Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 39x^{10} + 549x^{8} + 3500x^{6} + 10236x^{4} + 11952x^{2} + 4624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.8 | ||
Root | \(1.08600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.4.c.d.383.7 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.04120 | + | 4.21320i | 0.585280 | + | 0.810831i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.33303i | 0.834771i | 0.908729 | + | 0.417386i | \(0.137054\pi\) | ||||
−0.908729 | + | 0.417386i | \(0.862946\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 36.3792i | − | 1.96429i | −0.188120 | − | 0.982146i | \(-0.560240\pi\) | ||
0.188120 | − | 0.982146i | \(-0.439760\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.50216 | + | 25.6264i | −0.314895 | + | 0.949127i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 48.4408 | 1.32777 | 0.663884 | − | 0.747836i | \(-0.268907\pi\) | ||||
0.663884 | + | 0.747836i | \(0.268907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25.8988 | 0.552541 | 0.276270 | − | 0.961080i | \(-0.410901\pi\) | ||||
0.276270 | + | 0.961080i | \(0.410901\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −39.3219 | + | 28.3836i | −0.676859 | + | 0.488575i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 74.2219i | − | 1.05891i | −0.848338 | − | 0.529455i | \(-0.822397\pi\) | ||
0.848338 | − | 0.529455i | \(-0.177603\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 82.9826i | 1.00197i | 0.865455 | + | 0.500987i | \(0.167030\pi\) | ||||
−0.865455 | + | 0.500987i | \(0.832970\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 153.273 | − | 110.637i | 1.59271 | − | 1.14966i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 179.084 | 1.62355 | 0.811775 | − | 0.583971i | \(-0.198502\pi\) | ||||
0.811775 | + | 0.583971i | \(0.198502\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 37.8946 | 0.303157 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −133.826 | + | 42.1138i | −0.953883 | + | 0.300178i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 122.309i | − | 0.783180i | −0.920140 | − | 0.391590i | \(-0.871925\pi\) | ||
0.920140 | − | 0.391590i | \(-0.128075\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 64.1893i | 0.371895i | 0.982560 | + | 0.185947i | \(0.0595354\pi\) | ||||
−0.982560 | + | 0.185947i | \(0.940465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 147.318 | + | 204.091i | 0.777116 | + | 1.07660i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 339.528 | 1.63973 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.01487 | 0.0222822 | 0.0111411 | − | 0.999938i | \(-0.496454\pi\) | ||||
0.0111411 | + | 0.999938i | \(0.496454\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 78.7635 | + | 109.117i | 0.323391 | + | 0.448017i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 325.933i | 1.24152i | 0.784003 | + | 0.620758i | \(0.213175\pi\) | ||||
−0.784003 | + | 0.620758i | \(0.786825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 321.853i | 1.14144i | 0.821143 | + | 0.570722i | \(0.193337\pi\) | ||||
−0.821143 | + | 0.570722i | \(0.806663\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −239.172 | − | 79.3509i | −0.792304 | − | 0.262865i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −95.9780 | −0.297869 | −0.148934 | − | 0.988847i | \(-0.547584\pi\) | ||||
−0.148934 | + | 0.988847i | \(0.547584\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −980.446 | −2.85844 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 312.712 | − | 225.724i | 0.858597 | − | 0.619758i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 185.069i | − | 0.479645i | −0.970817 | − | 0.239822i | \(-0.922911\pi\) | ||
0.970817 | − | 0.239822i | \(-0.0770892\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 452.099i | 1.10838i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −349.623 | + | 252.367i | −0.812432 | + | 0.586436i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 226.316 | 0.499386 | 0.249693 | − | 0.968325i | \(-0.419670\pi\) | ||||
0.249693 | + | 0.968325i | \(0.419670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 198.851 | 0.417382 | 0.208691 | − | 0.977982i | \(-0.433080\pi\) | ||||
0.208691 | + | 0.977982i | \(0.433080\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 932.268 | + | 309.302i | 1.86436 | + | 0.618545i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 241.714i | 0.461245i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 23.9524i | − | 0.0436753i | −0.999762 | − | 0.0218377i | \(-0.993048\pi\) | ||
0.999762 | − | 0.0218377i | \(-0.00695170\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 544.632 | + | 754.518i | 0.950231 | + | 1.31642i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 399.741 | 0.668176 | 0.334088 | − | 0.942542i | \(-0.391572\pi\) | ||||
0.334088 | + | 0.942542i | \(0.391572\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 669.631 | 1.07362 | 0.536811 | − | 0.843703i | \(-0.319629\pi\) | ||||
0.536811 | + | 0.843703i | \(0.319629\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 115.245 | + | 159.658i | 0.177432 | + | 0.245809i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1762.24i | − | 2.60812i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 229.453i | 0.326778i | 0.986562 | + | 0.163389i | \(0.0522426\pi\) | ||||
−0.986562 | + | 0.163389i | \(0.947757\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −584.427 | − | 435.760i | −0.801683 | − | 0.597750i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −321.150 | −0.424709 | −0.212354 | − | 0.977193i | \(-0.568113\pi\) | ||||
−0.212354 | + | 0.977193i | \(0.568113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 692.715 | 0.883947 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 515.313 | − | 371.967i | 0.635027 | − | 0.458380i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 131.446i | 0.156554i | 0.996932 | + | 0.0782768i | \(0.0249418\pi\) | ||||
−0.996932 | + | 0.0782768i | \(0.975058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 942.177i | − | 1.08535i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −270.443 | + | 195.213i | −0.301544 | + | 0.217663i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −774.479 | −0.836420 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 136.371 | 0.142746 | 0.0713732 | − | 0.997450i | \(-0.477262\pi\) | ||||
0.0713732 | + | 0.997450i | \(0.477262\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −411.851 | + | 1241.36i | −0.418107 | + | 1.26022i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 411.095i | − | 0.405005i | −0.979282 | − | 0.202502i | \(-0.935093\pi\) | ||
0.979282 | − | 0.202502i | \(-0.0649074\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 137.507i | − | 0.131543i | −0.997835 | − | 0.0657716i | \(-0.979049\pi\) | ||
0.997835 | − | 0.0657716i | \(-0.0209509\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1032.57 | + | 1430.50i | 0.959704 | + | 1.32955i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2113.08 | 1.90915 | 0.954577 | − | 0.297964i | \(-0.0963076\pi\) | ||||
0.954577 | + | 0.297964i | \(0.0963076\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1310.07 | −1.15121 | −0.575606 | − | 0.817727i | \(-0.695234\pi\) | ||||
−0.575606 | + | 0.817727i | \(0.695234\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.2512 | + | 21.1287i | 0.0130413 | + | 0.0180671i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1403.62i | − | 1.16851i | −0.811571 | − | 0.584254i | \(-0.801387\pi\) | ||
0.811571 | − | 0.584254i | \(-0.198613\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1671.40i | 1.35529i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −220.196 | + | 663.693i | −0.173992 | + | 0.524431i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2700.13 | −2.08001 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1015.51 | 0.762967 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1373.22 | + | 991.227i | −1.00666 | + | 0.726634i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1520.30i | 1.08784i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1583.69i | − | 1.10653i | −0.833004 | − | 0.553267i | \(-0.813381\pi\) | ||
0.833004 | − | 0.553267i | \(-0.186619\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1356.03 | + | 978.820i | −0.925519 | + | 0.668065i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 160.326 | 0.106929 | 0.0534646 | − | 0.998570i | \(-0.482974\pi\) | ||||
0.0534646 | + | 0.998570i | \(0.482974\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3018.84 | 1.96817 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −393.050 | − | 1249.00i | −0.250580 | − | 0.796274i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1487.47i | − | 0.927614i | −0.885936 | − | 0.463807i | \(-0.846483\pi\) | ||
0.885936 | − | 0.463807i | \(-0.153517\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 58.7660i | − | 0.0358595i | −0.999839 | − | 0.0179298i | \(-0.994292\pi\) | ||
0.999839 | − | 0.0179298i | \(-0.00570752\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −291.889 | − | 404.375i | −0.174337 | − | 0.241521i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1254.56 | 0.733646 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1141.51 | 0.653776 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2981.74 | − | 4130.82i | −1.67299 | − | 2.31771i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 940.146i | 0.516911i | 0.966023 | + | 0.258456i | \(0.0832136\pi\) | ||||
−0.966023 | + | 0.258456i | \(0.916786\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1800.43i | 0.970308i | 0.874429 | + | 0.485154i | \(0.161237\pi\) | ||||
−0.874429 | + | 0.485154i | \(0.838763\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1902.04 | + | 631.046i | 1.00504 | + | 0.333445i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −599.081 | −0.310447 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3024.10 | −1.53726 | −0.768629 | − | 0.639695i | \(-0.779061\pi\) | ||||
−0.768629 | + | 0.639695i | \(0.779061\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 779.733 | − | 562.832i | 0.388911 | − | 0.280726i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6514.94i | − | 3.18913i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3124.46i | − | 1.50139i | −0.660650 | − | 0.750694i | \(-0.729719\pi\) | ||
0.660650 | − | 0.750694i | \(-0.270281\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1904.79 | + | 1374.93i | −0.898711 | + | 0.648714i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −371.384 | −0.172087 | −0.0860435 | − | 0.996291i | \(-0.527422\pi\) | ||||
−0.0860435 | + | 0.996291i | \(0.527422\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1526.25 | −0.694699 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2126.55 | − | 705.531i | −0.951001 | − | 0.315517i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2931.24i | − | 1.28820i | −0.764943 | − | 0.644099i | \(-0.777233\pi\) | ||
0.764943 | − | 0.644099i | \(-0.222767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1378.58i | − | 0.595489i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 688.272 | + | 953.513i | 0.292281 | + | 0.404918i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2834.46 | 1.18356 | 0.591781 | − | 0.806098i | \(-0.298425\pi\) | ||||
0.591781 | + | 0.806098i | \(0.298425\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1819.98 | −0.747392 | −0.373696 | − | 0.927551i | \(-0.621910\pi\) | ||||
−0.373696 | + | 0.927551i | \(0.621910\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 604.747 | + | 837.800i | 0.244285 | + | 0.338426i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 46.8039i | 0.0186005i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3595.37i | − | 1.40599i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1532.07 | + | 4868.49i | 0.589638 | + | 1.87370i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4627.06 | −1.75289 | −0.876446 | − | 0.481500i | \(-0.840092\pi\) | ||||
−0.876446 | + | 0.481500i | \(0.840092\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2770.29 | −1.03321 | −0.516606 | − | 0.856223i | \(-0.672805\pi\) | ||||
−0.516606 | + | 0.856223i | \(0.672805\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1018.39 | + | 735.102i | −0.373992 | + | 0.269958i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3880.01i | 1.40324i | 0.712550 | + | 0.701622i | \(0.247540\pi\) | ||||
−0.712550 | + | 0.701622i | \(0.752460\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2015.00i | − | 0.717785i | −0.933379 | − | 0.358893i | \(-0.883154\pi\) | ||
0.933379 | − | 0.358893i | \(-0.116846\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 100.916 | − | 72.8440i | 0.0354133 | − | 0.0255623i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4449.51 | −1.53839 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3041.94 | −1.03638 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1522.60 | + | 4589.29i | −0.511247 | + | 1.54095i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4019.74i | 1.33039i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5611.42i | 1.83084i | 0.402505 | + | 0.915418i | \(0.368140\pi\) | ||||
−0.402505 | + | 0.915418i | \(0.631860\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1215.69 | + | 1684.19i | 0.391070 | + | 0.541778i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3003.86 | −0.952845 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2335.16 | 0.730510 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2036.48 | + | 2821.29i | 0.628369 | + | 0.870526i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1922.26i | − | 0.585091i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2025.65i | − | 0.608285i | −0.952627 | − | 0.304142i | \(-0.901630\pi\) | ||
0.952627 | − | 0.304142i | \(-0.0983699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −322.186 | + | 971.103i | −0.0954625 | + | 0.287734i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −404.049 | −0.118140 | −0.0590698 | − | 0.998254i | \(-0.518813\pi\) | ||||
−0.0590698 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4735.42 | −1.36649 | −0.683243 | − | 0.730191i | \(-0.739431\pi\) | ||||
−0.683243 | + | 0.730191i | \(0.739431\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7424.66 | − | 5359.32i | 2.11475 | − | 1.52648i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3703.79i | − | 1.04139i | −0.853744 | − | 0.520694i | \(-0.825673\pi\) | ||
0.853744 | − | 0.520694i | \(-0.174327\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 895.765i | − | 0.248652i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −966.733 | + | 697.814i | −0.264962 | + | 0.191257i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6398.83 | −1.73182 | −0.865912 | − | 0.500197i | \(-0.833261\pi\) | ||||
−0.865912 | + | 0.500197i | \(0.833261\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3766.48 | 1.00672 | 0.503362 | − | 0.864076i | \(-0.332096\pi\) | ||||
0.503362 | + | 0.864076i | \(0.332096\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 58.5842 | − | 3787.54i | 0.0154658 | − | 0.999880i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 9150.53i | − | 2.38615i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2149.15i | 0.553632i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −976.683 | − | 1353.07i | −0.248573 | − | 0.344367i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1979.71 | 0.497841 | 0.248921 | − | 0.968524i | \(-0.419924\pi\) | ||||
0.248921 | + | 0.968524i | \(0.419924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8674.98 | 2.15570 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2106.69 | + | 2918.55i | 0.517356 | + | 0.716732i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1081.54i | 0.262508i | 0.991349 | + | 0.131254i | \(0.0419004\pi\) | ||||
−0.991349 | + | 0.131254i | \(0.958100\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 182.437i | − | 0.0437687i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3134.34 | + | 1039.89i | 0.743337 | + | 0.246619i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1121.20 | 0.262875 | 0.131438 | − | 0.991324i | \(-0.458041\pi\) | ||||
0.131438 | + | 0.991324i | \(0.458041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1727.25 | 0.400394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −553.810 | + | 399.755i | −0.126939 | + | 0.0916277i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1844.86i | 0.418153i | 0.977899 | + | 0.209076i | \(0.0670457\pi\) | ||||
−0.977899 | + | 0.209076i | \(0.932954\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 938.970i | − | 0.210474i | −0.994447 | − | 0.105237i | \(-0.966440\pi\) | ||
0.994447 | − | 0.105237i | \(-0.0335601\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3969.58 | − | 2865.35i | 0.880037 | − | 0.635234i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1835.64 | 0.402522 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1100.93 | 0.238803 | 0.119401 | − | 0.992846i | \(-0.461902\pi\) | ||||
0.119401 | + | 0.992846i | \(0.461902\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1644.94 | − | 545.748i | −0.352975 | − | 0.117108i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 748.208i | − | 0.158841i | −0.996841 | − | 0.0794205i | \(-0.974693\pi\) | ||
0.996841 | − | 0.0794205i | \(-0.0253070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2150.15i | 0.451636i | 0.974170 | + | 0.225818i | \(0.0725054\pi\) | ||||
−0.974170 | + | 0.225818i | \(0.927495\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2355.35 | − | 3263.04i | −0.489540 | − | 0.678195i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11857.2 | 2.43870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −595.891 | −0.121289 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 414.733 | + | 574.559i | 0.0835466 | + | 0.115743i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5252.83i | − | 1.04735i | −0.851918 | − | 0.523675i | \(-0.824561\pi\) | ||
0.851918 | − | 0.523675i | \(-0.175439\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2112.21i | 0.416873i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6482.64 | + | 2040.03i | −1.26654 | + | 0.398567i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4638.06 | 0.897077 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11708.8 | 2.24213 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1732.03 | − | 1250.22i | 0.328390 | − | 0.237041i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1855.88i | 0.348418i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5337.06i | 0.992190i | 0.868268 | + | 0.496095i | \(0.165233\pi\) | ||||
−0.868268 | + | 0.496095i | \(0.834767\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 579.344 | − | 418.186i | 0.106659 | − | 0.0769896i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1034.85 | −0.188685 | −0.0943424 | − | 0.995540i | \(-0.530075\pi\) | ||||
−0.0943424 | + | 0.995540i | \(0.530075\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9570.33 | −1.72826 | −0.864132 | − | 0.503265i | \(-0.832132\pi\) | ||||
−0.864132 | + | 0.503265i | \(0.832132\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2886.72 | + | 8700.89i | −0.516344 | + | 1.55632i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3593.05i | 0.636612i | 0.947988 | + | 0.318306i | \(0.103114\pi\) | ||||
−0.947988 | + | 0.318306i | \(0.896886\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5924.75i | − | 1.03988i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6426.32 | + | 8902.85i | 1.11739 | + | 1.54800i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6159.13 | 1.06100 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 981.425 | 0.167507 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3984.19 | − | 5519.60i | −0.673781 | − | 0.933438i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3491.60i | 0.585101i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4119.28i | − | 0.684037i | −0.939693 | − | 0.342018i | \(-0.888890\pi\) | ||
0.939693 | − | 0.342018i | \(-0.111110\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −42.6372 | + | 128.513i | −0.00701654 | + | 0.0211486i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 223.548 | 0.0364589 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6488.93 | −1.04889 | −0.524443 | − | 0.851446i | \(-0.675726\pi\) | ||||
−0.524443 | + | 0.851446i | \(0.675726\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5913.73 | − | 4268.69i | 0.947462 | − | 0.683904i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3109.38i | 0.493790i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 23189.8i | 3.65052i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7041.94 | + | 5083.06i | −1.09891 | + | 0.793225i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7085.97 | 1.09624 | 0.548119 | − | 0.836400i | \(-0.315344\pi\) | ||||
0.548119 | + | 0.836400i | \(0.315344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6075.79 | −0.931891 | −0.465945 | − | 0.884814i | \(-0.654286\pi\) | ||||
−0.465945 | + | 0.884814i | \(0.654286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3465.93 | + | 1090.70i | −0.527059 | + | 0.165861i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4451.86i | 0.671242i | 0.941997 | + | 0.335621i | \(0.108946\pi\) | ||||
−0.941997 | + | 0.335621i | \(0.891054\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3730.79i | 0.557774i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8211.66 | − | 11376.2i | −1.21739 | − | 1.68653i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10771.6 | 1.58357 | 0.791785 | − | 0.610800i | \(-0.209152\pi\) | ||||
0.791785 | + | 0.610800i | \(0.209152\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −27.1131 | −0.00395293 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3088.37 | + | 4278.54i | 0.446549 | + | 0.618637i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6249.68i | 0.896228i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6671.95i | 0.948973i | 0.880263 | + | 0.474486i | \(0.157366\pi\) | ||||
−0.880263 | + | 0.474486i | \(0.842634\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8352.48 | − | 2771.13i | −1.17835 | − | 0.390947i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6732.66 | −0.942162 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12618.5 | −1.75164 | −0.875819 | − | 0.482641i | \(-0.839678\pi\) | ||||
−0.875819 | + | 0.482641i | \(0.839678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6405.33 | + | 4623.54i | −0.882053 | + | 0.636690i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3167.66i | − | 0.432739i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7915.38i | − | 1.07279i | −0.843968 | − | 0.536393i | \(-0.819787\pi\) | ||
0.843968 | − | 0.536393i | \(-0.180213\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6672.40 | − | 4816.32i | 0.897212 | − | 0.647632i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10820.5 | 1.44360 | 0.721802 | − | 0.692099i | \(-0.243314\pi\) | ||||
0.721802 | + | 0.692099i | \(0.243314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16447.0 | 2.17719 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8247.94 | − | 2736.45i | −1.08338 | − | 0.359435i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 7990.57i | − | 1.04149i | −0.853714 | − | 0.520743i | \(-0.825655\pi\) | ||
0.853714 | − | 0.520743i | \(-0.174345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 13292.0i | − | 1.71919i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 487.583 | + | 675.485i | 0.0625835 | + | 0.0867016i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2141.49 | −0.272785 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5526.21 | 0.698620 | 0.349310 | − | 0.937007i | \(-0.386416\pi\) | ||||
0.349310 | + | 0.937007i | \(0.386416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9180.91 | + | 12719.0i | 1.15193 | + | 1.59585i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7844.55i | 0.976903i | 0.872591 | + | 0.488451i | \(0.162438\pi\) | ||||
−0.872591 | + | 0.488451i | \(0.837562\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1662.43i | 0.205487i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4066.96 | − | 5454.47i | 0.498985 | − | 0.669222i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 242.924 | 0.0295855 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4407.65 | −0.532871 | −0.266435 | − | 0.963853i | \(-0.585846\pi\) | ||||
−0.266435 | + | 0.963853i | \(0.585846\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6267.01 | − | 4523.70i | 0.752138 | − | 0.542914i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 8233.18i | − | 0.980940i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2997.30i | − | 0.354534i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 247.593 | − | 178.720i | 0.0290760 | − | 0.0209878i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12032.8 | −1.40296 | −0.701481 | − | 0.712688i | \(-0.747477\pi\) | ||||
−0.701481 | + | 0.712688i | \(0.747477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10320.3 | 1.19473 | 0.597365 | − | 0.801969i | \(-0.296214\pi\) | ||||
0.597365 | + | 0.801969i | \(0.296214\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 816.021 | − | 2459.57i | 0.0937973 | − | 0.282715i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2812.61i | − | 0.321016i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 7234.05i | − | 0.819860i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3815.36 | + | 5285.70i | 0.429388 | + | 0.594863i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8068.52 | −0.901733 | −0.450866 | − | 0.892591i | \(-0.648885\pi\) | ||||
−0.450866 | + | 0.892591i | \(0.648885\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3236.75 | −0.359234 | −0.179617 | − | 0.983737i | \(-0.557486\pi\) | ||||
−0.179617 | + | 0.983737i | \(0.557486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3471.58 | + | 4809.43i | 0.382642 | + | 0.530102i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14860.9i | 1.62676i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2207.71i | 0.240019i | 0.992773 | + | 0.120009i | \(0.0382924\pi\) | ||||
−0.992773 | + | 0.120009i | \(0.961708\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8335.91 | − | 25125.3i | 0.900109 | − | 2.71302i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1058.18 | 0.113489 | 0.0567447 | − | 0.998389i | \(-0.481928\pi\) | ||||
0.0567447 | + | 0.998389i | \(0.481928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1226.79 | −0.130686 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3961.03 | + | 2859.18i | −0.419128 | + | 0.302538i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10836.4i | 1.13898i | 0.822000 | + | 0.569488i | \(0.192858\pi\) | ||||
−0.822000 | + | 0.569488i | \(0.807142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15788.4i | 1.64844i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7585.56 | + | 5475.46i | −0.786756 | + | 0.567902i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8793.36 | 0.906020 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9827.12 | −1.00589 | −0.502947 | − | 0.864317i | \(-0.667751\pi\) | ||||
−0.502947 | + | 0.864317i | \(0.667751\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3125.77 | + | 9932.83i | 0.317861 | + | 1.01008i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9311.74i | 0.940761i | 0.882464 | + | 0.470381i | \(0.155883\pi\) | ||||
−0.882464 | + | 0.470381i | \(0.844117\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7601.37i | − | 0.762993i | −0.924370 | − | 0.381497i | \(-0.875409\pi\) | ||
0.924370 | − | 0.381497i | \(-0.124591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1821.93 | − | 2524.05i | −0.181699 | − | 0.251720i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4446.20 | −0.440569 | −0.220284 | − | 0.975436i | \(-0.570699\pi\) | ||||
−0.220284 | + | 0.975436i | \(0.570699\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −871.368 | −0.0857911 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9196.90 | − | 12741.1i | −0.899726 | − | 1.24646i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15590.8i | 1.51557i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3144.59i | 0.303756i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4742.65 | + | 1573.49i | 0.455244 | + | 0.151038i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12285.9 | −1.17194 | −0.585970 | − | 0.810333i | \(-0.699286\pi\) | ||||
−0.585970 | + | 0.810333i | \(0.699286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 129.879 | 0.0123118 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27448.8 | − | 19813.3i | 2.58584 | − | 1.86653i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1272.76i | 0.119161i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8464.78i | − | 0.787630i | −0.919190 | − | 0.393815i | \(-0.871155\pi\) | ||
0.919190 | − | 0.393815i | \(-0.128845\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13164.0 | − | 9502.11i | 1.21737 | − | 0.878732i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6356.37 | −0.584234 | −0.292117 | − | 0.956383i | \(-0.594360\pi\) | ||||
−0.292117 | + | 0.956383i | \(0.594360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9078.02 | −0.829317 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11585.7 | − | 3843.82i | −1.05200 | − | 0.349024i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 14542.2i | − | 1.31249i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 11856.6i | − | 1.06368i | −0.846845 | − | 0.531840i | \(-0.821501\pi\) | ||
0.846845 | − | 0.531840i | \(-0.178499\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1129.45 | − | 1564.72i | −0.100719 | − | 0.139534i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17032.5 | −1.50982 | −0.754912 | − | 0.655826i | \(-0.772321\pi\) | ||||
−0.754912 | + | 0.655826i | \(0.772321\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3836.76 | 0.338086 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4641.65 | − | 6430.41i | −0.406593 | − | 0.563283i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1563.18i | − | 0.136123i | −0.997681 | − | 0.0680617i | \(-0.978319\pi\) | ||
0.997681 | − | 0.0680617i | \(-0.0216815\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 24360.6i | − | 2.10891i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3494.72 | − | 11105.2i | −0.300771 | − | 0.955767i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1283.36 | 0.109809 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4649.25 | −0.395501 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12349.9 | − | 8914.50i | 1.04451 | − | 0.753956i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9096.23i | 0.764900i | 0.923976 | + | 0.382450i | \(0.124920\pi\) | ||||
−0.923976 | + | 0.382450i | \(0.875080\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10108.4i | 0.845143i | 0.906330 | + | 0.422572i | \(0.138873\pi\) | ||||
−0.906330 | + | 0.422572i | \(0.861127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5808.22 | − | 4192.53i | 0.482841 | − | 0.348528i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4764.25 | 0.393803 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19904.2 | 1.63591 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1924.17 | + | 5799.66i | −0.157254 | + | 0.473980i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8441.26i | 0.685988i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19721.5i | 1.59371i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8620.18 | + | 11942.2i | 0.692716 | + | 0.959670i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −47493.6 | −3.79535 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10097.6 | −0.802462 | −0.401231 | − | 0.915977i | \(-0.631417\pi\) | ||||
−0.401231 | + | 0.915977i | \(0.631417\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5534.93 | − | 7667.94i | −0.437434 | − | 0.606009i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 12226.9i | − | 0.960998i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2064.83i | 0.161400i | 0.996738 | + | 0.0806998i | \(0.0257155\pi\) | ||||
−0.996738 | + | 0.0806998i | \(0.974284\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1690.66 | + | 5095.84i | −0.131431 | + | 0.396148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10149.5 | 0.784727 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8347.32 | 0.641888 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −197.194 | + | 142.340i | −0.0150819 | + | 0.0108865i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12125.7i | 0.922409i | 0.887294 | + | 0.461204i | \(0.152583\pi\) | ||||
−0.887294 | + | 0.461204i | \(0.847417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8335.60i | 0.630695i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15148.0 | − | 10934.2i | 1.14002 | − | 0.822895i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7278.58 | −0.544859 | −0.272429 | − | 0.962176i | \(-0.587827\pi\) | ||||
−0.272429 | + | 0.962176i | \(0.587827\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13100.0 | 0.975436 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15852.6 | + | 21261.0i | −1.17416 | + | 1.57474i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 17428.1i | − | 1.28405i | −0.766685 | − | 0.642024i | \(-0.778095\pi\) | ||
0.766685 | − | 0.642024i | \(-0.221905\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2423.73i | 0.177635i | 0.996048 | + | 0.0888177i | \(0.0283089\pi\) | ||||
−0.996048 | + | 0.0888177i | \(0.971691\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14071.8 | − | 19494.7i | −1.02593 | − | 1.42130i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6786.33 | 0.492190 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17471.1 | −1.26054 | −0.630268 | − | 0.776377i | \(-0.717055\pi\) | ||||
−0.630268 | + | 0.776377i | \(0.717055\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8425.03 | − | 11671.8i | −0.604719 | − | 0.837761i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11683.2i | 0.834252i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8964.88i | − | 0.636857i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6194.27 | − | 2055.09i | −0.437780 | − | 0.145244i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7273.06 | 0.511399 | 0.255700 | − | 0.966756i | \(-0.417694\pi\) | ||||
0.255700 | + | 0.966756i | \(0.417694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5326.60 | −0.372629 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16347.3 | + | 11799.9i | −1.13779 | + | 0.821290i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19957.9i | 1.38208i | 0.722818 | + | 0.691038i | \(0.242846\pi\) | ||||
−0.722818 | + | 0.691038i | \(0.757154\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 25200.4i | − | 1.73633i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8489.59 | − | 6128.01i | 0.582003 | − | 0.420105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6101.48 | 0.416193 | 0.208097 | − | 0.978108i | \(-0.433273\pi\) | ||||
0.208097 | + | 0.978108i | \(0.433273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16659.6 | 1.13071 | 0.565357 | − | 0.824846i | \(-0.308738\pi\) | ||||
0.565357 | + | 0.824846i | \(0.308738\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 613.813 | + | 203.647i | 0.0414534 | + | 0.0137531i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9477.77i | 0.636903i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13728.6i | 0.917999i | 0.888437 | + | 0.458999i | \(0.151792\pi\) | ||||
−0.888437 | + | 0.458999i | \(0.848208\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13531.9 | − | 18746.7i | −0.900392 | − | 1.24738i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2485.71 | −0.164585 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7514.10 | 0.495093 | 0.247546 | − | 0.968876i | \(-0.420376\pi\) | ||||
0.247546 | + | 0.968876i | \(0.420376\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9251.15 | − | 12816.3i | −0.606573 | − | 0.840330i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8052.78i | − | 0.525434i | −0.964873 | − | 0.262717i | \(-0.915381\pi\) | ||
0.964873 | − | 0.262717i | \(-0.0846186\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 25194.4i | − | 1.63594i | −0.575261 | − | 0.817970i | \(-0.695100\pi\) | ||
0.575261 | − | 0.817970i | \(-0.304900\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23966.1 | + | 7541.92i | −1.54868 | + | 0.487354i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4781.91 | 0.307517 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9452.17 | −0.604939 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16936.0 | + | 12224.9i | −1.07872 | + | 0.778650i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 372.213i | − | 0.0235948i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14945.1i | − | 0.942876i | −0.881899 | − | 0.471438i | \(-0.843735\pi\) | ||
0.881899 | − | 0.471438i | \(-0.156265\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23642.1 | + | 17065.5i | −1.48450 | + | 1.07155i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14780.6 | 0.923702 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25392.4 | −1.57941 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3398.66 | + | 10243.9i | −0.210405 | + | 0.634184i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 13909.9i | − | 0.857109i | −0.903516 | − | 0.428555i | \(-0.859023\pi\) | ||
0.903516 | − | 0.428555i | \(-0.140977\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13338.7i | 0.818084i | 0.912516 | + | 0.409042i | \(0.134137\pi\) | ||||
−0.912516 | + | 0.409042i | \(0.865863\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9135.36 | − | 12655.9i | −0.557681 | − | 0.772597i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 719.190 | 0.0437006 | 0.0218503 | − | 0.999761i | \(-0.493044\pi\) | ||||
0.0218503 | + | 0.999761i | \(0.493044\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10962.9 | 0.663069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7101.69 | + | 9838.49i | 0.427553 | + | 0.592321i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19019.4i | 1.13980i | 0.821714 | + | 0.569899i | \(0.193018\pi\) | ||||
−0.821714 | + | 0.569899i | \(0.806982\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1496.32i | 0.0892615i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5693.31 | + | 17160.2i | −0.338078 | + | 1.01900i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22748.7 | 1.34471 | 0.672354 | − | 0.740230i | \(-0.265283\pi\) | ||||
0.672354 | + | 0.740230i | \(0.265283\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23275.3 | −1.36960 | −0.684798 | − | 0.728733i | \(-0.740110\pi\) | ||||
−0.684798 | + | 0.728733i | \(0.740110\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8098.86 | − | 5845.98i | 0.474410 | − | 0.342442i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28174.9i | 1.64297i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 21903.6i | − | 1.27153i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8534.47 | − | 6160.41i | 0.493216 | − | 0.356017i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9632.51 | 0.554186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28195.5 | −1.61495 | −0.807473 | − | 0.589905i | \(-0.799165\pi\) | ||||
−0.807473 | + | 0.589905i | \(0.799165\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5071.29 | + | 1595.89i | −0.289176 | + | 0.0910011i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32369.7i | 1.83762i | 0.394701 | + | 0.918809i | \(0.370848\pi\) | ||||
−0.394701 | + | 0.918809i | \(0.629152\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4961.07i | − | 0.280396i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1228.80 | − | 1702.34i | −0.0691447 | − | 0.0957913i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1227.33 | −0.0687592 | −0.0343796 | − | 0.999409i | \(-0.510946\pi\) | ||||
−0.0343796 | + | 0.999409i | \(0.510946\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13882.6 | 0.774345 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14401.4 | − | 19951.3i | −0.799776 | − | 1.10799i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 4793.06i | − | 0.265023i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3563.29i | 0.196170i | 0.995178 | + | 0.0980852i | \(0.0312718\pi\) | ||||
−0.995178 | + | 0.0980852i | \(0.968728\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 45159.8 | + | 14982.8i | 2.47544 | + | 0.821284i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 548.465 | 0.0299345 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24191.3 | 1.31465 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15604.8 | − | 11264.0i | 0.844389 | − | 0.609503i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 11942.4i | − | 0.643448i | −0.946834 | − | 0.321724i | \(-0.895738\pi\) | ||
0.946834 | − | 0.321724i | \(-0.104262\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 416.147i | 0.0223262i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3774.04 | − | 2724.21i | 0.201615 | − | 0.145531i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14955.3 | −0.795547 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22547.9 | 1.19436 | 0.597182 | − | 0.802105i | \(-0.296287\pi\) | ||||
0.597182 | + | 0.802105i | \(0.296287\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5880.06 | − | 1950.85i | −0.310154 | − | 0.102901i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11495.3i | 0.603790i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11708.8i | 0.612426i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19460.1 | − | 26959.6i | −1.01360 | − | 1.40422i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2034.54 | 0.105529 | 0.0527647 | − | 0.998607i | \(-0.483197\pi\) | ||||
0.0527647 | + | 0.998607i | \(0.483197\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5002.39 | −0.258389 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11454.6 | + | 15869.0i | 0.589215 | + | 0.816283i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 4634.86i | − | 0.237427i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26487.5i | 1.35126i | 0.737240 | + | 0.675631i | \(0.236129\pi\) | ||||
−0.737240 | + | 0.675631i | \(0.763871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16135.9 | − | 11271.9i | 0.819786 | − | 0.572670i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23888.5 | 1.20869 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38967.7 | 1.96358 | 0.981791 | − | 0.189964i | \(-0.0608370\pi\) | ||||
0.981791 | + | 0.189964i | \(0.0608370\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 38553.0 | − | 27828.6i | 1.93476 | − | 1.39656i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1160.27i | − | 0.0579907i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14312.2i | 0.712425i | 0.934405 | + | 0.356212i | \(0.115932\pi\) | ||||
−0.934405 | + | 0.356212i | \(0.884068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9054.80 | + | 6536.00i | −0.448902 | + | 0.324030i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12790.0 | 0.631520 | 0.315760 | − | 0.948839i | \(-0.397741\pi\) | ||||
0.315760 | + | 0.948839i | \(0.397741\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8774.41 | −0.431503 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2730.47 | − | 8229.93i | 0.133739 | − | 0.403102i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 76872.3i | − | 3.75014i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19441.6i | 0.944653i | 0.881424 | + | 0.472327i | \(0.156586\pi\) | ||||
−0.881424 | + | 0.472327i | \(0.843414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6020.70 | + | 8340.92i | 0.291376 | + | 0.403665i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16803.4 | −0.809985 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13901.0 | −0.667424 | −0.333712 | − | 0.942675i | \(-0.608301\pi\) | ||||
−0.333712 | + | 0.942675i | \(0.608301\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26382.4 | + | 36549.4i | 1.26169 | + | 1.74791i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8818.58i | − | 0.420070i | −0.977694 | − | 0.210035i | \(-0.932642\pi\) | ||
0.977694 | − | 0.210035i | \(-0.0673578\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 47659.3i | 2.26132i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5889.57 | + | 17751.8i | −0.278350 | + | 0.838978i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5861.30 | 0.275931 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1323.39 | 0.0620582 | 0.0310291 | − | 0.999518i | \(-0.490122\pi\) | ||||
0.0310291 | + | 0.999518i | \(0.490122\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4556.75 | + | 3289.18i | −0.212850 | + | 0.153641i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 34327.1i | − | 1.59723i | −0.601840 | − | 0.798617i | \(-0.705565\pi\) | ||
0.601840 | − | 0.798617i | \(-0.294435\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2432.43i | 0.112743i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 768.644 | − | 554.828i | 0.0354890 | − | 0.0256169i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27046.7 | −1.24397 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19363.8 | 0.887183 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5150.91 | + | 16368.2i | 0.235094 | + | 0.747063i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 28224.0i | − | 1.28326i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 15375.3i | − | 0.696405i | −0.937419 | − | 0.348203i | \(-0.886792\pi\) | ||
0.937419 | − | 0.348203i | \(-0.113208\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3409.80 | + | 4723.84i | 0.153856 | + | 0.213147i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −51062.5 | −2.29529 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5150.00 | 0.230620 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5252.93 | + | 7277.27i | 0.234342 | + | 0.324652i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3347.25i | 0.148765i | 0.997230 | + | 0.0743826i | \(0.0236986\pi\) | ||||
−0.997230 | + | 0.0743826i | \(0.976301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7123.67i | 0.315416i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3368.50 | − | 1117.58i | −0.148589 | − | 0.0492979i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32437.4 | 1.42552 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 60804.1 | 2.66219 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7772.76 | + | 5610.59i | −0.339051 | + | 0.244736i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39577.3i | 1.71998i | 0.510309 | + | 0.859991i | \(0.329531\pi\) | ||||
−0.510309 | + | 0.859991i | \(0.670469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12614.4i | 0.546180i | 0.961989 | + | 0.273090i | \(0.0880457\pi\) | ||||
−0.961989 | + | 0.273090i | \(0.911954\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3956.07 | − | 2855.60i | 0.170659 | − | 0.123186i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29160.6 | 1.25332 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26708.2 | −1.14370 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24144.6 | + | 8010.54i | 1.03014 | + | 0.341772i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 18243.6i | − | 0.775526i | −0.921759 | − | 0.387763i | \(-0.873248\pi\) | ||
0.921759 | − | 0.387763i | \(-0.126752\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18350.6i | − | 0.777230i | −0.921400 | − | 0.388615i | \(-0.872954\pi\) | ||
0.921400 | − | 0.388615i | \(-0.127046\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5582.57 | + | 7733.94i | 0.235588 | + | 0.326377i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15785.4 | 0.663739 | 0.331869 | − | 0.943325i | \(-0.392321\pi\) | ||||
0.331869 | + | 0.943325i | \(0.392321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36102.8 | −1.51255 | −0.756274 | − | 0.654255i | \(-0.772982\pi\) | ||||
−0.756274 | + | 0.654255i | \(0.772982\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3348.15 | + | 4638.43i | 0.139766 | + | 0.193629i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 72770.6i | 3.02683i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3466.13i | − | 0.143653i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2703.26 | − | 8590.21i | −0.111635 | − | 0.354744i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18961.8 | −0.780255 | −0.390127 | − | 0.920761i | \(-0.627569\pi\) | ||||
−0.390127 | + | 0.920761i | \(0.627569\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9429.48 | 0.386628 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3152.35 | − | 2275.45i | 0.128793 | − | 0.0929665i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 14244.6i | − | 0.579914i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 36943.4i | − | 1.49869i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9059.00 | + | 6539.03i | −0.366201 | + | 0.264333i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 898.084 | 0.0361762 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27761.8 | −1.11435 | −0.557177 | − | 0.830394i | \(-0.688116\pi\) | ||||
−0.557177 | + | 0.830394i | \(0.688116\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6584.74 | − | 19847.1i | 0.263384 | − | 0.793868i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2082.01i | − | 0.0829874i | −0.999139 | − | 0.0414937i | \(-0.986788\pi\) | ||
0.999139 | − | 0.0414937i | \(-0.0132117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34995.2i | 1.39001i | 0.719004 | + | 0.695005i | \(0.244598\pi\) | ||||
−0.719004 | + | 0.695005i | \(0.755402\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36060.1 | + | 49956.6i | 1.42732 | + | 1.97737i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6045.46 | −0.238459 | −0.119229 | − | 0.992867i | \(-0.538042\pi\) | ||||
−0.119229 | + | 0.992867i | \(0.538042\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27357.3 | 1.07535 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1812.23 | − | 2510.61i | −0.0709878 | − | 0.0983446i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11114.9i | 0.433886i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 620.337i | − | 0.0241324i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1159.45 | + | 3494.70i | −0.0449501 | + | 0.135484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 55307.3 | 2.13683 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30101.8 | −1.15903 | −0.579514 | − | 0.814963i | \(-0.696757\pi\) | ||||
−0.579514 | + | 0.814963i | \(0.696757\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22131.2 | − | 15974.9i | 0.849224 | − | 0.612993i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16655.3i | − | 0.636926i | −0.947935 | − | 0.318463i | \(-0.896833\pi\) | ||
0.947935 | − | 0.318463i | \(-0.103167\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24940.5i | 0.950528i | 0.879843 | + | 0.475264i | \(0.157647\pi\) | ||||
−0.879843 | + | 0.475264i | \(0.842353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8899.16 | + | 6423.66i | −0.338014 | + | 0.243987i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32143.9 | 1.21678 | 0.608391 | − | 0.793637i | \(-0.291815\pi\) | ||||
0.608391 | + | 0.793637i | \(0.291815\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −57613.3 | −2.17355 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28310.1 | − | 21108.5i | −1.06445 | − | 0.793673i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7964.51i | − | 0.298457i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26454.1i | 0.988004i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14105.3 | + | 19541.1i | 0.525041 | + | 0.727378i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7850.94 | 0.291261 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13736.2 | −0.507900 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 35608.7 | + | 49331.3i | 1.31227 | + | 1.81799i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 16985.9i | − | 0.623902i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3376.58i | 0.123613i | 0.998088 | + | 0.0618067i | \(0.0196862\pi\) | ||||
−0.998088 | + | 0.0618067i | \(0.980314\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10534.9 | + | 3495.19i | 0.384401 | + | 0.127534i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45248.4 | −1.64561 | −0.822803 | − | 0.568326i | \(-0.807591\pi\) | ||||
−0.822803 | + | 0.568326i | \(0.807591\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15556.8 | −0.563914 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7819.21 | + | 5644.12i | −0.282508 | + | 0.203922i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 5832.52i | − | 0.210040i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18545.2i | − | 0.665668i | −0.942985 | − | 0.332834i | \(-0.891995\pi\) | ||
0.942985 | − | 0.332834i | \(-0.108005\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22486.1 | + | 16231.1i | −0.804498 | + | 0.580709i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10352.8 | 0.369195 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 190.037 | 0.00675499 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3523.81 | + | 1169.11i | 0.124851 | + | 0.0414223i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 33976.7i | − | 1.19993i | −0.800024 | − | 0.599967i | \(-0.795180\pi\) | ||
0.800024 | − | 0.599967i | \(-0.204820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 81360.0i | − | 2.86409i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3147.19 | − | 4360.03i | −0.110433 | − | 0.152992i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33555.7 | 1.17368 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22803.1 | −0.795031 | −0.397516 | − | 0.917595i | \(-0.630128\pi\) | ||||
−0.397516 | + | 0.917595i | \(0.630128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29105.3 | − | 40321.7i | −1.01152 | − | 1.40133i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24174.7i | 0.837484i | 0.908105 | + | 0.418742i | \(0.137529\pi\) | ||||
−0.908105 | + | 0.418742i | \(0.862471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58369.4i | 2.01566i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −45437.7 | + | 14298.8i | −1.56412 | + | 0.492213i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8044.99 | 0.276058 | 0.138029 | − | 0.990428i | \(-0.455923\pi\) | ||||
0.138029 | + | 0.990428i | \(0.455923\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17342.6 | 0.593220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15138.3 | + | 10927.2i | −0.516185 | + | 0.372596i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 39730.8i | − | 1.35048i | −0.737598 | − | 0.675240i | \(-0.764040\pi\) | ||
0.737598 | − | 0.675240i | \(-0.235960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 43184.5i | − | 1.46326i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24962.2 | − | 18018.4i | 0.843169 | − | 0.608622i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −54112.9 | −1.82210 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25670.7 | 0.861694 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17965.8 | + | 54150.8i | −0.601183 | + | 1.81203i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 25855.2i | − | 0.862496i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17685.2i | − | 0.588126i | −0.955786 | − | 0.294063i | \(-0.904992\pi\) | ||
0.955786 | − | 0.294063i | \(-0.0950076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18731.2 | + | 25949.7i | 0.620982 | + | 0.860292i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44010.1 | −1.45453 | −0.727267 | − | 0.686355i | \(-0.759210\pi\) | ||||
−0.727267 | + | 0.686355i | \(0.759210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2137.86 | −0.0704385 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2984.71 | + | 4134.94i | 0.0980382 | + | 0.135820i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 33518.4i | − | 1.09759i | −0.835956 | − | 0.548796i | \(-0.815086\pi\) | ||
0.835956 | − | 0.548796i | \(-0.184914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6367.36i | 0.207867i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11138.4 | − | 33572.4i | 0.362511 | − | 1.09265i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43740.3 | 1.41923 | 0.709613 | − | 0.704592i | \(-0.248870\pi\) | ||||
0.709613 | + | 0.704592i | \(0.248870\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36212.2 | −1.17139 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14710.8 | + | 10618.7i | −0.474418 | + | 0.342448i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57638.8i | 1.85319i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10468.7i | 0.335568i | 0.985824 | + | 0.167784i | \(0.0536611\pi\) | ||||
−0.985824 | + | 0.167784i | \(0.946339\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17355.4 | − | 12527.6i | 0.554638 | − | 0.400353i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18806.0 | 0.599186 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9561.56 | −0.303729 | −0.151864 | − | 0.988401i | \(-0.548528\pi\) | ||||
−0.151864 | + | 0.988401i | \(0.548528\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −671.121 | + | 211.195i | −0.0212546 | + | 0.00668862i |
(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 | 384.4.c.d.383.8 | yes | 12 | |
3.2 | odd | 2 | 384.4.c.a.383.6 | yes | 12 | ||
4.3 | odd | 2 | 384.4.c.a.383.5 | ✓ | 12 | ||
8.3 | odd | 2 | 384.4.c.c.383.8 | yes | 12 | ||
8.5 | even | 2 | 384.4.c.b.383.5 | yes | 12 | ||
12.11 | even | 2 | inner | 384.4.c.d.383.7 | yes | 12 | |
16.3 | odd | 4 | 768.4.f.h.383.9 | 12 | |||
16.5 | even | 4 | 768.4.f.g.383.9 | 12 | |||
16.11 | odd | 4 | 768.4.f.e.383.4 | 12 | |||
16.13 | even | 4 | 768.4.f.f.383.4 | 12 | |||
24.5 | odd | 2 | 384.4.c.c.383.7 | yes | 12 | ||
24.11 | even | 2 | 384.4.c.b.383.6 | yes | 12 | ||
48.5 | odd | 4 | 768.4.f.h.383.10 | 12 | |||
48.11 | even | 4 | 768.4.f.f.383.3 | 12 | |||
48.29 | odd | 4 | 768.4.f.e.383.3 | 12 | |||
48.35 | even | 4 | 768.4.f.g.383.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.c.a.383.5 | ✓ | 12 | 4.3 | odd | 2 | ||
384.4.c.a.383.6 | yes | 12 | 3.2 | odd | 2 | ||
384.4.c.b.383.5 | yes | 12 | 8.5 | even | 2 | ||
384.4.c.b.383.6 | yes | 12 | 24.11 | even | 2 | ||
384.4.c.c.383.7 | yes | 12 | 24.5 | odd | 2 | ||
384.4.c.c.383.8 | yes | 12 | 8.3 | odd | 2 | ||
384.4.c.d.383.7 | yes | 12 | 12.11 | even | 2 | inner | |
384.4.c.d.383.8 | yes | 12 | 1.1 | even | 1 | trivial | |
768.4.f.e.383.3 | 12 | 48.29 | odd | 4 | |||
768.4.f.e.383.4 | 12 | 16.11 | odd | 4 | |||
768.4.f.f.383.3 | 12 | 48.11 | even | 4 | |||
768.4.f.f.383.4 | 12 | 16.13 | even | 4 | |||
768.4.f.g.383.9 | 12 | 16.5 | even | 4 | |||
768.4.f.g.383.10 | 12 | 48.35 | even | 4 | |||
768.4.f.h.383.9 | 12 | 16.3 | odd | 4 | |||
768.4.f.h.383.10 | 12 | 48.5 | odd | 4 |