Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(685,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.685");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.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: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 98) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 685.4 | ||
Root | \(0.765367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.685 |
Dual form | 882.3.c.a.685.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 8.15640i | 1.63128i | 0.578559 | + | 0.815640i | \(0.303615\pi\) | ||||
−0.578559 | + | 0.815640i | \(0.696385\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11.5349i | 1.15349i | ||||||||
\(11\) | −17.6569 | −1.60517 | −0.802584 | − | 0.596539i | \(-0.796542\pi\) | ||||
−0.802584 | + | 0.596539i | \(0.796542\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.21371i | − 0.0933622i | −0.998910 | − | 0.0466811i | \(-0.985136\pi\) | ||||
0.998910 | − | 0.0466811i | \(-0.0148645\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 16.6298i | 0.978225i | 0.872221 | + | 0.489113i | \(0.162679\pi\) | ||||
−0.872221 | + | 0.489113i | \(0.837321\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 0.371418i | − 0.0195483i | −0.999952 | − | 0.00977417i | \(-0.996889\pi\) | ||||
0.999952 | − | 0.00977417i | \(-0.00311126\pi\) | |||||||
\(20\) | 16.3128i | 0.815640i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −24.9706 | −1.13503 | ||||||||
\(23\) | −3.02944 | −0.131715 | −0.0658573 | − | 0.997829i | \(-0.520978\pi\) | ||||
−0.0658573 | + | 0.997829i | \(0.520978\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −41.5269 | −1.66108 | ||||||||
\(26\) | − 1.71644i | − 0.0660170i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.38478 | −0.0822337 | −0.0411168 | − | 0.999154i | \(-0.513092\pi\) | ||||
−0.0411168 | + | 0.999154i | \(0.513092\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1.26810i | − 0.0409065i | −0.999791 | − | 0.0204532i | \(-0.993489\pi\) | ||||
0.999791 | − | 0.0204532i | \(-0.00651092\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 23.5181i | 0.691710i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27.7574 | −0.750199 | −0.375099 | − | 0.926985i | \(-0.622391\pi\) | ||||
−0.375099 | + | 0.926985i | \(0.622391\pi\) | |||||||
\(38\) | − 0.525265i | − 0.0138228i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 23.0698i | 0.576745i | ||||||||
\(41\) | − 28.7988i | − 0.702409i | −0.936299 | − | 0.351205i | \(-0.885772\pi\) | ||||
0.936299 | − | 0.351205i | \(-0.114228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −55.3137 | −1.28637 | −0.643183 | − | 0.765713i | \(-0.722386\pi\) | ||||
−0.643183 | + | 0.765713i | \(0.722386\pi\) | |||||||
\(44\) | −35.3137 | −0.802584 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.28427 | −0.0931363 | ||||||||
\(47\) | 58.3855i | 1.24224i | 0.783714 | + | 0.621122i | \(0.213323\pi\) | ||||
−0.783714 | + | 0.621122i | \(0.786677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −58.7279 | −1.17456 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 2.42742i | − 0.0466811i | ||||||||
\(53\) | 1.37258 | 0.0258978 | 0.0129489 | − | 0.999916i | \(-0.495878\pi\) | ||||
0.0129489 | + | 0.999916i | \(0.495878\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 144.016i | − 2.61848i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.37258 | −0.0581480 | ||||||||
\(59\) | − 98.7735i | − 1.67413i | −0.547105 | − | 0.837064i | \(-0.684270\pi\) | ||||
0.547105 | − | 0.837064i | \(-0.315730\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 82.2975i | 1.34914i | 0.738211 | + | 0.674570i | \(0.235671\pi\) | ||||
−0.738211 | + | 0.674570i | \(0.764329\pi\) | |||||||
\(62\) | − 1.79337i | − 0.0289253i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 9.89949 | 0.152300 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 97.9411 | 1.46181 | 0.730904 | − | 0.682480i | \(-0.239099\pi\) | ||||
0.730904 | + | 0.682480i | \(0.239099\pi\) | |||||||
\(68\) | 33.2597i | 0.489113i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −64.5685 | −0.909416 | −0.454708 | − | 0.890641i | \(-0.650256\pi\) | ||||
−0.454708 | + | 0.890641i | \(0.650256\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 91.9940i | 1.26019i | 0.776517 | + | 0.630096i | \(0.216984\pi\) | ||||
−0.776517 | + | 0.630096i | \(0.783016\pi\) | |||||||
\(74\) | −39.2548 | −0.530471 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 0.742837i | − 0.00977417i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −19.7157 | −0.249566 | −0.124783 | − | 0.992184i | \(-0.539823\pi\) | ||||
−0.124783 | + | 0.992184i | \(0.539823\pi\) | |||||||
\(80\) | 32.6256i | 0.407820i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 40.7276i | − 0.496678i | ||||||||
\(83\) | − 43.4495i | − 0.523488i | −0.965137 | − | 0.261744i | \(-0.915702\pi\) | ||||
0.965137 | − | 0.261744i | \(-0.0842977\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −135.640 | −1.59576 | ||||||||
\(86\) | −78.2254 | −0.909598 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −49.9411 | −0.567513 | ||||||||
\(89\) | 7.86191i | 0.0883360i | 0.999024 | + | 0.0441680i | \(0.0140637\pi\) | ||||
−0.999024 | + | 0.0441680i | \(0.985936\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.05887 | −0.0658573 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 82.5695i | 0.878399i | ||||||||
\(95\) | 3.02944 | 0.0318888 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 47.2126i | 0.486728i | 0.969935 | + | 0.243364i | \(0.0782510\pi\) | ||||
−0.969935 | + | 0.243364i | \(0.921749\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −83.0538 | −0.830538 | ||||||||
\(101\) | 196.532i | 1.94586i | 0.231092 | + | 0.972932i | \(0.425770\pi\) | ||||
−0.231092 | + | 0.972932i | \(0.574230\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 119.090i | 1.15621i | 0.815963 | + | 0.578105i | \(0.196207\pi\) | ||||
−0.815963 | + | 0.578105i | \(0.803793\pi\) | |||||||
\(104\) | − 3.43289i | − 0.0330085i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.94113 | 0.0183125 | ||||||||
\(107\) | 147.480 | 1.37832 | 0.689160 | − | 0.724609i | \(-0.257980\pi\) | ||||
0.689160 | + | 0.724609i | \(0.257980\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −130.385 | −1.19619 | −0.598095 | − | 0.801425i | \(-0.704076\pi\) | ||||
−0.598095 | + | 0.801425i | \(0.704076\pi\) | |||||||
\(110\) | − 203.670i | − 1.85155i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.94113 | 0.0171781 | 0.00858905 | − | 0.999963i | \(-0.497266\pi\) | ||||
0.00858905 | + | 0.999963i | \(0.497266\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 24.7093i | − 0.214864i | ||||||||
\(116\) | −4.76955 | −0.0411168 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 139.687i | − 1.18379i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 190.765 | 1.57657 | ||||||||
\(122\) | 116.386i | 0.953986i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 2.53620i | − 0.0204532i | ||||||||
\(125\) | − 134.800i | − 1.07840i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.3431 | 0.175930 | 0.0879651 | − | 0.996124i | \(-0.471964\pi\) | ||||
0.0879651 | + | 0.996124i | \(0.471964\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 14.0000 | 0.107692 | ||||||||
\(131\) | 36.3662i | 0.277605i | 0.990320 | + | 0.138802i | \(0.0443252\pi\) | ||||
−0.990320 | + | 0.138802i | \(0.955675\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 138.510 | 1.03365 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 47.0363i | 0.345855i | ||||||||
\(137\) | 75.9239 | 0.554189 | 0.277094 | − | 0.960843i | \(-0.410629\pi\) | ||||
0.277094 | + | 0.960843i | \(0.410629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 109.751i | 0.789578i | 0.918772 | + | 0.394789i | \(0.129182\pi\) | ||||
−0.918772 | + | 0.394789i | \(0.870818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −91.3137 | −0.643054 | ||||||||
\(143\) | 21.4303i | 0.149862i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 19.4512i | − 0.134146i | ||||||||
\(146\) | 130.099i | 0.891090i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −55.5147 | −0.375099 | ||||||||
\(149\) | 184.000 | 1.23490 | 0.617450 | − | 0.786610i | \(-0.288166\pi\) | ||||
0.617450 | + | 0.786610i | \(0.288166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 216.284 | 1.43235 | 0.716173 | − | 0.697923i | \(-0.245892\pi\) | ||||
0.716173 | + | 0.697923i | \(0.245892\pi\) | |||||||
\(152\) | − 1.05053i | − 0.00691138i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3431 | 0.0667300 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 182.570i | 1.16287i | 0.813594 | + | 0.581433i | \(0.197508\pi\) | ||||
−0.813594 | + | 0.581433i | \(0.802492\pi\) | |||||||
\(158\) | −27.8823 | −0.176470 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 46.1396i | 0.288372i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −159.078 | −0.975940 | −0.487970 | − | 0.872860i | \(-0.662262\pi\) | ||||
−0.487970 | + | 0.872860i | \(0.662262\pi\) | |||||||
\(164\) | − 57.5976i | − 0.351205i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 61.4469i | − 0.370162i | ||||||||
\(167\) | − 74.3455i | − 0.445183i | −0.974912 | − | 0.222591i | \(-0.928548\pi\) | ||||
0.974912 | − | 0.222591i | \(-0.0714516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 167.527 | 0.991284 | ||||||||
\(170\) | −191.823 | −1.12837 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −110.627 | −0.643183 | ||||||||
\(173\) | 188.648i | 1.09045i | 0.838290 | + | 0.545225i | \(0.183556\pi\) | ||||
−0.838290 | + | 0.545225i | \(0.816444\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −70.6274 | −0.401292 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.1184i | 0.0624630i | ||||||||
\(179\) | 209.872 | 1.17247 | 0.586235 | − | 0.810141i | \(-0.300610\pi\) | ||||
0.586235 | + | 0.810141i | \(0.300610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 315.609i | − 1.74369i | −0.489778 | − | 0.871847i | \(-0.662922\pi\) | ||||
0.489778 | − | 0.871847i | \(-0.337078\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.56854 | −0.0465682 | ||||||||
\(185\) | − 226.400i | − 1.22378i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 293.631i | − 1.57022i | ||||||||
\(188\) | 116.771i | 0.621122i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.28427 | 0.0225488 | ||||||||
\(191\) | −326.794 | −1.71096 | −0.855482 | − | 0.517833i | \(-0.826739\pi\) | ||||
−0.855482 | + | 0.517833i | \(0.826739\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 108.451 | 0.561921 | 0.280961 | − | 0.959719i | \(-0.409347\pi\) | ||||
0.280961 | + | 0.959719i | \(0.409347\pi\) | |||||||
\(194\) | 66.7688i | 0.344169i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −40.5097 | −0.205633 | −0.102816 | − | 0.994700i | \(-0.532785\pi\) | ||||
−0.102816 | + | 0.994700i | \(0.532785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 245.390i | − 1.23311i | −0.787310 | − | 0.616557i | \(-0.788527\pi\) | ||||
0.787310 | − | 0.616557i | \(-0.211473\pi\) | |||||||
\(200\) | −117.456 | −0.587279 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 277.939i | 1.37593i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 234.894 | 1.14583 | ||||||||
\(206\) | 168.418i | 0.817563i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 4.85483i | − 0.0233405i | ||||||||
\(209\) | 6.55808i | 0.0313784i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −36.2843 | −0.171963 | −0.0859817 | − | 0.996297i | \(-0.527403\pi\) | ||||
−0.0859817 | + | 0.996297i | \(0.527403\pi\) | |||||||
\(212\) | 2.74517 | 0.0129489 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 208.569 | 0.974619 | ||||||||
\(215\) | − 451.161i | − 2.09842i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −184.392 | −0.845834 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 288.033i | − 1.30924i | ||||||||
\(221\) | 20.1838 | 0.0913293 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 88.9100i | 0.398700i | 0.979928 | + | 0.199350i | \(0.0638830\pi\) | ||||
−0.979928 | + | 0.199350i | \(0.936117\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.74517 | 0.0121468 | ||||||||
\(227\) | − 320.287i | − 1.41096i | −0.708732 | − | 0.705478i | \(-0.750732\pi\) | ||||
0.708732 | − | 0.705478i | \(-0.249268\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.90376i | 0.0126802i | 0.999980 | + | 0.00634008i | \(0.00201812\pi\) | ||||
−0.999980 | + | 0.00634008i | \(0.997982\pi\) | |||||||
\(230\) | − 34.9442i | − 0.151931i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.74517 | −0.0290740 | ||||||||
\(233\) | 16.6102 | 0.0712883 | 0.0356441 | − | 0.999365i | \(-0.488652\pi\) | ||||
0.0356441 | + | 0.999365i | \(0.488652\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −476.215 | −2.02645 | ||||||||
\(236\) | − 197.547i | − 0.837064i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 397.470 | 1.66305 | 0.831527 | − | 0.555484i | \(-0.187467\pi\) | ||||
0.831527 | + | 0.555484i | \(0.187467\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 302.018i | − 1.25319i | −0.779347 | − | 0.626593i | \(-0.784449\pi\) | ||||
0.779347 | − | 0.626593i | \(-0.215551\pi\) | |||||||
\(242\) | 269.782 | 1.11480 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 164.595i | 0.674570i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.450793 | −0.00182507 | ||||||||
\(248\) | − 3.58673i | − 0.0144626i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 190.636i | − 0.762545i | ||||||||
\(251\) | − 17.9974i | − 0.0717027i | −0.999357 | − | 0.0358514i | \(-0.988586\pi\) | ||||
0.999357 | − | 0.0358514i | \(-0.0114143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 53.4903 | 0.211424 | ||||||||
\(254\) | 31.5980 | 0.124401 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 445.668i | 1.73412i | 0.498206 | + | 0.867059i | \(0.333992\pi\) | ||||
−0.498206 | + | 0.867059i | \(0.666008\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 19.7990 | 0.0761500 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 51.4296i | 0.196296i | ||||||||
\(263\) | 33.5391 | 0.127525 | 0.0637626 | − | 0.997965i | \(-0.479690\pi\) | ||||
0.0637626 | + | 0.997965i | \(0.479690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.1953i | 0.0422466i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 195.882 | 0.730904 | ||||||||
\(269\) | − 131.716i | − 0.489651i | −0.969567 | − | 0.244826i | \(-0.921269\pi\) | ||||
0.969567 | − | 0.244826i | \(-0.0787307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 454.132i | 1.67576i | 0.545851 | + | 0.837882i | \(0.316207\pi\) | ||||
−0.545851 | + | 0.837882i | \(0.683793\pi\) | |||||||
\(272\) | 66.5193i | 0.244556i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 107.373 | 0.391871 | ||||||||
\(275\) | 733.235 | 2.66631 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 53.7645 | 0.194096 | 0.0970478 | − | 0.995280i | \(-0.469060\pi\) | ||||
0.0970478 | + | 0.995280i | \(0.469060\pi\) | |||||||
\(278\) | 155.212i | 0.558316i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 162.218 | 0.577289 | 0.288645 | − | 0.957436i | \(-0.406795\pi\) | ||||
0.288645 | + | 0.957436i | \(0.406795\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 225.037i | − 0.795182i | −0.917563 | − | 0.397591i | \(-0.869846\pi\) | ||||
0.917563 | − | 0.397591i | \(-0.130154\pi\) | |||||||
\(284\) | −129.137 | −0.454708 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 30.3070i | 0.105968i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.4487 | 0.0430751 | ||||||||
\(290\) | − 27.5081i | − 0.0948557i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 183.988i | 0.630096i | ||||||||
\(293\) | − 92.6226i | − 0.316118i | −0.987430 | − | 0.158059i | \(-0.949476\pi\) | ||||
0.987430 | − | 0.158059i | \(-0.0505236\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 805.637 | 2.73097 | ||||||||
\(296\) | −78.5097 | −0.265235 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 260.215 | 0.873206 | ||||||||
\(299\) | 3.67685i | 0.0122972i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 305.872 | 1.01282 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 1.48567i | − 0.00488708i | ||||||||
\(305\) | −671.252 | −2.20083 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 430.230i | 1.40140i | 0.713457 | + | 0.700700i | \(0.247129\pi\) | ||||
−0.713457 | + | 0.700700i | \(0.752871\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.6274 | 0.0471852 | ||||||||
\(311\) | − 59.0008i | − 0.189713i | −0.995491 | − | 0.0948567i | \(-0.969761\pi\) | ||||
0.995491 | − | 0.0948567i | \(-0.0302393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 313.725i | − 1.00232i | −0.865356 | − | 0.501158i | \(-0.832907\pi\) | ||||
0.865356 | − | 0.501158i | \(-0.167093\pi\) | |||||||
\(314\) | 258.193i | 0.822270i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −39.4315 | −0.124783 | ||||||||
\(317\) | −470.548 | −1.48438 | −0.742190 | − | 0.670190i | \(-0.766213\pi\) | ||||
−0.742190 | + | 0.670190i | \(0.766213\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.1076 | 0.131999 | ||||||||
\(320\) | 65.2512i | 0.203910i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.17662 | 0.0191227 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 50.4016i | 0.155082i | ||||||||
\(326\) | −224.971 | −0.690094 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 81.4552i | − 0.248339i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 308.666 | 0.932526 | 0.466263 | − | 0.884646i | \(-0.345600\pi\) | ||||
0.466263 | + | 0.884646i | \(0.345600\pi\) | |||||||
\(332\) | − 86.8991i | − 0.261744i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 105.140i | − 0.314792i | ||||||||
\(335\) | 798.847i | 2.38462i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 189.865 | 0.563398 | 0.281699 | − | 0.959503i | \(-0.409102\pi\) | ||||
0.281699 | + | 0.959503i | \(0.409102\pi\) | |||||||
\(338\) | 236.919 | 0.700943 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −271.279 | −0.797880 | ||||||||
\(341\) | 22.3907i | 0.0656618i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −156.451 | −0.454799 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 266.788i | 0.771064i | ||||||||
\(347\) | −288.950 | −0.832710 | −0.416355 | − | 0.909202i | \(-0.636693\pi\) | ||||
−0.416355 | + | 0.909202i | \(0.636693\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 339.050i | 0.971489i | 0.874101 | + | 0.485745i | \(0.161452\pi\) | ||||
−0.874101 | + | 0.485745i | \(0.838548\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −99.8823 | −0.283756 | ||||||||
\(353\) | 498.029i | 1.41085i | 0.708787 | + | 0.705423i | \(0.249243\pi\) | ||||
−0.708787 | + | 0.705423i | \(0.750757\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 526.647i | − 1.48351i | ||||||||
\(356\) | 15.7238i | 0.0441680i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 296.804 | 0.829062 | ||||||||
\(359\) | 117.941 | 0.328527 | 0.164263 | − | 0.986417i | \(-0.447475\pi\) | ||||
0.164263 | + | 0.986417i | \(0.447475\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 360.862 | 0.999618 | ||||||||
\(362\) | − 446.338i | − 1.23298i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −750.340 | −2.05573 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 175.066i | − 0.477020i | −0.971140 | − | 0.238510i | \(-0.923341\pi\) | ||||
0.971140 | − | 0.238510i | \(-0.0766589\pi\) | |||||||
\(368\) | −12.1177 | −0.0329287 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 320.178i | − 0.865347i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −526.156 | −1.41061 | −0.705304 | − | 0.708905i | \(-0.749189\pi\) | ||||
−0.705304 | + | 0.708905i | \(0.749189\pi\) | |||||||
\(374\) | − 415.256i | − 1.11031i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 165.139i | 0.439199i | ||||||||
\(377\) | 2.89442i | 0.00767751i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −383.245 | −1.01120 | −0.505600 | − | 0.862768i | \(-0.668729\pi\) | ||||
−0.505600 | + | 0.862768i | \(0.668729\pi\) | |||||||
\(380\) | 6.05887 | 0.0159444 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −462.156 | −1.20983 | ||||||||
\(383\) | 0.127451i | 0 0.000332769i | 1.00000 | 0.000166385i | \(5.29619e-5\pi\) | |||||
−1.00000 | 0.000166385i | \(0.999947\pi\) | ||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 153.373 | 0.397338 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 94.4253i | 0.243364i | ||||||||
\(389\) | 372.909 | 0.958634 | 0.479317 | − | 0.877642i | \(-0.340884\pi\) | ||||
0.479317 | + | 0.877642i | \(0.340884\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 50.3790i | − 0.128847i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −57.2893 | −0.145404 | ||||||||
\(395\) | − 160.809i | − 0.407112i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 72.5164i | 0.182661i | 0.995821 | + | 0.0913305i | \(0.0291120\pi\) | ||||
−0.995821 | + | 0.0913305i | \(0.970888\pi\) | |||||||
\(398\) | − 347.034i | − 0.871944i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −166.108 | −0.415269 | ||||||||
\(401\) | 12.3116 | 0.0307023 | 0.0153511 | − | 0.999882i | \(-0.495113\pi\) | ||||
0.0153511 | + | 0.999882i | \(0.495113\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.53911 | −0.00381912 | ||||||||
\(404\) | 393.064i | 0.972932i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 490.108 | 1.20420 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 185.279i | − 0.453004i | −0.974011 | − | 0.226502i | \(-0.927271\pi\) | ||||
0.974011 | − | 0.226502i | \(-0.0727290\pi\) | |||||||
\(410\) | 332.191 | 0.810222 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 238.179i | 0.578105i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 354.392 | 0.853956 | ||||||||
\(416\) | − 6.86577i | − 0.0165043i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.27452i | 0.0221879i | ||||||||
\(419\) | − 491.676i | − 1.17345i | −0.809785 | − | 0.586726i | \(-0.800417\pi\) | ||||
0.809785 | − | 0.586726i | \(-0.199583\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −471.373 | −1.11965 | −0.559825 | − | 0.828611i | \(-0.689132\pi\) | ||||
−0.559825 | + | 0.828611i | \(0.689132\pi\) | |||||||
\(422\) | −51.3137 | −0.121596 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.88225 | 0.00915625 | ||||||||
\(425\) | − 690.586i | − 1.62491i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 294.960 | 0.689160 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 638.038i | − 1.48381i | ||||||||
\(431\) | 457.255 | 1.06092 | 0.530458 | − | 0.847711i | \(-0.322020\pi\) | ||||
0.530458 | + | 0.847711i | \(0.322020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 248.941i | 0.574921i | 0.957792 | + | 0.287461i | \(0.0928110\pi\) | ||||
−0.957792 | + | 0.287461i | \(0.907189\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −260.770 | −0.598095 | ||||||||
\(437\) | 1.12519i | 0.00257480i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 430.001i | 0.979501i | 0.871863 | + | 0.489751i | \(0.162912\pi\) | ||||
−0.871863 | + | 0.489751i | \(0.837088\pi\) | |||||||
\(440\) | − 407.340i | − 0.925773i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 28.5442 | 0.0645795 | ||||||||
\(443\) | −380.353 | −0.858585 | −0.429293 | − | 0.903165i | \(-0.641237\pi\) | ||||
−0.429293 | + | 0.903165i | \(0.641237\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −64.1249 | −0.144101 | ||||||||
\(446\) | 125.738i | 0.281923i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −326.627 | −0.727455 | −0.363728 | − | 0.931505i | \(-0.618496\pi\) | ||||
−0.363728 | + | 0.931505i | \(0.618496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 508.496i | 1.12749i | ||||||||
\(452\) | 3.88225 | 0.00858905 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 452.954i | − 0.997697i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −621.117 | −1.35912 | −0.679559 | − | 0.733621i | \(-0.737829\pi\) | ||||
−0.679559 | + | 0.733621i | \(0.737829\pi\) | |||||||
\(458\) | 4.10653i | 0.00896622i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 49.4186i | − 0.107432i | ||||||||
\(461\) | 170.939i | 0.370801i | 0.982663 | + | 0.185401i | \(0.0593583\pi\) | ||||
−0.982663 | + | 0.185401i | \(0.940642\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 491.813 | 1.06223 | 0.531116 | − | 0.847299i | \(-0.321773\pi\) | ||||
0.531116 | + | 0.847299i | \(0.321773\pi\) | |||||||
\(464\) | −9.53911 | −0.0205584 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.4903 | 0.0504084 | ||||||||
\(467\) | − 300.342i | − 0.643132i | −0.946887 | − | 0.321566i | \(-0.895791\pi\) | ||||
0.946887 | − | 0.321566i | \(-0.104209\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −673.470 | −1.43292 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 279.374i | − 0.591893i | ||||||||
\(473\) | 976.666 | 2.06483 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.4239i | 0.0324713i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 562.108 | 1.17596 | ||||||||
\(479\) | 161.823i | 0.337834i | 0.985630 | + | 0.168917i | \(0.0540270\pi\) | ||||
−0.985630 | + | 0.168917i | \(0.945973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.6893i | 0.0700402i | ||||||||
\(482\) | − 427.118i | − 0.886136i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 381.529 | 0.788283 | ||||||||
\(485\) | −385.085 | −0.793990 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 770.392 | 1.58191 | 0.790957 | − | 0.611872i | \(-0.209583\pi\) | ||||
0.790957 | + | 0.611872i | \(0.209583\pi\) | |||||||
\(488\) | 232.773i | 0.476993i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 363.578 | 0.740484 | 0.370242 | − | 0.928935i | \(-0.379275\pi\) | ||||
0.370242 | + | 0.928935i | \(0.379275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 39.6584i | − 0.0804431i | ||||||||
\(494\) | −0.637518 | −0.00129052 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 5.07241i | − 0.0102266i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 224.402 | 0.449703 | 0.224852 | − | 0.974393i | \(-0.427810\pi\) | ||||
0.224852 | + | 0.974393i | \(0.427810\pi\) | |||||||
\(500\) | − 269.600i | − 0.539201i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 25.4521i | − 0.0507015i | ||||||||
\(503\) | 790.766i | 1.57210i | 0.618163 | + | 0.786050i | \(0.287877\pi\) | ||||
−0.618163 | + | 0.786050i | \(0.712123\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1603.00 | −3.17425 | ||||||||
\(506\) | 75.6468 | 0.149500 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 44.6863 | 0.0879651 | ||||||||
\(509\) | 409.968i | 0.805438i | 0.915324 | + | 0.402719i | \(0.131935\pi\) | ||||
−0.915324 | + | 0.402719i | \(0.868065\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 630.270i | 1.22621i | ||||||||
\(515\) | −971.342 | −1.88610 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1030.90i | − 1.99401i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 28.0000 | 0.0538462 | ||||||||
\(521\) | 420.351i | 0.806816i | 0.915020 | + | 0.403408i | \(0.132174\pi\) | ||||
−0.915020 | + | 0.403408i | \(0.867826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 319.672i | − 0.611227i | −0.952156 | − | 0.305613i | \(-0.901138\pi\) | ||||
0.952156 | − | 0.305613i | \(-0.0988615\pi\) | |||||||
\(524\) | 72.7324i | 0.138802i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 47.4315 | 0.0901739 | ||||||||
\(527\) | 21.0883 | 0.0400158 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −519.823 | −0.982651 | ||||||||
\(530\) | 15.8326i | 0.0298728i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.9533 | −0.0655785 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1202.91i | 2.24843i | ||||||||
\(536\) | 277.019 | 0.516827 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 186.275i | − 0.346236i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −361.608 | −0.668407 | −0.334203 | − | 0.942501i | \(-0.608467\pi\) | ||||
−0.334203 | + | 0.942501i | \(0.608467\pi\) | |||||||
\(542\) | 642.240i | 1.18494i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 94.0725i | 0.172927i | ||||||||
\(545\) | − 1063.47i | − 1.95132i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 93.4701 | 0.170878 | 0.0854389 | − | 0.996343i | \(-0.472771\pi\) | ||||
0.0854389 | + | 0.996343i | \(0.472771\pi\) | |||||||
\(548\) | 151.848 | 0.277094 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1036.95 | 1.88536 | ||||||||
\(551\) | 0.885750i | 0.00160753i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 76.0345 | 0.137246 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 219.503i | 0.394789i | ||||||||
\(557\) | −628.627 | −1.12860 | −0.564298 | − | 0.825572i | \(-0.690853\pi\) | ||||
−0.564298 | + | 0.825572i | \(0.690853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 67.1347i | 0.120098i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 229.411 | 0.408205 | ||||||||
\(563\) | − 282.424i | − 0.501642i | −0.968034 | − | 0.250821i | \(-0.919300\pi\) | ||||
0.968034 | − | 0.250821i | \(-0.0807005\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.8326i | 0.0280223i | ||||||||
\(566\) | − 318.250i | − 0.562279i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −182.627 | −0.321527 | ||||||||
\(569\) | −625.664 | −1.09959 | −0.549793 | − | 0.835301i | \(-0.685293\pi\) | ||||
−0.549793 | + | 0.835301i | \(0.685293\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −661.401 | −1.15832 | −0.579160 | − | 0.815214i | \(-0.696619\pi\) | ||||
−0.579160 | + | 0.815214i | \(0.696619\pi\) | |||||||
\(572\) | 42.8605i | 0.0749310i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 125.803 | 0.218788 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 334.988i | 0.580569i | 0.956940 | + | 0.290285i | \(0.0937499\pi\) | ||||
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(578\) | 17.6051 | 0.0304587 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 38.9024i | − 0.0670731i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.2355 | −0.0415703 | ||||||||
\(584\) | 260.198i | 0.445545i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 130.988i | − 0.223529i | ||||||||
\(587\) | 1083.88i | 1.84648i | 0.384227 | + | 0.923239i | \(0.374468\pi\) | ||||
−0.384227 | + | 0.923239i | \(0.625532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.470996 | −0.000799654 0 | ||||||||
\(590\) | 1139.34 | 1.93109 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −111.029 | −0.187550 | ||||||||
\(593\) | − 145.827i | − 0.245914i | −0.992412 | − | 0.122957i | \(-0.960762\pi\) | ||||
0.992412 | − | 0.122957i | \(-0.0392377\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 368.000 | 0.617450 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.19986i | 0.00869541i | ||||||||
\(599\) | 154.246 | 0.257505 | 0.128753 | − | 0.991677i | \(-0.458903\pi\) | ||||
0.128753 | + | 0.991677i | \(0.458903\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 361.658i | − 0.601760i | −0.953662 | − | 0.300880i | \(-0.902720\pi\) | ||||
0.953662 | − | 0.300880i | \(-0.0972804\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 432.569 | 0.716173 | ||||||||
\(605\) | 1555.95i | 2.57182i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 361.943i | − 0.596282i | −0.954522 | − | 0.298141i | \(-0.903633\pi\) | ||||
0.954522 | − | 0.298141i | \(-0.0963666\pi\) | |||||||
\(608\) | − 2.10106i | − 0.00345569i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −949.294 | −1.55622 | ||||||||
\(611\) | 70.8629 | 0.115979 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −513.360 | −0.837454 | −0.418727 | − | 0.908112i | \(-0.637524\pi\) | ||||
−0.418727 | + | 0.908112i | \(0.637524\pi\) | |||||||
\(614\) | 608.436i | 0.990939i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −613.767 | −0.994761 | −0.497380 | − | 0.867533i | \(-0.665705\pi\) | ||||
−0.497380 | + | 0.867533i | \(0.665705\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 454.594i | − 0.734400i | −0.930142 | − | 0.367200i | \(-0.880316\pi\) | ||||
0.930142 | − | 0.367200i | \(-0.119684\pi\) | |||||||
\(620\) | 20.6863 | 0.0333650 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 83.4398i | − 0.134148i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 61.3116 | 0.0980986 | ||||||||
\(626\) | − 443.674i | − 0.708745i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 365.140i | 0.581433i | ||||||||
\(629\) | − 461.600i | − 0.733864i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.7351 | 0.0645564 | 0.0322782 | − | 0.999479i | \(-0.489724\pi\) | ||||
0.0322782 | + | 0.999479i | \(0.489724\pi\) | |||||||
\(632\) | −55.7645 | −0.0882350 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −665.456 | −1.04961 | ||||||||
\(635\) | 182.240i | 0.286992i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 59.5492 | 0.0933373 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 92.2792i | 0.144186i | ||||||||
\(641\) | −153.650 | −0.239703 | −0.119852 | − | 0.992792i | \(-0.538242\pi\) | ||||
−0.119852 | + | 0.992792i | \(0.538242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 899.887i | − 1.39951i | −0.714382 | − | 0.699756i | \(-0.753292\pi\) | ||||
0.714382 | − | 0.699756i | \(-0.246708\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.73506 | 0.0135218 | ||||||||
\(647\) | 709.014i | 1.09585i | 0.836528 | + | 0.547924i | \(0.184582\pi\) | ||||
−0.836528 | + | 0.547924i | \(0.815418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1744.03i | 2.68726i | ||||||||
\(650\) | 71.2786i | 0.109659i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −318.156 | −0.487970 | ||||||||
\(653\) | 848.222 | 1.29896 | 0.649481 | − | 0.760378i | \(-0.274986\pi\) | ||||
0.649481 | + | 0.760378i | \(0.274986\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −296.617 | −0.452851 | ||||||||
\(656\) | − 115.195i | − 0.175602i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −437.803 | −0.664345 | −0.332172 | − | 0.943219i | \(-0.607782\pi\) | ||||
−0.332172 | + | 0.943219i | \(0.607782\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 333.242i | 0.504149i | 0.967708 | + | 0.252074i | \(0.0811128\pi\) | ||||
−0.967708 | + | 0.252074i | \(0.918887\pi\) | |||||||
\(662\) | 436.520 | 0.659395 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 122.894i | − 0.185081i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.22453 | 0.0108314 | ||||||||
\(668\) | − 148.691i | − 0.222591i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1129.74i | 1.68618i | ||||||||
\(671\) | − 1453.12i | − 2.16560i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 366.253 | 0.544209 | 0.272105 | − | 0.962268i | \(-0.412280\pi\) | ||||
0.272105 | + | 0.962268i | \(0.412280\pi\) | |||||||
\(674\) | 268.510 | 0.398382 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 335.054 | 0.495642 | ||||||||
\(677\) | − 942.533i | − 1.39222i | −0.717935 | − | 0.696110i | \(-0.754912\pi\) | ||||
0.717935 | − | 0.696110i | \(-0.245088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −383.647 | −0.564186 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 31.6652i | 0.0464299i | ||||||||
\(683\) | 215.500 | 0.315520 | 0.157760 | − | 0.987477i | \(-0.449573\pi\) | ||||
0.157760 | + | 0.987477i | \(0.449573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 619.266i | 0.904038i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −221.255 | −0.321591 | ||||||||
\(689\) | − 1.66592i | − 0.00241787i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 916.732i | − 1.32668i | −0.748320 | − | 0.663338i | \(-0.769139\pi\) | ||||
0.748320 | − | 0.663338i | \(-0.230861\pi\) | |||||||
\(692\) | 377.296i | 0.545225i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −408.638 | −0.588815 | ||||||||
\(695\) | −895.176 | −1.28802 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 478.919 | 0.687115 | ||||||||
\(698\) | 479.489i | 0.686947i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −541.894 | −0.773029 | −0.386515 | − | 0.922283i | \(-0.626321\pi\) | ||||
−0.386515 | + | 0.922283i | \(0.626321\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.3096i | 0.0146651i | ||||||||
\(704\) | −141.255 | −0.200646 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 704.319i | 0.997619i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −401.497 | −0.566287 | −0.283143 | − | 0.959078i | \(-0.591377\pi\) | ||||
−0.283143 | + | 0.959078i | \(0.591377\pi\) | |||||||
\(710\) | − 744.791i | − 1.04900i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22.2368i | 0.0312315i | ||||||||
\(713\) | 3.84163i | 0.00538799i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −174.794 | −0.244467 | ||||||||
\(716\) | 419.744 | 0.586235 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 166.794 | 0.232304 | ||||||||
\(719\) | 306.327i | 0.426046i | 0.977047 | + | 0.213023i | \(0.0683309\pi\) | ||||
−0.977047 | + | 0.213023i | \(0.931669\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 510.336 | 0.706837 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 631.217i | − 0.871847i | ||||||||
\(725\) | 99.0324 | 0.136596 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 520.704i | 0.716237i | 0.933676 | + | 0.358119i | \(0.116582\pi\) | ||||
−0.933676 | + | 0.358119i | \(0.883418\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1061.14 | −1.45362 | ||||||||
\(731\) | − 919.858i | − 1.25836i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 359.775i | − 0.490825i | −0.969419 | − | 0.245412i | \(-0.921077\pi\) | ||||
0.969419 | − | 0.245412i | \(-0.0789234\pi\) | |||||||
\(734\) | − 247.581i | − 0.337304i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.1371 | −0.0232841 | ||||||||
\(737\) | −1729.33 | −2.34645 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −857.588 | −1.16047 | −0.580235 | − | 0.814449i | \(-0.697039\pi\) | ||||
−0.580235 | + | 0.814449i | \(0.697039\pi\) | |||||||
\(740\) | − 452.800i | − 0.611892i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 863.038 | 1.16156 | 0.580779 | − | 0.814061i | \(-0.302748\pi\) | ||||
0.580779 | + | 0.814061i | \(0.302748\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1500.78i | 2.01447i | ||||||||
\(746\) | −744.098 | −0.997450 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 587.261i | − 0.785108i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1486.04 | −1.97875 | −0.989373 | − | 0.145398i | \(-0.953554\pi\) | ||||
−0.989373 | + | 0.145398i | \(0.953554\pi\) | |||||||
\(752\) | 233.542i | 0.310561i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.09333i | 0.00542882i | ||||||||
\(755\) | 1764.10i | 2.33656i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 480.693 | 0.634998 | 0.317499 | − | 0.948259i | \(-0.397157\pi\) | ||||
0.317499 | + | 0.948259i | \(0.397157\pi\) | |||||||
\(758\) | −541.990 | −0.715026 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.56854 | 0.0112744 | ||||||||
\(761\) | 1222.02i | 1.60581i | 0.596107 | + | 0.802905i | \(0.296713\pi\) | ||||
−0.596107 | + | 0.802905i | \(0.703287\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −653.588 | −0.855482 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.180242i | 0 0.000235303i | ||||||||
\(767\) | −119.882 | −0.156300 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 290.136i | − 0.377289i | −0.982045 | − | 0.188645i | \(-0.939591\pi\) | ||||
0.982045 | − | 0.188645i | \(-0.0604094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 216.902 | 0.280961 | ||||||||
\(773\) | − 1131.59i | − 1.46390i | −0.681359 | − | 0.731949i | \(-0.738611\pi\) | ||||
0.681359 | − | 0.731949i | \(-0.261389\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 52.6603i | 0.0679488i | ||||||||
\(776\) | 133.538i | 0.172084i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 527.373 | 0.677857 | ||||||||
\(779\) | −10.6964 | −0.0137309 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1140.08 | 1.45977 | ||||||||
\(782\) | − 71.2467i | − 0.0911083i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1489.11 | −1.89696 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 667.719i | − 0.848435i | −0.905560 | − | 0.424218i | \(-0.860549\pi\) | ||||
0.905560 | − | 0.424218i | \(-0.139451\pi\) | |||||||
\(788\) | −81.0193 | −0.102816 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 227.419i | − 0.287872i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 99.8852 | 0.125959 | ||||||||
\(794\) | 102.554i | 0.129161i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 490.780i | − 0.616557i | ||||||||
\(797\) | 779.700i | 0.978294i | 0.872201 | + | 0.489147i | \(0.162692\pi\) | ||||
−0.872201 | + | 0.489147i | \(0.837308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −970.940 | −1.21519 | ||||||||
\(800\) | −234.912 | −0.293640 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.4113 | 0.0217098 | ||||||||
\(803\) | − 1624.32i | − 2.02282i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.17662 | −0.00270053 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 555.877i | 0.687967i | ||||||||
\(809\) | −1379.82 | −1.70559 | −0.852796 | − | 0.522245i | \(-0.825095\pi\) | ||||
−0.852796 | + | 0.522245i | \(0.825095\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 736.976i | 0.908725i | 0.890817 | + | 0.454363i | \(0.150133\pi\) | ||||
−0.890817 | + | 0.454363i | \(0.849867\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 693.117 | 0.851495 | ||||||||
\(815\) | − 1297.51i | − 1.59203i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.5445i | 0.0251463i | ||||||||
\(818\) | − 262.024i | − 0.320322i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 469.789 | 0.572913 | ||||||||
\(821\) | −4.15642 | −0.00506263 | −0.00253132 | − | 0.999997i | \(-0.500806\pi\) | ||||
−0.00253132 | + | 0.999997i | \(0.500806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1228.08 | 1.49220 | 0.746098 | − | 0.665836i | \(-0.231925\pi\) | ||||
0.746098 | + | 0.665836i | \(0.231925\pi\) | |||||||
\(824\) | 336.836i | 0.408782i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.2548 | −0.0257011 | −0.0128506 | − | 0.999917i | \(-0.504091\pi\) | ||||
−0.0128506 | + | 0.999917i | \(0.504091\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1223.92i | − 1.47639i | −0.674590 | − | 0.738193i | \(-0.735679\pi\) | ||||
0.674590 | − | 0.738193i | \(-0.264321\pi\) | |||||||
\(830\) | 501.186 | 0.603838 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 9.70967i | − 0.0116703i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 606.392 | 0.726218 | ||||||||
\(836\) | 13.1162i | 0.0156892i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 695.335i | − 0.829756i | ||||||||
\(839\) | − 73.5125i | − 0.0876192i | −0.999040 | − | 0.0438096i | \(-0.986050\pi\) | ||||
0.999040 | − | 0.0438096i | \(-0.0139495\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −835.313 | −0.993238 | ||||||||
\(842\) | −666.621 | −0.791712 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −72.5685 | −0.0859817 | ||||||||
\(845\) | 1366.42i | 1.61706i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.49033 | 0.00647445 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 976.635i | − 1.14898i | ||||||||
\(851\) | 84.0892 | 0.0988122 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 704.025i | − 0.825352i | −0.910878 | − | 0.412676i | \(-0.864594\pi\) | ||||
0.910878 | − | 0.412676i | \(-0.135406\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 417.137 | 0.487310 | ||||||||
\(857\) | 161.299i | 0.188213i | 0.995562 | + | 0.0941067i | \(0.0299995\pi\) | ||||
−0.995562 | + | 0.0941067i | \(0.970001\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 902.603i | 1.05076i | 0.850868 | + | 0.525380i | \(0.176077\pi\) | ||||
−0.850868 | + | 0.525380i | \(0.823923\pi\) | |||||||
\(860\) | − 902.322i | − 1.04921i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 646.656 | 0.750181 | ||||||||
\(863\) | 802.705 | 0.930133 | 0.465066 | − | 0.885276i | \(-0.346030\pi\) | ||||
0.465066 | + | 0.885276i | \(0.346030\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1538.69 | −1.77883 | ||||||||
\(866\) | 352.056i | 0.406531i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 348.118 | 0.400596 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 118.872i | − 0.136478i | ||||||||
\(872\) | −368.784 | −0.422917 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.59126i | 0.00182066i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1462.85 | 1.66802 | 0.834008 | − | 0.551753i | \(-0.186041\pi\) | ||||
0.834008 | + | 0.551753i | \(0.186041\pi\) | |||||||
\(878\) | 608.113i | 0.692612i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 576.066i | − 0.654620i | ||||||||
\(881\) | − 851.416i | − 0.966420i | −0.875505 | − | 0.483210i | \(-0.839471\pi\) | ||||
0.875505 | − | 0.483210i | \(-0.160529\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −306.303 | −0.346889 | −0.173444 | − | 0.984844i | \(-0.555490\pi\) | ||||
−0.173444 | + | 0.984844i | \(0.555490\pi\) | |||||||
\(884\) | 40.3675 | 0.0456646 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −537.901 | −0.607111 | ||||||||
\(887\) | − 560.594i | − 0.632011i | −0.948757 | − | 0.316005i | \(-0.897658\pi\) | ||||
0.948757 | − | 0.316005i | \(-0.102342\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −90.6863 | −0.101895 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 177.820i | 0.199350i | ||||||||
\(893\) | 21.6854 | 0.0242838 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1711.80i | 1.91263i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −461.921 | −0.514389 | ||||||||
\(899\) | 3.02414i | 0.00336389i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.8258i | 0.0253339i | ||||||||
\(902\) | 719.122i | 0.797252i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.49033 | 0.00607338 | ||||||||
\(905\) | 2574.23 | 2.84445 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.70563 | 0.00188052 | 0.000940258 | − | 1.00000i | \(-0.499701\pi\) | ||||
0.000940258 | 1.00000i | \(0.499701\pi\) | ||||||||
\(908\) | − 640.574i | − 0.705478i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 629.539 | 0.691042 | 0.345521 | − | 0.938411i | \(-0.387702\pi\) | ||||
0.345521 | + | 0.938411i | \(0.387702\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 767.182i | 0.840287i | ||||||||
\(914\) | −878.392 | −0.961041 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.80751i | 0.00634008i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −562.940 | −0.612557 | −0.306279 | − | 0.951942i | \(-0.599084\pi\) | ||||
−0.306279 | + | 0.951942i | \(0.599084\pi\) | |||||||
\(920\) | − 69.8885i | − 0.0759657i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 241.745i | 0.262196i | ||||||||
\(923\) | 78.3674i | 0.0849051i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1152.68 | 1.24614 | ||||||||
\(926\) | 695.529 | 0.751111 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.4903 | −0.0145370 | ||||||||
\(929\) | 184.016i | 0.198080i | 0.995083 | + | 0.0990398i | \(0.0315771\pi\) | ||||
−0.995083 | + | 0.0990398i | \(0.968423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 33.2203 | 0.0356441 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 424.748i | − 0.454763i | ||||||||
\(935\) | 2394.97 | 2.56146 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 200.616i | 0.214104i | 0.994253 | + | 0.107052i | \(0.0341412\pi\) | ||||
−0.994253 | + | 0.107052i | \(0.965859\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −952.431 | −1.01322 | ||||||||
\(941\) | 715.285i | 0.760133i | 0.924959 | + | 0.380066i | \(0.124099\pi\) | ||||
−0.924959 | + | 0.380066i | \(0.875901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 87.2441i | 0.0925176i | ||||||||
\(944\) | − 395.094i | − 0.418532i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1381.21 | 1.46006 | ||||||||
\(947\) | −865.588 | −0.914032 | −0.457016 | − | 0.889459i | \(-0.651082\pi\) | ||||
−0.457016 | + | 0.889459i | \(0.651082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 111.654 | 0.117654 | ||||||||
\(950\) | 21.8126i | 0.0229607i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1499.57 | 1.57352 | 0.786762 | − | 0.617257i | \(-0.211756\pi\) | ||||
0.786762 | + | 0.617257i | \(0.211756\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2665.46i | − 2.79106i | ||||||||
\(956\) | 794.940 | 0.831527 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 228.852i | 0.238885i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 959.392 | 0.998327 | ||||||||
\(962\) | 47.6439i | 0.0495259i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 604.035i | − 0.626593i | ||||||||
\(965\) | 884.568i | 0.916651i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 606.969 | 0.627682 | 0.313841 | − | 0.949475i | \(-0.398384\pi\) | ||||
0.313841 | + | 0.949475i | \(0.398384\pi\) | |||||||
\(968\) | 539.563 | 0.557400 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −544.593 | −0.561436 | ||||||||
\(971\) | 406.226i | 0.418358i | 0.977877 | + | 0.209179i | \(0.0670791\pi\) | ||||
−0.977877 | + | 0.209179i | \(0.932921\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1089.50 | 1.11858 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 329.190i | 0.337285i | ||||||||
\(977\) | −283.591 | −0.290267 | −0.145133 | − | 0.989412i | \(-0.546361\pi\) | ||||
−0.145133 | + | 0.989412i | \(0.546361\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 138.817i | − 0.141794i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 514.177 | 0.523601 | ||||||||
\(983\) | 956.266i | 0.972803i | 0.873735 | + | 0.486402i | \(0.161691\pi\) | ||||
−0.873735 | + | 0.486402i | \(0.838309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 330.413i | − 0.335445i | ||||||||
\(986\) | − 56.0855i | − 0.0568818i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.901587 | −0.000912537 0 | ||||||||
\(989\) | 167.569 | 0.169433 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −945.568 | −0.954155 | −0.477078 | − | 0.878861i | \(-0.658304\pi\) | ||||
−0.477078 | + | 0.878861i | \(0.658304\pi\) | |||||||
\(992\) | − 7.17346i | − 0.00723131i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2001.50 | 2.01156 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 940.358i | 0.943187i | 0.881816 | + | 0.471594i | \(0.156321\pi\) | ||||
−0.881816 | + | 0.471594i | \(0.843679\pi\) | |||||||
\(998\) | 317.352 | 0.317988 | ||||||||
\(999\) | 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 | 882.3.c.a.685.4 | 4 | ||
3.2 | odd | 2 | 98.3.b.a.97.2 | yes | 4 | ||
7.2 | even | 3 | 882.3.n.j.325.2 | 8 | |||
7.3 | odd | 6 | 882.3.n.j.19.2 | 8 | |||
7.4 | even | 3 | 882.3.n.j.19.1 | 8 | |||
7.5 | odd | 6 | 882.3.n.j.325.1 | 8 | |||
7.6 | odd | 2 | inner | 882.3.c.a.685.3 | 4 | ||
12.11 | even | 2 | 784.3.c.b.97.2 | 4 | |||
21.2 | odd | 6 | 98.3.d.b.31.3 | 8 | |||
21.5 | even | 6 | 98.3.d.b.31.4 | 8 | |||
21.11 | odd | 6 | 98.3.d.b.19.4 | 8 | |||
21.17 | even | 6 | 98.3.d.b.19.3 | 8 | |||
21.20 | even | 2 | 98.3.b.a.97.1 | ✓ | 4 | ||
84.11 | even | 6 | 784.3.s.j.705.2 | 8 | |||
84.23 | even | 6 | 784.3.s.j.129.3 | 8 | |||
84.47 | odd | 6 | 784.3.s.j.129.2 | 8 | |||
84.59 | odd | 6 | 784.3.s.j.705.3 | 8 | |||
84.83 | odd | 2 | 784.3.c.b.97.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.3.b.a.97.1 | ✓ | 4 | 21.20 | even | 2 | ||
98.3.b.a.97.2 | yes | 4 | 3.2 | odd | 2 | ||
98.3.d.b.19.3 | 8 | 21.17 | even | 6 | |||
98.3.d.b.19.4 | 8 | 21.11 | odd | 6 | |||
98.3.d.b.31.3 | 8 | 21.2 | odd | 6 | |||
98.3.d.b.31.4 | 8 | 21.5 | even | 6 | |||
784.3.c.b.97.2 | 4 | 12.11 | even | 2 | |||
784.3.c.b.97.3 | 4 | 84.83 | odd | 2 | |||
784.3.s.j.129.2 | 8 | 84.47 | odd | 6 | |||
784.3.s.j.129.3 | 8 | 84.23 | even | 6 | |||
784.3.s.j.705.2 | 8 | 84.11 | even | 6 | |||
784.3.s.j.705.3 | 8 | 84.59 | odd | 6 | |||
882.3.c.a.685.3 | 4 | 7.6 | odd | 2 | inner | ||
882.3.c.a.685.4 | 4 | 1.1 | even | 1 | trivial | ||
882.3.n.j.19.1 | 8 | 7.4 | even | 3 | |||
882.3.n.j.19.2 | 8 | 7.3 | odd | 6 | |||
882.3.n.j.325.1 | 8 | 7.5 | odd | 6 | |||
882.3.n.j.325.2 | 8 | 7.2 | even | 3 |