Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8464,2,Mod(1,8464)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8464, 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("8464.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8464 = 2^{4} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8464.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: | \(67.5853802708\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 30 x^{13} + 28 x^{12} + 354 x^{11} - 302 x^{10} - 2111 x^{9} + 1596 x^{8} + 6777 x^{7} + \cdots - 419 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 184) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.593309\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8464.1 |
$q$-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 | ||||||||
\(3\) | 0.593309 | 0.342547 | 0.171273 | − | 0.985224i | \(-0.445212\pi\) | ||||
0.171273 | + | 0.985224i | \(0.445212\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.48229 | 1.11011 | 0.555057 | − | 0.831812i | \(-0.312696\pi\) | ||||
0.555057 | + | 0.831812i | \(0.312696\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.58382 | 1.35455 | 0.677277 | − | 0.735728i | \(-0.263160\pi\) | ||||
0.677277 | + | 0.735728i | \(0.263160\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.64799 | −0.882662 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.309711 | −0.0933815 | −0.0466907 | − | 0.998909i | \(-0.514868\pi\) | ||||
−0.0466907 | + | 0.998909i | \(0.514868\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.08036 | −0.299637 | −0.149819 | − | 0.988713i | \(-0.547869\pi\) | ||||
−0.149819 | + | 0.988713i | \(0.547869\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.47276 | 0.380266 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.71863 | −1.38697 | −0.693485 | − | 0.720471i | \(-0.743926\pi\) | ||||
−0.693485 | + | 0.720471i | \(0.743926\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.82587 | −0.418884 | −0.209442 | − | 0.977821i | \(-0.567165\pi\) | ||||
−0.209442 | + | 0.977821i | \(0.567165\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.12631 | 0.463999 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.16177 | 0.232353 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.35100 | −0.644900 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00622 | −1.11533 | −0.557664 | − | 0.830067i | \(-0.688302\pi\) | ||||
−0.557664 | + | 0.830067i | \(0.688302\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.94727 | −1.24777 | −0.623883 | − | 0.781518i | \(-0.714446\pi\) | ||||
−0.623883 | + | 0.781518i | \(0.714446\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.183754 | −0.0319875 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.89607 | 1.50371 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.89141 | 1.62614 | 0.813069 | − | 0.582168i | \(-0.197795\pi\) | ||||
0.813069 | + | 0.582168i | \(0.197795\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.640986 | −0.102640 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.59824 | −1.03047 | −0.515236 | − | 0.857048i | \(-0.672296\pi\) | ||||
−0.515236 | + | 0.857048i | \(0.672296\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.87615 | −0.438608 | −0.219304 | − | 0.975657i | \(-0.570379\pi\) | ||||
−0.219304 | + | 0.975657i | \(0.570379\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.57307 | −0.979855 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.3753 | −1.80513 | −0.902563 | − | 0.430557i | \(-0.858317\pi\) | ||||
−0.902563 | + | 0.430557i | \(0.858317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.84373 | 0.834819 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.39291 | −0.475102 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.28037 | −1.13740 | −0.568698 | − | 0.822546i | \(-0.692553\pi\) | ||||
−0.568698 | + | 0.822546i | \(0.692553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.768793 | −0.103664 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.08331 | −0.143487 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.48827 | −0.454134 | −0.227067 | − | 0.973879i | \(-0.572914\pi\) | ||||
−0.227067 | + | 0.973879i | \(0.572914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.06229 | 1.03227 | 0.516135 | − | 0.856507i | \(-0.327370\pi\) | ||||
0.516135 | + | 0.856507i | \(0.327370\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.48989 | −1.19561 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.68176 | −0.332632 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.48841 | 0.181839 | 0.0909193 | − | 0.995858i | \(-0.471019\pi\) | ||||
0.0909193 | + | 0.995858i | \(0.471019\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.32836 | −0.632361 | −0.316180 | − | 0.948699i | \(-0.602400\pi\) | ||||
−0.316180 | + | 0.948699i | \(0.602400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.52126 | 0.997338 | 0.498669 | − | 0.866792i | \(-0.333822\pi\) | ||||
0.498669 | + | 0.866792i | \(0.333822\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.689285 | 0.0795918 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.10995 | −0.126490 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.48841 | −0.955020 | −0.477510 | − | 0.878626i | \(-0.658461\pi\) | ||||
−0.477510 | + | 0.878626i | \(0.658461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.95578 | 0.661753 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.51157 | 0.385445 | 0.192723 | − | 0.981253i | \(-0.438268\pi\) | ||||
0.192723 | + | 0.981253i | \(0.438268\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.1953 | −1.53970 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.56354 | −0.382052 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.08382 | −0.114885 | −0.0574424 | − | 0.998349i | \(-0.518295\pi\) | ||||
−0.0574424 | + | 0.998349i | \(0.518295\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.87180 | −0.405875 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.12187 | −0.427418 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.53235 | −0.465009 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.05757 | −0.107380 | −0.0536898 | − | 0.998558i | \(-0.517098\pi\) | ||||
−0.0536898 | + | 0.998558i | \(0.517098\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.820111 | 0.0824243 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.92537 | −0.689100 | −0.344550 | − | 0.938768i | \(-0.611969\pi\) | ||||
−0.344550 | + | 0.938768i | \(0.611969\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.6189 | −1.53898 | −0.769490 | − | 0.638659i | \(-0.779489\pi\) | ||||
−0.769490 | + | 0.638659i | \(0.779489\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.27811 | 0.515091 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.6594 | −1.51385 | −0.756924 | − | 0.653502i | \(-0.773299\pi\) | ||||
−0.756924 | + | 0.653502i | \(0.773299\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9341 | 1.43042 | 0.715212 | − | 0.698907i | \(-0.246330\pi\) | ||||
0.715212 | + | 0.698907i | \(0.246330\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.86866 | 0.557028 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.4972 | 1.55193 | 0.775963 | − | 0.630778i | \(-0.217264\pi\) | ||||
0.775963 | + | 0.630778i | \(0.217264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.86077 | 0.264478 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −20.4945 | −1.87873 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9041 | −0.991280 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.91479 | −0.352985 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.52761 | −0.852176 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6044 | 1.38467 | 0.692334 | − | 0.721578i | \(-0.256583\pi\) | ||||
0.692334 | + | 0.721578i | \(0.256583\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.70644 | −0.150244 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.58127 | −0.749749 | −0.374874 | − | 0.927076i | \(-0.622314\pi\) | ||||
−0.374874 | + | 0.927076i | \(0.622314\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.54359 | −0.567401 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.31815 | −0.715912 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.38302 | 0.545338 | 0.272669 | − | 0.962108i | \(-0.412094\pi\) | ||||
0.272669 | + | 0.962108i | \(0.412094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.1827 | 1.79670 | 0.898348 | − | 0.439284i | \(-0.144768\pi\) | ||||
0.898348 | + | 0.439284i | \(0.144768\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.34238 | −0.618340 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.334599 | 0.0279806 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.9092 | −1.23814 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.46714 | 0.285965 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.50002 | −0.450579 | −0.225289 | − | 0.974292i | \(-0.572333\pi\) | ||||
−0.225289 | + | 0.974292i | \(0.572333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.944676 | 0.0768767 | 0.0384383 | − | 0.999261i | \(-0.487762\pi\) | ||||
0.0384383 | + | 0.999261i | \(0.487762\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.1428 | 1.22423 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.2451 | −1.38516 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.1040 | −1.76409 | −0.882047 | − | 0.471162i | \(-0.843835\pi\) | ||||
−0.882047 | + | 0.471162i | \(0.843835\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.91282 | −0.389612 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.9082 | −1.55933 | −0.779665 | − | 0.626197i | \(-0.784611\pi\) | ||||
−0.779665 | + | 0.626197i | \(0.784611\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.456132 | −0.0355098 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.38102 | −0.493778 | −0.246889 | − | 0.969044i | \(-0.579408\pi\) | ||||
−0.246889 | + | 0.969044i | \(0.579408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8328 | −0.910217 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.83488 | 0.369733 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.982165 | 0.0746726 | 0.0373363 | − | 0.999303i | \(-0.488113\pi\) | ||||
0.0373363 | + | 0.999303i | \(0.488113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.16355 | 0.314735 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.06962 | −0.155562 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.9804 | 1.86712 | 0.933561 | − | 0.358420i | \(-0.116684\pi\) | ||||
0.933561 | + | 0.358420i | \(0.116684\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3447 | 1.21489 | 0.607446 | − | 0.794361i | \(-0.292194\pi\) | ||||
0.607446 | + | 0.794361i | \(0.292194\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.78342 | 0.353601 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.5533 | 1.80520 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.77112 | 0.129517 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.0094 | −0.873552 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.79988 | −0.709094 | −0.354547 | − | 0.935038i | \(-0.615365\pi\) | ||||
−0.354547 | + | 0.935038i | \(0.615365\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.9095 | 1.43312 | 0.716558 | − | 0.697528i | \(-0.245717\pi\) | ||||
0.716558 | + | 0.697528i | \(0.245717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.59111 | −0.113942 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.39454 | 0.455592 | 0.227796 | − | 0.973709i | \(-0.426848\pi\) | ||||
0.227796 | + | 0.973709i | \(0.426848\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.7933 | −1.11956 | −0.559778 | − | 0.828643i | \(-0.689114\pi\) | ||||
−0.559778 | + | 0.828643i | \(0.689114\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.883088 | 0.0622882 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21.5252 | −1.51077 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.3788 | −1.14394 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.565493 | 0.0391160 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.48312 | 0.515160 | 0.257580 | − | 0.966257i | \(-0.417075\pi\) | ||||
0.257580 | + | 0.966257i | \(0.417075\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.16136 | −0.216613 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.13943 | −0.486905 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.8977 | −1.69017 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.05574 | 0.341635 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.17816 | 0.415588 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4545 | 1.30277 | 0.651385 | − | 0.758747i | \(-0.274188\pi\) | ||||
0.651385 | + | 0.758747i | \(0.274188\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.07634 | −0.205089 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.0195 | 1.26237 | 0.631183 | − | 0.775634i | \(-0.282570\pi\) | ||||
0.631183 | + | 0.775634i | \(0.282570\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.93124 | 0.325865 | 0.162933 | − | 0.986637i | \(-0.447905\pi\) | ||||
0.162933 | + | 0.986637i | \(0.447905\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.658542 | −0.0433289 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.6337 | −0.827661 | −0.413831 | − | 0.910354i | \(-0.635809\pi\) | ||||
−0.413831 | + | 0.910354i | \(0.635809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.7191 | −2.00390 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.03624 | −0.327139 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.81067 | 0.375861 | 0.187930 | − | 0.982182i | \(-0.439822\pi\) | ||||
0.187930 | + | 0.982182i | \(0.439822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1708 | 0.783993 | 0.391996 | − | 0.919967i | \(-0.371785\pi\) | ||||
0.391996 | + | 0.919967i | \(0.371785\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5866 | 0.871581 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.5058 | 0.926744 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.97260 | 0.125513 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.08345 | 0.132033 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.5690 | −1.48766 | −0.743831 | − | 0.668368i | \(-0.766993\pi\) | ||||
−0.743831 | + | 0.668368i | \(0.766993\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.42219 | −0.527418 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.5339 | 1.28087 | 0.640434 | − | 0.768013i | \(-0.278754\pi\) | ||||
0.640434 | + | 0.768013i | \(0.278754\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 35.4490 | 2.20269 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.9044 | 0.984457 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.49432 | 0.215469 | 0.107734 | − | 0.994180i | \(-0.465640\pi\) | ||||
0.107734 | + | 0.994180i | \(0.465640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.5543 | −1.26264 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.643040 | −0.0393534 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.136318 | 0.00831147 | 0.00415573 | − | 0.999991i | \(-0.498677\pi\) | ||||
0.00415573 | + | 0.999991i | \(0.498677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.9988 | 0.971858 | 0.485929 | − | 0.873998i | \(-0.338481\pi\) | ||||
0.485929 | + | 0.873998i | \(0.338481\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.29717 | −0.139031 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.359812 | −0.0216975 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.2361 | 1.51629 | 0.758147 | − | 0.652084i | \(-0.226105\pi\) | ||||
0.758147 | + | 0.652084i | \(0.226105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.3963 | 1.10136 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8972 | 0.829037 | 0.414518 | − | 0.910041i | \(-0.363950\pi\) | ||||
0.414518 | + | 0.910041i | \(0.363950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.32674 | −0.376086 | −0.188043 | − | 0.982161i | \(-0.560214\pi\) | ||||
−0.188043 | + | 0.982161i | \(0.560214\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.68908 | −0.159287 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.6469 | −1.39583 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.7027 | 0.923687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.627464 | −0.0367826 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.42772 | −0.0834080 | −0.0417040 | − | 0.999130i | \(-0.513279\pi\) | ||||
−0.0417040 | + | 0.999130i | \(0.513279\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.65889 | −0.504140 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.03784 | 0.0602217 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3076 | −0.594119 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.10888 | −0.236049 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.0129 | 1.14594 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.2169 | −1.15384 | −0.576918 | − | 0.816802i | \(-0.695745\pi\) | ||||
−0.576918 | + | 0.816802i | \(0.695745\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.26685 | −0.527172 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.14913 | 0.518799 | 0.259400 | − | 0.965770i | \(-0.416475\pi\) | ||||
0.259400 | + | 0.965770i | \(0.416475\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0420 | 1.07632 | 0.538159 | − | 0.842844i | \(-0.319120\pi\) | ||||
0.538159 | + | 0.842844i | \(0.319120\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −23.5567 | −1.32727 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.0855 | 0.847284 | 0.423642 | − | 0.905830i | \(-0.360751\pi\) | ||||
0.423642 | + | 0.905830i | \(0.360751\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.86020 | 0.104151 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.29084 | −0.518564 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.4415 | 0.580980 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.25512 | −0.0696217 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.86051 | 0.489987 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −44.3509 | −2.44514 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.86945 | 0.542474 | 0.271237 | − | 0.962513i | \(-0.412567\pi\) | ||||
0.271237 | + | 0.962513i | \(0.412567\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.1923 | −1.43533 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.69467 | 0.201862 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.39577 | −0.511820 | −0.255910 | − | 0.966701i | \(-0.582375\pi\) | ||||
−0.255910 | + | 0.966701i | \(0.582375\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.78793 | 0.531607 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.15165 | 0.116518 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.14384 | −0.223747 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.4905 | 0.563161 | 0.281581 | − | 0.959538i | \(-0.409141\pi\) | ||||
0.281581 | + | 0.959538i | \(0.409141\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.7716 | −1.64717 | −0.823583 | − | 0.567196i | \(-0.808028\pi\) | ||||
−0.823583 | + | 0.567196i | \(0.808028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.62028 | 0.193236 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0753 | −0.802378 | −0.401189 | − | 0.915995i | \(-0.631403\pi\) | ||||
−0.401189 | + | 0.915995i | \(0.631403\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.2265 | −0.701992 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.1596 | −0.643552 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.36983 | −0.0722970 | −0.0361485 | − | 0.999346i | \(-0.511509\pi\) | ||||
−0.0361485 | + | 0.999346i | \(0.511509\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6662 | −0.824536 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.46948 | −0.339560 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.1523 | 1.10716 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.6797 | −1.65367 | −0.826834 | − | 0.562447i | \(-0.809860\pi\) | ||||
−0.826834 | + | 0.562447i | \(0.809860\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.4720 | 0.909558 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.6753 | −1.54067 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.1443 | 1.09481 | 0.547404 | − | 0.836868i | \(-0.315616\pi\) | ||||
0.547404 | + | 0.836868i | \(0.315616\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.65281 | −0.291910 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.48887 | 0.334194 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0257 | 1.18275 | 0.591375 | − | 0.806396i | \(-0.298585\pi\) | ||||
0.591375 | + | 0.806396i | \(0.298585\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.25823 | 0.474313 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.9058 | 0.608358 | 0.304179 | − | 0.952615i | \(-0.401618\pi\) | ||||
0.304179 | + | 0.952615i | \(0.401618\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.75521 | −0.140419 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.61599 | 0.387143 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.1143 | 1.17194 | 0.585970 | − | 0.810333i | \(-0.300714\pi\) | ||||
0.585970 | + | 0.810333i | \(0.300714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.09134 | −0.256824 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.0707 | −1.06018 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.16095 | −0.309209 | −0.154605 | − | 0.987976i | \(-0.549410\pi\) | ||||
−0.154605 | + | 0.987976i | \(0.549410\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.88237 | −0.194361 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3034 | 0.514527 | 0.257264 | − | 0.966341i | \(-0.417179\pi\) | ||||
0.257264 | + | 0.966341i | \(0.417179\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.50554 | 0.373877 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.7840 | 0.734622 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.06348 | −0.151851 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.00814518 | 0.000402753 0 | 0.000201377 | − | 1.00000i | \(-0.499936\pi\) | ||||
0.000201377 | 1.00000i | \(0.499936\pi\) | ||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.78710 | 0.186804 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.5013 | −0.615149 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.71675 | 0.427888 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.5679 | 0.615453 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.8859 | −1.31346 | −0.656730 | − | 0.754126i | \(-0.728061\pi\) | ||||
−0.656730 | + | 0.754126i | \(0.728061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.30579 | −0.161115 | −0.0805573 | − | 0.996750i | \(-0.525670\pi\) | ||||
−0.0805573 | + | 0.996750i | \(0.525670\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 32.7697 | 1.59332 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.64370 | −0.322267 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.8938 | 1.39827 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.198520 | 0.00958466 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.2487 | −0.589997 | −0.294999 | − | 0.955498i | \(-0.595319\pi\) | ||||
−0.294999 | + | 0.955498i | \(0.595319\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.62340 | −0.126072 | −0.0630362 | − | 0.998011i | \(-0.520078\pi\) | ||||
−0.0630362 | + | 0.998011i | \(0.520078\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.84575 | −0.424121 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.11062 | −0.291644 | −0.145822 | − | 0.989311i | \(-0.546583\pi\) | ||||
−0.145822 | + | 0.989311i | \(0.546583\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.4741 | −0.736863 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.2860 | 1.15386 | 0.576932 | − | 0.816792i | \(-0.304250\pi\) | ||||
0.576932 | + | 0.816792i | \(0.304250\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.69036 | −0.127535 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.26321 | −0.154344 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.8960 | 1.69404 | 0.847018 | − | 0.531564i | \(-0.178395\pi\) | ||||
0.847018 | + | 0.531564i | \(0.178395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.04355 | 0.0962270 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.560485 | 0.0263339 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.61094 | −0.450568 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.2842 | 1.27630 | 0.638151 | − | 0.769911i | \(-0.279699\pi\) | ||||
0.638151 | + | 0.769911i | \(0.279699\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.1631 | 0.894457 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.54919 | −0.165302 | −0.0826510 | − | 0.996579i | \(-0.526339\pi\) | ||||
−0.0826510 | + | 0.996579i | \(0.526339\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.4936 | −1.13831 | −0.569157 | − | 0.822229i | \(-0.692731\pi\) | ||||
−0.569157 | + | 0.822229i | \(0.692731\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.2317 | −0.474483 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.8164 | −1.47229 | −0.736145 | − | 0.676824i | \(-0.763356\pi\) | ||||
−0.736145 | + | 0.676824i | \(0.763356\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.33420 | 0.246310 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.1145 | −0.604285 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.890775 | 0.0409579 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.12124 | −0.0973290 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.9263 | 1.00394 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.5961 | 0.712603 | 0.356301 | − | 0.934371i | \(-0.384038\pi\) | ||||
0.356301 | + | 0.934371i | \(0.384038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.6863 | −0.487251 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.62519 | −0.119204 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.5151 | −1.51871 | −0.759357 | − | 0.650675i | \(-0.774486\pi\) | ||||
−0.759357 | + | 0.650675i | \(0.774486\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.8117 | −0.534144 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.5885 | −0.748626 | −0.374313 | − | 0.927302i | \(-0.622121\pi\) | ||||
−0.374313 | + | 0.927302i | \(0.622121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.3473 | 1.54693 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.03575 | 0.0915003 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.0959 | −0.856567 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5815 | 0.742288 | 0.371144 | − | 0.928575i | \(-0.378966\pi\) | ||||
0.371144 | + | 0.928575i | \(0.378966\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.78591 | −0.169142 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.1612 | 1.21106 | 0.605530 | − | 0.795823i | \(-0.292961\pi\) | ||||
0.605530 | + | 0.795823i | \(0.292961\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.1908 | −0.764980 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.02052 | −0.311792 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.51627 | 0.421801 | 0.210901 | − | 0.977508i | \(-0.432360\pi\) | ||||
0.210901 | + | 0.977508i | \(0.432360\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.5386 | 1.35095 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.11849 | 0.270138 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38.7707 | −1.70844 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.83278 | 0.168565 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.582727 | 0.0255789 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.97611 | −0.437061 | −0.218531 | − | 0.975830i | \(-0.570126\pi\) | ||||
−0.218531 | + | 0.975830i | \(0.570126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.37220 | 0.234910 | 0.117455 | − | 0.993078i | \(-0.462526\pi\) | ||||
0.117455 | + | 0.993078i | \(0.462526\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.47027 | 0.107811 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.7288 | 1.73061 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.23688 | 0.400846 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.12846 | 0.308768 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.8711 | −1.68054 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.8211 | 0.639576 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.80987 | −0.0779566 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.8030 | 1.41031 | 0.705155 | − | 0.709053i | \(-0.250877\pi\) | ||||
0.705155 | + | 0.709053i | \(0.250877\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.69745 | 0.416157 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37.0707 | 1.58793 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.5457 | −1.77636 | −0.888182 | − | 0.459491i | \(-0.848032\pi\) | ||||
−0.888182 | + | 0.459491i | \(0.848032\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.3488 | −0.911145 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.9666 | 0.467193 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.4209 | −1.29363 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.5677 | 0.618365 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.8796 | −1.39316 | −0.696578 | − | 0.717481i | \(-0.745295\pi\) | ||||
−0.696578 | + | 0.717481i | \(0.745295\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.10727 | 0.131423 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.05082 | 0.0443658 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.55565 | −0.360578 | −0.180289 | − | 0.983614i | \(-0.557703\pi\) | ||||
−0.180289 | + | 0.983614i | \(0.557703\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.9509 | 1.72282 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.3444 | 0.896381 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.1498 | −1.01241 | −0.506207 | − | 0.862412i | \(-0.668953\pi\) | ||||
−0.506207 | + | 0.862412i | \(0.668953\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.6468 | −0.864043 | −0.432021 | − | 0.901863i | \(-0.642199\pi\) | ||||
−0.432021 | + | 0.901863i | \(0.642199\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.81435 | −0.242898 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.28441 | −0.261623 | −0.130812 | − | 0.991407i | \(-0.541758\pi\) | ||||
−0.130812 | + | 0.991407i | \(0.541758\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.8125 | 0.490909 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.5848 | 0.522107 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.56453 | 0.106212 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.10127 | 0.293601 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.2070 | −1.32932 | −0.664662 | − | 0.747144i | \(-0.731424\pi\) | ||||
−0.664662 | + | 0.747144i | \(0.731424\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.6848 | 0.522669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.79393 | 0.156062 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.20462 | −0.254793 | −0.127397 | − | 0.991852i | \(-0.540662\pi\) | ||||
−0.127397 | + | 0.991852i | \(0.540662\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −50.8733 | −2.08560 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.37029 | −0.383500 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.67037 | −0.109108 | −0.0545542 | − | 0.998511i | \(-0.517374\pi\) | ||||
−0.0545542 | + | 0.998511i | \(0.517374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.828318 | 0.0337878 | 0.0168939 | − | 0.999857i | \(-0.494622\pi\) | ||||
0.0168939 | + | 0.999857i | \(0.494622\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.94129 | −0.160502 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.0671 | −1.10043 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.2415 | −0.699810 | −0.349905 | − | 0.936785i | \(-0.613786\pi\) | ||||
−0.349905 | + | 0.936785i | \(0.613786\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.7711 | −0.517510 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.3698 | 0.540883 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.9368 | 0.845630 | 0.422815 | − | 0.906216i | \(-0.361042\pi\) | ||||
0.422815 | + | 0.906216i | \(0.361042\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.71765 | −0.391854 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.4417 | −0.581403 | −0.290701 | − | 0.956814i | \(-0.593889\pi\) | ||||
−0.290701 | + | 0.956814i | \(0.593889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.08672 | −0.0436788 | −0.0218394 | − | 0.999761i | \(-0.506952\pi\) | ||||
−0.0218394 | + | 0.999761i | \(0.506952\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.88421 | −0.155618 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.4591 | −1.17837 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.335512 | 0.0133991 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −56.5653 | −2.25540 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.1753 | 0.405071 | 0.202536 | − | 0.979275i | \(-0.435082\pi\) | ||||
0.202536 | + | 0.979275i | \(0.435082\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.43980 | 0.176466 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 38.7347 | 1.53714 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.31332 | −0.250143 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.1094 | 0.558160 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.0504 | −1.14742 | −0.573710 | − | 0.819058i | \(-0.694496\pi\) | ||||
−0.573710 | + | 0.819058i | \(0.694496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.2701 | −1.50922 | −0.754612 | − | 0.656171i | \(-0.772175\pi\) | ||||
−0.754612 | + | 0.656171i | \(0.772175\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.23588 | −0.166788 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.00577 | −0.196797 | −0.0983985 | − | 0.995147i | \(-0.531372\pi\) | ||||
−0.0983985 | + | 0.995147i | \(0.531372\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.08036 | 0.0424077 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.7720 | −0.578962 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.09064 | −0.0426802 | −0.0213401 | − | 0.999772i | \(-0.506793\pi\) | ||||
−0.0213401 | + | 0.999772i | \(0.506793\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.3012 | −0.832307 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.5642 | −0.880312 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.7118 | 0.962634 | 0.481317 | − | 0.876547i | \(-0.340159\pi\) | ||||
0.481317 | + | 0.876547i | \(0.340159\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.5858 | −1.30633 | −0.653167 | − | 0.757214i | \(-0.726560\pi\) | ||||
−0.653167 | + | 0.757214i | \(0.726560\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.66556 | 0.142358 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.2431 | −0.629880 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.5425 | 0.446260 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.49698 | −0.0963949 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.20521 | −0.354835 | −0.177417 | − | 0.984136i | \(-0.556774\pi\) | ||||
−0.177417 | + | 0.984136i | \(0.556774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.89307 | −0.149844 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.0216 | −0.462028 | −0.231014 | − | 0.972950i | \(-0.574204\pi\) | ||||
−0.231014 | + | 0.972950i | \(0.574204\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.79013 | −0.145452 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.2844 | 0.432419 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.1023 | −1.26663 | −0.633313 | − | 0.773896i | \(-0.718305\pi\) | ||||
−0.633313 | + | 0.773896i | \(0.718305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.8445 | 0.605388 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.92575 | 0.111624 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.94577 | 0.340807 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0797 | 1.06820 | 0.534102 | − | 0.845420i | \(-0.320650\pi\) | ||||
0.534102 | + | 0.845420i | \(0.320650\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.93913 | 0.111648 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 52.5817 | 1.99454 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.7329 | 1.42923 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.49568 | −0.283513 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.84360 | −0.145171 | −0.0725854 | − | 0.997362i | \(-0.523125\pi\) | ||||
−0.0725854 | + | 0.997362i | \(0.523125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0604 | −0.681163 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.2259 | −0.686428 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.8193 | −0.933424 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.63312 | −0.174000 | −0.0870002 | − | 0.996208i | \(-0.527728\pi\) | ||||
−0.0870002 | + | 0.996208i | \(0.527728\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.4772 | 0.842960 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.830572 | 0.0310616 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.44752 | 0.128750 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9053 | −1.15257 | −0.576286 | − | 0.817248i | \(-0.695499\pi\) | ||||
−0.576286 | + | 0.817248i | \(0.695499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −55.9754 | −2.08463 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.22107 | 0.268554 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.97782 | −0.259150 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.4685 | 0.759134 | 0.379567 | − | 0.925164i | \(-0.376073\pi\) | ||||
0.379567 | + | 0.925164i | \(0.376073\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.80629 | −0.363196 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.4476 | 0.608337 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.8697 | −0.992456 | −0.496228 | − | 0.868192i | \(-0.665282\pi\) | ||||
−0.496228 | + | 0.868192i | \(0.665282\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.60644 | 0.317453 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.460978 | −0.0169804 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.8142 | 1.20709 | 0.603544 | − | 0.797329i | \(-0.293755\pi\) | ||||
0.603544 | + | 0.797329i | \(0.293755\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.17036 | 0.0429942 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.5291 | −0.679767 | −0.339883 | − | 0.940468i | \(-0.610388\pi\) | ||||
−0.339883 | + | 0.940468i | \(0.610388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.6526 | −0.500194 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.29860 | −0.340218 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −56.1203 | −2.05059 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.4057 | 0.744615 | 0.372307 | − | 0.928109i | \(-0.378567\pi\) | ||||
0.372307 | + | 0.928109i | \(0.378567\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.9837 | −0.509594 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.34496 | 0.0853419 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.53188 | 0.201060 | 0.100530 | − | 0.994934i | \(-0.467946\pi\) | ||||
0.100530 | + | 0.994934i | \(0.467946\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.5746 | 0.564579 | 0.282289 | − | 0.959329i | \(-0.408906\pi\) | ||||
0.282289 | + | 0.959329i | \(0.408906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 53.5209 | 1.93759 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 37.5889 | 1.35903 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.76858 | 0.136075 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.76741 | −0.352222 | −0.176111 | − | 0.984370i | \(-0.556352\pi\) | ||||
−0.176111 | + | 0.984370i | \(0.556352\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.1829 | 0.438758 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.0970 | −0.578968 | −0.289484 | − | 0.957183i | \(-0.593484\pi\) | ||||
−0.289484 | + | 0.957183i | \(0.593484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.07110 | −0.289922 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.0322 | 0.754525 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0475 | 0.431648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.65025 | 0.0590508 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.1268 | 0.719274 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −54.8686 | −1.95835 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.3012 | −0.402845 | −0.201422 | − | 0.979504i | \(-0.564556\pi\) | ||||
−0.201422 | + | 0.979504i | \(0.564556\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.07321 | 0.0738082 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 59.1229 | 2.10217 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.71016 | −0.309307 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.1950 | −0.432513 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −49.4017 | −1.74990 | −0.874949 | − | 0.484216i | \(-0.839105\pi\) | ||||
−0.874949 | + | 0.484216i | \(0.839105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 70.7699 | 2.50366 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.86994 | 0.101404 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.63913 | −0.0931329 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.0808788 | 0.00284707 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −55.1319 | −1.93834 | −0.969168 | − | 0.246401i | \(-0.920752\pi\) | ||||
−0.969168 | + | 0.246401i | \(0.920752\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.0399 | −1.75714 | −0.878570 | − | 0.477614i | \(-0.841502\pi\) | ||||
−0.878570 | + | 0.477614i | \(0.841502\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.49222 | 0.332907 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −49.4179 | −1.73103 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.25147 | 0.183726 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.2525 | 0.358251 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.1147 | −0.667109 | −0.333554 | − | 0.942731i | \(-0.608248\pi\) | ||||
−0.333554 | + | 0.942731i | \(0.608248\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.799459 | 0.0278674 | 0.0139337 | − | 0.999903i | \(-0.495565\pi\) | ||||
0.0139337 | + | 0.999903i | \(0.495565\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.213479 | −0.00743240 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.1707 | −0.910046 | −0.455023 | − | 0.890480i | \(-0.650369\pi\) | ||||
−0.455023 | + | 0.890480i | \(0.650369\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0541 | −0.800703 | −0.400352 | − | 0.916362i | \(-0.631112\pi\) | ||||
−0.400352 | + | 0.916362i | \(0.631112\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.9728 | 0.519401 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.4181 | −1.15787 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.8395 | −0.548150 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.2803 | 0.804684 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.7809 | 1.85672 | 0.928361 | − | 0.371679i | \(-0.121218\pi\) | ||||
0.928361 | + | 0.371679i | \(0.121218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.07471 | 0.243955 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.24532 | 0.283984 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.3725 | −1.01045 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.0782 | −1.34274 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.75371 | −0.128827 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.8558 | −0.988003 | −0.494002 | − | 0.869461i | \(-0.664466\pi\) | ||||
−0.494002 | + | 0.869461i | \(0.664466\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.0016 | 0.410445 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.88284 | −0.166794 | −0.0833972 | − | 0.996516i | \(-0.526577\pi\) | ||||
−0.0833972 | + | 0.996516i | \(0.526577\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.7917 | 0.811764 | 0.405882 | − | 0.913926i | \(-0.366964\pi\) | ||||
0.405882 | + | 0.913926i | \(0.366964\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.0299 | −0.478138 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.3772 | 1.03405 | 0.517026 | − | 0.855970i | \(-0.327039\pi\) | ||||
0.517026 | + | 0.855970i | \(0.327039\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.43802 | 0.0828951 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.31654 | 0.316406 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.62896 | 0.0891812 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.60802 | −0.0544856 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.80042 | 0.0947799 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −34.1452 | −1.15432 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.8762 | −0.434798 | −0.217399 | − | 0.976083i | \(-0.569757\pi\) | ||||
−0.217399 | + | 0.976083i | \(0.569757\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.847076 | −0.0285711 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.7139 | 0.798943 | 0.399472 | − | 0.916746i | \(-0.369194\pi\) | ||||
0.399472 | + | 0.916746i | \(0.369194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.8223 | −0.599769 | −0.299885 | − | 0.953976i | \(-0.596948\pi\) | ||||
−0.299885 | + | 0.953976i | \(0.596948\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.13739 | −0.172692 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.1050 | −1.11156 | −0.555778 | − | 0.831331i | \(-0.687580\pi\) | ||||
−0.555778 | + | 0.831331i | \(0.687580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.9233 | 1.87561 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.84457 | −0.0617955 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.5958 | 0.756138 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62.0086 | 2.07272 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41.7268 | 1.39167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.3524 | 1.57754 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.11557 | −0.203514 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 40.5723 | 1.34867 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.0149 | 1.79354 | 0.896768 | − | 0.442502i | \(-0.145909\pi\) | ||||
0.896768 | + | 0.442502i | \(0.145909\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.3383 | 0.608242 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.2595 | −1.36699 | −0.683493 | − | 0.729957i | \(-0.739540\pi\) | ||||
−0.683493 | + | 0.729957i | \(0.739540\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.08757 | −0.0359935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.8738 | 0.392537 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.7537 | −1.01558 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.8698 | 1.38116 | 0.690579 | − | 0.723257i | \(-0.257356\pi\) | ||||
0.690579 | + | 0.723257i | \(0.257356\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.9948 | −0.395243 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.75654 | 0.189479 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.4915 | 0.377838 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41.3587 | 1.35840 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.30456 | −0.108419 | −0.0542095 | − | 0.998530i | \(-0.517264\pi\) | ||||
−0.0542095 | + | 0.998530i | \(0.517264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.6699 | −0.349692 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.42826 | 0.177713 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.39644 | 0.143779 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.5552 | 0.377493 | 0.188746 | − | 0.982026i | \(-0.439558\pi\) | ||||
0.188746 | + | 0.982026i | \(0.439558\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.2978 | 0.368689 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0702 | −0.360878 | −0.180439 | − | 0.983586i | \(-0.557752\pi\) | ||||
−0.180439 | + | 0.983586i | \(0.557752\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −29.8107 | −0.969743 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.9486 | 1.59062 | 0.795308 | − | 0.606206i | \(-0.207309\pi\) | ||||
0.795308 | + | 0.606206i | \(0.207309\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.20601 | −0.298840 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.95034 | 0.290235 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.11432 | 0.198062 | 0.0990311 | − | 0.995084i | \(-0.468426\pi\) | ||||
0.0990311 | + | 0.995084i | \(0.468426\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.3261 | −0.787175 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.10367 | 0.0356766 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.8756 | 0.738691 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.2645 | 0.556920 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.4658 | 1.33622 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 49.4211 | 1.59092 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.52591 | 0.274175 | 0.137087 | − | 0.990559i | \(-0.456226\pi\) | ||||
0.137087 | + | 0.990559i | \(0.456226\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.19502 | 0.199013 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.0062 | −0.834579 | −0.417290 | − | 0.908774i | \(-0.637020\pi\) | ||||
−0.417290 | + | 0.908774i | \(0.637020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 75.9150 | 2.43372 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.744675 | −0.0238487 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.31555 | −0.266038 | −0.133019 | − | 0.991113i | \(-0.542467\pi\) | ||||
−0.133019 | + | 0.991113i | \(0.542467\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.335671 | 0.0107281 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.5452 | −1.26258 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.2291 | 0.485733 | 0.242867 | − | 0.970060i | \(-0.421912\pi\) | ||||
0.242867 | + | 0.970060i | \(0.421912\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.8731 | 0.505759 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.3138 | −0.837576 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.7796 | −0.787150 | −0.393575 | − | 0.919293i | \(-0.628762\pi\) | ||||
−0.393575 | + | 0.919293i | \(0.628762\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.85563 | 0.185823 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.2035 | −1.24283 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.5183 | −1.44158 | −0.720790 | − | 0.693153i | \(-0.756221\pi\) | ||||
−0.720790 | + | 0.693153i | \(0.756221\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −33.1461 | −1.04870 |
(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 | 8464.2.a.cg.1.9 | 15 | ||
4.3 | odd | 2 | 4232.2.a.bb.1.7 | 15 | |||
23.13 | even | 11 | 368.2.m.e.353.2 | 30 | |||
23.16 | even | 11 | 368.2.m.e.49.2 | 30 | |||
23.22 | odd | 2 | 8464.2.a.ch.1.9 | 15 | |||
92.39 | odd | 22 | 184.2.i.b.49.2 | ✓ | 30 | ||
92.59 | odd | 22 | 184.2.i.b.169.2 | yes | 30 | ||
92.91 | even | 2 | 4232.2.a.ba.1.7 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
184.2.i.b.49.2 | ✓ | 30 | 92.39 | odd | 22 | ||
184.2.i.b.169.2 | yes | 30 | 92.59 | odd | 22 | ||
368.2.m.e.49.2 | 30 | 23.16 | even | 11 | |||
368.2.m.e.353.2 | 30 | 23.13 | even | 11 | |||
4232.2.a.ba.1.7 | 15 | 92.91 | even | 2 | |||
4232.2.a.bb.1.7 | 15 | 4.3 | odd | 2 | |||
8464.2.a.cg.1.9 | 15 | 1.1 | even | 1 | trivial | ||
8464.2.a.ch.1.9 | 15 | 23.22 | odd | 2 |