Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 315) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.828427 | −0.249780 | −0.124890 | − | 0.992171i | \(-0.539858\pi\) | ||||
−0.124890 | + | 0.992171i | \(0.539858\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.82843 | 1.33916 | 0.669582 | − | 0.742738i | \(-0.266473\pi\) | ||||
0.669582 | + | 0.742738i | \(0.266473\pi\) | |||||||
\(14\) | −2.41421 | −0.645226 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 3.65685 | 0.886917 | 0.443459 | − | 0.896295i | \(-0.353751\pi\) | ||||
0.443459 | + | 0.896295i | \(0.353751\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | −7.65685 | −1.59656 | −0.798282 | − | 0.602284i | \(-0.794258\pi\) | ||||
−0.798282 | + | 0.602284i | \(0.794258\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −11.6569 | −2.28610 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.82843 | 0.723505 | ||||||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.48528 | −1.52400 | −0.762001 | − | 0.647576i | \(-0.775783\pi\) | ||||
−0.762001 | + | 0.647576i | \(0.775783\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.82843 | −1.51406 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | −6.82843 | −1.10772 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.65685 | 0.571105 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.65685 | 1.47266 | 0.736328 | − | 0.676625i | \(-0.236558\pi\) | ||||
0.736328 | + | 0.676625i | \(0.236558\pi\) | |||||||
\(44\) | −3.17157 | −0.478133 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.4853 | 2.72551 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 18.4853 | 2.56345 | ||||||||
\(53\) | −10.8284 | −1.48740 | −0.743699 | − | 0.668514i | \(-0.766931\pi\) | ||||
−0.743699 | + | 0.668514i | \(0.766931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.41421 | −0.589874 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.3137 | −2.53601 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 20.4853 | 2.60163 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.31371 | −0.893512 | −0.446756 | − | 0.894656i | \(-0.647421\pi\) | ||||
−0.446756 | + | 0.894656i | \(0.647421\pi\) | |||||||
\(68\) | 14.0000 | 1.69775 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.48528 | −0.769661 | −0.384831 | − | 0.922987i | \(-0.625740\pi\) | ||||
−0.384831 | + | 0.922987i | \(0.625740\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.1421 | −1.88929 | −0.944647 | − | 0.328088i | \(-0.893596\pi\) | ||||
−0.944647 | + | 0.328088i | \(0.893596\pi\) | |||||||
\(74\) | −14.4853 | −1.68388 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.8284 | 1.24211 | ||||||||
\(77\) | −0.828427 | −0.0944080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.65685 | −0.636446 | −0.318223 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318223 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.82843 | −0.974937 | ||||||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −23.3137 | −2.51398 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.65685 | 0.389822 | ||||||||
\(89\) | 17.3137 | 1.83525 | 0.917625 | − | 0.397448i | \(-0.130104\pi\) | ||||
0.917625 | + | 0.397448i | \(0.130104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.82843 | 0.506157 | ||||||||
\(92\) | −29.3137 | −3.05617 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.65685 | −0.996028 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.82843 | 0.896391 | 0.448195 | − | 0.893936i | \(-0.352067\pi\) | ||||
0.448195 | + | 0.893936i | \(0.352067\pi\) | |||||||
\(98\) | −2.41421 | −0.243872 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6569 | 1.55792 | 0.778958 | − | 0.627077i | \(-0.215749\pi\) | ||||
0.778958 | + | 0.627077i | \(0.215749\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.31371 | −0.720641 | −0.360321 | − | 0.932829i | \(-0.617333\pi\) | ||||
−0.360321 | + | 0.932829i | \(0.617333\pi\) | |||||||
\(104\) | −21.3137 | −2.08998 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 26.1421 | 2.53915 | ||||||||
\(107\) | 2.00000 | 0.193347 | 0.0966736 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966736 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.00000 | 0.283473 | ||||||||
\(113\) | 4.48528 | 0.421940 | 0.210970 | − | 0.977493i | \(-0.432338\pi\) | ||||
0.210970 | + | 0.977493i | \(0.432338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 30.6274 | 2.84368 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.65685 | 0.888985 | ||||||||
\(119\) | 3.65685 | 0.335223 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | −14.4853 | −1.31144 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −32.4853 | −2.91726 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.6569 | −1.21185 | −0.605925 | − | 0.795522i | \(-0.707197\pi\) | ||||
−0.605925 | + | 0.795522i | \(0.707197\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.34315 | −0.204722 | −0.102361 | − | 0.994747i | \(-0.532640\pi\) | ||||
−0.102361 | + | 0.994747i | \(0.532640\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.82843 | 0.245256 | ||||||||
\(134\) | 17.6569 | 1.52532 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.1421 | −1.38418 | ||||||||
\(137\) | 6.14214 | 0.524758 | 0.262379 | − | 0.964965i | \(-0.415493\pi\) | ||||
0.262379 | + | 0.964965i | \(0.415493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.82843 | 0.579180 | 0.289590 | − | 0.957151i | \(-0.406481\pi\) | ||||
0.289590 | + | 0.957151i | \(0.406481\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.6569 | 1.31389 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 38.9706 | 3.22523 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 22.9706 | 1.88817 | ||||||||
\(149\) | −1.65685 | −0.135735 | −0.0678674 | − | 0.997694i | \(-0.521619\pi\) | ||||
−0.0678674 | + | 0.997694i | \(0.521619\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.65685 | 0.460348 | 0.230174 | − | 0.973149i | \(-0.426070\pi\) | ||||
0.230174 | + | 0.973149i | \(0.426070\pi\) | |||||||
\(152\) | −12.4853 | −1.01269 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.17157 | 0.253119 | 0.126560 | − | 0.991959i | \(-0.459607\pi\) | ||||
0.126560 | + | 0.991959i | \(0.459607\pi\) | |||||||
\(158\) | 13.6569 | 1.08648 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.65685 | −0.603445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6569 | 1.38299 | 0.691496 | − | 0.722380i | \(-0.256952\pi\) | ||||
0.691496 | + | 0.722380i | \(0.256952\pi\) | |||||||
\(164\) | 14.0000 | 1.09322 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.3137 | −1.49903 | ||||||||
\(167\) | 23.3137 | 1.80407 | 0.902034 | − | 0.431664i | \(-0.142073\pi\) | ||||
0.902034 | + | 0.431664i | \(0.142073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 36.9706 | 2.81898 | ||||||||
\(173\) | −4.34315 | −0.330203 | −0.165102 | − | 0.986277i | \(-0.552795\pi\) | ||||
−0.165102 | + | 0.986277i | \(0.552795\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.48528 | −0.187335 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −41.7990 | −3.13297 | ||||||||
\(179\) | 22.4853 | 1.68063 | 0.840314 | − | 0.542099i | \(-0.182370\pi\) | ||||
0.840314 | + | 0.542099i | \(0.182370\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.343146 | −0.0255058 | −0.0127529 | − | 0.999919i | \(-0.504059\pi\) | ||||
−0.0127529 | + | 0.999919i | \(0.504059\pi\) | |||||||
\(182\) | −11.6569 | −0.864064 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 33.7990 | 2.49169 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.02944 | −0.221534 | ||||||||
\(188\) | 15.3137 | 1.11687 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.828427 | −0.0599429 | −0.0299714 | − | 0.999551i | \(-0.509542\pi\) | ||||
−0.0299714 | + | 0.999551i | \(0.509542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.9706 | 1.36553 | 0.682765 | − | 0.730638i | \(-0.260777\pi\) | ||||
0.682765 | + | 0.730638i | \(0.260777\pi\) | |||||||
\(194\) | −21.3137 | −1.53024 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.82843 | 0.273459 | ||||||||
\(197\) | 2.82843 | 0.201517 | 0.100759 | − | 0.994911i | \(-0.467873\pi\) | ||||
0.100759 | + | 0.994911i | \(0.467873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.8284 | 1.61826 | 0.809132 | − | 0.587627i | \(-0.199938\pi\) | ||||
0.809132 | + | 0.587627i | \(0.199938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −37.7990 | −2.65953 | ||||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.6569 | 1.23021 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.4853 | 1.00437 | ||||||||
\(209\) | −2.34315 | −0.162079 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | −41.4558 | −2.84720 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.82843 | −0.330064 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.48528 | −0.576018 | ||||||||
\(218\) | −24.1421 | −1.63511 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.6569 | 1.18773 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.65685 | 0.378811 | 0.189405 | − | 0.981899i | \(-0.439344\pi\) | ||||
0.189405 | + | 0.981899i | \(0.439344\pi\) | |||||||
\(224\) | 1.58579 | 0.105955 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.8284 | −0.720296 | ||||||||
\(227\) | 20.0000 | 1.32745 | 0.663723 | − | 0.747978i | \(-0.268975\pi\) | ||||
0.663723 | + | 0.747978i | \(0.268975\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.31371 | 0.351140 | 0.175570 | − | 0.984467i | \(-0.443823\pi\) | ||||
0.175570 | + | 0.984467i | \(0.443823\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −35.3137 | −2.31846 | ||||||||
\(233\) | −6.14214 | −0.402385 | −0.201192 | − | 0.979552i | \(-0.564482\pi\) | ||||
−0.201192 | + | 0.979552i | \(0.564482\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.3137 | −0.996838 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.82843 | −0.572262 | ||||||||
\(239\) | 4.14214 | 0.267932 | 0.133966 | − | 0.990986i | \(-0.457229\pi\) | ||||
0.133966 | + | 0.990986i | \(0.457229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.65685 | 0.235559 | 0.117779 | − | 0.993040i | \(-0.462422\pi\) | ||||
0.117779 | + | 0.993040i | \(0.462422\pi\) | |||||||
\(242\) | 24.8995 | 1.60060 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.9706 | 1.47054 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.6569 | 0.868965 | ||||||||
\(248\) | 37.4558 | 2.37845 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.6274 | 1.17575 | 0.587876 | − | 0.808951i | \(-0.299964\pi\) | ||||
0.587876 | + | 0.808951i | \(0.299964\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.34315 | 0.398790 | ||||||||
\(254\) | 32.9706 | 2.06876 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | −17.3137 | −1.08000 | −0.540000 | − | 0.841665i | \(-0.681576\pi\) | ||||
−0.540000 | + | 0.841665i | \(0.681576\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.65685 | 0.349482 | ||||||||
\(263\) | 25.3137 | 1.56091 | 0.780455 | − | 0.625212i | \(-0.214987\pi\) | ||||
0.780455 | + | 0.625212i | \(0.214987\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.82843 | −0.418678 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −28.0000 | −1.71037 | ||||||||
\(269\) | −18.9706 | −1.15666 | −0.578328 | − | 0.815804i | \(-0.696295\pi\) | ||||
−0.578328 | + | 0.815804i | \(0.696295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.51472 | −0.456487 | −0.228243 | − | 0.973604i | \(-0.573298\pi\) | ||||
−0.228243 | + | 0.973604i | \(0.573298\pi\) | |||||||
\(272\) | 10.9706 | 0.665188 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.8284 | −0.895818 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.34315 | 0.260954 | 0.130477 | − | 0.991451i | \(-0.458349\pi\) | ||||
0.130477 | + | 0.991451i | \(0.458349\pi\) | |||||||
\(278\) | −16.4853 | −0.988721 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.3431 | −0.855640 | −0.427820 | − | 0.903864i | \(-0.640718\pi\) | ||||
−0.427820 | + | 0.903864i | \(0.640718\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | −24.8284 | −1.47330 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.65685 | 0.571022 | ||||||||
\(287\) | 3.65685 | 0.215857 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −61.7990 | −3.61651 | ||||||||
\(293\) | −2.00000 | −0.116841 | −0.0584206 | − | 0.998292i | \(-0.518606\pi\) | ||||
−0.0584206 | + | 0.998292i | \(0.518606\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −26.4853 | −1.53943 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.00000 | 0.231714 | ||||||||
\(299\) | −36.9706 | −2.13806 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.65685 | 0.556612 | ||||||||
\(302\) | −13.6569 | −0.785864 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.48528 | 0.486664 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.97056 | 0.283685 | 0.141843 | − | 0.989889i | \(-0.454697\pi\) | ||||
0.141843 | + | 0.989889i | \(0.454697\pi\) | |||||||
\(308\) | −3.17157 | −0.180717 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.6569 | −1.90851 | −0.954253 | − | 0.299002i | \(-0.903346\pi\) | ||||
−0.954253 | + | 0.299002i | \(0.903346\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.8284 | 1.17729 | 0.588646 | − | 0.808391i | \(-0.299661\pi\) | ||||
0.588646 | + | 0.808391i | \(0.299661\pi\) | |||||||
\(314\) | −7.65685 | −0.432101 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −21.6569 | −1.21829 | ||||||||
\(317\) | −14.1421 | −0.794301 | −0.397151 | − | 0.917753i | \(-0.630001\pi\) | ||||
−0.397151 | + | 0.917753i | \(0.630001\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.62742 | −0.371064 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.4853 | 1.03014 | ||||||||
\(323\) | 10.3431 | 0.575508 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −42.6274 | −2.36091 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16.1421 | −0.891300 | ||||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 30.6274 | 1.68090 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −56.2843 | −3.07974 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2843 | 1.21390 | 0.606951 | − | 0.794739i | \(-0.292392\pi\) | ||||
0.606951 | + | 0.794739i | \(0.292392\pi\) | |||||||
\(338\) | −24.8995 | −1.35435 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.02944 | 0.380665 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −42.6274 | −2.29832 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.4853 | 0.563692 | ||||||||
\(347\) | 0.343146 | 0.0184210 | 0.00921051 | − | 0.999958i | \(-0.497068\pi\) | ||||
0.00921051 | + | 0.999958i | \(0.497068\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.3137 | −1.56913 | −0.784563 | − | 0.620049i | \(-0.787113\pi\) | ||||
−0.784563 | + | 0.620049i | \(0.787113\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.31371 | −0.0700209 | ||||||||
\(353\) | −16.6274 | −0.884988 | −0.442494 | − | 0.896771i | \(-0.645906\pi\) | ||||
−0.442494 | + | 0.896771i | \(0.645906\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 66.2843 | 3.51306 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −54.2843 | −2.86901 | ||||||||
\(359\) | 10.4853 | 0.553392 | 0.276696 | − | 0.960958i | \(-0.410761\pi\) | ||||
0.276696 | + | 0.960958i | \(0.410761\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 0.828427 | 0.0435412 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.4853 | 0.968892 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.9706 | −1.30345 | −0.651726 | − | 0.758454i | \(-0.725955\pi\) | ||||
−0.651726 | + | 0.758454i | \(0.725955\pi\) | |||||||
\(368\) | −22.9706 | −1.19742 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.8284 | −0.562184 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 7.31371 | 0.378183 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.6569 | −0.910583 | ||||||||
\(377\) | 38.6274 | 1.98941 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.34315 | 0.325826 | 0.162913 | − | 0.986640i | \(-0.447911\pi\) | ||||
0.162913 | + | 0.986640i | \(0.447911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.00000 | 0.102329 | ||||||||
\(383\) | −27.3137 | −1.39567 | −0.697833 | − | 0.716261i | \(-0.745852\pi\) | ||||
−0.697833 | + | 0.716261i | \(0.745852\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −45.7990 | −2.33111 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 33.7990 | 1.71588 | ||||||||
\(389\) | 29.6569 | 1.50366 | 0.751831 | − | 0.659356i | \(-0.229171\pi\) | ||||
0.751831 | + | 0.659356i | \(0.229171\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.0000 | −1.41602 | ||||||||
\(392\) | −4.41421 | −0.222951 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.82843 | −0.344011 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.85786 | −0.193621 | −0.0968103 | − | 0.995303i | \(-0.530864\pi\) | ||||
−0.0968103 | + | 0.995303i | \(0.530864\pi\) | |||||||
\(398\) | −55.1127 | −2.76255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6274 | −0.930209 | −0.465104 | − | 0.885256i | \(-0.653983\pi\) | ||||
−0.465104 | + | 0.885256i | \(0.653983\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40.9706 | −2.04089 | ||||||||
\(404\) | 59.9411 | 2.98218 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.3137 | −0.958523 | ||||||||
\(407\) | −4.97056 | −0.246382 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.68629 | 0.132829 | 0.0664143 | − | 0.997792i | \(-0.478844\pi\) | ||||
0.0664143 | + | 0.997792i | \(0.478844\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −28.0000 | −1.37946 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.65685 | 0.375408 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.65685 | 0.276686 | ||||||||
\(419\) | −10.6274 | −0.519183 | −0.259592 | − | 0.965718i | \(-0.583588\pi\) | ||||
−0.259592 | + | 0.965718i | \(0.583588\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 28.9706 | 1.41026 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 47.7990 | 2.32132 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | 0.290360 | ||||||||
\(428\) | 7.65685 | 0.370108 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.8284 | 0.617924 | 0.308962 | − | 0.951074i | \(-0.400018\pi\) | ||||
0.308962 | + | 0.951074i | \(0.400018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.7990 | −1.23982 | −0.619910 | − | 0.784673i | \(-0.712831\pi\) | ||||
−0.619910 | + | 0.784673i | \(0.712831\pi\) | |||||||
\(434\) | 20.4853 | 0.983325 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 38.2843 | 1.83348 | ||||||||
\(437\) | −21.6569 | −1.03599 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.4558 | 0.642212 | 0.321106 | − | 0.947043i | \(-0.395945\pi\) | ||||
0.321106 | + | 0.947043i | \(0.395945\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −42.6274 | −2.02758 | ||||||||
\(443\) | −1.02944 | −0.0489100 | −0.0244550 | − | 0.999701i | \(-0.507785\pi\) | ||||
−0.0244550 | + | 0.999701i | \(0.507785\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.6569 | −0.646671 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.82843 | −0.464350 | ||||||||
\(449\) | 3.31371 | 0.156384 | 0.0781918 | − | 0.996938i | \(-0.475085\pi\) | ||||
0.0781918 | + | 0.996938i | \(0.475085\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.02944 | −0.142651 | ||||||||
\(452\) | 17.1716 | 0.807683 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −48.2843 | −2.26609 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.31371 | −0.0614527 | −0.0307263 | − | 0.999528i | \(-0.509782\pi\) | ||||
−0.0307263 | + | 0.999528i | \(0.509782\pi\) | |||||||
\(458\) | −12.8284 | −0.599433 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.6274 | −1.33331 | −0.666656 | − | 0.745366i | \(-0.732275\pi\) | ||||
−0.666656 | + | 0.745366i | \(0.732275\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3431 | 0.480687 | 0.240343 | − | 0.970688i | \(-0.422740\pi\) | ||||
0.240343 | + | 0.970688i | \(0.422740\pi\) | |||||||
\(464\) | 24.0000 | 1.11417 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.8284 | 0.686914 | ||||||||
\(467\) | −8.68629 | −0.401954 | −0.200977 | − | 0.979596i | \(-0.564412\pi\) | ||||
−0.200977 | + | 0.979596i | \(0.564412\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.31371 | −0.337716 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17.6569 | 0.812723 | ||||||||
\(473\) | −8.00000 | −0.367840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14.0000 | 0.641689 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.0000 | −0.457389 | ||||||||
\(479\) | −41.6569 | −1.90335 | −0.951675 | − | 0.307107i | \(-0.900639\pi\) | ||||
−0.951675 | + | 0.307107i | \(0.900639\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.9706 | 1.32094 | ||||||||
\(482\) | −8.82843 | −0.402124 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.4853 | −1.79479 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.6569 | 0.618851 | 0.309426 | − | 0.950924i | \(-0.399863\pi\) | ||||
0.309426 | + | 0.950924i | \(0.399863\pi\) | |||||||
\(488\) | −26.4853 | −1.19893 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.1421 | −0.728484 | −0.364242 | − | 0.931304i | \(-0.618672\pi\) | ||||
−0.364242 | + | 0.931304i | \(0.618672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.2548 | 1.31757 | ||||||||
\(494\) | −32.9706 | −1.48342 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.4558 | −1.14300 | ||||||||
\(497\) | −6.48528 | −0.290905 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6569 | 1.14856 | 0.574279 | − | 0.818659i | \(-0.305282\pi\) | ||||
0.574279 | + | 0.818659i | \(0.305282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −44.9706 | −2.00713 | ||||||||
\(503\) | 14.6274 | 0.652204 | 0.326102 | − | 0.945335i | \(-0.394265\pi\) | ||||
0.326102 | + | 0.945335i | \(0.394265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.3137 | −0.680777 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −52.2843 | −2.31974 | ||||||||
\(509\) | 16.3431 | 0.724397 | 0.362199 | − | 0.932101i | \(-0.382026\pi\) | ||||
0.362199 | + | 0.932101i | \(0.382026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.1421 | −0.714086 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 41.7990 | 1.84367 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.31371 | −0.145737 | ||||||||
\(518\) | −14.4853 | −0.636447 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9706 | 1.18160 | 0.590801 | − | 0.806817i | \(-0.298812\pi\) | ||||
0.590801 | + | 0.806817i | \(0.298812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.3431 | 0.802090 | 0.401045 | − | 0.916058i | \(-0.368647\pi\) | ||||
0.401045 | + | 0.916058i | \(0.368647\pi\) | |||||||
\(524\) | −8.97056 | −0.391881 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −61.1127 | −2.66464 | ||||||||
\(527\) | −31.0294 | −1.35166 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.6274 | 1.54902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.8284 | 0.469472 | ||||||||
\(533\) | 17.6569 | 0.764803 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 32.2843 | 1.39447 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 45.7990 | 1.97453 | ||||||||
\(539\) | −0.828427 | −0.0356829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.3137 | 1.43227 | 0.716134 | − | 0.697963i | \(-0.245910\pi\) | ||||
0.716134 | + | 0.697963i | \(0.245910\pi\) | |||||||
\(542\) | 18.1421 | 0.779271 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.79899 | 0.248630 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.686292 | −0.0293437 | −0.0146719 | − | 0.999892i | \(-0.504670\pi\) | ||||
−0.0146719 | + | 0.999892i | \(0.504670\pi\) | |||||||
\(548\) | 23.5147 | 1.00450 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.6274 | 0.963960 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.65685 | −0.240554 | ||||||||
\(554\) | −10.4853 | −0.445477 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 26.1421 | 1.10867 | ||||||||
\(557\) | −26.8284 | −1.13676 | −0.568378 | − | 0.822767i | \(-0.692429\pi\) | ||||
−0.568378 | + | 0.822767i | \(0.692429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.6274 | 1.97213 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 34.6274 | 1.46067 | ||||||||
\(563\) | −29.9411 | −1.26187 | −0.630934 | − | 0.775837i | \(-0.717328\pi\) | ||||
−0.630934 | + | 0.775837i | \(0.717328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.65685 | −0.405908 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 28.6274 | 1.20118 | ||||||||
\(569\) | −39.3137 | −1.64812 | −0.824058 | − | 0.566505i | \(-0.808295\pi\) | ||||
−0.824058 | + | 0.566505i | \(0.808295\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.3137 | −0.975648 | −0.487824 | − | 0.872942i | \(-0.662209\pi\) | ||||
−0.487824 | + | 0.872942i | \(0.662209\pi\) | |||||||
\(572\) | −15.3137 | −0.640298 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.82843 | −0.368491 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.5147 | 1.06219 | 0.531096 | − | 0.847312i | \(-0.321780\pi\) | ||||
0.531096 | + | 0.847312i | \(0.321780\pi\) | |||||||
\(578\) | 8.75736 | 0.364258 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | 0.331896 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.97056 | 0.371523 | ||||||||
\(584\) | 71.2548 | 2.94855 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.82843 | 0.199460 | ||||||||
\(587\) | −34.6274 | −1.42923 | −0.714613 | − | 0.699520i | \(-0.753397\pi\) | ||||
−0.714613 | + | 0.699520i | \(0.753397\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.0000 | 0.739795 | ||||||||
\(593\) | 17.3137 | 0.710989 | 0.355494 | − | 0.934678i | \(-0.384313\pi\) | ||||
0.355494 | + | 0.934678i | \(0.384313\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.34315 | −0.259825 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 89.2548 | 3.64990 | ||||||||
\(599\) | −20.1421 | −0.822985 | −0.411493 | − | 0.911413i | \(-0.634992\pi\) | ||||
−0.411493 | + | 0.911413i | \(0.634992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.2843 | −1.07216 | −0.536079 | − | 0.844168i | \(-0.680095\pi\) | ||||
−0.536079 | + | 0.844168i | \(0.680095\pi\) | |||||||
\(602\) | −23.3137 | −0.950196 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.6569 | 0.881205 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.0294 | −0.610026 | −0.305013 | − | 0.952348i | \(-0.598661\pi\) | ||||
−0.305013 | + | 0.952348i | \(0.598661\pi\) | |||||||
\(608\) | 4.48528 | 0.181902 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.3137 | 0.781349 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.9706 | −0.604655 | −0.302328 | − | 0.953204i | \(-0.597764\pi\) | ||||
−0.302328 | + | 0.953204i | \(0.597764\pi\) | |||||||
\(614\) | −12.0000 | −0.484281 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.65685 | 0.147339 | ||||||||
\(617\) | 21.1716 | 0.852335 | 0.426168 | − | 0.904644i | \(-0.359863\pi\) | ||||
0.426168 | + | 0.904644i | \(0.359863\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.4853 | −1.14492 | −0.572460 | − | 0.819933i | \(-0.694011\pi\) | ||||
−0.572460 | + | 0.819933i | \(0.694011\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 81.2548 | 3.25802 | ||||||||
\(623\) | 17.3137 | 0.693659 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −50.2843 | −2.00976 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.1421 | 0.484524 | ||||||||
\(629\) | 21.9411 | 0.874850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.65685 | −0.225196 | −0.112598 | − | 0.993641i | \(-0.535917\pi\) | ||||
−0.112598 | + | 0.993641i | \(0.535917\pi\) | |||||||
\(632\) | 24.9706 | 0.993276 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 34.1421 | 1.35596 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.82843 | 0.191309 | ||||||||
\(638\) | 16.0000 | 0.633446 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.9706 | 0.512306 | 0.256153 | − | 0.966636i | \(-0.417545\pi\) | ||||
0.256153 | + | 0.966636i | \(0.417545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.3431 | −0.881128 | −0.440564 | − | 0.897721i | \(-0.645221\pi\) | ||||
−0.440564 | + | 0.897721i | \(0.645221\pi\) | |||||||
\(644\) | −29.3137 | −1.15512 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.9706 | −0.982454 | ||||||||
\(647\) | −18.6274 | −0.732319 | −0.366160 | − | 0.930552i | \(-0.619328\pi\) | ||||
−0.366160 | + | 0.930552i | \(0.619328\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.31371 | 0.130074 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 67.5980 | 2.64734 | ||||||||
\(653\) | −5.85786 | −0.229236 | −0.114618 | − | 0.993410i | \(-0.536564\pi\) | ||||
−0.114618 | + | 0.993410i | \(0.536564\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.9706 | 0.428329 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.65685 | −0.376463 | ||||||||
\(659\) | 32.1421 | 1.25208 | 0.626040 | − | 0.779791i | \(-0.284675\pi\) | ||||
0.626040 | + | 0.779791i | \(0.284675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.3137 | 1.91808 | 0.959040 | − | 0.283269i | \(-0.0914189\pi\) | ||||
0.959040 | + | 0.283269i | \(0.0914189\pi\) | |||||||
\(662\) | 28.9706 | 1.12597 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −35.3137 | −1.37044 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −61.2548 | −2.37180 | ||||||||
\(668\) | 89.2548 | 3.45337 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.97056 | −0.191886 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.62742 | −0.178374 | −0.0891869 | − | 0.996015i | \(-0.528427\pi\) | ||||
−0.0891869 | + | 0.996015i | \(0.528427\pi\) | |||||||
\(674\) | −53.7990 | −2.07226 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 39.4853 | 1.51866 | ||||||||
\(677\) | −21.3137 | −0.819152 | −0.409576 | − | 0.912276i | \(-0.634323\pi\) | ||||
−0.409576 | + | 0.912276i | \(0.634323\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.82843 | 0.338804 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.9706 | −0.649836 | ||||||||
\(683\) | −1.02944 | −0.0393903 | −0.0196952 | − | 0.999806i | \(-0.506270\pi\) | ||||
−0.0196952 | + | 0.999806i | \(0.506270\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.41421 | −0.0921751 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28.9706 | 1.10449 | ||||||||
\(689\) | −52.2843 | −1.99187 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.1421 | −0.385825 | −0.192913 | − | 0.981216i | \(-0.561793\pi\) | ||||
−0.192913 | + | 0.981216i | \(0.561793\pi\) | |||||||
\(692\) | −16.6274 | −0.632080 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.828427 | −0.0314467 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.3726 | 0.506523 | ||||||||
\(698\) | 70.7696 | 2.67867 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.31371 | 0.125157 | 0.0625785 | − | 0.998040i | \(-0.480068\pi\) | ||||
0.0625785 | + | 0.998040i | \(0.480068\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9706 | 0.640057 | ||||||||
\(704\) | 8.14214 | 0.306868 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40.1421 | 1.51077 | ||||||||
\(707\) | 15.6569 | 0.588837 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.6274 | 0.624456 | 0.312228 | − | 0.950007i | \(-0.398925\pi\) | ||||
0.312228 | + | 0.950007i | \(0.398925\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −76.4264 | −2.86420 | ||||||||
\(713\) | 64.9706 | 2.43317 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 86.0833 | 3.21708 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −25.3137 | −0.944699 | ||||||||
\(719\) | 20.6863 | 0.771468 | 0.385734 | − | 0.922610i | \(-0.373948\pi\) | ||||
0.385734 | + | 0.922610i | \(0.373948\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.31371 | −0.272377 | ||||||||
\(722\) | 26.5563 | 0.988325 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.31371 | −0.0488236 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.34315 | 0.235254 | 0.117627 | − | 0.993058i | \(-0.462471\pi\) | ||||
0.117627 | + | 0.993058i | \(0.462471\pi\) | |||||||
\(728\) | −21.3137 | −0.789939 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.3137 | 1.30612 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.51472 | 0.0559474 | 0.0279737 | − | 0.999609i | \(-0.491095\pi\) | ||||
0.0279737 | + | 0.999609i | \(0.491095\pi\) | |||||||
\(734\) | 60.2843 | 2.22513 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.1421 | −0.447565 | ||||||||
\(737\) | 6.05887 | 0.223182 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.6274 | −0.685221 | −0.342610 | − | 0.939478i | \(-0.611311\pi\) | ||||
−0.342610 | + | 0.939478i | \(0.611311\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.1421 | 0.959708 | ||||||||
\(743\) | 29.3137 | 1.07542 | 0.537708 | − | 0.843131i | \(-0.319290\pi\) | ||||
0.537708 | + | 0.843131i | \(0.319290\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24.1421 | −0.883906 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.5980 | −0.424064 | ||||||||
\(749\) | 2.00000 | 0.0730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.6274 | 1.70146 | 0.850729 | − | 0.525604i | \(-0.176161\pi\) | ||||
0.850729 | + | 0.525604i | \(0.176161\pi\) | |||||||
\(752\) | 12.0000 | 0.437595 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −93.2548 | −3.39614 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.9706 | −1.27103 | −0.635513 | − | 0.772090i | \(-0.719211\pi\) | ||||
−0.635513 | + | 0.772090i | \(0.719211\pi\) | |||||||
\(758\) | −15.3137 | −0.556219 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.6274 | −0.892743 | −0.446372 | − | 0.894848i | \(-0.647284\pi\) | ||||
−0.446372 | + | 0.894848i | \(0.647284\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0000 | 0.362024 | ||||||||
\(764\) | −3.17157 | −0.114743 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 65.9411 | 2.38255 | ||||||||
\(767\) | −19.3137 | −0.697378 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.6569 | −0.708844 | −0.354422 | − | 0.935086i | \(-0.615322\pi\) | ||||
−0.354422 | + | 0.935086i | \(0.615322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 72.6274 | 2.61392 | ||||||||
\(773\) | −36.3431 | −1.30717 | −0.653586 | − | 0.756852i | \(-0.726736\pi\) | ||||
−0.653586 | + | 0.756852i | \(0.726736\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −38.9706 | −1.39896 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −71.5980 | −2.56691 | ||||||||
\(779\) | 10.3431 | 0.370582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.37258 | 0.192246 | ||||||||
\(782\) | 67.5980 | 2.41730 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.34315 | −0.0835241 | −0.0417621 | − | 0.999128i | \(-0.513297\pi\) | ||||
−0.0417621 | + | 0.999128i | \(0.513297\pi\) | |||||||
\(788\) | 10.8284 | 0.385747 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.48528 | 0.159478 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.9706 | 1.02877 | ||||||||
\(794\) | 9.31371 | 0.330531 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 87.3970 | 3.09770 | ||||||||
\(797\) | −50.9706 | −1.80547 | −0.902735 | − | 0.430197i | \(-0.858444\pi\) | ||||
−0.902735 | + | 0.430197i | \(0.858444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.6274 | 0.517481 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 44.9706 | 1.58797 | ||||||||
\(803\) | 13.3726 | 0.471908 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 98.9117 | 3.48402 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −69.1127 | −2.43138 | ||||||||
\(809\) | −2.34315 | −0.0823806 | −0.0411903 | − | 0.999151i | \(-0.513115\pi\) | ||||
−0.0411903 | + | 0.999151i | \(0.513115\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.1716 | −0.883893 | −0.441947 | − | 0.897041i | \(-0.645712\pi\) | ||||
−0.441947 | + | 0.897041i | \(0.645712\pi\) | |||||||
\(812\) | 30.6274 | 1.07481 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.3137 | 0.955586 | ||||||||
\(818\) | −6.48528 | −0.226753 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.9411 | 1.04495 | 0.522476 | − | 0.852654i | \(-0.325008\pi\) | ||||
0.522476 | + | 0.852654i | \(0.325008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3431 | −0.360539 | −0.180270 | − | 0.983617i | \(-0.557697\pi\) | ||||
−0.180270 | + | 0.983617i | \(0.557697\pi\) | |||||||
\(824\) | 32.2843 | 1.12468 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.65685 | 0.336005 | ||||||||
\(827\) | −46.0000 | −1.59958 | −0.799788 | − | 0.600282i | \(-0.795055\pi\) | ||||
−0.799788 | + | 0.600282i | \(0.795055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.6569 | −0.404859 | −0.202430 | − | 0.979297i | \(-0.564884\pi\) | ||||
−0.202430 | + | 0.979297i | \(0.564884\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −47.4558 | −1.64524 | ||||||||
\(833\) | 3.65685 | 0.126702 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.97056 | −0.310253 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.6569 | 0.886301 | ||||||||
\(839\) | 17.6569 | 0.609582 | 0.304791 | − | 0.952419i | \(-0.401413\pi\) | ||||
0.304791 | + | 0.952419i | \(0.401413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | −33.7990 | −1.16479 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −45.9411 | −1.58136 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.3137 | −0.354383 | ||||||||
\(848\) | −32.4853 | −1.11555 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45.9411 | −1.57484 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.4853 | −1.45467 | −0.727334 | − | 0.686283i | \(-0.759241\pi\) | ||||
−0.727334 | + | 0.686283i | \(0.759241\pi\) | |||||||
\(854\) | −14.4853 | −0.495676 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.82843 | −0.301749 | ||||||||
\(857\) | −0.343146 | −0.0117216 | −0.00586082 | − | 0.999983i | \(-0.501866\pi\) | ||||
−0.00586082 | + | 0.999983i | \(0.501866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.1421 | −1.30139 | −0.650696 | − | 0.759338i | \(-0.725523\pi\) | ||||
−0.650696 | + | 0.759338i | \(0.725523\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.9706 | −1.05486 | ||||||||
\(863\) | −54.2843 | −1.84786 | −0.923929 | − | 0.382564i | \(-0.875041\pi\) | ||||
−0.923929 | + | 0.382564i | \(0.875041\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 62.2843 | 2.11651 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −32.4853 | −1.10262 | ||||||||
\(869\) | 4.68629 | 0.158972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.3137 | −1.19656 | ||||||||
\(872\) | −44.1421 | −1.49484 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 52.2843 | 1.76854 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.3431 | 0.686939 | 0.343470 | − | 0.939164i | \(-0.388398\pi\) | ||||
0.343470 | + | 0.939164i | \(0.388398\pi\) | |||||||
\(878\) | −32.4853 | −1.09633 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.6863 | −0.360030 | −0.180015 | − | 0.983664i | \(-0.557615\pi\) | ||||
−0.180015 | + | 0.983664i | \(0.557615\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.31371 | −0.246126 | −0.123063 | − | 0.992399i | \(-0.539272\pi\) | ||||
−0.123063 | + | 0.992399i | \(0.539272\pi\) | |||||||
\(884\) | 67.5980 | 2.27357 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.48528 | 0.0834947 | ||||||||
\(887\) | 31.3137 | 1.05141 | 0.525706 | − | 0.850667i | \(-0.323801\pi\) | ||||
0.525706 | + | 0.850667i | \(0.323801\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.6569 | −0.458036 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.6569 | 0.725125 | ||||||||
\(893\) | 11.3137 | 0.378599 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 20.5563 | 0.686739 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.00000 | −0.266963 | ||||||||
\(899\) | −67.8823 | −2.26400 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.5980 | −1.31920 | ||||||||
\(902\) | 7.31371 | 0.243520 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.7990 | −0.658505 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.00000 | −0.132818 | −0.0664089 | − | 0.997792i | \(-0.521154\pi\) | ||||
−0.0664089 | + | 0.997792i | \(0.521154\pi\) | |||||||
\(908\) | 76.5685 | 2.54102 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.85786 | 0.127817 | 0.0639084 | − | 0.997956i | \(-0.479643\pi\) | ||||
0.0639084 | + | 0.997956i | \(0.479643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.62742 | −0.219335 | ||||||||
\(914\) | 3.17157 | 0.104906 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.3431 | 0.672156 | ||||||||
\(917\) | −2.34315 | −0.0773775 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.6274 | −0.746410 | −0.373205 | − | 0.927749i | \(-0.621741\pi\) | ||||
−0.373205 | + | 0.927749i | \(0.621741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 69.1127 | 2.27611 | ||||||||
\(923\) | −31.3137 | −1.03070 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −24.9706 | −0.820584 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.6863 | 0.416448 | ||||||||
\(929\) | −51.9411 | −1.70413 | −0.852067 | − | 0.523434i | \(-0.824651\pi\) | ||||
−0.852067 | + | 0.523434i | \(0.824651\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.82843 | 0.0926980 | ||||||||
\(932\) | −23.5147 | −0.770250 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.9706 | 0.686178 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.7990 | 0.450793 | 0.225397 | − | 0.974267i | \(-0.427632\pi\) | ||||
0.225397 | + | 0.974267i | \(0.427632\pi\) | |||||||
\(938\) | 17.6569 | 0.576517 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.62742 | 0.150849 | 0.0754247 | − | 0.997151i | \(-0.475969\pi\) | ||||
0.0754247 | + | 0.997151i | \(0.475969\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.0000 | −0.911805 | ||||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.3137 | 0.627943 | ||||||||
\(947\) | 18.9706 | 0.616460 | 0.308230 | − | 0.951312i | \(-0.400263\pi\) | ||||
0.308230 | + | 0.951312i | \(0.400263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −77.9411 | −2.53008 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16.1421 | −0.523170 | ||||||||
\(953\) | 51.1127 | 1.65570 | 0.827851 | − | 0.560948i | \(-0.189563\pi\) | ||||
0.827851 | + | 0.560948i | \(0.189563\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.8579 | 0.512880 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 100.569 | 3.24922 | ||||||||
\(959\) | 6.14214 | 0.198340 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.0000 | 1.32258 | ||||||||
\(962\) | −69.9411 | −2.25499 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.0000 | 0.450910 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.6274 | 1.24217 | 0.621087 | − | 0.783742i | \(-0.286691\pi\) | ||||
0.621087 | + | 0.783742i | \(0.286691\pi\) | |||||||
\(968\) | 45.5269 | 1.46329 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.9706 | −0.544611 | −0.272306 | − | 0.962211i | \(-0.587786\pi\) | ||||
−0.272306 | + | 0.962211i | \(0.587786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.82843 | 0.218909 | ||||||||
\(974\) | −32.9706 | −1.05644 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.0000 | 0.576166 | ||||||||
\(977\) | −6.14214 | −0.196504 | −0.0982522 | − | 0.995162i | \(-0.531325\pi\) | ||||
−0.0982522 | + | 0.995162i | \(0.531325\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.3431 | −0.458409 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 38.9706 | 1.24360 | ||||||||
\(983\) | 41.9411 | 1.33771 | 0.668857 | − | 0.743391i | \(-0.266784\pi\) | ||||
0.668857 | + | 0.743391i | \(0.266784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −70.6274 | −2.24924 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 52.2843 | 1.66338 | ||||||||
\(989\) | −73.9411 | −2.35119 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.3137 | −1.63003 | −0.815017 | − | 0.579437i | \(-0.803272\pi\) | ||||
−0.815017 | + | 0.579437i | \(0.803272\pi\) | |||||||
\(992\) | −13.4558 | −0.427223 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.6569 | 0.496605 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.5147 | 1.18810 | 0.594052 | − | 0.804427i | \(-0.297528\pi\) | ||||
0.594052 | + | 0.804427i | \(0.297528\pi\) | |||||||
\(998\) | −61.9411 | −1.96071 | ||||||||
\(999\) | 0 | 0 |
(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 | 1575.2.a.m.1.1 | 2 | ||
3.2 | odd | 2 | 1575.2.a.u.1.2 | 2 | |||
5.2 | odd | 4 | 1575.2.d.j.1324.1 | 4 | |||
5.3 | odd | 4 | 1575.2.d.j.1324.4 | 4 | |||
5.4 | even | 2 | 315.2.a.f.1.2 | yes | 2 | ||
15.2 | even | 4 | 1575.2.d.h.1324.4 | 4 | |||
15.8 | even | 4 | 1575.2.d.h.1324.1 | 4 | |||
15.14 | odd | 2 | 315.2.a.c.1.1 | ✓ | 2 | ||
20.19 | odd | 2 | 5040.2.a.bx.1.2 | 2 | |||
35.34 | odd | 2 | 2205.2.a.y.1.2 | 2 | |||
60.59 | even | 2 | 5040.2.a.bu.1.1 | 2 | |||
105.104 | even | 2 | 2205.2.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.a.c.1.1 | ✓ | 2 | 15.14 | odd | 2 | ||
315.2.a.f.1.2 | yes | 2 | 5.4 | even | 2 | ||
1575.2.a.m.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1575.2.a.u.1.2 | 2 | 3.2 | odd | 2 | |||
1575.2.d.h.1324.1 | 4 | 15.8 | even | 4 | |||
1575.2.d.h.1324.4 | 4 | 15.2 | even | 4 | |||
1575.2.d.j.1324.1 | 4 | 5.2 | odd | 4 | |||
1575.2.d.j.1324.4 | 4 | 5.3 | odd | 4 | |||
2205.2.a.p.1.1 | 2 | 105.104 | even | 2 | |||
2205.2.a.y.1.2 | 2 | 35.34 | odd | 2 | |||
5040.2.a.bu.1.1 | 2 | 60.59 | even | 2 | |||
5040.2.a.bx.1.2 | 2 | 20.19 | odd | 2 |