Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(1,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.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: | \(36.4117833217\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 285) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | −0.534522 | −0.267261 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267261 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.24264 | −1.88223 | −0.941113 | − | 0.338091i | \(-0.890219\pi\) | ||||
−0.941113 | + | 0.338091i | \(0.890219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.585786 | −0.162468 | −0.0812340 | − | 0.996695i | \(-0.525886\pi\) | ||||
−0.0812340 | + | 0.996695i | \(0.525886\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.82843 | 1.65614 | 0.828068 | − | 0.560627i | \(-0.189440\pi\) | ||||
0.828068 | + | 0.560627i | \(0.189440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41421 | 0.308607 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.65685 | 0.762507 | 0.381253 | − | 0.924471i | \(-0.375493\pi\) | ||||
0.381253 | + | 0.924471i | \(0.375493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.41421 | −0.262613 | −0.131306 | − | 0.991342i | \(-0.541917\pi\) | ||||
−0.131306 | + | 0.991342i | \(0.541917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.82843 | 1.58563 | 0.792816 | − | 0.609461i | \(-0.208614\pi\) | ||||
0.792816 | + | 0.609461i | \(0.208614\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.24264 | 1.08670 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41421 | 0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.585786 | −0.0963027 | −0.0481513 | − | 0.998840i | \(-0.515333\pi\) | ||||
−0.0481513 | + | 0.998840i | \(0.515333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.585786 | 0.0938009 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.24264 | 1.28728 | 0.643642 | − | 0.765327i | \(-0.277423\pi\) | ||||
0.643642 | + | 0.765327i | \(0.277423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.75736 | −0.572992 | −0.286496 | − | 0.958081i | \(-0.592491\pi\) | ||||
−0.286496 | + | 0.958081i | \(0.592491\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.65685 | −0.533407 | −0.266704 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266704 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.82843 | −0.956171 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.00000 | 1.09888 | 0.549442 | − | 0.835532i | \(-0.314840\pi\) | ||||
0.549442 | + | 0.835532i | \(0.314840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.24264 | 0.841757 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.48528 | 0.583934 | 0.291967 | − | 0.956428i | \(-0.405690\pi\) | ||||
0.291967 | + | 0.956428i | \(0.405690\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.3137 | −1.96072 | −0.980360 | − | 0.197218i | \(-0.936809\pi\) | ||||
−0.980360 | + | 0.197218i | \(0.936809\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.41421 | −0.178174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.585786 | 0.0726579 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.65685 | −0.202417 | −0.101208 | − | 0.994865i | \(-0.532271\pi\) | ||||
−0.101208 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.65685 | −0.440234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.17157 | 0.613753 | 0.306876 | − | 0.951749i | \(-0.400716\pi\) | ||||
0.306876 | + | 0.951749i | \(0.400716\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.65685 | 0.428002 | 0.214001 | − | 0.976833i | \(-0.431350\pi\) | ||||
0.214001 | + | 0.976833i | \(0.431350\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.82843 | 1.00609 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.17157 | −0.787182 | −0.393591 | − | 0.919286i | \(-0.628767\pi\) | ||||
−0.393591 | + | 0.919286i | \(0.628767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.82843 | −0.740647 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.41421 | 0.151620 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8995 | −1.47334 | −0.736672 | − | 0.676250i | \(-0.763604\pi\) | ||||
−0.736672 | + | 0.676250i | \(0.763604\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.828427 | 0.0868428 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.82843 | −0.915465 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.2426 | −1.85226 | −0.926130 | − | 0.377205i | \(-0.876885\pi\) | ||||
−0.926130 | + | 0.377205i | \(0.876885\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.24264 | −0.627409 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.82843 | −0.878461 | −0.439231 | − | 0.898374i | \(-0.644749\pi\) | ||||
−0.439231 | + | 0.898374i | \(0.644749\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.3137 | −1.50890 | −0.754452 | − | 0.656355i | \(-0.772097\pi\) | ||||
−0.754452 | + | 0.656355i | \(0.772097\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.41421 | −0.138013 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.31371 | 0.320348 | 0.160174 | − | 0.987089i | \(-0.448794\pi\) | ||||
0.160174 | + | 0.987089i | \(0.448794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4853 | 1.00431 | 0.502154 | − | 0.864778i | \(-0.332541\pi\) | ||||
0.502154 | + | 0.864778i | \(0.332541\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.585786 | 0.0556004 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.1421 | −1.70667 | −0.853334 | − | 0.521364i | \(-0.825423\pi\) | ||||
−0.853334 | + | 0.521364i | \(0.825423\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.65685 | −0.341003 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.585786 | −0.0541560 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.65685 | −0.885242 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.9706 | 2.54278 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.24264 | −0.743214 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.31371 | 0.294044 | 0.147022 | − | 0.989133i | \(-0.453031\pi\) | ||||
0.147022 | + | 0.989133i | \(0.453031\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.75736 | 0.330817 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4142 | 0.997264 | 0.498632 | − | 0.866814i | \(-0.333836\pi\) | ||||
0.498632 | + | 0.866814i | \(0.333836\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.41421 | −0.122628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000 | 0.854358 | 0.427179 | − | 0.904167i | \(-0.359507\pi\) | ||||
0.427179 | + | 0.904167i | \(0.359507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.1421 | −1.19952 | −0.599760 | − | 0.800180i | \(-0.704737\pi\) | ||||
−0.599760 | + | 0.800180i | \(0.704737\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.65685 | 0.307963 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.65685 | 0.305802 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.41421 | 0.117444 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00000 | 0.412393 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4853 | −0.853280 | −0.426640 | − | 0.904422i | \(-0.640303\pi\) | ||||
−0.426640 | + | 0.904422i | \(0.640303\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.82843 | 0.552046 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.82843 | −0.709116 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.48528 | −0.517582 | −0.258791 | − | 0.965933i | \(-0.583324\pi\) | ||||
−0.258791 | + | 0.965933i | \(0.583324\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.00000 | −0.634441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.17157 | −0.407577 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.10051 | −0.164524 | −0.0822621 | − | 0.996611i | \(-0.526214\pi\) | ||||
−0.0822621 | + | 0.996611i | \(0.526214\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.24264 | −0.485989 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.31371 | −0.411187 | −0.205594 | − | 0.978637i | \(-0.565912\pi\) | ||||
−0.205594 | + | 0.978637i | \(0.565912\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6569 | −0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.7990 | 1.50529 | 0.752645 | − | 0.658427i | \(-0.228778\pi\) | ||||
0.752645 | + | 0.658427i | \(0.228778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.41421 | −0.106904 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.48528 | −0.337134 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.485281 | 0.0362716 | 0.0181358 | − | 0.999836i | \(-0.494227\pi\) | ||||
0.0181358 | + | 0.999836i | \(0.494227\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.1716 | −1.12769 | −0.563847 | − | 0.825879i | \(-0.690679\pi\) | ||||
−0.563847 | + | 0.825879i | \(0.690679\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.3137 | 1.13202 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.585786 | 0.0430679 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −42.6274 | −3.11723 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.41421 | 0.102869 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.75736 | −0.127158 | −0.0635790 | − | 0.997977i | \(-0.520251\pi\) | ||||
−0.0635790 | + | 0.997977i | \(0.520251\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.07107 | −0.652950 | −0.326475 | − | 0.945206i | \(-0.605861\pi\) | ||||
−0.326475 | + | 0.945206i | \(0.605861\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.585786 | −0.0419490 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.17157 | 0.0834711 | 0.0417356 | − | 0.999129i | \(-0.486711\pi\) | ||||
0.0417356 | + | 0.999129i | \(0.486711\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1421 | 0.718957 | 0.359478 | − | 0.933153i | \(-0.382955\pi\) | ||||
0.359478 | + | 0.933153i | \(0.382955\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.65685 | 0.116865 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.00000 | 0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.24264 | −0.575691 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.65685 | 0.254169 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.24264 | −0.431812 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3137 | 1.05424 | 0.527120 | − | 0.849791i | \(-0.323272\pi\) | ||||
0.527120 | + | 0.849791i | \(0.323272\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.17157 | −0.354350 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.75736 | 0.256250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.4853 | −0.847556 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.65685 | −0.247107 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.6274 | 1.78310 | 0.891552 | − | 0.452919i | \(-0.149617\pi\) | ||||
0.891552 | + | 0.452919i | \(0.149617\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.9706 | 1.25912 | 0.629560 | − | 0.776952i | \(-0.283235\pi\) | ||||
0.629560 | + | 0.776952i | \(0.283235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.6274 | 1.49526 | 0.747631 | − | 0.664114i | \(-0.231191\pi\) | ||||
0.747631 | + | 0.664114i | \(0.231191\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.82843 | −0.580868 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.6569 | −0.763666 | −0.381833 | − | 0.924231i | \(-0.624707\pi\) | ||||
−0.381833 | + | 0.924231i | \(0.624707\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.65685 | 0.238547 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.27208 | 0.0822839 | 0.0411419 | − | 0.999153i | \(-0.486900\pi\) | ||||
0.0411419 | + | 0.999153i | \(0.486900\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.34315 | −0.537429 | −0.268715 | − | 0.963220i | \(-0.586599\pi\) | ||||
−0.268715 | + | 0.963220i | \(0.586599\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.00000 | 0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.585786 | −0.0372727 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.17157 | 0.454480 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.2426 | 0.646510 | 0.323255 | − | 0.946312i | \(-0.395223\pi\) | ||||
0.323255 | + | 0.946312i | \(0.395223\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.8284 | −1.43521 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.82843 | 0.427613 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.4853 | 0.778810 | 0.389405 | − | 0.921067i | \(-0.372681\pi\) | ||||
0.389405 | + | 0.921067i | \(0.372681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.828427 | 0.0514760 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.41421 | −0.0875376 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.4558 | −1.69300 | −0.846500 | − | 0.532389i | \(-0.821294\pi\) | ||||
−0.846500 | + | 0.532389i | \(0.821294\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00000 | −0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.8995 | 0.850635 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.0711 | 0.675015 | 0.337507 | − | 0.941323i | \(-0.390416\pi\) | ||||
0.337507 | + | 0.941323i | \(0.390416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.17157 | 0.314151 | 0.157075 | − | 0.987587i | \(-0.449793\pi\) | ||||
0.157075 | + | 0.987587i | \(0.449793\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.828427 | −0.0501387 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.24264 | −0.376445 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.82843 | 0.528544 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.4142 | −1.03884 | −0.519422 | − | 0.854518i | \(-0.673853\pi\) | ||||
−0.519422 | + | 0.854518i | \(0.673853\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.3848 | −1.56841 | −0.784206 | − | 0.620500i | \(-0.786929\pi\) | ||||
−0.784206 | + | 0.620500i | \(0.786929\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.6569 | −0.688082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.6274 | 1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.2426 | 1.06940 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.4853 | −1.66413 | −0.832064 | − | 0.554680i | \(-0.812841\pi\) | ||||
−0.832064 | + | 0.554680i | \(0.812841\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.48528 | −0.261143 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.24264 | 0.362235 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.14214 | −0.123883 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.31371 | 0.306277 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.82843 | 0.507180 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.3137 | 0.876860 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.8284 | −1.53118 | −0.765590 | − | 0.643329i | \(-0.777553\pi\) | ||||
−0.765590 | + | 0.643329i | \(0.777553\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.3137 | 0.871166 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.24264 | −0.127168 | −0.0635842 | − | 0.997976i | \(-0.520253\pi\) | ||||
−0.0635842 | + | 0.997976i | \(0.520253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.7990 | −1.91043 | −0.955216 | − | 0.295910i | \(-0.904377\pi\) | ||||
−0.955216 | + | 0.295910i | \(0.904377\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.41421 | 0.0796819 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.6274 | 1.04622 | 0.523110 | − | 0.852265i | \(-0.324772\pi\) | ||||
0.523110 | + | 0.852265i | \(0.324772\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.82843 | 0.494297 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.31371 | −0.184953 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.82843 | 0.379944 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.585786 | −0.0324936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.4853 | −0.579837 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.17157 | 0.285118 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.142136 | 0.00781248 | 0.00390624 | − | 0.999992i | \(-0.498757\pi\) | ||||
0.00390624 | + | 0.999992i | \(0.498757\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.585786 | −0.0321009 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.65685 | 0.0905236 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.4142 | −1.49335 | −0.746674 | − | 0.665191i | \(-0.768350\pi\) | ||||
−0.746674 | + | 0.665191i | \(0.768350\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.1421 | 0.985346 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −55.1127 | −2.98452 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.65685 | 0.196878 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.4558 | −1.25918 | −0.629588 | − | 0.776929i | \(-0.716776\pi\) | ||||
−0.629588 | + | 0.776929i | \(0.716776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0000 | 0.963518 | 0.481759 | − | 0.876304i | \(-0.339998\pi\) | ||||
0.481759 | + | 0.876304i | \(0.339998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.585786 | 0.0312670 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.65685 | −0.407533 | −0.203767 | − | 0.979019i | \(-0.565318\pi\) | ||||
−0.203767 | + | 0.979019i | \(0.565318\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.17157 | −0.274479 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.65685 | 0.511095 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.8701 | 1.52370 | 0.761852 | − | 0.647752i | \(-0.224290\pi\) | ||||
0.761852 | + | 0.647752i | \(0.224290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −27.9706 | −1.46807 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.65685 | −0.191408 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.3848 | −1.16848 | −0.584238 | − | 0.811582i | \(-0.698606\pi\) | ||||
−0.584238 | + | 0.811582i | \(0.698606\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.24264 | 0.429095 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3137 | −0.587378 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.41421 | 0.176781 | 0.0883906 | − | 0.996086i | \(-0.471828\pi\) | ||||
0.0883906 | + | 0.996086i | \(0.471828\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.828427 | 0.0426662 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.82843 | −0.453486 | −0.226743 | − | 0.973955i | \(-0.572808\pi\) | ||||
−0.226743 | + | 0.973955i | \(0.572808\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.31371 | −0.169766 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.0000 | −1.43073 | −0.715367 | − | 0.698749i | \(-0.753740\pi\) | ||||
−0.715367 | + | 0.698749i | \(0.753740\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.82843 | −0.449938 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.75736 | −0.190997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.97056 | −0.150614 | −0.0753068 | − | 0.997160i | \(-0.523994\pi\) | ||||
−0.0753068 | + | 0.997160i | \(0.523994\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9706 | 1.26282 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.4142 | −0.575771 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.6274 | −0.834506 | −0.417253 | − | 0.908790i | \(-0.637007\pi\) | ||||
−0.417253 | + | 0.908790i | \(0.637007\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.41421 | 0.0707992 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.2426 | −0.811119 | −0.405559 | − | 0.914069i | \(-0.632923\pi\) | ||||
−0.405559 | + | 0.914069i | \(0.632923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.17157 | −0.257614 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.65685 | 0.181264 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.17157 | −0.354611 | −0.177306 | − | 0.984156i | \(-0.556738\pi\) | ||||
−0.177306 | + | 0.984156i | \(0.556738\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.0000 | −0.493264 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.34315 | −0.312126 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.17157 | 0.352039 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.1421 | 0.692543 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.585786 | −0.0286175 | −0.0143088 | − | 0.999898i | \(-0.504555\pi\) | ||||
−0.0143088 | + | 0.999898i | \(0.504555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.3137 | −0.648870 | −0.324435 | − | 0.945908i | \(-0.605174\pi\) | ||||
−0.324435 | + | 0.945908i | \(0.605174\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.65685 | −0.177802 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.82843 | 0.331227 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.6569 | 1.04805 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.65685 | −0.176555 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.1127 | −1.49865 | −0.749323 | − | 0.662205i | \(-0.769621\pi\) | ||||
−0.749323 | + | 0.662205i | \(0.769621\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0711 | −1.20484 | −0.602419 | − | 0.798180i | \(-0.705796\pi\) | ||||
−0.602419 | + | 0.798180i | \(0.705796\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41421 | −0.0678064 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.65685 | 0.174931 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.3431 | 0.493651 | 0.246826 | − | 0.969060i | \(-0.420612\pi\) | ||||
0.246826 | + | 0.969060i | \(0.420612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.0000 | −0.855206 | −0.427603 | − | 0.903967i | \(-0.640642\pi\) | ||||
−0.427603 | + | 0.903967i | \(0.640642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.8995 | 0.658899 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.8701 | 1.26808 | 0.634038 | − | 0.773302i | \(-0.281396\pi\) | ||||
0.634038 | + | 0.773302i | \(0.281396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −51.4558 | −2.42296 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.4853 | 0.492641 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.828427 | −0.0388373 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.1716 | 1.27103 | 0.635516 | − | 0.772087i | \(-0.280787\pi\) | ||||
0.635516 | + | 0.772087i | \(0.280787\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.82843 | −0.318724 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.34315 | 0.388579 | 0.194290 | − | 0.980944i | \(-0.437760\pi\) | ||||
0.194290 | + | 0.980944i | \(0.437760\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7574 | −0.732307 | −0.366153 | − | 0.930555i | \(-0.619325\pi\) | ||||
−0.366153 | + | 0.930555i | \(0.619325\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.82843 | 0.409409 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.3431 | −1.12647 | −0.563233 | − | 0.826298i | \(-0.690443\pi\) | ||||
−0.563233 | + | 0.826298i | \(0.690443\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.34315 | 0.108196 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.48528 | 0.298826 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.4558 | 1.07850 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.00000 | 0.366295 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.92893 | −0.133826 | −0.0669132 | − | 0.997759i | \(-0.521315\pi\) | ||||
−0.0669132 | + | 0.997759i | \(0.521315\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.343146 | 0.0156461 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.17157 | 0.235315 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.2426 | 0.828356 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.51472 | −0.159267 | −0.0796336 | − | 0.996824i | \(-0.525375\pi\) | ||||
−0.0796336 | + | 0.996824i | \(0.525375\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.10051 | 0.0949881 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2426 | 0.462244 | 0.231122 | − | 0.972925i | \(-0.425760\pi\) | ||||
0.231122 | + | 0.972925i | \(0.425760\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.65685 | −0.434923 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.24264 | 0.280586 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.31371 | −0.328065 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8284 | 0.484747 | 0.242373 | − | 0.970183i | \(-0.422074\pi\) | ||||
0.242373 | + | 0.970183i | \(0.422074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.31371 | 0.237399 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.828427 | 0.0369377 | 0.0184689 | − | 0.999829i | \(-0.494121\pi\) | ||||
0.0184689 | + | 0.999829i | \(0.494121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.82843 | 0.392860 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.6569 | 0.562111 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.7279 | 1.09605 | 0.548023 | − | 0.836463i | \(-0.315381\pi\) | ||||
0.548023 | + | 0.836463i | \(0.315381\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.17157 | −0.228777 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.3137 | 0.674803 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.8284 | 1.00399 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.7990 | −0.869079 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.2426 | 0.711603 | 0.355802 | − | 0.934562i | \(-0.384208\pi\) | ||||
0.355802 | + | 0.934562i | \(0.384208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.4853 | 1.42048 | 0.710241 | − | 0.703959i | \(-0.248586\pi\) | ||||
0.710241 | + | 0.703959i | \(0.248586\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.41421 | 0.0617213 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 60.2843 | 2.62602 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.62742 | −0.418583 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.48528 | 0.194645 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.82843 | −0.209142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.31371 | −0.143264 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.485281 | −0.0209414 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.2132 | 1.34445 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.1716 | 0.651075 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.4853 | −0.449140 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.51472 | −0.321306 | −0.160653 | − | 0.987011i | \(-0.551360\pi\) | ||||
−0.160653 | + | 0.987011i | \(0.551360\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.3137 | −0.653573 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.41421 | −0.0602475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.585786 | −0.0248652 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.68629 | −0.113822 | −0.0569109 | − | 0.998379i | \(-0.518125\pi\) | ||||
−0.0569109 | + | 0.998379i | \(0.518125\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.20101 | 0.0930928 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 42.6274 | 1.79973 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.2843 | −1.10775 | −0.553875 | − | 0.832600i | \(-0.686851\pi\) | ||||
−0.553875 | + | 0.832600i | \(0.686851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.1421 | 0.763245 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.41421 | −0.0593914 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.9289 | 0.709698 | 0.354849 | − | 0.934924i | \(-0.384532\pi\) | ||||
0.354849 | + | 0.934924i | \(0.384532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8284 | −0.620550 | −0.310275 | − | 0.950647i | \(-0.600421\pi\) | ||||
−0.310275 | + | 0.950647i | \(0.600421\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.75736 | 0.0734147 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.65685 | 0.152501 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.4558 | −1.30952 | −0.654762 | − | 0.755835i | \(-0.727231\pi\) | ||||
−0.654762 | + | 0.755835i | \(0.727231\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.07107 | 0.376981 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.1421 | 0.420767 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.9411 | −2.06835 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.585786 | 0.0242193 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.6569 | 0.976423 | 0.488211 | − | 0.872725i | \(-0.337649\pi\) | ||||
0.488211 | + | 0.872725i | \(0.337649\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.82843 | 0.363769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.17157 | −0.0481921 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.62742 | −0.354286 | −0.177143 | − | 0.984185i | \(-0.556685\pi\) | ||||
−0.177143 | + | 0.984185i | \(0.556685\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.65685 | 0.395892 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.1421 | −0.415090 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.9706 | 1.51058 | 0.755288 | − | 0.655393i | \(-0.227497\pi\) | ||||
0.755288 | + | 0.655393i | \(0.227497\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.1421 | −0.821615 | −0.410807 | − | 0.911722i | \(-0.634753\pi\) | ||||
−0.410807 | + | 0.911722i | \(0.634753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.65685 | −0.0674723 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.9706 | −1.13717 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.485281 | 0.0196970 | 0.00984848 | − | 0.999952i | \(-0.496865\pi\) | ||||
0.00984848 | + | 0.999952i | \(0.496865\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.00000 | −0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.14214 | 0.0866615 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.48528 | 0.261938 | 0.130969 | − | 0.991386i | \(-0.458191\pi\) | ||||
0.130969 | + | 0.991386i | \(0.458191\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.24264 | 0.332375 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.5147 | 0.463565 | 0.231783 | − | 0.972768i | \(-0.425544\pi\) | ||||
0.231783 | + | 0.972768i | \(0.425544\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.51472 | 0.141268 | 0.0706342 | − | 0.997502i | \(-0.477498\pi\) | ||||
0.0706342 | + | 0.997502i | \(0.477498\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.65685 | −0.146745 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.6569 | 0.787535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.24264 | 0.249307 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.3137 | −0.608665 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.31371 | −0.131501 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.92893 | 0.116049 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.17157 | 0.204584 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.3553 | 1.55444 | 0.777221 | − | 0.629227i | \(-0.216629\pi\) | ||||
0.777221 | + | 0.629227i | \(0.216629\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.61522 | −0.221443 | −0.110721 | − | 0.993851i | \(-0.535316\pi\) | ||||
−0.110721 | + | 0.993851i | \(0.535316\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.75736 | −0.147946 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.85786 | 0.308925 | 0.154462 | − | 0.987999i | \(-0.450635\pi\) | ||||
0.154462 | + | 0.987999i | \(0.450635\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.0000 | −1.09910 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.4853 | 0.489337 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.1716 | 1.45464 | 0.727318 | − | 0.686301i | \(-0.240767\pi\) | ||||
0.727318 | + | 0.686301i | \(0.240767\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.4142 | −0.445990 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.65685 | 0.142667 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.6274 | −1.03726 | −0.518628 | − | 0.855000i | \(-0.673557\pi\) | ||||
−0.518628 | + | 0.855000i | \(0.673557\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.4558 | −1.69024 | −0.845118 | − | 0.534579i | \(-0.820470\pi\) | ||||
−0.845118 | + | 0.534579i | \(0.820470\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.00000 | 0.155347 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.41421 | 0.0548408 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.17157 | −0.200244 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.6274 | −1.02948 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 95.5980 | 3.69052 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.1838 | 1.24059 | 0.620297 | − | 0.784367i | \(-0.287012\pi\) | ||||
0.620297 | + | 0.784367i | \(0.287012\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.9706 | −0.652232 | −0.326116 | − | 0.945330i | \(-0.605740\pi\) | ||||
−0.326116 | + | 0.945330i | \(0.605740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.7990 | 0.990074 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.9706 | −0.726954 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.6569 | −1.13479 | −0.567394 | − | 0.823446i | \(-0.692048\pi\) | ||||
−0.567394 | + | 0.823446i | \(0.692048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.0000 | −0.382080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.6274 | −0.863290 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.68629 | −0.178533 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.1716 | −1.56624 | −0.783120 | − | 0.621870i | \(-0.786373\pi\) | ||||
−0.783120 | + | 0.621870i | \(0.786373\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.82843 | 0.335364 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.1421 | 0.536442 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56.2843 | 2.13192 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.6569 | 0.440903 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.3137 | 1.10716 | 0.553582 | − | 0.832795i | \(-0.313261\pi\) | ||||
0.553582 | + | 0.832795i | \(0.313261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.585786 | −0.0220934 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.65685 | −0.137725 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.4853 | 0.469557 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.97056 | −0.186673 | −0.0933367 | − | 0.995635i | \(-0.529753\pi\) | ||||
−0.0933367 | + | 0.995635i | \(0.529753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.2843 | 1.20906 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.65685 | −0.136759 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.27208 | −0.0475066 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.0711 | −0.487469 | −0.243734 | − | 0.969842i | \(-0.578372\pi\) | ||||
−0.243734 | + | 0.969842i | \(0.578372\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.6569 | 0.806543 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.34315 | 0.310285 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.41421 | −0.0525226 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.3553 | 0.866202 | 0.433101 | − | 0.901345i | \(-0.357419\pi\) | ||||
0.433101 | + | 0.901345i | \(0.357419\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.6569 | −0.948953 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.00000 | −0.184428 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.3431 | 0.380995 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.6569 | −0.943803 | −0.471901 | − | 0.881651i | \(-0.656432\pi\) | ||||
−0.471901 | + | 0.881651i | \(0.656432\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.585786 | 0.0215194 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.00000 | 0.146746 | 0.0733729 | − | 0.997305i | \(-0.476624\pi\) | ||||
0.0733729 | + | 0.997305i | \(0.476624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.17157 | −0.262394 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.68629 | −0.171233 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.14214 | −0.151149 | −0.0755743 | − | 0.997140i | \(-0.524079\pi\) | ||||
−0.0755743 | + | 0.997140i | \(0.524079\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.2426 | −0.373263 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.4853 | 0.381598 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.4264 | 1.90547 | 0.952735 | − | 0.303802i | \(-0.0982562\pi\) | ||||
0.952735 | + | 0.303802i | \(0.0982562\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.8284 | 0.828619 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.9411 | −0.867865 | −0.433933 | − | 0.900945i | \(-0.642874\pi\) | ||||
−0.433933 | + | 0.900945i | \(0.642874\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.8284 | −0.536825 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.82843 | −0.246882 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.62742 | −0.0948705 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.02944 | 0.325610 | 0.162805 | − | 0.986658i | \(-0.447946\pi\) | ||||
0.162805 | + | 0.986658i | \(0.447946\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.4853 | −0.449646 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.3431 | −0.515887 | −0.257944 | − | 0.966160i | \(-0.583045\pi\) | ||||
−0.257944 | + | 0.966160i | \(0.583045\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.82843 | 0.317126 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.828427 | −0.0297197 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.24264 | 0.295323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.2843 | −1.15522 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.41421 | 0.0505399 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.48528 | 0.231470 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.1716 | 1.32502 | 0.662512 | − | 0.749052i | \(-0.269490\pi\) | ||||
0.662512 | + | 0.749052i | \(0.269490\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.4558 | 0.977454 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.6569 | 0.912253 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.97056 | 0.318554 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.00000 | 0.283731 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.1421 | 0.500940 | 0.250470 | − | 0.968124i | \(-0.419415\pi\) | ||||
0.250470 | + | 0.968124i | \(0.419415\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.9706 | −0.883395 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.8995 | −0.491115 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.8284 | −0.805598 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.17157 | 0.182274 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.0711 | −0.389720 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.00000 | −0.0703163 | −0.0351581 | − | 0.999382i | \(-0.511193\pi\) | ||||
−0.0351581 | + | 0.999382i | \(0.511193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.3137 | −1.09957 | −0.549787 | − | 0.835305i | \(-0.685291\pi\) | ||||
−0.549787 | + | 0.835305i | \(0.685291\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.17157 | −0.181375 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.10051 | 0.0735775 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.75736 | −0.131453 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.828427 | 0.0289476 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.48528 | −0.0867369 | −0.0433685 | − | 0.999059i | \(-0.513809\pi\) | ||||
−0.0433685 | + | 0.999059i | \(0.513809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −57.0122 | −1.98732 | −0.993660 | − | 0.112426i | \(-0.964138\pi\) | ||||
−0.993660 | + | 0.112426i | \(0.964138\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.24264 | 0.217341 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.3137 | 0.880244 | 0.440122 | − | 0.897938i | \(-0.354935\pi\) | ||||
0.440122 | + | 0.897938i | \(0.354935\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.5147 | 1.02509 | 0.512544 | − | 0.858661i | \(-0.328703\pi\) | ||||
0.512544 | + | 0.858661i | \(0.328703\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.0000 | 0.763172 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.1421 | −1.18295 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.31371 | 0.183888 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.82843 | −0.305155 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.1421 | 1.31681 | 0.658406 | − | 0.752663i | \(-0.271231\pi\) | ||||
0.658406 | + | 0.752663i | \(0.271231\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0000 | −0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.4142 | 0.599777 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6569 | 0.435409 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.5563 | −1.35917 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.3848 | 0.905523 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.14214 | −0.0734315 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.1716 | −0.382507 | −0.191254 | − | 0.981541i | \(-0.561255\pi\) | ||||
−0.191254 | + | 0.981541i | \(0.561255\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.3137 | 1.20629 | 0.603147 | − | 0.797630i | \(-0.293913\pi\) | ||||
0.603147 | + | 0.797630i | \(0.293913\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.9411 | −0.612143 | −0.306072 | − | 0.952008i | \(-0.599015\pi\) | ||||
−0.306072 | + | 0.952008i | \(0.599015\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.6569 | 0.397265 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.3137 | −1.06593 | −0.532966 | − | 0.846137i | \(-0.678922\pi\) | ||||
−0.532966 | + | 0.846137i | \(0.678922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.7990 | −0.673186 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.6274 | −1.00620 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.970563 | 0.0328863 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.2426 | −0.617420 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.41421 | 0.0478091 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.0711 | −1.65701 | −0.828506 | − | 0.559980i | \(-0.810809\pi\) | ||||
−0.828506 | + | 0.559980i | \(0.810809\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.4853 | 0.960785 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.7990 | 1.13872 | 0.569358 | − | 0.822089i | \(-0.307192\pi\) | ||||
0.569358 | + | 0.822089i | \(0.307192\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.0416 | −1.21290 | −0.606449 | − | 0.795123i | \(-0.707406\pi\) | ||||
−0.606449 | + | 0.795123i | \(0.707406\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.48528 | 0.150771 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.9411 | 1.40825 | 0.704123 | − | 0.710078i | \(-0.251341\pi\) | ||||
0.704123 | + | 0.710078i | \(0.251341\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.68629 | −0.157173 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.24264 | −0.209136 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.65685 | −0.122372 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.485281 | −0.0162212 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.14214 | 0.0715238 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.4853 | −0.416407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.6274 | 1.81990 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.31371 | −0.176829 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.1716 | 0.504320 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.1421 | −0.336764 | −0.168382 | − | 0.985722i | \(-0.553854\pi\) | ||||
−0.168382 | + | 0.985722i | \(0.553854\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.82843 | −0.292820 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.3137 | −1.03747 | −0.518735 | − | 0.854935i | \(-0.673597\pi\) | ||||
−0.518735 | + | 0.854935i | \(0.673597\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.7696 | 1.48166 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.3137 | −0.506256 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.1421 | −0.533060 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.0000 | 0.395843 | 0.197922 | − | 0.980218i | \(-0.436581\pi\) | ||||
0.197922 | + | 0.980218i | \(0.436581\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.8284 | 0.884027 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.02944 | −0.0997151 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.585786 | −0.0192605 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.3137 | −0.502968 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.1127 | −0.955157 | −0.477578 | − | 0.878589i | \(-0.658485\pi\) | ||||
−0.477578 | + | 0.878589i | \(0.658485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.00000 | −0.163868 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.24264 | 0.0734208 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.6274 | 1.39407 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.79899 | 0.320119 | 0.160060 | − | 0.987107i | \(-0.448831\pi\) | ||||
0.160060 | + | 0.987107i | \(0.448831\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.7990 | 1.10299 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.8701 | −1.00634 | −0.503168 | − | 0.864189i | \(-0.667832\pi\) | ||||
−0.503168 | + | 0.864189i | \(0.667832\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.1421 | 0.981563 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.41421 | −0.0460044 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.8284 | 1.71669 | 0.858347 | − | 0.513070i | \(-0.171492\pi\) | ||||
0.858347 | + | 0.513070i | \(0.171492\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.14214 | −0.0695367 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.6274 | −0.604035 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.54416 | −0.0824133 | −0.0412066 | − | 0.999151i | \(-0.513120\pi\) | ||||
−0.0412066 | + | 0.999151i | \(0.513120\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.75736 | 0.0568668 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.82843 | −0.285383 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.1421 | −0.456673 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.9411 | 1.51423 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.31371 | 0.106783 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.07107 | 0.292008 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.0416 | 1.28765 | 0.643826 | − | 0.765172i | \(-0.277346\pi\) | ||||
0.643826 | + | 0.765172i | \(0.277346\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.82843 | −0.219361 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.6569 | −1.08010 | −0.540050 | − | 0.841633i | \(-0.681595\pi\) | ||||
−0.540050 | + | 0.841633i | \(0.681595\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000 | 0.641171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.585786 | 0.0187602 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.2843 | −0.776923 | −0.388461 | − | 0.921465i | \(-0.626993\pi\) | ||||
−0.388461 | + | 0.921465i | \(0.626993\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 86.7696 | 2.77317 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4853 | 0.334769 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.6274 | −0.657912 | −0.328956 | − | 0.944345i | \(-0.606697\pi\) | ||||
−0.328956 | + | 0.944345i | \(0.606697\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.17157 | −0.0373294 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.17157 | −0.164613 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.7401 | −0.436910 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.6569 | −0.433824 | −0.216912 | − | 0.976191i | \(-0.569599\pi\) | ||||
−0.216912 | + | 0.976191i | \(0.569599\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.142136 | −0.00451054 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.1421 | −0.321527 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.0833 | 1.83952 | 0.919758 | − | 0.392487i | \(-0.128385\pi\) | ||||
0.919758 | + | 0.392487i | \(0.128385\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.585786 | 0.0185335 |
(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 | 4560.2.a.bf.1.1 | 2 | ||
4.3 | odd | 2 | 285.2.a.g.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 855.2.a.d.1.2 | 2 | |||
20.3 | even | 4 | 1425.2.c.l.799.3 | 4 | |||
20.7 | even | 4 | 1425.2.c.l.799.2 | 4 | |||
20.19 | odd | 2 | 1425.2.a.k.1.2 | 2 | |||
60.59 | even | 2 | 4275.2.a.y.1.1 | 2 | |||
76.75 | even | 2 | 5415.2.a.n.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.a.g.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
855.2.a.d.1.2 | 2 | 12.11 | even | 2 | |||
1425.2.a.k.1.2 | 2 | 20.19 | odd | 2 | |||
1425.2.c.l.799.2 | 4 | 20.7 | even | 4 | |||
1425.2.c.l.799.3 | 4 | 20.3 | even | 4 | |||
4275.2.a.y.1.1 | 2 | 60.59 | even | 2 | |||
4560.2.a.bf.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5415.2.a.n.1.2 | 2 | 76.75 | even | 2 |