Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,1,Mod(68,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(28))
chi = DirichletCharacter(H, H._module([14, 14, 23]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.68");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.bf (of order \(28\), degree \(12\), 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: | \(0.998629090279\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{28})\) |
Coefficient field: | \(\Q(\zeta_{84})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{84}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{84} - \cdots)\) |
Embedding invariants
Embedding label | 137.1 | ||
Root | \(0.149042 + 0.988831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.137 |
Dual form | 2001.1.bf.d.482.1 |
$q$-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 \(\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times\).
\(n\) | \(553\) | \(668\) | \(1132\) |
\(\chi(n)\) | \(e\left(\frac{17}{28}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.85486 | − | 0.649042i | −1.85486 | − | 0.649042i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.866025 | − | 0.500000i | \(-0.833333\pi\) | |||||||
\(3\) | −0.563320 | − | 0.826239i | −0.563320 | − | 0.826239i | ||||
\(4\) | 2.23740 | + | 1.78427i | 2.23740 | + | 1.78427i | ||||
\(5\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(6\) | 0.508614 | + | 1.89817i | 0.508614 | + | 1.89817i | ||||
\(7\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(8\) | −1.94648 | − | 3.09781i | −1.94648 | − | 3.09781i | ||||
\(9\) | −0.365341 | + | 0.930874i | −0.365341 | + | 0.930874i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(12\) | 0.213859 | − | 2.85375i | 0.213859 | − | 2.85375i | ||||
\(13\) | −1.61105 | + | 0.367711i | −1.61105 | + | 0.367711i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.963038 | + | 4.21934i | 0.963038 | + | 4.21934i | ||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | 1.28183 | − | 1.48952i | 1.28183 | − | 1.48952i | ||||
\(19\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.433884 | + | 0.900969i | −0.433884 | + | 0.900969i | ||||
\(24\) | −1.46304 | + | 3.35332i | −1.46304 | + | 3.35332i | ||||
\(25\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(26\) | 3.22692 | + | 0.363587i | 3.22692 | + | 0.363587i | ||||
\(27\) | 0.974928 | − | 0.222521i | 0.974928 | − | 0.222521i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.149042 | − | 0.988831i | 0.149042 | − | 0.988831i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.170965 | − | 0.488590i | 0.170965 | − | 0.488590i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
0.997204 | + | 0.0747301i | \(0.0238095\pi\) | |||||||
\(32\) | 0.542605 | − | 4.81575i | 0.542605 | − | 4.81575i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.47835 | + | 1.43087i | −2.47835 | + | 1.43087i | ||||
\(37\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.21135 | + | 1.12397i | 1.21135 | + | 1.12397i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.25033 | + | 1.25033i | −1.25033 | + | 1.25033i | −0.294755 | + | 0.955573i | \(0.595238\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.38956 | − | 1.38956i | 1.38956 | − | 1.38956i | ||||
\(47\) | 1.36254 | + | 0.856144i | 1.36254 | + | 0.856144i | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(48\) | 2.94369 | − | 3.17254i | 2.94369 | − | 3.17254i | ||||
\(49\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(50\) | −1.66393 | + | 1.04551i | −1.66393 | + | 1.04551i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.26066 | − | 2.05182i | −4.26066 | − | 2.05182i | ||||
\(53\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(54\) | −1.95278 | − | 0.220025i | −1.95278 | − | 0.220025i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.918245 | + | 1.73740i | −0.918245 | + | 1.73740i | ||||
\(59\) | 1.24698i | 1.24698i | 0.781831 | + | 0.623490i | \(0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(62\) | −0.634231 | + | 0.795301i | −0.634231 | + | 0.795301i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.25429 | + | 4.68109i | −2.25429 | + | 4.68109i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.988831 | − | 0.149042i | 0.988831 | − | 0.149042i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.443797 | + | 1.94440i | 0.443797 | + | 1.94440i | 0.294755 | + | 0.955573i | \(0.404762\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(72\) | 3.59480 | − | 0.680173i | 3.59480 | − | 0.680173i | ||||
\(73\) | 0.605443 | + | 1.73026i | 0.605443 | + | 1.73026i | 0.680173 | + | 0.733052i | \(0.261905\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.997204 | − | 0.0747301i | −0.997204 | − | 0.0747301i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.51738 | − | 2.87102i | −1.51738 | − | 2.87102i | ||||
\(79\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(82\) | 3.13069 | − | 1.50766i | 3.13069 | − | 1.50766i | ||||
\(83\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.57835 | + | 1.24167i | −2.57835 | + | 1.24167i | ||||
\(93\) | −0.500000 | + | 0.133975i | −0.500000 | + | 0.133975i | ||||
\(94\) | −1.97165 | − | 2.47237i | −1.97165 | − | 2.47237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.28462 | + | 2.26449i | −4.28462 | + | 2.26449i | ||||
\(97\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(98\) | 1.04551 | − | 1.66393i | 1.04551 | − | 1.66393i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.79000 | − | 0.636799i | 2.79000 | − | 0.636799i | ||||
\(101\) | −0.0739590 | − | 0.211363i | −0.0739590 | − | 0.211363i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(104\) | 4.27497 | + | 4.27497i | 4.27497 | + | 4.27497i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(108\) | 2.57835 | + | 1.24167i | 2.57835 | + | 1.24167i | ||||
\(109\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.09781 | − | 1.94648i | 2.09781 | − | 1.94648i | ||||
\(117\) | 0.246289 | − | 1.63402i | 0.246289 | − | 1.63402i | ||||
\(118\) | 0.809342 | − | 2.31297i | 0.809342 | − | 2.31297i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.433884 | − | 0.900969i | −0.433884 | − | 0.900969i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.73740 | + | 0.328735i | 1.73740 | + | 0.328735i | ||||
\(124\) | 1.25429 | − | 0.788125i | 1.25429 | − | 0.788125i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0633201 | − | 0.0397866i | −0.0633201 | − | 0.0397866i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(128\) | 3.79282 | − | 3.79282i | 3.79282 | − | 3.79282i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.350958 | − | 0.122805i | 0.350958 | − | 0.122805i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(138\) | −1.93087 | − | 0.365341i | −1.93087 | − | 0.365341i | ||||
\(139\) | 1.79690 | + | 0.865341i | 1.79690 | + | 0.865341i | 0.930874 | + | 0.365341i | \(0.119048\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0601697 | − | 1.60807i | −0.0601697 | − | 1.60807i | ||||
\(142\) | 0.438820 | − | 3.89463i | 0.438820 | − | 3.89463i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.27951 | − | 0.645033i | −4.27951 | − | 0.645033i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 3.60233i | − | 3.60233i | ||||||
\(147\) | 0.930874 | − | 0.365341i | 0.930874 | − | 0.365341i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(150\) | 1.80117 | + | 0.785841i | 1.80117 | + | 0.785841i | ||||
\(151\) | −0.433884 | + | 0.900969i | −0.433884 | + | 0.900969i | 0.563320 | + | 0.826239i | \(0.309524\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.704817 | + | 4.67615i | 0.704817 | + | 4.67615i | ||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.918245 | + | 1.73740i | 0.918245 | + | 1.73740i | ||||
\(163\) | −0.856144 | + | 1.36254i | −0.856144 | + | 1.36254i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(164\) | −5.02841 | + | 0.566566i | −5.02841 | + | 0.566566i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.12349 | + | 1.40881i | 1.12349 | + | 1.40881i | 0.900969 | + | 0.433884i | \(0.142857\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.55929 | − | 0.750915i | 1.55929 | − | 0.750915i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.445042 | −0.445042 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(174\) | 1.95278 | − | 0.220025i | 1.95278 | − | 0.220025i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.03030 | − | 0.702449i | 1.03030 | − | 0.702449i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.32091 | − | 0.636119i | 1.32091 | − | 0.636119i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.63558 | − | 0.409631i | 3.63558 | − | 0.409631i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.01438 | + | 0.0760175i | 1.01438 | + | 0.0760175i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.52097 | + | 4.34669i | 1.52097 | + | 4.34669i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(192\) | 5.13759 | − | 0.774367i | 5.13759 | − | 0.774367i | ||||
\(193\) | −0.0895474 | − | 0.794755i | −0.0895474 | − | 0.794755i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.23740 | + | 1.78427i | −2.23740 | + | 1.78427i | ||||
\(197\) | −0.751509 | + | 1.56052i | −0.751509 | + | 1.56052i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(200\) | −3.63558 | − | 0.409631i | −3.63558 | − | 0.409631i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.440050i | 0.440050i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.680173 | − | 0.733052i | −0.680173 | − | 0.733052i | ||||
\(208\) | −3.10300 | − | 6.44344i | −3.10300 | − | 6.44344i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.19745 | − | 0.752407i | 1.19745 | − | 0.752407i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.35654 | − | 1.46200i | 1.35654 | − | 1.46200i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.58701 | − | 2.58701i | −2.58701 | − | 2.58701i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.08855 | − | 1.47493i | 1.08855 | − | 1.47493i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.0990311 | + | 0.433884i | −0.0990311 | + | 0.433884i | 0.900969 | + | 0.433884i | \(0.142857\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.35332 | + | 1.46304i | −3.35332 | + | 1.46304i | ||||
\(233\) | − | 1.91115i | − | 1.91115i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) | ||
0.294755 | − | 0.955573i | \(-0.404762\pi\) | |||||||
\(234\) | −1.51738 | + | 2.87102i | −1.51738 | + | 2.87102i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.22495 | + | 2.79000i | −2.22495 | + | 2.79000i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.460898 | − | 0.367554i | 0.460898 | − | 0.367554i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(242\) | 0.220025 | + | 1.95278i | 0.220025 | + | 1.95278i | ||||
\(243\) | −0.149042 | + | 0.988831i | −0.149042 | + | 0.988831i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.00927 | − | 1.73740i | −3.00927 | − | 1.73740i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.84634 | + | 0.421415i | −1.84634 | + | 0.421415i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.0916264 | + | 0.114896i | 0.0916264 | + | 0.114896i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.81575 | + | 2.31914i | −4.81575 | + | 2.31914i | ||||
\(257\) | −0.233052 | − | 0.185853i | −0.233052 | − | 0.185853i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(262\) | −0.730682 | −0.730682 | ||||||||
\(263\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.0397866 | − | 0.0633201i | −0.0397866 | − | 0.0633201i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.87590 | + | 0.211363i | −1.87590 | + | 0.211363i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.47835 | + | 1.43087i | 2.47835 | + | 1.43087i | ||||
\(277\) | −0.0332580 | − | 0.145713i | −0.0332580 | − | 0.145713i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(278\) | −2.77135 | − | 2.77135i | −2.77135 | − | 2.77135i | ||||
\(279\) | 0.392355 | + | 0.337649i | 0.392355 | + | 0.337649i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(282\) | −0.932099 | + | 3.02179i | −0.932099 | + | 3.02179i | ||||
\(283\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(284\) | −2.47639 | + | 5.14227i | −2.47639 | + | 5.14227i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.28462 | + | 2.26449i | 4.28462 | + | 2.26449i | ||||
\(289\) | 1.00000i | 1.00000i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.73262 | + | 4.95155i | −1.73262 | + | 4.95155i | ||||
\(293\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(294\) | −1.96376 | + | 0.0734787i | −1.96376 | + | 0.0734787i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.367711 | − | 1.61105i | 0.367711 | − | 1.61105i | ||||
\(300\) | −2.09781 | − | 1.94648i | −2.09781 | − | 1.94648i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.38956 | − | 1.38956i | 1.38956 | − | 1.38956i | ||||
\(303\) | −0.132974 | + | 0.180173i | −0.132974 | + | 0.180173i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.40532 | + | 1.40532i | −1.40532 | + | 1.40532i | −0.623490 | + | 0.781831i | \(0.714286\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.10462 | + | 0.694076i | −1.10462 | + | 0.694076i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(312\) | 1.12397 | − | 5.94033i | 1.12397 | − | 5.94033i | ||||
\(313\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.218169 | − | 0.623490i | 0.218169 | − | 0.623490i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
1.00000 | \(0\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.426521 | − | 2.82978i | −0.426521 | − | 2.82978i | ||||
\(325\) | −0.716983 | + | 1.48883i | −0.716983 | + | 1.48883i | ||||
\(326\) | 2.47237 | − | 1.97165i | 2.47237 | − | 1.97165i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.30702 | + | 1.43954i | 6.30702 | + | 1.43954i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.41322 | − | 1.41322i | −1.41322 | − | 1.41322i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.680173 | − | 0.733052i | \(-0.738095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.16953 | − | 3.34234i | −1.16953 | − | 3.34234i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(338\) | −3.37964 | + | 0.380793i | −3.37964 | + | 0.380793i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.825489 | + | 0.288851i | 0.825489 | + | 0.288851i | ||||
\(347\) | 1.94986 | 1.94986 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(348\) | −2.79000 | − | 0.636799i | −2.79000 | − | 0.636799i | ||||
\(349\) | −1.97766 | −1.97766 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.48883 | + | 0.716983i | −1.48883 | + | 0.716983i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.22563 | − | 0.590232i | 1.22563 | − | 0.590232i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(354\) | −2.36698 | + | 0.634231i | −2.36698 | + | 0.634231i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.86297 | + | 0.322580i | −2.86297 | + | 0.322580i | ||||
\(359\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.974928 | + | 0.222521i | −0.974928 | + | 0.222521i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(368\) | −4.21934 | − | 0.963038i | −4.21934 | − | 0.963038i | ||||
\(369\) | −0.707101 | − | 1.62069i | −0.707101 | − | 1.62069i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.35775 | − | 0.592380i | −1.35775 | − | 0.592380i | ||||
\(373\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 5.88737i | − | 5.88737i | ||||||
\(377\) | 0.123490 | + | 1.64786i | 0.123490 | + | 1.64786i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.00279620 | + | 0.0747301i | 0.00279620 | + | 0.0747301i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(384\) | −5.27035 | − | 0.997204i | −5.27035 | − | 0.997204i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.349732 | + | 1.53228i | −0.349732 | + | 1.53228i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.45327 | − | 1.20835i | 3.45327 | − | 1.20835i | ||||
\(393\) | −0.299168 | − | 0.220796i | −0.299168 | − | 0.220796i | ||||
\(394\) | 2.40679 | − | 2.40679i | 2.40679 | − | 2.40679i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.131178 | − | 0.574730i | 0.131178 | − | 0.574730i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.89926 | + | 1.87778i | 3.89926 | + | 1.87778i | ||||
\(401\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0957728 | + | 0.850007i | −0.0957728 | + | 0.850007i | ||||
\(404\) | 0.211652 | − | 0.604867i | 0.211652 | − | 0.604867i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.75711 | + | 0.197979i | 1.75711 | + | 0.197979i | 0.930874 | − | 0.365341i | \(-0.119048\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.785841 | + | 1.80117i | 0.785841 | + | 1.80117i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.896642 | + | 7.95792i | 0.896642 | + | 7.95792i | ||||
\(417\) | −0.297251 | − | 1.97213i | −0.297251 | − | 1.97213i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(422\) | −2.70944 | + | 0.618412i | −2.70944 | + | 0.618412i | ||||
\(423\) | −1.29476 | + | 0.955573i | −1.29476 | + | 0.955573i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.46509 | + | 1.83135i | −3.46509 | + | 1.83135i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(432\) | 1.87778 | + | 3.89926i | 1.87778 | + | 3.89926i | ||||
\(433\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −2.97639 | + | 2.02927i | −2.97639 | + | 2.02927i | ||||
\(439\) | −0.460898 | − | 0.367554i | −0.460898 | − | 0.367554i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.826239 | − | 0.563320i | −0.826239 | − | 0.563320i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.425511 | + | 0.677197i | 0.425511 | + | 0.677197i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.465297 | − | 0.740517i | 0.465297 | − | 0.740517i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.623490 | − | 1.78183i | −0.623490 | − | 1.78183i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(450\) | −0.365341 | − | 1.93087i | −0.365341 | − | 1.93087i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.988831 | − | 0.149042i | 0.988831 | − | 0.149042i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.98603 | − | 0.223772i | −1.98603 | − | 0.223772i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) |
−0.988831 | − | 0.149042i | \(-0.952381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.80194i | 1.80194i | 0.433884 | + | 0.900969i | \(0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(464\) | 4.31575 | − | 0.323421i | 4.31575 | − | 0.323421i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.24041 | + | 3.54490i | −1.24041 | + | 3.54490i | ||||
\(467\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(468\) | 3.46658 | − | 3.21652i | 3.46658 | − | 3.21652i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.86291 | − | 2.42722i | 3.86291 | − | 2.42722i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.09346 | + | 0.382617i | −1.09346 | + | 0.382617i | ||||
\(479\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.636799 | − | 2.79000i | 0.636799 | − | 2.79000i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.918245 | − | 1.73740i | 0.918245 | − | 1.73740i | ||||
\(487\) | −1.22563 | − | 0.590232i | −1.22563 | − | 0.590232i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.60807 | − | 0.0601697i | 1.60807 | − | 0.0601697i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.308658 | + | 0.882094i | −0.308658 | + | 0.882094i | 0.680173 | + | 0.733052i | \(0.261905\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(492\) | 3.30072 | + | 3.83551i | 3.30072 | + | 3.83551i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.22617 | + | 0.250830i | 2.22617 | + | 0.250830i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.858075 | − | 1.78181i | 0.858075 | − | 1.78181i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
0.563320 | − | 0.826239i | \(-0.309524\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.531130 | − | 1.72188i | 0.531130 | − | 1.72188i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.49881 | − | 0.865341i | −1.49881 | − | 0.865341i | ||||
\(508\) | −0.0706825 | − | 0.201999i | −0.0706825 | − | 0.201999i | ||||
\(509\) | 1.81507 | − | 0.414278i | 1.81507 | − | 0.414278i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.10761 | − | 0.575490i | 5.10761 | − | 0.575490i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.311651 | + | 0.495990i | 0.311651 | + | 0.495990i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.250701 | + | 0.367711i | 0.250701 | + | 0.367711i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | −1.28183 | − | 1.48952i | −1.28183 | − | 1.48952i | ||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 1.00435 | + | 0.351438i | 1.00435 | + | 0.351438i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.16078 | − | 0.455573i | −1.16078 | − | 0.455573i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.55458 | − | 2.47410i | 1.55458 | − | 2.47410i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.26968 | − | 0.733052i | −1.26968 | − | 0.733052i | ||||
\(538\) | 0.0327011 | + | 0.143273i | 0.0327011 | + | 0.143273i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.132974 | − | 1.18017i | −0.132974 | − | 1.18017i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.733052 | − | 0.680173i | \(-0.238095\pi\) | |||||||
\(542\) | 3.61670 | + | 0.825489i | 3.61670 | + | 0.825489i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.19158 | + | 1.49419i | −1.19158 | + | 1.49419i | −0.365341 | + | 0.930874i | \(0.619048\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.38645 | − | 2.77310i | −2.38645 | − | 2.77310i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.0328850 | + | 0.291862i | −0.0328850 | + | 0.291862i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.47639 | + | 5.14227i | 2.47639 | + | 5.14227i | ||||
\(557\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(558\) | −0.508614 | − | 0.880945i | −0.508614 | − | 0.880945i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 2.73461 | − | 3.70526i | 2.73461 | − | 3.70526i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.15955 | − | 5.15955i | 5.15955 | − | 5.15955i | ||||
\(569\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.433884 | + | 0.900969i | 0.433884 | + | 0.900969i | ||||
\(576\) | −3.53392 | − | 3.80866i | −3.53392 | − | 3.80866i | ||||
\(577\) | −0.223772 | + | 1.98603i | −0.223772 | + | 1.98603i | −0.0747301 | + | 0.997204i | \(0.523810\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(578\) | 0.649042 | − | 1.85486i | 0.649042 | − | 1.85486i | ||||
\(579\) | −0.606214 | + | 0.521689i | −0.606214 | + | 0.521689i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.18152 | − | 5.24346i | 4.18152 | − | 5.24346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.06356 | + | 0.848162i | −1.06356 | + | 0.848162i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(588\) | 2.73461 | + | 0.843515i | 2.73461 | + | 0.843515i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.71271 | − | 0.258149i | 1.71271 | − | 0.258149i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.433884 | + | 1.90097i | 0.433884 | + | 1.90097i | 0.433884 | + | 0.900969i | \(0.357143\pi\) |
1.00000i | \(0.500000\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.72769 | + | 2.74960i | −1.72769 | + | 2.74960i | ||||
\(599\) | −1.87590 | + | 0.211363i | −1.87590 | + | 0.211363i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(600\) | 1.70954 | + | 3.23461i | 1.70954 | + | 3.23461i | ||||
\(601\) | 1.02781 | + | 1.63575i | 1.02781 | + | 1.63575i | 0.733052 | + | 0.680173i | \(0.238095\pi\) |
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.57835 | + | 1.24167i | −2.57835 | + | 1.24167i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.363587 | − | 0.247889i | 0.363587 | − | 0.247889i | ||||
\(607\) | 1.00435 | + | 0.351438i | 1.00435 | + | 0.351438i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.50994 | − | 0.878265i | −2.50994 | − | 0.878265i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(614\) | 3.51878 | − | 1.69456i | 3.51878 | − | 1.69456i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(622\) | 2.49939 | − | 0.570469i | 2.49939 | − | 0.570469i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.57584 | + | 6.19353i | −3.57584 | + | 6.19353i | ||||
\(625\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.29621 | − | 0.565533i | −1.29621 | − | 0.565533i | ||||
\(634\) | −0.809342 | + | 1.01488i | −0.809342 | + | 1.01488i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.65248i | − | 1.65248i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.97213 | − | 0.297251i | −1.97213 | − | 0.297251i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.414278 | − | 1.81507i | 0.414278 | − | 1.81507i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
0.563320 | − | 0.826239i | \(-0.309524\pi\) | |||||||
\(648\) | −0.680173 | + | 3.59480i | −0.680173 | + | 3.59480i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.29621 | − | 2.29621i | 2.29621 | − | 2.29621i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.34669 | + | 1.52097i | −4.34669 | + | 1.52097i | ||||
\(653\) | −1.82344 | + | 0.638050i | −1.82344 | + | 0.638050i | −0.826239 | + | 0.563320i | \(0.809524\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.47968 | − | 4.07145i | −6.47968 | − | 4.07145i | ||||
\(657\) | −1.83184 | − | 0.0685427i | −1.83184 | − | 0.0685427i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(662\) | 1.70409 | + | 3.53857i | 1.70409 | + | 3.53857i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.826239 | + | 0.563320i | 0.826239 | + | 0.563320i | ||||
\(668\) | 5.15669i | 5.15669i | ||||||||
\(669\) | 0.414278 | − | 0.162592i | 0.414278 | − | 0.162592i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.590232 | + | 1.22563i | −0.590232 | + | 1.22563i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.433884 | − | 0.900969i | 0.433884 | − | 0.900969i | ||||
\(676\) | 4.82860 | + | 1.10210i | 4.82860 | + | 1.10210i | ||||
\(677\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.290611 | − | 0.0663300i | 0.290611 | − | 0.0663300i | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.781831 | − | 0.376510i | 0.781831 | − | 0.376510i | − | 1.00000i | \(-0.5\pi\) | |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(692\) | −0.995739 | − | 0.794075i | −0.995739 | − | 0.794075i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.61670 | − | 1.26554i | −3.61670 | − | 1.26554i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.09781 | + | 1.94648i | 3.09781 | + | 1.94648i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 3.66828 | + | 1.28359i | 3.66828 | + | 1.28359i | ||||
\(699\) | −1.57906 | + | 1.07659i | −1.57906 | + | 1.07659i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(702\) | 3.22692 | − | 0.363587i | 3.22692 | − | 0.363587i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.65645 | + | 0.299310i | −2.65645 | + | 0.299310i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.55856 | + | 0.266677i | 3.55856 | + | 0.266677i | ||||
\(709\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.366025 | + | 0.366025i | 0.366025 | + | 0.366025i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.09043 | + | 0.933613i | 4.09043 | + | 0.933613i | ||||
\(717\) | −0.563320 | − | 0.173761i | −0.563320 | − | 0.173761i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.376510 | + | 0.781831i | −0.376510 | + | 0.781831i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.95278 | + | 0.220025i | 1.95278 | + | 0.220025i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.680173 | − | 0.733052i | −0.680173 | − | 0.733052i | ||||
\(726\) | 1.48952 | − | 1.28183i | 1.48952 | − | 1.28183i | ||||
\(727\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.10341 | + | 2.57835i | 4.10341 | + | 2.57835i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.259673 | + | 3.46509i | 0.259673 | + | 3.46509i | ||||
\(739\) | 1.66900 | − | 0.584010i | 1.66900 | − | 0.584010i | 0.680173 | − | 0.733052i | \(-0.261905\pi\) |
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(744\) | 1.38827 | + | 1.28813i | 1.38827 | + | 1.28813i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(752\) | −2.30018 | + | 6.57354i | −2.30018 | + | 6.57354i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.840473 | − | 3.13669i | 0.840473 | − | 3.13669i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.116853 | − | 0.0931869i | 0.116853 | − | 0.0931869i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) |
0.680173 | + | 0.733052i | \(0.261905\pi\) | |||||||
\(762\) | 0.0433164 | − | 0.140428i | 0.0433164 | − | 0.140428i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.458528 | − | 2.00894i | −0.458528 | − | 2.00894i | ||||
\(768\) | 4.62897 | + | 2.67254i | 4.62897 | + | 2.67254i | ||||
\(769\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.0222759 | + | 0.297251i | −0.0222759 | + | 0.297251i | ||||
\(772\) | 1.21770 | − | 1.93797i | 1.21770 | − | 1.93797i | ||||
\(773\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.275400 | − | 0.438297i | −0.275400 | − | 0.438297i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.0747301 | − | 0.997204i | −0.0747301 | − | 0.997204i | ||||
\(784\) | −4.32785 | −4.32785 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.411608 | + | 0.603718i | 0.411608 | + | 0.603718i | ||||
\(787\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(788\) | −4.46583 | + | 2.15063i | −4.46583 | + | 2.15063i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.616341 | + | 0.980901i | −0.616341 | + | 0.980901i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −3.42680 | − | 3.42680i | −3.42680 | − | 3.42680i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.729335 | − | 1.51448i | 0.729335 | − | 1.51448i | ||||
\(807\) | −0.0299049 | + | 0.0685427i | −0.0299049 | + | 0.0685427i | ||||
\(808\) | −0.510802 | + | 0.640525i | −0.510802 | + | 0.640525i | ||||
\(809\) | −1.05737 | − | 0.119137i | −1.05737 | − | 0.119137i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.23137 | + | 1.43087i | 1.23137 | + | 1.43087i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3.13069 | − | 1.50766i | −3.13069 | − | 1.50766i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.347948 | − | 1.52446i | 0.347948 | − | 1.52446i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.781831 | − | 0.623490i | \(-0.214286\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.791295 | − | 0.497204i | −0.791295 | − | 0.497204i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(828\) | −0.213859 | − | 2.85375i | −0.213859 | − | 2.85375i | ||||
\(829\) | −0.467085 | + | 0.467085i | −0.467085 | + | 0.467085i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.101659 | + | 0.109562i | −0.101659 | + | 0.109562i | ||||
\(832\) | 1.91049 | − | 8.37038i | 1.91049 | − | 8.37038i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.728639 | + | 3.85095i | −0.728639 | + | 3.85095i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.0579571 | − | 0.514383i | 0.0579571 | − | 0.514383i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.955573 | − | 0.294755i | −0.955573 | − | 0.294755i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.02167 | + | 0.453134i | 4.02167 | + | 0.453134i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.02179 | − | 0.932099i | 3.02179 | − | 0.932099i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 5.64374 | − | 0.850657i | 5.64374 | − | 0.850657i | ||||
\(853\) | 0.158342 | + | 0.158342i | 0.158342 | + | 0.158342i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.974928 | + | 0.222521i | −0.974928 | + | 0.222521i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.497204 | − | 0.791295i | 0.497204 | − | 0.791295i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.997204 | + | 0.0747301i | \(0.0238095\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(864\) | −0.542605 | − | 4.81575i | −0.542605 | − | 4.81575i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.826239 | − | 0.563320i | 0.826239 | − | 0.563320i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.06719 | − | 1.35775i | 5.06719 | − | 1.35775i | ||||
\(877\) | −0.974928 | − | 1.22252i | −0.974928 | − | 1.22252i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(878\) | 0.616341 | + | 0.980901i | 0.616341 | + | 0.980901i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(882\) | 1.16694 | + | 1.58114i | 1.16694 | + | 1.58114i | ||||
\(883\) | 1.21572 | − | 0.277479i | 1.21572 | − | 0.277479i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.349732 | − | 1.53228i | −0.349732 | − | 1.53228i | ||||
\(887\) | −0.0528791 | − | 0.0528791i | −0.0528791 | − | 0.0528791i | 0.680173 | − | 0.733052i | \(-0.261905\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.995739 | + | 0.794075i | −0.995739 | + | 0.794075i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.53825 | + | 0.603718i | −1.53825 | + | 0.603718i | ||||
\(898\) | 3.70971i | 3.70971i | ||||||||
\(899\) | −0.457652 | − | 0.241876i | −0.457652 | − | 0.241876i | ||||
\(900\) | −0.426521 | + | 2.82978i | −0.426521 | + | 2.82978i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.93087 | − | 0.365341i | −1.93087 | − | 0.365341i | ||||
\(907\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.223772 | + | 0.00837297i | 0.223772 | + | 0.00837297i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.95278 | + | 0.369485i | 1.95278 | + | 0.369485i | ||||
\(922\) | 3.53857 | + | 1.70409i | 3.53857 | + | 1.70409i | ||||
\(923\) | −1.42996 | − | 2.96934i | −1.42996 | − | 2.96934i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.16953 | − | 3.34234i | 1.16953 | − | 3.34234i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.68109 | − | 1.25429i | −4.68109 | − | 1.25429i | ||||
\(929\) | 1.65248i | 1.65248i | 0.563320 | + | 0.826239i | \(0.309524\pi\) | ||||
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.41000 | − | 4.27601i | 3.41000 | − | 4.27601i | ||||
\(933\) | 1.19572 | + | 0.521689i | 1.19572 | + | 0.521689i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.54128 | + | 2.41764i | −5.54128 | + | 2.41764i | ||||
\(937\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.584010 | − | 1.66900i | −0.584010 | − | 1.66900i | ||||
\(944\) | −5.26143 | + | 1.20089i | −5.26143 | + | 1.20089i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.0743122 | − | 0.00837297i | 0.0743122 | − | 0.00837297i | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.61163 | − | 2.56489i | −1.61163 | − | 2.56489i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.638050 | + | 0.170965i | −0.638050 | + | 0.170965i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.68703 | 1.68703 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.572340 | + | 0.456426i | 0.572340 | + | 0.456426i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.794755 | − | 0.0895474i | 0.794755 | − | 0.0895474i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(968\) | −1.94648 | + | 3.09781i | −1.94648 | + | 3.09781i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(972\) | −2.09781 | + | 1.94648i | −2.09781 | + | 1.94648i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.89028 | + | 1.89028i | 1.89028 | + | 1.89028i | ||||
\(975\) | 1.63402 | − | 0.246289i | 1.63402 | − | 0.246289i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(978\) | −3.02179 | − | 0.932099i | −3.02179 | − | 0.932099i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.14503 | − | 1.43583i | 1.14503 | − | 1.43583i | ||||
\(983\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(984\) | −2.36347 | − | 6.02202i | −2.36347 | − | 6.02202i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.846011 | + | 1.75676i | 0.846011 | + | 1.75676i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(992\) | −2.26016 | − | 1.08844i | −2.26016 | − | 1.08844i | ||||
\(993\) | −0.371563 | + | 1.96376i | −0.371563 | + | 1.96376i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.59842 | + | 1.00435i | 1.59842 | + | 1.00435i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(998\) | −2.74808 | + | 2.74808i | −2.74808 | + | 2.74808i | ||||
\(999\) | 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 | 2001.1.bf.d.137.1 | yes | 24 | |
3.2 | odd | 2 | 2001.1.bf.c.137.2 | ✓ | 24 | ||
23.22 | odd | 2 | CM | 2001.1.bf.d.137.1 | yes | 24 | |
29.18 | odd | 28 | 2001.1.bf.c.482.2 | yes | 24 | ||
69.68 | even | 2 | 2001.1.bf.c.137.2 | ✓ | 24 | ||
87.47 | even | 28 | inner | 2001.1.bf.d.482.1 | yes | 24 | |
667.482 | even | 28 | 2001.1.bf.c.482.2 | yes | 24 | ||
2001.482 | odd | 28 | inner | 2001.1.bf.d.482.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.1.bf.c.137.2 | ✓ | 24 | 3.2 | odd | 2 | ||
2001.1.bf.c.137.2 | ✓ | 24 | 69.68 | even | 2 | ||
2001.1.bf.c.482.2 | yes | 24 | 29.18 | odd | 28 | ||
2001.1.bf.c.482.2 | yes | 24 | 667.482 | even | 28 | ||
2001.1.bf.d.137.1 | yes | 24 | 1.1 | even | 1 | trivial | |
2001.1.bf.d.137.1 | yes | 24 | 23.22 | odd | 2 | CM | |
2001.1.bf.d.482.1 | yes | 24 | 87.47 | even | 28 | inner | |
2001.1.bf.d.482.1 | yes | 24 | 2001.482 | odd | 28 | inner |