Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,6,Mod(19,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.19");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.21727189158\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-5}, \sqrt{-14})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 38x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(-1.50559i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.19 |
Dual form | 45.6.b.d.19.3 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.47214i | − | 0.790569i | −0.918559 | − | 0.395285i | \(-0.870646\pi\) | ||
0.918559 | − | 0.395285i | \(-0.129354\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 12.0000 | 0.375000 | ||||||||
\(5\) | −50.1996 | + | 24.5967i | −0.897998 | + | 0.440000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 224.499i | − | 1.73169i | −0.500312 | − | 0.865845i | \(-0.666781\pi\) | ||
0.500312 | − | 0.865845i | \(-0.333219\pi\) | |||||||
\(8\) | − | 196.774i | − | 1.08703i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 110.000 | + | 224.499i | 0.347851 | + | 0.709930i | ||||
\(11\) | −501.996 | −1.25089 | −0.625444 | − | 0.780269i | \(-0.715082\pi\) | ||||
−0.625444 | + | 0.780269i | \(0.715082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 224.499i | 0.368432i | 0.982886 | + | 0.184216i | \(0.0589745\pi\) | ||||
−0.982886 | + | 0.184216i | \(0.941025\pi\) | |||||||
\(14\) | −1003.99 | −1.36902 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −496.000 | −0.484375 | ||||||||
\(17\) | − | 1668.11i | − | 1.39991i | −0.714185 | − | 0.699957i | \(-0.753202\pi\) | ||
0.714185 | − | 0.699957i | \(-0.246798\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −484.000 | −0.307582 | −0.153791 | − | 0.988103i | \(-0.549148\pi\) | ||||
−0.153791 | + | 0.988103i | \(0.549148\pi\) | |||||||
\(20\) | −602.395 | + | 295.161i | −0.336749 | + | 0.165000i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2244.99i | 0.988914i | ||||||||
\(23\) | 2262.90i | 0.891961i | 0.895043 | + | 0.445981i | \(0.147145\pi\) | ||||
−0.895043 | + | 0.445981i | \(0.852855\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1915.00 | − | 2469.49i | 0.612800 | − | 0.790238i | ||||
\(26\) | 1003.99 | 0.291271 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 2693.99i | − | 0.649384i | ||||||
\(29\) | 5521.96 | 1.21926 | 0.609632 | − | 0.792684i | \(-0.291317\pi\) | ||||
0.609632 | + | 0.792684i | \(0.291317\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3608.00 | 0.674314 | 0.337157 | − | 0.941448i | \(-0.390535\pi\) | ||||
0.337157 | + | 0.941448i | \(0.390535\pi\) | |||||||
\(32\) | − | 4078.59i | − | 0.704101i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7460.00 | −1.10673 | ||||||||
\(35\) | 5521.96 | + | 11269.8i | 0.761944 | + | 1.55505i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7408.48i | − | 0.889662i | −0.895615 | − | 0.444831i | \(-0.853264\pi\) | ||
0.895615 | − | 0.444831i | \(-0.146736\pi\) | |||||||
\(38\) | 2164.51i | 0.243165i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4840.00 | + | 9877.98i | 0.478294 | + | 0.976153i | ||||
\(41\) | 11043.9 | 1.02604 | 0.513019 | − | 0.858377i | \(-0.328527\pi\) | ||||
0.513019 | + | 0.858377i | \(0.328527\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12572.0i | 1.03689i | 0.855111 | + | 0.518444i | \(0.173489\pi\) | ||||
−0.855111 | + | 0.518444i | \(0.826511\pi\) | |||||||
\(44\) | −6023.95 | −0.469083 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10120.0 | 0.705157 | ||||||||
\(47\) | − | 9543.54i | − | 0.630180i | −0.949062 | − | 0.315090i | \(-0.897965\pi\) | ||
0.949062 | − | 0.315090i | \(-0.102035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33593.0 | −1.99875 | ||||||||
\(50\) | −11043.9 | − | 8564.14i | −0.624738 | − | 0.484461i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2693.99i | 0.138162i | ||||||||
\(53\) | 4771.77i | 0.233340i | 0.993171 | + | 0.116670i | \(0.0372220\pi\) | ||||
−0.993171 | + | 0.116670i | \(0.962778\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 25200.0 | − | 12347.5i | 1.12329 | − | 0.550391i | ||||
\(56\) | −44175.6 | −1.88240 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 24694.9i | − | 0.963913i | ||||||
\(59\) | −5521.96 | −0.206520 | −0.103260 | − | 0.994654i | \(-0.532927\pi\) | ||||
−0.103260 | + | 0.994654i | \(0.532927\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 21362.0 | 0.735051 | 0.367525 | − | 0.930013i | \(-0.380205\pi\) | ||||
0.367525 | + | 0.930013i | \(0.380205\pi\) | |||||||
\(62\) | − | 16135.5i | − | 0.533092i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −34112.0 | −1.04102 | ||||||||
\(65\) | −5521.96 | − | 11269.8i | −0.162110 | − | 0.330851i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34572.9i | 0.940912i | 0.882423 | + | 0.470456i | \(0.155911\pi\) | ||||
−0.882423 | + | 0.470456i | \(0.844089\pi\) | |||||||
\(68\) | − | 20017.3i | − | 0.524968i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 50400.0 | − | 24694.9i | 1.22938 | − | 0.602369i | ||||
\(71\) | 33131.7 | 0.780007 | 0.390003 | − | 0.920813i | \(-0.372474\pi\) | ||||
0.390003 | + | 0.920813i | \(0.372474\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2693.99i | − | 0.0591683i | −0.999562 | − | 0.0295842i | \(-0.990582\pi\) | ||
0.999562 | − | 0.0295842i | \(-0.00941831\pi\) | |||||||
\(74\) | −33131.7 | −0.703339 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5808.00 | −0.115343 | ||||||||
\(77\) | 112698.i | 2.16615i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −99616.0 | −1.79581 | −0.897907 | − | 0.440185i | \(-0.854913\pi\) | ||||
−0.897907 | + | 0.440185i | \(0.854913\pi\) | |||||||
\(80\) | 24899.0 | − | 12200.0i | 0.434968 | − | 0.213125i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 49389.9i | − | 0.811154i | ||||||
\(83\) | − | 57118.1i | − | 0.910078i | −0.890471 | − | 0.455039i | \(-0.849625\pi\) | ||
0.890471 | − | 0.455039i | \(-0.150375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41030.0 | + | 83738.3i | 0.615962 | + | 1.25712i | ||||
\(86\) | 56223.6 | 0.819733 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 98779.8i | 1.35976i | ||||||||
\(89\) | 120479. | 1.61227 | 0.806133 | − | 0.591735i | \(-0.201557\pi\) | ||||
0.806133 | + | 0.591735i | \(0.201557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 50400.0 | 0.638009 | ||||||||
\(92\) | 27154.8i | 0.334485i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −42680.0 | −0.498201 | ||||||||
\(95\) | 24296.6 | − | 11904.8i | 0.276208 | − | 0.135336i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 64206.8i | − | 0.692870i | −0.938074 | − | 0.346435i | \(-0.887392\pi\) | ||
0.938074 | − | 0.346435i | \(-0.112608\pi\) | |||||||
\(98\) | 150232.i | 1.58015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 22980.0 | − | 29633.9i | 0.229800 | − | 0.296339i | ||||
\(101\) | −60741.5 | −0.592492 | −0.296246 | − | 0.955112i | \(-0.595735\pi\) | ||||
−0.296246 | + | 0.955112i | \(0.595735\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 150639.i | − | 1.39909i | −0.714590 | − | 0.699544i | \(-0.753387\pi\) | ||
0.714590 | − | 0.699544i | \(-0.246613\pi\) | |||||||
\(104\) | 44175.6 | 0.400497 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21340.0 | 0.184472 | ||||||||
\(107\) | 1914.07i | 0.0161622i | 0.999967 | + | 0.00808108i | \(0.00257232\pi\) | ||||
−0.999967 | + | 0.00808108i | \(0.997428\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1694.00 | 0.0136567 | 0.00682837 | − | 0.999977i | \(-0.497826\pi\) | ||||
0.00682837 | + | 0.999977i | \(0.497826\pi\) | |||||||
\(110\) | −55219.6 | − | 112698.i | −0.435122 | − | 0.888043i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 111352.i | 0.838787i | ||||||||
\(113\) | − | 148712.i | − | 1.09559i | −0.836611 | − | 0.547797i | \(-0.815467\pi\) | ||
0.836611 | − | 0.547797i | \(-0.184533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −55660.0 | − | 113597.i | −0.392463 | − | 0.800979i | ||||
\(116\) | 66263.5 | 0.457224 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24694.9i | 0.163269i | ||||||||
\(119\) | −374489. | −2.42422 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 90949.0 | 0.564722 | ||||||||
\(122\) | − | 95533.8i | − | 0.581109i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 43296.0 | 0.252868 | ||||||||
\(125\) | −35390.7 | + | 171070.i | −0.202588 | + | 0.979264i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 173089.i | 0.952271i | 0.879372 | + | 0.476135i | \(0.157963\pi\) | ||||
−0.879372 | + | 0.476135i | \(0.842037\pi\) | |||||||
\(128\) | 22038.7i | 0.118894i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −50400.0 | + | 24694.9i | −0.261560 | + | 0.128159i | ||||
\(131\) | −270576. | −1.37756 | −0.688780 | − | 0.724970i | \(-0.741854\pi\) | ||||
−0.688780 | + | 0.724970i | \(0.741854\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 108658.i | 0.532637i | ||||||||
\(134\) | 154615. | 0.743856 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −328240. | −1.52175 | ||||||||
\(137\) | − | 319020.i | − | 1.45217i | −0.687607 | − | 0.726083i | \(-0.741339\pi\) | ||
0.687607 | − | 0.726083i | \(-0.258661\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 226556. | 0.994577 | 0.497289 | − | 0.867585i | \(-0.334329\pi\) | ||||
0.497289 | + | 0.867585i | \(0.334329\pi\) | |||||||
\(140\) | 66263.5 | + | 135237.i | 0.285729 | + | 0.583145i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 148170.i | − | 0.616649i | ||||||
\(143\) | − | 112698.i | − | 0.460867i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −277200. | + | 135822.i | −1.09490 | + | 0.536476i | ||||
\(146\) | −12047.9 | −0.0467767 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 88901.8i | − | 0.333623i | ||||||
\(149\) | 160137. | 0.590915 | 0.295458 | − | 0.955356i | \(-0.404528\pi\) | ||||
0.295458 | + | 0.955356i | \(0.404528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8888.00 | 0.0317221 | 0.0158610 | − | 0.999874i | \(-0.494951\pi\) | ||||
0.0158610 | + | 0.999874i | \(0.494951\pi\) | |||||||
\(152\) | 95238.6i | 0.334352i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 504000. | 1.71249 | ||||||||
\(155\) | −181120. | + | 88745.1i | −0.605533 | + | 0.296698i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 506246.i | − | 1.63913i | −0.572988 | − | 0.819564i | \(-0.694216\pi\) | ||
0.572988 | − | 0.819564i | \(-0.305784\pi\) | |||||||
\(158\) | 445496.i | 1.41972i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 100320. | + | 204743.i | 0.309804 | + | 0.632281i | ||||
\(161\) | 508020. | 1.54460 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 222254.i | 0.655211i | 0.944815 | + | 0.327606i | \(0.106242\pi\) | ||||
−0.944815 | + | 0.327606i | \(0.893758\pi\) | |||||||
\(164\) | 132527. | 0.384764 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −255440. | −0.719480 | ||||||||
\(167\) | − | 97555.2i | − | 0.270682i | −0.990799 | − | 0.135341i | \(-0.956787\pi\) | ||
0.990799 | − | 0.135341i | \(-0.0432130\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 320893. | 0.864258 | ||||||||
\(170\) | 374489. | − | 183492.i | 0.993841 | − | 0.486961i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 150864.i | 0.388833i | ||||||||
\(173\) | 276669.i | 0.702821i | 0.936221 | + | 0.351411i | \(0.114298\pi\) | ||||
−0.936221 | + | 0.351411i | \(0.885702\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −554400. | − | 429916.i | −1.36845 | − | 1.06118i | ||||
\(176\) | 248990. | 0.605899 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 538799.i | − | 1.27461i | ||||||
\(179\) | 28613.8 | 0.0667487 | 0.0333743 | − | 0.999443i | \(-0.489375\pi\) | ||||
0.0333743 | + | 0.999443i | \(0.489375\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −81862.0 | −0.185732 | −0.0928658 | − | 0.995679i | \(-0.529603\pi\) | ||||
−0.0928658 | + | 0.995679i | \(0.529603\pi\) | |||||||
\(182\) | − | 225396.i | − | 0.504391i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 445280. | 0.969591 | ||||||||
\(185\) | 182225. | + | 371903.i | 0.391451 | + | 0.798914i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 837383.i | 1.75114i | ||||||||
\(188\) | − | 114522.i | − | 0.236318i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −53240.0 | − | 108658.i | −0.106993 | − | 0.218362i | ||||
\(191\) | −486936. | −0.965803 | −0.482902 | − | 0.875675i | \(-0.660417\pi\) | ||||
−0.482902 | + | 0.875675i | \(0.660417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 541044.i | 1.04554i | 0.852475 | + | 0.522768i | \(0.175101\pi\) | ||||
−0.852475 | + | 0.522768i | \(0.824899\pi\) | |||||||
\(194\) | −287142. | −0.547762 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −403116. | −0.749531 | ||||||||
\(197\) | 812976.i | 1.49249i | 0.665670 | + | 0.746246i | \(0.268146\pi\) | ||||
−0.665670 | + | 0.746246i | \(0.731854\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 146144. | 0.261606 | 0.130803 | − | 0.991408i | \(-0.458244\pi\) | ||||
0.130803 | + | 0.991408i | \(0.458244\pi\) | |||||||
\(200\) | −485932. | − | 376822.i | −0.859015 | − | 0.666134i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 271644.i | 0.468406i | ||||||||
\(203\) | − | 1.23968e6i | − | 2.11139i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −554400. | + | 271644.i | −0.921380 | + | 0.451457i | ||||
\(206\) | −673679. | −1.10608 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 111352.i | − | 0.178459i | ||||||
\(209\) | 242966. | 0.384751 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 846692. | 1.30924 | 0.654620 | − | 0.755958i | \(-0.272829\pi\) | ||||
0.654620 | + | 0.755958i | \(0.272829\pi\) | |||||||
\(212\) | 57261.2i | 0.0875026i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8560.00 | 0.0127773 | ||||||||
\(215\) | −309230. | − | 631108.i | −0.456231 | − | 0.931124i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 809994.i | − | 1.16770i | ||||||
\(218\) | − | 7575.80i | − | 0.0107966i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 302400. | − | 148170.i | 0.421236 | − | 0.206397i | ||||
\(221\) | 374489. | 0.515773 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 812463.i | − | 1.09406i | −0.837113 | − | 0.547031i | \(-0.815758\pi\) | ||
0.837113 | − | 0.547031i | \(-0.184242\pi\) | |||||||
\(224\) | −915641. | −1.21928 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −665060. | −0.866143 | ||||||||
\(227\) | 355034.i | 0.457304i | 0.973508 | + | 0.228652i | \(0.0734318\pi\) | ||||
−0.973508 | + | 0.228652i | \(0.926568\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −411094. | −0.518027 | −0.259014 | − | 0.965874i | \(-0.583397\pi\) | ||||
−0.259014 | + | 0.965874i | \(0.583397\pi\) | |||||||
\(230\) | −508020. | + | 248919.i | −0.633230 | + | 0.310269i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 1.08658e6i | − | 1.32538i | ||||||
\(233\) | 738193.i | 0.890800i | 0.895332 | + | 0.445400i | \(0.146939\pi\) | ||||
−0.895332 | + | 0.445400i | \(0.853061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 234740. | + | 479082.i | 0.277279 | + | 0.565900i | ||||
\(236\) | −66263.5 | −0.0774451 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.67477e6i | 1.91651i | ||||||||
\(239\) | −121483. | −0.137569 | −0.0687845 | − | 0.997632i | \(-0.521912\pi\) | ||||
−0.0687845 | + | 0.997632i | \(0.521912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.12224e6 | 1.24464 | 0.622320 | − | 0.782763i | \(-0.286190\pi\) | ||||
0.622320 | + | 0.782763i | \(0.286190\pi\) | |||||||
\(242\) | − | 406736.i | − | 0.446452i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 256344. | 0.275644 | ||||||||
\(245\) | 1.68636e6 | − | 826279.i | 1.79487 | − | 0.879450i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 108658.i | − | 0.113323i | ||||||
\(248\) | − | 709961.i | − | 0.733002i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 765050. | + | 158272.i | 0.774176 | + | 0.160160i | ||||
\(251\) | 16565.9 | 0.0165970 | 0.00829851 | − | 0.999966i | \(-0.497358\pi\) | ||||
0.00829851 | + | 0.999966i | \(0.497358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.13597e6i | − | 1.11574i | ||||||
\(254\) | 774078. | 0.752836 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −993024. | −0.947021 | ||||||||
\(257\) | 1.10779e6i | 1.04622i | 0.852264 | + | 0.523111i | \(0.175229\pi\) | ||||
−0.852264 | + | 0.523111i | \(0.824771\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.66320e6 | −1.54062 | ||||||||
\(260\) | −66263.5 | − | 135237.i | −0.0607912 | − | 0.124069i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.21005e6i | 1.08906i | ||||||||
\(263\) | 1.82582e6i | 1.62768i | 0.581090 | + | 0.813840i | \(0.302627\pi\) | ||||
−0.581090 | + | 0.813840i | \(0.697373\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −117370. | − | 239541.i | −0.102670 | − | 0.209539i | ||||
\(266\) | 485932. | 0.421087 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 414875.i | 0.352842i | ||||||||
\(269\) | 1.34184e6 | 1.13062 | 0.565312 | − | 0.824877i | \(-0.308756\pi\) | ||||
0.565312 | + | 0.824877i | \(0.308756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 724592. | 0.599336 | 0.299668 | − | 0.954044i | \(-0.403124\pi\) | ||||
0.299668 | + | 0.954044i | \(0.403124\pi\) | |||||||
\(272\) | 827381.i | 0.678084i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.42670e6 | −1.14804 | ||||||||
\(275\) | −961322. | + | 1.23968e6i | −0.766544 | + | 0.988500i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00007e6i | 1.56619i | 0.621901 | + | 0.783096i | \(0.286361\pi\) | ||||
−0.621901 | + | 0.783096i | \(0.713639\pi\) | |||||||
\(278\) | − | 1.01319e6i | − | 0.786282i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.21760e6 | − | 1.08658e6i | 1.69039 | − | 0.828258i | ||||
\(281\) | 2.20878e6 | 1.66873 | 0.834367 | − | 0.551209i | \(-0.185833\pi\) | ||||
0.834367 | + | 0.551209i | \(0.185833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 442264.i | − | 0.328258i | −0.986439 | − | 0.164129i | \(-0.947519\pi\) | ||
0.986439 | − | 0.164129i | \(-0.0524813\pi\) | |||||||
\(284\) | 397581. | 0.292503 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −504000. | −0.364347 | ||||||||
\(287\) | − | 2.47935e6i | − | 1.77678i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.36272e6 | −0.959761 | ||||||||
\(290\) | 607415. | + | 1.23968e6i | 0.424122 | + | 0.865592i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 32327.9i | − | 0.0221881i | ||||||
\(293\) | − | 1.01093e6i | − | 0.687943i | −0.938980 | − | 0.343971i | \(-0.888228\pi\) | ||
0.938980 | − | 0.343971i | \(-0.111772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 277200. | − | 135822.i | 0.185455 | − | 0.0908690i | ||||
\(296\) | −1.45780e6 | −0.967092 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 716153.i | − | 0.467160i | ||||||
\(299\) | −508020. | −0.328627 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.82240e6 | 1.79557 | ||||||||
\(302\) | − | 39748.3i | − | 0.0250785i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 240064. | 0.148985 | ||||||||
\(305\) | −1.07236e6 | + | 525436.i | −0.660074 | + | 0.323422i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.37341e6i | − | 1.43723i | −0.695408 | − | 0.718615i | \(-0.744776\pi\) | ||
0.695408 | − | 0.718615i | \(-0.255224\pi\) | |||||||
\(308\) | 1.35237e6i | 0.812307i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 396880. | + | 809994.i | 0.234561 | + | 0.478716i | ||||
\(311\) | −2.57323e6 | −1.50861 | −0.754307 | − | 0.656522i | \(-0.772027\pi\) | ||||
−0.754307 | + | 0.656522i | \(0.772027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.53603e6i | 0.886212i | 0.896469 | + | 0.443106i | \(0.146123\pi\) | ||||
−0.896469 | + | 0.443106i | \(0.853877\pi\) | |||||||
\(314\) | −2.26400e6 | −1.29584 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.19539e6 | −0.673430 | ||||||||
\(317\) | − | 2.26708e6i | − | 1.26712i | −0.773692 | − | 0.633562i | \(-0.781592\pi\) | ||
0.773692 | − | 0.633562i | \(-0.218408\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.77200e6 | −1.52516 | ||||||||
\(320\) | 1.71241e6 | − | 839044.i | 0.934830 | − | 0.458047i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 2.27193e6i | − | 1.22111i | ||||||
\(323\) | 807364.i | 0.430589i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 554400. | + | 429916.i | 0.291149 | + | 0.225775i | ||||
\(326\) | 993952. | 0.517990 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 2.17315e6i | − | 1.11534i | ||||||
\(329\) | −2.14252e6 | −1.09128 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.65981e6 | 0.832701 | 0.416350 | − | 0.909204i | \(-0.363309\pi\) | ||||
0.416350 | + | 0.909204i | \(0.363309\pi\) | |||||||
\(332\) | − | 685417.i | − | 0.341279i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −436280. | −0.213993 | ||||||||
\(335\) | −850381. | − | 1.73555e6i | −0.414001 | − | 0.844937i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 822566.i | 0.394544i | 0.980349 | + | 0.197272i | \(0.0632083\pi\) | ||||
−0.980349 | + | 0.197272i | \(0.936792\pi\) | |||||||
\(338\) | − | 1.43508e6i | − | 0.683256i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 492360. | + | 1.00486e6i | 0.230986 | + | 0.471420i | ||||
\(341\) | −1.81120e6 | −0.843492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.76845e6i | 1.72953i | ||||||||
\(344\) | 2.47384e6 | 1.12713 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.23730e6 | 0.555629 | ||||||||
\(347\) | − | 977323.i | − | 0.435727i | −0.975979 | − | 0.217863i | \(-0.930091\pi\) | ||
0.975979 | − | 0.217863i | \(-0.0699087\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −774994. | −0.340592 | −0.170296 | − | 0.985393i | \(-0.554472\pi\) | ||||
−0.170296 | + | 0.985393i | \(0.554472\pi\) | |||||||
\(350\) | −1.92264e6 | + | 2.47935e6i | −0.838936 | + | 1.08185i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.04743e6i | 0.880752i | ||||||||
\(353\) | 2.76069e6i | 1.17918i | 0.807702 | + | 0.589591i | \(0.200711\pi\) | ||||
−0.807702 | + | 0.589591i | \(0.799289\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.66320e6 | + | 814933.i | −0.700444 | + | 0.343203i | ||||
\(356\) | 1.44575e6 | 0.604599 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 127965.i | − | 0.0527694i | ||||||
\(359\) | −1.12648e6 | −0.461304 | −0.230652 | − | 0.973036i | \(-0.574086\pi\) | ||||
−0.230652 | + | 0.973036i | \(0.574086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.24184e6 | −0.905393 | ||||||||
\(362\) | 366098.i | 0.146834i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 604800. | 0.239254 | ||||||||
\(365\) | 66263.5 | + | 135237.i | 0.0260341 | + | 0.0531330i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 264236.i | − | 0.102406i | −0.998688 | − | 0.0512031i | \(-0.983694\pi\) | ||
0.998688 | − | 0.0512031i | \(-0.0163056\pi\) | |||||||
\(368\) | − | 1.12240e6i | − | 0.432044i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.66320e6 | − | 814933.i | 0.631597 | − | 0.309469i | ||||
\(371\) | 1.07126e6 | 0.404073 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.07227e6i | − | 1.14337i | −0.820472 | − | 0.571687i | \(-0.806289\pi\) | ||
0.820472 | − | 0.571687i | \(-0.193711\pi\) | |||||||
\(374\) | 3.74489e6 | 1.38440 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.87792e6 | −0.685027 | ||||||||
\(377\) | 1.23968e6i | 0.449216i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.52304e6 | 0.544643 | 0.272322 | − | 0.962206i | \(-0.412209\pi\) | ||||
0.272322 | + | 0.962206i | \(0.412209\pi\) | |||||||
\(380\) | 291559. | − | 142858.i | 0.103578 | − | 0.0507511i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.17764e6i | 0.763534i | ||||||||
\(383\) | − | 2.40625e6i | − | 0.838193i | −0.907942 | − | 0.419096i | \(-0.862347\pi\) | ||
0.907942 | − | 0.419096i | \(-0.137653\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.77200e6 | − | 5.65739e6i | −0.953106 | − | 1.94520i | ||||
\(386\) | 2.41962e6 | 0.826569 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 770482.i | − | 0.259826i | ||||||
\(389\) | 1.26453e6 | 0.423696 | 0.211848 | − | 0.977303i | \(-0.432052\pi\) | ||||
0.211848 | + | 0.977303i | \(0.432052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.77476e6 | 1.24867 | ||||||||
\(392\) | 6.61023e6i | 2.17271i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.63574e6 | 1.17992 | ||||||||
\(395\) | 5.00068e6 | − | 2.45023e6i | 1.61264 | − | 0.790158i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.56319e6i | 0.497778i | 0.968532 | + | 0.248889i | \(0.0800654\pi\) | ||||
−0.968532 | + | 0.248889i | \(0.919935\pi\) | |||||||
\(398\) | − | 653576.i | − | 0.206818i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −949840. | + | 1.22487e6i | −0.296825 | + | 0.382772i | ||||
\(401\) | −1.36844e6 | −0.424977 | −0.212488 | − | 0.977164i | \(-0.568157\pi\) | ||||
−0.212488 | + | 0.977164i | \(0.568157\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 809994.i | 0.248439i | ||||||||
\(404\) | −728898. | −0.222184 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.54400e6 | −1.66920 | ||||||||
\(407\) | 3.71903e6i | 1.11287i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.31427e6 | 1.27526 | 0.637630 | − | 0.770343i | \(-0.279915\pi\) | ||||
0.637630 | + | 0.770343i | \(0.279915\pi\) | |||||||
\(410\) | 1.21483e6 | + | 2.47935e6i | 0.356908 | + | 0.728414i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1.80767e6i | − | 0.524658i | ||||||
\(413\) | 1.23968e6i | 0.357629i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.40492e6 | + | 2.86731e6i | 0.400434 | + | 0.817248i | ||||
\(416\) | 915641. | 0.259413 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1.08658e6i | − | 0.304172i | ||||||
\(419\) | −689241. | −0.191794 | −0.0958972 | − | 0.995391i | \(-0.530572\pi\) | ||||
−0.0958972 | + | 0.995391i | \(0.530572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.03556e6 | −0.284755 | −0.142377 | − | 0.989812i | \(-0.545475\pi\) | ||||
−0.142377 | + | 0.989812i | \(0.545475\pi\) | |||||||
\(422\) | − | 3.78652e6i | − | 1.03505i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 938960. | 0.253649 | ||||||||
\(425\) | −4.11938e6 | − | 3.19442e6i | −1.10627 | − | 0.857868i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.79576e6i | − | 1.27288i | ||||||
\(428\) | 22968.9i | 0.00606081i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.82240e6 | + | 1.38292e6i | −0.736118 | + | 0.360682i | ||||
\(431\) | 2.78307e6 | 0.721656 | 0.360828 | − | 0.932632i | \(-0.382494\pi\) | ||||
0.360828 | + | 0.932632i | \(0.382494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 400058.i | 0.102542i | 0.998685 | + | 0.0512712i | \(0.0163273\pi\) | ||||
−0.998685 | + | 0.0512712i | \(0.983673\pi\) | |||||||
\(434\) | −3.62240e6 | −0.923150 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20328.0 | 0.00512128 | ||||||||
\(437\) | − | 1.09524e6i | − | 0.274351i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.10006e6 | 0.767731 | 0.383866 | − | 0.923389i | \(-0.374593\pi\) | ||||
0.383866 | + | 0.923389i | \(0.374593\pi\) | |||||||
\(440\) | −2.42966e6 | − | 4.95870e6i | −0.598293 | − | 1.22106i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.67477e6i | − | 0.407754i | ||||||
\(443\) | 219797.i | 0.0532122i | 0.999646 | + | 0.0266061i | \(0.00846999\pi\) | ||||
−0.999646 | + | 0.0266061i | \(0.991530\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.04800e6 | + | 2.96339e6i | −1.44781 | + | 0.709397i | ||||
\(446\) | −3.63345e6 | −0.864931 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.65813e6i | 1.80272i | ||||||||
\(449\) | 2.47283e6 | 0.578867 | 0.289434 | − | 0.957198i | \(-0.406533\pi\) | ||||
0.289434 | + | 0.957198i | \(0.406533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.54400e6 | −1.28346 | ||||||||
\(452\) | − | 1.78454e6i | − | 0.410848i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.58776e6 | 0.361531 | ||||||||
\(455\) | −2.53006e6 | + | 1.23968e6i | −0.572931 | + | 0.280724i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.89649e6i | 0.648757i | 0.945927 | + | 0.324378i | \(0.105155\pi\) | ||||
−0.945927 | + | 0.324378i | \(0.894845\pi\) | |||||||
\(458\) | 1.83847e6i | 0.409536i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −667920. | − | 1.36316e6i | −0.147174 | − | 0.300367i | ||||
\(461\) | −7.05154e6 | −1.54537 | −0.772683 | − | 0.634792i | \(-0.781086\pi\) | ||||
−0.772683 | + | 0.634792i | \(0.781086\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.89178e6i | − | 0.626920i | −0.949601 | − | 0.313460i | \(-0.898512\pi\) | ||
0.949601 | − | 0.313460i | \(-0.101488\pi\) | |||||||
\(464\) | −2.73889e6 | −0.590581 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.30130e6 | 0.704239 | ||||||||
\(467\) | 7.71866e6i | 1.63776i | 0.573967 | + | 0.818879i | \(0.305404\pi\) | ||||
−0.573967 | + | 0.818879i | \(0.694596\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.76160e6 | 1.62937 | ||||||||
\(470\) | 2.14252e6 | − | 1.04979e6i | 0.447384 | − | 0.219209i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.08658e6i | 0.224494i | ||||||||
\(473\) | − | 6.31108e6i | − | 1.29703i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −926860. | + | 1.19524e6i | −0.188486 | + | 0.243063i | ||||
\(476\) | −4.49387e6 | −0.909082 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 543289.i | 0.108758i | ||||||||
\(479\) | −209834. | −0.0417867 | −0.0208933 | − | 0.999782i | \(-0.506651\pi\) | ||||
−0.0208933 | + | 0.999782i | \(0.506651\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.66320e6 | 0.327779 | ||||||||
\(482\) | − | 5.01882e6i | − | 0.983975i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.09139e6 | 0.211771 | ||||||||
\(485\) | 1.57928e6 | + | 3.22316e6i | 0.304863 | + | 0.622196i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 777891.i | 0.148626i | 0.997235 | + | 0.0743132i | \(0.0236765\pi\) | ||||
−0.997235 | + | 0.0743132i | \(0.976324\pi\) | |||||||
\(488\) | − | 4.20349e6i | − | 0.799024i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.69523e6 | − | 7.54161e6i | −0.695266 | − | 1.41897i | ||||
\(491\) | 9.93400e6 | 1.85960 | 0.929802 | − | 0.368061i | \(-0.119978\pi\) | ||||
0.929802 | + | 0.368061i | \(0.119978\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9.21121e6i | − | 1.70687i | ||||||
\(494\) | −485932. | −0.0895897 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.78957e6 | −0.326621 | ||||||||
\(497\) | − | 7.43806e6i | − | 1.35073i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.10332e6 | −0.917489 | −0.458745 | − | 0.888568i | \(-0.651701\pi\) | ||||
−0.458745 | + | 0.888568i | \(0.651701\pi\) | |||||||
\(500\) | −424689. | + | 2.05284e6i | −0.0759706 | + | 0.367224i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 74084.8i | − | 0.0131211i | ||||||
\(503\) | 4.00824e6i | 0.706373i | 0.935553 | + | 0.353186i | \(0.114902\pi\) | ||||
−0.935553 | + | 0.353186i | \(0.885098\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.04920e6 | − | 1.49404e6i | 0.532056 | − | 0.260696i | ||||
\(506\) | −5.08020e6 | −0.882073 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.07707e6i | 0.357101i | ||||||||
\(509\) | −1.96029e6 | −0.335372 | −0.167686 | − | 0.985840i | \(-0.553629\pi\) | ||||
−0.167686 | + | 0.985840i | \(0.553629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −604800. | −0.102461 | ||||||||
\(512\) | 5.14618e6i | 0.867580i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.95418e6 | 0.827111 | ||||||||
\(515\) | 3.70523e6 | + | 7.56202e6i | 0.615598 | + | 1.25638i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.79082e6i | 0.788285i | ||||||||
\(518\) | 7.43806e6i | 1.21797i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.21760e6 | + | 1.08658e6i | −0.359646 | + | 0.176219i | ||||
\(521\) | 9.65338e6 | 1.55806 | 0.779032 | − | 0.626984i | \(-0.215711\pi\) | ||||
0.779032 | + | 0.626984i | \(0.215711\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 462020.i | − | 0.0738595i | −0.999318 | − | 0.0369298i | \(-0.988242\pi\) | ||
0.999318 | − | 0.0369298i | \(-0.0117578\pi\) | |||||||
\(524\) | −3.24691e6 | −0.516585 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.16532e6 | 1.28679 | ||||||||
\(527\) | − | 6.01853e6i | − | 0.943982i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.31562e6 | 0.204405 | ||||||||
\(530\) | −1.07126e6 | + | 524895.i | −0.165655 | + | 0.0811675i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.30389e6i | 0.199739i | ||||||||
\(533\) | 2.47935e6i | 0.378025i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −47080.0 | − | 96085.8i | −0.00711135 | − | 0.0145136i | ||||
\(536\) | 6.80305e6 | 1.02280 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 6.00087e6i | − | 0.893837i | ||||||
\(539\) | 1.68636e7 | 2.50021 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.08238e7 | −1.58996 | −0.794978 | − | 0.606639i | \(-0.792517\pi\) | ||||
−0.794978 | + | 0.606639i | \(0.792517\pi\) | |||||||
\(542\) | − | 3.24047e6i | − | 0.473817i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.80352e6 | −0.985681 | ||||||||
\(545\) | −85038.1 | + | 41666.9i | −0.0122637 | + | 0.00600897i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.02229e6i | 0.288985i | 0.989506 | + | 0.144493i | \(0.0461550\pi\) | ||||
−0.989506 | + | 0.144493i | \(0.953845\pi\) | |||||||
\(548\) | − | 3.82824e6i | − | 0.544562i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.54400e6 | + | 4.29916e6i | 0.781478 | + | 0.606007i | ||||
\(551\) | −2.67263e6 | −0.375024 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.23637e7i | 3.10979i | ||||||||
\(554\) | 8.94457e6 | 1.23818 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.71867e6 | 0.372967 | ||||||||
\(557\) | 3.92593e6i | 0.536173i | 0.963395 | + | 0.268086i | \(0.0863913\pi\) | ||||
−0.963395 | + | 0.268086i | \(0.913609\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.82240e6 | −0.382023 | ||||||||
\(560\) | −2.73889e6 | − | 5.58981e6i | −0.369066 | − | 0.753229i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 9.87798e6i | − | 1.31925i | ||||||
\(563\) | 1.12906e7i | 1.50123i | 0.660739 | + | 0.750616i | \(0.270243\pi\) | ||||
−0.660739 | + | 0.750616i | \(0.729757\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.65783e6 | + | 7.46528e6i | 0.482061 | + | 0.983841i | ||||
\(566\) | −1.97786e6 | −0.259511 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.51946e6i | − | 0.847893i | ||||||
\(569\) | −1.10770e7 | −1.43431 | −0.717155 | − | 0.696913i | \(-0.754556\pi\) | ||||
−0.717155 | + | 0.696913i | \(0.754556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.28605e6 | 0.421778 | 0.210889 | − | 0.977510i | \(-0.432364\pi\) | ||||
0.210889 | + | 0.977510i | \(0.432364\pi\) | |||||||
\(572\) | − | 1.35237e6i | − | 0.172825i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.10880e7 | −1.40467 | ||||||||
\(575\) | 5.58822e6 | + | 4.33346e6i | 0.704862 | + | 0.546594i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.42539e7i | − | 1.78236i | −0.453653 | − | 0.891179i | \(-0.649879\pi\) | ||
0.453653 | − | 0.891179i | \(-0.350121\pi\) | |||||||
\(578\) | 6.09428e6i | 0.758757i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.32640e6 | + | 1.62987e6i | −0.410586 | + | 0.201179i | ||||
\(581\) | −1.28230e7 | −1.57597 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.39541e6i | − | 0.291883i | ||||||
\(584\) | −530108. | −0.0643179 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.52102e6 | −0.543867 | ||||||||
\(587\) | − | 6.12026e6i | − | 0.733119i | −0.930395 | − | 0.366560i | \(-0.880536\pi\) | ||
0.930395 | − | 0.366560i | \(-0.119464\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.74627e6 | −0.207407 | ||||||||
\(590\) | −607415. | − | 1.23968e6i | −0.0718382 | − | 0.146615i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.67461e6i | 0.430930i | ||||||||
\(593\) | − | 1.38377e7i | − | 1.61595i | −0.589215 | − | 0.807976i | \(-0.700563\pi\) | ||
0.589215 | − | 0.807976i | \(-0.299437\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.87992e7 | − | 9.21121e6i | 2.17694 | − | 1.06666i | ||||
\(596\) | 1.92164e6 | 0.221593 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.27193e6i | 0.259802i | ||||||||
\(599\) | −6.37133e6 | −0.725543 | −0.362772 | − | 0.931878i | \(-0.618169\pi\) | ||||
−0.362772 | + | 0.931878i | \(0.618169\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.06116e6 | 0.232769 | 0.116384 | − | 0.993204i | \(-0.462870\pi\) | ||||
0.116384 | + | 0.993204i | \(0.462870\pi\) | |||||||
\(602\) | − | 1.26222e7i | − | 1.41952i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 106656. | 0.0118958 | ||||||||
\(605\) | −4.56560e6 | + | 2.23705e6i | −0.507119 | + | 0.248478i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.89040e6i | 0.979377i | 0.871898 | + | 0.489688i | \(0.162889\pi\) | ||||
−0.871898 | + | 0.489688i | \(0.837111\pi\) | |||||||
\(608\) | 1.97404e6i | 0.216569i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.34982e6 | + | 4.79576e6i | 0.255688 | + | 0.521834i | ||||
\(611\) | 2.14252e6 | 0.232178 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9.20605e6i | − | 0.989514i | −0.869031 | − | 0.494757i | \(-0.835257\pi\) | ||
0.869031 | − | 0.494757i | \(-0.164743\pi\) | |||||||
\(614\) | −1.06142e7 | −1.13623 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.21760e7 | 2.35468 | ||||||||
\(617\) | 1.07622e7i | 1.13812i | 0.822296 | + | 0.569061i | \(0.192693\pi\) | ||||
−0.822296 | + | 0.569061i | \(0.807307\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.40448e7 | −1.47329 | −0.736644 | − | 0.676281i | \(-0.763591\pi\) | ||||
−0.736644 | + | 0.676281i | \(0.763591\pi\) | |||||||
\(620\) | −2.17344e6 | + | 1.06494e6i | −0.227075 | + | 0.111262i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.15078e7i | 1.19266i | ||||||||
\(623\) | − | 2.70475e7i | − | 2.79194i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.43118e6 | − | 9.45816e6i | −0.248952 | − | 0.968516i | ||||
\(626\) | 6.86931e6 | 0.700612 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 6.07495e6i | − | 0.614673i | ||||||
\(629\) | −1.23581e7 | −1.24545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00120e7 | −1.00104 | −0.500518 | − | 0.865726i | \(-0.666857\pi\) | ||||
−0.500518 | + | 0.865726i | \(0.666857\pi\) | |||||||
\(632\) | 1.96018e7i | 1.95211i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.01387e7 | −1.00175 | ||||||||
\(635\) | −4.25743e6 | − | 8.68900e6i | −0.418999 | − | 0.855137i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 7.54161e6i | − | 0.736403i | ||||||
\(638\) | 1.23968e7i | 1.20575i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −542080. | − | 1.10633e6i | −0.0523135 | − | 0.106767i | ||||
\(641\) | −9.60720e6 | −0.923532 | −0.461766 | − | 0.887002i | \(-0.652784\pi\) | ||||
−0.461766 | + | 0.887002i | \(0.652784\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.21761e6i | − | 0.211523i | −0.994392 | − | 0.105761i | \(-0.966272\pi\) | ||
0.994392 | − | 0.105761i | \(-0.0337280\pi\) | |||||||
\(644\) | 6.09624e6 | 0.579225 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.61064e6 | 0.340410 | ||||||||
\(647\) | 5.71481e6i | 0.536712i | 0.963320 | + | 0.268356i | \(0.0864803\pi\) | ||||
−0.963320 | + | 0.268356i | \(0.913520\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.77200e6 | 0.258334 | ||||||||
\(650\) | 1.92264e6 | − | 2.47935e6i | 0.178491 | − | 0.230173i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.66705e6i | 0.245704i | ||||||||
\(653\) | − | 4.71603e6i | − | 0.432807i | −0.976304 | − | 0.216403i | \(-0.930567\pi\) | ||
0.976304 | − | 0.216403i | \(-0.0694326\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.35828e7 | − | 6.65529e6i | 1.23705 | − | 0.606127i | ||||
\(656\) | −5.47778e6 | −0.496987 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.58164e6i | 0.862730i | ||||||||
\(659\) | 2.01496e7 | 1.80740 | 0.903698 | − | 0.428171i | \(-0.140842\pi\) | ||||
0.903698 | + | 0.428171i | \(0.140842\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −564742. | −0.0502743 | −0.0251372 | − | 0.999684i | \(-0.508002\pi\) | ||||
−0.0251372 | + | 0.999684i | \(0.508002\pi\) | |||||||
\(662\) | − | 7.42290e6i | − | 0.658308i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.12394e7 | −0.989285 | ||||||||
\(665\) | −2.67263e6 | − | 5.45457e6i | −0.234360 | − | 0.478307i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.24956e7i | 1.08754i | ||||||||
\(668\) | − | 1.17066e6i | − | 0.101506i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.76160e6 | + | 3.80302e6i | −0.667981 | + | 0.327297i | ||||
\(671\) | −1.07236e7 | −0.919466 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.07198e7i | 0.912328i | 0.889896 | + | 0.456164i | \(0.150777\pi\) | ||||
−0.889896 | + | 0.456164i | \(0.849223\pi\) | |||||||
\(674\) | 3.67863e6 | 0.311915 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.85072e6 | 0.324097 | ||||||||
\(677\) | 3.36926e6i | 0.282529i | 0.989972 | + | 0.141264i | \(0.0451168\pi\) | ||||
−0.989972 | + | 0.141264i | \(0.954883\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.44144e7 | −1.19984 | ||||||||
\(680\) | 1.64775e7 | − | 8.07364e6i | 1.36653 | − | 0.669571i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.09994e6i | 0.666839i | ||||||||
\(683\) | 1.55817e7i | 1.27810i | 0.769166 | + | 0.639049i | \(0.220672\pi\) | ||||
−0.769166 | + | 0.639049i | \(0.779328\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.84685e6 | + | 1.60147e7i | 0.638953 | + | 1.30404i | ||||
\(686\) | 1.68530e7 | 1.36731 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 6.23570e6i | − | 0.502243i | ||||||
\(689\) | −1.07126e6 | −0.0859699 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.73771e6 | 0.775821 | 0.387911 | − | 0.921697i | \(-0.373197\pi\) | ||||
0.387911 | + | 0.921697i | \(0.373197\pi\) | |||||||
\(692\) | 3.32002e6i | 0.263558i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.37072e6 | −0.344472 | ||||||||
\(695\) | −1.13730e7 | + | 5.57254e6i | −0.893128 | + | 0.437614i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.84224e7i | − | 1.43637i | ||||||
\(698\) | 3.46588e6i | 0.269262i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.65280e6 | − | 5.15900e6i | −0.513168 | − | 0.397942i | ||||
\(701\) | 1.72451e7 | 1.32547 | 0.662735 | − | 0.748854i | \(-0.269396\pi\) | ||||
0.662735 | + | 0.748854i | \(0.269396\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.58571e6i | 0.273644i | ||||||||
\(704\) | 1.71241e7 | 1.30219 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.23462e7 | 0.932225 | ||||||||
\(707\) | 1.36364e7i | 1.02601i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.81083e7 | 1.35289 | 0.676443 | − | 0.736495i | \(-0.263520\pi\) | ||||
0.676443 | + | 0.736495i | \(0.263520\pi\) | |||||||
\(710\) | 3.64449e6 | + | 7.43806e6i | 0.271326 | + | 0.553750i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 2.37071e7i | − | 1.75259i | ||||||
\(713\) | 8.16455e6i | 0.601462i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.77200e6 | + | 5.65739e6i | 0.202781 | + | 0.413857i | ||||
\(716\) | 343365. | 0.0250307 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.03777e6i | 0.364693i | ||||||||
\(719\) | −1.77044e7 | −1.27720 | −0.638600 | − | 0.769539i | \(-0.720486\pi\) | ||||
−0.638600 | + | 0.769539i | \(0.720486\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.38184e7 | −2.42279 | ||||||||
\(722\) | 1.00258e7i | 0.715776i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −982344. | −0.0696494 | ||||||||
\(725\) | 1.05745e7 | − | 1.36364e7i | 0.747165 | − | 0.963509i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.80607e6i | − | 0.547768i | −0.961763 | − | 0.273884i | \(-0.911692\pi\) | ||
0.961763 | − | 0.273884i | \(-0.0883084\pi\) | |||||||
\(728\) | − | 9.91741e6i | − | 0.693537i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 604800. | − | 296339.i | 0.0420054 | − | 0.0205817i | ||||
\(731\) | 2.09714e7 | 1.45156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 2.11490e7i | − | 1.45388i | −0.686700 | − | 0.726941i | \(-0.740941\pi\) | ||
0.686700 | − | 0.726941i | \(-0.259059\pi\) | |||||||
\(734\) | −1.18170e6 | −0.0809593 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.22944e6 | 0.628031 | ||||||||
\(737\) | − | 1.73555e7i | − | 1.17698i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.20256e6 | 0.619865 | 0.309933 | − | 0.950759i | \(-0.399693\pi\) | ||||
0.309933 | + | 0.950759i | \(0.399693\pi\) | |||||||
\(740\) | 2.18669e6 | + | 4.46283e6i | 0.146794 | + | 0.299593i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 4.79082e6i | − | 0.319448i | ||||||
\(743\) | − | 4.78756e6i | − | 0.318157i | −0.987266 | − | 0.159079i | \(-0.949148\pi\) | ||
0.987266 | − | 0.159079i | \(-0.0508523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.03880e6 | + | 3.93884e6i | −0.530641 | + | 0.260003i | ||||
\(746\) | −1.37396e7 | −0.903916 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.00486e7i | 0.656676i | ||||||||
\(749\) | 429709. | 0.0279878 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.03369e6 | 0.455075 | 0.227538 | − | 0.973769i | \(-0.426933\pi\) | ||||
0.227538 | + | 0.973769i | \(0.426933\pi\) | |||||||
\(752\) | 4.73359e6i | 0.305244i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.54400e6 | 0.355136 | ||||||||
\(755\) | −446174. | + | 218616.i | −0.0284864 | + | 0.0139577i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.99807e7i | 1.26727i | 0.773631 | + | 0.633637i | \(0.218439\pi\) | ||||
−0.773631 | + | 0.633637i | \(0.781561\pi\) | |||||||
\(758\) | − | 6.81122e6i | − | 0.430578i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.34256e6 | − | 4.78094e6i | −0.147115 | − | 0.300247i | ||||
\(761\) | −1.15851e7 | −0.725165 | −0.362582 | − | 0.931952i | \(-0.618105\pi\) | ||||
−0.362582 | + | 0.931952i | \(0.618105\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 380302.i | − | 0.0236492i | ||||||
\(764\) | −5.84323e6 | −0.362176 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.07611e7 | −0.662650 | ||||||||
\(767\) | − | 1.23968e6i | − | 0.0760886i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.88308e7 | 1.14830 | 0.574148 | − | 0.818752i | \(-0.305333\pi\) | ||||
0.574148 | + | 0.818752i | \(0.305333\pi\) | |||||||
\(770\) | −2.53006e7 | + | 1.23968e7i | −1.53781 | + | 0.753497i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.49252e6i | 0.392076i | ||||||||
\(773\) | − | 9.80638e6i | − | 0.590283i | −0.955454 | − | 0.295141i | \(-0.904633\pi\) | ||
0.955454 | − | 0.295141i | \(-0.0953667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.90932e6 | − | 8.90993e6i | 0.413220 | − | 0.532869i | ||||
\(776\) | −1.26342e7 | −0.753173 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 5.65514e6i | − | 0.334961i | ||||||
\(779\) | −5.34525e6 | −0.315591 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.66320e7 | −0.975701 | ||||||||
\(782\) | − | 1.68812e7i | − | 0.987160i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.66621e7 | 0.968145 | ||||||||
\(785\) | 1.24520e7 | + | 2.54134e7i | 0.721216 | + | 1.47193i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.21012e7i | 1.84750i | 0.382998 | + | 0.923749i | \(0.374892\pi\) | ||||
−0.382998 | + | 0.923749i | \(0.625108\pi\) | |||||||
\(788\) | 9.75571e6i | 0.559685i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.09578e7 | − | 2.23637e7i | −0.624675 | − | 1.27490i | ||||
\(791\) | −3.33857e7 | −1.89723 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.79576e6i | 0.270816i | ||||||||
\(794\) | 6.99080e6 | 0.393528 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.75373e6 | 0.0981024 | ||||||||
\(797\) | − | 3.06076e7i | − | 1.70680i | −0.521256 | − | 0.853400i | \(-0.674536\pi\) | ||
0.521256 | − | 0.853400i | \(-0.325464\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.59196e7 | −0.882198 | ||||||||
\(800\) | −1.00720e7 | − | 7.81050e6i | −0.556407 | − | 0.431473i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.11985e6i | 0.335974i | ||||||||
\(803\) | 1.35237e6i | 0.0740130i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.55024e7 | + | 1.24956e7i | −1.38705 | + | 0.679624i | ||||
\(806\) | 3.62240e6 | 0.196408 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.19524e7i | 0.644058i | ||||||||
\(809\) | 1.30208e7 | 0.699464 | 0.349732 | − | 0.936850i | \(-0.386273\pi\) | ||||
0.349732 | + | 0.936850i | \(0.386273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.58466e7 | −1.37991 | −0.689956 | − | 0.723851i | \(-0.742370\pi\) | ||||
−0.689956 | + | 0.723851i | \(0.742370\pi\) | |||||||
\(812\) | − | 1.48761e7i | − | 0.791771i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.66320e7 | 0.879799 | ||||||||
\(815\) | −5.46674e6 | − | 1.11571e7i | −0.288293 | − | 0.588378i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.08483e6i | − | 0.318929i | ||||||
\(818\) | − | 1.92940e7i | − | 1.00818i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.65280e6 | + | 3.25973e6i | −0.345517 | + | 0.169296i | ||||
\(821\) | 1.88575e7 | 0.976396 | 0.488198 | − | 0.872733i | \(-0.337654\pi\) | ||||
0.488198 | + | 0.872733i | \(0.337654\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.90126e7i | − | 0.978459i | −0.872155 | − | 0.489230i | \(-0.837278\pi\) | ||
0.872155 | − | 0.489230i | \(-0.162722\pi\) | |||||||
\(824\) | −2.96419e7 | −1.52085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.54400e6 | 0.282731 | ||||||||
\(827\) | − | 823839.i | − | 0.0418869i | −0.999781 | − | 0.0209435i | \(-0.993333\pi\) | ||
0.999781 | − | 0.0209435i | \(-0.00666700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.60900e7 | 1.82390 | 0.911948 | − | 0.410305i | \(-0.134578\pi\) | ||||
0.911948 | + | 0.410305i | \(0.134578\pi\) | |||||||
\(830\) | 1.28230e7 | − | 6.28299e6i | 0.646091 | − | 0.316571i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 7.65813e6i | − | 0.383543i | ||||||
\(833\) | 5.60367e7i | 2.79808i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.39954e6 | + | 4.89723e6i | 0.119100 | + | 0.243072i | ||||
\(836\) | 2.91559e6 | 0.144282 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.08238e6i | 0.151627i | ||||||||
\(839\) | −1.23692e7 | −0.606647 | −0.303324 | − | 0.952888i | \(-0.598096\pi\) | ||||
−0.303324 | + | 0.952888i | \(0.598096\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.98085e6 | 0.486606 | ||||||||
\(842\) | 4.63117e6i | 0.225118i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.01603e7 | 0.490965 | ||||||||
\(845\) | −1.61087e7 | + | 7.89292e6i | −0.776102 | + | 0.380274i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.04180e7i | − | 0.977923i | ||||||
\(848\) | − | 2.36680e6i | − | 0.113024i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.42859e7 | + | 1.84224e7i | −0.678204 | + | 0.874580i | ||||
\(851\) | 1.67647e7 | 0.793544 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.97159e6i | 0.469237i | 0.972088 | + | 0.234618i | \(0.0753840\pi\) | ||||
−0.972088 | + | 0.234618i | \(0.924616\pi\) | |||||||
\(854\) | −2.14473e7 | −1.00630 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 376640. | 0.0175688 | ||||||||
\(857\) | 1.48619e7i | 0.691231i | 0.938376 | + | 0.345616i | \(0.112330\pi\) | ||||
−0.938376 | + | 0.345616i | \(0.887670\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.41452e7 | 0.654071 | 0.327036 | − | 0.945012i | \(-0.393950\pi\) | ||||
0.327036 | + | 0.945012i | \(0.393950\pi\) | |||||||
\(860\) | −3.71075e6 | − | 7.57329e6i | −0.171087 | − | 0.349171i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 1.24462e7i | − | 0.570519i | ||||||
\(863\) | − | 1.72325e6i | − | 0.0787627i | −0.999224 | − | 0.0393814i | \(-0.987461\pi\) | ||
0.999224 | − | 0.0393814i | \(-0.0125387\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.80515e6 | − | 1.38887e7i | −0.309241 | − | 0.631132i | ||||
\(866\) | 1.78911e6 | 0.0810668 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 9.71993e6i | − | 0.437889i | ||||||
\(869\) | 5.00068e7 | 2.24636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.76160e6 | −0.346662 | ||||||||
\(872\) | − | 333335.i | − | 0.0148453i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.89808e6 | −0.216894 | ||||||||
\(875\) | 3.84052e7 | + | 7.94520e6i | 1.69578 | + | 0.350820i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 8.53435e6i | − | 0.374689i | −0.982294 | − | 0.187345i | \(-0.940012\pi\) | ||
0.982294 | − | 0.187345i | \(-0.0599881\pi\) | |||||||
\(878\) | − | 1.38639e7i | − | 0.606945i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.24992e7 | + | 6.12434e6i | −0.544096 | + | 0.266596i | ||||
\(881\) | 7.09019e6 | 0.307764 | 0.153882 | − | 0.988089i | \(-0.450822\pi\) | ||||
0.153882 | + | 0.988089i | \(0.450822\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.54183e6i | 0.325518i | 0.986666 | + | 0.162759i | \(0.0520393\pi\) | ||||
−0.986666 | + | 0.162759i | \(0.947961\pi\) | |||||||
\(884\) | 4.49387e6 | 0.193415 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 982960. | 0.0420680 | ||||||||
\(887\) | − | 4.11968e7i | − | 1.75815i | −0.476687 | − | 0.879073i | \(-0.658163\pi\) | ||
0.476687 | − | 0.879073i | \(-0.341837\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.88584e7 | 1.64904 | ||||||||
\(890\) | 1.32527e7 | + | 2.70475e7i | 0.560827 | + | 1.14459i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 9.74956e6i | − | 0.410273i | ||||||
\(893\) | 4.61907e6i | 0.193832i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.43640e6 | + | 703806.i | −0.0599401 | + | 0.0293694i | ||||
\(896\) | 4.94767e6 | 0.205888 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 1.10588e7i | − | 0.457635i | ||||||
\(899\) | 1.99232e7 | 0.822167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.95982e6 | 0.326656 | ||||||||
\(902\) | 2.47935e7i | 1.01466i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.92626e7 | −1.19095 | ||||||||
\(905\) | 4.10944e6 | − | 2.01354e6i | 0.166787 | − | 0.0817219i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 3.99367e7i | − | 1.61196i | −0.591945 | − | 0.805979i | \(-0.701640\pi\) | ||
0.591945 | − | 0.805979i | \(-0.298360\pi\) | |||||||
\(908\) | 4.26041e6i | 0.171489i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.54400e6 | + | 1.13148e7i | 0.221932 | + | 0.452942i | ||||
\(911\) | −9.30901e6 | −0.371627 | −0.185814 | − | 0.982585i | \(-0.559492\pi\) | ||||
−0.185814 | + | 0.982585i | \(0.559492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.86731e7i | 1.13841i | ||||||||
\(914\) | 1.29535e7 | 0.512887 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.93313e6 | −0.194260 | ||||||||
\(917\) | 6.07441e7i | 2.38551i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.88035e7 | −1.12501 | −0.562506 | − | 0.826793i | \(-0.690163\pi\) | ||||
−0.562506 | + | 0.826793i | \(0.690163\pi\) | |||||||
\(920\) | −2.23529e7 | + | 1.09524e7i | −0.870691 | + | 0.426620i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.15354e7i | 1.22172i | ||||||||
\(923\) | 7.43806e6i | 0.287379i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.82952e7 | − | 1.41872e7i | −0.703045 | − | 0.545185i | ||||
\(926\) | −1.29324e7 | −0.495624 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 2.25218e7i | − | 0.858485i | ||||||
\(929\) | 2.03981e7 | 0.775444 | 0.387722 | − | 0.921776i | \(-0.373262\pi\) | ||||
0.387722 | + | 0.921776i | \(0.373262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.62590e7 | 0.614780 | ||||||||
\(932\) | 8.85832e6i | 0.334050i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.45189e7 | 1.29476 | ||||||||
\(935\) | −2.05969e7 | − | 4.20363e7i | −0.770500 | − | 1.57252i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.91357e7i | 1.82830i | 0.405371 | + | 0.914152i | \(0.367142\pi\) | ||||
−0.405371 | + | 0.914152i | \(0.632858\pi\) | |||||||
\(938\) | − | 3.47109e7i | − | 1.28813i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.81688e6 | + | 5.74898e6i | 0.103980 | + | 0.212213i | ||||
\(941\) | 3.80960e7 | 1.40251 | 0.701254 | − | 0.712912i | \(-0.252624\pi\) | ||||
0.701254 | + | 0.712912i | \(0.252624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.49913e7i | 0.915186i | ||||||||
\(944\) | 2.73889e6 | 0.100033 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.82240e7 | −1.02539 | ||||||||
\(947\) | 1.45947e6i | 0.0528836i | 0.999650 | + | 0.0264418i | \(0.00841767\pi\) | ||||
−0.999650 | + | 0.0264418i | \(0.991582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 604800. | 0.0217995 | ||||||||
\(950\) | 5.34525e6 | + | 4.14504e6i | 0.192158 | + | 0.149012i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.36897e7i | 2.63520i | ||||||||
\(953\) | − | 1.94841e7i | − | 0.694940i | −0.937691 | − | 0.347470i | \(-0.887041\pi\) | ||
0.937691 | − | 0.347470i | \(-0.112959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.44440e7 | − | 1.19770e7i | 0.867289 | − | 0.424953i | ||||
\(956\) | −1.45780e6 | −0.0515884 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 938408.i | 0.0330353i | ||||||||
\(959\) | −7.16198e7 | −2.51470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.56115e7 | −0.545300 | ||||||||
\(962\) | − | 7.43806e6i | − | 0.259132i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.34669e7 | 0.466740 | ||||||||
\(965\) | −1.33079e7 | − | 2.71602e7i | −0.460036 | − | 0.938889i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.65207e7i | − | 0.568149i | −0.958802 | − | 0.284074i | \(-0.908314\pi\) | ||
0.958802 | − | 0.284074i | \(-0.0916862\pi\) | |||||||
\(968\) | − | 1.78964e7i | − | 0.613871i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.44144e7 | − | 7.06275e6i | 0.491889 | − | 0.241015i | ||||
\(971\) | −1.02422e7 | −0.348615 | −0.174308 | − | 0.984691i | \(-0.555769\pi\) | ||||
−0.174308 | + | 0.984691i | \(0.555769\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 5.08617e7i | − | 1.72230i | ||||||
\(974\) | 3.47883e6 | 0.117500 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.05956e7 | −0.356040 | ||||||||
\(977\) | 1.95090e7i | 0.653881i | 0.945045 | + | 0.326941i | \(0.106018\pi\) | ||||
−0.945045 | + | 0.326941i | \(0.893982\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.04800e7 | −2.01676 | ||||||||
\(980\) | 2.02363e7 | − | 9.91534e6i | 0.673078 | − | 0.329794i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 4.44262e7i | − | 1.47015i | ||||||
\(983\) | 1.91895e7i | 0.633403i | 0.948525 | + | 0.316701i | \(0.102575\pi\) | ||||
−0.948525 | + | 0.316701i | \(0.897425\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.99966e7 | − | 4.08111e7i | −0.656697 | − | 1.34026i | ||||
\(986\) | −4.11938e7 | −1.34940 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 1.30389e6i | − | 0.0424961i | ||||||
\(989\) | −2.84491e7 | −0.924864 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.38361e7 | 1.74136 | 0.870682 | − | 0.491846i | \(-0.163678\pi\) | ||||
0.870682 | + | 0.491846i | \(0.163678\pi\) | |||||||
\(992\) | − | 1.47155e7i | − | 0.474785i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.32640e7 | −1.06785 | ||||||||
\(995\) | −7.33637e6 | + | 3.59467e6i | −0.234922 | + | 0.115107i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.25008e6i | 0.103551i | 0.998659 | + | 0.0517757i | \(0.0164881\pi\) | ||||
−0.998659 | + | 0.0517757i | \(0.983512\pi\) | |||||||
\(998\) | 2.28227e7i | 0.725339i | ||||||||
\(999\) | 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 | 45.6.b.d.19.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 45.6.b.d.19.4 | yes | 4 | |
4.3 | odd | 2 | 720.6.f.k.289.2 | 4 | |||
5.2 | odd | 4 | 225.6.a.v.1.4 | 4 | |||
5.3 | odd | 4 | 225.6.a.v.1.1 | 4 | |||
5.4 | even | 2 | inner | 45.6.b.d.19.3 | yes | 4 | |
12.11 | even | 2 | 720.6.f.k.289.3 | 4 | |||
15.2 | even | 4 | 225.6.a.v.1.2 | 4 | |||
15.8 | even | 4 | 225.6.a.v.1.3 | 4 | |||
15.14 | odd | 2 | inner | 45.6.b.d.19.2 | yes | 4 | |
20.19 | odd | 2 | 720.6.f.k.289.1 | 4 | |||
60.59 | even | 2 | 720.6.f.k.289.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.6.b.d.19.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
45.6.b.d.19.2 | yes | 4 | 15.14 | odd | 2 | inner | |
45.6.b.d.19.3 | yes | 4 | 5.4 | even | 2 | inner | |
45.6.b.d.19.4 | yes | 4 | 3.2 | odd | 2 | inner | |
225.6.a.v.1.1 | 4 | 5.3 | odd | 4 | |||
225.6.a.v.1.2 | 4 | 15.2 | even | 4 | |||
225.6.a.v.1.3 | 4 | 15.8 | even | 4 | |||
225.6.a.v.1.4 | 4 | 5.2 | odd | 4 | |||
720.6.f.k.289.1 | 4 | 20.19 | odd | 2 | |||
720.6.f.k.289.2 | 4 | 4.3 | odd | 2 | |||
720.6.f.k.289.3 | 4 | 12.11 | even | 2 | |||
720.6.f.k.289.4 | 4 | 60.59 | even | 2 |