Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,3,Mod(701,3150)]
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, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.701");
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.e (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: | \(85.8312832735\) |
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: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 701.1 | ||
Root | \(2.57794i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.701 |
Dual form | 3150.3.e.e.701.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.41421i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64575 | −0.377964 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 17.7951i | − 1.61773i | −0.587993 | − | 0.808866i | \(-0.700082\pi\) | ||||
0.587993 | − | 0.808866i | \(-0.299918\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.58301 | −0.198693 | −0.0993464 | − | 0.995053i | \(-0.531675\pi\) | ||||
−0.0993464 | + | 0.995053i | \(0.531675\pi\) | |||||||
\(14\) | 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 | \(0.323573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 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 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.65292i | 0.140497i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.29150 | 0.188982 | ||||||||
\(29\) | − 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 | \(0.589298\pi\) | |||||||
\(32\) | − 5.65685i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −36.5830 | −1.07597 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −38.0000 | −1.02703 | −0.513514 | − | 0.858082i | \(-0.671656\pi\) | ||||
−0.513514 | + | 0.858082i | \(0.671656\pi\) | |||||||
\(38\) | − 28.2843i | − 0.744323i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15.7338i | 0.383752i | 0.981419 | + | 0.191876i | \(0.0614571\pi\) | ||||
−0.981419 | + | 0.191876i | \(0.938543\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.4980 | 1.01158 | 0.505791 | − | 0.862656i | \(-0.331201\pi\) | ||||
0.505791 | + | 0.862656i | \(0.331201\pi\) | |||||||
\(44\) | 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 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 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 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 7.48331i | − 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −16.8340 | −0.290241 | ||||||||
\(59\) | − 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 | \(0.192638\pi\) | |||||||
\(62\) | 24.2764i | 0.391555i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −36.6640 | −0.547225 | −0.273612 | − | 0.961840i | \(-0.588219\pi\) | ||||
−0.273612 | + | 0.961840i | \(0.588219\pi\) | |||||||
\(68\) | 51.7362i | 0.760826i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 17.7951i | − 0.250635i | −0.992117 | − | 0.125317i | \(-0.960005\pi\) | ||||
0.992117 | − | 0.125317i | \(-0.0399949\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −28.9150 | −0.396096 | −0.198048 | − | 0.980192i | \(-0.563460\pi\) | ||||
−0.198048 | + | 0.980192i | \(0.563460\pi\) | |||||||
\(74\) | 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 | \(0.230565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 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 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − 61.5155i | − 0.715297i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 50.3320 | 0.571955 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | − 35.5901i | − 0.386849i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −24.0000 | −0.255319 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −44.4131 | −0.457867 | −0.228933 | − | 0.973442i | \(-0.573524\pi\) | ||||
−0.228933 | + | 0.973442i | \(0.573524\pi\) | |||||||
\(98\) | − 9.89949i | − 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 31.8799i | − 0.315642i | −0.987468 | − | 0.157821i | \(-0.949553\pi\) | ||||
0.987468 | − | 0.157821i | \(-0.0504470\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.50197 | −0.0437084 | −0.0218542 | − | 0.999761i | \(-0.506957\pi\) | ||||
−0.0218542 | + | 0.999761i | \(0.506957\pi\) | |||||||
\(104\) | − 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 | \(0.803667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 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 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −214.332 | −1.68765 | −0.843827 | − | 0.536616i | \(-0.819703\pi\) | ||||
−0.843827 | + | 0.536616i | \(0.819703\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 91.4488i | − 0.698082i | −0.937107 | − | 0.349041i | \(-0.886507\pi\) | ||||
0.937107 | − | 0.349041i | \(-0.113493\pi\) | |||||||
\(132\) | 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 | \(0.643758\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −25.1660 | −0.177225 | ||||||||
\(143\) | 45.9647i | 0.321432i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 40.8920i | 0.280082i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 76.0000 | 0.513514 | ||||||||
\(149\) | 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 | \(0.553836\pi\) | |||||||
\(152\) | 56.5685i | 0.372161i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 66.5830 | 0.432357 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −68.9961 | −0.439465 | −0.219733 | − | 0.975560i | \(-0.570519\pi\) | ||||
−0.219733 | + | 0.975560i | \(0.570519\pi\) | |||||||
\(158\) | − 167.347i | − 1.05916i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 47.0813i | − 0.292430i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 166.996 | 1.02452 | 0.512258 | − | 0.858832i | \(-0.328809\pi\) | ||||
0.512258 | + | 0.858832i | \(0.328809\pi\) | |||||||
\(164\) | − 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 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 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 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 71.1802i | − 0.404433i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 197.247 | 1.10813 | ||||||||
\(179\) | − 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 | \(0.426286\pi\) | |||||||
\(182\) | − 9.66472i | − 0.0531029i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −50.3320 | −0.273544 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −460.324 | −2.46163 | ||||||||
\(188\) | 33.9411i | 0.180538i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 41.3616i | − 0.216553i | −0.994121 | − | 0.108276i | \(-0.965467\pi\) | ||||
0.994121 | − | 0.108276i | \(-0.0345331\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −134.000 | −0.694301 | −0.347150 | − | 0.937810i | \(-0.612851\pi\) | ||||
−0.347150 | + | 0.937810i | \(0.612851\pi\) | |||||||
\(194\) | 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 | \(0.746698\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −45.0850 | −0.223193 | ||||||||
\(203\) | 31.4935i | 0.155140i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 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 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 45.4170 | 0.209295 | ||||||||
\(218\) | 251.490i | 1.15362i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 66.8174i | 0.302341i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −222.494 | −0.997731 | −0.498866 | − | 0.866679i | \(-0.666250\pi\) | ||||
−0.498866 | + | 0.866679i | \(0.666250\pi\) | |||||||
\(224\) | 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 | \(0.615887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 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 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.29798i | 0.0139745i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 96.7895 | 0.406679 | ||||||||
\(239\) | 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 | \(0.397353\pi\) | |||||||
\(242\) | 276.711i | 1.14343i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −200.664 | −0.822394 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −51.6601 | −0.209150 | ||||||||
\(248\) | − 48.5528i | − 0.195777i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 356.382i | − 1.41985i | −0.704278 | − | 0.709924i | \(-0.748729\pi\) | ||||
0.704278 | − | 0.709924i | \(-0.251271\pi\) | |||||||
\(252\) | 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 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 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 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 74.8331i | 0.281328i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 73.3281 | 0.273612 | ||||||||
\(269\) | 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 | \(0.524200\pi\) | |||||||
\(272\) | − 103.472i | − 0.380413i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −151.166 | −0.551701 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.0000 | −0.115523 | −0.0577617 | − | 0.998330i | \(-0.518396\pi\) | ||||
−0.0577617 | + | 0.998330i | \(0.518396\pi\) | |||||||
\(278\) | 171.584i | 0.617208i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 17.0907i | − 0.0608211i | −0.999537 | − | 0.0304106i | \(-0.990319\pi\) | ||||
0.999537 | − | 0.0304106i | \(-0.00968147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −439.660 | −1.55357 | −0.776785 | − | 0.629766i | \(-0.783151\pi\) | ||||
−0.776785 | + | 0.629766i | \(0.783151\pi\) | |||||||
\(284\) | 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 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 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 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − 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 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.3360 | 0.0760129 | 0.0380064 | − | 0.999277i | \(-0.487899\pi\) | ||||
0.0380064 | + | 0.999277i | \(0.487899\pi\) | |||||||
\(308\) | − 94.1626i | − 0.305723i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 527.256i | 1.69536i | 0.530511 | + | 0.847678i | \(0.322000\pi\) | ||||
−0.530511 | + | 0.847678i | \(0.678000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 295.328 | 0.943540 | 0.471770 | − | 0.881722i | \(-0.343615\pi\) | ||||
0.471770 | + | 0.881722i | \(0.343615\pi\) | |||||||
\(314\) | 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 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −66.5830 | −0.206780 | ||||||||
\(323\) | − 517.362i | − 1.60174i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − 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 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 341.166 | 1.01236 | 0.506181 | − | 0.862427i | \(-0.331057\pi\) | ||||
0.506181 | + | 0.862427i | \(0.331057\pi\) | |||||||
\(338\) | 229.567i | 0.679191i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 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 | \(0.572835\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 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 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − 278.949i | − 0.783566i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −188.502 | −0.526542 | ||||||||
\(359\) | − 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 | ||||||||
\(362\) | − 117.500i | − 0.324585i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.6680 | −0.0375494 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −517.490 | −1.41005 | −0.705027 | − | 0.709180i | \(-0.749065\pi\) | ||||
−0.705027 | + | 0.709180i | \(0.749065\pi\) | |||||||
\(368\) | 71.1802i | 0.193425i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 226.363i | 0.610143i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 233.336 | 0.625566 | 0.312783 | − | 0.949825i | \(-0.398739\pi\) | ||||
0.312783 | + | 0.949825i | \(0.398739\pi\) | |||||||
\(374\) | 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 | \(0.302265\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 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 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 189.505i | 0.490945i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 88.8261 | 0.228933 | ||||||||
\(389\) | 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 | ||||||||
\(392\) | 19.7990i | 0.0505076i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −97.3360 | −0.247046 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −498.324 | −1.25522 | −0.627612 | − | 0.778526i | \(-0.715968\pi\) | ||||
−0.627612 | + | 0.778526i | \(0.715968\pi\) | |||||||
\(398\) | 393.850i | 0.989573i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 193.392i | 0.482275i | 0.970491 | + | 0.241138i | \(0.0775205\pi\) | ||||
−0.970491 | + | 0.241138i | \(0.922480\pi\) | |||||||
\(402\) | 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 | \(0.687400\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.00394 | 0.0218542 | ||||||||
\(413\) | 4.36281i | 0.0105637i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14.6117i | 0.0351242i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −503.320 | −1.20412 | ||||||||
\(419\) | − 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 | \(0.405104\pi\) | |||||||
\(422\) | 299.103i | 0.708776i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 241.992 | 0.570736 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −265.454 | −0.621671 | ||||||||
\(428\) | − 344.358i | − 0.804575i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 456.419i | 1.05898i | 0.848317 | + | 0.529489i | \(0.177616\pi\) | ||||
−0.848317 | + | 0.529489i | \(0.822384\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 637.984 | 1.47340 | 0.736702 | − | 0.676217i | \(-0.236382\pi\) | ||||
0.736702 | + | 0.676217i | \(0.236382\pi\) | |||||||
\(434\) | − 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 | \(0.851478\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 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 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 314.654i | 0.705503i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21.1660 | 0.0472456 | ||||||||
\(449\) | − 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 | ||||||||
\(452\) | − 62.6949i | − 0.138706i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 144.000 | 0.317181 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 248.324 | 0.543379 | 0.271689 | − | 0.962385i | \(-0.412418\pi\) | ||||
0.271689 | + | 0.962385i | \(0.412418\pi\) | |||||||
\(458\) | 230.637i | 0.503574i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 355.970i | 0.772168i | 0.922464 | + | 0.386084i | \(0.126173\pi\) | ||||
−0.922464 | + | 0.386084i | \(0.873827\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.33202 | 0.0136761 | 0.00683804 | − | 0.999977i | \(-0.497823\pi\) | ||||
0.00683804 | + | 0.999977i | \(0.497823\pi\) | |||||||
\(464\) | − 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 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.66404 | 0.00988144 | ||||||||
\(473\) | − 774.050i | − 1.63647i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − 136.881i | − 0.287565i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 250.494 | 0.524046 | ||||||||
\(479\) | 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 | ||||||||
\(482\) | − 216.025i | − 0.448185i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 391.328 | 0.808529 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 717.490 | 1.47329 | 0.736643 | − | 0.676282i | \(-0.236410\pi\) | ||||
0.736643 | + | 0.676282i | \(0.236410\pi\) | |||||||
\(488\) | 283.782i | 0.581520i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 274.002i | 0.558050i | 0.960284 | + | 0.279025i | \(0.0900112\pi\) | ||||
−0.960284 | + | 0.279025i | \(0.909989\pi\) | |||||||
\(492\) | 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 | \(0.760606\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 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 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − 447.831i | − 0.885041i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 428.664 | 0.843827 | ||||||||
\(509\) | − 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 | ||||||||
\(512\) | − 22.6274i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 84.2431 | 0.163897 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −301.992 | −0.584124 | ||||||||
\(518\) | − 142.183i | − 0.274485i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 40.8459i | − 0.0783990i | −0.999231 | − | 0.0391995i | \(-0.987519\pi\) | ||||
0.999231 | − | 0.0391995i | \(-0.0124808\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 232.000 | 0.443595 | 0.221797 | − | 0.975093i | \(-0.428808\pi\) | ||||
0.221797 | + | 0.975093i | \(0.428808\pi\) | |||||||
\(524\) | 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 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 105.830 | 0.198929 | ||||||||
\(533\) | − 40.6405i | − 0.0762487i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − 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 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −888.324 | −1.62399 | −0.811996 | − | 0.583662i | \(-0.801619\pi\) | ||||
−0.811996 | + | 0.583662i | \(0.801619\pi\) | |||||||
\(548\) | 213.781i | 0.390111i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 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 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 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 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 621.773i | 1.09854i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 50.3320 | 0.0886127 | ||||||||
\(569\) | − 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 | \(0.640433\pi\) | |||||||
\(572\) | − 91.9294i | − 0.160716i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −58.8706 | −0.102562 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 487.328 | 0.844589 | 0.422295 | − | 0.906459i | \(-0.361225\pi\) | ||||
0.422295 | + | 0.906459i | \(0.361225\pi\) | |||||||
\(578\) | 537.625i | 0.930147i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 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 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 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 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 35.3498i | − 0.0593117i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −65.0039 | −0.108702 | ||||||||
\(599\) | 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 | \(0.613055\pi\) | |||||||
\(602\) | 162.755i | 0.270357i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 101.668 | 0.168324 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −76.8419 | −0.126593 | −0.0632964 | − | 0.997995i | \(-0.520161\pi\) | ||||
−0.0632964 | + | 0.997995i | \(0.520161\pi\) | |||||||
\(608\) | − 113.137i | − 0.186081i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 43.8351i | 0.0717431i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −59.3281 | −0.0967832 | −0.0483916 | − | 0.998828i | \(-0.515410\pi\) | ||||
−0.0483916 | + | 0.998828i | \(0.515410\pi\) | |||||||
\(614\) | − 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 | \(0.380026\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 745.652 | 1.19880 | ||||||||
\(623\) | − 369.015i | − 0.592320i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 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 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.0810 | −0.0283847 | ||||||||
\(638\) | 299.562i | 0.469533i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 641.223i | 1.00035i | 0.865925 | + | 0.500174i | \(0.166731\pi\) | ||||
−0.865925 | + | 0.500174i | \(0.833269\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 604.000 | 0.939347 | 0.469673 | − | 0.882840i | \(-0.344372\pi\) | ||||
0.469673 | + | 0.882840i | \(0.344372\pi\) | |||||||
\(644\) | 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 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 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 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 62.9353i | 0.0959379i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 63.4980 | 0.0965016 | ||||||||
\(659\) | − 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 | \(0.255788\pi\) | |||||||
\(662\) | 386.773i | 0.584250i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 340.664 | 0.513048 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 211.822 | 0.317574 | ||||||||
\(668\) | − 240.886i | − 0.360608i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1785.41i | − 2.66083i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 152.008 | 0.225866 | 0.112933 | − | 0.993603i | \(-0.463975\pi\) | ||||
0.112933 | + | 0.993603i | \(0.463975\pi\) | |||||||
\(674\) | − 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 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 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 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 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 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 407.004 | 0.583937 | ||||||||
\(698\) | 223.904i | 0.320780i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 427.202i | 0.609417i | 0.952446 | + | 0.304709i | \(0.0985591\pi\) | ||||
−0.952446 | + | 0.304709i | \(0.901441\pi\) | |||||||
\(702\) | 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 | \(0.483943\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −394.494 | −0.554065 | ||||||||
\(713\) | − 305.470i | − 0.428429i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 266.582i | 0.372321i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −242.818 | −0.338187 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | − 55.1543i | − 0.0763910i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −166.170 | −0.229517 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1338.82 | 1.84157 | 0.920783 | − | 0.390076i | \(-0.127551\pi\) | ||||
0.920783 | + | 0.390076i | \(0.127551\pi\) | |||||||
\(728\) | 19.3294i | 0.0265514i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1125.21i | − 1.53928i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.0771 | −0.0669538 | −0.0334769 | − | 0.999439i | \(-0.510658\pi\) | ||||
−0.0334769 | + | 0.999439i | \(0.510658\pi\) | |||||||
\(734\) | 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 | \(0.0810751\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 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 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − 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 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −289.830 | −0.382867 | −0.191433 | − | 0.981506i | \(-0.561314\pi\) | ||||
−0.191433 | + | 0.981506i | \(0.561314\pi\) | |||||||
\(758\) | − 623.903i | − 0.823091i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 704.657i | 0.925962i | 0.886368 | + | 0.462981i | \(0.153220\pi\) | ||||
−0.886368 | + | 0.462981i | \(0.846780\pi\) | |||||||
\(762\) | 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 | \(0.524305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 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 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − 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 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1200.65 | 1.52560 | 0.762801 | − | 0.646634i | \(-0.223824\pi\) | ||||
0.762801 | + | 0.646634i | \(0.223824\pi\) | |||||||
\(788\) | 137.654i | 0.174688i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 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 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 273.498 | 0.341020 | ||||||||
\(803\) | 514.545i | 0.640778i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 62.7061i | − 0.0777991i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 90.1699 | 0.111596 | ||||||||
\(809\) | 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 | \(0.620257\pi\) | |||||||
\(812\) | − 62.9870i | − 0.0775702i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 956.308 | 1.17483 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 869.961 | 1.06482 | ||||||||
\(818\) | 642.397i | 0.785326i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 980.978i | 1.19486i | 0.801922 | + | 0.597429i | \(0.203811\pi\) | ||||
−0.801922 | + | 0.597429i | \(0.796189\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 431.336 | 0.524102 | 0.262051 | − | 0.965054i | \(-0.415601\pi\) | ||||
0.262051 | + | 0.965054i | \(0.415601\pi\) | |||||||
\(824\) | − 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 | \(0.653753\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.6640 | 0.0248366 | ||||||||
\(833\) | − 181.077i | − 0.217379i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 711.802i | 0.851438i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −480.000 | −0.572792 | ||||||||
\(839\) | − 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 | ||||||||
\(842\) | − 349.764i | − 0.415396i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 422.996 | 0.501180 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 517.678 | 0.611191 | ||||||||
\(848\) | − 342.229i | − 0.403571i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 676.212i | − 0.794609i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −898.988 | −1.05391 | −0.526957 | − | 0.849892i | \(-0.676667\pi\) | ||||
−0.526957 | + | 0.849892i | \(0.676667\pi\) | |||||||
\(854\) | 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 | \(0.695935\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 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 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − 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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 865.304 | 0.986664 | 0.493332 | − | 0.869841i | \(-0.335779\pi\) | ||||
0.493332 | + | 0.869841i | \(0.335779\pi\) | |||||||
\(878\) | 1108.95i | 1.26304i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 995.046i | 1.12945i | 0.825279 | + | 0.564725i | \(0.191018\pi\) | ||||
−0.825279 | + | 0.564725i | \(0.808982\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −101.474 | −0.114920 | −0.0574600 | − | 0.998348i | \(-0.518300\pi\) | ||||
−0.0574600 | + | 0.998348i | \(0.518300\pi\) | |||||||
\(884\) | − 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 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 444.988 | 0.498866 | ||||||||
\(893\) | − 339.411i | − 0.380080i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 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 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 432.162 | 0.476474 | 0.238237 | − | 0.971207i | \(-0.423430\pi\) | ||||
0.238237 | + | 0.971207i | \(0.423430\pi\) | |||||||
\(908\) | − 203.647i | − 0.224281i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 104.984i | − 0.115241i | −0.998339 | − | 0.0576205i | \(-0.981649\pi\) | ||||
0.998339 | − | 0.0576205i | \(-0.0183513\pi\) | |||||||
\(912\) | 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 | \(0.515911\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 503.417 | 0.546005 | ||||||||
\(923\) | 45.9647i | 0.0497993i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − 8.95483i | − 0.00967044i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −67.3360 | −0.0725603 | ||||||||
\(929\) | − 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 | ||||||||
\(932\) | − 725.715i | − 0.778664i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1242.66 | −1.33047 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1262.00 | −1.34685 | −0.673426 | − | 0.739255i | \(-0.735178\pi\) | ||||
−0.673426 | + | 0.739255i | \(0.735178\pi\) | |||||||
\(938\) | − 137.184i | − 0.146252i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1315.97i | − 1.39849i | −0.714884 | − | 0.699243i | \(-0.753521\pi\) | ||||
0.714884 | − | 0.699243i | \(-0.246479\pi\) | |||||||
\(942\) | 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 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 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 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − 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 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1648.99 | −1.70526 | −0.852631 | − | 0.522514i | \(-0.824994\pi\) | ||||
−0.852631 | + | 0.522514i | \(0.824994\pi\) | |||||||
\(968\) | − 553.421i | − 0.571716i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 518.323i | 0.533803i | 0.963724 | + | 0.266902i | \(0.0859999\pi\) | ||||
−0.963724 | + | 0.266902i | \(0.914000\pi\) | |||||||
\(972\) | 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 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 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 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 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 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1222.99 | −1.22667 | −0.613334 | − | 0.789824i | \(-0.710172\pi\) | ||||
−0.613334 | + | 0.789824i | \(0.710172\pi\) | |||||||
\(998\) | 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 | 3150.3.e.e.701.1 | 4 | ||
3.2 | odd | 2 | inner | 3150.3.e.e.701.3 | 4 | ||
5.2 | odd | 4 | 3150.3.c.b.449.5 | 8 | |||
5.3 | odd | 4 | 3150.3.c.b.449.3 | 8 | |||
5.4 | even | 2 | 126.3.b.a.71.3 | yes | 4 | ||
15.2 | even | 4 | 3150.3.c.b.449.2 | 8 | |||
15.8 | even | 4 | 3150.3.c.b.449.8 | 8 | |||
15.14 | odd | 2 | 126.3.b.a.71.2 | ✓ | 4 | ||
20.19 | odd | 2 | 1008.3.d.a.449.1 | 4 | |||
35.4 | even | 6 | 882.3.s.e.863.2 | 8 | |||
35.9 | even | 6 | 882.3.s.e.557.3 | 8 | |||
35.19 | odd | 6 | 882.3.s.i.557.4 | 8 | |||
35.24 | odd | 6 | 882.3.s.i.863.1 | 8 | |||
35.34 | odd | 2 | 882.3.b.f.197.4 | 4 | |||
40.19 | odd | 2 | 4032.3.d.j.449.4 | 4 | |||
40.29 | even | 2 | 4032.3.d.i.449.4 | 4 | |||
45.4 | even | 6 | 1134.3.q.c.1079.1 | 8 | |||
45.14 | odd | 6 | 1134.3.q.c.1079.4 | 8 | |||
45.29 | odd | 6 | 1134.3.q.c.701.1 | 8 | |||
45.34 | even | 6 | 1134.3.q.c.701.4 | 8 | |||
60.59 | even | 2 | 1008.3.d.a.449.4 | 4 | |||
105.44 | odd | 6 | 882.3.s.e.557.2 | 8 | |||
105.59 | even | 6 | 882.3.s.i.863.4 | 8 | |||
105.74 | odd | 6 | 882.3.s.e.863.3 | 8 | |||
105.89 | even | 6 | 882.3.s.i.557.1 | 8 | |||
105.104 | even | 2 | 882.3.b.f.197.1 | 4 | |||
120.29 | odd | 2 | 4032.3.d.i.449.1 | 4 | |||
120.59 | even | 2 | 4032.3.d.j.449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.b.a.71.2 | ✓ | 4 | 15.14 | odd | 2 | ||
126.3.b.a.71.3 | yes | 4 | 5.4 | even | 2 | ||
882.3.b.f.197.1 | 4 | 105.104 | even | 2 | |||
882.3.b.f.197.4 | 4 | 35.34 | odd | 2 | |||
882.3.s.e.557.2 | 8 | 105.44 | odd | 6 | |||
882.3.s.e.557.3 | 8 | 35.9 | even | 6 | |||
882.3.s.e.863.2 | 8 | 35.4 | even | 6 | |||
882.3.s.e.863.3 | 8 | 105.74 | odd | 6 | |||
882.3.s.i.557.1 | 8 | 105.89 | even | 6 | |||
882.3.s.i.557.4 | 8 | 35.19 | odd | 6 | |||
882.3.s.i.863.1 | 8 | 35.24 | odd | 6 | |||
882.3.s.i.863.4 | 8 | 105.59 | even | 6 | |||
1008.3.d.a.449.1 | 4 | 20.19 | odd | 2 | |||
1008.3.d.a.449.4 | 4 | 60.59 | even | 2 | |||
1134.3.q.c.701.1 | 8 | 45.29 | odd | 6 | |||
1134.3.q.c.701.4 | 8 | 45.34 | even | 6 | |||
1134.3.q.c.1079.1 | 8 | 45.4 | even | 6 | |||
1134.3.q.c.1079.4 | 8 | 45.14 | odd | 6 | |||
3150.3.c.b.449.2 | 8 | 15.2 | even | 4 | |||
3150.3.c.b.449.3 | 8 | 5.3 | odd | 4 | |||
3150.3.c.b.449.5 | 8 | 5.2 | odd | 4 | |||
3150.3.c.b.449.8 | 8 | 15.8 | even | 4 | |||
3150.3.e.e.701.1 | 4 | 1.1 | even | 1 | trivial | ||
3150.3.e.e.701.3 | 4 | 3.2 | odd | 2 | inner | ||
4032.3.d.i.449.1 | 4 | 120.29 | odd | 2 | |||
4032.3.d.i.449.4 | 4 | 40.29 | even | 2 | |||
4032.3.d.j.449.1 | 4 | 120.59 | even | 2 | |||
4032.3.d.j.449.4 | 4 | 40.19 | odd | 2 |