Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,2,Mod(43,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.k (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: | \(1.59700804043\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 9 \)
|
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 | 43.2 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.43 |
Dual form | 200.2.k.e.107.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.707107 | + | 0.707107i | ||||
\(3\) | 2.22474 | + | 2.22474i | 1.28446 | + | 1.28446i | 0.938104 | + | 0.346353i | \(0.112580\pi\) |
0.346353 | + | 0.938104i | \(0.387420\pi\) | |||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.44949 | −1.81650 | ||||||||
\(7\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 6.89898i | 2.29966i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.550510 | 0.165985 | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) | ||||
0.0829925 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(12\) | 4.44949 | − | 4.44949i | 1.28446 | − | 1.28446i | ||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −1.67423 | + | 1.67423i | −0.406062 | + | 0.406062i | −0.880363 | − | 0.474301i | \(-0.842701\pi\) |
0.474301 | + | 0.880363i | \(0.342701\pi\) | |||||||
\(18\) | −6.89898 | − | 6.89898i | −1.62611 | − | 1.62611i | ||||
\(19\) | − | 8.34847i | − | 1.91527i | −0.287984 | − | 0.957635i | \(-0.592985\pi\) | ||
0.287984 | − | 0.957635i | \(-0.407015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.550510 | + | 0.550510i | −0.117369 | + | 0.117369i | ||||
\(23\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(24\) | 8.89898i | 1.81650i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.67423 | + | 8.67423i | −1.66936 | + | 1.66936i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 4.00000 | − | 4.00000i | 0.707107 | − | 0.707107i | ||||
\(33\) | 1.22474 | + | 1.22474i | 0.213201 | + | 0.213201i | ||||
\(34\) | − | 3.34847i | − | 0.574258i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 13.7980 | 2.29966 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 8.34847 | + | 8.34847i | 1.35430 | + | 1.35430i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.7980 | 1.99871 | 0.999353 | − | 0.0359748i | \(-0.0114536\pi\) | ||||
0.999353 | + | 0.0359748i | \(0.0114536\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | − | 6.00000i | −0.914991 | − | 0.914991i | 0.0816682 | − | 0.996660i | \(-0.473975\pi\) |
−0.996660 | + | 0.0816682i | \(0.973975\pi\) | |||||||
\(44\) | − | 1.10102i | − | 0.165985i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | −8.89898 | − | 8.89898i | −1.28446 | − | 1.28446i | ||||
\(49\) | − | 7.00000i | − | 1.00000i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.44949 | −1.04314 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | − | 17.3485i | − | 2.36083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.5732 | − | 18.5732i | 2.46008 | − | 2.46008i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000i | 0.781133i | 0.920575 | + | 0.390567i | \(0.127721\pi\) | ||||
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.44949 | −0.301511 | ||||||||
\(67\) | 5.57321 | − | 5.57321i | 0.680876 | − | 0.680876i | −0.279321 | − | 0.960198i | \(-0.590109\pi\) |
0.960198 | + | 0.279321i | \(0.0901094\pi\) | |||||||
\(68\) | 3.34847 | + | 3.34847i | 0.406062 | + | 0.406062i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −13.7980 | + | 13.7980i | −1.62611 | + | 1.62611i | ||||
\(73\) | 7.22474 | + | 7.22474i | 0.845592 | + | 0.845592i | 0.989580 | − | 0.143987i | \(-0.0459924\pi\) |
−0.143987 | + | 0.989580i | \(0.545992\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −16.6969 | −1.91527 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −17.8990 | −1.98878 | ||||||||
\(82\) | −12.7980 | + | 12.7980i | −1.41330 | + | 1.41330i | ||||
\(83\) | −10.0227 | − | 10.0227i | −1.10013 | − | 1.10013i | −0.994394 | − | 0.105741i | \(-0.966279\pi\) |
−0.105741 | − | 0.994394i | \(-0.533721\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.0000 | 1.29399 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.10102 | + | 1.10102i | 0.117369 | + | 0.117369i | ||||
\(89\) | 13.8990i | 1.47329i | 0.676280 | + | 0.736644i | \(0.263591\pi\) | ||||
−0.676280 | + | 0.736644i | \(0.736409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 17.7980 | 1.81650 | ||||||||
\(97\) | −12.0000 | + | 12.0000i | −1.21842 | + | 1.21842i | −0.250229 | + | 0.968187i | \(0.580506\pi\) |
−0.968187 | + | 0.250229i | \(0.919494\pi\) | |||||||
\(98\) | 7.00000 | + | 7.00000i | 0.707107 | + | 0.707107i | ||||
\(99\) | 3.79796i | 0.381709i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 7.44949 | − | 7.44949i | 0.737609 | − | 0.737609i | ||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.32577 | − | 3.32577i | 0.321514 | − | 0.321514i | −0.527834 | − | 0.849348i | \(-0.676996\pi\) |
0.849348 | + | 0.527834i | \(0.176996\pi\) | |||||||
\(108\) | 17.3485 | + | 17.3485i | 1.66936 | + | 1.66936i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0227 | − | 15.0227i | −1.41322 | − | 1.41322i | −0.733148 | − | 0.680069i | \(-0.761950\pi\) |
−0.680069 | − | 0.733148i | \(-0.738050\pi\) | |||||||
\(114\) | 37.1464i | 3.47908i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.00000 | − | 6.00000i | −0.552345 | − | 0.552345i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6969 | −0.972449 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.4722 | + | 28.4722i | 2.56725 | + | 2.56725i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.707107 | − | 0.707107i | ||||
\(129\) | − | 26.6969i | − | 2.35053i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0000 | −1.57267 | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 2.44949 | − | 2.44949i | 0.213201 | − | 0.213201i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.1464i | 0.962905i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.69694 | −0.574258 | ||||||||
\(137\) | −11.6742 | + | 11.6742i | −0.997397 | + | 0.997397i | −0.999997 | − | 0.00259945i | \(-0.999173\pi\) |
0.00259945 | + | 0.999997i | \(0.499173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 18.3485i | − | 1.55630i | −0.628080 | − | 0.778148i | \(-0.716159\pi\) | ||
0.628080 | − | 0.778148i | \(-0.283841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 27.5959i | − | 2.29966i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.4495 | −1.19585 | ||||||||
\(147\) | 15.5732 | − | 15.5732i | 1.28446 | − | 1.28446i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 16.6969 | − | 16.6969i | 1.35430 | − | 1.35430i | ||||
\(153\) | −11.5505 | − | 11.5505i | −0.933803 | − | 0.933803i | ||||
\(154\) | 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 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 17.8990 | − | 17.8990i | 1.40628 | − | 1.40628i | ||||
\(163\) | −7.77526 | − | 7.77526i | −0.609005 | − | 0.609005i | 0.333681 | − | 0.942686i | \(-0.391709\pi\) |
−0.942686 | + | 0.333681i | \(0.891709\pi\) | |||||||
\(164\) | − | 25.5959i | − | 1.99871i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 20.0454 | 1.55583 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 57.5959 | 4.40447 | ||||||||
\(172\) | −12.0000 | + | 12.0000i | −0.914991 | + | 0.914991i | ||||
\(173\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.20204 | −0.165985 | ||||||||
\(177\) | −13.3485 | + | 13.3485i | −1.00333 | + | 1.00333i | ||||
\(178\) | −13.8990 | − | 13.8990i | −1.04177 | − | 1.04177i | ||||
\(179\) | 26.1464i | 1.95428i | 0.212607 | + | 0.977138i | \(0.431805\pi\) | ||||
−0.212607 | + | 0.977138i | \(0.568195\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.921683 | + | 0.921683i | −0.0674002 | + | 0.0674002i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | −17.7980 | + | 17.7980i | −1.28446 | + | 1.28446i | ||||
\(193\) | 19.4722 | + | 19.4722i | 1.40164 | + | 1.40164i | 0.794904 | + | 0.606735i | \(0.207521\pi\) |
0.606735 | + | 0.794904i | \(0.292479\pi\) | |||||||
\(194\) | − | 24.0000i | − | 1.72310i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −1.00000 | ||||||||
\(197\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | −3.79796 | − | 3.79796i | −0.269909 | − | 0.269909i | ||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.7980 | 1.74911 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 14.8990i | 1.04314i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.59592i | − | 0.317906i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.0454 | 1.03577 | 0.517884 | − | 0.855451i | \(-0.326720\pi\) | ||||
0.517884 | + | 0.855451i | \(0.326720\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.65153i | 0.454689i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −34.6969 | −2.36083 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 32.1464i | 2.17225i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 30.0454 | 1.99859 | ||||||||
\(227\) | −2.00000 | + | 2.00000i | −0.132745 | + | 0.132745i | −0.770357 | − | 0.637613i | \(-0.779922\pi\) |
0.637613 | + | 0.770357i | \(0.279922\pi\) | |||||||
\(228\) | −37.1464 | − | 37.1464i | −2.46008 | − | 2.46008i | ||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00000 | + | 4.00000i | 0.262049 | + | 0.262049i | 0.825886 | − | 0.563837i | \(-0.190675\pi\) |
−0.563837 | + | 0.825886i | \(0.690675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.69694 | −0.109309 | −0.0546547 | − | 0.998505i | \(-0.517406\pi\) | ||||
−0.0546547 | + | 0.998505i | \(0.517406\pi\) | |||||||
\(242\) | 10.6969 | − | 10.6969i | 0.687625 | − | 0.687625i | ||||
\(243\) | −13.7980 | − | 13.7980i | −0.885139 | − | 0.885139i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −56.9444 | −3.63064 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 44.5959i | − | 2.82615i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.9444 | −1.51136 | −0.755678 | − | 0.654943i | \(-0.772693\pi\) | ||||
−0.755678 | + | 0.654943i | \(0.772693\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 8.00000 | − | 8.00000i | 0.499026 | − | 0.499026i | −0.412108 | − | 0.911135i | \(-0.635208\pi\) |
0.911135 | + | 0.412108i | \(0.135208\pi\) | |||||||
\(258\) | 26.6969 | + | 26.6969i | 1.66208 | + | 1.66208i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.0000 | − | 18.0000i | 1.11204 | − | 1.11204i | ||||
\(263\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(264\) | 4.89898i | 0.301511i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −30.9217 | + | 30.9217i | −1.89238 | + | 1.89238i | ||||
\(268\) | −11.1464 | − | 11.1464i | −0.680876 | − | 0.680876i | ||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 6.69694 | − | 6.69694i | 0.406062 | − | 0.406062i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 23.3485i | − | 1.41053i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(278\) | 18.3485 | + | 18.3485i | 1.10047 | + | 1.10047i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.47219 | + | 4.47219i | 0.265844 | + | 0.265844i | 0.827423 | − | 0.561579i | \(-0.189806\pi\) |
−0.561579 | + | 0.827423i | \(0.689806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 27.5959 | + | 27.5959i | 1.62611 | + | 1.62611i | ||||
\(289\) | 11.3939i | 0.670228i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −53.3939 | −3.13000 | ||||||||
\(292\) | 14.4495 | − | 14.4495i | 0.845592 | − | 0.845592i | ||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | 31.1464i | 1.81650i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.77526 | + | 4.77526i | −0.277088 | + | 0.277088i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 33.3939i | 1.91527i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 23.1010 | 1.32060 | ||||||||
\(307\) | 17.8207 | − | 17.8207i | 1.01708 | − | 1.01708i | 0.0172273 | − | 0.999852i | \(-0.494516\pi\) |
0.999852 | − | 0.0172273i | \(-0.00548391\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0000 | + | 24.0000i | 1.35656 | + | 1.35656i | 0.878120 | + | 0.478440i | \(0.158798\pi\) |
0.478440 | + | 0.878120i | \(0.341202\pi\) | |||||||
\(314\) | 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 | ||||||||
\(321\) | 14.7980 | 0.825942 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9773 | + | 13.9773i | 0.777718 | + | 0.777718i | ||||
\(324\) | 35.7980i | 1.98878i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.5505 | 0.861263 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 25.5959 | + | 25.5959i | 1.41330 | + | 1.41330i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.0454 | 1.92627 | 0.963135 | − | 0.269019i | \(-0.0866994\pi\) | ||||
0.963135 | + | 0.269019i | \(0.0866994\pi\) | |||||||
\(332\) | −20.0454 | + | 20.0454i | −1.10013 | + | 1.10013i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.5732 | − | 20.5732i | 1.12069 | − | 1.12069i | 0.129057 | − | 0.991637i | \(-0.458805\pi\) |
0.991637 | − | 0.129057i | \(-0.0411951\pi\) | |||||||
\(338\) | −13.0000 | − | 13.0000i | −0.707107 | − | 0.707107i | ||||
\(339\) | − | 66.8434i | − | 3.63043i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −57.5959 | + | 57.5959i | −3.11443 | + | 3.11443i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 24.0000i | − | 1.29399i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.6742 | + | 16.6742i | −0.895120 | + | 0.895120i | −0.995000 | − | 0.0998797i | \(-0.968154\pi\) |
0.0998797 | + | 0.995000i | \(0.468154\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.20204 | − | 2.20204i | 0.117369 | − | 0.117369i | ||||
\(353\) | −16.0000 | − | 16.0000i | −0.851594 | − | 0.851594i | 0.138735 | − | 0.990329i | \(-0.455696\pi\) |
−0.990329 | + | 0.138735i | \(0.955696\pi\) | |||||||
\(354\) | − | 26.6969i | − | 1.41893i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 27.7980 | 1.47329 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.1464 | − | 26.1464i | −1.38188 | − | 1.38188i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −50.6969 | −2.66826 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −23.7980 | − | 23.7980i | −1.24907 | − | 1.24907i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 88.2929i | 4.59634i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(374\) | − | 1.84337i | − | 0.0953182i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6515i | 0.598499i | 0.954175 | + | 0.299249i | \(0.0967363\pi\) | ||||
−0.954175 | + | 0.299249i | \(0.903264\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | − | 35.5959i | − | 1.81650i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −38.9444 | −1.98222 | ||||||||
\(387\) | 41.3939 | − | 41.3939i | 2.10417 | − | 2.10417i | ||||
\(388\) | 24.0000 | + | 24.0000i | 1.21842 | + | 1.21842i | ||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 14.0000 | − | 14.0000i | 0.707107 | − | 0.707107i | ||||
\(393\) | −40.0454 | − | 40.0454i | −2.02002 | − | 2.02002i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.59592 | 0.381709 | ||||||||
\(397\) | 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 | ||||||||
\(401\) | 37.2929 | 1.86232 | 0.931158 | − | 0.364615i | \(-0.118800\pi\) | ||||
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | −24.7980 | + | 24.7980i | −1.23681 | + | 1.23681i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −14.8990 | − | 14.8990i | −0.737609 | − | 0.737609i | ||||
\(409\) | 18.3939i | 0.909519i | 0.890614 | + | 0.454759i | \(0.150275\pi\) | ||||
−0.890614 | + | 0.454759i | \(0.849725\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −51.9444 | −2.56223 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.8207 | − | 40.8207i | 1.99900 | − | 1.99900i | ||||
\(418\) | 4.59592 | + | 4.59592i | 0.224794 | + | 0.224794i | ||||
\(419\) | − | 22.8434i | − | 1.11597i | −0.829851 | − | 0.557986i | \(-0.811574\pi\) | ||
0.829851 | − | 0.557986i | \(-0.188426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | −15.0454 | + | 15.0454i | −0.732399 | + | 0.732399i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.65153 | − | 6.65153i | −0.321514 | − | 0.321514i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 34.6969 | − | 34.6969i | 1.66936 | − | 1.66936i | ||||
\(433\) | −17.2702 | − | 17.2702i | −0.829951 | − | 0.829951i | 0.157559 | − | 0.987510i | \(-0.449638\pi\) |
−0.987510 | + | 0.157559i | \(0.949638\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −32.1464 | − | 32.1464i | −1.53602 | − | 1.53602i | ||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 48.2929 | 2.29966 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.7196 | + | 26.7196i | 1.26949 | + | 1.26949i | 0.946353 | + | 0.323136i | \(0.104737\pi\) |
0.323136 | + | 0.946353i | \(0.395263\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.1010i | − | 0.759854i | −0.925016 | − | 0.379927i | \(-0.875949\pi\) | ||
0.925016 | − | 0.379927i | \(-0.124051\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.04541 | 0.331755 | ||||||||
\(452\) | −30.0454 | + | 30.0454i | −1.41322 | + | 1.41322i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4.00000i | − | 0.187729i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 74.2929 | 3.47908 | ||||||||
\(457\) | −3.92168 | + | 3.92168i | −0.183449 | + | 0.183449i | −0.792857 | − | 0.609408i | \(-0.791407\pi\) |
0.609408 | + | 0.792857i | \(0.291407\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 29.0454i | − | 1.35572i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.00000 | −0.370593 | ||||||||
\(467\) | −22.0000 | + | 22.0000i | −1.01804 | + | 1.01804i | −0.0182043 | + | 0.999834i | \(0.505795\pi\) |
−0.999834 | + | 0.0182043i | \(0.994205\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.0000 | + | 12.0000i | −0.552345 | + | 0.552345i | ||||
\(473\) | −3.30306 | − | 3.30306i | −0.151875 | − | 0.151875i | ||||
\(474\) | 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 | ||||||||
\(482\) | 1.69694 | − | 1.69694i | 0.0772934 | − | 0.0772934i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.3939i | 0.972449i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 27.5959 | 1.25178 | ||||||||
\(487\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 34.5959i | − | 1.56448i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.0000 | 1.89543 | 0.947717 | − | 0.319113i | \(-0.103385\pi\) | ||||
0.947717 | + | 0.319113i | \(0.103385\pi\) | |||||||
\(492\) | 56.9444 | − | 56.9444i | 2.56725 | − | 2.56725i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 44.5959 | + | 44.5959i | 1.99839 | + | 1.99839i | ||||
\(499\) | − | 14.0000i | − | 0.626726i | −0.949633 | − | 0.313363i | \(-0.898544\pi\) | ||
0.949633 | − | 0.313363i | \(-0.101456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23.9444 | − | 23.9444i | 1.06869 | − | 1.06869i | ||||
\(503\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.9217 | + | 28.9217i | −1.28446 | + | 1.28446i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 72.4166 | + | 72.4166i | 3.19727 | + | 3.19727i | ||||
\(514\) | 16.0000i | 0.705730i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −53.3939 | −2.35053 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.1918 | −1.58559 | −0.792797 | − | 0.609486i | \(-0.791376\pi\) | ||||
−0.792797 | + | 0.609486i | \(0.791376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.2702 | − | 32.2702i | −1.41108 | − | 1.41108i | −0.752619 | − | 0.658456i | \(-0.771210\pi\) |
−0.658456 | − | 0.752619i | \(-0.728790\pi\) | |||||||
\(524\) | 36.0000i | 1.57267i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −4.89898 | − | 4.89898i | −0.213201 | − | 0.213201i | ||||
\(529\) | 23.0000i | 1.00000i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −41.3939 | −1.79634 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | − | 61.8434i | − | 2.67622i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 22.2929 | 0.962905 | ||||||||
\(537\) | −58.1691 | + | 58.1691i | −2.51018 | + | 2.51018i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3.85357i | − | 0.165985i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.3939i | 0.574258i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.1691 | + | 31.1691i | −1.33270 | + | 1.33270i | −0.429746 | + | 0.902950i | \(0.641397\pi\) |
−0.902950 | + | 0.429746i | \(0.858603\pi\) | |||||||
\(548\) | 23.3485 | + | 23.3485i | 0.997397 | + | 0.997397i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −36.6969 | −1.55630 | ||||||||
\(557\) | 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 | ||||||||
\(561\) | −4.10102 | −0.173145 | ||||||||
\(562\) | 18.0000 | − | 18.0000i | 0.759284 | − | 0.759284i | ||||
\(563\) | −26.0000 | − | 26.0000i | −1.09577 | − | 1.09577i | −0.994900 | − | 0.100870i | \(-0.967837\pi\) |
−0.100870 | − | 0.994900i | \(-0.532163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.94439 | −0.375961 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 40.5959i | − | 1.70187i | −0.525271 | − | 0.850935i | \(-0.676036\pi\) | ||
0.525271 | − | 0.850935i | \(-0.323964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0000 | 0.920671 | 0.460336 | − | 0.887745i | \(-0.347729\pi\) | ||||
0.460336 | + | 0.887745i | \(0.347729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −55.1918 | −2.29966 | ||||||||
\(577\) | 32.8207 | − | 32.8207i | 1.36634 | − | 1.36634i | 0.500750 | − | 0.865592i | \(-0.333058\pi\) |
0.865592 | − | 0.500750i | \(-0.166942\pi\) | |||||||
\(578\) | −11.3939 | − | 11.3939i | −0.473923 | − | 0.473923i | ||||
\(579\) | 86.6413i | 3.60069i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 53.3939 | − | 53.3939i | 2.21325 | − | 2.21325i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 28.8990i | 1.19585i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.3258 | − | 13.3258i | 0.550013 | − | 0.550013i | −0.376431 | − | 0.926445i | \(-0.622849\pi\) |
0.926445 | + | 0.376431i | \(0.122849\pi\) | |||||||
\(588\) | −31.1464 | − | 31.1464i | −1.28446 | − | 1.28446i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.97730 | + | 4.97730i | 0.204393 | + | 0.204393i | 0.801879 | − | 0.597486i | \(-0.203834\pi\) |
−0.597486 | + | 0.801879i | \(0.703834\pi\) | |||||||
\(594\) | − | 9.55051i | − | 0.391862i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.30306 | 0.338689 | 0.169344 | − | 0.985557i | \(-0.445835\pi\) | ||||
0.169344 | + | 0.985557i | \(0.445835\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.4495 | + | 38.4495i | 1.56578 | + | 1.56578i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(608\) | −33.3939 | − | 33.3939i | −1.35430 | − | 1.35430i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −23.1010 | + | 23.1010i | −0.933803 | + | 0.933803i | ||||
\(613\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(614\) | 35.6413i | 1.43837i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.0000 | − | 28.0000i | 1.12724 | − | 1.12724i | 0.136613 | − | 0.990624i | \(-0.456378\pi\) |
0.990624 | − | 0.136613i | \(-0.0436217\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.0000i | 1.04503i | 0.852631 | + | 0.522514i | \(0.175006\pi\) | ||||
−0.852631 | + | 0.522514i | \(0.824994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −48.0000 | −1.91847 | ||||||||
\(627\) | 10.2247 | − | 10.2247i | 0.408337 | − | 0.408337i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.4722 | + | 33.4722i | 1.33040 | + | 1.33040i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.0000 | 1.65890 | 0.829450 | − | 0.558581i | \(-0.188654\pi\) | ||||
0.829450 | + | 0.558581i | \(0.188654\pi\) | |||||||
\(642\) | −14.7980 | + | 14.7980i | −0.584029 | + | 0.584029i | ||||
\(643\) | −6.00000 | − | 6.00000i | −0.236617 | − | 0.236617i | 0.578831 | − | 0.815448i | \(-0.303509\pi\) |
−0.815448 | + | 0.578831i | \(0.803509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.9546 | −1.09986 | ||||||||
\(647\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | −35.7980 | − | 35.7980i | −1.40628 | − | 1.40628i | ||||
\(649\) | 3.30306i | 0.129657i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.5505 | + | 15.5505i | −0.609005 | + | 0.609005i | ||||
\(653\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −51.1918 | −1.99871 | ||||||||
\(657\) | −49.8434 | + | 49.8434i | −1.94457 | + | 1.94457i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 50.6413i | 1.97271i | 0.164644 | + | 0.986353i | \(0.447352\pi\) | ||||
−0.164644 | + | 0.986353i | \(0.552648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | −35.0454 | + | 35.0454i | −1.36208 | + | 1.36208i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 40.0908i | − | 1.55583i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.0000 | − | 36.0000i | −1.38770 | − | 1.38770i | −0.830134 | − | 0.557564i | \(-0.811736\pi\) |
−0.557564 | − | 0.830134i | \(-0.688264\pi\) | |||||||
\(674\) | 41.1464i | 1.58490i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.0000 | 1.00000 | ||||||||
\(677\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(678\) | 66.8434 | + | 66.8434i | 2.56710 | + | 2.56710i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.89898 | −0.341010 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.7196 | + | 36.7196i | 1.40504 | + | 1.40504i | 0.782937 | + | 0.622101i | \(0.213721\pi\) |
0.622101 | + | 0.782937i | \(0.286279\pi\) | |||||||
\(684\) | − | 115.192i | − | 4.40447i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 24.0000 | + | 24.0000i | 0.914991 | + | 0.914991i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.0454 | 1.71361 | 0.856804 | − | 0.515642i | \(-0.172447\pi\) | ||||
0.856804 | + | 0.515642i | \(0.172447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 33.3485i | − | 1.26589i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.4268 | + | 21.4268i | −0.811597 | + | 0.811597i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.7980i | 0.673181i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.40408i | 0.165985i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.0000 | 1.20434 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 26.6969 | + | 26.6969i | 1.00333 | + | 1.00333i | ||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −27.7980 | + | 27.7980i | −1.04177 | + | 1.04177i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 52.2929 | 1.95428 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 50.6969 | − | 50.6969i | 1.88674 | − | 1.88674i | ||||
\(723\) | −3.77526 | − | 3.77526i | −0.140403 | − | 0.140403i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 47.5959 | 1.76645 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 7.69694i | − | 0.285072i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.0908 | 0.743086 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.06811 | − | 3.06811i | 0.113015 | − | 0.113015i | ||||
\(738\) | −88.2929 | − | 88.2929i | −3.25010 | − | 3.25010i | ||||
\(739\) | − | 34.0000i | − | 1.25071i | −0.780340 | − | 0.625355i | \(-0.784954\pi\) | ||
0.780340 | − | 0.625355i | \(-0.215046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 69.1464 | − | 69.1464i | 2.52994 | − | 2.52994i | ||||
\(748\) | 1.84337 | + | 1.84337i | 0.0674002 | + | 0.0674002i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −53.2702 | − | 53.2702i | −1.94127 | − | 1.94127i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(758\) | −11.6515 | − | 11.6515i | −0.423203 | − | 0.423203i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.2020 | −0.623574 | −0.311787 | − | 0.950152i | \(-0.600927\pi\) | ||||
−0.311787 | + | 0.950152i | \(0.600927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 35.5959 | + | 35.5959i | 1.28446 | + | 1.28446i | ||||
\(769\) | − | 55.0908i | − | 1.98663i | −0.115454 | − | 0.993313i | \(-0.536832\pi\) | ||
0.115454 | − | 0.993313i | \(-0.463168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.5959 | 1.28196 | ||||||||
\(772\) | 38.9444 | − | 38.9444i | 1.40164 | − | 1.40164i | ||||
\(773\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(774\) | 82.7878i | 2.97574i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −48.0000 | −1.72310 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 106.843i | − | 3.82806i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000i | 1.00000i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 80.0908 | 2.85674 | ||||||||
\(787\) | 18.0000 | − | 18.0000i | 0.641631 | − | 0.641631i | −0.309326 | − | 0.950956i | \(-0.600103\pi\) |
0.950956 | + | 0.309326i | \(0.100103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.59592 | + | 7.59592i | −0.269909 | + | 0.269909i | ||||
\(793\) | 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 | ||||||||
\(801\) | −95.8888 | −3.38806 | ||||||||
\(802\) | −37.2929 | + | 37.2929i | −1.31686 | + | 1.31686i | ||||
\(803\) | 3.97730 | + | 3.97730i | 0.140356 | + | 0.140356i | ||||
\(804\) | − | 49.5959i | − | 1.74911i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.00000i | 0.210949i | 0.994422 | + | 0.105474i | \(0.0336361\pi\) | ||||
−0.994422 | + | 0.105474i | \(0.966364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.0000 | −1.33436 | −0.667180 | − | 0.744896i | \(-0.732499\pi\) | ||||
−0.667180 | + | 0.744896i | \(0.732499\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 29.7980 | 1.04314 | ||||||||
\(817\) | −50.0908 | + | 50.0908i | −1.75246 | + | 1.75246i | ||||
\(818\) | −18.3939 | − | 18.3939i | −0.643127 | − | 0.643127i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 51.9444 | − | 51.9444i | 1.81177 | − | 1.81177i | ||||
\(823\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.0681 | − | 40.0681i | 1.39330 | − | 1.39330i | 0.575510 | − | 0.817795i | \(-0.304804\pi\) |
0.817795 | − | 0.575510i | \(-0.195196\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.7196 | + | 11.7196i | 0.406062 | + | 0.406062i | ||||
\(834\) | 81.6413i | 2.82701i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.19184 | −0.317906 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.8434 | + | 22.8434i | 0.789111 | + | 0.789111i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −40.0454 | − | 40.0454i | −1.37924 | − | 1.37924i | ||||
\(844\) | − | 30.0908i | − | 1.03577i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.8990i | 0.682931i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.3031 | 0.454689 | ||||||||
\(857\) | 25.0681 | − | 25.0681i | 0.856310 | − | 0.856310i | −0.134591 | − | 0.990901i | \(-0.542972\pi\) |
0.990901 | + | 0.134591i | \(0.0429720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.6515i | 0.738741i | 0.929282 | + | 0.369370i | \(0.120427\pi\) | ||||
−0.929282 | + | 0.369370i | \(0.879573\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | 69.3939i | 2.36083i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.5403 | 1.17373 | ||||||||
\(867\) | −25.3485 | + | 25.3485i | −0.860879 | + | 0.860879i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −82.7878 | − | 82.7878i | −2.80194 | − | 2.80194i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 64.2929 | 2.17225 | ||||||||
\(877\) | 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 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | −48.2929 | + | 48.2929i | −1.62611 | + | 1.62611i | ||||
\(883\) | 22.2247 | + | 22.2247i | 0.747922 | + | 0.747922i | 0.974089 | − | 0.226166i | \(-0.0726193\pi\) |
−0.226166 | + | 0.974089i | \(0.572619\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −53.4393 | −1.79533 | ||||||||
\(887\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.85357 | −0.330107 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.1010 | + | 16.1010i | 0.537298 | + | 0.537298i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −7.04541 | + | 7.04541i | −0.234586 | + | 0.234586i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 60.0908i | − | 1.99859i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.0000 | + | 42.0000i | −1.39459 | + | 1.39459i | −0.579898 | + | 0.814689i | \(0.696908\pi\) |
−0.814689 | + | 0.579898i | \(0.803092\pi\) | |||||||
\(908\) | 4.00000 | + | 4.00000i | 0.132745 | + | 0.132745i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −74.2929 | + | 74.2929i | −2.46008 | + | 2.46008i | ||||
\(913\) | −5.51760 | − | 5.51760i | −0.182606 | − | 0.182606i | ||||
\(914\) | − | 7.84337i | − | 0.259436i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 29.0454 | + | 29.0454i | 0.958641 | + | 0.958641i | ||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 79.2929 | 2.61279 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 54.0000i | − | 1.77168i | −0.463988 | − | 0.885841i | \(-0.653582\pi\) | ||
0.463988 | − | 0.885841i | \(-0.346418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −58.4393 | −1.91527 | ||||||||
\(932\) | 8.00000 | − | 8.00000i | 0.262049 | − | 0.262049i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 44.0000i | − | 1.43972i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.82066 | − | 2.82066i | 0.0921470 | − | 0.0921470i | −0.659531 | − | 0.751678i | \(-0.729245\pi\) |
0.751678 | + | 0.659531i | \(0.229245\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 106.788i | 3.48489i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 24.0000i | − | 0.781133i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.60612 | 0.214784 | ||||||||
\(947\) | 38.0000 | − | 38.0000i | 1.23483 | − | 1.23483i | 0.272749 | − | 0.962085i | \(-0.412067\pi\) |
0.962085 | − | 0.272749i | \(-0.0879328\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.7196 | + | 41.7196i | 1.35143 | + | 1.35143i | 0.884062 | + | 0.467370i | \(0.154798\pi\) |
0.467370 | + | 0.884062i | \(0.345202\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.9444 | + | 22.9444i | 0.739373 | + | 0.739373i | ||||
\(964\) | 3.39388i | 0.109309i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(968\) | −21.3939 | − | 21.3939i | −0.687625 | − | 0.687625i | ||||
\(969\) | 62.1918i | 1.99789i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.9444 | −1.73116 | −0.865579 | − | 0.500773i | \(-0.833049\pi\) | ||||
−0.865579 | + | 0.500773i | \(0.833049\pi\) | |||||||
\(972\) | −27.5959 | + | 27.5959i | −0.885139 | + | 0.885139i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.3258 | − | 18.3258i | 0.586293 | − | 0.586293i | −0.350332 | − | 0.936625i | \(-0.613931\pi\) |
0.936625 | + | 0.350332i | \(0.113931\pi\) | |||||||
\(978\) | 34.5959 | + | 34.5959i | 1.10626 | + | 1.10626i | ||||
\(979\) | 7.65153i | 0.244544i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −42.0000 | + | 42.0000i | −1.34027 | + | 1.34027i | ||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 113.889i | 3.63064i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 77.9671 | + | 77.9671i | 2.47421 | + | 2.47421i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −89.1918 | −2.82615 | ||||||||
\(997\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(998\) | 14.0000 | + | 14.0000i | 0.443162 | + | 0.443162i | ||||
\(999\) | 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 | 200.2.k.e.43.2 | ✓ | 4 | |
4.3 | odd | 2 | 800.2.o.e.143.1 | 4 | |||
5.2 | odd | 4 | inner | 200.2.k.e.107.2 | yes | 4 | |
5.3 | odd | 4 | 200.2.k.f.107.1 | yes | 4 | ||
5.4 | even | 2 | 200.2.k.f.43.1 | yes | 4 | ||
8.3 | odd | 2 | CM | 200.2.k.e.43.2 | ✓ | 4 | |
8.5 | even | 2 | 800.2.o.e.143.1 | 4 | |||
20.3 | even | 4 | 800.2.o.f.207.2 | 4 | |||
20.7 | even | 4 | 800.2.o.e.207.1 | 4 | |||
20.19 | odd | 2 | 800.2.o.f.143.2 | 4 | |||
40.3 | even | 4 | 200.2.k.f.107.1 | yes | 4 | ||
40.13 | odd | 4 | 800.2.o.f.207.2 | 4 | |||
40.19 | odd | 2 | 200.2.k.f.43.1 | yes | 4 | ||
40.27 | even | 4 | inner | 200.2.k.e.107.2 | yes | 4 | |
40.29 | even | 2 | 800.2.o.f.143.2 | 4 | |||
40.37 | odd | 4 | 800.2.o.e.207.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.2.k.e.43.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
200.2.k.e.43.2 | ✓ | 4 | 8.3 | odd | 2 | CM | |
200.2.k.e.107.2 | yes | 4 | 5.2 | odd | 4 | inner | |
200.2.k.e.107.2 | yes | 4 | 40.27 | even | 4 | inner | |
200.2.k.f.43.1 | yes | 4 | 5.4 | even | 2 | ||
200.2.k.f.43.1 | yes | 4 | 40.19 | odd | 2 | ||
200.2.k.f.107.1 | yes | 4 | 5.3 | odd | 4 | ||
200.2.k.f.107.1 | yes | 4 | 40.3 | even | 4 | ||
800.2.o.e.143.1 | 4 | 4.3 | odd | 2 | |||
800.2.o.e.143.1 | 4 | 8.5 | even | 2 | |||
800.2.o.e.207.1 | 4 | 20.7 | even | 4 | |||
800.2.o.e.207.1 | 4 | 40.37 | odd | 4 | |||
800.2.o.f.143.2 | 4 | 20.19 | odd | 2 | |||
800.2.o.f.143.2 | 4 | 40.29 | even | 2 | |||
800.2.o.f.207.2 | 4 | 20.3 | even | 4 | |||
800.2.o.f.207.2 | 4 | 40.13 | odd | 4 |