Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,6,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.a (trivial) |
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: | yes |
Analytic conductor: | \(36.0863594579\) |
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: | \( x^{4} - 2x^{3} - 29x^{2} + 30x + 155 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.35969\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.47214 | −0.790569 | −0.395285 | − | 0.918559i | \(-0.629354\pi\) | ||||
−0.395285 | + | 0.918559i | \(0.629354\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −12.0000 | −0.375000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −224.499 | −1.73169 | −0.865845 | − | 0.500312i | \(-0.833219\pi\) | ||||
−0.865845 | + | 0.500312i | \(0.833219\pi\) | |||||||
\(8\) | 196.774 | 1.08703 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −501.996 | −1.25089 | −0.625444 | − | 0.780269i | \(-0.715082\pi\) | ||||
−0.625444 | + | 0.780269i | \(0.715082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −224.499 | −0.368432 | −0.184216 | − | 0.982886i | \(-0.558975\pi\) | ||||
−0.184216 | + | 0.982886i | \(0.558975\pi\) | |||||||
\(14\) | 1003.99 | 1.36902 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −496.000 | −0.484375 | ||||||||
\(17\) | −1668.11 | −1.39991 | −0.699957 | − | 0.714185i | \(-0.746798\pi\) | ||||
−0.699957 | + | 0.714185i | \(0.746798\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 484.000 | 0.307582 | 0.153791 | − | 0.988103i | \(-0.450852\pi\) | ||||
0.153791 | + | 0.988103i | \(0.450852\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2244.99 | 0.988914 | ||||||||
\(23\) | −2262.90 | −0.891961 | −0.445981 | − | 0.895043i | \(-0.647145\pi\) | ||||
−0.445981 | + | 0.895043i | \(0.647145\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1003.99 | 0.291271 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2693.99 | 0.649384 | ||||||||
\(29\) | −5521.96 | −1.21926 | −0.609632 | − | 0.792684i | \(-0.708683\pi\) | ||||
−0.609632 | + | 0.792684i | \(0.708683\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3608.00 | 0.674314 | 0.337157 | − | 0.941448i | \(-0.390535\pi\) | ||||
0.337157 | + | 0.941448i | \(0.390535\pi\) | |||||||
\(32\) | −4078.59 | −0.704101 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7460.00 | 1.10673 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7408.48 | −0.889662 | −0.444831 | − | 0.895615i | \(-0.646736\pi\) | ||||
−0.444831 | + | 0.895615i | \(0.646736\pi\) | |||||||
\(38\) | −2164.51 | −0.243165 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11043.9 | 1.02604 | 0.513019 | − | 0.858377i | \(-0.328527\pi\) | ||||
0.513019 | + | 0.858377i | \(0.328527\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12572.0 | −1.03689 | −0.518444 | − | 0.855111i | \(-0.673489\pi\) | ||||
−0.518444 | + | 0.855111i | \(0.673489\pi\) | |||||||
\(44\) | 6023.95 | 0.469083 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10120.0 | 0.705157 | ||||||||
\(47\) | −9543.54 | −0.630180 | −0.315090 | − | 0.949062i | \(-0.602035\pi\) | ||||
−0.315090 | + | 0.949062i | \(0.602035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 33593.0 | 1.99875 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2693.99 | 0.138162 | ||||||||
\(53\) | −4771.77 | −0.233340 | −0.116670 | − | 0.993171i | \(-0.537222\pi\) | ||||
−0.116670 | + | 0.993171i | \(0.537222\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −44175.6 | −1.88240 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 24694.9 | 0.963913 | ||||||||
\(59\) | 5521.96 | 0.206520 | 0.103260 | − | 0.994654i | \(-0.467073\pi\) | ||||
0.103260 | + | 0.994654i | \(0.467073\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 21362.0 | 0.735051 | 0.367525 | − | 0.930013i | \(-0.380205\pi\) | ||||
0.367525 | + | 0.930013i | \(0.380205\pi\) | |||||||
\(62\) | −16135.5 | −0.533092 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 34112.0 | 1.04102 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34572.9 | 0.940912 | 0.470456 | − | 0.882423i | \(-0.344089\pi\) | ||||
0.470456 | + | 0.882423i | \(0.344089\pi\) | |||||||
\(68\) | 20017.3 | 0.524968 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 33131.7 | 0.780007 | 0.390003 | − | 0.920813i | \(-0.372474\pi\) | ||||
0.390003 | + | 0.920813i | \(0.372474\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2693.99 | 0.0591683 | 0.0295842 | − | 0.999562i | \(-0.490582\pi\) | ||||
0.0295842 | + | 0.999562i | \(0.490582\pi\) | |||||||
\(74\) | 33131.7 | 0.703339 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5808.00 | −0.115343 | ||||||||
\(77\) | 112698. | 2.16615 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 99616.0 | 1.79581 | 0.897907 | − | 0.440185i | \(-0.145087\pi\) | ||||
0.897907 | + | 0.440185i | \(0.145087\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −49389.9 | −0.811154 | ||||||||
\(83\) | 57118.1 | 0.910078 | 0.455039 | − | 0.890471i | \(-0.349625\pi\) | ||||
0.455039 | + | 0.890471i | \(0.349625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 56223.6 | 0.819733 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −98779.8 | −1.35976 | ||||||||
\(89\) | −120479. | −1.61227 | −0.806133 | − | 0.591735i | \(-0.798443\pi\) | ||||
−0.806133 | + | 0.591735i | \(0.798443\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 50400.0 | 0.638009 | ||||||||
\(92\) | 27154.8 | 0.334485 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 42680.0 | 0.498201 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −64206.8 | −0.692870 | −0.346435 | − | 0.938074i | \(-0.612608\pi\) | ||||
−0.346435 | + | 0.938074i | \(0.612608\pi\) | |||||||
\(98\) | −150232. | −1.58015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −60741.5 | −0.592492 | −0.296246 | − | 0.955112i | \(-0.595735\pi\) | ||||
−0.296246 | + | 0.955112i | \(0.595735\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 150639. | 1.39909 | 0.699544 | − | 0.714590i | \(-0.253387\pi\) | ||||
0.699544 | + | 0.714590i | \(0.253387\pi\) | |||||||
\(104\) | −44175.6 | −0.400497 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21340.0 | 0.184472 | ||||||||
\(107\) | 1914.07 | 0.0161622 | 0.00808108 | − | 0.999967i | \(-0.497428\pi\) | ||||
0.00808108 | + | 0.999967i | \(0.497428\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1694.00 | −0.0136567 | −0.00682837 | − | 0.999977i | \(-0.502174\pi\) | ||||
−0.00682837 | + | 0.999977i | \(0.502174\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 111352. | 0.838787 | ||||||||
\(113\) | 148712. | 1.09559 | 0.547797 | − | 0.836611i | \(-0.315467\pi\) | ||||
0.547797 | + | 0.836611i | \(0.315467\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 66263.5 | 0.457224 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −24694.9 | −0.163269 | ||||||||
\(119\) | 374489. | 2.42422 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 90949.0 | 0.564722 | ||||||||
\(122\) | −95533.8 | −0.581109 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −43296.0 | −0.252868 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 173089. | 0.952271 | 0.476135 | − | 0.879372i | \(-0.342037\pi\) | ||||
0.476135 | + | 0.879372i | \(0.342037\pi\) | |||||||
\(128\) | −22038.7 | −0.118894 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −270576. | −1.37756 | −0.688780 | − | 0.724970i | \(-0.741854\pi\) | ||||
−0.688780 | + | 0.724970i | \(0.741854\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −108658. | −0.532637 | ||||||||
\(134\) | −154615. | −0.743856 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −328240. | −1.52175 | ||||||||
\(137\) | −319020. | −1.45217 | −0.726083 | − | 0.687607i | \(-0.758661\pi\) | ||||
−0.726083 | + | 0.687607i | \(0.758661\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −226556. | −0.994577 | −0.497289 | − | 0.867585i | \(-0.665671\pi\) | ||||
−0.497289 | + | 0.867585i | \(0.665671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −148170. | −0.616649 | ||||||||
\(143\) | 112698. | 0.460867 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12047.9 | −0.0467767 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 88901.8 | 0.333623 | ||||||||
\(149\) | −160137. | −0.590915 | −0.295458 | − | 0.955356i | \(-0.595472\pi\) | ||||
−0.295458 | + | 0.955356i | \(0.595472\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8888.00 | 0.0317221 | 0.0158610 | − | 0.999874i | \(-0.494951\pi\) | ||||
0.0158610 | + | 0.999874i | \(0.494951\pi\) | |||||||
\(152\) | 95238.6 | 0.334352 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −504000. | −1.71249 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −506246. | −1.63913 | −0.819564 | − | 0.572988i | \(-0.805784\pi\) | ||||
−0.819564 | + | 0.572988i | \(0.805784\pi\) | |||||||
\(158\) | −445496. | −1.41972 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 508020. | 1.54460 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −222254. | −0.655211 | −0.327606 | − | 0.944815i | \(-0.606242\pi\) | ||||
−0.327606 | + | 0.944815i | \(0.606242\pi\) | |||||||
\(164\) | −132527. | −0.384764 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −255440. | −0.719480 | ||||||||
\(167\) | −97555.2 | −0.270682 | −0.135341 | − | 0.990799i | \(-0.543213\pi\) | ||||
−0.135341 | + | 0.990799i | \(0.543213\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −320893. | −0.864258 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 150864. | 0.388833 | ||||||||
\(173\) | −276669. | −0.702821 | −0.351411 | − | 0.936221i | \(-0.614298\pi\) | ||||
−0.351411 | + | 0.936221i | \(0.614298\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 248990. | 0.605899 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 538799. | 1.27461 | ||||||||
\(179\) | −28613.8 | −0.0667487 | −0.0333743 | − | 0.999443i | \(-0.510625\pi\) | ||||
−0.0333743 | + | 0.999443i | \(0.510625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −81862.0 | −0.185732 | −0.0928658 | − | 0.995679i | \(-0.529603\pi\) | ||||
−0.0928658 | + | 0.995679i | \(0.529603\pi\) | |||||||
\(182\) | −225396. | −0.504391 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −445280. | −0.969591 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 837383. | 1.75114 | ||||||||
\(188\) | 114522. | 0.236318 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −486936. | −0.965803 | −0.482902 | − | 0.875675i | \(-0.660417\pi\) | ||||
−0.482902 | + | 0.875675i | \(0.660417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −541044. | −1.04554 | −0.522768 | − | 0.852475i | \(-0.675101\pi\) | ||||
−0.522768 | + | 0.852475i | \(0.675101\pi\) | |||||||
\(194\) | 287142. | 0.547762 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −403116. | −0.749531 | ||||||||
\(197\) | 812976. | 1.49249 | 0.746246 | − | 0.665670i | \(-0.231854\pi\) | ||||
0.746246 | + | 0.665670i | \(0.231854\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −146144. | −0.261606 | −0.130803 | − | 0.991408i | \(-0.541756\pi\) | ||||
−0.130803 | + | 0.991408i | \(0.541756\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 271644. | 0.468406 | ||||||||
\(203\) | 1.23968e6 | 2.11139 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −673679. | −1.10608 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 111352. | 0.178459 | ||||||||
\(209\) | −242966. | −0.384751 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 846692. | 1.30924 | 0.654620 | − | 0.755958i | \(-0.272829\pi\) | ||||
0.654620 | + | 0.755958i | \(0.272829\pi\) | |||||||
\(212\) | 57261.2 | 0.0875026 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8560.00 | −0.0127773 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −809994. | −1.16770 | ||||||||
\(218\) | 7575.80 | 0.0107966 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 374489. | 0.515773 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 812463. | 1.09406 | 0.547031 | − | 0.837113i | \(-0.315758\pi\) | ||||
0.547031 | + | 0.837113i | \(0.315758\pi\) | |||||||
\(224\) | 915641. | 1.21928 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −665060. | −0.866143 | ||||||||
\(227\) | 355034. | 0.457304 | 0.228652 | − | 0.973508i | \(-0.426568\pi\) | ||||
0.228652 | + | 0.973508i | \(0.426568\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 411094. | 0.518027 | 0.259014 | − | 0.965874i | \(-0.416603\pi\) | ||||
0.259014 | + | 0.965874i | \(0.416603\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.08658e6 | −1.32538 | ||||||||
\(233\) | −738193. | −0.890800 | −0.445400 | − | 0.895332i | \(-0.646939\pi\) | ||||
−0.445400 | + | 0.895332i | \(0.646939\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −66263.5 | −0.0774451 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.67477e6 | −1.91651 | ||||||||
\(239\) | 121483. | 0.137569 | 0.0687845 | − | 0.997632i | \(-0.478088\pi\) | ||||
0.0687845 | + | 0.997632i | \(0.478088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.12224e6 | 1.24464 | 0.622320 | − | 0.782763i | \(-0.286190\pi\) | ||||
0.622320 | + | 0.782763i | \(0.286190\pi\) | |||||||
\(242\) | −406736. | −0.446452 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −256344. | −0.275644 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −108658. | −0.113323 | ||||||||
\(248\) | 709961. | 0.733002 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16565.9 | 0.0165970 | 0.00829851 | − | 0.999966i | \(-0.497358\pi\) | ||||
0.00829851 | + | 0.999966i | \(0.497358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.13597e6 | 1.11574 | ||||||||
\(254\) | −774078. | −0.752836 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −993024. | −0.947021 | ||||||||
\(257\) | 1.10779e6 | 1.04622 | 0.523111 | − | 0.852264i | \(-0.324771\pi\) | ||||
0.523111 | + | 0.852264i | \(0.324771\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.66320e6 | 1.54062 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.21005e6 | 1.08906 | ||||||||
\(263\) | −1.82582e6 | −1.62768 | −0.813840 | − | 0.581090i | \(-0.802627\pi\) | ||||
−0.813840 | + | 0.581090i | \(0.802627\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 485932. | 0.421087 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −414875. | −0.352842 | ||||||||
\(269\) | −1.34184e6 | −1.13062 | −0.565312 | − | 0.824877i | \(-0.691244\pi\) | ||||
−0.565312 | + | 0.824877i | \(0.691244\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 724592. | 0.599336 | 0.299668 | − | 0.954044i | \(-0.403124\pi\) | ||||
0.299668 | + | 0.954044i | \(0.403124\pi\) | |||||||
\(272\) | 827381. | 0.678084 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.42670e6 | 1.14804 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00007e6 | 1.56619 | 0.783096 | − | 0.621901i | \(-0.213639\pi\) | ||||
0.783096 | + | 0.621901i | \(0.213639\pi\) | |||||||
\(278\) | 1.01319e6 | 0.786282 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.20878e6 | 1.66873 | 0.834367 | − | 0.551209i | \(-0.185833\pi\) | ||||
0.834367 | + | 0.551209i | \(0.185833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 442264. | 0.328258 | 0.164129 | − | 0.986439i | \(-0.447519\pi\) | ||||
0.164129 | + | 0.986439i | \(0.447519\pi\) | |||||||
\(284\) | −397581. | −0.292503 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −504000. | −0.364347 | ||||||||
\(287\) | −2.47935e6 | −1.77678 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.36272e6 | 0.959761 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −32327.9 | −0.0221881 | ||||||||
\(293\) | 1.01093e6 | 0.687943 | 0.343971 | − | 0.938980i | \(-0.388228\pi\) | ||||
0.343971 | + | 0.938980i | \(0.388228\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.45780e6 | −0.967092 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 716153. | 0.467160 | ||||||||
\(299\) | 508020. | 0.328627 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.82240e6 | 1.79557 | ||||||||
\(302\) | −39748.3 | −0.0250785 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −240064. | −0.148985 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.37341e6 | −1.43723 | −0.718615 | − | 0.695408i | \(-0.755224\pi\) | ||||
−0.718615 | + | 0.695408i | \(0.755224\pi\) | |||||||
\(308\) | −1.35237e6 | −0.812307 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.57323e6 | −1.50861 | −0.754307 | − | 0.656522i | \(-0.772027\pi\) | ||||
−0.754307 | + | 0.656522i | \(0.772027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.53603e6 | −0.886212 | −0.443106 | − | 0.896469i | \(-0.646123\pi\) | ||||
−0.443106 | + | 0.896469i | \(0.646123\pi\) | |||||||
\(314\) | 2.26400e6 | 1.29584 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.19539e6 | −0.673430 | ||||||||
\(317\) | −2.26708e6 | −1.26712 | −0.633562 | − | 0.773692i | \(-0.718408\pi\) | ||||
−0.633562 | + | 0.773692i | \(0.718408\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.77200e6 | 1.52516 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.27193e6 | −1.22111 | ||||||||
\(323\) | −807364. | −0.430589 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 993952. | 0.517990 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.17315e6 | 1.11534 | ||||||||
\(329\) | 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. | −0.341279 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 436280. | 0.213993 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 822566. | 0.394544 | 0.197272 | − | 0.980349i | \(-0.436792\pi\) | ||||
0.197272 | + | 0.980349i | \(0.436792\pi\) | |||||||
\(338\) | 1.43508e6 | 0.683256 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.81120e6 | −0.843492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.76845e6 | −1.72953 | ||||||||
\(344\) | −2.47384e6 | −1.12713 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.23730e6 | 0.555629 | ||||||||
\(347\) | −977323. | −0.435727 | −0.217863 | − | 0.975979i | \(-0.569909\pi\) | ||||
−0.217863 | + | 0.975979i | \(0.569909\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 774994. | 0.340592 | 0.170296 | − | 0.985393i | \(-0.445528\pi\) | ||||
0.170296 | + | 0.985393i | \(0.445528\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.04743e6 | 0.880752 | ||||||||
\(353\) | −2.76069e6 | −1.17918 | −0.589591 | − | 0.807702i | \(-0.700711\pi\) | ||||
−0.589591 | + | 0.807702i | \(0.700711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.44575e6 | 0.604599 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 127965. | 0.0527694 | ||||||||
\(359\) | 1.12648e6 | 0.461304 | 0.230652 | − | 0.973036i | \(-0.425914\pi\) | ||||
0.230652 | + | 0.973036i | \(0.425914\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.24184e6 | −0.905393 | ||||||||
\(362\) | 366098. | 0.146834 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −604800. | −0.239254 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −264236. | −0.102406 | −0.0512031 | − | 0.998688i | \(-0.516306\pi\) | ||||
−0.0512031 | + | 0.998688i | \(0.516306\pi\) | |||||||
\(368\) | 1.12240e6 | 0.432044 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.07126e6 | 0.404073 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.07227e6 | 1.14337 | 0.571687 | − | 0.820472i | \(-0.306289\pi\) | ||||
0.571687 | + | 0.820472i | \(0.306289\pi\) | |||||||
\(374\) | −3.74489e6 | −1.38440 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.87792e6 | −0.685027 | ||||||||
\(377\) | 1.23968e6 | 0.449216 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.52304e6 | −0.544643 | −0.272322 | − | 0.962206i | \(-0.587791\pi\) | ||||
−0.272322 | + | 0.962206i | \(0.587791\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.17764e6 | 0.763534 | ||||||||
\(383\) | 2.40625e6 | 0.838193 | 0.419096 | − | 0.907942i | \(-0.362347\pi\) | ||||
0.419096 | + | 0.907942i | \(0.362347\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.41962e6 | 0.826569 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 770482. | 0.259826 | ||||||||
\(389\) | −1.26453e6 | −0.423696 | −0.211848 | − | 0.977303i | \(-0.567948\pi\) | ||||
−0.211848 | + | 0.977303i | \(0.567948\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.77476e6 | 1.24867 | ||||||||
\(392\) | 6.61023e6 | 2.17271 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.63574e6 | −1.17992 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.56319e6 | 0.497778 | 0.248889 | − | 0.968532i | \(-0.419935\pi\) | ||||
0.248889 | + | 0.968532i | \(0.419935\pi\) | |||||||
\(398\) | 653576. | 0.206818 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.36844e6 | −0.424977 | −0.212488 | − | 0.977164i | \(-0.568157\pi\) | ||||
−0.212488 | + | 0.977164i | \(0.568157\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −809994. | −0.248439 | ||||||||
\(404\) | 728898. | 0.222184 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.54400e6 | −1.66920 | ||||||||
\(407\) | 3.71903e6 | 1.11287 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.31427e6 | −1.27526 | −0.637630 | − | 0.770343i | \(-0.720085\pi\) | ||||
−0.637630 | + | 0.770343i | \(0.720085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.80767e6 | −0.524658 | ||||||||
\(413\) | −1.23968e6 | −0.357629 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 915641. | 0.259413 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.08658e6 | 0.304172 | ||||||||
\(419\) | 689241. | 0.191794 | 0.0958972 | − | 0.995391i | \(-0.469428\pi\) | ||||
0.0958972 | + | 0.995391i | \(0.469428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.03556e6 | −0.284755 | −0.142377 | − | 0.989812i | \(-0.545475\pi\) | ||||
−0.142377 | + | 0.989812i | \(0.545475\pi\) | |||||||
\(422\) | −3.78652e6 | −1.03505 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −938960. | −0.253649 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.79576e6 | −1.27288 | ||||||||
\(428\) | −22968.9 | −0.00606081 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.78307e6 | 0.721656 | 0.360828 | − | 0.932632i | \(-0.382494\pi\) | ||||
0.360828 | + | 0.932632i | \(0.382494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −400058. | −0.102542 | −0.0512712 | − | 0.998685i | \(-0.516327\pi\) | ||||
−0.0512712 | + | 0.998685i | \(0.516327\pi\) | |||||||
\(434\) | 3.62240e6 | 0.923150 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20328.0 | 0.00512128 | ||||||||
\(437\) | −1.09524e6 | −0.274351 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.10006e6 | −0.767731 | −0.383866 | − | 0.923389i | \(-0.625407\pi\) | ||||
−0.383866 | + | 0.923389i | \(0.625407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.67477e6 | −0.407754 | ||||||||
\(443\) | −219797. | −0.0532122 | −0.0266061 | − | 0.999646i | \(-0.508470\pi\) | ||||
−0.0266061 | + | 0.999646i | \(0.508470\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.63345e6 | −0.864931 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.65813e6 | −1.80272 | ||||||||
\(449\) | −2.47283e6 | −0.578867 | −0.289434 | − | 0.957198i | \(-0.593467\pi\) | ||||
−0.289434 | + | 0.957198i | \(0.593467\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.54400e6 | −1.28346 | ||||||||
\(452\) | −1.78454e6 | −0.410848 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.58776e6 | −0.361531 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.89649e6 | 0.648757 | 0.324378 | − | 0.945927i | \(-0.394845\pi\) | ||||
0.324378 | + | 0.945927i | \(0.394845\pi\) | |||||||
\(458\) | −1.83847e6 | −0.409536 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.05154e6 | −1.54537 | −0.772683 | − | 0.634792i | \(-0.781086\pi\) | ||||
−0.772683 | + | 0.634792i | \(0.781086\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.89178e6 | 0.626920 | 0.313460 | − | 0.949601i | \(-0.398512\pi\) | ||||
0.313460 | + | 0.949601i | \(0.398512\pi\) | |||||||
\(464\) | 2.73889e6 | 0.590581 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.30130e6 | 0.704239 | ||||||||
\(467\) | 7.71866e6 | 1.63776 | 0.818879 | − | 0.573967i | \(-0.194596\pi\) | ||||
0.818879 | + | 0.573967i | \(0.194596\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.76160e6 | −1.62937 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.08658e6 | 0.224494 | ||||||||
\(473\) | 6.31108e6 | 1.29703 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.49387e6 | −0.909082 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −543289. | −0.108758 | ||||||||
\(479\) | 209834. | 0.0417867 | 0.0208933 | − | 0.999782i | \(-0.493349\pi\) | ||||
0.0208933 | + | 0.999782i | \(0.493349\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.66320e6 | 0.327779 | ||||||||
\(482\) | −5.01882e6 | −0.983975 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.09139e6 | −0.211771 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 777891. | 0.148626 | 0.0743132 | − | 0.997235i | \(-0.476324\pi\) | ||||
0.0743132 | + | 0.997235i | \(0.476324\pi\) | |||||||
\(488\) | 4.20349e6 | 0.799024 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.93400e6 | 1.85960 | 0.929802 | − | 0.368061i | \(-0.119978\pi\) | ||||
0.929802 | + | 0.368061i | \(0.119978\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.21121e6 | 1.70687 | ||||||||
\(494\) | 485932. | 0.0895897 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.78957e6 | −0.326621 | ||||||||
\(497\) | −7.43806e6 | −1.35073 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.10332e6 | 0.917489 | 0.458745 | − | 0.888568i | \(-0.348299\pi\) | ||||
0.458745 | + | 0.888568i | \(0.348299\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −74084.8 | −0.0131211 | ||||||||
\(503\) | −4.00824e6 | −0.706373 | −0.353186 | − | 0.935553i | \(-0.614902\pi\) | ||||
−0.353186 | + | 0.935553i | \(0.614902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.08020e6 | −0.882073 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.07707e6 | −0.357101 | ||||||||
\(509\) | 1.96029e6 | 0.335372 | 0.167686 | − | 0.985840i | \(-0.446371\pi\) | ||||
0.167686 | + | 0.985840i | \(0.446371\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −604800. | −0.102461 | ||||||||
\(512\) | 5.14618e6 | 0.867580 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.95418e6 | −0.827111 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.79082e6 | 0.788285 | ||||||||
\(518\) | −7.43806e6 | −1.21797 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.65338e6 | 1.55806 | 0.779032 | − | 0.626984i | \(-0.215711\pi\) | ||||
0.779032 | + | 0.626984i | \(0.215711\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 462020. | 0.0738595 | 0.0369298 | − | 0.999318i | \(-0.488242\pi\) | ||||
0.0369298 | + | 0.999318i | \(0.488242\pi\) | |||||||
\(524\) | 3.24691e6 | 0.516585 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.16532e6 | 1.28679 | ||||||||
\(527\) | −6.01853e6 | −0.943982 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.31562e6 | −0.204405 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.30389e6 | 0.199739 | ||||||||
\(533\) | −2.47935e6 | −0.378025 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.80305e6 | 1.02280 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.00087e6 | 0.893837 | ||||||||
\(539\) | −1.68636e7 | −2.50021 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.08238e7 | −1.58996 | −0.794978 | − | 0.606639i | \(-0.792517\pi\) | ||||
−0.794978 | + | 0.606639i | \(0.792517\pi\) | |||||||
\(542\) | −3.24047e6 | −0.473817 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.80352e6 | 0.985681 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.02229e6 | 0.288985 | 0.144493 | − | 0.989506i | \(-0.453845\pi\) | ||||
0.144493 | + | 0.989506i | \(0.453845\pi\) | |||||||
\(548\) | 3.82824e6 | 0.544562 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.67263e6 | −0.375024 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.23637e7 | −3.10979 | ||||||||
\(554\) | −8.94457e6 | −1.23818 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.71867e6 | 0.372967 | ||||||||
\(557\) | 3.92593e6 | 0.536173 | 0.268086 | − | 0.963395i | \(-0.413609\pi\) | ||||
0.268086 | + | 0.963395i | \(0.413609\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.82240e6 | 0.382023 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.87798e6 | −1.31925 | ||||||||
\(563\) | −1.12906e7 | −1.50123 | −0.750616 | − | 0.660739i | \(-0.770243\pi\) | ||||
−0.750616 | + | 0.660739i | \(0.770243\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.97786e6 | −0.259511 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.51946e6 | 0.847893 | ||||||||
\(569\) | 1.10770e7 | 1.43431 | 0.717155 | − | 0.696913i | \(-0.245444\pi\) | ||||
0.717155 | + | 0.696913i | \(0.245444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.28605e6 | 0.421778 | 0.210889 | − | 0.977510i | \(-0.432364\pi\) | ||||
0.210889 | + | 0.977510i | \(0.432364\pi\) | |||||||
\(572\) | −1.35237e6 | −0.172825 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.10880e7 | 1.40467 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.42539e7 | −1.78236 | −0.891179 | − | 0.453653i | \(-0.850121\pi\) | ||||
−0.891179 | + | 0.453653i | \(0.850121\pi\) | |||||||
\(578\) | −6.09428e6 | −0.758757 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.28230e7 | −1.57597 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.39541e6 | 0.291883 | ||||||||
\(584\) | 530108. | 0.0643179 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.52102e6 | −0.543867 | ||||||||
\(587\) | −6.12026e6 | −0.733119 | −0.366560 | − | 0.930395i | \(-0.619464\pi\) | ||||
−0.366560 | + | 0.930395i | \(0.619464\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.74627e6 | 0.207407 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.67461e6 | 0.430930 | ||||||||
\(593\) | 1.38377e7 | 1.61595 | 0.807976 | − | 0.589215i | \(-0.200563\pi\) | ||||
0.807976 | + | 0.589215i | \(0.200563\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.92164e6 | 0.221593 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.27193e6 | −0.259802 | ||||||||
\(599\) | 6.37133e6 | 0.725543 | 0.362772 | − | 0.931878i | \(-0.381831\pi\) | ||||
0.362772 | + | 0.931878i | \(0.381831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.06116e6 | 0.232769 | 0.116384 | − | 0.993204i | \(-0.462870\pi\) | ||||
0.116384 | + | 0.993204i | \(0.462870\pi\) | |||||||
\(602\) | −1.26222e7 | −1.41952 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −106656. | −0.0118958 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.89040e6 | 0.979377 | 0.489688 | − | 0.871898i | \(-0.337111\pi\) | ||||
0.489688 | + | 0.871898i | \(0.337111\pi\) | |||||||
\(608\) | −1.97404e6 | −0.216569 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.14252e6 | 0.232178 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.20605e6 | 0.989514 | 0.494757 | − | 0.869031i | \(-0.335257\pi\) | ||||
0.494757 | + | 0.869031i | \(0.335257\pi\) | |||||||
\(614\) | 1.06142e7 | 1.13623 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.21760e7 | 2.35468 | ||||||||
\(617\) | 1.07622e7 | 1.13812 | 0.569061 | − | 0.822296i | \(-0.307307\pi\) | ||||
0.569061 | + | 0.822296i | \(0.307307\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.40448e7 | 1.47329 | 0.736644 | − | 0.676281i | \(-0.236409\pi\) | ||||
0.736644 | + | 0.676281i | \(0.236409\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.15078e7 | 1.19266 | ||||||||
\(623\) | 2.70475e7 | 2.79194 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.86931e6 | 0.700612 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.07495e6 | 0.614673 | ||||||||
\(629\) | 1.23581e7 | 1.24545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00120e7 | −1.00104 | −0.500518 | − | 0.865726i | \(-0.666857\pi\) | ||||
−0.500518 | + | 0.865726i | \(0.666857\pi\) | |||||||
\(632\) | 1.96018e7 | 1.95211 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.01387e7 | 1.00175 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.54161e6 | −0.736403 | ||||||||
\(638\) | −1.23968e7 | −1.20575 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.60720e6 | −0.923532 | −0.461766 | − | 0.887002i | \(-0.652784\pi\) | ||||
−0.461766 | + | 0.887002i | \(0.652784\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.21761e6 | 0.211523 | 0.105761 | − | 0.994392i | \(-0.466272\pi\) | ||||
0.105761 | + | 0.994392i | \(0.466272\pi\) | |||||||
\(644\) | −6.09624e6 | −0.579225 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.61064e6 | 0.340410 | ||||||||
\(647\) | 5.71481e6 | 0.536712 | 0.268356 | − | 0.963320i | \(-0.413520\pi\) | ||||
0.268356 | + | 0.963320i | \(0.413520\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.77200e6 | −0.258334 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.66705e6 | 0.245704 | ||||||||
\(653\) | 4.71603e6 | 0.432807 | 0.216403 | − | 0.976304i | \(-0.430567\pi\) | ||||
0.216403 | + | 0.976304i | \(0.430567\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.47778e6 | −0.496987 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.58164e6 | −0.862730 | ||||||||
\(659\) | −2.01496e7 | −1.80740 | −0.903698 | − | 0.428171i | \(-0.859158\pi\) | ||||
−0.903698 | + | 0.428171i | \(0.859158\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −564742. | −0.0502743 | −0.0251372 | − | 0.999684i | \(-0.508002\pi\) | ||||
−0.0251372 | + | 0.999684i | \(0.508002\pi\) | |||||||
\(662\) | −7.42290e6 | −0.658308 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.12394e7 | 0.989285 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.24956e7 | 1.08754 | ||||||||
\(668\) | 1.17066e6 | 0.101506 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.07236e7 | −0.919466 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.07198e7 | −0.912328 | −0.456164 | − | 0.889896i | \(-0.650777\pi\) | ||||
−0.456164 | + | 0.889896i | \(0.650777\pi\) | |||||||
\(674\) | −3.67863e6 | −0.311915 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.85072e6 | 0.324097 | ||||||||
\(677\) | 3.36926e6 | 0.282529 | 0.141264 | − | 0.989972i | \(-0.454883\pi\) | ||||
0.141264 | + | 0.989972i | \(0.454883\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.44144e7 | 1.19984 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.09994e6 | 0.666839 | ||||||||
\(683\) | −1.55817e7 | −1.27810 | −0.639049 | − | 0.769166i | \(-0.720672\pi\) | ||||
−0.639049 | + | 0.769166i | \(0.720672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.68530e7 | 1.36731 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.23570e6 | 0.502243 | ||||||||
\(689\) | 1.07126e6 | 0.0859699 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.73771e6 | 0.775821 | 0.387911 | − | 0.921697i | \(-0.373197\pi\) | ||||
0.387911 | + | 0.921697i | \(0.373197\pi\) | |||||||
\(692\) | 3.32002e6 | 0.263558 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.37072e6 | 0.344472 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.84224e7 | −1.43637 | ||||||||
\(698\) | −3.46588e6 | −0.269262 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.72451e7 | 1.32547 | 0.662735 | − | 0.748854i | \(-0.269396\pi\) | ||||
0.662735 | + | 0.748854i | \(0.269396\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.58571e6 | −0.273644 | ||||||||
\(704\) | −1.71241e7 | −1.30219 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.23462e7 | 0.932225 | ||||||||
\(707\) | 1.36364e7 | 1.02601 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.81083e7 | −1.35289 | −0.676443 | − | 0.736495i | \(-0.736480\pi\) | ||||
−0.676443 | + | 0.736495i | \(0.736480\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.37071e7 | −1.75259 | ||||||||
\(713\) | −8.16455e6 | −0.601462 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 343365. | 0.0250307 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.03777e6 | −0.364693 | ||||||||
\(719\) | 1.77044e7 | 1.27720 | 0.638600 | − | 0.769539i | \(-0.279514\pi\) | ||||
0.638600 | + | 0.769539i | \(0.279514\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.38184e7 | −2.42279 | ||||||||
\(722\) | 1.00258e7 | 0.715776 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 982344. | 0.0696494 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.80607e6 | −0.547768 | −0.273884 | − | 0.961763i | \(-0.588308\pi\) | ||||
−0.273884 | + | 0.961763i | \(0.588308\pi\) | |||||||
\(728\) | 9.91741e6 | 0.693537 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.09714e7 | 1.45156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.11490e7 | 1.45388 | 0.726941 | − | 0.686700i | \(-0.240941\pi\) | ||||
0.726941 | + | 0.686700i | \(0.240941\pi\) | |||||||
\(734\) | 1.18170e6 | 0.0809593 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.22944e6 | 0.628031 | ||||||||
\(737\) | −1.73555e7 | −1.17698 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.20256e6 | −0.619865 | −0.309933 | − | 0.950759i | \(-0.600307\pi\) | ||||
−0.309933 | + | 0.950759i | \(0.600307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.79082e6 | −0.319448 | ||||||||
\(743\) | 4.78756e6 | 0.318157 | 0.159079 | − | 0.987266i | \(-0.449148\pi\) | ||||
0.159079 | + | 0.987266i | \(0.449148\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.37396e7 | −0.903916 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.00486e7 | −0.656676 | ||||||||
\(749\) | −429709. | −0.0279878 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.03369e6 | 0.455075 | 0.227538 | − | 0.973769i | \(-0.426933\pi\) | ||||
0.227538 | + | 0.973769i | \(0.426933\pi\) | |||||||
\(752\) | 4.73359e6 | 0.305244 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.54400e6 | −0.355136 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.99807e7 | 1.26727 | 0.633637 | − | 0.773631i | \(-0.281561\pi\) | ||||
0.633637 | + | 0.773631i | \(0.281561\pi\) | |||||||
\(758\) | 6.81122e6 | 0.430578 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.15851e7 | −0.725165 | −0.362582 | − | 0.931952i | \(-0.618105\pi\) | ||||
−0.362582 | + | 0.931952i | \(0.618105\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 380302. | 0.0236492 | ||||||||
\(764\) | 5.84323e6 | 0.362176 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.07611e7 | −0.662650 | ||||||||
\(767\) | −1.23968e6 | −0.0760886 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.88308e7 | −1.14830 | −0.574148 | − | 0.818752i | \(-0.694667\pi\) | ||||
−0.574148 | + | 0.818752i | \(0.694667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.49252e6 | 0.392076 | ||||||||
\(773\) | 9.80638e6 | 0.590283 | 0.295141 | − | 0.955454i | \(-0.404633\pi\) | ||||
0.295141 | + | 0.955454i | \(0.404633\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.26342e7 | −0.753173 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.65514e6 | 0.334961 | ||||||||
\(779\) | 5.34525e6 | 0.315591 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.66320e7 | −0.975701 | ||||||||
\(782\) | −1.68812e7 | −0.987160 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.66621e7 | −0.968145 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.21012e7 | 1.84750 | 0.923749 | − | 0.382998i | \(-0.125108\pi\) | ||||
0.923749 | + | 0.382998i | \(0.125108\pi\) | |||||||
\(788\) | −9.75571e6 | −0.559685 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.33857e7 | −1.89723 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.79576e6 | −0.270816 | ||||||||
\(794\) | −6.99080e6 | −0.393528 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.75373e6 | 0.0981024 | ||||||||
\(797\) | −3.06076e7 | −1.70680 | −0.853400 | − | 0.521256i | \(-0.825464\pi\) | ||||
−0.853400 | + | 0.521256i | \(0.825464\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.59196e7 | 0.882198 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.11985e6 | 0.335974 | ||||||||
\(803\) | −1.35237e6 | −0.0740130 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.62240e6 | 0.196408 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.19524e7 | −0.644058 | ||||||||
\(809\) | −1.30208e7 | −0.699464 | −0.349732 | − | 0.936850i | \(-0.613727\pi\) | ||||
−0.349732 | + | 0.936850i | \(0.613727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.58466e7 | −1.37991 | −0.689956 | − | 0.723851i | \(-0.742370\pi\) | ||||
−0.689956 | + | 0.723851i | \(0.742370\pi\) | |||||||
\(812\) | −1.48761e7 | −0.791771 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.66320e7 | −0.879799 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.08483e6 | −0.318929 | ||||||||
\(818\) | 1.92940e7 | 1.00818 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.88575e7 | 0.976396 | 0.488198 | − | 0.872733i | \(-0.337654\pi\) | ||||
0.488198 | + | 0.872733i | \(0.337654\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.90126e7 | 0.978459 | 0.489230 | − | 0.872155i | \(-0.337278\pi\) | ||||
0.489230 | + | 0.872155i | \(0.337278\pi\) | |||||||
\(824\) | 2.96419e7 | 1.52085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.54400e6 | 0.282731 | ||||||||
\(827\) | −823839. | −0.0418869 | −0.0209435 | − | 0.999781i | \(-0.506667\pi\) | ||||
−0.0209435 | + | 0.999781i | \(0.506667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.60900e7 | −1.82390 | −0.911948 | − | 0.410305i | \(-0.865422\pi\) | ||||
−0.911948 | + | 0.410305i | \(0.865422\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.65813e6 | −0.383543 | ||||||||
\(833\) | −5.60367e7 | −2.79808 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.91559e6 | 0.144282 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.08238e6 | −0.151627 | ||||||||
\(839\) | 1.23692e7 | 0.606647 | 0.303324 | − | 0.952888i | \(-0.401904\pi\) | ||||
0.303324 | + | 0.952888i | \(0.401904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.98085e6 | 0.486606 | ||||||||
\(842\) | 4.63117e6 | 0.225118 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.01603e7 | −0.490965 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.04180e7 | −0.977923 | ||||||||
\(848\) | 2.36680e6 | 0.113024 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.67647e7 | 0.793544 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.97159e6 | −0.469237 | −0.234618 | − | 0.972088i | \(-0.575384\pi\) | ||||
−0.234618 | + | 0.972088i | \(0.575384\pi\) | |||||||
\(854\) | 2.14473e7 | 1.00630 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 376640. | 0.0175688 | ||||||||
\(857\) | 1.48619e7 | 0.691231 | 0.345616 | − | 0.938376i | \(-0.387670\pi\) | ||||
0.345616 | + | 0.938376i | \(0.387670\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.41452e7 | −0.654071 | −0.327036 | − | 0.945012i | \(-0.606050\pi\) | ||||
−0.327036 | + | 0.945012i | \(0.606050\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.24462e7 | −0.570519 | ||||||||
\(863\) | 1.72325e6 | 0.0787627 | 0.0393814 | − | 0.999224i | \(-0.487461\pi\) | ||||
0.0393814 | + | 0.999224i | \(0.487461\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.78911e6 | 0.0810668 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.71993e6 | 0.437889 | ||||||||
\(869\) | −5.00068e7 | −2.24636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.76160e6 | −0.346662 | ||||||||
\(872\) | −333335. | −0.0148453 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.89808e6 | 0.216894 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.53435e6 | −0.374689 | −0.187345 | − | 0.982294i | \(-0.559988\pi\) | ||||
−0.187345 | + | 0.982294i | \(0.559988\pi\) | |||||||
\(878\) | 1.38639e7 | 0.606945 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.09019e6 | 0.307764 | 0.153882 | − | 0.988089i | \(-0.450822\pi\) | ||||
0.153882 | + | 0.988089i | \(0.450822\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.54183e6 | −0.325518 | −0.162759 | − | 0.986666i | \(-0.552039\pi\) | ||||
−0.162759 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(884\) | −4.49387e6 | −0.193415 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 982960. | 0.0420680 | ||||||||
\(887\) | −4.11968e7 | −1.75815 | −0.879073 | − | 0.476687i | \(-0.841837\pi\) | ||||
−0.879073 | + | 0.476687i | \(0.841837\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.88584e7 | −1.64904 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.74956e6 | −0.410273 | ||||||||
\(893\) | −4.61907e6 | −0.193832 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.94767e6 | 0.205888 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.10588e7 | 0.457635 | ||||||||
\(899\) | −1.99232e7 | −0.822167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.95982e6 | 0.326656 | ||||||||
\(902\) | 2.47935e7 | 1.01466 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.92626e7 | 1.19095 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.99367e7 | −1.61196 | −0.805979 | − | 0.591945i | \(-0.798360\pi\) | ||||
−0.805979 | + | 0.591945i | \(0.798360\pi\) | |||||||
\(908\) | −4.26041e6 | −0.171489 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.30901e6 | −0.371627 | −0.185814 | − | 0.982585i | \(-0.559492\pi\) | ||||
−0.185814 | + | 0.982585i | \(0.559492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.86731e7 | −1.13841 | ||||||||
\(914\) | −1.29535e7 | −0.512887 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.93313e6 | −0.194260 | ||||||||
\(917\) | 6.07441e7 | 2.38551 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.88035e7 | 1.12501 | 0.562506 | − | 0.826793i | \(-0.309837\pi\) | ||||
0.562506 | + | 0.826793i | \(0.309837\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.15354e7 | 1.22172 | ||||||||
\(923\) | −7.43806e6 | −0.287379 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.29324e7 | −0.495624 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.25218e7 | 0.858485 | ||||||||
\(929\) | −2.03981e7 | −0.775444 | −0.387722 | − | 0.921776i | \(-0.626738\pi\) | ||||
−0.387722 | + | 0.921776i | \(0.626738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.62590e7 | 0.614780 | ||||||||
\(932\) | 8.85832e6 | 0.334050 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.45189e7 | −1.29476 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.91357e7 | 1.82830 | 0.914152 | − | 0.405371i | \(-0.132858\pi\) | ||||
0.914152 | + | 0.405371i | \(0.132858\pi\) | |||||||
\(938\) | 3.47109e7 | 1.28813 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.80960e7 | 1.40251 | 0.701254 | − | 0.712912i | \(-0.252624\pi\) | ||||
0.701254 | + | 0.712912i | \(0.252624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.49913e7 | −0.915186 | ||||||||
\(944\) | −2.73889e6 | −0.100033 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.82240e7 | −1.02539 | ||||||||
\(947\) | 1.45947e6 | 0.0528836 | 0.0264418 | − | 0.999650i | \(-0.491582\pi\) | ||||
0.0264418 | + | 0.999650i | \(0.491582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −604800. | −0.0217995 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.36897e7 | 2.63520 | ||||||||
\(953\) | 1.94841e7 | 0.694940 | 0.347470 | − | 0.937691i | \(-0.387041\pi\) | ||||
0.347470 | + | 0.937691i | \(0.387041\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.45780e6 | −0.0515884 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −938408. | −0.0330353 | ||||||||
\(959\) | 7.16198e7 | 2.51470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.56115e7 | −0.545300 | ||||||||
\(962\) | −7.43806e6 | −0.259132 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.34669e7 | −0.466740 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.65207e7 | −0.568149 | −0.284074 | − | 0.958802i | \(-0.591686\pi\) | ||||
−0.284074 | + | 0.958802i | \(0.591686\pi\) | |||||||
\(968\) | 1.78964e7 | 0.613871 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.02422e7 | −0.348615 | −0.174308 | − | 0.984691i | \(-0.555769\pi\) | ||||
−0.174308 | + | 0.984691i | \(0.555769\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.08617e7 | 1.72230 | ||||||||
\(974\) | −3.47883e6 | −0.117500 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.05956e7 | −0.356040 | ||||||||
\(977\) | 1.95090e7 | 0.653881 | 0.326941 | − | 0.945045i | \(-0.393982\pi\) | ||||
0.326941 | + | 0.945045i | \(0.393982\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.04800e7 | 2.01676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.44262e7 | −1.47015 | ||||||||
\(983\) | −1.91895e7 | −0.633403 | −0.316701 | − | 0.948525i | \(-0.602575\pi\) | ||||
−0.316701 | + | 0.948525i | \(0.602575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.11938e7 | −1.34940 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.30389e6 | 0.0424961 | ||||||||
\(989\) | 2.84491e7 | 0.924864 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.38361e7 | 1.74136 | 0.870682 | − | 0.491846i | \(-0.163678\pi\) | ||||
0.870682 | + | 0.491846i | \(0.163678\pi\) | |||||||
\(992\) | −1.47155e7 | −0.474785 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.32640e7 | 1.06785 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.25008e6 | 0.103551 | 0.0517757 | − | 0.998659i | \(-0.483512\pi\) | ||||
0.0517757 | + | 0.998659i | \(0.483512\pi\) | |||||||
\(998\) | −2.28227e7 | −0.725339 | ||||||||
\(999\) | 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 | 225.6.a.v.1.1 | 4 | ||
3.2 | odd | 2 | inner | 225.6.a.v.1.3 | 4 | ||
5.2 | odd | 4 | 45.6.b.d.19.1 | ✓ | 4 | ||
5.3 | odd | 4 | 45.6.b.d.19.3 | yes | 4 | ||
5.4 | even | 2 | inner | 225.6.a.v.1.4 | 4 | ||
15.2 | even | 4 | 45.6.b.d.19.4 | yes | 4 | ||
15.8 | even | 4 | 45.6.b.d.19.2 | yes | 4 | ||
15.14 | odd | 2 | inner | 225.6.a.v.1.2 | 4 | ||
20.3 | even | 4 | 720.6.f.k.289.1 | 4 | |||
20.7 | even | 4 | 720.6.f.k.289.2 | 4 | |||
60.23 | odd | 4 | 720.6.f.k.289.4 | 4 | |||
60.47 | odd | 4 | 720.6.f.k.289.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.6.b.d.19.1 | ✓ | 4 | 5.2 | odd | 4 | ||
45.6.b.d.19.2 | yes | 4 | 15.8 | even | 4 | ||
45.6.b.d.19.3 | yes | 4 | 5.3 | odd | 4 | ||
45.6.b.d.19.4 | yes | 4 | 15.2 | even | 4 | ||
225.6.a.v.1.1 | 4 | 1.1 | even | 1 | trivial | ||
225.6.a.v.1.2 | 4 | 15.14 | odd | 2 | inner | ||
225.6.a.v.1.3 | 4 | 3.2 | odd | 2 | inner | ||
225.6.a.v.1.4 | 4 | 5.4 | even | 2 | inner | ||
720.6.f.k.289.1 | 4 | 20.3 | even | 4 | |||
720.6.f.k.289.2 | 4 | 20.7 | even | 4 | |||
720.6.f.k.289.3 | 4 | 60.47 | odd | 4 | |||
720.6.f.k.289.4 | 4 | 60.23 | odd | 4 |