Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(1,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.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: | \(2.20387109579\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 276.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.41421 | 1.52688 | 0.763441 | − | 0.645877i | \(-0.223508\pi\) | ||||
0.763441 | + | 0.645877i | \(0.223508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421 | 0.534522 | 0.267261 | − | 0.963624i | \(-0.413881\pi\) | ||||
0.267261 | + | 0.963624i | \(0.413881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.65685 | −1.70561 | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.65685 | −1.56893 | −0.784465 | − | 0.620174i | \(-0.787062\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.24264 | 1.51406 | 0.757031 | − | 0.653379i | \(-0.226649\pi\) | ||||
0.757031 | + | 0.653379i | \(0.226649\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.242641 | 0.0556656 | 0.0278328 | − | 0.999613i | \(-0.491139\pi\) | ||||
0.0278328 | + | 0.999613i | \(0.491139\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41421 | 0.308607 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.17157 | 0.588946 | 0.294473 | − | 0.955660i | \(-0.404856\pi\) | ||||
0.294473 | + | 0.955660i | \(0.404856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.82843 | −1.22642 | −0.613211 | − | 0.789919i | \(-0.710122\pi\) | ||||
−0.613211 | + | 0.789919i | \(0.710122\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.65685 | −0.984732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.82843 | 0.816153 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.82843 | −1.45138 | −0.725692 | − | 0.688019i | \(-0.758480\pi\) | ||||
−0.725692 | + | 0.688019i | \(0.758480\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.65685 | −0.905822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.58579 | −0.394329 | −0.197164 | − | 0.980370i | \(-0.563173\pi\) | ||||
−0.197164 | + | 0.980370i | \(0.563173\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.41421 | 0.508961 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.48528 | 0.945976 | 0.472988 | − | 0.881069i | \(-0.343175\pi\) | ||||
0.472988 | + | 0.881069i | \(0.343175\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.24264 | 0.874145 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.41421 | 1.01842 | 0.509210 | − | 0.860642i | \(-0.329938\pi\) | ||||
0.509210 | + | 0.860642i | \(0.329938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.3137 | −2.60426 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.242641 | 0.0321385 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.17157 | −0.412904 | −0.206452 | − | 0.978457i | \(-0.566192\pi\) | ||||
−0.206452 | + | 0.978457i | \(0.566192\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82843 | 1.13036 | 0.565182 | − | 0.824966i | \(-0.308806\pi\) | ||||
0.565182 | + | 0.824966i | \(0.308806\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.41421 | 0.178174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −19.3137 | −2.39557 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.2426 | −1.98435 | −0.992177 | − | 0.124838i | \(-0.960159\pi\) | ||||
−0.992177 | + | 0.124838i | \(0.960159\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3137 | −1.34269 | −0.671345 | − | 0.741145i | \(-0.734283\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6569 | 1.36433 | 0.682166 | − | 0.731198i | \(-0.261038\pi\) | ||||
0.682166 | + | 0.731198i | \(0.261038\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.65685 | 0.768667 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.00000 | −0.911685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.07107 | 0.795557 | 0.397779 | − | 0.917481i | \(-0.369781\pi\) | ||||
0.397779 | + | 0.917481i | \(0.369781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.65685 | 0.181863 | 0.0909317 | − | 0.995857i | \(-0.471016\pi\) | ||||
0.0909317 | + | 0.995857i | \(0.471016\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.3137 | 2.31180 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.17157 | 0.340028 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.07107 | −0.113533 | −0.0567665 | − | 0.998387i | \(-0.518079\pi\) | ||||
−0.0567665 | + | 0.998387i | \(0.518079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.82843 | −0.708075 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.828427 | 0.0849948 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.1421 | −1.23285 | −0.616424 | − | 0.787415i | \(-0.711419\pi\) | ||||
−0.616424 | + | 0.787415i | \(0.711419\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.65685 | −0.568535 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.3137 | 1.72278 | 0.861389 | − | 0.507946i | \(-0.169595\pi\) | ||||
0.861389 | + | 0.507946i | \(0.169595\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7279 | 1.25412 | 0.627060 | − | 0.778971i | \(-0.284258\pi\) | ||||
0.627060 | + | 0.778971i | \(0.284258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.82843 | 0.471206 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.65685 | −0.546869 | −0.273434 | − | 0.961891i | \(-0.588160\pi\) | ||||
−0.273434 | + | 0.961891i | \(0.588160\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.65685 | −0.733394 | −0.366697 | − | 0.930341i | \(-0.619511\pi\) | ||||
−0.366697 | + | 0.930341i | \(0.619511\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.82843 | −0.837957 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.4142 | −1.07376 | −0.536879 | − | 0.843659i | \(-0.680397\pi\) | ||||
−0.536879 | + | 0.843659i | \(0.680397\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.41421 | 0.318377 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.65685 | −0.522976 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.82843 | 0.809301 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.0000 | 1.90909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.485281 | −0.0430618 | −0.0215309 | − | 0.999768i | \(-0.506854\pi\) | ||||
−0.0215309 | + | 0.999768i | \(0.506854\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.58579 | −0.227666 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.65685 | −0.144760 | −0.0723800 | − | 0.997377i | \(-0.523059\pi\) | ||||
−0.0723800 | + | 0.997377i | \(0.523059\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.343146 | 0.0297545 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.41421 | 0.293849 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.07107 | 0.0915075 | 0.0457537 | − | 0.998953i | \(-0.485431\pi\) | ||||
0.0457537 | + | 0.998953i | \(0.485431\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.65685 | −0.140533 | −0.0702663 | − | 0.997528i | \(-0.522385\pi\) | ||||
−0.0702663 | + | 0.997528i | \(0.522385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.48528 | 0.546159 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 32.0000 | 2.67597 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.8284 | 0.899252 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.00000 | −0.412393 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.24264 | 0.183724 | 0.0918621 | − | 0.995772i | \(-0.470718\pi\) | ||||
0.0918621 | + | 0.995772i | \(0.470718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.6569 | 1.11138 | 0.555690 | − | 0.831390i | \(-0.312454\pi\) | ||||
0.555690 | + | 0.831390i | \(0.312454\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.24264 | 0.504688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.3137 | −1.87260 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.17157 | −0.253119 | −0.126560 | − | 0.991959i | \(-0.540393\pi\) | ||||
−0.126560 | + | 0.991959i | \(0.540393\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.41421 | 0.587985 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.41421 | 0.111456 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.17157 | 0.405069 | 0.202534 | − | 0.979275i | \(-0.435082\pi\) | ||||
0.202534 | + | 0.979275i | \(0.435082\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −19.3137 | −1.50357 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.6569 | 1.05680 | 0.528400 | − | 0.848996i | \(-0.322792\pi\) | ||||
0.528400 | + | 0.848996i | \(0.322792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.242641 | 0.0185552 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.51472 | 0.419276 | 0.209638 | − | 0.977779i | \(-0.432771\pi\) | ||||
0.209638 | + | 0.977779i | \(0.432771\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.41421 | 0.711648 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.17157 | −0.238390 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.4853 | 1.08268 | 0.541340 | − | 0.840804i | \(-0.317917\pi\) | ||||
0.541340 | + | 0.840804i | \(0.317917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.31371 | 0.394965 | 0.197482 | − | 0.980306i | \(-0.436723\pi\) | ||||
0.197482 | + | 0.980306i | \(0.436723\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.82843 | 0.652616 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −30.1421 | −2.21609 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −35.3137 | −2.58239 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.41421 | 0.102869 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.17157 | −0.0847720 | −0.0423860 | − | 0.999101i | \(-0.513496\pi\) | ||||
−0.0423860 | + | 0.999101i | \(0.513496\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3137 | 0.814379 | 0.407189 | − | 0.913344i | \(-0.366509\pi\) | ||||
0.407189 | + | 0.913344i | \(0.366509\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.3137 | −1.38308 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.82843 | −0.628999 | −0.314500 | − | 0.949258i | \(-0.601837\pi\) | ||||
−0.314500 | + | 0.949258i | \(0.601837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.2426 | 1.43496 | 0.717481 | − | 0.696578i | \(-0.245295\pi\) | ||||
0.717481 | + | 0.696578i | \(0.245295\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.2426 | −1.14567 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.48528 | 0.314805 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.82843 | −0.476918 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.37258 | −0.0949436 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.485281 | −0.0334081 | −0.0167041 | − | 0.999860i | \(-0.505317\pi\) | ||||
−0.0167041 | + | 0.999860i | \(0.505317\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.3137 | −0.775203 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.82843 | −0.602094 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.65685 | −0.655550 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.6569 | 0.787697 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −35.3137 | −2.37546 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0000 | 0.803579 | 0.401790 | − | 0.915732i | \(-0.368388\pi\) | ||||
0.401790 | + | 0.915732i | \(0.368388\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8284 | 0.718708 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.9706 | −1.78226 | −0.891132 | − | 0.453743i | \(-0.850088\pi\) | ||||
−0.891132 | + | 0.453743i | \(0.850088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.6569 | −1.02571 | −0.512857 | − | 0.858474i | \(-0.671413\pi\) | ||||
−0.512857 | + | 0.858474i | \(0.671413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.1421 | 1.44439 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.07107 | 0.459315 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3431 | 0.669042 | 0.334521 | − | 0.942388i | \(-0.391425\pi\) | ||||
0.334521 | + | 0.942388i | \(0.391425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.7990 | −1.40420 | −0.702098 | − | 0.712080i | \(-0.747753\pi\) | ||||
−0.702098 | + | 0.712080i | \(0.747753\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.0711 | −1.09063 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.37258 | −0.0873354 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.65685 | 0.104999 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.4558 | 1.35428 | 0.677140 | − | 0.735854i | \(-0.263219\pi\) | ||||
0.677140 | + | 0.735854i | \(0.263219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.65685 | −0.355643 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.3137 | 1.33472 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −29.3137 | −1.82854 | −0.914269 | − | 0.405107i | \(-0.867234\pi\) | ||||
−0.914269 | + | 0.405107i | \(0.867234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.4853 | −0.775798 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.17157 | 0.196315 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.7990 | −0.974207 | −0.487104 | − | 0.873344i | \(-0.661947\pi\) | ||||
−0.487104 | + | 0.873344i | \(0.661947\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.3137 | 1.55501 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.07107 | −0.0655483 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.1716 | 1.41280 | 0.706398 | − | 0.707815i | \(-0.250319\pi\) | ||||
0.706398 | + | 0.707815i | \(0.250319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.8284 | 1.14375 | 0.571873 | − | 0.820342i | \(-0.306217\pi\) | ||||
0.571873 | + | 0.820342i | \(0.306217\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.00000 | −0.484182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −37.6569 | −2.27079 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.6274 | 0.758708 | 0.379354 | − | 0.925252i | \(-0.376146\pi\) | ||||
0.379354 | + | 0.925252i | \(0.376146\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.82843 | −0.408807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.0711 | 1.49561 | 0.747807 | − | 0.663916i | \(-0.231107\pi\) | ||||
0.747807 | + | 0.663916i | \(0.231107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.8995 | −1.30179 | −0.650895 | − | 0.759168i | \(-0.725606\pi\) | ||||
−0.650895 | + | 0.759168i | \(0.725606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.828427 | 0.0490718 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.82843 | −0.166957 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.9706 | 1.29239 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.1421 | −0.711785 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.75736 | −0.570031 | −0.285016 | − | 0.958523i | \(-0.591999\pi\) | ||||
−0.285016 | + | 0.958523i | \(0.591999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.8284 | −0.630455 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.65685 | −0.328244 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.65685 | −0.327144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.65685 | −0.210778 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.3137 | 0.994647 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 30.1421 | 1.72593 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4558 | 1.22455 | 0.612275 | − | 0.790645i | \(-0.290255\pi\) | ||||
0.612275 | + | 0.790645i | \(0.290255\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.7279 | 0.724066 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.82843 | 0.500614 | 0.250307 | − | 0.968166i | \(-0.419468\pi\) | ||||
0.250307 | + | 0.968166i | \(0.419468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.34315 | −0.245489 | −0.122745 | − | 0.992438i | \(-0.539170\pi\) | ||||
−0.122745 | + | 0.992438i | \(0.539170\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.82843 | 0.272051 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.82843 | −0.495854 | −0.247927 | − | 0.968779i | \(-0.579749\pi\) | ||||
−0.247927 | + | 0.968779i | \(0.579749\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.9411 | −1.00451 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.65685 | −0.315735 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.51472 | 0.0842812 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −37.6569 | −2.08883 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.65685 | −0.423425 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.17157 | 0.505645 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.14214 | 0.117742 | 0.0588712 | − | 0.998266i | \(-0.481250\pi\) | ||||
0.0588712 | + | 0.998266i | \(0.481250\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.82843 | −0.483795 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −55.4558 | −3.02988 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.17157 | 0.390660 | 0.195330 | − | 0.980738i | \(-0.437422\pi\) | ||||
0.195330 | + | 0.980738i | \(0.437422\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.4142 | −0.619935 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 38.6274 | 2.09179 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.41421 | 0.183815 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.17157 | −0.384990 | −0.192495 | − | 0.981298i | \(-0.561658\pi\) | ||||
−0.192495 | + | 0.981298i | \(0.561658\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.31371 | 0.177379 | 0.0886894 | − | 0.996059i | \(-0.471732\pi\) | ||||
0.0886894 | + | 0.996059i | \(0.471732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.65685 | −0.301941 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.1421 | 0.859159 | 0.429580 | − | 0.903029i | \(-0.358662\pi\) | ||||
0.429580 | + | 0.903029i | \(0.358662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −38.6274 | −2.05013 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.82843 | 0.467250 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.8284 | 1.62706 | 0.813531 | − | 0.581521i | \(-0.197542\pi\) | ||||
0.813531 | + | 0.581521i | \(0.197542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9411 | −0.996901 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.0000 | 1.10221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 39.7990 | 2.08317 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.2426 | −1.05666 | −0.528329 | − | 0.849040i | \(-0.677181\pi\) | ||||
−0.528329 | + | 0.849040i | \(0.677181\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.4853 | 0.544369 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.8284 | −0.871343 | −0.435671 | − | 0.900106i | \(-0.643489\pi\) | ||||
−0.435671 | + | 0.900106i | \(0.643489\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.9411 | −0.924015 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7279 | 0.859256 | 0.429628 | − | 0.903006i | \(-0.358645\pi\) | ||||
0.429628 | + | 0.903006i | \(0.358645\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.485281 | −0.0248617 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.7990 | 0.602900 | 0.301450 | − | 0.953482i | \(-0.402529\pi\) | ||||
0.301450 | + | 0.953482i | \(0.402529\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −27.3137 | −1.39204 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.58579 | −0.131443 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.7279 | −0.543927 | −0.271964 | − | 0.962308i | \(-0.587673\pi\) | ||||
−0.271964 | + | 0.962308i | \(0.587673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.24264 | 0.315704 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.65685 | −0.0835772 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.1421 | 1.21472 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.6274 | 1.43677 | 0.718384 | − | 0.695646i | \(-0.244882\pi\) | ||||
0.718384 | + | 0.695646i | \(0.244882\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.343146 | 0.0171788 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.89949 | 0.194731 | 0.0973657 | − | 0.995249i | \(-0.468958\pi\) | ||||
0.0973657 | + | 0.995249i | \(0.468958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.6274 | 1.92417 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.41421 | 0.169654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 49.9411 | 2.47549 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.6569 | 0.873075 | 0.436538 | − | 0.899686i | \(-0.356205\pi\) | ||||
0.436538 | + | 0.899686i | \(0.356205\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.07107 | 0.0528319 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.48528 | −0.220706 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.65685 | 0.277684 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.65685 | −0.0811365 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.68629 | 0.424353 | 0.212177 | − | 0.977231i | \(-0.431945\pi\) | ||||
0.212177 | + | 0.977231i | \(0.431945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.68629 | 0.325870 | 0.162935 | − | 0.986637i | \(-0.447904\pi\) | ||||
0.162935 | + | 0.986637i | \(0.447904\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.48528 | 0.315325 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 41.5563 | 2.01578 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4853 | 0.604205 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 32.0000 | 1.54497 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.00000 | −0.192673 | −0.0963366 | − | 0.995349i | \(-0.530713\pi\) | ||||
−0.0963366 | + | 0.995349i | \(0.530713\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.9706 | −1.48835 | −0.744175 | − | 0.667985i | \(-0.767157\pi\) | ||||
−0.744175 | + | 0.667985i | \(0.767157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.8284 | 0.519183 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.242641 | 0.0116071 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.6569 | −0.651806 | −0.325903 | − | 0.945403i | \(-0.605668\pi\) | ||||
−0.325903 | + | 0.945403i | \(0.605668\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.2843 | −0.773689 | −0.386845 | − | 0.922145i | \(-0.626435\pi\) | ||||
−0.386845 | + | 0.922145i | \(0.626435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.65685 | −0.173352 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.24264 | 0.106073 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.3431 | 1.33760 | 0.668798 | − | 0.743444i | \(-0.266809\pi\) | ||||
0.668798 | + | 0.743444i | \(0.266809\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3137 | 0.532742 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.6569 | 0.641655 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.3137 | −1.28049 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.8284 | −1.72276 | −0.861381 | − | 0.507960i | \(-0.830400\pi\) | ||||
−0.861381 | + | 0.507960i | \(0.830400\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.24264 | 0.291382 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.4558 | −1.27875 | −0.639373 | − | 0.768897i | \(-0.720806\pi\) | ||||
−0.639373 | + | 0.768897i | \(0.720806\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.9706 | 1.34638 | 0.673188 | − | 0.739471i | \(-0.264924\pi\) | ||||
0.673188 | + | 0.739471i | \(0.264924\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −23.3137 | −1.08115 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.1127 | −1.25463 | −0.627313 | − | 0.778767i | \(-0.715845\pi\) | ||||
−0.627313 | + | 0.778767i | \(0.715845\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.9706 | −1.06068 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.17157 | −0.146138 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.6274 | 0.672569 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.61522 | 0.0741115 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.41421 | 0.339474 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −42.6274 | −1.94770 | −0.973848 | − | 0.227200i | \(-0.927043\pi\) | ||||
−0.973848 | + | 0.227200i | \(0.927043\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 49.9411 | 2.27712 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.41421 | 0.0643489 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −41.4558 | −1.88241 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.6569 | −1.16262 | −0.581312 | − | 0.813681i | \(-0.697460\pi\) | ||||
−0.581312 | + | 0.813681i | \(0.697460\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.17157 | 0.233867 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.1421 | −1.27004 | −0.635018 | − | 0.772497i | \(-0.719007\pi\) | ||||
−0.635018 | + | 0.772497i | \(0.719007\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.7990 | 0.891702 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.3137 | −0.868087 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | −0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.51472 | −0.336405 | −0.168203 | − | 0.985752i | \(-0.553796\pi\) | ||||
−0.168203 | + | 0.985752i | \(0.553796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.6569 | 0.610143 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.3137 | 1.03951 | 0.519753 | − | 0.854316i | \(-0.326024\pi\) | ||||
0.519753 | + | 0.854316i | \(0.326024\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 59.1127 | 2.63048 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.0000 | 0.843820 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.51472 | −0.244436 | −0.122218 | − | 0.992503i | \(-0.539001\pi\) | ||||
−0.122218 | + | 0.992503i | \(0.539001\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.4853 | 0.729266 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.242641 | 0.0107128 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 43.4558 | 1.91489 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.6863 | −1.61346 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.51472 | 0.242069 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.24264 | 0.0982519 | 0.0491259 | − | 0.998793i | \(-0.484356\pi\) | ||||
0.0491259 | + | 0.998793i | \(0.484356\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.2132 | −1.80213 | −0.901064 | − | 0.433687i | \(-0.857213\pi\) | ||||
−0.901064 | + | 0.433687i | \(0.857213\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.41421 | 0.410870 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42.6274 | −1.85688 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.17157 | −0.137635 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.3137 | 0.490051 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.3137 | −0.835004 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.4853 | 0.625086 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.2843 | 1.21829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.2843 | −1.38801 | −0.694005 | − | 0.719971i | \(-0.744155\pi\) | ||||
−0.694005 | + | 0.719971i | \(0.744155\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.31371 | 0.228033 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.1421 | −1.11981 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.85786 | 0.0794365 | 0.0397183 | − | 0.999211i | \(-0.487354\pi\) | ||||
0.0397183 | + | 0.999211i | \(0.487354\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.82843 | 0.376788 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.769553 | 0.0327840 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0000 | 0.425243 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −30.1421 | −1.27946 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.2426 | 1.28142 | 0.640711 | − | 0.767782i | \(-0.278640\pi\) | ||||
0.640711 | + | 0.767782i | \(0.278640\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6274 | 0.618674 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.3137 | −1.49095 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.1716 | 0.892275 | 0.446138 | − | 0.894964i | \(-0.352799\pi\) | ||||
0.446138 | + | 0.894964i | \(0.352799\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.9706 | −1.63950 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.41421 | 0.0593914 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.75736 | 0.409050 | 0.204525 | − | 0.978861i | \(-0.434435\pi\) | ||||
0.204525 | + | 0.978861i | \(0.434435\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.7279 | −1.03483 | −0.517416 | − | 0.855734i | \(-0.673106\pi\) | ||||
−0.517416 | + | 0.855734i | \(0.673106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.17157 | −0.0489432 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.65685 | 0.277610 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −46.6274 | −1.94112 | −0.970562 | − | 0.240850i | \(-0.922574\pi\) | ||||
−0.970562 | + | 0.240850i | \(0.922574\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.3137 | 0.470182 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.34315 | 0.0972101 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −41.9411 | −1.73702 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.3137 | −0.798524 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.6569 | −1.38917 | −0.694584 | − | 0.719412i | \(-0.744411\pi\) | ||||
−0.694584 | + | 0.719412i | \(0.744411\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.65685 | −0.0682695 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.82843 | −0.363153 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.3431 | −1.32817 | −0.664087 | − | 0.747655i | \(-0.731180\pi\) | ||||
−0.664087 | + | 0.747655i | \(0.731180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.1421 | 1.23571 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.2426 | 0.828476 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 44.2843 | 1.80941 | 0.904703 | − | 0.426043i | \(-0.140093\pi\) | ||||
0.904703 | + | 0.426043i | \(0.140093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.3137 | 1.44048 | 0.720238 | − | 0.693727i | \(-0.244033\pi\) | ||||
0.720238 | + | 0.693727i | \(0.244033\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.2426 | −0.661451 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 71.6985 | 2.91496 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.6569 | −0.879025 | −0.439512 | − | 0.898237i | \(-0.644849\pi\) | ||||
−0.439512 | + | 0.898237i | \(0.644849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.48528 | 0.181753 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.6863 | −1.48417 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.51472 | 0.0611789 | 0.0305895 | − | 0.999532i | \(-0.490262\pi\) | ||||
0.0305895 | + | 0.999532i | \(0.490262\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.82843 | −0.275349 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.89949 | 0.318022 | 0.159011 | − | 0.987277i | \(-0.449170\pi\) | ||||
0.159011 | + | 0.987277i | \(0.449170\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.24264 | 0.331300 | 0.165650 | − | 0.986185i | \(-0.447028\pi\) | ||||
0.165650 | + | 0.986185i | \(0.447028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.51472 | −0.0606859 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.37258 | −0.0548157 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −55.1127 | −2.19749 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.24264 | 0.168897 | 0.0844484 | − | 0.996428i | \(-0.473087\pi\) | ||||
0.0844484 | + | 0.996428i | \(0.473087\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.485281 | −0.0192882 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.65685 | −0.0657503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.2843 | 1.12066 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.3137 | −0.447563 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.6985 | −0.778043 | −0.389022 | − | 0.921229i | \(-0.627187\pi\) | ||||
−0.389022 | + | 0.921229i | \(0.627187\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.7279 | 0.659685 | 0.329842 | − | 0.944036i | \(-0.393004\pi\) | ||||
0.329842 | + | 0.944036i | \(0.393004\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.82843 | −0.347619 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.79899 | −0.385238 | −0.192619 | − | 0.981274i | \(-0.561698\pi\) | ||||
−0.192619 | + | 0.981274i | \(0.561698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.9411 | 0.704251 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.65685 | −0.378482 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.9706 | 0.742375 | 0.371188 | − | 0.928558i | \(-0.378951\pi\) | ||||
0.371188 | + | 0.928558i | \(0.378951\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.65685 | −0.221032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.6569 | 0.454777 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.201010 | −0.00783024 | −0.00391512 | − | 0.999992i | \(-0.501246\pi\) | ||||
−0.00391512 | + | 0.999992i | \(0.501246\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.14214 | 0.316692 | 0.158346 | − | 0.987384i | \(-0.449384\pi\) | ||||
0.158346 | + | 0.987384i | \(0.449384\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −35.3137 | −1.37147 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.17157 | 0.0454316 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.17157 | 0.122804 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0000 | 0.463947 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49.9411 | −1.92796 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3137 | 0.898677 | 0.449339 | − | 0.893361i | \(-0.351660\pi\) | ||||
0.449339 | + | 0.893361i | \(0.351660\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.65685 | 0.256222 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.6985 | −0.603342 | −0.301671 | − | 0.953412i | \(-0.597544\pi\) | ||||
−0.301671 | + | 0.953412i | \(0.597544\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.1716 | −0.658984 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.8284 | 0.414946 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.6274 | −0.712758 | −0.356379 | − | 0.934341i | \(-0.615989\pi\) | ||||
−0.356379 | + | 0.934341i | \(0.615989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.65685 | 0.139721 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.9706 | −1.02899 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.9411 | −1.59783 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4558 | −0.968386 | −0.484193 | − | 0.874961i | \(-0.660887\pi\) | ||||
−0.484193 | + | 0.874961i | \(0.660887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.00000 | −0.303895 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.65685 | −0.214577 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.4853 | −0.472914 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.6569 | −0.592197 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.78680 | 0.180795 | 0.0903974 | − | 0.995906i | \(-0.471186\pi\) | ||||
0.0903974 | + | 0.995906i | \(0.471186\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.14214 | −0.0807922 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.1421 | 0.833921 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.4853 | 0.920864 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.3137 | 0.650230 | 0.325115 | − | 0.945674i | \(-0.394597\pi\) | ||||
0.325115 | + | 0.945674i | \(0.394597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.07107 | 0.265186 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.82843 | −0.255727 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 109.255 | 4.08590 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.3431 | 0.386272 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.14214 | 0.303650 | 0.151825 | − | 0.988407i | \(-0.451485\pi\) | ||||
0.151825 | + | 0.988407i | \(0.451485\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0000 | 0.670355 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.7990 | −0.810713 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.1127 | 0.784106 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.0416 | −0.891655 | −0.445827 | − | 0.895119i | \(-0.647090\pi\) | ||||
−0.445827 | + | 0.895119i | \(0.647090\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.1421 | −0.597038 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.9706 | −0.848437 | −0.424219 | − | 0.905560i | \(-0.639451\pi\) | ||||
−0.424219 | + | 0.905560i | \(0.639451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.0711 | −0.629676 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 91.8823 | 3.38453 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.3137 | 1.74046 | 0.870231 | − | 0.492643i | \(-0.163969\pi\) | ||||
0.870231 | + | 0.492643i | \(0.163969\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.37258 | −0.0504231 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.4558 | 1.22738 | 0.613688 | − | 0.789549i | \(-0.289685\pi\) | ||||
0.613688 | + | 0.789549i | \(0.289685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.65685 | 0.280525 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.65685 | 0.0606211 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.6985 | 1.95949 | 0.979743 | − | 0.200260i | \(-0.0641787\pi\) | ||||
0.979743 | + | 0.200260i | \(0.0641787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.4558 | 0.781894 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46.6274 | 1.69695 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.31371 | −0.0477475 | −0.0238738 | − | 0.999715i | \(-0.507600\pi\) | ||||
−0.0238738 | + | 0.999715i | \(0.507600\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.65685 | −0.205331 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.8284 | −1.48003 | −0.740015 | − | 0.672591i | \(-0.765181\pi\) | ||||
−0.740015 | + | 0.672591i | \(0.765181\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8284 | −0.392015 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.3137 | 0.770599 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.9411 | 0.647816 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.34315 | 0.300862 | 0.150431 | − | 0.988621i | \(-0.451934\pi\) | ||||
0.150431 | + | 0.988621i | \(0.451934\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −29.3137 | −1.05571 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.87006 | 0.319034 | 0.159517 | − | 0.987195i | \(-0.449006\pi\) | ||||
0.159517 | + | 0.987195i | \(0.449006\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −45.4558 | −1.63282 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.4853 | −0.447907 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.485281 | −0.0173870 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.0000 | 2.29010 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.17157 | 0.113343 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.8284 | −0.386483 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.5269 | −0.731705 | −0.365853 | − | 0.930673i | \(-0.619223\pi\) | ||||
−0.365853 | + | 0.930673i | \(0.619223\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.7990 | −0.562459 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.1421 | −0.573948 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.9411 | −1.77346 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.3137 | 0.897785 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.8995 | −0.704876 | −0.352438 | − | 0.935835i | \(-0.614647\pi\) | ||||
−0.352438 | + | 0.935835i | \(0.614647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.4853 | 1.43227 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.07107 | −0.0378443 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −65.9411 | −2.32701 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.82843 | 0.170180 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.1716 | 0.815678 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.1716 | 1.51783 | 0.758916 | − | 0.651189i | \(-0.225729\pi\) | ||||
0.758916 | + | 0.651189i | \(0.225729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.17157 | −0.181598 | −0.0907992 | − | 0.995869i | \(-0.528942\pi\) | ||||
−0.0907992 | + | 0.995869i | \(0.528942\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.8284 | 0.660342 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.6569 | 0.618493 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.627417 | −0.0219505 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.00000 | −0.279543 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.68629 | 0.0937522 | 0.0468761 | − | 0.998901i | \(-0.485073\pi\) | ||||
0.0468761 | + | 0.998901i | \(0.485073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.7990 | 1.52674 | 0.763368 | − | 0.645963i | \(-0.223544\pi\) | ||||
0.763368 | + | 0.645963i | \(0.223544\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −37.6569 | −1.31104 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.7696 | −1.69588 | −0.847942 | − | 0.530089i | \(-0.822158\pi\) | ||||
−0.847942 | + | 0.530089i | \(0.822158\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.9706 | −1.83974 | −0.919872 | − | 0.392219i | \(-0.871708\pi\) | ||||
−0.919872 | + | 0.392219i | \(0.871708\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.6274 | 0.438040 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.2132 | −1.08147 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.6274 | 1.61361 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.82843 | −0.236025 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.82843 | −0.235743 | −0.117872 | − | 0.993029i | \(-0.537607\pi\) | ||||
−0.117872 | + | 0.993029i | \(0.537607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9411 | −0.653142 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.0711 | 0.863493 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 64.8701 | 2.23160 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.6985 | 1.02045 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.8995 | −0.751589 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.82843 | −0.302635 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.9411 | 0.682771 | 0.341386 | − | 0.939923i | \(-0.389104\pi\) | ||||
0.341386 | + | 0.939923i | \(0.389104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.828427 | 0.0283316 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.9706 | −0.921297 | −0.460648 | − | 0.887583i | \(-0.652383\pi\) | ||||
−0.460648 | + | 0.887583i | \(0.652383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.00000 | −0.272956 | −0.136478 | − | 0.990643i | \(-0.543578\pi\) | ||||
−0.136478 | + | 0.990643i | \(0.543578\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.82843 | −0.0963925 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.51472 | −0.323885 | −0.161942 | − | 0.986800i | \(-0.551776\pi\) | ||||
−0.161942 | + | 0.986800i | \(0.551776\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.8284 | 0.640186 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.9706 | 0.746159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.0000 | −1.35691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 91.8823 | 3.11331 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.1421 | −0.410949 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.00000 | 0.270449 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.9706 | −1.04580 | −0.522901 | − | 0.852394i | \(-0.675150\pi\) | ||||
−0.522901 | + | 0.852394i | \(0.675150\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.75736 | −0.329108 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.2426 | −1.69272 | −0.846359 | − | 0.532613i | \(-0.821210\pi\) | ||||
−0.846359 | + | 0.532613i | \(0.821210\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.79899 | −0.262457 | −0.131228 | − | 0.991352i | \(-0.541892\pi\) | ||||
−0.131228 | + | 0.991352i | \(0.541892\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.8284 | −0.363994 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.7990 | 1.00055 | 0.500276 | − | 0.865866i | \(-0.333232\pi\) | ||||
0.500276 | + | 0.865866i | \(0.333232\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.686292 | −0.0230175 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.65685 | −0.189512 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.57359 | 0.0526583 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 49.4558 | 1.65313 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.65685 | −0.188877 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.6569 | −0.722297 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.2843 | 1.54195 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.65685 | −0.121692 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.1421 | 0.603065 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.07107 | 0.101973 | 0.0509866 | − | 0.998699i | \(-0.483763\pi\) | ||||
0.0509866 | + | 0.998699i | \(0.483763\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.3137 | 0.574259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.9411 | −0.726942 | −0.363471 | − | 0.931606i | \(-0.618408\pi\) | ||||
−0.363471 | + | 0.931606i | \(0.618408\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.37258 | −0.310187 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.1421 | 0.996468 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.34315 | −0.0773775 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0416 | −0.793060 | −0.396530 | − | 0.918022i | \(-0.629786\pi\) | ||||
−0.396530 | + | 0.918022i | \(0.629786\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.4558 | 0.706994 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 64.0000 | 2.10659 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58.7696 | −1.93233 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.7279 | 0.418040 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.9706 | 1.01611 | 0.508056 | − | 0.861324i | \(-0.330364\pi\) | ||||
0.508056 | + | 0.861324i | \(0.330364\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.21320 | −0.0397611 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.82843 | 0.289030 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −120.569 | −3.94301 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.0000 | 0.588034 | 0.294017 | − | 0.955800i | \(-0.405008\pi\) | ||||
0.294017 | + | 0.955800i | \(0.405008\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.34315 | −0.141733 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0416 | 0.588140 | 0.294070 | − | 0.955784i | \(-0.404990\pi\) | ||||
0.294070 | + | 0.955784i | \(0.404990\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.00000 | −0.0651290 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.82843 | 0.157069 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.79899 | 0.318424 | 0.159212 | − | 0.987244i | \(-0.449105\pi\) | ||||
0.159212 | + | 0.987244i | \(0.449105\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −65.9411 | −2.14054 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.82843 | −0.286281 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.89949 | −0.126317 | −0.0631585 | − | 0.998004i | \(-0.520117\pi\) | ||||
−0.0631585 | + | 0.998004i | \(0.520117\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.00000 | −0.129437 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.9411 | −0.579954 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.51472 | 0.0489128 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.6274 | 0.504110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.65685 | −0.182290 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 38.6274 | 1.24346 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.45584 | −0.175448 | −0.0877241 | − | 0.996145i | \(-0.527959\pi\) | ||||
−0.0877241 | + | 0.996145i | \(0.527959\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.51472 | 0.0486598 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.4558 | 1.33038 | 0.665191 | − | 0.746674i | \(-0.268350\pi\) | ||||
0.665191 | + | 0.746674i | \(0.268350\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.34315 | −0.0751178 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −37.6569 | −1.20598 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.2132 | 1.38251 | 0.691256 | − | 0.722610i | \(-0.257058\pi\) | ||||
0.691256 | + | 0.722610i | \(0.257058\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.05887 | 0.193642 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.65685 | −0.244465 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.0000 | 0.637901 | 0.318950 | − | 0.947771i | \(-0.396670\pi\) | ||||
0.318950 | + | 0.947771i | \(0.396670\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.1421 | −0.960408 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.17157 | 0.291934 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.58579 | −0.0822232 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7696 | −0.405638 | −0.202819 | − | 0.979216i | \(-0.565010\pi\) | ||||
−0.202819 | + | 0.979216i | \(0.565010\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.14214 | 0.0679786 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 69.1127 | 2.19102 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.68629 | −0.148416 | −0.0742082 | − | 0.997243i | \(-0.523643\pi\) | ||||
−0.0742082 | + | 0.997243i | \(0.523643\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.82843 | −0.279319 |
(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 | 276.2.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 828.2.a.e.1.1 | 2 | |||
4.3 | odd | 2 | 1104.2.a.l.1.2 | 2 | |||
5.2 | odd | 4 | 6900.2.f.l.6349.2 | 4 | |||
5.3 | odd | 4 | 6900.2.f.l.6349.3 | 4 | |||
5.4 | even | 2 | 6900.2.a.m.1.1 | 2 | |||
8.3 | odd | 2 | 4416.2.a.bi.1.1 | 2 | |||
8.5 | even | 2 | 4416.2.a.bc.1.1 | 2 | |||
12.11 | even | 2 | 3312.2.a.s.1.1 | 2 | |||
23.22 | odd | 2 | 6348.2.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
828.2.a.e.1.1 | 2 | 3.2 | odd | 2 | |||
1104.2.a.l.1.2 | 2 | 4.3 | odd | 2 | |||
3312.2.a.s.1.1 | 2 | 12.11 | even | 2 | |||
4416.2.a.bc.1.1 | 2 | 8.5 | even | 2 | |||
4416.2.a.bi.1.1 | 2 | 8.3 | odd | 2 | |||
6348.2.a.h.1.1 | 2 | 23.22 | odd | 2 | |||
6900.2.a.m.1.1 | 2 | 5.4 | even | 2 | |||
6900.2.f.l.6349.2 | 4 | 5.2 | odd | 4 | |||
6900.2.f.l.6349.3 | 4 | 5.3 | odd | 4 |