Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3620,1,Mod(219,3620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3620, base_ring=CyclotomicField(90))
chi = DirichletCharacter(H, H._module([45, 45, 68]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3620.219");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3620 = 2^{2} \cdot 5 \cdot 181 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3620.dy (of order \(90\), degree \(24\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.80661534573\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Coefficient field: | \(\Q(\zeta_{45})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{45}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{45} - \cdots)\) |
Embedding invariants
Embedding label | 2139.1 | ||
Root | \(-0.241922 - 0.970296i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3620.2139 |
Dual form | 3620.1.dy.a.1799.1 |
$q$-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 \(\left(\mathbb{Z}/3620\mathbb{Z}\right)^\times\).
\(n\) | \(1811\) | \(2897\) | \(3441\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{45}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.882948 | + | 0.469472i | 0.882948 | + | 0.469472i | ||||
\(3\) | −1.20442 | + | 1.54158i | −1.20442 | + | 1.54158i | −0.438371 | + | 0.898794i | \(0.644444\pi\) |
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(4\) | 0.559193 | + | 0.829038i | 0.559193 | + | 0.829038i | ||||
\(5\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(6\) | −1.78716 | + | 0.795697i | −1.78716 | + | 0.795697i | ||||
\(7\) | 0.766044 | + | 1.32683i | 0.766044 | + | 1.32683i | 0.939693 | + | 0.342020i | \(0.111111\pi\) |
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(8\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(9\) | −0.683935 | − | 2.74311i | −0.683935 | − | 2.74311i | ||||
\(10\) | 0.241922 | + | 0.970296i | 0.241922 | + | 0.970296i | ||||
\(11\) | 0 | 0 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
−0.438371 | + | 0.898794i | \(0.644444\pi\) | |||||||
\(12\) | −1.95153 | − | 0.136464i | −1.95153 | − | 0.136464i | ||||
\(13\) | 0 | 0 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
−0.0348995 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(14\) | 0.0534691 | + | 1.53116i | 0.0534691 | + | 1.53116i | ||||
\(15\) | −1.95153 | + | 0.136464i | −1.95153 | + | 0.136464i | ||||
\(16\) | −0.374607 | + | 0.927184i | −0.374607 | + | 0.927184i | ||||
\(17\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(18\) | 0.683935 | − | 2.74311i | 0.683935 | − | 2.74311i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | −0.241922 | + | 0.970296i | −0.241922 | + | 0.970296i | ||||
\(21\) | −2.96805 | − | 0.417132i | −2.96805 | − | 0.417132i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.885740 | − | 0.855349i | −0.885740 | − | 0.855349i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(24\) | −1.65903 | − | 1.03668i | −1.65903 | − | 1.03668i | ||||
\(25\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.26531 | + | 1.45381i | 3.26531 | + | 1.45381i | ||||
\(28\) | −0.671624 | + | 1.37703i | −0.671624 | + | 1.37703i | ||||
\(29\) | −0.207022 | − | 1.96969i | −0.207022 | − | 1.96969i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
0.0348995 | − | 0.999391i | \(-0.488889\pi\) | |||||||
\(30\) | −1.78716 | − | 0.795697i | −1.78716 | − | 0.795697i | ||||
\(31\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(32\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.473442 | + | 1.45710i | −0.473442 | + | 1.45710i | ||||
\(36\) | 1.89169 | − | 2.10094i | 1.89169 | − | 2.10094i | ||||
\(37\) | 0 | 0 | −0.990268 | − | 0.139173i | \(-0.955556\pi\) | ||||
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(41\) | 0.333843 | − | 0.0957278i | 0.333843 | − | 0.0957278i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(42\) | −2.42480 | − | 1.76172i | −2.42480 | − | 1.76172i | ||||
\(43\) | 1.59381 | + | 0.580099i | 1.59381 | + | 0.580099i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
0.615661 | + | 0.788011i | \(0.288889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.58089 | − | 2.34376i | 1.58089 | − | 2.34376i | ||||
\(46\) | −0.380500 | − | 1.17106i | −0.380500 | − | 1.17106i | ||||
\(47\) | −0.208548 | − | 0.0145831i | −0.208548 | − | 0.0145831i | −0.0348995 | − | 0.999391i | \(-0.511111\pi\) |
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(48\) | −0.978148 | − | 1.69420i | −0.978148 | − | 1.69420i | ||||
\(49\) | −0.673648 | + | 1.16679i | −0.673648 | + | 1.16679i | ||||
\(50\) | −0.559193 | + | 0.829038i | −0.559193 | + | 0.829038i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.961262 | − | 0.275637i | \(-0.911111\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(54\) | 2.20058 | + | 2.81661i | 2.20058 | + | 2.81661i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.23949 | + | 0.900539i | −1.23949 | + | 0.900539i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.741922 | − | 1.83632i | 0.741922 | − | 1.83632i | ||||
\(59\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(60\) | −1.20442 | − | 1.54158i | −1.20442 | − | 1.54158i | ||||
\(61\) | 0.333843 | + | 1.89332i | 0.333843 | + | 1.89332i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.11572 | − | 3.00881i | 3.11572 | − | 3.00881i | ||||
\(64\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.22256 | + | 0.544320i | −1.22256 | + | 0.544320i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.38539 | − | 0.335245i | 2.38539 | − | 0.335245i | ||||
\(70\) | −1.10209 | + | 1.06428i | −1.10209 | + | 1.06428i | ||||
\(71\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(72\) | 2.65660 | − | 0.966922i | 2.65660 | − | 0.966922i | ||||
\(73\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.40724 | − | 1.35896i | −1.40724 | − | 1.35896i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.961262 | − | 0.275637i | \(-0.911111\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(80\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(81\) | −3.67779 | + | 1.95551i | −3.67779 | + | 1.95551i | ||||
\(82\) | 0.339707 | + | 0.0722070i | 0.339707 | + | 0.0722070i | ||||
\(83\) | 1.37217 | − | 0.857427i | 1.37217 | − | 0.857427i | 0.374607 | − | 0.927184i | \(-0.377778\pi\) |
0.997564 | + | 0.0697565i | \(0.0222222\pi\) | |||||||
\(84\) | −1.31389 | − | 2.69388i | −1.31389 | − | 2.69388i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.13491 | + | 1.26045i | 1.13491 | + | 1.26045i | ||||
\(87\) | 3.28577 | + | 2.05318i | 3.28577 | + | 2.05318i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.194206 | − | 1.10140i | 0.194206 | − | 1.10140i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(90\) | 2.49617 | − | 1.32724i | 2.49617 | − | 1.32724i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.213817 | − | 1.21262i | 0.213817 | − | 1.21262i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.177290 | − | 0.110783i | −0.177290 | − | 0.110783i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.0682737 | − | 1.95510i | −0.0682737 | − | 1.95510i | ||||
\(97\) | 0 | 0 | −0.438371 | − | 0.898794i | \(-0.644444\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(98\) | −1.14257 | + | 0.713958i | −1.14257 | + | 0.713958i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.882948 | + | 0.469472i | −0.882948 | + | 0.469472i | ||||
\(101\) | 1.87481 | − | 0.682374i | 1.87481 | − | 0.682374i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.961262 | − | 0.275637i | \(-0.0888889\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.732841 | − | 1.81385i | −0.732841 | − | 1.81385i | −0.559193 | − | 0.829038i | \(-0.688889\pi\) |
−0.173648 | − | 0.984808i | \(-0.555556\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.67602 | − | 2.48481i | −1.67602 | − | 2.48481i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(108\) | 0.620676 | + | 3.52003i | 0.620676 | + | 3.52003i | ||||
\(109\) | 1.35192 | − | 0.492057i | 1.35192 | − | 0.492057i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.51718 | + | 0.213226i | −1.51718 | + | 0.213226i | ||||
\(113\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0429726 | − | 1.23057i | 0.0429726 | − | 1.23057i | ||||
\(116\) | 1.51718 | − | 1.27306i | 1.51718 | − | 1.27306i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.339707 | − | 1.92657i | −0.339707 | − | 1.92657i | ||||
\(121\) | −0.615661 | − | 0.788011i | −0.615661 | − | 0.788011i | ||||
\(122\) | −0.594092 | + | 1.82843i | −0.594092 | + | 1.82843i | ||||
\(123\) | −0.254513 | + | 0.629942i | −0.254513 | + | 0.629942i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(126\) | 4.16357 | − | 1.19388i | 4.16357 | − | 1.19388i | ||||
\(127\) | −1.15707 | − | 1.48098i | −1.15707 | − | 1.48098i | −0.848048 | − | 0.529919i | \(-0.822222\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(128\) | −0.961262 | − | 0.275637i | −0.961262 | − | 0.275637i | ||||
\(129\) | −2.81388 | + | 1.75831i | −2.81388 | + | 1.75831i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.33500 | − | 0.0933524i | −1.33500 | − | 0.0933524i | ||||
\(135\) | 1.10453 | + | 3.39939i | 1.10453 | + | 3.39939i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) | ||||
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(138\) | 2.26356 | + | 0.823869i | 2.26356 | + | 0.823869i | ||||
\(139\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(140\) | −1.47274 | + | 0.422301i | −1.47274 | + | 0.422301i | ||||
\(141\) | 0.273659 | − | 0.303929i | 0.273659 | − | 0.303929i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.79958 | + | 0.393455i | 2.79958 | + | 0.393455i | ||||
\(145\) | 1.32524 | − | 1.47183i | 1.32524 | − | 1.47183i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.987354 | − | 2.44379i | −0.987354 | − | 2.44379i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.573931 | + | 0.481585i | −0.573931 | + | 0.481585i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(150\) | −0.604528 | − | 1.86055i | −0.604528 | − | 1.86055i | ||||
\(151\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.848048 | − | 0.529919i | \(-0.822222\pi\) | ||||
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.990268 | − | 0.139173i | −0.990268 | − | 0.139173i | ||||
\(161\) | 0.456385 | − | 1.83046i | 0.456385 | − | 1.83046i | ||||
\(162\) | −4.16535 | −4.16535 | ||||||||
\(163\) | −0.117052 | + | 0.469472i | −0.117052 | + | 0.469472i | 0.882948 | + | 0.469472i | \(0.155556\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(164\) | 0.266044 | + | 0.223238i | 0.266044 | + | 0.223238i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.61409 | − | 0.112868i | 1.61409 | − | 0.112868i | ||||
\(167\) | 0.0502092 | + | 1.43780i | 0.0502092 | + | 1.43780i | 0.719340 | + | 0.694658i | \(0.244444\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(168\) | 0.104601 | − | 2.99539i | 0.104601 | − | 2.99539i | ||||
\(169\) | −0.997564 | − | 0.0697565i | −0.997564 | − | 0.0697565i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.410323 | + | 1.64571i | 0.410323 | + | 1.64571i | ||||
\(173\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(174\) | 1.93726 | + | 3.35543i | 1.93726 | + | 3.35543i | ||||
\(175\) | −1.39963 | + | 0.623157i | −1.39963 | + | 0.623157i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.688547 | − | 0.881300i | 0.688547 | − | 0.881300i | ||||
\(179\) | 0 | 0 | −0.882948 | − | 0.469472i | \(-0.844444\pi\) | ||||
0.882948 | + | 0.469472i | \(0.155556\pi\) | |||||||
\(180\) | 2.82709 | 2.82709 | ||||||||
\(181\) | 0.559193 | + | 0.829038i | 0.559193 | + | 0.829038i | ||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.32079 | − | 1.76569i | −3.32079 | − | 1.76569i | ||||
\(184\) | 0.758078 | − | 0.970296i | 0.758078 | − | 0.970296i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.104528 | − | 0.181049i | −0.104528 | − | 0.181049i | ||||
\(189\) | 0.572418 | + | 5.44619i | 0.572418 | + | 5.44619i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
0.241922 | + | 0.970296i | \(0.422222\pi\) | |||||||
\(192\) | 0.857583 | − | 1.75831i | 0.857583 | − | 1.75831i | ||||
\(193\) | 0 | 0 | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) | ||||
0.997564 | + | 0.0697565i | \(0.0222222\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.34401 | + | 0.0939826i | −1.34401 | + | 0.0939826i | ||||
\(197\) | 0 | 0 | 0.374607 | − | 0.927184i | \(-0.377778\pi\) | ||||
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.241922 | − | 0.970296i | \(-0.422222\pi\) | ||||
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(200\) | −1.00000 | −1.00000 | ||||||||
\(201\) | 0.633360 | − | 2.54027i | 0.633360 | − | 2.54027i | ||||
\(202\) | 1.97571 | + | 0.277668i | 1.97571 | + | 0.277668i | ||||
\(203\) | 2.45485 | − | 1.78355i | 2.45485 | − | 1.78355i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.294524 | + | 0.184039i | 0.294524 | + | 0.184039i | ||||
\(206\) | 0.204489 | − | 1.94558i | 0.204489 | − | 1.94558i | ||||
\(207\) | −1.74053 | + | 3.01469i | −1.74053 | + | 3.01469i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.313295 | − | 2.98080i | −0.313295 | − | 2.98080i | ||||
\(211\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.270928 | + | 0.555485i | 0.270928 | + | 0.555485i | ||||
\(215\) | 0.635369 | + | 1.57259i | 0.635369 | + | 1.57259i | ||||
\(216\) | −1.10453 | + | 3.39939i | −1.10453 | + | 3.39939i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.42468 | + | 0.200226i | 1.42468 | + | 0.200226i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.0564686 | + | 0.0410268i | 0.0564686 | + | 0.0410268i | 0.615661 | − | 0.788011i | \(-0.288889\pi\) |
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(224\) | −1.43969 | − | 0.524005i | −1.43969 | − | 0.524005i | ||||
\(225\) | 2.79958 | − | 0.393455i | 2.79958 | − | 0.393455i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.149516 | + | 0.460163i | 0.149516 | + | 0.460163i | 0.997564 | − | 0.0697565i | \(-0.0222222\pi\) |
−0.848048 | + | 0.529919i | \(0.822222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(230\) | 0.615661 | − | 1.06636i | 0.615661 | − | 1.06636i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.93726 | − | 0.411777i | 1.93726 | − | 0.411777i | ||||
\(233\) | 0 | 0 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
−0.848048 | + | 0.529919i | \(0.822222\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.128708 | − | 0.164739i | −0.128708 | − | 0.164739i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.374607 | − | 0.927184i | \(-0.377778\pi\) | ||||
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(240\) | 0.604528 | − | 1.86055i | 0.604528 | − | 1.86055i | ||||
\(241\) | 0.615661 | + | 0.788011i | 0.615661 | + | 0.788011i | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(242\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(243\) | 0.794324 | − | 4.50483i | 0.794324 | − | 4.50483i | ||||
\(244\) | −1.38295 | + | 1.33550i | −1.38295 | + | 1.33550i | ||||
\(245\) | −1.31785 | + | 0.280119i | −1.31785 | + | 0.280119i | ||||
\(246\) | −0.520461 | + | 0.436719i | −0.520461 | + | 0.436719i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.330869 | + | 3.14801i | −0.330869 | + | 3.14801i | ||||
\(250\) | −0.990268 | + | 0.139173i | −0.990268 | + | 0.139173i | ||||
\(251\) | 0 | 0 | 0.719340 | − | 0.694658i | \(-0.244444\pi\) | ||||
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(252\) | 4.23670 | + | 0.900539i | 4.23670 | + | 0.900539i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.326352 | − | 1.85083i | −0.326352 | − | 1.85083i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.719340 | − | 0.694658i | −0.719340 | − | 0.694658i | ||||
\(257\) | 0 | 0 | −0.559193 | − | 0.829038i | \(-0.688889\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(258\) | −3.30998 | + | 0.231457i | −3.30998 | + | 0.231457i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.26149 | + | 1.91502i | −5.26149 | + | 1.91502i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.204489 | − | 0.0434654i | −0.204489 | − | 0.0434654i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.46399 | + | 1.62592i | 1.46399 | + | 1.62592i | ||||
\(268\) | −1.13491 | − | 0.709170i | −1.13491 | − | 0.709170i | ||||
\(269\) | 1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | 1.00000 | \(0\) | ||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(270\) | −0.620676 | + | 3.52003i | −0.620676 | + | 3.52003i | ||||
\(271\) | 0 | 0 | 0.882948 | − | 0.469472i | \(-0.155556\pi\) | ||||
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.61182 | + | 1.79011i | 1.61182 | + | 1.79011i | ||||
\(277\) | 0 | 0 | −0.0348995 | − | 0.999391i | \(-0.511111\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.49861 | − | 0.318539i | −1.49861 | − | 0.318539i | ||||
\(281\) | −0.774117 | + | 0.411606i | −0.774117 | + | 0.411606i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(282\) | 0.384313 | − | 0.139878i | 0.384313 | − | 0.139878i | ||||
\(283\) | −0.594092 | − | 0.170353i | −0.594092 | − | 0.170353i | −0.0348995 | − | 0.999391i | \(-0.511111\pi\) |
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.382753 | + | 0.369620i | 0.382753 | + | 0.369620i | ||||
\(288\) | 2.28716 | + | 1.66172i | 2.28716 | + | 1.66172i | ||||
\(289\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(290\) | 1.86110 | − | 0.677383i | 1.86110 | − | 0.677383i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) | ||||
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(294\) | 0.275507 | − | 2.62127i | 0.275507 | − | 2.62127i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.732841 | + | 0.155770i | −0.732841 | + | 0.155770i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.339707 | − | 1.92657i | 0.339707 | − | 1.92657i | ||||
\(301\) | 0.451237 | + | 2.55909i | 0.451237 | + | 2.55909i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.20611 | + | 3.71203i | −1.20611 | + | 3.71203i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.18362 | + | 1.51497i | −1.18362 | + | 1.51497i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.75631 | + | 0.503615i | −1.75631 | + | 0.503615i | −0.990268 | − | 0.139173i | \(-0.955556\pi\) |
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.67884 | + | 1.05489i | 3.67884 | + | 1.05489i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.32080 | + | 0.302140i | 4.32080 | + | 0.302140i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(321\) | −1.16222 | + | 0.333261i | −1.16222 | + | 0.333261i | ||||
\(322\) | 1.26231 | − | 1.40194i | 1.26231 | − | 1.40194i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3.67779 | − | 1.95551i | −3.67779 | − | 1.95551i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.323755 | + | 0.359566i | −0.323755 | + | 0.359566i | ||||
\(327\) | −0.869723 | + | 2.67673i | −0.869723 | + | 2.67673i | ||||
\(328\) | 0.130100 | + | 0.322008i | 0.130100 | + | 0.322008i | ||||
\(329\) | −0.140408 | − | 0.287878i | −0.140408 | − | 0.287878i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(332\) | 1.47815 | + | 0.658114i | 1.47815 | + | 0.658114i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.630676 | + | 1.29308i | −0.630676 | + | 1.29308i | ||||
\(335\) | −1.22256 | − | 0.544320i | −1.22256 | − | 0.544320i | ||||
\(336\) | 1.49861 | − | 2.59567i | 1.49861 | − | 2.59567i | ||||
\(337\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(338\) | −0.848048 | − | 0.529919i | −0.848048 | − | 0.529919i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.532089 | −0.532089 | ||||||||
\(344\) | −0.410323 | + | 1.64571i | −0.410323 | + | 1.64571i | ||||
\(345\) | 1.84527 | + | 1.54837i | 1.84527 | + | 1.54837i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.874607 | − | 0.0611585i | 0.874607 | − | 0.0611585i | 0.374607 | − | 0.927184i | \(-0.377778\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0.135219 | + | 3.87215i | 0.135219 | + | 3.87215i | ||||
\(349\) | −0.00729598 | + | 0.208930i | −0.00729598 | + | 0.208930i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(350\) | −1.52836 | − | 0.106873i | −1.52836 | − | 0.106873i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
0.241922 | + | 0.970296i | \(0.422222\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.02170 | − | 0.454888i | 1.02170 | − | 0.454888i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.615661 | − | 0.788011i | \(-0.288889\pi\) | ||||
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(360\) | 2.49617 | + | 1.32724i | 2.49617 | + | 1.32724i | ||||
\(361\) | 1.00000 | 1.00000 | ||||||||
\(362\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(363\) | 1.95630 | 1.95630 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.10314 | − | 3.11803i | −2.10314 | − | 3.11803i | ||||
\(367\) | −1.33826 | − | 1.48629i | −1.33826 | − | 1.48629i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.669131 | − | 0.743145i | \(-0.733333\pi\) | |||||||
\(368\) | 1.12487 | − | 0.500824i | 1.12487 | − | 0.500824i | ||||
\(369\) | −0.490919 | − | 0.850297i | −0.490919 | − | 0.850297i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
−0.438371 | + | 0.898794i | \(0.644444\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.0682737 | − | 1.95510i | 0.0682737 | − | 1.95510i | ||||
\(376\) | −0.00729598 | − | 0.208930i | −0.00729598 | − | 0.208930i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.05142 | + | 5.07743i | −2.05142 | + | 5.07743i | ||||
\(379\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.67663 | 3.67663 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.10750 | − | 0.155649i | −1.10750 | − | 0.155649i | −0.438371 | − | 0.898794i | \(-0.644444\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(384\) | 1.58268 | − | 1.14988i | 1.58268 | − | 1.14988i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.501216 | − | 4.76875i | 0.501216 | − | 4.76875i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.02170 | + | 0.454888i | 1.02170 | + | 0.454888i | 0.848048 | − | 0.529919i | \(-0.177778\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.23082 | − | 0.547995i | −1.23082 | − | 0.547995i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.882948 | − | 0.469472i | −0.882948 | − | 0.469472i | ||||
\(401\) | −1.35275 | − | 1.13510i | −1.35275 | − | 1.13510i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.374607 | − | 0.927184i | \(-0.622222\pi\) | |||||||
\(402\) | 1.75181 | − | 1.94558i | 1.75181 | − | 1.94558i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.61409 | + | 1.17271i | 1.61409 | + | 1.17271i | ||||
\(405\) | −3.91415 | − | 1.42463i | −3.91415 | − | 1.42463i | ||||
\(406\) | 3.00483 | − | 0.422301i | 3.00483 | − | 0.422301i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.997564 | + | 0.0697565i | 0.997564 | + | 0.0697565i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(410\) | 0.173648 | + | 0.300767i | 0.173648 | + | 0.300767i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.09395 | − | 1.62184i | 1.09395 | − | 1.62184i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.95211 | + | 1.84468i | −2.95211 | + | 1.84468i | ||||
\(415\) | 1.55535 | + | 0.445991i | 1.55535 | + | 0.445991i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.615661 | − | 0.788011i | \(-0.288889\pi\) | ||||
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(420\) | 1.12278 | − | 2.77897i | 1.12278 | − | 2.77897i | ||||
\(421\) | −0.231520 | + | 0.712544i | −0.231520 | + | 0.712544i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.102630 | + | 0.582044i | 0.102630 | + | 0.582044i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.25637 | + | 1.89332i | −2.25637 | + | 1.89332i | ||||
\(428\) | −0.0215691 | + | 0.617657i | −0.0215691 | + | 0.617657i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.177290 | + | 1.68680i | −0.177290 | + | 1.68680i | ||||
\(431\) | 0 | 0 | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) | ||||
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(432\) | −2.57116 | + | 2.48294i | −2.57116 | + | 2.48294i | ||||
\(433\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.672802 | + | 3.81565i | 0.672802 | + | 3.81565i | ||||
\(436\) | 1.16392 | + | 0.845635i | 1.16392 | + | 0.845635i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.997564 | − | 0.0697565i | \(-0.0222222\pi\) | ||||
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.66138 | + | 1.04988i | 3.66138 | + | 1.04988i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.65940 | + | 0.882318i | −1.65940 | + | 0.882318i | −0.669131 | + | 0.743145i | \(0.733333\pi\) |
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.948445 | − | 0.592654i | 0.948445 | − | 0.592654i | ||||
\(446\) | 0.0305979 | + | 0.0627349i | 0.0305979 | + | 0.0627349i | ||||
\(447\) | −0.0511516 | − | 1.46479i | −0.0511516 | − | 1.46479i | ||||
\(448\) | −1.02517 | − | 1.13856i | −1.02517 | − | 1.13856i | ||||
\(449\) | −1.49756 | − | 0.935782i | −1.49756 | − | 0.935782i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(450\) | 2.65660 | + | 0.966922i | 2.65660 | + | 0.966922i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.0840186 | + | 0.476493i | −0.0840186 | + | 0.476493i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(458\) | −0.0215691 | − | 0.617657i | −0.0215691 | − | 0.617657i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.04422 | − | 0.652502i | 1.04422 | − | 0.652502i | ||||
\(461\) | 0.732841 | + | 0.155770i | 0.732841 | + | 0.155770i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.86110 | − | 0.677383i | 1.86110 | − | 0.677383i | 0.882948 | − | 0.469472i | \(-0.155556\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(464\) | 1.90381 | + | 0.545910i | 1.90381 | + | 0.545910i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.194206 | − | 0.287922i | −0.194206 | − | 0.287922i | 0.719340 | − | 0.694658i | \(-0.244444\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.65876 | − | 1.20516i | −1.65876 | − | 1.20516i | ||||
\(470\) | −0.0363024 | − | 0.205881i | −0.0363024 | − | 0.205881i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(480\) | 1.40724 | − | 1.35896i | 1.40724 | − | 1.35896i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(483\) | 2.27213 | + | 2.90819i | 2.27213 | + | 2.90819i | ||||
\(484\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.81624 | − | 3.60462i | 2.81624 | − | 3.60462i | ||||
\(487\) | 0.709299 | − | 0.515336i | 0.709299 | − | 0.515336i | −0.173648 | − | 0.984808i | \(-0.555556\pi\) |
0.882948 | + | 0.469472i | \(0.155556\pi\) | |||||||
\(488\) | −1.84805 | + | 0.529919i | −1.84805 | + | 0.529919i | ||||
\(489\) | −0.582749 | − | 0.745885i | −0.582749 | − | 0.745885i | ||||
\(490\) | −1.29510 | − | 0.371365i | −1.29510 | − | 0.371365i | ||||
\(491\) | 0 | 0 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
−0.848048 | + | 0.529919i | \(0.822222\pi\) | |||||||
\(492\) | −0.664567 | + | 0.141258i | −0.664567 | + | 0.141258i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.77004 | + | 2.62420i | −1.77004 | + | 2.62420i | ||||
\(499\) | 0 | 0 | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) | ||||
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(500\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(501\) | −2.27696 | − | 1.65431i | −2.27696 | − | 1.65431i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.748346 | + | 0.831123i | −0.748346 | + | 0.831123i | −0.990268 | − | 0.139173i | \(-0.955556\pi\) |
0.241922 | + | 0.970296i | \(0.422222\pi\) | |||||||
\(504\) | 3.31801 | + | 2.78414i | 3.31801 | + | 2.78414i | ||||
\(505\) | 1.76159 | + | 0.936656i | 1.76159 | + | 0.936656i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.30902 | − | 1.45381i | 1.30902 | − | 1.45381i | ||||
\(508\) | 0.580762 | − | 1.78740i | 0.580762 | − | 1.78740i | ||||
\(509\) | −0.635369 | − | 1.57259i | −0.635369 | − | 1.57259i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.857583 | − | 1.75831i | 0.857583 | − | 1.75831i | ||||
\(516\) | −3.03120 | − | 1.34958i | −3.03120 | − | 1.34958i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(522\) | −5.54467 | − | 0.779252i | −5.54467 | − | 0.779252i | ||||
\(523\) | 0.0840186 | − | 0.336980i | 0.0840186 | − | 0.336980i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.997564 | + | 0.0697565i | \(0.0222222\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.725093 | − | 2.90819i | 0.725093 | − | 2.90819i | ||||
\(526\) | −0.160147 | − | 0.134379i | −0.160147 | − | 0.134379i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.0180136 | + | 0.515842i | 0.0180136 | + | 0.515842i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.529299 | + | 2.12290i | 0.529299 | + | 2.12290i | ||||
\(535\) | 0.0646021 | + | 0.614648i | 0.0646021 | + | 0.614648i | ||||
\(536\) | −0.669131 | − | 1.15897i | −0.669131 | − | 1.15897i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.25755 | + | 1.39666i | 1.25755 | + | 1.39666i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.20058 | + | 2.81661i | −2.20058 | + | 2.81661i | ||||
\(541\) | −1.76590 | − | 0.938943i | −1.76590 | − | 0.938943i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
−0.882948 | − | 0.469472i | \(-0.844444\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.95153 | − | 0.136464i | −1.95153 | − | 0.136464i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.27028 | + | 0.675419i | 1.27028 | + | 0.675419i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.10750 | − | 1.64194i | −1.10750 | − | 1.64194i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.438371 | − | 0.898794i | \(-0.644444\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.96526 | − | 2.21067i | 4.96526 | − | 2.21067i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.582749 | + | 2.33728i | 0.582749 | + | 2.33728i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.0348995 | − | 0.999391i | \(-0.511111\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.17365 | − | 0.984808i | −1.17365 | − | 0.984808i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.876742 | −0.876742 | ||||||||
\(563\) | −0.181251 | + | 0.726958i | −0.181251 | + | 0.726958i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(564\) | 0.404997 | + | 0.0569186i | 0.404997 | + | 0.0569186i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.444576 | − | 0.429322i | −0.444576 | − | 0.429322i | ||||
\(567\) | −5.41198 | − | 3.38178i | −5.41198 | − | 3.38178i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
−0.438371 | + | 0.898794i | \(0.644444\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.164425 | + | 0.506047i | 0.164425 | + | 0.506047i | ||||
\(575\) | 0.943248 | − | 0.791479i | 0.943248 | − | 0.791479i | ||||
\(576\) | 1.23932 | + | 2.54097i | 1.23932 | + | 2.54097i | ||||
\(577\) | 0 | 0 | −0.374607 | − | 0.927184i | \(-0.622222\pi\) | ||||
0.374607 | + | 0.927184i | \(0.377778\pi\) | |||||||
\(578\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.96126 | + | 0.275637i | 1.96126 | + | 0.275637i | ||||
\(581\) | 2.18880 | + | 1.16381i | 2.18880 | + | 1.16381i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.479135 | − | 0.0673380i | 0.479135 | − | 0.0673380i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
0.374607 | + | 0.927184i | \(0.377778\pi\) | |||||||
\(588\) | 1.47387 | − | 2.18510i | 1.47387 | − | 2.18510i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.720190 | − | 0.206511i | −0.720190 | − | 0.206511i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(600\) | 1.20442 | − | 1.54158i | 1.20442 | − | 1.54158i | ||||
\(601\) | −0.684440 | + | 1.69405i | −0.684440 | + | 1.69405i | 0.0348995 | + | 0.999391i | \(0.488889\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(602\) | −0.803002 | + | 2.47139i | −0.803002 | + | 2.47139i | ||||
\(603\) | 2.32929 | + | 2.98135i | 2.32929 | + | 2.98135i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(606\) | −2.80763 | + | 2.71129i | −2.80763 | + | 2.71129i | ||||
\(607\) | 1.49861 | − | 0.318539i | 1.49861 | − | 0.318539i | 0.615661 | − | 0.788011i | \(-0.288889\pi\) |
0.882948 | + | 0.469472i | \(0.155556\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.207167 | + | 5.93248i | −0.207167 | + | 5.93248i | ||||
\(610\) | −1.75631 | + | 0.781961i | −1.75631 | + | 0.781961i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.719340 | − | 0.694658i | \(-0.244444\pi\) | ||||
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(614\) | −1.78716 | − | 0.379874i | −1.78716 | − | 0.379874i | ||||
\(615\) | −0.638441 | + | 0.232373i | −0.638441 | + | 0.232373i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(618\) | 2.75298 | + | 2.65852i | 2.75298 | + | 2.65852i | ||||
\(619\) | 0 | 0 | −0.559193 | − | 0.829038i | \(-0.688889\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.64870 | − | 4.08068i | −1.64870 | − | 4.08068i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.61013 | − | 0.586040i | 1.61013 | − | 0.586040i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 3.67320 | + | 2.29527i | 3.67320 | + | 2.29527i | ||||
\(631\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.326352 | − | 1.85083i | 0.326352 | − | 1.85083i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.438371 | − | 0.898794i | −0.438371 | − | 0.898794i | ||||
\(641\) | 0.0591929 | − | 0.0369878i | 0.0591929 | − | 0.0369878i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(642\) | −1.18264 | − | 0.251377i | −1.18264 | − | 0.251377i | ||||
\(643\) | −0.882948 | + | 0.469472i | −0.882948 | + | 0.469472i | −0.848048 | − | 0.529919i | \(-0.822222\pi\) |
−0.0348995 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(644\) | 1.77273 | − | 0.645220i | 1.77273 | − | 0.645220i | ||||
\(645\) | −3.18953 | − | 0.914583i | −3.18953 | − | 0.914583i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.874607 | − | 0.0611585i | 0.874607 | − | 0.0611585i | 0.374607 | − | 0.927184i | \(-0.377778\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(648\) | −2.32924 | − | 3.45323i | −2.32924 | − | 3.45323i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.454664 | + | 0.165484i | −0.454664 | + | 0.165484i | ||||
\(653\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(654\) | −2.02457 | + | 1.95510i | −2.02457 | + | 1.95510i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.0363024 | + | 0.345394i | −0.0363024 | + | 0.345394i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.0111781 | − | 0.320099i | 0.0111781 | − | 0.320099i | ||||
\(659\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.31430 | + | 1.26920i | −1.31430 | + | 1.26920i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.996161 | + | 1.27503i | 0.996161 | + | 1.27503i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.50140 | + | 1.92171i | −1.50140 | + | 1.92171i | ||||
\(668\) | −1.16392 | + | 0.845635i | −1.16392 | + | 0.845635i | ||||
\(669\) | −0.131258 | + | 0.0376376i | −0.131258 | + | 0.0376376i | ||||
\(670\) | −0.823916 | − | 1.05456i | −0.823916 | − | 1.05456i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.54179 | − | 1.58828i | 2.54179 | − | 1.58828i | ||||
\(673\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.78716 | + | 3.09546i | −1.78716 | + | 3.09546i | ||||
\(676\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(677\) | 0 | 0 | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) | ||||
0.997564 | + | 0.0697565i | \(0.0222222\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.889458 | − | 0.323736i | −0.889458 | − | 0.323736i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.63039 | + | 0.467507i | −1.63039 | + | 0.467507i | −0.961262 | − | 0.275637i | \(-0.911111\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.469807 | − | 0.249801i | −0.469807 | − | 0.249801i | ||||
\(687\) | 1.19729 | + | 0.168268i | 1.19729 | + | 0.168268i | ||||
\(688\) | −1.13491 | + | 1.26045i | −1.13491 | + | 1.26045i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.902364 | + | 2.23343i | 0.902364 | + | 2.23343i | ||||
\(691\) | 0 | 0 | −0.438371 | − | 0.898794i | \(-0.644444\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.800944 | + | 0.356603i | 0.800944 | + | 0.356603i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.69847 | + | 3.48239i | −1.69847 | + | 3.48239i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −0.104528 | + | 0.181049i | −0.104528 | + | 0.181049i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.29929 | − | 0.811883i | −1.29929 | − | 0.811883i | ||||
\(701\) | 0.348048 | + | 0.336106i | 0.348048 | + | 0.336106i | 0.848048 | − | 0.529919i | \(-0.177778\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.408977 | 0.408977 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.34158 | + | 1.96482i | 2.34158 | + | 1.96482i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.747388 | − | 0.0522625i | 0.747388 | − | 0.0522625i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.11566 | + | 0.0780147i | 1.11566 | + | 0.0780147i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(720\) | 1.58089 | + | 2.34376i | 1.58089 | + | 2.34376i | ||||
\(721\) | 1.84527 | − | 2.36184i | 1.84527 | − | 2.36184i | ||||
\(722\) | 0.882948 | + | 0.469472i | 0.882948 | + | 0.469472i | ||||
\(723\) | −1.95630 | −1.95630 | ||||||||
\(724\) | −0.374607 | + | 0.927184i | −0.374607 | + | 0.927184i | ||||
\(725\) | 1.98054 | 1.98054 | ||||||||
\(726\) | 1.72731 | + | 0.918425i | 1.72731 | + | 0.918425i | ||||
\(727\) | 0.380500 | − | 0.487017i | 0.380500 | − | 0.487017i | −0.559193 | − | 0.829038i | \(-0.688889\pi\) |
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.20071 | + | 3.55475i | 3.20071 | + | 3.55475i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.393134 | − | 3.74042i | −0.393134 | − | 3.74042i | ||||
\(733\) | 0 | 0 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
0.241922 | + | 0.970296i | \(0.422222\pi\) | |||||||
\(734\) | −0.483844 | − | 1.94059i | −0.483844 | − | 1.94059i | ||||
\(735\) | 1.15542 | − | 2.36896i | 1.15542 | − | 2.36896i | ||||
\(736\) | 1.22832 | + | 0.0858927i | 1.22832 | + | 0.0858927i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.0342657 | − | 0.981240i | −0.0342657 | − | 0.981240i | ||||
\(739\) | 0 | 0 | 0.997564 | − | 0.0697565i | \(-0.0222222\pi\) | ||||
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.43868 | 1.43868 | 0.719340 | − | 0.694658i | \(-0.244444\pi\) | ||||
0.719340 | + | 0.694658i | \(0.244444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.741922 | − | 0.104270i | −0.741922 | − | 0.104270i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.29050 | − | 3.17760i | −3.29050 | − | 3.17760i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.0989762 | + | 0.941696i | −0.0989762 | + | 0.941696i | ||||
\(750\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | ||||
\(751\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(752\) | 0.0916445 | − | 0.187899i | 0.0916445 | − | 0.187899i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.19500 | + | 3.52003i | −4.19500 | + | 3.52003i | ||||
\(757\) | 0 | 0 | −0.438371 | − | 0.898794i | \(-0.644444\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.32524 | + | 0.186250i | 1.32524 | + | 0.186250i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(762\) | 3.24627 | + | 1.72607i | 3.24627 | + | 1.72607i | ||||
\(763\) | 1.68850 | + | 1.41682i | 1.68850 | + | 1.41682i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.904793 | − | 0.657371i | −0.904793 | − | 0.657371i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.93726 | − | 0.272264i | 1.93726 | − | 0.272264i | ||||
\(769\) | −0.987476 | + | 1.46399i | −0.987476 | + | 1.46399i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 2.68134 | − | 3.97525i | 2.68134 | − | 3.97525i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.688547 | + | 0.881300i | 0.688547 | + | 0.881300i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.18756 | − | 6.73261i | 2.18756 | − | 6.73261i | ||||
\(784\) | −0.829478 | − | 1.06168i | −0.829478 | − | 1.06168i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.38295 | − | 1.33550i | 1.38295 | − | 1.33550i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.882948 | − | 0.469472i | \(-0.155556\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.313295 | − | 0.262885i | 0.313295 | − | 0.262885i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.559193 | − | 0.829038i | −0.559193 | − | 0.829038i | ||||
\(801\) | −3.15408 | + | 0.220555i | −3.15408 | + | 0.220555i | ||||
\(802\) | −0.661516 | − | 1.63731i | −0.661516 | − | 1.63731i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.46015 | − | 0.895420i | 2.46015 | − | 0.895420i | ||||
\(805\) | 1.66568 | − | 0.885656i | 1.66568 | − | 0.885656i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.11796 | + | 1.94832i | −3.11796 | + | 1.94832i | ||||
\(808\) | 0.874607 | + | 1.79321i | 0.874607 | + | 1.79321i | ||||
\(809\) | 0.0467046 | + | 1.33745i | 0.0467046 | + | 1.33745i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(810\) | −2.78716 | − | 3.09546i | −2.78716 | − | 3.09546i | ||||
\(811\) | 0 | 0 | −0.848048 | − | 0.529919i | \(-0.822222\pi\) | ||||
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(812\) | 2.85136 | + | 1.03781i | 2.85136 | + | 1.03781i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.427209 | + | 0.227151i | −0.427209 | + | 0.227151i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.848048 | + | 0.529919i | 0.848048 | + | 0.529919i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0121205 | + | 0.347085i | 0.0121205 | + | 0.347085i | ||||
\(821\) | 0.743520 | + | 1.52444i | 0.743520 | + | 1.52444i | 0.848048 | + | 0.529919i | \(0.177778\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.20442 | − | 0.256006i | −1.20442 | − | 0.256006i | −0.438371 | − | 0.898794i | \(-0.644444\pi\) |
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(824\) | 1.72731 | − | 0.918425i | 1.72731 | − | 0.918425i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.747388 | − | 1.84985i | −0.747388 | − | 1.84985i | −0.438371 | − | 0.898794i | \(-0.644444\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(828\) | −3.47258 | + | 0.242827i | −3.47258 | + | 0.242827i | ||||
\(829\) | −0.904793 | − | 1.34141i | −0.904793 | − | 1.34141i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.0348995 | − | 0.999391i | \(-0.488889\pi\) | |||||||
\(830\) | 1.16392 | + | 1.12398i | 1.16392 | + | 1.12398i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.03490 | + | 0.999391i | −1.03490 | + | 0.999391i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
−0.0348995 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(840\) | 2.29600 | − | 1.92657i | 2.29600 | − | 1.92657i | ||||
\(841\) | −2.85866 | + | 0.607627i | −2.85866 | + | 0.607627i | ||||
\(842\) | −0.538939 | + | 0.520447i | −0.538939 | + | 0.520447i | ||||
\(843\) | 0.297836 | − | 1.68911i | 0.297836 | − | 1.68911i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.615661 | − | 0.788011i | −0.615661 | − | 0.788011i | ||||
\(846\) | −0.182636 | + | 0.562096i | −0.182636 | + | 0.562096i | ||||
\(847\) | 0.573931 | − | 1.42053i | 0.573931 | − | 1.42053i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.978148 | − | 0.710666i | 0.978148 | − | 0.710666i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
−0.848048 | + | 0.529919i | \(0.822222\pi\) | |||||||
\(854\) | −2.88111 | + | 0.612399i | −2.88111 | + | 0.612399i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | ||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(860\) | −0.948445 | + | 1.40613i | −0.948445 | + | 1.40613i | ||||
\(861\) | −1.03079 | + | 0.144868i | −1.03079 | + | 0.144868i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.61409 | − | 1.17271i | −1.61409 | − | 1.17271i | −0.848048 | − | 0.529919i | \(-0.822222\pi\) |
−0.766044 | − | 0.642788i | \(-0.777778\pi\) | |||||||
\(864\) | −3.43587 | + | 0.985219i | −3.43587 | + | 0.985219i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.72731 | − | 0.918425i | −1.72731 | − | 0.918425i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.19729 | + | 3.68488i | −1.19729 | + | 3.68488i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.630676 | + | 1.29308i | 0.630676 | + | 1.29308i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.39963 | − | 0.623157i | −1.39963 | − | 0.623157i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
−0.438371 | + | 0.898794i | \(0.644444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.410323 | − | 0.256398i | −0.410323 | − | 0.256398i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(882\) | 2.73991 | + | 2.64590i | 2.73991 | + | 2.64590i | ||||
\(883\) | −1.52045 | + | 1.10467i | −1.52045 | + | 1.10467i | −0.559193 | + | 0.829038i | \(0.688889\pi\) |
−0.961262 | + | 0.275637i | \(0.911111\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.87939 | −1.87939 | ||||||||
\(887\) | 0.465101 | − | 1.86542i | 0.465101 | − | 1.86542i | −0.0348995 | − | 0.999391i | \(-0.511111\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.07864 | − | 2.66972i | 1.07864 | − | 2.66972i | ||||
\(890\) | 1.11566 | − | 0.0780147i | 1.11566 | − | 0.0780147i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.00243595 | + | 0.0697565i | −0.00243595 | + | 0.0697565i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.642513 | − | 1.31735i | 0.642513 | − | 1.31735i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.370646 | − | 1.48658i | −0.370646 | − | 1.48658i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.882948 | − | 1.52931i | −0.882948 | − | 1.52931i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.89169 | + | 2.10094i | 1.89169 | + | 2.10094i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.48853 | − | 2.38659i | −4.48853 | − | 2.38659i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.241922 | + | 0.970296i | −0.241922 | + | 0.970296i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.74871 | + | 0.929805i | 1.74871 | + | 0.929805i | 0.939693 | + | 0.342020i | \(0.111111\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(908\) | −0.297884 | + | 0.381274i | −0.297884 | + | 0.381274i | ||||
\(909\) | −3.15408 | − | 4.67611i | −3.15408 | − | 4.67611i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.909874 | − | 3.64930i | −0.909874 | − | 3.64930i | ||||
\(916\) | 0.270928 | − | 0.555485i | 0.270928 | − | 0.555485i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.0348995 | − | 0.999391i | \(-0.511111\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(920\) | 1.22832 | − | 0.0858927i | 1.22832 | − | 0.0858927i | ||||
\(921\) | 1.33897 | − | 3.31406i | 1.33897 | − | 3.31406i | ||||
\(922\) | 0.573931 | + | 0.481585i | 0.573931 | + | 0.481585i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.96126 | + | 0.275637i | 1.96126 | + | 0.275637i | ||||
\(927\) | −4.47437 | + | 3.25082i | −4.47437 | + | 3.25082i | ||||
\(928\) | 1.42468 | + | 1.37580i | 1.42468 | + | 1.37580i | ||||
\(929\) | −1.37217 | − | 0.857427i | −1.37217 | − | 0.857427i | −0.374607 | − | 0.927184i | \(-0.622222\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.0363024 | − | 0.345394i | −0.0363024 | − | 0.345394i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(938\) | −0.898808 | − | 1.84283i | −0.898808 | − | 1.84283i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.0646021 | − | 0.198825i | 0.0646021 | − | 0.198825i | ||||
\(941\) | 1.28642 | − | 1.42871i | 1.28642 | − | 1.42871i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
0.848048 | − | 0.529919i | \(-0.177778\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.377578 | − | 0.200762i | −0.377578 | − | 0.200762i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.66429 | + | 4.06960i | −3.66429 | + | 4.06960i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.904793 | + | 0.657371i | 0.904793 | + | 0.657371i | 0.939693 | − | 0.342020i | \(-0.111111\pi\) |
−0.0348995 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.88051 | − | 0.539228i | 1.88051 | − | 0.539228i | ||||
\(961\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.654527 | − | 1.62001i | 0.654527 | − | 1.62001i | ||||
\(964\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.640856 | + | 3.63448i | 0.640856 | + | 3.63448i | ||||
\(967\) | −0.294524 | + | 1.67033i | −0.294524 | + | 1.67033i | 0.374607 | + | 0.927184i | \(0.377778\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(968\) | 0.719340 | − | 0.694658i | 0.719340 | − | 0.694658i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
−0.0348995 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(972\) | 4.17886 | − | 1.86055i | 4.17886 | − | 1.86055i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.868210 | − | 0.122019i | 0.868210 | − | 0.122019i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.88051 | − | 0.399715i | −1.88051 | − | 0.399715i | ||||
\(977\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(978\) | −0.164365 | − | 0.932161i | −0.164365 | − | 0.932161i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.969164 | − | 0.935911i | −0.969164 | − | 0.935911i | ||||
\(981\) | −2.27439 | − | 3.37193i | −2.27439 | − | 3.37193i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.374607 | − | 0.927184i | −0.374607 | − | 0.927184i | −0.990268 | − | 0.139173i | \(-0.955556\pi\) |
0.615661 | − | 0.788011i | \(-0.288889\pi\) | |||||||
\(984\) | −0.653095 | − | 0.187272i | −0.653095 | − | 0.187272i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.612897 | + | 0.130275i | 0.612897 | + | 0.130275i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.915513 | − | 1.87708i | −0.915513 | − | 1.87708i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.79484 | + | 1.48604i | −2.79484 | + | 1.48604i | ||||
\(997\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3620.1.dy.a.2139.1 | yes | 24 | |
4.3 | odd | 2 | 3620.1.dy.b.2139.1 | yes | 24 | ||
5.4 | even | 2 | 3620.1.dy.b.2139.1 | yes | 24 | ||
20.19 | odd | 2 | CM | 3620.1.dy.a.2139.1 | yes | 24 | |
181.170 | even | 45 | inner | 3620.1.dy.a.1799.1 | ✓ | 24 | |
724.351 | odd | 90 | 3620.1.dy.b.1799.1 | yes | 24 | ||
905.894 | even | 90 | 3620.1.dy.b.1799.1 | yes | 24 | ||
3620.1799 | odd | 90 | inner | 3620.1.dy.a.1799.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3620.1.dy.a.1799.1 | ✓ | 24 | 181.170 | even | 45 | inner | |
3620.1.dy.a.1799.1 | ✓ | 24 | 3620.1799 | odd | 90 | inner | |
3620.1.dy.a.2139.1 | yes | 24 | 1.1 | even | 1 | trivial | |
3620.1.dy.a.2139.1 | yes | 24 | 20.19 | odd | 2 | CM | |
3620.1.dy.b.1799.1 | yes | 24 | 724.351 | odd | 90 | ||
3620.1.dy.b.1799.1 | yes | 24 | 905.894 | even | 90 | ||
3620.1.dy.b.2139.1 | yes | 24 | 4.3 | odd | 2 | ||
3620.1.dy.b.2139.1 | yes | 24 | 5.4 | even | 2 |