Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9280,2,Mod(1,9280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9280 = 2^{6} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9280.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: | \(74.1011730757\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4640) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.93185\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9280.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.41421 | 0.816497 | 0.408248 | − | 0.912871i | \(-0.366140\pi\) | ||||
0.408248 | + | 0.912871i | \(0.366140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421 | 0.534522 | 0.267261 | − | 0.963624i | \(-0.413881\pi\) | ||||
0.267261 | + | 0.963624i | \(0.413881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.46410 | −0.406069 | −0.203034 | − | 0.979172i | \(-0.565080\pi\) | ||||
−0.203034 | + | 0.979172i | \(0.565080\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.19615 | −1.50279 | −0.751394 | − | 0.659854i | \(-0.770618\pi\) | ||||
−0.751394 | + | 0.659854i | \(0.770618\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.44949 | −0.561951 | −0.280976 | − | 0.959715i | \(-0.590658\pi\) | ||||
−0.280976 | + | 0.959715i | \(0.590658\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.378937 | 0.0790139 | 0.0395070 | − | 0.999219i | \(-0.487421\pi\) | ||||
0.0395070 | + | 0.999219i | \(0.487421\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.20736 | 0.576060 | 0.288030 | − | 0.957621i | \(-0.407000\pi\) | ||||
0.288030 | + | 0.957621i | \(0.407000\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41421 | −0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.732051 | −0.120348 | −0.0601742 | − | 0.998188i | \(-0.519166\pi\) | ||||
−0.0601742 | + | 0.998188i | \(0.519166\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.07055 | −0.331554 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.24264 | 0.646997 | 0.323498 | − | 0.946229i | \(-0.395141\pi\) | ||||
0.323498 | + | 0.946229i | \(0.395141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.2122 | 1.63546 | 0.817732 | − | 0.575600i | \(-0.195231\pi\) | ||||
0.817732 | + | 0.575600i | \(0.195231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.76268 | −1.22702 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.53590 | 0.348332 | 0.174166 | − | 0.984716i | \(-0.444277\pi\) | ||||
0.174166 | + | 0.984716i | \(0.444277\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41421 | −0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | −0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.76268 | 1.14080 | 0.570402 | − | 0.821366i | \(-0.306787\pi\) | ||||
0.570402 | + | 0.821366i | \(0.306787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.3923 | 1.58667 | 0.793336 | − | 0.608784i | \(-0.208342\pi\) | ||||
0.793336 | + | 0.608784i | \(0.208342\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.41421 | −0.178174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.46410 | 0.181599 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.0759 | 1.84181 | 0.920906 | − | 0.389785i | \(-0.127451\pi\) | ||||
0.920906 | + | 0.389785i | \(0.127451\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.535898 | 0.0645146 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.45001 | 0.884153 | 0.442076 | − | 0.896977i | \(-0.354242\pi\) | ||||
0.442076 | + | 0.896977i | \(0.354242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.19615 | −0.959287 | −0.479644 | − | 0.877463i | \(-0.659234\pi\) | ||||
−0.479644 | + | 0.877463i | \(0.659234\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.41421 | 0.163299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.38375 | 0.943245 | 0.471623 | − | 0.881801i | \(-0.343669\pi\) | ||||
0.471623 | + | 0.881801i | \(0.343669\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.89949 | 1.08661 | 0.543305 | − | 0.839535i | \(-0.317173\pi\) | ||||
0.543305 | + | 0.839535i | \(0.317173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.19615 | 0.672067 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.41421 | −0.151620 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.8564 | 1.25678 | 0.628388 | − | 0.777900i | \(-0.283715\pi\) | ||||
0.628388 | + | 0.777900i | \(0.283715\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.07055 | −0.217053 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.53590 | 0.470351 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.44949 | 0.251312 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.1962 | −1.23833 | −0.619166 | − | 0.785260i | \(-0.712529\pi\) | ||||
−0.619166 | + | 0.785260i | \(0.712529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.41421 | −0.142134 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.39230 | −0.238043 | −0.119022 | − | 0.992892i | \(-0.537976\pi\) | ||||
−0.119022 | + | 0.992892i | \(0.537976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.9043 | 1.76416 | 0.882082 | − | 0.471096i | \(-0.156142\pi\) | ||||
0.882082 | + | 0.471096i | \(0.156142\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.2827 | −1.28409 | −0.642045 | − | 0.766667i | \(-0.721914\pi\) | ||||
−0.642045 | + | 0.766667i | \(0.721914\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.92820 | 0.663602 | 0.331801 | − | 0.943349i | \(-0.392344\pi\) | ||||
0.331801 | + | 0.943349i | \(0.392344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.03528 | −0.0982641 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.5885 | 1.93680 | 0.968400 | − | 0.249404i | \(-0.0802347\pi\) | ||||
0.968400 | + | 0.249404i | \(0.0802347\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.378937 | −0.0353361 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.46410 | 0.135356 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.76268 | −0.803274 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.65685 | −0.510061 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.1817 | −1.61337 | −0.806683 | − | 0.590985i | \(-0.798739\pi\) | ||||
−0.806683 | + | 0.590985i | \(0.798739\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.69161 | 0.147797 | 0.0738985 | − | 0.997266i | \(-0.476456\pi\) | ||||
0.0738985 | + | 0.997266i | \(0.476456\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.46410 | −0.300376 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.65685 | 0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.73205 | 0.404286 | 0.202143 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202143 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4548 | 1.31086 | 0.655430 | − | 0.755256i | \(-0.272487\pi\) | ||||
0.655430 | + | 0.755256i | \(0.272487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.8564 | 1.33535 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.07055 | −0.173148 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.07107 | −0.583212 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.5359 | 1.02698 | 0.513490 | − | 0.858095i | \(-0.328352\pi\) | ||||
0.513490 | + | 0.858095i | \(0.328352\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.69213 | 0.544598 | 0.272299 | − | 0.962213i | \(-0.412216\pi\) | ||||
0.272299 | + | 0.962213i | \(0.412216\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.19615 | 0.500929 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.20736 | −0.257622 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.1962 | −1.61183 | −0.805914 | − | 0.592032i | \(-0.798326\pi\) | ||||
−0.805914 | + | 0.592032i | \(0.798326\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.58630 | 0.284412 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.535898 | 0.0422347 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.07107 | 0.553849 | 0.276924 | − | 0.960892i | \(-0.410685\pi\) | ||||
0.276924 | + | 0.960892i | \(0.410685\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.00000 | −0.155700 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.3495 | 1.34254 | 0.671272 | − | 0.741211i | \(-0.265748\pi\) | ||||
0.671272 | + | 0.741211i | \(0.265748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8564 | −0.835108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.44949 | 0.187317 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.8564 | 1.66171 | 0.830856 | − | 0.556488i | \(-0.187851\pi\) | ||||
0.830856 | + | 0.556488i | \(0.187851\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.41421 | 0.106904 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.3923 | 0.931463 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.04008 | −0.675688 | −0.337844 | − | 0.941202i | \(-0.609698\pi\) | ||||
−0.337844 | + | 0.941202i | \(0.609698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.5359 | 1.37776 | 0.688881 | − | 0.724874i | \(-0.258102\pi\) | ||||
0.688881 | + | 0.724874i | \(0.258102\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.5254 | 1.29551 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.732051 | 0.0538214 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.76268 | −0.640791 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.00000 | −0.581914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.656339 | 0.0474910 | 0.0237455 | − | 0.999718i | \(-0.492441\pi\) | ||||
0.0237455 | + | 0.999718i | \(0.492441\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.1244 | −1.52056 | −0.760282 | − | 0.649593i | \(-0.774939\pi\) | ||||
−0.760282 | + | 0.649593i | \(0.774939\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.07055 | 0.148275 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.9282 | 0.921096 | 0.460548 | − | 0.887635i | \(-0.347653\pi\) | ||||
0.460548 | + | 0.887635i | \(0.347653\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0363 | −0.782343 | −0.391172 | − | 0.920318i | \(-0.627930\pi\) | ||||
−0.391172 | + | 0.920318i | \(0.627930\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.3205 | 1.50383 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.41421 | −0.0992583 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.378937 | −0.0263380 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.46410 | −0.239617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0406 | 0.966595 | 0.483297 | − | 0.875456i | \(-0.339439\pi\) | ||||
0.483297 | + | 0.875456i | \(0.339439\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.5359 | 0.721908 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.24264 | −0.289346 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.53590 | 0.307917 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.5911 | −0.783255 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.07180 | 0.610235 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29.2180 | −1.95658 | −0.978291 | − | 0.207234i | \(-0.933554\pi\) | ||||
−0.978291 | + | 0.207234i | \(0.933554\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.9749 | −1.32578 | −0.662889 | − | 0.748718i | \(-0.730670\pi\) | ||||
−0.662889 | + | 0.748718i | \(0.730670\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.92820 | 0.325665 | 0.162832 | − | 0.986654i | \(-0.447937\pi\) | ||||
0.162832 | + | 0.986654i | \(0.447937\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.82843 | 0.186097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.2487 | −1.32654 | −0.663269 | − | 0.748381i | \(-0.730831\pi\) | ||||
−0.663269 | + | 0.748381i | \(0.730831\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2122 | −0.731401 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.8564 | 0.770156 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.20788 | −0.530924 | −0.265462 | − | 0.964121i | \(-0.585524\pi\) | ||||
−0.265462 | + | 0.964121i | \(0.585524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.85641 | 0.248413 | 0.124206 | − | 0.992256i | \(-0.460361\pi\) | ||||
0.124206 | + | 0.992256i | \(0.460361\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.89949 | 0.635053 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.00000 | 0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.58630 | 0.228191 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.0000 | 0.887214 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.1112 | 1.01693 | 0.508463 | − | 0.861084i | \(-0.330214\pi\) | ||||
0.508463 | + | 0.861084i | \(0.330214\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.535898 | 0.0336916 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.76268 | 0.548740 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.92820 | −0.182656 | −0.0913281 | − | 0.995821i | \(-0.529111\pi\) | ||||
−0.0913281 | + | 0.995821i | \(0.529111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.03528 | −0.0643289 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.79744 | −0.295823 | −0.147912 | − | 0.989001i | \(-0.547255\pi\) | ||||
−0.147912 | + | 0.989001i | \(0.547255\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.53590 | −0.155779 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.7675 | 1.02615 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.85641 | −0.113187 | −0.0565935 | − | 0.998397i | \(-0.518024\pi\) | ||||
−0.0565935 | + | 0.998397i | \(0.518024\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3142 | −0.991019 | −0.495509 | − | 0.868603i | \(-0.665019\pi\) | ||||
−0.495509 | + | 0.868603i | \(0.665019\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.92820 | −0.177223 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.41421 | 0.0852803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.392305 | −0.0235713 | −0.0117857 | − | 0.999931i | \(-0.503752\pi\) | ||||
−0.0117857 | + | 0.999931i | \(0.503752\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.20736 | −0.192020 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8564 | −0.826604 | −0.413302 | − | 0.910594i | \(-0.635625\pi\) | ||||
−0.413302 | + | 0.910594i | \(0.635625\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.2180 | 1.73683 | 0.868415 | − | 0.495838i | \(-0.165139\pi\) | ||||
0.868415 | + | 0.495838i | \(0.165139\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.46410 | 0.205196 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.65685 | −0.333914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.3923 | 1.25837 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.2480 | −1.01109 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.66025 | −0.0969931 | −0.0484965 | − | 0.998823i | \(-0.515443\pi\) | ||||
−0.0484965 | + | 0.998823i | \(0.515443\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.76268 | −0.510183 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.00000 | −0.464207 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.554803 | −0.0320851 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | 0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.38323 | −0.194361 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.3923 | −0.709581 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.41421 | −0.0807134 | −0.0403567 | − | 0.999185i | \(-0.512849\pi\) | ||||
−0.0403567 | + | 0.999185i | \(0.512849\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.3205 | 1.44043 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.7632 | −0.780439 | −0.390220 | − | 0.920722i | \(-0.627601\pi\) | ||||
−0.390220 | + | 0.920722i | \(0.627601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.53590 | 0.143337 | 0.0716687 | − | 0.997428i | \(-0.477168\pi\) | ||||
0.0716687 | + | 0.997428i | \(0.477168\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.41421 | 0.0796819 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.5167 | −1.43316 | −0.716579 | − | 0.697506i | \(-0.754293\pi\) | ||||
−0.716579 | + | 0.697506i | \(0.754293\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.41421 | −0.0791808 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.7846 | −1.04845 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.1774 | 0.844494 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.46410 | −0.0812137 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.79796 | 0.541828 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.8564 | 0.874192 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.8033 | −1.25338 | −0.626691 | − | 0.779268i | \(-0.715591\pi\) | ||||
−0.626691 | + | 0.779268i | \(0.715591\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.732051 | 0.0401161 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.0759 | −0.823683 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5885 | 0.685737 | 0.342868 | − | 0.939383i | \(-0.388601\pi\) | ||||
0.342868 | + | 0.939383i | \(0.388601\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.1165 | 1.58139 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.53590 | 0.245633 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.535898 | −0.0288518 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.0406 | 0.753739 | 0.376869 | − | 0.926266i | \(-0.377001\pi\) | ||||
0.376869 | + | 0.926266i | \(0.377001\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.85641 | −0.420544 | −0.210272 | − | 0.977643i | \(-0.567435\pi\) | ||||
−0.210272 | + | 0.977643i | \(0.567435\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.28221 | 0.442072 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.5359 | 1.41236 | 0.706182 | − | 0.708031i | \(-0.250416\pi\) | ||||
0.706182 | + | 0.708031i | \(0.250416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.45001 | −0.395405 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.3923 | −0.655870 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.41902 | 0.497117 | 0.248558 | − | 0.968617i | \(-0.420043\pi\) | ||||
0.248558 | + | 0.968617i | \(0.420043\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | −0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.7279 | −0.668043 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.19615 | 0.429006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.9101 | 1.87449 | 0.937247 | − | 0.348666i | \(-0.113365\pi\) | ||||
0.937247 | + | 0.348666i | \(0.113365\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.58630 | 0.186192 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.3923 | 0.952317 | 0.476159 | − | 0.879359i | \(-0.342029\pi\) | ||||
0.476159 | + | 0.879359i | \(0.342029\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.41421 | −0.0730297 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.46410 | 0.0754051 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.69642 | −0.498072 | −0.249036 | − | 0.968494i | \(-0.580114\pi\) | ||||
−0.249036 | + | 0.968494i | \(0.580114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.7128 | −1.31731 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.2827 | 0.678716 | 0.339358 | − | 0.940657i | \(-0.389790\pi\) | ||||
0.339358 | + | 0.940657i | \(0.389790\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.00000 | −0.101929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.24264 | −0.215666 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.7846 | 1.66225 | 0.831123 | − | 0.556089i | \(-0.187699\pi\) | ||||
0.831123 | + | 0.556089i | \(0.187699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.34795 | −0.118741 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.39230 | 0.120676 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.38375 | −0.421832 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.8564 | −0.795810 | −0.397905 | − | 0.917427i | \(-0.630263\pi\) | ||||
−0.397905 | + | 0.917427i | \(0.630263\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.89898 | −0.245256 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.392305 | 0.0195908 | 0.00979538 | − | 0.999952i | \(-0.496882\pi\) | ||||
0.00979538 | + | 0.999952i | \(0.496882\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.69591 | −0.233920 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.00000 | 0.248452 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.03528 | −0.0513167 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.3205 | −0.757550 | −0.378775 | − | 0.925489i | \(-0.623655\pi\) | ||||
−0.378775 | + | 0.925489i | \(0.623655\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.69213 | 0.330098 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.3923 | 0.609785 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.89949 | −0.485947 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.8564 | 1.07031 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.1459 | 0.593367 | 0.296683 | − | 0.954976i | \(-0.404119\pi\) | ||||
0.296683 | + | 0.954976i | \(0.404119\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.9282 | 1.70230 | 0.851148 | − | 0.524925i | \(-0.175907\pi\) | ||||
0.851148 | + | 0.524925i | \(0.175907\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.2122 | −0.545154 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.19615 | −0.300558 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.5254 | 0.848112 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.92820 | −0.141375 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.4548 | −0.744432 | −0.372216 | − | 0.928146i | \(-0.621402\pi\) | ||||
−0.372216 | + | 0.928146i | \(0.621402\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.19615 | 0.297768 | 0.148884 | − | 0.988855i | \(-0.452432\pi\) | ||||
0.148884 | + | 0.988855i | \(0.452432\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.41421 | 0.0678064 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.928203 | −0.0444020 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.9144 | −1.85728 | −0.928642 | − | 0.370976i | \(-0.879023\pi\) | ||||
−0.928642 | + | 0.370976i | \(0.879023\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.6574 | −0.506347 | −0.253173 | − | 0.967421i | \(-0.581474\pi\) | ||||
−0.253173 | + | 0.967421i | \(0.581474\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.8564 | −0.562048 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.7284 | 0.838526 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5359 | 1.06353 | 0.531767 | − | 0.846890i | \(-0.321528\pi\) | ||||
0.531767 | + | 0.846890i | \(0.321528\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.65685 | −0.266371 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.46410 | 0.444662 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.07055 | 0.0970690 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.46410 | −0.0684878 | −0.0342439 | − | 0.999414i | \(-0.510902\pi\) | ||||
−0.0342439 | + | 0.999414i | \(0.510902\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 35.0507 | 1.63603 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.46410 | −0.161339 | −0.0806696 | − | 0.996741i | \(-0.525706\pi\) | ||||
−0.0806696 | + | 0.996741i | \(0.525706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.175865 | 0.00817316 | 0.00408658 | − | 0.999992i | \(-0.498699\pi\) | ||||
0.00408658 | + | 0.999992i | \(0.498699\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.53590 | −0.210347 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.8081 | 1.42563 | 0.712814 | − | 0.701353i | \(-0.247420\pi\) | ||||
0.712814 | + | 0.701353i | \(0.247420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.3205 | 0.984490 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.5617 | −1.31605 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | 0.275880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.44949 | −0.112390 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.53590 | −0.116111 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.6985 | −1.35696 | −0.678479 | − | 0.734620i | \(-0.737361\pi\) | ||||
−0.678479 | + | 0.734620i | \(0.737361\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.07180 | 0.0488697 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.757875 | 0.0344845 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.1962 | 0.553799 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.2934 | 1.78055 | 0.890276 | − | 0.455421i | \(-0.150511\pi\) | ||||
0.890276 | + | 0.455421i | \(0.150511\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.0000 | 0.452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.6622 | 0.842212 | 0.421106 | − | 0.907011i | \(-0.361642\pi\) | ||||
0.421106 | + | 0.907011i | \(0.361642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.19615 | 0.279061 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.41421 | 0.0635642 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.5359 | 0.472600 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −43.7391 | −1.95803 | −0.979015 | − | 0.203787i | \(-0.934675\pi\) | ||||
−0.979015 | + | 0.203787i | \(0.934675\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.5359 | 1.09618 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.96902 | 0.0877941 | 0.0438971 | − | 0.999036i | \(-0.486023\pi\) | ||||
0.0438971 | + | 0.999036i | \(0.486023\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.39230 | 0.106456 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.3533 | −0.681863 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.7846 | 0.743965 | 0.371982 | − | 0.928240i | \(-0.378678\pi\) | ||||
0.371982 | + | 0.928240i | \(0.378678\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.5911 | −0.512761 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.8564 | 0.611775 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.9043 | −0.788958 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.8564 | 0.697364 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.9096 | 1.35678 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.07180 | −0.0469563 | −0.0234781 | − | 0.999724i | \(-0.507474\pi\) | ||||
−0.0234781 | + | 0.999724i | \(0.507474\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.13681 | 0.0497093 | 0.0248547 | − | 0.999691i | \(-0.492088\pi\) | ||||
0.0248547 | + | 0.999691i | \(0.492088\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.00000 | 0.0872872 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.8733 | −0.865695 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8564 | −0.993757 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.76268 | −0.380268 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.85641 | 0.253669 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.2827 | 0.574262 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.7846 | −0.551697 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.07107 | −0.304572 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.143594 | −0.00617357 | −0.00308678 | − | 0.999995i | \(-0.500983\pi\) | ||||
−0.00308678 | + | 0.999995i | \(0.500983\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26.2137 | 1.12494 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.92820 | −0.296772 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.8386 | −1.01926 | −0.509632 | − | 0.860393i | \(-0.670218\pi\) | ||||
−0.509632 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.3923 | −0.528891 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.44949 | 0.104352 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.8564 | 0.504186 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.03528 | 0.0439450 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.2487 | 1.19694 | 0.598468 | − | 0.801147i | \(-0.295776\pi\) | ||||
0.598468 | + | 0.801147i | \(0.295776\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.21166 | −0.262725 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.3923 | −0.523204 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.3553 | −1.49005 | −0.745025 | − | 0.667037i | \(-0.767562\pi\) | ||||
−0.745025 | + | 0.667037i | \(0.767562\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.5885 | −0.866163 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.07107 | −0.296957 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.8564 | 0.748580 | 0.374290 | − | 0.927312i | \(-0.377887\pi\) | ||||
0.374290 | + | 0.927312i | \(0.377887\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.6274 | 0.946928 | 0.473464 | − | 0.880813i | \(-0.343003\pi\) | ||||
0.473464 | + | 0.880813i | \(0.343003\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.928203 | 0.0387762 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.378937 | 0.0158028 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.5167 | 1.72836 | 0.864181 | − | 0.503182i | \(-0.167837\pi\) | ||||
0.864181 | + | 0.503182i | \(0.167837\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.8744 | −1.24154 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.0000 | 0.580818 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.58630 | 0.148529 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.46410 | −0.0605332 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.34847 | −0.303304 | −0.151652 | − | 0.988434i | \(-0.548459\pi\) | ||||
−0.151652 | + | 0.988434i | \(0.548459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.85641 | −0.323718 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.2832 | 0.752072 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.1436 | 0.416547 | 0.208274 | − | 0.978071i | \(-0.433216\pi\) | ||||
0.208274 | + | 0.978071i | \(0.433216\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.76268 | 0.359235 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.6077 | −0.638780 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0416 | 0.982314 | 0.491157 | − | 0.871071i | \(-0.336574\pi\) | ||||
0.491157 | + | 0.871071i | \(0.336574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.9282 | −1.42475 | −0.712376 | − | 0.701798i | \(-0.752381\pi\) | ||||
−0.712376 | + | 0.701798i | \(0.752381\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.0759 | −0.613937 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.00000 | 0.365902 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.5269 | −1.32023 | −0.660113 | − | 0.751166i | \(-0.729492\pi\) | ||||
−0.660113 | + | 0.751166i | \(0.729492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.00000 | −0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.4158 | −0.664111 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.8564 | −0.478876 | −0.239438 | − | 0.970912i | \(-0.576963\pi\) | ||||
−0.239438 | + | 0.970912i | \(0.576963\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.65685 | 0.228106 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.1244 | −0.447850 | −0.223925 | − | 0.974606i | \(-0.571887\pi\) | ||||
−0.223925 | + | 0.974606i | \(0.571887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.2827 | 0.533878 | 0.266939 | − | 0.963713i | \(-0.413988\pi\) | ||||
0.266939 | + | 0.963713i | \(0.413988\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.14359 | −0.0860194 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.7675 | 0.671775 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.89898 | −0.195646 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.53590 | 0.180858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.7685 | 1.06564 | 0.532819 | − | 0.846229i | \(-0.321133\pi\) | ||||
0.532819 | + | 0.846229i | \(0.321133\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.8564 | 0.789221 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.1817 | 0.721519 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.32051 | 0.290049 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.45001 | −0.294718 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.92820 | −0.115657 | −0.0578285 | − | 0.998327i | \(-0.518418\pi\) | ||||
−0.0578285 | + | 0.998327i | \(0.518418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.8749 | 1.37533 | 0.687665 | − | 0.726028i | \(-0.258636\pi\) | ||||
0.687665 | + | 0.726028i | \(0.258636\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.62587 | −0.299804 | −0.149902 | − | 0.988701i | \(-0.547896\pi\) | ||||
−0.149902 | + | 0.988701i | \(0.547896\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.3923 | 0.486441 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.41473 | 0.251413 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.58846 | −0.336092 | −0.168046 | − | 0.985779i | \(-0.553746\pi\) | ||||
−0.168046 | + | 0.985779i | \(0.553746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.69161 | −0.0660969 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.19615 | 0.319762 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.66115 | −0.337390 | −0.168695 | − | 0.985668i | \(-0.553955\pi\) | ||||
−0.168695 | + | 0.985668i | \(0.553955\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.8564 | 0.850116 | 0.425058 | − | 0.905166i | \(-0.360254\pi\) | ||||
0.425058 | + | 0.905166i | \(0.360254\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.8295 | 0.498255 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.46410 | 0.134332 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.378937 | −0.0146725 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −41.3205 | −1.59754 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.5254 | 0.676559 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.8564 | 1.07379 | 0.536893 | − | 0.843650i | \(-0.319598\pi\) | ||||
0.536893 | + | 0.843650i | \(0.319598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.65685 | −0.217732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.94744 | −0.382311 | −0.191156 | − | 0.981560i | \(-0.561224\pi\) | ||||
−0.191156 | + | 0.981560i | \(0.561224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.2480 | −0.661916 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.2487 | −1.08249 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.6718 | 1.32668 | 0.663340 | − | 0.748318i | \(-0.269138\pi\) | ||||
0.663340 | + | 0.748318i | \(0.269138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.73205 | −0.180802 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.96953 | 0.265904 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.71281 | −0.141447 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.66063 | 0.139257 | 0.0696285 | − | 0.997573i | \(-0.477819\pi\) | ||||
0.0696285 | + | 0.997573i | \(0.477819\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.00000 | −0.0759737 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.4548 | −0.586234 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.7846 | 0.938784 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.6360 | −1.08311 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.92820 | 0.110597 | 0.0552984 | − | 0.998470i | \(-0.482389\pi\) | ||||
0.0552984 | + | 0.998470i | \(0.482389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.79315 | 0.0676300 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.8564 | −0.597187 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.38323 | −0.127239 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.0000 | 0.600893 | 0.300446 | − | 0.953799i | \(-0.402864\pi\) | ||||
0.300446 | + | 0.953799i | \(0.402864\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.38375 | −0.314415 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.21539 | 0.0455167 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.07055 | 0.0774343 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.6077 | −0.433497 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.8754 | −1.48710 | −0.743550 | − | 0.668680i | \(-0.766860\pi\) | ||||
−0.743550 | + | 0.668680i | \(0.766860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.3205 | 0.942985 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.45378 | 0.202828 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00000 | −0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.8091 | 1.51353 | 0.756763 | − | 0.653689i | \(-0.226780\pi\) | ||||
0.756763 | + | 0.653689i | \(0.226780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.2880 | −0.972299 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.4115 | 0.495367 | 0.247683 | − | 0.968841i | \(-0.420331\pi\) | ||||
0.247683 | + | 0.968841i | \(0.420331\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.07107 | 0.260820 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.3205 | 0.785351 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.6632 | −1.05439 | −0.527197 | − | 0.849743i | \(-0.676757\pi\) | ||||
−0.527197 | + | 0.849743i | \(0.676757\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.07180 | 0.186317 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.11012 | −0.224159 | −0.112079 | − | 0.993699i | \(-0.535751\pi\) | ||||
−0.112079 | + | 0.993699i | \(0.535751\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.5359 | −0.459280 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.89949 | −0.362204 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.7846 | −0.686375 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.48854 | −0.0543177 | −0.0271589 | − | 0.999631i | \(-0.508646\pi\) | ||||
−0.0271589 | + | 0.999631i | \(0.508646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.7846 | 0.830317 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.69213 | −0.243552 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.3397 | −0.521187 | −0.260593 | − | 0.965449i | \(-0.583918\pi\) | ||||
−0.260593 | + | 0.965449i | \(0.583918\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.757875 | 0.0275091 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.71281 | 0.207089 | 0.103545 | − | 0.994625i | \(-0.466982\pi\) | ||||
0.103545 | + | 0.994625i | \(0.466982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.79796 | 0.354710 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.19615 | −0.224022 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.8295 | −0.463245 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.46410 | −0.124919 | −0.0624593 | − | 0.998048i | \(-0.519894\pi\) | ||||
−0.0624593 | + | 0.998048i | \(0.519894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.14110 | −0.149138 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.9090 | −1.50736 | −0.753680 | − | 0.657241i | \(-0.771723\pi\) | ||||
−0.753680 | + | 0.657241i | \(0.771723\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.20736 | 0.115212 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.46410 | −0.0525244 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.79796 | 0.351048 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5359 | 0.377004 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.65685 | 0.202159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.1962 | 0.720832 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.5975 | −1.23327 | −0.616633 | − | 0.787251i | \(-0.711504\pi\) | ||||
−0.616633 | + | 0.787251i | \(0.711504\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.78461 | −0.241539 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.1165 | 1.03526 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.1436 | −0.644298 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.58630 | −0.127193 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.1244 | −1.38586 | −0.692928 | − | 0.721007i | \(-0.743680\pi\) | ||||
−0.692928 | + | 0.721007i | \(0.743680\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −69.4723 | −2.45775 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.8564 | −0.418926 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.5911 | −0.409041 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.535898 | −0.0188879 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.62536 | −0.0924169 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.9282 | 1.29833 | 0.649163 | − | 0.760649i | \(-0.275119\pi\) | ||||
0.649163 | + | 0.760649i | \(0.275119\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6990 | 1.21845 | 0.609223 | − | 0.792999i | \(-0.291481\pi\) | ||||
0.609223 | + | 0.792999i | \(0.291481\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.0718 | −0.809163 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.07107 | −0.247689 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.3923 | −0.363581 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.07055 | 0.0723510 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5359 | 0.437506 | 0.218753 | − | 0.975780i | \(-0.429801\pi\) | ||||
0.218753 | + | 0.975780i | \(0.429801\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.6269 | 0.614435 | 0.307218 | − | 0.951639i | \(-0.400602\pi\) | ||||
0.307218 | + | 0.951639i | \(0.400602\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | 0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.0817 | −1.15036 | −0.575182 | − | 0.818025i | \(-0.695069\pi\) | ||||
−0.575182 | + | 0.818025i | \(0.695069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.8564 | −0.620179 | −0.310089 | − | 0.950707i | \(-0.600359\pi\) | ||||
−0.310089 | + | 0.950707i | \(0.600359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.554803 | −0.0192459 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.9808 | 1.07342 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.3495 | −0.600404 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.1436 | −0.627134 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.69642 | 0.334758 | 0.167379 | − | 0.985893i | \(-0.446470\pi\) | ||||
0.167379 | + | 0.985893i | \(0.446470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.5959 | −0.674919 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.8564 | 0.373472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.7279 | −0.437337 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.3205 | 1.41812 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.277401 | −0.00950920 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.0525589 | 0.00179958 | 0.000899791 | − | 1.00000i | \(-0.499714\pi\) | ||||
0.000899791 | 1.00000i | \(0.499714\pi\) | ||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.44949 | −0.0837708 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.7846 | 1.52981 | 0.764907 | − | 0.644141i | \(-0.222785\pi\) | ||||
0.764907 | + | 0.644141i | \(0.222785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.61729 | −0.0551811 | −0.0275905 | − | 0.999619i | \(-0.508783\pi\) | ||||
−0.0275905 | + | 0.999619i | \(0.508783\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | −0.272639 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.9396 | 0.644711 | 0.322355 | − | 0.946619i | \(-0.395525\pi\) | ||||
0.322355 | + | 0.946619i | \(0.395525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.8564 | −0.743140 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.2533 | 1.02746 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.8564 | 0.402201 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.0726 | −0.747902 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.1962 | 0.412777 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.41421 | −0.0478091 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.0333 | −1.45313 | −0.726566 | − | 0.687097i | \(-0.758885\pi\) | ||||
−0.726566 | + | 0.687097i | \(0.758885\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.34795 | −0.0791945 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.53590 | 0.0854366 | 0.0427183 | − | 0.999087i | \(-0.486398\pi\) | ||||
0.0427183 | + | 0.999087i | \(0.486398\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.2533 | −1.01810 | −0.509052 | − | 0.860736i | \(-0.670004\pi\) | ||||
−0.509052 | + | 0.860736i | \(0.670004\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.3923 | −0.416563 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.2142 | −1.04807 | −0.524036 | − | 0.851696i | \(-0.675574\pi\) | ||||
−0.524036 | + | 0.851696i | \(0.675574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.7128 | −0.862380 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.07107 | −0.236890 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.4641 | −0.919051 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.04008 | 0.302177 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.784610 | −0.0261974 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.20736 | −0.106972 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.7128 | −0.523470 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.48528 | 0.282372 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.5359 | −0.616154 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.55532 | 0.184461 | 0.0922307 | − | 0.995738i | \(-0.470600\pi\) | ||||
0.0922307 | + | 0.995738i | \(0.470600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.39230 | 0.0793477 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.1779 | 0.668525 | 0.334262 | − | 0.942480i | \(-0.391513\pi\) | ||||
0.334262 | + | 0.942480i | \(0.391513\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.0000 | 0.463332 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.5254 | −0.579371 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.39230 | 0.0790009 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.8840 | 1.51357 | 0.756786 | − | 0.653662i | \(-0.226768\pi\) | ||||
0.756786 | + | 0.653662i | \(0.226768\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.00000 | −0.0659022 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9076 | −0.359027 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.732051 | −0.0240697 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.9043 | −0.588054 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.2487 | −0.533103 | −0.266551 | − | 0.963821i | \(-0.585884\pi\) | ||||
−0.266551 | + | 0.963821i | \(0.585884\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.2474 | 0.401394 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.4641 | −0.637226 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.76268 | 0.286570 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.7846 | −1.33238 | −0.666188 | − | 0.745784i | \(-0.732075\pi\) | ||||
−0.666188 | + | 0.745784i | \(0.732075\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.58630 | 0.117035 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.0000 | 0.325991 | 0.162995 | − | 0.986627i | \(-0.447884\pi\) | ||||
0.162995 | + | 0.986627i | \(0.447884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.51575 | −0.0493596 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.00000 | 0.260240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.55532 | 0.180524 | 0.0902618 | − | 0.995918i | \(-0.471230\pi\) | ||||
0.0902618 | + | 0.995918i | \(0.471230\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | 0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.0860 | −1.17017 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.6410 | −0.539055 | −0.269528 | − | 0.962993i | \(-0.586868\pi\) | ||||
−0.269528 | + | 0.962993i | \(0.586868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.656339 | −0.0212386 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.00000 | −0.0646508 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.69213 | 0.216100 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7128 | −0.668155 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.2827 | 0.428030 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.1244 | 0.680017 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.4543 | −0.336188 | −0.168094 | − | 0.985771i | \(-0.553761\pi\) | ||||
−0.168094 | + | 0.985771i | \(0.553761\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.4641 | 0.689526 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.3601 | 1.39149 | 0.695747 | − | 0.718287i | \(-0.255074\pi\) | ||||
0.695747 | + | 0.718287i | \(0.255074\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.8564 | 0.700684 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.07055 | −0.0663107 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.7128 | −0.502697 | −0.251349 | − | 0.967897i | \(-0.580874\pi\) | ||||
−0.251349 | + | 0.967897i | \(0.580874\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.7675 | 0.535891 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.92820 | −0.221201 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.62587 | −0.243227 | −0.121614 | − | 0.992578i | \(-0.538807\pi\) | ||||
−0.121614 | + | 0.992578i | \(0.538807\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.9282 | −0.411927 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.4243 | 0.713775 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.60770 | 0.0511217 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.4997 | 1.03239 | 0.516194 | − | 0.856472i | \(-0.327349\pi\) | ||||
0.516194 | + | 0.856472i | \(0.327349\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.2487 | −1.02338 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.0363 | 0.349874 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.6603 | −0.812668 | −0.406334 | − | 0.913725i | \(-0.633193\pi\) | ||||
−0.406334 | + | 0.913725i | \(0.633193\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.14110 | 0.131019 |
(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 | 9280.2.a.cb.1.3 | 4 | ||
4.3 | odd | 2 | inner | 9280.2.a.cb.1.1 | 4 | ||
8.3 | odd | 2 | 4640.2.a.p.1.4 | yes | 4 | ||
8.5 | even | 2 | 4640.2.a.p.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4640.2.a.p.1.2 | ✓ | 4 | 8.5 | even | 2 | ||
4640.2.a.p.1.4 | yes | 4 | 8.3 | odd | 2 | ||
9280.2.a.cb.1.1 | 4 | 4.3 | odd | 2 | inner | ||
9280.2.a.cb.1.3 | 4 | 1.1 | even | 1 | trivial |