Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,3,Mod(449,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("3150.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.c (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: | \(85.8312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.2 | ||
Root | \(-0.581861 - 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.449 |
Dual form | 3150.3.c.b.449.3 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.64575i | − 0.377964i | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.7951i | 1.61773i | 0.587993 | + | 0.808866i | \(0.299918\pi\) | ||||
−0.587993 | + | 0.808866i | \(0.700082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.58301i | 0.198693i | 0.995053 | + | 0.0993464i | \(0.0316752\pi\) | ||||
−0.995053 | + | 0.0993464i | \(0.968325\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −25.8681 | −1.52165 | −0.760826 | − | 0.648956i | \(-0.775206\pi\) | ||||
−0.760826 | + | 0.648956i | \(0.775206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.0000 | −1.05263 | −0.526316 | − | 0.850289i | \(-0.676427\pi\) | ||||
−0.526316 | + | 0.850289i | \(0.676427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 25.1660i | − 1.14391i | ||||||||
\(23\) | −17.7951 | −0.773698 | −0.386849 | − | 0.922143i | \(-0.626437\pi\) | ||||
−0.386849 | + | 0.922143i | \(0.626437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − 3.65292i | − 0.140497i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 5.29150i | − 0.188982i | ||||||||
\(29\) | − 11.9034i | − 0.410463i | −0.978713 | − | 0.205232i | \(-0.934205\pi\) | ||||
0.978713 | − | 0.205232i | \(-0.0657947\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −17.1660 | −0.553742 | −0.276871 | − | 0.960907i | \(-0.589298\pi\) | ||||
−0.276871 | + | 0.960907i | \(0.589298\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 36.5830 | 1.07597 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 38.0000i | − 1.02703i | −0.858082 | − | 0.513514i | \(-0.828344\pi\) | ||||
0.858082 | − | 0.513514i | \(-0.171656\pi\) | |||||||
\(38\) | 28.2843 | 0.744323 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 15.7338i | − 0.383752i | −0.981419 | − | 0.191876i | \(-0.938543\pi\) | ||||
0.981419 | − | 0.191876i | \(-0.0614571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 43.4980i | − 1.01158i | −0.862656 | − | 0.505791i | \(-0.831201\pi\) | ||||
0.862656 | − | 0.505791i | \(-0.168799\pi\) | |||||||
\(44\) | 35.5901i | 0.808866i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 25.1660 | 0.547087 | ||||||||
\(47\) | −16.9706 | −0.361076 | −0.180538 | − | 0.983568i | \(-0.557784\pi\) | ||||
−0.180538 | + | 0.983568i | \(0.557784\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.16601i | 0.0993464i | ||||||||
\(53\) | 85.5571 | 1.61429 | 0.807143 | − | 0.590356i | \(-0.201013\pi\) | ||||
0.807143 | + | 0.590356i | \(0.201013\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 16.8340i | 0.290241i | ||||||||
\(59\) | − 1.64899i | − 0.0279489i | −0.999902 | − | 0.0139745i | \(-0.995552\pi\) | ||||
0.999902 | − | 0.0139745i | \(-0.00444836\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 100.332 | 1.64479 | 0.822394 | − | 0.568919i | \(-0.192638\pi\) | ||||
0.822394 | + | 0.568919i | \(0.192638\pi\) | |||||||
\(62\) | 24.2764 | 0.391555 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 36.6640i | − 0.547225i | −0.961840 | − | 0.273612i | \(-0.911781\pi\) | ||||
0.961840 | − | 0.273612i | \(-0.0882185\pi\) | |||||||
\(68\) | −51.7362 | −0.760826 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 17.7951i | 0.250635i | 0.992117 | + | 0.125317i | \(0.0399949\pi\) | ||||
−0.992117 | + | 0.125317i | \(0.960005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28.9150i | 0.396096i | 0.980192 | + | 0.198048i | \(0.0634602\pi\) | ||||
−0.980192 | + | 0.198048i | \(0.936540\pi\) | |||||||
\(74\) | 53.7401i | 0.726218i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −40.0000 | −0.526316 | ||||||||
\(77\) | 47.0813 | 0.611445 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −118.332 | −1.49787 | −0.748937 | − | 0.662641i | \(-0.769435\pi\) | ||||
−0.748937 | + | 0.662641i | \(0.769435\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 22.2510i | 0.271353i | ||||||||
\(83\) | 120.443 | 1.45112 | 0.725560 | − | 0.688159i | \(-0.241581\pi\) | ||||
0.725560 | + | 0.688159i | \(0.241581\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 61.5155i | 0.715297i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 50.3320i | − 0.571955i | ||||||||
\(89\) | 139.475i | 1.56713i | 0.621309 | + | 0.783566i | \(0.286601\pi\) | ||||
−0.621309 | + | 0.783566i | \(0.713399\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.83399 | 0.0750988 | ||||||||
\(92\) | −35.5901 | −0.386849 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 24.0000 | 0.255319 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 44.4131i | − 0.457867i | −0.973442 | − | 0.228933i | \(-0.926476\pi\) | ||||
0.973442 | − | 0.228933i | \(-0.0735238\pi\) | |||||||
\(98\) | 9.89949 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 31.8799i | 0.315642i | 0.987468 | + | 0.157821i | \(0.0504470\pi\) | ||||
−0.987468 | + | 0.157821i | \(0.949553\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.50197i | 0.0437084i | 0.999761 | + | 0.0218542i | \(0.00695697\pi\) | ||||
−0.999761 | + | 0.0218542i | \(0.993043\pi\) | |||||||
\(104\) | − 7.30584i | − 0.0702485i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −120.996 | −1.14147 | ||||||||
\(107\) | 172.179 | 1.60915 | 0.804575 | − | 0.593851i | \(-0.202393\pi\) | ||||
0.804575 | + | 0.593851i | \(0.202393\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 177.830 | 1.63147 | 0.815734 | − | 0.578427i | \(-0.196333\pi\) | ||||
0.815734 | + | 0.578427i | \(0.196333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 10.5830i | − 0.0944911i | ||||||||
\(113\) | −31.3475 | −0.277411 | −0.138706 | − | 0.990334i | \(-0.544294\pi\) | ||||
−0.138706 | + | 0.990334i | \(0.544294\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − 23.8069i | − 0.205232i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.33202i | 0.0197629i | ||||||||
\(119\) | 68.4405i | 0.575131i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −195.664 | −1.61706 | ||||||||
\(122\) | −141.891 | −1.16304 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −34.3320 | −0.276871 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 214.332i | − 1.68765i | −0.536616 | − | 0.843827i | \(-0.680297\pi\) | ||||
0.536616 | − | 0.843827i | \(-0.319703\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 91.4488i | 0.698082i | 0.937107 | + | 0.349041i | \(0.113493\pi\) | ||||
−0.937107 | + | 0.349041i | \(0.886507\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 52.9150i | 0.397857i | ||||||||
\(134\) | 51.8508i | 0.386946i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 73.1660 | 0.537985 | ||||||||
\(137\) | −106.891 | −0.780223 | −0.390111 | − | 0.920768i | \(-0.627563\pi\) | ||||
−0.390111 | + | 0.920768i | \(0.627563\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 121.328 | 0.872864 | 0.436432 | − | 0.899737i | \(-0.356242\pi\) | ||||
0.436432 | + | 0.899737i | \(0.356242\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 25.1660i | − 0.177225i | ||||||||
\(143\) | −45.9647 | −0.321432 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − 40.8920i | − 0.280082i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 76.0000i | − 0.513514i | ||||||||
\(149\) | 17.6749i | 0.118623i | 0.998240 | + | 0.0593117i | \(0.0188906\pi\) | ||||
−0.998240 | + | 0.0593117i | \(0.981109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −50.8340 | −0.336649 | −0.168324 | − | 0.985732i | \(-0.553836\pi\) | ||||
−0.168324 | + | 0.985732i | \(0.553836\pi\) | |||||||
\(152\) | 56.5685 | 0.372161 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −66.5830 | −0.432357 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 68.9961i | − 0.439465i | −0.975560 | − | 0.219733i | \(-0.929481\pi\) | ||||
0.975560 | − | 0.219733i | \(-0.0705185\pi\) | |||||||
\(158\) | 167.347 | 1.05916 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 47.0813i | 0.292430i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 166.996i | − 1.02452i | −0.858832 | − | 0.512258i | \(-0.828809\pi\) | ||||
0.858832 | − | 0.512258i | \(-0.171191\pi\) | |||||||
\(164\) | − 31.4676i | − 0.191876i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −170.332 | −1.02610 | ||||||||
\(167\) | 120.443 | 0.721215 | 0.360608 | − | 0.932718i | \(-0.382569\pi\) | ||||
0.360608 | + | 0.932718i | \(0.382569\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 162.328 | 0.960521 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 86.9961i | − 0.505791i | ||||||||
\(173\) | 91.8610 | 0.530989 | 0.265494 | − | 0.964112i | \(-0.414465\pi\) | ||||
0.265494 | + | 0.964112i | \(0.414465\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 71.1802i | 0.404433i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 197.247i | − 1.10813i | ||||||||
\(179\) | − 133.291i | − 0.744643i | −0.928104 | − | 0.372321i | \(-0.878562\pi\) | ||||
0.928104 | − | 0.372321i | \(-0.121438\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 83.0850 | 0.459033 | 0.229517 | − | 0.973305i | \(-0.426286\pi\) | ||||
0.229517 | + | 0.973305i | \(0.426286\pi\) | |||||||
\(182\) | −9.66472 | −0.0531029 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 50.3320 | 0.273544 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 460.324i | − 2.46163i | ||||||||
\(188\) | −33.9411 | −0.180538 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 41.3616i | 0.216553i | 0.994121 | + | 0.108276i | \(0.0345331\pi\) | ||||
−0.994121 | + | 0.108276i | \(0.965467\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 134.000i | 0.694301i | 0.937810 | + | 0.347150i | \(0.112851\pi\) | ||||
−0.937810 | + | 0.347150i | \(0.887149\pi\) | |||||||
\(194\) | 62.8095i | 0.323761i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −68.8269 | −0.349375 | −0.174688 | − | 0.984624i | \(-0.555892\pi\) | ||||
−0.174688 | + | 0.984624i | \(0.555892\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 278.494 | 1.39947 | 0.699734 | − | 0.714404i | \(-0.253302\pi\) | ||||
0.699734 | + | 0.714404i | \(0.253302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 45.0850i | − 0.223193i | ||||||||
\(203\) | −31.4935 | −0.155140 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − 6.36674i | − 0.0309065i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.3320i | 0.0496732i | ||||||||
\(209\) | − 355.901i | − 1.70288i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −211.498 | −1.00236 | −0.501180 | − | 0.865343i | \(-0.667101\pi\) | ||||
−0.501180 | + | 0.865343i | \(0.667101\pi\) | |||||||
\(212\) | 171.114 | 0.807143 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −243.498 | −1.13784 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 45.4170i | 0.209295i | ||||||||
\(218\) | −251.490 | −1.15362 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 66.8174i | − 0.302341i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 222.494i | 0.997731i | 0.866679 | + | 0.498866i | \(0.166250\pi\) | ||||
−0.866679 | + | 0.498866i | \(0.833750\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 44.3320 | 0.196159 | ||||||||
\(227\) | 101.823 | 0.448561 | 0.224281 | − | 0.974525i | \(-0.427997\pi\) | ||||
0.224281 | + | 0.974525i | \(0.427997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 163.085 | 0.712161 | 0.356081 | − | 0.934455i | \(-0.384113\pi\) | ||||
0.356081 | + | 0.934455i | \(0.384113\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 33.6680i | 0.145121i | ||||||||
\(233\) | −362.858 | −1.55733 | −0.778664 | − | 0.627441i | \(-0.784102\pi\) | ||||
−0.778664 | + | 0.627441i | \(0.784102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − 3.29798i | − 0.0139745i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 96.7895i | − 0.406679i | ||||||||
\(239\) | 177.126i | 0.741113i | 0.928810 | + | 0.370557i | \(0.120833\pi\) | ||||
−0.928810 | + | 0.370557i | \(0.879167\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 152.753 | 0.633830 | 0.316915 | − | 0.948454i | \(-0.397353\pi\) | ||||
0.316915 | + | 0.948454i | \(0.397353\pi\) | |||||||
\(242\) | 276.711 | 1.14343 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 200.664 | 0.822394 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 51.6601i | − 0.209150i | ||||||||
\(248\) | 48.5528 | 0.195777 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 356.382i | 1.41985i | 0.704278 | + | 0.709924i | \(0.251271\pi\) | ||||
−0.704278 | + | 0.709924i | \(0.748729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 316.664i | − 1.25164i | ||||||||
\(254\) | 303.111i | 1.19335i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 59.5689 | 0.231786 | 0.115893 | − | 0.993262i | \(-0.463027\pi\) | ||||
0.115893 | + | 0.993262i | \(0.463027\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −100.539 | −0.388180 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 129.328i | − 0.493619i | ||||||||
\(263\) | 7.42045 | 0.0282146 | 0.0141073 | − | 0.999900i | \(-0.495509\pi\) | ||||
0.0141073 | + | 0.999900i | \(0.495509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − 74.8331i | − 0.281328i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 73.3281i | − 0.273612i | ||||||||
\(269\) | 430.207i | 1.59928i | 0.600477 | + | 0.799642i | \(0.294977\pi\) | ||||
−0.600477 | + | 0.799642i | \(0.705023\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −41.1660 | −0.151904 | −0.0759520 | − | 0.997111i | \(-0.524200\pi\) | ||||
−0.0759520 | + | 0.997111i | \(0.524200\pi\) | |||||||
\(272\) | −103.472 | −0.380413 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 151.166 | 0.551701 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 32.0000i | − 0.115523i | −0.998330 | − | 0.0577617i | \(-0.981604\pi\) | ||||
0.998330 | − | 0.0577617i | \(-0.0183964\pi\) | |||||||
\(278\) | −171.584 | −0.617208 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0907i | 0.0608211i | 0.999537 | + | 0.0304106i | \(0.00968147\pi\) | ||||
−0.999537 | + | 0.0304106i | \(0.990319\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 439.660i | 1.55357i | 0.629766 | + | 0.776785i | \(0.283151\pi\) | ||||
−0.629766 | + | 0.776785i | \(0.716849\pi\) | |||||||
\(284\) | 35.5901i | 0.125317i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 65.0039 | 0.227286 | ||||||||
\(287\) | −41.6278 | −0.145045 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 380.158 | 1.31543 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 57.8301i | 0.198048i | ||||||||
\(293\) | 394.377 | 1.34600 | 0.672998 | − | 0.739644i | \(-0.265006\pi\) | ||||
0.672998 | + | 0.739644i | \(0.265006\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 107.480i | 0.363109i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 24.9961i | − 0.0838794i | ||||||||
\(299\) | − 45.9647i | − 0.153728i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −115.085 | −0.382342 | ||||||||
\(302\) | 71.8901 | 0.238047 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −80.0000 | −0.263158 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.3360i | 0.0760129i | 0.999277 | + | 0.0380064i | \(0.0121007\pi\) | ||||
−0.999277 | + | 0.0380064i | \(0.987899\pi\) | |||||||
\(308\) | 94.1626 | 0.305723 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 527.256i | − 1.69536i | −0.530511 | − | 0.847678i | \(-0.678000\pi\) | ||||
0.530511 | − | 0.847678i | \(-0.322000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 295.328i | − 0.943540i | −0.881722 | − | 0.471770i | \(-0.843615\pi\) | ||||
0.881722 | − | 0.471770i | \(-0.156385\pi\) | |||||||
\(314\) | 97.5752i | 0.310749i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −236.664 | −0.748937 | ||||||||
\(317\) | 107.475 | 0.339037 | 0.169518 | − | 0.985527i | \(-0.445779\pi\) | ||||
0.169518 | + | 0.985527i | \(0.445779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 211.822 | 0.664019 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 66.5830i | − 0.206780i | ||||||||
\(323\) | 517.362 | 1.60174 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 236.168i | 0.724442i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 44.5020i | 0.135677i | ||||||||
\(329\) | 44.8999i | 0.136474i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −273.490 | −0.826254 | −0.413127 | − | 0.910673i | \(-0.635563\pi\) | ||||
−0.413127 | + | 0.910673i | \(0.635563\pi\) | |||||||
\(332\) | 240.886 | 0.725560 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −170.332 | −0.509976 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 341.166i | 1.01236i | 0.862427 | + | 0.506181i | \(0.168943\pi\) | ||||
−0.862427 | + | 0.506181i | \(0.831057\pi\) | |||||||
\(338\) | −229.567 | −0.679191 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 305.470i | − 0.895807i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 123.031i | 0.357648i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −129.911 | −0.375466 | ||||||||
\(347\) | 116.320 | 0.335217 | 0.167609 | − | 0.985854i | \(-0.446395\pi\) | ||||
0.167609 | + | 0.985854i | \(0.446395\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 158.324 | 0.453651 | 0.226825 | − | 0.973935i | \(-0.427165\pi\) | ||||
0.226825 | + | 0.973935i | \(0.427165\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 100.664i | − 0.285977i | ||||||||
\(353\) | 230.339 | 0.652519 | 0.326260 | − | 0.945280i | \(-0.394212\pi\) | ||||
0.326260 | + | 0.945280i | \(0.394212\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 278.949i | 0.783566i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 188.502i | 0.526542i | ||||||||
\(359\) | − 171.698i | − 0.478269i | −0.970987 | − | 0.239134i | \(-0.923136\pi\) | ||||
0.970987 | − | 0.239134i | \(-0.0768636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.0000 | 0.108033 | ||||||||
\(362\) | −117.500 | −0.324585 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.6680 | 0.0375494 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 517.490i | − 1.41005i | −0.709180 | − | 0.705027i | \(-0.750935\pi\) | ||||
0.709180 | − | 0.705027i | \(-0.249065\pi\) | |||||||
\(368\) | −71.1802 | −0.193425 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 226.363i | − 0.610143i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 233.336i | − 0.625566i | −0.949825 | − | 0.312783i | \(-0.898739\pi\) | ||||
0.949825 | − | 0.312783i | \(-0.101261\pi\) | |||||||
\(374\) | 650.997i | 1.74063i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 48.0000 | 0.127660 | ||||||||
\(377\) | 30.7466 | 0.0815560 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −441.166 | −1.16403 | −0.582013 | − | 0.813179i | \(-0.697735\pi\) | ||||
−0.582013 | + | 0.813179i | \(0.697735\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 58.4941i | − 0.153126i | ||||||||
\(383\) | 213.060 | 0.556292 | 0.278146 | − | 0.960539i | \(-0.410280\pi\) | ||||
0.278146 | + | 0.960539i | \(0.410280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 189.505i | − 0.490945i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 88.8261i | − 0.228933i | ||||||||
\(389\) | 565.096i | 1.45269i | 0.687331 | + | 0.726344i | \(0.258782\pi\) | ||||
−0.687331 | + | 0.726344i | \(0.741218\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 460.324 | 1.17730 | ||||||||
\(392\) | 19.7990 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 97.3360 | 0.247046 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 498.324i | − 1.25522i | −0.778526 | − | 0.627612i | \(-0.784032\pi\) | ||||
0.778526 | − | 0.627612i | \(-0.215968\pi\) | |||||||
\(398\) | −393.850 | −0.989573 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 193.392i | − 0.482275i | −0.970491 | − | 0.241138i | \(-0.922480\pi\) | ||||
0.970491 | − | 0.241138i | \(-0.0775205\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 44.3399i | − 0.110025i | ||||||||
\(404\) | 63.7598i | 0.157821i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 44.5385 | 0.109701 | ||||||||
\(407\) | 676.212 | 1.66145 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 454.243 | 1.11062 | 0.555309 | − | 0.831644i | \(-0.312600\pi\) | ||||
0.555309 | + | 0.831644i | \(0.312600\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.00394i | 0.0218542i | ||||||||
\(413\) | −4.36281 | −0.0105637 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − 14.6117i | − 0.0351242i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 503.320i | 1.20412i | ||||||||
\(419\) | − 339.411i | − 0.810051i | −0.914305 | − | 0.405025i | \(-0.867263\pi\) | ||||
0.914305 | − | 0.405025i | \(-0.132737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 247.320 | 0.587459 | 0.293729 | − | 0.955889i | \(-0.405104\pi\) | ||||
0.293729 | + | 0.955889i | \(0.405104\pi\) | |||||||
\(422\) | 299.103 | 0.708776 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −241.992 | −0.570736 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 265.454i | − 0.621671i | ||||||||
\(428\) | 344.358 | 0.804575 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 456.419i | − 1.05898i | −0.848317 | − | 0.529489i | \(-0.822384\pi\) | ||||
0.848317 | − | 0.529489i | \(-0.177616\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 637.984i | − 1.47340i | −0.676217 | − | 0.736702i | \(-0.736382\pi\) | ||||
0.676217 | − | 0.736702i | \(-0.263618\pi\) | |||||||
\(434\) | − 64.2293i | − 0.147994i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 355.660 | 0.815734 | ||||||||
\(437\) | 355.901 | 0.814419 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 784.146 | 1.78621 | 0.893105 | − | 0.449848i | \(-0.148522\pi\) | ||||
0.893105 | + | 0.449848i | \(0.148522\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 94.4941i | 0.213788i | ||||||||
\(443\) | 472.222 | 1.06596 | 0.532981 | − | 0.846127i | \(-0.321072\pi\) | ||||
0.532981 | + | 0.846127i | \(0.321072\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − 314.654i | − 0.705503i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 21.1660i | − 0.0472456i | ||||||||
\(449\) | − 739.852i | − 1.64778i | −0.566752 | − | 0.823888i | \(-0.691800\pi\) | ||||
0.566752 | − | 0.823888i | \(-0.308200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 279.984 | 0.620808 | ||||||||
\(452\) | −62.6949 | −0.138706 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −144.000 | −0.317181 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 248.324i | 0.543379i | 0.962385 | + | 0.271689i | \(0.0875824\pi\) | ||||
−0.962385 | + | 0.271689i | \(0.912418\pi\) | |||||||
\(458\) | −230.637 | −0.503574 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 355.970i | − 0.772168i | −0.922464 | − | 0.386084i | \(-0.873827\pi\) | ||||
0.922464 | − | 0.386084i | \(-0.126173\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 6.33202i | − 0.0136761i | −0.999977 | − | 0.00683804i | \(-0.997823\pi\) | ||||
0.999977 | − | 0.00683804i | \(-0.00217663\pi\) | |||||||
\(464\) | − 47.6137i | − 0.102616i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 513.158 | 1.10120 | ||||||||
\(467\) | −878.691 | −1.88156 | −0.940782 | − | 0.339011i | \(-0.889907\pi\) | ||||
−0.940782 | + | 0.339011i | \(0.889907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −97.0039 | −0.206831 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.66404i | 0.00988144i | ||||||||
\(473\) | 774.050 | 1.63647 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 136.881i | 0.287565i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 250.494i | − 0.524046i | ||||||||
\(479\) | 224.396i | 0.468468i | 0.972180 | + | 0.234234i | \(0.0752581\pi\) | ||||
−0.972180 | + | 0.234234i | \(0.924742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 98.1542 | 0.204063 | ||||||||
\(482\) | −216.025 | −0.448185 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −391.328 | −0.808529 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 717.490i | 1.47329i | 0.676282 | + | 0.736643i | \(0.263590\pi\) | ||||
−0.676282 | + | 0.736643i | \(0.736410\pi\) | |||||||
\(488\) | −283.782 | −0.581520 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 274.002i | − 0.558050i | −0.960284 | − | 0.279025i | \(-0.909989\pi\) | ||||
0.960284 | − | 0.279025i | \(-0.0900112\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 307.919i | 0.624582i | ||||||||
\(494\) | 73.0584i | 0.147892i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −68.6640 | −0.138436 | ||||||||
\(497\) | 47.0813 | 0.0947310 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 728.810 | 1.46054 | 0.730271 | − | 0.683158i | \(-0.239394\pi\) | ||||
0.730271 | + | 0.683158i | \(0.239394\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 504.000i | − 1.00398i | ||||||||
\(503\) | −594.657 | −1.18222 | −0.591111 | − | 0.806590i | \(-0.701310\pi\) | ||||
−0.591111 | + | 0.806590i | \(0.701310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 447.831i | 0.885041i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 428.664i | − 0.843827i | ||||||||
\(509\) | − 994.015i | − 1.95288i | −0.215795 | − | 0.976439i | \(-0.569234\pi\) | ||||
0.215795 | − | 0.976439i | \(-0.430766\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 76.5020 | 0.149710 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −84.2431 | −0.163897 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 301.992i | − 0.584124i | ||||||||
\(518\) | 142.183 | 0.274485 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.8459i | 0.0783990i | 0.999231 | + | 0.0391995i | \(0.0124808\pi\) | ||||
−0.999231 | + | 0.0391995i | \(0.987519\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 232.000i | − 0.443595i | −0.975093 | − | 0.221797i | \(-0.928808\pi\) | ||||
0.975093 | − | 0.221797i | \(-0.0711923\pi\) | |||||||
\(524\) | 182.898i | 0.349041i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.4941 | −0.0199507 | ||||||||
\(527\) | 444.052 | 0.842603 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −212.336 | −0.401391 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 105.830i | 0.198929i | ||||||||
\(533\) | 40.6405 | 0.0762487 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 103.702i | 0.193473i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 608.405i | − 1.13086i | ||||||||
\(539\) | − 124.565i | − 0.231105i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 250.332 | 0.462721 | 0.231360 | − | 0.972868i | \(-0.425682\pi\) | ||||
0.231360 | + | 0.972868i | \(0.425682\pi\) | |||||||
\(542\) | 58.2175 | 0.107412 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 146.332 | 0.268993 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 888.324i | − 1.62399i | −0.583662 | − | 0.811996i | \(-0.698381\pi\) | ||||
0.583662 | − | 0.811996i | \(-0.301619\pi\) | |||||||
\(548\) | −213.781 | −0.390111 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 238.069i | 0.432066i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 313.077i | 0.566143i | ||||||||
\(554\) | 45.2548i | 0.0816874i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 242.656 | 0.436432 | ||||||||
\(557\) | 316.309 | 0.567879 | 0.283940 | − | 0.958842i | \(-0.408358\pi\) | ||||
0.283940 | + | 0.958842i | \(0.408358\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 112.356 | 0.200994 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 24.1699i | − 0.0430070i | ||||||||
\(563\) | −58.4690 | −0.103853 | −0.0519263 | − | 0.998651i | \(-0.516536\pi\) | ||||
−0.0519263 | + | 0.998651i | \(0.516536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − 621.773i | − 1.09854i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 50.3320i | − 0.0886127i | ||||||||
\(569\) | − 221.665i | − 0.389570i | −0.980846 | − | 0.194785i | \(-0.937599\pi\) | ||||
0.980846 | − | 0.194785i | \(-0.0624009\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −487.644 | −0.854018 | −0.427009 | − | 0.904247i | \(-0.640433\pi\) | ||||
−0.427009 | + | 0.904247i | \(0.640433\pi\) | |||||||
\(572\) | −91.9294 | −0.160716 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 58.8706 | 0.102562 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 487.328i | 0.844589i | 0.906459 | + | 0.422295i | \(0.138775\pi\) | ||||
−0.906459 | + | 0.422295i | \(0.861225\pi\) | |||||||
\(578\) | −537.625 | −0.930147 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 318.662i | − 0.548472i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1522.49i | 2.61148i | ||||||||
\(584\) | − 81.7840i | − 0.140041i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −557.733 | −0.951763 | ||||||||
\(587\) | −445.701 | −0.759286 | −0.379643 | − | 0.925133i | \(-0.623953\pi\) | ||||
−0.379643 | + | 0.925133i | \(0.623953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 343.320 | 0.582887 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 152.000i | − 0.256757i | ||||||||
\(593\) | 276.648 | 0.466523 | 0.233261 | − | 0.972414i | \(-0.425060\pi\) | ||||
0.233261 | + | 0.972414i | \(0.425060\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 35.3498i | 0.0593117i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 65.0039i | 0.108702i | ||||||||
\(599\) | 82.3793i | 0.137528i | 0.997633 | + | 0.0687641i | \(0.0219056\pi\) | ||||
−0.997633 | + | 0.0687641i | \(0.978094\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −418.000 | −0.695507 | −0.347754 | − | 0.937586i | \(-0.613055\pi\) | ||||
−0.347754 | + | 0.937586i | \(0.613055\pi\) | |||||||
\(602\) | 162.755 | 0.270357 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −101.668 | −0.168324 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 76.8419i | − 0.126593i | −0.997995 | − | 0.0632964i | \(-0.979839\pi\) | ||||
0.997995 | − | 0.0632964i | \(-0.0201614\pi\) | |||||||
\(608\) | 113.137 | 0.186081 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 43.8351i | − 0.0717431i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 59.3281i | 0.0967832i | 0.998828 | + | 0.0483916i | \(0.0154095\pi\) | ||||
−0.998828 | + | 0.0483916i | \(0.984590\pi\) | |||||||
\(614\) | − 33.0020i | − 0.0537492i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −133.166 | −0.216179 | ||||||||
\(617\) | 29.1143 | 0.0471869 | 0.0235935 | − | 0.999722i | \(-0.492489\pi\) | ||||
0.0235935 | + | 0.999722i | \(0.492489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −455.644 | −0.736098 | −0.368049 | − | 0.929806i | \(-0.619974\pi\) | ||||
−0.368049 | + | 0.929806i | \(0.619974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 745.652i | 1.19880i | ||||||||
\(623\) | 369.015 | 0.592320 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 417.657i | 0.667184i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 137.992i | − 0.219733i | ||||||||
\(629\) | 982.987i | 1.56278i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.0039 | −0.0713216 | −0.0356608 | − | 0.999364i | \(-0.511354\pi\) | ||||
−0.0356608 | + | 0.999364i | \(0.511354\pi\) | |||||||
\(632\) | 334.693 | 0.529578 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −151.992 | −0.239735 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 18.0810i | − 0.0283847i | ||||||||
\(638\) | −299.562 | −0.469533 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 641.223i | − 1.00035i | −0.865925 | − | 0.500174i | \(-0.833269\pi\) | ||||
0.865925 | − | 0.500174i | \(-0.166731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 604.000i | − 0.939347i | −0.882840 | − | 0.469673i | \(-0.844372\pi\) | ||||
0.882840 | − | 0.469673i | \(-0.155628\pi\) | |||||||
\(644\) | 94.1626i | 0.146215i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −731.660 | −1.13260 | ||||||||
\(647\) | −179.600 | −0.277588 | −0.138794 | − | 0.990321i | \(-0.544323\pi\) | ||||
−0.138794 | + | 0.990321i | \(0.544323\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.3438 | 0.0452139 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 333.992i | − 0.512258i | ||||||||
\(653\) | −392.092 | −0.600447 | −0.300224 | − | 0.953869i | \(-0.597061\pi\) | ||||
−0.300224 | + | 0.953869i | \(0.597061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − 62.9353i | − 0.0959379i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 63.4980i | − 0.0965016i | ||||||||
\(659\) | − 1266.54i | − 1.92191i | −0.276701 | − | 0.960956i | \(-0.589241\pi\) | ||||
0.276701 | − | 0.960956i | \(-0.410759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 917.644 | 1.38827 | 0.694133 | − | 0.719846i | \(-0.255788\pi\) | ||||
0.694133 | + | 0.719846i | \(0.255788\pi\) | |||||||
\(662\) | 386.773 | 0.584250 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −340.664 | −0.513048 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 211.822i | 0.317574i | ||||||||
\(668\) | 240.886 | 0.360608 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1785.41i | 2.66083i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 152.008i | − 0.225866i | −0.993603 | − | 0.112933i | \(-0.963975\pi\) | ||||
0.993603 | − | 0.112933i | \(-0.0360246\pi\) | |||||||
\(674\) | − 482.482i | − 0.715848i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 324.656 | 0.480261 | ||||||||
\(677\) | 163.178 | 0.241031 | 0.120516 | − | 0.992711i | \(-0.461545\pi\) | ||||
0.120516 | + | 0.992711i | \(0.461545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −117.506 | −0.173057 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 432.000i | 0.633431i | ||||||||
\(683\) | 324.914 | 0.475716 | 0.237858 | − | 0.971300i | \(-0.423555\pi\) | ||||
0.237858 | + | 0.971300i | \(0.423555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − 26.1916i | − 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 173.992i | − 0.252896i | ||||||||
\(689\) | 220.995i | 0.320747i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1218.98 | 1.76408 | 0.882041 | − | 0.471173i | \(-0.156169\pi\) | ||||
0.882041 | + | 0.471173i | \(0.156169\pi\) | |||||||
\(692\) | 183.722 | 0.265494 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −164.502 | −0.237035 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 407.004i | 0.583937i | ||||||||
\(698\) | −223.904 | −0.320780 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 427.202i | − 0.609417i | −0.952446 | − | 0.304709i | \(-0.901441\pi\) | ||||
0.952446 | − | 0.304709i | \(-0.0985591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 760.000i | 1.08108i | ||||||||
\(704\) | 142.360i | 0.202217i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −325.749 | −0.461401 | ||||||||
\(707\) | 84.3463 | 0.119302 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −71.4980 | −0.100843 | −0.0504217 | − | 0.998728i | \(-0.516057\pi\) | ||||
−0.0504217 | + | 0.998728i | \(0.516057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 394.494i | − 0.554065i | ||||||||
\(713\) | 305.470 | 0.428429 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 266.582i | − 0.372321i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 242.818i | 0.338187i | ||||||||
\(719\) | 111.030i | 0.154422i | 0.997015 | + | 0.0772112i | \(0.0246016\pi\) | ||||
−0.997015 | + | 0.0772112i | \(0.975398\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.9111 | 0.0165202 | ||||||||
\(722\) | −55.1543 | −0.0763910 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 166.170 | 0.229517 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1338.82i | 1.84157i | 0.390076 | + | 0.920783i | \(0.372449\pi\) | ||||
−0.390076 | + | 0.920783i | \(0.627551\pi\) | |||||||
\(728\) | −19.3294 | −0.0265514 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1125.21i | 1.53928i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.0771i | 0.0669538i | 0.999439 | + | 0.0334769i | \(0.0106580\pi\) | ||||
−0.999439 | + | 0.0334769i | \(0.989342\pi\) | |||||||
\(734\) | 731.842i | 0.997059i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 100.664 | 0.136772 | ||||||||
\(737\) | 652.439 | 0.885263 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1430.32 | −1.93548 | −0.967738 | − | 0.251960i | \(-0.918925\pi\) | ||||
−0.967738 | + | 0.251960i | \(0.918925\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 320.125i | 0.431436i | ||||||||
\(743\) | −875.736 | −1.17865 | −0.589325 | − | 0.807896i | \(-0.700606\pi\) | ||||
−0.589325 | + | 0.807896i | \(0.700606\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 329.987i | 0.442342i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 920.648i | − 1.23081i | ||||||||
\(749\) | − 455.543i | − 0.608202i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 320.826 | 0.427199 | 0.213599 | − | 0.976921i | \(-0.431481\pi\) | ||||
0.213599 | + | 0.976921i | \(0.431481\pi\) | |||||||
\(752\) | −67.8823 | −0.0902690 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −43.4823 | −0.0576688 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 289.830i | − 0.382867i | −0.981506 | − | 0.191433i | \(-0.938686\pi\) | ||||
0.981506 | − | 0.191433i | \(-0.0613136\pi\) | |||||||
\(758\) | 623.903 | 0.823091 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 704.657i | − 0.925962i | −0.886368 | − | 0.462981i | \(-0.846780\pi\) | ||||
0.886368 | − | 0.462981i | \(-0.153220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 470.494i | − 0.616637i | ||||||||
\(764\) | 82.7231i | 0.108276i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −301.312 | −0.393358 | ||||||||
\(767\) | 4.25934 | 0.00555325 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 117.320 | 0.152562 | 0.0762810 | − | 0.997086i | \(-0.475695\pi\) | ||||
0.0762810 | + | 0.997086i | \(0.475695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 268.000i | 0.347150i | ||||||||
\(773\) | −658.005 | −0.851235 | −0.425618 | − | 0.904903i | \(-0.639943\pi\) | ||||
−0.425618 | + | 0.904903i | \(0.639943\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 125.619i | 0.161880i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 799.166i | − 1.02721i | ||||||||
\(779\) | 314.676i | 0.403949i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −316.664 | −0.405460 | ||||||||
\(782\) | −650.997 | −0.832477 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1200.65i | 1.52560i | 0.646634 | + | 0.762801i | \(0.276176\pi\) | ||||
−0.646634 | + | 0.762801i | \(0.723824\pi\) | |||||||
\(788\) | −137.654 | −0.174688 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 82.9376i | 0.104852i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 259.158i | 0.326807i | ||||||||
\(794\) | 704.737i | 0.887578i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 556.988 | 0.699734 | ||||||||
\(797\) | 797.411 | 1.00052 | 0.500258 | − | 0.865876i | \(-0.333239\pi\) | ||||
0.500258 | + | 0.865876i | \(0.333239\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 438.996 | 0.549432 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 273.498i | 0.341020i | ||||||||
\(803\) | −514.545 | −0.640778 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 62.7061i | 0.0777991i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 90.1699i | − 0.111596i | ||||||||
\(809\) | 156.016i | 0.192851i | 0.995340 | + | 0.0964254i | \(0.0307409\pi\) | ||||
−0.995340 | + | 0.0964254i | \(0.969259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −598.316 | −0.737751 | −0.368876 | − | 0.929479i | \(-0.620257\pi\) | ||||
−0.368876 | + | 0.929479i | \(0.620257\pi\) | |||||||
\(812\) | −62.9870 | −0.0775702 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −956.308 | −1.17483 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 869.961i | 1.06482i | ||||||||
\(818\) | −642.397 | −0.785326 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 980.978i | − 1.19486i | −0.801922 | − | 0.597429i | \(-0.796189\pi\) | ||||
0.801922 | − | 0.597429i | \(-0.203811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 431.336i | − 0.524102i | −0.965054 | − | 0.262051i | \(-0.915601\pi\) | ||||
0.965054 | − | 0.262051i | \(-0.0843989\pi\) | |||||||
\(824\) | − 12.7335i | − 0.0154533i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.16995 | 0.00746967 | ||||||||
\(827\) | −1219.41 | −1.47449 | −0.737247 | − | 0.675623i | \(-0.763875\pi\) | ||||
−0.737247 | + | 0.675623i | \(0.763875\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 770.081 | 0.928928 | 0.464464 | − | 0.885592i | \(-0.346247\pi\) | ||||
0.464464 | + | 0.885592i | \(0.346247\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.6640i | 0.0248366i | ||||||||
\(833\) | 181.077 | 0.217379 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − 711.802i | − 0.851438i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 480.000i | 0.572792i | ||||||||
\(839\) | − 1310.03i | − 1.56142i | −0.624894 | − | 0.780710i | \(-0.714858\pi\) | ||||
0.624894 | − | 0.780710i | \(-0.285142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 699.308 | 0.831520 | ||||||||
\(842\) | −349.764 | −0.415396 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −422.996 | −0.501180 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 517.678i | 0.611191i | ||||||||
\(848\) | 342.229 | 0.403571 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 676.212i | 0.794609i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 898.988i | 1.05391i | 0.849892 | + | 0.526957i | \(0.176667\pi\) | ||||
−0.849892 | + | 0.526957i | \(0.823333\pi\) | |||||||
\(854\) | 375.408i | 0.439588i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −486.996 | −0.568921 | ||||||||
\(857\) | −746.156 | −0.870660 | −0.435330 | − | 0.900271i | \(-0.643368\pi\) | ||||
−0.435330 | + | 0.900271i | \(0.643368\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 991.984 | 1.15481 | 0.577406 | − | 0.816457i | \(-0.304065\pi\) | ||||
0.577406 | + | 0.816457i | \(0.304065\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 645.474i | 0.748810i | ||||||||
\(863\) | 209.418 | 0.242663 | 0.121332 | − | 0.992612i | \(-0.461284\pi\) | ||||
0.121332 | + | 0.992612i | \(0.461284\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 902.246i | 1.04185i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 90.8340i | 0.104647i | ||||||||
\(869\) | − 2105.73i | − 2.42316i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 94.7034 | 0.108730 | ||||||||
\(872\) | −502.979 | −0.576811 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −503.320 | −0.575881 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 865.304i | 0.986664i | 0.869841 | + | 0.493332i | \(0.164221\pi\) | ||||
−0.869841 | + | 0.493332i | \(0.835779\pi\) | |||||||
\(878\) | −1108.95 | −1.26304 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 995.046i | − 1.12945i | −0.825279 | − | 0.564725i | \(-0.808982\pi\) | ||||
0.825279 | − | 0.564725i | \(-0.191018\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 101.474i | 0.114920i | 0.998348 | + | 0.0574600i | \(0.0183002\pi\) | ||||
−0.998348 | + | 0.0574600i | \(0.981700\pi\) | |||||||
\(884\) | − 133.635i | − 0.151171i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −667.822 | −0.753750 | ||||||||
\(887\) | −1074.09 | −1.21093 | −0.605464 | − | 0.795873i | \(-0.707012\pi\) | ||||
−0.605464 | + | 0.795873i | \(0.707012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −567.069 | −0.637873 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 444.988i | 0.498866i | ||||||||
\(893\) | 339.411 | 0.380080 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1046.31i | 1.16515i | ||||||||
\(899\) | 204.334i | 0.227291i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2213.20 | −2.45638 | ||||||||
\(902\) | −395.958 | −0.438977 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 88.6640 | 0.0980797 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 432.162i | 0.476474i | 0.971207 | + | 0.238237i | \(0.0765695\pi\) | ||||
−0.971207 | + | 0.238237i | \(0.923430\pi\) | |||||||
\(908\) | 203.647 | 0.224281 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 104.984i | 0.115241i | 0.998339 | + | 0.0576205i | \(0.0183513\pi\) | ||||
−0.998339 | + | 0.0576205i | \(0.981649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2143.29i | 2.34752i | ||||||||
\(914\) | − 351.183i | − 0.384227i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 326.170 | 0.356081 | ||||||||
\(917\) | 241.951 | 0.263850 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 91.8379 | 0.0999325 | 0.0499662 | − | 0.998751i | \(-0.484089\pi\) | ||||
0.0499662 | + | 0.998751i | \(0.484089\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 503.417i | 0.546005i | ||||||||
\(923\) | −45.9647 | −0.0497993 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.95483i | 0.00967044i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 67.3360i | 0.0725603i | ||||||||
\(929\) | − 1309.00i | − 1.40904i | −0.709682 | − | 0.704522i | \(-0.751162\pi\) | ||||
0.709682 | − | 0.704522i | \(-0.248838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 140.000 | 0.150376 | ||||||||
\(932\) | −725.715 | −0.778664 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1242.66 | 1.33047 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1262.00i | − 1.34685i | −0.739255 | − | 0.673426i | \(-0.764822\pi\) | ||||
0.739255 | − | 0.673426i | \(-0.235178\pi\) | |||||||
\(938\) | 137.184 | 0.146252 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1315.97i | 1.39849i | 0.714884 | + | 0.699243i | \(0.246479\pi\) | ||||
−0.714884 | + | 0.699243i | \(0.753521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 279.984i | 0.296908i | ||||||||
\(944\) | − 6.59595i | − 0.00698724i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1094.67 | −1.15716 | ||||||||
\(947\) | −486.582 | −0.513814 | −0.256907 | − | 0.966436i | \(-0.582703\pi\) | ||||
−0.256907 | + | 0.966436i | \(0.582703\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −74.6877 | −0.0787014 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 193.579i | − 0.203339i | ||||||||
\(953\) | 43.3711 | 0.0455100 | 0.0227550 | − | 0.999741i | \(-0.492756\pi\) | ||||
0.0227550 | + | 0.999741i | \(0.492756\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 354.252i | 0.370557i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 317.344i | − 0.331257i | ||||||||
\(959\) | 282.806i | 0.294896i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −666.328 | −0.693369 | ||||||||
\(962\) | −138.811 | −0.144294 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 305.506 | 0.316915 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1648.99i | − 1.70526i | −0.522514 | − | 0.852631i | \(-0.675006\pi\) | ||||
0.522514 | − | 0.852631i | \(-0.324994\pi\) | |||||||
\(968\) | 553.421 | 0.571716 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 518.323i | − 0.533803i | −0.963724 | − | 0.266902i | \(-0.914000\pi\) | ||||
0.963724 | − | 0.266902i | \(-0.0859999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 321.004i | − 0.329912i | ||||||||
\(974\) | − 1014.68i | − 1.04177i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 401.328 | 0.411197 | ||||||||
\(977\) | −109.948 | −0.112536 | −0.0562682 | − | 0.998416i | \(-0.517920\pi\) | ||||
−0.0562682 | + | 0.998416i | \(0.517920\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2481.96 | −2.53520 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 387.498i | 0.394601i | ||||||||
\(983\) | −589.710 | −0.599909 | −0.299954 | − | 0.953954i | \(-0.596971\pi\) | ||||
−0.299954 | + | 0.953954i | \(0.596971\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − 435.463i | − 0.441646i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 103.320i | − 0.104575i | ||||||||
\(989\) | 774.050i | 0.782659i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 713.474 | 0.719954 | 0.359977 | − | 0.932961i | \(-0.382785\pi\) | ||||
0.359977 | + | 0.932961i | \(0.382785\pi\) | |||||||
\(992\) | 97.1056 | 0.0978887 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −66.5830 | −0.0669849 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1222.99i | − 1.22667i | −0.789824 | − | 0.613334i | \(-0.789828\pi\) | ||||
0.789824 | − | 0.613334i | \(-0.210172\pi\) | |||||||
\(998\) | −1030.69 | −1.03276 | ||||||||
\(999\) | 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 | 3150.3.c.b.449.2 | 8 | ||
3.2 | odd | 2 | inner | 3150.3.c.b.449.5 | 8 | ||
5.2 | odd | 4 | 126.3.b.a.71.2 | ✓ | 4 | ||
5.3 | odd | 4 | 3150.3.e.e.701.3 | 4 | |||
5.4 | even | 2 | inner | 3150.3.c.b.449.8 | 8 | ||
15.2 | even | 4 | 126.3.b.a.71.3 | yes | 4 | ||
15.8 | even | 4 | 3150.3.e.e.701.1 | 4 | |||
15.14 | odd | 2 | inner | 3150.3.c.b.449.3 | 8 | ||
20.7 | even | 4 | 1008.3.d.a.449.4 | 4 | |||
35.2 | odd | 12 | 882.3.s.e.557.2 | 8 | |||
35.12 | even | 12 | 882.3.s.i.557.1 | 8 | |||
35.17 | even | 12 | 882.3.s.i.863.4 | 8 | |||
35.27 | even | 4 | 882.3.b.f.197.1 | 4 | |||
35.32 | odd | 12 | 882.3.s.e.863.3 | 8 | |||
40.27 | even | 4 | 4032.3.d.j.449.1 | 4 | |||
40.37 | odd | 4 | 4032.3.d.i.449.1 | 4 | |||
45.2 | even | 12 | 1134.3.q.c.701.4 | 8 | |||
45.7 | odd | 12 | 1134.3.q.c.701.1 | 8 | |||
45.22 | odd | 12 | 1134.3.q.c.1079.4 | 8 | |||
45.32 | even | 12 | 1134.3.q.c.1079.1 | 8 | |||
60.47 | odd | 4 | 1008.3.d.a.449.1 | 4 | |||
105.2 | even | 12 | 882.3.s.e.557.3 | 8 | |||
105.17 | odd | 12 | 882.3.s.i.863.1 | 8 | |||
105.32 | even | 12 | 882.3.s.e.863.2 | 8 | |||
105.47 | odd | 12 | 882.3.s.i.557.4 | 8 | |||
105.62 | odd | 4 | 882.3.b.f.197.4 | 4 | |||
120.77 | even | 4 | 4032.3.d.i.449.4 | 4 | |||
120.107 | odd | 4 | 4032.3.d.j.449.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.b.a.71.2 | ✓ | 4 | 5.2 | odd | 4 | ||
126.3.b.a.71.3 | yes | 4 | 15.2 | even | 4 | ||
882.3.b.f.197.1 | 4 | 35.27 | even | 4 | |||
882.3.b.f.197.4 | 4 | 105.62 | odd | 4 | |||
882.3.s.e.557.2 | 8 | 35.2 | odd | 12 | |||
882.3.s.e.557.3 | 8 | 105.2 | even | 12 | |||
882.3.s.e.863.2 | 8 | 105.32 | even | 12 | |||
882.3.s.e.863.3 | 8 | 35.32 | odd | 12 | |||
882.3.s.i.557.1 | 8 | 35.12 | even | 12 | |||
882.3.s.i.557.4 | 8 | 105.47 | odd | 12 | |||
882.3.s.i.863.1 | 8 | 105.17 | odd | 12 | |||
882.3.s.i.863.4 | 8 | 35.17 | even | 12 | |||
1008.3.d.a.449.1 | 4 | 60.47 | odd | 4 | |||
1008.3.d.a.449.4 | 4 | 20.7 | even | 4 | |||
1134.3.q.c.701.1 | 8 | 45.7 | odd | 12 | |||
1134.3.q.c.701.4 | 8 | 45.2 | even | 12 | |||
1134.3.q.c.1079.1 | 8 | 45.32 | even | 12 | |||
1134.3.q.c.1079.4 | 8 | 45.22 | odd | 12 | |||
3150.3.c.b.449.2 | 8 | 1.1 | even | 1 | trivial | ||
3150.3.c.b.449.3 | 8 | 15.14 | odd | 2 | inner | ||
3150.3.c.b.449.5 | 8 | 3.2 | odd | 2 | inner | ||
3150.3.c.b.449.8 | 8 | 5.4 | even | 2 | inner | ||
3150.3.e.e.701.1 | 4 | 15.8 | even | 4 | |||
3150.3.e.e.701.3 | 4 | 5.3 | odd | 4 | |||
4032.3.d.i.449.1 | 4 | 40.37 | odd | 4 | |||
4032.3.d.i.449.4 | 4 | 120.77 | even | 4 | |||
4032.3.d.j.449.1 | 4 | 40.27 | even | 4 | |||
4032.3.d.j.449.4 | 4 | 120.107 | odd | 4 |