Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,3,Mod(71,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.71");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.43325133094\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 8x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.2 | ||
Root | \(2.57794i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.71 |
Dual form | 126.3.b.a.71.3 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.41421i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 8.89753i | 1.77951i | 0.456443 | + | 0.889753i | \(0.349123\pi\) | ||||
−0.456443 | + | 0.889753i | \(0.650877\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575 | 0.377964 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 12.5830 | 1.25830 | ||||||||
\(11\) | 17.7951i | 1.61773i | 0.587993 | + | 0.808866i | \(0.299918\pi\) | ||||
−0.587993 | + | 0.808866i | \(0.700082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.58301 | 0.198693 | 0.0993464 | − | 0.995053i | \(-0.468325\pi\) | ||||
0.0993464 | + | 0.995053i | \(0.468325\pi\) | |||||||
\(14\) | − 3.74166i | − 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 25.8681i | − 1.52165i | −0.648956 | − | 0.760826i | \(-0.724794\pi\) | ||||
0.648956 | − | 0.760826i | \(-0.275206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.0000 | 1.05263 | 0.526316 | − | 0.850289i | \(-0.323573\pi\) | ||||
0.526316 | + | 0.850289i | \(0.323573\pi\) | |||||||
\(20\) | − 17.7951i | − 0.889753i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 25.1660 | 1.14391 | ||||||||
\(23\) | 17.7951i | 0.773698i | 0.922143 | + | 0.386849i | \(0.126437\pi\) | ||||
−0.922143 | + | 0.386849i | \(0.873563\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −54.1660 | −2.16664 | ||||||||
\(26\) | − 3.65292i | − 0.140497i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.29150 | −0.188982 | ||||||||
\(29\) | 11.9034i | 0.410463i | 0.978713 | + | 0.205232i | \(0.0657947\pi\) | ||||
−0.978713 | + | 0.205232i | \(0.934205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −17.1660 | −0.553742 | −0.276871 | − | 0.960907i | \(-0.589298\pi\) | ||||
−0.276871 | + | 0.960907i | \(0.589298\pi\) | |||||||
\(32\) | − 5.65685i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −36.5830 | −1.07597 | ||||||||
\(35\) | 23.5406i | 0.672590i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38.0000 | 1.02703 | 0.513514 | − | 0.858082i | \(-0.328344\pi\) | ||||
0.513514 | + | 0.858082i | \(0.328344\pi\) | |||||||
\(38\) | − 28.2843i | − 0.744323i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −25.1660 | −0.629150 | ||||||||
\(41\) | − 15.7338i | − 0.383752i | −0.981419 | − | 0.191876i | \(-0.938543\pi\) | ||||
0.981419 | − | 0.191876i | \(-0.0614571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −43.4980 | −1.01158 | −0.505791 | − | 0.862656i | \(-0.668799\pi\) | ||||
−0.505791 | + | 0.862656i | \(0.668799\pi\) | |||||||
\(44\) | − 35.5901i | − 0.808866i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 25.1660 | 0.547087 | ||||||||
\(47\) | − 16.9706i | − 0.361076i | −0.983568 | − | 0.180538i | \(-0.942216\pi\) | ||||
0.983568 | − | 0.180538i | \(-0.0577838\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 76.6023i | 1.53205i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.16601 | −0.0993464 | ||||||||
\(53\) | − 85.5571i | − 1.61429i | −0.590356 | − | 0.807143i | \(-0.701013\pi\) | ||||
0.590356 | − | 0.807143i | \(-0.298987\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −158.332 | −2.87876 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 16.8340 | 0.290241 | ||||||||
\(59\) | 1.64899i | 0.0279489i | 0.999902 | + | 0.0139745i | \(0.00444836\pi\) | ||||
−0.999902 | + | 0.0139745i | \(0.995552\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 100.332 | 1.64479 | 0.822394 | − | 0.568919i | \(-0.192638\pi\) | ||||
0.822394 | + | 0.568919i | \(0.192638\pi\) | |||||||
\(62\) | 24.2764i | 0.391555i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 22.9824i | 0.353575i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 36.6640 | 0.547225 | 0.273612 | − | 0.961840i | \(-0.411781\pi\) | ||||
0.273612 | + | 0.961840i | \(0.411781\pi\) | |||||||
\(68\) | 51.7362i | 0.760826i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 33.2915 | 0.475593 | ||||||||
\(71\) | 17.7951i | 0.250635i | 0.992117 | + | 0.125317i | \(0.0399949\pi\) | ||||
−0.992117 | + | 0.125317i | \(0.960005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28.9150 | 0.396096 | 0.198048 | − | 0.980192i | \(-0.436540\pi\) | ||||
0.198048 | + | 0.980192i | \(0.436540\pi\) | |||||||
\(74\) | − 53.7401i | − 0.726218i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −40.0000 | −0.526316 | ||||||||
\(77\) | 47.0813i | 0.611445i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 118.332 | 1.49787 | 0.748937 | − | 0.662641i | \(-0.230565\pi\) | ||||
0.748937 | + | 0.662641i | \(0.230565\pi\) | |||||||
\(80\) | 35.5901i | 0.444876i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −22.2510 | −0.271353 | ||||||||
\(83\) | − 120.443i | − 1.45112i | −0.688159 | − | 0.725560i | \(-0.741581\pi\) | ||||
0.688159 | − | 0.725560i | \(-0.258419\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 230.162 | 2.70779 | ||||||||
\(86\) | 61.5155i | 0.715297i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −50.3320 | −0.571955 | ||||||||
\(89\) | − 139.475i | − 1.56713i | −0.621309 | − | 0.783566i | \(-0.713399\pi\) | ||||
0.621309 | − | 0.783566i | \(-0.286601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.83399 | 0.0750988 | ||||||||
\(92\) | − 35.5901i | − 0.386849i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −24.0000 | −0.255319 | ||||||||
\(95\) | 177.951i | 1.87316i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 44.4131 | 0.457867 | 0.228933 | − | 0.973442i | \(-0.426476\pi\) | ||||
0.228933 | + | 0.973442i | \(0.426476\pi\) | |||||||
\(98\) | − 9.89949i | − 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 108.332 | 1.08332 | ||||||||
\(101\) | 31.8799i | 0.315642i | 0.987468 | + | 0.157821i | \(0.0504470\pi\) | ||||
−0.987468 | + | 0.157821i | \(0.949553\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.50197 | 0.0437084 | 0.0218542 | − | 0.999761i | \(-0.493043\pi\) | ||||
0.0218542 | + | 0.999761i | \(0.493043\pi\) | |||||||
\(104\) | 7.30584i | 0.0702485i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −120.996 | −1.14147 | ||||||||
\(107\) | 172.179i | 1.60915i | 0.593851 | + | 0.804575i | \(0.297607\pi\) | ||||
−0.593851 | + | 0.804575i | \(0.702393\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −177.830 | −1.63147 | −0.815734 | − | 0.578427i | \(-0.803667\pi\) | ||||
−0.815734 | + | 0.578427i | \(0.803667\pi\) | |||||||
\(110\) | 223.915i | 2.03559i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.5830 | 0.0944911 | ||||||||
\(113\) | 31.3475i | 0.277411i | 0.990334 | + | 0.138706i | \(0.0442942\pi\) | ||||
−0.990334 | + | 0.138706i | \(0.955706\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −158.332 | −1.37680 | ||||||||
\(116\) | − 23.8069i | − 0.205232i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.33202 | 0.0197629 | ||||||||
\(119\) | − 68.4405i | − 0.575131i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −195.664 | −1.61706 | ||||||||
\(122\) | − 141.891i | − 1.16304i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 34.3320 | 0.276871 | ||||||||
\(125\) | − 259.505i | − 2.07604i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 214.332 | 1.68765 | 0.843827 | − | 0.536616i | \(-0.180297\pi\) | ||||
0.843827 | + | 0.536616i | \(0.180297\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 32.5020 | 0.250015 | ||||||||
\(131\) | 91.4488i | 0.698082i | 0.937107 | + | 0.349041i | \(0.113493\pi\) | ||||
−0.937107 | + | 0.349041i | \(0.886507\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 52.9150 | 0.397857 | ||||||||
\(134\) | − 51.8508i | − 0.386946i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 73.1660 | 0.537985 | ||||||||
\(137\) | − 106.891i | − 0.780223i | −0.920768 | − | 0.390111i | \(-0.872437\pi\) | ||||
0.920768 | − | 0.390111i | \(-0.127563\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −121.328 | −0.872864 | −0.436432 | − | 0.899737i | \(-0.643758\pi\) | ||||
−0.436432 | + | 0.899737i | \(0.643758\pi\) | |||||||
\(140\) | − 47.0813i | − 0.336295i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.1660 | 0.177225 | ||||||||
\(143\) | 45.9647i | 0.321432i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −105.911 | −0.730421 | ||||||||
\(146\) | − 40.8920i | − 0.280082i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −76.0000 | −0.513514 | ||||||||
\(149\) | − 17.6749i | − 0.118623i | −0.998240 | − | 0.0593117i | \(-0.981109\pi\) | ||||
0.998240 | − | 0.0593117i | \(-0.0188906\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −50.8340 | −0.336649 | −0.168324 | − | 0.985732i | \(-0.553836\pi\) | ||||
−0.168324 | + | 0.985732i | \(0.553836\pi\) | |||||||
\(152\) | 56.5685i | 0.372161i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 66.5830 | 0.432357 | ||||||||
\(155\) | − 152.735i | − 0.985388i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 68.9961 | 0.439465 | 0.219733 | − | 0.975560i | \(-0.429481\pi\) | ||||
0.219733 | + | 0.975560i | \(0.429481\pi\) | |||||||
\(158\) | − 167.347i | − 1.05916i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 50.3320 | 0.314575 | ||||||||
\(161\) | 47.0813i | 0.292430i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −166.996 | −1.02452 | −0.512258 | − | 0.858832i | \(-0.671191\pi\) | ||||
−0.512258 | + | 0.858832i | \(0.671191\pi\) | |||||||
\(164\) | 31.4676i | 0.191876i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −170.332 | −1.02610 | ||||||||
\(167\) | 120.443i | 0.721215i | 0.932718 | + | 0.360608i | \(0.117431\pi\) | ||||
−0.932718 | + | 0.360608i | \(0.882569\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −162.328 | −0.960521 | ||||||||
\(170\) | − 325.498i | − 1.91470i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 86.9961 | 0.505791 | ||||||||
\(173\) | − 91.8610i | − 0.530989i | −0.964112 | − | 0.265494i | \(-0.914465\pi\) | ||||
0.964112 | − | 0.265494i | \(-0.0855351\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −143.310 | −0.818913 | ||||||||
\(176\) | 71.1802i | 0.404433i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −197.247 | −1.10813 | ||||||||
\(179\) | 133.291i | 0.744643i | 0.928104 | + | 0.372321i | \(0.121438\pi\) | ||||
−0.928104 | + | 0.372321i | \(0.878562\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 83.0850 | 0.459033 | 0.229517 | − | 0.973305i | \(-0.426286\pi\) | ||||
0.229517 | + | 0.973305i | \(0.426286\pi\) | |||||||
\(182\) | − 9.66472i | − 0.0531029i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −50.3320 | −0.273544 | ||||||||
\(185\) | 338.106i | 1.82760i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 460.324 | 2.46163 | ||||||||
\(188\) | 33.9411i | 0.180538i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 251.660 | 1.32453 | ||||||||
\(191\) | 41.3616i | 0.216553i | 0.994121 | + | 0.108276i | \(0.0345331\pi\) | ||||
−0.994121 | + | 0.108276i | \(0.965467\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 134.000 | 0.694301 | 0.347150 | − | 0.937810i | \(-0.387149\pi\) | ||||
0.347150 | + | 0.937810i | \(0.387149\pi\) | |||||||
\(194\) | − 62.8095i | − 0.323761i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | − 68.8269i | − 0.349375i | −0.984624 | − | 0.174688i | \(-0.944108\pi\) | ||||
0.984624 | − | 0.174688i | \(-0.0558916\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −278.494 | −1.39947 | −0.699734 | − | 0.714404i | \(-0.746698\pi\) | ||||
−0.699734 | + | 0.714404i | \(0.746698\pi\) | |||||||
\(200\) | − 153.205i | − 0.766023i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 45.0850 | 0.223193 | ||||||||
\(203\) | 31.4935i | 0.155140i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 139.992 | 0.682888 | ||||||||
\(206\) | − 6.36674i | − 0.0309065i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.3320 | 0.0496732 | ||||||||
\(209\) | 355.901i | 1.70288i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −211.498 | −1.00236 | −0.501180 | − | 0.865343i | \(-0.667101\pi\) | ||||
−0.501180 | + | 0.865343i | \(0.667101\pi\) | |||||||
\(212\) | 171.114i | 0.807143i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 243.498 | 1.13784 | ||||||||
\(215\) | − 387.025i | − 1.80012i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −45.4170 | −0.209295 | ||||||||
\(218\) | 251.490i | 1.15362i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 316.664 | 1.43938 | ||||||||
\(221\) | − 66.8174i | − 0.302341i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 222.494 | 0.997731 | 0.498866 | − | 0.866679i | \(-0.333750\pi\) | ||||
0.498866 | + | 0.866679i | \(0.333750\pi\) | |||||||
\(224\) | − 14.9666i | − 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 44.3320 | 0.196159 | ||||||||
\(227\) | 101.823i | 0.448561i | 0.974525 | + | 0.224281i | \(0.0720032\pi\) | ||||
−0.974525 | + | 0.224281i | \(0.927997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −163.085 | −0.712161 | −0.356081 | − | 0.934455i | \(-0.615887\pi\) | ||||
−0.356081 | + | 0.934455i | \(0.615887\pi\) | |||||||
\(230\) | 223.915i | 0.973545i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −33.6680 | −0.145121 | ||||||||
\(233\) | 362.858i | 1.55733i | 0.627441 | + | 0.778664i | \(0.284102\pi\) | ||||
−0.627441 | + | 0.778664i | \(0.715898\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 150.996 | 0.642536 | ||||||||
\(236\) | − 3.29798i | − 0.0139745i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −96.7895 | −0.406679 | ||||||||
\(239\) | − 177.126i | − 0.741113i | −0.928810 | − | 0.370557i | \(-0.879167\pi\) | ||||
0.928810 | − | 0.370557i | \(-0.120833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 152.753 | 0.633830 | 0.316915 | − | 0.948454i | \(-0.397353\pi\) | ||||
0.316915 | + | 0.948454i | \(0.397353\pi\) | |||||||
\(242\) | 276.711i | 1.14343i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −200.664 | −0.822394 | ||||||||
\(245\) | 62.2827i | 0.254215i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 51.6601 | 0.209150 | ||||||||
\(248\) | − 48.5528i | − 0.195777i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −366.996 | −1.46798 | ||||||||
\(251\) | 356.382i | 1.41985i | 0.704278 | + | 0.709924i | \(0.251271\pi\) | ||||
−0.704278 | + | 0.709924i | \(0.748729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −316.664 | −1.25164 | ||||||||
\(254\) | − 303.111i | − 1.19335i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 59.5689i | 0.231786i | 0.993262 | + | 0.115893i | \(0.0369729\pi\) | ||||
−0.993262 | + | 0.115893i | \(0.963027\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 100.539 | 0.388180 | ||||||||
\(260\) | − 45.9647i | − 0.176787i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 129.328 | 0.493619 | ||||||||
\(263\) | − 7.42045i | − 0.0282146i | −0.999900 | − | 0.0141073i | \(-0.995509\pi\) | ||||
0.999900 | − | 0.0141073i | \(-0.00449065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 761.247 | 2.87263 | ||||||||
\(266\) | − 74.8331i | − 0.281328i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −73.3281 | −0.273612 | ||||||||
\(269\) | − 430.207i | − 1.59928i | −0.600477 | − | 0.799642i | \(-0.705023\pi\) | ||||
0.600477 | − | 0.799642i | \(-0.294977\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −41.1660 | −0.151904 | −0.0759520 | − | 0.997111i | \(-0.524200\pi\) | ||||
−0.0759520 | + | 0.997111i | \(0.524200\pi\) | |||||||
\(272\) | − 103.472i | − 0.380413i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −151.166 | −0.551701 | ||||||||
\(275\) | − 963.887i | − 3.50504i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.0000 | 0.115523 | 0.0577617 | − | 0.998330i | \(-0.481604\pi\) | ||||
0.0577617 | + | 0.998330i | \(0.481604\pi\) | |||||||
\(278\) | 171.584i | 0.617208i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −66.5830 | −0.237796 | ||||||||
\(281\) | 17.0907i | 0.0608211i | 0.999537 | + | 0.0304106i | \(0.00968147\pi\) | ||||
−0.999537 | + | 0.0304106i | \(0.990319\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 439.660 | 1.55357 | 0.776785 | − | 0.629766i | \(-0.216849\pi\) | ||||
0.776785 | + | 0.629766i | \(0.216849\pi\) | |||||||
\(284\) | − 35.5901i | − 0.125317i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 65.0039 | 0.227286 | ||||||||
\(287\) | − 41.6278i | − 0.145045i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −380.158 | −1.31543 | ||||||||
\(290\) | 149.781i | 0.516486i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −57.8301 | −0.198048 | ||||||||
\(293\) | − 394.377i | − 1.34600i | −0.739644 | − | 0.672998i | \(-0.765006\pi\) | ||||
0.739644 | − | 0.672998i | \(-0.234994\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.6719 | −0.0497353 | ||||||||
\(296\) | 107.480i | 0.363109i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.9961 | −0.0838794 | ||||||||
\(299\) | 45.9647i | 0.153728i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −115.085 | −0.382342 | ||||||||
\(302\) | 71.8901i | 0.238047i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 80.0000 | 0.263158 | ||||||||
\(305\) | 892.707i | 2.92691i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.3360 | −0.0760129 | −0.0380064 | − | 0.999277i | \(-0.512101\pi\) | ||||
−0.0380064 | + | 0.999277i | \(0.512101\pi\) | |||||||
\(308\) | − 94.1626i | − 0.305723i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −216.000 | −0.696774 | ||||||||
\(311\) | − 527.256i | − 1.69536i | −0.530511 | − | 0.847678i | \(-0.678000\pi\) | ||||
0.530511 | − | 0.847678i | \(-0.322000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −295.328 | −0.943540 | −0.471770 | − | 0.881722i | \(-0.656385\pi\) | ||||
−0.471770 | + | 0.881722i | \(0.656385\pi\) | |||||||
\(314\) | − 97.5752i | − 0.310749i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −236.664 | −0.748937 | ||||||||
\(317\) | 107.475i | 0.339037i | 0.985527 | + | 0.169518i | \(0.0542212\pi\) | ||||
−0.985527 | + | 0.169518i | \(0.945779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −211.822 | −0.664019 | ||||||||
\(320\) | − 71.1802i | − 0.222438i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 66.5830 | 0.206780 | ||||||||
\(323\) | − 517.362i | − 1.60174i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −139.911 | −0.430496 | ||||||||
\(326\) | 236.168i | 0.724442i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 44.5020 | 0.135677 | ||||||||
\(329\) | − 44.8999i | − 0.136474i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −273.490 | −0.826254 | −0.413127 | − | 0.910673i | \(-0.635563\pi\) | ||||
−0.413127 | + | 0.910673i | \(0.635563\pi\) | |||||||
\(332\) | 240.886i | 0.725560i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 170.332 | 0.509976 | ||||||||
\(335\) | 326.219i | 0.973789i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −341.166 | −1.01236 | −0.506181 | − | 0.862427i | \(-0.668943\pi\) | ||||
−0.506181 | + | 0.862427i | \(0.668943\pi\) | |||||||
\(338\) | 229.567i | 0.679191i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −460.324 | −1.35389 | ||||||||
\(341\) | − 305.470i | − 0.895807i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 0.0539949 | ||||||||
\(344\) | − 123.031i | − 0.357648i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −129.911 | −0.375466 | ||||||||
\(347\) | 116.320i | 0.335217i | 0.985854 | + | 0.167609i | \(0.0536045\pi\) | ||||
−0.985854 | + | 0.167609i | \(0.946395\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −158.324 | −0.453651 | −0.226825 | − | 0.973935i | \(-0.572835\pi\) | ||||
−0.226825 | + | 0.973935i | \(0.572835\pi\) | |||||||
\(350\) | 202.671i | 0.579059i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 100.664 | 0.285977 | ||||||||
\(353\) | − 230.339i | − 0.652519i | −0.945280 | − | 0.326260i | \(-0.894212\pi\) | ||||
0.945280 | − | 0.326260i | \(-0.105788\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −158.332 | −0.446006 | ||||||||
\(356\) | 278.949i | 0.783566i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 188.502 | 0.526542 | ||||||||
\(359\) | 171.698i | 0.478269i | 0.970987 | + | 0.239134i | \(0.0768636\pi\) | ||||
−0.970987 | + | 0.239134i | \(0.923136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.0000 | 0.108033 | ||||||||
\(362\) | − 117.500i | − 0.324585i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.6680 | −0.0375494 | ||||||||
\(365\) | 257.272i | 0.704856i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 517.490 | 1.41005 | 0.705027 | − | 0.709180i | \(-0.250935\pi\) | ||||
0.705027 | + | 0.709180i | \(0.250935\pi\) | |||||||
\(368\) | 71.1802i | 0.193425i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 478.154 | 1.29231 | ||||||||
\(371\) | − 226.363i | − 0.610143i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −233.336 | −0.625566 | −0.312783 | − | 0.949825i | \(-0.601261\pi\) | ||||
−0.312783 | + | 0.949825i | \(0.601261\pi\) | |||||||
\(374\) | − 650.997i | − 1.74063i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 48.0000 | 0.127660 | ||||||||
\(377\) | 30.7466i | 0.0815560i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 441.166 | 1.16403 | 0.582013 | − | 0.813179i | \(-0.302265\pi\) | ||||
0.582013 | + | 0.813179i | \(0.302265\pi\) | |||||||
\(380\) | − 355.901i | − 0.936582i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 58.4941 | 0.153126 | ||||||||
\(383\) | − 213.060i | − 0.556292i | −0.960539 | − | 0.278146i | \(-0.910280\pi\) | ||||
0.960539 | − | 0.278146i | \(-0.0897200\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −418.907 | −1.08807 | ||||||||
\(386\) | − 189.505i | − 0.490945i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −88.8261 | −0.228933 | ||||||||
\(389\) | − 565.096i | − 1.45269i | −0.687331 | − | 0.726344i | \(-0.741218\pi\) | ||||
0.687331 | − | 0.726344i | \(-0.258782\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 460.324 | 1.17730 | ||||||||
\(392\) | 19.7990i | 0.0505076i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −97.3360 | −0.247046 | ||||||||
\(395\) | 1052.86i | 2.66547i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 498.324 | 1.25522 | 0.627612 | − | 0.778526i | \(-0.284032\pi\) | ||||
0.627612 | + | 0.778526i | \(0.284032\pi\) | |||||||
\(398\) | 393.850i | 0.989573i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −216.664 | −0.541660 | ||||||||
\(401\) | − 193.392i | − 0.482275i | −0.970491 | − | 0.241138i | \(-0.922480\pi\) | ||||
0.970491 | − | 0.241138i | \(-0.0775205\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −44.3399 | −0.110025 | ||||||||
\(404\) | − 63.7598i | − 0.157821i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 44.5385 | 0.109701 | ||||||||
\(407\) | 676.212i | 1.66145i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −454.243 | −1.11062 | −0.555309 | − | 0.831644i | \(-0.687400\pi\) | ||||
−0.555309 | + | 0.831644i | \(0.687400\pi\) | |||||||
\(410\) | − 197.979i | − 0.482875i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.00394 | −0.0218542 | ||||||||
\(413\) | 4.36281i | 0.0105637i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1071.64 | 2.58228 | ||||||||
\(416\) | − 14.6117i | − 0.0351242i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 503.320 | 1.20412 | ||||||||
\(419\) | 339.411i | 0.810051i | 0.914305 | + | 0.405025i | \(0.132737\pi\) | ||||
−0.914305 | + | 0.405025i | \(0.867263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 247.320 | 0.587459 | 0.293729 | − | 0.955889i | \(-0.405104\pi\) | ||||
0.293729 | + | 0.955889i | \(0.405104\pi\) | |||||||
\(422\) | 299.103i | 0.708776i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 241.992 | 0.570736 | ||||||||
\(425\) | 1401.17i | 3.29687i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 265.454 | 0.621671 | ||||||||
\(428\) | − 344.358i | − 0.804575i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −547.336 | −1.27287 | ||||||||
\(431\) | − 456.419i | − 1.05898i | −0.848317 | − | 0.529489i | \(-0.822384\pi\) | ||||
0.848317 | − | 0.529489i | \(-0.177616\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −637.984 | −1.47340 | −0.736702 | − | 0.676217i | \(-0.763618\pi\) | ||||
−0.736702 | + | 0.676217i | \(0.763618\pi\) | |||||||
\(434\) | 64.2293i | 0.147994i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 355.660 | 0.815734 | ||||||||
\(437\) | 355.901i | 0.814419i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −784.146 | −1.78621 | −0.893105 | − | 0.449848i | \(-0.851478\pi\) | ||||
−0.893105 | + | 0.449848i | \(0.851478\pi\) | |||||||
\(440\) | − 447.831i | − 1.01780i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −94.4941 | −0.213788 | ||||||||
\(443\) | − 472.222i | − 1.06596i | −0.846127 | − | 0.532981i | \(-0.821072\pi\) | ||||
0.846127 | − | 0.532981i | \(-0.178928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1240.98 | 2.78872 | ||||||||
\(446\) | − 314.654i | − 0.705503i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.1660 | −0.0472456 | ||||||||
\(449\) | 739.852i | 1.64778i | 0.566752 | + | 0.823888i | \(0.308200\pi\) | ||||
−0.566752 | + | 0.823888i | \(0.691800\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 279.984 | 0.620808 | ||||||||
\(452\) | − 62.6949i | − 0.138706i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 144.000 | 0.317181 | ||||||||
\(455\) | 60.8056i | 0.133639i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −248.324 | −0.543379 | −0.271689 | − | 0.962385i | \(-0.587582\pi\) | ||||
−0.271689 | + | 0.962385i | \(0.587582\pi\) | |||||||
\(458\) | 230.637i | 0.503574i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 316.664 | 0.688400 | ||||||||
\(461\) | − 355.970i | − 0.772168i | −0.922464 | − | 0.386084i | \(-0.873827\pi\) | ||||
0.922464 | − | 0.386084i | \(-0.126173\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.33202 | −0.0136761 | −0.00683804 | − | 0.999977i | \(-0.502177\pi\) | ||||
−0.00683804 | + | 0.999977i | \(0.502177\pi\) | |||||||
\(464\) | 47.6137i | 0.102616i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 513.158 | 1.10120 | ||||||||
\(467\) | − 878.691i | − 1.88156i | −0.339011 | − | 0.940782i | \(-0.610093\pi\) | ||||
0.339011 | − | 0.940782i | \(-0.389907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 97.0039 | 0.206831 | ||||||||
\(470\) | − 213.541i | − 0.454342i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.66404 | −0.00988144 | ||||||||
\(473\) | − 774.050i | − 1.63647i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1083.32 | −2.28067 | ||||||||
\(476\) | 136.881i | 0.287565i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −250.494 | −0.524046 | ||||||||
\(479\) | − 224.396i | − 0.468468i | −0.972180 | − | 0.234234i | \(-0.924742\pi\) | ||||
0.972180 | − | 0.234234i | \(-0.0752581\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 98.1542 | 0.204063 | ||||||||
\(482\) | − 216.025i | − 0.448185i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 391.328 | 0.808529 | ||||||||
\(485\) | 395.166i | 0.814776i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −717.490 | −1.47329 | −0.736643 | − | 0.676282i | \(-0.763590\pi\) | ||||
−0.736643 | + | 0.676282i | \(0.763590\pi\) | |||||||
\(488\) | 283.782i | 0.581520i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 88.0810 | 0.179757 | ||||||||
\(491\) | − 274.002i | − 0.558050i | −0.960284 | − | 0.279025i | \(-0.909989\pi\) | ||||
0.960284 | − | 0.279025i | \(-0.0900112\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 307.919 | 0.624582 | ||||||||
\(494\) | − 73.0584i | − 0.147892i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −68.6640 | −0.138436 | ||||||||
\(497\) | 47.0813i | 0.0947310i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −728.810 | −1.46054 | −0.730271 | − | 0.683158i | \(-0.760606\pi\) | ||||
−0.730271 | + | 0.683158i | \(0.760606\pi\) | |||||||
\(500\) | 519.011i | 1.03802i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 504.000 | 1.00398 | ||||||||
\(503\) | 594.657i | 1.18222i | 0.806590 | + | 0.591111i | \(0.201310\pi\) | ||||
−0.806590 | + | 0.591111i | \(0.798690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −283.652 | −0.561688 | ||||||||
\(506\) | 447.831i | 0.885041i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −428.664 | −0.843827 | ||||||||
\(509\) | 994.015i | 1.95288i | 0.215795 | + | 0.976439i | \(0.430766\pi\) | ||||
−0.215795 | + | 0.976439i | \(0.569234\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 76.5020 | 0.149710 | ||||||||
\(512\) | − 22.6274i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 84.2431 | 0.163897 | ||||||||
\(515\) | 40.0564i | 0.0777794i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 301.992 | 0.584124 | ||||||||
\(518\) | − 142.183i | − 0.274485i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −65.0039 | −0.125008 | ||||||||
\(521\) | 40.8459i | 0.0783990i | 0.999231 | + | 0.0391995i | \(0.0124808\pi\) | ||||
−0.999231 | + | 0.0391995i | \(0.987519\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −232.000 | −0.443595 | −0.221797 | − | 0.975093i | \(-0.571192\pi\) | ||||
−0.221797 | + | 0.975093i | \(0.571192\pi\) | |||||||
\(524\) | − 182.898i | − 0.349041i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.4941 | −0.0199507 | ||||||||
\(527\) | 444.052i | 0.842603i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 212.336 | 0.401391 | ||||||||
\(530\) | − 1076.57i | − 2.03126i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −105.830 | −0.198929 | ||||||||
\(533\) | − 40.6405i | − 0.0762487i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1531.97 | −2.86349 | ||||||||
\(536\) | 103.702i | 0.193473i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −608.405 | −1.13086 | ||||||||
\(539\) | 124.565i | 0.231105i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 250.332 | 0.462721 | 0.231360 | − | 0.972868i | \(-0.425682\pi\) | ||||
0.231360 | + | 0.972868i | \(0.425682\pi\) | |||||||
\(542\) | 58.2175i | 0.107412i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −146.332 | −0.268993 | ||||||||
\(545\) | − 1582.25i | − 2.90321i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 888.324 | 1.62399 | 0.811996 | − | 0.583662i | \(-0.198381\pi\) | ||||
0.811996 | + | 0.583662i | \(0.198381\pi\) | |||||||
\(548\) | 213.781i | 0.390111i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1363.14 | −2.47844 | ||||||||
\(551\) | 238.069i | 0.432066i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 313.077 | 0.566143 | ||||||||
\(554\) | − 45.2548i | − 0.0816874i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 242.656 | 0.436432 | ||||||||
\(557\) | 316.309i | 0.567879i | 0.958842 | + | 0.283940i | \(0.0916415\pi\) | ||||
−0.958842 | + | 0.283940i | \(0.908358\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −112.356 | −0.200994 | ||||||||
\(560\) | 94.1626i | 0.168147i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.1699 | 0.0430070 | ||||||||
\(563\) | 58.4690i | 0.103853i | 0.998651 | + | 0.0519263i | \(0.0165361\pi\) | ||||
−0.998651 | + | 0.0519263i | \(0.983464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −278.915 | −0.493655 | ||||||||
\(566\) | − 621.773i | − 1.09854i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −50.3320 | −0.0886127 | ||||||||
\(569\) | 221.665i | 0.389570i | 0.980846 | + | 0.194785i | \(0.0624009\pi\) | ||||
−0.980846 | + | 0.194785i | \(0.937599\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −487.644 | −0.854018 | −0.427009 | − | 0.904247i | \(-0.640433\pi\) | ||||
−0.427009 | + | 0.904247i | \(0.640433\pi\) | |||||||
\(572\) | − 91.9294i | − 0.160716i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −58.8706 | −0.102562 | ||||||||
\(575\) | − 963.887i | − 1.67633i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −487.328 | −0.844589 | −0.422295 | − | 0.906459i | \(-0.638775\pi\) | ||||
−0.422295 | + | 0.906459i | \(0.638775\pi\) | |||||||
\(578\) | 537.625i | 0.930147i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 211.822 | 0.365211 | ||||||||
\(581\) | − 318.662i | − 0.548472i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1522.49 | 2.61148 | ||||||||
\(584\) | 81.7840i | 0.140041i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −557.733 | −0.951763 | ||||||||
\(587\) | − 445.701i | − 0.759286i | −0.925133 | − | 0.379643i | \(-0.876047\pi\) | ||||
0.925133 | − | 0.379643i | \(-0.123953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −343.320 | −0.582887 | ||||||||
\(590\) | 20.7492i | 0.0351682i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 152.000 | 0.256757 | ||||||||
\(593\) | − 276.648i | − 0.466523i | −0.972414 | − | 0.233261i | \(-0.925060\pi\) | ||||
0.972414 | − | 0.233261i | \(-0.0749397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 608.952 | 1.02345 | ||||||||
\(596\) | 35.3498i | 0.0593117i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 65.0039 | 0.108702 | ||||||||
\(599\) | − 82.3793i | − 0.137528i | −0.997633 | − | 0.0687641i | \(-0.978094\pi\) | ||||
0.997633 | − | 0.0687641i | \(-0.0219056\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −418.000 | −0.695507 | −0.347754 | − | 0.937586i | \(-0.613055\pi\) | ||||
−0.347754 | + | 0.937586i | \(0.613055\pi\) | |||||||
\(602\) | 162.755i | 0.270357i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 101.668 | 0.168324 | ||||||||
\(605\) | − 1740.93i | − 2.87756i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 76.8419 | 0.126593 | 0.0632964 | − | 0.997995i | \(-0.479839\pi\) | ||||
0.0632964 | + | 0.997995i | \(0.479839\pi\) | |||||||
\(608\) | − 113.137i | − 0.186081i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1262.48 | 2.06964 | ||||||||
\(611\) | − 43.8351i | − 0.0717431i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 59.3281 | 0.0967832 | 0.0483916 | − | 0.998828i | \(-0.484590\pi\) | ||||
0.0483916 | + | 0.998828i | \(0.484590\pi\) | |||||||
\(614\) | 33.0020i | 0.0537492i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −133.166 | −0.216179 | ||||||||
\(617\) | 29.1143i | 0.0471869i | 0.999722 | + | 0.0235935i | \(0.00751073\pi\) | ||||
−0.999722 | + | 0.0235935i | \(0.992489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 455.644 | 0.736098 | 0.368049 | − | 0.929806i | \(-0.380026\pi\) | ||||
0.368049 | + | 0.929806i | \(0.380026\pi\) | |||||||
\(620\) | 305.470i | 0.492694i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −745.652 | −1.19880 | ||||||||
\(623\) | − 369.015i | − 0.592320i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 954.806 | 1.52769 | ||||||||
\(626\) | 417.657i | 0.667184i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −137.992 | −0.219733 | ||||||||
\(629\) | − 982.987i | − 1.56278i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.0039 | −0.0713216 | −0.0356608 | − | 0.999364i | \(-0.511354\pi\) | ||||
−0.0356608 | + | 0.999364i | \(0.511354\pi\) | |||||||
\(632\) | 334.693i | 0.529578i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 151.992 | 0.239735 | ||||||||
\(635\) | 1907.03i | 3.00319i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0810 | 0.0283847 | ||||||||
\(638\) | 299.562i | 0.469533i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −100.664 | −0.157288 | ||||||||
\(641\) | − 641.223i | − 1.00035i | −0.865925 | − | 0.500174i | \(-0.833269\pi\) | ||||
0.865925 | − | 0.500174i | \(-0.166731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −604.000 | −0.939347 | −0.469673 | − | 0.882840i | \(-0.655628\pi\) | ||||
−0.469673 | + | 0.882840i | \(0.655628\pi\) | |||||||
\(644\) | − 94.1626i | − 0.146215i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −731.660 | −1.13260 | ||||||||
\(647\) | − 179.600i | − 0.277588i | −0.990321 | − | 0.138794i | \(-0.955677\pi\) | ||||
0.990321 | − | 0.138794i | \(-0.0443226\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.3438 | −0.0452139 | ||||||||
\(650\) | 197.864i | 0.304406i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 333.992 | 0.512258 | ||||||||
\(653\) | 392.092i | 0.600447i | 0.953869 | + | 0.300224i | \(0.0970613\pi\) | ||||
−0.953869 | + | 0.300224i | \(0.902939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −813.668 | −1.24224 | ||||||||
\(656\) | − 62.9353i | − 0.0959379i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −63.4980 | −0.0965016 | ||||||||
\(659\) | 1266.54i | 1.92191i | 0.276701 | + | 0.960956i | \(0.410759\pi\) | ||||
−0.276701 | + | 0.960956i | \(0.589241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 917.644 | 1.38827 | 0.694133 | − | 0.719846i | \(-0.255788\pi\) | ||||
0.694133 | + | 0.719846i | \(0.255788\pi\) | |||||||
\(662\) | 386.773i | 0.584250i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 340.664 | 0.513048 | ||||||||
\(665\) | 470.813i | 0.707989i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −211.822 | −0.317574 | ||||||||
\(668\) | − 240.886i | − 0.360608i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 461.344 | 0.688573 | ||||||||
\(671\) | 1785.41i | 2.66083i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −152.008 | −0.225866 | −0.112933 | − | 0.993603i | \(-0.536025\pi\) | ||||
−0.112933 | + | 0.993603i | \(0.536025\pi\) | |||||||
\(674\) | 482.482i | 0.715848i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 324.656 | 0.480261 | ||||||||
\(677\) | 163.178i | 0.241031i | 0.992711 | + | 0.120516i | \(0.0384548\pi\) | ||||
−0.992711 | + | 0.120516i | \(0.961545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 117.506 | 0.173057 | ||||||||
\(680\) | 650.997i | 0.957348i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −432.000 | −0.633431 | ||||||||
\(683\) | − 324.914i | − 0.475716i | −0.971300 | − | 0.237858i | \(-0.923555\pi\) | ||||
0.971300 | − | 0.237858i | \(-0.0764453\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 951.061 | 1.38841 | ||||||||
\(686\) | − 26.1916i | − 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −173.992 | −0.252896 | ||||||||
\(689\) | − 220.995i | − 0.320747i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1218.98 | 1.76408 | 0.882041 | − | 0.471173i | \(-0.156169\pi\) | ||||
0.882041 | + | 0.471173i | \(0.156169\pi\) | |||||||
\(692\) | 183.722i | 0.265494i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 164.502 | 0.237035 | ||||||||
\(695\) | − 1079.52i | − 1.55327i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −407.004 | −0.583937 | ||||||||
\(698\) | 223.904i | 0.320780i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 286.620 | 0.409457 | ||||||||
\(701\) | − 427.202i | − 0.609417i | −0.952446 | − | 0.304709i | \(-0.901441\pi\) | ||||
0.952446 | − | 0.304709i | \(-0.0985591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 760.000 | 1.08108 | ||||||||
\(704\) | − 142.360i | − 0.202217i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −325.749 | −0.461401 | ||||||||
\(707\) | 84.3463i | 0.119302i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 71.4980 | 0.100843 | 0.0504217 | − | 0.998728i | \(-0.483943\pi\) | ||||
0.0504217 | + | 0.998728i | \(0.483943\pi\) | |||||||
\(710\) | 223.915i | 0.315374i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 394.494 | 0.554065 | ||||||||
\(713\) | − 305.470i | − 0.428429i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −408.972 | −0.571989 | ||||||||
\(716\) | − 266.582i | − 0.372321i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 242.818 | 0.338187 | ||||||||
\(719\) | − 111.030i | − 0.154422i | −0.997015 | − | 0.0772112i | \(-0.975398\pi\) | ||||
0.997015 | − | 0.0772112i | \(-0.0246016\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.9111 | 0.0165202 | ||||||||
\(722\) | − 55.1543i | − 0.0763910i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −166.170 | −0.229517 | ||||||||
\(725\) | − 644.761i | − 0.889326i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1338.82 | −1.84157 | −0.920783 | − | 0.390076i | \(-0.872449\pi\) | ||||
−0.920783 | + | 0.390076i | \(0.872449\pi\) | |||||||
\(728\) | 19.3294i | 0.0265514i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 363.838 | 0.498408 | ||||||||
\(731\) | 1125.21i | 1.53928i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.0771 | 0.0669538 | 0.0334769 | − | 0.999439i | \(-0.489342\pi\) | ||||
0.0334769 | + | 0.999439i | \(0.489342\pi\) | |||||||
\(734\) | − 731.842i | − 0.997059i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 100.664 | 0.136772 | ||||||||
\(737\) | 652.439i | 0.885263i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1430.32 | 1.93548 | 0.967738 | − | 0.251960i | \(-0.0810751\pi\) | ||||
0.967738 | + | 0.251960i | \(0.0810751\pi\) | |||||||
\(740\) | − 676.212i | − 0.913800i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −320.125 | −0.431436 | ||||||||
\(743\) | 875.736i | 1.17865i | 0.807896 | + | 0.589325i | \(0.200606\pi\) | ||||
−0.807896 | + | 0.589325i | \(0.799394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 157.263 | 0.211091 | ||||||||
\(746\) | 329.987i | 0.442342i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −920.648 | −1.23081 | ||||||||
\(749\) | 455.543i | 0.608202i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 320.826 | 0.427199 | 0.213599 | − | 0.976921i | \(-0.431481\pi\) | ||||
0.213599 | + | 0.976921i | \(0.431481\pi\) | |||||||
\(752\) | − 67.8823i | − 0.0902690i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 43.4823 | 0.0576688 | ||||||||
\(755\) | − 452.297i | − 0.599069i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 289.830 | 0.382867 | 0.191433 | − | 0.981506i | \(-0.438686\pi\) | ||||
0.191433 | + | 0.981506i | \(0.438686\pi\) | |||||||
\(758\) | − 623.903i | − 0.823091i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −503.320 | −0.662263 | ||||||||
\(761\) | − 704.657i | − 0.925962i | −0.886368 | − | 0.462981i | \(-0.846780\pi\) | ||||
0.886368 | − | 0.462981i | \(-0.153220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −470.494 | −0.616637 | ||||||||
\(764\) | − 82.7231i | − 0.108276i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −301.312 | −0.393358 | ||||||||
\(767\) | 4.25934i | 0.00555325i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −117.320 | −0.152562 | −0.0762810 | − | 0.997086i | \(-0.524305\pi\) | ||||
−0.0762810 | + | 0.997086i | \(0.524305\pi\) | |||||||
\(770\) | 592.424i | 0.769382i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −268.000 | −0.347150 | ||||||||
\(773\) | 658.005i | 0.851235i | 0.904903 | + | 0.425618i | \(0.139943\pi\) | ||||
−0.904903 | + | 0.425618i | \(0.860057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 929.814 | 1.19976 | ||||||||
\(776\) | 125.619i | 0.161880i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −799.166 | −1.02721 | ||||||||
\(779\) | − 314.676i | − 0.403949i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −316.664 | −0.405460 | ||||||||
\(782\) | − 650.997i | − 0.832477i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | 613.894i | 0.782031i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1200.65 | −1.52560 | −0.762801 | − | 0.646634i | \(-0.776176\pi\) | ||||
−0.762801 | + | 0.646634i | \(0.776176\pi\) | |||||||
\(788\) | 137.654i | 0.174688i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1488.97 | 1.88478 | ||||||||
\(791\) | 82.9376i | 0.104852i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 259.158 | 0.326807 | ||||||||
\(794\) | − 704.737i | − 0.887578i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 556.988 | 0.699734 | ||||||||
\(797\) | 797.411i | 1.00052i | 0.865876 | + | 0.500258i | \(0.166761\pi\) | ||||
−0.865876 | + | 0.500258i | \(0.833239\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −438.996 | −0.549432 | ||||||||
\(800\) | 306.409i | 0.383012i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −273.498 | −0.341020 | ||||||||
\(803\) | 514.545i | 0.640778i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −418.907 | −0.520382 | ||||||||
\(806\) | 62.7061i | 0.0777991i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −90.1699 | −0.111596 | ||||||||
\(809\) | − 156.016i | − 0.192851i | −0.995340 | − | 0.0964254i | \(-0.969259\pi\) | ||||
0.995340 | − | 0.0964254i | \(-0.0307409\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −598.316 | −0.737751 | −0.368876 | − | 0.929479i | \(-0.620257\pi\) | ||||
−0.368876 | + | 0.929479i | \(0.620257\pi\) | |||||||
\(812\) | − 62.9870i | − 0.0775702i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 956.308 | 1.17483 | ||||||||
\(815\) | − 1485.85i | − 1.82313i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −869.961 | −1.06482 | ||||||||
\(818\) | 642.397i | 0.785326i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −279.984 | −0.341444 | ||||||||
\(821\) | − 980.978i | − 1.19486i | −0.801922 | − | 0.597429i | \(-0.796189\pi\) | ||||
0.801922 | − | 0.597429i | \(-0.203811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −431.336 | −0.524102 | −0.262051 | − | 0.965054i | \(-0.584399\pi\) | ||||
−0.262051 | + | 0.965054i | \(0.584399\pi\) | |||||||
\(824\) | 12.7335i | 0.0154533i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.16995 | 0.00746967 | ||||||||
\(827\) | − 1219.41i | − 1.47449i | −0.675623 | − | 0.737247i | \(-0.736125\pi\) | ||||
0.675623 | − | 0.737247i | \(-0.263875\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −770.081 | −0.928928 | −0.464464 | − | 0.885592i | \(-0.653753\pi\) | ||||
−0.464464 | + | 0.885592i | \(0.653753\pi\) | |||||||
\(830\) | − 1515.53i | − 1.82594i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.6640 | −0.0248366 | ||||||||
\(833\) | − 181.077i | − 0.217379i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1071.64 | −1.28341 | ||||||||
\(836\) | − 711.802i | − 0.851438i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 480.000 | 0.572792 | ||||||||
\(839\) | 1310.03i | 1.56142i | 0.624894 | + | 0.780710i | \(0.285142\pi\) | ||||
−0.624894 | + | 0.780710i | \(0.714858\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 699.308 | 0.831520 | ||||||||
\(842\) | − 349.764i | − 0.415396i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 422.996 | 0.501180 | ||||||||
\(845\) | − 1444.32i | − 1.70925i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −517.678 | −0.611191 | ||||||||
\(848\) | − 342.229i | − 0.403571i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1981.56 | 2.33124 | ||||||||
\(851\) | 676.212i | 0.794609i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 898.988 | 1.05391 | 0.526957 | − | 0.849892i | \(-0.323333\pi\) | ||||
0.526957 | + | 0.849892i | \(0.323333\pi\) | |||||||
\(854\) | − 375.408i | − 0.439588i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −486.996 | −0.568921 | ||||||||
\(857\) | − 746.156i | − 0.870660i | −0.900271 | − | 0.435330i | \(-0.856632\pi\) | ||||
0.900271 | − | 0.435330i | \(-0.143368\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −991.984 | −1.15481 | −0.577406 | − | 0.816457i | \(-0.695935\pi\) | ||||
−0.577406 | + | 0.816457i | \(0.695935\pi\) | |||||||
\(860\) | 774.050i | 0.900058i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −645.474 | −0.748810 | ||||||||
\(863\) | − 209.418i | − 0.242663i | −0.992612 | − | 0.121332i | \(-0.961284\pi\) | ||||
0.992612 | − | 0.121332i | \(-0.0387164\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 817.336 | 0.944897 | ||||||||
\(866\) | 902.246i | 1.04185i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 90.8340 | 0.104647 | ||||||||
\(869\) | 2105.73i | 2.42316i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 94.7034 | 0.108730 | ||||||||
\(872\) | − 502.979i | − 0.576811i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 503.320 | 0.575881 | ||||||||
\(875\) | − 686.587i | − 0.784671i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −865.304 | −0.986664 | −0.493332 | − | 0.869841i | \(-0.664221\pi\) | ||||
−0.493332 | + | 0.869841i | \(0.664221\pi\) | |||||||
\(878\) | 1108.95i | 1.26304i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −633.328 | −0.719691 | ||||||||
\(881\) | − 995.046i | − 1.12945i | −0.825279 | − | 0.564725i | \(-0.808982\pi\) | ||||
0.825279 | − | 0.564725i | \(-0.191018\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 101.474 | 0.114920 | 0.0574600 | − | 0.998348i | \(-0.481700\pi\) | ||||
0.0574600 | + | 0.998348i | \(0.481700\pi\) | |||||||
\(884\) | 133.635i | 0.151171i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −667.822 | −0.753750 | ||||||||
\(887\) | − 1074.09i | − 1.21093i | −0.795873 | − | 0.605464i | \(-0.792988\pi\) | ||||
0.795873 | − | 0.605464i | \(-0.207012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 567.069 | 0.637873 | ||||||||
\(890\) | − 1755.01i | − 1.97192i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −444.988 | −0.498866 | ||||||||
\(893\) | − 339.411i | − 0.380080i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1185.96 | −1.32510 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1046.31 | 1.16515 | ||||||||
\(899\) | − 204.334i | − 0.227291i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2213.20 | −2.45638 | ||||||||
\(902\) | − 395.958i | − 0.438977i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −88.6640 | −0.0980797 | ||||||||
\(905\) | 739.251i | 0.816852i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −432.162 | −0.476474 | −0.238237 | − | 0.971207i | \(-0.576570\pi\) | ||||
−0.238237 | + | 0.971207i | \(0.576570\pi\) | |||||||
\(908\) | − 203.647i | − 0.224281i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 85.9921 | 0.0944968 | ||||||||
\(911\) | 104.984i | 0.115241i | 0.998339 | + | 0.0576205i | \(0.0183513\pi\) | ||||
−0.998339 | + | 0.0576205i | \(0.981649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2143.29 | 2.34752 | ||||||||
\(914\) | 351.183i | 0.384227i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 326.170 | 0.356081 | ||||||||
\(917\) | 241.951i | 0.263850i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −91.8379 | −0.0999325 | −0.0499662 | − | 0.998751i | \(-0.515911\pi\) | ||||
−0.0499662 | + | 0.998751i | \(0.515911\pi\) | |||||||
\(920\) | − 447.831i | − 0.486772i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −503.417 | −0.546005 | ||||||||
\(923\) | 45.9647i | 0.0497993i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2058.31 | −2.22520 | ||||||||
\(926\) | 8.95483i | 0.00967044i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 67.3360 | 0.0725603 | ||||||||
\(929\) | 1309.00i | 1.40904i | 0.709682 | + | 0.704522i | \(0.248838\pi\) | ||||
−0.709682 | + | 0.704522i | \(0.751162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 140.000 | 0.150376 | ||||||||
\(932\) | − 725.715i | − 0.778664i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1242.66 | −1.33047 | ||||||||
\(935\) | 4095.75i | 4.38048i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1262.00 | 1.34685 | 0.673426 | − | 0.739255i | \(-0.264822\pi\) | ||||
0.673426 | + | 0.739255i | \(0.264822\pi\) | |||||||
\(938\) | − 137.184i | − 0.146252i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −301.992 | −0.321268 | ||||||||
\(941\) | 1315.97i | 1.39849i | 0.714884 | + | 0.699243i | \(0.246479\pi\) | ||||
−0.714884 | + | 0.699243i | \(0.753521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 279.984 | 0.296908 | ||||||||
\(944\) | 6.59595i | 0.00698724i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1094.67 | −1.15716 | ||||||||
\(947\) | − 486.582i | − 0.513814i | −0.966436 | − | 0.256907i | \(-0.917297\pi\) | ||||
0.966436 | − | 0.256907i | \(-0.0827034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 74.6877 | 0.0787014 | ||||||||
\(950\) | 1532.05i | 1.61268i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 193.579 | 0.203339 | ||||||||
\(953\) | − 43.3711i | − 0.0455100i | −0.999741 | − | 0.0227550i | \(-0.992756\pi\) | ||||
0.999741 | − | 0.0227550i | \(-0.00724377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −368.016 | −0.385357 | ||||||||
\(956\) | 354.252i | 0.370557i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −317.344 | −0.331257 | ||||||||
\(959\) | − 282.806i | − 0.294896i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −666.328 | −0.693369 | ||||||||
\(962\) | − 138.811i | − 0.144294i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −305.506 | −0.316915 | ||||||||
\(965\) | 1192.27i | 1.23551i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1648.99 | 1.70526 | 0.852631 | − | 0.522514i | \(-0.175006\pi\) | ||||
0.852631 | + | 0.522514i | \(0.175006\pi\) | |||||||
\(968\) | − 553.421i | − 0.571716i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 558.850 | 0.576134 | ||||||||
\(971\) | − 518.323i | − 0.533803i | −0.963724 | − | 0.266902i | \(-0.914000\pi\) | ||||
0.963724 | − | 0.266902i | \(-0.0859999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −321.004 | −0.329912 | ||||||||
\(974\) | 1014.68i | 1.04177i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 401.328 | 0.411197 | ||||||||
\(977\) | − 109.948i | − 0.112536i | −0.998416 | − | 0.0562682i | \(-0.982080\pi\) | ||||
0.998416 | − | 0.0562682i | \(-0.0179202\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2481.96 | 2.53520 | ||||||||
\(980\) | − 124.565i | − 0.127108i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −387.498 | −0.394601 | ||||||||
\(983\) | 589.710i | 0.599909i | 0.953954 | + | 0.299954i | \(0.0969715\pi\) | ||||
−0.953954 | + | 0.299954i | \(0.903029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 612.389 | 0.621715 | ||||||||
\(986\) | − 435.463i | − 0.441646i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −103.320 | −0.104575 | ||||||||
\(989\) | − 774.050i | − 0.782659i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 713.474 | 0.719954 | 0.359977 | − | 0.932961i | \(-0.382785\pi\) | ||||
0.359977 | + | 0.932961i | \(0.382785\pi\) | |||||||
\(992\) | 97.1056i | 0.0978887i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 66.5830 | 0.0669849 | ||||||||
\(995\) | − 2477.91i | − 2.49036i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1222.99 | 1.22667 | 0.613334 | − | 0.789824i | \(-0.289828\pi\) | ||||
0.613334 | + | 0.789824i | \(0.289828\pi\) | |||||||
\(998\) | 1030.69i | 1.03276i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 126.3.b.a.71.2 | ✓ | 4 | |
3.2 | odd | 2 | inner | 126.3.b.a.71.3 | yes | 4 | |
4.3 | odd | 2 | 1008.3.d.a.449.4 | 4 | |||
5.2 | odd | 4 | 3150.3.c.b.449.8 | 8 | |||
5.3 | odd | 4 | 3150.3.c.b.449.2 | 8 | |||
5.4 | even | 2 | 3150.3.e.e.701.3 | 4 | |||
7.2 | even | 3 | 882.3.s.e.557.2 | 8 | |||
7.3 | odd | 6 | 882.3.s.i.863.4 | 8 | |||
7.4 | even | 3 | 882.3.s.e.863.3 | 8 | |||
7.5 | odd | 6 | 882.3.s.i.557.1 | 8 | |||
7.6 | odd | 2 | 882.3.b.f.197.1 | 4 | |||
8.3 | odd | 2 | 4032.3.d.j.449.1 | 4 | |||
8.5 | even | 2 | 4032.3.d.i.449.1 | 4 | |||
9.2 | odd | 6 | 1134.3.q.c.701.4 | 8 | |||
9.4 | even | 3 | 1134.3.q.c.1079.4 | 8 | |||
9.5 | odd | 6 | 1134.3.q.c.1079.1 | 8 | |||
9.7 | even | 3 | 1134.3.q.c.701.1 | 8 | |||
12.11 | even | 2 | 1008.3.d.a.449.1 | 4 | |||
15.2 | even | 4 | 3150.3.c.b.449.3 | 8 | |||
15.8 | even | 4 | 3150.3.c.b.449.5 | 8 | |||
15.14 | odd | 2 | 3150.3.e.e.701.1 | 4 | |||
21.2 | odd | 6 | 882.3.s.e.557.3 | 8 | |||
21.5 | even | 6 | 882.3.s.i.557.4 | 8 | |||
21.11 | odd | 6 | 882.3.s.e.863.2 | 8 | |||
21.17 | even | 6 | 882.3.s.i.863.1 | 8 | |||
21.20 | even | 2 | 882.3.b.f.197.4 | 4 | |||
24.5 | odd | 2 | 4032.3.d.i.449.4 | 4 | |||
24.11 | even | 2 | 4032.3.d.j.449.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.b.a.71.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
126.3.b.a.71.3 | yes | 4 | 3.2 | odd | 2 | inner | |
882.3.b.f.197.1 | 4 | 7.6 | odd | 2 | |||
882.3.b.f.197.4 | 4 | 21.20 | even | 2 | |||
882.3.s.e.557.2 | 8 | 7.2 | even | 3 | |||
882.3.s.e.557.3 | 8 | 21.2 | odd | 6 | |||
882.3.s.e.863.2 | 8 | 21.11 | odd | 6 | |||
882.3.s.e.863.3 | 8 | 7.4 | even | 3 | |||
882.3.s.i.557.1 | 8 | 7.5 | odd | 6 | |||
882.3.s.i.557.4 | 8 | 21.5 | even | 6 | |||
882.3.s.i.863.1 | 8 | 21.17 | even | 6 | |||
882.3.s.i.863.4 | 8 | 7.3 | odd | 6 | |||
1008.3.d.a.449.1 | 4 | 12.11 | even | 2 | |||
1008.3.d.a.449.4 | 4 | 4.3 | odd | 2 | |||
1134.3.q.c.701.1 | 8 | 9.7 | even | 3 | |||
1134.3.q.c.701.4 | 8 | 9.2 | odd | 6 | |||
1134.3.q.c.1079.1 | 8 | 9.5 | odd | 6 | |||
1134.3.q.c.1079.4 | 8 | 9.4 | even | 3 | |||
3150.3.c.b.449.2 | 8 | 5.3 | odd | 4 | |||
3150.3.c.b.449.3 | 8 | 15.2 | even | 4 | |||
3150.3.c.b.449.5 | 8 | 15.8 | even | 4 | |||
3150.3.c.b.449.8 | 8 | 5.2 | odd | 4 | |||
3150.3.e.e.701.1 | 4 | 15.14 | odd | 2 | |||
3150.3.e.e.701.3 | 4 | 5.4 | even | 2 | |||
4032.3.d.i.449.1 | 4 | 8.5 | even | 2 | |||
4032.3.d.i.449.4 | 4 | 24.5 | odd | 2 | |||
4032.3.d.j.449.1 | 4 | 8.3 | odd | 2 | |||
4032.3.d.j.449.4 | 4 | 24.11 | even | 2 |