Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(239,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.239");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.h (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: | \(19.8246417619\) |
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: | \( x^{12} + 152x^{10} + 8222x^{8} + 194132x^{6} + 1882697x^{4} + 5152508x^{2} + 4008004 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.1 | ||
Root | \(4.19902i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.239 |
Dual form | 336.4.h.a.239.2 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −4.90731 | − | 1.70829i | −0.944413 | − | 0.328761i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 20.5781i | − | 1.84056i | −0.391259 | − | 0.920281i | \(-0.627960\pi\) | ||
0.391259 | − | 0.920281i | \(-0.372040\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 21.1635 | + | 16.7663i | 0.783832 | + | 0.620973i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 63.9252 | 1.75220 | 0.876099 | − | 0.482131i | \(-0.160137\pi\) | ||||
0.876099 | + | 0.482131i | \(0.160137\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 56.5700 | 1.20690 | 0.603450 | − | 0.797401i | \(-0.293792\pi\) | ||||
0.603450 | + | 0.797401i | \(0.293792\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −35.1534 | + | 100.983i | −0.605105 | + | 1.73825i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 81.6568i | − | 1.16498i | −0.812837 | − | 0.582491i | \(-0.802078\pi\) | ||
0.812837 | − | 0.582491i | \(-0.197922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.4109i | 0.270600i | 0.990805 | + | 0.135300i | \(0.0431998\pi\) | ||||
−0.990805 | + | 0.135300i | \(0.956800\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.9580 | − | 34.3512i | 0.124260 | − | 0.356955i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 114.603 | 1.03897 | 0.519486 | − | 0.854479i | \(-0.326124\pi\) | ||||
0.519486 | + | 0.854479i | \(0.326124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −298.458 | −2.38767 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −75.2141 | − | 118.431i | −0.536110 | − | 0.844148i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 62.7161i | − | 0.401589i | −0.979633 | − | 0.200795i | \(-0.935648\pi\) | ||
0.979633 | − | 0.200795i | \(-0.0643524\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 88.6606i | − | 0.513675i | −0.966455 | − | 0.256837i | \(-0.917320\pi\) | ||
0.966455 | − | 0.256837i | \(-0.0826805\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −313.701 | − | 109.203i | −1.65480 | − | 0.576055i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 144.047 | 0.695667 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −51.3374 | −0.228103 | −0.114052 | − | 0.993475i | \(-0.536383\pi\) | ||||
−0.114052 | + | 0.993475i | \(0.536383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −277.607 | − | 96.6381i | −1.13981 | − | 0.396782i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 165.933i | − | 0.632057i | −0.948750 | − | 0.316029i | \(-0.897650\pi\) | ||
0.948750 | − | 0.316029i | \(-0.102350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 393.078i | 1.39404i | 0.717051 | + | 0.697021i | \(0.245491\pi\) | ||||
−0.717051 | + | 0.697021i | \(0.754509\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 345.018 | − | 435.504i | 1.14294 | − | 1.44269i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −164.421 | −0.510282 | −0.255141 | − | 0.966904i | \(-0.582122\pi\) | ||||
−0.255141 | + | 0.966904i | \(0.582122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −139.494 | + | 400.716i | −0.383001 | + | 1.10022i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 231.927i | − | 0.601087i | −0.953768 | − | 0.300543i | \(-0.902832\pi\) | ||
0.953768 | − | 0.300543i | \(-0.0971680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1315.46i | − | 3.22503i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 38.2843 | − | 109.977i | 0.0889628 | − | 0.255558i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.4719 | 0.0297269 | 0.0148634 | − | 0.999890i | \(-0.495269\pi\) | ||||
0.0148634 | + | 0.999890i | \(0.495269\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 665.952 | 1.39781 | 0.698905 | − | 0.715215i | \(-0.253671\pi\) | ||||
0.698905 | + | 0.715215i | \(0.253671\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −117.364 | + | 148.144i | −0.234706 | + | 0.296261i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1164.10i | − | 2.22137i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 837.255i | − | 1.52667i | −0.646002 | − | 0.763336i | \(-0.723560\pi\) | ||
0.646002 | − | 0.763336i | \(-0.276440\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −562.392 | − | 195.775i | −0.981218 | − | 0.341573i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −175.804 | −0.293860 | −0.146930 | − | 0.989147i | \(-0.546939\pi\) | ||||
−0.146930 | + | 0.989147i | \(0.546939\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 301.790 | 0.483861 | 0.241931 | − | 0.970294i | \(-0.422219\pi\) | ||||
0.241931 | + | 0.970294i | \(0.422219\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1464.63 | + | 509.854i | 2.25494 | + | 0.784972i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 447.477i | 0.662269i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1049.12i | 1.49411i | 0.664762 | + | 0.747055i | \(0.268533\pi\) | ||||
−0.664762 | + | 0.747055i | \(0.731467\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 166.785 | + | 709.664i | 0.228786 | + | 0.973477i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1263.02 | −1.67030 | −0.835149 | − | 0.550023i | \(-0.814619\pi\) | ||||
−0.835149 | + | 0.550023i | \(0.814619\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1680.34 | −2.14422 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −107.137 | + | 307.768i | −0.132027 | + | 0.379266i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 780.001i | − | 0.928988i | −0.885576 | − | 0.464494i | \(-0.846236\pi\) | ||
0.885576 | − | 0.464494i | \(-0.153764\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 395.990i | 0.456165i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −151.458 | + | 435.085i | −0.168876 | + | 0.485121i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 461.173 | 0.498056 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −780.280 | −0.816757 | −0.408378 | − | 0.912813i | \(-0.633906\pi\) | ||||
−0.408378 | + | 0.912813i | \(0.633906\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1352.88 | + | 1071.79i | 1.37343 | + | 1.08807i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 47.4348i | 0.0467321i | 0.999727 | + | 0.0233661i | \(0.00743832\pi\) | ||||
−0.999727 | + | 0.0233661i | \(0.992562\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 24.0000i | 0.0229591i | 0.999934 | + | 0.0114796i | \(0.00365414\pi\) | ||||
−0.999934 | + | 0.0114796i | \(0.996346\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −706.883 | − | 246.074i | −0.656997 | − | 0.228708i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −432.110 | −0.390408 | −0.195204 | − | 0.980763i | \(-0.562537\pi\) | ||||
−0.195204 | + | 0.980763i | \(0.562537\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 323.801 | 0.284537 | 0.142268 | − | 0.989828i | \(-0.454560\pi\) | ||||
0.142268 | + | 0.989828i | \(0.454560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 251.929 | + | 87.6994i | 0.215424 | + | 0.0749915i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1972.82i | 1.64236i | 0.570667 | + | 0.821181i | \(0.306685\pi\) | ||||
−0.570667 | + | 0.821181i | \(0.693315\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2358.31i | − | 1.91229i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1197.22 | + | 948.467i | 0.946007 | + | 0.749451i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 571.598 | 0.440322 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2755.44 | 2.07020 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −283.462 | + | 814.284i | −0.207796 | + | 0.596923i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3569.44i | 2.55408i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1694.77i | − | 1.18415i | −0.805883 | − | 0.592074i | \(-0.798309\pi\) | ||
0.805883 | − | 0.592074i | \(-0.201691\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 671.492 | − | 1928.96i | 0.458306 | − | 1.31655i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1240.10 | −0.827084 | −0.413542 | − | 0.910485i | \(-0.635709\pi\) | ||||
−0.413542 | + | 0.910485i | \(0.635709\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −156.876 | −0.102277 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2437.08 | + | 1547.76i | −1.55371 | + | 0.986743i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1698.55i | − | 1.05925i | −0.848233 | − | 0.529623i | \(-0.822334\pi\) | ||
0.848233 | − | 0.529623i | \(-0.177666\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1234.84i | 0.753508i | 0.926313 | + | 0.376754i | \(0.122960\pi\) | ||||
−0.926313 | + | 0.376754i | \(0.877040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 806.864 | + | 280.879i | 0.481917 | + | 0.167761i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3616.25 | 2.11473 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1290.58 | −0.739149 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 240.458 | + | 83.7063i | 0.134916 | + | 0.0469659i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2080.66i | 1.14399i | 0.820257 | + | 0.571995i | \(0.193830\pi\) | ||||
−0.820257 | + | 0.571995i | \(0.806170\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1209.99i | − | 0.652102i | −0.945352 | − | 0.326051i | \(-0.894282\pi\) | ||
0.945352 | − | 0.326051i | \(-0.105718\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1369.08 | − | 1728.14i | 0.723422 | − | 0.913150i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1824.47 | −0.945450 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3193.69 | 1.62347 | 0.811734 | − | 0.584027i | \(-0.198524\pi\) | ||||
0.811734 | + | 0.584027i | \(0.198524\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −396.199 | + | 1138.14i | −0.197614 | + | 0.567674i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 802.220i | 0.392694i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3417.95i | − | 1.64242i | −0.570624 | − | 0.821211i | \(-0.693299\pi\) | ||
0.570624 | − | 0.821211i | \(-0.306701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2247.19 | + | 6455.38i | −1.06026 | + | 3.04576i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −626.793 | −0.290435 | −0.145218 | − | 0.989400i | \(-0.546388\pi\) | ||||
−0.145218 | + | 0.989400i | \(0.546388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1003.16 | 0.456606 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −375.746 | + | 474.291i | −0.168035 | + | 0.212105i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1310.07i | − | 0.575740i | −0.957669 | − | 0.287870i | \(-0.907053\pi\) | ||
0.957669 | − | 0.287870i | \(-0.0929472\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2089.21i | − | 0.902453i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −66.1106 | − | 23.0139i | −0.0280745 | − | 0.00977304i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3826.17 | 1.59766 | 0.798830 | − | 0.601557i | \(-0.205453\pi\) | ||||
0.798830 | + | 0.601557i | \(0.205453\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 305.944 | 0.125639 | 0.0628195 | − | 0.998025i | \(-0.479991\pi\) | ||||
0.0628195 | + | 0.998025i | \(0.479991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3268.03 | − | 1137.64i | −1.32011 | − | 0.459545i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1056.43i | 0.419838i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5219.93i | − | 2.04128i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 829.015 | − | 526.499i | 0.319058 | − | 0.202631i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4263.10 | −1.61501 | −0.807505 | − | 0.589861i | \(-0.799183\pi\) | ||||
−0.807505 | + | 0.589861i | \(0.799183\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3859.28 | −1.43936 | −0.719681 | − | 0.694305i | \(-0.755712\pi\) | ||||
−0.719681 | + | 0.694305i | \(0.755712\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1988.63 | + | 5712.62i | −0.730301 | + | 2.09789i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2956.09i | 1.06910i | 0.845137 | + | 0.534550i | \(0.179519\pi\) | ||||
−0.845137 | + | 0.534550i | \(0.820481\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3601.86i | 1.28306i | 0.767098 | + | 0.641530i | \(0.221700\pi\) | ||||
−0.767098 | + | 0.641530i | \(0.778300\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1430.28 | + | 4108.67i | −0.501910 | + | 1.44181i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 439.013 | 0.151786 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3414.58 | −1.16334 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2425.39 | + | 1921.46i | 0.814379 | + | 0.645173i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1432.62i | 0.474145i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1210.52i | − | 0.394957i | −0.980307 | − | 0.197478i | \(-0.936725\pi\) | ||
0.980307 | − | 0.197478i | \(-0.0632752\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 862.724 | + | 300.324i | 0.277525 | + | 0.0966097i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8088.79 | 2.56582 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 620.624 | 0.194151 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1480.98 | − | 515.546i | −0.456965 | − | 0.159075i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4619.33i | − | 1.40602i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4434.61i | 1.33168i | 0.746096 | + | 0.665838i | \(0.231926\pi\) | ||||
−0.746096 | + | 0.665838i | \(0.768074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6316.41 | − | 5004.03i | −1.87153 | − | 1.48267i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1003.61 | 0.293444 | 0.146722 | − | 0.989178i | \(-0.453128\pi\) | ||||
0.146722 | + | 0.989178i | \(0.453128\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3572.10 | 1.03079 | 0.515396 | − | 0.856952i | \(-0.327645\pi\) | ||||
0.515396 | + | 0.856952i | \(0.327645\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 764.421 | − | 2195.91i | 0.217728 | − | 0.625455i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5058.93i | − | 1.42241i | −0.702985 | − | 0.711204i | \(-0.748150\pi\) | ||
0.702985 | − | 0.711204i | \(-0.251850\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3383.47i | 0.939205i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1792.20 | − | 5148.34i | 0.491205 | − | 1.41106i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −859.569 | −0.232640 | −0.116320 | − | 0.993212i | \(-0.537110\pi\) | ||||
−0.116320 | + | 0.993212i | \(0.537110\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1789.17 | −0.478218 | −0.239109 | − | 0.970993i | \(-0.576855\pi\) | ||||
−0.239109 | + | 0.970993i | \(0.576855\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 393.847 | − | 3767.46i | 0.103972 | − | 0.994580i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1008.33i | 0.262937i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1267.78i | 0.326587i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6198.05 | + | 2157.61i | 1.57745 | + | 0.549129i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3442.21 | 0.865618 | 0.432809 | − | 0.901486i | \(-0.357522\pi\) | ||||
0.432809 | + | 0.901486i | \(0.357522\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7326.01 | 1.82048 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8245.97 | + | 2870.52i | 2.02503 | + | 0.704936i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3520.64i | − | 0.854519i | −0.904129 | − | 0.427259i | \(-0.859479\pi\) | ||
0.904129 | − | 0.427259i | \(-0.140521\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 359.362i | − | 0.0862149i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1051.51 | − | 1327.29i | 0.249376 | − | 0.314779i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5073.74 | −1.18958 | −0.594792 | − | 0.803880i | \(-0.702765\pi\) | ||||
−0.594792 | + | 0.803880i | \(0.702765\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4772.61 | −1.10634 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1332.47 | + | 3827.71i | −0.305415 | + | 0.877349i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4866.95i | 1.10313i | 0.834130 | + | 0.551567i | \(0.185970\pi\) | ||||
−0.834130 | + | 0.551567i | \(0.814030\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1174.35i | − | 0.263234i | −0.991301 | − | 0.131617i | \(-0.957983\pi\) | ||
0.991301 | − | 0.131617i | \(-0.0420169\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 676.467 | − | 1943.25i | 0.149969 | − | 0.430808i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19079.0 | −4.18367 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4246.00 | 0.921001 | 0.460501 | − | 0.887659i | \(-0.347670\pi\) | ||||
0.460501 | + | 0.887659i | \(0.347670\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1486.51 | − | 1876.37i | 0.318978 | − | 0.402635i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3654.37i | − | 0.775806i | −0.921700 | − | 0.387903i | \(-0.873200\pi\) | ||
0.921700 | − | 0.387903i | \(-0.126800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9256.48i | − | 1.94431i | −0.234331 | − | 0.972157i | \(-0.575290\pi\) | ||
0.234331 | − | 0.972157i | \(-0.424710\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2263.12 | − | 787.818i | −0.470371 | − | 0.163741i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1161.53 | 0.238895 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1754.84 | −0.357182 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3829.08 | + | 1332.95i | 0.771356 | + | 0.268518i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 310.759i | 0.0619615i | 0.999520 | + | 0.0309807i | \(0.00986305\pi\) | ||||
−0.999520 | + | 0.0309807i | \(0.990137\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 277.225i | − | 0.0547142i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4808.08 | − | 7570.71i | −0.939371 | − | 1.47912i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6483.08 | 1.25393 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2751.54 | −0.526898 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 81.0326 | − | 232.778i | 0.0153637 | − | 0.0441344i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 13704.0i | − | 2.57275i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2309.44i | 0.429338i | 0.976687 | + | 0.214669i | \(0.0688673\pi\) | ||||
−0.976687 | + | 0.214669i | \(0.931133\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40.9990 | − | 117.775i | 0.00754806 | − | 0.0216829i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1750.76 | −0.319216 | −0.159608 | − | 0.987180i | \(-0.551023\pi\) | ||||
−0.159608 | + | 0.987180i | \(0.551023\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4130.16 | −0.745847 | −0.372924 | − | 0.927862i | \(-0.621645\pi\) | ||||
−0.372924 | + | 0.927862i | \(0.621645\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3048.53 | + | 2415.12i | 0.545286 | + | 0.431990i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3470.62i | 0.614919i | 0.951561 | + | 0.307460i | \(0.0994789\pi\) | ||||
−0.951561 | + | 0.307460i | \(0.900521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4009.14i | − | 0.703664i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2120.50 | + | 738.171i | 0.368707 | + | 0.128351i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1830.00 | 0.315244 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16883.8 | −2.88167 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1588.99 | − | 553.147i | −0.268720 | − | 0.0935447i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1150.95i | − | 0.192868i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6625.10i | 1.10015i | 0.835116 | + | 0.550073i | \(0.185400\pi\) | ||||
−0.835116 | + | 0.550073i | \(0.814600\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1086.48 | − | 860.737i | −0.178795 | − | 0.141646i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17229.1 | −2.80993 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1193.87 | −0.192979 | −0.0964897 | − | 0.995334i | \(-0.530761\pi\) | ||||
−0.0964897 | + | 0.995334i | \(0.530761\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3370.15 | − | 9681.23i | 0.539945 | − | 1.55107i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5667.65i | − | 0.900060i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 343.000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4028.68 | + | 11573.0i | −0.628687 | + | 1.80599i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9431.38 | 1.45909 | 0.729543 | − | 0.683935i | \(-0.239733\pi\) | ||||
0.729543 | + | 0.683935i | \(0.239733\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4294.01 | −0.658604 | −0.329302 | − | 0.944225i | \(-0.606813\pi\) | ||||
−0.329302 | + | 0.944225i | \(0.606813\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4254.86 | − | 6699.62i | −0.647031 | − | 1.01880i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5205.64i | 0.784896i | 0.919774 | + | 0.392448i | \(0.128372\pi\) | ||||
−0.919774 | + | 0.392448i | \(0.871628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3617.71i | 0.540867i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2805.01 | − | 976.456i | −0.415846 | − | 0.144761i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1696.11 | −0.249352 | −0.124676 | − | 0.992197i | \(-0.539789\pi\) | ||||
−0.124676 | + | 0.992197i | \(0.539789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6356.75 | 0.926776 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13521.8 | − | 4707.09i | −1.95512 | − | 0.680601i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6210.27i | − | 0.890576i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6924.96i | 0.984959i | 0.870324 | + | 0.492479i | \(0.163909\pi\) | ||||
−0.870324 | + | 0.492479i | \(0.836091\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2782.07 | − | 3511.71i | 0.392490 | − | 0.495427i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1623.49 | 0.227189 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10377.2 | 1.44052 | 0.720258 | − | 0.693707i | \(-0.244024\pi\) | ||||
0.720258 | + | 0.693707i | \(0.244024\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6097.65 | − | 17516.4i | 0.839683 | − | 2.41211i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3547.85i | − | 0.484678i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10635.6i | 1.44146i | 0.693215 | + | 0.720730i | \(0.256193\pi\) | ||||
−0.693215 | + | 0.720730i | \(0.743807\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2895.17 | + | 8316.79i | −0.389302 | + | 1.11833i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8069.79 | 1.07662 | 0.538312 | − | 0.842745i | \(-0.319062\pi\) | ||||
0.538312 | + | 0.842745i | \(0.319062\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9208.22 | 1.21895 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6590.44 | + | 8318.89i | −0.865661 | + | 1.09269i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6771.67i | 0.882615i | 0.897356 | + | 0.441307i | \(0.145485\pi\) | ||||
−0.897356 | + | 0.441307i | \(0.854515\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9358.10i | − | 1.21038i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6085.56 | + | 2118.45i | 0.781109 | + | 0.271913i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21588.8 | 2.75000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −357.176 | −0.0451541 | −0.0225770 | − | 0.999745i | \(-0.507187\pi\) | ||||
−0.0225770 | + | 0.999745i | \(0.507187\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 769.840 | + | 267.990i | 0.0965920 | + | 0.0336248i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7785.56i | − | 0.969557i | −0.874637 | − | 0.484779i | \(-0.838900\pi\) | ||
0.874637 | − | 0.484779i | \(-0.161100\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5015.53i | − | 0.619954i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14603.5 | − | 3432.12i | 1.79174 | − | 0.421095i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3281.76 | −0.399682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11301.2 | 1.36628 | 0.683139 | − | 0.730288i | \(-0.260614\pi\) | ||||
0.683139 | + | 0.730288i | \(0.260614\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2901.61 | + | 8335.30i | −0.348239 | + | 1.00037i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 94.3030i | 0.0112357i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25990.6i | 3.07429i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2109.46 | − | 6059.74i | 0.247724 | − | 0.711623i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1022.70 | 0.119241 | 0.0596207 | − | 0.998221i | \(-0.481011\pi\) | ||||
0.0596207 | + | 0.998221i | \(0.481011\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4810.60 | 0.556898 | 0.278449 | − | 0.960451i | \(-0.410180\pi\) | ||||
0.278449 | + | 0.960451i | \(0.410180\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3479.71 | − | 2756.72i | −0.399975 | − | 0.316871i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24371.2i | 2.78159i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4661.66i | 0.528322i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17746.1 | − | 6177.61i | −1.99718 | − | 0.695240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −189.365 | −0.0211633 | −0.0105816 | − | 0.999944i | \(-0.503368\pi\) | ||||
−0.0105816 | + | 0.999944i | \(0.503368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6284.67 | 0.697510 | 0.348755 | − | 0.937214i | \(-0.386604\pi\) | ||||
0.348755 | + | 0.937214i | \(0.386604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6333.27 | + | 2204.68i | 0.698062 | + | 0.243004i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2568.35i | 0.281146i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14240.9i | 1.54825i | 0.633035 | + | 0.774123i | \(0.281809\pi\) | ||||
−0.633035 | + | 0.774123i | \(0.718191\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1037.01 | − | 821.547i | −0.111976 | − | 0.0887104i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4560.34 | −0.489093 | −0.244547 | − | 0.969638i | \(-0.578639\pi\) | ||||
−0.244547 | + | 0.969638i | \(0.578639\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16050.9 | −1.70986 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3554.38 | − | 10210.5i | 0.376099 | − | 1.08040i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7453.68i | 0.783432i | 0.920086 | + | 0.391716i | \(0.128118\pi\) | ||||
−0.920086 | + | 0.391716i | \(0.871882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 10607.3i | − | 1.10749i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2067.01 | + | 5937.79i | −0.214386 | + | 0.615854i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8148.72 | 0.839600 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5124.39 | −0.524527 | −0.262264 | − | 0.964996i | \(-0.584469\pi\) | ||||
−0.262264 | + | 0.964996i | \(0.584469\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9670.67 | + | 6141.75i | −0.983417 | + | 0.624558i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2810.43i | − | 0.283936i | −0.989871 | − | 0.141968i | \(-0.954657\pi\) | ||
0.989871 | − | 0.141968i | \(-0.0453431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9716.28i | 0.975278i | 0.873045 | + | 0.487639i | \(0.162142\pi\) | ||||
−0.873045 | + | 0.487639i | \(0.837858\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8953.23 | + | 3116.72i | 0.892895 | + | 0.310827i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1200.36 | 0.118942 | 0.0594709 | − | 0.998230i | \(-0.481059\pi\) | ||||
0.0594709 | + | 0.998230i | \(0.481059\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5860.78 | 0.577027 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15672.5 | − | 5455.76i | −1.53322 | − | 0.533733i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25127.6i | 2.44264i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6688.70i | − | 0.646103i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3888.54 | − | 4908.38i | 0.373258 | − | 0.471151i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8213.87 | 0.783510 | 0.391755 | − | 0.920070i | \(-0.371868\pi\) | ||||
0.391755 | + | 0.920070i | \(0.371868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2904.16 | −0.275298 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1370.43 | − | 3936.74i | 0.129103 | − | 0.370866i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16056.7i | 1.50329i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1756.97i | 0.163482i | 0.996654 | + | 0.0817411i | \(0.0260481\pi\) | ||||
−0.996654 | + | 0.0817411i | \(0.973952\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5838.87 | + | 16773.0i | −0.539965 | + | 1.55113i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3491.44 | 0.320910 | 0.160455 | − | 0.987043i | \(-0.448704\pi\) | ||||
0.160455 | + | 0.987043i | \(0.448704\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5121.20 | −0.467844 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22055.3 | − | 27839.7i | 2.00265 | − | 2.52788i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1230.63i | − | 0.111069i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2052.58i | − | 0.184140i | −0.995753 | − | 0.0920702i | \(-0.970652\pi\) | ||
0.995753 | − | 0.0920702i | \(-0.0293484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3075.87 | + | 1070.75i | 0.274291 | + | 0.0954838i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11456.0 | −1.01550 | −0.507752 | − | 0.861503i | \(-0.669523\pi\) | ||||
−0.507752 | + | 0.861503i | \(0.669523\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 976.119 | 0.0860133 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4922.84 | − | 1713.70i | −0.431225 | − | 0.150114i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 8286.73i | − | 0.721616i | −0.932640 | − | 0.360808i | \(-0.882501\pi\) | ||
0.932640 | − | 0.360808i | \(-0.117499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2112.53i | 0.182882i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2654.13 | − | 1685.61i | 0.228427 | − | 0.145071i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 493.874 | 0.0422576 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10510.6 | −0.894115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2237.99 | + | 6428.94i | −0.189281 | + | 0.543737i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4530.21i | 0.380944i | 0.981693 | + | 0.190472i | \(0.0610019\pi\) | ||||
−0.981693 | + | 0.190472i | \(0.938998\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 6344.62i | − | 0.530460i | −0.964185 | − | 0.265230i | \(-0.914552\pi\) | ||
0.964185 | − | 0.265230i | \(-0.0854480\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3568.98 | + | 10252.4i | −0.296691 | + | 0.852288i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7239.74 | −0.598422 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 966.807 | 0.0794614 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 285.111 | + | 225.873i | 0.0233009 | + | 0.0184596i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9386.82i | − | 0.762830i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8892.01i | 0.718570i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18776.2 | − | 6536.21i | −1.50885 | − | 0.525248i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3132.34 | −0.250314 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11240.5 | 0.893285 | 0.446643 | − | 0.894713i | \(-0.352620\pi\) | ||||
0.446643 | + | 0.894713i | \(0.352620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1501.37 | − | 522.642i | −0.118655 | − | 0.0413052i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 6663.21i | − | 0.523708i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 910.522i | − | 0.0711721i | −0.999367 | − | 0.0355860i | \(-0.988670\pi\) | ||
0.999367 | − | 0.0355860i | \(-0.0113298\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14093.8 | + | 11165.5i | 1.09565 | + | 0.868001i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1405.52 | 0.108670 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7343.81 | −0.564721 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1804.69 | − | 5184.22i | 0.138026 | − | 0.396501i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1315.08i | − | 0.100039i | −0.998748 | − | 0.0500194i | \(-0.984072\pi\) | ||
0.998748 | − | 0.0500194i | \(-0.0159283\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22236.4i | 1.68247i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8917.17 | + | 25615.8i | −0.671093 | + | 1.92781i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18890.6 | −1.41411 | −0.707055 | − | 0.707159i | \(-0.749977\pi\) | ||||
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40596.8 | 3.02287 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4967.65 | + | 1167.50i | −0.367940 | + | 0.0864731i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10534.7i | 0.776166i | 0.921624 | + | 0.388083i | \(0.126863\pi\) | ||||
−0.921624 | + | 0.388083i | \(0.873137\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5473.47i | 0.401151i | 0.979678 | + | 0.200576i | \(0.0642813\pi\) | ||||
−0.979678 | + | 0.200576i | \(0.935719\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20920.4 | + | 7282.62i | 1.52524 | + | 0.530952i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34204.2 | −2.48072 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10941.0 | −0.789390 | −0.394695 | − | 0.918812i | \(-0.629150\pi\) | ||||
−0.394695 | + | 0.918812i | \(0.629150\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18938.7 | + | 6592.77i | 1.35935 | + | 0.473206i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 8841.16i | − | 0.631313i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 14826.0i | − | 1.05322i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19517.7 | − | 24636.5i | 1.37941 | − | 1.74118i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7729.23 | −0.543474 | −0.271737 | − | 0.962372i | \(-0.587598\pi\) | ||||
−0.271737 | + | 0.962372i | \(0.587598\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1986.96 | 0.139000 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5049.87 | − | 14506.5i | 0.351478 | − | 1.00967i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5216.63i | 0.361250i | 0.983552 | + | 0.180625i | \(0.0578121\pi\) | ||||
−0.983552 | + | 0.180625i | \(0.942188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 11762.4i | − | 0.810439i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6153.03 | − | 17675.5i | 0.421820 | − | 1.21174i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24351.3 | 1.66105 | 0.830525 | − | 0.556982i | \(-0.188041\pi\) | ||||
0.830525 | + | 0.556982i | \(0.188041\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22958.3 | −1.55822 | −0.779109 | − | 0.626889i | \(-0.784328\pi\) | ||||
−0.779109 | + | 0.626889i | \(0.784328\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14037.6 | − | 17719.2i | 0.948021 | − | 1.19665i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 56701.7i | − | 3.81033i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27664.8i | − | 1.84988i | −0.380111 | − | 0.924941i | \(-0.624114\pi\) | ||
0.380111 | − | 0.924941i | \(-0.375886\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2154.37 | − | 749.962i | −0.143349 | − | 0.0499015i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9301.28 | −0.615859 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14975.3 | −0.986697 | −0.493349 | − | 0.869832i | \(-0.664227\pi\) | ||||
−0.493349 | + | 0.869832i | \(0.664227\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16756.4 | + | 5833.10i | 1.09867 | + | 0.382461i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10894.6i | 0.710862i | 0.934702 | + | 0.355431i | \(0.115666\pi\) | ||||
−0.934702 | + | 0.355431i | \(0.884334\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14213.8i | 0.922942i | 0.887155 | + | 0.461471i | \(0.152678\pi\) | ||||
−0.887155 | + | 0.461471i | \(0.847322\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8619.75 | − | 13572.5i | −0.557003 | − | 0.877046i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5460.01 | 0.351125 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 36145.0 | 2.31328 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2447.33 | − | 7030.31i | 0.155880 | − | 0.447789i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4192.05i | 0.265736i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12822.4i | 0.808957i | 0.914548 | + | 0.404478i | \(0.132547\pi\) | ||||
−0.914548 | + | 0.404478i | \(0.867453\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2067.93 | + | 5940.42i | −0.129846 | + | 0.373002i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34875.2 | −2.17950 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2771.93 | −0.172414 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3720.62 | − | 2947.57i | −0.230337 | − | 0.182479i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18120.3i | 1.11655i | 0.829657 | + | 0.558274i | \(0.188536\pi\) | ||||
−0.829657 | + | 0.558274i | \(0.811464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15848.0i | 0.971982i | 0.873964 | + | 0.485991i | \(0.161541\pi\) | ||||
−0.873964 | + | 0.485991i | \(0.838459\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −39694.2 | − | 13818.0i | −2.42319 | − | 0.843541i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7882.76 | 0.478985 | 0.239493 | − | 0.970898i | \(-0.423019\pi\) | ||||
0.239493 | + | 0.970898i | \(0.423019\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 861.192 | 0.0520874 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3045.60 | − | 1060.21i | −0.183359 | − | 0.0638292i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5732.96i | 0.343565i | 0.985135 | + | 0.171782i | \(0.0549526\pi\) | ||||
−0.985135 | + | 0.171782i | \(0.945047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25518.9i | 1.52230i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6386.93 | + | 5059.89i | 0.379266 | + | 0.300465i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8321.00 | 0.491867 | 0.245933 | − | 0.969287i | \(-0.420906\pi\) | ||||
0.245933 | + | 0.969287i | \(0.420906\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −658.617 | −0.0387553 | −0.0193776 | − | 0.999812i | \(-0.506168\pi\) | ||||
−0.0193776 | + | 0.999812i | \(0.506168\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7891.16 | + | 22668.5i | −0.462243 | + | 1.32786i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3228.21i | 0.188248i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7187.44i | − | 0.417240i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7575.62 | − | 21762.0i | 0.437803 | − | 1.25765i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42571.1 | 2.44924 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 433.488 | 0.0248287 | 0.0124144 | − | 0.999923i | \(-0.496048\pi\) | ||||
0.0124144 | + | 0.999923i | \(0.496048\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 22448.3 | + | 35346.6i | 1.28005 | + | 2.01554i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 15477.7i | − | 0.878663i | −0.898325 | − | 0.439332i | \(-0.855215\pi\) | ||
0.898325 | − | 0.439332i | \(-0.144785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5461.96i | − | 0.308705i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4925.02 | − | 1714.45i | −0.277132 | − | 0.0964729i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8246.35 | −0.461988 | −0.230994 | − | 0.972955i | \(-0.574198\pi\) | ||||
−0.230994 | + | 0.972955i | \(0.574198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34952.9 | −1.94961 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17529.4 | − | 6102.20i | −0.973493 | − | 0.338884i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 13120.1i | − | 0.725451i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9543.79i | 0.525417i | 0.964875 | + | 0.262708i | \(0.0846157\pi\) | ||||
−0.964875 | + | 0.262708i | \(0.915384\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7502.51 | + | 9470.16i | −0.411251 | + | 0.519108i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25410.6 | 1.38688 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13549.5 | −0.736335 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8642.12 | + | 24825.7i | −0.467633 | + | 1.34334i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 468.446i | − | 0.0252396i | −0.999920 | − | 0.0126198i | \(-0.995983\pi\) | ||
0.999920 | − | 0.0126198i | \(-0.00401712\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1150.52i | − | 0.0617248i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5779.95 | − | 16603.7i | 0.308774 | − | 0.886997i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −332.044 | −0.0176631 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29596.7 | −1.56774 | −0.783869 | − | 0.620926i | \(-0.786757\pi\) | ||||
−0.783869 | + | 0.620926i | \(0.786757\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17589.7 | + | 22202.9i | −0.927802 | + | 1.17113i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 10160.8i | − | 0.533693i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 74415.6i | − | 3.89229i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4218.18 | + | 1468.40i | 0.219708 | + | 0.0764829i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9175.10 | −0.475902 | −0.237951 | − | 0.971277i | \(-0.576476\pi\) | ||||
−0.237951 | + | 0.971277i | \(0.576476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −168.000 | −0.00867773 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8780.03 | + | 3056.43i | 0.451636 | + | 0.157220i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18718.1i | 0.958861i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28785.0i | 1.46847i | 0.678897 | + | 0.734233i | \(0.262458\pi\) | ||||
−0.678897 | + | 0.734233i | \(0.737542\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8368.66 | + | 17815.3i | −0.425172 | + | 0.905112i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32097.5 | 1.62403 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16765.7 | −0.844822 | −0.422411 | − | 0.906404i | \(-0.638816\pi\) | ||||
−0.422411 | + | 0.906404i | \(0.638816\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1722.52 | − | 4948.18i | 0.0864436 | − | 0.248321i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 53521.7i | − | 2.67503i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20608.6i | − | 1.02585i | −0.858434 | − | 0.512924i | \(-0.828562\pi\) | ||
0.858434 | − | 0.512924i | \(-0.171438\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2165.74 | − | 6221.40i | 0.107369 | − | 0.308433i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28519.6 | 1.40818 | 0.704092 | − | 0.710108i | \(-0.251354\pi\) | ||||
0.704092 | + | 0.710108i | \(0.251354\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42816.1 | 2.10558 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26729.9 | − | 21176.2i | −1.30923 | − | 1.03721i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 3024.77i | − | 0.147560i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 27316.0i | − | 1.32726i | −0.748059 | − | 0.663632i | \(-0.769014\pi\) | ||
0.748059 | − | 0.663632i | \(-0.230986\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16892.0 | − | 5880.29i | −0.817501 | − | 0.284581i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24899.2 | −1.20023 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17115.2 | 0.821749 | 0.410874 | − | 0.911692i | \(-0.365223\pi\) | ||||
0.410874 | + | 0.911692i | \(0.365223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −35951.1 | − | 12515.0i | −1.71929 | − | 0.598504i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28590.3i | 1.36189i | 0.732336 | + | 0.680944i | \(0.238430\pi\) | ||||
−0.732336 | + | 0.680944i | \(0.761570\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2266.61i | 0.107545i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −35561.9 | − | 28173.1i | −1.68071 | − | 1.33150i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 762.103 | 0.0358774 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25114.9 | −1.17772 | −0.588860 | − | 0.808235i | \(-0.700423\pi\) | ||||
−0.588860 | + | 0.808235i | \(0.700423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6014.28 | + | 17276.9i | −0.280932 | + | 0.807019i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3680.65i | 0.171260i | 0.996327 | + | 0.0856298i | \(0.0272902\pi\) | ||||
−0.996327 | + | 0.0856298i | \(0.972710\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26461.5i | 1.22648i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −613.896 | + | 1763.50i | −0.0283441 | + | 0.0814225i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3718.70 | 0.171035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11238.3 | −0.514901 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7427.51 | + | 4717.14i | −0.339001 | + | 0.215296i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 65720.2i | − | 2.98809i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 16721.5i | − | 0.757377i | −0.925524 | − | 0.378689i | \(-0.876375\pi\) | ||
0.925524 | − | 0.378689i | \(-0.123625\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24898.4 | + | 8667.44i | 1.12346 | + | 0.391089i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13809.7 | −0.620755 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37672.9 | 1.68702 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23420.7 | + | 8153.02i | 1.04484 | + | 0.363721i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 44061.5i | − | 1.95827i | −0.203219 | − | 0.979133i | \(-0.565140\pi\) | ||
0.203219 | − | 0.979133i | \(-0.434860\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13426.1i | 0.594469i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13077.7 | − | 16507.5i | 0.576876 | − | 0.728171i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19292.0 | 0.847821 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16508.2 | 0.722778 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8314.18 | − | 23883.7i | 0.362668 | − | 1.04182i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27091.4i | 1.17736i | 0.808366 | + | 0.588680i | \(0.200352\pi\) | ||||
−0.808366 | + | 0.588680i | \(0.799648\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23726.8i | − | 1.02733i | −0.857992 | − | 0.513663i | \(-0.828288\pi\) | ||
0.857992 | − | 0.513663i | \(-0.171712\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2006.13 | + | 5762.88i | −0.0865411 | + | 0.248602i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −70335.0 | −3.02298 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8809.20 | −0.377228 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6639.27 | + | 8380.52i | −0.283266 | + | 0.357557i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23146.9i | 0.983961i | 0.870606 | + | 0.491981i | \(0.163727\pi\) | ||||
−0.870606 | + | 0.491981i | \(0.836273\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 7929.61i | − | 0.335855i | −0.985799 | − | 0.167928i | \(-0.946293\pi\) | ||
0.985799 | − | 0.167928i | \(-0.0537075\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 93626.7 | + | 32592.5i | 3.95111 | + | 1.37543i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11422.2 | 0.480277 | 0.240138 | − | 0.970739i | \(-0.422807\pi\) | ||||
0.240138 | + | 0.970739i | \(0.422807\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34636.9 | 1.45113 | 0.725566 | − | 0.688152i | \(-0.241578\pi\) | ||||
0.725566 | + | 0.688152i | \(0.241578\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20836.5 | − | 7253.41i | −0.869806 | − | 0.302789i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4001.18i | 0.166426i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12898.2i | 0.534564i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10500.1 | + | 6668.53i | −0.433618 | + | 0.275386i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43031.9 | 1.77071 | 0.885355 | − | 0.464916i | \(-0.153916\pi\) | ||||
0.885355 | + | 0.464916i | \(0.153916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20455.7 | 0.838726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6242.73 | + | 17933.1i | −0.255055 | + | 0.732681i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 20643.2i | − | 0.840412i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19288.1i | 0.782462i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15812.8 | + | 45424.5i | −0.639215 | + | 1.83624i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5883.41 | −0.236993 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23460.4 | −0.941697 | −0.470849 | − | 0.882214i | \(-0.656052\pi\) | ||||
−0.470849 | + | 0.882214i | \(0.656052\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9760.02 | + | 7732.14i | 0.390392 | + | 0.309279i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1212.42i | − | 0.0483261i | −0.999708 | − | 0.0241630i | \(-0.992308\pi\) | ||
0.999708 | − | 0.0241630i | \(-0.00769208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 28844.2i | − | 1.14570i | −0.819662 | − | 0.572848i | \(-0.805839\pi\) | ||
0.819662 | − | 0.572848i | \(-0.194161\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5699.99 | − | 1984.23i | −0.225616 | − | 0.0785394i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20058.6 | 0.791195 | 0.395598 | − | 0.918424i | \(-0.370537\pi\) | ||||
0.395598 | + | 0.918424i | \(0.370537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26958.8 | −1.05969 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8611.53 | + | 2997.77i | 0.337328 | + | 0.117428i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 67065.0i | 2.61798i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 47363.5i | − | 1.84254i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16513.4 | − | 13082.4i | −0.640201 | − | 0.507184i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24986.1 | −0.965353 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17663.8 | 0.680120 | 0.340060 | − | 0.940404i | \(-0.389553\pi\) | ||||
0.340060 | + | 0.940404i | \(0.389553\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 530.866 | − | 1524.99i | 0.0203705 | − | 0.0585172i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5168.58i | 0.197655i | 0.995105 | + | 0.0988273i | \(0.0315092\pi\) | ||||
−0.995105 | + | 0.0988273i | \(0.968491\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5686.84i | 0.216735i | 0.994111 | + | 0.108368i | \(0.0345624\pi\) | ||||
−0.994111 | + | 0.108368i | \(0.965438\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −473.582 | + | 1360.43i | −0.0179879 | + | 0.0516728i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36753.5 | 1.39128 | 0.695638 | − | 0.718393i | \(-0.255122\pi\) | ||||
0.695638 | + | 0.718393i | \(0.255122\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11863.4 | 0.447566 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10661.8 | + | 45365.5i | 0.400879 | + | 1.70572i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3684.81i | − | 0.138082i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 78735.2i | − | 2.94059i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31814.5 | − | 11075.0i | −1.18423 | − | 0.412245i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5560.45 | −0.206286 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18938.4 | −0.700255 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13502.7 | + | 4700.44i | 0.497609 | + | 0.173224i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 6295.75i | − | 0.231246i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 18480.7i | − | 0.676563i | −0.941045 | − | 0.338281i | \(-0.890154\pi\) | ||
0.941045 | − | 0.338281i | \(-0.109846\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −795.305 | + | 1003.89i | −0.0290194 | + | 0.0366301i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13991.3 | −0.508839 | −0.254419 | − | 0.967094i | \(-0.581884\pi\) | ||||
−0.254419 | + | 0.967094i | \(0.581884\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −80739.0 | −2.92669 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23410.5 | + | 67249.9i | −0.845821 | + | 2.42974i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 8680.70i | − | 0.312608i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28803.2i | − | 1.03387i | −0.856023 | − | 0.516937i | \(-0.827072\pi\) | ||
0.856023 | − | 0.516937i | \(-0.172928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3945.20 | − | 11333.2i | 0.141150 | − | 0.405473i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9945.21 | −0.354659 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15322.1 | 0.544635 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −402.390 | + | 507.923i | −0.0142570 | + | 0.0179961i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50020.7i | 1.76655i | 0.468855 | + | 0.883275i | \(0.344667\pi\) | ||||
−0.468855 | + | 0.883275i | \(0.655333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1098.13i | − | 0.0386572i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8591.51 | + | 2990.80i | 0.301472 | + | 0.104946i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −107416. | −3.75710 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32852.9 | −1.14542 | −0.572709 | − | 0.819759i | \(-0.694108\pi\) | ||||
−0.572709 | + | 0.819759i | \(0.694108\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20268.0 | + | 7055.52i | 0.704388 | + | 0.245206i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23711.2i | 0.821426i | 0.911765 | + | 0.410713i | \(0.134720\pi\) | ||||
−0.911765 | + | 0.410713i | \(0.865280\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 19016.4i | − | 0.656689i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10834.4 | − | 17059.6i | −0.372954 | − | 0.587246i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45052.9 | 1.54596 | 0.772979 | − | 0.634431i | \(-0.218766\pi\) | ||||
0.772979 | + | 0.634431i | \(0.218766\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17072.3 | 0.583972 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5928.83 | − | 17031.4i | 0.202161 | − | 0.580738i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32569.1i | 1.10705i | 0.832833 | + | 0.553525i | \(0.186717\pi\) | ||||
−0.832833 | + | 0.553525i | \(0.813283\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 87726.4i | 2.97252i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6848.79 | + | 19674.1i | −0.231337 | + | 0.664550i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11889.8 | 0.400357 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21930.3 | 0.736138 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9144.96 | − | 7244.87i | −0.306015 | − | 0.242433i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 79416.6i | 2.64923i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45524.5i | 1.51393i | 0.653456 | + | 0.756965i | \(0.273319\pi\) | ||||
−0.653456 | + | 0.756965i | \(0.726681\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8980.38 | − | 3126.17i | −0.297721 | − | 0.103640i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20237.7 | −0.668857 | −0.334429 | − | 0.942421i | \(-0.608543\pi\) | ||||
−0.334429 | + | 0.942421i | \(0.608543\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8643.87 | −0.284799 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 82854.0 | + | 28842.4i | 2.72149 | + | 0.947382i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 29052.2i | − | 0.951342i | −0.879623 | − | 0.475671i | \(-0.842205\pi\) | ||
0.879623 | − | 0.475671i | \(-0.157795\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 49861.8i | − | 1.62777i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6852.76 | + | 5428.93i | 0.223029 | + | 0.176690i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26099.1 | −0.846827 | −0.423414 | − | 0.905937i | \(-0.639168\pi\) | ||||
−0.423414 | + | 0.905937i | \(0.639168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 60830.7 | 1.96774 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1966.15 | + | 5648.05i | −0.0634076 | + | 0.182147i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45047.8i | 1.44837i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48391.3i | 1.55116i | 0.631249 | + | 0.775580i | \(0.282543\pi\) | ||||
−0.631249 | + | 0.775580i | \(0.717457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11317.6 | − | 32511.5i | 0.361685 | − | 1.03899i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 74119.4 | 2.36155 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22646.0 | −0.719365 | −0.359683 | − | 0.933075i | \(-0.617115\pi\) | ||||
−0.359683 | + | 0.933075i | \(0.617115\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3861.30 | + | 6079.93i | 0.122288 | + | 0.192553i |
(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 | 336.4.h.a.239.1 | ✓ | 12 | |
3.2 | odd | 2 | inner | 336.4.h.a.239.11 | yes | 12 | |
4.3 | odd | 2 | inner | 336.4.h.a.239.12 | yes | 12 | |
12.11 | even | 2 | inner | 336.4.h.a.239.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.h.a.239.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
336.4.h.a.239.2 | yes | 12 | 12.11 | even | 2 | inner | |
336.4.h.a.239.11 | yes | 12 | 3.2 | odd | 2 | inner | |
336.4.h.a.239.12 | yes | 12 | 4.3 | odd | 2 | inner |