Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(383,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.383");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.f (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: | \(45.3134668844\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 39x^{10} + 549x^{8} + 3500x^{6} + 10236x^{4} + 11952x^{2} + 4624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.7 | ||
Root | \(2.29679i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.383 |
Dual form | 768.4.f.e.383.8 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.40813 | − | 5.00172i | 0.270995 | − | 0.962581i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.86626 | −0.524694 | −0.262347 | − | 0.964974i | \(-0.584497\pi\) | ||||
−0.262347 | + | 0.964974i | \(0.584497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 5.92149i | − | 0.319730i | −0.987139 | − | 0.159865i | \(-0.948894\pi\) | ||
0.987139 | − | 0.159865i | \(-0.0511060\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −23.0343 | − | 14.0861i | −0.853124 | − | 0.521709i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27.9652i | 0.766531i | 0.923638 | + | 0.383265i | \(0.125201\pi\) | ||||
−0.923638 | + | 0.383265i | \(0.874799\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.0653967i | − | 0.00139521i | −1.00000 | 0.000697607i | \(-0.999778\pi\) | |||
1.00000 | 0.000697607i | \(-0.000222055\pi\) | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.26046 | + | 29.3414i | −0.142189 | + | 0.505061i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 36.9675i | 0.527408i | 0.964604 | + | 0.263704i | \(0.0849443\pi\) | ||||
−0.964604 | + | 0.263704i | \(0.915056\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −30.7691 | −0.371522 | −0.185761 | − | 0.982595i | \(-0.559475\pi\) | ||||
−0.185761 | + | 0.982595i | \(0.559475\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −29.6176 | − | 8.33823i | −0.307766 | − | 0.0866452i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 61.2864 | 0.555613 | 0.277806 | − | 0.960637i | \(-0.410393\pi\) | ||||
0.277806 | + | 0.960637i | \(0.410393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −90.5870 | −0.724696 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −102.890 | + | 95.3761i | −0.733379 | + | 0.679820i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 143.566 | 0.919294 | 0.459647 | − | 0.888102i | \(-0.347976\pi\) | ||||
0.459647 | + | 0.888102i | \(0.347976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 299.568i | 1.73562i | 0.496900 | + | 0.867808i | \(0.334471\pi\) | ||||
−0.496900 | + | 0.867808i | \(0.665529\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 139.874 | + | 39.3787i | 0.737848 | + | 0.207726i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 34.7370i | 0.167761i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 340.559i | − | 1.51318i | −0.653891 | − | 0.756589i | \(-0.726865\pi\) | ||
0.653891 | − | 0.756589i | \(-0.273135\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.327096 | − | 0.0920870i | −0.00134301 | − | 0.000378095i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 379.315i | 1.44486i | 0.691447 | + | 0.722428i | \(0.256974\pi\) | ||||
−0.691447 | + | 0.722428i | \(0.743026\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −470.926 | −1.67013 | −0.835065 | − | 0.550152i | \(-0.814570\pi\) | ||||
−0.835065 | + | 0.550152i | \(0.814570\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 135.125 | + | 82.6330i | 0.447629 | + | 0.273738i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 428.593 | 1.33014 | 0.665072 | − | 0.746779i | \(-0.268401\pi\) | ||||
0.665072 | + | 0.746779i | \(0.268401\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 307.936 | 0.897772 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 184.901 | + | 52.0551i | 0.507673 | + | 0.142925i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 505.868 | 1.31106 | 0.655531 | − | 0.755168i | \(-0.272445\pi\) | ||||
0.655531 | + | 0.755168i | \(0.272445\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 164.051i | − | 0.402194i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −43.3269 | + | 153.898i | −0.100681 | + | 0.357620i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 207.827i | − | 0.458589i | −0.973357 | − | 0.229295i | \(-0.926358\pi\) | ||
0.973357 | − | 0.229295i | \(-0.0736419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 578.221i | 1.21367i | 0.794830 | + | 0.606833i | \(0.207560\pi\) | ||||
−0.794830 | + | 0.606833i | \(0.792440\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −83.4109 | + | 136.398i | −0.166806 | + | 0.272770i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.383634i | 0.000732061i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 415.350 | 0.757359 | 0.378679 | − | 0.925528i | \(-0.376378\pi\) | ||||
0.378679 | + | 0.925528i | \(0.376378\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 86.2992 | − | 306.537i | 0.150568 | − | 0.534822i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −547.669 | −0.915441 | −0.457721 | − | 0.889096i | \(-0.651334\pi\) | ||||
−0.457721 | + | 0.889096i | \(0.651334\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −194.572 | −0.311957 | −0.155979 | − | 0.987760i | \(-0.549853\pi\) | ||||
−0.155979 | + | 0.987760i | \(0.549853\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −127.558 | + | 453.090i | −0.196389 | + | 0.697578i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 165.596 | 0.245083 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 308.374i | 0.439175i | 0.975593 | + | 0.219587i | \(0.0704711\pi\) | ||||
−0.975593 | + | 0.219587i | \(0.929529\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 332.162 | + | 648.930i | 0.455640 | + | 0.890164i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 62.3019i | − | 0.0823918i | −0.999151 | − | 0.0411959i | \(-0.986883\pi\) | ||
0.999151 | − | 0.0411959i | \(-0.0131168\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 216.861i | − | 0.276728i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 202.159 | − | 718.076i | 0.249124 | − | 0.884895i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1065.01i | 1.26844i | 0.773153 | + | 0.634220i | \(0.218679\pi\) | ||||
−0.773153 | + | 0.634220i | \(0.781321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.387246 | −0.000446092 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1498.36 | + | 421.831i | 1.67067 | + | 0.470343i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 180.500 | 0.194936 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 703.293 | 0.736171 | 0.368085 | − | 0.929792i | \(-0.380013\pi\) | ||||
0.368085 | + | 0.929792i | \(0.380013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 393.922 | − | 644.161i | 0.399906 | − | 0.653946i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 942.553 | 0.928589 | 0.464295 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464295 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 86.0316i | − | 0.0823005i | −0.999153 | − | 0.0411502i | \(-0.986898\pi\) | ||
0.999153 | − | 0.0411502i | \(-0.0131022\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 173.745 | + | 48.9142i | 0.161483 | + | 0.0454623i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 688.082i | − | 0.621676i | −0.950463 | − | 0.310838i | \(-0.899390\pi\) | ||
0.950463 | − | 0.310838i | \(-0.100610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1849.94i | − | 1.62561i | −0.582534 | − | 0.812807i | \(-0.697939\pi\) | ||
0.582534 | − | 0.812807i | \(-0.302061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1703.38 | − | 479.551i | −1.45656 | − | 0.410063i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1054.54i | 0.877902i | 0.898511 | + | 0.438951i | \(0.144650\pi\) | ||||
−0.898511 | + | 0.438951i | \(0.855350\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −359.522 | −0.291527 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.921186 | + | 1.50637i | −0.000727895 | + | 0.00119029i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 218.903 | 0.168628 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 548.945 | 0.412431 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1897.23 | + | 534.125i | 1.39079 | + | 0.391548i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1264.69 | 0.904938 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 957.493i | − | 0.669006i | −0.942395 | − | 0.334503i | \(-0.891432\pi\) | ||
0.942395 | − | 0.334503i | \(-0.108568\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −663.125 | + | 2355.44i | −0.452596 | + | 1.60763i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 550.306i | 0.367026i | 0.983017 | + | 0.183513i | \(0.0587470\pi\) | ||||
−0.983017 | + | 0.183513i | \(0.941253\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 182.199i | 0.118787i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 603.581 | − | 559.501i | 0.384800 | − | 0.356698i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1991.37i | 1.24185i | 0.783869 | + | 0.620926i | \(0.213243\pi\) | ||||
−0.783869 | + | 0.620926i | \(0.786757\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 746.850 | 0.455733 | 0.227867 | − | 0.973692i | \(-0.426825\pi\) | ||||
0.227867 | + | 0.973692i | \(0.426825\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 603.515 | − | 2143.70i | 0.360462 | − | 1.28037i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.82883 | 0.00106947 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −842.195 | −0.482348 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 433.614 | − | 1540.21i | 0.243292 | − | 0.864179i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3198.80 | 1.75877 | 0.879383 | − | 0.476114i | \(-0.157955\pi\) | ||||
0.879383 | + | 0.476114i | \(0.157955\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1475.50i | 0.795195i | 0.917560 | + | 0.397598i | \(0.130156\pi\) | ||||
−0.917560 | + | 0.397598i | \(0.869844\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 520.730 | − | 851.523i | 0.275154 | − | 0.449945i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1757.35i | − | 0.910668i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 713.140i | 0.362514i | 0.983436 | + | 0.181257i | \(0.0580166\pi\) | ||||
−0.983436 | + | 0.181257i | \(0.941983\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 712.328 | − | 2530.21i | 0.355291 | − | 1.26200i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 362.907i | − | 0.177646i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1986.44 | −0.954538 | −0.477269 | − | 0.878757i | \(-0.658373\pi\) | ||||
−0.477269 | + | 0.878757i | \(0.658373\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −820.539 | − | 231.006i | −0.387145 | − | 0.108993i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3376.74 | −1.56467 | −0.782336 | − | 0.622857i | \(-0.785972\pi\) | ||||
−0.782336 | + | 0.622857i | \(0.785972\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2197.00 | 0.999998 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 708.747 | + | 433.418i | 0.316954 | + | 0.193826i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2696.12 | −1.18487 | −0.592435 | − | 0.805619i | \(-0.701833\pi\) | ||||
−0.592435 | + | 0.805619i | \(0.701833\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 536.410i | 0.231707i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1039.49 | − | 292.647i | −0.441429 | − | 0.124275i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3347.25i | 1.39768i | 0.715276 | + | 0.698842i | \(0.246301\pi\) | ||||
−0.715276 | + | 0.698842i | \(0.753699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1843.89i | 0.757210i | 0.925558 | + | 0.378605i | \(0.123596\pi\) | ||||
−0.925558 | + | 0.378605i | \(0.876404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2892.10 | + | 814.210i | 1.16825 | + | 0.328897i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1997.81i | 0.793956i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1033.81 | −0.404275 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 564.769 | + | 609.263i | 0.217359 | + | 0.234483i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2382.31 | 0.902501 | 0.451251 | − | 0.892397i | \(-0.350978\pi\) | ||||
0.451251 | + | 0.892397i | \(0.350978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2546.25 | −0.949654 | −0.474827 | − | 0.880079i | \(-0.657489\pi\) | ||||
−0.474827 | + | 0.880079i | \(0.657489\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.91883 | + | 0.540207i | 0.000704668 | + | 0.000198385i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2189.58 | 0.791885 | 0.395943 | − | 0.918275i | \(-0.370418\pi\) | ||||
0.395943 | + | 0.918275i | \(0.370418\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5379.16i | 1.91617i | 0.286476 | + | 0.958087i | \(0.407516\pi\) | ||||
−0.286476 | + | 0.958087i | \(0.592484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 584.866 | − | 2077.46i | 0.205240 | − | 0.729019i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 850.124i | − | 0.293926i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2225.16i | − | 0.758107i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1411.69 | − | 863.288i | −0.474006 | − | 0.289868i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 860.466i | − | 0.284783i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5320.28 | −1.73584 | −0.867922 | − | 0.496701i | \(-0.834544\pi\) | ||||
−0.867922 | + | 0.496701i | \(0.834544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −771.189 | + | 2739.28i | −0.248080 | + | 0.881186i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2762.58 | 0.876307 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1773.89 | 0.554929 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −273.982 | + | 973.192i | −0.0845388 | + | 0.300284i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.41755 | 0.000735847 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2708.41i | 0.813310i | 0.913582 | + | 0.406655i | \(0.133305\pi\) | ||||
−0.913582 | + | 0.406655i | \(0.866695\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2086.61 | + | 1276.02i | 0.618255 | + | 0.378080i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2335.26i | 0.682806i | 0.939917 | + | 0.341403i | \(0.110902\pi\) | ||||
−0.939917 | + | 0.341403i | \(0.889098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 139.302i | − | 0.0401980i | −0.999798 | − | 0.0200990i | \(-0.993602\pi\) | ||
0.999798 | − | 0.0200990i | \(-0.00639814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 233.181 | − | 828.264i | 0.0664162 | − | 0.235912i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.07987i | 0.00199064i | 1.00000 | 0.000995318i | \(0.000316819\pi\) | |||||
−1.00000 | 0.000995318i | \(0.999683\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2514.24 | −0.697919 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1542.40 | + | 434.231i | 0.422741 | + | 0.119014i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −890.272 | −0.240949 | −0.120475 | − | 0.992716i | \(-0.538442\pi\) | ||||
−0.120475 | + | 0.992716i | \(0.538442\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1273.98 | 0.340515 | 0.170258 | − | 0.985400i | \(-0.445540\pi\) | ||||
0.170258 | + | 0.985400i | \(0.445540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3713.49 | − | 747.601i | 0.980331 | − | 0.197361i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1806.43 | −0.471056 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.01220i | 0.000518353i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −311.616 | − | 87.7291i | −0.0793088 | − | 0.0223277i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3032.85i | 0.762678i | 0.924435 | + | 0.381339i | \(0.124537\pi\) | ||||
−0.924435 | + | 0.381339i | \(0.875463\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1713.89i | 0.425894i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1084.68 | − | 305.369i | −0.266373 | − | 0.0749919i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2585.22i | − | 0.627478i | −0.949509 | − | 0.313739i | \(-0.898418\pi\) | ||
0.949509 | − | 0.313739i | \(-0.101582\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2016.62 | −0.483809 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3306.95 | − | 2022.29i | −0.784271 | − | 0.479604i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5444.20 | −1.27644 | −0.638220 | − | 0.769854i | \(-0.720329\pi\) | ||||
−0.638220 | + | 0.769854i | \(0.720329\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2967.55 | −0.687907 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5326.89 | + | 1499.68i | 1.22098 | + | 0.343740i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2061.38 | −0.467229 | −0.233614 | − | 0.972329i | \(-0.575055\pi\) | ||||
−0.233614 | + | 0.972329i | \(0.575055\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5846.72i | 1.31056i | 0.755384 | + | 0.655282i | \(0.227450\pi\) | ||||
−0.755384 | + | 0.655282i | \(0.772550\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.545292 | + | 1.93689i | −0.000120889 | + | 0.000429400i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2533.29i | − | 0.555502i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1488.28i | − | 0.322823i | −0.986887 | − | 0.161412i | \(-0.948395\pi\) | ||
0.986887 | − | 0.161412i | \(-0.0516046\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4219.76 | − | 6900.36i | 0.905485 | − | 1.48069i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6456.97i | − | 1.37079i | −0.728174 | − | 0.685393i | \(-0.759631\pi\) | ||
0.728174 | − | 0.685393i | \(-0.240369\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5390.67 | −1.13231 | −0.566153 | − | 0.824301i | \(-0.691569\pi\) | ||||
−0.566153 | + | 0.824301i | \(0.691569\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 254.167 | − | 902.809i | 0.0528265 | − | 0.187641i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2246.11 | 0.461964 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3546.40 | 0.721840 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 990.328 | − | 3517.67i | 0.199498 | − | 0.708624i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5400.85 | −1.07686 | −0.538432 | − | 0.842669i | \(-0.680983\pi\) | ||||
−0.538432 | + | 0.842669i | \(0.680983\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1219.17i | 0.240619i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2667.22 | − | 2877.35i | −0.521103 | − | 0.562157i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 4.00793i | − | 0.000775198i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2788.58i | 0.533991i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1327.24 | − | 4714.38i | 0.251643 | − | 0.893842i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3391.99i | − | 0.636803i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3598.12 | 0.668910 | 0.334455 | − | 0.942412i | \(-0.391448\pi\) | ||||
0.334455 | + | 0.942412i | \(0.391448\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −430.306 | − | 121.144i | −0.0792209 | − | 0.0223030i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7894.55 | 1.43942 | 0.719709 | − | 0.694276i | \(-0.244275\pi\) | ||||
0.719709 | + | 0.694276i | \(0.244275\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8500.57 | −1.53508 | −0.767541 | − | 0.641000i | \(-0.778520\pi\) | ||||
−0.767541 | + | 0.641000i | \(0.778520\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 489.310 | − | 800.144i | 0.0875222 | − | 0.143121i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7352.01 | −1.30262 | −0.651309 | − | 0.758813i | \(-0.725780\pi\) | ||||
−0.651309 | + | 0.758813i | \(0.725780\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4014.86i | 0.704667i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3441.59 | − | 968.908i | −0.598414 | − | 0.168471i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1137.46i | − | 0.195944i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.92409i | 0.00101111i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9252.86 | − | 2604.95i | −1.56478 | − | 0.440533i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2537.91i | − | 0.425287i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4348.48 | −0.722097 | −0.361048 | − | 0.932547i | \(-0.617581\pi\) | ||||
−0.361048 | + | 0.932547i | \(0.617581\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4797.16 | + | 7844.55i | −0.789438 | + | 1.29093i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2436.55 | −0.397382 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2451.75 | −0.396307 | −0.198153 | − | 0.980171i | \(-0.563494\pi\) | ||||
−0.198153 | + | 0.980171i | \(0.563494\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5274.52 | + | 1484.93i | 0.845051 | + | 0.237907i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8377.50 | −1.33040 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3854.51i | − | 0.606776i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −506.254 | + | 1798.23i | −0.0790023 | + | 0.280618i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3671.15i | − | 0.567947i | −0.958832 | − | 0.283974i | \(-0.908347\pi\) | ||
0.958832 | − | 0.283974i | \(-0.0916528\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2543.31i | 0.390086i | 0.980795 | + | 0.195043i | \(0.0624847\pi\) | ||||
−0.980795 | + | 0.195043i | \(0.937515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.23728 | + | 6.72868i | 0.000948494 | + | 0.00102322i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12015.9i | − | 1.81173i | −0.423562 | − | 0.905867i | \(-0.639221\pi\) | ||
0.423562 | − | 0.905867i | \(-0.360779\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3212.77 | 0.480327 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 308.244 | − | 1094.89i | 0.0456974 | − | 0.162319i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11569.3 | −1.70085 | −0.850424 | − | 0.526097i | \(-0.823655\pi\) | ||||
−0.850424 | + | 0.526097i | \(0.823655\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5912.26 | −0.861971 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 772.986 | − | 2745.67i | 0.111767 | − | 0.396998i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1141.41 | 0.163682 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 675.208i | − | 0.0960370i | −0.998846 | − | 0.0480185i | \(-0.984709\pi\) | ||
0.998846 | − | 0.0480185i | \(-0.0152906\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5343.08 | − | 8737.27i | 0.753793 | − | 1.23264i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2995.49i | − | 0.419186i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9000.61i | − | 1.24942i | −0.780857 | − | 0.624710i | \(-0.785217\pi\) | ||
0.780857 | − | 0.624710i | \(-0.214783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1780.85 | − | 6325.62i | 0.245234 | − | 0.871076i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 9.38873i | − | 0.00128261i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6453.84 | −0.874700 | −0.437350 | − | 0.899291i | \(-0.644083\pi\) | ||||
−0.437350 | + | 0.899291i | \(0.644083\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4789.11 | − | 1348.28i | −0.643973 | − | 0.181297i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5211.10 | 0.695234 | 0.347617 | − | 0.937637i | \(-0.386991\pi\) | ||||
0.347617 | + | 0.937637i | \(0.386991\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −971.429 | −0.128594 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10847.5 | + | 6633.53i | 1.42483 | + | 0.871321i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1399.05 | −0.182351 | −0.0911756 | − | 0.995835i | \(-0.529062\pi\) | ||||
−0.0911756 | + | 0.995835i | \(0.529062\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2265.61i | 0.293035i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2752.47 | + | 774.902i | 0.353292 | + | 0.0994622i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1809.00i | − | 0.230433i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6624.77i | 0.837500i | 0.908101 | + | 0.418750i | \(0.137532\pi\) | ||||
−0.908101 | + | 0.418750i | \(0.862468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 911.308 | + | 256.560i | 0.114342 | + | 0.0321906i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5283.09i | 0.657918i | 0.944344 | + | 0.328959i | \(0.106698\pi\) | ||||
−0.944344 | + | 0.328959i | \(0.893302\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.5908 | 0.00242155 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1948.55 | − | 3806.79i | −0.239072 | − | 0.467064i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9523.81 | 1.15990 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7555.96 | 0.913492 | 0.456746 | − | 0.889597i | \(-0.349015\pi\) | ||||
0.456746 | + | 0.889597i | \(0.349015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9960.25 | + | 2804.10i | 1.19538 | + | 0.336536i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1230.65 | −0.146625 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 365.479i | 0.0432305i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1051.66 | − | 3735.53i | 0.123501 | − | 0.438680i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6784.17i | − | 0.790999i | −0.918466 | − | 0.395500i | \(-0.870571\pi\) | ||
0.918466 | − | 0.395500i | \(-0.129429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12740.9i | 1.47495i | 0.675374 | + | 0.737476i | \(0.263982\pi\) | ||||
−0.675374 | + | 0.737476i | \(0.736018\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9872.36 | − | 6037.22i | −1.13478 | − | 0.693947i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3348.78i | − | 0.382211i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3423.93 | 0.388046 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.57524 | − | 9.14731i | 0.000289822 | − | 0.00102946i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16239.7 | −1.81493 | −0.907467 | − | 0.420123i | \(-0.861987\pi\) | ||||
−0.907467 | + | 0.420123i | \(0.861987\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4832.73 | 0.536365 | 0.268183 | − | 0.963368i | \(-0.413577\pi\) | ||||
0.268183 | + | 0.963368i | \(0.413577\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1185.92 | + | 4212.42i | −0.130714 | + | 0.464299i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1885.73 | −0.206422 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4286.58i | 0.466031i | 0.972473 | + | 0.233015i | \(0.0748592\pi\) | ||||
−0.972473 | + | 0.233015i | \(0.925141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7093.10 | − | 4337.63i | −0.765911 | − | 0.468376i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2140.54i | 0.229572i | 0.993390 | + | 0.114786i | \(0.0366182\pi\) | ||||
−0.993390 | + | 0.114786i | \(0.963382\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 6247.64i | − | 0.665543i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4504.33 | − | 15999.5i | 0.476617 | − | 1.69296i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9598.09i | 1.00882i | 0.863463 | + | 0.504412i | \(0.168291\pi\) | ||||
−0.863463 | + | 0.504412i | \(0.831709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10607.6 | −1.10753 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7380.03 | + | 2077.70i | 0.765440 | + | 0.215494i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.27168 | 0.000234062 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9542.53 | 0.976763 | 0.488382 | − | 0.872630i | \(-0.337587\pi\) | ||||
0.488382 | + | 0.872630i | \(0.337587\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3525.82 | − | 3803.60i | −0.358543 | − | 0.386790i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8017.02 | 0.809956 | 0.404978 | − | 0.914326i | \(-0.367279\pi\) | ||||
0.404978 | + | 0.914326i | \(0.367279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10933.1i | 1.09742i | 0.836014 | + | 0.548709i | \(0.184880\pi\) | ||||
−0.836014 | + | 0.548709i | \(0.815120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8789.75 | − | 2474.57i | −0.876591 | − | 0.246786i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 3991.55i | − | 0.395518i | −0.980251 | − | 0.197759i | \(-0.936634\pi\) | ||
0.980251 | − | 0.197759i | \(-0.0633664\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2459.49i | − | 0.242151i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3566.92 | + | 1004.19i | 0.348949 | + | 0.0982394i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 13169.6i | − | 1.28021i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2787.28 | 0.269241 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11652.3 | − | 7125.72i | −1.11850 | − | 0.683993i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10524.5 | 1.00392 | 0.501958 | − | 0.864892i | \(-0.332613\pi\) | ||||
0.501958 | + | 0.864892i | \(0.332613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.2714 | −0.00211120 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1815.16 | − | 511.020i | −0.170999 | − | 0.0481412i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4125.70 | −0.386265 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10750.1i | 1.00028i | 0.865946 | + | 0.500138i | \(0.166717\pi\) | ||||
−0.865946 | + | 0.500138i | \(0.833283\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2797.16 | + | 9935.60i | −0.258675 | + | 0.918820i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18059.8i | 1.65994i | 0.557811 | + | 0.829968i | \(0.311641\pi\) | ||||
−0.557811 | + | 0.829968i | \(0.688359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5307.28i | 0.484843i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2310.85 | + | 3778.82i | −0.209828 | + | 0.343122i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3243.02i | 0.292694i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15164.6 | −1.36044 | −0.680221 | − | 0.733007i | \(-0.738116\pi\) | ||||
−0.680221 | + | 0.733007i | \(0.738116\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4754.89 | + | 16889.5i | −0.424018 | + | 1.50612i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21362.1 | 1.89362 | 0.946808 | − | 0.321799i | \(-0.104288\pi\) | ||||
0.946808 | + | 0.321799i | \(0.104288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5529.26 | −0.487226 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3093.66 | − | 10988.8i | 0.270994 | − | 0.962579i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4921.82 | 0.428597 | 0.214299 | − | 0.976768i | \(-0.431253\pi\) | ||||
0.214299 | + | 0.976768i | \(0.431253\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1152.15i | 0.0997422i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3165.84 | − | 2934.64i | 0.272467 | − | 0.252568i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 504.684i | 0.0431826i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11985.7i | 1.01960i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3796.49 | + | 13485.2i | −0.321093 | + | 1.14053i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9816.25i | − | 0.825446i | −0.910857 | − | 0.412723i | \(-0.864578\pi\) | ||
0.910857 | − | 0.412723i | \(-0.135422\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11120.7 | −0.929783 | −0.464891 | − | 0.885368i | \(-0.653907\pi\) | ||||
−0.464891 | + | 0.885368i | \(0.653907\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2682.97 | + | 755.335i | 0.223037 | + | 0.0627914i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11074.3 | −0.915378 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8410.98 | −0.691295 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2927.48 | + | 4787.16i | −0.239250 | + | 0.391233i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.8059 | 0.00201588 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4036.47i | 0.326190i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16742.0 | + | 4713.37i | 1.34538 | + | 0.378765i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8611.50i | 0.688170i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 15949.1i | − | 1.26748i | −0.773546 | − | 0.633740i | \(-0.781519\pi\) | ||
0.773546 | − | 0.633740i | \(-0.218481\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9222.60 | + | 2596.43i | 0.728876 | + | 0.205200i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10852.2i | 0.852950i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12775.8 | −0.998637 | −0.499318 | − | 0.866419i | \(-0.666416\pi\) | ||||
−0.499318 | + | 0.866419i | \(0.666416\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8144.89 | − | 13318.9i | 0.633180 | − | 1.03541i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4417.40 | −0.341538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1826.04 | 0.140418 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9992.47 | + | 2813.17i | 0.764246 | + | 0.215158i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9120.09 | 0.693772 | 0.346886 | − | 0.937907i | \(-0.387239\pi\) | ||||
0.346886 | + | 0.937907i | \(0.387239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.7970i | 0.00233019i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1455.73 | + | 5170.80i | −0.109556 | + | 0.389147i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4530.65i | 0.339155i | 0.985517 | + | 0.169577i | \(0.0542403\pi\) | ||||
−0.985517 | + | 0.169577i | \(0.945760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6186.21i | − | 0.460630i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3842.63 | − | 1966.89i | 0.284612 | − | 0.145682i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17896.0i | 1.31853i | 0.751913 | + | 0.659263i | \(0.229132\pi\) | ||||
−0.751913 | + | 0.659263i | \(0.770868\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11840.1 | 0.867760 | 0.433880 | − | 0.900971i | \(-0.357144\pi\) | ||||
0.433880 | + | 0.900971i | \(0.357144\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3354.60 | − | 11915.6i | 0.244573 | − | 0.868731i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5551.75 | −0.402650 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18102.9 | −1.30612 | −0.653060 | − | 0.757306i | \(-0.726515\pi\) | ||||
−0.653060 | + | 0.757306i | \(0.726515\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3585.45 | + | 12735.6i | −0.257351 | + | 0.914119i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −368.920 | −0.0263432 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14146.7i | 1.00497i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.40392 | − | 8.83676i | 0.000381922 | − | 0.000624538i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 21946.7i | − | 1.54317i | −0.636129 | − | 0.771583i | \(-0.719465\pi\) | ||
0.636129 | − | 0.771583i | \(-0.280535\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9217.46i | − | 0.644820i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3083.22 | − | 10951.7i | 0.214597 | − | 0.762253i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8554.64i | 0.592406i | 0.955125 | + | 0.296203i | \(0.0957206\pi\) | ||||
−0.955125 | + | 0.296203i | \(0.904279\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1284.14 | −0.0884784 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26905.0 | + | 7574.56i | 1.84447 | + | 0.519273i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19321.4 | 1.31795 | 0.658973 | − | 0.752167i | \(-0.270991\pi\) | ||||
0.658973 | + | 0.752167i | \(0.270991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18248.6 | 1.23856 | 0.619281 | − | 0.785170i | \(-0.287424\pi\) | ||||
0.619281 | + | 0.785170i | \(0.287424\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9567.30 | − | 5850.67i | −0.646121 | − | 0.395121i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3220.26 | −0.216400 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18473.4i | − | 1.23528i | −0.786462 | − | 0.617639i | \(-0.788089\pi\) | ||
0.786462 | − | 0.617639i | \(-0.211911\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4252.08 | − | 1197.08i | −0.282928 | − | 0.0796524i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 28.0286i | − | 0.00185583i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1007.68i | 0.0663946i | 0.999449 | + | 0.0331973i | \(0.0105690\pi\) | ||||
−0.999449 | + | 0.0331973i | \(0.989431\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11129.6 | − | 3133.32i | −0.729740 | − | 0.205443i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8342.82i | 0.544359i | 0.962247 | + | 0.272179i | \(0.0877444\pi\) | ||||
−0.962247 | + | 0.272179i | \(0.912256\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5153.14 | −0.334608 | −0.167304 | − | 0.985905i | \(-0.553506\pi\) | ||||
−0.167304 | + | 0.985905i | \(0.553506\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6305.77 | + | 5845.26i | −0.407475 | + | 0.377717i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6306.46 | 0.405559 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3904.37 | 0.249880 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4303.81 | − | 1211.65i | −0.274127 | − | 0.0771748i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12589.6 | 0.798062 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3224.67i | 0.203442i | 0.994813 | + | 0.101721i | \(0.0324350\pi\) | ||||
−0.994813 | + | 0.101721i | \(0.967565\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7491.64 | + | 26610.5i | −0.470404 | + | 1.67089i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5616.91i | 0.351024i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 20.1380i | − | 0.00125258i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12615.2 | + | 7714.54i | 0.780985 | + | 0.477594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13243.1i | 0.816025i | 0.912976 | + | 0.408013i | \(0.133778\pi\) | ||||
−0.912976 | + | 0.408013i | \(0.866222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17030.3 | 1.04449 | 0.522246 | − | 0.852795i | \(-0.325094\pi\) | ||||
0.522246 | + | 0.852795i | \(0.325094\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3890.07 | − | 13817.6i | 0.237475 | − | 0.843517i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29077.9 | −1.76688 | −0.883438 | − | 0.468548i | \(-0.844777\pi\) | ||||
−0.883438 | + | 0.468548i | \(0.844777\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5811.93 | 0.351523 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2497.87 | − | 8872.50i | 0.150383 | − | 0.534164i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14617.7 | 0.876008 | 0.438004 | − | 0.898973i | \(-0.355685\pi\) | ||||
0.438004 | + | 0.898973i | \(0.355685\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3228.24i | − | 0.192577i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4481.83 | + | 2740.76i | 0.266138 | + | 0.162751i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3426.04i | 0.202518i | 0.994860 | + | 0.101259i | \(0.0322871\pi\) | ||||
−0.994860 | + | 0.101259i | \(0.967713\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 9256.76i | − | 0.544699i | −0.962198 | − | 0.272350i | \(-0.912199\pi\) | ||
0.962198 | − | 0.272350i | \(-0.0878008\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.40423 | − | 12.0919i | 0.000199411 | − | 0.000708312i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1068.83i | − | 0.0623269i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8798.63 | 0.510771 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13546.7 | + | 3813.79i | 0.782877 | + | 0.220403i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16170.1 | −0.930312 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26622.1 | 1.52482 | 0.762412 | − | 0.647092i | \(-0.224015\pi\) | ||||
0.762412 | + | 0.647092i | \(0.224015\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9320.51 | − | 8639.84i | 0.531476 | − | 0.492663i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23048.4 | 1.30845 | 0.654225 | − | 0.756300i | \(-0.272995\pi\) | ||||
0.654225 | + | 0.756300i | \(0.272995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4164.54i | − | 0.235376i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11680.3 | + | 3288.36i | 0.657256 | + | 0.185037i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27884.8i | 1.56220i | 0.624406 | + | 0.781100i | \(0.285341\pi\) | ||||
−0.624406 | + | 0.781100i | \(0.714659\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 11681.9i | − | 0.651593i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −696.749 | − | 196.155i | −0.0386938 | − | 0.0108934i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 33.0821i | − | 0.00182921i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8029.81 | 0.442067 | 0.221034 | − | 0.975266i | \(-0.429057\pi\) | ||||
0.221034 | + | 0.975266i | \(0.429057\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3814.39 | − | 2332.61i | −0.209086 | − | 0.127862i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4381.22 | −0.239121 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14022.3 | −0.762029 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.4115 | + | 9.96938i | 0.00191615 | + | 0.000539452i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19827.7 | 1.06830 | 0.534152 | − | 0.845388i | \(-0.320631\pi\) | ||||
0.534152 | + | 0.845388i | \(0.320631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10478.7i | 0.562179i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3540.38 | + | 12575.5i | −0.189132 | + | 0.671803i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 5581.32i | − | 0.296898i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5444.68i | 0.288405i | 0.989548 | + | 0.144202i | \(0.0460617\pi\) | ||||
−0.989548 | + | 0.144202i | \(0.953938\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4343.80 | − | 7103.20i | 0.229121 | − | 0.374671i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18359.5i | 0.964330i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.7284 | −0.000561147 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1253.62 | + | 4452.89i | −0.0652960 | + | 0.231933i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4118.06 | −0.213599 | −0.106799 | − | 0.994281i | \(-0.534060\pi\) | ||||
−0.106799 | + | 0.994281i | \(0.534060\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −509.435 | −0.0263140 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1793.93 | − | 6372.08i | 0.0922779 | − | 0.327774i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13005.2 | −0.666208 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26169.4i | − | 1.33504i | −0.744594 | − | 0.667518i | \(-0.767357\pi\) | ||
0.744594 | − | 0.667518i | \(-0.232643\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1489.78 | − | 19626.5i | 0.0756889 | − | 0.997131i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 17409.0i | − | 0.880840i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28634.0i | 1.44286i | 0.692485 | + | 0.721432i | \(0.256516\pi\) | ||||
−0.692485 | + | 0.721432i | \(0.743484\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2543.69 | + | 9035.27i | −0.127654 | + | 0.453430i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11615.4i | 0.580539i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1607.43 | 0.0800139 | 0.0400070 | − | 0.999199i | \(-0.487262\pi\) | ||||
0.0400070 | + | 0.999199i | \(0.487262\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.0644 | + | 2.83344i | 0.000498957 | + | 0.000140471i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 600.872 | 0.0296687 | 0.0148344 | − | 0.999890i | \(-0.495278\pi\) | ||||
0.0148344 | + | 0.999890i | \(0.495278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18765.0 | −0.922815 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −877.593 | + | 1435.08i | −0.0429845 | + | 0.0702904i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4074.47 | −0.198769 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 16005.7i | − | 0.777707i | −0.921300 | − | 0.388854i | \(-0.872871\pi\) | ||
0.921300 | − | 0.388854i | \(-0.127129\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15169.5 | + | 4270.65i | 0.734139 | + | 0.206682i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 8655.67i | − | 0.417235i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 16731.0i | − | 0.803300i | −0.915793 | − | 0.401650i | \(-0.868437\pi\) | ||
0.915793 | − | 0.401650i | \(-0.131563\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8572.38 | + | 2413.38i | 0.409958 | + | 0.115415i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2885.92i | − | 0.137470i | −0.997635 | − | 0.0687349i | \(-0.978104\pi\) | ||
0.997635 | − | 0.0687349i | \(-0.0218963\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10954.4 | −0.519758 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3054.74 | + | 4995.26i | −0.144372 | + | 0.236083i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.5912 | −0.000639830 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5456.60 | 0.255878 | 0.127939 | − | 0.991782i | \(-0.459164\pi\) | ||||
0.127939 | + | 0.991782i | \(0.459164\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12930.6 | − | 3640.33i | −0.603998 | − | 0.170043i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1995.30 | −0.0928407 | −0.0464204 | − | 0.998922i | \(-0.514781\pi\) | ||||
−0.0464204 | + | 0.998922i | \(0.514781\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 27137.0i | − | 1.25779i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2839.66 | + | 10086.5i | −0.131110 | + | 0.465705i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 11671.2i | − | 0.536796i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 15315.7i | − | 0.701714i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14771.5 | + | 13692.8i | −0.674191 | + | 0.624954i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4183.46i | − | 0.190209i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38385.1 | 1.73860 | 0.869302 | − | 0.494282i | \(-0.164569\pi\) | ||||
0.869302 | + | 0.494282i | \(0.164569\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7666.14 | + | 27230.4i | −0.345909 | + | 1.22868i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6244.45 | 0.280692 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.8137 | 0.00169332 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4178.70 | + | 14842.9i | −0.186419 | + | 0.662166i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27449.4 | 1.21996 | 0.609980 | − | 0.792417i | \(-0.291178\pi\) | ||||
0.609980 | + | 0.792417i | \(0.291178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15844.0i | 0.701529i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15001.9 | − | 24531.9i | 0.661756 | − | 1.08214i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 5441.24i | − | 0.239125i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2128.91i | 0.0932100i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2902.69 | + | 10310.4i | −0.126617 | + | 0.449745i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 430.948i | 0.0187285i | 0.999956 | + | 0.00936424i | \(0.00298077\pi\) | ||||
−0.999956 | + | 0.00936424i | \(0.997019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30047.5 | 1.30100 | 0.650500 | − | 0.759506i | \(-0.274559\pi\) | ||||
0.650500 | + | 0.759506i | \(0.274559\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29243.6 | + | 8232.94i | 1.26152 | + | 0.355156i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11653.0 | 0.500841 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14490.0 | 0.620490 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.91995 | + | 5.45480i | 0.000380572 | + | 0.000232730i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27225.8 | 1.15736 | 0.578678 | − | 0.815556i | \(-0.303569\pi\) | ||||
0.578678 | + | 0.815556i | \(0.303569\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 41196.3i | − | 1.74485i | −0.488748 | − | 0.872425i | \(-0.662546\pi\) | ||
0.488748 | − | 0.872425i | \(-0.337454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12670.8 | − | 3567.20i | −0.534715 | − | 0.150538i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9322.06i | 0.391971i | 0.980607 | + | 0.195985i | \(0.0627905\pi\) | ||||
−0.980607 | + | 0.195985i | \(0.937209\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39860.8i | 1.66999i | 0.550256 | + | 0.834996i | \(0.314530\pi\) | ||||
−0.550256 | + | 0.834996i | \(0.685470\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7443.95 | − | 2095.69i | −0.310743 | − | 0.0874833i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11383.6i | 0.473493i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19808.9 | 0.820975 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28571.7 | − | 30822.6i | −1.17991 | − | 1.27286i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8509.74 | −0.350165 | −0.175083 | − | 0.984554i | \(-0.556019\pi\) | ||||
−0.175083 | + | 0.984554i | \(0.556019\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3777.83 | −0.154899 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32295.9 | − | 9092.26i | −1.31949 | − | 0.371476i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12888.2 | −0.524693 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3250.57i | − | 0.131867i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7590.77 | + | 26962.6i | −0.306849 | + | 1.08994i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 20871.6i | − | 0.840740i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 37505.9i | − | 1.50548i | −0.658317 | − | 0.752741i | \(-0.728731\pi\) | ||
0.658317 | − | 0.752741i | \(-0.271269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4157.69 | − | 2542.54i | −0.166304 | − | 0.101700i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40647.9i | 1.62019i | 0.586296 | + | 0.810097i | \(0.300585\pi\) | ||||
−0.586296 | + | 0.810097i | \(0.699415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14040.1 | −0.557673 | −0.278836 | − | 0.960339i | \(-0.589949\pi\) | ||||
−0.278836 | + | 0.960339i | \(0.589949\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3162.81 | − | 11234.4i | 0.125190 | − | 0.444678i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12519.6 | 0.493826 | 0.246913 | − | 0.969038i | \(-0.420584\pi\) | ||||
0.246913 | + | 0.969038i | \(0.420584\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15816.2 | 0.621694 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4993.79 | − | 17738.1i | 0.195615 | − | 0.694830i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8623.76 | −0.336641 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 27.1625i | − | 0.00105668i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16199.9 | − | 9906.68i | −0.628045 | − | 0.384067i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 7488.85i | − | 0.289336i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 27995.4i | − | 1.07792i | −0.842330 | − | 0.538962i | \(-0.818817\pi\) | ||
0.842330 | − | 0.538962i | \(-0.181183\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7605.11 | + | 27013.5i | −0.291825 | + | 1.03657i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16934.0i | − | 0.647583i | −0.946128 | − | 0.323792i | \(-0.895042\pi\) | ||
0.946128 | − | 0.323792i | \(-0.104958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5835.41 | 0.222398 | 0.111199 | − | 0.993798i | \(-0.464531\pi\) | ||||
0.111199 | + | 0.993798i | \(0.464531\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6097.93 | + | 1716.75i | 0.231615 | + | 0.0652066i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12966.0 | −0.490818 | −0.245409 | − | 0.969420i | \(-0.578922\pi\) | ||||
−0.245409 | + | 0.969420i | \(0.578922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5669.79 | −0.213902 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18147.5 | + | 9288.98i | −0.682338 | + | 0.349262i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13187.4 | −0.494178 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 19635.9i | − | 0.733357i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.0465 | − | 5.64368i | −0.000746191 | − | 0.000210075i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43007.8i | 1.59554i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18700.7i | 0.691465i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13947.7 | + | 3926.69i | 0.514009 | + | 0.144709i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 10816.7i | − | 0.397304i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14718.0 | 0.538812 | 0.269406 | − | 0.963027i | \(-0.413173\pi\) | ||||
0.269406 | + | 0.963027i | \(0.413173\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21711.1 | − | 13276.9i | −0.792202 | − | 0.484453i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38859.8 | 1.41326 | 0.706632 | − | 0.707581i | \(-0.250214\pi\) | ||||
0.706632 | + | 0.707581i | \(0.250214\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1742.29 | 0.0631559 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16965.8 | − | 4776.37i | −0.612975 | − | 0.172570i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3258.63 | 0.117349 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38295.3i | 1.37459i | 0.726380 | + | 0.687294i | \(0.241201\pi\) | ||||
−0.726380 | + | 0.687294i | \(0.758799\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5066.61 | − | 17996.8i | 0.181271 | − | 0.643880i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.8157i | 0.00127724i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30850.2i | 1.09659i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1211.85 | + | 1981.68i | −0.0429369 | + | 0.0702125i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 43777.6i | − | 1.54607i | −0.634364 | − | 0.773034i | \(-0.718738\pi\) | ||
0.634364 | − | 0.773034i | \(-0.281262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9474.92 | −0.333542 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11116.6 | − | 39486.3i | 0.390075 | − | 1.38556i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6064.58 | 0.212121 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28384.6 | 0.989631 | 0.494816 | − | 0.868998i | \(-0.335236\pi\) | ||||
0.494816 | + | 0.868998i | \(0.335236\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11969.9 | + | 42517.4i | −0.415999 | + | 1.47764i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54057.6 | −1.87272 | −0.936359 | − | 0.351044i | \(-0.885827\pi\) | ||||
−0.936359 | + | 0.351044i | \(0.885827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23246.8i | 0.802780i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3313.08 | − | 3574.10i | −0.114047 | − | 0.123032i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54179.3i | 1.85912i | 0.368665 | + | 0.929562i | \(0.379815\pi\) | ||||
−0.368665 | + | 0.929562i | \(0.620185\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.7243i | 0.000435247i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10352.6 | + | 36772.7i | −0.353003 | + | 1.25388i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2964.61i | − | 0.100769i | −0.998730 | − | 0.0503846i | \(-0.983955\pi\) | ||
0.998730 | − | 0.0503846i | \(-0.0160447\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13975.2 | −0.473537 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20081.2 | + | 5653.44i | 0.678299 | + | 0.190961i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11791.8 | 0.397058 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −59950.2 | −2.01236 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9692.41 | + | 15849.5i | −0.324334 | + | 0.530367i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14937.0 | 0.498278 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 12087.0i | − | 0.401956i | −0.979596 | − | 0.200978i | \(-0.935588\pi\) | ||
0.979596 | − | 0.200978i | \(-0.0644119\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5689.25 | − | 1601.69i | −0.188612 | − | 0.0530998i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 34336.2i | − | 1.13481i | −0.823439 | − | 0.567405i | \(-0.807947\pi\) | ||
0.823439 | − | 0.567405i | \(-0.192053\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4422.46i | − | 0.145712i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29.6306 | + | 8.34188i | 0.000973271 | + | 0.000274004i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 12445.9i | − | 0.407555i | −0.979017 | − | 0.203777i | \(-0.934678\pi\) | ||
0.979017 | − | 0.203777i | \(-0.0653218\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29783.3 | −0.972298 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26058.5 | + | 42612.1i | −0.848097 | + | 1.38685i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50850.7 | −1.64994 | −0.824968 | − | 0.565180i | \(-0.808807\pi\) | ||||
−0.824968 | + | 0.565180i | \(0.808807\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12844.7 | −0.415498 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12693.9 | − | 3573.71i | −0.409373 | − | 0.115251i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28861.3 | −0.927945 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 16973.3i | − | 0.544071i | −0.962287 | − | 0.272035i | \(-0.912303\pi\) | ||
0.962287 | − | 0.272035i | \(-0.0876968\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6123.23 | + | 21749.9i | −0.195684 | + | 0.695077i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 31555.6i | − | 1.00541i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20434.2i | 0.649104i | 0.945868 | + | 0.324552i | \(0.105213\pi\) | ||||
−0.945868 | + | 0.324552i | \(0.894787\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32481.2 | + | 35040.2i | 1.02869 | + | 1.10973i |
(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 | 768.4.f.e.383.7 | 12 | ||
3.2 | odd | 2 | 768.4.f.f.383.8 | 12 | |||
4.3 | odd | 2 | 768.4.f.g.383.6 | 12 | |||
8.3 | odd | 2 | 768.4.f.f.383.7 | 12 | |||
8.5 | even | 2 | 768.4.f.h.383.6 | 12 | |||
12.11 | even | 2 | 768.4.f.h.383.5 | 12 | |||
16.3 | odd | 4 | 384.4.c.d.383.1 | yes | 12 | ||
16.5 | even | 4 | 384.4.c.c.383.1 | yes | 12 | ||
16.11 | odd | 4 | 384.4.c.b.383.12 | yes | 12 | ||
16.13 | even | 4 | 384.4.c.a.383.12 | yes | 12 | ||
24.5 | odd | 2 | 768.4.f.g.383.5 | 12 | |||
24.11 | even | 2 | inner | 768.4.f.e.383.8 | 12 | ||
48.5 | odd | 4 | 384.4.c.b.383.11 | yes | 12 | ||
48.11 | even | 4 | 384.4.c.c.383.2 | yes | 12 | ||
48.29 | odd | 4 | 384.4.c.d.383.2 | yes | 12 | ||
48.35 | even | 4 | 384.4.c.a.383.11 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.c.a.383.11 | ✓ | 12 | 48.35 | even | 4 | ||
384.4.c.a.383.12 | yes | 12 | 16.13 | even | 4 | ||
384.4.c.b.383.11 | yes | 12 | 48.5 | odd | 4 | ||
384.4.c.b.383.12 | yes | 12 | 16.11 | odd | 4 | ||
384.4.c.c.383.1 | yes | 12 | 16.5 | even | 4 | ||
384.4.c.c.383.2 | yes | 12 | 48.11 | even | 4 | ||
384.4.c.d.383.1 | yes | 12 | 16.3 | odd | 4 | ||
384.4.c.d.383.2 | yes | 12 | 48.29 | odd | 4 | ||
768.4.f.e.383.7 | 12 | 1.1 | even | 1 | trivial | ||
768.4.f.e.383.8 | 12 | 24.11 | even | 2 | inner | ||
768.4.f.f.383.7 | 12 | 8.3 | odd | 2 | |||
768.4.f.f.383.8 | 12 | 3.2 | odd | 2 | |||
768.4.f.g.383.5 | 12 | 24.5 | odd | 2 | |||
768.4.f.g.383.6 | 12 | 4.3 | odd | 2 | |||
768.4.f.h.383.5 | 12 | 12.11 | even | 2 | |||
768.4.f.h.383.6 | 12 | 8.5 | even | 2 |