Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [100,4,Mod(7,100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("100.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.e (of order \(4\), degree \(2\), 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: | \(5.90019100057\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 100.7 |
Dual form | 100.4.e.c.43.1 |
$q$-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 \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(77\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(3\) | −7.00000 | − | 7.00000i | −1.34715 | − | 1.34715i | −0.888741 | − | 0.458410i | \(-0.848419\pi\) |
−0.458410 | − | 0.888741i | \(-0.651581\pi\) | |||||||
\(4\) | − | 8.00000i | − | 1.00000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −28.0000 | −1.90516 | ||||||||
\(7\) | 9.00000 | − | 9.00000i | 0.485954 | − | 0.485954i | −0.421073 | − | 0.907027i | \(-0.638346\pi\) |
0.907027 | + | 0.421073i | \(0.138346\pi\) | |||||||
\(8\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(9\) | 71.0000i | 2.62963i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | −56.0000 | + | 56.0000i | −1.34715 | + | 1.34715i | ||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | − | 36.0000i | − | 0.687243i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | 142.000 | + | 142.000i | 1.85943 | + | 1.85943i | ||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −126.000 | −1.30931 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −67.0000 | − | 67.0000i | −0.607412 | − | 0.607412i | 0.334857 | − | 0.942269i | \(-0.391312\pi\) |
−0.942269 | + | 0.334857i | \(0.891312\pi\) | |||||||
\(24\) | 224.000i | 1.90516i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 308.000 | − | 308.000i | 2.19536 | − | 2.19536i | ||||
\(28\) | −72.0000 | − | 72.0000i | −0.485954 | − | 0.485954i | ||||
\(29\) | − | 306.000i | − | 1.95941i | −0.200455 | − | 0.979703i | \(-0.564242\pi\) | ||
0.200455 | − | 0.979703i | \(-0.435758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −128.000 | + | 128.000i | −0.707107 | + | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 568.000 | 2.62963 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 252.000 | 0.959897 | 0.479949 | − | 0.877297i | \(-0.340655\pi\) | ||||
0.479949 | + | 0.877297i | \(0.340655\pi\) | |||||||
\(42\) | −252.000 | + | 252.000i | −0.925820 | + | 0.925820i | ||||
\(43\) | −297.000 | − | 297.000i | −1.05330 | − | 1.05330i | −0.998497 | − | 0.0548071i | \(-0.982546\pi\) |
−0.0548071 | − | 0.998497i | \(-0.517454\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −268.000 | −0.859010 | ||||||||
\(47\) | −301.000 | + | 301.000i | −0.934157 | + | 0.934157i | −0.997962 | − | 0.0638057i | \(-0.979676\pi\) |
0.0638057 | + | 0.997962i | \(0.479676\pi\) | |||||||
\(48\) | 448.000 | + | 448.000i | 1.34715 | + | 1.34715i | ||||
\(49\) | 181.000i | 0.527697i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | − | 1232.00i | − | 3.10470i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −288.000 | −0.687243 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −612.000 | − | 612.000i | −1.38551 | − | 1.38551i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 952.000 | 1.99821 | 0.999107 | − | 0.0422409i | \(-0.0134497\pi\) | ||||
0.999107 | + | 0.0422409i | \(0.0134497\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 639.000 | + | 639.000i | 1.27788 | + | 1.27788i | ||||
\(64\) | 512.000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 549.000 | − | 549.000i | 1.00106 | − | 1.00106i | 0.00106064 | − | 0.999999i | \(-0.499662\pi\) |
0.999999 | − | 0.00106064i | \(-0.000337611\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 938.000i | 1.63655i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 1136.00 | − | 1136.00i | 1.85943 | − | 1.85943i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2395.00 | −3.28532 | ||||||||
\(82\) | 504.000 | − | 504.000i | 0.678750 | − | 0.678750i | ||||
\(83\) | −77.0000 | − | 77.0000i | −0.101829 | − | 0.101829i | 0.654357 | − | 0.756186i | \(-0.272940\pi\) |
−0.756186 | + | 0.654357i | \(0.772940\pi\) | |||||||
\(84\) | 1008.00i | 1.30931i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1188.00 | −1.48960 | ||||||||
\(87\) | −2142.00 | + | 2142.00i | −2.63961 | + | 2.63961i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1386.00i | − | 1.65074i | −0.564593 | − | 0.825369i | \(-0.690967\pi\) | ||
0.564593 | − | 0.825369i | \(-0.309033\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −536.000 | + | 536.000i | −0.607412 | + | 0.607412i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1204.00i | 1.32110i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1792.00 | 1.90516 | ||||||||
\(97\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | 362.000 | + | 362.000i | 0.373138 | + | 0.373138i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −378.000 | −0.372400 | −0.186200 | − | 0.982512i | \(-0.559617\pi\) | ||||
−0.186200 | + | 0.982512i | \(0.559617\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1323.00 | + | 1323.00i | 1.26562 | + | 1.26562i | 0.948327 | + | 0.317295i | \(0.102775\pi\) |
0.317295 | + | 0.948327i | \(0.397225\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −221.000 | + | 221.000i | −0.199672 | + | 0.199672i | −0.799859 | − | 0.600188i | \(-0.795093\pi\) |
0.600188 | + | 0.799859i | \(0.295093\pi\) | |||||||
\(108\) | −2464.00 | − | 2464.00i | −2.19536 | − | 2.19536i | ||||
\(109\) | − | 1136.00i | − | 0.998248i | −0.866530 | − | 0.499124i | \(-0.833655\pi\) | ||
0.866530 | − | 0.499124i | \(-0.166345\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −576.000 | + | 576.000i | −0.485954 | + | 0.485954i | ||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2448.00 | −1.95941 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1331.00 | 1.00000 | ||||||||
\(122\) | 1904.00 | − | 1904.00i | 1.41295 | − | 1.41295i | ||||
\(123\) | −1764.00 | − | 1764.00i | −1.29313 | − | 1.29313i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2556.00 | 1.80720 | ||||||||
\(127\) | 1089.00 | − | 1089.00i | 0.760891 | − | 0.760891i | −0.215593 | − | 0.976483i | \(-0.569168\pi\) |
0.976483 | + | 0.215593i | \(0.0691683\pi\) | |||||||
\(128\) | 1024.00 | + | 1024.00i | 0.707107 | + | 0.707107i | ||||
\(129\) | 4158.00i | 2.83792i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2196.00i | − | 1.41571i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(138\) | 1876.00 | + | 1876.00i | 1.15722 | + | 1.15722i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4214.00 | 2.51690 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 4544.00i | − | 2.62963i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1267.00 | − | 1267.00i | 0.710887 | − | 0.710887i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 3096.00i | − | 1.70224i | −0.524969 | − | 0.851121i | \(-0.675923\pi\) | ||
0.524969 | − | 0.851121i | \(-0.324077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1206.00 | −0.590349 | ||||||||
\(162\) | −4790.00 | + | 4790.00i | −2.32307 | + | 2.32307i | ||||
\(163\) | 2943.00 | + | 2943.00i | 1.41419 | + | 1.41419i | 0.710858 | + | 0.703336i | \(0.248307\pi\) |
0.703336 | + | 0.710858i | \(0.251693\pi\) | |||||||
\(164\) | − | 2016.00i | − | 0.959897i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −308.000 | −0.144009 | ||||||||
\(167\) | 1309.00 | − | 1309.00i | 0.606548 | − | 0.606548i | −0.335494 | − | 0.942042i | \(-0.608903\pi\) |
0.942042 | + | 0.335494i | \(0.108903\pi\) | |||||||
\(168\) | 2016.00 | + | 2016.00i | 0.925820 | + | 0.925820i | ||||
\(169\) | 2197.00i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2376.00 | + | 2376.00i | −1.05330 | + | 1.05330i | ||||
\(173\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(174\) | 8568.00i | 3.73298i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2772.00 | − | 2772.00i | −1.16725 | − | 1.16725i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1078.00 | −0.442691 | −0.221346 | − | 0.975195i | \(-0.571045\pi\) | ||||
−0.221346 | + | 0.975195i | \(0.571045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6664.00 | − | 6664.00i | −2.69190 | − | 2.69190i | ||||
\(184\) | 2144.00i | 0.859010i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2408.00 | + | 2408.00i | 0.934157 | + | 0.934157i | ||||
\(189\) | − | 5544.00i | − | 2.13369i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 3584.00 | − | 3584.00i | 1.34715 | − | 1.34715i | ||||
\(193\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1448.00 | 0.527697 | ||||||||
\(197\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7686.00 | −2.69716 | ||||||||
\(202\) | −756.000 | + | 756.000i | −0.263327 | + | 0.263327i | ||||
\(203\) | −2754.00 | − | 2754.00i | −0.952182 | − | 0.952182i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5292.00 | 1.78986 | ||||||||
\(207\) | 4757.00 | − | 4757.00i | 1.59727 | − | 1.59727i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 884.000i | 0.282378i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9856.00 | −3.10470 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2272.00 | − | 2272.00i | −0.705868 | − | 0.705868i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4473.00 | + | 4473.00i | 1.34320 | + | 1.34320i | 0.892851 | + | 0.450352i | \(0.148701\pi\) |
0.450352 | + | 0.892851i | \(0.351299\pi\) | |||||||
\(224\) | 2304.00i | 0.687243i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4081.00 | + | 4081.00i | −1.19324 | + | 1.19324i | −0.217088 | + | 0.976152i | \(0.569656\pi\) |
−0.976152 | + | 0.217088i | \(0.930344\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6874.00i | 1.98361i | 0.127761 | + | 0.991805i | \(0.459221\pi\) | ||||
−0.127761 | + | 0.991805i | \(0.540779\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4896.00 | + | 4896.00i | −1.38551 | + | 1.38551i | ||||
\(233\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1708.00 | −0.456523 | −0.228261 | − | 0.973600i | \(-0.573304\pi\) | ||||
−0.228261 | + | 0.973600i | \(0.573304\pi\) | |||||||
\(242\) | 2662.00 | − | 2662.00i | 0.707107 | − | 0.707107i | ||||
\(243\) | 8449.00 | + | 8449.00i | 2.23047 | + | 2.23047i | ||||
\(244\) | − | 7616.00i | − | 1.99821i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7056.00 | −1.82876 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1078.00i | 0.274359i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 5112.00 | − | 5112.00i | 1.27788 | − | 1.27788i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 4356.00i | − | 1.07606i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 8316.00 | + | 8316.00i | 2.00671 | + | 2.00671i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21726.0 | 5.15251 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6017.00 | − | 6017.00i | −1.41074 | − | 1.41074i | −0.754912 | − | 0.655826i | \(-0.772321\pi\) |
−0.655826 | − | 0.754912i | \(-0.727679\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9702.00 | + | 9702.00i | −2.22379 | + | 2.22379i | ||||
\(268\) | −4392.00 | − | 4392.00i | −1.00106 | − | 1.00106i | ||||
\(269\) | 5544.00i | 1.25659i | 0.777974 | + | 0.628297i | \(0.216248\pi\) | ||||
−0.777974 | + | 0.628297i | \(0.783752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7504.00 | 1.63655 | ||||||||
\(277\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8388.00 | −1.78073 | −0.890367 | − | 0.455244i | \(-0.849552\pi\) | ||||
−0.890367 | + | 0.455244i | \(0.849552\pi\) | |||||||
\(282\) | 8428.00 | − | 8428.00i | 1.77972 | − | 1.77972i | ||||
\(283\) | 693.000 | + | 693.000i | 0.145564 | + | 0.145564i | 0.776133 | − | 0.630569i | \(-0.217178\pi\) |
−0.630569 | + | 0.776133i | \(0.717178\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2268.00 | − | 2268.00i | 0.466466 | − | 0.466466i | ||||
\(288\) | −9088.00 | − | 9088.00i | −1.85943 | − | 1.85943i | ||||
\(289\) | − | 4913.00i | − | 1.00000i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | − | 5068.00i | − | 1.00535i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6192.00 | − | 6192.00i | −1.20367 | − | 1.20367i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5346.00 | −1.02372 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2646.00 | + | 2646.00i | 0.501679 | + | 0.501679i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2709.00 | − | 2709.00i | 0.503618 | − | 0.503618i | −0.408942 | − | 0.912560i | \(-0.634102\pi\) |
0.912560 | + | 0.408942i | \(0.134102\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 18522.0i | − | 3.40997i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3094.00 | 0.537976 | ||||||||
\(322\) | −2412.00 | + | 2412.00i | −0.417439 | + | 0.417439i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 19160.0i | 3.28532i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11772.0 | 1.99997 | ||||||||
\(327\) | −7952.00 | + | 7952.00i | −1.34479 | + | 1.34479i | ||||
\(328\) | −4032.00 | − | 4032.00i | −0.678750 | − | 0.678750i | ||||
\(329\) | 5418.00i | 0.907915i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | −616.000 | + | 616.000i | −0.101829 | + | 0.101829i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 5236.00i | − | 0.857788i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8064.00 | 1.30931 | ||||||||
\(337\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(338\) | 4394.00 | + | 4394.00i | 0.707107 | + | 0.707107i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4716.00 | + | 4716.00i | 0.742391 | + | 0.742391i | ||||
\(344\) | 9504.00i | 1.48960i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7871.00 | + | 7871.00i | −1.21769 | + | 1.21769i | −0.249247 | + | 0.968440i | \(0.580183\pi\) |
−0.968440 | + | 0.249247i | \(0.919817\pi\) | |||||||
\(348\) | 17136.0 | + | 17136.0i | 2.63961 | + | 2.63961i | ||||
\(349\) | − | 9646.00i | − | 1.47948i | −0.672893 | − | 0.739740i | \(-0.734948\pi\) | ||
0.672893 | − | 0.739740i | \(-0.265052\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −11088.0 | −1.65074 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6859.00 | −1.00000 | ||||||||
\(362\) | −2156.00 | + | 2156.00i | −0.313030 | + | 0.313030i | ||||
\(363\) | −9317.00 | − | 9317.00i | −1.34715 | − | 1.34715i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −26656.0 | −3.80692 | ||||||||
\(367\) | 9639.00 | − | 9639.00i | 1.37099 | − | 1.37099i | 0.512000 | − | 0.858985i | \(-0.328905\pi\) |
0.858985 | − | 0.512000i | \(-0.171095\pi\) | |||||||
\(368\) | 4288.00 | + | 4288.00i | 0.607412 | + | 0.607412i | ||||
\(369\) | 17892.0i | 2.52417i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9632.00 | 1.32110 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −11088.0 | − | 11088.0i | −1.50874 | − | 1.50874i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15246.0 | −2.05007 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8113.00 | + | 8113.00i | 1.08239 | + | 1.08239i | 0.996286 | + | 0.0861026i | \(0.0274413\pi\) |
0.0861026 | + | 0.996286i | \(0.472559\pi\) | |||||||
\(384\) | − | 14336.0i | − | 1.90516i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21087.0 | − | 21087.0i | 2.76980 | − | 2.76980i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14184.0i | 1.84873i | 0.381505 | + | 0.924367i | \(0.375406\pi\) | ||||
−0.381505 | + | 0.924367i | \(0.624594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2896.00 | − | 2896.00i | 0.373138 | − | 0.373138i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15822.0 | 1.97036 | 0.985178 | − | 0.171534i | \(-0.0548722\pi\) | ||||
0.985178 | + | 0.171534i | \(0.0548722\pi\) | |||||||
\(402\) | −15372.0 | + | 15372.0i | −1.90718 | + | 1.90718i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3024.00i | 0.372400i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11016.0 | −1.34659 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4844.00i | 0.585624i | 0.956170 | + | 0.292812i | \(0.0945911\pi\) | ||||
−0.956170 | + | 0.292812i | \(0.905409\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10584.0 | − | 10584.0i | 1.26562 | − | 1.26562i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 19028.0i | − | 2.25888i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9592.00 | 1.11042 | 0.555208 | − | 0.831711i | \(-0.312638\pi\) | ||||
0.555208 | + | 0.831711i | \(0.312638\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21371.0 | − | 21371.0i | −2.45649 | − | 2.45649i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8568.00 | − | 8568.00i | 0.971041 | − | 0.971041i | ||||
\(428\) | 1768.00 | + | 1768.00i | 0.199672 | + | 0.199672i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | −19712.0 | + | 19712.0i | −2.19536 | + | 2.19536i | ||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9088.00 | −0.998248 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12851.0 | −1.38765 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10237.0 | − | 10237.0i | −1.09791 | − | 1.09791i | −0.994655 | − | 0.103256i | \(-0.967074\pi\) |
−0.103256 | − | 0.994655i | \(-0.532926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17892.0 | 1.89958 | ||||||||
\(447\) | −21672.0 | + | 21672.0i | −2.29318 | + | 2.29318i | ||||
\(448\) | 4608.00 | + | 4608.00i | 0.485954 | + | 0.485954i | ||||
\(449\) | − | 1836.00i | − | 0.192976i | −0.995334 | − | 0.0964880i | \(-0.969239\pi\) | ||
0.995334 | − | 0.0964880i | \(-0.0307609\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16324.0i | 1.68750i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(458\) | 13748.0 | + | 13748.0i | 1.40262 | + | 1.40262i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16002.0 | 1.61668 | 0.808338 | − | 0.588719i | \(-0.200368\pi\) | ||||
0.808338 | + | 0.588719i | \(0.200368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11043.0 | + | 11043.0i | 1.10845 | + | 1.10845i | 0.993355 | + | 0.115094i | \(0.0367169\pi\) |
0.115094 | + | 0.993355i | \(0.463283\pi\) | |||||||
\(464\) | 19584.0i | 1.95941i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7889.00 | − | 7889.00i | 0.781712 | − | 0.781712i | −0.198408 | − | 0.980120i | \(-0.563577\pi\) |
0.980120 | + | 0.198408i | \(0.0635770\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9882.00i | − | 0.972939i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −3416.00 | + | 3416.00i | −0.322810 | + | 0.322810i | ||||
\(483\) | 8442.00 | + | 8442.00i | 0.795288 | + | 0.795288i | ||||
\(484\) | − | 10648.0i | − | 1.00000i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 33796.0 | 3.15436 | ||||||||
\(487\) | −81.0000 | + | 81.0000i | −0.00753688 | + | 0.00753688i | −0.710865 | − | 0.703328i | \(-0.751696\pi\) |
0.703328 | + | 0.710865i | \(0.251696\pi\) | |||||||
\(488\) | −15232.0 | − | 15232.0i | −1.41295 | − | 1.41295i | ||||
\(489\) | − | 41202.0i | − | 3.81026i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | −14112.0 | + | 14112.0i | −1.29313 | + | 1.29313i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2156.00 | + | 2156.00i | 0.194001 | + | 0.194001i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18326.0 | −1.63422 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12803.0 | + | 12803.0i | 1.13491 | + | 1.13491i | 0.989350 | + | 0.145556i | \(0.0464970\pi\) |
0.145556 | + | 0.989350i | \(0.453503\pi\) | |||||||
\(504\) | − | 20448.0i | − | 1.80720i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15379.0 | − | 15379.0i | 1.34715 | − | 1.34715i | ||||
\(508\) | −8712.00 | − | 8712.00i | −0.760891 | − | 0.760891i | ||||
\(509\) | − | 8946.00i | − | 0.779026i | −0.921021 | − | 0.389513i | \(-0.872643\pi\) | ||
0.921021 | − | 0.389513i | \(-0.127357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8192.00 | − | 8192.00i | 0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 33264.0 | 2.83792 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8442.00 | 0.709886 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(522\) | 43452.0 | − | 43452.0i | 3.64338 | − | 3.64338i | ||||
\(523\) | −14427.0 | − | 14427.0i | −1.20621 | − | 1.20621i | −0.972245 | − | 0.233967i | \(-0.924829\pi\) |
−0.233967 | − | 0.972245i | \(-0.575171\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24068.0 | −1.99508 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 3189.00i | − | 0.262102i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 38808.0i | 3.14492i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −17568.0 | −1.41571 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11088.0 | + | 11088.0i | 0.888546 | + | 0.888546i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6802.00 | 0.540556 | 0.270278 | − | 0.962782i | \(-0.412884\pi\) | ||||
0.270278 | + | 0.962782i | \(0.412884\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7546.00 | + | 7546.00i | 0.596372 | + | 0.596372i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17721.0 | + | 17721.0i | −1.38518 | + | 1.38518i | −0.550055 | + | 0.835129i | \(0.685393\pi\) |
−0.835129 | + | 0.550055i | \(0.814607\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 67592.0i | 5.25457i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 15008.0 | − | 15008.0i | 1.15722 | − | 1.15722i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16776.0 | + | 16776.0i | −1.25917 | + | 1.25917i | ||||
\(563\) | −1687.00 | − | 1687.00i | −0.126285 | − | 0.126285i | 0.641139 | − | 0.767425i | \(-0.278462\pi\) |
−0.767425 | + | 0.641139i | \(0.778462\pi\) | |||||||
\(564\) | − | 33712.0i | − | 2.51690i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2772.00 | 0.205858 | ||||||||
\(567\) | −21555.0 | + | 21555.0i | −1.59652 | + | 1.59652i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 14796.0i | − | 1.09012i | −0.838396 | − | 0.545062i | \(-0.816506\pi\) | ||
0.838396 | − | 0.545062i | \(-0.183494\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 9072.00i | − | 0.659683i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −36352.0 | −2.62963 | ||||||||
\(577\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(578\) | −9826.00 | − | 9826.00i | −0.707107 | − | 0.707107i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1386.00 | −0.0989690 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11641.0 | + | 11641.0i | −0.818527 | + | 0.818527i | −0.985895 | − | 0.167367i | \(-0.946473\pi\) |
0.167367 | + | 0.985895i | \(0.446473\pi\) | |||||||
\(588\) | −10136.0 | − | 10136.0i | −0.710887 | − | 0.710887i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −24768.0 | −1.70224 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28532.0 | 1.93651 | 0.968257 | − | 0.249958i | \(-0.0804168\pi\) | ||||
0.968257 | + | 0.249958i | \(0.0804168\pi\) | |||||||
\(602\) | −10692.0 | + | 10692.0i | −0.723876 | + | 0.723876i | ||||
\(603\) | 38979.0 | + | 38979.0i | 2.63242 | + | 2.63242i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10584.0 | 0.709481 | ||||||||
\(607\) | −11781.0 | + | 11781.0i | −0.787769 | + | 0.787769i | −0.981128 | − | 0.193359i | \(-0.938062\pi\) |
0.193359 | + | 0.981128i | \(0.438062\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 38556.0i | 2.56546i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(614\) | − | 10836.0i | − | 0.712224i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(618\) | −37044.0 | − | 37044.0i | −2.41121 | − | 2.41121i | ||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −41272.0 | −2.66697 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12474.0 | − | 12474.0i | −0.802183 | − | 0.802183i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21348.0 | −1.31544 | −0.657719 | − | 0.753264i | \(-0.728478\pi\) | ||||
−0.657719 | + | 0.753264i | \(0.728478\pi\) | |||||||
\(642\) | 6188.00 | − | 6188.00i | 0.380406 | − | 0.380406i | ||||
\(643\) | −21987.0 | − | 21987.0i | −1.34850 | − | 1.34850i | −0.887297 | − | 0.461199i | \(-0.847420\pi\) |
−0.461199 | − | 0.887297i | \(-0.652580\pi\) | |||||||
\(644\) | 9648.00i | 0.590349i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20839.0 | − | 20839.0i | 1.26625 | − | 1.26625i | 0.318244 | − | 0.948009i | \(-0.396907\pi\) |
0.948009 | − | 0.318244i | \(-0.103093\pi\) | |||||||
\(648\) | 38320.0 | + | 38320.0i | 2.32307 | + | 2.32307i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23544.0 | − | 23544.0i | 1.41419 | − | 1.41419i | ||||
\(653\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(654\) | 31808.0i | 1.90182i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −16128.0 | −0.959897 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10836.0 | + | 10836.0i | 0.641993 | + | 0.641993i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30688.0 | −1.80579 | −0.902893 | − | 0.429865i | \(-0.858561\pi\) | ||||
−0.902893 | + | 0.429865i | \(0.858561\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2464.00i | 0.144009i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20502.0 | + | 20502.0i | −1.19017 | + | 1.19017i | ||||
\(668\) | −10472.0 | − | 10472.0i | −0.606548 | − | 0.606548i | ||||
\(669\) | − | 62622.0i | − | 3.61899i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 16128.0 | − | 16128.0i | 0.925820 | − | 0.925820i | ||||
\(673\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17576.0 | 1.00000 | ||||||||
\(677\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 57134.0 | 3.21495 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3937.00 | − | 3937.00i | −0.220564 | − | 0.220564i | 0.588172 | − | 0.808736i | \(-0.299848\pi\) |
−0.808736 | + | 0.588172i | \(0.799848\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18864.0 | 1.04990 | ||||||||
\(687\) | 48118.0 | − | 48118.0i | 2.67222 | − | 2.67222i | ||||
\(688\) | 19008.0 | + | 19008.0i | 1.05330 | + | 1.05330i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31484.0i | 1.72207i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 68544.0 | 3.73298 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −19292.0 | − | 19292.0i | −1.04615 | − | 1.04615i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9648.00 | −0.519829 | −0.259914 | − | 0.965632i | \(-0.583694\pi\) | ||||
−0.259914 | + | 0.965632i | \(0.583694\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3402.00 | + | 3402.00i | −0.180969 | + | 0.180969i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 506.000i | − | 0.0268029i | −0.999910 | − | 0.0134014i | \(-0.995734\pi\) | ||
0.999910 | − | 0.0134014i | \(-0.00426594\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −22176.0 | + | 22176.0i | −1.16725 | + | 1.16725i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23814.0 | 1.23007 | ||||||||
\(722\) | −13718.0 | + | 13718.0i | −0.707107 | + | 0.707107i | ||||
\(723\) | 11956.0 | + | 11956.0i | 0.615005 | + | 0.615005i | ||||
\(724\) | 8624.00i | 0.442691i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −37268.0 | −1.90516 | ||||||||
\(727\) | 6489.00 | − | 6489.00i | 0.331037 | − | 0.331037i | −0.521943 | − | 0.852980i | \(-0.674793\pi\) |
0.852980 | + | 0.521943i | \(0.174793\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 53621.0i | − | 2.72423i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −53312.0 | + | 53312.0i | −2.69190 | + | 2.69190i | ||||
\(733\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(734\) | − | 38556.0i | − | 1.93887i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17152.0 | 0.859010 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 35784.0 | + | 35784.0i | 1.78486 | + | 1.78486i | ||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28633.0 | + | 28633.0i | 1.41379 | + | 1.41379i | 0.724282 | + | 0.689504i | \(0.242171\pi\) |
0.689504 | + | 0.724282i | \(0.257829\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5467.00 | − | 5467.00i | 0.267774 | − | 0.267774i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3978.00i | 0.194063i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 19264.0 | − | 19264.0i | 0.934157 | − | 0.934157i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −44352.0 | −2.13369 | ||||||||
\(757\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21798.0 | −1.03834 | −0.519170 | − | 0.854671i | \(-0.673759\pi\) | ||||
−0.519170 | + | 0.854671i | \(0.673759\pi\) | |||||||
\(762\) | −30492.0 | + | 30492.0i | −1.44962 | + | 1.44962i | ||||
\(763\) | −10224.0 | − | 10224.0i | −0.485103 | − | 0.485103i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32452.0 | 1.53073 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −28672.0 | − | 28672.0i | −1.34715 | − | 1.34715i | ||||
\(769\) | 29554.0i | 1.38588i | 0.720994 | + | 0.692942i | \(0.243686\pi\) | ||||
−0.720994 | + | 0.692942i | \(0.756314\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(774\) | − | 84348.0i | − | 3.91709i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28368.0 | + | 28368.0i | 1.30725 | + | 1.30725i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −94248.0 | − | 94248.0i | −4.30159 | − | 4.30159i | ||||
\(784\) | − | 11584.0i | − | 0.527697i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24381.0 | + | 24381.0i | −1.10431 | + | 1.10431i | −0.110421 | + | 0.993885i | \(0.535220\pi\) |
−0.993885 | + | 0.110421i | \(0.964780\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 84238.0i | 3.80095i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 98406.0 | 4.34083 | ||||||||
\(802\) | 31644.0 | − | 31644.0i | 1.39325 | − | 1.39325i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 61488.0i | 2.69716i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38808.0 | − | 38808.0i | 1.69282 | − | 1.69282i | ||||
\(808\) | 6048.00 | + | 6048.00i | 0.263327 | + | 0.263327i | ||||
\(809\) | − | 26406.0i | − | 1.14757i | −0.819005 | − | 0.573786i | \(-0.805474\pi\) | ||
0.819005 | − | 0.573786i | \(-0.194526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −22032.0 | + | 22032.0i | −0.952182 | + | 0.952182i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 9688.00 | + | 9688.00i | 0.414099 | + | 0.414099i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7632.00 | 0.324432 | 0.162216 | − | 0.986755i | \(-0.448136\pi\) | ||||
0.162216 | + | 0.986755i | \(0.448136\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22347.0 | − | 22347.0i | −0.946498 | − | 0.946498i | 0.0521422 | − | 0.998640i | \(-0.483395\pi\) |
−0.998640 | + | 0.0521422i | \(0.983395\pi\) | |||||||
\(824\) | − | 42336.0i | − | 1.78986i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32729.0 | − | 32729.0i | 1.37618 | − | 1.37618i | 0.525197 | − | 0.850981i | \(-0.323992\pi\) |
0.850981 | − | 0.525197i | \(-0.176008\pi\) | |||||||
\(828\) | −38056.0 | − | 38056.0i | −1.59727 | − | 1.59727i | ||||
\(829\) | 36344.0i | 1.52265i | 0.648369 | + | 0.761326i | \(0.275452\pi\) | ||||
−0.648369 | + | 0.761326i | \(0.724548\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −69247.0 | −2.83927 | ||||||||
\(842\) | 19184.0 | − | 19184.0i | 0.785183 | − | 0.785183i | ||||
\(843\) | 58716.0 | + | 58716.0i | 2.39892 | + | 2.39892i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −85484.0 | −3.47400 | ||||||||
\(847\) | 11979.0 | − | 11979.0i | 0.485954 | − | 0.485954i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 9702.00i | − | 0.392193i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(854\) | − | 34272.0i | − | 1.37326i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7072.00 | 0.282378 | ||||||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −31752.0 | −1.25680 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31693.0 | + | 31693.0i | 1.25011 | + | 1.25011i | 0.955671 | + | 0.294436i | \(0.0951316\pi\) |
0.294436 | + | 0.955671i | \(0.404868\pi\) | |||||||
\(864\) | 78848.0i | 3.10470i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34391.0 | + | 34391.0i | −1.34715 | + | 1.34715i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −18176.0 | + | 18176.0i | −0.705868 | + | 0.705868i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29988.0 | −1.14679 | −0.573395 | − | 0.819279i | \(-0.694374\pi\) | ||||
−0.573395 | + | 0.819279i | \(0.694374\pi\) | |||||||
\(882\) | −25702.0 | + | 25702.0i | −0.981215 | + | 0.981215i | ||||
\(883\) | −15327.0 | − | 15327.0i | −0.584139 | − | 0.584139i | 0.351899 | − | 0.936038i | \(-0.385536\pi\) |
−0.936038 | + | 0.351899i | \(0.885536\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40948.0 | −1.55268 | ||||||||
\(887\) | 2849.00 | − | 2849.00i | 0.107847 | − | 0.107847i | −0.651124 | − | 0.758971i | \(-0.725702\pi\) |
0.758971 | + | 0.651124i | \(0.225702\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 19602.0i | − | 0.739516i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 35784.0 | − | 35784.0i | 1.34320 | − | 1.34320i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 86688.0i | 3.24304i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 18432.0 | 0.687243 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3672.00 | − | 3672.00i | −0.136455 | − | 0.136455i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37422.0 | + | 37422.0i | 1.37910 | + | 1.37910i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8109.00 | − | 8109.00i | 0.296863 | − | 0.296863i | −0.542921 | − | 0.839784i | \(-0.682682\pi\) |
0.839784 | + | 0.542921i | \(0.182682\pi\) | |||||||
\(908\) | 32648.0 | + | 32648.0i | 1.19324 | + | 1.19324i | ||||
\(909\) | − | 26838.0i | − | 0.979274i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 54992.0 | 1.98361 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −37926.0 | −1.35690 | ||||||||
\(922\) | 32004.0 | − | 32004.0i | 1.14316 | − | 1.14316i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 44172.0 | 1.56758 | ||||||||
\(927\) | −93933.0 | + | 93933.0i | −3.32812 | + | 3.32812i | ||||
\(928\) | 39168.0 | + | 39168.0i | 1.38551 | + | 1.38551i | ||||
\(929\) | − | 53676.0i | − | 1.89564i | −0.318801 | − | 0.947822i | \(-0.603280\pi\) | ||
0.318801 | − | 0.947822i | \(-0.396720\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 31556.0i | − | 1.10551i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | −19764.0 | − | 19764.0i | −0.687972 | − | 0.687972i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44478.0 | −1.54085 | −0.770426 | − | 0.637530i | \(-0.779956\pi\) | ||||
−0.770426 | + | 0.637530i | \(0.779956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16884.0 | − | 16884.0i | −0.583053 | − | 0.583053i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36851.0 | + | 36851.0i | −1.26452 | + | 1.26452i | −0.315635 | + | 0.948881i | \(0.602218\pi\) |
−0.948881 | + | 0.315635i | \(0.897782\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29791.0 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15691.0 | − | 15691.0i | −0.525063 | − | 0.525063i | ||||
\(964\) | 13664.0i | 0.456523i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 33768.0 | 1.12471 | ||||||||
\(967\) | 23859.0 | − | 23859.0i | 0.793437 | − | 0.793437i | −0.188614 | − | 0.982051i | \(-0.560400\pi\) |
0.982051 | + | 0.188614i | \(0.0603995\pi\) | |||||||
\(968\) | −21296.0 | − | 21296.0i | −0.707107 | − | 0.707107i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 67592.0 | − | 67592.0i | 2.23047 | − | 2.23047i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 324.000i | 0.0106588i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −60928.0 | −1.99821 | ||||||||
\(977\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | −82404.0 | − | 82404.0i | −2.69426 | − | 2.69426i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 80656.0 | 2.62502 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36743.0 | + | 36743.0i | 1.19219 | + | 1.19219i | 0.976452 | + | 0.215735i | \(0.0692147\pi\) |
0.215735 | + | 0.976452i | \(0.430785\pi\) | |||||||
\(984\) | 56448.0i | 1.82876i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 37926.0 | − | 37926.0i | 1.22310 | − | 1.22310i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39798.0i | 1.27958i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8624.00 | 0.274359 | ||||||||
\(997\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(998\) | 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 | 100.4.e.c.7.1 | yes | 2 | |
4.3 | odd | 2 | 100.4.e.b.7.1 | ✓ | 2 | ||
5.2 | odd | 4 | inner | 100.4.e.c.43.1 | yes | 2 | |
5.3 | odd | 4 | 100.4.e.b.43.1 | yes | 2 | ||
5.4 | even | 2 | 100.4.e.b.7.1 | ✓ | 2 | ||
20.3 | even | 4 | inner | 100.4.e.c.43.1 | yes | 2 | |
20.7 | even | 4 | 100.4.e.b.43.1 | yes | 2 | ||
20.19 | odd | 2 | CM | 100.4.e.c.7.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.4.e.b.7.1 | ✓ | 2 | 4.3 | odd | 2 | ||
100.4.e.b.7.1 | ✓ | 2 | 5.4 | even | 2 | ||
100.4.e.b.43.1 | yes | 2 | 5.3 | odd | 4 | ||
100.4.e.b.43.1 | yes | 2 | 20.7 | even | 4 | ||
100.4.e.c.7.1 | yes | 2 | 1.1 | even | 1 | trivial | |
100.4.e.c.7.1 | yes | 2 | 20.19 | odd | 2 | CM | |
100.4.e.c.43.1 | yes | 2 | 5.2 | odd | 4 | inner | |
100.4.e.c.43.1 | yes | 2 | 20.3 | even | 4 | inner |