Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,3,Mod(127,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.d (of order \(2\), degree \(1\), not 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: | \(12.2071158433\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.4 | ||
Root | \(-0.895644 + 1.09445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.127 |
Dual form | 448.3.d.b.127.1 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.37780i | 1.45927i | 0.683838 | + | 0.729634i | \(0.260309\pi\) | ||||
−0.683838 | + | 0.729634i | \(0.739691\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.58258 | 1.11652 | 0.558258 | − | 0.829668i | \(-0.311470\pi\) | ||||
0.558258 | + | 0.829668i | \(0.311470\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.64575i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −10.1652 | −1.12946 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.82740i | 0.166127i | 0.996544 | + | 0.0830637i | \(0.0264705\pi\) | ||||
−0.996544 | + | 0.0830637i | \(0.973530\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.7477 | 1.59598 | 0.797990 | − | 0.602671i | \(-0.205897\pi\) | ||||
0.797990 | + | 0.602671i | \(0.205897\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.4394i | 1.62929i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.1652 | 1.48030 | 0.740152 | − | 0.672440i | \(-0.234754\pi\) | ||||
0.740152 | + | 0.672440i | \(0.234754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.6446i | 1.61287i | 0.591320 | + | 0.806437i | \(0.298607\pi\) | ||||
−0.591320 | + | 0.806437i | \(0.701393\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.5826 | 0.551551 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3.27340i | − 0.142322i | −0.997465 | − | 0.0711609i | \(-0.977330\pi\) | ||||
0.997465 | − | 0.0711609i | \(-0.0226704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.16515 | 0.246606 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.10080i | − 0.188919i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −53.8258 | −1.85606 | −0.928030 | − | 0.372505i | \(-0.878499\pi\) | ||||
−0.928030 | + | 0.372505i | \(0.878499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 29.1588i | − 0.940607i | −0.882505 | − | 0.470303i | \(-0.844144\pi\) | ||||
0.882505 | − | 0.470303i | \(-0.155856\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.00000 | −0.242424 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 14.7701i | − 0.422003i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −17.1652 | −0.463923 | −0.231962 | − | 0.972725i | \(-0.574514\pi\) | ||||
−0.231962 | + | 0.972725i | \(0.574514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 90.8294i | 2.32896i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.49545 | 0.182816 | 0.0914080 | − | 0.995814i | \(-0.470863\pi\) | ||||
0.0914080 | + | 0.995814i | \(0.470863\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 57.2530i | − 1.33147i | −0.746190 | − | 0.665733i | \(-0.768119\pi\) | ||||
0.746190 | − | 0.665733i | \(-0.231881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −56.7477 | −1.26106 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 37.2312i | 0.792154i | 0.918217 | + | 0.396077i | \(0.129629\pi\) | ||||
−0.918217 | + | 0.396077i | \(0.870371\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 110.168i | 2.16016i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 46.0000 | 0.867925 | 0.433962 | − | 0.900931i | \(-0.357115\pi\) | ||||
0.433962 | + | 0.900931i | \(0.357115\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.2016i | 0.185484i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −134.156 | −2.35362 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 75.1058i | 1.27298i | 0.771285 | + | 0.636490i | \(0.219614\pi\) | ||||
−0.771285 | + | 0.636490i | \(0.780386\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −28.0871 | −0.460445 | −0.230222 | − | 0.973138i | \(-0.573945\pi\) | ||||
−0.230222 | + | 0.973138i | \(0.573945\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 26.8945i | 0.426896i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 115.826 | 1.78193 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 81.3906i | 1.21479i | 0.794402 | + | 0.607393i | \(0.207785\pi\) | ||||
−0.794402 | + | 0.607393i | \(0.792215\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.3303 | 0.207686 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 32.1304i | − 0.452541i | −0.974064 | − | 0.226271i | \(-0.927347\pi\) | ||||
0.974064 | − | 0.226271i | \(-0.0726533\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −45.6515 | −0.625363 | −0.312682 | − | 0.949858i | \(-0.601227\pi\) | ||||
−0.312682 | + | 0.949858i | \(0.601227\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 26.9898i | 0.359864i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.83485 | 0.0627902 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9644i | 0.138790i | 0.997589 | + | 0.0693950i | \(0.0221069\pi\) | ||||
−0.997589 | + | 0.0693950i | \(0.977893\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −69.1561 | −0.853779 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 143.705i | − 1.73138i | −0.500579 | − | 0.865691i | \(-0.666880\pi\) | ||||
0.500579 | − | 0.865691i | \(-0.333120\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 140.486 | 1.65278 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 235.639i | − 2.70849i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 59.3212 | 0.666530 | 0.333265 | − | 0.942833i | \(-0.391850\pi\) | ||||
0.333265 | + | 0.942833i | \(0.391850\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 54.8933i | − 0.603223i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 127.652 | 1.37260 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 171.076i | 1.80080i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1652 | 0.176960 | 0.0884802 | − | 0.996078i | \(-0.471799\pi\) | ||||
0.0884802 | + | 0.996078i | \(0.471799\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 18.5758i | − 0.187634i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.74773 | −0.0866112 | −0.0433056 | − | 0.999062i | \(-0.513789\pi\) | ||||
−0.0433056 | + | 0.999062i | \(0.513789\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 54.7424i | − 0.531480i | −0.964045 | − | 0.265740i | \(-0.914384\pi\) | ||||
0.964045 | − | 0.265740i | \(-0.0856162\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 64.6606 | 0.615815 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 127.377i | − 1.19044i | −0.803561 | − | 0.595222i | \(-0.797064\pi\) | ||||
0.803561 | − | 0.595222i | \(-0.202936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 48.5045 | 0.444996 | 0.222498 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222498 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 75.1456i | − 0.676988i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −36.5045 | −0.323049 | −0.161525 | − | 0.986869i | \(-0.551641\pi\) | ||||
−0.161525 | + | 0.986869i | \(0.551641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 18.2740i | − 0.158904i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −210.904 | −1.80260 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 66.5807i | − 0.559502i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 117.661 | 0.972402 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 32.8136i | 0.266777i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −105.147 | −0.841176 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 41.9506i | 0.330320i | 0.986267 | + | 0.165160i | \(0.0528140\pi\) | ||||
−0.986267 | + | 0.165160i | \(0.947186\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 250.642 | 1.94296 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 47.3930i | 0.361779i | 0.983503 | + | 0.180889i | \(0.0578976\pi\) | ||||
−0.983503 | + | 0.180889i | \(0.942102\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 81.0780 | 0.609609 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 28.4756i | − 0.210930i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 153.652 | 1.12154 | 0.560772 | − | 0.827970i | \(-0.310504\pi\) | ||||
0.560772 | + | 0.827970i | \(0.310504\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 147.439i | − 1.06071i | −0.847775 | − | 0.530356i | \(-0.822058\pi\) | ||||
0.847775 | − | 0.530356i | \(-0.177942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −162.991 | −1.15596 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 37.9144i | 0.265136i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −300.486 | −2.07232 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 30.6446i | − 0.208467i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −78.3121 | −0.525585 | −0.262792 | − | 0.964852i | \(-0.584643\pi\) | ||||
−0.262792 | + | 0.964852i | \(0.584643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 154.327i | − 1.02204i | −0.859570 | − | 0.511018i | \(-0.829268\pi\) | ||||
0.859570 | − | 0.511018i | \(-0.170732\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −255.808 | −1.67194 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 162.781i | − 1.05020i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 161.408 | 1.02808 | 0.514039 | − | 0.857767i | \(-0.328149\pi\) | ||||
0.514039 | + | 0.857767i | \(0.328149\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 201.379i | 1.26653i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.66061 | −0.0537926 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 139.788i | 0.857594i | 0.903401 | + | 0.428797i | \(0.141062\pi\) | ||||
−0.903401 | + | 0.428797i | \(0.858938\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −44.6606 | −0.270670 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 115.348i | − 0.690709i | −0.938472 | − | 0.345355i | \(-0.887759\pi\) | ||||
0.938472 | − | 0.345355i | \(-0.112241\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 261.468 | 1.54715 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 311.507i | − 1.82168i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 85.7205 | 0.495494 | 0.247747 | − | 0.968825i | \(-0.420310\pi\) | ||||
0.247747 | + | 0.968825i | \(0.420310\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 16.3115i | − 0.0932083i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −328.798 | −1.85762 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 112.758i | − 0.629934i | −0.949103 | − | 0.314967i | \(-0.898006\pi\) | ||||
0.949103 | − | 0.314967i | \(-0.101994\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −65.9311 | −0.364260 | −0.182130 | − | 0.983274i | \(-0.558299\pi\) | ||||
−0.182130 | + | 0.983274i | \(0.558299\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 122.960i | − 0.671912i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −95.8258 | −0.517977 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 45.9868i | 0.245919i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.4955 | −0.0714045 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 207.243i | − 1.08504i | −0.840043 | − | 0.542520i | \(-0.817470\pi\) | ||||
0.840043 | − | 0.542520i | \(-0.182530\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 127.183 | 0.658981 | 0.329491 | − | 0.944159i | \(-0.393123\pi\) | ||||
0.329491 | + | 0.944159i | \(0.393123\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 507.062i | 2.60032i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −227.670 | −1.15568 | −0.577842 | − | 0.816149i | \(-0.696105\pi\) | ||||
−0.577842 | + | 0.816149i | \(0.696105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 171.378i | 0.861194i | 0.902544 | + | 0.430597i | \(0.141697\pi\) | ||||
−0.902544 | + | 0.430597i | \(0.858303\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −356.312 | −1.77270 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 142.410i | 0.701525i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 41.8439 | 0.204117 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 33.2746i | 0.160747i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −56.0000 | −0.267943 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 149.910i | 0.710473i | 0.934776 | + | 0.355237i | \(0.115600\pi\) | ||||
−0.934776 | + | 0.355237i | \(0.884400\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 140.661 | 0.660378 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 319.619i | − 1.48660i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −77.1470 | −0.355516 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 199.853i | − 0.912572i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 522.120 | 2.36253 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 85.2676i | − 0.382366i | −0.981554 | − | 0.191183i | \(-0.938768\pi\) | ||||
0.981554 | − | 0.191183i | \(-0.0612324\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −62.6697 | −0.278532 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 154.510i | − 0.680660i | −0.940306 | − | 0.340330i | \(-0.889461\pi\) | ||||
0.940306 | − | 0.340330i | \(-0.110539\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −330.555 | −1.44347 | −0.721736 | − | 0.692168i | \(-0.756656\pi\) | ||||
−0.721736 | + | 0.692168i | \(0.756656\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.1660i | 0.0916278i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 213.339 | 0.915620 | 0.457810 | − | 0.889050i | \(-0.348634\pi\) | ||||
0.457810 | + | 0.889050i | \(0.348634\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 207.846i | 0.884451i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −48.0000 | −0.202532 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 266.545i | − 1.11525i | −0.830092 | − | 0.557626i | \(-0.811712\pi\) | ||||
0.830092 | − | 0.557626i | \(-0.188288\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.4864 | 0.109902 | 0.0549510 | − | 0.998489i | \(-0.482500\pi\) | ||||
0.0549510 | + | 0.998489i | \(0.482500\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 348.659i | − 1.43481i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −39.0780 | −0.159502 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 635.806i | 2.57411i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 629.111 | 2.52655 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 372.796i | − 1.48524i | −0.669711 | − | 0.742622i | \(-0.733582\pi\) | ||||
0.669711 | − | 0.742622i | \(-0.266418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.98182 | 0.0236435 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 615.021i | 2.41185i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −206.000 | −0.801556 | −0.400778 | − | 0.916175i | \(-0.631260\pi\) | ||||
−0.400778 | + | 0.916175i | \(0.631260\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 45.4147i | 0.175346i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 547.147 | 2.09635 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 465.493i | − 1.76994i | −0.465652 | − | 0.884968i | \(-0.654180\pi\) | ||||
0.465652 | − | 0.884968i | \(-0.345820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 256.798 | 0.969051 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 259.697i | 0.972646i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 390.417 | 1.45137 | 0.725683 | − | 0.688029i | \(-0.241524\pi\) | ||||
0.725683 | + | 0.688029i | \(0.241524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 133.543i | 0.492778i | 0.969171 | + | 0.246389i | \(0.0792441\pi\) | ||||
−0.969171 | + | 0.246389i | \(0.920756\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 240.312 | 0.880264 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.2662i | 0.0409680i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −306.624 | −1.10695 | −0.553473 | − | 0.832867i | \(-0.686698\pi\) | ||||
−0.553473 | + | 0.832867i | \(0.686698\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 296.404i | 1.06238i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −112.642 | −0.400863 | −0.200431 | − | 0.979708i | \(-0.564234\pi\) | ||||
−0.200431 | + | 0.979708i | \(0.564234\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 474.368i | 1.67621i | 0.545507 | + | 0.838106i | \(0.316337\pi\) | ||||
−0.545507 | + | 0.838106i | \(0.683663\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −748.936 | −2.62785 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 19.8311i | − 0.0690979i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 344.285 | 1.19130 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 75.1456i | 0.258232i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.0962 | −0.0583489 | −0.0291744 | − | 0.999574i | \(-0.509288\pi\) | ||||
−0.0291744 | + | 0.999574i | \(0.509288\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 419.284i | 1.42130i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.32121 | 0.0313845 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 67.9156i | − 0.227143i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −151.477 | −0.503247 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 38.2958i | − 0.126389i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −156.798 | −0.514093 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 508.468i | 1.65625i | 0.560544 | + | 0.828124i | \(0.310592\pi\) | ||||
−0.560544 | + | 0.828124i | \(0.689408\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 239.652 | 0.775571 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.2084i | 0.100349i | 0.998740 | + | 0.0501743i | \(0.0159777\pi\) | ||||
−0.998740 | + | 0.0501743i | \(0.984022\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −175.183 | −0.559691 | −0.279846 | − | 0.960045i | \(-0.590283\pi\) | ||||
−0.279846 | + | 0.960045i | \(0.590283\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 150.140i | 0.476636i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −217.652 | −0.686598 | −0.343299 | − | 0.939226i | \(-0.611544\pi\) | ||||
−0.343299 | + | 0.939226i | \(0.611544\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 98.3612i | − 0.308342i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 557.633 | 1.73718 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 771.176i | 2.38754i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 127.913 | 0.393578 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 212.343i | 0.649368i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 98.5045 | 0.299406 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 601.467i | − 1.81712i | −0.417754 | − | 0.908560i | \(-0.637183\pi\) | ||||
0.417754 | − | 0.908560i | \(-0.362817\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 174.486 | 0.523983 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 454.369i | 1.35633i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −445.477 | −1.32189 | −0.660946 | − | 0.750434i | \(-0.729845\pi\) | ||||
−0.660946 | + | 0.750434i | \(0.729845\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 159.810i | − 0.471415i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 53.2848 | 0.156261 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 80.0000 | 0.231884 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 404.426i | − 1.16549i | −0.812654 | − | 0.582746i | \(-0.801978\pi\) | ||||
0.812654 | − | 0.582746i | \(-0.198022\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −157.895 | −0.452420 | −0.226210 | − | 0.974079i | \(-0.572634\pi\) | ||||
−0.226210 | + | 0.974079i | \(0.572634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 105.830i | − 0.301510i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −321.267 | −0.910104 | −0.455052 | − | 0.890465i | \(-0.650379\pi\) | ||||
−0.455052 | + | 0.890465i | \(0.650379\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 179.370i | − 0.505269i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 291.477 | 0.816463 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 173.968i | − 0.484590i | −0.970203 | − | 0.242295i | \(-0.922100\pi\) | ||||
0.970203 | − | 0.242295i | \(-0.0779002\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −578.092 | −1.60136 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 515.095i | 1.41899i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −254.853 | −0.698227 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 278.050i | 0.757630i | 0.925472 | + | 0.378815i | \(0.123668\pi\) | ||||
−0.925472 | + | 0.378815i | \(0.876332\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −76.1924 | −0.206484 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 121.705i | − 0.328045i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 342.973 | 0.919498 | 0.459749 | − | 0.888049i | \(-0.347939\pi\) | ||||
0.459749 | + | 0.888049i | \(0.347939\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 460.313i | − 1.22750i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1116.76 | −2.96223 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 145.731i | 0.384515i | 0.981345 | + | 0.192257i | \(0.0615808\pi\) | ||||
−0.981345 | + | 0.192257i | \(0.938419\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −183.652 | −0.482025 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 224.071i | − 0.585040i | −0.956259 | − | 0.292520i | \(-0.905506\pi\) | ||||
0.956259 | − | 0.292520i | \(-0.0944939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.9909 | 0.0701063 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 581.986i | 1.50384i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −99.8076 | −0.256575 | −0.128287 | − | 0.991737i | \(-0.540948\pi\) | ||||
−0.128287 | + | 0.991737i | \(0.540948\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 82.3756i | − 0.210679i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −207.477 | −0.527932 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 61.2096i | 0.154961i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 163.354 | 0.411470 | 0.205735 | − | 0.978608i | \(-0.434041\pi\) | ||||
0.205735 | + | 0.978608i | \(0.434041\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 354.944i | 0.889583i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −123.459 | −0.307878 | −0.153939 | − | 0.988080i | \(-0.549196\pi\) | ||||
−0.153939 | + | 0.988080i | \(0.549196\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 604.979i | − 1.50119i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −386.069 | −0.953257 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 31.3676i | − 0.0770703i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.84394 | 0.0191783 | 0.00958917 | − | 0.999954i | \(-0.496948\pi\) | ||||
0.00958917 | + | 0.999954i | \(0.496948\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 672.656i | 1.63663i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 198.711 | 0.481141 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 802.242i | − 1.93311i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 645.459 | 1.54786 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 364.565i | − 0.870083i | −0.900410 | − | 0.435041i | \(-0.856734\pi\) | ||||
0.900410 | − | 0.435041i | \(-0.143266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −708.570 | −1.68306 | −0.841532 | − | 0.540208i | \(-0.818346\pi\) | ||||
−0.841532 | + | 0.540208i | \(0.818346\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 378.461i | − 0.894707i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 155.147 | 0.365052 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 74.3115i | 0.174032i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −165.982 | −0.386904 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 80.9463i | − 0.187810i | −0.995581 | − | 0.0939052i | \(-0.970065\pi\) | ||||
0.995581 | − | 0.0939052i | \(-0.0299350\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 295.495 | 0.682438 | 0.341219 | − | 0.939984i | \(-0.389160\pi\) | ||||
0.341219 | + | 0.939984i | \(0.389160\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1315.47i | − 3.02407i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 100.312 | 0.229547 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 11.5680i | − 0.0263508i | −0.999913 | − | 0.0131754i | \(-0.995806\pi\) | ||||
0.999913 | − | 0.0131754i | \(-0.00419398\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 71.1561 | 0.161352 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 284.660i | 0.642573i | 0.946982 | + | 0.321287i | \(0.104115\pi\) | ||||
−0.946982 | + | 0.321287i | \(0.895885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 331.165 | 0.744191 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 342.835i | − 0.766969i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 154.624 | 0.344375 | 0.172187 | − | 0.985064i | \(-0.444917\pi\) | ||||
0.172187 | + | 0.985064i | \(0.444917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.6972i | 0.0303707i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 675.615 | 1.49142 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 306.446i | − 0.673508i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 410.450 | 0.898140 | 0.449070 | − | 0.893497i | \(-0.351755\pi\) | ||||
0.449070 | + | 0.893497i | \(0.351755\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 128.362i | − 0.279657i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 595.078 | 1.29084 | 0.645421 | − | 0.763827i | \(-0.276682\pi\) | ||||
0.645421 | + | 0.763827i | \(0.276682\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 511.924i | 1.10567i | 0.833291 | + | 0.552834i | \(0.186454\pi\) | ||||
−0.833291 | + | 0.552834i | \(0.813546\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 712.624 | 1.53253 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 365.122i | − 0.781846i | −0.920423 | − | 0.390923i | \(-0.872156\pi\) | ||||
0.920423 | − | 0.390923i | \(-0.127844\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 215.339 | 0.459146 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 706.614i | 1.50024i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 104.624 | 0.221193 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 188.929i | 0.397745i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −467.597 | −0.980287 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 202.745i | − 0.423268i | −0.977349 | − | 0.211634i | \(-0.932122\pi\) | ||||
0.977349 | − | 0.211634i | \(-0.0678785\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −356.138 | −0.740411 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 37.9144i | − 0.0784978i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 95.8258 | 0.197579 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 821.120i | 1.68608i | 0.537853 | + | 0.843039i | \(0.319236\pi\) | ||||
−0.537853 | + | 0.843039i | \(0.680764\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −611.964 | −1.25146 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 316.505i | − 0.644613i | −0.946635 | − | 0.322307i | \(-0.895542\pi\) | ||||
0.946635 | − | 0.322307i | \(-0.104458\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1354.53 | −2.74753 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 103.701i | − 0.209497i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −85.0091 | −0.171044 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 176.415i | − 0.353538i | −0.984252 | − | 0.176769i | \(-0.943435\pi\) | ||||
0.984252 | − | 0.176769i | \(-0.0565646\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 504.973 | 1.00793 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 883.918i | 1.75729i | 0.477474 | + | 0.878646i | \(0.341553\pi\) | ||||
−0.477474 | + | 0.878646i | \(0.658447\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −48.8348 | −0.0967027 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1144.66i | 2.25770i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −519.216 | −1.02007 | −0.510035 | − | 0.860153i | \(-0.670368\pi\) | ||||
−0.510035 | + | 0.860153i | \(0.670368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 120.783i | 0.236365i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 156.312 | 0.304702 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 305.604i | − 0.593405i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −68.0364 | −0.131598 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 375.267i | 0.723058i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1037.40 | 1.99118 | 0.995590 | − | 0.0938137i | \(-0.0299058\pi\) | ||||
0.995590 | + | 0.0938137i | \(0.0299058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 525.900i | − 1.00555i | −0.864419 | − | 0.502773i | \(-0.832313\pi\) | ||||
0.864419 | − | 0.502773i | \(-0.167687\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 71.4083 | 0.136016 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 733.786i | − 1.39238i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 518.285 | 0.979745 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 763.462i | − 1.43778i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 155.514 | 0.291770 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 711.094i | − 1.32915i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 493.633 | 0.919243 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 12.7918i | − 0.0237325i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 776.221 | 1.43479 | 0.717395 | − | 0.696667i | \(-0.245334\pi\) | ||||
0.717395 | + | 0.696667i | \(0.245334\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 288.633i | − 0.531553i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 270.780 | 0.496845 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 153.041i | 0.279782i | 0.990167 | + | 0.139891i | \(0.0446752\pi\) | ||||
−0.990167 | + | 0.139891i | \(0.955325\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 285.510 | 0.520054 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1649.47i | − 2.99359i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.0091 | 0.0524577 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 419.506i | − 0.755867i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −481.579 | −0.864594 | −0.432297 | − | 0.901731i | \(-0.642297\pi\) | ||||
−0.432297 | + | 0.901731i | \(0.642297\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1187.87i | − 2.12499i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −201.321 | −0.358861 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 489.909i | − 0.870176i | −0.900388 | − | 0.435088i | \(-0.856717\pi\) | ||||
0.900388 | − | 0.435088i | \(-0.143283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −203.789 | −0.360689 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 182.970i | 0.322698i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 97.8985 | 0.172054 | 0.0860268 | − | 0.996293i | \(-0.472583\pi\) | ||||
0.0860268 | + | 0.996293i | \(0.472583\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 752.680i | 1.31818i | 0.752065 | + | 0.659089i | \(0.229058\pi\) | ||||
−0.752065 | + | 0.659089i | \(0.770942\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 907.267 | 1.58336 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 20.1810i | − 0.0350974i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −924.533 | −1.60231 | −0.801155 | − | 0.598456i | \(-0.795781\pi\) | ||||
−0.801155 | + | 0.598456i | \(0.795781\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 556.783i | 0.961629i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −380.207 | −0.654401 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 84.0604i | 0.144186i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1177.39 | −2.01263 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1110.24i | − 1.89138i | −0.325077 | − | 0.945688i | \(-0.605390\pi\) | ||||
0.325077 | − | 0.945688i | \(-0.394610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 893.561 | 1.51708 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 996.693i | − 1.68645i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.9909 | 0.0758700 | 0.0379350 | − | 0.999280i | \(-0.487922\pi\) | ||||
0.0379350 | + | 0.999280i | \(0.487922\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 371.692i | − 0.624692i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −750.258 | −1.25671 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 988.382i | 1.65005i | 0.565094 | + | 0.825026i | \(0.308840\pi\) | ||||
−0.565094 | + | 0.825026i | \(0.691160\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 732.570 | 1.21892 | 0.609459 | − | 0.792818i | \(-0.291387\pi\) | ||||
0.609459 | + | 0.792818i | \(0.291387\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 827.348i | − 1.37205i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 656.849 | 1.08570 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 145.874i | 0.240319i | 0.992755 | + | 0.120160i | \(0.0383406\pi\) | ||||
−0.992755 | + | 0.120160i | \(0.961659\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −623.441 | −1.02371 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 772.463i | 1.26426i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −100.577 | −0.164074 | −0.0820369 | − | 0.996629i | \(-0.526143\pi\) | ||||
−0.0820369 | + | 0.996629i | \(0.526143\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 183.184i | 0.297861i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −342.102 | −0.554459 | −0.277230 | − | 0.960804i | \(-0.589416\pi\) | ||||
−0.277230 | + | 0.960804i | \(0.589416\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 512.123i | 0.827340i | 0.910427 | + | 0.413670i | \(0.135753\pi\) | ||||
−0.910427 | + | 0.413670i | \(0.864247\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.6970 | −0.0268872 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 156.949i | − 0.251925i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −741.120 | −1.18579 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 245.157i | − 0.391000i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −431.964 | −0.686747 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 530.517i | − 0.840755i | −0.907349 | − | 0.420378i | \(-0.861898\pi\) | ||||
0.907349 | − | 0.420378i | \(-0.138102\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −656.276 | −1.03677 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 234.193i | 0.368807i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −145.234 | −0.227997 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 326.611i | 0.511128i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1054.80 | −1.64555 | −0.822776 | − | 0.568366i | \(-0.807576\pi\) | ||||
−0.822776 | + | 0.568366i | \(0.807576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 107.316i | 0.166899i | 0.996512 | + | 0.0834493i | \(0.0265937\pi\) | ||||
−0.996512 | + | 0.0834493i | \(0.973406\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1399.23 | 2.16935 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 202.142i | 0.312429i | 0.987723 | + | 0.156215i | \(0.0499291\pi\) | ||||
−0.987723 | + | 0.156215i | \(0.950071\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −137.248 | −0.211477 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 337.734i | − 0.518793i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1278.73 | −1.95823 | −0.979116 | − | 0.203301i | \(-0.934833\pi\) | ||||
−0.979116 | + | 0.203301i | \(0.934833\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 264.575i | 0.403931i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 464.055 | 0.706324 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 835.500i | 1.26783i | 0.773403 | + | 0.633915i | \(0.218553\pi\) | ||||
−0.773403 | + | 0.633915i | \(0.781447\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −998.381 | −1.51041 | −0.755205 | − | 0.655489i | \(-0.772463\pi\) | ||||
−0.755205 | + | 0.655489i | \(0.772463\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2285.74i | 3.44757i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 452.624 | 0.680638 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 176.193i | 0.264158i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 373.285 | 0.557974 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 51.3264i | − 0.0764925i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −572.330 | −0.850416 | −0.425208 | − | 0.905096i | \(-0.639799\pi\) | ||||
−0.425208 | + | 0.905096i | \(0.639799\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 31.4472i | − 0.0465885i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1079.77 | −1.59493 | −0.797465 | − | 0.603365i | \(-0.793826\pi\) | ||||
−0.797465 | + | 0.603365i | \(0.793826\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 45.4147i | − 0.0668847i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 676.414 | 0.993265 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 444.708i | 0.651110i | 0.945523 | + | 0.325555i | \(0.105551\pi\) | ||||
−0.945523 | + | 0.325555i | \(0.894449\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 857.771 | 1.25222 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 1447.11i | − 2.10641i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 954.395 | 1.38519 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 214.227i | − 0.310025i | −0.987913 | − | 0.155012i | \(-0.950458\pi\) | ||||
0.987913 | − | 0.155012i | \(-0.0495417\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −49.1470 | −0.0709191 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 823.090i | − 1.18430i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 188.624 | 0.270623 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 933.958i | 1.33613i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −573.477 | −0.818085 | −0.409042 | − | 0.912515i | \(-0.634137\pi\) | ||||
−0.409042 | + | 0.912515i | \(0.634137\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 526.019i | − 0.748250i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −909.909 | −1.29065 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.1443i | 0.0327359i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 436.817 | 0.616102 | 0.308051 | − | 0.951370i | \(-0.400323\pi\) | ||||
0.308051 | + | 0.951370i | \(0.400323\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 111.455i | − 0.156758i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −95.4485 | −0.133869 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 211.660i | 0.296028i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1166.88 | 1.62745 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1279.32i | 1.77930i | 0.456639 | + | 0.889652i | \(0.349053\pi\) | ||||
−0.456639 | + | 0.889652i | \(0.650947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −144.835 | −0.200881 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 115.952i | 0.160376i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −331.844 | −0.457716 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 166.834i | 0.229483i | 0.993395 | + | 0.114741i | \(0.0366040\pi\) | ||||
−0.993395 | + | 0.114741i | \(0.963396\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 903.955 | 1.23999 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1440.78i | − 1.97097i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −105.299 | −0.143655 | −0.0718276 | − | 0.997417i | \(-0.522883\pi\) | ||||
−0.0718276 | + | 0.997417i | \(0.522883\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 171.076i | − 0.232756i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −148.733 | −0.201809 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 898.713i | 1.21612i | 0.793891 | + | 0.608060i | \(0.208052\pi\) | ||||
−0.793891 | + | 0.608060i | \(0.791948\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2783.43 | −3.75632 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1154.15i | 1.55337i | 0.629891 | + | 0.776683i | \(0.283099\pi\) | ||||
−0.629891 | + | 0.776683i | \(0.716901\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −437.183 | −0.586823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1460.78i | 1.95553i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −337.009 | −0.449945 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 561.025i | 0.747038i | 0.927623 | + | 0.373519i | \(0.121849\pi\) | ||||
−0.927623 | + | 0.373519i | \(0.878151\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1632.03 | 2.16737 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 861.545i | − 1.14112i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 860.120 | 1.13622 | 0.568111 | − | 0.822952i | \(-0.307675\pi\) | ||||
0.568111 | + | 0.822952i | \(0.307675\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.1872i | 0.0345023i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1336.47 | 1.75620 | 0.878100 | − | 0.478477i | \(-0.158811\pi\) | ||||
0.878100 | + | 0.478477i | \(0.158811\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 128.331i | − 0.168193i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1428.07 | −1.86675 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1558.28i | 2.03165i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −716.323 | −0.931499 | −0.465749 | − | 0.884917i | \(-0.654215\pi\) | ||||
−0.465749 | + | 0.884917i | \(0.654215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 901.827i | − 1.16969i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 98.6644 | 0.127638 | 0.0638191 | − | 0.997961i | \(-0.479672\pi\) | ||||
0.0638191 | + | 0.997961i | \(0.479672\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 179.768i | − 0.231959i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −198.817 | −0.255877 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 229.695i | 0.294859i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 58.7152 | 0.0751795 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 274.555i | 0.350644i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 901.074 | 1.14787 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 673.903i | − 0.856293i | −0.903709 | − | 0.428147i | \(-0.859167\pi\) | ||||
0.903709 | − | 0.428147i | \(-0.140833\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2037.84 | 2.58281 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 96.5819i | 0.122101i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −582.744 | −0.734860 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1124.21i | 1.41410i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1097.76 | 1.37736 | 0.688681 | − | 0.725065i | \(-0.258190\pi\) | ||||
0.688681 | + | 0.725065i | \(0.258190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 936.929i | 1.17263i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −603.009 | −0.752820 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 83.4236i | − 0.103890i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48.3485 | −0.0600602 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1709.17i | 2.11793i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −340.853 | −0.421326 | −0.210663 | − | 0.977559i | \(-0.567562\pi\) | ||||
−0.210663 | + | 0.977559i | \(0.567562\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 112.655i | − 0.138909i | −0.997585 | − | 0.0694547i | \(-0.977874\pi\) | ||||
0.997585 | − | 0.0694547i | \(-0.0221259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −584.624 | −0.719095 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 780.376i | 0.957517i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1754.50 | 2.14749 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 557.999i | 0.681317i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1267.91 | 1.54435 | 0.772174 | − | 0.635412i | \(-0.219170\pi\) | ||||
0.772174 | + | 0.635412i | \(0.219170\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 743.669i | − 0.903608i | −0.892117 | − | 0.451804i | \(-0.850781\pi\) | ||||
0.892117 | − | 0.451804i | \(-0.149219\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −49.3212 | −0.0597833 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1473.29i | 1.78149i | 0.454503 | + | 0.890745i | \(0.349817\pi\) | ||||
−0.454503 | + | 0.890745i | \(0.650183\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 379.840 | 0.458191 | 0.229095 | − | 0.973404i | \(-0.426423\pi\) | ||||
0.229095 | + | 0.973404i | \(0.426423\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1342.34i | − 1.61533i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −176.156 | −0.211472 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 643.941i | − 0.771187i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −148.733 | −0.177698 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1080.75i | − 1.28814i | −0.764965 | − | 0.644072i | \(-0.777244\pi\) | ||||
0.764965 | − | 0.644072i | \(-0.222756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2056.21 | 2.44496 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 493.126i | − 0.584966i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1459.67 | 1.72742 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 311.301i | − 0.367533i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2076.69 | −2.44604 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56.1884i | 0.0660264i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 125.372 | 0.146978 | 0.0734888 | − | 0.997296i | \(-0.476587\pi\) | ||||
0.0734888 | + | 0.997296i | \(0.476587\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 1739.01i | − 2.03393i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 721.717 | 0.842143 | 0.421072 | − | 0.907027i | \(-0.361654\pi\) | ||||
0.421072 | + | 0.907027i | \(0.361654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 104.742i | 0.121935i | 0.998140 | + | 0.0609676i | \(0.0194186\pi\) | ||||
−0.998140 | + | 0.0609676i | \(0.980581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 86.8167 | 0.100832 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 425.005i | 0.492474i | 0.969210 | + | 0.246237i | \(0.0791941\pi\) | ||||
−0.969210 | + | 0.246237i | \(0.920806\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 478.541 | 0.553226 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1507.21i | 1.73842i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.0364 | −0.0230568 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1688.67i | 1.93877i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −174.486 | −0.199870 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 278.193i | 0.317935i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 469.368 | 0.535197 | 0.267599 | − | 0.963530i | \(-0.413770\pi\) | ||||
0.267599 | + | 0.963530i | \(0.413770\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 74.8438i | − 0.0851466i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1116.11 | −1.26687 | −0.633435 | − | 0.773796i | \(-0.718356\pi\) | ||||
−0.633435 | + | 0.773796i | \(0.718356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 271.281i | − 0.307227i | −0.988131 | − | 0.153613i | \(-0.950909\pi\) | ||||
0.988131 | − | 0.153613i | \(-0.0490910\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1835.54 | −2.07406 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 211.421i | − 0.238355i | −0.992873 | − | 0.119178i | \(-0.961974\pi\) | ||||
0.992873 | − | 0.119178i | \(-0.0380258\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 110.991 | 0.124849 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 126.376i | − 0.141836i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1140.94 | −1.27764 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 629.481i | − 0.703331i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 297.321 | 0.331462 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1569.50i | 1.74582i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1157.60 | 1.28479 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 663.138i | − 0.734372i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −368.065 | −0.406702 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 410.290i | 0.452359i | 0.974086 | + | 0.226179i | \(0.0726236\pi\) | ||||
−0.974086 | + | 0.226179i | \(0.927376\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 88.9220 | 0.0978239 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 608.982i | − 0.668476i | −0.942489 | − | 0.334238i | \(-0.891521\pi\) | ||||
0.942489 | − | 0.334238i | \(-0.108479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 262.606 | 0.287630 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 686.433i | − 0.750200i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 125.390 | 0.136740 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 497.942i | − 0.541830i | −0.962603 | − | 0.270915i | \(-0.912674\pi\) | ||||
0.962603 | − | 0.270915i | \(-0.0873262\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2225.97 | −2.41691 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 666.633i | − 0.722246i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −105.826 | −0.114406 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 556.465i | 0.600286i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −65.4045 | −0.0704032 | −0.0352016 | − | 0.999380i | \(-0.511207\pi\) | ||||
−0.0352016 | + | 0.999380i | \(0.511207\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 214.512i | − 0.230411i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −136.624 | −0.146435 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 256.725i | 0.274572i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −600.918 | −0.641321 | −0.320661 | − | 0.947194i | \(-0.603905\pi\) | ||||
−0.320661 | + | 0.947194i | \(0.603905\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 766.918i | − 0.816739i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1482.87 | 1.57584 | 0.787921 | − | 0.615776i | \(-0.211157\pi\) | ||||
0.787921 | + | 0.615776i | \(0.211157\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 24.5356i | − 0.0260187i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −75.3394 | −0.0797242 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 806.865i | − 0.852023i | −0.904718 | − | 0.426011i | \(-0.859918\pi\) | ||||
0.904718 | − | 0.426011i | \(-0.140082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −947.165 | −0.998067 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 952.835i | − 1.00193i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 899.945 | 0.944329 | 0.472164 | − | 0.881510i | \(-0.343473\pi\) | ||||
0.472164 | + | 0.881510i | \(0.343473\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1156.95i | − 1.21146i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 430.606 | 0.449954 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 406.524i | − 0.423904i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 110.764 | 0.115259 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1294.81i | 1.34456i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 710.011 | 0.735762 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1725.92i | 1.78482i | 0.451228 | + | 0.892409i | \(0.350986\pi\) | ||||
−0.451228 | + | 0.892409i | \(0.649014\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3376.06 | −3.48406 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 657.951i | − 0.677601i | −0.940858 | − | 0.338800i | \(-0.889979\pi\) | ||||
0.940858 | − | 0.338800i | \(-0.110021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −390.087 | −0.400912 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 559.977i | 0.574336i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.9364 | 0.0480413 | 0.0240207 | − | 0.999711i | \(-0.492353\pi\) | ||||
0.0240207 | + | 0.999711i | \(0.492353\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 108.404i | 0.110729i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −493.056 | −0.502606 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 377.095i | 0.383616i | 0.981432 | + | 0.191808i | \(0.0614351\pi\) | ||||
−0.981432 | + | 0.191808i | \(0.938565\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1270.98 | −1.29034 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 431.233i | 0.436913i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −187.412 | −0.189497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 926.283i | − 0.934696i | −0.884074 | − | 0.467348i | \(-0.845210\pi\) | ||||
0.884074 | − | 0.467348i | \(-0.154790\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2633.10 | 2.65166 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 956.729i | 0.961537i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.6462 | 0.0568167 | 0.0284083 | − | 0.999596i | \(-0.490956\pi\) | ||||
0.0284083 | + | 0.999596i | \(0.490956\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 87.5560i | 0.0876437i |
(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 | 448.3.d.b.127.4 | 4 | ||
4.3 | odd | 2 | inner | 448.3.d.b.127.1 | 4 | ||
8.3 | odd | 2 | 112.3.d.b.15.4 | yes | 4 | ||
8.5 | even | 2 | 112.3.d.b.15.1 | ✓ | 4 | ||
16.3 | odd | 4 | 1792.3.g.e.127.7 | 8 | |||
16.5 | even | 4 | 1792.3.g.e.127.8 | 8 | |||
16.11 | odd | 4 | 1792.3.g.e.127.2 | 8 | |||
16.13 | even | 4 | 1792.3.g.e.127.1 | 8 | |||
24.5 | odd | 2 | 1008.3.m.d.127.3 | 4 | |||
24.11 | even | 2 | 1008.3.m.d.127.4 | 4 | |||
56.3 | even | 6 | 784.3.r.i.79.1 | 4 | |||
56.5 | odd | 6 | 784.3.r.i.655.1 | 4 | |||
56.11 | odd | 6 | 784.3.r.o.79.2 | 4 | |||
56.13 | odd | 2 | 784.3.d.j.687.4 | 4 | |||
56.19 | even | 6 | 784.3.r.n.655.2 | 4 | |||
56.27 | even | 2 | 784.3.d.j.687.1 | 4 | |||
56.37 | even | 6 | 784.3.r.o.655.2 | 4 | |||
56.45 | odd | 6 | 784.3.r.n.79.2 | 4 | |||
56.51 | odd | 6 | 784.3.r.j.655.1 | 4 | |||
56.53 | even | 6 | 784.3.r.j.79.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.3.d.b.15.1 | ✓ | 4 | 8.5 | even | 2 | ||
112.3.d.b.15.4 | yes | 4 | 8.3 | odd | 2 | ||
448.3.d.b.127.1 | 4 | 4.3 | odd | 2 | inner | ||
448.3.d.b.127.4 | 4 | 1.1 | even | 1 | trivial | ||
784.3.d.j.687.1 | 4 | 56.27 | even | 2 | |||
784.3.d.j.687.4 | 4 | 56.13 | odd | 2 | |||
784.3.r.i.79.1 | 4 | 56.3 | even | 6 | |||
784.3.r.i.655.1 | 4 | 56.5 | odd | 6 | |||
784.3.r.j.79.1 | 4 | 56.53 | even | 6 | |||
784.3.r.j.655.1 | 4 | 56.51 | odd | 6 | |||
784.3.r.n.79.2 | 4 | 56.45 | odd | 6 | |||
784.3.r.n.655.2 | 4 | 56.19 | even | 6 | |||
784.3.r.o.79.2 | 4 | 56.11 | odd | 6 | |||
784.3.r.o.655.2 | 4 | 56.37 | even | 6 | |||
1008.3.m.d.127.3 | 4 | 24.5 | odd | 2 | |||
1008.3.m.d.127.4 | 4 | 24.11 | even | 2 | |||
1792.3.g.e.127.1 | 8 | 16.13 | even | 4 | |||
1792.3.g.e.127.2 | 8 | 16.11 | odd | 4 | |||
1792.3.g.e.127.7 | 8 | 16.3 | odd | 4 | |||
1792.3.g.e.127.8 | 8 | 16.5 | even | 4 |