Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3864,2,Mod(1,3864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3864.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: | \(30.8541953410\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.39605.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 8x^{2} + 9x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.57685\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.57685 | −1.59961 | −0.799807 | − | 0.600257i | \(-0.795065\pi\) | ||||
−0.799807 | + | 0.600257i | \(0.795065\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.81840 | −1.45280 | −0.726401 | − | 0.687271i | \(-0.758809\pi\) | ||||
−0.726401 | + | 0.687271i | \(0.758809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.91214 | −1.08503 | −0.542516 | − | 0.840045i | \(-0.682528\pi\) | ||||
−0.542516 | + | 0.840045i | \(0.682528\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.57685 | −0.923538 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.21699 | −1.75038 | −0.875189 | − | 0.483782i | \(-0.839263\pi\) | ||||
−0.875189 | + | 0.483782i | \(0.839263\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.335294 | −0.0769217 | −0.0384608 | − | 0.999260i | \(-0.512245\pi\) | ||||
−0.0384608 | + | 0.999260i | \(0.512245\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.79384 | 1.55877 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.11144 | 1.32056 | 0.660280 | − | 0.751019i | \(-0.270438\pi\) | ||||
0.660280 | + | 0.751019i | \(0.270438\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.21699 | −0.218578 | −0.109289 | − | 0.994010i | \(-0.534857\pi\) | ||||
−0.109289 | + | 0.994010i | \(0.534857\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.81840 | −0.838776 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.57685 | 0.604598 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.55915 | 0.256323 | 0.128161 | − | 0.991753i | \(-0.459092\pi\) | ||||
0.128161 | + | 0.991753i | \(0.459092\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.91214 | −0.626444 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0422591 | −0.00659976 | −0.00329988 | − | 0.999995i | \(-0.501050\pi\) | ||||
−0.00329988 | + | 0.999995i | \(0.501050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.12325 | 1.23878 | 0.619392 | − | 0.785082i | \(-0.287379\pi\) | ||||
0.619392 | + | 0.785082i | \(0.287379\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.57685 | −0.533205 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.10555 | 0.598857 | 0.299428 | − | 0.954119i | \(-0.403204\pi\) | ||||
0.299428 | + | 0.954119i | \(0.403204\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.21699 | −1.01058 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.35299 | 0.872650 | 0.436325 | − | 0.899789i | \(-0.356280\pi\) | ||||
0.436325 | + | 0.899789i | \(0.356280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.2347 | 2.32392 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.335294 | −0.0444107 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.08099 | −0.270922 | −0.135461 | − | 0.990783i | \(-0.543252\pi\) | ||||
−0.135461 | + | 0.990783i | \(0.543252\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9603 | 1.40332 | 0.701660 | − | 0.712512i | \(-0.252443\pi\) | ||||
0.701660 | + | 0.712512i | \(0.252443\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.9931 | 1.73563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.19929 | 0.146517 | 0.0732586 | − | 0.997313i | \(-0.476660\pi\) | ||||
0.0732586 | + | 0.997313i | \(0.476660\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.89939 | −0.818807 | −0.409404 | − | 0.912353i | \(-0.634263\pi\) | ||||
−0.409404 | + | 0.912353i | \(0.634263\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.73388 | −0.319977 | −0.159988 | − | 0.987119i | \(-0.551146\pi\) | ||||
−0.159988 | + | 0.987119i | \(0.551146\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.79384 | 0.899955 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.81840 | 0.549108 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.5582 | 1.86294 | 0.931470 | − | 0.363819i | \(-0.118527\pi\) | ||||
0.931470 | + | 0.363819i | \(0.118527\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.0413 | −1.43147 | −0.715733 | − | 0.698374i | \(-0.753907\pi\) | ||||
−0.715733 | + | 0.698374i | \(0.753907\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 25.8141 | 2.79993 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.11144 | 0.762426 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.17139 | −0.972165 | −0.486083 | − | 0.873913i | \(-0.661575\pi\) | ||||
−0.486083 | + | 0.873913i | \(0.661575\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.91214 | 0.410104 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.21699 | −0.126196 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.19929 | 0.123045 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.7820 | −1.39935 | −0.699676 | − | 0.714460i | \(-0.746672\pi\) | ||||
−0.699676 | + | 0.714460i | \(0.746672\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.81840 | −0.484268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.7178 | 1.56398 | 0.781989 | − | 0.623292i | \(-0.214205\pi\) | ||||
0.781989 | + | 0.623292i | \(0.214205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.70697 | 0.365258 | 0.182629 | − | 0.983182i | \(-0.441539\pi\) | ||||
0.182629 | + | 0.983182i | \(0.441539\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.57685 | 0.349065 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.65289 | −0.256465 | −0.128232 | − | 0.991744i | \(-0.540930\pi\) | ||||
−0.128232 | + | 0.991744i | \(0.540930\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.85713 | −0.656794 | −0.328397 | − | 0.944540i | \(-0.606508\pi\) | ||||
−0.328397 | + | 0.944540i | \(0.606508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.55915 | 0.147988 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.54306 | 0.803664 | 0.401832 | − | 0.915713i | \(-0.368374\pi\) | ||||
0.401832 | + | 0.915713i | \(0.368374\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.57685 | 0.333543 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.91214 | −0.361678 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.21699 | 0.661580 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.2170 | 1.11064 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0422591 | −0.00381037 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.99313 | −0.893813 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.7718 | −1.39952 | −0.699761 | − | 0.714377i | \(-0.746710\pi\) | ||||
−0.699761 | + | 0.714377i | \(0.746710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.12325 | 0.715212 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0987 | −1.05707 | −0.528534 | − | 0.848912i | \(-0.677258\pi\) | ||||
−0.528534 | + | 0.848912i | \(0.677258\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.335294 | 0.0290737 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.57685 | −0.307846 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.7145 | −1.85519 | −0.927595 | − | 0.373586i | \(-0.878128\pi\) | ||||
−0.927595 | + | 0.373586i | \(0.878128\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.30485 | 0.619589 | 0.309795 | − | 0.950804i | \(-0.399740\pi\) | ||||
0.309795 | + | 0.950804i | \(0.399740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.10555 | 0.345750 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.8503 | 1.57634 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −25.4365 | −2.11239 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.39030 | 0.277744 | 0.138872 | − | 0.990310i | \(-0.455652\pi\) | ||||
0.138872 | + | 0.990310i | \(0.455652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.8469 | −1.53374 | −0.766871 | − | 0.641802i | \(-0.778187\pi\) | ||||
−0.766871 | + | 0.641802i | \(0.778187\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.21699 | −0.583459 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.35299 | 0.349641 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.8243 | 1.10330 | 0.551649 | − | 0.834076i | \(-0.313999\pi\) | ||||
0.551649 | + | 0.834076i | \(0.313999\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.35299 | 0.503825 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7433 | 1.07646 | 0.538229 | − | 0.842799i | \(-0.319094\pi\) | ||||
0.538229 | + | 0.842799i | \(0.319094\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 17.2347 | 1.34172 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.335294 | −0.0259458 | −0.0129729 | − | 0.999916i | \(-0.504130\pi\) | ||||
−0.0129729 | + | 0.999916i | \(0.504130\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.30485 | 0.177296 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.335294 | −0.0256406 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.323531 | 0.0245976 | 0.0122988 | − | 0.999924i | \(-0.496085\pi\) | ||||
0.0122988 | + | 0.999924i | \(0.496085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.79384 | −0.589159 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.08099 | −0.156417 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.06824 | 0.378818 | 0.189409 | − | 0.981898i | \(-0.439343\pi\) | ||||
0.189409 | + | 0.981898i | \(0.439343\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.5818 | −0.935197 | −0.467599 | − | 0.883941i | \(-0.654881\pi\) | ||||
−0.467599 | + | 0.883941i | \(0.654881\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.9603 | 0.810207 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.57685 | −0.410018 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.7744 | 2.54295 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.06918 | 0.511508 | 0.255754 | − | 0.966742i | \(-0.417676\pi\) | ||||
0.255754 | + | 0.966742i | \(0.417676\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4247 | 1.47020 | 0.735101 | − | 0.677957i | \(-0.237135\pi\) | ||||
0.735101 | + | 0.677957i | \(0.237135\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.9931 | 1.00207 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.87836 | −0.490063 | −0.245031 | − | 0.969515i | \(-0.578798\pi\) | ||||
−0.245031 | + | 0.969515i | \(0.578798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3182 | −1.29854 | −0.649272 | − | 0.760556i | \(-0.724926\pi\) | ||||
−0.649272 | + | 0.760556i | \(0.724926\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.19929 | 0.0845917 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.11144 | −0.499125 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.151154 | 0.0105571 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.61558 | 0.111752 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1596 | 1.25016 | 0.625078 | − | 0.780562i | \(-0.285067\pi\) | ||||
0.625078 | + | 0.780562i | \(0.285067\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.89939 | −0.472739 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −29.0556 | −1.98158 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.21699 | 0.0826147 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.73388 | −0.184739 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.2339 | 1.89922 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.5421 | 1.71042 | 0.855212 | − | 0.518278i | \(-0.173427\pi\) | ||||
0.855212 | + | 0.518278i | \(0.173427\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.79384 | 0.519589 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.7423 | 1.11123 | 0.555613 | − | 0.831441i | \(-0.312484\pi\) | ||||
0.555613 | + | 0.831441i | \(0.312484\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.5504 | 1.75450 | 0.877249 | − | 0.480036i | \(-0.159376\pi\) | ||||
0.877249 | + | 0.480036i | \(0.159376\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.81840 | 0.317028 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.76692 | 0.377804 | 0.188902 | − | 0.981996i | \(-0.439507\pi\) | ||||
0.188902 | + | 0.981996i | \(0.439507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.6849 | −0.957940 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.5582 | 1.07557 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.8023 | 1.53964 | 0.769822 | − | 0.638259i | \(-0.220345\pi\) | ||||
0.769822 | + | 0.638259i | \(0.220345\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.1031 | −0.779632 | −0.389816 | − | 0.920893i | \(-0.627461\pi\) | ||||
−0.389816 | + | 0.920893i | \(0.627461\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.57685 | −0.228516 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.31172 | 0.0834625 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.0413 | −0.826457 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.80993 | −0.492958 | −0.246479 | − | 0.969148i | \(-0.579274\pi\) | ||||
−0.246479 | + | 0.969148i | \(0.579274\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.81840 | 0.302930 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 25.8141 | 1.61654 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.26024 | −0.140990 | −0.0704948 | − | 0.997512i | \(-0.522458\pi\) | ||||
−0.0704948 | + | 0.997512i | \(0.522458\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.55915 | −0.0968810 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.11144 | 0.440187 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.0168 | −1.23429 | −0.617143 | − | 0.786851i | \(-0.711710\pi\) | ||||
−0.617143 | + | 0.786851i | \(0.711710\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.7237 | −1.39590 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.17139 | −0.561280 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.1730 | 1.83968 | 0.919840 | − | 0.392294i | \(-0.128318\pi\) | ||||
0.919840 | + | 0.392294i | \(0.128318\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5735 | 1.18901 | 0.594503 | − | 0.804093i | \(-0.297349\pi\) | ||||
0.594503 | + | 0.804093i | \(0.297349\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.91214 | 0.236774 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −37.5538 | −2.26458 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.1140 | −1.32870 | −0.664350 | − | 0.747422i | \(-0.731292\pi\) | ||||
−0.664350 | + | 0.747422i | \(0.731292\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.21699 | −0.0728593 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.7424 | −1.29704 | −0.648520 | − | 0.761197i | \(-0.724612\pi\) | ||||
−0.648520 | + | 0.761197i | \(0.724612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.59788 | 0.332760 | 0.166380 | − | 0.986062i | \(-0.446792\pi\) | ||||
0.166380 | + | 0.986062i | \(0.446792\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.19929 | 0.0710401 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0422591 | 0.00249447 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.0850 | 2.06382 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.7820 | −0.807917 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6706 | −0.857065 | −0.428532 | − | 0.903526i | \(-0.640969\pi\) | ||||
−0.428532 | + | 0.903526i | \(0.640969\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.44339 | 0.433371 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.81840 | −0.279592 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.91214 | 0.226245 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.12325 | −0.468216 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.7178 | 0.902964 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −39.2033 | −2.24477 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.07604 | 0.517997 | 0.258999 | − | 0.965878i | \(-0.416607\pi\) | ||||
0.258999 | + | 0.965878i | \(0.416607\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.70697 | 0.210882 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.10221 | −0.232615 | −0.116308 | − | 0.993213i | \(-0.537106\pi\) | ||||
−0.116308 | + | 0.993213i | \(0.537106\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.09628 | 0.118489 | 0.0592444 | − | 0.998244i | \(-0.481131\pi\) | ||||
0.0592444 | + | 0.998244i | \(0.481131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.57685 | 0.201533 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.9063 | 0.612557 | 0.306278 | − | 0.951942i | \(-0.400916\pi\) | ||||
0.306278 | + | 0.951942i | \(0.400916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34.2658 | −1.91851 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.65289 | −0.148070 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.41981 | 0.134642 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −30.4906 | −1.69131 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.85713 | −0.379200 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.10555 | −0.226347 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.6368 | 1.62899 | 0.814493 | − | 0.580173i | \(-0.197015\pi\) | ||||
0.814493 | + | 0.580173i | \(0.197015\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.55915 | 0.0854410 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.28969 | −0.234371 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.0731 | −1.69266 | −0.846331 | − | 0.532658i | \(-0.821193\pi\) | ||||
−0.846331 | + | 0.532658i | \(0.821193\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.54306 | 0.463995 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.86395 | 0.317551 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.57685 | 0.192571 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.9019 | 0.746295 | 0.373147 | − | 0.927772i | \(-0.378279\pi\) | ||||
0.373147 | + | 0.927772i | \(0.378279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.8868 | −0.850403 | −0.425201 | − | 0.905099i | \(-0.639797\pi\) | ||||
−0.425201 | + | 0.905099i | \(0.639797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.91214 | −0.208815 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.3917 | −1.40469 | −0.702345 | − | 0.711837i | \(-0.747864\pi\) | ||||
−0.702345 | + | 0.711837i | \(0.747864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.6781 | 1.30978 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.21699 | 0.381964 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.1208 | 1.16749 | 0.583747 | − | 0.811936i | \(-0.301586\pi\) | ||||
0.583747 | + | 0.811936i | \(0.301586\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8876 | −0.994083 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.2170 | 0.641226 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.77868 | 0.511840 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.69756 | 0.140811 | 0.0704057 | − | 0.997518i | \(-0.477571\pi\) | ||||
0.0704057 | + | 0.997518i | \(0.477571\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0422591 | −0.00219992 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.35299 | −0.329831 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.2862 | −0.636154 | −0.318077 | − | 0.948065i | \(-0.603037\pi\) | ||||
−0.318077 | + | 0.948065i | \(0.603037\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.99313 | −0.516043 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.8209 | −1.43285 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.8198 | 1.01808 | 0.509038 | − | 0.860744i | \(-0.330001\pi\) | ||||
0.509038 | + | 0.860744i | \(0.330001\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.7718 | −0.808015 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.92297 | 0.404845 | 0.202422 | − | 0.979298i | \(-0.435119\pi\) | ||||
0.202422 | + | 0.979298i | \(0.435119\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.2347 | −0.878361 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.12325 | 0.412928 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.2508 | −0.621139 | −0.310569 | − | 0.950551i | \(-0.600520\pi\) | ||||
−0.310569 | + | 0.950551i | \(0.600520\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.21699 | 0.364979 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0987 | −0.610298 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −59.2260 | −2.97999 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.19924 | −0.411508 | −0.205754 | − | 0.978604i | \(-0.565965\pi\) | ||||
−0.205754 | + | 0.978604i | \(0.565965\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.335294 | 0.0167857 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.88758 | −0.294012 | −0.147006 | − | 0.989136i | \(-0.546964\pi\) | ||||
−0.147006 | + | 0.989136i | \(0.546964\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.76104 | 0.237164 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.57685 | −0.177735 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.51262 | −0.372387 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.83684 | 0.239167 | 0.119583 | − | 0.992824i | \(-0.461844\pi\) | ||||
0.119583 | + | 0.992824i | \(0.461844\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.7145 | −1.07109 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.08099 | 0.102399 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 46.6466 | 2.28979 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.30485 | 0.357720 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.31920 | −0.162154 | −0.0810769 | − | 0.996708i | \(-0.525836\pi\) | ||||
−0.0810769 | + | 0.996708i | \(0.525836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.8209 | −1.45338 | −0.726692 | − | 0.686964i | \(-0.758943\pi\) | ||||
−0.726692 | + | 0.686964i | \(0.758943\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.10555 | 0.199619 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −56.2481 | −2.72843 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.9603 | −0.530405 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.8503 | 0.910099 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.23611 | 0.396719 | 0.198360 | − | 0.980129i | \(-0.436439\pi\) | ||||
0.198360 | + | 0.980129i | \(0.436439\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.2101 | −0.827066 | −0.413533 | − | 0.910489i | \(-0.635705\pi\) | ||||
−0.413533 | + | 0.910489i | \(0.635705\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.4365 | −1.21959 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.335294 | 0.0160393 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.8200 | 1.13687 | 0.568433 | − | 0.822729i | \(-0.307550\pi\) | ||||
0.568433 | + | 0.822729i | \(0.307550\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.7050 | 1.79142 | 0.895709 | − | 0.444640i | \(-0.146669\pi\) | ||||
0.895709 | + | 0.444640i | \(0.146669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.8047 | 1.55509 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.39030 | 0.160356 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.1552 | 1.56469 | 0.782346 | − | 0.622843i | \(-0.214023\pi\) | ||||
0.782346 | + | 0.622843i | \(0.214023\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.203621 | 0.00958815 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.8469 | −0.885506 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.9931 | −0.656008 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.92062 | −0.417289 | −0.208644 | − | 0.977992i | \(-0.566905\pi\) | ||||
−0.208644 | + | 0.977992i | \(0.566905\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.21699 | −0.336860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.2484 | −0.617040 | −0.308520 | − | 0.951218i | \(-0.599834\pi\) | ||||
−0.308520 | + | 0.951218i | \(0.599834\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9357 | 0.601174 | 0.300587 | − | 0.953754i | \(-0.402817\pi\) | ||||
0.300587 | + | 0.953754i | \(0.402817\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.35299 | 0.201865 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.959348 | 0.0443933 | 0.0221967 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221967 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.19929 | −0.0553783 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.8243 | 0.636989 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −39.1411 | −1.79971 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.61323 | −0.119903 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.35299 | 0.290883 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.8621 | 1.36443 | 0.682217 | − | 0.731150i | \(-0.261016\pi\) | ||||
0.682217 | + | 0.731150i | \(0.261016\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.09962 | −0.278119 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 49.2962 | 2.23842 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.3021 | 1.69032 | 0.845160 | − | 0.534513i | \(-0.179505\pi\) | ||||
0.845160 | + | 0.534513i | \(0.179505\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.7433 | 0.621493 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.2794 | 1.14084 | 0.570422 | − | 0.821351i | \(-0.306780\pi\) | ||||
0.570422 | + | 0.821351i | \(0.306780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −51.3232 | −2.31148 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.2347 | 0.774642 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.89939 | 0.309480 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.0944 | −1.12338 | −0.561689 | − | 0.827348i | \(-0.689848\pi\) | ||||
−0.561689 | + | 0.827348i | \(0.689848\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.335294 | −0.0149798 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.2736 | −1.17148 | −0.585740 | − | 0.810499i | \(-0.699196\pi\) | ||||
−0.585740 | + | 0.810499i | \(0.699196\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −56.2202 | −2.50176 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.30485 | 0.102362 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.86636 | −0.171373 | −0.0856866 | − | 0.996322i | \(-0.527308\pi\) | ||||
−0.0856866 | + | 0.996322i | \(0.527308\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.73388 | 0.120940 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.335294 | −0.0148036 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.2592 | −0.584272 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.7822 | −0.870021 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.323531 | 0.0142014 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.2599 | 1.19428 | 0.597138 | − | 0.802138i | \(-0.296304\pi\) | ||||
0.597138 | + | 0.802138i | \(0.296304\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.7634 | −0.514377 | −0.257189 | − | 0.966361i | \(-0.582796\pi\) | ||||
−0.257189 | + | 0.966361i | \(0.582796\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.79384 | −0.340151 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.78301 | 0.382594 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.08099 | −0.0903073 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.165323 | 0.00716096 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.48899 | 0.410245 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.06824 | 0.218711 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.81840 | −0.207543 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.8833 | 1.71472 | 0.857359 | − | 0.514720i | \(-0.172104\pi\) | ||||
0.857359 | + | 0.514720i | \(0.172104\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.5818 | −0.539936 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.5269 | 1.05062 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.5504 | −0.536615 | −0.268307 | − | 0.963333i | \(-0.586464\pi\) | ||||
−0.268307 | + | 0.963333i | \(0.586464\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.9603 | 0.467773 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.38442 | −0.101580 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.5582 | −0.704125 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.57685 | −0.236724 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.8951 | −1.60567 | −0.802833 | − | 0.596204i | \(-0.796675\pi\) | ||||
−0.802833 | + | 0.596204i | \(0.796675\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.7793 | −1.34412 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.7744 | 1.46817 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.2498 | −0.769139 | −0.384570 | − | 0.923096i | \(-0.625650\pi\) | ||||
−0.384570 | + | 0.923096i | \(0.625650\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.5572 | −1.28555 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.5076 | 0.650113 | 0.325057 | − | 0.945695i | \(-0.394617\pi\) | ||||
0.325057 | + | 0.945695i | \(0.394617\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.8773 | 1.37587 | 0.687936 | − | 0.725771i | \(-0.258517\pi\) | ||||
0.687936 | + | 0.725771i | \(0.258517\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.06918 | 0.295319 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.79384 | −0.325026 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.1384 | −1.00489 | −0.502446 | − | 0.864608i | \(-0.667567\pi\) | ||||
−0.502446 | + | 0.864608i | \(0.667567\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.4247 | 0.848822 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.0413 | 0.541043 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.6113 | −1.26779 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.9931 | 0.578545 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.53806 | 0.352404 | 0.176202 | − | 0.984354i | \(-0.443619\pi\) | ||||
0.176202 | + | 0.984354i | \(0.443619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.408049 | 0.0168134 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.87836 | −0.282938 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.8469 | 0.691820 | 0.345910 | − | 0.938268i | \(-0.387570\pi\) | ||||
0.345910 | + | 0.938268i | \(0.387570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.8141 | −1.05827 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.3182 | −0.749715 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.7000 | −1.17265 | −0.586326 | − | 0.810075i | \(-0.699426\pi\) | ||||
−0.586326 | + | 0.810075i | \(0.699426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6840 | 0.435810 | 0.217905 | − | 0.975970i | \(-0.430078\pi\) | ||||
0.217905 | + | 0.975970i | \(0.430078\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.19929 | 0.0488391 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −43.6983 | −1.77659 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.751144 | 0.0304880 | 0.0152440 | − | 0.999884i | \(-0.495147\pi\) | ||||
0.0152440 | + | 0.999884i | \(0.495147\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.11144 | −0.288170 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.0615 | −0.649779 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.1618 | 1.90485 | 0.952424 | − | 0.304777i | \(-0.0985820\pi\) | ||||
0.952424 | + | 0.304777i | \(0.0985820\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.151154 | 0.00609513 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.8503 | 0.678366 | 0.339183 | − | 0.940720i | \(-0.389849\pi\) | ||||
0.339183 | + | 0.940720i | \(0.389849\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.0665 | −1.73099 | −0.865494 | − | 0.500920i | \(-0.832995\pi\) | ||||
−0.865494 | + | 0.500920i | \(0.832995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.17139 | 0.367444 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.22528 | −0.129011 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.61558 | 0.0645200 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.2524 | −0.448662 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.5881 | 1.65560 | 0.827798 | − | 0.561026i | \(-0.189593\pi\) | ||||
0.827798 | + | 0.561026i | \(0.189593\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.1596 | 0.721778 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 56.4134 | 2.23870 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.91214 | −0.155005 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.89939 | −0.272936 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.08786 | −0.0824655 | −0.0412327 | − | 0.999150i | \(-0.513129\pi\) | ||||
−0.0412327 | + | 0.999150i | \(0.513129\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.3997 | 0.804486 | 0.402243 | − | 0.915533i | \(-0.368231\pi\) | ||||
0.402243 | + | 0.915533i | \(0.368231\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −29.0556 | −1.14406 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.8750 | 0.859994 | 0.429997 | − | 0.902830i | \(-0.358515\pi\) | ||||
0.429997 | + | 0.902830i | \(0.358515\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0271 | 0.393596 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.21699 | 0.0476976 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.8788 | −0.738784 | −0.369392 | − | 0.929274i | \(-0.620434\pi\) | ||||
−0.369392 | + | 0.929274i | \(0.620434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.2752 | 1.69090 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.73388 | −0.106659 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.4552 | 0.407277 | 0.203638 | − | 0.979046i | \(-0.434723\pi\) | ||||
0.203638 | + | 0.979046i | \(0.434723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.21860 | 0.0862934 | 0.0431467 | − | 0.999069i | \(-0.486262\pi\) | ||||
0.0431467 | + | 0.999069i | \(0.486262\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.2339 | 1.09651 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.19929 | −0.0465067 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.11144 | −0.275356 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.5421 | 0.987514 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52.8110 | −2.03875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8037 | 1.22594 | 0.612971 | − | 0.790105i | \(-0.289974\pi\) | ||||
0.612971 | + | 0.790105i | \(0.289974\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.79384 | 0.299985 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.2001 | 1.50658 | 0.753291 | − | 0.657687i | \(-0.228465\pi\) | ||||
0.753291 | + | 0.657687i | \(0.228465\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.7820 | 0.528906 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.7423 | 0.641567 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.1242 | −0.846558 | −0.423279 | − | 0.905999i | \(-0.639121\pi\) | ||||
−0.423279 | + | 0.905999i | \(0.639121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 77.6693 | 2.96759 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.5504 | 1.01296 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.8538 | −0.946854 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.1115 | −0.841161 | −0.420580 | − | 0.907255i | \(-0.638174\pi\) | ||||
−0.420580 | + | 0.907255i | \(0.638174\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.81840 | 0.183036 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.1283 | −0.991104 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.304983 | 0.0115521 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.76692 | 0.218125 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.0353 | −1.24773 | −0.623864 | − | 0.781533i | \(-0.714438\pi\) | ||||
−0.623864 | + | 0.781533i | \(0.714438\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.522774 | −0.0197168 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.6849 | −0.553067 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.7178 | −0.591128 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.9265 | −0.447909 | −0.223954 | − | 0.974600i | \(-0.571897\pi\) | ||||
−0.223954 | + | 0.974600i | \(0.571897\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.5582 | 0.620980 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.21699 | 0.0455767 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −67.4245 | −2.52153 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.8023 | 0.888914 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.0840 | −1.45759 | −0.728793 | − | 0.684734i | \(-0.759918\pi\) | ||||
−0.728793 | + | 0.684734i | \(0.759918\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.70697 | −0.138055 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.1031 | −0.450121 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 55.4254 | 2.05845 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.2170 | 1.00942 | 0.504711 | − | 0.863288i | \(-0.331599\pi\) | ||||
0.504711 | + | 0.863288i | \(0.331599\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −58.6254 | −2.16834 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.6585 | 1.76031 | 0.880153 | − | 0.474691i | \(-0.157440\pi\) | ||||
0.880153 | + | 0.474691i | \(0.157440\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.57685 | −0.131934 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.77868 | −0.212861 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.1341 | 0.593502 | 0.296751 | − | 0.954955i | \(-0.404097\pi\) | ||||
0.296751 | + | 0.954955i | \(0.404097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.31172 | 0.0481871 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.2347 | −0.925771 | −0.462885 | − | 0.886418i | \(-0.653186\pi\) | ||||
−0.462885 | + | 0.886418i | \(0.653186\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1266 | −0.444284 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.0413 | −0.477155 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.65289 | 0.0969346 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.57586 | 0.0939945 | 0.0469973 | − | 0.998895i | \(-0.485035\pi\) | ||||
0.0469973 | + | 0.998895i | \(0.485035\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.80993 | −0.284610 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 67.4126 | 2.45339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.1086 | −1.31239 | −0.656194 | − | 0.754592i | \(-0.727835\pi\) | ||||
−0.656194 | + | 0.754592i | \(0.727835\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.81840 | 0.174897 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.687163 | 0.0249097 | 0.0124548 | − | 0.999922i | \(-0.496035\pi\) | ||||
0.0124548 | + | 0.999922i | \(0.496035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.85713 | 0.248245 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 25.8141 | 0.933310 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.14113 | 0.293959 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.1426 | 1.12303 | 0.561515 | − | 0.827467i | \(-0.310219\pi\) | ||||
0.561515 | + | 0.827467i | \(0.310219\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.26024 | −0.0814004 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.8425 | 1.61287 | 0.806437 | − | 0.591320i | \(-0.201393\pi\) | ||||
0.806437 | + | 0.591320i | \(0.201393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.48503 | −0.340712 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.55915 | −0.0559343 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0141692 | 0.000507665 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.2440 | 1.18957 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.11144 | 0.254142 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −49.4474 | −1.76485 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.3412 | 0.439917 | 0.219959 | − | 0.975509i | \(-0.429408\pi\) | ||||
0.219959 | + | 0.975509i | \(0.429408\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.0168 | −0.712616 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.54306 | −0.303756 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.8782 | −1.52265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −22.7237 | −0.805926 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 52.4818 | 1.85900 | 0.929500 | − | 0.368823i | \(-0.120239\pi\) | ||||
0.929500 | + | 0.368823i | \(0.120239\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.6297 | −1.04823 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.17139 | −0.324055 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.1729 | 0.464863 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.57685 | −0.126067 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.1730 | 1.06214 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.6408 | −1.18275 | −0.591373 | − | 0.806398i | \(-0.701414\pi\) | ||||
−0.591373 | + | 0.806398i | \(0.701414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.6500 | −0.373972 | −0.186986 | − | 0.982363i | \(-0.559872\pi\) | ||||
−0.186986 | + | 0.982363i | \(0.559872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.5735 | 0.686473 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −49.1577 | −1.72192 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.72368 | −0.0952893 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.91214 | 0.136701 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.3310 | 1.75656 | 0.878282 | − | 0.478142i | \(-0.158690\pi\) | ||||
0.878282 | + | 0.478142i | \(0.158690\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.1916 | −0.634120 | −0.317060 | − | 0.948405i | \(-0.602696\pi\) | ||||
−0.317060 | + | 0.948405i | \(0.602696\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −37.5538 | −1.30746 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.1298 | 1.15203 | 0.576017 | − | 0.817438i | \(-0.304606\pi\) | ||||
0.576017 | + | 0.817438i | \(0.304606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.34555 | −0.324584 | −0.162292 | − | 0.986743i | \(-0.551889\pi\) | ||||
−0.162292 | + | 0.986743i | \(0.551889\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.1140 | −0.767125 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.21699 | −0.250054 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.19929 | 0.0415033 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.21699 | −0.0420653 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.4482 | 0.395236 | 0.197618 | − | 0.980279i | \(-0.436679\pi\) | ||||
0.197618 | + | 0.980279i | \(0.436679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.5725 | 0.743880 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.7424 | −0.748847 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.24409 | −0.283605 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.2170 | −0.419781 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.59788 | 0.192119 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.55915 | −0.0534470 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.2336 | −1.82269 | −0.911343 | − | 0.411648i | \(-0.864953\pi\) | ||||
−0.911343 | + | 0.411648i | \(0.864953\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.19929 | 0.0410150 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.95025 | −0.271575 | −0.135788 | − | 0.990738i | \(-0.543357\pi\) | ||||
−0.135788 | + | 0.990738i | \(0.543357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.1664 | −0.551592 | −0.275796 | − | 0.961216i | \(-0.588941\pi\) | ||||
−0.275796 | + | 0.961216i | \(0.588941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0422591 | 0.00144019 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.2500 | −0.859519 | −0.429760 | − | 0.902943i | \(-0.641402\pi\) | ||||
−0.429760 | + | 0.902943i | \(0.641402\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.15722 | −0.0393467 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.0850 | 1.19155 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −79.7839 | −2.70648 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.69181 | −0.158976 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.7820 | −0.466451 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.99313 | 0.337830 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.08452 | −0.0703892 | −0.0351946 | − | 0.999380i | \(-0.511205\pi\) | ||||
−0.0351946 | + | 0.999380i | \(0.511205\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.6706 | −0.494827 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.69769 | 0.259342 | 0.129671 | − | 0.991557i | \(-0.458608\pi\) | ||||
0.129671 | + | 0.991557i | \(0.458608\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.9600 | 1.95051 | 0.975255 | − | 0.221083i | \(-0.0709592\pi\) | ||||
0.975255 | + | 0.221083i | \(0.0709592\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.44339 | 0.250207 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.4481 | 1.32454 | 0.662269 | − | 0.749266i | \(-0.269594\pi\) | ||||
0.662269 | + | 0.749266i | \(0.269594\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.7718 | 0.528970 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.81840 | −0.161423 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.37657 | −0.0460651 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.1283 | −0.605963 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.91214 | 0.130623 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.65455 | −0.288645 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.8495 | −1.52747 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.12325 | −0.270325 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45.0032 | 1.49596 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.4448 | −1.01090 | −0.505452 | − | 0.862855i | \(-0.668674\pi\) | ||||
−0.505452 | + | 0.862855i | \(0.668674\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.7178 | 0.521326 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.3234 | 1.50163 | 0.750815 | − | 0.660513i | \(-0.229661\pi\) | ||||
0.750815 | + | 0.660513i | \(0.229661\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 62.8381 | 2.07964 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −39.2033 | −1.29602 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.0987 | 0.399534 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.2201 | 1.55765 | 0.778824 | − | 0.627243i | \(-0.215817\pi\) | ||||
0.778824 | + | 0.627243i | \(0.215817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.07604 | 0.299066 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26.9914 | 0.888433 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.1518 | 0.399548 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.70697 | 0.121753 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.4145 | −1.39157 | −0.695787 | − | 0.718248i | \(-0.744944\pi\) | ||||
−0.695787 | + | 0.718248i | \(0.744944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.335294 | −0.0109888 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.10221 | −0.134300 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −124.383 | −4.06774 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.68451 | −0.0876991 | −0.0438495 | − | 0.999038i | \(-0.513962\pi\) | ||||
−0.0438495 | + | 0.999038i | \(0.513962\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.09628 | 0.0684095 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.9923 | −1.40151 | −0.700755 | − | 0.713402i | \(-0.747153\pi\) | ||||
−0.700755 | + | 0.713402i | \(0.747153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.0422591 | 0.00137615 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.57685 | 0.116355 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.2997 | −0.887122 | −0.443561 | − | 0.896244i | \(-0.646285\pi\) | ||||
−0.443561 | + | 0.896244i | \(0.646285\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.6953 | 0.347185 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.9063 | 0.353660 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.8015 | −1.19212 | −0.596059 | − | 0.802941i | \(-0.703268\pi\) | ||||
−0.596059 | + | 0.802941i | \(0.703268\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.2854 | −0.818215 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −34.2658 | −1.10765 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.7145 | 0.701196 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5189 | −0.952224 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.65289 | −0.0854882 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −73.0561 | −2.35176 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.9270 | −1.25181 | −0.625904 | − | 0.779900i | \(-0.715270\pi\) | ||||
−0.625904 | + | 0.779900i | \(0.715270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.41981 | 0.0777356 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.2523 | −1.80522 | −0.902612 | − | 0.430456i | \(-0.858353\pi\) | ||||
−0.902612 | + | 0.430456i | \(0.858353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.30485 | −0.234183 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −30.4906 | −0.976481 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.0147 | 1.37616 | 0.688082 | − | 0.725633i | \(-0.258453\pi\) | ||||
0.688082 | + | 0.725633i | \(0.258453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.1914 | 1.41236 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.85713 | −0.218931 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.3824 | −1.03284 | −0.516420 | − | 0.856336i | \(-0.672736\pi\) | ||||
−0.516420 | + | 0.856336i | \(0.672736\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.6028 | 0.783911 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.10555 | −0.130681 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.12325 | −0.258304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9957 | −0.539885 | −0.269943 | − | 0.962876i | \(-0.587005\pi\) | ||||
−0.269943 | + | 0.962876i | \(0.587005\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.6368 | 0.940495 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 65.5215 | 2.07717 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.6882 | 0.560192 | 0.280096 | − | 0.959972i | \(-0.409634\pi\) | ||||
0.280096 | + | 0.959972i | \(0.409634\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.55915 | 0.0493294 |
(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 | 3864.2.a.t.1.1 | ✓ | 4 | |
4.3 | odd | 2 | 7728.2.a.bz.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.t.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7728.2.a.bz.1.1 | 4 | 4.3 | odd | 2 |