Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1666,2,Mod(1,1666)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1666, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1666.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1666 = 2 \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1666.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: | \(13.3030769767\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1666.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.585786 | 0.261972 | 0.130986 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130986 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(6\) | 1.41421 | 0.577350 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.585786 | −0.185242 | ||||||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | −1.41421 | −0.408248 | ||||||||
\(13\) | −4.82843 | −1.33916 | −0.669582 | − | 0.742738i | \(-0.733527\pi\) | ||||
−0.669582 | + | 0.742738i | \(0.733527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.828427 | −0.213899 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.82843 | 1.56655 | 0.783274 | − | 0.621676i | \(-0.213548\pi\) | ||||
0.783274 | + | 0.621676i | \(0.213548\pi\) | |||||||
\(20\) | 0.585786 | 0.130986 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.24264 | 0.904534 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 1.41421 | 0.288675 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 4.82843 | 0.946932 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.07107 | 1.68446 | 0.842228 | − | 0.539122i | \(-0.181244\pi\) | ||||
0.842228 | + | 0.539122i | \(0.181244\pi\) | |||||||
\(30\) | 0.828427 | 0.151249 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.00000 | 1.04447 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 1.75736 | 0.288908 | 0.144454 | − | 0.989512i | \(-0.453857\pi\) | ||||
0.144454 | + | 0.989512i | \(0.453857\pi\) | |||||||
\(38\) | −6.82843 | −1.10772 | ||||||||
\(39\) | 6.82843 | 1.09342 | ||||||||
\(40\) | −0.585786 | −0.0926210 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.48528 | −1.29399 | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | −4.24264 | −0.639602 | ||||||||
\(45\) | −0.585786 | −0.0873239 | ||||||||
\(46\) | 2.82843 | 0.417029 | ||||||||
\(47\) | 12.8284 | 1.87122 | 0.935609 | − | 0.353037i | \(-0.114851\pi\) | ||||
0.935609 | + | 0.353037i | \(0.114851\pi\) | |||||||
\(48\) | −1.41421 | −0.204124 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.65685 | 0.658579 | ||||||||
\(51\) | 1.41421 | 0.198030 | ||||||||
\(52\) | −4.82843 | −0.669582 | ||||||||
\(53\) | −3.17157 | −0.435649 | −0.217825 | − | 0.975988i | \(-0.569896\pi\) | ||||
−0.217825 | + | 0.975988i | \(0.569896\pi\) | |||||||
\(54\) | −5.65685 | −0.769800 | ||||||||
\(55\) | −2.48528 | −0.335115 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.65685 | −1.27908 | ||||||||
\(58\) | −9.07107 | −1.19109 | ||||||||
\(59\) | 11.3137 | 1.47292 | 0.736460 | − | 0.676481i | \(-0.236496\pi\) | ||||
0.736460 | + | 0.676481i | \(0.236496\pi\) | |||||||
\(60\) | −0.828427 | −0.106949 | ||||||||
\(61\) | −2.24264 | −0.287141 | −0.143570 | − | 0.989640i | \(-0.545858\pi\) | ||||
−0.143570 | + | 0.989640i | \(0.545858\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.82843 | −0.350823 | ||||||||
\(66\) | −6.00000 | −0.738549 | ||||||||
\(67\) | −1.17157 | −0.143130 | −0.0715652 | − | 0.997436i | \(-0.522799\pi\) | ||||
−0.0715652 | + | 0.997436i | \(0.522799\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.82843 | −0.810385 | −0.405193 | − | 0.914231i | \(-0.632796\pi\) | ||||
−0.405193 | + | 0.914231i | \(0.632796\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −10.4853 | −1.22721 | −0.613605 | − | 0.789613i | \(-0.710281\pi\) | ||||
−0.613605 | + | 0.789613i | \(0.710281\pi\) | |||||||
\(74\) | −1.75736 | −0.204289 | ||||||||
\(75\) | 6.58579 | 0.760461 | ||||||||
\(76\) | 6.82843 | 0.783274 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.82843 | −0.773167 | ||||||||
\(79\) | 4.48528 | 0.504634 | 0.252317 | − | 0.967645i | \(-0.418807\pi\) | ||||
0.252317 | + | 0.967645i | \(0.418807\pi\) | |||||||
\(80\) | 0.585786 | 0.0654929 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | 5.65685 | 0.620920 | 0.310460 | − | 0.950586i | \(-0.399517\pi\) | ||||
0.310460 | + | 0.950586i | \(0.399517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.585786 | −0.0635375 | ||||||||
\(86\) | 8.48528 | 0.914991 | ||||||||
\(87\) | −12.8284 | −1.37535 | ||||||||
\(88\) | 4.24264 | 0.452267 | ||||||||
\(89\) | −1.65685 | −0.175626 | −0.0878131 | − | 0.996137i | \(-0.527988\pi\) | ||||
−0.0878131 | + | 0.996137i | \(0.527988\pi\) | |||||||
\(90\) | 0.585786 | 0.0617473 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.82843 | −0.294884 | ||||||||
\(93\) | 5.65685 | 0.586588 | ||||||||
\(94\) | −12.8284 | −1.32315 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 1.41421 | 0.144338 | ||||||||
\(97\) | 14.9706 | 1.52003 | 0.760015 | − | 0.649905i | \(-0.225191\pi\) | ||||
0.760015 | + | 0.649905i | \(0.225191\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.24264 | 0.426401 | ||||||||
\(100\) | −4.65685 | −0.465685 | ||||||||
\(101\) | 3.17157 | 0.315583 | 0.157792 | − | 0.987472i | \(-0.449563\pi\) | ||||
0.157792 | + | 0.987472i | \(0.449563\pi\) | |||||||
\(102\) | −1.41421 | −0.140028 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 4.82843 | 0.473466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.17157 | 0.308050 | ||||||||
\(107\) | 4.24264 | 0.410152 | 0.205076 | − | 0.978746i | \(-0.434256\pi\) | ||||
0.205076 | + | 0.978746i | \(0.434256\pi\) | |||||||
\(108\) | 5.65685 | 0.544331 | ||||||||
\(109\) | 7.89949 | 0.756634 | 0.378317 | − | 0.925676i | \(-0.376503\pi\) | ||||
0.378317 | + | 0.925676i | \(0.376503\pi\) | |||||||
\(110\) | 2.48528 | 0.236962 | ||||||||
\(111\) | −2.48528 | −0.235892 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.31371 | 0.876160 | 0.438080 | − | 0.898936i | \(-0.355659\pi\) | ||||
0.438080 | + | 0.898936i | \(0.355659\pi\) | |||||||
\(114\) | 9.65685 | 0.904447 | ||||||||
\(115\) | −1.65685 | −0.154502 | ||||||||
\(116\) | 9.07107 | 0.842228 | ||||||||
\(117\) | 4.82843 | 0.446388 | ||||||||
\(118\) | −11.3137 | −1.04151 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.828427 | 0.0756247 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 2.24264 | 0.203039 | ||||||||
\(123\) | −8.48528 | −0.765092 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.8284 | 1.49328 | 0.746641 | − | 0.665228i | \(-0.231665\pi\) | ||||
0.746641 | + | 0.665228i | \(0.231665\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.0000 | 1.05654 | ||||||||
\(130\) | 2.82843 | 0.248069 | ||||||||
\(131\) | 14.5858 | 1.27437 | 0.637183 | − | 0.770713i | \(-0.280100\pi\) | ||||
0.637183 | + | 0.770713i | \(0.280100\pi\) | |||||||
\(132\) | 6.00000 | 0.522233 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.17157 | 0.101208 | ||||||||
\(135\) | 3.31371 | 0.285199 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −1.65685 | −0.141555 | −0.0707773 | − | 0.997492i | \(-0.522548\pi\) | ||||
−0.0707773 | + | 0.997492i | \(0.522548\pi\) | |||||||
\(138\) | −4.00000 | −0.340503 | ||||||||
\(139\) | 0.928932 | 0.0787910 | 0.0393955 | − | 0.999224i | \(-0.487457\pi\) | ||||
0.0393955 | + | 0.999224i | \(0.487457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.1421 | −1.52784 | ||||||||
\(142\) | 6.82843 | 0.573029 | ||||||||
\(143\) | 20.4853 | 1.71307 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 5.31371 | 0.441279 | ||||||||
\(146\) | 10.4853 | 0.867768 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.75736 | 0.144454 | ||||||||
\(149\) | −17.3137 | −1.41839 | −0.709197 | − | 0.705010i | \(-0.750942\pi\) | ||||
−0.709197 | + | 0.705010i | \(0.750942\pi\) | |||||||
\(150\) | −6.58579 | −0.537727 | ||||||||
\(151\) | 14.4853 | 1.17880 | 0.589398 | − | 0.807843i | \(-0.299365\pi\) | ||||
0.589398 | + | 0.807843i | \(0.299365\pi\) | |||||||
\(152\) | −6.82843 | −0.553859 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.34315 | −0.188206 | ||||||||
\(156\) | 6.82843 | 0.546712 | ||||||||
\(157\) | 14.9706 | 1.19478 | 0.597390 | − | 0.801950i | \(-0.296204\pi\) | ||||
0.597390 | + | 0.801950i | \(0.296204\pi\) | |||||||
\(158\) | −4.48528 | −0.356830 | ||||||||
\(159\) | 4.48528 | 0.355706 | ||||||||
\(160\) | −0.585786 | −0.0463105 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 5.00000 | 0.392837 | ||||||||
\(163\) | 4.24264 | 0.332309 | 0.166155 | − | 0.986100i | \(-0.446865\pi\) | ||||
0.166155 | + | 0.986100i | \(0.446865\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 3.51472 | 0.273620 | ||||||||
\(166\) | −5.65685 | −0.439057 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 0.585786 | 0.0449278 | ||||||||
\(171\) | −6.82843 | −0.522183 | ||||||||
\(172\) | −8.48528 | −0.646997 | ||||||||
\(173\) | 4.10051 | 0.311756 | 0.155878 | − | 0.987776i | \(-0.450179\pi\) | ||||
0.155878 | + | 0.987776i | \(0.450179\pi\) | |||||||
\(174\) | 12.8284 | 0.972521 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.24264 | −0.319801 | ||||||||
\(177\) | −16.0000 | −1.20263 | ||||||||
\(178\) | 1.65685 | 0.124186 | ||||||||
\(179\) | 21.6569 | 1.61871 | 0.809355 | − | 0.587320i | \(-0.199817\pi\) | ||||
0.809355 | + | 0.587320i | \(0.199817\pi\) | |||||||
\(180\) | −0.585786 | −0.0436619 | ||||||||
\(181\) | −18.2426 | −1.35596 | −0.677982 | − | 0.735078i | \(-0.737145\pi\) | ||||
−0.677982 | + | 0.735078i | \(0.737145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.17157 | 0.234449 | ||||||||
\(184\) | 2.82843 | 0.208514 | ||||||||
\(185\) | 1.02944 | 0.0756857 | ||||||||
\(186\) | −5.65685 | −0.414781 | ||||||||
\(187\) | 4.24264 | 0.310253 | ||||||||
\(188\) | 12.8284 | 0.935609 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 11.3137 | 0.818631 | 0.409316 | − | 0.912393i | \(-0.365768\pi\) | ||||
0.409316 | + | 0.912393i | \(0.365768\pi\) | |||||||
\(192\) | −1.41421 | −0.102062 | ||||||||
\(193\) | −24.8284 | −1.78719 | −0.893595 | − | 0.448875i | \(-0.851825\pi\) | ||||
−0.893595 | + | 0.448875i | \(0.851825\pi\) | |||||||
\(194\) | −14.9706 | −1.07482 | ||||||||
\(195\) | 4.00000 | 0.286446 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.2426 | −1.58472 | −0.792361 | − | 0.610052i | \(-0.791148\pi\) | ||||
−0.792361 | + | 0.610052i | \(0.791148\pi\) | |||||||
\(198\) | −4.24264 | −0.301511 | ||||||||
\(199\) | 7.51472 | 0.532704 | 0.266352 | − | 0.963876i | \(-0.414182\pi\) | ||||
0.266352 | + | 0.963876i | \(0.414182\pi\) | |||||||
\(200\) | 4.65685 | 0.329289 | ||||||||
\(201\) | 1.65685 | 0.116865 | ||||||||
\(202\) | −3.17157 | −0.223151 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.41421 | 0.0990148 | ||||||||
\(205\) | 3.51472 | 0.245479 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82843 | 0.196589 | ||||||||
\(208\) | −4.82843 | −0.334791 | ||||||||
\(209\) | −28.9706 | −2.00394 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.55635 | −0.520201 | −0.260100 | − | 0.965582i | \(-0.583756\pi\) | ||||
−0.260100 | + | 0.965582i | \(0.583756\pi\) | |||||||
\(212\) | −3.17157 | −0.217825 | ||||||||
\(213\) | 9.65685 | 0.661677 | ||||||||
\(214\) | −4.24264 | −0.290021 | ||||||||
\(215\) | −4.97056 | −0.338990 | ||||||||
\(216\) | −5.65685 | −0.384900 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.89949 | −0.535021 | ||||||||
\(219\) | 14.8284 | 1.00201 | ||||||||
\(220\) | −2.48528 | −0.167558 | ||||||||
\(221\) | 4.82843 | 0.324795 | ||||||||
\(222\) | 2.48528 | 0.166801 | ||||||||
\(223\) | 21.7990 | 1.45977 | 0.729884 | − | 0.683571i | \(-0.239574\pi\) | ||||
0.729884 | + | 0.683571i | \(0.239574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.65685 | 0.310457 | ||||||||
\(226\) | −9.31371 | −0.619539 | ||||||||
\(227\) | −21.2132 | −1.40797 | −0.703985 | − | 0.710215i | \(-0.748598\pi\) | ||||
−0.703985 | + | 0.710215i | \(0.748598\pi\) | |||||||
\(228\) | −9.65685 | −0.639541 | ||||||||
\(229\) | −26.0000 | −1.71813 | −0.859064 | − | 0.511868i | \(-0.828954\pi\) | ||||
−0.859064 | + | 0.511868i | \(0.828954\pi\) | |||||||
\(230\) | 1.65685 | 0.109250 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.07107 | −0.595545 | ||||||||
\(233\) | −11.6569 | −0.763666 | −0.381833 | − | 0.924231i | \(-0.624707\pi\) | ||||
−0.381833 | + | 0.924231i | \(0.624707\pi\) | |||||||
\(234\) | −4.82843 | −0.315644 | ||||||||
\(235\) | 7.51472 | 0.490206 | ||||||||
\(236\) | 11.3137 | 0.736460 | ||||||||
\(237\) | −6.34315 | −0.412032 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6569 | 0.883388 | 0.441694 | − | 0.897166i | \(-0.354378\pi\) | ||||
0.441694 | + | 0.897166i | \(0.354378\pi\) | |||||||
\(240\) | −0.828427 | −0.0534747 | ||||||||
\(241\) | 25.3137 | 1.63060 | 0.815300 | − | 0.579039i | \(-0.196572\pi\) | ||||
0.815300 | + | 0.579039i | \(0.196572\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | −2.24264 | −0.143570 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.48528 | 0.541002 | ||||||||
\(247\) | −32.9706 | −2.09787 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −8.00000 | −0.506979 | ||||||||
\(250\) | 5.65685 | 0.357771 | ||||||||
\(251\) | 5.65685 | 0.357057 | 0.178529 | − | 0.983935i | \(-0.442866\pi\) | ||||
0.178529 | + | 0.983935i | \(0.442866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | −16.8284 | −1.05591 | ||||||||
\(255\) | 0.828427 | 0.0518781 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.6274 | 1.03719 | 0.518595 | − | 0.855020i | \(-0.326455\pi\) | ||||
0.518595 | + | 0.855020i | \(0.326455\pi\) | |||||||
\(258\) | −12.0000 | −0.747087 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.82843 | −0.175412 | ||||||||
\(261\) | −9.07107 | −0.561485 | ||||||||
\(262\) | −14.5858 | −0.901113 | ||||||||
\(263\) | 19.4558 | 1.19970 | 0.599849 | − | 0.800113i | \(-0.295227\pi\) | ||||
0.599849 | + | 0.800113i | \(0.295227\pi\) | |||||||
\(264\) | −6.00000 | −0.369274 | ||||||||
\(265\) | −1.85786 | −0.114128 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.34315 | 0.143398 | ||||||||
\(268\) | −1.17157 | −0.0715652 | ||||||||
\(269\) | 18.7279 | 1.14186 | 0.570931 | − | 0.820998i | \(-0.306582\pi\) | ||||
0.570931 | + | 0.820998i | \(0.306582\pi\) | |||||||
\(270\) | −3.31371 | −0.201666 | ||||||||
\(271\) | −9.79899 | −0.595246 | −0.297623 | − | 0.954683i | \(-0.596194\pi\) | ||||
−0.297623 | + | 0.954683i | \(0.596194\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.65685 | 0.100094 | ||||||||
\(275\) | 19.7574 | 1.19141 | ||||||||
\(276\) | 4.00000 | 0.240772 | ||||||||
\(277\) | 2.24264 | 0.134747 | 0.0673736 | − | 0.997728i | \(-0.478538\pi\) | ||||
0.0673736 | + | 0.997728i | \(0.478538\pi\) | |||||||
\(278\) | −0.928932 | −0.0557137 | ||||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.6274 | 1.34984 | 0.674919 | − | 0.737892i | \(-0.264178\pi\) | ||||
0.674919 | + | 0.737892i | \(0.264178\pi\) | |||||||
\(282\) | 18.1421 | 1.08035 | ||||||||
\(283\) | 12.7279 | 0.756596 | 0.378298 | − | 0.925684i | \(-0.376509\pi\) | ||||
0.378298 | + | 0.925684i | \(0.376509\pi\) | |||||||
\(284\) | −6.82843 | −0.405193 | ||||||||
\(285\) | −5.65685 | −0.335083 | ||||||||
\(286\) | −20.4853 | −1.21132 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −5.31371 | −0.312032 | ||||||||
\(291\) | −21.1716 | −1.24110 | ||||||||
\(292\) | −10.4853 | −0.613605 | ||||||||
\(293\) | −29.3137 | −1.71253 | −0.856263 | − | 0.516541i | \(-0.827219\pi\) | ||||
−0.856263 | + | 0.516541i | \(0.827219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.62742 | 0.385863 | ||||||||
\(296\) | −1.75736 | −0.102144 | ||||||||
\(297\) | −24.0000 | −1.39262 | ||||||||
\(298\) | 17.3137 | 1.00296 | ||||||||
\(299\) | 13.6569 | 0.789796 | ||||||||
\(300\) | 6.58579 | 0.380231 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14.4853 | −0.833534 | ||||||||
\(303\) | −4.48528 | −0.257673 | ||||||||
\(304\) | 6.82843 | 0.391637 | ||||||||
\(305\) | −1.31371 | −0.0752227 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −24.4853 | −1.39745 | −0.698724 | − | 0.715391i | \(-0.746249\pi\) | ||||
−0.698724 | + | 0.715391i | \(0.746249\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.34315 | 0.133082 | ||||||||
\(311\) | 25.6569 | 1.45487 | 0.727433 | − | 0.686178i | \(-0.240713\pi\) | ||||
0.727433 | + | 0.686178i | \(0.240713\pi\) | |||||||
\(312\) | −6.82843 | −0.386584 | ||||||||
\(313\) | −22.0000 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | −14.9706 | −0.844838 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.48528 | 0.252317 | ||||||||
\(317\) | 10.9289 | 0.613830 | 0.306915 | − | 0.951737i | \(-0.400703\pi\) | ||||
0.306915 | + | 0.951737i | \(0.400703\pi\) | |||||||
\(318\) | −4.48528 | −0.251522 | ||||||||
\(319\) | −38.4853 | −2.15476 | ||||||||
\(320\) | 0.585786 | 0.0327465 | ||||||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.82843 | −0.379944 | ||||||||
\(324\) | −5.00000 | −0.277778 | ||||||||
\(325\) | 22.4853 | 1.24726 | ||||||||
\(326\) | −4.24264 | −0.234978 | ||||||||
\(327\) | −11.1716 | −0.617789 | ||||||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.51472 | −0.193479 | ||||||||
\(331\) | −27.7990 | −1.52797 | −0.763985 | − | 0.645234i | \(-0.776760\pi\) | ||||
−0.763985 | + | 0.645234i | \(0.776760\pi\) | |||||||
\(332\) | 5.65685 | 0.310460 | ||||||||
\(333\) | −1.75736 | −0.0963027 | ||||||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | −0.686292 | −0.0374961 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00000 | 0.326841 | 0.163420 | − | 0.986557i | \(-0.447747\pi\) | ||||
0.163420 | + | 0.986557i | \(0.447747\pi\) | |||||||
\(338\) | −10.3137 | −0.560992 | ||||||||
\(339\) | −13.1716 | −0.715382 | ||||||||
\(340\) | −0.585786 | −0.0317687 | ||||||||
\(341\) | 16.9706 | 0.919007 | ||||||||
\(342\) | 6.82843 | 0.369239 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.48528 | 0.457496 | ||||||||
\(345\) | 2.34315 | 0.126151 | ||||||||
\(346\) | −4.10051 | −0.220445 | ||||||||
\(347\) | −7.55635 | −0.405646 | −0.202823 | − | 0.979215i | \(-0.565012\pi\) | ||||
−0.202823 | + | 0.979215i | \(0.565012\pi\) | |||||||
\(348\) | −12.8284 | −0.687676 | ||||||||
\(349\) | 4.82843 | 0.258460 | 0.129230 | − | 0.991615i | \(-0.458749\pi\) | ||||
0.129230 | + | 0.991615i | \(0.458749\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.3137 | −1.45790 | ||||||||
\(352\) | 4.24264 | 0.226134 | ||||||||
\(353\) | −1.31371 | −0.0699216 | −0.0349608 | − | 0.999389i | \(-0.511131\pi\) | ||||
−0.0349608 | + | 0.999389i | \(0.511131\pi\) | |||||||
\(354\) | 16.0000 | 0.850390 | ||||||||
\(355\) | −4.00000 | −0.212298 | ||||||||
\(356\) | −1.65685 | −0.0878131 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.6569 | −1.14460 | ||||||||
\(359\) | 16.9706 | 0.895672 | 0.447836 | − | 0.894116i | \(-0.352195\pi\) | ||||
0.447836 | + | 0.894116i | \(0.352195\pi\) | |||||||
\(360\) | 0.585786 | 0.0308737 | ||||||||
\(361\) | 27.6274 | 1.45407 | ||||||||
\(362\) | 18.2426 | 0.958812 | ||||||||
\(363\) | −9.89949 | −0.519589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.14214 | −0.321494 | ||||||||
\(366\) | −3.17157 | −0.165781 | ||||||||
\(367\) | −22.1421 | −1.15581 | −0.577905 | − | 0.816104i | \(-0.696130\pi\) | ||||
−0.577905 | + | 0.816104i | \(0.696130\pi\) | |||||||
\(368\) | −2.82843 | −0.147442 | ||||||||
\(369\) | −6.00000 | −0.312348 | ||||||||
\(370\) | −1.02944 | −0.0535179 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.65685 | 0.293294 | ||||||||
\(373\) | −12.8284 | −0.664231 | −0.332115 | − | 0.943239i | \(-0.607762\pi\) | ||||
−0.332115 | + | 0.943239i | \(0.607762\pi\) | |||||||
\(374\) | −4.24264 | −0.219382 | ||||||||
\(375\) | 8.00000 | 0.413118 | ||||||||
\(376\) | −12.8284 | −0.661576 | ||||||||
\(377\) | −43.7990 | −2.25576 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.21320 | 0.267784 | 0.133892 | − | 0.990996i | \(-0.457252\pi\) | ||||
0.133892 | + | 0.990996i | \(0.457252\pi\) | |||||||
\(380\) | 4.00000 | 0.205196 | ||||||||
\(381\) | −23.7990 | −1.21926 | ||||||||
\(382\) | −11.3137 | −0.578860 | ||||||||
\(383\) | −2.34315 | −0.119729 | −0.0598646 | − | 0.998207i | \(-0.519067\pi\) | ||||
−0.0598646 | + | 0.998207i | \(0.519067\pi\) | |||||||
\(384\) | 1.41421 | 0.0721688 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.8284 | 1.26373 | ||||||||
\(387\) | 8.48528 | 0.431331 | ||||||||
\(388\) | 14.9706 | 0.760015 | ||||||||
\(389\) | 4.34315 | 0.220206 | 0.110103 | − | 0.993920i | \(-0.464882\pi\) | ||||
0.110103 | + | 0.993920i | \(0.464882\pi\) | |||||||
\(390\) | −4.00000 | −0.202548 | ||||||||
\(391\) | 2.82843 | 0.143040 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.6274 | −1.04052 | ||||||||
\(394\) | 22.2426 | 1.12057 | ||||||||
\(395\) | 2.62742 | 0.132200 | ||||||||
\(396\) | 4.24264 | 0.213201 | ||||||||
\(397\) | −37.5563 | −1.88490 | −0.942450 | − | 0.334348i | \(-0.891484\pi\) | ||||
−0.942450 | + | 0.334348i | \(0.891484\pi\) | |||||||
\(398\) | −7.51472 | −0.376679 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.65685 | −0.232843 | ||||||||
\(401\) | −17.7990 | −0.888839 | −0.444420 | − | 0.895819i | \(-0.646590\pi\) | ||||
−0.444420 | + | 0.895819i | \(0.646590\pi\) | |||||||
\(402\) | −1.65685 | −0.0826364 | ||||||||
\(403\) | 19.3137 | 0.962084 | ||||||||
\(404\) | 3.17157 | 0.157792 | ||||||||
\(405\) | −2.92893 | −0.145540 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.45584 | −0.369572 | ||||||||
\(408\) | −1.41421 | −0.0700140 | ||||||||
\(409\) | 2.00000 | 0.0988936 | 0.0494468 | − | 0.998777i | \(-0.484254\pi\) | ||||
0.0494468 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(410\) | −3.51472 | −0.173580 | ||||||||
\(411\) | 2.34315 | 0.115579 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.82843 | −0.139010 | ||||||||
\(415\) | 3.31371 | 0.162664 | ||||||||
\(416\) | 4.82843 | 0.236733 | ||||||||
\(417\) | −1.31371 | −0.0643326 | ||||||||
\(418\) | 28.9706 | 1.41700 | ||||||||
\(419\) | 1.41421 | 0.0690889 | 0.0345444 | − | 0.999403i | \(-0.489002\pi\) | ||||
0.0345444 | + | 0.999403i | \(0.489002\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.4853 | 0.705969 | 0.352985 | − | 0.935629i | \(-0.385167\pi\) | ||||
0.352985 | + | 0.935629i | \(0.385167\pi\) | |||||||
\(422\) | 7.55635 | 0.367837 | ||||||||
\(423\) | −12.8284 | −0.623739 | ||||||||
\(424\) | 3.17157 | 0.154025 | ||||||||
\(425\) | 4.65685 | 0.225891 | ||||||||
\(426\) | −9.65685 | −0.467876 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.24264 | 0.205076 | ||||||||
\(429\) | −28.9706 | −1.39871 | ||||||||
\(430\) | 4.97056 | 0.239702 | ||||||||
\(431\) | −38.8284 | −1.87030 | −0.935150 | − | 0.354253i | \(-0.884735\pi\) | ||||
−0.935150 | + | 0.354253i | \(0.884735\pi\) | |||||||
\(432\) | 5.65685 | 0.272166 | ||||||||
\(433\) | −12.0000 | −0.576683 | −0.288342 | − | 0.957528i | \(-0.593104\pi\) | ||||
−0.288342 | + | 0.957528i | \(0.593104\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.51472 | −0.360303 | ||||||||
\(436\) | 7.89949 | 0.378317 | ||||||||
\(437\) | −19.3137 | −0.923900 | ||||||||
\(438\) | −14.8284 | −0.708530 | ||||||||
\(439\) | −15.5147 | −0.740477 | −0.370239 | − | 0.928937i | \(-0.620724\pi\) | ||||
−0.370239 | + | 0.928937i | \(0.620724\pi\) | |||||||
\(440\) | 2.48528 | 0.118481 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.82843 | −0.229665 | ||||||||
\(443\) | 22.8284 | 1.08461 | 0.542306 | − | 0.840181i | \(-0.317551\pi\) | ||||
0.542306 | + | 0.840181i | \(0.317551\pi\) | |||||||
\(444\) | −2.48528 | −0.117946 | ||||||||
\(445\) | −0.970563 | −0.0460091 | ||||||||
\(446\) | −21.7990 | −1.03221 | ||||||||
\(447\) | 24.4853 | 1.15811 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.7990 | 1.97262 | 0.986308 | − | 0.164913i | \(-0.0527343\pi\) | ||||
0.986308 | + | 0.164913i | \(0.0527343\pi\) | |||||||
\(450\) | −4.65685 | −0.219526 | ||||||||
\(451\) | −25.4558 | −1.19867 | ||||||||
\(452\) | 9.31371 | 0.438080 | ||||||||
\(453\) | −20.4853 | −0.962482 | ||||||||
\(454\) | 21.2132 | 0.995585 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.65685 | 0.452224 | ||||||||
\(457\) | 39.9411 | 1.86837 | 0.934184 | − | 0.356793i | \(-0.116130\pi\) | ||||
0.934184 | + | 0.356793i | \(0.116130\pi\) | |||||||
\(458\) | 26.0000 | 1.21490 | ||||||||
\(459\) | −5.65685 | −0.264039 | ||||||||
\(460\) | −1.65685 | −0.0772512 | ||||||||
\(461\) | 19.4558 | 0.906149 | 0.453074 | − | 0.891473i | \(-0.350327\pi\) | ||||
0.453074 | + | 0.891473i | \(0.350327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.828427 | −0.0385003 | −0.0192501 | − | 0.999815i | \(-0.506128\pi\) | ||||
−0.0192501 | + | 0.999815i | \(0.506128\pi\) | |||||||
\(464\) | 9.07107 | 0.421114 | ||||||||
\(465\) | 3.31371 | 0.153670 | ||||||||
\(466\) | 11.6569 | 0.539993 | ||||||||
\(467\) | 13.1716 | 0.609508 | 0.304754 | − | 0.952431i | \(-0.401426\pi\) | ||||
0.304754 | + | 0.952431i | \(0.401426\pi\) | |||||||
\(468\) | 4.82843 | 0.223194 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.51472 | −0.346628 | ||||||||
\(471\) | −21.1716 | −0.975535 | ||||||||
\(472\) | −11.3137 | −0.520756 | ||||||||
\(473\) | 36.0000 | 1.65528 | ||||||||
\(474\) | 6.34315 | 0.291350 | ||||||||
\(475\) | −31.7990 | −1.45904 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.17157 | 0.145216 | ||||||||
\(478\) | −13.6569 | −0.624650 | ||||||||
\(479\) | 5.17157 | 0.236295 | 0.118148 | − | 0.992996i | \(-0.462304\pi\) | ||||
0.118148 | + | 0.992996i | \(0.462304\pi\) | |||||||
\(480\) | 0.828427 | 0.0378124 | ||||||||
\(481\) | −8.48528 | −0.386896 | ||||||||
\(482\) | −25.3137 | −1.15301 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 8.76955 | 0.398205 | ||||||||
\(486\) | 9.89949 | 0.449050 | ||||||||
\(487\) | 6.14214 | 0.278327 | 0.139163 | − | 0.990269i | \(-0.455559\pi\) | ||||
0.139163 | + | 0.990269i | \(0.455559\pi\) | |||||||
\(488\) | 2.24264 | 0.101520 | ||||||||
\(489\) | −6.00000 | −0.271329 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.6569 | 0.977360 | 0.488680 | − | 0.872463i | \(-0.337479\pi\) | ||||
0.488680 | + | 0.872463i | \(0.337479\pi\) | |||||||
\(492\) | −8.48528 | −0.382546 | ||||||||
\(493\) | −9.07107 | −0.408540 | ||||||||
\(494\) | 32.9706 | 1.48342 | ||||||||
\(495\) | 2.48528 | 0.111705 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.00000 | 0.358489 | ||||||||
\(499\) | 23.5563 | 1.05453 | 0.527264 | − | 0.849702i | \(-0.323218\pi\) | ||||
0.527264 | + | 0.849702i | \(0.323218\pi\) | |||||||
\(500\) | −5.65685 | −0.252982 | ||||||||
\(501\) | −16.9706 | −0.758189 | ||||||||
\(502\) | −5.65685 | −0.252478 | ||||||||
\(503\) | 3.51472 | 0.156714 | 0.0783568 | − | 0.996925i | \(-0.475033\pi\) | ||||
0.0783568 | + | 0.996925i | \(0.475033\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.85786 | 0.0826739 | ||||||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | −14.5858 | −0.647778 | ||||||||
\(508\) | 16.8284 | 0.746641 | ||||||||
\(509\) | −16.6274 | −0.736997 | −0.368499 | − | 0.929628i | \(-0.620128\pi\) | ||||
−0.368499 | + | 0.929628i | \(0.620128\pi\) | |||||||
\(510\) | −0.828427 | −0.0366834 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 38.6274 | 1.70544 | ||||||||
\(514\) | −16.6274 | −0.733404 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.0000 | 0.528271 | ||||||||
\(517\) | −54.4264 | −2.39367 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.79899 | −0.254547 | ||||||||
\(520\) | 2.82843 | 0.124035 | ||||||||
\(521\) | 5.31371 | 0.232798 | 0.116399 | − | 0.993203i | \(-0.462865\pi\) | ||||
0.116399 | + | 0.993203i | \(0.462865\pi\) | |||||||
\(522\) | 9.07107 | 0.397030 | ||||||||
\(523\) | −22.3431 | −0.976998 | −0.488499 | − | 0.872565i | \(-0.662455\pi\) | ||||
−0.488499 | + | 0.872565i | \(0.662455\pi\) | |||||||
\(524\) | 14.5858 | 0.637183 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.4558 | −0.848315 | ||||||||
\(527\) | 4.00000 | 0.174243 | ||||||||
\(528\) | 6.00000 | 0.261116 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 1.85786 | 0.0807005 | ||||||||
\(531\) | −11.3137 | −0.490973 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.9706 | −1.25485 | ||||||||
\(534\) | −2.34315 | −0.101398 | ||||||||
\(535\) | 2.48528 | 0.107448 | ||||||||
\(536\) | 1.17157 | 0.0506042 | ||||||||
\(537\) | −30.6274 | −1.32167 | ||||||||
\(538\) | −18.7279 | −0.807418 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.31371 | 0.142599 | ||||||||
\(541\) | −1.75736 | −0.0755548 | −0.0377774 | − | 0.999286i | \(-0.512028\pi\) | ||||
−0.0377774 | + | 0.999286i | \(0.512028\pi\) | |||||||
\(542\) | 9.79899 | 0.420903 | ||||||||
\(543\) | 25.7990 | 1.10714 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 4.62742 | 0.198217 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.2426 | −1.54962 | −0.774812 | − | 0.632192i | \(-0.782155\pi\) | ||||
−0.774812 | + | 0.632192i | \(0.782155\pi\) | |||||||
\(548\) | −1.65685 | −0.0707773 | ||||||||
\(549\) | 2.24264 | 0.0957136 | ||||||||
\(550\) | −19.7574 | −0.842457 | ||||||||
\(551\) | 61.9411 | 2.63878 | ||||||||
\(552\) | −4.00000 | −0.170251 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.24264 | −0.0952807 | ||||||||
\(555\) | −1.45584 | −0.0617971 | ||||||||
\(556\) | 0.928932 | 0.0393955 | ||||||||
\(557\) | −36.8284 | −1.56047 | −0.780235 | − | 0.625486i | \(-0.784901\pi\) | ||||
−0.780235 | + | 0.625486i | \(0.784901\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | 40.9706 | 1.73287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | −22.6274 | −0.954480 | ||||||||
\(563\) | −12.0000 | −0.505740 | −0.252870 | − | 0.967500i | \(-0.581374\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581374\pi\) | |||||||
\(564\) | −18.1421 | −0.763922 | ||||||||
\(565\) | 5.45584 | 0.229529 | ||||||||
\(566\) | −12.7279 | −0.534994 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.82843 | 0.286514 | ||||||||
\(569\) | 22.2843 | 0.934205 | 0.467103 | − | 0.884203i | \(-0.345298\pi\) | ||||
0.467103 | + | 0.884203i | \(0.345298\pi\) | |||||||
\(570\) | 5.65685 | 0.236940 | ||||||||
\(571\) | 6.10051 | 0.255298 | 0.127649 | − | 0.991819i | \(-0.459257\pi\) | ||||
0.127649 | + | 0.991819i | \(0.459257\pi\) | |||||||
\(572\) | 20.4853 | 0.856533 | ||||||||
\(573\) | −16.0000 | −0.668410 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.1716 | 0.549293 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 2.97056 | 0.123666 | 0.0618331 | − | 0.998087i | \(-0.480305\pi\) | ||||
0.0618331 | + | 0.998087i | \(0.480305\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 35.1127 | 1.45923 | ||||||||
\(580\) | 5.31371 | 0.220640 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 21.1716 | 0.877590 | ||||||||
\(583\) | 13.4558 | 0.557284 | ||||||||
\(584\) | 10.4853 | 0.433884 | ||||||||
\(585\) | 2.82843 | 0.116941 | ||||||||
\(586\) | 29.3137 | 1.21094 | ||||||||
\(587\) | 25.4558 | 1.05068 | 0.525338 | − | 0.850894i | \(-0.323939\pi\) | ||||
0.525338 | + | 0.850894i | \(0.323939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.3137 | −1.12544 | ||||||||
\(590\) | −6.62742 | −0.272846 | ||||||||
\(591\) | 31.4558 | 1.29392 | ||||||||
\(592\) | 1.75736 | 0.0722270 | ||||||||
\(593\) | −1.65685 | −0.0680388 | −0.0340194 | − | 0.999421i | \(-0.510831\pi\) | ||||
−0.0340194 | + | 0.999421i | \(0.510831\pi\) | |||||||
\(594\) | 24.0000 | 0.984732 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.3137 | −0.709197 | ||||||||
\(597\) | −10.6274 | −0.434951 | ||||||||
\(598\) | −13.6569 | −0.558470 | ||||||||
\(599\) | 0.828427 | 0.0338486 | 0.0169243 | − | 0.999857i | \(-0.494613\pi\) | ||||
0.0169243 | + | 0.999857i | \(0.494613\pi\) | |||||||
\(600\) | −6.58579 | −0.268864 | ||||||||
\(601\) | 40.1421 | 1.63743 | 0.818716 | − | 0.574199i | \(-0.194686\pi\) | ||||
0.818716 | + | 0.574199i | \(0.194686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.17157 | 0.0477101 | ||||||||
\(604\) | 14.4853 | 0.589398 | ||||||||
\(605\) | 4.10051 | 0.166709 | ||||||||
\(606\) | 4.48528 | 0.182202 | ||||||||
\(607\) | 20.0000 | 0.811775 | 0.405887 | − | 0.913923i | \(-0.366962\pi\) | ||||
0.405887 | + | 0.913923i | \(0.366962\pi\) | |||||||
\(608\) | −6.82843 | −0.276929 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.31371 | 0.0531905 | ||||||||
\(611\) | −61.9411 | −2.50587 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 38.9706 | 1.57401 | 0.787003 | − | 0.616949i | \(-0.211632\pi\) | ||||
0.787003 | + | 0.616949i | \(0.211632\pi\) | |||||||
\(614\) | 24.4853 | 0.988146 | ||||||||
\(615\) | −4.97056 | −0.200432 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.3431 | −0.980018 | −0.490009 | − | 0.871717i | \(-0.663007\pi\) | ||||
−0.490009 | + | 0.871717i | \(0.663007\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.7574 | 0.472568 | 0.236284 | − | 0.971684i | \(-0.424070\pi\) | ||||
0.236284 | + | 0.971684i | \(0.424070\pi\) | |||||||
\(620\) | −2.34315 | −0.0941030 | ||||||||
\(621\) | −16.0000 | −0.642058 | ||||||||
\(622\) | −25.6569 | −1.02875 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.82843 | 0.273356 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 22.0000 | 0.879297 | ||||||||
\(627\) | 40.9706 | 1.63621 | ||||||||
\(628\) | 14.9706 | 0.597390 | ||||||||
\(629\) | −1.75736 | −0.0700705 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0000 | −0.955425 | −0.477712 | − | 0.878516i | \(-0.658534\pi\) | ||||
−0.477712 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(632\) | −4.48528 | −0.178415 | ||||||||
\(633\) | 10.6863 | 0.424742 | ||||||||
\(634\) | −10.9289 | −0.434043 | ||||||||
\(635\) | 9.85786 | 0.391197 | ||||||||
\(636\) | 4.48528 | 0.177853 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 38.4853 | 1.52365 | ||||||||
\(639\) | 6.82843 | 0.270128 | ||||||||
\(640\) | −0.585786 | −0.0231552 | ||||||||
\(641\) | 3.85786 | 0.152376 | 0.0761882 | − | 0.997093i | \(-0.475725\pi\) | ||||
0.0761882 | + | 0.997093i | \(0.475725\pi\) | |||||||
\(642\) | 6.00000 | 0.236801 | ||||||||
\(643\) | 0.443651 | 0.0174959 | 0.00874794 | − | 0.999962i | \(-0.497215\pi\) | ||||
0.00874794 | + | 0.999962i | \(0.497215\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.02944 | 0.276784 | ||||||||
\(646\) | 6.82843 | 0.268661 | ||||||||
\(647\) | −15.1716 | −0.596456 | −0.298228 | − | 0.954495i | \(-0.596396\pi\) | ||||
−0.298228 | + | 0.954495i | \(0.596396\pi\) | |||||||
\(648\) | 5.00000 | 0.196419 | ||||||||
\(649\) | −48.0000 | −1.88416 | ||||||||
\(650\) | −22.4853 | −0.881945 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.24264 | 0.166155 | ||||||||
\(653\) | −9.07107 | −0.354978 | −0.177489 | − | 0.984123i | \(-0.556797\pi\) | ||||
−0.177489 | + | 0.984123i | \(0.556797\pi\) | |||||||
\(654\) | 11.1716 | 0.436843 | ||||||||
\(655\) | 8.54416 | 0.333848 | ||||||||
\(656\) | 6.00000 | 0.234261 | ||||||||
\(657\) | 10.4853 | 0.409070 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.68629 | −0.338370 | −0.169185 | − | 0.985584i | \(-0.554114\pi\) | ||||
−0.169185 | + | 0.985584i | \(0.554114\pi\) | |||||||
\(660\) | 3.51472 | 0.136810 | ||||||||
\(661\) | −2.48528 | −0.0966662 | −0.0483331 | − | 0.998831i | \(-0.515391\pi\) | ||||
−0.0483331 | + | 0.998831i | \(0.515391\pi\) | |||||||
\(662\) | 27.7990 | 1.08044 | ||||||||
\(663\) | −6.82843 | −0.265194 | ||||||||
\(664\) | −5.65685 | −0.219529 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.75736 | 0.0680963 | ||||||||
\(667\) | −25.6569 | −0.993437 | ||||||||
\(668\) | 12.0000 | 0.464294 | ||||||||
\(669\) | −30.8284 | −1.19190 | ||||||||
\(670\) | 0.686292 | 0.0265138 | ||||||||
\(671\) | 9.51472 | 0.367312 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.1716 | −0.893198 | −0.446599 | − | 0.894734i | \(-0.647365\pi\) | ||||
−0.446599 | + | 0.894734i | \(0.647365\pi\) | |||||||
\(674\) | −6.00000 | −0.231111 | ||||||||
\(675\) | −26.3431 | −1.01395 | ||||||||
\(676\) | 10.3137 | 0.396681 | ||||||||
\(677\) | −3.21320 | −0.123493 | −0.0617467 | − | 0.998092i | \(-0.519667\pi\) | ||||
−0.0617467 | + | 0.998092i | \(0.519667\pi\) | |||||||
\(678\) | 13.1716 | 0.505851 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.585786 | 0.0224639 | ||||||||
\(681\) | 30.0000 | 1.14960 | ||||||||
\(682\) | −16.9706 | −0.649836 | ||||||||
\(683\) | −0.443651 | −0.0169758 | −0.00848791 | − | 0.999964i | \(-0.502702\pi\) | ||||
−0.00848791 | + | 0.999964i | \(0.502702\pi\) | |||||||
\(684\) | −6.82843 | −0.261091 | ||||||||
\(685\) | −0.970563 | −0.0370833 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.7696 | 1.40285 | ||||||||
\(688\) | −8.48528 | −0.323498 | ||||||||
\(689\) | 15.3137 | 0.583406 | ||||||||
\(690\) | −2.34315 | −0.0892020 | ||||||||
\(691\) | −13.2132 | −0.502654 | −0.251327 | − | 0.967902i | \(-0.580867\pi\) | ||||
−0.251327 | + | 0.967902i | \(0.580867\pi\) | |||||||
\(692\) | 4.10051 | 0.155878 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.55635 | 0.286835 | ||||||||
\(695\) | 0.544156 | 0.0206410 | ||||||||
\(696\) | 12.8284 | 0.486260 | ||||||||
\(697\) | −6.00000 | −0.227266 | ||||||||
\(698\) | −4.82843 | −0.182759 | ||||||||
\(699\) | 16.4853 | 0.623531 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.1127 | −1.09957 | −0.549786 | − | 0.835306i | \(-0.685291\pi\) | ||||
−0.549786 | + | 0.835306i | \(0.685291\pi\) | |||||||
\(702\) | 27.3137 | 1.03089 | ||||||||
\(703\) | 12.0000 | 0.452589 | ||||||||
\(704\) | −4.24264 | −0.159901 | ||||||||
\(705\) | −10.6274 | −0.400252 | ||||||||
\(706\) | 1.31371 | 0.0494421 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −16.0000 | −0.601317 | ||||||||
\(709\) | −36.5858 | −1.37401 | −0.687004 | − | 0.726654i | \(-0.741075\pi\) | ||||
−0.687004 | + | 0.726654i | \(0.741075\pi\) | |||||||
\(710\) | 4.00000 | 0.150117 | ||||||||
\(711\) | −4.48528 | −0.168211 | ||||||||
\(712\) | 1.65685 | 0.0620932 | ||||||||
\(713\) | 11.3137 | 0.423702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | 21.6569 | 0.809355 | ||||||||
\(717\) | −19.3137 | −0.721284 | ||||||||
\(718\) | −16.9706 | −0.633336 | ||||||||
\(719\) | −48.7696 | −1.81880 | −0.909399 | − | 0.415925i | \(-0.863458\pi\) | ||||
−0.909399 | + | 0.415925i | \(0.863458\pi\) | |||||||
\(720\) | −0.585786 | −0.0218310 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −27.6274 | −1.02819 | ||||||||
\(723\) | −35.7990 | −1.33138 | ||||||||
\(724\) | −18.2426 | −0.677982 | ||||||||
\(725\) | −42.2426 | −1.56885 | ||||||||
\(726\) | 9.89949 | 0.367405 | ||||||||
\(727\) | 25.5147 | 0.946289 | 0.473144 | − | 0.880985i | \(-0.343119\pi\) | ||||
0.473144 | + | 0.880985i | \(0.343119\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 6.14214 | 0.227331 | ||||||||
\(731\) | 8.48528 | 0.313839 | ||||||||
\(732\) | 3.17157 | 0.117225 | ||||||||
\(733\) | 19.4558 | 0.718618 | 0.359309 | − | 0.933219i | \(-0.383012\pi\) | ||||
0.359309 | + | 0.933219i | \(0.383012\pi\) | |||||||
\(734\) | 22.1421 | 0.817281 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.82843 | 0.104257 | ||||||||
\(737\) | 4.97056 | 0.183093 | ||||||||
\(738\) | 6.00000 | 0.220863 | ||||||||
\(739\) | −30.6274 | −1.12665 | −0.563324 | − | 0.826236i | \(-0.690478\pi\) | ||||
−0.563324 | + | 0.826236i | \(0.690478\pi\) | |||||||
\(740\) | 1.02944 | 0.0378429 | ||||||||
\(741\) | 46.6274 | 1.71290 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.686292 | −0.0251776 | −0.0125888 | − | 0.999921i | \(-0.504007\pi\) | ||||
−0.0125888 | + | 0.999921i | \(0.504007\pi\) | |||||||
\(744\) | −5.65685 | −0.207390 | ||||||||
\(745\) | −10.1421 | −0.371579 | ||||||||
\(746\) | 12.8284 | 0.469682 | ||||||||
\(747\) | −5.65685 | −0.206973 | ||||||||
\(748\) | 4.24264 | 0.155126 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.00000 | −0.292119 | ||||||||
\(751\) | 3.51472 | 0.128254 | 0.0641270 | − | 0.997942i | \(-0.479574\pi\) | ||||
0.0641270 | + | 0.997942i | \(0.479574\pi\) | |||||||
\(752\) | 12.8284 | 0.467805 | ||||||||
\(753\) | −8.00000 | −0.291536 | ||||||||
\(754\) | 43.7990 | 1.59507 | ||||||||
\(755\) | 8.48528 | 0.308811 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.9411 | 1.88783 | 0.943916 | − | 0.330185i | \(-0.107111\pi\) | ||||
0.943916 | + | 0.330185i | \(0.107111\pi\) | |||||||
\(758\) | −5.21320 | −0.189352 | ||||||||
\(759\) | −16.9706 | −0.615992 | ||||||||
\(760\) | −4.00000 | −0.145095 | ||||||||
\(761\) | 52.6274 | 1.90774 | 0.953871 | − | 0.300216i | \(-0.0970588\pi\) | ||||
0.953871 | + | 0.300216i | \(0.0970588\pi\) | |||||||
\(762\) | 23.7990 | 0.862146 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.3137 | 0.409316 | ||||||||
\(765\) | 0.585786 | 0.0211792 | ||||||||
\(766\) | 2.34315 | 0.0846613 | ||||||||
\(767\) | −54.6274 | −1.97248 | ||||||||
\(768\) | −1.41421 | −0.0510310 | ||||||||
\(769\) | 33.3137 | 1.20132 | 0.600662 | − | 0.799503i | \(-0.294904\pi\) | ||||
0.600662 | + | 0.799503i | \(0.294904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.5147 | −0.846862 | ||||||||
\(772\) | −24.8284 | −0.893595 | ||||||||
\(773\) | −29.5980 | −1.06457 | −0.532283 | − | 0.846567i | \(-0.678666\pi\) | ||||
−0.532283 | + | 0.846567i | \(0.678666\pi\) | |||||||
\(774\) | −8.48528 | −0.304997 | ||||||||
\(775\) | 18.6274 | 0.669117 | ||||||||
\(776\) | −14.9706 | −0.537412 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.34315 | −0.155709 | ||||||||
\(779\) | 40.9706 | 1.46792 | ||||||||
\(780\) | 4.00000 | 0.143223 | ||||||||
\(781\) | 28.9706 | 1.03665 | ||||||||
\(782\) | −2.82843 | −0.101144 | ||||||||
\(783\) | 51.3137 | 1.83380 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.76955 | 0.312999 | ||||||||
\(786\) | 20.6274 | 0.735756 | ||||||||
\(787\) | −19.2721 | −0.686975 | −0.343488 | − | 0.939157i | \(-0.611608\pi\) | ||||
−0.343488 | + | 0.939157i | \(0.611608\pi\) | |||||||
\(788\) | −22.2426 | −0.792361 | ||||||||
\(789\) | −27.5147 | −0.979550 | ||||||||
\(790\) | −2.62742 | −0.0934793 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.24264 | −0.150756 | ||||||||
\(793\) | 10.8284 | 0.384529 | ||||||||
\(794\) | 37.5563 | 1.33282 | ||||||||
\(795\) | 2.62742 | 0.0931849 | ||||||||
\(796\) | 7.51472 | 0.266352 | ||||||||
\(797\) | −2.48528 | −0.0880332 | −0.0440166 | − | 0.999031i | \(-0.514015\pi\) | ||||
−0.0440166 | + | 0.999031i | \(0.514015\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.8284 | −0.453837 | ||||||||
\(800\) | 4.65685 | 0.164645 | ||||||||
\(801\) | 1.65685 | 0.0585421 | ||||||||
\(802\) | 17.7990 | 0.628504 | ||||||||
\(803\) | 44.4853 | 1.56985 | ||||||||
\(804\) | 1.65685 | 0.0584327 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.3137 | −0.680296 | ||||||||
\(807\) | −26.4853 | −0.932326 | ||||||||
\(808\) | −3.17157 | −0.111576 | ||||||||
\(809\) | −14.4853 | −0.509275 | −0.254638 | − | 0.967037i | \(-0.581956\pi\) | ||||
−0.254638 | + | 0.967037i | \(0.581956\pi\) | |||||||
\(810\) | 2.92893 | 0.102912 | ||||||||
\(811\) | 44.7279 | 1.57061 | 0.785305 | − | 0.619109i | \(-0.212506\pi\) | ||||
0.785305 | + | 0.619109i | \(0.212506\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.8579 | 0.486017 | ||||||||
\(814\) | 7.45584 | 0.261327 | ||||||||
\(815\) | 2.48528 | 0.0870556 | ||||||||
\(816\) | 1.41421 | 0.0495074 | ||||||||
\(817\) | −57.9411 | −2.02710 | ||||||||
\(818\) | −2.00000 | −0.0699284 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.51472 | 0.122739 | ||||||||
\(821\) | −20.8701 | −0.728370 | −0.364185 | − | 0.931327i | \(-0.618652\pi\) | ||||
−0.364185 | + | 0.931327i | \(0.618652\pi\) | |||||||
\(822\) | −2.34315 | −0.0817266 | ||||||||
\(823\) | −32.4853 | −1.13237 | −0.566183 | − | 0.824280i | \(-0.691580\pi\) | ||||
−0.566183 | + | 0.824280i | \(0.691580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.9411 | −0.972785 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.1005 | 0.490323 | 0.245161 | − | 0.969482i | \(-0.421159\pi\) | ||||
0.245161 | + | 0.969482i | \(0.421159\pi\) | |||||||
\(828\) | 2.82843 | 0.0982946 | ||||||||
\(829\) | 19.6569 | 0.682711 | 0.341355 | − | 0.939934i | \(-0.389114\pi\) | ||||
0.341355 | + | 0.939934i | \(0.389114\pi\) | |||||||
\(830\) | −3.31371 | −0.115021 | ||||||||
\(831\) | −3.17157 | −0.110021 | ||||||||
\(832\) | −4.82843 | −0.167396 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.31371 | 0.0454900 | ||||||||
\(835\) | 7.02944 | 0.243264 | ||||||||
\(836\) | −28.9706 | −1.00197 | ||||||||
\(837\) | −22.6274 | −0.782118 | ||||||||
\(838\) | −1.41421 | −0.0488532 | ||||||||
\(839\) | 18.3431 | 0.633276 | 0.316638 | − | 0.948547i | \(-0.397446\pi\) | ||||
0.316638 | + | 0.948547i | \(0.397446\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.2843 | 1.83739 | ||||||||
\(842\) | −14.4853 | −0.499196 | ||||||||
\(843\) | −32.0000 | −1.10214 | ||||||||
\(844\) | −7.55635 | −0.260100 | ||||||||
\(845\) | 6.04163 | 0.207838 | ||||||||
\(846\) | 12.8284 | 0.441050 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.17157 | −0.108912 | ||||||||
\(849\) | −18.0000 | −0.617758 | ||||||||
\(850\) | −4.65685 | −0.159729 | ||||||||
\(851\) | −4.97056 | −0.170389 | ||||||||
\(852\) | 9.65685 | 0.330838 | ||||||||
\(853\) | 48.5858 | 1.66355 | 0.831773 | − | 0.555116i | \(-0.187326\pi\) | ||||
0.831773 | + | 0.555116i | \(0.187326\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | −4.24264 | −0.145010 | ||||||||
\(857\) | 25.5980 | 0.874410 | 0.437205 | − | 0.899362i | \(-0.355968\pi\) | ||||
0.437205 | + | 0.899362i | \(0.355968\pi\) | |||||||
\(858\) | 28.9706 | 0.989039 | ||||||||
\(859\) | 44.9706 | 1.53438 | 0.767188 | − | 0.641422i | \(-0.221655\pi\) | ||||
0.767188 | + | 0.641422i | \(0.221655\pi\) | |||||||
\(860\) | −4.97056 | −0.169495 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 38.8284 | 1.32250 | ||||||||
\(863\) | −21.7990 | −0.742046 | −0.371023 | − | 0.928624i | \(-0.620993\pi\) | ||||
−0.371023 | + | 0.928624i | \(0.620993\pi\) | |||||||
\(864\) | −5.65685 | −0.192450 | ||||||||
\(865\) | 2.40202 | 0.0816711 | ||||||||
\(866\) | 12.0000 | 0.407777 | ||||||||
\(867\) | −1.41421 | −0.0480292 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.0294 | −0.645529 | ||||||||
\(870\) | 7.51472 | 0.254773 | ||||||||
\(871\) | 5.65685 | 0.191675 | ||||||||
\(872\) | −7.89949 | −0.267511 | ||||||||
\(873\) | −14.9706 | −0.506677 | ||||||||
\(874\) | 19.3137 | 0.653296 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.8284 | 0.501006 | ||||||||
\(877\) | 44.3848 | 1.49877 | 0.749384 | − | 0.662136i | \(-0.230350\pi\) | ||||
0.749384 | + | 0.662136i | \(0.230350\pi\) | |||||||
\(878\) | 15.5147 | 0.523596 | ||||||||
\(879\) | 41.4558 | 1.39827 | ||||||||
\(880\) | −2.48528 | −0.0837788 | ||||||||
\(881\) | −49.1127 | −1.65465 | −0.827324 | − | 0.561724i | \(-0.810138\pi\) | ||||
−0.827324 | + | 0.561724i | \(0.810138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.4558 | 1.52971 | 0.764855 | − | 0.644202i | \(-0.222810\pi\) | ||||
0.764855 | + | 0.644202i | \(0.222810\pi\) | |||||||
\(884\) | 4.82843 | 0.162398 | ||||||||
\(885\) | −9.37258 | −0.315056 | ||||||||
\(886\) | −22.8284 | −0.766936 | ||||||||
\(887\) | −5.17157 | −0.173644 | −0.0868222 | − | 0.996224i | \(-0.527671\pi\) | ||||
−0.0868222 | + | 0.996224i | \(0.527671\pi\) | |||||||
\(888\) | 2.48528 | 0.0834006 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.970563 | 0.0325333 | ||||||||
\(891\) | 21.2132 | 0.710669 | ||||||||
\(892\) | 21.7990 | 0.729884 | ||||||||
\(893\) | 87.5980 | 2.93135 | ||||||||
\(894\) | −24.4853 | −0.818910 | ||||||||
\(895\) | 12.6863 | 0.424056 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.3137 | −0.644866 | ||||||||
\(898\) | −41.7990 | −1.39485 | ||||||||
\(899\) | −36.2843 | −1.21015 | ||||||||
\(900\) | 4.65685 | 0.155228 | ||||||||
\(901\) | 3.17157 | 0.105660 | ||||||||
\(902\) | 25.4558 | 0.847587 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.31371 | −0.309769 | ||||||||
\(905\) | −10.6863 | −0.355224 | ||||||||
\(906\) | 20.4853 | 0.680578 | ||||||||
\(907\) | −38.5858 | −1.28122 | −0.640610 | − | 0.767866i | \(-0.721318\pi\) | ||||
−0.640610 | + | 0.767866i | \(0.721318\pi\) | |||||||
\(908\) | −21.2132 | −0.703985 | ||||||||
\(909\) | −3.17157 | −0.105194 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.3431 | 0.607736 | 0.303868 | − | 0.952714i | \(-0.401722\pi\) | ||||
0.303868 | + | 0.952714i | \(0.401722\pi\) | |||||||
\(912\) | −9.65685 | −0.319770 | ||||||||
\(913\) | −24.0000 | −0.794284 | ||||||||
\(914\) | −39.9411 | −1.32114 | ||||||||
\(915\) | 1.85786 | 0.0614191 | ||||||||
\(916\) | −26.0000 | −0.859064 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.65685 | 0.186704 | ||||||||
\(919\) | 24.9706 | 0.823703 | 0.411851 | − | 0.911251i | \(-0.364882\pi\) | ||||
0.411851 | + | 0.911251i | \(0.364882\pi\) | |||||||
\(920\) | 1.65685 | 0.0546249 | ||||||||
\(921\) | 34.6274 | 1.14101 | ||||||||
\(922\) | −19.4558 | −0.640744 | ||||||||
\(923\) | 32.9706 | 1.08524 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.18377 | −0.269081 | ||||||||
\(926\) | 0.828427 | 0.0272238 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.07107 | −0.297772 | ||||||||
\(929\) | 37.5980 | 1.23355 | 0.616775 | − | 0.787140i | \(-0.288439\pi\) | ||||
0.616775 | + | 0.787140i | \(0.288439\pi\) | |||||||
\(930\) | −3.31371 | −0.108661 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.6569 | −0.381833 | ||||||||
\(933\) | −36.2843 | −1.18789 | ||||||||
\(934\) | −13.1716 | −0.430987 | ||||||||
\(935\) | 2.48528 | 0.0812774 | ||||||||
\(936\) | −4.82843 | −0.157822 | ||||||||
\(937\) | −22.9706 | −0.750416 | −0.375208 | − | 0.926941i | \(-0.622429\pi\) | ||||
−0.375208 | + | 0.926941i | \(0.622429\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.1127 | 1.01532 | ||||||||
\(940\) | 7.51472 | 0.245103 | ||||||||
\(941\) | 26.4437 | 0.862038 | 0.431019 | − | 0.902343i | \(-0.358154\pi\) | ||||
0.431019 | + | 0.902343i | \(0.358154\pi\) | |||||||
\(942\) | 21.1716 | 0.689807 | ||||||||
\(943\) | −16.9706 | −0.552638 | ||||||||
\(944\) | 11.3137 | 0.368230 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.0000 | −1.17046 | ||||||||
\(947\) | −31.5563 | −1.02544 | −0.512722 | − | 0.858555i | \(-0.671363\pi\) | ||||
−0.512722 | + | 0.858555i | \(0.671363\pi\) | |||||||
\(948\) | −6.34315 | −0.206016 | ||||||||
\(949\) | 50.6274 | 1.64344 | ||||||||
\(950\) | 31.7990 | 1.03170 | ||||||||
\(951\) | −15.4558 | −0.501190 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.5980 | −1.08835 | −0.544173 | − | 0.838973i | \(-0.683156\pi\) | ||||
−0.544173 | + | 0.838973i | \(0.683156\pi\) | |||||||
\(954\) | −3.17157 | −0.102683 | ||||||||
\(955\) | 6.62742 | 0.214458 | ||||||||
\(956\) | 13.6569 | 0.441694 | ||||||||
\(957\) | 54.4264 | 1.75936 | ||||||||
\(958\) | −5.17157 | −0.167086 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.828427 | −0.0267374 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 8.48528 | 0.273576 | ||||||||
\(963\) | −4.24264 | −0.136717 | ||||||||
\(964\) | 25.3137 | 0.815300 | ||||||||
\(965\) | −14.5442 | −0.468193 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3431 | 0.332613 | 0.166307 | − | 0.986074i | \(-0.446816\pi\) | ||||
0.166307 | + | 0.986074i | \(0.446816\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 9.65685 | 0.310223 | ||||||||
\(970\) | −8.76955 | −0.281573 | ||||||||
\(971\) | −2.62742 | −0.0843178 | −0.0421589 | − | 0.999111i | \(-0.513424\pi\) | ||||
−0.0421589 | + | 0.999111i | \(0.513424\pi\) | |||||||
\(972\) | −9.89949 | −0.317526 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.14214 | −0.196807 | ||||||||
\(975\) | −31.7990 | −1.01838 | ||||||||
\(976\) | −2.24264 | −0.0717852 | ||||||||
\(977\) | 42.2843 | 1.35279 | 0.676397 | − | 0.736537i | \(-0.263540\pi\) | ||||
0.676397 | + | 0.736537i | \(0.263540\pi\) | |||||||
\(978\) | 6.00000 | 0.191859 | ||||||||
\(979\) | 7.02944 | 0.224662 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.89949 | −0.252211 | ||||||||
\(982\) | −21.6569 | −0.691098 | ||||||||
\(983\) | −25.4558 | −0.811915 | −0.405958 | − | 0.913892i | \(-0.633062\pi\) | ||||
−0.405958 | + | 0.913892i | \(0.633062\pi\) | |||||||
\(984\) | 8.48528 | 0.270501 | ||||||||
\(985\) | −13.0294 | −0.415152 | ||||||||
\(986\) | 9.07107 | 0.288882 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −32.9706 | −1.04893 | ||||||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | −2.48528 | −0.0789874 | ||||||||
\(991\) | −46.4264 | −1.47478 | −0.737392 | − | 0.675465i | \(-0.763943\pi\) | ||||
−0.737392 | + | 0.675465i | \(0.763943\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | 39.3137 | 1.24758 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.40202 | 0.139553 | ||||||||
\(996\) | −8.00000 | −0.253490 | ||||||||
\(997\) | −35.4142 | −1.12158 | −0.560790 | − | 0.827958i | \(-0.689502\pi\) | ||||
−0.560790 | + | 0.827958i | \(0.689502\pi\) | |||||||
\(998\) | −23.5563 | −0.745663 | ||||||||
\(999\) | 9.94113 | 0.314523 |
(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 | 1666.2.a.q.1.1 | yes | 2 | |
7.6 | odd | 2 | 1666.2.a.p.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1666.2.a.p.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
1666.2.a.q.1.1 | yes | 2 | 1.1 | even | 1 | trivial |