Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [480,4,Mod(431,480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(480, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("480.431");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.b (of order \(2\), degree \(1\), not 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: | \(28.3209168028\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 431.23 | ||
Character | \(\chi\) | \(=\) | 480.431 |
Dual form | 480.4.b.b.431.24 |
$q$-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 \(\left(\mathbb{Z}/480\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(421\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 5.19284 | − | 0.185395i | 0.999363 | − | 0.0356793i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 11.8996i | − | 0.642519i | −0.946991 | − | 0.321259i | \(-0.895894\pi\) | ||
0.946991 | − | 0.321259i | \(-0.104106\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 26.9313 | − | 1.92545i | 0.997454 | − | 0.0713131i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 19.5939i | − | 0.537072i | −0.963270 | − | 0.268536i | \(-0.913460\pi\) | ||
0.963270 | − | 0.268536i | \(-0.0865398\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 80.7203i | − | 1.72214i | −0.508488 | − | 0.861069i | \(-0.669795\pi\) | ||
0.508488 | − | 0.861069i | \(-0.330205\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.9642 | − | 0.926975i | 0.446929 | − | 0.0159563i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.9580i | 0.184869i | 0.995719 | + | 0.0924345i | \(0.0294649\pi\) | ||||
−0.995719 | + | 0.0924345i | \(0.970535\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −81.9017 | −0.988923 | −0.494462 | − | 0.869200i | \(-0.664635\pi\) | ||||
−0.494462 | + | 0.869200i | \(0.664635\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.20613 | − | 61.7928i | −0.0229246 | − | 0.642110i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −147.701 | −1.33904 | −0.669519 | − | 0.742795i | \(-0.733500\pi\) | ||||
−0.669519 | + | 0.742795i | \(0.733500\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 139.493 | − | 14.9915i | 0.994274 | − | 0.106856i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 217.553 | 1.39305 | 0.696527 | − | 0.717531i | \(-0.254728\pi\) | ||||
0.696527 | + | 0.717531i | \(0.254728\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 139.101i | − | 0.805909i | −0.915220 | − | 0.402955i | \(-0.867983\pi\) | ||
0.915220 | − | 0.402955i | \(-0.132017\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.63262 | − | 101.748i | −0.0191624 | − | 0.536730i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 59.4981i | − | 0.287343i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 272.588i | − | 1.21117i | −0.795781 | − | 0.605584i | \(-0.792940\pi\) | ||
0.795781 | − | 0.605584i | \(-0.207060\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.9651 | − | 419.168i | −0.0614447 | − | 1.72104i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 480.713i | 1.83109i | 0.402212 | + | 0.915547i | \(0.368242\pi\) | ||||
−0.402212 | + | 0.915547i | \(0.631758\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24.1939 | 0.0858033 | 0.0429016 | − | 0.999079i | \(-0.486340\pi\) | ||||
0.0429016 | + | 0.999079i | \(0.486340\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 134.656 | − | 9.62727i | 0.446075 | − | 0.0318922i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −370.290 | −1.14920 | −0.574599 | − | 0.818435i | \(-0.694842\pi\) | ||||
−0.574599 | + | 0.818435i | \(0.694842\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 201.399 | 0.587170 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.40235 | + | 67.2888i | 0.00659600 | + | 0.184751i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 271.318 | 0.703178 | 0.351589 | − | 0.936155i | \(-0.385642\pi\) | ||||
0.351589 | + | 0.936155i | \(0.385642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 97.9697i | − | 0.240186i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −425.303 | + | 15.1842i | −0.988293 | + | 0.0352841i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 323.342i | − | 0.713485i | −0.934203 | − | 0.356742i | \(-0.883887\pi\) | ||
0.934203 | − | 0.356742i | \(-0.116113\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 79.6391i | − | 0.167160i | −0.996501 | − | 0.0835799i | \(-0.973365\pi\) | ||
0.996501 | − | 0.0835799i | \(-0.0266354\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −22.9122 | − | 320.472i | −0.0458200 | − | 0.640883i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 403.602i | − | 0.770164i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 563.244 | 1.02703 | 0.513517 | − | 0.858080i | \(-0.328342\pi\) | ||||
0.513517 | + | 0.858080i | \(0.328342\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −766.991 | + | 27.3831i | −1.33819 | + | 0.0477759i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 537.552 | 0.898531 | 0.449265 | − | 0.893398i | \(-0.351686\pi\) | ||||
0.449265 | + | 0.893398i | \(0.351686\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 98.9937 | 0.158717 | 0.0793585 | − | 0.996846i | \(-0.474713\pi\) | ||||
0.0793585 | + | 0.996846i | \(0.474713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 129.821 | − | 4.63488i | 0.199873 | − | 0.00713586i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −233.160 | −0.345079 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 292.524i | 0.416602i | 0.978065 | + | 0.208301i | \(0.0667933\pi\) | ||||
−0.978065 | + | 0.208301i | \(0.933207\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 721.585 | − | 103.710i | 0.989829 | − | 0.142263i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1235.15i | 1.63344i | 0.577033 | + | 0.816721i | \(0.304210\pi\) | ||||
−0.577033 | + | 0.816721i | \(0.695790\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 64.7900i | 0.0826760i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1129.72 | − | 40.3332i | 1.39217 | − | 0.0497032i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 657.532i | − | 0.783126i | −0.920151 | − | 0.391563i | \(-0.871935\pi\) | ||
0.920151 | − | 0.391563i | \(-0.128065\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −960.541 | −1.10651 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25.7885 | − | 722.327i | −0.0287543 | − | 0.805396i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −409.508 | −0.442260 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −574.564 | −0.601424 | −0.300712 | − | 0.953715i | \(-0.597224\pi\) | ||||
−0.300712 | + | 0.953715i | \(0.597224\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −37.7272 | − | 527.689i | −0.0383003 | − | 0.535705i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −95.4087 | −0.0939953 | −0.0469976 | − | 0.998895i | \(-0.514965\pi\) | ||||
−0.0469976 | + | 0.998895i | \(0.514965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 190.207i | − | 0.181957i | −0.995853 | − | 0.0909787i | \(-0.971000\pi\) | ||
0.995853 | − | 0.0909787i | \(-0.0289995\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.0306 | − | 308.964i | −0.0102522 | − | 0.287160i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1394.13i | − | 1.25958i | −0.776764 | − | 0.629792i | \(-0.783140\pi\) | ||
0.776764 | − | 0.629792i | \(-0.216860\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1052.71i | − | 0.925061i | −0.886603 | − | 0.462531i | \(-0.846942\pi\) | ||
0.886603 | − | 0.462531i | \(-0.153058\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −50.5365 | − | 1415.51i | −0.0432136 | − | 1.21040i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1385.09i | 1.15308i | 0.817069 | + | 0.576540i | \(0.195598\pi\) | ||||
−0.817069 | + | 0.576540i | \(0.804402\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −738.507 | −0.598836 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −155.423 | − | 2173.90i | −0.122811 | − | 1.71775i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 154.195 | 0.118782 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 947.078 | 0.711554 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 89.1219 | + | 2496.27i | 0.0653321 | + | 1.82993i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 345.019i | 0.241067i | 0.992709 | + | 0.120533i | \(0.0384605\pi\) | ||||
−0.992709 | + | 0.120533i | \(0.961540\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 125.635 | − | 4.48544i | 0.0857487 | − | 0.00306140i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 481.159i | − | 0.320909i | −0.987043 | − | 0.160454i | \(-0.948704\pi\) | ||
0.987043 | − | 0.160454i | \(-0.0512960\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 974.599i | 0.635402i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 697.464 | − | 74.9575i | 0.444653 | − | 0.0477875i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1207.42i | − | 0.752967i | −0.926423 | − | 0.376483i | \(-0.877133\pi\) | ||
0.926423 | − | 0.376483i | \(-0.122867\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2439.69 | 1.48872 | 0.744359 | − | 0.667779i | \(-0.232755\pi\) | ||||
0.744359 | + | 0.667779i | \(0.232755\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1922.86 | + | 68.6499i | −1.14847 | + | 0.0410026i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1581.63 | −0.924912 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1087.76 | 0.622993 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1045.83 | − | 37.3384i | 0.586796 | − | 0.0209498i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2052.93 | 1.12874 | 0.564372 | − | 0.825521i | \(-0.309118\pi\) | ||||
0.564372 | + | 0.825521i | \(0.309118\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 232.344i | 0.125218i | 0.998038 | + | 0.0626088i | \(0.0199420\pi\) | ||||
−0.998038 | + | 0.0626088i | \(0.980058\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 24.9500 | + | 348.975i | 0.0131836 | + | 0.184398i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 695.503i | − | 0.360414i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3057.94i | 1.55446i | 0.629216 | + | 0.777231i | \(0.283376\pi\) | ||||
−0.629216 | + | 0.777231i | \(0.716624\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1408.91 | − | 50.3010i | 0.702730 | − | 0.0250889i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1757.59i | 0.860358i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −621.974 | −0.298876 | −0.149438 | − | 0.988771i | \(-0.547746\pi\) | ||||
−0.149438 | + | 0.988771i | \(0.547746\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.1631 | − | 508.741i | −0.00856966 | − | 0.240033i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1489.97 | 0.690402 | 0.345201 | − | 0.938529i | \(-0.387811\pi\) | ||||
0.345201 | + | 0.938529i | \(0.387811\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4318.77 | −1.96576 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2205.72 | + | 157.698i | −0.986405 | + | 0.0705232i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2319.39 | −1.01930 | −0.509652 | − | 0.860381i | \(-0.670226\pi\) | ||||
−0.509652 | + | 0.860381i | \(0.670226\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 297.490i | − | 0.128504i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −59.9461 | − | 1679.07i | −0.0254566 | − | 0.713031i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2525.19i | 1.05442i | 0.849734 | + | 0.527212i | \(0.176763\pi\) | ||||
−0.849734 | + | 0.527212i | \(0.823237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3943.26i | 1.61934i | 0.586888 | + | 0.809668i | \(0.300353\pi\) | ||||
−0.586888 | + | 0.809668i | \(0.699647\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.7647 | − | 413.554i | −0.00596414 | − | 0.167053i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1362.94i | − | 0.541651i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 253.898 | 0.0992880 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −178.393 | − | 1659.91i | −0.0686571 | − | 0.638840i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1918.68 | −0.726862 | −0.363431 | − | 0.931621i | \(-0.618395\pi\) | ||||
−0.363431 | + | 0.931621i | \(0.618395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1417.65 | −0.528731 | −0.264365 | − | 0.964423i | \(-0.585162\pi\) | ||||
−0.264365 | + | 0.964423i | \(0.585162\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −74.8257 | − | 2095.84i | −0.0274789 | − | 0.769673i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3744.03 | 1.35407 | 0.677033 | − | 0.735952i | \(-0.263265\pi\) | ||||
0.677033 | + | 0.735952i | \(0.263265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4872.55i | 1.73571i | 0.496820 | + | 0.867854i | \(0.334501\pi\) | ||||
−0.496820 | + | 0.867854i | \(0.665499\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2924.84 | − | 104.423i | 1.02638 | − | 0.0366438i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2588.80i | − | 0.895063i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2403.57i | 0.818890i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3977.79 | + | 284.393i | −1.33563 | + | 0.0954911i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1604.78i | 0.531123i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2120.64 | −0.691900 | −0.345950 | − | 0.938253i | \(-0.612443\pi\) | ||||
−0.345950 | + | 0.938253i | \(0.612443\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2791.42 | − | 99.6594i | 0.897958 | − | 0.0320589i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 120.970 | 0.0383724 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1655.24 | −0.517812 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 514.059 | − | 18.3529i | 0.158616 | − | 0.00566291i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1045.97 | 0.318370 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5310.83i | 1.59480i | 0.603454 | + | 0.797398i | \(0.293791\pi\) | ||||
−0.603454 | + | 0.797398i | \(0.706209\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 673.281 | − | 48.1364i | 0.199491 | − | 0.0142626i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 3911.60i | − | 1.14371i | −0.820355 | − | 0.571854i | \(-0.806224\pi\) | ||
0.820355 | − | 0.571854i | \(-0.193776\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5988.71i | 1.72814i | 0.503368 | + | 0.864072i | \(0.332094\pi\) | ||||
−0.503368 | + | 0.864072i | \(0.667906\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1210.76 | + | 43.2268i | −0.344859 | + | 0.0123122i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3640.14i | 1.02349i | 0.859137 | + | 0.511745i | \(0.171001\pi\) | ||||
−0.859137 | + | 0.511745i | \(0.828999\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1851.45 | −0.513937 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 54.2325 | + | 1519.03i | 0.0148640 | + | 0.416336i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6300.66 | −1.70525 | −0.852627 | − | 0.522521i | \(-0.824992\pi\) | ||||
−0.852627 | + | 0.522521i | \(0.824992\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −186.979 | −0.0499766 | −0.0249883 | − | 0.999688i | \(-0.507955\pi\) | ||||
−0.0249883 | + | 0.999688i | \(0.507955\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3727.85 | − | 672.327i | 0.984123 | − | 0.177489i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1007.00 | 0.262590 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6611.13i | 1.70306i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 228.991 | + | 6413.96i | 0.0582800 | + | 1.63240i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5717.83i | 1.43787i | 0.695075 | + | 0.718937i | \(0.255371\pi\) | ||||
−0.695075 | + | 0.718937i | \(0.744629\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2894.05i | 0.719160i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.0117 | + | 336.444i | 0.00294982 | + | 0.0826233i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6608.04i | − | 1.60388i | −0.597402 | − | 0.801942i | \(-0.703800\pi\) | ||
0.597402 | − | 0.801942i | \(-0.296200\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3243.69 | −0.778198 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5858.97 | − | 418.888i | 1.38951 | − | 0.0993431i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5341.51 | 1.25236 | 0.626182 | − | 0.779677i | \(-0.284617\pi\) | ||||
0.626182 | + | 0.779677i | \(0.284617\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1356.59 | 0.314471 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −121.903 | − | 3414.46i | −0.0279414 | − | 0.782627i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7051.54 | −1.59829 | −0.799144 | − | 0.601139i | \(-0.794714\pi\) | ||||
−0.799144 | + | 0.601139i | \(0.794714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4785.65i | 1.07272i | 0.843989 | + | 0.536361i | \(0.180201\pi\) | ||||
−0.843989 | + | 0.536361i | \(0.819799\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4987.94 | + | 178.080i | −1.10580 | + | 0.0394794i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 489.848i | − | 0.107414i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4080.47i | − | 0.885097i | −0.896745 | − | 0.442548i | \(-0.854074\pi\) | ||
0.896745 | − | 0.442548i | \(-0.145926\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −267.832 | − | 3746.15i | −0.0574719 | − | 0.803858i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1042.56i | − | 0.221331i | −0.993858 | − | 0.110665i | \(-0.964702\pi\) | ||
0.993858 | − | 0.110665i | \(-0.0352982\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2816.83 | −0.591672 | −0.295836 | − | 0.955239i | \(-0.595598\pi\) | ||||
−0.295836 | + | 0.955239i | \(0.595598\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2126.51 | + | 75.9208i | −0.441978 | + | 0.0157795i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5720.30 | 1.17651 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4745.09 | 0.965823 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2983.62 | + | 106.521i | −0.601041 | + | 0.0214584i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4373.43 | −0.872009 | −0.436005 | − | 0.899944i | \(-0.643607\pi\) | ||||
−0.436005 | + | 0.899944i | \(0.643607\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1616.71i | − | 0.319080i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −293.743 | − | 2733.21i | −0.0573895 | − | 0.533997i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11922.5i | 2.30601i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 287.899i | − | 0.0551302i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −495.443 | + | 17.6883i | −0.0939354 | + | 0.00335369i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 398.196i | − | 0.0747561i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4848.29 | 0.901324 | 0.450662 | − | 0.892695i | \(-0.351188\pi\) | ||||
0.450662 | + | 0.892695i | \(0.351188\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −35.2634 | − | 987.714i | −0.00649211 | − | 0.181842i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4111.79 | 0.749705 | 0.374853 | − | 0.927084i | \(-0.377693\pi\) | ||||
0.374853 | + | 0.927084i | \(0.377693\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7169.64 | 1.29474 | 0.647368 | − | 0.762178i | \(-0.275870\pi\) | ||||
0.647368 | + | 0.762178i | \(0.275870\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −114.561 | − | 1602.36i | −0.0204913 | − | 0.286612i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4371.23 | −0.774489 | −0.387244 | − | 0.921977i | \(-0.626573\pi\) | ||||
−0.387244 | + | 0.921977i | \(0.626573\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4262.72i | − | 0.748170i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −258.465 | − | 7239.49i | −0.0449411 | − | 1.25878i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1061.28i | − | 0.182821i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2018.01i | − | 0.344428i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −195.168 | − | 5466.58i | −0.0330055 | − | 0.924472i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4406.31i | 0.738381i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5590.60 | 0.928360 | 0.464180 | − | 0.885741i | \(-0.346349\pi\) | ||||
0.464180 | + | 0.885741i | \(0.346349\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −524.856 | − | 7341.14i | −0.0863722 | − | 1.20808i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2816.22 | 0.459303 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7898.02 | −1.27665 | −0.638327 | − | 0.769765i | \(-0.720373\pi\) | ||||
−0.638327 | + | 0.769765i | \(0.720373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 256.788 | + | 7192.54i | 0.0411411 | + | 1.15235i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2725.53 | −0.432831 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6478.14i | − | 1.01979i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3834.95 | + | 136.916i | −0.598455 | + | 0.0213661i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 10863.8i | − | 1.68069i | −0.542048 | − | 0.840347i | \(-0.682351\pi\) | ||
0.542048 | − | 0.840347i | \(-0.317649\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4377.57i | − | 0.671421i | −0.941965 | − | 0.335711i | \(-0.891024\pi\) | ||
0.941965 | − | 0.335711i | \(-0.108976\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1210.12 | − | 11259.9i | −0.184021 | − | 1.71228i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1333.66i | 0.201086i | 0.994933 | + | 0.100543i | \(0.0320580\pi\) | ||||
−0.994933 | + | 0.100543i | \(0.967942\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2687.76 | 0.401835 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 800.711 | − | 28.5870i | 0.118706 | − | 0.00423805i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3527.91 | 0.518651 | 0.259326 | − | 0.965790i | \(-0.416500\pi\) | ||||
0.259326 | + | 0.965790i | \(0.416500\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −151.112 | −0.0220312 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4918.03 | − | 175.584i | 0.711101 | − | 0.0253877i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 494.969 | 0.0709804 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4297.18i | − | 0.611202i | −0.952160 | − | 0.305601i | \(-0.901143\pi\) | ||
0.952160 | − | 0.305601i | \(-0.0988574\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 925.592 | + | 12946.2i | 0.130581 | + | 1.82643i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3228.58i | − | 0.451805i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1702.18i | 0.236288i | 0.992996 | + | 0.118144i | \(0.0376944\pi\) | ||||
−0.992996 | + | 0.118144i | \(0.962306\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 649.105 | − | 23.1744i | 0.0893858 | − | 0.00319125i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 17560.9i | − | 2.39903i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1377.13 | −0.186645 | −0.0933223 | − | 0.995636i | \(-0.529749\pi\) | ||||
−0.0933223 | + | 0.995636i | \(0.529749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 63.9648 | + | 1791.63i | 0.00860109 | + | 0.240913i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1957.46 | 0.261152 | 0.130576 | − | 0.991438i | \(-0.458317\pi\) | ||||
0.130576 | + | 0.991438i | \(0.458317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1165.80 | −0.154324 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 651.573 | − | 46.5843i | 0.0855848 | − | 0.00611890i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7121.90 | 0.928264 | 0.464132 | − | 0.885766i | \(-0.346366\pi\) | ||||
0.464132 | + | 0.885766i | \(0.346366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1913.91i | − | 0.247547i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −89.2045 | − | 2498.58i | −0.0114498 | − | 0.320705i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1462.62i | 0.186310i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3576.18i | − | 0.452099i | −0.974116 | − | 0.226050i | \(-0.927419\pi\) | ||
0.974116 | − | 0.226050i | \(-0.0725811\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 180.686 | + | 5060.94i | 0.0226707 | + | 0.634997i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4642.92i | 0.578196i | 0.957300 | + | 0.289098i | \(0.0933553\pi\) | ||||
−0.957300 | + | 0.289098i | \(0.906645\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11228.2 | −1.38789 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3607.93 | − | 518.549i | 0.442665 | − | 0.0636220i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5341.07 | −0.650485 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2880.41 | −0.348233 | −0.174116 | − | 0.984725i | \(-0.555707\pi\) | ||||
−0.174116 | + | 0.984725i | \(0.555707\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −223.849 | − | 6269.92i | −0.0268653 | − | 0.752487i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3847.65 | −0.458427 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6175.77i | 0.730497i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12668.9 | − | 452.307i | 1.48777 | − | 0.0531164i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11503.6i | 1.34126i | 0.741792 | + | 0.670630i | \(0.233976\pi\) | ||||
−0.741792 | + | 0.670630i | \(0.766024\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12380.8i | − | 1.43327i | −0.697450 | − | 0.716633i | \(-0.745682\pi\) | ||
0.697450 | − | 0.716633i | \(-0.254318\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9972.37 | + | 712.976i | −1.14627 | + | 0.0819529i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 323.950i | 0.0369738i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −947.675 | −0.107403 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8213.15 | + | 293.226i | −0.924323 | + | 0.0330002i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1329.74 | 0.148611 | 0.0743053 | − | 0.997236i | \(-0.476326\pi\) | ||||
0.0743053 | + | 0.997236i | \(0.476326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7568.50 | 0.839997 | 0.419999 | − | 0.907525i | \(-0.362031\pi\) | ||||
0.419999 | + | 0.907525i | \(0.362031\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5648.59 | − | 201.666i | 0.622596 | − | 0.0222279i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12097.0 | 1.32421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6198.59i | − | 0.673901i | −0.941522 | − | 0.336951i | \(-0.890604\pi\) | ||
0.941522 | − | 0.336951i | \(-0.109396\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5423.93 | − | 387.785i | 0.585675 | − | 0.0418729i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4385.56i | 0.470349i | 0.971953 | + | 0.235174i | \(0.0755661\pi\) | ||||
−0.971953 | + | 0.235174i | \(0.924434\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 3287.66i | − | 0.350225i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10660.6 | − | 380.604i | 1.12803 | − | 0.0402728i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10366.2i | 1.08955i | 0.838581 | + | 0.544777i | \(0.183386\pi\) | ||||
−0.838581 | + | 0.544777i | \(0.816614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9419.07 | 0.983429 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 43.0754 | + | 1206.52i | 0.00446768 | + | 0.125138i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4802.71 | −0.494845 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8503.91 | 0.870451 | 0.435226 | − | 0.900321i | \(-0.356669\pi\) | ||||
0.435226 | + | 0.900321i | \(0.356669\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 194.260 | + | 1807.55i | 0.0197544 | + | 0.183811i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14344.7 | −1.44924 | −0.724618 | − | 0.689151i | \(-0.757984\pi\) | ||||
−0.724618 | + | 0.689151i | \(0.757984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14521.6i | − | 1.45762i | −0.684717 | − | 0.728809i | \(-0.740074\pi\) | ||
0.684717 | − | 0.728809i | \(-0.259926\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −128.943 | − | 3611.64i | −0.0128593 | − | 0.360184i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 15334.2i | − | 1.51945i | −0.650247 | − | 0.759723i | \(-0.725335\pi\) | ||
0.650247 | − | 0.759723i | \(-0.274665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6702.39i | − | 0.659888i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 566.928 | + | 15879.4i | 0.0554621 | + | 1.55347i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 474.054i | − | 0.0460825i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2047.54 | −0.197785 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7306.94 | − | 522.411i | 0.701387 | − | 0.0501458i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2635.56 | −0.251403 | −0.125701 | − | 0.992068i | \(-0.540118\pi\) | ||||
−0.125701 | + | 0.992068i | \(0.540118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22003.4 | −2.08580 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 325.849 | + | 9126.90i | 0.0306969 | + | 0.859810i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2872.82 | −0.268965 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 627.098i | 0.0583502i | 0.999574 | + | 0.0291751i | \(0.00928803\pi\) | ||||
−0.999574 | + | 0.0291751i | \(0.990712\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3229.82 | + | 115.311i | −0.298686 | + | 0.0106637i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 106.671i | − | 0.00980444i | −0.999988 | − | 0.00490222i | \(-0.998440\pi\) | ||
0.999988 | − | 0.00490222i | \(-0.00156043\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2819.05i | 0.257533i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −188.636 | − | 2638.45i | −0.0171284 | − | 0.239574i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6396.66i | − | 0.577323i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3347.75 | −0.300332 | −0.150166 | − | 0.988661i | \(-0.547981\pi\) | ||||
−0.150166 | + | 0.988661i | \(0.547981\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7737.16 | − | 276.232i | 0.689962 | − | 0.0246330i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −574.905 | −0.0509617 | −0.0254809 | − | 0.999675i | \(-0.508112\pi\) | ||||
−0.0254809 | + | 0.999675i | \(0.508112\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −477.044 | −0.0420360 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22426.7 | + | 800.679i | −1.96451 | + | 0.0701369i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −846.131 | −0.0736819 | −0.0368410 | − | 0.999321i | \(-0.511729\pi\) | ||||
−0.0368410 | + | 0.999321i | \(0.511729\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1177.99i | − | 0.101979i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11424.7 | + | 1227.83i | −0.983261 | + | 0.105673i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 951.033i | − | 0.0813739i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7255.43i | 0.617202i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12044.2 | + | 430.003i | −1.01866 | + | 0.0363680i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12770.5i | 1.07387i | 0.843624 | + | 0.536935i | \(0.180418\pi\) | ||||
−0.843624 | + | 0.536935i | \(0.819582\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5813.64 | 0.486067 | 0.243033 | − | 0.970018i | \(-0.421858\pi\) | ||||
0.243033 | + | 0.970018i | \(0.421858\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −55.1532 | − | 1544.82i | −0.00458492 | − | 0.128422i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1802.46 | 0.148988 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9648.73 | 0.793025 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −622.581 | − | 8708.02i | −0.0508808 | − | 0.711668i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38803.4 | 3.15340 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6970.64i | − | 0.563303i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 468.158 | + | 13112.9i | 0.0376211 | + | 1.05375i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3946.20i | − | 0.315352i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 4442.49i | − | 0.353045i | −0.984297 | − | 0.176523i | \(-0.943515\pi\) | ||
0.984297 | − | 0.176523i | \(-0.0564849\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 731.060 | + | 20476.7i | 0.0577768 | + | 1.61831i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 5263.57i | − | 0.413700i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2460.07 | 0.192295 | 0.0961473 | − | 0.995367i | \(-0.469348\pi\) | ||||
0.0961473 | + | 0.995367i | \(0.469348\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −153.342 | − | 2144.78i | −0.0119207 | − | 0.166734i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17818.0 | −1.37762 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3480.92 | 0.267674 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −252.682 | − | 7077.54i | −0.0193257 | − | 0.541306i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20307.0 | −1.54477 | −0.772385 | − | 0.635155i | \(-0.780936\pi\) | ||||
−0.772385 | + | 0.635155i | \(0.780936\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1952.94i | − | 0.147765i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1318.45 | − | 47.0714i | 0.0992248 | − | 0.00354253i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1927.79i | 0.144310i | 0.997393 | + | 0.0721550i | \(0.0229876\pi\) | ||||
−0.997393 | + | 0.0721550i | \(0.977012\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6925.44i | 0.515673i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1234.11 | − | 8586.59i | −0.0914068 | − | 0.635984i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5528.65i | 0.407334i | 0.979040 | + | 0.203667i | \(0.0652861\pi\) | ||||
−0.979040 | + | 0.203667i | \(0.934714\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22158.5 | 1.62400 | 0.812001 | − | 0.583656i | \(-0.198379\pi\) | ||||
0.812001 | + | 0.583656i | \(0.198379\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9963.39 | + | 355.713i | −0.726399 | + | 0.0259339i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3692.54 | −0.267808 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16291.1 | 1.17541 | 0.587703 | − | 0.809077i | \(-0.300032\pi\) | ||||
0.587703 | + | 0.809077i | \(0.300032\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7361.66 | + | 262.826i | −0.528394 | + | 0.0188647i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14697.8 | 1.04952 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5316.19i | − | 0.377657i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −777.117 | − | 10869.5i | −0.0549228 | − | 0.768203i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 14991.4i | − | 1.05411i | −0.849831 | − | 0.527055i | \(-0.823296\pi\) | ||
0.849831 | − | 0.527055i | \(-0.176704\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11392.6i | 0.796982i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19442.2 | − | 694.125i | 1.35320 | − | 0.0483121i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11604.3i | − | 0.803591i | −0.915729 | − | 0.401796i | \(-0.868386\pi\) | ||
0.915729 | − | 0.401796i | \(-0.131614\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 770.976 | 0.0531209 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 903.346 | + | 25302.4i | 0.0619288 | + | 1.73460i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2109.64 | −0.143902 | −0.0719511 | − | 0.997408i | \(-0.522923\pi\) | ||||
−0.0719511 | + | 0.997408i | \(0.522923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17029.9 | −1.15585 | −0.577923 | − | 0.816091i | \(-0.696137\pi\) | ||||
−0.577923 | + | 0.816091i | \(0.696137\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15168.9 | − | 1084.50i | 1.02442 | − | 0.0732410i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4735.39 | 0.318216 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18341.5i | − | 1.22646i | −0.789905 | − | 0.613229i | \(-0.789870\pi\) | ||
0.789905 | − | 0.613229i | \(-0.210130\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −479.950 | − | 13443.2i | −0.0319352 | − | 0.894494i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29889.9i | 1.97908i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9663.26i | − | 0.636697i | −0.947974 | − | 0.318349i | \(-0.896872\pi\) | ||
0.947974 | − | 0.318349i | \(-0.103128\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 445.609 | + | 12481.3i | 0.0292174 | + | 0.818368i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2815.64i | 0.183717i | 0.995772 | + | 0.0918586i | \(0.0292808\pi\) | ||||
−0.995772 | + | 0.0918586i | \(0.970719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14824.5 | 0.962596 | 0.481298 | − | 0.876557i | \(-0.340166\pi\) | ||||
0.481298 | + | 0.876557i | \(0.340166\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20603.3 | + | 2214.27i | −1.33137 | + | 0.143085i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7824.37 | −0.503173 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 297.518 | + | 8333.35i | 0.0189501 | + | 0.530785i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3532.20 | 0.223908 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2273.51i | 0.143434i | 0.997425 | + | 0.0717171i | \(0.0228479\pi\) | ||||
−0.997425 | + | 0.0717171i | \(0.977152\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11012.2 | + | 393.156i | −0.691460 | + | 0.0246865i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1725.09i | 0.107808i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 16257.0i | − | 1.01119i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14476.9 | − | 1035.03i | 0.896243 | − | 0.0640770i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19455.2i | 1.19880i | 0.800448 | + | 0.599402i | \(0.204595\pi\) | ||||
−0.800448 | + | 0.599402i | \(0.795405\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15696.0 | −0.962657 | −0.481328 | − | 0.876540i | \(-0.659846\pi\) | ||||
−0.481328 | + | 0.876540i | \(0.659846\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 628.177 | − | 22.4272i | 0.0383480 | − | 0.00136910i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10884.6 | 0.661389 | 0.330694 | − | 0.943738i | \(-0.392717\pi\) | ||||
0.330694 | + | 0.943738i | \(0.392717\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6335.55 | −0.383193 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8595.42 | + | 306.874i | −0.517482 | + | 0.0184752i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27481.9 | −1.64694 | −0.823469 | − | 0.567361i | \(-0.807964\pi\) | ||||
−0.823469 | + | 0.567361i | \(0.807964\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2405.80i | − | 0.143515i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2666.03 | − | 190.608i | 0.158313 | − | 0.0113186i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 31077.7i | − | 1.83705i | −0.395367 | − | 0.918523i | \(-0.629383\pi\) | ||
0.395367 | − | 0.918523i | \(-0.370617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 7446.83i | − | 0.438197i | −0.975703 | − | 0.219098i | \(-0.929688\pi\) | ||
0.975703 | − | 0.219098i | \(-0.0703116\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5431.58 | − | 193.918i | 0.318167 | − | 0.0113592i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4872.99i | 0.284160i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32132.9 | −1.86535 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 984.602 | + | 27578.3i | 0.0569012 | + | 1.59378i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1560.44 | −0.0897768 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11727.3 | 0.671700 | 0.335850 | − | 0.941915i | \(-0.390976\pi\) | ||||
0.335850 | + | 0.941915i | \(0.390976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3487.32 | − | 374.788i | 0.198855 | − | 0.0213712i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16194.0 | 0.919331 | 0.459666 | − | 0.888092i | \(-0.347969\pi\) | ||||
0.459666 | + | 0.888092i | \(0.347969\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6837.09i | 0.386426i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −725.190 | − | 20312.3i | −0.0408067 | − | 1.14298i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22713.8i | 1.27250i | 0.771481 | + | 0.636252i | \(0.219516\pi\) | ||||
−0.771481 | + | 0.636252i | \(0.780484\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6037.08i | − | 0.336737i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1110.28 | + | 31098.4i | 0.0616590 | + | 1.72704i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 21900.9i | − | 1.21097i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10207.3 | 0.561945 | 0.280972 | − | 0.959716i | \(-0.409343\pi\) | ||||
0.280972 | + | 0.959716i | \(0.409343\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6279.30 | + | 448.940i | −0.344200 | + | 0.0246087i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12198.5 | 0.665775 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6229.08 | −0.338513 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 674.863 | + | 18902.7i | 0.0365174 | + | 1.02284i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2137.78 | −0.115182 | −0.0575911 | − | 0.998340i | \(-0.518342\pi\) | ||||
−0.0575911 | + | 0.998340i | \(0.518342\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22325.4i | 1.19775i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9614.28 | + | 343.249i | −0.513610 | + | 0.0183369i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1135.33i | 0.0603937i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 7932.80i | − | 0.420201i | −0.977680 | − | 0.210101i | \(-0.932621\pi\) | ||
0.977680 | − | 0.210101i | \(-0.0673792\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 563.242 | + | 7878.04i | 0.0297092 | + | 0.415541i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20545.4i | 1.07914i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7908.15 | −0.413633 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32718.3 | + | 1168.11i | −1.70417 | + | 0.0608422i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24949.4 | 1.29410 | 0.647048 | − | 0.762449i | \(-0.276003\pi\) | ||||
0.647048 | + | 0.762449i | \(0.276003\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2263.39 | −0.116911 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −970.951 | + | 34.6649i | −0.0499447 | + | 0.00178313i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5438.82 | 0.278611 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13284.0i | 0.677685i | 0.940843 | + | 0.338843i | \(0.110035\pi\) | ||||
−0.940843 | + | 0.338843i | \(0.889965\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19233.5 | − | 4182.42i | 0.977164 | − | 0.212489i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 313.505i | 0.0158624i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16860.0i | 0.849575i | 0.905293 | + | 0.424788i | \(0.139651\pi\) | ||||
−0.905293 | + | 0.424788i | \(0.860349\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5229.17 | − | 186.692i | 0.262423 | − | 0.00936903i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 11036.2i | − | 0.551591i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21665.0 | −1.07843 | −0.539216 | − | 0.842168i | \(-0.681279\pi\) | ||||
−0.539216 | + | 0.842168i | \(0.681279\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1225.67 | + | 34330.6i | 0.0607640 | + | 1.70198i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23700.7 | −1.17025 | −0.585123 | − | 0.810944i | \(-0.698954\pi\) | ||||
−0.585123 | + | 0.810944i | \(0.698954\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10264.7 | 0.504790 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2378.23 | + | 33264.2i | 0.116486 | + | 1.62928i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16589.6 | −0.809307 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38822.5i | 1.88636i | 0.332286 | + | 0.943179i | \(0.392180\pi\) | ||||
−0.332286 | + | 0.943179i | \(0.607820\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1060.06 | + | 29691.8i | 0.0513023 | + | 1.43696i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1161.72i | 0.0559990i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21198.9i | 1.01782i | 0.860821 | + | 0.508908i | \(0.169951\pi\) | ||||
−0.860821 | + | 0.508908i | \(0.830049\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 536.543 | + | 15028.4i | 0.0256591 | + | 0.718702i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2028.32i | 0.0966185i | 0.998832 | + | 0.0483092i | \(0.0153833\pi\) | ||||
−0.998832 | + | 0.0483092i | \(0.984617\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12526.9 | −0.594369 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 124.750 | + | 1744.88i | 0.00589588 | + | 0.0824655i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26100.3 | −1.22872 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −257.053 | −0.0120541 | −0.00602703 | − | 0.999982i | \(-0.501918\pi\) | ||||
−0.00602703 | + | 0.999982i | \(0.501918\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1225.10 | − | 34314.5i | −0.0572254 | − | 1.60286i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19191.4 | −0.892971 | −0.446486 | − | 0.894791i | \(-0.647325\pi\) | ||||
−0.446486 | + | 0.894791i | \(0.647325\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3477.51i | − | 0.161182i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16844.0 | + | 601.365i | −0.777703 | + | 0.0277656i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 39371.2i | − | 1.81081i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 10532.8i | − | 0.482576i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30347.1 | − | 3261.45i | 1.38508 | − | 0.148856i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15289.7i | 0.695176i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41816.6 | 1.89403 | 0.947015 | − | 0.321191i | \(-0.104083\pi\) | ||||
0.947015 | + | 0.321191i | \(0.104083\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27737.6 | − | 990.289i | 1.25157 | − | 0.0446834i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16482.0 | 0.740876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6428.50 | −0.287872 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7044.57 | − | 251.505i | 0.314270 | − | 0.0112201i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25232.5 | 1.12143 | 0.560717 | − | 0.828008i | \(-0.310526\pi\) | ||||
0.560717 | + | 0.828008i | \(0.310526\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4798.21i | − | 0.212451i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1266.05 | − | 17708.2i | −0.0558472 | − | 0.781132i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1939.68i | − | 0.0852425i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8787.96i | 0.384764i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36617.5 | + | 1307.32i | −1.59727 | + | 0.0570258i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 35880.6i | − | 1.55933i | −0.626199 | − | 0.779663i | \(-0.715390\pi\) | ||
0.626199 | − | 0.779663i | \(-0.284610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24028.6 | −1.04039 | −0.520196 | − | 0.854047i | \(-0.674141\pi\) | ||||
−0.520196 | + | 0.854047i | \(0.674141\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 887.235 | + | 24851.1i | 0.0382739 | + | 1.07204i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3109.87 | −0.133661 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1981.52 | −0.0848528 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25868.6 | + | 1849.48i | −1.10369 | + | 0.0789084i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9237.39 | 0.392676 | 0.196338 | − | 0.980536i | \(-0.437095\pi\) | ||||
0.196338 | + | 0.980536i | \(0.437095\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2873.15i | − | 0.121691i | −0.998147 | − | 0.0608454i | \(-0.980620\pi\) | ||
0.998147 | − | 0.0608454i | \(-0.0193797\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −90.8154 | − | 2543.71i | −0.00383247 | − | 0.107346i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15113.0i | 0.635465i | 0.948180 | + | 0.317733i | \(0.102921\pi\) | ||||
−0.948180 | + | 0.317733i | \(0.897079\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10373.3i | − | 0.434595i | −0.976105 | − | 0.217298i | \(-0.930276\pi\) | ||
0.976105 | − | 0.217298i | \(-0.0697242\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −756.499 | − | 21189.3i | −0.0315796 | − | 0.884533i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2609.73i | 0.108549i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7449.83 | 0.308757 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2085.33 | − | 19403.5i | −0.0861164 | − | 0.801295i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14010.2 | −0.576502 | −0.288251 | − | 0.957555i | \(-0.593074\pi\) | ||||
−0.288251 | + | 0.957555i | \(0.593074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22940.3 | 0.940599 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −193.285 | − | 5413.85i | −0.00789692 | − | 0.221190i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21593.9 | −0.879114 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11269.9i | − | 0.457187i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14627.4 | + | 522.227i | −0.591296 | + | 0.0211104i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40261.7i | 1.62180i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 11697.1i | − | 0.469520i | −0.972053 | − | 0.234760i | \(-0.924570\pi\) | ||
0.972053 | − | 0.234760i | \(-0.0754304\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11028.6 | + | 788.490i | −0.441134 | + | 0.0315389i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 4954.60i | − | 0.197486i | −0.995113 | − | 0.0987432i | \(-0.968518\pi\) | ||
0.995113 | − | 0.0987432i | \(-0.0314822\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31596.1 | 1.25500 | 0.627499 | − | 0.778617i | \(-0.284079\pi\) | ||||
0.627499 | + | 0.778617i | \(0.284079\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29704.7 | − | 1060.52i | 1.17576 | − | 0.0419771i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6703.04 | 0.264396 | 0.132198 | − | 0.991223i | \(-0.457796\pi\) | ||||
0.132198 | + | 0.991223i | \(0.457796\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11596.9 | −0.455847 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24640.5 | − | 879.716i | 0.965208 | − | 0.0344599i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5731.70 | 0.223745 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 45465.3i | − | 1.76869i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15473.7 | + | 1106.30i | −0.599893 | + | 0.0428894i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1487.45i | − | 0.0574686i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 2640.85i | − | 0.101682i | −0.998707 | − | 0.0508411i | \(-0.983810\pi\) | ||
0.998707 | − | 0.0508411i | \(-0.0161902\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22710.6 | + | 810.813i | −0.871454 | + | 0.0311127i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 948.785i | − | 0.0362831i | −0.999835 | − | 0.0181415i | \(-0.994225\pi\) | ||
0.999835 | − | 0.0181415i | \(-0.00577495\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7226.54 | 0.275416 | 0.137708 | − | 0.990473i | \(-0.456026\pi\) | ||||
0.137708 | + | 0.990473i | \(0.456026\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −299.730 | − | 8395.34i | −0.0113846 | − | 0.318877i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48118.6 | 1.82149 | 0.910746 | − | 0.412966i | \(-0.135507\pi\) | ||||
0.910746 | + | 0.412966i | \(0.135507\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4105.59 | 0.154890 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2032.08 | − | 14138.7i | −0.0764056 | − | 0.531609i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30327.4 | 1.13647 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12626.0i | 0.471553i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2210.37 | + | 61911.8i | 0.0822768 | + | 2.30454i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 30261.7i | − | 1.12268i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3515.74i | 0.129996i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −53.3750 | − | 1495.01i | −0.00196701 | − | 0.0550951i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19716.3i | 0.724189i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3998.99 | −0.146399 | −0.0731997 | − | 0.997317i | \(-0.523321\pi\) | ||||
−0.0731997 | + | 0.997317i | \(0.523321\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2569.48 | + | 183.705i | −0.0937560 | + | 0.00670310i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44298.6 | −1.61106 | −0.805532 | − | 0.592552i | \(-0.798120\pi\) | ||||
−0.805532 | + | 0.592552i | \(0.798120\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24201.5 | 0.877276 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −73.8235 | − | 2067.77i | −0.00266725 | − | 0.0747085i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5725.61 | −0.206190 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2554.93i | − | 0.0917078i | −0.998948 | − | 0.0458539i | \(-0.985399\pi\) | ||
0.998948 | − | 0.0458539i | \(-0.0146009\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25176.4 | − | 898.849i | 0.900751 | − | 0.0321586i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 43391.4i | − | 1.54739i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6814.70i | − | 0.242234i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −366.234 | − | 5122.51i | −0.0129760 | − | 0.181494i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 11706.4i | − | 0.413428i | −0.978401 | − | 0.206714i | \(-0.933723\pi\) | ||
0.978401 | − | 0.206714i | \(-0.0662770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16494.9 | −0.580665 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21351.9 | − | 762.306i | 0.749228 | − | 0.0267490i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1269.49 | 0.0444030 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41893.6 | −1.46062 | −0.730311 | − | 0.683114i | \(-0.760625\pi\) | ||||
−0.730311 | + | 0.683114i | \(0.760625\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 37230.8 | − | 1329.22i | 1.29391 | − | 0.0461952i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3148.26 | −0.109065 | −0.0545326 | − | 0.998512i | \(-0.517367\pi\) | ||||
−0.0545326 | + | 0.998512i | \(0.517367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 71002.1i | − | 2.45190i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −891.966 | − | 8299.56i | −0.0307044 | − | 0.285698i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24539.5i | 0.842055i | 0.907048 | + | 0.421028i | \(0.138330\pi\) | ||||
−0.907048 | + | 0.421028i | \(0.861670\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 7990.81i | − | 0.273333i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22699.1 | + | 810.405i | −0.773996 | + | 0.0276332i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 34706.3i | − | 1.17969i | −0.807515 | − | 0.589847i | \(-0.799188\pi\) | ||
0.807515 | − | 0.589847i | \(-0.200812\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9593.39 | −0.325063 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −790.287 | − | 22135.6i | −0.0266942 | − | 0.747694i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14367.8 | −0.483795 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10442.0 | 0.350510 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2684.33 | − | 37545.6i | −0.0898249 | − | 1.25638i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7088.27 | −0.236455 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8683.49i | 0.288772i | 0.989521 | + | 0.144386i | \(0.0461207\pi\) | ||||
−0.989521 | + | 0.144386i | \(0.953879\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −196.756 | − | 5511.07i | −0.00652293 | − | 0.182705i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35296.8i | 1.16656i | 0.812272 | + | 0.583279i | \(0.198231\pi\) | ||||
−0.812272 | + | 0.583279i | \(0.801769\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 29031.4i | − | 0.956530i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −374.129 | − | 10479.2i | −0.0122889 | − | 0.344208i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22443.3i | 0.734927i | 0.930038 | + | 0.367463i | \(0.119774\pi\) | ||||
−0.930038 | + | 0.367463i | \(0.880226\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12883.6 | −0.420595 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2026.95 | − | 28350.9i | −0.0659690 | − | 0.922706i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47336.6 | 1.53591 | 0.767957 | − | 0.640502i | \(-0.221274\pi\) | ||||
0.767957 | + | 0.640502i | \(0.221274\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18720.2 | 0.605557 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 816.907 | + | 22881.3i | 0.0263449 | + | 0.737911i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3573.48 | −0.114894 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 34234.4i | − | 1.09737i | −0.836030 | − | 0.548683i | \(-0.815129\pi\) | ||
0.836030 | − | 0.548683i | \(-0.184871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29031.1 | − | 1036.47i | 0.927769 | − | 0.0331232i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24362.7i | 0.776232i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 50553.3i | − | 1.60586i | −0.596076 | − | 0.802928i | \(-0.703274\pi\) | ||
0.596076 | − | 0.802928i | \(-0.296726\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4086.51 | − | 38024.1i | −0.129421 | − | 1.20423i |
(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 | 480.4.b.b.431.23 | 24 | ||
3.2 | odd | 2 | 480.4.b.a.431.24 | 24 | |||
4.3 | odd | 2 | 120.4.b.a.11.11 | ✓ | 24 | ||
8.3 | odd | 2 | 480.4.b.a.431.23 | 24 | |||
8.5 | even | 2 | 120.4.b.b.11.13 | yes | 24 | ||
12.11 | even | 2 | 120.4.b.b.11.14 | yes | 24 | ||
24.5 | odd | 2 | 120.4.b.a.11.12 | yes | 24 | ||
24.11 | even | 2 | inner | 480.4.b.b.431.24 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.b.a.11.11 | ✓ | 24 | 4.3 | odd | 2 | ||
120.4.b.a.11.12 | yes | 24 | 24.5 | odd | 2 | ||
120.4.b.b.11.13 | yes | 24 | 8.5 | even | 2 | ||
120.4.b.b.11.14 | yes | 24 | 12.11 | even | 2 | ||
480.4.b.a.431.23 | 24 | 8.3 | odd | 2 | |||
480.4.b.a.431.24 | 24 | 3.2 | odd | 2 | |||
480.4.b.b.431.23 | 24 | 1.1 | even | 1 | trivial | ||
480.4.b.b.431.24 | 24 | 24.11 | even | 2 | inner |