Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,4,Mod(123,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("124.123");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.31623684071\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-31}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 123.2 | ||
Root | \(0.500000 + 2.78388i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 124.123 |
Dual form | 124.4.d.a.123.1 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 2.78388i | 0.176777 | + | 0.984251i | ||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | −7.50000 | + | 2.78388i | −0.937500 | + | 0.347985i | ||||
\(5\) | −2.00000 | −0.178885 | −0.0894427 | − | 0.995992i | \(-0.528509\pi\) | ||||
−0.0894427 | + | 0.995992i | \(0.528509\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 33.4066i | − | 1.80379i | −0.431959 | − | 0.901893i | \(-0.642178\pi\) | ||
0.431959 | − | 0.901893i | \(-0.357822\pi\) | |||||||
\(8\) | −11.5000 | − | 19.4872i | −0.508233 | − | 0.861220i | ||||
\(9\) | −27.0000 | −1.00000 | ||||||||
\(10\) | −1.00000 | − | 5.56776i | −0.0316228 | − | 0.176068i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 93.0000 | − | 16.7033i | 1.77538 | − | 0.318867i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 48.5000 | − | 41.7582i | 0.757812 | − | 0.652472i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −13.5000 | − | 75.1648i | −0.176777 | − | 0.984251i | ||||
\(19\) | − | 55.6776i | − | 0.672280i | −0.941812 | − | 0.336140i | \(-0.890878\pi\) | ||
0.941812 | − | 0.336140i | \(-0.109122\pi\) | |||||||
\(20\) | 15.0000 | − | 5.56776i | 0.167705 | − | 0.0622495i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −121.000 | −0.968000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 93.0000 | + | 250.549i | 0.627691 | + | 1.69105i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 172.601i | − | 1.00000i | ||||||
\(32\) | 140.500 | + | 114.139i | 0.776160 | + | 0.630536i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 66.8132i | 0.322671i | ||||||||
\(36\) | 202.500 | − | 75.1648i | 0.937500 | − | 0.347985i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 155.000 | − | 27.8388i | 0.661693 | − | 0.118844i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 23.0000 | + | 38.9744i | 0.0909155 | + | 0.154060i | ||||
\(41\) | −278.000 | −1.05893 | −0.529467 | − | 0.848330i | \(-0.677608\pi\) | ||||
−0.529467 | + | 0.848330i | \(0.677608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 54.0000 | 0.178885 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 189.304i | 0.587507i | 0.955881 | + | 0.293753i | \(0.0949045\pi\) | ||||
−0.955881 | + | 0.293753i | \(0.905096\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −773.000 | −2.25364 | ||||||||
\(50\) | −60.5000 | − | 336.850i | −0.171120 | − | 0.952755i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −651.000 | + | 384.176i | −1.55346 | + | 0.916744i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 523.370i | 1.15486i | 0.816439 | + | 0.577432i | \(0.195945\pi\) | ||||
−0.816439 | + | 0.577432i | \(0.804055\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 480.500 | − | 86.3003i | 0.984251 | − | 0.176777i | ||||
\(63\) | 901.978i | 1.80379i | ||||||||
\(64\) | −247.500 | + | 448.205i | −0.483398 | + | 0.875400i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 857.436i | − | 1.56347i | −0.623611 | − | 0.781735i | \(-0.714335\pi\) | ||
0.623611 | − | 0.781735i | \(-0.285665\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −186.000 | + | 33.4066i | −0.317589 | + | 0.0570407i | ||||
\(71\) | − | 656.996i | − | 1.09818i | −0.835762 | − | 0.549092i | \(-0.814974\pi\) | ||
0.835762 | − | 0.549092i | \(-0.185026\pi\) | |||||||
\(72\) | 310.500 | + | 526.154i | 0.508233 | + | 0.861220i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 155.000 | + | 417.582i | 0.233944 | + | 0.630263i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −97.0000 | + | 83.5165i | −0.135562 | + | 0.116718i | ||||
\(81\) | 729.000 | 1.00000 | ||||||||
\(82\) | −139.000 | − | 773.919i | −0.187195 | − | 1.04226i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 27.0000 | + | 150.330i | 0.0316228 | + | 0.176068i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −527.000 | + | 94.6520i | −0.578254 | + | 0.103858i | ||||
\(95\) | 111.355i | 0.120261i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1906.00 | 1.99510 | 0.997551 | − | 0.0699366i | \(-0.0222797\pi\) | ||||
0.997551 | + | 0.0699366i | \(0.0222797\pi\) | |||||||
\(98\) | −386.500 | − | 2151.94i | −0.398392 | − | 2.21815i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 907.500 | − | 336.850i | 0.907500 | − | 0.336850i | ||||
\(101\) | 1790.00 | 1.76348 | 0.881741 | − | 0.471734i | \(-0.156372\pi\) | ||||
0.881741 | + | 0.471734i | \(0.156372\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1659.19i | 1.58724i | 0.608417 | + | 0.793618i | \(0.291805\pi\) | ||||
−0.608417 | + | 0.793618i | \(0.708195\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1525.57i | − | 1.37834i | −0.724601 | − | 0.689169i | \(-0.757976\pi\) | ||
0.724601 | − | 0.689169i | \(-0.242024\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1546.00 | −1.35853 | −0.679266 | − | 0.733892i | \(-0.737702\pi\) | ||||
−0.679266 | + | 0.733892i | \(0.737702\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1395.00 | − | 1620.22i | −1.17692 | − | 1.36693i | ||||
\(113\) | 2402.00 | 1.99966 | 0.999828 | − | 0.0185406i | \(-0.00590199\pi\) | ||||
0.999828 | + | 0.0185406i | \(0.00590199\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1457.00 | + | 261.685i | −1.13668 | + | 0.204153i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1331.00 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 480.500 | + | 1294.51i | 0.347985 | + | 0.937500i | ||||
\(125\) | 492.000 | 0.352047 | ||||||||
\(126\) | −2511.00 | + | 450.989i | −1.77538 | + | 0.318867i | ||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | −1371.50 | − | 464.908i | −0.947067 | − | 0.321035i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2995.46i | − | 1.99782i | −0.0466865 | − | 0.998910i | \(-0.514866\pi\) | ||
0.0466865 | − | 0.998910i | \(-0.485134\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1860.00 | −1.21265 | ||||||||
\(134\) | 2387.00 | − | 428.718i | 1.53885 | − | 0.276385i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | −186.000 | − | 501.099i | −0.112285 | − | 0.302504i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1829.00 | − | 328.498i | 1.08089 | − | 0.194133i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1309.50 | + | 1127.47i | −0.757812 | + | 0.652472i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3470.00 | 1.90788 | 0.953938 | − | 0.300004i | \(-0.0969881\pi\) | ||||
0.953938 | + | 0.300004i | \(0.0969881\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | −1085.00 | + | 640.293i | −0.578981 | + | 0.341675i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 345.201i | 0.178885i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1146.00 | −0.582553 | −0.291276 | − | 0.956639i | \(-0.594080\pi\) | ||||
−0.291276 | + | 0.956639i | \(0.594080\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −281.000 | − | 228.278i | −0.138844 | − | 0.112794i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 364.500 | + | 2029.45i | 0.176777 | + | 0.984251i | ||||
\(163\) | 3240.44i | 1.55712i | 0.627569 | + | 0.778561i | \(0.284050\pi\) | ||||
−0.627569 | + | 0.778561i | \(0.715950\pi\) | |||||||
\(164\) | 2085.00 | − | 773.919i | 0.992751 | − | 0.368494i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2197.00 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1503.30i | 0.672280i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4522.00 | −1.98729 | −0.993645 | − | 0.112556i | \(-0.964096\pi\) | ||||
−0.993645 | + | 0.112556i | \(0.964096\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4042.20i | 1.74606i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −405.000 | + | 150.330i | −0.167705 | + | 0.0622495i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −527.000 | − | 1419.78i | −0.204444 | − | 0.550788i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −310.000 | + | 55.6776i | −0.118367 | + | 0.0212594i | ||||
\(191\) | 278.388i | 0.105463i | 0.998609 | + | 0.0527316i | \(0.0167928\pi\) | ||||
−0.998609 | + | 0.0527316i | \(0.983207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4542.00 | −1.69399 | −0.846996 | − | 0.531600i | \(-0.821591\pi\) | ||||
−0.846996 | + | 0.531600i | \(0.821591\pi\) | |||||||
\(194\) | 953.000 | + | 5306.08i | 0.352688 | + | 1.96368i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5797.50 | − | 2151.94i | 2.11279 | − | 0.784235i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 1391.50 | + | 2357.95i | 0.491970 | + | 0.833661i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 895.000 | + | 4983.15i | 0.311742 | + | 1.73571i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 556.000 | 0.189428 | ||||||||
\(206\) | −4619.00 | + | 829.597i | −1.56224 | + | 0.280586i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5578.90i | − | 1.82022i | −0.414362 | − | 0.910112i | \(-0.635995\pi\) | ||
0.414362 | − | 0.910112i | \(-0.364005\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4247.00 | − | 762.784i | 1.35663 | − | 0.243658i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5766.00 | −1.80379 | ||||||||
\(218\) | −773.000 | − | 4303.88i | −0.240157 | − | 1.33714i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 3813.00 | − | 4693.63i | 1.13735 | − | 1.40003i | ||||
\(225\) | 3267.00 | 0.968000 | ||||||||
\(226\) | 1201.00 | + | 6686.88i | 0.353493 | + | 1.96816i | ||||
\(227\) | − | 6202.49i | − | 1.81354i | −0.421625 | − | 0.906770i | \(-0.638540\pi\) | ||
0.421625 | − | 0.906770i | \(-0.361460\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5398.00 | −1.51775 | −0.758873 | − | 0.651239i | \(-0.774250\pi\) | ||||
−0.758873 | + | 0.651239i | \(0.774250\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 378.608i | − | 0.105096i | ||||||
\(236\) | −1457.00 | − | 3925.27i | −0.401876 | − | 1.08268i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −665.500 | − | 3705.35i | −0.176777 | − | 0.984251i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1546.00 | 0.403144 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3363.50 | + | 1984.91i | −0.861220 | + | 0.508233i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 246.000 | + | 1369.67i | 0.0622336 | + | 0.346502i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −2511.00 | − | 6764.83i | −0.627691 | − | 1.69105i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 608.500 | − | 4050.55i | 0.148560 | − | 0.988903i | ||||
\(257\) | −4286.00 | −1.04029 | −0.520143 | − | 0.854079i | \(-0.674121\pi\) | ||||
−0.520143 | + | 0.854079i | \(0.674121\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8339.00 | − | 1497.73i | 1.96636 | − | 0.353168i | ||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −930.000 | − | 5178.02i | −0.214368 | − | 1.19355i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2387.00 | + | 6430.77i | 0.544064 | + | 1.46575i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4660.22i | 1.00000i | ||||||||
\(280\) | 1302.00 | − | 768.351i | 0.277891 | − | 0.163992i | ||||
\(281\) | 650.000 | 0.137992 | 0.0689960 | − | 0.997617i | \(-0.478020\pi\) | ||||
0.0689960 | + | 0.997617i | \(0.478020\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8919.56i | − | 1.87354i | −0.349941 | − | 0.936772i | \(-0.613799\pi\) | ||
0.349941 | − | 0.936772i | \(-0.386201\pi\) | |||||||
\(284\) | 1829.00 | + | 4927.47i | 0.382152 | + | 1.02955i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9287.03i | 1.91009i | ||||||||
\(288\) | −3793.50 | − | 3081.76i | −0.776160 | − | 0.630536i | ||||
\(289\) | 4913.00 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5278.00 | 1.05237 | 0.526184 | − | 0.850371i | \(-0.323622\pi\) | ||||
0.526184 | + | 0.850371i | \(0.323622\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1046.74i | − | 0.206588i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1735.00 | + | 9660.07i | 0.337268 | + | 1.87783i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2325.00 | − | 2700.37i | −0.438644 | − | 0.509462i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4153.55i | − | 0.772169i | −0.922464 | − | 0.386084i | \(-0.873827\pi\) | ||
0.922464 | − | 0.386084i | \(-0.126173\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −961.000 | + | 172.601i | −0.176068 | + | 0.0316228i | ||||
\(311\) | − | 3953.11i | − | 0.720773i | −0.932803 | − | 0.360387i | \(-0.882645\pi\) | ||
0.932803 | − | 0.360387i | \(-0.117355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | −573.000 | − | 3190.33i | −0.102982 | − | 0.573378i | ||||
\(315\) | − | 1803.96i | − | 0.322671i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11206.0 | 1.98546 | 0.992731 | − | 0.120352i | \(-0.0384022\pi\) | ||||
0.992731 | + | 0.120352i | \(0.0384022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 495.000 | − | 896.410i | 0.0864729 | − | 0.156596i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −5467.50 | + | 2029.45i | −0.937500 | + | 0.347985i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9021.00 | + | 1620.22i | −1.53260 | + | 0.275263i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3197.00 | + | 5417.43i | 0.538185 | + | 0.911975i | ||||
\(329\) | 6324.00 | 1.05974 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1714.87i | 0.279682i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 1098.50 | + | 6116.19i | 0.176777 | + | 0.984251i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4185.00 | + | 751.648i | −0.661693 | + | 0.118844i | ||||
\(343\) | 14364.8i | 2.26131i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2261.00 | − | 12588.7i | −0.351307 | − | 1.95599i | ||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4410.00 | −0.676395 | −0.338198 | − | 0.941075i | \(-0.609817\pi\) | ||||
−0.338198 | + | 0.941075i | \(0.609817\pi\) | |||||||
\(350\) | −11253.0 | + | 2021.10i | −1.71857 | + | 0.308664i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1313.99i | 0.196449i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12972.9i | 1.90719i | 0.301084 | + | 0.953597i | \(0.402651\pi\) | ||||
−0.301084 | + | 0.953597i | \(0.597349\pi\) | |||||||
\(360\) | −621.000 | − | 1052.31i | −0.0909155 | − | 0.154060i | ||||
\(361\) | 3759.00 | 0.548039 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7506.00 | 1.05893 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14258.0 | −1.97923 | −0.989613 | − | 0.143758i | \(-0.954081\pi\) | ||||
−0.989613 | + | 0.143758i | \(0.954081\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3689.00 | − | 2177.00i | 0.505972 | − | 0.298590i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 701.538i | 0.0950807i | 0.998869 | + | 0.0475404i | \(0.0151383\pi\) | ||||
−0.998869 | + | 0.0475404i | \(0.984862\pi\) | |||||||
\(380\) | −310.000 | − | 835.165i | −0.0418491 | − | 0.112745i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −775.000 | + | 139.194i | −0.103802 | + | 0.0186434i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2271.00 | − | 12644.4i | −0.299458 | − | 1.66731i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14295.0 | + | 5306.08i | −1.87041 | + | 0.694266i | ||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 8889.50 | + | 15063.6i | 1.14538 | + | 1.94088i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15626.0 | −1.97543 | −0.987716 | − | 0.156260i | \(-0.950056\pi\) | ||||
−0.987716 | + | 0.156260i | \(0.950056\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5868.50 | + | 5052.75i | −0.733563 | + | 0.631593i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −13425.0 | + | 4983.15i | −1.65326 | + | 0.613666i | ||||
\(405\) | −1458.00 | −0.178885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 278.000 | + | 1547.84i | 0.0334864 | + | 0.186445i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4619.00 | − | 12444.0i | −0.552334 | − | 1.48803i | ||||
\(413\) | 17484.0 | 2.08313 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 16892.6i | − | 1.96959i | −0.173726 | − | 0.984794i | \(-0.555581\pi\) | ||
0.173726 | − | 0.984794i | \(-0.444419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11838.0 | 1.37042 | 0.685212 | − | 0.728343i | \(-0.259709\pi\) | ||||
0.685212 | + | 0.728343i | \(0.259709\pi\) | |||||||
\(422\) | 15531.0 | − | 2789.45i | 1.79156 | − | 0.321773i | ||||
\(423\) | − | 5111.21i | − | 0.587507i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4247.00 | + | 11441.8i | 0.479641 | + | 1.29219i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13017.4i | 1.45482i | 0.686203 | + | 0.727410i | \(0.259276\pi\) | ||||
−0.686203 | + | 0.727410i | \(0.740724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | −2883.00 | − | 16051.9i | −0.318867 | − | 1.77538i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11595.0 | − | 4303.88i | 1.27362 | − | 0.472749i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 18295.7i | − | 1.98908i | −0.104370 | − | 0.994539i | \(-0.533283\pi\) | ||
0.104370 | − | 0.994539i | \(-0.466717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20871.0 | 2.25364 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 7137.87i | − | 0.765532i | −0.923845 | − | 0.382766i | \(-0.874972\pi\) | ||
0.923845 | − | 0.382766i | \(-0.125028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14973.0 | + | 8268.13i | 1.57904 | + | 0.871947i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 1633.50 | + | 9094.94i | 0.171120 | + | 0.952755i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −18015.0 | + | 6686.88i | −1.87468 | + | 0.695851i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17267.0 | − | 3101.24i | 1.78498 | − | 0.320592i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2699.00 | − | 15027.4i | −0.268302 | − | 1.49384i | ||||
\(467\) | 18295.7i | 1.81290i | 0.422317 | + | 0.906448i | \(0.361217\pi\) | ||||
−0.422317 | + | 0.906448i | \(0.638783\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28644.0 | −2.82016 | ||||||||
\(470\) | 1054.00 | − | 189.304i | 0.103441 | − | 0.0185786i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10199.0 | − | 6018.75i | 0.994591 | − | 0.586940i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6736.99i | 0.650767i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 12104.3i | − | 1.15461i | −0.816527 | − | 0.577307i | \(-0.804103\pi\) | ||
0.816527 | − | 0.577307i | \(-0.195897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9982.50 | − | 3705.35i | 0.937500 | − | 0.347985i | ||||
\(485\) | −3812.00 | −0.356895 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 773.000 | + | 4303.88i | 0.0712665 | + | 0.396795i | ||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7207.50 | − | 8371.13i | −0.652472 | − | 0.757812i | ||||
\(497\) | −21948.0 | −1.98089 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | −3690.00 | + | 1369.67i | −0.330044 | + | 0.122507i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 679.267i | 0.0602128i | 0.999547 | + | 0.0301064i | \(0.00958461\pi\) | ||||
−0.999547 | + | 0.0301064i | \(0.990415\pi\) | |||||||
\(504\) | 17577.0 | − | 10372.7i | 1.55346 | − | 0.916744i | ||||
\(505\) | −3580.00 | −0.315461 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11580.5 | − | 331.282i | 0.999591 | − | 0.0285952i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2143.00 | − | 11931.7i | −0.183898 | − | 1.02390i | ||||
\(515\) | − | 3318.39i | − | 0.283933i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14630.0 | −1.23023 | −0.615117 | − | 0.788436i | \(-0.710891\pi\) | ||||
−0.615117 | + | 0.788436i | \(0.710891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | 8339.00 | + | 22465.9i | 0.695212 | + | 1.87296i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12167.0 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 14131.0i | − | 1.15486i | ||||||
\(532\) | 13950.0 | − | 5178.02i | 1.13686 | − | 0.421984i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3051.13i | 0.246565i | ||||||||
\(536\) | −16709.0 | + | 9860.51i | −1.34649 | + | 0.794607i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24870.0 | 1.97642 | 0.988211 | − | 0.153095i | \(-0.0489241\pi\) | ||||
0.988211 | + | 0.153095i | \(0.0489241\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3092.00 | 0.243022 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24910.2i | − | 1.94713i | −0.228402 | − | 0.973567i | \(-0.573350\pi\) | ||
0.228402 | − | 0.973567i | \(-0.426650\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | −12973.5 | + | 2330.11i | −0.984251 | + | 0.176777i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2790.00 | + | 3240.44i | 0.210534 | + | 0.244524i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 325.000 | + | 1809.52i | 0.0243938 | + | 0.135819i | ||||
\(563\) | 22393.5i | 1.67633i | 0.545414 | + | 0.838167i | \(0.316372\pi\) | ||||
−0.545414 | + | 0.838167i | \(0.683628\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4804.00 | −0.357709 | ||||||||
\(566\) | 24831.0 | − | 4459.78i | 1.84404 | − | 0.331199i | ||||
\(567\) | − | 24353.4i | − | 1.80379i | ||||||
\(568\) | −12803.0 | + | 7555.46i | −0.945778 | + | 0.558134i | ||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −25854.0 | + | 4643.52i | −1.88001 | + | 0.337660i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6682.50 | − | 12101.5i | 0.483398 | − | 0.875400i | ||||
\(577\) | −25326.0 | −1.82727 | −0.913635 | − | 0.406535i | \(-0.866737\pi\) | ||||
−0.913635 | + | 0.406535i | \(0.866737\pi\) | |||||||
\(578\) | 2456.50 | + | 13677.2i | 0.176777 | + | 0.984251i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2639.00 | + | 14693.3i | 0.186034 | + | 1.03580i | ||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9610.00 | −0.672280 | ||||||||
\(590\) | 2914.00 | − | 523.370i | 0.203335 | − | 0.0365200i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25342.0 | −1.75493 | −0.877463 | − | 0.479644i | \(-0.840766\pi\) | ||||
−0.877463 | + | 0.479644i | \(0.840766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −26025.0 | + | 9660.07i | −1.78863 | + | 0.663913i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26780.9i | 1.82678i | 0.407088 | + | 0.913389i | \(0.366544\pi\) | ||||
−0.407088 | + | 0.913389i | \(0.633456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23150.8i | 1.56347i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2662.00 | 0.178885 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18897.0i | 1.26360i | 0.775131 | + | 0.631800i | \(0.217684\pi\) | ||||
−0.775131 | + | 0.631800i | \(0.782316\pi\) | |||||||
\(608\) | 6355.00 | − | 7822.71i | 0.423897 | − | 0.521797i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 11563.0 | − | 2076.78i | 0.760008 | − | 0.136501i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30074.0 | 1.96229 | 0.981146 | − | 0.193270i | \(-0.0619094\pi\) | ||||
0.981146 | + | 0.193270i | \(0.0619094\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | −961.000 | − | 2589.01i | −0.0622495 | − | 0.167705i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11005.0 | − | 1976.56i | 0.709422 | − | 0.127416i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14141.0 | 0.905024 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8595.00 | − | 3190.33i | 0.546143 | − | 0.202720i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 5022.00 | − | 901.978i | 0.317589 | − | 0.0570407i | ||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5603.00 | + | 31196.2i | 0.350984 | + | 1.95419i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17738.9i | 1.09818i | ||||||||
\(640\) | 2743.00 | + | 929.817i | 0.169417 | + | 0.0574285i | ||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −8383.50 | − | 14206.2i | −0.508233 | − | 0.861220i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9021.00 | − | 24303.3i | −0.541855 | − | 1.45980i | ||||
\(653\) | 7222.00 | 0.432800 | 0.216400 | − | 0.976305i | \(-0.430568\pi\) | ||||
0.216400 | + | 0.976305i | \(0.430568\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5990.91i | 0.357381i | ||||||||
\(656\) | −13483.0 | + | 11608.8i | −0.802474 | + | 0.690925i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3162.00 | + | 17605.3i | 0.187337 | + | 1.04305i | ||||
\(659\) | 33796.3i | 1.99775i | 0.0474074 | + | 0.998876i | \(0.484904\pi\) | ||||
−0.0474074 | + | 0.998876i | \(0.515096\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30350.0 | 1.78590 | 0.892949 | − | 0.450158i | \(-0.148632\pi\) | ||||
0.892949 | + | 0.450158i | \(0.148632\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3720.00 | 0.216925 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4774.00 | + | 857.436i | −0.275277 | + | 0.0494412i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16477.5 | + | 6116.19i | −0.937500 | + | 0.347985i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 63673.0i | − | 3.59874i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25377.9i | 1.42175i | 0.703317 | + | 0.710876i | \(0.251701\pi\) | ||||
−0.703317 | + | 0.710876i | \(0.748299\pi\) | |||||||
\(684\) | −4185.00 | − | 11274.7i | −0.233944 | − | 0.630263i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −39990.0 | + | 7182.42i | −2.22569 | + | 0.399746i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 17872.5i | − | 0.983940i | −0.870612 | − | 0.491970i | \(-0.836277\pi\) | ||
0.870612 | − | 0.491970i | \(-0.163723\pi\) | |||||||
\(692\) | 33915.0 | − | 12588.7i | 1.86309 | − | 0.691548i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −2205.00 | − | 12276.9i | −0.119571 | − | 0.665743i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11253.0 | − | 30316.5i | −0.607605 | − | 1.63694i | ||||
\(701\) | 17702.0 | 0.953774 | 0.476887 | − | 0.878965i | \(-0.341765\pi\) | ||||
0.476887 | + | 0.878965i | \(0.341765\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 59797.8i | − | 3.18094i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | −3658.00 | + | 656.996i | −0.193355 | + | 0.0347276i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −36115.0 | + | 6486.45i | −1.87716 | + | 0.337148i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 2619.00 | − | 2254.94i | 0.135562 | − | 0.116718i | ||||
\(721\) | 55428.0 | 2.86303 | ||||||||
\(722\) | 1879.50 | + | 10464.6i | 0.0968805 | + | 0.539408i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23017.1i | − | 1.17422i | −0.809507 | − | 0.587110i | \(-0.800265\pi\) | ||
0.809507 | − | 0.587110i | \(-0.199735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27078.0 | 1.36446 | 0.682230 | − | 0.731138i | \(-0.261010\pi\) | ||||
0.682230 | + | 0.731138i | \(0.261010\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 3753.00 | + | 20895.8i | 0.187195 | + | 1.04226i | ||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6940.00 | −0.341291 | ||||||||
\(746\) | −7129.00 | − | 39692.6i | −0.349881 | − | 1.94806i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −50964.0 | −2.48623 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7672.38i | 0.372795i | 0.982474 | + | 0.186398i | \(0.0596812\pi\) | ||||
−0.982474 | + | 0.186398i | \(0.940319\pi\) | |||||||
\(752\) | 7905.00 | + | 9181.24i | 0.383332 | + | 0.445220i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | −1953.00 | + | 350.769i | −0.0935833 | + | 0.0168081i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2170.00 | − | 1280.59i | 0.103571 | − | 0.0611207i | ||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51646.6i | 2.45050i | ||||||||
\(764\) | −775.000 | − | 2087.91i | −0.0366996 | − | 0.0988717i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25170.0 | 1.18030 | 0.590152 | − | 0.807292i | \(-0.299068\pi\) | ||||
0.590152 | + | 0.807292i | \(0.299068\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 34065.0 | − | 12644.4i | 1.58812 | − | 0.589484i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20884.7i | 0.968000i | ||||||||
\(776\) | −21919.0 | − | 37142.6i | −1.01398 | − | 1.71822i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15478.4i | 0.711901i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −37490.5 | + | 32279.1i | −1.70784 | + | 1.47044i | ||||
\(785\) | 2292.00 | 0.104210 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 80242.6i | − | 3.60695i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −7813.00 | − | 43500.9i | −0.349210 | − | 1.94432i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −17000.5 | − | 13810.8i | −0.751323 | − | 0.610359i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20585.0 | − | 34882.0i | −0.896260 | − | 1.51875i | ||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | −729.000 | − | 4058.90i | −0.0316228 | − | 0.176068i | ||||
\(811\) | 37137.0i | 1.60796i | 0.594656 | + | 0.803980i | \(0.297288\pi\) | ||||
−0.594656 | + | 0.803980i | \(0.702712\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 6480.88i | − | 0.278546i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4170.00 | + | 1547.84i | −0.177589 | + | 0.0659181i | ||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 32333.0 | − | 19080.7i | 1.36696 | − | 0.806685i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8742.00 | + | 48673.4i | 0.368248 | + | 2.05032i | ||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 47027.0 | − | 8446.30i | 1.93857 | − | 0.348177i | ||||
\(839\) | − | 32460.1i | − | 1.33569i | −0.744299 | − | 0.667846i | \(-0.767216\pi\) | ||
0.744299 | − | 0.667846i | \(-0.232784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24389.0 | 1.00000 | ||||||||
\(842\) | 5919.00 | + | 32955.6i | 0.242259 | + | 1.34884i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15531.0 | + | 41841.7i | 0.633411 | + | 1.70646i | ||||
\(845\) | −4394.00 | −0.178885 | ||||||||
\(846\) | 14229.0 | − | 2555.60i | 0.578254 | − | 0.103858i | ||||
\(847\) | 44464.2i | 1.80379i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19278.0 | 0.773817 | 0.386909 | − | 0.922118i | \(-0.373543\pi\) | ||||
0.386909 | + | 0.922118i | \(0.373543\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 3006.59i | − | 0.120261i | ||||||
\(856\) | −29729.0 | + | 17544.0i | −1.18705 | + | 0.700517i | ||||
\(857\) | 42826.0 | 1.70701 | 0.853505 | − | 0.521084i | \(-0.174472\pi\) | ||||
0.853505 | + | 0.521084i | \(0.174472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36239.0 | + | 6508.72i | −1.43191 | + | 0.257178i | ||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9044.00 | 0.355497 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 43245.0 | − | 16051.9i | 1.69105 | − | 0.627691i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 17779.0 | + | 30127.2i | 0.690451 | + | 1.16999i | ||||
\(873\) | −51462.0 | −1.99510 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 16436.0i | − | 0.635017i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38634.0 | −1.48755 | −0.743773 | − | 0.668433i | \(-0.766966\pi\) | ||||
−0.743773 | + | 0.668433i | \(0.766966\pi\) | |||||||
\(878\) | 50933.0 | − | 9147.84i | 1.95775 | − | 0.351622i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 10435.5 | + | 58102.4i | 0.398392 | + | 2.21815i | ||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19871.0 | − | 3568.94i | 0.753476 | − | 0.135328i | ||||
\(887\) | 11280.3i | 0.427007i | 0.976942 | + | 0.213503i | \(0.0684875\pi\) | ||||
−0.976942 | + | 0.213503i | \(0.931513\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10540.0 | 0.394969 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −15531.0 | + | 45817.1i | −0.579078 | + | 1.70831i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −24502.5 | + | 9094.94i | −0.907500 | + | 0.336850i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27623.0 | − | 46808.2i | −1.01629 | − | 1.72214i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50856.0i | 1.86179i | 0.365286 | + | 0.930895i | \(0.380971\pi\) | ||||
−0.365286 | + | 0.930895i | \(0.619029\pi\) | |||||||
\(908\) | 17267.0 | + | 46518.7i | 0.631085 | + | 1.70019i | ||||
\(909\) | −48330.0 | −1.76348 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −100068. | −3.60364 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 19097.4i | − | 0.685491i | −0.939428 | − | 0.342745i | \(-0.888643\pi\) | ||
0.939428 | − | 0.342745i | \(-0.111357\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 44798.2i | − | 1.58724i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43038.8i | 1.51508i | ||||||||
\(932\) | 40485.0 | − | 15027.4i | 1.42289 | − | 0.528153i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −50933.0 | + | 9147.84i | −1.78435 | + | 0.320478i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43974.0 | −1.53316 | −0.766578 | − | 0.642151i | \(-0.778042\pi\) | ||||
−0.766578 | + | 0.642151i | \(0.778042\pi\) | |||||||
\(938\) | −14322.0 | − | 79741.5i | −0.498539 | − | 2.77575i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1054.00 | + | 2839.56i | 0.0365720 | + | 0.0985279i | ||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 21855.0 | + | 25383.4i | 0.753517 | + | 0.875170i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −18755.0 | + | 3368.50i | −0.640518 | + | 0.115041i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 556.776i | − | 0.0188658i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33697.0 | − | 6052.16i | 1.13643 | − | 0.204109i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29791.0 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41190.3i | 1.37834i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9084.00 | 0.303030 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(968\) | 15306.5 | + | 25937.4i | 0.508233 | + | 0.861220i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1906.00 | − | 10612.2i | −0.0630907 | − | 0.351274i | ||||
\(971\) | 10411.7i | 0.344107i | 0.985088 | + | 0.172054i | \(0.0550402\pi\) | ||||
−0.985088 | + | 0.172054i | \(0.944960\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23246.0 | −0.761213 | −0.380607 | − | 0.924737i | \(-0.624285\pi\) | ||||
−0.380607 | + | 0.924737i | \(0.624285\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −11595.0 | + | 4303.88i | −0.377948 | + | 0.140288i | ||||
\(981\) | 41742.0 | 1.35853 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 19700.5 | − | 24250.4i | 0.630536 | − | 0.776160i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10974.0 | − | 61100.6i | −0.350175 | − | 1.94969i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54686.0 | 1.73713 | 0.868567 | − | 0.495571i | \(-0.165041\pi\) | ||||
0.868567 | + | 0.495571i | \(0.165041\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 124.4.d.a.123.2 | yes | 2 | |
4.3 | odd | 2 | inner | 124.4.d.a.123.1 | ✓ | 2 | |
31.30 | odd | 2 | CM | 124.4.d.a.123.2 | yes | 2 | |
124.123 | even | 2 | inner | 124.4.d.a.123.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.4.d.a.123.1 | ✓ | 2 | 4.3 | odd | 2 | inner | |
124.4.d.a.123.1 | ✓ | 2 | 124.123 | even | 2 | inner | |
124.4.d.a.123.2 | yes | 2 | 1.1 | even | 1 | trivial | |
124.4.d.a.123.2 | yes | 2 | 31.30 | odd | 2 | CM |