Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,5,Mod(61,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.61");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.c (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: | \(12.8178754224\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 478x^{8} + 69668x^{6} + 4198200x^{4} + 101304000x^{2} + 622080000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 61.6 | ||
Root | \(3.01087i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 124.61 |
Dual form | 124.5.c.a.61.5 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.01087i | 0.334541i | 0.985911 | + | 0.167270i | \(0.0534953\pi\) | ||||
−0.985911 | + | 0.167270i | \(0.946505\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 16.1544 | 0.646177 | 0.323089 | − | 0.946369i | \(-0.395279\pi\) | ||||
0.323089 | + | 0.946369i | \(0.395279\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −66.9407 | −1.36614 | −0.683069 | − | 0.730354i | \(-0.739355\pi\) | ||||
−0.683069 | + | 0.730354i | \(0.739355\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 71.9347 | 0.888082 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 221.831i | 1.83331i | 0.399679 | + | 0.916655i | \(0.369122\pi\) | ||||
−0.399679 | + | 0.916655i | \(0.630878\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 65.3555i | − | 0.386719i | −0.981128 | − | 0.193360i | \(-0.938062\pi\) | ||
0.981128 | − | 0.193360i | \(-0.0619384\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 48.6389i | 0.216173i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 59.5422i | 0.206028i | 0.994680 | + | 0.103014i | \(0.0328487\pi\) | ||||
−0.994680 | + | 0.103014i | \(0.967151\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −328.553 | −0.910118 | −0.455059 | − | 0.890461i | \(-0.650382\pi\) | ||||
−0.455059 | + | 0.890461i | \(0.650382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 201.550i | − | 0.457029i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 623.356i | 1.17837i | 0.807999 | + | 0.589183i | \(0.200550\pi\) | ||||
−0.807999 | + | 0.589183i | \(0.799450\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −364.034 | −0.582455 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 460.466i | 0.631641i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1273.53i | 1.51430i | 0.653240 | + | 0.757151i | \(0.273409\pi\) | ||||
−0.653240 | + | 0.757151i | \(0.726591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 328.048 | + | 903.275i | 0.341361 | + | 0.939932i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −667.902 | −0.613317 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1081.39 | −0.882767 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 477.045i | 0.348462i | 0.984705 | + | 0.174231i | \(0.0557440\pi\) | ||||
−0.984705 | + | 0.174231i | \(0.944256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 196.777 | 0.129373 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 329.250 | 0.195866 | 0.0979328 | − | 0.995193i | \(-0.468777\pi\) | ||||
0.0979328 | + | 0.995193i | \(0.468777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3327.48i | − | 1.79961i | −0.436293 | − | 0.899804i | \(-0.643709\pi\) | ||
0.436293 | − | 0.899804i | \(-0.356291\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1162.06 | 0.573859 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 742.126 | 0.335956 | 0.167978 | − | 0.985791i | \(-0.446276\pi\) | ||||
0.167978 | + | 0.985791i | \(0.446276\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2080.06 | 0.866332 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −179.274 | −0.0689249 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1744.76i | 0.621131i | 0.950552 | + | 0.310566i | \(0.100518\pi\) | ||||
−0.950552 | + | 0.310566i | \(0.899482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3583.55i | 1.18464i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 989.229i | − | 0.304472i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4726.44 | −1.35778 | −0.678891 | − | 0.734239i | \(-0.737539\pi\) | ||||
−0.678891 | + | 0.734239i | \(0.737539\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4981.21i | − | 1.33867i | −0.742959 | − | 0.669337i | \(-0.766578\pi\) | ||
0.742959 | − | 0.669337i | \(-0.233422\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4815.36 | −1.21324 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1055.78i | − | 0.249889i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6596.77 | 1.46954 | 0.734770 | − | 0.678316i | \(-0.237290\pi\) | ||||
0.734770 | + | 0.678316i | \(0.237290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1876.84 | −0.394212 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8230.46 | 1.63270 | 0.816351 | − | 0.577555i | \(-0.195993\pi\) | ||||
0.816351 | + | 0.577555i | \(0.195993\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7160.56i | − | 1.34370i | −0.740688 | − | 0.671849i | \(-0.765500\pi\) | ||
0.740688 | − | 0.671849i | \(-0.234500\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1096.06i | − | 0.194855i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 14849.5i | − | 2.50455i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6391.96i | 1.02419i | 0.858929 | + | 0.512094i | \(0.171130\pi\) | ||||
−0.858929 | + | 0.512094i | \(0.828870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4440.31 | 0.676773 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 9782.20i | − | 1.41997i | −0.704215 | − | 0.709987i | \(-0.748701\pi\) | ||
0.704215 | − | 0.709987i | \(-0.251299\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 961.871i | 0.133131i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3834.42 | −0.506596 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2278.45i | 0.287647i | 0.989603 | + | 0.143824i | \(0.0459398\pi\) | ||||
−0.989603 | + | 0.143824i | \(0.954060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4374.95i | 0.528311i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2719.64 | + | 987.710i | −0.314446 | + | 0.114199i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5307.58 | −0.588098 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3409.25 | −0.362339 | −0.181170 | − | 0.983452i | \(-0.557988\pi\) | ||||
−0.181170 | + | 0.983452i | \(0.557988\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15957.3i | 1.62813i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15736.6 | 1.54265 | 0.771327 | − | 0.636439i | \(-0.219593\pi\) | ||||
0.771327 | + | 0.636439i | \(0.219593\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9560.46 | −0.901165 | −0.450583 | − | 0.892735i | \(-0.648784\pi\) | ||||
−0.450583 | + | 0.892735i | \(0.648784\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 3255.92i | − | 0.295322i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11127.3 | 0.971899 | 0.485949 | − | 0.873987i | \(-0.338474\pi\) | ||||
0.485949 | + | 0.873987i | \(0.338474\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 114.812 | 0.00966352 | 0.00483176 | − | 0.999988i | \(-0.498462\pi\) | ||||
0.00483176 | + | 0.999988i | \(0.498462\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1436.32 | −0.116575 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15726.7 | 1.23163 | 0.615815 | − | 0.787891i | \(-0.288827\pi\) | ||||
0.615815 | + | 0.787891i | \(0.288827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10070.0i | 0.761434i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 4701.33i | − | 0.343438i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3985.80i | − | 0.281463i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −34567.8 | −2.36103 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 991.328i | 0.0655250i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15977.3 | −1.02255 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15947.7i | 0.988759i | 0.869246 | + | 0.494380i | \(0.164605\pi\) | ||||
−0.869246 | + | 0.494380i | \(0.835395\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10018.6 | 0.602043 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −26656.7 | −1.55333 | −0.776666 | − | 0.629913i | \(-0.783091\pi\) | ||||
−0.776666 | + | 0.629913i | \(0.783091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21993.6 | 1.24335 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7438.57i | 0.408152i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1658.69i | 0.0883741i | 0.999023 | + | 0.0441870i | \(0.0140697\pi\) | ||||
−0.999023 | + | 0.0441870i | \(0.985930\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 24655.9i | 1.27612i | 0.769987 | + | 0.638059i | \(0.220263\pi\) | ||||
−0.769987 | + | 0.638059i | \(0.779737\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2234.44i | 0.112391i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14497.9 | 0.708976 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20573.1i | 0.978507i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6262.79i | 0.289823i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21164.6 | −0.953317 | −0.476658 | − | 0.879089i | \(-0.658152\pi\) | ||||
−0.476658 | + | 0.879089i | \(0.658152\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15194.7i | − | 0.666406i | −0.942855 | − | 0.333203i | \(-0.891871\pi\) | ||
0.942855 | − | 0.333203i | \(-0.108129\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4283.15i | 0.182970i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5299.44 | + | 14591.9i | 0.220580 | + | 0.607363i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −695.584 | −0.0282196 | −0.0141098 | − | 0.999900i | \(-0.504491\pi\) | ||||
−0.0141098 | + | 0.999900i | \(0.504491\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5253.23 | −0.207794 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 41727.9i | − | 1.60981i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14204.3 | −0.534619 | −0.267309 | − | 0.963611i | \(-0.586135\pi\) | ||||
−0.267309 | + | 0.963611i | \(0.586135\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10789.6 | −0.396312 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14959.2i | 0.536384i | 0.963365 | + | 0.268192i | \(0.0864262\pi\) | ||||
−0.963365 | + | 0.268192i | \(0.913574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24289.7 | 0.850448 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23634.3 | −0.808260 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18495.1 | 0.617965 | 0.308983 | − | 0.951068i | \(-0.400011\pi\) | ||||
0.308983 | + | 0.951068i | \(0.400011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24368.7 | 0.795713 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 14230.7i | − | 0.454234i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 16289.5i | − | 0.508394i | −0.967152 | − | 0.254197i | \(-0.918189\pi\) | ||
0.967152 | − | 0.254197i | \(-0.0818112\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23603.4i | 0.720471i | 0.932861 | + | 0.360236i | \(0.117304\pi\) | ||||
−0.932861 | + | 0.360236i | \(0.882696\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14997.8 | 0.447841 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7706.39i | 0.225168i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13208.3 | −0.377714 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 30823.9i | − | 0.862908i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9319.69 | 0.255467 | 0.127733 | − | 0.991809i | \(-0.459230\pi\) | ||||
0.127733 | + | 0.991809i | \(0.459230\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 41176.9 | 1.10545 | 0.552725 | − | 0.833364i | \(-0.313588\pi\) | ||||
0.552725 | + | 0.833364i | \(0.313588\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3178.82 | 0.0835981 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 30012.5i | 0.773339i | 0.922218 | + | 0.386669i | \(0.126375\pi\) | ||||
−0.922218 | + | 0.386669i | \(0.873625\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 57165.7i | − | 1.44354i | −0.692132 | − | 0.721771i | \(-0.743328\pi\) | ||
0.692132 | − | 0.721771i | \(-0.256672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19862.0i | 0.491621i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 85250.9i | − | 2.06874i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5318.85 | 0.126564 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 44840.9i | 1.04649i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 72883.0i | − | 1.66853i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −56296.3 | −1.26449 | −0.632244 | − | 0.774769i | \(-0.717866\pi\) | ||||
−0.632244 | + | 0.774769i | \(0.717866\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24780.8i | 0.546206i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 53753.5i | − | 1.16287i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21959.8 | − | 60465.9i | −0.466347 | − | 1.28408i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21559.5 | 0.449522 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3891.41 | 0.0796751 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5569.33i | 0.111994i | 0.998431 | + | 0.0559968i | \(0.0178337\pi\) | ||||
−0.998431 | + | 0.0559968i | \(0.982166\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26186.7 | −0.517268 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 47715.7 | 0.925996 | 0.462998 | − | 0.886359i | \(-0.346774\pi\) | ||||
0.462998 | + | 0.886359i | \(0.346774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 68963.9i | 1.31508i | 0.753422 | + | 0.657538i | \(0.228402\pi\) | ||||
−0.753422 | + | 0.657538i | \(0.771598\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 44709.9 | 0.837876 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7500.46 | 0.138158 | 0.0690790 | − | 0.997611i | \(-0.477994\pi\) | ||||
0.0690790 | + | 0.997611i | \(0.477994\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11988.6 | 0.217087 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19245.3 | −0.342633 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 52994.8i | − | 0.927763i | −0.885897 | − | 0.463882i | \(-0.846456\pi\) | ||
0.885897 | − | 0.463882i | \(-0.153544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 56610.9i | − | 0.974689i | −0.873210 | − | 0.487345i | \(-0.837966\pi\) | ||
0.873210 | − | 0.487345i | \(-0.162034\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 50666.9i | 0.858049i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 33602.2 | 0.559804 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21472.7i | 0.351960i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 29452.9 | 0.475039 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30642.8i | 0.486387i | 0.969978 | + | 0.243193i | \(0.0781949\pi\) | ||||
−0.969978 | + | 0.243193i | \(0.921805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −138279. | −2.16031 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2896.07 | −0.0445377 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3213.28 | −0.0486500 | −0.0243250 | − | 0.999704i | \(-0.507744\pi\) | ||||
−0.0243250 | + | 0.999704i | \(0.507744\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 31933.7i | − | 0.476047i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 91610.8i | 1.34482i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 69055.0i | − | 0.998352i | −0.866501 | − | 0.499176i | \(-0.833636\pi\) | ||
0.866501 | − | 0.499176i | \(-0.166364\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28185.6i | 0.401361i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6860.12 | −0.0962297 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 49330.7i | 0.681731i | 0.940112 | + | 0.340866i | \(0.110720\pi\) | ||||
−0.940112 | + | 0.340866i | \(0.889280\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 56069.0i | 0.763457i | 0.924275 | + | 0.381728i | \(0.124671\pi\) | ||||
−0.924275 | + | 0.381728i | \(0.875329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13172.4 | −0.176742 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 80753.9i | − | 1.06782i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 43505.6i | 0.567003i | 0.958972 | + | 0.283502i | \(0.0914961\pi\) | ||||
−0.958972 | + | 0.283502i | \(0.908504\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23598.1 | + | 64976.8i | 0.303157 | + | 0.834737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 76538.0 | 0.969314 | 0.484657 | − | 0.874704i | \(-0.338944\pi\) | ||||
0.484657 | + | 0.874704i | \(0.338944\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32018.4 | 0.399785 | 0.199893 | − | 0.979818i | \(-0.435941\pi\) | ||||
0.199893 | + | 0.979818i | \(0.435941\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 15980.4i | − | 0.196743i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22040.2 | −0.267579 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 79975.7 | 0.957552 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 10264.8i | − | 0.121217i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −83976.9 | −0.978194 | −0.489097 | − | 0.872230i | \(-0.662674\pi\) | ||||
−0.489097 | + | 0.872230i | \(0.662674\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −76353.0 | −0.877368 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −102145. | −1.15799 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 40739.8 | 0.455697 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 222744.i | 2.45851i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 47380.9i | 0.516081i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 80468.6i | − | 0.865021i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 180118. | 1.91109 | 0.955544 | − | 0.294849i | \(-0.0952694\pi\) | ||||
0.955544 | + | 0.294849i | \(0.0952694\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 28785.3i | − | 0.301477i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14764.7 | −0.152653 | −0.0763265 | − | 0.997083i | \(-0.524319\pi\) | ||||
−0.0763265 | + | 0.997083i | \(0.524319\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 117215.i | 1.19645i | 0.801328 | + | 0.598225i | \(0.204127\pi\) | ||||
−0.801328 | + | 0.598225i | \(0.795873\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −77789.4 | −0.783970 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 39990.7 | 0.397961 | 0.198980 | − | 0.980003i | \(-0.436237\pi\) | ||||
0.198980 | + | 0.980003i | \(0.436237\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −282507. | −2.77618 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33502.7i | 0.325140i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 19562.8i | − | 0.187510i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23791.6i | 0.225246i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 345.684i | 0.00323284i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −49678.5 | −0.458962 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 118136.i | − | 1.07827i | −0.842219 | − | 0.539135i | \(-0.818751\pi\) | ||
0.842219 | − | 0.539135i | \(-0.181249\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 34316.0i | 0.309463i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 106567. | 0.949584 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 92291.6i | 0.812648i | 0.913729 | + | 0.406324i | \(0.133189\pi\) | ||||
−0.913729 | + | 0.406324i | \(0.866811\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 47351.0i | 0.412030i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −200374. | + | 72771.1i | −1.72319 | + | 0.625821i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21483.8 | 0.182609 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30319.3 | −0.254731 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 127823.i | 1.06157i | 0.847506 | + | 0.530786i | \(0.178103\pi\) | ||||
−0.847506 | + | 0.530786i | \(0.821897\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 132077. | 1.08437 | 0.542183 | − | 0.840260i | \(-0.317598\pi\) | ||||
0.542183 | + | 0.840260i | \(0.317598\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 30094.0 | 0.244268 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 155311.i | − | 1.24639i | −0.782068 | − | 0.623193i | \(-0.785835\pi\) | ||
0.782068 | − | 0.623193i | \(-0.214165\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 132958. | 1.05502 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12000.7 | 0.0941609 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 97187.0 | 0.754083 | 0.377042 | − | 0.926196i | \(-0.376941\pi\) | ||||
0.377042 | + | 0.926196i | \(0.376941\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22374.1 | −0.171685 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 104079.i | − | 0.789860i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 115675.i | − | 0.868267i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12139.6i | 0.0901302i | 0.998984 | + | 0.0450651i | \(0.0143495\pi\) | ||||
−0.998984 | + | 0.0450651i | \(0.985650\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 23684.5 | 0.173945 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 116795.i | − | 0.848550i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −60713.5 | −0.436383 | −0.218191 | − | 0.975906i | \(-0.570016\pi\) | ||||
−0.218191 | + | 0.975906i | \(0.570016\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 48105.5i | − | 0.342084i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 83232.1 | 0.585609 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17514.0 | −0.121929 | −0.0609645 | − | 0.998140i | \(-0.519418\pi\) | ||||
−0.0609645 | + | 0.998140i | \(0.519418\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −48016.4 | −0.330780 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 167299.i | − | 1.14050i | −0.821471 | − | 0.570250i | \(-0.806846\pi\) | ||
0.821471 | − | 0.570250i | \(-0.193154\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 239885.i | − | 1.61839i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 239361.i | − | 1.59820i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 117046.i | 0.773492i | 0.922186 | + | 0.386746i | \(0.126401\pi\) | ||||
−0.922186 | + | 0.386746i | \(0.873599\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37116.0 | −0.242777 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 80259.9i | − | 0.519653i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 103259.i | 0.661808i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 138674. | 0.879858 | 0.439929 | − | 0.898033i | \(-0.355004\pi\) | ||||
0.439929 | + | 0.898033i | \(0.355004\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 66219.7i | 0.415950i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 243942.i | 1.51704i | 0.651650 | + | 0.758520i | \(0.274077\pi\) | ||||
−0.651650 | + | 0.758520i | \(0.725923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 59034.0 | − | 21439.8i | 0.363490 | − | 0.132011i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 71730.6 | 0.437315 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −105823. | −0.638839 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11473.9i | 0.0685907i | 0.999412 | + | 0.0342954i | \(0.0109187\pi\) | ||||
−0.999412 | + | 0.0342954i | \(0.989081\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4994.10 | −0.0295647 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 316391. | 1.85492 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 158026.i | − | 0.917555i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −74235.6 | −0.426914 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −64305.6 | −0.366286 | −0.183143 | − | 0.983086i | \(-0.558627\pi\) | ||||
−0.183143 | + | 0.983086i | \(0.558627\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −178277. | −1.00585 | −0.502923 | − | 0.864331i | \(-0.667742\pi\) | ||||
−0.502923 | + | 0.864331i | \(0.667742\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 53384.6 | 0.298356 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 21675.4i | − | 0.120002i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 333446.i | 1.82881i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 43651.1i | 0.237181i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 153293. | 0.825214 | 0.412607 | − | 0.910909i | \(-0.364618\pi\) | ||||
0.412607 | + | 0.910909i | \(0.364618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 234185.i | − | 1.24906i | −0.781000 | − | 0.624530i | \(-0.785290\pi\) | ||
0.781000 | − | 0.624530i | \(-0.214710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −61942.9 | −0.327351 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 204805.i | − | 1.07245i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15890.9 | 0.0824553 | 0.0412276 | − | 0.999150i | \(-0.486873\pi\) | ||||
0.0412276 | + | 0.999150i | \(0.486873\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 149629. | 0.769374 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −262700. | −1.33860 | −0.669302 | − | 0.742990i | \(-0.733407\pi\) | ||||
−0.669302 | + | 0.742990i | \(0.733407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36807.1i | 0.185871i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 63723.8i | − | 0.318923i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 79750.8i | − | 0.395587i | −0.980244 | − | 0.197794i | \(-0.936622\pi\) | ||
0.980244 | − | 0.197794i | \(-0.0633776\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 73037.7i | 0.359082i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 45749.3 | 0.222940 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 70674.8i | 0.341383i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 377226.i | − | 1.80621i | −0.429416 | − | 0.903107i | \(-0.641281\pi\) | ||
0.429416 | − | 0.903107i | \(-0.358719\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27417.2 | −0.130136 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 119252.i | − | 0.561130i | −0.959835 | − | 0.280565i | \(-0.909478\pi\) | ||
0.959835 | − | 0.280565i | \(-0.0905218\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 286927.i | − | 1.33847i | −0.743050 | − | 0.669236i | \(-0.766621\pi\) | ||
0.743050 | − | 0.669236i | \(-0.233379\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −43934.3 | + | 15955.9i | −0.203188 | + | 0.0737930i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −366554. | −1.68075 | −0.840377 | − | 0.542002i | \(-0.817666\pi\) | ||||
−0.840377 | + | 0.542002i | \(0.817666\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −441593. | −2.00759 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2094.31i | − | 0.00944059i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 738136. | 3.29924 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 119604. | 0.530103 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 125509.i | 0.551616i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 191449. | 0.834414 | 0.417207 | − | 0.908812i | \(-0.363009\pi\) | ||||
0.417207 | + | 0.908812i | \(0.363009\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31177.5 | 0.134757 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 125637. | 0.538547 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −55074.5 | −0.234136 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 263460.i | 1.11085i | 0.831566 | + | 0.555426i | \(0.187445\pi\) | ||||
−0.831566 | + | 0.555426i | \(0.812555\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 42767.2i | − | 0.178852i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 172003.i | 0.713464i | 0.934207 | + | 0.356732i | \(0.116109\pi\) | ||||
−0.934207 | + | 0.356732i | \(0.883891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −75828.6 | −0.311989 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 257781.i | 1.05206i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −550953. | −2.23050 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 264134.i | 1.06077i | 0.847756 | + | 0.530387i | \(0.177953\pi\) | ||||
−0.847756 | + | 0.530387i | \(0.822047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −45040.2 | −0.179442 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 72423.1 | 0.286247 | 0.143124 | − | 0.989705i | \(-0.454285\pi\) | ||||
0.143124 | + | 0.989705i | \(0.454285\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 254216. | 0.996829 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 73132.9i | 0.284510i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 378639.i | 1.46147i | 0.682662 | + | 0.730734i | \(0.260822\pi\) | ||||
−0.682662 | + | 0.730734i | \(0.739178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 479333.i | 1.83568i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 151287.i | − | 0.574868i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −154444. | −0.582313 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 164626.i | 0.615911i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 55686.3i | 0.206735i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −306109. | −1.12772 | −0.563859 | − | 0.825871i | \(-0.690684\pi\) | ||||
−0.563859 | + | 0.825871i | \(0.690684\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 87718.5i | − | 0.320692i | −0.987061 | − | 0.160346i | \(-0.948739\pi\) | ||
0.987061 | − | 0.160346i | \(-0.0512610\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 73371.0i | 0.266199i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −53783.0 | + | 19532.7i | −0.193653 | + | 0.0703301i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −108732. | −0.388548 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −339995. | −1.20582 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 21518.3i | − | 0.0757450i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 179755. | 0.628019 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 49045.4 | 0.170079 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 461421.i | 1.58825i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 114508. | 0.391240 | 0.195620 | − | 0.980680i | \(-0.437328\pi\) | ||||
0.195620 | + | 0.980680i | \(0.437328\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −71066.6 | −0.241027 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1854.73 | 0.00624435 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 415415. | 1.38838 | 0.694188 | − | 0.719794i | \(-0.255764\pi\) | ||||
0.694188 | + | 0.719794i | \(0.255764\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 358321.i | − | 1.18885i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 418421.i | − | 1.37819i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 427883.i | − | 1.39918i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23202.9 | −0.0753280 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 522689.i | 1.68474i | 0.538900 | + | 0.842370i | \(0.318840\pi\) | ||||
−0.538900 | + | 0.842370i | \(0.681160\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −217469. | −0.695943 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 39768.4i | − | 0.126361i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 383486. | 1.20985 | 0.604926 | − | 0.796282i | \(-0.293203\pi\) | ||||
0.604926 | + | 0.796282i | \(0.293203\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 254056. | 0.795851 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −297237. | −0.924565 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 73389.1i | 0.226677i | 0.993556 | + | 0.113338i | \(0.0361544\pi\) | ||||
−0.993556 | + | 0.113338i | \(0.963846\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 60865.1i | 0.186679i | 0.995634 | + | 0.0933397i | \(0.0297543\pi\) | ||||
−0.995634 | + | 0.0933397i | \(0.970246\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28060.3i | 0.0854641i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 226923.i | − | 0.686345i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 561989. | 1.68802 | 0.844008 | − | 0.536331i | \(-0.180190\pi\) | ||||
0.844008 | + | 0.536331i | \(0.180190\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 123978.i | 0.369818i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 654827.i | 1.93988i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −387040. | −1.13873 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 75947.3i | − | 0.221922i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18401.2i | 0.0534036i | 0.999643 | + | 0.0267018i | \(0.00850045\pi\) | ||||
−0.999643 | + | 0.0267018i | \(0.991500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −107781. | − | 296773.i | −0.310679 | − | 0.855449i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −90363.7 | −0.258713 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −376357. | −1.07026 | −0.535132 | − | 0.844769i | \(-0.679738\pi\) | ||||
−0.535132 | + | 0.844769i | \(0.679738\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 64388.3i | − | 0.181875i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 172118. | 0.482924 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −287857. | −0.802275 | −0.401137 | − | 0.916018i | \(-0.631385\pi\) | ||||
−0.401137 | + | 0.916018i | \(0.631385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 89490.0i | 0.247757i | 0.992297 | + | 0.123878i | \(0.0395333\pi\) | ||||
−0.992297 | + | 0.123878i | \(0.960467\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 474536. | 1.30507 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −558423. | −1.52564 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −391296. | −1.06201 | −0.531004 | − | 0.847369i | \(-0.678185\pi\) | ||||
−0.531004 | + | 0.847369i | \(0.678185\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 256679. | 0.692079 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 48502.1i | − | 0.129921i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 189074.i | − | 0.503165i | −0.967836 | − | 0.251583i | \(-0.919049\pi\) | ||
0.967836 | − | 0.251583i | \(-0.0809510\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16014.3i | 0.0423408i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 110621. | 0.290581 | 0.145291 | − | 0.989389i | \(-0.453588\pi\) | ||||
0.145291 | + | 0.989389i | \(0.453588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 235880.i | − | 0.615616i | −0.951448 | − | 0.307808i | \(-0.900405\pi\) | ||
0.951448 | − | 0.307808i | \(-0.0995955\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −287034. | −0.744304 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 152521.i | − | 0.392966i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30582.7 | −0.0782917 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 219441. | 0.558191 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28404.3 | −0.0717931 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 725427.i | 1.82194i | 0.412468 | + | 0.910972i | \(0.364667\pi\) | ||||
−0.412468 | + | 0.910972i | \(0.635333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 169501.i | − | 0.423023i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 257626.i | 0.638914i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 135944.i | − | 0.335027i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 592055. | 1.44997 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 42234.9i | − | 0.102791i | −0.998678 | − | 0.0513955i | \(-0.983633\pi\) | ||
0.998678 | − | 0.0513955i | \(-0.0163669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 765165.i | − | 1.85069i | −0.379130 | − | 0.925343i | \(-0.623777\pi\) | ||
0.379130 | − | 0.925343i | \(-0.376223\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 161845. | 0.389026 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 137859.i | 0.329327i | 0.986350 | + | 0.164663i | \(0.0526538\pi\) | ||||
−0.986350 | + | 0.164663i | \(0.947346\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.04847e6i | − | 2.48924i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 182055. | − | 66118.0i | 0.429576 | − | 0.156012i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −101837. | −0.238825 | −0.119412 | − | 0.992845i | \(-0.538101\pi\) | ||||
−0.119412 | + | 0.992845i | \(0.538101\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −430624. | −1.00373 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 515093.i | − | 1.19331i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 479706. | 1.10460 | 0.552300 | − | 0.833646i | \(-0.313750\pi\) | ||||
0.552300 | + | 0.833646i | \(0.313750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 600294. | 1.37392 | 0.686959 | − | 0.726696i | \(-0.258945\pi\) | ||||
0.686959 | + | 0.726696i | \(0.258945\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11716.5i | 0.0266546i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 355294. | 0.803423 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −793861. | −1.78440 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16768.5 | −0.0374664 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.10498e6 | 2.45420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 467721.i | − | 1.03266i | −0.856390 | − | 0.516329i | \(-0.827298\pi\) | ||
0.856390 | − | 0.516329i | \(-0.172702\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 167625.i | − | 0.367902i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 518012.i | 1.13022i | 0.825016 | + | 0.565109i | \(0.191166\pi\) | ||||
−0.825016 | + | 0.565109i | \(0.808834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 228218. | 0.495005 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 143666.i | 0.309784i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −341401. | −0.731852 | −0.365926 | − | 0.930644i | \(-0.619248\pi\) | ||||
−0.365926 | + | 0.930644i | \(0.619248\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26795.2i | 0.0571053i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −207641. | −0.439946 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 114030. | 0.240203 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −561520. | −1.17600 | −0.588002 | − | 0.808859i | \(-0.700085\pi\) | ||||
−0.588002 | + | 0.808859i | \(0.700085\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.06819e6i | − | 2.22425i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 398302.i | 0.824599i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19604.3i | 0.0403539i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22582.9i | 0.0462195i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48521.5 | −0.0987412 | −0.0493706 | − | 0.998781i | \(-0.515722\pi\) | ||||
−0.0493706 | + | 0.998781i | \(0.515722\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 156734.i | − | 0.317142i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 36096.2i | 0.0726245i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.05342e6 | −2.10748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 329285.i | 0.655059i | 0.944841 | + | 0.327529i | \(0.106216\pi\) | ||||
−0.944841 | + | 0.327529i | \(0.893784\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 459804.i | 0.909564i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −563062. | + | 204491.i | −1.10758 | + | 0.402249i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 234205. | 0.458124 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 159560. | 0.310375 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 829911.i | − | 1.60537i | −0.596407 | − | 0.802683i | \(-0.703405\pi\) | ||
0.596407 | − | 0.802683i | \(-0.296595\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 639984. | 1.23112 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 170448. | 0.326073 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 463608.i | − | 0.882012i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.01055e6 | 1.91201 | 0.956004 | − | 0.293353i | \(-0.0947712\pi\) | ||||
0.956004 | + | 0.293353i | \(0.0947712\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 207113. | 0.389720 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 198125. | 0.370771 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 540023. | 1.00509 | 0.502544 | − | 0.864552i | \(-0.332398\pi\) | ||||
0.502544 | + | 0.864552i | \(0.332398\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 101172.i | 0.187277i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.46336e6i | 2.69412i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 69857.3i | − | 0.127915i | −0.997953 | − | 0.0639577i | \(-0.979628\pi\) | ||
0.997953 | − | 0.0639577i | \(-0.0203723\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −64651.6 | −0.117745 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 64118.2i | − | 0.116146i | −0.998312 | − | 0.0580729i | \(-0.981504\pi\) | ||
0.998312 | − | 0.0580729i | \(-0.0184956\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −341902. | −0.616012 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 703679.i | − | 1.26105i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −744868. | −1.32775 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 217979. | 0.386488 | 0.193244 | − | 0.981151i | \(-0.438099\pi\) | ||||
0.193244 | + | 0.981151i | \(0.438099\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −92261.5 | −0.162716 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 245462.i | − | 0.430616i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 270275.i | − | 0.471643i | −0.971796 | − | 0.235822i | \(-0.924222\pi\) | ||
0.971796 | − | 0.235822i | \(-0.0757781\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 416341.i | − | 0.722712i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 218980.i | 0.378124i | 0.981965 | + | 0.189062i | \(0.0605448\pi\) | ||||
−0.981965 | + | 0.189062i | \(0.939455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7685.62 | −0.0132017 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 69191.9i | 0.118231i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 308899.i | 0.525080i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −686317. | −1.16057 | −0.580286 | − | 0.814413i | \(-0.697059\pi\) | ||||
−0.580286 | + | 0.814413i | \(0.697059\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 9674.76i | − | 0.0162754i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 750379.i | 1.25580i | 0.778293 | + | 0.627901i | \(0.216086\pi\) | ||||
−0.778293 | + | 0.627901i | \(0.783914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −119421. | − | 328823.i | −0.198828 | − | 0.547468i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 96148.2 | 0.159257 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −108176. | −0.178261 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.82577e6i | 2.99325i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −586416. | −0.956494 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11236.8 | −0.0182348 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 727065.i | − | 1.17388i | −0.809630 | − | 0.586940i | \(-0.800332\pi\) | ||
0.809630 | − | 0.586940i | \(-0.199668\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 207916. | 0.333990 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.05276e6 | −1.68258 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −325549. | −0.517691 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −84863.0 | −0.134272 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 101857.i | 0.160352i | 0.996781 | + | 0.0801758i | \(0.0255482\pi\) | ||||
−0.996781 | + | 0.0801758i | \(0.974452\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44187.8i | 0.0692164i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 163900.i | 0.255454i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.58843e6 | 2.46341 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 674091.i | − | 1.04022i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −148528. | −0.228067 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 994694.i | 1.51982i | 0.650028 | + | 0.759911i | \(0.274757\pi\) | ||||
−0.650028 | + | 0.759911i | \(0.725243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −968962. | −1.47321 | −0.736606 | − | 0.676322i | \(-0.763573\pi\) | ||||
−0.736606 | + | 0.676322i | \(0.763573\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −168816. | −0.255407 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −229462. | −0.345458 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.09325e6i | 1.63786i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 314710.i | 0.469184i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25477.6i | 0.0377983i | 0.999821 | + | 0.0188991i | \(0.00601614\pi\) | ||||
−0.999821 | + | 0.0188991i | \(0.993984\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.23265e6i | 1.81988i | 0.414745 | + | 0.909938i | \(0.363871\pi\) | ||||
−0.414745 | + | 0.909938i | \(0.636129\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 243139. | 0.357229 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 923364.i | − | 1.35009i | −0.737778 | − | 0.675044i | \(-0.764125\pi\) | ||
0.737778 | − | 0.675044i | \(-0.235875\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 309988.i | 0.451061i | 0.974236 | + | 0.225531i | \(0.0724116\pi\) | ||||
−0.974236 | + | 0.225531i | \(0.927588\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −130990. | −0.189686 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 123851.i | 0.178489i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 241658.i | 0.346599i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −415927. | + | 151055.i | −0.593699 | + | 0.215618i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.26783e6 | 1.80109 | 0.900547 | − | 0.434759i | \(-0.143166\pi\) | ||||
0.900547 | + | 0.434759i | \(0.143166\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −914592. | −1.29311 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 230446.i | 0.324275i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 392386. | 0.549541 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.31399e6 | 3.22549 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 96403.2i | 0.133745i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −297369. | −0.410616 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 240725. | 0.330844 | 0.165422 | − | 0.986223i | \(-0.447101\pi\) | ||||
0.165422 | + | 0.986223i | \(0.447101\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −381799. | −0.522279 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −209842. | −0.285714 | −0.142857 | − | 0.989743i | \(-0.545629\pi\) | ||||
−0.142857 | + | 0.989743i | \(0.545629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 733682.i | 0.994310i | 0.867662 | + | 0.497155i | \(0.165622\pi\) | ||||
−0.867662 | + | 0.497155i | \(0.834378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 66360.2i | − | 0.0895162i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.46308e6i | − | 1.96447i | −0.187648 | − | 0.982236i | \(-0.560086\pi\) | ||
0.187648 | − | 0.982236i | \(-0.439914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 298778. | 0.399315 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 240796.i | 0.320340i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.41793e6 | −1.87766 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 431135.i | − | 0.568299i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −245243. | −0.321787 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.06953e6 | 1.39694 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.34294e6 | −1.74605 | −0.873024 | − | 0.487678i | \(-0.837844\pi\) | ||||
−0.873024 | + | 0.487678i | \(0.837844\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 252843.i | − | 0.327246i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 259075.i | − | 0.333790i | −0.985975 | − | 0.166895i | \(-0.946626\pi\) | ||
0.985975 | − | 0.166895i | \(-0.0533741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 41148.7i | − | 0.0527758i | −0.999652 | − | 0.0263879i | \(-0.991599\pi\) | ||
0.999652 | − | 0.0263879i | \(-0.00840051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 229889.i | − | 0.293515i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −519280. | −0.660016 | −0.330008 | − | 0.943978i | \(-0.607051\pi\) | ||||
−0.330008 | + | 0.943978i | \(0.607051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.06755e6i | − | 1.35078i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 984996.i | 1.24073i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −243828. | −0.305760 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 263147.i | − | 0.328513i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 122662.i | 0.152449i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.15035e6 | + | 417779.i | −1.42334 | + | 0.516924i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −103887. | −0.127971 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −670652. | −0.822473 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 381299.i | 0.465552i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 463052. | 0.562879 | 0.281439 | − | 0.959579i | \(-0.409188\pi\) | ||||
0.281439 | + | 0.959579i | \(0.409188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.13201e6 | 1.37000 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 499296.i | 0.601618i | 0.953684 | + | 0.300809i | \(0.0972567\pi\) | ||||
−0.953684 | + | 0.300809i | \(0.902743\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.16999e6 | 2.60325 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 242280. | 0.289385 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.78442e6 | 2.12207 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 263056. | 0.311471 | 0.155736 | − | 0.987799i | \(-0.450225\pi\) | ||||
0.155736 | + | 0.987799i | \(0.450225\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 542312.i | 0.639337i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 537906.i | − | 0.631397i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 173661.i | − | 0.202963i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −687729. | −0.800309 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 696545.i | 0.807082i | 0.914962 | + | 0.403541i | \(0.132221\pi\) | ||||
−0.914962 | + | 0.403541i | \(0.867779\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −683410. | −0.788464 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 44454.7i | − | 0.0510686i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −213372. | −0.244070 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −684691. | −0.779858 | −0.389929 | − | 0.920845i | \(-0.627500\pi\) | ||||
−0.389929 | + | 0.920845i | \(0.627500\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −352919. | −0.400261 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.09654e6i | − | 1.23835i | −0.785252 | − | 0.619176i | \(-0.787467\pi\) | ||
0.785252 | − | 0.619176i | \(-0.212533\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 205240.i | 0.230801i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 497943.i | − | 0.557592i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 439438.i | 0.490002i | 0.969523 | + | 0.245001i | \(0.0787883\pi\) | ||||
−0.969523 | + | 0.245001i | \(0.921212\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −467982. | −0.519633 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 120407.i | 0.133134i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 701926.i | − | 0.772868i | −0.922317 | − | 0.386434i | \(-0.873707\pi\) | ||
0.922317 | − | 0.386434i | \(-0.126293\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 150554. | 0.165077 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 850592.i | − | 0.928747i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 111034.i | − | 0.120731i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −708290. | + | 592636.i | −0.766945 | + | 0.641713i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 800437. | 0.863126 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 665190. | 0.714317 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 554085.i | − | 0.592548i | −0.955103 | − | 0.296274i | \(-0.904256\pi\) | ||
0.955103 | − | 0.296274i | \(-0.0957442\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 58900.9 | 0.0627298 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 902421. | 0.957129 | 0.478565 | − | 0.878052i | \(-0.341157\pi\) | ||||
0.478565 | + | 0.878052i | \(0.341157\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.65048e6i | − | 1.74335i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −71633.5 | −0.0753541 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.65718e6 | −1.73612 | −0.868060 | − | 0.496459i | \(-0.834633\pi\) | ||||
−0.868060 | + | 0.496459i | \(0.834633\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −505431. | −0.527347 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8258.98 | 0.00858200 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 919314.i | − | 0.951386i | −0.879611 | − | 0.475693i | \(-0.842197\pi\) | ||
0.879611 | − | 0.475693i | \(-0.157803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 484835.i | 0.499714i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 149575.i | − | 0.153541i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.07420e6 | 2.12060 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 857735.i | − | 0.873385i | −0.899611 | − | 0.436692i | \(-0.856150\pi\) | ||
0.899611 | − | 0.436692i | \(-0.143850\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 355693. | 0.360725 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 923479.i | − | 0.932784i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.04357e6 | −1.04986 | −0.524928 | − | 0.851147i | \(-0.675908\pi\) | ||||
−0.524928 | + | 0.851147i | \(0.675908\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −219663. | −0.220103 |
(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 | 124.5.c.a.61.6 | yes | 10 | |
3.2 | odd | 2 | 1116.5.h.b.433.3 | 10 | |||
4.3 | odd | 2 | 496.5.e.c.433.5 | 10 | |||
31.30 | odd | 2 | inner | 124.5.c.a.61.5 | ✓ | 10 | |
93.92 | even | 2 | 1116.5.h.b.433.4 | 10 | |||
124.123 | even | 2 | 496.5.e.c.433.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.5.c.a.61.5 | ✓ | 10 | 31.30 | odd | 2 | inner | |
124.5.c.a.61.6 | yes | 10 | 1.1 | even | 1 | trivial | |
496.5.e.c.433.5 | 10 | 4.3 | odd | 2 | |||
496.5.e.c.433.6 | 10 | 124.123 | even | 2 | |||
1116.5.h.b.433.3 | 10 | 3.2 | odd | 2 | |||
1116.5.h.b.433.4 | 10 | 93.92 | even | 2 |