Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,5,Mod(8,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.8");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(0.930329667755\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.8 |
Dual form | 9.5.b.a.8.1 |
$q$-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 \(\left(\mathbb{Z}/9\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.24264i | 1.06066i | 0.847791 | + | 0.530330i | \(0.177932\pi\) | ||||
−0.847791 | + | 0.530330i | \(0.822068\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.125000 | ||||||||
\(5\) | − 29.6985i | − 1.18794i | −0.804487 | − | 0.593970i | \(-0.797560\pi\) | ||||
0.804487 | − | 0.593970i | \(-0.202440\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −28.0000 | −0.571429 | −0.285714 | − | 0.958315i | \(-0.592231\pi\) | ||||
−0.285714 | + | 0.958315i | \(0.592231\pi\) | |||||||
\(8\) | 59.3970i | 0.928078i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 126.000 | 1.26000 | ||||||||
\(11\) | 16.9706i | 0.140253i | 0.997538 | + | 0.0701263i | \(0.0223402\pi\) | ||||
−0.997538 | + | 0.0701263i | \(0.977660\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −112.000 | −0.662722 | −0.331361 | − | 0.943504i | \(-0.607508\pi\) | ||||
−0.331361 | + | 0.943504i | \(0.607508\pi\) | |||||||
\(14\) | − 118.794i | − 0.606092i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −284.000 | −1.10938 | ||||||||
\(17\) | − 89.0955i | − 0.308289i | −0.988048 | − | 0.154144i | \(-0.950738\pi\) | ||||
0.988048 | − | 0.154144i | \(-0.0492621\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 560.000 | 1.55125 | 0.775623 | − | 0.631196i | \(-0.217436\pi\) | ||||
0.775623 | + | 0.631196i | \(0.217436\pi\) | |||||||
\(20\) | 59.3970i | 0.148492i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −72.0000 | −0.148760 | ||||||||
\(23\) | 797.616i | 1.50778i | 0.657000 | + | 0.753891i | \(0.271825\pi\) | ||||
−0.657000 | + | 0.753891i | \(0.728175\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −257.000 | −0.411200 | ||||||||
\(26\) | − 475.176i | − 0.702923i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 56.0000 | 0.0714286 | ||||||||
\(29\) | − 988.535i | − 1.17543i | −0.809069 | − | 0.587714i | \(-0.800028\pi\) | ||||
0.809069 | − | 0.587714i | \(-0.199972\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −364.000 | −0.378772 | −0.189386 | − | 0.981903i | \(-0.560650\pi\) | ||||
−0.189386 | + | 0.981903i | \(0.560650\pi\) | |||||||
\(32\) | − 254.558i | − 0.248592i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 378.000 | 0.326990 | ||||||||
\(35\) | 831.558i | 0.678823i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −826.000 | −0.603360 | −0.301680 | − | 0.953409i | \(-0.597547\pi\) | ||||
−0.301680 | + | 0.953409i | \(0.597547\pi\) | |||||||
\(38\) | 2375.88i | 1.64535i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1764.00 | 1.10250 | ||||||||
\(41\) | − 1811.61i | − 1.07770i | −0.842403 | − | 0.538848i | \(-0.818860\pi\) | ||||
0.842403 | − | 0.538848i | \(-0.181140\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1736.00 | 0.938886 | 0.469443 | − | 0.882963i | \(-0.344455\pi\) | ||||
0.469443 | + | 0.882963i | \(0.344455\pi\) | |||||||
\(44\) | − 33.9411i | − 0.0175316i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3384.00 | −1.59924 | ||||||||
\(47\) | − 1306.73i | − 0.591550i | −0.955258 | − | 0.295775i | \(-0.904422\pi\) | ||||
0.955258 | − | 0.295775i | \(-0.0955778\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1617.00 | −0.673469 | ||||||||
\(50\) | − 1090.36i | − 0.436143i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 224.000 | 0.0828402 | ||||||||
\(53\) | 1794.64i | 0.638888i | 0.947605 | + | 0.319444i | \(0.103496\pi\) | ||||
−0.947605 | + | 0.319444i | \(0.896504\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 504.000 | 0.166612 | ||||||||
\(56\) | − 1663.12i | − 0.530330i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4194.00 | 1.24673 | ||||||||
\(59\) | 4514.17i | 1.29680i | 0.761299 | + | 0.648401i | \(0.224562\pi\) | ||||
−0.761299 | + | 0.648401i | \(0.775438\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2618.00 | 0.703574 | 0.351787 | − | 0.936080i | \(-0.385574\pi\) | ||||
0.351787 | + | 0.936080i | \(0.385574\pi\) | |||||||
\(62\) | − 1544.32i | − 0.401748i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3464.00 | −0.845703 | ||||||||
\(65\) | 3326.23i | 0.787273i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3784.00 | −0.842949 | −0.421475 | − | 0.906840i | \(-0.638487\pi\) | ||||
−0.421475 | + | 0.906840i | \(0.638487\pi\) | |||||||
\(68\) | 178.191i | 0.0385361i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3528.00 | −0.720000 | ||||||||
\(71\) | − 8604.08i | − 1.70682i | −0.521241 | − | 0.853410i | \(-0.674531\pi\) | ||||
0.521241 | − | 0.853410i | \(-0.325469\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6608.00 | 1.24001 | 0.620004 | − | 0.784599i | \(-0.287131\pi\) | ||||
0.620004 | + | 0.784599i | \(0.287131\pi\) | |||||||
\(74\) | − 3504.42i | − 0.639960i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1120.00 | −0.193906 | ||||||||
\(77\) | − 475.176i | − 0.0801443i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4276.00 | −0.685147 | −0.342573 | − | 0.939491i | \(-0.611299\pi\) | ||||
−0.342573 | + | 0.939491i | \(0.611299\pi\) | |||||||
\(80\) | 8434.37i | 1.31787i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7686.00 | 1.14307 | ||||||||
\(83\) | 118.794i | 0.0172440i | 0.999963 | + | 0.00862200i | \(0.00274450\pi\) | ||||
−0.999963 | + | 0.00862200i | \(0.997255\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2646.00 | −0.366228 | ||||||||
\(86\) | 7365.22i | 0.995839i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1008.00 | −0.130165 | ||||||||
\(89\) | 4365.68i | 0.551152i | 0.961279 | + | 0.275576i | \(0.0888686\pi\) | ||||
−0.961279 | + | 0.275576i | \(0.911131\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3136.00 | 0.378698 | ||||||||
\(92\) | − 1595.23i | − 0.188473i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5544.00 | 0.627433 | ||||||||
\(95\) | − 16631.2i | − 1.84279i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5824.00 | −0.618982 | −0.309491 | − | 0.950902i | \(-0.600159\pi\) | ||||
−0.309491 | + | 0.950902i | \(0.600159\pi\) | |||||||
\(98\) | − 6860.35i | − 0.714322i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 514.000 | 0.0514000 | ||||||||
\(101\) | 8048.29i | 0.788971i | 0.918902 | + | 0.394485i | \(0.129077\pi\) | ||||
−0.918902 | + | 0.394485i | \(0.870923\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14980.0 | −1.41201 | −0.706004 | − | 0.708208i | \(-0.749504\pi\) | ||||
−0.706004 | + | 0.708208i | \(0.749504\pi\) | |||||||
\(104\) | − 6652.46i | − 0.615057i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7614.00 | −0.677643 | ||||||||
\(107\) | 9775.04i | 0.853790i | 0.904301 | + | 0.426895i | \(0.140393\pi\) | ||||
−0.904301 | + | 0.426895i | \(0.859607\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10640.0 | 0.895548 | 0.447774 | − | 0.894147i | \(-0.352217\pi\) | ||||
0.447774 | + | 0.894147i | \(0.352217\pi\) | |||||||
\(110\) | 2138.29i | 0.176718i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7952.00 | 0.633929 | ||||||||
\(113\) | 2872.27i | 0.224941i | 0.993655 | + | 0.112470i | \(0.0358763\pi\) | ||||
−0.993655 | + | 0.112470i | \(0.964124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23688.0 | 1.79115 | ||||||||
\(116\) | 1977.07i | 0.146929i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19152.0 | −1.37547 | ||||||||
\(119\) | 2494.67i | 0.176165i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14353.0 | 0.980329 | ||||||||
\(122\) | 11107.2i | 0.746253i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 728.000 | 0.0473465 | ||||||||
\(125\) | − 10929.0i | − 0.699459i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19420.0 | −1.20404 | −0.602021 | − | 0.798480i | \(-0.705638\pi\) | ||||
−0.602021 | + | 0.798480i | \(0.705638\pi\) | |||||||
\(128\) | − 18769.4i | − 1.14560i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14112.0 | −0.835030 | ||||||||
\(131\) | 20195.0i | 1.17679i | 0.808572 | + | 0.588397i | \(0.200241\pi\) | ||||
−0.808572 | + | 0.588397i | \(0.799759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15680.0 | −0.886427 | ||||||||
\(134\) | − 16054.2i | − 0.894083i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5292.00 | 0.286116 | ||||||||
\(137\) | − 17331.2i | − 0.923394i | −0.887038 | − | 0.461697i | \(-0.847241\pi\) | ||||
0.887038 | − | 0.461697i | \(-0.152759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18536.0 | 0.959371 | 0.479685 | − | 0.877441i | \(-0.340751\pi\) | ||||
0.479685 | + | 0.877441i | \(0.340751\pi\) | |||||||
\(140\) | − 1663.12i | − 0.0848528i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 36504.0 | 1.81036 | ||||||||
\(143\) | − 1900.70i | − 0.0929485i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −29358.0 | −1.39634 | ||||||||
\(146\) | 28035.4i | 1.31523i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1652.00 | 0.0754200 | ||||||||
\(149\) | 3152.28i | 0.141988i | 0.997477 | + | 0.0709941i | \(0.0226172\pi\) | ||||
−0.997477 | + | 0.0709941i | \(0.977383\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7028.00 | 0.308232 | 0.154116 | − | 0.988053i | \(-0.450747\pi\) | ||||
0.154116 | + | 0.988053i | \(0.450747\pi\) | |||||||
\(152\) | 33262.3i | 1.43968i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2016.00 | 0.0850059 | ||||||||
\(155\) | 10810.2i | 0.449958i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5530.00 | −0.224350 | −0.112175 | − | 0.993688i | \(-0.535782\pi\) | ||||
−0.112175 | + | 0.993688i | \(0.535782\pi\) | |||||||
\(158\) | − 18141.5i | − 0.726708i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7560.00 | −0.295312 | ||||||||
\(161\) | − 22333.3i | − 0.861589i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10856.0 | 0.408596 | 0.204298 | − | 0.978909i | \(-0.434509\pi\) | ||||
0.204298 | + | 0.978909i | \(0.434509\pi\) | |||||||
\(164\) | 3623.22i | 0.134712i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −504.000 | −0.0182900 | ||||||||
\(167\) | − 29698.5i | − 1.06488i | −0.846467 | − | 0.532441i | \(-0.821275\pi\) | ||||
0.846467 | − | 0.532441i | \(-0.178725\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16017.0 | −0.560800 | ||||||||
\(170\) | − 11226.0i | − 0.388444i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3472.00 | −0.117361 | ||||||||
\(173\) | − 27589.9i | − 0.921845i | −0.887440 | − | 0.460922i | \(-0.847519\pi\) | ||||
0.887440 | − | 0.460922i | \(-0.152481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7196.00 | 0.234971 | ||||||||
\(176\) | − 4819.64i | − 0.155593i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −18522.0 | −0.584585 | ||||||||
\(179\) | 54781.0i | 1.70971i | 0.518863 | + | 0.854857i | \(0.326356\pi\) | ||||
−0.518863 | + | 0.854857i | \(0.673644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18704.0 | 0.570923 | 0.285461 | − | 0.958390i | \(-0.407853\pi\) | ||||
0.285461 | + | 0.958390i | \(0.407853\pi\) | |||||||
\(182\) | 13304.9i | 0.401670i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −47376.0 | −1.39934 | ||||||||
\(185\) | 24530.9i | 0.716755i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1512.00 | 0.0432383 | ||||||||
\(188\) | 2613.47i | 0.0739437i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 70560.0 | 1.95457 | ||||||||
\(191\) | 8519.22i | 0.233525i | 0.993160 | + | 0.116762i | \(0.0372516\pi\) | ||||
−0.993160 | + | 0.116762i | \(0.962748\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 48398.0 | 1.29931 | 0.649655 | − | 0.760229i | \(-0.274913\pi\) | ||||
0.649655 | + | 0.760229i | \(0.274913\pi\) | |||||||
\(194\) | − 24709.1i | − 0.656529i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3234.00 | 0.0841837 | ||||||||
\(197\) | 10016.9i | 0.258107i | 0.991638 | + | 0.129054i | \(0.0411939\pi\) | ||||
−0.991638 | + | 0.129054i | \(0.958806\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13300.0 | −0.335850 | −0.167925 | − | 0.985800i | \(-0.553707\pi\) | ||||
−0.167925 | + | 0.985800i | \(0.553707\pi\) | |||||||
\(200\) | − 15265.0i | − 0.381626i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −34146.0 | −0.836830 | ||||||||
\(203\) | 27679.0i | 0.671673i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −53802.0 | −1.28024 | ||||||||
\(206\) | − 63554.8i | − 1.49766i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 31808.0 | 0.735207 | ||||||||
\(209\) | 9503.52i | 0.217566i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −36904.0 | −0.828912 | −0.414456 | − | 0.910069i | \(-0.636028\pi\) | ||||
−0.414456 | + | 0.910069i | \(0.636028\pi\) | |||||||
\(212\) | − 3589.27i | − 0.0798610i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −41472.0 | −0.905581 | ||||||||
\(215\) | − 51556.6i | − 1.11534i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10192.0 | 0.216441 | ||||||||
\(218\) | 45141.7i | 0.949872i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1008.00 | −0.0208264 | ||||||||
\(221\) | 9978.69i | 0.204310i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 51380.0 | 1.03320 | 0.516600 | − | 0.856227i | \(-0.327197\pi\) | ||||
0.516600 | + | 0.856227i | \(0.327197\pi\) | |||||||
\(224\) | 7127.64i | 0.142053i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12186.0 | −0.238586 | ||||||||
\(227\) | − 90402.2i | − 1.75439i | −0.480130 | − | 0.877197i | \(-0.659411\pi\) | ||||
0.480130 | − | 0.877197i | \(-0.340589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 78512.0 | 1.49715 | 0.748575 | − | 0.663051i | \(-0.230739\pi\) | ||||
0.748575 | + | 0.663051i | \(0.230739\pi\) | |||||||
\(230\) | 100500.i | 1.89980i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 58716.0 | 1.09089 | ||||||||
\(233\) | 52451.8i | 0.966158i | 0.875577 | + | 0.483079i | \(0.160482\pi\) | ||||
−0.875577 | + | 0.483079i | \(0.839518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −38808.0 | −0.702725 | ||||||||
\(236\) | − 9028.34i | − 0.162100i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10584.0 | −0.186851 | ||||||||
\(239\) | − 22265.4i | − 0.389793i | −0.980824 | − | 0.194897i | \(-0.937563\pi\) | ||||
0.980824 | − | 0.194897i | \(-0.0624371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −53200.0 | −0.915962 | −0.457981 | − | 0.888962i | \(-0.651427\pi\) | ||||
−0.457981 | + | 0.888962i | \(0.651427\pi\) | |||||||
\(242\) | 60894.6i | 1.03980i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5236.00 | −0.0879468 | ||||||||
\(245\) | 48022.4i | 0.800041i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −62720.0 | −1.02805 | ||||||||
\(248\) | − 21620.5i | − 0.351530i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 46368.0 | 0.741888 | ||||||||
\(251\) | − 83037.0i | − 1.31803i | −0.752131 | − | 0.659013i | \(-0.770974\pi\) | ||||
0.752131 | − | 0.659013i | \(-0.229026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13536.0 | −0.211470 | ||||||||
\(254\) | − 82392.1i | − 1.27708i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 24208.0 | 0.369385 | ||||||||
\(257\) | − 84670.4i | − 1.28193i | −0.767569 | − | 0.640966i | \(-0.778534\pi\) | ||||
0.767569 | − | 0.640966i | \(-0.221466\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23128.0 | 0.344777 | ||||||||
\(260\) | − 6652.46i | − 0.0984092i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −85680.0 | −1.24818 | ||||||||
\(263\) | 110343.i | 1.59526i | 0.603146 | + | 0.797630i | \(0.293913\pi\) | ||||
−0.603146 | + | 0.797630i | \(0.706087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 53298.0 | 0.758960 | ||||||||
\(266\) | − 66524.6i | − 0.940197i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7568.00 | 0.105369 | ||||||||
\(269\) | 27530.5i | 0.380460i | 0.981740 | + | 0.190230i | \(0.0609234\pi\) | ||||
−0.981740 | + | 0.190230i | \(0.939077\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −73276.0 | −0.997753 | −0.498877 | − | 0.866673i | \(-0.666254\pi\) | ||||
−0.498877 | + | 0.866673i | \(0.666254\pi\) | |||||||
\(272\) | 25303.1i | 0.342008i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 73530.0 | 0.979408 | ||||||||
\(275\) | − 4361.43i | − 0.0576719i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 46736.0 | 0.609105 | 0.304552 | − | 0.952496i | \(-0.401493\pi\) | ||||
0.304552 | + | 0.952496i | \(0.401493\pi\) | |||||||
\(278\) | 78641.6i | 1.01757i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −49392.0 | −0.630000 | ||||||||
\(281\) | 112774.i | 1.42822i | 0.700034 | + | 0.714110i | \(0.253168\pi\) | ||||
−0.700034 | + | 0.714110i | \(0.746832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24304.0 | −0.303462 | −0.151731 | − | 0.988422i | \(-0.548485\pi\) | ||||
−0.151731 | + | 0.988422i | \(0.548485\pi\) | |||||||
\(284\) | 17208.2i | 0.213352i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8064.00 | 0.0985867 | ||||||||
\(287\) | 50725.0i | 0.615826i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 75583.0 | 0.904958 | ||||||||
\(290\) | − 124555.i | − 1.48104i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13216.0 | −0.155001 | ||||||||
\(293\) | − 9473.82i | − 0.110354i | −0.998477 | − | 0.0551772i | \(-0.982428\pi\) | ||||
0.998477 | − | 0.0551772i | \(-0.0175724\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 134064. | 1.54052 | ||||||||
\(296\) | − 49061.9i | − 0.559965i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13374.0 | −0.150601 | ||||||||
\(299\) | − 89333.0i | − 0.999240i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −48608.0 | −0.536506 | ||||||||
\(302\) | 29817.3i | 0.326930i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −159040. | −1.72091 | ||||||||
\(305\) | − 77750.6i | − 0.835804i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19208.0 | 0.203801 | 0.101900 | − | 0.994795i | \(-0.467508\pi\) | ||||
0.101900 | + | 0.994795i | \(0.467508\pi\) | |||||||
\(308\) | 950.352i | 0.0100180i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −45864.0 | −0.477253 | ||||||||
\(311\) | 78641.6i | 0.813077i | 0.913634 | + | 0.406538i | \(0.133264\pi\) | ||||
−0.913634 | + | 0.406538i | \(0.866736\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −127918. | −1.30570 | −0.652849 | − | 0.757488i | \(-0.726427\pi\) | ||||
−0.652849 | + | 0.757488i | \(0.726427\pi\) | |||||||
\(314\) | − 23461.8i | − 0.237959i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8552.00 | 0.0856433 | ||||||||
\(317\) | − 65875.5i | − 0.655549i | −0.944756 | − | 0.327775i | \(-0.893701\pi\) | ||||
0.944756 | − | 0.327775i | \(-0.106299\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16776.0 | 0.164857 | ||||||||
\(320\) | 102876.i | 1.00464i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 94752.0 | 0.913854 | ||||||||
\(323\) | − 49893.5i | − 0.478232i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28784.0 | 0.272511 | ||||||||
\(326\) | 46058.1i | 0.433382i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 107604. | 1.00019 | ||||||||
\(329\) | 36588.5i | 0.338028i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15848.0 | 0.144650 | 0.0723250 | − | 0.997381i | \(-0.476958\pi\) | ||||
0.0723250 | + | 0.997381i | \(0.476958\pi\) | |||||||
\(332\) | − 237.588i | − 0.00215550i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 126000. | 1.12948 | ||||||||
\(335\) | 112379.i | 1.00137i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −127120. | −1.11932 | −0.559660 | − | 0.828722i | \(-0.689068\pi\) | ||||
−0.559660 | + | 0.828722i | \(0.689068\pi\) | |||||||
\(338\) | − 67954.4i | − 0.594818i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5292.00 | 0.0457785 | ||||||||
\(341\) | − 6177.28i | − 0.0531238i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 112504. | 0.956268 | ||||||||
\(344\) | 103113.i | 0.871359i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 117054. | 0.977764 | ||||||||
\(347\) | 21875.1i | 0.181673i | 0.995866 | + | 0.0908365i | \(0.0289541\pi\) | ||||
−0.995866 | + | 0.0908365i | \(0.971046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −200998. | −1.65022 | −0.825108 | − | 0.564975i | \(-0.808886\pi\) | ||||
−0.825108 | + | 0.564975i | \(0.808886\pi\) | |||||||
\(350\) | 30530.0i | 0.249225i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4320.00 | 0.0348657 | ||||||||
\(353\) | − 241775.i | − 1.94027i | −0.242561 | − | 0.970136i | \(-0.577988\pi\) | ||||
0.242561 | − | 0.970136i | \(-0.422012\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −255528. | −2.02760 | ||||||||
\(356\) | − 8731.35i | − 0.0688940i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −232416. | −1.81343 | ||||||||
\(359\) | 108187.i | 0.839436i | 0.907655 | + | 0.419718i | \(0.137871\pi\) | ||||
−0.907655 | + | 0.419718i | \(0.862129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 183279. | 1.40637 | ||||||||
\(362\) | 79354.4i | 0.605555i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6272.00 | −0.0473373 | ||||||||
\(365\) | − 196248.i | − 1.47305i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 221732. | 1.64625 | 0.823126 | − | 0.567859i | \(-0.192228\pi\) | ||||
0.823126 | + | 0.567859i | \(0.192228\pi\) | |||||||
\(368\) | − 226523.i | − 1.67270i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −104076. | −0.760234 | ||||||||
\(371\) | − 50249.8i | − 0.365079i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 87674.0 | 0.630163 | 0.315082 | − | 0.949065i | \(-0.397968\pi\) | ||||
0.315082 | + | 0.949065i | \(0.397968\pi\) | |||||||
\(374\) | 6414.87i | 0.0458611i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 77616.0 | 0.549004 | ||||||||
\(377\) | 110716.i | 0.778982i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −40768.0 | −0.283819 | −0.141909 | − | 0.989880i | \(-0.545324\pi\) | ||||
−0.141909 | + | 0.989880i | \(0.545324\pi\) | |||||||
\(380\) | 33262.3i | 0.230348i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −36144.0 | −0.247691 | ||||||||
\(383\) | 75077.8i | 0.511816i | 0.966701 | + | 0.255908i | \(0.0823744\pi\) | ||||
−0.966701 | + | 0.255908i | \(0.917626\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14112.0 | −0.0952066 | ||||||||
\(386\) | 205335.i | 1.37813i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11648.0 | 0.0773727 | ||||||||
\(389\) | 123236.i | 0.814401i | 0.913339 | + | 0.407201i | \(0.133495\pi\) | ||||
−0.913339 | + | 0.407201i | \(0.866505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 71064.0 | 0.464832 | ||||||||
\(392\) | − 96044.9i | − 0.625032i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −42498.0 | −0.273764 | ||||||||
\(395\) | 126991.i | 0.813913i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8134.00 | −0.0516087 | −0.0258044 | − | 0.999667i | \(-0.508215\pi\) | ||||
−0.0258044 | + | 0.999667i | \(0.508215\pi\) | |||||||
\(398\) | − 56427.1i | − 0.356223i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 72988.0 | 0.456175 | ||||||||
\(401\) | 133639.i | 0.831083i | 0.909574 | + | 0.415541i | \(0.136408\pi\) | ||||
−0.909574 | + | 0.415541i | \(0.863592\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 40768.0 | 0.251021 | ||||||||
\(404\) | − 16096.6i | − 0.0986213i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −117432. | −0.712417 | ||||||||
\(407\) | − 14017.7i | − 0.0846228i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35168.0 | 0.210233 | 0.105117 | − | 0.994460i | \(-0.466478\pi\) | ||||
0.105117 | + | 0.994460i | \(0.466478\pi\) | |||||||
\(410\) | − 228263.i | − 1.35790i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 29960.0 | 0.176501 | ||||||||
\(413\) | − 126397.i | − 0.741030i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3528.00 | 0.0204848 | ||||||||
\(416\) | 28510.5i | 0.164748i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −40320.0 | −0.230764 | ||||||||
\(419\) | − 157640.i | − 0.897919i | −0.893552 | − | 0.448959i | \(-0.851795\pi\) | ||||
0.893552 | − | 0.448959i | \(-0.148205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18800.0 | 0.106070 | 0.0530351 | − | 0.998593i | \(-0.483110\pi\) | ||||
0.0530351 | + | 0.998593i | \(0.483110\pi\) | |||||||
\(422\) | − 156570.i | − 0.879194i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −106596. | −0.592938 | ||||||||
\(425\) | 22897.5i | 0.126768i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −73304.0 | −0.402042 | ||||||||
\(428\) | − 19550.1i | − 0.106724i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 218736. | 1.18300 | ||||||||
\(431\) | − 72243.7i | − 0.388907i | −0.980912 | − | 0.194453i | \(-0.937707\pi\) | ||||
0.980912 | − | 0.194453i | \(-0.0622933\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −351106. | −1.87268 | −0.936338 | − | 0.351101i | \(-0.885807\pi\) | ||||
−0.936338 | + | 0.351101i | \(0.885807\pi\) | |||||||
\(434\) | 43241.0i | 0.229571i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21280.0 | −0.111943 | ||||||||
\(437\) | 446665.i | 2.33894i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −60508.0 | −0.313967 | −0.156983 | − | 0.987601i | \(-0.550177\pi\) | ||||
−0.156983 | + | 0.987601i | \(0.550177\pi\) | |||||||
\(440\) | 29936.1i | 0.154628i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −42336.0 | −0.216703 | ||||||||
\(443\) | − 57105.9i | − 0.290987i | −0.989359 | − | 0.145494i | \(-0.953523\pi\) | ||||
0.989359 | − | 0.145494i | \(-0.0464770\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 129654. | 0.654736 | ||||||||
\(446\) | 217987.i | 1.09587i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 96992.0 | 0.483259 | ||||||||
\(449\) | − 210482.i | − 1.04405i | −0.852930 | − | 0.522025i | \(-0.825177\pi\) | ||||
0.852930 | − | 0.522025i | \(-0.174823\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30744.0 | 0.151150 | ||||||||
\(452\) | − 5744.54i | − 0.0281176i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 383544. | 1.86082 | ||||||||
\(455\) | − 93134.4i | − 0.449871i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 324800. | 1.55519 | 0.777595 | − | 0.628765i | \(-0.216439\pi\) | ||||
0.777595 | + | 0.628765i | \(0.216439\pi\) | |||||||
\(458\) | 333098.i | 1.58797i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −47376.0 | −0.223894 | ||||||||
\(461\) | − 165331.i | − 0.777954i | −0.921248 | − | 0.388977i | \(-0.872829\pi\) | ||||
0.921248 | − | 0.388977i | \(-0.127171\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −117220. | −0.546814 | −0.273407 | − | 0.961898i | \(-0.588151\pi\) | ||||
−0.273407 | + | 0.961898i | \(0.588151\pi\) | |||||||
\(464\) | 280744.i | 1.30399i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −222534. | −1.02477 | ||||||||
\(467\) | − 170707.i | − 0.782740i | −0.920233 | − | 0.391370i | \(-0.872001\pi\) | ||||
0.920233 | − | 0.391370i | \(-0.127999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 105952. | 0.481685 | ||||||||
\(470\) | − 164648.i | − 0.745353i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −268128. | −1.20353 | ||||||||
\(473\) | 29460.9i | 0.131681i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −143920. | −0.637873 | ||||||||
\(476\) | − 4989.35i | − 0.0220206i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 94464.0 | 0.413438 | ||||||||
\(479\) | − 99668.1i | − 0.434395i | −0.976128 | − | 0.217198i | \(-0.930308\pi\) | ||||
0.976128 | − | 0.217198i | \(-0.0696916\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 92512.0 | 0.399860 | ||||||||
\(482\) | − 225708.i | − 0.971525i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −28706.0 | −0.122541 | ||||||||
\(485\) | 172964.i | 0.735313i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −416500. | −1.75613 | −0.878066 | − | 0.478540i | \(-0.841166\pi\) | ||||
−0.878066 | + | 0.478540i | \(0.841166\pi\) | |||||||
\(488\) | 155501.i | 0.652972i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −203742. | −0.848571 | ||||||||
\(491\) | − 355024.i | − 1.47263i | −0.676637 | − | 0.736317i | \(-0.736563\pi\) | ||||
0.676637 | − | 0.736317i | \(-0.263437\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −88074.0 | −0.362371 | ||||||||
\(494\) | − 266098.i | − 1.09041i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 103376. | 0.420200 | ||||||||
\(497\) | 240914.i | 0.975325i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 135968. | 0.546054 | 0.273027 | − | 0.962006i | \(-0.411975\pi\) | ||||
0.273027 | + | 0.962006i | \(0.411975\pi\) | |||||||
\(500\) | 21858.1i | 0.0874323i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 352296. | 1.39798 | ||||||||
\(503\) | 170707.i | 0.674707i | 0.941378 | + | 0.337353i | \(0.109532\pi\) | ||||
−0.941378 | + | 0.337353i | \(0.890468\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 239022. | 0.937249 | ||||||||
\(506\) | − 57428.4i | − 0.224298i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 38840.0 | 0.150505 | ||||||||
\(509\) | − 193367.i | − 0.746357i | −0.927760 | − | 0.373178i | \(-0.878268\pi\) | ||||
0.927760 | − | 0.373178i | \(-0.121732\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −185024. | −0.708576 | ||||||||
\(512\) | − 197605.i | − 0.753804i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 359226. | 1.35970 | ||||||||
\(515\) | 444883.i | 1.67738i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22176.0 | 0.0829664 | ||||||||
\(518\) | 98123.8i | 0.365691i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −197568. | −0.730651 | ||||||||
\(521\) | 391931.i | 1.44389i | 0.691951 | + | 0.721945i | \(0.256752\pi\) | ||||
−0.691951 | + | 0.721945i | \(0.743248\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 410816. | 1.50191 | 0.750955 | − | 0.660353i | \(-0.229593\pi\) | ||||
0.750955 | + | 0.660353i | \(0.229593\pi\) | |||||||
\(524\) | − 40389.9i | − 0.147099i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −468144. | −1.69203 | ||||||||
\(527\) | 32430.7i | 0.116771i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −356351. | −1.27341 | ||||||||
\(530\) | 226124.i | 0.804999i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 31360.0 | 0.110803 | ||||||||
\(533\) | 202900.i | 0.714213i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 290304. | 1.01425 | ||||||||
\(536\) | − 224758.i | − 0.782323i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −116802. | −0.403539 | ||||||||
\(539\) | − 27441.4i | − 0.0944558i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −57616.0 | −0.196856 | −0.0984280 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984280 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(542\) | − 310884.i | − 1.05828i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −22680.0 | −0.0766382 | ||||||||
\(545\) | − 315992.i | − 1.06386i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 78920.0 | 0.263762 | 0.131881 | − | 0.991266i | \(-0.457898\pi\) | ||||
0.131881 | + | 0.991266i | \(0.457898\pi\) | |||||||
\(548\) | 34662.4i | 0.115424i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18504.0 | 0.0611702 | ||||||||
\(551\) | − 553580.i | − 1.82338i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 119728. | 0.391512 | ||||||||
\(554\) | 198284.i | 0.646053i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −37072.0 | −0.119921 | ||||||||
\(557\) | − 178025.i | − 0.573815i | −0.957958 | − | 0.286907i | \(-0.907373\pi\) | ||||
0.957958 | − | 0.286907i | \(-0.0926272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −194432. | −0.622220 | ||||||||
\(560\) | − 236162.i | − 0.753069i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −478458. | −1.51486 | ||||||||
\(563\) | 431816.i | 1.36233i | 0.732131 | + | 0.681164i | \(0.238526\pi\) | ||||
−0.732131 | + | 0.681164i | \(0.761474\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 85302.0 | 0.267216 | ||||||||
\(566\) | − 103113.i | − 0.321870i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 511056. | 1.58406 | ||||||||
\(569\) | 65756.7i | 0.203103i | 0.994830 | + | 0.101551i | \(0.0323806\pi\) | ||||
−0.994830 | + | 0.101551i | \(0.967619\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 111632. | 0.342386 | 0.171193 | − | 0.985237i | \(-0.445238\pi\) | ||||
0.171193 | + | 0.985237i | \(0.445238\pi\) | |||||||
\(572\) | 3801.41i | 0.0116186i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −215208. | −0.653183 | ||||||||
\(575\) | − 204987.i | − 0.620000i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −164878. | −0.495235 | −0.247617 | − | 0.968858i | \(-0.579648\pi\) | ||||
−0.247617 | + | 0.968858i | \(0.579648\pi\) | |||||||
\(578\) | 320672.i | 0.959853i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 58716.0 | 0.174542 | ||||||||
\(581\) | − 3326.23i | − 0.00985372i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30456.0 | −0.0896057 | ||||||||
\(584\) | 392495.i | 1.15082i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 40194.0 | 0.117049 | ||||||||
\(587\) | 568548.i | 1.65003i | 0.565114 | + | 0.825013i | \(0.308832\pi\) | ||||
−0.565114 | + | 0.825013i | \(0.691168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −203840. | −0.587569 | ||||||||
\(590\) | 568785.i | 1.63397i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 234584. | 0.669353 | ||||||||
\(593\) | − 580279.i | − 1.65016i | −0.565013 | − | 0.825082i | \(-0.691129\pi\) | ||||
0.565013 | − | 0.825082i | \(-0.308871\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 74088.0 | 0.209273 | ||||||||
\(596\) | − 6304.56i | − 0.0177485i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 379008. | 1.05985 | ||||||||
\(599\) | − 5719.08i | − 0.0159394i | −0.999968 | − | 0.00796971i | \(-0.997463\pi\) | ||||
0.999968 | − | 0.00796971i | \(-0.00253686\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 233198. | 0.645618 | 0.322809 | − | 0.946464i | \(-0.395373\pi\) | ||||
0.322809 | + | 0.946464i | \(0.395373\pi\) | |||||||
\(602\) | − 206226.i | − 0.569051i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14056.0 | −0.0385290 | ||||||||
\(605\) | − 426262.i | − 1.16457i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 154868. | 0.420324 | 0.210162 | − | 0.977667i | \(-0.432601\pi\) | ||||
0.210162 | + | 0.977667i | \(0.432601\pi\) | |||||||
\(608\) | − 142553.i | − 0.385628i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 329868. | 0.886504 | ||||||||
\(611\) | 146354.i | 0.392033i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −333862. | −0.888477 | −0.444238 | − | 0.895909i | \(-0.646526\pi\) | ||||
−0.444238 | + | 0.895909i | \(0.646526\pi\) | |||||||
\(614\) | 81492.6i | 0.216163i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28224.0 | 0.0743802 | ||||||||
\(617\) | − 19325.2i | − 0.0507638i | −0.999678 | − | 0.0253819i | \(-0.991920\pi\) | ||||
0.999678 | − | 0.0253819i | \(-0.00808018\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −473536. | −1.23587 | −0.617933 | − | 0.786230i | \(-0.712030\pi\) | ||||
−0.617933 | + | 0.786230i | \(0.712030\pi\) | |||||||
\(620\) | − 21620.5i | − 0.0562448i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −333648. | −0.862398 | ||||||||
\(623\) | − 122239.i | − 0.314944i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −485201. | −1.24211 | ||||||||
\(626\) | − 542710.i | − 1.38490i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11060.0 | 0.0280437 | ||||||||
\(629\) | 73592.8i | 0.186009i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −384820. | −0.966493 | −0.483247 | − | 0.875484i | \(-0.660543\pi\) | ||||
−0.483247 | + | 0.875484i | \(0.660543\pi\) | |||||||
\(632\) | − 253981.i | − 0.635869i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 279486. | 0.695315 | ||||||||
\(635\) | 576745.i | 1.43033i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 181104. | 0.446323 | ||||||||
\(638\) | 71174.5i | 0.174857i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −557424. | −1.36090 | ||||||||
\(641\) | − 145832.i | − 0.354926i | −0.984127 | − | 0.177463i | \(-0.943211\pi\) | ||||
0.984127 | − | 0.177463i | \(-0.0567890\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 528584. | 1.27847 | 0.639237 | − | 0.769010i | \(-0.279250\pi\) | ||||
0.639237 | + | 0.769010i | \(0.279250\pi\) | |||||||
\(644\) | 44666.5i | 0.107699i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 211680. | 0.507242 | ||||||||
\(647\) | − 176409.i | − 0.421417i | −0.977549 | − | 0.210709i | \(-0.932423\pi\) | ||||
0.977549 | − | 0.210709i | \(-0.0675771\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −76608.0 | −0.181880 | ||||||||
\(650\) | 122120.i | 0.289042i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21712.0 | −0.0510746 | ||||||||
\(653\) | − 403250.i | − 0.945689i | −0.881146 | − | 0.472844i | \(-0.843227\pi\) | ||||
0.881146 | − | 0.472844i | \(-0.156773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 599760. | 1.39796 | ||||||||
\(656\) | 514497.i | 1.19557i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −155232. | −0.358533 | ||||||||
\(659\) | 137020.i | 0.315511i | 0.987478 | + | 0.157755i | \(0.0504257\pi\) | ||||
−0.987478 | + | 0.157755i | \(0.949574\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 286790. | 0.656389 | 0.328194 | − | 0.944610i | \(-0.393560\pi\) | ||||
0.328194 | + | 0.944610i | \(0.393560\pi\) | |||||||
\(662\) | 67237.4i | 0.153425i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7056.00 | −0.0160038 | ||||||||
\(665\) | 465672.i | 1.05302i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 788472. | 1.77229 | ||||||||
\(668\) | 59397.0i | 0.133110i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −476784. | −1.06212 | ||||||||
\(671\) | 44428.9i | 0.0986781i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 121058. | 0.267278 | 0.133639 | − | 0.991030i | \(-0.457334\pi\) | ||||
0.133639 | + | 0.991030i | \(0.457334\pi\) | |||||||
\(674\) | − 539324.i | − 1.18722i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 32034.0 | 0.0701000 | ||||||||
\(677\) | 377260.i | 0.823120i | 0.911383 | + | 0.411560i | \(0.135016\pi\) | ||||
−0.911383 | + | 0.411560i | \(0.864984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 163072. | 0.353704 | ||||||||
\(680\) | − 157164.i | − 0.339888i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26208.0 | 0.0563463 | ||||||||
\(683\) | 335457.i | 0.719110i | 0.933124 | + | 0.359555i | \(0.117072\pi\) | ||||
−0.933124 | + | 0.359555i | \(0.882928\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −514710. | −1.09694 | ||||||||
\(686\) | 477314.i | 1.01428i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −493024. | −1.04158 | ||||||||
\(689\) | − 200999.i | − 0.423405i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −578872. | −1.21235 | −0.606173 | − | 0.795333i | \(-0.707296\pi\) | ||||
−0.606173 | + | 0.795333i | \(0.707296\pi\) | |||||||
\(692\) | 55179.8i | 0.115231i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −92808.0 | −0.192693 | ||||||||
\(695\) | − 550491.i | − 1.13967i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −161406. | −0.332242 | ||||||||
\(698\) | − 852762.i | − 1.75032i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14392.0 | −0.0293714 | ||||||||
\(701\) | 654279.i | 1.33146i | 0.746194 | + | 0.665728i | \(0.231879\pi\) | ||||
−0.746194 | + | 0.665728i | \(0.768121\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −462560. | −0.935960 | ||||||||
\(704\) | − 58786.0i | − 0.118612i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.02577e6 | 2.05797 | ||||||||
\(707\) | − 225352.i | − 0.450840i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 779408. | 1.55050 | 0.775251 | − | 0.631653i | \(-0.217623\pi\) | ||||
0.775251 | + | 0.631653i | \(0.217623\pi\) | |||||||
\(710\) | − 1.08411e6i | − 2.15059i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −259308. | −0.511512 | ||||||||
\(713\) | − 290332.i | − 0.571106i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −56448.0 | −0.110417 | ||||||||
\(716\) | − 109562.i | − 0.213714i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −459000. | −0.890356 | ||||||||
\(719\) | − 147898.i | − 0.286092i | −0.989716 | − | 0.143046i | \(-0.954310\pi\) | ||||
0.989716 | − | 0.143046i | \(-0.0456897\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 419440. | 0.806862 | ||||||||
\(722\) | 777587.i | 1.49168i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −37408.0 | −0.0713653 | ||||||||
\(725\) | 254054.i | 0.483336i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −713188. | −1.34938 | −0.674691 | − | 0.738100i | \(-0.735723\pi\) | ||||
−0.674691 | + | 0.738100i | \(0.735723\pi\) | |||||||
\(728\) | 186269.i | 0.351461i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 832608. | 1.56241 | ||||||||
\(731\) | − 154670.i | − 0.289448i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −826672. | −1.53860 | −0.769299 | − | 0.638889i | \(-0.779394\pi\) | ||||
−0.769299 | + | 0.638889i | \(0.779394\pi\) | |||||||
\(734\) | 940729.i | 1.74611i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 203040. | 0.374823 | ||||||||
\(737\) | − 64216.6i | − 0.118226i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 703280. | 1.28777 | 0.643887 | − | 0.765121i | \(-0.277321\pi\) | ||||
0.643887 | + | 0.765121i | \(0.277321\pi\) | |||||||
\(740\) | − 49061.9i | − 0.0895944i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 213192. | 0.387225 | ||||||||
\(743\) | 469643.i | 0.850728i | 0.905022 | + | 0.425364i | \(0.139854\pi\) | ||||
−0.905022 | + | 0.425364i | \(0.860146\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 93618.0 | 0.168673 | ||||||||
\(746\) | 371969.i | 0.668389i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3024.00 | −0.00540479 | ||||||||
\(749\) | − 273701.i | − 0.487880i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −963004. | −1.70745 | −0.853725 | − | 0.520723i | \(-0.825662\pi\) | ||||
−0.853725 | + | 0.520723i | \(0.825662\pi\) | |||||||
\(752\) | 371112.i | 0.656250i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −469728. | −0.826235 | ||||||||
\(755\) | − 208721.i | − 0.366161i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 899696. | 1.57002 | 0.785008 | − | 0.619486i | \(-0.212659\pi\) | ||||
0.785008 | + | 0.619486i | \(0.212659\pi\) | |||||||
\(758\) | − 172964.i | − 0.301035i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 987840. | 1.71025 | ||||||||
\(761\) | 886292.i | 1.53041i | 0.643787 | + | 0.765204i | \(0.277362\pi\) | ||||
−0.643787 | + | 0.765204i | \(0.722638\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −297920. | −0.511741 | ||||||||
\(764\) | − 17038.4i | − 0.0291906i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −318528. | −0.542863 | ||||||||
\(767\) | − 505587.i | − 0.859419i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 183218. | 0.309824 | 0.154912 | − | 0.987928i | \(-0.450491\pi\) | ||||
0.154912 | + | 0.987928i | \(0.450491\pi\) | |||||||
\(770\) | − 59872.1i | − 0.100982i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −96796.0 | −0.162414 | ||||||||
\(773\) | − 1.11521e6i | − 1.86637i | −0.359402 | − | 0.933183i | \(-0.617019\pi\) | ||||
0.359402 | − | 0.933183i | \(-0.382981\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 93548.0 | 0.155751 | ||||||||
\(776\) | − 345928.i | − 0.574463i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −522846. | −0.863803 | ||||||||
\(779\) | − 1.01450e6i | − 1.67177i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 146016. | 0.239386 | ||||||||
\(782\) | 301499.i | 0.493029i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 459228. | 0.747130 | ||||||||
\(785\) | 164233.i | 0.266514i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −276304. | −0.446106 | −0.223053 | − | 0.974806i | \(-0.571602\pi\) | ||||
−0.223053 | + | 0.974806i | \(0.571602\pi\) | |||||||
\(788\) | − 20033.7i | − 0.0322634i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −538776. | −0.863285 | ||||||||
\(791\) | − 80423.5i | − 0.128538i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −293216. | −0.466274 | ||||||||
\(794\) | − 34509.6i | − 0.0547393i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26600.0 | 0.0419813 | ||||||||
\(797\) | 249438.i | 0.392686i | 0.980535 | + | 0.196343i | \(0.0629066\pi\) | ||||
−0.980535 | + | 0.196343i | \(0.937093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −116424. | −0.182368 | ||||||||
\(800\) | 65421.5i | 0.102221i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −566982. | −0.881496 | ||||||||
\(803\) | 112141.i | 0.173914i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −663264. | −1.02352 | ||||||||
\(806\) | 172964.i | 0.266248i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −478044. | −0.732226 | ||||||||
\(809\) | 657868.i | 1.00518i | 0.864526 | + | 0.502588i | \(0.167619\pi\) | ||||
−0.864526 | + | 0.502588i | \(0.832381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 660800. | 1.00468 | 0.502341 | − | 0.864670i | \(-0.332472\pi\) | ||||
0.502341 | + | 0.864670i | \(0.332472\pi\) | |||||||
\(812\) | − 55358.0i | − 0.0839592i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 59472.0 | 0.0897561 | ||||||||
\(815\) | − 322407.i | − 0.485388i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 972160. | 1.45644 | ||||||||
\(818\) | 149205.i | 0.222986i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 107604. | 0.160030 | ||||||||
\(821\) | 1.23522e6i | 1.83256i | 0.400533 | + | 0.916282i | \(0.368825\pi\) | ||||
−0.400533 | + | 0.916282i | \(0.631175\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.07330e6 | 1.58461 | 0.792303 | − | 0.610127i | \(-0.208882\pi\) | ||||
0.792303 | + | 0.610127i | \(0.208882\pi\) | |||||||
\(824\) | − 889767.i | − 1.31045i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 536256. | 0.785981 | ||||||||
\(827\) | − 356687.i | − 0.521527i | −0.965403 | − | 0.260763i | \(-0.916026\pi\) | ||||
0.965403 | − | 0.260763i | \(-0.0839742\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 91280.0 | 0.132821 | 0.0664105 | − | 0.997792i | \(-0.478845\pi\) | ||||
0.0664105 | + | 0.997792i | \(0.478845\pi\) | |||||||
\(830\) | 14968.0i | 0.0217274i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 387968. | 0.560466 | ||||||||
\(833\) | 144067.i | 0.207623i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −882000. | −1.26501 | ||||||||
\(836\) | − 19007.0i | − 0.0271958i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 668808. | 0.952387 | ||||||||
\(839\) | 1.18473e6i | 1.68305i | 0.540221 | + | 0.841523i | \(0.318341\pi\) | ||||
−0.540221 | + | 0.841523i | \(0.681659\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −269921. | −0.381632 | ||||||||
\(842\) | 79761.6i | 0.112505i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 73808.0 | 0.103614 | ||||||||
\(845\) | 475681.i | 0.666196i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −401884. | −0.560188 | ||||||||
\(848\) | − 509677.i | − 0.708767i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −97146.0 | −0.134458 | ||||||||
\(851\) | − 658831.i | − 0.909735i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 429254. | 0.589951 | 0.294976 | − | 0.955505i | \(-0.404688\pi\) | ||||
0.294976 | + | 0.955505i | \(0.404688\pi\) | |||||||
\(854\) | − 311003.i | − 0.426430i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −580608. | −0.792384 | ||||||||
\(857\) | − 337286.i | − 0.459236i | −0.973281 | − | 0.229618i | \(-0.926252\pi\) | ||||
0.973281 | − | 0.229618i | \(-0.0737477\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −535864. | −0.726220 | −0.363110 | − | 0.931746i | \(-0.618285\pi\) | ||||
−0.363110 | + | 0.931746i | \(0.618285\pi\) | |||||||
\(860\) | 103113.i | 0.139417i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 306504. | 0.412498 | ||||||||
\(863\) | 894722.i | 1.20134i | 0.799496 | + | 0.600671i | \(0.205100\pi\) | ||||
−0.799496 | + | 0.600671i | \(0.794900\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −819378. | −1.09510 | ||||||||
\(866\) | − 1.48962e6i | − 1.98627i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −20384.0 | −0.0270552 | ||||||||
\(869\) | − 72566.1i | − 0.0960936i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 423808. | 0.558641 | ||||||||
\(872\) | 631984.i | 0.831138i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.89504e6 | −2.48082 | ||||||||
\(875\) | 306013.i | 0.399691i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −179878. | −0.233872 | −0.116936 | − | 0.993139i | \(-0.537307\pi\) | ||||
−0.116936 | + | 0.993139i | \(0.537307\pi\) | |||||||
\(878\) | − 256714.i | − 0.333012i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −143136. | −0.184835 | ||||||||
\(881\) | − 1.27451e6i | − 1.64207i | −0.570878 | − | 0.821035i | \(-0.693397\pi\) | ||||
0.570878 | − | 0.821035i | \(-0.306603\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 383096. | 0.491345 | 0.245672 | − | 0.969353i | \(-0.420991\pi\) | ||||
0.245672 | + | 0.969353i | \(0.420991\pi\) | |||||||
\(884\) | − 19957.4i | − 0.0255387i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 242280. | 0.308639 | ||||||||
\(887\) | − 450229.i | − 0.572251i | −0.958192 | − | 0.286125i | \(-0.907633\pi\) | ||||
0.958192 | − | 0.286125i | \(-0.0923674\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 543760. | 0.688024 | ||||||||
\(890\) | 550075.i | 0.694452i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −102760. | −0.129150 | ||||||||
\(893\) | − 731771.i | − 0.917639i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.62691e6 | 2.03104 | ||||||||
\(896\) | 525544.i | 0.654626i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 892998. | 1.10738 | ||||||||
\(899\) | 359827.i | 0.445219i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 159894. | 0.196962 | ||||||||
\(902\) | 130436.i | 0.160318i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −170604. | −0.208762 | ||||||||
\(905\) | − 555480.i | − 0.678222i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.09900e6 | −1.33593 | −0.667964 | − | 0.744193i | \(-0.732834\pi\) | ||||
−0.667964 | + | 0.744193i | \(0.732834\pi\) | |||||||
\(908\) | 180804.i | 0.219299i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 395136. | 0.477160 | ||||||||
\(911\) | 284461.i | 0.342756i | 0.985205 | + | 0.171378i | \(0.0548220\pi\) | ||||
−0.985205 | + | 0.171378i | \(0.945178\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2016.00 | −0.00241852 | ||||||||
\(914\) | 1.37801e6i | 1.64953i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −157024. | −0.187144 | ||||||||
\(917\) | − 565459.i | − 0.672454i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −490588. | −0.580879 | −0.290440 | − | 0.956893i | \(-0.593802\pi\) | ||||
−0.290440 | + | 0.956893i | \(0.593802\pi\) | |||||||
\(920\) | 1.40700e6i | 1.66233i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 701442. | 0.825144 | ||||||||
\(923\) | 963656.i | 1.13115i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 212282. | 0.248102 | ||||||||
\(926\) | − 497322.i | − 0.579984i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −251640. | −0.292202 | ||||||||
\(929\) | 651852.i | 0.755297i | 0.925949 | + | 0.377648i | \(0.123267\pi\) | ||||
−0.925949 | + | 0.377648i | \(0.876733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −905520. | −1.04472 | ||||||||
\(932\) | − 104904.i | − 0.120770i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 724248. | 0.830221 | ||||||||
\(935\) | − 44904.1i | − 0.0513645i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −947842. | −1.07958 | −0.539792 | − | 0.841798i | \(-0.681497\pi\) | ||||
−0.539792 | + | 0.841798i | \(0.681497\pi\) | |||||||
\(938\) | 449516.i | 0.510905i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 77616.0 | 0.0878407 | ||||||||
\(941\) | − 214750.i | − 0.242523i | −0.992621 | − | 0.121262i | \(-0.961306\pi\) | ||||
0.992621 | − | 0.121262i | \(-0.0386940\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.44497e6 | 1.62493 | ||||||||
\(944\) | − 1.28202e6i | − 1.43864i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −124992. | −0.139669 | ||||||||
\(947\) | − 1.18220e6i | − 1.31823i | −0.752041 | − | 0.659117i | \(-0.770930\pi\) | ||||
0.752041 | − | 0.659117i | \(-0.229070\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −740096. | −0.821780 | ||||||||
\(950\) | − 610601.i | − 0.676566i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −148176. | −0.163495 | ||||||||
\(953\) | − 426729.i | − 0.469858i | −0.972013 | − | 0.234929i | \(-0.924514\pi\) | ||||
0.972013 | − | 0.234929i | \(-0.0754857\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 253008. | 0.277413 | ||||||||
\(956\) | 44530.8i | 0.0487242i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 422856. | 0.460746 | ||||||||
\(959\) | 485273.i | 0.527654i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −791025. | −0.856532 | ||||||||
\(962\) | 392495.i | 0.424116i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 106400. | 0.114495 | ||||||||
\(965\) | − 1.43735e6i | − 1.54350i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 392828. | 0.420097 | 0.210048 | − | 0.977691i | \(-0.432638\pi\) | ||||
0.210048 | + | 0.977691i | \(0.432638\pi\) | |||||||
\(968\) | 852525.i | 0.909822i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −733824. | −0.779917 | ||||||||
\(971\) | − 567716.i | − 0.602134i | −0.953603 | − | 0.301067i | \(-0.902657\pi\) | ||||
0.953603 | − | 0.301067i | \(-0.0973427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −519008. | −0.548212 | ||||||||
\(974\) | − 1.76706e6i | − 1.86266i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −743512. | −0.780528 | ||||||||
\(977\) | − 122370.i | − 0.128200i | −0.997943 | − | 0.0640999i | \(-0.979582\pi\) | ||||
0.997943 | − | 0.0640999i | \(-0.0204176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −74088.0 | −0.0773005 | ||||||||
\(980\) | − 96044.9i | − 0.100005i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.50624e6 | 1.56196 | ||||||||
\(983\) | 1.58495e6i | 1.64024i | 0.572189 | + | 0.820121i | \(0.306094\pi\) | ||||
−0.572189 | + | 0.820121i | \(0.693906\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 297486. | 0.306615 | ||||||||
\(986\) | − 373666.i | − 0.384353i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 125440. | 0.128506 | ||||||||
\(989\) | 1.38466e6i | 1.41563i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7364.00 | 0.00749836 | 0.00374918 | − | 0.999993i | \(-0.498807\pi\) | ||||
0.00374918 | + | 0.999993i | \(0.498807\pi\) | |||||||
\(992\) | 92659.3i | 0.0941598i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.02211e6 | −1.03449 | ||||||||
\(995\) | 394990.i | 0.398970i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.43479e6 | −1.44344 | −0.721719 | − | 0.692186i | \(-0.756648\pi\) | ||||
−0.721719 | + | 0.692186i | \(0.756648\pi\) | |||||||
\(998\) | 576863.i | 0.579178i | ||||||||
\(999\) | 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 | 9.5.b.a.8.2 | yes | 2 | |
3.2 | odd | 2 | inner | 9.5.b.a.8.1 | ✓ | 2 | |
4.3 | odd | 2 | 144.5.e.c.17.1 | 2 | |||
5.2 | odd | 4 | 225.5.d.a.224.1 | 4 | |||
5.3 | odd | 4 | 225.5.d.a.224.4 | 4 | |||
5.4 | even | 2 | 225.5.c.a.26.1 | 2 | |||
7.6 | odd | 2 | 441.5.b.a.197.2 | 2 | |||
8.3 | odd | 2 | 576.5.e.g.449.2 | 2 | |||
8.5 | even | 2 | 576.5.e.d.449.2 | 2 | |||
9.2 | odd | 6 | 81.5.d.c.53.1 | 4 | |||
9.4 | even | 3 | 81.5.d.c.26.1 | 4 | |||
9.5 | odd | 6 | 81.5.d.c.26.2 | 4 | |||
9.7 | even | 3 | 81.5.d.c.53.2 | 4 | |||
12.11 | even | 2 | 144.5.e.c.17.2 | 2 | |||
15.2 | even | 4 | 225.5.d.a.224.3 | 4 | |||
15.8 | even | 4 | 225.5.d.a.224.2 | 4 | |||
15.14 | odd | 2 | 225.5.c.a.26.2 | 2 | |||
21.20 | even | 2 | 441.5.b.a.197.1 | 2 | |||
24.5 | odd | 2 | 576.5.e.d.449.1 | 2 | |||
24.11 | even | 2 | 576.5.e.g.449.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.5.b.a.8.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
9.5.b.a.8.2 | yes | 2 | 1.1 | even | 1 | trivial | |
81.5.d.c.26.1 | 4 | 9.4 | even | 3 | |||
81.5.d.c.26.2 | 4 | 9.5 | odd | 6 | |||
81.5.d.c.53.1 | 4 | 9.2 | odd | 6 | |||
81.5.d.c.53.2 | 4 | 9.7 | even | 3 | |||
144.5.e.c.17.1 | 2 | 4.3 | odd | 2 | |||
144.5.e.c.17.2 | 2 | 12.11 | even | 2 | |||
225.5.c.a.26.1 | 2 | 5.4 | even | 2 | |||
225.5.c.a.26.2 | 2 | 15.14 | odd | 2 | |||
225.5.d.a.224.1 | 4 | 5.2 | odd | 4 | |||
225.5.d.a.224.2 | 4 | 15.8 | even | 4 | |||
225.5.d.a.224.3 | 4 | 15.2 | even | 4 | |||
225.5.d.a.224.4 | 4 | 5.3 | odd | 4 | |||
441.5.b.a.197.1 | 2 | 21.20 | even | 2 | |||
441.5.b.a.197.2 | 2 | 7.6 | odd | 2 | |||
576.5.e.d.449.1 | 2 | 24.5 | odd | 2 | |||
576.5.e.d.449.2 | 2 | 8.5 | even | 2 | |||
576.5.e.g.449.1 | 2 | 24.11 | even | 2 | |||
576.5.e.g.449.2 | 2 | 8.3 | odd | 2 |