Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 637) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421 | 1.70711 | 0.853553 | − | 0.521005i | \(-0.174443\pi\) | ||||
0.853553 | + | 0.521005i | \(0.174443\pi\) | |||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | −3.82843 | −1.71212 | −0.856062 | − | 0.516873i | \(-0.827096\pi\) | ||||
−0.856062 | + | 0.516873i | \(0.827096\pi\) | |||||||
\(6\) | −3.41421 | −1.39385 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4.41421 | 1.56066 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −9.24264 | −2.92278 | ||||||||
\(11\) | −3.41421 | −1.02942 | −0.514712 | − | 0.857363i | \(-0.672101\pi\) | ||||
−0.514712 | + | 0.857363i | \(0.672101\pi\) | |||||||
\(12\) | −5.41421 | −1.56295 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.41421 | 1.39794 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −0.171573 | −0.0416125 | −0.0208063 | − | 0.999784i | \(-0.506623\pi\) | ||||
−0.0208063 | + | 0.999784i | \(0.506623\pi\) | |||||||
\(18\) | −2.41421 | −0.569036 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | −14.6569 | −3.27737 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.24264 | −1.75734 | ||||||||
\(23\) | 1.41421 | 0.294884 | 0.147442 | − | 0.989071i | \(-0.452896\pi\) | ||||
0.147442 | + | 0.989071i | \(0.452896\pi\) | |||||||
\(24\) | −6.24264 | −1.27427 | ||||||||
\(25\) | 9.65685 | 1.93137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.82843 | 1.82509 | 0.912547 | − | 0.408973i | \(-0.134113\pi\) | ||||
0.912547 | + | 0.408973i | \(0.134113\pi\) | |||||||
\(30\) | 13.0711 | 2.38644 | ||||||||
\(31\) | −5.41421 | −0.972421 | −0.486211 | − | 0.873842i | \(-0.661621\pi\) | ||||
−0.486211 | + | 0.873842i | \(0.661621\pi\) | |||||||
\(32\) | −1.58579 | −0.280330 | ||||||||
\(33\) | 4.82843 | 0.840521 | ||||||||
\(34\) | −0.414214 | −0.0710370 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.82843 | −0.638071 | ||||||||
\(37\) | −7.48528 | −1.23057 | −0.615286 | − | 0.788304i | \(-0.710960\pi\) | ||||
−0.615286 | + | 0.788304i | \(0.710960\pi\) | |||||||
\(38\) | −14.4853 | −2.34982 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −16.8995 | −2.67204 | ||||||||
\(41\) | −5.82843 | −0.910247 | −0.455124 | − | 0.890428i | \(-0.650405\pi\) | ||||
−0.455124 | + | 0.890428i | \(0.650405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.585786 | 0.0893316 | 0.0446658 | − | 0.999002i | \(-0.485778\pi\) | ||||
0.0446658 | + | 0.999002i | \(0.485778\pi\) | |||||||
\(44\) | −13.0711 | −1.97054 | ||||||||
\(45\) | 3.82843 | 0.570708 | ||||||||
\(46\) | 3.41421 | 0.503398 | ||||||||
\(47\) | −7.65685 | −1.11687 | −0.558433 | − | 0.829549i | \(-0.688597\pi\) | ||||
−0.558433 | + | 0.829549i | \(0.688597\pi\) | |||||||
\(48\) | −4.24264 | −0.612372 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 23.3137 | 3.29706 | ||||||||
\(51\) | 0.242641 | 0.0339765 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | 13.6569 | 1.85846 | ||||||||
\(55\) | 13.0711 | 1.76250 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.48528 | 1.12390 | ||||||||
\(58\) | 23.7279 | 3.11563 | ||||||||
\(59\) | 1.75736 | 0.228789 | 0.114394 | − | 0.993435i | \(-0.463507\pi\) | ||||
0.114394 | + | 0.993435i | \(0.463507\pi\) | |||||||
\(60\) | 20.7279 | 2.67596 | ||||||||
\(61\) | 9.82843 | 1.25840 | 0.629201 | − | 0.777243i | \(-0.283382\pi\) | ||||
0.629201 | + | 0.777243i | \(0.283382\pi\) | |||||||
\(62\) | −13.0711 | −1.66003 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.6569 | 1.43486 | ||||||||
\(67\) | 4.24264 | 0.518321 | 0.259161 | − | 0.965834i | \(-0.416554\pi\) | ||||
0.259161 | + | 0.965834i | \(0.416554\pi\) | |||||||
\(68\) | −0.656854 | −0.0796553 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.343146 | 0.0407239 | 0.0203620 | − | 0.999793i | \(-0.493518\pi\) | ||||
0.0203620 | + | 0.999793i | \(0.493518\pi\) | |||||||
\(72\) | −4.41421 | −0.520220 | ||||||||
\(73\) | −0.656854 | −0.0768790 | −0.0384395 | − | 0.999261i | \(-0.512239\pi\) | ||||
−0.0384395 | + | 0.999261i | \(0.512239\pi\) | |||||||
\(74\) | −18.0711 | −2.10072 | ||||||||
\(75\) | −13.6569 | −1.57696 | ||||||||
\(76\) | −22.9706 | −2.63490 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2426 | 1.15239 | 0.576194 | − | 0.817313i | \(-0.304537\pi\) | ||||
0.576194 | + | 0.817313i | \(0.304537\pi\) | |||||||
\(80\) | −11.4853 | −1.28409 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −14.0711 | −1.55389 | ||||||||
\(83\) | 13.0711 | 1.43474 | 0.717368 | − | 0.696694i | \(-0.245347\pi\) | ||||
0.717368 | + | 0.696694i | \(0.245347\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.656854 | 0.0712458 | ||||||||
\(86\) | 1.41421 | 0.152499 | ||||||||
\(87\) | −13.8995 | −1.49018 | ||||||||
\(88\) | −15.0711 | −1.60658 | ||||||||
\(89\) | 7.31371 | 0.775252 | 0.387626 | − | 0.921817i | \(-0.373295\pi\) | ||||
0.387626 | + | 0.921817i | \(0.373295\pi\) | |||||||
\(90\) | 9.24264 | 0.974260 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.41421 | 0.564471 | ||||||||
\(93\) | 7.65685 | 0.793979 | ||||||||
\(94\) | −18.4853 | −1.90661 | ||||||||
\(95\) | 22.9706 | 2.35673 | ||||||||
\(96\) | 2.24264 | 0.228889 | ||||||||
\(97\) | 5.17157 | 0.525094 | 0.262547 | − | 0.964919i | \(-0.415438\pi\) | ||||
0.262547 | + | 0.964919i | \(0.415438\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.41421 | 0.343141 | ||||||||
\(100\) | 36.9706 | 3.69706 | ||||||||
\(101\) | 3.34315 | 0.332655 | 0.166328 | − | 0.986071i | \(-0.446809\pi\) | ||||
0.166328 | + | 0.986071i | \(0.446809\pi\) | |||||||
\(102\) | 0.585786 | 0.0580015 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.24264 | −0.703467 | ||||||||
\(107\) | −5.31371 | −0.513696 | −0.256848 | − | 0.966452i | \(-0.582684\pi\) | ||||
−0.256848 | + | 0.966452i | \(0.582684\pi\) | |||||||
\(108\) | 21.6569 | 2.08393 | ||||||||
\(109\) | 2.34315 | 0.224433 | 0.112216 | − | 0.993684i | \(-0.464205\pi\) | ||||
0.112216 | + | 0.993684i | \(0.464205\pi\) | |||||||
\(110\) | 31.5563 | 3.00878 | ||||||||
\(111\) | 10.5858 | 1.00476 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.31371 | −0.217655 | −0.108828 | − | 0.994061i | \(-0.534710\pi\) | ||||
−0.108828 | + | 0.994061i | \(0.534710\pi\) | |||||||
\(114\) | 20.4853 | 1.91862 | ||||||||
\(115\) | −5.41421 | −0.504878 | ||||||||
\(116\) | 37.6274 | 3.49362 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.24264 | 0.390567 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 23.8995 | 2.18172 | ||||||||
\(121\) | 0.656854 | 0.0597140 | ||||||||
\(122\) | 23.7279 | 2.14823 | ||||||||
\(123\) | 8.24264 | 0.743214 | ||||||||
\(124\) | −20.7279 | −1.86142 | ||||||||
\(125\) | −17.8284 | −1.59462 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.31371 | −0.826458 | −0.413229 | − | 0.910627i | \(-0.635599\pi\) | ||||
−0.413229 | + | 0.910627i | \(0.635599\pi\) | |||||||
\(128\) | −20.5563 | −1.81694 | ||||||||
\(129\) | −0.828427 | −0.0729389 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.31371 | −0.114779 | −0.0573896 | − | 0.998352i | \(-0.518278\pi\) | ||||
−0.0573896 | + | 0.998352i | \(0.518278\pi\) | |||||||
\(132\) | 18.4853 | 1.60894 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.2426 | 0.884829 | ||||||||
\(135\) | −21.6569 | −1.86393 | ||||||||
\(136\) | −0.757359 | −0.0649430 | ||||||||
\(137\) | 5.82843 | 0.497956 | 0.248978 | − | 0.968509i | \(-0.419905\pi\) | ||||
0.248978 | + | 0.968509i | \(0.419905\pi\) | |||||||
\(138\) | −4.82843 | −0.411023 | ||||||||
\(139\) | 7.89949 | 0.670026 | 0.335013 | − | 0.942213i | \(-0.391259\pi\) | ||||
0.335013 | + | 0.942213i | \(0.391259\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.8284 | 0.911918 | ||||||||
\(142\) | 0.828427 | 0.0695201 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | −37.6274 | −3.12479 | ||||||||
\(146\) | −1.58579 | −0.131241 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −28.6569 | −2.35558 | ||||||||
\(149\) | −3.00000 | −0.245770 | −0.122885 | − | 0.992421i | \(-0.539215\pi\) | ||||
−0.122885 | + | 0.992421i | \(0.539215\pi\) | |||||||
\(150\) | −32.9706 | −2.69204 | ||||||||
\(151\) | 18.9706 | 1.54380 | 0.771901 | − | 0.635742i | \(-0.219306\pi\) | ||||
0.771901 | + | 0.635742i | \(0.219306\pi\) | |||||||
\(152\) | −26.4853 | −2.14824 | ||||||||
\(153\) | 0.171573 | 0.0138708 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.7279 | 1.66491 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4853 | −0.916625 | −0.458313 | − | 0.888791i | \(-0.651546\pi\) | ||||
−0.458313 | + | 0.888791i | \(0.651546\pi\) | |||||||
\(158\) | 24.7279 | 1.96725 | ||||||||
\(159\) | 4.24264 | 0.336463 | ||||||||
\(160\) | 6.07107 | 0.479960 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.0711 | −0.948393 | ||||||||
\(163\) | −15.4142 | −1.20733 | −0.603667 | − | 0.797236i | \(-0.706294\pi\) | ||||
−0.603667 | + | 0.797236i | \(0.706294\pi\) | |||||||
\(164\) | −22.3137 | −1.74241 | ||||||||
\(165\) | −18.4853 | −1.43908 | ||||||||
\(166\) | 31.5563 | 2.44925 | ||||||||
\(167\) | 18.7279 | 1.44921 | 0.724605 | − | 0.689164i | \(-0.242022\pi\) | ||||
0.724605 | + | 0.689164i | \(0.242022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.58579 | 0.121624 | ||||||||
\(171\) | 6.00000 | 0.458831 | ||||||||
\(172\) | 2.24264 | 0.171000 | ||||||||
\(173\) | 18.1421 | 1.37932 | 0.689661 | − | 0.724133i | \(-0.257760\pi\) | ||||
0.689661 | + | 0.724133i | \(0.257760\pi\) | |||||||
\(174\) | −33.5563 | −2.54390 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.2426 | −0.772068 | ||||||||
\(177\) | −2.48528 | −0.186805 | ||||||||
\(178\) | 17.6569 | 1.32344 | ||||||||
\(179\) | 5.65685 | 0.422813 | 0.211407 | − | 0.977398i | \(-0.432196\pi\) | ||||
0.211407 | + | 0.977398i | \(0.432196\pi\) | |||||||
\(180\) | 14.6569 | 1.09246 | ||||||||
\(181\) | −19.1421 | −1.42282 | −0.711412 | − | 0.702775i | \(-0.751944\pi\) | ||||
−0.711412 | + | 0.702775i | \(0.751944\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.8995 | −1.02748 | ||||||||
\(184\) | 6.24264 | 0.460214 | ||||||||
\(185\) | 28.6569 | 2.10689 | ||||||||
\(186\) | 18.4853 | 1.35541 | ||||||||
\(187\) | 0.585786 | 0.0428369 | ||||||||
\(188\) | −29.3137 | −2.13792 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 55.4558 | 4.02319 | ||||||||
\(191\) | 7.75736 | 0.561303 | 0.280651 | − | 0.959810i | \(-0.409450\pi\) | ||||
0.280651 | + | 0.959810i | \(0.409450\pi\) | |||||||
\(192\) | 13.8995 | 1.00311 | ||||||||
\(193\) | 21.1421 | 1.52184 | 0.760922 | − | 0.648843i | \(-0.224747\pi\) | ||||
0.760922 | + | 0.648843i | \(0.224747\pi\) | |||||||
\(194\) | 12.4853 | 0.896391 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.17157 | −0.653448 | −0.326724 | − | 0.945120i | \(-0.605945\pi\) | ||||
−0.326724 | + | 0.945120i | \(0.605945\pi\) | |||||||
\(198\) | 8.24264 | 0.585779 | ||||||||
\(199\) | 18.9706 | 1.34479 | 0.672394 | − | 0.740194i | \(-0.265266\pi\) | ||||
0.672394 | + | 0.740194i | \(0.265266\pi\) | |||||||
\(200\) | 42.6274 | 3.01421 | ||||||||
\(201\) | −6.00000 | −0.423207 | ||||||||
\(202\) | 8.07107 | 0.567878 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.928932 | 0.0650383 | ||||||||
\(205\) | 22.3137 | 1.55846 | ||||||||
\(206\) | 33.7990 | 2.35489 | ||||||||
\(207\) | −1.41421 | −0.0982946 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.4853 | 1.41700 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.727922 | −0.0501122 | −0.0250561 | − | 0.999686i | \(-0.507976\pi\) | ||||
−0.0250561 | + | 0.999686i | \(0.507976\pi\) | |||||||
\(212\) | −11.4853 | −0.788812 | ||||||||
\(213\) | −0.485281 | −0.0332509 | ||||||||
\(214\) | −12.8284 | −0.876933 | ||||||||
\(215\) | −2.24264 | −0.152947 | ||||||||
\(216\) | 24.9706 | 1.69903 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.65685 | 0.383131 | ||||||||
\(219\) | 0.928932 | 0.0627714 | ||||||||
\(220\) | 50.0416 | 3.37381 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 25.5563 | 1.71523 | ||||||||
\(223\) | −2.00000 | −0.133930 | −0.0669650 | − | 0.997755i | \(-0.521332\pi\) | ||||
−0.0669650 | + | 0.997755i | \(0.521332\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.65685 | −0.643790 | ||||||||
\(226\) | −5.58579 | −0.371561 | ||||||||
\(227\) | 13.8995 | 0.922542 | 0.461271 | − | 0.887259i | \(-0.347394\pi\) | ||||
0.461271 | + | 0.887259i | \(0.347394\pi\) | |||||||
\(228\) | 32.4853 | 2.15139 | ||||||||
\(229\) | −4.48528 | −0.296396 | −0.148198 | − | 0.988958i | \(-0.547347\pi\) | ||||
−0.148198 | + | 0.988958i | \(0.547347\pi\) | |||||||
\(230\) | −13.0711 | −0.861881 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 43.3848 | 2.84835 | ||||||||
\(233\) | −2.82843 | −0.185296 | −0.0926482 | − | 0.995699i | \(-0.529533\pi\) | ||||
−0.0926482 | + | 0.995699i | \(0.529533\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.3137 | 1.91222 | ||||||||
\(236\) | 6.72792 | 0.437950 | ||||||||
\(237\) | −14.4853 | −0.940920 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.3848 | 0.801105 | 0.400552 | − | 0.916274i | \(-0.368818\pi\) | ||||
0.400552 | + | 0.916274i | \(0.368818\pi\) | |||||||
\(240\) | 16.2426 | 1.04846 | ||||||||
\(241\) | 1.48528 | 0.0956754 | 0.0478377 | − | 0.998855i | \(-0.484767\pi\) | ||||
0.0478377 | + | 0.998855i | \(0.484767\pi\) | |||||||
\(242\) | 1.58579 | 0.101938 | ||||||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | 37.6274 | 2.40885 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 19.8995 | 1.26875 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −23.8995 | −1.51762 | ||||||||
\(249\) | −18.4853 | −1.17146 | ||||||||
\(250\) | −43.0416 | −2.72219 | ||||||||
\(251\) | −10.9706 | −0.692456 | −0.346228 | − | 0.938150i | \(-0.612538\pi\) | ||||
−0.346228 | + | 0.938150i | \(0.612538\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.82843 | −0.303561 | ||||||||
\(254\) | −22.4853 | −1.41085 | ||||||||
\(255\) | −0.928932 | −0.0581720 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 15.0000 | 0.935674 | 0.467837 | − | 0.883815i | \(-0.345033\pi\) | ||||
0.467837 | + | 0.883815i | \(0.345033\pi\) | |||||||
\(258\) | −2.00000 | −0.124515 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.82843 | −0.608364 | ||||||||
\(262\) | −3.17157 | −0.195940 | ||||||||
\(263\) | 18.7279 | 1.15481 | 0.577407 | − | 0.816457i | \(-0.304065\pi\) | ||||
0.577407 | + | 0.816457i | \(0.304065\pi\) | |||||||
\(264\) | 21.3137 | 1.31177 | ||||||||
\(265\) | 11.4853 | 0.705535 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.3431 | −0.632990 | ||||||||
\(268\) | 16.2426 | 0.992177 | ||||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | −52.2843 | −3.18192 | ||||||||
\(271\) | 6.92893 | 0.420903 | 0.210451 | − | 0.977604i | \(-0.432507\pi\) | ||||
0.210451 | + | 0.977604i | \(0.432507\pi\) | |||||||
\(272\) | −0.514719 | −0.0312094 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.0711 | 0.850064 | ||||||||
\(275\) | −32.9706 | −1.98820 | ||||||||
\(276\) | −7.65685 | −0.460888 | ||||||||
\(277\) | −31.9706 | −1.92092 | −0.960462 | − | 0.278409i | \(-0.910193\pi\) | ||||
−0.960462 | + | 0.278409i | \(0.910193\pi\) | |||||||
\(278\) | 19.0711 | 1.14381 | ||||||||
\(279\) | 5.41421 | 0.324140 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.514719 | 0.0307055 | 0.0153528 | − | 0.999882i | \(-0.495113\pi\) | ||||
0.0153528 | + | 0.999882i | \(0.495113\pi\) | |||||||
\(282\) | 26.1421 | 1.55674 | ||||||||
\(283\) | −0.100505 | −0.00597441 | −0.00298720 | − | 0.999996i | \(-0.500951\pi\) | ||||
−0.00298720 | + | 0.999996i | \(0.500951\pi\) | |||||||
\(284\) | 1.31371 | 0.0779543 | ||||||||
\(285\) | −32.4853 | −1.92426 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.58579 | 0.0934434 | ||||||||
\(289\) | −16.9706 | −0.998268 | ||||||||
\(290\) | −90.8406 | −5.33434 | ||||||||
\(291\) | −7.31371 | −0.428737 | ||||||||
\(292\) | −2.51472 | −0.147163 | ||||||||
\(293\) | 22.4558 | 1.31188 | 0.655942 | − | 0.754811i | \(-0.272271\pi\) | ||||
0.655942 | + | 0.754811i | \(0.272271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.72792 | −0.391715 | ||||||||
\(296\) | −33.0416 | −1.92051 | ||||||||
\(297\) | −19.3137 | −1.12070 | ||||||||
\(298\) | −7.24264 | −0.419555 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −52.2843 | −3.01863 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 45.7990 | 2.63544 | ||||||||
\(303\) | −4.72792 | −0.271612 | ||||||||
\(304\) | −18.0000 | −1.03237 | ||||||||
\(305\) | −37.6274 | −2.15454 | ||||||||
\(306\) | 0.414214 | 0.0236790 | ||||||||
\(307\) | 7.27208 | 0.415039 | 0.207520 | − | 0.978231i | \(-0.433461\pi\) | ||||
0.207520 | + | 0.978231i | \(0.433461\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.7990 | −1.12633 | ||||||||
\(310\) | 50.0416 | 2.84217 | ||||||||
\(311\) | −27.0711 | −1.53506 | −0.767530 | − | 0.641013i | \(-0.778514\pi\) | ||||
−0.767530 | + | 0.641013i | \(0.778514\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0000 | −0.791327 | −0.395663 | − | 0.918396i | \(-0.629485\pi\) | ||||
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(314\) | −27.7279 | −1.56478 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 39.2132 | 2.20592 | ||||||||
\(317\) | −21.3431 | −1.19875 | −0.599375 | − | 0.800468i | \(-0.704584\pi\) | ||||
−0.599375 | + | 0.800468i | \(0.704584\pi\) | |||||||
\(318\) | 10.2426 | 0.574379 | ||||||||
\(319\) | −33.5563 | −1.87879 | ||||||||
\(320\) | 37.6274 | 2.10344 | ||||||||
\(321\) | 7.51472 | 0.419431 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.02944 | 0.0572794 | ||||||||
\(324\) | −19.1421 | −1.06345 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −37.2132 | −2.06105 | ||||||||
\(327\) | −3.31371 | −0.183248 | ||||||||
\(328\) | −25.7279 | −1.42059 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −44.6274 | −2.45666 | ||||||||
\(331\) | −28.8701 | −1.58684 | −0.793421 | − | 0.608673i | \(-0.791702\pi\) | ||||
−0.793421 | + | 0.608673i | \(0.791702\pi\) | |||||||
\(332\) | 50.0416 | 2.74639 | ||||||||
\(333\) | 7.48528 | 0.410191 | ||||||||
\(334\) | 45.2132 | 2.47396 | ||||||||
\(335\) | −16.2426 | −0.887430 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4853 | 0.734590 | 0.367295 | − | 0.930104i | \(-0.380284\pi\) | ||||
0.367295 | + | 0.930104i | \(0.380284\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.27208 | 0.177715 | ||||||||
\(340\) | 2.51472 | 0.136380 | ||||||||
\(341\) | 18.4853 | 1.00103 | ||||||||
\(342\) | 14.4853 | 0.783274 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.58579 | 0.139416 | ||||||||
\(345\) | 7.65685 | 0.412231 | ||||||||
\(346\) | 43.7990 | 2.35465 | ||||||||
\(347\) | −25.8995 | −1.39036 | −0.695179 | − | 0.718837i | \(-0.744675\pi\) | ||||
−0.695179 | + | 0.718837i | \(0.744675\pi\) | |||||||
\(348\) | −53.2132 | −2.85253 | ||||||||
\(349\) | 13.3137 | 0.712666 | 0.356333 | − | 0.934359i | \(-0.384027\pi\) | ||||
0.356333 | + | 0.934359i | \(0.384027\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.41421 | 0.288579 | ||||||||
\(353\) | −0.171573 | −0.00913190 | −0.00456595 | − | 0.999990i | \(-0.501453\pi\) | ||||
−0.00456595 | + | 0.999990i | \(0.501453\pi\) | |||||||
\(354\) | −6.00000 | −0.318896 | ||||||||
\(355\) | −1.31371 | −0.0697244 | ||||||||
\(356\) | 28.0000 | 1.48400 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.6569 | 0.721787 | ||||||||
\(359\) | −16.9706 | −0.895672 | −0.447836 | − | 0.894116i | \(-0.647805\pi\) | ||||
−0.447836 | + | 0.894116i | \(0.647805\pi\) | |||||||
\(360\) | 16.8995 | 0.890682 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | −46.2132 | −2.42891 | ||||||||
\(363\) | −0.928932 | −0.0487563 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.51472 | 0.131626 | ||||||||
\(366\) | −33.5563 | −1.75402 | ||||||||
\(367\) | −3.27208 | −0.170801 | −0.0854005 | − | 0.996347i | \(-0.527217\pi\) | ||||
−0.0854005 | + | 0.996347i | \(0.527217\pi\) | |||||||
\(368\) | 4.24264 | 0.221163 | ||||||||
\(369\) | 5.82843 | 0.303416 | ||||||||
\(370\) | 69.1838 | 3.59669 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 29.3137 | 1.51984 | ||||||||
\(373\) | −24.4558 | −1.26628 | −0.633138 | − | 0.774039i | \(-0.718233\pi\) | ||||
−0.633138 | + | 0.774039i | \(0.718233\pi\) | |||||||
\(374\) | 1.41421 | 0.0731272 | ||||||||
\(375\) | 25.2132 | 1.30200 | ||||||||
\(376\) | −33.7990 | −1.74305 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.24264 | −0.423396 | −0.211698 | − | 0.977335i | \(-0.567899\pi\) | ||||
−0.211698 | + | 0.977335i | \(0.567899\pi\) | |||||||
\(380\) | 87.9411 | 4.51128 | ||||||||
\(381\) | 13.1716 | 0.674800 | ||||||||
\(382\) | 18.7279 | 0.958204 | ||||||||
\(383\) | −14.0416 | −0.717494 | −0.358747 | − | 0.933435i | \(-0.616796\pi\) | ||||
−0.358747 | + | 0.933435i | \(0.616796\pi\) | |||||||
\(384\) | 29.0711 | 1.48353 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 51.0416 | 2.59795 | ||||||||
\(387\) | −0.585786 | −0.0297772 | ||||||||
\(388\) | 19.7990 | 1.00514 | ||||||||
\(389\) | −1.14214 | −0.0579086 | −0.0289543 | − | 0.999581i | \(-0.509218\pi\) | ||||
−0.0289543 | + | 0.999581i | \(0.509218\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.242641 | −0.0122709 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.85786 | 0.0937169 | ||||||||
\(394\) | −22.1421 | −1.11550 | ||||||||
\(395\) | −39.2132 | −1.97303 | ||||||||
\(396\) | 13.0711 | 0.656846 | ||||||||
\(397\) | 38.6274 | 1.93865 | 0.969327 | − | 0.245774i | \(-0.0790420\pi\) | ||||
0.969327 | + | 0.245774i | \(0.0790420\pi\) | |||||||
\(398\) | 45.7990 | 2.29570 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 28.9706 | 1.44853 | ||||||||
\(401\) | 30.7990 | 1.53803 | 0.769014 | − | 0.639232i | \(-0.220748\pi\) | ||||
0.769014 | + | 0.639232i | \(0.220748\pi\) | |||||||
\(402\) | −14.4853 | −0.722460 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12.7990 | 0.636774 | ||||||||
\(405\) | 19.1421 | 0.951180 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.5563 | 1.26678 | ||||||||
\(408\) | 1.07107 | 0.0530258 | ||||||||
\(409\) | −11.9706 | −0.591906 | −0.295953 | − | 0.955202i | \(-0.595637\pi\) | ||||
−0.295953 | + | 0.955202i | \(0.595637\pi\) | |||||||
\(410\) | 53.8701 | 2.66045 | ||||||||
\(411\) | −8.24264 | −0.406579 | ||||||||
\(412\) | 53.5980 | 2.64058 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.41421 | −0.167799 | ||||||||
\(415\) | −50.0416 | −2.45645 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.1716 | −0.547074 | ||||||||
\(418\) | 49.4558 | 2.41896 | ||||||||
\(419\) | 19.5563 | 0.955390 | 0.477695 | − | 0.878526i | \(-0.341472\pi\) | ||||
0.477695 | + | 0.878526i | \(0.341472\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.51472 | −0.220034 | −0.110017 | − | 0.993930i | \(-0.535091\pi\) | ||||
−0.110017 | + | 0.993930i | \(0.535091\pi\) | |||||||
\(422\) | −1.75736 | −0.0855469 | ||||||||
\(423\) | 7.65685 | 0.372289 | ||||||||
\(424\) | −13.2426 | −0.643119 | ||||||||
\(425\) | −1.65685 | −0.0803692 | ||||||||
\(426\) | −1.17157 | −0.0567629 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −20.3431 | −0.983323 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.41421 | −0.261097 | ||||||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 16.9706 | 0.816497 | ||||||||
\(433\) | 0.514719 | 0.0247358 | 0.0123679 | − | 0.999924i | \(-0.496063\pi\) | ||||
0.0123679 | + | 0.999924i | \(0.496063\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 53.2132 | 2.55138 | ||||||||
\(436\) | 8.97056 | 0.429612 | ||||||||
\(437\) | −8.48528 | −0.405906 | ||||||||
\(438\) | 2.24264 | 0.107158 | ||||||||
\(439\) | −26.7279 | −1.27565 | −0.637827 | − | 0.770180i | \(-0.720167\pi\) | ||||
−0.637827 | + | 0.770180i | \(0.720167\pi\) | |||||||
\(440\) | 57.6985 | 2.75067 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.3431 | 0.681463 | 0.340732 | − | 0.940161i | \(-0.389325\pi\) | ||||
0.340732 | + | 0.940161i | \(0.389325\pi\) | |||||||
\(444\) | 40.5269 | 1.92332 | ||||||||
\(445\) | −28.0000 | −1.32733 | ||||||||
\(446\) | −4.82843 | −0.228633 | ||||||||
\(447\) | 4.24264 | 0.200670 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.5147 | −0.732185 | −0.366092 | − | 0.930578i | \(-0.619305\pi\) | ||||
−0.366092 | + | 0.930578i | \(0.619305\pi\) | |||||||
\(450\) | −23.3137 | −1.09902 | ||||||||
\(451\) | 19.8995 | 0.937031 | ||||||||
\(452\) | −8.85786 | −0.416639 | ||||||||
\(453\) | −26.8284 | −1.26051 | ||||||||
\(454\) | 33.5563 | 1.57488 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 37.4558 | 1.75403 | ||||||||
\(457\) | 25.0000 | 1.16945 | 0.584725 | − | 0.811231i | \(-0.301202\pi\) | ||||
0.584725 | + | 0.811231i | \(0.301202\pi\) | |||||||
\(458\) | −10.8284 | −0.505979 | ||||||||
\(459\) | −0.970563 | −0.0453020 | ||||||||
\(460\) | −20.7279 | −0.966444 | ||||||||
\(461\) | −12.6569 | −0.589488 | −0.294744 | − | 0.955576i | \(-0.595234\pi\) | ||||
−0.294744 | + | 0.955576i | \(0.595234\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7279 | 0.870360 | 0.435180 | − | 0.900343i | \(-0.356685\pi\) | ||||
0.435180 | + | 0.900343i | \(0.356685\pi\) | |||||||
\(464\) | 29.4853 | 1.36882 | ||||||||
\(465\) | −29.3137 | −1.35939 | ||||||||
\(466\) | −6.82843 | −0.316321 | ||||||||
\(467\) | 8.58579 | 0.397303 | 0.198651 | − | 0.980070i | \(-0.436344\pi\) | ||||
0.198651 | + | 0.980070i | \(0.436344\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 70.7696 | 3.26436 | ||||||||
\(471\) | 16.2426 | 0.748421 | ||||||||
\(472\) | 7.75736 | 0.357061 | ||||||||
\(473\) | −2.00000 | −0.0919601 | ||||||||
\(474\) | −34.9706 | −1.60625 | ||||||||
\(475\) | −57.9411 | −2.65852 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | 0.137361 | ||||||||
\(478\) | 29.8995 | 1.36757 | ||||||||
\(479\) | 38.3848 | 1.75385 | 0.876923 | − | 0.480632i | \(-0.159593\pi\) | ||||
0.876923 | + | 0.480632i | \(0.159593\pi\) | |||||||
\(480\) | −8.58579 | −0.391886 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.58579 | 0.163328 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.51472 | 0.114305 | ||||||||
\(485\) | −19.7990 | −0.899026 | ||||||||
\(486\) | −23.8995 | −1.08410 | ||||||||
\(487\) | −20.9706 | −0.950267 | −0.475133 | − | 0.879914i | \(-0.657600\pi\) | ||||
−0.475133 | + | 0.879914i | \(0.657600\pi\) | |||||||
\(488\) | 43.3848 | 1.96394 | ||||||||
\(489\) | 21.7990 | 0.985784 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.3137 | 1.59369 | 0.796843 | − | 0.604187i | \(-0.206502\pi\) | ||||
0.796843 | + | 0.604187i | \(0.206502\pi\) | |||||||
\(492\) | 31.5563 | 1.42267 | ||||||||
\(493\) | −1.68629 | −0.0759467 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.0711 | −0.587501 | ||||||||
\(496\) | −16.2426 | −0.729316 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −44.6274 | −1.99980 | ||||||||
\(499\) | 28.0416 | 1.25532 | 0.627658 | − | 0.778489i | \(-0.284014\pi\) | ||||
0.627658 | + | 0.778489i | \(0.284014\pi\) | |||||||
\(500\) | −68.2548 | −3.05245 | ||||||||
\(501\) | −26.4853 | −1.18328 | ||||||||
\(502\) | −26.4853 | −1.18210 | ||||||||
\(503\) | −33.5563 | −1.49620 | −0.748102 | − | 0.663584i | \(-0.769035\pi\) | ||||
−0.748102 | + | 0.663584i | \(0.769035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.7990 | −0.569548 | ||||||||
\(506\) | −11.6569 | −0.518210 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −35.6569 | −1.58202 | ||||||||
\(509\) | 6.65685 | 0.295060 | 0.147530 | − | 0.989058i | \(-0.452868\pi\) | ||||
0.147530 | + | 0.989058i | \(0.452868\pi\) | |||||||
\(510\) | −2.24264 | −0.0993058 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −31.2426 | −1.38074 | ||||||||
\(513\) | −33.9411 | −1.49854 | ||||||||
\(514\) | 36.2132 | 1.59730 | ||||||||
\(515\) | −53.5980 | −2.36181 | ||||||||
\(516\) | −3.17157 | −0.139621 | ||||||||
\(517\) | 26.1421 | 1.14973 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.6569 | −1.12621 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.3431 | −0.584574 | −0.292287 | − | 0.956331i | \(-0.594416\pi\) | ||||
−0.292287 | + | 0.956331i | \(0.594416\pi\) | |||||||
\(522\) | −23.7279 | −1.03854 | ||||||||
\(523\) | 16.9706 | 0.742071 | 0.371035 | − | 0.928619i | \(-0.379003\pi\) | ||||
0.371035 | + | 0.928619i | \(0.379003\pi\) | |||||||
\(524\) | −5.02944 | −0.219712 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 45.2132 | 1.97139 | ||||||||
\(527\) | 0.928932 | 0.0404649 | ||||||||
\(528\) | 14.4853 | 0.630391 | ||||||||
\(529\) | −21.0000 | −0.913043 | ||||||||
\(530\) | 27.7279 | 1.20442 | ||||||||
\(531\) | −1.75736 | −0.0762629 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −24.9706 | −1.08058 | ||||||||
\(535\) | 20.3431 | 0.879511 | ||||||||
\(536\) | 18.7279 | 0.808923 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | −43.4558 | −1.87351 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −82.9117 | −3.56795 | ||||||||
\(541\) | −5.48528 | −0.235831 | −0.117915 | − | 0.993024i | \(-0.537621\pi\) | ||||
−0.117915 | + | 0.993024i | \(0.537621\pi\) | |||||||
\(542\) | 16.7279 | 0.718526 | ||||||||
\(543\) | 27.0711 | 1.16173 | ||||||||
\(544\) | 0.272078 | 0.0116652 | ||||||||
\(545\) | −8.97056 | −0.384257 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0711 | 0.644392 | 0.322196 | − | 0.946673i | \(-0.395579\pi\) | ||||
0.322196 | + | 0.946673i | \(0.395579\pi\) | |||||||
\(548\) | 22.3137 | 0.953194 | ||||||||
\(549\) | −9.82843 | −0.419467 | ||||||||
\(550\) | −79.5980 | −3.39407 | ||||||||
\(551\) | −58.9706 | −2.51223 | ||||||||
\(552\) | −8.82843 | −0.375763 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −77.1838 | −3.27922 | ||||||||
\(555\) | −40.5269 | −1.72027 | ||||||||
\(556\) | 30.2426 | 1.28257 | ||||||||
\(557\) | 10.3137 | 0.437006 | 0.218503 | − | 0.975836i | \(-0.429883\pi\) | ||||
0.218503 | + | 0.975836i | \(0.429883\pi\) | |||||||
\(558\) | 13.0711 | 0.553342 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.828427 | −0.0349762 | ||||||||
\(562\) | 1.24264 | 0.0524176 | ||||||||
\(563\) | 19.8995 | 0.838664 | 0.419332 | − | 0.907833i | \(-0.362264\pi\) | ||||
0.419332 | + | 0.907833i | \(0.362264\pi\) | |||||||
\(564\) | 41.4558 | 1.74561 | ||||||||
\(565\) | 8.85786 | 0.372653 | ||||||||
\(566\) | −0.242641 | −0.0101989 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.51472 | 0.0635562 | ||||||||
\(569\) | 13.1716 | 0.552181 | 0.276091 | − | 0.961132i | \(-0.410961\pi\) | ||||
0.276091 | + | 0.961132i | \(0.410961\pi\) | |||||||
\(570\) | −78.4264 | −3.28492 | ||||||||
\(571\) | −4.97056 | −0.208012 | −0.104006 | − | 0.994577i | \(-0.533166\pi\) | ||||
−0.104006 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.9706 | −0.458302 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.6569 | 0.569530 | ||||||||
\(576\) | 9.82843 | 0.409518 | ||||||||
\(577\) | 36.3137 | 1.51176 | 0.755880 | − | 0.654710i | \(-0.227209\pi\) | ||||
0.755880 | + | 0.654710i | \(0.227209\pi\) | |||||||
\(578\) | −40.9706 | −1.70415 | ||||||||
\(579\) | −29.8995 | −1.24258 | ||||||||
\(580\) | −144.054 | −5.98151 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −17.6569 | −0.731900 | ||||||||
\(583\) | 10.2426 | 0.424207 | ||||||||
\(584\) | −2.89949 | −0.119982 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 54.2132 | 2.23953 | ||||||||
\(587\) | 18.3431 | 0.757103 | 0.378551 | − | 0.925580i | \(-0.376422\pi\) | ||||
0.378551 | + | 0.925580i | \(0.376422\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.4853 | 1.33853 | ||||||||
\(590\) | −16.2426 | −0.668699 | ||||||||
\(591\) | 12.9706 | 0.533538 | ||||||||
\(592\) | −22.4558 | −0.922930 | ||||||||
\(593\) | 31.2843 | 1.28469 | 0.642346 | − | 0.766415i | \(-0.277961\pi\) | ||||
0.642346 | + | 0.766415i | \(0.277961\pi\) | |||||||
\(594\) | −46.6274 | −1.91315 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.4853 | −0.470455 | ||||||||
\(597\) | −26.8284 | −1.09801 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.6569 | 1.62034 | 0.810168 | − | 0.586198i | \(-0.199376\pi\) | ||||
0.810168 | + | 0.586198i | \(0.199376\pi\) | |||||||
\(600\) | −60.2843 | −2.46110 | ||||||||
\(601\) | −36.9411 | −1.50686 | −0.753430 | − | 0.657528i | \(-0.771602\pi\) | ||||
−0.753430 | + | 0.657528i | \(0.771602\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.24264 | −0.172774 | ||||||||
\(604\) | 72.6274 | 2.95517 | ||||||||
\(605\) | −2.51472 | −0.102238 | ||||||||
\(606\) | −11.4142 | −0.463671 | ||||||||
\(607\) | −43.6569 | −1.77198 | −0.885989 | − | 0.463707i | \(-0.846519\pi\) | ||||
−0.885989 | + | 0.463707i | \(0.846519\pi\) | |||||||
\(608\) | 9.51472 | 0.385873 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −90.8406 | −3.67803 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.656854 | 0.0265518 | ||||||||
\(613\) | −24.7990 | −1.00162 | −0.500811 | − | 0.865557i | \(-0.666965\pi\) | ||||
−0.500811 | + | 0.865557i | \(0.666965\pi\) | |||||||
\(614\) | 17.5563 | 0.708517 | ||||||||
\(615\) | −31.5563 | −1.27247 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.85786 | 0.115053 | 0.0575266 | − | 0.998344i | \(-0.481679\pi\) | ||||
0.0575266 | + | 0.998344i | \(0.481679\pi\) | |||||||
\(618\) | −47.7990 | −1.92276 | ||||||||
\(619\) | −10.4437 | −0.419766 | −0.209883 | − | 0.977727i | \(-0.567308\pi\) | ||||
−0.209883 | + | 0.977727i | \(0.567308\pi\) | |||||||
\(620\) | 79.3553 | 3.18699 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | −65.3553 | −2.62051 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | −33.7990 | −1.35088 | ||||||||
\(627\) | −28.9706 | −1.15697 | ||||||||
\(628\) | −43.9706 | −1.75462 | ||||||||
\(629\) | 1.28427 | 0.0512072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2843 | 1.28522 | 0.642608 | − | 0.766195i | \(-0.277852\pi\) | ||||
0.642608 | + | 0.766195i | \(0.277852\pi\) | |||||||
\(632\) | 45.2132 | 1.79848 | ||||||||
\(633\) | 1.02944 | 0.0409165 | ||||||||
\(634\) | −51.5269 | −2.04640 | ||||||||
\(635\) | 35.6569 | 1.41500 | ||||||||
\(636\) | 16.2426 | 0.644063 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −81.0122 | −3.20730 | ||||||||
\(639\) | −0.343146 | −0.0135746 | ||||||||
\(640\) | 78.6985 | 3.11083 | ||||||||
\(641\) | 24.7990 | 0.979501 | 0.489751 | − | 0.871863i | \(-0.337088\pi\) | ||||
0.489751 | + | 0.871863i | \(0.337088\pi\) | |||||||
\(642\) | 18.1421 | 0.716013 | ||||||||
\(643\) | −48.9706 | −1.93121 | −0.965605 | − | 0.260013i | \(-0.916273\pi\) | ||||
−0.965605 | + | 0.260013i | \(0.916273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.17157 | 0.124881 | ||||||||
\(646\) | 2.48528 | 0.0977821 | ||||||||
\(647\) | 5.31371 | 0.208903 | 0.104452 | − | 0.994530i | \(-0.466691\pi\) | ||||
0.104452 | + | 0.994530i | \(0.466691\pi\) | |||||||
\(648\) | −22.0711 | −0.867033 | ||||||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −59.0122 | −2.31110 | ||||||||
\(653\) | −2.14214 | −0.0838282 | −0.0419141 | − | 0.999121i | \(-0.513346\pi\) | ||||
−0.0419141 | + | 0.999121i | \(0.513346\pi\) | |||||||
\(654\) | −8.00000 | −0.312825 | ||||||||
\(655\) | 5.02944 | 0.196516 | ||||||||
\(656\) | −17.4853 | −0.682686 | ||||||||
\(657\) | 0.656854 | 0.0256263 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.31371 | 0.284902 | 0.142451 | − | 0.989802i | \(-0.454502\pi\) | ||||
0.142451 | + | 0.989802i | \(0.454502\pi\) | |||||||
\(660\) | −70.7696 | −2.75470 | ||||||||
\(661\) | 4.85786 | 0.188949 | 0.0944745 | − | 0.995527i | \(-0.469883\pi\) | ||||
0.0944745 | + | 0.995527i | \(0.469883\pi\) | |||||||
\(662\) | −69.6985 | −2.70891 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 57.6985 | 2.23914 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.0711 | 0.700240 | ||||||||
\(667\) | 13.8995 | 0.538191 | ||||||||
\(668\) | 71.6985 | 2.77410 | ||||||||
\(669\) | 2.82843 | 0.109353 | ||||||||
\(670\) | −39.2132 | −1.51494 | ||||||||
\(671\) | −33.5563 | −1.29543 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.4853 | 1.21367 | 0.606834 | − | 0.794828i | \(-0.292439\pi\) | ||||
0.606834 | + | 0.794828i | \(0.292439\pi\) | |||||||
\(674\) | 32.5563 | 1.25402 | ||||||||
\(675\) | 54.6274 | 2.10261 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.34315 | −0.243787 | −0.121893 | − | 0.992543i | \(-0.538897\pi\) | ||||
−0.121893 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(678\) | 7.89949 | 0.303378 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.89949 | 0.111191 | ||||||||
\(681\) | −19.6569 | −0.753252 | ||||||||
\(682\) | 44.6274 | 1.70887 | ||||||||
\(683\) | 17.3137 | 0.662491 | 0.331245 | − | 0.943545i | \(-0.392531\pi\) | ||||
0.331245 | + | 0.943545i | \(0.392531\pi\) | |||||||
\(684\) | 22.9706 | 0.878301 | ||||||||
\(685\) | −22.3137 | −0.852563 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.34315 | 0.242006 | ||||||||
\(688\) | 1.75736 | 0.0669987 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.4853 | 0.703723 | ||||||||
\(691\) | 37.9411 | 1.44335 | 0.721674 | − | 0.692233i | \(-0.243373\pi\) | ||||
0.721674 | + | 0.692233i | \(0.243373\pi\) | |||||||
\(692\) | 69.4558 | 2.64032 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −62.5269 | −2.37349 | ||||||||
\(695\) | −30.2426 | −1.14717 | ||||||||
\(696\) | −61.3553 | −2.32567 | ||||||||
\(697\) | 1.00000 | 0.0378777 | ||||||||
\(698\) | 32.1421 | 1.21660 | ||||||||
\(699\) | 4.00000 | 0.151294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.1421 | 1.59169 | 0.795843 | − | 0.605503i | \(-0.207028\pi\) | ||||
0.795843 | + | 0.605503i | \(0.207028\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.9117 | 1.69388 | ||||||||
\(704\) | 33.5563 | 1.26470 | ||||||||
\(705\) | −41.4558 | −1.56132 | ||||||||
\(706\) | −0.414214 | −0.0155891 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.51472 | −0.357585 | ||||||||
\(709\) | 27.6274 | 1.03757 | 0.518785 | − | 0.854905i | \(-0.326385\pi\) | ||||
0.518785 | + | 0.854905i | \(0.326385\pi\) | |||||||
\(710\) | −3.17157 | −0.119027 | ||||||||
\(711\) | −10.2426 | −0.384129 | ||||||||
\(712\) | 32.2843 | 1.20990 | ||||||||
\(713\) | −7.65685 | −0.286751 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.6569 | 0.809355 | ||||||||
\(717\) | −17.5147 | −0.654099 | ||||||||
\(718\) | −40.9706 | −1.52901 | ||||||||
\(719\) | −36.3848 | −1.35692 | −0.678462 | − | 0.734636i | \(-0.737353\pi\) | ||||
−0.678462 | + | 0.734636i | \(0.737353\pi\) | |||||||
\(720\) | 11.4853 | 0.428031 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 41.0416 | 1.52741 | ||||||||
\(723\) | −2.10051 | −0.0781186 | ||||||||
\(724\) | −73.2843 | −2.72359 | ||||||||
\(725\) | 94.9117 | 3.52493 | ||||||||
\(726\) | −2.24264 | −0.0832322 | ||||||||
\(727\) | −8.97056 | −0.332700 | −0.166350 | − | 0.986067i | \(-0.553198\pi\) | ||||
−0.166350 | + | 0.986067i | \(0.553198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 6.07107 | 0.224700 | ||||||||
\(731\) | −0.100505 | −0.00371731 | ||||||||
\(732\) | −53.2132 | −1.96682 | ||||||||
\(733\) | 21.0000 | 0.775653 | 0.387826 | − | 0.921732i | \(-0.373226\pi\) | ||||
0.387826 | + | 0.921732i | \(0.373226\pi\) | |||||||
\(734\) | −7.89949 | −0.291576 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.24264 | −0.0826648 | ||||||||
\(737\) | −14.4853 | −0.533572 | ||||||||
\(738\) | 14.0711 | 0.517963 | ||||||||
\(739\) | −36.2843 | −1.33474 | −0.667369 | − | 0.744727i | \(-0.732580\pi\) | ||||
−0.667369 | + | 0.744727i | \(0.732580\pi\) | |||||||
\(740\) | 109.711 | 4.03304 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.5980 | 1.74620 | 0.873100 | − | 0.487541i | \(-0.162106\pi\) | ||||
0.873100 | + | 0.487541i | \(0.162106\pi\) | |||||||
\(744\) | 33.7990 | 1.23913 | ||||||||
\(745\) | 11.4853 | 0.420788 | ||||||||
\(746\) | −59.0416 | −2.16167 | ||||||||
\(747\) | −13.0711 | −0.478245 | ||||||||
\(748\) | 2.24264 | 0.0819991 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 60.8701 | 2.22266 | ||||||||
\(751\) | 13.5563 | 0.494678 | 0.247339 | − | 0.968929i | \(-0.420444\pi\) | ||||
0.247339 | + | 0.968929i | \(0.420444\pi\) | |||||||
\(752\) | −22.9706 | −0.837650 | ||||||||
\(753\) | 15.5147 | 0.565388 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −72.6274 | −2.64318 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.4558 | −0.779826 | −0.389913 | − | 0.920852i | \(-0.627495\pi\) | ||||
−0.389913 | + | 0.920852i | \(0.627495\pi\) | |||||||
\(758\) | −19.8995 | −0.722782 | ||||||||
\(759\) | 6.82843 | 0.247856 | ||||||||
\(760\) | 101.397 | 3.67805 | ||||||||
\(761\) | −46.1421 | −1.67265 | −0.836326 | − | 0.548233i | \(-0.815301\pi\) | ||||
−0.836326 | + | 0.548233i | \(0.815301\pi\) | |||||||
\(762\) | 31.7990 | 1.15196 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 29.6985 | 1.07445 | ||||||||
\(765\) | −0.656854 | −0.0237486 | ||||||||
\(766\) | −33.8995 | −1.22484 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 42.3848 | 1.52943 | ||||||||
\(769\) | −1.45584 | −0.0524991 | −0.0262495 | − | 0.999655i | \(-0.508356\pi\) | ||||
−0.0262495 | + | 0.999655i | \(0.508356\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.2132 | −0.763975 | ||||||||
\(772\) | 80.9411 | 2.91313 | ||||||||
\(773\) | −17.6569 | −0.635073 | −0.317536 | − | 0.948246i | \(-0.602856\pi\) | ||||
−0.317536 | + | 0.948246i | \(0.602856\pi\) | |||||||
\(774\) | −1.41421 | −0.0508329 | ||||||||
\(775\) | −52.2843 | −1.87811 | ||||||||
\(776\) | 22.8284 | 0.819493 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.75736 | −0.0988561 | ||||||||
\(779\) | 34.9706 | 1.25295 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.17157 | −0.0419222 | ||||||||
\(782\) | −0.585786 | −0.0209477 | ||||||||
\(783\) | 55.5980 | 1.98691 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43.9706 | 1.56938 | ||||||||
\(786\) | 4.48528 | 0.159985 | ||||||||
\(787\) | −5.89949 | −0.210294 | −0.105147 | − | 0.994457i | \(-0.533531\pi\) | ||||
−0.105147 | + | 0.994457i | \(0.533531\pi\) | |||||||
\(788\) | −35.1127 | −1.25084 | ||||||||
\(789\) | −26.4853 | −0.942901 | ||||||||
\(790\) | −94.6690 | −3.36817 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 15.0711 | 0.535527 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 93.2548 | 3.30949 | ||||||||
\(795\) | −16.2426 | −0.576067 | ||||||||
\(796\) | 72.6274 | 2.57421 | ||||||||
\(797\) | 10.1421 | 0.359253 | 0.179626 | − | 0.983735i | \(-0.442511\pi\) | ||||
0.179626 | + | 0.983735i | \(0.442511\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.31371 | 0.0464757 | ||||||||
\(800\) | −15.3137 | −0.541421 | ||||||||
\(801\) | −7.31371 | −0.258417 | ||||||||
\(802\) | 74.3553 | 2.62558 | ||||||||
\(803\) | 2.24264 | 0.0791411 | ||||||||
\(804\) | −22.9706 | −0.810109 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.4558 | 0.896088 | ||||||||
\(808\) | 14.7574 | 0.519162 | ||||||||
\(809\) | 6.85786 | 0.241110 | 0.120555 | − | 0.992707i | \(-0.461533\pi\) | ||||
0.120555 | + | 0.992707i | \(0.461533\pi\) | |||||||
\(810\) | 46.2132 | 1.62377 | ||||||||
\(811\) | −34.1838 | −1.20035 | −0.600177 | − | 0.799867i | \(-0.704903\pi\) | ||||
−0.600177 | + | 0.799867i | \(0.704903\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.79899 | −0.343666 | ||||||||
\(814\) | 61.6985 | 2.16253 | ||||||||
\(815\) | 59.0122 | 2.06711 | ||||||||
\(816\) | 0.727922 | 0.0254824 | ||||||||
\(817\) | −3.51472 | −0.122964 | ||||||||
\(818\) | −28.8995 | −1.01045 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 85.4264 | 2.98322 | ||||||||
\(821\) | −27.9411 | −0.975152 | −0.487576 | − | 0.873081i | \(-0.662119\pi\) | ||||
−0.487576 | + | 0.873081i | \(0.662119\pi\) | |||||||
\(822\) | −19.8995 | −0.694075 | ||||||||
\(823\) | −3.31371 | −0.115509 | −0.0577543 | − | 0.998331i | \(-0.518394\pi\) | ||||
−0.0577543 | + | 0.998331i | \(0.518394\pi\) | |||||||
\(824\) | 61.7990 | 2.15287 | ||||||||
\(825\) | 46.6274 | 1.62336 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.6690 | −1.41420 | −0.707101 | − | 0.707113i | \(-0.749997\pi\) | ||||
−0.707101 | + | 0.707113i | \(0.749997\pi\) | |||||||
\(828\) | −5.41421 | −0.188157 | ||||||||
\(829\) | 23.6863 | 0.822659 | 0.411329 | − | 0.911487i | \(-0.365065\pi\) | ||||
0.411329 | + | 0.911487i | \(0.365065\pi\) | |||||||
\(830\) | −120.811 | −4.19342 | ||||||||
\(831\) | 45.2132 | 1.56843 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −26.9706 | −0.933914 | ||||||||
\(835\) | −71.6985 | −2.48123 | ||||||||
\(836\) | 78.4264 | 2.71243 | ||||||||
\(837\) | −30.6274 | −1.05864 | ||||||||
\(838\) | 47.2132 | 1.63095 | ||||||||
\(839\) | −37.5980 | −1.29803 | −0.649013 | − | 0.760777i | \(-0.724818\pi\) | ||||
−0.649013 | + | 0.760777i | \(0.724818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 67.5980 | 2.33096 | ||||||||
\(842\) | −10.8995 | −0.375621 | ||||||||
\(843\) | −0.727922 | −0.0250710 | ||||||||
\(844\) | −2.78680 | −0.0959255 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.4853 | 0.635537 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.00000 | −0.309061 | ||||||||
\(849\) | 0.142136 | 0.00487808 | ||||||||
\(850\) | −4.00000 | −0.137199 | ||||||||
\(851\) | −10.5858 | −0.362876 | ||||||||
\(852\) | −1.85786 | −0.0636494 | ||||||||
\(853\) | 35.0000 | 1.19838 | 0.599189 | − | 0.800608i | \(-0.295490\pi\) | ||||
0.599189 | + | 0.800608i | \(0.295490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.9706 | −0.785577 | ||||||||
\(856\) | −23.4558 | −0.801704 | ||||||||
\(857\) | 40.7990 | 1.39367 | 0.696833 | − | 0.717233i | \(-0.254592\pi\) | ||||
0.696833 | + | 0.717233i | \(0.254592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.0711 | −0.923653 | −0.461826 | − | 0.886970i | \(-0.652806\pi\) | ||||
−0.461826 | + | 0.886970i | \(0.652806\pi\) | |||||||
\(860\) | −8.58579 | −0.292773 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.9706 | −0.986741 | ||||||||
\(863\) | −56.1838 | −1.91252 | −0.956259 | − | 0.292522i | \(-0.905506\pi\) | ||||
−0.956259 | + | 0.292522i | \(0.905506\pi\) | |||||||
\(864\) | −8.97056 | −0.305185 | ||||||||
\(865\) | −69.4558 | −2.36157 | ||||||||
\(866\) | 1.24264 | 0.0422266 | ||||||||
\(867\) | 24.0000 | 0.815083 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34.9706 | −1.18630 | ||||||||
\(870\) | 128.468 | 4.35547 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.3431 | 0.350263 | ||||||||
\(873\) | −5.17157 | −0.175031 | ||||||||
\(874\) | −20.4853 | −0.692925 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.55635 | 0.120158 | ||||||||
\(877\) | −17.0000 | −0.574049 | −0.287025 | − | 0.957923i | \(-0.592666\pi\) | ||||
−0.287025 | + | 0.957923i | \(0.592666\pi\) | |||||||
\(878\) | −64.5269 | −2.17768 | ||||||||
\(879\) | −31.7574 | −1.07115 | ||||||||
\(880\) | 39.2132 | 1.32188 | ||||||||
\(881\) | −46.4558 | −1.56514 | −0.782569 | − | 0.622564i | \(-0.786091\pi\) | ||||
−0.782569 | + | 0.622564i | \(0.786091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.95837 | 0.267820 | 0.133910 | − | 0.990993i | \(-0.457247\pi\) | ||||
0.133910 | + | 0.990993i | \(0.457247\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.51472 | 0.319834 | ||||||||
\(886\) | 34.6274 | 1.16333 | ||||||||
\(887\) | 10.6274 | 0.356834 | 0.178417 | − | 0.983955i | \(-0.442902\pi\) | ||||
0.178417 | + | 0.983955i | \(0.442902\pi\) | |||||||
\(888\) | 46.7279 | 1.56809 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −67.5980 | −2.26589 | ||||||||
\(891\) | 17.0711 | 0.571902 | ||||||||
\(892\) | −7.65685 | −0.256370 | ||||||||
\(893\) | 45.9411 | 1.53736 | ||||||||
\(894\) | 10.2426 | 0.342565 | ||||||||
\(895\) | −21.6569 | −0.723909 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −37.4558 | −1.24992 | ||||||||
\(899\) | −53.2132 | −1.77476 | ||||||||
\(900\) | −36.9706 | −1.23235 | ||||||||
\(901\) | 0.514719 | 0.0171478 | ||||||||
\(902\) | 48.0416 | 1.59961 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.2132 | −0.339686 | ||||||||
\(905\) | 73.2843 | 2.43605 | ||||||||
\(906\) | −64.7696 | −2.15182 | ||||||||
\(907\) | 18.7279 | 0.621850 | 0.310925 | − | 0.950434i | \(-0.399361\pi\) | ||||
0.310925 | + | 0.950434i | \(0.399361\pi\) | |||||||
\(908\) | 53.2132 | 1.76594 | ||||||||
\(909\) | −3.34315 | −0.110885 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.3431 | −0.607736 | −0.303868 | − | 0.952714i | \(-0.598278\pi\) | ||||
−0.303868 | + | 0.952714i | \(0.598278\pi\) | |||||||
\(912\) | 25.4558 | 0.842927 | ||||||||
\(913\) | −44.6274 | −1.47695 | ||||||||
\(914\) | 60.3553 | 1.99638 | ||||||||
\(915\) | 53.2132 | 1.75917 | ||||||||
\(916\) | −17.1716 | −0.567365 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.34315 | −0.0773353 | ||||||||
\(919\) | 25.3137 | 0.835022 | 0.417511 | − | 0.908672i | \(-0.362902\pi\) | ||||
0.417511 | + | 0.908672i | \(0.362902\pi\) | |||||||
\(920\) | −23.8995 | −0.787943 | ||||||||
\(921\) | −10.2843 | −0.338878 | ||||||||
\(922\) | −30.5563 | −1.00632 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −72.2843 | −2.37669 | ||||||||
\(926\) | 45.2132 | 1.48580 | ||||||||
\(927\) | −14.0000 | −0.459820 | ||||||||
\(928\) | −15.5858 | −0.511629 | ||||||||
\(929\) | 18.9411 | 0.621438 | 0.310719 | − | 0.950502i | \(-0.399430\pi\) | ||||
0.310719 | + | 0.950502i | \(0.399430\pi\) | |||||||
\(930\) | −70.7696 | −2.32063 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.8284 | −0.354697 | ||||||||
\(933\) | 38.2843 | 1.25337 | ||||||||
\(934\) | 20.7279 | 0.678238 | ||||||||
\(935\) | −2.24264 | −0.0733422 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.85786 | −0.289374 | −0.144687 | − | 0.989477i | \(-0.546217\pi\) | ||||
−0.144687 | + | 0.989477i | \(0.546217\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.7990 | 0.646116 | ||||||||
\(940\) | 112.225 | 3.66039 | ||||||||
\(941\) | −19.0294 | −0.620342 | −0.310171 | − | 0.950681i | \(-0.600386\pi\) | ||||
−0.310171 | + | 0.950681i | \(0.600386\pi\) | |||||||
\(942\) | 39.2132 | 1.27764 | ||||||||
\(943\) | −8.24264 | −0.268417 | ||||||||
\(944\) | 5.27208 | 0.171592 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.82843 | −0.156986 | ||||||||
\(947\) | −18.5858 | −0.603957 | −0.301978 | − | 0.953315i | \(-0.597647\pi\) | ||||
−0.301978 | + | 0.953315i | \(0.597647\pi\) | |||||||
\(948\) | −55.4558 | −1.80112 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −139.882 | −4.53838 | ||||||||
\(951\) | 30.1838 | 0.978776 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.6274 | −1.25126 | −0.625632 | − | 0.780118i | \(-0.715159\pi\) | ||||
−0.625632 | + | 0.780118i | \(0.715159\pi\) | |||||||
\(954\) | 7.24264 | 0.234489 | ||||||||
\(955\) | −29.6985 | −0.961020 | ||||||||
\(956\) | 47.4142 | 1.53349 | ||||||||
\(957\) | 47.4558 | 1.53403 | ||||||||
\(958\) | 92.6690 | 2.99400 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −53.2132 | −1.71745 | ||||||||
\(961\) | −1.68629 | −0.0543965 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.31371 | 0.171232 | ||||||||
\(964\) | 5.68629 | 0.183143 | ||||||||
\(965\) | −80.9411 | −2.60559 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.2426 | 0.908222 | 0.454111 | − | 0.890945i | \(-0.349957\pi\) | ||||
0.454111 | + | 0.890945i | \(0.349957\pi\) | |||||||
\(968\) | 2.89949 | 0.0931933 | ||||||||
\(969\) | −1.45584 | −0.0467685 | ||||||||
\(970\) | −47.7990 | −1.53473 | ||||||||
\(971\) | 40.3431 | 1.29467 | 0.647337 | − | 0.762204i | \(-0.275883\pi\) | ||||
0.647337 | + | 0.762204i | \(0.275883\pi\) | |||||||
\(972\) | −37.8995 | −1.21563 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −50.6274 | −1.62221 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.4853 | 0.943801 | ||||||||
\(977\) | 48.5980 | 1.55479 | 0.777394 | − | 0.629015i | \(-0.216541\pi\) | ||||
0.777394 | + | 0.629015i | \(0.216541\pi\) | |||||||
\(978\) | 52.6274 | 1.68284 | ||||||||
\(979\) | −24.9706 | −0.798063 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.34315 | −0.0748109 | ||||||||
\(982\) | 85.2548 | 2.72059 | ||||||||
\(983\) | 42.0000 | 1.33959 | 0.669796 | − | 0.742545i | \(-0.266382\pi\) | ||||
0.669796 | + | 0.742545i | \(0.266382\pi\) | |||||||
\(984\) | 36.3848 | 1.15990 | ||||||||
\(985\) | 35.1127 | 1.11878 | ||||||||
\(986\) | −4.07107 | −0.129649 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.828427 | 0.0263425 | ||||||||
\(990\) | −31.5563 | −1.00293 | ||||||||
\(991\) | 28.2426 | 0.897157 | 0.448579 | − | 0.893743i | \(-0.351930\pi\) | ||||
0.448579 | + | 0.893743i | \(0.351930\pi\) | |||||||
\(992\) | 8.58579 | 0.272599 | ||||||||
\(993\) | 40.8284 | 1.29565 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −72.6274 | −2.30244 | ||||||||
\(996\) | −70.7696 | −2.24242 | ||||||||
\(997\) | −19.9706 | −0.632474 | −0.316237 | − | 0.948680i | \(-0.602419\pi\) | ||||
−0.316237 | + | 0.948680i | \(0.602419\pi\) | |||||||
\(998\) | 67.6985 | 2.14296 | ||||||||
\(999\) | −42.3431 | −1.33968 |
(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 | 8281.2.a.x.1.2 | 2 | ||
7.6 | odd | 2 | 8281.2.a.y.1.2 | 2 | |||
13.4 | even | 6 | 637.2.f.f.393.2 | yes | 4 | ||
13.10 | even | 6 | 637.2.f.f.295.2 | yes | 4 | ||
13.12 | even | 2 | 8281.2.a.p.1.1 | 2 | |||
91.4 | even | 6 | 637.2.h.b.471.1 | 4 | |||
91.10 | odd | 6 | 637.2.g.g.373.2 | 4 | |||
91.17 | odd | 6 | 637.2.h.c.471.1 | 4 | |||
91.23 | even | 6 | 637.2.h.b.165.1 | 4 | |||
91.30 | even | 6 | 637.2.g.f.263.2 | 4 | |||
91.62 | odd | 6 | 637.2.f.e.295.2 | ✓ | 4 | ||
91.69 | odd | 6 | 637.2.f.e.393.2 | yes | 4 | ||
91.75 | odd | 6 | 637.2.h.c.165.1 | 4 | |||
91.82 | odd | 6 | 637.2.g.g.263.2 | 4 | |||
91.88 | even | 6 | 637.2.g.f.373.2 | 4 | |||
91.90 | odd | 2 | 8281.2.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.e.295.2 | ✓ | 4 | 91.62 | odd | 6 | ||
637.2.f.e.393.2 | yes | 4 | 91.69 | odd | 6 | ||
637.2.f.f.295.2 | yes | 4 | 13.10 | even | 6 | ||
637.2.f.f.393.2 | yes | 4 | 13.4 | even | 6 | ||
637.2.g.f.263.2 | 4 | 91.30 | even | 6 | |||
637.2.g.f.373.2 | 4 | 91.88 | even | 6 | |||
637.2.g.g.263.2 | 4 | 91.82 | odd | 6 | |||
637.2.g.g.373.2 | 4 | 91.10 | odd | 6 | |||
637.2.h.b.165.1 | 4 | 91.23 | even | 6 | |||
637.2.h.b.471.1 | 4 | 91.4 | even | 6 | |||
637.2.h.c.165.1 | 4 | 91.75 | odd | 6 | |||
637.2.h.c.471.1 | 4 | 91.17 | odd | 6 | |||
8281.2.a.o.1.1 | 2 | 91.90 | odd | 2 | |||
8281.2.a.p.1.1 | 2 | 13.12 | even | 2 | |||
8281.2.a.x.1.2 | 2 | 1.1 | even | 1 | trivial | ||
8281.2.a.y.1.2 | 2 | 7.6 | odd | 2 |