Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(104,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.104");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.g (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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-5}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 104.4 | ||
Root | \(-1.32288 + 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.104 |
Dual form | 105.4.g.a.104.3 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 2.64575 | + | 4.47214i | 0.509175 | + | 0.860663i | ||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | − | 11.1803i | − | 1.00000i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.5203 | −1.00000 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −13.0000 | + | 23.6643i | −0.481481 | + | 0.876456i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 11.8322i | − | 0.324321i | −0.986764 | − | 0.162160i | \(-0.948154\pi\) | ||
0.986764 | − | 0.162160i | \(-0.0518462\pi\) | |||||||
\(12\) | −21.1660 | − | 35.7771i | −0.509175 | − | 0.860663i | ||||
\(13\) | −84.6640 | −1.80628 | −0.903138 | − | 0.429351i | \(-0.858742\pi\) | ||||
−0.903138 | + | 0.429351i | \(0.858742\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 50.0000 | − | 29.5804i | 0.860663 | − | 0.509175i | ||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | − | 102.859i | − | 1.46747i | −0.679435 | − | 0.733735i | \(-0.737775\pi\) | ||
0.679435 | − | 0.733735i | \(-0.262225\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 89.4427i | 1.00000i | ||||||||
\(21\) | −49.0000 | − | 82.8251i | −0.509175 | − | 0.860663i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −125.000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −140.225 | + | 4.47214i | −0.999492 | + | 0.0318764i | ||||
\(28\) | 148.162 | 1.00000 | ||||||||
\(29\) | 307.636i | 1.96988i | 0.172889 | + | 0.984941i | \(0.444690\pi\) | ||||
−0.172889 | + | 0.984941i | \(0.555310\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 52.9150 | − | 31.3050i | 0.279131 | − | 0.165136i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 207.063i | 1.00000i | ||||||||
\(36\) | 104.000 | − | 189.315i | 0.481481 | − | 0.876456i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −224.000 | − | 378.629i | −0.919710 | − | 1.55459i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 94.6573i | 0.324321i | ||||||||
\(45\) | 264.575 | + | 145.344i | 0.876456 | + | 0.481481i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 178.885i | 0.555173i | 0.960701 | + | 0.277586i | \(0.0895345\pi\) | ||||
−0.960701 | + | 0.277586i | \(0.910466\pi\) | |||||||
\(48\) | 169.328 | + | 286.217i | 0.509175 | + | 0.860663i | ||||
\(49\) | 343.000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 460.000 | − | 272.140i | 1.26300 | − | 0.747200i | ||||
\(52\) | 677.312 | 1.80628 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −132.288 | −0.324321 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −400.000 | + | 236.643i | −0.860663 | + | 0.509175i | ||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 240.763 | − | 438.269i | 0.481481 | − | 0.876456i | ||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 946.573i | 1.80628i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 822.873i | 1.46747i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 863.748i | − | 1.44377i | −0.692011 | − | 0.721887i | \(-0.743275\pi\) | ||
0.692011 | − | 0.721887i | \(-0.256725\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1132.38 | −1.81555 | −0.907776 | − | 0.419456i | \(-0.862221\pi\) | ||||
−0.907776 | + | 0.419456i | \(0.862221\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −330.719 | − | 559.017i | −0.509175 | − | 0.860663i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 219.135i | 0.324321i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 236.000 | 0.336102 | 0.168051 | − | 0.985778i | \(-0.446253\pi\) | ||||
0.168051 | + | 0.985778i | \(0.446253\pi\) | |||||||
\(80\) | − | 715.542i | − | 1.00000i | ||||||
\(81\) | −391.000 | − | 615.272i | −0.536351 | − | 0.843995i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1511.58i | − | 1.99901i | −0.0314901 | − | 0.999504i | \(-0.510025\pi\) | ||
0.0314901 | − | 0.999504i | \(-0.489975\pi\) | |||||||
\(84\) | 392.000 | + | 662.601i | 0.509175 | + | 0.860663i | ||||
\(85\) | −1150.00 | −1.46747 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1375.79 | + | 813.929i | −1.69541 | + | 1.00302i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1568.00 | 1.80628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 963.053 | 1.00807 | 0.504037 | − | 0.863682i | \(-0.331847\pi\) | ||||
0.504037 | + | 0.863682i | \(0.331847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 280.000 | + | 153.818i | 0.284253 | + | 0.156155i | ||||
\(100\) | 1000.00 | 1.00000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −799.017 | −0.764364 | −0.382182 | − | 0.924087i | \(-0.624827\pi\) | ||||
−0.382182 | + | 0.924087i | \(0.624827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −926.013 | + | 547.837i | −0.860663 | + | 0.509175i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 1121.80 | − | 35.7771i | 0.999492 | − | 0.0318764i | ||||
\(109\) | −2266.00 | −1.99122 | −0.995612 | − | 0.0935765i | \(-0.970170\pi\) | ||||
−0.995612 | + | 0.0935765i | \(0.970170\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1185.30 | −1.00000 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 2461.09i | − | 1.96988i | ||||||
\(117\) | 1100.63 | − | 2003.52i | 0.869688 | − | 1.58312i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1904.98i | 1.46747i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1191.00 | 0.894816 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1397.54i | 1.00000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −423.320 | + | 250.440i | −0.279131 | + | 0.165136i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 50.0000 | + | 1567.76i | 0.0318764 | + | 0.999492i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | − | 1656.50i | − | 1.00000i | ||||||
\(141\) | −800.000 | + | 473.286i | −0.477817 | + | 0.282680i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1001.76i | 0.585813i | ||||||||
\(144\) | −832.000 | + | 1514.52i | −0.481481 | + | 0.876456i | ||||
\(145\) | 3439.48 | 1.96988 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 907.493 | + | 1533.94i | 0.509175 | + | 0.860663i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2674.07i | − | 1.47026i | −0.677928 | − | 0.735128i | \(-0.737122\pi\) | ||
0.677928 | − | 0.735128i | \(-0.262878\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2788.00 | −1.50254 | −0.751272 | − | 0.659992i | \(-0.770559\pi\) | ||||
−0.751272 | + | 0.659992i | \(0.770559\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2434.09 | + | 1337.17i | 1.28617 | + | 0.706560i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1792.00 | + | 3029.03i | 0.919710 | + | 1.55459i | ||||
\(157\) | 486.818 | 0.247467 | 0.123734 | − | 0.992315i | \(-0.460513\pi\) | ||||
0.123734 | + | 0.992315i | \(0.460513\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −350.000 | − | 591.608i | −0.165136 | − | 0.279131i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2558.06i | − | 1.18532i | −0.805452 | − | 0.592661i | \(-0.798077\pi\) | ||
0.805452 | − | 0.592661i | \(-0.201923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4971.00 | 2.26263 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4405.05i | 1.93590i | 0.251150 | + | 0.967948i | \(0.419191\pi\) | ||||
−0.251150 | + | 0.967948i | \(0.580809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2315.03 | 1.00000 | ||||||||
\(176\) | − | 757.258i | − | 0.324321i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4697.37i | − | 1.96144i | −0.195419 | − | 0.980720i | \(-0.562607\pi\) | ||
0.195419 | − | 0.980720i | \(-0.437393\pi\) | |||||||
\(180\) | −2116.60 | − | 1162.76i | −0.876456 | − | 0.481481i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1217.05 | −0.475931 | ||||||||
\(188\) | − | 1431.08i | − | 0.555173i | ||||||
\(189\) | 2597.00 | − | 82.8251i | 0.999492 | − | 0.0318764i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3182.85i | 1.20577i | 0.797826 | + | 0.602887i | \(0.205983\pi\) | ||||
−0.797826 | + | 0.602887i | \(0.794017\pi\) | |||||||
\(192\) | −1354.62 | − | 2289.73i | −0.509175 | − | 0.860663i | ||||
\(193\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4233.20 | + | 2504.40i | −1.55459 | + | 0.919710i | ||||
\(196\) | −2744.00 | −1.00000 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 5697.50i | − | 1.96988i | ||||||
\(204\) | −3680.00 | + | 2177.12i | −1.26300 | + | 0.747200i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5418.50 | −1.80628 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2392.00 | −0.780436 | −0.390218 | − | 0.920722i | \(-0.627600\pi\) | ||||
−0.390218 | + | 0.920722i | \(0.627600\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3862.80 | − | 2285.26i | 1.24260 | − | 0.735134i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2996.00 | − | 5064.16i | −0.924433 | − | 1.56258i | ||||
\(220\) | 1058.30 | 0.324321 | ||||||||
\(221\) | 8708.47i | 2.65066i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5180.38 | −1.55562 | −0.777812 | − | 0.628498i | \(-0.783670\pi\) | ||||
−0.777812 | + | 0.628498i | \(0.783670\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1625.00 | − | 2958.04i | 0.481481 | − | 0.876456i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4767.30i | 1.39391i | 0.717117 | + | 0.696953i | \(0.245461\pi\) | ||||
−0.717117 | + | 0.696953i | \(0.754539\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −980.000 | + | 579.776i | −0.279131 | + | 0.165136i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2000.00 | 0.555173 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 624.397 | + | 1055.42i | 0.171135 | + | 0.289271i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4673.70i | 1.26492i | 0.774592 | + | 0.632462i | \(0.217955\pi\) | ||||
−0.774592 | + | 0.632462i | \(0.782045\pi\) | |||||||
\(240\) | 3200.00 | − | 1893.15i | 0.860663 | − | 0.509175i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1717.09 | − | 3376.46i | 0.453299 | − | 0.891359i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 3834.86i | − | 1.00000i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6760.00 | − | 3999.27i | 1.72047 | − | 1.01785i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −1926.11 | + | 3506.15i | −0.481481 | + | 0.876456i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3042.61 | − | 5142.96i | −0.747200 | − | 1.26300i | ||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 3358.57i | 0.815183i | 0.913164 | + | 0.407592i | \(0.133631\pi\) | ||||
−0.913164 | + | 0.407592i | \(0.866369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 7572.58i | − | 1.80628i | ||||||
\(261\) | −7280.00 | − | 3999.27i | −1.72652 | − | 0.948462i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | − | 6582.98i | − | 1.46747i | ||||||
\(273\) | 4148.54 | + | 7012.31i | 0.919710 | + | 1.55459i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1479.02i | 0.324321i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4780.19i | 1.01481i | 0.861707 | + | 0.507406i | \(0.169396\pi\) | ||||
−0.861707 | + | 0.507406i | \(0.830604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2227.72 | −0.467931 | −0.233965 | − | 0.972245i | \(-0.575170\pi\) | ||||
−0.233965 | + | 0.972245i | \(0.575170\pi\) | |||||||
\(284\) | 6909.98i | 1.44377i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5667.00 | −1.15347 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2548.00 | + | 4306.91i | 0.513287 | + | 0.867613i | ||||
\(292\) | 9059.05 | 1.81555 | ||||||||
\(293\) | 6739.51i | 1.34378i | 0.740653 | + | 0.671888i | \(0.234516\pi\) | ||||
−0.740653 | + | 0.671888i | \(0.765484\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 52.9150 | + | 1659.16i | 0.0103382 | + | 0.324156i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2645.75 | + | 4472.14i | 0.509175 | + | 0.860663i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9011.43 | 1.67527 | 0.837637 | − | 0.546227i | \(-0.183936\pi\) | ||||
0.837637 | + | 0.546227i | \(0.183936\pi\) | |||||||
\(308\) | − | 1753.08i | − | 0.324321i | ||||||
\(309\) | −2114.00 | − | 3573.31i | −0.389195 | − | 0.657860i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2677.50 | 0.483518 | 0.241759 | − | 0.970336i | \(-0.422276\pi\) | ||||
0.241759 | + | 0.970336i | \(0.422276\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4900.00 | − | 2691.82i | −0.876456 | − | 0.481481i | ||||
\(316\) | −1888.00 | −0.336102 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3640.00 | 0.638874 | ||||||||
\(320\) | 5724.33i | 1.00000i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 3128.00 | + | 4922.18i | 0.536351 | + | 0.843995i | ||||
\(325\) | 10583.0 | 1.80628 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5995.27 | − | 10133.9i | −1.01388 | − | 1.71377i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3313.00i | − | 0.555173i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7432.00 | −1.23414 | −0.617069 | − | 0.786909i | \(-0.711680\pi\) | ||||
−0.617069 | + | 0.786909i | \(0.711680\pi\) | |||||||
\(332\) | 12092.7i | 1.99901i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3136.00 | − | 5300.81i | −0.509175 | − | 0.860663i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9200.00 | 1.46747 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6352.45 | −1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 11006.3 | − | 6511.43i | 1.69541 | − | 1.00302i | ||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11872.0 | − | 378.629i | 1.80536 | − | 0.0575776i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6220.74i | − | 0.937951i | −0.883211 | − | 0.468975i | \(-0.844623\pi\) | ||
0.883211 | − | 0.468975i | \(-0.155377\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9656.99 | −1.44377 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8519.32 | + | 5040.10i | −1.26300 | + | 0.747200i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11086.7i | − | 1.62990i | −0.579529 | − | 0.814952i | \(-0.696763\pi\) | ||
0.579529 | − | 0.814952i | \(-0.303237\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6859.00 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3151.09 | + | 5326.31i | 0.455618 | + | 0.770135i | ||||
\(364\) | −12544.0 | −1.80628 | ||||||||
\(365\) | 12660.4i | 1.81555i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14038.4 | −1.99672 | −0.998360 | − | 0.0572477i | \(-0.981768\pi\) | ||||
−0.998360 | + | 0.0572477i | \(0.981768\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6250.00 | + | 3697.55i | −0.860663 | + | 0.509175i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 26045.7i | − | 3.55815i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14096.0 | 1.91046 | 0.955228 | − | 0.295870i | \(-0.0956097\pi\) | ||||
0.955228 | + | 0.295870i | \(0.0956097\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4686.80i | 0.625285i | 0.949871 | + | 0.312643i | \(0.101214\pi\) | ||||
−0.949871 | + | 0.312643i | \(0.898786\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2450.00 | 0.324321 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7704.43 | −1.00807 | ||||||||
\(389\) | 6697.00i | 0.872883i | 0.899733 | + | 0.436442i | \(0.143761\pi\) | ||||
−0.899733 | + | 0.436442i | \(0.856239\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 2638.56i | − | 0.336102i | ||||||
\(396\) | −2240.00 | − | 1230.54i | −0.284253 | − | 0.156155i | ||||
\(397\) | −275.158 | −0.0347854 | −0.0173927 | − | 0.999849i | \(-0.505537\pi\) | ||||
−0.0173927 | + | 0.999849i | \(0.505537\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8000.00 | −1.00000 | ||||||||
\(401\) | − | 9702.37i | − | 1.20826i | −0.796885 | − | 0.604131i | \(-0.793520\pi\) | ||
0.796885 | − | 0.604131i | \(-0.206480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6878.95 | + | 4371.51i | −0.843995 | + | 0.536351i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6392.14 | 0.764364 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16900.0 | −1.99901 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 7408.10 | − | 4382.69i | 0.860663 | − | 0.509175i | ||||
\(421\) | −3922.00 | −0.454030 | −0.227015 | − | 0.973891i | \(-0.572897\pi\) | ||||
−0.227015 | + | 0.973891i | \(0.572897\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4233.20 | − | 2325.51i | −0.486585 | − | 0.267305i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12857.4i | 1.46747i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4480.00 | + | 2650.40i | −0.504188 | + | 0.298281i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17476.1i | − | 1.95312i | −0.215249 | − | 0.976559i | \(-0.569056\pi\) | ||
0.215249 | − | 0.976559i | \(-0.430944\pi\) | |||||||
\(432\) | −8974.39 | + | 286.217i | −0.999492 | + | 0.0318764i | ||||
\(433\) | −12562.0 | −1.39421 | −0.697105 | − | 0.716970i | \(-0.745529\pi\) | ||||
−0.697105 | + | 0.716970i | \(0.745529\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9100.00 | + | 15381.8i | 1.00302 | + | 1.69541i | ||||
\(436\) | 18128.0 | 1.99122 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4459.00 | + | 8116.86i | −0.481481 | + | 0.876456i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11958.8 | − | 7074.92i | 1.26540 | − | 0.748618i | ||||
\(448\) | 9482.37 | 1.00000 | ||||||||
\(449\) | − | 15239.8i | − | 1.60181i | −0.598793 | − | 0.800904i | \(-0.704353\pi\) | ||
0.598793 | − | 0.800904i | \(-0.295647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7376.35 | − | 12468.3i | −0.765058 | − | 1.29318i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 17530.8i | − | 1.80628i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 460.000 | + | 14423.4i | 0.0467777 | + | 1.46673i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 19688.7i | 1.96988i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17164.1i | 1.70077i | 0.526164 | + | 0.850383i | \(0.323630\pi\) | ||||
−0.526164 | + | 0.850383i | \(0.676370\pi\) | |||||||
\(468\) | −8805.06 | + | 16028.1i | −0.869688 | + | 1.58312i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1288.00 | + | 2177.12i | 0.126004 | + | 0.212986i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 15239.8i | − | 1.46747i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9528.00 | −0.894816 | ||||||||
\(485\) | − | 10767.3i | − | 1.00807i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 17689.1i | − | 1.62586i | −0.582362 | − | 0.812930i | \(-0.697871\pi\) | ||
0.582362 | − | 0.812930i | \(-0.302129\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31643.2 | 2.89075 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1719.74 | − | 3130.50i | 0.156155 | − | 0.284253i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15996.8i | 1.44377i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7544.00 | 0.676785 | 0.338393 | − | 0.941005i | \(-0.390117\pi\) | ||||
0.338393 | + | 0.941005i | \(0.390117\pi\) | |||||||
\(500\) | − | 11180.3i | − | 1.00000i | ||||||
\(501\) | 11440.0 | − | 6768.00i | 1.02016 | − | 0.603536i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2432.84i | 0.215656i | 0.994170 | + | 0.107828i | \(0.0343896\pi\) | ||||
−0.994170 | + | 0.107828i | \(0.965610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13152.0 | + | 22231.0i | 1.15208 | + | 1.94736i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20972.0 | 1.81555 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8933.28i | 0.764364i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2116.60 | 0.180054 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19700.0 | + | 11654.7i | −1.66615 | + | 0.985710i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7296.98 | 0.610086 | 0.305043 | − | 0.952339i | \(-0.401329\pi\) | ||||
0.305043 | + | 0.952339i | \(0.401329\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6125.00 | + | 10353.1i | 0.509175 | + | 0.860663i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3386.56 | − | 2003.52i | 0.279131 | − | 0.165136i | ||||
\(529\) | −12167.0 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21007.3 | − | 12428.1i | 1.68814 | − | 0.998716i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 4058.43i | − | 0.324321i | ||||||
\(540\) | −400.000 | − | 12542.1i | −0.0318764 | − | 0.999492i | ||||
\(541\) | −9718.00 | −0.772291 | −0.386146 | − | 0.922438i | \(-0.626194\pi\) | ||||
−0.386146 | + | 0.922438i | \(0.626194\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25334.7i | 1.99122i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4370.78 | −0.336102 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 13252.0i | 1.00000i | ||||||||
\(561\) | −3220.00 | − | 5442.79i | −0.242332 | − | 0.409617i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 13908.3i | − | 1.04115i | −0.853816 | − | 0.520574i | \(-0.825718\pi\) | ||
0.853816 | − | 0.520574i | \(-0.174282\pi\) | |||||||
\(564\) | 6400.00 | − | 3786.29i | 0.477817 | − | 0.282680i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7241.42 | + | 11395.0i | 0.536351 | + | 0.843995i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25226.2i | 1.85859i | 0.369343 | + | 0.929293i | \(0.379583\pi\) | ||||
−0.369343 | + | 0.929293i | \(0.620417\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22048.0 | −1.61590 | −0.807951 | − | 0.589250i | \(-0.799423\pi\) | ||||
−0.807951 | + | 0.589250i | \(0.799423\pi\) | |||||||
\(572\) | − | 8014.07i | − | 0.585813i | ||||||
\(573\) | −14234.1 | + | 8421.03i | −1.03777 | + | 0.613951i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6656.00 | − | 12116.1i | 0.481481 | − | 0.876456i | ||||
\(577\) | −18848.3 | −1.35991 | −0.679954 | − | 0.733255i | \(-0.738000\pi\) | ||||
−0.679954 | + | 0.733255i | \(0.738000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −27515.8 | −1.96988 | ||||||||
\(581\) | 27994.9i | 1.99901i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22400.0 | − | 12305.4i | −1.58312 | − | 0.869688i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 15035.3i | − | 1.05720i | −0.848872 | − | 0.528598i | \(-0.822718\pi\) | ||
0.848872 | − | 0.528598i | \(-0.177282\pi\) | |||||||
\(588\) | −7259.94 | − | 12271.5i | −0.509175 | − | 0.860663i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1104.62i | 0.0764944i | 0.999268 | + | 0.0382472i | \(0.0121774\pi\) | ||||
−0.999268 | + | 0.0382472i | \(0.987823\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21298.3 | 1.46747 | ||||||||
\(596\) | 21392.5i | 1.47026i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 27273.1i | − | 1.86035i | −0.367116 | − | 0.930175i | \(-0.619655\pi\) | ||
0.367116 | − | 0.930175i | \(-0.380345\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22304.0 | 1.50254 | ||||||||
\(605\) | − | 13315.8i | − | 0.894816i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9085.51 | −0.607528 | −0.303764 | − | 0.952747i | \(-0.598243\pi\) | ||||
−0.303764 | + | 0.952747i | \(0.598243\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25480.0 | − | 15074.2i | 1.69541 | − | 1.00302i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 15145.2i | − | 1.00280i | ||||||
\(612\) | −19472.7 | − | 10697.3i | −1.28617 | − | 0.706560i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −14336.0 | − | 24232.3i | −0.919710 | − | 1.55459i | ||||
\(625\) | 15625.0 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3894.55 | −0.247467 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14852.0 | 0.937003 | 0.468501 | − | 0.883463i | \(-0.344794\pi\) | ||||
0.468501 | + | 0.883463i | \(0.344794\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6328.64 | − | 10697.3i | −0.397379 | − | 0.671693i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29039.8 | −1.80628 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20440.0 | + | 11228.7i | 1.26541 | + | 0.695151i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15003.2i | 0.924477i | 0.886756 | + | 0.462239i | \(0.152954\pi\) | ||||
−0.886756 | + | 0.462239i | \(0.847046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30061.0 | 1.84369 | 0.921844 | − | 0.387562i | \(-0.126683\pi\) | ||||
0.921844 | + | 0.387562i | \(0.126683\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28997.3i | 1.76198i | 0.473133 | + | 0.880991i | \(0.343123\pi\) | ||||
−0.473133 | + | 0.880991i | \(0.656877\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14721.0 | − | 26797.0i | 0.874154 | − | 1.59125i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11489.0i | 0.679133i | 0.940582 | + | 0.339567i | \(0.110280\pi\) | ||||
−0.940582 | + | 0.339567i | \(0.889720\pi\) | |||||||
\(660\) | 2800.00 | + | 4732.86i | 0.165136 | + | 0.279131i | ||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −38945.5 | + | 23040.4i | −2.28132 | + | 1.34965i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 20464.5i | 1.18532i | ||||||||
\(669\) | −13706.0 | − | 23167.4i | −0.792085 | − | 1.33887i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17528.1 | − | 559.017i | 0.999492 | − | 0.0318764i | ||||
\(676\) | −39768.0 | −2.26263 | ||||||||
\(677\) | − | 31577.8i | − | 1.79266i | −0.443386 | − | 0.896331i | \(-0.646223\pi\) | ||
0.443386 | − | 0.896331i | \(-0.353777\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17836.0 | −1.00807 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21320.0 | + | 12613.1i | −1.19968 | + | 0.709742i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | − | 35240.4i | − | 1.93590i | ||||||
\(693\) | −5185.67 | − | 2848.75i | −0.284253 | − | 0.156155i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18520.3 | −1.00000 | ||||||||
\(701\) | 16068.1i | 0.865739i | 0.901457 | + | 0.432869i | \(0.142499\pi\) | ||||
−0.901457 | + | 0.432869i | \(0.857501\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 6058.07i | 0.324321i | ||||||||
\(705\) | 5291.50 | + | 8944.27i | 0.282680 | + | 0.477817i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2126.00 | 0.112614 | 0.0563072 | − | 0.998413i | \(-0.482067\pi\) | ||||
0.0563072 | + | 0.998413i | \(0.482067\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3068.00 | + | 5584.78i | −0.161827 | + | 0.294579i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11200.0 | 0.585813 | ||||||||
\(716\) | 37578.9i | 1.96144i | ||||||||
\(717\) | −20901.4 | + | 12365.5i | −1.08867 | + | 0.644068i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 16932.8 | + | 9302.04i | 0.876456 | + | 0.481481i | ||||
\(721\) | 14798.0 | 0.764364 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 38454.5i | − | 1.96988i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11392.6 | 0.581194 | 0.290597 | − | 0.956845i | \(-0.406146\pi\) | ||||
0.290597 | + | 0.956845i | \(0.406146\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19643.0 | − | 1254.21i | 0.997968 | − | 0.0637204i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16488.3 | 0.830846 | 0.415423 | − | 0.909628i | \(-0.363634\pi\) | ||||
0.415423 | + | 0.909628i | \(0.363634\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17150.0 | − | 10146.1i | 0.860663 | − | 0.509175i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23056.0 | −1.14767 | −0.573835 | − | 0.818971i | \(-0.694545\pi\) | ||||
−0.573835 | + | 0.818971i | \(0.694545\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29897.0 | −1.47026 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35770.6 | + | 19650.6i | 1.75204 | + | 0.962485i | ||||
\(748\) | 9736.36 | 0.475931 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27092.0 | 1.31638 | 0.658190 | − | 0.752852i | \(-0.271322\pi\) | ||||
0.658190 | + | 0.752852i | \(0.271322\pi\) | |||||||
\(752\) | 11448.7i | 0.555173i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31170.8i | 1.50254i | ||||||||
\(756\) | −20776.0 | + | 662.601i | −0.999492 | + | 0.0318764i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41966.9 | 1.99122 | ||||||||
\(764\) | − | 25462.8i | − | 1.20577i | ||||||
\(765\) | 14950.0 | − | 27214.0i | 0.706560 | − | 1.28617i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 10837.0 | + | 18317.9i | 0.509175 | + | 0.860663i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15020.0 | + | 8885.95i | −0.701598 | + | 0.415071i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 5174.26i | − | 0.240757i | −0.992728 | − | 0.120379i | \(-0.961589\pi\) | ||
0.992728 | − | 0.120379i | \(-0.0384108\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 33865.6 | − | 20035.2i | 1.55459 | − | 0.919710i | ||||
\(781\) | −10220.0 | −0.468246 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1375.79 | − | 43138.2i | −0.0627928 | − | 1.96888i | ||||
\(784\) | 21952.0 | 1.00000 | ||||||||
\(785\) | − | 5442.79i | − | 0.247467i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15202.5 | 0.688577 | 0.344289 | − | 0.938864i | \(-0.388120\pi\) | ||||
0.344289 | + | 0.938864i | \(0.388120\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41031.8i | 1.82362i | 0.410616 | + | 0.911808i | \(0.365314\pi\) | ||||
−0.410616 | + | 0.911808i | \(0.634686\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18400.0 | 0.814700 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13398.5i | 0.588821i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29485.7i | 1.28141i | 0.767786 | + | 0.640707i | \(0.221359\pi\) | ||||
−0.767786 | + | 0.640707i | \(0.778641\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 45580.0i | 1.96988i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 29440.0 | − | 17416.9i | 1.26300 | − | 0.747200i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20384.0 | + | 37105.7i | −0.869688 | + | 1.58312i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14364.2i | 0.610616i | 0.952254 | + | 0.305308i | \(0.0987594\pi\) | ||||
−0.952254 | + | 0.305308i | \(0.901241\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6614.38 | + | 3913.12i | −0.279131 | + | 0.165136i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 43348.0 | 1.80628 | ||||||||
\(833\) | − | 35280.7i | − | 1.46747i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28600.0 | −1.18532 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −70251.0 | −2.88044 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21377.7 | + | 12647.2i | −0.873412 | + | 0.516717i | ||||
\(844\) | 19136.0 | 0.780436 | ||||||||
\(845\) | − | 55577.5i | − | 2.26263i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22057.6 | −0.894816 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5894.00 | − | 9962.68i | −0.238259 | − | 0.402731i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −30902.4 | + | 18282.1i | −1.24260 | + | 0.735134i | ||||
\(853\) | −32468.7 | −1.30329 | −0.651645 | − | 0.758524i | \(-0.725921\pi\) | ||||
−0.651645 | + | 0.758524i | \(0.725921\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7428.22i | − | 0.296083i | −0.988981 | − | 0.148041i | \(-0.952703\pi\) | ||
0.988981 | − | 0.148041i | \(-0.0472969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49250.0 | 1.93590 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14993.5 | − | 25343.6i | −0.587318 | − | 0.992749i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2792.39i | − | 0.109005i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12519.7 | + | 22790.0i | −0.485369 | + | 0.883534i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 25882.8i | − | 1.00000i | ||||||
\(876\) | 23968.0 | + | 40513.3i | 0.924433 | + | 1.56258i | ||||
\(877\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30140.0 | + | 17831.1i | −1.15654 | + | 0.684217i | ||||
\(880\) | −8466.40 | −0.324321 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | − | 69667.8i | − | 2.65066i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 49408.2i | − | 1.87031i | −0.354241 | − | 0.935154i | \(-0.615261\pi\) | ||
0.354241 | − | 0.935154i | \(-0.384739\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7280.00 | + | 4626.37i | −0.273725 | + | 0.173950i | ||||
\(892\) | 41443.0 | 1.55562 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −52518.2 | −1.96144 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −13000.0 | + | 23664.3i | −0.481481 | + | 0.876456i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(908\) | − | 38138.4i | − | 1.39391i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45376.3i | − | 1.65026i | −0.564944 | − | 0.825129i | \(-0.691102\pi\) | ||
0.564944 | − | 0.825129i | \(-0.308898\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17885.3 | −0.648320 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55564.0 | −1.99444 | −0.997218 | − | 0.0745363i | \(-0.976252\pi\) | ||||
−0.997218 | + | 0.0745363i | \(0.976252\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23842.0 | + | 40300.3i | 0.853008 | + | 1.44185i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 73128.4i | 2.60785i | ||||||||
\(924\) | 7840.00 | − | 4638.21i | 0.279131 | − | 0.165136i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10387.2 | − | 18908.2i | 0.368027 | − | 0.669931i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13607.0i | 0.475931i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54280.2 | −1.89248 | −0.946242 | − | 0.323459i | \(-0.895154\pi\) | ||||
−0.946242 | + | 0.323459i | \(0.895154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7084.00 | + | 11974.1i | 0.246196 | + | 0.416146i | ||||
\(940\) | −16000.0 | −0.555173 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −926.013 | − | 29035.3i | −0.0318764 | − | 0.999492i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | −4995.18 | − | 8443.39i | −0.171135 | − | 0.289271i | ||||
\(949\) | 95872.0 | 3.27939 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35585.4 | 1.20577 | ||||||||
\(956\) | − | 37389.6i | − | 1.26492i | ||||||
\(957\) | 9630.53 | + | 16278.6i | 0.325299 | + | 0.549855i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −25600.0 | + | 15145.2i | −0.860663 | + | 0.509175i | ||||
\(961\) | 29791.0 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −13736.7 | + | 27011.7i | −0.453299 | + | 0.891359i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28000.0 | + | 47328.6i | 0.919710 | + | 1.55459i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 30678.9i | 1.00000i | ||||||||
\(981\) | 29458.0 | − | 53623.3i | 0.958738 | − | 1.74522i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 61160.9i | − | 1.98447i | −0.124390 | − | 0.992233i | \(-0.539698\pi\) | ||
0.124390 | − | 0.992233i | \(-0.460302\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14816.2 | − | 8765.39i | 0.477817 | − | 0.282680i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13988.0 | 0.448379 | 0.224189 | − | 0.974546i | \(-0.428027\pi\) | ||||
0.224189 | + | 0.974546i | \(0.428027\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19663.2 | − | 33236.9i | −0.628392 | − | 1.06218i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −54080.0 | + | 31994.2i | −1.72047 | + | 1.01785i | ||||
\(997\) | −49041.6 | −1.55784 | −0.778919 | − | 0.627125i | \(-0.784232\pi\) | ||||
−0.778919 | + | 0.627125i | \(0.784232\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 105.4.g.a.104.4 | yes | 4 | |
3.2 | odd | 2 | inner | 105.4.g.a.104.3 | yes | 4 | |
5.4 | even | 2 | inner | 105.4.g.a.104.1 | ✓ | 4 | |
7.6 | odd | 2 | inner | 105.4.g.a.104.1 | ✓ | 4 | |
15.14 | odd | 2 | inner | 105.4.g.a.104.2 | yes | 4 | |
21.20 | even | 2 | inner | 105.4.g.a.104.2 | yes | 4 | |
35.34 | odd | 2 | CM | 105.4.g.a.104.4 | yes | 4 | |
105.104 | even | 2 | inner | 105.4.g.a.104.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.g.a.104.1 | ✓ | 4 | 5.4 | even | 2 | inner | |
105.4.g.a.104.1 | ✓ | 4 | 7.6 | odd | 2 | inner | |
105.4.g.a.104.2 | yes | 4 | 15.14 | odd | 2 | inner | |
105.4.g.a.104.2 | yes | 4 | 21.20 | even | 2 | inner | |
105.4.g.a.104.3 | yes | 4 | 3.2 | odd | 2 | inner | |
105.4.g.a.104.3 | yes | 4 | 105.104 | even | 2 | inner | |
105.4.g.a.104.4 | yes | 4 | 1.1 | even | 1 | trivial | |
105.4.g.a.104.4 | yes | 4 | 35.34 | odd | 2 | CM |