Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [712,1,Mod(99,712)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(712, base_ring=CyclotomicField(44))
chi = DirichletCharacter(H, H._module([22, 22, 43]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("712.99");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 712 = 2^{3} \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 712.y (of order \(44\), degree \(20\), 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: | \(0.355334288995\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{44})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{44}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{44} - \cdots)\) |
Embedding invariants
Embedding label | 427.1 | ||
Root | \(-0.909632 + 0.415415i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 712.427 |
Dual form | 712.1.y.a.707.1 |
$q$-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 \(\left(\mathbb{Z}/712\mathbb{Z}\right)^\times\).
\(n\) | \(357\) | \(535\) | \(537\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{31}{44}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(3\) | 1.12299 | − | 1.50013i | 1.12299 | − | 1.50013i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(4\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(5\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(6\) | 1.86912 | − | 0.133682i | 1.86912 | − | 0.133682i | ||||
\(7\) | 0 | 0 | −0.977147 | − | 0.212565i | \(-0.931818\pi\) | ||||
0.977147 | + | 0.212565i | \(0.0681818\pi\) | |||||||
\(8\) | −0.841254 | + | 0.540641i | −0.841254 | + | 0.540641i | ||||
\(9\) | −0.707571 | − | 2.40977i | −0.707571 | − | 2.40977i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.909632 | − | 0.584585i | −0.909632 | − | 0.584585i | − | 1.00000i | \(-0.5\pi\) | |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(12\) | 1.32505 | + | 1.32505i | 1.32505 | + | 1.32505i | ||||
\(13\) | 0 | 0 | −0.800541 | − | 0.599278i | \(-0.795455\pi\) | ||||
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(17\) | 0.989821 | + | 0.857685i | 0.989821 | + | 0.857685i | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 1.35782 | − | 2.11281i | 1.35782 | − | 2.11281i | ||||
\(19\) | −0.936593 | + | 1.71524i | −0.936593 | + | 1.71524i | −0.281733 | + | 0.959493i | \(0.590909\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.153882 | − | 1.07028i | −0.153882 | − | 1.07028i | ||||
\(23\) | 0 | 0 | −0.877679 | − | 0.479249i | \(-0.840909\pi\) | ||||
0.877679 | + | 0.479249i | \(0.159091\pi\) | |||||||
\(24\) | −0.133682 | + | 1.86912i | −0.133682 | + | 1.86912i | ||||
\(25\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.65381 | − | 0.989821i | −2.65381 | − | 0.989821i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.212565 | − | 0.977147i | \(-0.431818\pi\) | ||||
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(32\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(33\) | −1.89846 | + | 0.708089i | −1.89846 | + | 0.708089i | ||||
\(34\) | 1.30972i | 1.30972i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.48594 | − | 0.357424i | 2.48594 | − | 0.357424i | ||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | −1.90963 | + | 0.415415i | −1.90963 | + | 0.415415i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.13214 | − | 0.847507i | 1.13214 | − | 0.847507i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0303285 | − | 0.139418i | −0.0303285 | − | 0.139418i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(44\) | 0.708089 | − | 0.817178i | 0.708089 | − | 0.817178i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(48\) | −1.50013 | + | 1.12299i | −1.50013 | + | 1.12299i | ||||
\(49\) | 0.909632 | + | 0.415415i | 0.909632 | + | 0.415415i | ||||
\(50\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(51\) | 2.39820 | − | 0.521696i | 2.39820 | − | 0.521696i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(54\) | −0.989821 | − | 2.65381i | −0.989821 | − | 2.65381i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.52131 | + | 3.33121i | 1.52131 | + | 3.33121i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.19550 | − | 1.59700i | −1.19550 | − | 1.59700i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.540641 | − | 0.841254i | \(-0.681818\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.349464 | − | 0.936950i | \(-0.386364\pi\) | ||||
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.77836 | − | 0.971061i | −1.77836 | − | 0.971061i | ||||
\(67\) | −0.0801894 | − | 0.557730i | −0.0801894 | − | 0.557730i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
0.909632 | − | 0.415415i | \(-0.136364\pi\) | |||||||
\(68\) | −0.989821 | + | 0.857685i | −0.989821 | + | 0.857685i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(72\) | 1.89806 | + | 1.64468i | 1.89806 | + | 1.64468i | ||||
\(73\) | −1.74557 | − | 0.512546i | −1.74557 | − | 0.512546i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.898064 | + | 1.64468i | 0.898064 | + | 1.64468i | ||||
\(76\) | −1.56449 | − | 1.17116i | −1.56449 | − | 1.17116i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.35225 | + | 1.51170i | −2.35225 | + | 1.51170i | ||||
\(82\) | 1.38189 | + | 0.300613i | 1.38189 | + | 0.300613i | ||||
\(83\) | 1.19550 | − | 0.0855040i | 1.19550 | − | 0.0855040i | 0.540641 | − | 0.841254i | \(-0.318182\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.0855040 | − | 0.114220i | 0.0855040 | − | 0.114220i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.08128 | 1.08128 | ||||||||
\(89\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.83107 | − | 0.398326i | −1.83107 | − | 0.398326i | ||||
\(97\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | −0.654861 | + | 0.755750i | \(0.727273\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(98\) | 0.281733 | + | 0.959493i | 0.281733 | + | 0.959493i | ||||
\(99\) | −0.765084 | + | 2.60564i | −0.765084 | + | 2.60564i | ||||
\(100\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(101\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(102\) | 1.96476 | + | 1.47080i | 1.96476 | + | 1.47080i | ||||
\(103\) | 0 | 0 | −0.479249 | − | 0.877679i | \(-0.659091\pi\) | ||||
0.479249 | + | 0.877679i | \(0.340909\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(108\) | 1.35742 | − | 2.48594i | 1.35742 | − | 2.48594i | ||||
\(109\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.0855040 | + | 1.19550i | −0.0855040 | + | 1.19550i | 0.755750 | + | 0.654861i | \(0.227273\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(114\) | −1.52131 | + | 3.33121i | −1.52131 | + | 3.33121i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.424047 | − | 1.94931i | 0.424047 | − | 1.94931i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0702757 | + | 0.153882i | 0.0702757 | + | 0.153882i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 2.65009i | − | 2.65009i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(128\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(129\) | −0.243204 | − | 0.111067i | −0.243204 | − | 0.111067i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.822373 | + | 0.118239i | 0.822373 | + | 0.118239i | 0.540641 | − | 0.841254i | \(-0.318182\pi\) |
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(132\) | −0.430703 | − | 1.97991i | −0.430703 | − | 1.97991i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.368991 | − | 0.425839i | 0.368991 | − | 0.425839i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.29639 | − | 0.186393i | −1.29639 | − | 0.186393i | ||||
\(137\) | 1.59700 | − | 1.19550i | 1.59700 | − | 1.19550i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.61435 | − | 0.474017i | 1.61435 | − | 0.474017i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.51150i | 2.51150i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.755750 | − | 1.65486i | −0.755750 | − | 1.65486i | ||||
\(147\) | 1.64468 | − | 0.898064i | 1.64468 | − | 0.898064i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.212565 | − | 0.977147i | \(-0.431818\pi\) | ||||
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(150\) | −0.654861 | + | 1.75575i | −0.654861 | + | 1.75575i | ||||
\(151\) | 0 | 0 | −0.936950 | − | 0.349464i | \(-0.886364\pi\) | ||||
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(152\) | −0.139418 | − | 1.94931i | −0.139418 | − | 1.94931i | ||||
\(153\) | 1.36645 | − | 2.99211i | 1.36645 | − | 2.99211i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.68287 | − | 0.787761i | −2.68287 | − | 0.787761i | ||||
\(163\) | −0.697148 | − | 0.0498610i | −0.697148 | − | 0.0498610i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(164\) | 0.677760 | + | 1.24123i | 0.677760 | + | 1.24123i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.847507 | + | 0.847507i | 0.847507 | + | 0.847507i | ||||
\(167\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.281733 | + | 0.959493i | 0.281733 | + | 0.959493i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.79604 | + | 1.04331i | 4.79604 | + | 1.04331i | ||||
\(172\) | 0.142315 | − | 0.0101786i | 0.142315 | − | 0.0101786i | ||||
\(173\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.708089 | + | 0.817178i | 0.708089 | + | 0.817178i | ||||
\(177\) | −3.73825 | −3.73825 | ||||||||
\(178\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(179\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.599278 | − | 0.800541i | \(-0.295455\pi\) | ||||
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.398983 | − | 1.35881i | −0.398983 | − | 1.35881i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.800541 | − | 0.599278i | \(-0.795455\pi\) | ||||
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(192\) | −0.898064 | − | 1.64468i | −0.898064 | − | 1.64468i | ||||
\(193\) | 1.75089 | + | 0.125226i | 1.75089 | + | 0.125226i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(194\) | −1.84125 | − | 0.540641i | −1.84125 | − | 0.540641i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.540641 | + | 0.841254i | −0.540641 | + | 0.841254i | ||||
\(197\) | 0 | 0 | 0.479249 | − | 0.877679i | \(-0.340909\pi\) | ||||
−0.479249 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(198\) | −2.47023 | + | 1.12812i | −2.47023 | + | 1.12812i | ||||
\(199\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(200\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(201\) | −0.926721 | − | 0.506028i | −0.926721 | − | 0.506028i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.175087 | + | 2.44803i | 0.175087 | + | 2.44803i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.85466 | − | 1.01272i | 1.85466 | − | 1.01272i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.133682 | − | 0.0498610i | 0.133682 | − | 0.0498610i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.76767 | − | 0.602069i | 2.76767 | − | 0.602069i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.72914 | + | 2.04301i | −2.72914 | + | 2.04301i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.48594 | + | 0.357424i | 2.48594 | + | 0.357424i | ||||
\(226\) | −0.959493 | + | 0.718267i | −0.959493 | + | 0.718267i | ||||
\(227\) | −1.65486 | − | 0.755750i | −1.65486 | − | 0.755750i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(228\) | −3.51381 | + | 1.03175i | −3.51381 | + | 1.03175i | ||||
\(229\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 0.284630i | − | 0.284630i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||
0.989821 | − | 0.142315i | \(-0.0454545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.75089 | − | 0.956056i | 1.75089 | − | 0.956056i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.349464 | − | 0.936950i | \(-0.386364\pi\) | ||||
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.114220 | + | 1.59700i | 0.114220 | + | 1.59700i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(242\) | −0.0702757 | + | 0.153882i | −0.0702757 | + | 0.153882i | ||||
\(243\) | −0.171732 | + | 2.40113i | −0.171732 | + | 2.40113i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.00281 | − | 1.73544i | 2.00281 | − | 1.73544i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.21426 | − | 1.88943i | 1.21426 | − | 1.88943i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(257\) | 0.474017 | − | 1.61435i | 0.474017 | − | 1.61435i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
0.755750 | − | 0.654861i | \(-0.227273\pi\) | |||||||
\(258\) | −0.0753254 | − | 0.256535i | −0.0753254 | − | 0.256535i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.449181 | + | 0.698939i | 0.449181 | + | 0.698939i | ||||
\(263\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(264\) | 1.21426 | − | 1.62207i | 1.21426 | − | 1.62207i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.83107 | − | 0.398326i | −1.83107 | − | 0.398326i | ||||
\(268\) | 0.563465 | 0.563465 | ||||||||
\(269\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(272\) | −0.708089 | − | 1.10181i | −0.708089 | − | 1.10181i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.94931 | + | 0.424047i | 1.94931 | + | 0.424047i | ||||
\(275\) | 0.909632 | − | 0.584585i | 0.909632 | − | 0.584585i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(278\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.203743 | + | 0.373128i | 0.203743 | + | 0.373128i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.89945 | + | 0.557730i | 1.89945 | + | 0.557730i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.89806 | + | 1.64468i | −1.89806 | + | 1.64468i | ||||
\(289\) | 0.101808 | + | 0.708089i | 0.101808 | + | 0.708089i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.256535 | + | 3.58682i | −0.256535 | + | 3.58682i | ||||
\(292\) | 0.755750 | − | 1.65486i | 0.755750 | − | 1.65486i | ||||
\(293\) | 0 | 0 | −0.0713392 | − | 0.997452i | \(-0.522727\pi\) | ||||
0.0713392 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(294\) | 1.75575 | + | 0.654861i | 1.75575 | + | 0.654861i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.83536 | + | 2.45175i | 1.83536 | + | 2.45175i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.75575 | + | 0.654861i | −1.75575 | + | 0.654861i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.38189 | − | 1.38189i | 1.38189 | − | 1.38189i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.15612 | − | 0.926721i | 3.15612 | − | 0.926721i | ||||
\(307\) | −0.258908 | − | 0.118239i | −0.258908 | − | 0.118239i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.373128 | + | 1.71524i | 0.373128 | + | 1.71524i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.39820 | + | 0.894482i | −2.39820 | + | 0.894482i | ||||
\(324\) | −1.16155 | − | 2.54345i | −1.16155 | − | 2.54345i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.418852 | − | 0.559521i | −0.418852 | − | 0.559521i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.494217 | + | 1.32505i | −0.494217 | + | 1.32505i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.698939 | + | 1.53046i | −0.698939 | + | 1.53046i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(332\) | −0.0855040 | + | 1.19550i | −0.0855040 | + | 1.19550i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.203743 | − | 0.373128i | 0.203743 | − | 0.373128i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(338\) | −0.540641 | + | 0.841254i | −0.540641 | + | 0.841254i | ||||
\(339\) | 1.69739 | + | 1.47080i | 1.69739 | + | 1.47080i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.35225 | + | 4.30783i | 2.35225 | + | 4.30783i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.100889 | + | 0.100889i | 0.100889 | + | 0.100889i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.557730 | + | 1.89945i | 0.557730 | + | 1.89945i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.977147 | − | 0.212565i | \(-0.931818\pi\) | ||||
0.977147 | + | 0.212565i | \(0.0681818\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.153882 | + | 1.07028i | −0.153882 | + | 1.07028i | ||||
\(353\) | 1.05195 | − | 1.40524i | 1.05195 | − | 1.40524i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.909632 | − | 0.415415i | \(-0.136364\pi\) | |||||||
\(354\) | −2.44803 | − | 2.82518i | −2.44803 | − | 2.82518i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.25667 | − | 1.45027i | −1.25667 | − | 1.45027i | ||||
\(359\) | 0 | 0 | 0.599278 | − | 0.800541i | \(-0.295455\pi\) | ||||
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.52421 | − | 2.37172i | −1.52421 | − | 2.37172i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.309763 | + | 0.0673848i | 0.309763 | + | 0.0673848i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.84336 | − | 2.12851i | −2.84336 | − | 2.12851i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(374\) | 0.765644 | − | 1.19136i | 0.765644 | − | 1.19136i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.841254 | + | 0.459359i | 0.841254 | + | 0.459359i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.936950 | − | 0.349464i | \(-0.886364\pi\) | ||||
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(384\) | 0.654861 | − | 1.75575i | 0.654861 | − | 1.75575i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.05195 | + | 1.40524i | 1.05195 | + | 1.40524i | ||||
\(387\) | −0.314505 | + | 0.171732i | −0.314505 | + | 0.171732i | ||||
\(388\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(389\) | 0 | 0 | 0.936950 | − | 0.349464i | \(-0.113636\pi\) | ||||
−0.936950 | + | 0.349464i | \(0.886364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.989821 | + | 0.142315i | −0.989821 | + | 0.142315i | ||||
\(393\) | 1.10089 | − | 1.10089i | 1.10089 | − | 1.10089i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.47023 | − | 1.12812i | −2.47023 | − | 1.12812i | ||||
\(397\) | 0 | 0 | 0.800541 | − | 0.599278i | \(-0.204545\pi\) | ||||
−0.800541 | + | 0.599278i | \(0.795455\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(401\) | −0.368991 | + | 0.425839i | −0.368991 | + | 0.425839i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(402\) | −0.224443 | − | 1.03175i | −0.224443 | − | 1.03175i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.73544 | + | 1.73544i | −1.73544 | + | 1.73544i | ||||
\(409\) | −1.89945 | + | 0.273100i | −1.89945 | + | 0.273100i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 3.73825i | − | 3.73825i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.10181 | − | 2.95406i | 1.10181 | − | 2.95406i | ||||
\(418\) | 1.97991 | + | 0.738467i | 1.97991 | + | 0.738467i | ||||
\(419\) | 0.125226 | + | 1.75089i | 0.125226 | + | 1.75089i | 0.540641 | + | 0.841254i | \(0.318182\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.0713392 | − | 0.997452i | \(-0.477273\pi\) | ||||
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(422\) | 0.125226 | + | 0.0683785i | 0.125226 | + | 0.0683785i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.19136 | + | 0.544078i | −1.19136 | + | 0.544078i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.479249 | − | 0.877679i | \(-0.659091\pi\) | ||||
0.479249 | + | 0.877679i | \(0.340909\pi\) | |||||||
\(432\) | 2.26745 | + | 1.69739i | 2.26745 | + | 1.69739i | ||||
\(433\) | −0.494217 | − | 0.494217i | −0.494217 | − | 0.494217i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.33121 | − | 0.724660i | −3.33121 | − | 0.724660i | ||||
\(439\) | 0 | 0 | 0.997452 | − | 0.0713392i | \(-0.0227273\pi\) | ||||
−0.997452 | + | 0.0713392i | \(0.977273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.357424 | − | 2.48594i | 0.357424 | − | 2.48594i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.29639 | − | 1.49611i | −1.29639 | − | 1.49611i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
−0.540641 | − | 0.841254i | \(-0.681818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.281733 | + | 1.95949i | −0.281733 | + | 1.95949i | 1.00000i | \(0.5\pi\) | ||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(450\) | 1.35782 | + | 2.11281i | 1.35782 | + | 2.11281i | ||||
\(451\) | −1.52527 | + | 0.109089i | −1.52527 | + | 0.109089i | ||||
\(452\) | −1.17116 | − | 0.254771i | −1.17116 | − | 0.254771i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.512546 | − | 1.74557i | −0.512546 | − | 1.74557i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.08080 | − | 1.97991i | −3.08080 | − | 1.97991i | ||||
\(457\) | −0.677760 | − | 0.677760i | −0.677760 | − | 0.677760i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.77785 | − | 3.25588i | −1.77785 | − | 3.25588i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.215109 | − | 0.186393i | 0.215109 | − | 0.186393i | ||||
\(467\) | −0.186393 | − | 1.29639i | −0.186393 | − | 1.29639i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.86912 | + | 0.697148i | 1.86912 | + | 0.697148i | ||||
\(473\) | −0.0539138 | + | 0.144548i | −0.0539138 | + | 0.144548i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.17116 | − | 1.56449i | −1.17116 | − | 1.56449i | ||||
\(476\) | 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 | ||||||||
\(482\) | −1.13214 | + | 1.13214i | −1.13214 | + | 1.13214i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.162317 | + | 0.0476607i | −0.162317 | + | 0.0476607i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.92712 | + | 1.44262i | −1.92712 | + | 1.44262i | ||||
\(487\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.857685 | + | 0.989821i | −0.857685 | + | 0.989821i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.0903680 | + | 0.415415i | 0.0903680 | + | 0.415415i | 1.00000 | \(0\) | ||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(492\) | 2.62312 | + | 0.377148i | 2.62312 | + | 0.377148i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.22311 | − | 0.319635i | 2.22311 | − | 0.319635i | ||||
\(499\) | 0.559521 | + | 1.50013i | 0.559521 | + | 1.50013i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.118239 | + | 0.258908i | 0.118239 | + | 0.258908i | ||||
\(503\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.75575 | + | 0.654861i | 1.75575 | + | 0.654861i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(513\) | 4.18333 | − | 3.62487i | 4.18333 | − | 3.62487i | ||||
\(514\) | 1.53046 | − | 0.698939i | 1.53046 | − | 0.698939i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.144548 | − | 0.224922i | 0.144548 | − | 0.224922i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.114220 | + | 0.0855040i | 0.114220 | + | 0.0855040i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.53046 | + | 0.983568i | 1.53046 | + | 0.983568i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(524\) | −0.234072 | + | 0.797176i | −0.234072 | + | 0.797176i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.02105 | − | 0.144548i | 2.02105 | − | 0.144548i | ||||
\(529\) | 0.540641 | + | 0.841254i | 0.540641 | + | 0.841254i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.00250 | + | 4.01087i | −3.00250 | + | 4.01087i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.898064 | − | 1.64468i | −0.898064 | − | 1.64468i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.368991 | + | 0.425839i | 0.368991 | + | 0.425839i | ||||
\(537\) | −2.15499 | + | 2.87874i | −2.15499 | + | 2.87874i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.584585 | − | 0.909632i | −0.584585 | − | 0.909632i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.977147 | − | 0.212565i | \(-0.931818\pi\) | ||||
0.977147 | + | 0.212565i | \(0.0681818\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.368991 | − | 1.25667i | 0.368991 | − | 1.25667i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.340335 | − | 0.254771i | −0.340335 | − | 0.254771i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(548\) | 0.956056 | + | 1.75089i | 0.956056 | + | 1.75089i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.03748 | + | 0.304632i | 1.03748 | + | 0.304632i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.239446 | + | 1.66538i | 0.239446 | + | 1.66538i | ||||
\(557\) | 0 | 0 | −0.877679 | − | 0.479249i | \(-0.840909\pi\) | ||||
0.877679 | + | 0.479249i | \(0.159091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.48645 | − | 0.927399i | −2.48645 | − | 0.927399i | ||||
\(562\) | −0.148568 | + | 0.398326i | −0.148568 | + | 0.398326i | ||||
\(563\) | 0.0903680 | − | 0.415415i | 0.0903680 | − | 0.415415i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
1.00000 | \(0\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.822373 | + | 1.80075i | 0.822373 | + | 1.80075i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.334961 | + | 0.898064i | 0.334961 | + | 0.898064i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.48594 | − | 0.357424i | −2.48594 | − | 0.357424i | ||||
\(577\) | −0.415415 | − | 1.90963i | −0.415415 | − | 1.90963i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(578\) | −0.468468 | + | 0.540641i | −0.468468 | + | 0.540641i | ||||
\(579\) | 2.15408 | − | 2.48594i | 2.15408 | − | 2.48594i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.87874 | + | 2.15499i | −2.87874 | + | 2.15499i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.74557 | − | 0.512546i | 1.74557 | − | 0.512546i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.66538 | + | 0.239446i | −1.66538 | + | 0.239446i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(588\) | 0.654861 | + | 1.75575i | 0.654861 | + | 1.75575i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.574406 | − | 0.767317i | −0.574406 | − | 0.767317i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(594\) | −0.651007 | + | 2.99263i | −0.651007 | + | 2.99263i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.0713392 | − | 0.997452i | \(-0.477273\pi\) | ||||
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(600\) | −1.64468 | − | 0.898064i | −1.64468 | − | 0.898064i | ||||
\(601\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.28726 | + | 0.587871i | −1.28726 | + | 0.587871i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(608\) | 1.94931 | + | 0.139418i | 1.94931 | + | 0.139418i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.76719 | + | 1.77836i | 2.76719 | + | 1.77836i | ||||
\(613\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(614\) | −0.0801894 | − | 0.273100i | −0.0801894 | − | 0.273100i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.697148 | − | 0.0498610i | 0.697148 | − | 0.0498610i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.118239 | − | 0.822373i | 0.118239 | − | 0.822373i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(626\) | −1.05195 | + | 1.40524i | −1.05195 | + | 1.40524i | ||||
\(627\) | 0.563541 | − | 3.91951i | 0.563541 | − | 3.91951i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0753254 | − | 0.256535i | 0.0753254 | − | 0.256535i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.449181 | + | 0.698939i | −0.449181 | + | 0.698939i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.74557 | − | 0.797176i | 1.74557 | − | 0.797176i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
0.989821 | − | 0.142315i | \(-0.0454545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.24649 | − | 1.22668i | −2.24649 | − | 1.22668i | ||||
\(647\) | 0 | 0 | 0.0713392 | − | 0.997452i | \(-0.477273\pi\) | ||||
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(648\) | 1.16155 | − | 2.54345i | 1.16155 | − | 2.54345i | ||||
\(649\) | 0.153882 | + | 2.15156i | 0.153882 | + | 2.15156i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.148568 | − | 0.682956i | 0.148568 | − | 0.682956i | ||||
\(653\) | 0 | 0 | −0.599278 | − | 0.800541i | \(-0.704545\pi\) | ||||
0.599278 | + | 0.800541i | \(0.295455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.32505 | + | 0.494217i | −1.32505 | + | 0.494217i | ||||
\(657\) | 4.56908i | 4.56908i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.822373 | − | 0.118239i | 0.822373 | − | 0.118239i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(662\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.959493 | + | 0.718267i | −0.959493 | + | 0.718267i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(674\) | 0.415415 | − | 0.0903680i | 0.415415 | − | 0.0903680i | ||||
\(675\) | 2.00281 | − | 2.00281i | 2.00281 | − | 2.00281i | ||||
\(676\) | −0.989821 | + | 0.142315i | −0.989821 | + | 0.142315i | ||||
\(677\) | 0 | 0 | −0.349464 | − | 0.936950i | \(-0.613636\pi\) | ||||
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(678\) | 2.24597i | 2.24597i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.99211 | + | 1.63382i | −2.99211 | + | 1.63382i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.148568 | + | 0.682956i | −0.148568 | + | 0.682956i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(684\) | −1.71524 | + | 4.59874i | −1.71524 | + | 4.59874i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.0101786 | + | 0.142315i | −0.0101786 | + | 0.142315i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.215109 | − | 0.186393i | 0.215109 | − | 0.186393i | −0.540641 | − | 0.841254i | \(-0.681818\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.07028 | + | 1.66538i | −1.07028 | + | 1.66538i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.84751 | + | 0.132136i | 1.84751 | + | 0.132136i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.426983 | − | 0.319635i | −0.426983 | − | 0.319635i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.909632 | + | 0.584585i | −0.909632 | + | 0.584585i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.75089 | − | 0.125226i | 1.75089 | − | 0.125226i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.532008 | − | 3.70020i | 0.532008 | − | 3.70020i | ||||
\(709\) | 0 | 0 | 0.599278 | − | 0.800541i | \(-0.295455\pi\) | ||||
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.977147 | − | 0.212565i | \(-0.931818\pi\) | ||||
0.977147 | + | 0.212565i | \(0.0681818\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.794278 | − | 2.70506i | 0.794278 | − | 2.70506i | ||||
\(723\) | 2.52399 | + | 1.62207i | 2.52399 | + | 1.62207i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.151926 | + | 0.278231i | 0.151926 | + | 0.278231i | ||||
\(727\) | 0 | 0 | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) | ||||
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.29600 | + | 1.12299i | 1.29600 | + | 1.12299i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0895567 | − | 0.164011i | 0.0895567 | − | 0.164011i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.253098 | + | 0.554206i | −0.253098 | + | 0.554206i | ||||
\(738\) | −0.253382 | − | 3.54275i | −0.253382 | − | 3.54275i | ||||
\(739\) | 1.64468 | + | 0.613435i | 1.64468 | + | 0.613435i | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.05195 | − | 2.82038i | −1.05195 | − | 2.82038i | ||||
\(748\) | 1.40176 | − | 0.201543i | 1.40176 | − | 0.201543i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.426983 | − | 0.319635i | 0.426983 | − | 0.319635i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(758\) | 0.203743 | + | 0.936593i | 0.203743 | + | 0.936593i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.983568 | − | 0.449181i | −0.983568 | − | 0.449181i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.75575 | − | 0.654861i | 1.75575 | − | 0.654861i | ||||
\(769\) | −0.822373 | − | 1.80075i | −0.822373 | − | 1.80075i | −0.540641 | − | 0.841254i | \(-0.681818\pi\) |
−0.281733 | − | 0.959493i | \(-0.590909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.88943 | − | 2.52399i | −1.88943 | − | 2.52399i | ||||
\(772\) | −0.373128 | + | 1.71524i | −0.373128 | + | 1.71524i | ||||
\(773\) | 0 | 0 | 0.349464 | − | 0.936950i | \(-0.386364\pi\) | ||||
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(774\) | −0.335743 | − | 0.125226i | −0.335743 | − | 0.125226i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.797176 | − | 1.74557i | 0.797176 | − | 1.74557i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.393328 | + | 2.73566i | 0.393328 | + | 2.73566i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.755750 | − | 0.654861i | −0.755750 | − | 0.654861i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.55293 | + | 0.111067i | 1.55293 | + | 0.111067i | ||||
\(787\) | −0.767317 | − | 1.40524i | −0.767317 | − | 1.40524i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.765084 | − | 2.60564i | −0.765084 | − | 2.60564i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.00000 | 1.00000 | ||||||||
\(801\) | −1.89806 | + | 1.64468i | −1.89806 | + | 1.64468i | ||||
\(802\) | −0.563465 | −0.563465 | ||||||||
\(803\) | 1.28820 | + | 1.48666i | 1.28820 | + | 1.48666i | ||||
\(804\) | 0.632763 | − | 0.845273i | 0.632763 | − | 0.845273i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.44803 | − | 0.175087i | −2.44803 | − | 0.175087i | ||||
\(817\) | 0.267541 | + | 0.0785570i | 0.267541 | + | 0.0785570i | ||||
\(818\) | −1.45027 | − | 1.25667i | −1.45027 | − | 1.25667i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(822\) | 2.82518 | − | 2.44803i | 2.82518 | − | 2.44803i | ||||
\(823\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.144548 | − | 2.02105i | 0.144548 | − | 2.02105i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.114220 | + | 1.59700i | 0.114220 | + | 1.59700i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.349464 | − | 0.936950i | \(-0.386364\pi\) | ||||
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.544078 | + | 1.19136i | 0.544078 | + | 1.19136i | ||||
\(834\) | 2.95406 | − | 1.10181i | 2.95406 | − | 1.10181i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.738467 | + | 1.97991i | 0.738467 | + | 1.97991i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.24123 | + | 1.24123i | −1.24123 | + | 1.24123i | ||||
\(839\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.909632 | − | 0.415415i | −0.909632 | − | 0.415415i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.788543 | + | 0.113375i | 0.788543 | + | 0.113375i | ||||
\(844\) | 0.0303285 | + | 0.139418i | 0.0303285 | + | 0.139418i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.96973 | − | 2.22311i | 2.96973 | − | 2.22311i | ||||
\(850\) | −1.19136 | − | 0.544078i | −1.19136 | − | 0.544078i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.83107 | + | 0.682956i | −1.83107 | + | 0.682956i | −0.841254 | + | 0.540641i | \(0.818182\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.05195 | + | 0.574406i | −1.05195 | + | 0.574406i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.936950 | − | 0.349464i | \(-0.886364\pi\) | ||||
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(864\) | 0.202061 | + | 2.82518i | 0.202061 | + | 2.82518i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.0498610 | − | 0.697148i | 0.0498610 | − | 0.697148i | ||||
\(867\) | 1.17656 | + | 0.642449i | 1.17656 | + | 0.642449i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.64236 | + | 3.15612i | 3.64236 | + | 3.15612i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.63382 | − | 2.99211i | −1.63382 | − | 2.99211i | ||||
\(877\) | 0 | 0 | −0.800541 | − | 0.599278i | \(-0.795455\pi\) | ||||
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.425839 | − | 1.45027i | −0.425839 | − | 1.45027i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(882\) | 2.11281 | − | 1.35782i | 2.11281 | − | 1.35782i | ||||
\(883\) | 1.56449 | + | 0.340335i | 1.56449 | + | 0.340335i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.281733 | − | 1.95949i | 0.281733 | − | 1.95949i | ||||
\(887\) | 0 | 0 | 0.599278 | − | 0.800541i | \(-0.295455\pi\) | ||||
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.02340 | 3.02340 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.66538 | + | 1.07028i | −1.66538 | + | 1.07028i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.707571 | + | 2.40977i | −0.707571 | + | 2.40977i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1.08128 | − | 1.08128i | −1.08128 | − | 1.08128i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.574406 | − | 1.05195i | −0.574406 | − | 1.05195i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.14231 | − | 0.989821i | −1.14231 | − | 0.989821i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(908\) | 0.983568 | − | 1.53046i | 0.983568 | − | 1.53046i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(912\) | −0.521178 | − | 3.62487i | −0.521178 | − | 3.62487i | ||||
\(913\) | −1.13745 | − | 0.621095i | −1.13745 | − | 0.621095i | ||||
\(914\) | 0.0683785 | − | 0.956056i | 0.0683785 | − | 0.956056i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.29639 | − | 3.47576i | 1.29639 | − | 3.47576i | ||||
\(919\) | 0 | 0 | 0.212565 | − | 0.977147i | \(-0.431818\pi\) | ||||
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.468125 | + | 0.255616i | −0.468125 | + | 0.255616i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.273100 | + | 0.0801894i | −0.273100 | + | 0.0801894i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.56449 | + | 1.17116i | −1.56449 | + | 1.17116i | ||||
\(932\) | 0.281733 | + | 0.0405070i | 0.281733 | + | 0.0405070i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.49611 | − | 0.215109i | −1.49611 | − | 0.215109i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.99211 | + | 1.36645i | 2.99211 | + | 1.36645i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.697148 | + | 1.86912i | 0.697148 | + | 1.86912i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.144548 | + | 0.0539138i | −0.144548 | + | 0.0539138i | ||||
\(947\) | −0.234072 | − | 0.512546i | −0.234072 | − | 0.512546i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.415415 | − | 1.90963i | 0.415415 | − | 1.90963i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.0498610 | − | 0.697148i | −0.0498610 | − | 0.697148i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.909632 | − | 0.415415i | \(-0.136364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.540641 | − | 0.841254i | 0.540641 | − | 0.841254i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.59700 | − | 0.114220i | −1.59700 | − | 0.114220i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | −0.142315 | − | 0.0914602i | −0.142315 | − | 0.0914602i | ||||
\(969\) | −1.35130 | + | 4.60211i | −1.35130 | + | 4.60211i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | −0.654861 | + | 0.755750i | \(0.727273\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(972\) | −2.35225 | − | 0.511701i | −2.35225 | − | 0.511701i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.19136 | + | 1.37491i | 1.19136 | + | 1.37491i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(978\) | −1.30972 | −1.30972 | ||||||||
\(979\) | −0.153882 | + | 1.07028i | −0.153882 | + | 1.07028i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.254771 | + | 0.340335i | −0.254771 | + | 0.340335i | ||||
\(983\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(984\) | 1.43275 | + | 2.22940i | 1.43275 | + | 2.22940i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.51100 | + | 2.76719i | 1.51100 | + | 2.76719i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.69739 | + | 1.47080i | 1.69739 | + | 1.47080i | ||||
\(997\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(998\) | −0.767317 | + | 1.40524i | −0.767317 | + | 1.40524i | ||||
\(999\) | 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 | 712.1.y.a.427.1 | ✓ | 20 | |
4.3 | odd | 2 | 2848.1.cc.a.783.1 | 20 | |||
8.3 | odd | 2 | CM | 712.1.y.a.427.1 | ✓ | 20 | |
8.5 | even | 2 | 2848.1.cc.a.783.1 | 20 | |||
89.84 | even | 44 | inner | 712.1.y.a.707.1 | yes | 20 | |
356.351 | odd | 44 | 2848.1.cc.a.1775.1 | 20 | |||
712.173 | even | 44 | 2848.1.cc.a.1775.1 | 20 | |||
712.707 | odd | 44 | inner | 712.1.y.a.707.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
712.1.y.a.427.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
712.1.y.a.427.1 | ✓ | 20 | 8.3 | odd | 2 | CM | |
712.1.y.a.707.1 | yes | 20 | 89.84 | even | 44 | inner | |
712.1.y.a.707.1 | yes | 20 | 712.707 | odd | 44 | inner | |
2848.1.cc.a.783.1 | 20 | 4.3 | odd | 2 | |||
2848.1.cc.a.783.1 | 20 | 8.5 | even | 2 | |||
2848.1.cc.a.1775.1 | 20 | 356.351 | odd | 44 | |||
2848.1.cc.a.1775.1 | 20 | 712.173 | even | 44 |