Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(197,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.197");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.197 |
Dual form | 882.3.b.i.197.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.41421i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | − 2.00000i | − 0.400000i | −0.979796 | − | 0.200000i | \(-0.935906\pi\) | ||||
0.979796 | − | 0.200000i | \(-0.0640942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.82843 | −0.282843 | ||||||||
\(11\) | 2.82843i | 0.257130i | 0.991701 | + | 0.128565i | \(0.0410371\pi\) | ||||
−0.991701 | + | 0.128565i | \(0.958963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.7279 | 0.979071 | 0.489535 | − | 0.871983i | \(-0.337166\pi\) | ||||
0.489535 | + | 0.871983i | \(0.337166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 22.0000i | 1.29412i | 0.762440 | + | 0.647059i | \(0.224001\pi\) | ||||
−0.762440 | + | 0.647059i | \(0.775999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65685 | −0.297729 | −0.148865 | − | 0.988858i | \(-0.547562\pi\) | ||||
−0.148865 | + | 0.988858i | \(0.547562\pi\) | |||||||
\(20\) | 4.00000i | 0.200000i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.181818 | ||||||||
\(23\) | − 2.82843i | − 0.122975i | −0.998108 | − | 0.0614875i | \(-0.980416\pi\) | ||||
0.998108 | − | 0.0614875i | \(-0.0195844\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 21.0000 | 0.840000 | ||||||||
\(26\) | − 18.0000i | − 0.692308i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 35.3553i | 1.21915i | 0.792729 | + | 0.609575i | \(0.208660\pi\) | ||||
−0.792729 | + | 0.609575i | \(0.791340\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −33.9411 | −1.09488 | −0.547438 | − | 0.836847i | \(-0.684397\pi\) | ||||
−0.547438 | + | 0.836847i | \(0.684397\pi\) | |||||||
\(32\) | − 5.65685i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 31.1127 | 0.915079 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 64.0000 | 1.72973 | 0.864865 | − | 0.502005i | \(-0.167404\pi\) | ||||
0.864865 | + | 0.502005i | \(0.167404\pi\) | |||||||
\(38\) | 8.00000i | 0.210526i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.65685 | 0.141421 | ||||||||
\(41\) | − 20.0000i | − 0.487805i | −0.969800 | − | 0.243902i | \(-0.921572\pi\) | ||||
0.969800 | − | 0.243902i | \(-0.0784277\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 44.0000 | 1.02326 | 0.511628 | − | 0.859207i | \(-0.329043\pi\) | ||||
0.511628 | + | 0.859207i | \(0.329043\pi\) | |||||||
\(44\) | − 5.65685i | − 0.128565i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | −0.0869565 | ||||||||
\(47\) | − 68.0000i | − 1.44681i | −0.690425 | − | 0.723404i | \(-0.742576\pi\) | ||||
0.690425 | − | 0.723404i | \(-0.257424\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 29.6985i | − 0.593970i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −25.4558 | −0.489535 | ||||||||
\(53\) | − 18.3848i | − 0.346883i | −0.984844 | − | 0.173441i | \(-0.944511\pi\) | ||||
0.984844 | − | 0.173441i | \(-0.0554887\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.65685 | 0.102852 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 50.0000 | 0.862069 | ||||||||
\(59\) | 100.000i | 1.69492i | 0.530863 | + | 0.847458i | \(0.321868\pi\) | ||||
−0.530863 | + | 0.847458i | \(0.678132\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 52.3259 | 0.857802 | 0.428901 | − | 0.903352i | \(-0.358901\pi\) | ||||
0.428901 | + | 0.903352i | \(0.358901\pi\) | |||||||
\(62\) | 48.0000i | 0.774194i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − 25.4558i | − 0.391628i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 120.000 | 1.79104 | 0.895522 | − | 0.445016i | \(-0.146802\pi\) | ||||
0.895522 | + | 0.445016i | \(0.146802\pi\) | |||||||
\(68\) | − 44.0000i | − 0.647059i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 8.48528i | − 0.119511i | −0.998213 | − | 0.0597555i | \(-0.980968\pi\) | ||||
0.998213 | − | 0.0597555i | \(-0.0190321\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −74.9533 | −1.02676 | −0.513379 | − | 0.858162i | \(-0.671606\pi\) | ||||
−0.513379 | + | 0.858162i | \(0.671606\pi\) | |||||||
\(74\) | − 90.5097i | − 1.22310i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.3137 | 0.148865 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 92.0000 | 1.16456 | 0.582278 | − | 0.812989i | \(-0.302161\pi\) | ||||
0.582278 | + | 0.812989i | \(0.302161\pi\) | |||||||
\(80\) | − 8.00000i | − 0.100000i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −28.2843 | −0.344930 | ||||||||
\(83\) | − 112.000i | − 1.34940i | −0.738093 | − | 0.674699i | \(-0.764274\pi\) | ||||
0.738093 | − | 0.674699i | \(-0.235726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 44.0000 | 0.517647 | ||||||||
\(86\) | − 62.2254i | − 0.723551i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.00000 | −0.0909091 | ||||||||
\(89\) | 20.0000i | 0.224719i | 0.993668 | + | 0.112360i | \(0.0358408\pi\) | ||||
−0.993668 | + | 0.112360i | \(0.964159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.65685i | 0.0614875i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −96.1665 | −1.02305 | ||||||||
\(95\) | 11.3137i | 0.119092i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −26.8701 | −0.277011 | −0.138505 | − | 0.990362i | \(-0.544230\pi\) | ||||
−0.138505 | + | 0.990362i | \(0.544230\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −42.0000 | −0.420000 | ||||||||
\(101\) | 84.0000i | 0.831683i | 0.909437 | + | 0.415842i | \(0.136513\pi\) | ||||
−0.909437 | + | 0.415842i | \(0.863487\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 158.392 | 1.53779 | 0.768893 | − | 0.639378i | \(-0.220808\pi\) | ||||
0.768893 | + | 0.639378i | \(0.220808\pi\) | |||||||
\(104\) | 36.0000i | 0.346154i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −26.0000 | −0.245283 | ||||||||
\(107\) | − 138.593i | − 1.29526i | −0.761955 | − | 0.647631i | \(-0.775760\pi\) | ||||
0.761955 | − | 0.647631i | \(-0.224240\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 70.0000 | 0.642202 | 0.321101 | − | 0.947045i | \(-0.395947\pi\) | ||||
0.321101 | + | 0.947045i | \(0.395947\pi\) | |||||||
\(110\) | − 8.00000i | − 0.0727273i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 21.2132i | − 0.187727i | −0.995585 | − | 0.0938637i | \(-0.970078\pi\) | ||||
0.995585 | − | 0.0938637i | \(-0.0299218\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.65685 | −0.0491900 | ||||||||
\(116\) | − 70.7107i | − 0.609575i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 141.421 | 1.19849 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 113.000 | 0.933884 | ||||||||
\(122\) | − 74.0000i | − 0.606557i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 67.8823 | 0.547438 | ||||||||
\(125\) | − 92.0000i | − 0.736000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.0000 | −0.157480 | −0.0787402 | − | 0.996895i | \(-0.525090\pi\) | ||||
−0.0787402 | + | 0.996895i | \(0.525090\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −36.0000 | −0.276923 | ||||||||
\(131\) | 144.000i | 1.09924i | 0.835416 | + | 0.549618i | \(0.185227\pi\) | ||||
−0.835416 | + | 0.549618i | \(0.814773\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 169.706i | − 1.26646i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −62.2254 | −0.457540 | ||||||||
\(137\) | 199.404i | 1.45550i | 0.685840 | + | 0.727752i | \(0.259435\pi\) | ||||
−0.685840 | + | 0.727752i | \(0.740565\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.65685 | −0.0406968 | −0.0203484 | − | 0.999793i | \(-0.506478\pi\) | ||||
−0.0203484 | + | 0.999793i | \(0.506478\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0000 | −0.0845070 | ||||||||
\(143\) | 36.0000i | 0.251748i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 70.7107 | 0.487660 | ||||||||
\(146\) | 106.000i | 0.726027i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −128.000 | −0.864865 | ||||||||
\(149\) | − 18.3848i | − 0.123388i | −0.998095 | − | 0.0616939i | \(-0.980350\pi\) | ||||
0.998095 | − | 0.0616939i | \(-0.0196503\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −64.0000 | −0.423841 | −0.211921 | − | 0.977287i | \(-0.567972\pi\) | ||||
−0.211921 | + | 0.977287i | \(0.567972\pi\) | |||||||
\(152\) | − 16.0000i | − 0.105263i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 67.8823i | 0.437950i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −162.635 | −1.03589 | −0.517944 | − | 0.855414i | \(-0.673303\pi\) | ||||
−0.517944 | + | 0.855414i | \(0.673303\pi\) | |||||||
\(158\) | − 130.108i | − 0.823466i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −11.3137 | −0.0707107 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −224.000 | −1.37423 | −0.687117 | − | 0.726547i | \(-0.741124\pi\) | ||||
−0.687117 | + | 0.726547i | \(0.741124\pi\) | |||||||
\(164\) | 40.0000i | 0.243902i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −158.392 | −0.954168 | ||||||||
\(167\) | − 292.000i | − 1.74850i | −0.485473 | − | 0.874251i | \(-0.661353\pi\) | ||||
0.485473 | − | 0.874251i | \(-0.338647\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.0414201 | ||||||||
\(170\) | − 62.2254i | − 0.366032i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −88.0000 | −0.511628 | ||||||||
\(173\) | 156.000i | 0.901734i | 0.892591 | + | 0.450867i | \(0.148885\pi\) | ||||
−0.892591 | + | 0.450867i | \(0.851115\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.3137i | 0.0642824i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 28.2843 | 0.158900 | ||||||||
\(179\) | − 93.3381i | − 0.521442i | −0.965414 | − | 0.260721i | \(-0.916040\pi\) | ||||
0.965414 | − | 0.260721i | \(-0.0839602\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −190.919 | −1.05480 | −0.527400 | − | 0.849617i | \(-0.676833\pi\) | ||||
−0.527400 | + | 0.849617i | \(0.676833\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000 | 0.0434783 | ||||||||
\(185\) | − 128.000i | − 0.691892i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −62.2254 | −0.332756 | ||||||||
\(188\) | 136.000i | 0.723404i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.0000 | 0.0842105 | ||||||||
\(191\) | 132.936i | 0.696000i | 0.937494 | + | 0.348000i | \(0.113139\pi\) | ||||
−0.937494 | + | 0.348000i | \(0.886861\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 122.000 | 0.632124 | 0.316062 | − | 0.948738i | \(-0.397639\pi\) | ||||
0.316062 | + | 0.948738i | \(0.397639\pi\) | |||||||
\(194\) | 38.0000i | 0.195876i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 7.07107i | − 0.0358937i | −0.999839 | − | 0.0179469i | \(-0.994287\pi\) | ||||
0.999839 | − | 0.0179469i | \(-0.00571297\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 373.352 | 1.87614 | 0.938071 | − | 0.346442i | \(-0.112610\pi\) | ||||
0.938071 | + | 0.346442i | \(0.112610\pi\) | |||||||
\(200\) | 59.3970i | 0.296985i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 118.794 | 0.588089 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −40.0000 | −0.195122 | ||||||||
\(206\) | − 224.000i | − 1.08738i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 50.9117 | 0.244768 | ||||||||
\(209\) | − 16.0000i | − 0.0765550i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.0568720 | −0.0284360 | − | 0.999596i | \(-0.509053\pi\) | ||||
−0.0284360 | + | 0.999596i | \(0.509053\pi\) | |||||||
\(212\) | 36.7696i | 0.173441i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −196.000 | −0.915888 | ||||||||
\(215\) | − 88.0000i | − 0.409302i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 98.9949i | − 0.454105i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −11.3137 | −0.0514259 | ||||||||
\(221\) | 280.014i | 1.26703i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −203.647 | −0.913214 | −0.456607 | − | 0.889668i | \(-0.650935\pi\) | ||||
−0.456607 | + | 0.889668i | \(0.650935\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −30.0000 | −0.132743 | ||||||||
\(227\) | 204.000i | 0.898678i | 0.893361 | + | 0.449339i | \(0.148341\pi\) | ||||
−0.893361 | + | 0.449339i | \(0.851659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −46.6690 | −0.203795 | −0.101897 | − | 0.994795i | \(-0.532491\pi\) | ||||
−0.101897 | + | 0.994795i | \(0.532491\pi\) | |||||||
\(230\) | 8.00000i | 0.0347826i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −100.000 | −0.431034 | ||||||||
\(233\) | 309.713i | 1.32924i | 0.747182 | + | 0.664620i | \(0.231406\pi\) | ||||
−0.747182 | + | 0.664620i | \(0.768594\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −136.000 | −0.578723 | ||||||||
\(236\) | − 200.000i | − 0.847458i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 42.4264i | 0.177516i | 0.996053 | + | 0.0887582i | \(0.0282898\pi\) | ||||
−0.996053 | + | 0.0887582i | \(0.971710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 377.595 | 1.56678 | 0.783392 | − | 0.621528i | \(-0.213488\pi\) | ||||
0.783392 | + | 0.621528i | \(0.213488\pi\) | |||||||
\(242\) | − 159.806i | − 0.660356i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −104.652 | −0.428901 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −72.0000 | −0.291498 | ||||||||
\(248\) | − 96.0000i | − 0.387097i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −130.108 | −0.520431 | ||||||||
\(251\) | 332.000i | 1.32271i | 0.750073 | + | 0.661355i | \(0.230018\pi\) | ||||
−0.750073 | + | 0.661355i | \(0.769982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.0316206 | ||||||||
\(254\) | 28.2843i | 0.111355i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 180.000i | 0.700389i | 0.936677 | + | 0.350195i | \(0.113885\pi\) | ||||
−0.936677 | + | 0.350195i | \(0.886115\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 50.9117i | 0.195814i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 203.647 | 0.777278 | ||||||||
\(263\) | 161.220i | 0.613005i | 0.951870 | + | 0.306503i | \(0.0991588\pi\) | ||||
−0.951870 | + | 0.306503i | \(0.900841\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −36.7696 | −0.138753 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −240.000 | −0.895522 | ||||||||
\(269\) | − 526.000i | − 1.95539i | −0.210029 | − | 0.977695i | \(-0.567356\pi\) | ||||
0.210029 | − | 0.977695i | \(-0.432644\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −429.921 | −1.58642 | −0.793212 | − | 0.608946i | \(-0.791593\pi\) | ||||
−0.793212 | + | 0.608946i | \(0.791593\pi\) | |||||||
\(272\) | 88.0000i | 0.323529i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 282.000 | 1.02920 | ||||||||
\(275\) | 59.3970i | 0.215989i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 64.0000 | 0.231047 | 0.115523 | − | 0.993305i | \(-0.463145\pi\) | ||||
0.115523 | + | 0.993305i | \(0.463145\pi\) | |||||||
\(278\) | 8.00000i | 0.0287770i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 448.306i | 1.59539i | 0.603058 | + | 0.797697i | \(0.293949\pi\) | ||||
−0.603058 | + | 0.797697i | \(0.706051\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 124.451 | 0.439755 | 0.219878 | − | 0.975527i | \(-0.429434\pi\) | ||||
0.219878 | + | 0.975527i | \(0.429434\pi\) | |||||||
\(284\) | 16.9706i | 0.0597555i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 50.9117 | 0.178013 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −195.000 | −0.674740 | ||||||||
\(290\) | − 100.000i | − 0.344828i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 149.907 | 0.513379 | ||||||||
\(293\) | 284.000i | 0.969283i | 0.874713 | + | 0.484642i | \(0.161050\pi\) | ||||
−0.874713 | + | 0.484642i | \(0.838950\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 200.000 | 0.677966 | ||||||||
\(296\) | 181.019i | 0.611552i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.0000 | −0.0872483 | ||||||||
\(299\) | − 36.0000i | − 0.120401i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 90.5097i | 0.299701i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −22.6274 | −0.0744323 | ||||||||
\(305\) | − 104.652i | − 0.343121i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −282.843 | −0.921312 | −0.460656 | − | 0.887579i | \(-0.652386\pi\) | ||||
−0.460656 | + | 0.887579i | \(0.652386\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 96.0000 | 0.309677 | ||||||||
\(311\) | 188.000i | 0.604502i | 0.953228 | + | 0.302251i | \(0.0977380\pi\) | ||||
−0.953228 | + | 0.302251i | \(0.902262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −216.375 | −0.691293 | −0.345646 | − | 0.938365i | \(-0.612340\pi\) | ||||
−0.345646 | + | 0.938365i | \(0.612340\pi\) | |||||||
\(314\) | 230.000i | 0.732484i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −184.000 | −0.582278 | ||||||||
\(317\) | 456.791i | 1.44098i | 0.693465 | + | 0.720491i | \(0.256083\pi\) | ||||
−0.693465 | + | 0.720491i | \(0.743917\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −100.000 | −0.313480 | ||||||||
\(320\) | 16.0000i | 0.0500000i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 124.451i | − 0.385297i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 267.286 | 0.822420 | ||||||||
\(326\) | 316.784i | 0.971730i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 56.5685 | 0.172465 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −500.000 | −1.51057 | −0.755287 | − | 0.655394i | \(-0.772503\pi\) | ||||
−0.755287 | + | 0.655394i | \(0.772503\pi\) | |||||||
\(332\) | 224.000i | 0.674699i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −412.950 | −1.23638 | ||||||||
\(335\) | − 240.000i | − 0.716418i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 86.0000 | 0.255193 | 0.127596 | − | 0.991826i | \(-0.459274\pi\) | ||||
0.127596 | + | 0.991826i | \(0.459274\pi\) | |||||||
\(338\) | 9.89949i | 0.0292884i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −88.0000 | −0.258824 | ||||||||
\(341\) | − 96.0000i | − 0.281525i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 124.451i | 0.361776i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 220.617 | 0.637622 | ||||||||
\(347\) | 246.073i | 0.709145i | 0.935029 | + | 0.354572i | \(0.115374\pi\) | ||||
−0.935029 | + | 0.354572i | \(0.884626\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 445.477 | 1.27644 | 0.638220 | − | 0.769854i | \(-0.279671\pi\) | ||||
0.638220 | + | 0.769854i | \(0.279671\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.0000 | 0.0454545 | ||||||||
\(353\) | − 218.000i | − 0.617564i | −0.951133 | − | 0.308782i | \(-0.900079\pi\) | ||||
0.951133 | − | 0.308782i | \(-0.0999213\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.9706 | −0.0478044 | ||||||||
\(356\) | − 40.0000i | − 0.112360i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −132.000 | −0.368715 | ||||||||
\(359\) | − 370.524i | − 1.03210i | −0.856558 | − | 0.516050i | \(-0.827402\pi\) | ||||
0.856558 | − | 0.516050i | \(-0.172598\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −329.000 | −0.911357 | ||||||||
\(362\) | 270.000i | 0.745856i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 149.907i | 0.410703i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 446.891 | 1.21769 | 0.608844 | − | 0.793290i | \(-0.291634\pi\) | ||||
0.608844 | + | 0.793290i | \(0.291634\pi\) | |||||||
\(368\) | − 11.3137i | − 0.0307438i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −181.019 | −0.489241 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 286.000 | 0.766756 | 0.383378 | − | 0.923592i | \(-0.374761\pi\) | ||||
0.383378 | + | 0.923592i | \(0.374761\pi\) | |||||||
\(374\) | 88.0000i | 0.235294i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 192.333 | 0.511524 | ||||||||
\(377\) | 450.000i | 1.19363i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −188.000 | −0.496042 | −0.248021 | − | 0.968755i | \(-0.579780\pi\) | ||||
−0.248021 | + | 0.968755i | \(0.579780\pi\) | |||||||
\(380\) | − 22.6274i | − 0.0595458i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 188.000 | 0.492147 | ||||||||
\(383\) | − 352.000i | − 0.919060i | −0.888162 | − | 0.459530i | \(-0.848018\pi\) | ||||
0.888162 | − | 0.459530i | \(-0.151982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 172.534i | − 0.446979i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 53.7401 | 0.138505 | ||||||||
\(389\) | 205.061i | 0.527149i | 0.964639 | + | 0.263575i | \(0.0849015\pi\) | ||||
−0.964639 | + | 0.263575i | \(0.915099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 62.2254 | 0.159144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.0000 | −0.0253807 | ||||||||
\(395\) | − 184.000i | − 0.465823i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 244.659 | 0.616269 | 0.308135 | − | 0.951343i | \(-0.400295\pi\) | ||||
0.308135 | + | 0.951343i | \(0.400295\pi\) | |||||||
\(398\) | − 528.000i | − 1.32663i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 84.0000 | 0.210000 | ||||||||
\(401\) | 445.477i | 1.11092i | 0.831545 | + | 0.555458i | \(0.187457\pi\) | ||||
−0.831545 | + | 0.555458i | \(0.812543\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −432.000 | −1.07196 | ||||||||
\(404\) | − 168.000i | − 0.415842i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 181.019i | 0.444765i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −750.947 | −1.83606 | −0.918029 | − | 0.396514i | \(-0.870220\pi\) | ||||
−0.918029 | + | 0.396514i | \(0.870220\pi\) | |||||||
\(410\) | 56.5685i | 0.137972i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −316.784 | −0.768893 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −224.000 | −0.539759 | ||||||||
\(416\) | − 72.0000i | − 0.173077i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.6274 | −0.0541326 | ||||||||
\(419\) | − 236.000i | − 0.563246i | −0.959525 | − | 0.281623i | \(-0.909127\pi\) | ||||
0.959525 | − | 0.281623i | \(-0.0908727\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −96.0000 | −0.228029 | −0.114014 | − | 0.993479i | \(-0.536371\pi\) | ||||
−0.114014 | + | 0.993479i | \(0.536371\pi\) | |||||||
\(422\) | 16.9706i | 0.0402146i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 52.0000 | 0.122642 | ||||||||
\(425\) | 462.000i | 1.08706i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 277.186i | 0.647631i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −124.451 | −0.289420 | ||||||||
\(431\) | − 857.013i | − 1.98843i | −0.107407 | − | 0.994215i | \(-0.534255\pi\) | ||||
0.107407 | − | 0.994215i | \(-0.465745\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 156.978 | 0.362535 | 0.181268 | − | 0.983434i | \(-0.441980\pi\) | ||||
0.181268 | + | 0.983434i | \(0.441980\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −140.000 | −0.321101 | ||||||||
\(437\) | 16.0000i | 0.0366133i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −644.881 | −1.46898 | −0.734489 | − | 0.678621i | \(-0.762578\pi\) | ||||
−0.734489 | + | 0.678621i | \(0.762578\pi\) | |||||||
\(440\) | 16.0000i | 0.0363636i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 396.000 | 0.895928 | ||||||||
\(443\) | − 579.828i | − 1.30887i | −0.756120 | − | 0.654433i | \(-0.772907\pi\) | ||||
0.756120 | − | 0.654433i | \(-0.227093\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 40.0000 | 0.0898876 | ||||||||
\(446\) | 288.000i | 0.645740i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 869.741i | − 1.93706i | −0.248891 | − | 0.968532i | \(-0.580066\pi\) | ||||
0.248891 | − | 0.968532i | \(-0.419934\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 56.5685 | 0.125429 | ||||||||
\(452\) | 42.4264i | 0.0938637i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 288.500 | 0.635462 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 384.000 | 0.840263 | 0.420131 | − | 0.907463i | \(-0.361984\pi\) | ||||
0.420131 | + | 0.907463i | \(0.361984\pi\) | |||||||
\(458\) | 66.0000i | 0.144105i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.3137 | 0.0245950 | ||||||||
\(461\) | − 268.000i | − 0.581345i | −0.956823 | − | 0.290672i | \(-0.906121\pi\) | ||||
0.956823 | − | 0.290672i | \(-0.0938790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −716.000 | −1.54644 | −0.773218 | − | 0.634140i | \(-0.781354\pi\) | ||||
−0.773218 | + | 0.634140i | \(0.781354\pi\) | |||||||
\(464\) | 141.421i | 0.304787i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 438.000 | 0.939914 | ||||||||
\(467\) | − 308.000i | − 0.659529i | −0.944063 | − | 0.329764i | \(-0.893031\pi\) | ||||
0.944063 | − | 0.329764i | \(-0.106969\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 192.333i | 0.409219i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −282.843 | −0.599243 | ||||||||
\(473\) | 124.451i | 0.263109i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −118.794 | −0.250093 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 60.0000 | 0.125523 | ||||||||
\(479\) | 388.000i | 0.810021i | 0.914312 | + | 0.405010i | \(0.132732\pi\) | ||||
−0.914312 | + | 0.405010i | \(0.867268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 814.587 | 1.69353 | ||||||||
\(482\) | − 534.000i | − 1.10788i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −226.000 | −0.466942 | ||||||||
\(485\) | 53.7401i | 0.110804i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 120.000 | 0.246407 | 0.123203 | − | 0.992381i | \(-0.460683\pi\) | ||||
0.123203 | + | 0.992381i | \(0.460683\pi\) | |||||||
\(488\) | 148.000i | 0.303279i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 619.426i | − 1.26156i | −0.775962 | − | 0.630780i | \(-0.782735\pi\) | ||||
0.775962 | − | 0.630780i | \(-0.217265\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −777.817 | −1.57772 | ||||||||
\(494\) | 101.823i | 0.206120i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −135.765 | −0.273719 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 476.000 | 0.953908 | 0.476954 | − | 0.878928i | \(-0.341741\pi\) | ||||
0.476954 | + | 0.878928i | \(0.341741\pi\) | |||||||
\(500\) | 184.000i | 0.368000i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 469.519 | 0.935297 | ||||||||
\(503\) | 968.000i | 1.92445i | 0.272250 | + | 0.962227i | \(0.412232\pi\) | ||||
−0.272250 | + | 0.962227i | \(0.587768\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 168.000 | 0.332673 | ||||||||
\(506\) | − 11.3137i | − 0.0223591i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 40.0000 | 0.0787402 | ||||||||
\(509\) | 254.000i | 0.499018i | 0.968373 | + | 0.249509i | \(0.0802692\pi\) | ||||
−0.968373 | + | 0.249509i | \(0.919731\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 22.6274i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 254.558 | 0.495250 | ||||||||
\(515\) | − 316.784i | − 0.615114i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 192.333 | 0.372017 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 72.0000 | 0.138462 | ||||||||
\(521\) | − 806.000i | − 1.54702i | −0.633781 | − | 0.773512i | \(-0.718498\pi\) | ||||
0.633781 | − | 0.773512i | \(-0.281502\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 610.940 | 1.16815 | 0.584073 | − | 0.811701i | \(-0.301458\pi\) | ||||
0.584073 | + | 0.811701i | \(0.301458\pi\) | |||||||
\(524\) | − 288.000i | − 0.549618i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 228.000 | 0.433460 | ||||||||
\(527\) | − 746.705i | − 1.41690i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 521.000 | 0.984877 | ||||||||
\(530\) | 52.0000i | 0.0981132i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 254.558i | − 0.477596i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −277.186 | −0.518104 | ||||||||
\(536\) | 339.411i | 0.633230i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −743.876 | −1.38267 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −80.0000 | −0.147874 | −0.0739372 | − | 0.997263i | \(-0.523556\pi\) | ||||
−0.0739372 | + | 0.997263i | \(0.523556\pi\) | |||||||
\(542\) | 608.000i | 1.12177i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 124.451 | 0.228770 | ||||||||
\(545\) | − 140.000i | − 0.256881i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 256.000 | 0.468007 | 0.234004 | − | 0.972236i | \(-0.424817\pi\) | ||||
0.234004 | + | 0.972236i | \(0.424817\pi\) | |||||||
\(548\) | − 398.808i | − 0.727752i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 84.0000 | 0.152727 | ||||||||
\(551\) | − 200.000i | − 0.362976i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 90.5097i | − 0.163375i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.3137 | 0.0203484 | ||||||||
\(557\) | − 784.889i | − 1.40914i | −0.709637 | − | 0.704568i | \(-0.751141\pi\) | ||||
0.709637 | − | 0.704568i | \(-0.248859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 560.029 | 1.00184 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 634.000 | 1.12811 | ||||||||
\(563\) | 604.000i | 1.07282i | 0.843956 | + | 0.536412i | \(0.180221\pi\) | ||||
−0.843956 | + | 0.536412i | \(0.819779\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −42.4264 | −0.0750910 | ||||||||
\(566\) | − 176.000i | − 0.310954i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.0000 | 0.0422535 | ||||||||
\(569\) | − 434.164i | − 0.763029i | −0.924363 | − | 0.381515i | \(-0.875403\pi\) | ||||
0.924363 | − | 0.381515i | \(-0.124597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −248.000 | −0.434326 | −0.217163 | − | 0.976135i | \(-0.569680\pi\) | ||||
−0.217163 | + | 0.976135i | \(0.569680\pi\) | |||||||
\(572\) | − 72.0000i | − 0.125874i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 59.3970i | − 0.103299i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −767.918 | −1.33088 | −0.665440 | − | 0.746451i | \(-0.731756\pi\) | ||||
−0.665440 | + | 0.746451i | \(0.731756\pi\) | |||||||
\(578\) | 275.772i | 0.477114i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −141.421 | −0.243830 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.0000 | 0.0891938 | ||||||||
\(584\) | − 212.000i | − 0.363014i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 401.637 | 0.685387 | ||||||||
\(587\) | − 1140.00i | − 1.94208i | −0.238920 | − | 0.971039i | \(-0.576793\pi\) | ||||
0.238920 | − | 0.971039i | \(-0.423207\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 192.000 | 0.325976 | ||||||||
\(590\) | − 282.843i | − 0.479394i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 256.000 | 0.432432 | ||||||||
\(593\) | − 682.000i | − 1.15008i | −0.818124 | − | 0.575042i | \(-0.804986\pi\) | ||||
0.818124 | − | 0.575042i | \(-0.195014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36.7696i | 0.0616939i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −50.9117 | −0.0851366 | ||||||||
\(599\) | − 1055.00i | − 1.76127i | −0.473791 | − | 0.880637i | \(-0.657115\pi\) | ||||
0.473791 | − | 0.880637i | \(-0.342885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 555.786 | 0.924769 | 0.462384 | − | 0.886680i | \(-0.346994\pi\) | ||||
0.462384 | + | 0.886680i | \(0.346994\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 128.000 | 0.211921 | ||||||||
\(605\) | − 226.000i | − 0.373554i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 424.264 | 0.698952 | 0.349476 | − | 0.936945i | \(-0.386360\pi\) | ||||
0.349476 | + | 0.936945i | \(0.386360\pi\) | |||||||
\(608\) | 32.0000i | 0.0526316i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −148.000 | −0.242623 | ||||||||
\(611\) | − 865.499i | − 1.41653i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 312.000 | 0.508972 | 0.254486 | − | 0.967076i | \(-0.418094\pi\) | ||||
0.254486 | + | 0.967076i | \(0.418094\pi\) | |||||||
\(614\) | 400.000i | 0.651466i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 490.732i | 0.795352i | 0.917526 | + | 0.397676i | \(0.130183\pi\) | ||||
−0.917526 | + | 0.397676i | \(0.869817\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −277.186 | −0.447796 | −0.223898 | − | 0.974613i | \(-0.571878\pi\) | ||||
−0.223898 | + | 0.974613i | \(0.571878\pi\) | |||||||
\(620\) | − 135.765i | − 0.218975i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 265.872 | 0.427447 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 341.000 | 0.545600 | ||||||||
\(626\) | 306.000i | 0.488818i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 325.269 | 0.517944 | ||||||||
\(629\) | 1408.00i | 2.23847i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −316.000 | −0.500792 | −0.250396 | − | 0.968143i | \(-0.580561\pi\) | ||||
−0.250396 | + | 0.968143i | \(0.580561\pi\) | |||||||
\(632\) | 260.215i | 0.411733i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 646.000 | 1.01893 | ||||||||
\(635\) | 40.0000i | 0.0629921i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 141.421i | 0.221664i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 22.6274 | 0.0353553 | ||||||||
\(641\) | 434.164i | 0.677322i | 0.940908 | + | 0.338661i | \(0.109974\pi\) | ||||
−0.940908 | + | 0.338661i | \(0.890026\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −158.392 | −0.246333 | −0.123166 | − | 0.992386i | \(-0.539305\pi\) | ||||
−0.123166 | + | 0.992386i | \(0.539305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −176.000 | −0.272446 | ||||||||
\(647\) | 876.000i | 1.35394i | 0.736010 | + | 0.676971i | \(0.236708\pi\) | ||||
−0.736010 | + | 0.676971i | \(0.763292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −282.843 | −0.435813 | ||||||||
\(650\) | − 378.000i | − 0.581538i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 448.000 | 0.687117 | ||||||||
\(653\) | 292.742i | 0.448304i | 0.974554 | + | 0.224152i | \(0.0719611\pi\) | ||||
−0.974554 | + | 0.224152i | \(0.928039\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 288.000 | 0.439695 | ||||||||
\(656\) | − 80.0000i | − 0.121951i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 907.925i | − 1.37773i | −0.724889 | − | 0.688866i | \(-0.758109\pi\) | ||||
0.724889 | − | 0.688866i | \(-0.241891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −784.889 | −1.18743 | −0.593713 | − | 0.804677i | \(-0.702339\pi\) | ||||
−0.593713 | + | 0.804677i | \(0.702339\pi\) | |||||||
\(662\) | 707.107i | 1.06814i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 316.784 | 0.477084 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 100.000 | 0.149925 | ||||||||
\(668\) | 584.000i | 0.874251i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −339.411 | −0.506584 | ||||||||
\(671\) | 148.000i | 0.220566i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −264.000 | −0.392273 | −0.196137 | − | 0.980577i | \(-0.562840\pi\) | ||||
−0.196137 | + | 0.980577i | \(0.562840\pi\) | |||||||
\(674\) | − 121.622i | − 0.180449i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.0000 | 0.0207101 | ||||||||
\(677\) | 300.000i | 0.443131i | 0.975145 | + | 0.221566i | \(0.0711167\pi\) | ||||
−0.975145 | + | 0.221566i | \(0.928883\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 124.451i | 0.183016i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −135.765 | −0.199068 | ||||||||
\(683\) | − 1162.48i | − 1.70203i | −0.525145 | − | 0.851013i | \(-0.675989\pi\) | ||||
0.525145 | − | 0.851013i | \(-0.324011\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 398.808 | 0.582202 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 176.000 | 0.255814 | ||||||||
\(689\) | − 234.000i | − 0.339623i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −509.117 | −0.736783 | −0.368391 | − | 0.929671i | \(-0.620091\pi\) | ||||
−0.368391 | + | 0.929671i | \(0.620091\pi\) | |||||||
\(692\) | − 312.000i | − 0.450867i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 348.000 | 0.501441 | ||||||||
\(695\) | 11.3137i | 0.0162787i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 440.000 | 0.631277 | ||||||||
\(698\) | − 630.000i | − 0.902579i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 182.434i | − 0.260248i | −0.991498 | − | 0.130124i | \(-0.958463\pi\) | ||||
0.991498 | − | 0.130124i | \(-0.0415375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −362.039 | −0.514991 | ||||||||
\(704\) | − 22.6274i | − 0.0321412i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −308.299 | −0.436684 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1318.00 | 1.85896 | 0.929478 | − | 0.368877i | \(-0.120258\pi\) | ||||
0.929478 | + | 0.368877i | \(0.120258\pi\) | |||||||
\(710\) | 24.0000i | 0.0338028i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −56.5685 | −0.0794502 | ||||||||
\(713\) | 96.0000i | 0.134642i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 72.0000 | 0.100699 | ||||||||
\(716\) | 186.676i | 0.260721i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −524.000 | −0.729805 | ||||||||
\(719\) | − 1016.00i | − 1.41307i | −0.707676 | − | 0.706537i | \(-0.750256\pi\) | ||||
0.707676 | − | 0.706537i | \(-0.249744\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 465.276i | 0.644427i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 381.838 | 0.527400 | ||||||||
\(725\) | 742.462i | 1.02409i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 384.666 | 0.529114 | 0.264557 | − | 0.964370i | \(-0.414774\pi\) | ||||
0.264557 | + | 0.964370i | \(0.414774\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 212.000 | 0.290411 | ||||||||
\(731\) | 968.000i | 1.32421i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 555.786 | 0.758235 | 0.379117 | − | 0.925349i | \(-0.376228\pi\) | ||||
0.379117 | + | 0.925349i | \(0.376228\pi\) | |||||||
\(734\) | − 632.000i | − 0.861035i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.0000 | −0.0217391 | ||||||||
\(737\) | 339.411i | 0.460531i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1200.00 | −1.62382 | −0.811908 | − | 0.583785i | \(-0.801571\pi\) | ||||
−0.811908 | + | 0.583785i | \(0.801571\pi\) | |||||||
\(740\) | 256.000i | 0.345946i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1309.56i | 1.76253i | 0.472620 | + | 0.881266i | \(0.343308\pi\) | ||||
−0.472620 | + | 0.881266i | \(0.656692\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.7696 | −0.0493551 | ||||||||
\(746\) | − 404.465i | − 0.542178i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 124.451 | 0.166378 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −568.000 | −0.756325 | −0.378162 | − | 0.925739i | \(-0.623444\pi\) | ||||
−0.378162 | + | 0.925739i | \(0.623444\pi\) | |||||||
\(752\) | − 272.000i | − 0.361702i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 636.396 | 0.844027 | ||||||||
\(755\) | 128.000i | 0.169536i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −358.000 | −0.472919 | −0.236460 | − | 0.971641i | \(-0.575987\pi\) | ||||
−0.236460 | + | 0.971641i | \(0.575987\pi\) | |||||||
\(758\) | 265.872i | 0.350755i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −32.0000 | −0.0421053 | ||||||||
\(761\) | − 508.000i | − 0.667543i | −0.942654 | − | 0.333771i | \(-0.891679\pi\) | ||||
0.942654 | − | 0.333771i | \(-0.108321\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 265.872i | − 0.348000i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −497.803 | −0.649874 | ||||||||
\(767\) | 1272.79i | 1.65944i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 861.256 | 1.11997 | 0.559984 | − | 0.828503i | \(-0.310807\pi\) | ||||
0.559984 | + | 0.828503i | \(0.310807\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −244.000 | −0.316062 | ||||||||
\(773\) | − 892.000i | − 1.15395i | −0.816763 | − | 0.576973i | \(-0.804234\pi\) | ||||
0.816763 | − | 0.576973i | \(-0.195766\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −712.764 | −0.919695 | ||||||||
\(776\) | − 76.0000i | − 0.0979381i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 290.000 | 0.372751 | ||||||||
\(779\) | 113.137i | 0.145234i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.0307298 | ||||||||
\(782\) | − 88.0000i | − 0.112532i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 325.269i | 0.414356i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 429.921 | 0.546278 | 0.273139 | − | 0.961975i | \(-0.411938\pi\) | ||||
0.273139 | + | 0.961975i | \(0.411938\pi\) | |||||||
\(788\) | 14.1421i | 0.0179469i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −260.215 | −0.329386 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 666.000 | 0.839849 | ||||||||
\(794\) | − 346.000i | − 0.435768i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −746.705 | −0.938071 | ||||||||
\(797\) | − 540.000i | − 0.677541i | −0.940869 | − | 0.338770i | \(-0.889989\pi\) | ||||
0.940869 | − | 0.338770i | \(-0.110011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1496.00 | 1.87234 | ||||||||
\(800\) | − 118.794i | − 0.148492i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 630.000 | 0.785536 | ||||||||
\(803\) | − 212.000i | − 0.264010i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 610.940i | 0.757990i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −237.588 | −0.294044 | ||||||||
\(809\) | − 872.570i | − 1.07858i | −0.842121 | − | 0.539289i | \(-0.818693\pi\) | ||||
0.842121 | − | 0.539289i | \(-0.181307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −492.146 | −0.606839 | −0.303419 | − | 0.952857i | \(-0.598128\pi\) | ||||
−0.303419 | + | 0.952857i | \(0.598128\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 256.000 | 0.314496 | ||||||||
\(815\) | 448.000i | 0.549693i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −248.902 | −0.304653 | ||||||||
\(818\) | 1062.00i | 1.29829i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 80.0000 | 0.0975610 | ||||||||
\(821\) | 750.947i | 0.914674i | 0.889293 | + | 0.457337i | \(0.151197\pi\) | ||||
−0.889293 | + | 0.457337i | \(0.848803\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −116.000 | −0.140948 | −0.0704739 | − | 0.997514i | \(-0.522451\pi\) | ||||
−0.0704739 | + | 0.997514i | \(0.522451\pi\) | |||||||
\(824\) | 448.000i | 0.543689i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 873.984i | − 1.05681i | −0.848992 | − | 0.528406i | \(-0.822790\pi\) | ||||
0.848992 | − | 0.528406i | \(-0.177210\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 272.943 | 0.329244 | 0.164622 | − | 0.986357i | \(-0.447360\pi\) | ||||
0.164622 | + | 0.986357i | \(0.447360\pi\) | |||||||
\(830\) | 316.784i | 0.381667i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −101.823 | −0.122384 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −584.000 | −0.699401 | ||||||||
\(836\) | 32.0000i | 0.0382775i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −333.754 | −0.398275 | ||||||||
\(839\) | − 188.000i | − 0.224076i | −0.993704 | − | 0.112038i | \(-0.964262\pi\) | ||||
0.993704 | − | 0.112038i | \(-0.0357379\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −409.000 | −0.486326 | ||||||||
\(842\) | 135.765i | 0.161241i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.0000 | 0.0284360 | ||||||||
\(845\) | 14.0000i | 0.0165680i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 73.5391i | − 0.0867206i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 653.367 | 0.768667 | ||||||||
\(851\) | − 181.019i | − 0.212714i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 63.6396 | 0.0746068 | 0.0373034 | − | 0.999304i | \(-0.488123\pi\) | ||||
0.0373034 | + | 0.999304i | \(0.488123\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 392.000 | 0.457944 | ||||||||
\(857\) | 260.000i | 0.303384i | 0.988428 | + | 0.151692i | \(0.0484722\pi\) | ||||
−0.988428 | + | 0.151692i | \(0.951528\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −791.960 | −0.921955 | −0.460978 | − | 0.887412i | \(-0.652501\pi\) | ||||
−0.460978 | + | 0.887412i | \(0.652501\pi\) | |||||||
\(860\) | 176.000i | 0.204651i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1212.00 | −1.40603 | ||||||||
\(863\) | 421.436i | 0.488338i | 0.969733 | + | 0.244169i | \(0.0785152\pi\) | ||||
−0.969733 | + | 0.244169i | \(0.921485\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 312.000 | 0.360694 | ||||||||
\(866\) | − 222.000i | − 0.256351i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 260.215i | 0.299442i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1527.35 | 1.75356 | ||||||||
\(872\) | 197.990i | 0.227053i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22.6274 | 0.0258895 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −952.000 | −1.08552 | −0.542759 | − | 0.839888i | \(-0.682620\pi\) | ||||
−0.542759 | + | 0.839888i | \(0.682620\pi\) | |||||||
\(878\) | 912.000i | 1.03872i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22.6274 | 0.0257130 | ||||||||
\(881\) | 1158.00i | 1.31442i | 0.753710 | + | 0.657208i | \(0.228263\pi\) | ||||
−0.753710 | + | 0.657208i | \(0.771737\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1036.00 | −1.17327 | −0.586636 | − | 0.809850i | \(-0.699548\pi\) | ||||
−0.586636 | + | 0.809850i | \(0.699548\pi\) | |||||||
\(884\) | − 560.029i | − 0.633516i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −820.000 | −0.925508 | ||||||||
\(887\) | − 460.000i | − 0.518602i | −0.965797 | − | 0.259301i | \(-0.916508\pi\) | ||||
0.965797 | − | 0.259301i | \(-0.0834922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 56.5685i | − 0.0635602i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 407.294 | 0.456607 | ||||||||
\(893\) | 384.666i | 0.430757i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −186.676 | −0.208577 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1230.00 | −1.36971 | ||||||||
\(899\) | − 1200.00i | − 1.33482i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 404.465 | 0.448907 | ||||||||
\(902\) | − 80.0000i | − 0.0886918i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 60.0000 | 0.0663717 | ||||||||
\(905\) | 381.838i | 0.421920i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 220.000 | 0.242558 | 0.121279 | − | 0.992618i | \(-0.461300\pi\) | ||||
0.121279 | + | 0.992618i | \(0.461300\pi\) | |||||||
\(908\) | − 408.000i | − 0.449339i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1049.35i | 1.15186i | 0.817498 | + | 0.575931i | \(0.195360\pi\) | ||||
−0.817498 | + | 0.575931i | \(0.804640\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 316.784 | 0.346970 | ||||||||
\(914\) | − 543.058i | − 0.594155i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 93.3381 | 0.101897 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −320.000 | −0.348205 | −0.174102 | − | 0.984728i | \(-0.555702\pi\) | ||||
−0.174102 | + | 0.984728i | \(0.555702\pi\) | |||||||
\(920\) | − 16.0000i | − 0.0173913i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −379.009 | −0.411073 | ||||||||
\(923\) | − 108.000i | − 0.117010i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1344.00 | 1.45297 | ||||||||
\(926\) | 1012.58i | 1.09350i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 200.000 | 0.215517 | ||||||||
\(929\) | 1756.00i | 1.89020i | 0.326775 | + | 0.945102i | \(0.394038\pi\) | ||||
−0.326775 | + | 0.945102i | \(0.605962\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 619.426i | − 0.664620i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −435.578 | −0.466357 | ||||||||
\(935\) | 124.451i | 0.133102i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1740.90 | −1.85795 | −0.928974 | − | 0.370145i | \(-0.879308\pi\) | ||||
−0.928974 | + | 0.370145i | \(0.879308\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 272.000 | 0.289362 | ||||||||
\(941\) | − 626.000i | − 0.665250i | −0.943059 | − | 0.332625i | \(-0.892066\pi\) | ||||
0.943059 | − | 0.332625i | \(-0.107934\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56.5685 | −0.0599878 | ||||||||
\(944\) | 400.000i | 0.423729i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 176.000 | 0.186047 | ||||||||
\(947\) | − 789.131i | − 0.833296i | −0.909068 | − | 0.416648i | \(-0.863205\pi\) | ||||
0.909068 | − | 0.416648i | \(-0.136795\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −954.000 | −1.00527 | ||||||||
\(950\) | 168.000i | 0.176842i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 193.747i | 0.203302i | 0.994820 | + | 0.101651i | \(0.0324126\pi\) | ||||
−0.994820 | + | 0.101651i | \(0.967587\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 265.872 | 0.278400 | ||||||||
\(956\) | − 84.8528i | − 0.0887582i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 548.715 | 0.572771 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 191.000 | 0.198751 | ||||||||
\(962\) | − 1152.00i | − 1.19751i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −755.190 | −0.783392 | ||||||||
\(965\) | − 244.000i | − 0.252850i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 132.000 | 0.136505 | 0.0682523 | − | 0.997668i | \(-0.478258\pi\) | ||||
0.0682523 | + | 0.997668i | \(0.478258\pi\) | |||||||
\(968\) | 319.612i | 0.330178i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 76.0000 | 0.0783505 | ||||||||
\(971\) | 160.000i | 0.164779i | 0.996600 | + | 0.0823893i | \(0.0262551\pi\) | ||||
−0.996600 | + | 0.0823893i | \(0.973745\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 169.706i | − 0.174236i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 209.304 | 0.214450 | ||||||||
\(977\) | 1497.65i | 1.53291i | 0.642299 | + | 0.766455i | \(0.277981\pi\) | ||||
−0.642299 | + | 0.766455i | \(0.722019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −56.5685 | −0.0577820 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −876.000 | −0.892057 | ||||||||
\(983\) | − 328.000i | − 0.333672i | −0.985985 | − | 0.166836i | \(-0.946645\pi\) | ||||
0.985985 | − | 0.166836i | \(-0.0533551\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.1421 | −0.0143575 | ||||||||
\(986\) | 1100.00i | 1.11562i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 144.000 | 0.145749 | ||||||||
\(989\) | − 124.451i | − 0.125835i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.0161453 | −0.00807265 | − | 0.999967i | \(-0.502570\pi\) | ||||
−0.00807265 | + | 0.999967i | \(0.502570\pi\) | |||||||
\(992\) | 192.000i | 0.193548i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 746.705i | − 0.750457i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 875.398 | 0.878032 | 0.439016 | − | 0.898479i | \(-0.355327\pi\) | ||||
0.439016 | + | 0.898479i | \(0.355327\pi\) | |||||||
\(998\) | − 673.166i | − 0.674515i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.3.b.i.197.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 882.3.b.i.197.4 | yes | 4 | |
7.2 | even | 3 | 882.3.s.f.557.1 | 8 | |||
7.3 | odd | 6 | 882.3.s.f.863.3 | 8 | |||
7.4 | even | 3 | 882.3.s.f.863.4 | 8 | |||
7.5 | odd | 6 | 882.3.s.f.557.2 | 8 | |||
7.6 | odd | 2 | inner | 882.3.b.i.197.2 | yes | 4 | |
21.2 | odd | 6 | 882.3.s.f.557.4 | 8 | |||
21.5 | even | 6 | 882.3.s.f.557.3 | 8 | |||
21.11 | odd | 6 | 882.3.s.f.863.1 | 8 | |||
21.17 | even | 6 | 882.3.s.f.863.2 | 8 | |||
21.20 | even | 2 | inner | 882.3.b.i.197.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.3.b.i.197.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
882.3.b.i.197.2 | yes | 4 | 7.6 | odd | 2 | inner | |
882.3.b.i.197.3 | yes | 4 | 21.20 | even | 2 | inner | |
882.3.b.i.197.4 | yes | 4 | 3.2 | odd | 2 | inner | |
882.3.s.f.557.1 | 8 | 7.2 | even | 3 | |||
882.3.s.f.557.2 | 8 | 7.5 | odd | 6 | |||
882.3.s.f.557.3 | 8 | 21.5 | even | 6 | |||
882.3.s.f.557.4 | 8 | 21.2 | odd | 6 | |||
882.3.s.f.863.1 | 8 | 21.11 | odd | 6 | |||
882.3.s.f.863.2 | 8 | 21.17 | even | 6 | |||
882.3.s.f.863.3 | 8 | 7.3 | odd | 6 | |||
882.3.s.f.863.4 | 8 | 7.4 | even | 3 |