Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,1,Mod(53,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([0, 21, 21, 10]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.53");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.ck (of order \(42\), 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: | \(0.586900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\Q(\zeta_{21})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{21}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{21} + \cdots)\) |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-0.733052 - 0.680173i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.149 |
Dual form | 1176.1.ck.b.221.1 |
$q$-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 \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{13}{21}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(3\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(4\) | 0.826239 | + | 0.563320i | 0.826239 | + | 0.563320i | ||||
\(5\) | 1.44973 | − | 0.218511i | 1.44973 | − | 0.218511i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(6\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(7\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(8\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(9\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(10\) | 1.44973 | + | 0.218511i | 1.44973 | + | 0.218511i | ||||
\(11\) | −1.21135 | + | 1.12397i | −1.21135 | + | 1.12397i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(12\) | 0.826239 | − | 0.563320i | 0.826239 | − | 0.563320i | ||||
\(13\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(14\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(15\) | 0.326239 | − | 1.42935i | 0.326239 | − | 1.42935i | ||||
\(16\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | ||||
\(17\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(19\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | 1.32091 | + | 0.636119i | 1.32091 | + | 0.636119i | ||||
\(21\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(22\) | −1.48883 | + | 0.716983i | −1.48883 | + | 0.716983i | ||||
\(23\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(24\) | 0.955573 | − | 0.294755i | 0.955573 | − | 0.294755i | ||||
\(25\) | 1.09839 | − | 0.338809i | 1.09839 | − | 0.338809i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(28\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(29\) | −1.72188 | − | 0.829215i | −1.72188 | − | 0.829215i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.733052 | − | 0.680173i | \(-0.761905\pi\) | |||||||
\(30\) | 0.733052 | − | 1.26968i | 0.733052 | − | 1.26968i | ||||
\(31\) | −0.365341 | − | 0.632789i | −0.365341 | − | 0.632789i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(32\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(33\) | 0.603718 | + | 1.53825i | 0.603718 | + | 1.53825i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.46610 | −1.46610 | ||||||||
\(36\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(37\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.07473 | + | 0.997204i | 1.07473 | + | 0.997204i | ||||
\(41\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(42\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(43\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(44\) | −1.63402 | + | 0.246289i | −1.63402 | + | 0.246289i | ||||
\(45\) | −1.21135 | − | 0.825886i | −1.21135 | − | 0.825886i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(48\) | 1.00000 | 1.00000 | ||||||||
\(49\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(50\) | 1.14946 | 1.14946 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.826239 | − | 0.563320i | −0.826239 | − | 0.563320i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(54\) | −0.988831 | + | 0.149042i | −0.988831 | + | 0.149042i | ||||
\(55\) | −1.51053 | + | 1.89415i | −1.51053 | + | 1.89415i | ||||
\(56\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.40097 | − | 1.29991i | −1.40097 | − | 1.29991i | ||||
\(59\) | 0.988831 | + | 0.149042i | 0.988831 | + | 0.149042i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(60\) | 1.07473 | − | 0.997204i | 1.07473 | − | 0.997204i | ||||
\(61\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(62\) | −0.162592 | − | 0.712362i | −0.162592 | − | 0.712362i | ||||
\(63\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(64\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.123490 | + | 1.64786i | 0.123490 | + | 1.64786i | ||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.40097 | − | 0.432142i | −1.40097 | − | 0.432142i | ||||
\(71\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(72\) | 0.0747301 | − | 0.997204i | 0.0747301 | − | 0.997204i | ||||
\(73\) | 1.19158 | − | 0.367554i | 1.19158 | − | 0.367554i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0858993 | − | 1.14625i | 0.0858993 | − | 1.14625i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.36534 | − | 0.930874i | 1.36534 | − | 0.930874i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.988831 | − | 1.71271i | 0.988831 | − | 1.71271i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(80\) | 0.733052 | + | 1.26968i | 0.733052 | + | 1.26968i | ||||
\(81\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.425270 | + | 1.86323i | −0.425270 | + | 1.86323i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(84\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.40097 | + | 1.29991i | −1.40097 | + | 1.29991i | ||||
\(88\) | −1.63402 | − | 0.246289i | −1.63402 | − | 0.246289i | ||||
\(89\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(90\) | −0.914101 | − | 1.14625i | −0.914101 | − | 1.14625i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.722521 | + | 0.108903i | −0.722521 | + | 0.108903i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(97\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(98\) | 0.826239 | + | 0.563320i | 0.826239 | + | 0.563320i | ||||
\(99\) | 1.65248 | 1.65248 | ||||||||
\(100\) | 1.09839 | + | 0.338809i | 1.09839 | + | 0.338809i | ||||
\(101\) | −0.658322 | + | 1.67738i | −0.658322 | + | 1.67738i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.78181 | − | 0.268565i | 1.78181 | − | 0.268565i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.535628 | + | 1.36476i | −0.535628 | + | 1.36476i | ||||
\(106\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | ||||
\(107\) | 1.44973 | + | 1.34515i | 1.44973 | + | 1.34515i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(108\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(109\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(110\) | −2.00173 | + | 1.36476i | −2.00173 | + | 1.36476i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(113\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.955573 | − | 1.65510i | −0.955573 | − | 1.65510i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.900969 | + | 0.433884i | 0.900969 | + | 0.433884i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.32091 | − | 0.636119i | 1.32091 | − | 0.636119i | ||||
\(121\) | 0.129334 | − | 1.72584i | 0.129334 | − | 1.72584i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.0546039 | − | 0.728639i | 0.0546039 | − | 0.728639i | ||||
\(125\) | 0.197424 | − | 0.0950744i | 0.197424 | − | 0.0950744i | ||||
\(126\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | ||||
\(127\) | −0.658322 | − | 0.317031i | −0.658322 | − | 0.317031i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.722521 | − | 1.84095i | −0.722521 | − | 1.84095i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(132\) | −0.367711 | + | 1.61105i | −0.367711 | + | 1.61105i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.21135 | + | 0.825886i | −1.21135 | + | 0.825886i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(140\) | −1.21135 | − | 0.825886i | −1.21135 | − | 0.825886i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(145\) | −2.67746 | − | 0.825886i | −2.67746 | − | 0.825886i | ||||
\(146\) | 1.24698 | 1.24698 | ||||||||
\(147\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.19158 | + | 0.367554i | 1.19158 | + | 0.367554i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(150\) | 0.419945 | − | 1.07000i | 0.419945 | − | 1.07000i | ||||
\(151\) | −0.826239 | − | 0.563320i | −0.826239 | − | 0.563320i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.57906 | − | 0.487076i | 1.57906 | − | 0.487076i | ||||
\(155\) | −0.667917 | − | 0.837541i | −0.667917 | − | 0.837541i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(158\) | 1.44973 | − | 1.34515i | 1.44973 | − | 1.34515i | ||||
\(159\) | −0.826239 | + | 0.563320i | −0.826239 | + | 0.563320i | ||||
\(160\) | 0.326239 | + | 1.42935i | 0.326239 | + | 1.42935i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(163\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.21135 | + | 2.09812i | 1.21135 | + | 2.09812i | ||||
\(166\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | ||||
\(167\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(168\) | −0.988831 | + | 0.149042i | −0.988831 | + | 0.149042i | ||||
\(169\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.0332580 | + | 0.443797i | −0.0332580 | + | 0.443797i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(174\) | −1.72188 | + | 0.829215i | −1.72188 | + | 0.829215i | ||||
\(175\) | −1.13662 | + | 0.171318i | −1.13662 | + | 0.171318i | ||||
\(176\) | −1.48883 | − | 0.716983i | −1.48883 | − | 0.716983i | ||||
\(177\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.0332580 | − | 0.443797i | −0.0332580 | − | 0.443797i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(180\) | −0.535628 | − | 1.36476i | −0.535628 | − | 1.36476i | ||||
\(181\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.722521 | − | 0.108903i | −0.722521 | − | 0.108903i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.955573 | − | 0.294755i | 0.955573 | − | 0.294755i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(192\) | 0.826239 | + | 0.563320i | 0.826239 | + | 0.563320i | ||||
\(193\) | −0.722521 | + | 1.84095i | −0.722521 | + | 1.84095i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | 0.142820 | + | 0.0440542i | 0.142820 | + | 0.0440542i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(197\) | −1.80194 | −1.80194 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(198\) | 1.57906 | + | 0.487076i | 1.57906 | + | 0.487076i | ||||
\(199\) | 0.455573 | − | 1.16078i | 0.455573 | − | 1.16078i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(200\) | 0.949729 | + | 0.647514i | 0.949729 | + | 0.647514i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.12349 | + | 1.40881i | −1.12349 | + | 1.40881i | ||||
\(203\) | 1.57906 | + | 1.07659i | 1.57906 | + | 1.07659i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.78181 | + | 0.268565i | 1.78181 | + | 0.268565i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.914101 | + | 1.14625i | −0.914101 | + | 1.14625i | ||||
\(211\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(212\) | −0.365341 | − | 0.930874i | −0.365341 | − | 0.930874i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.988831 | + | 1.71271i | 0.988831 | + | 1.71271i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(217\) | 0.266948 | + | 0.680173i | 0.266948 | + | 0.680173i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0931869 | − | 1.24349i | 0.0931869 | − | 1.24349i | ||||
\(220\) | −2.31507 | + | 0.714104i | −2.31507 | + | 0.714104i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.134659 | + | 0.0648483i | −0.134659 | + | 0.0648483i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(224\) | 0.0747301 | − | 0.997204i | 0.0747301 | − | 0.997204i | ||||
\(225\) | −1.03563 | − | 0.498732i | −1.03563 | − | 0.498732i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.826239 | − | 1.43109i | −0.826239 | − | 1.43109i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.0747301 | − | 0.997204i | \(-0.476190\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.367711 | − | 1.61105i | −0.367711 | − | 1.61105i | ||||
\(232\) | −0.425270 | − | 1.86323i | −0.425270 | − | 1.86323i | ||||
\(233\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.733052 | + | 0.680173i | 0.733052 | + | 0.680173i | ||||
\(237\) | −1.23305 | − | 1.54620i | −1.23305 | − | 1.54620i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(240\) | 1.44973 | − | 0.218511i | 1.44973 | − | 0.218511i | ||||
\(241\) | 1.57906 | + | 1.07659i | 1.57906 | + | 1.07659i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(242\) | 0.632289 | − | 1.61105i | 0.632289 | − | 1.61105i | ||||
\(243\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.44973 | + | 0.218511i | 1.44973 | + | 0.218511i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.266948 | − | 0.680173i | 0.266948 | − | 0.680173i | ||||
\(249\) | 1.57906 | + | 1.07659i | 1.57906 | + | 1.07659i | ||||
\(250\) | 0.216677 | − | 0.0326588i | 0.216677 | − | 0.0326588i | ||||
\(251\) | 0.455573 | − | 0.571270i | 0.455573 | − | 0.571270i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(252\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.535628 | − | 0.496990i | −0.535628 | − | 0.496990i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(257\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.698220 | + | 1.77904i | 0.698220 | + | 1.77904i | ||||
\(262\) | −0.147791 | − | 1.97213i | −0.147791 | − | 1.97213i | ||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | −0.826239 | + | 1.43109i | −0.826239 | + | 1.43109i | ||||
\(265\) | −1.32091 | − | 0.636119i | −1.32091 | − | 0.636119i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.82624 | − | 0.563320i | 1.82624 | − | 0.563320i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
1.00000 | \(0\) | |||||||||
\(270\) | −1.40097 | + | 0.432142i | −1.40097 | + | 0.432142i | ||||
\(271\) | 0.0111692 | − | 0.149042i | 0.0111692 | − | 0.149042i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
1.00000 | \(0\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.949729 | + | 1.64498i | −0.949729 | + | 1.64498i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.162592 | + | 0.712362i | −0.162592 | + | 0.712362i | ||||
\(280\) | −0.914101 | − | 1.14625i | −0.914101 | − | 1.14625i | ||||
\(281\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(289\) | −0.988831 | + | 0.149042i | −0.988831 | + | 0.149042i | ||||
\(290\) | −2.31507 | − | 1.57839i | −2.31507 | − | 1.57839i | ||||
\(291\) | 0.0546039 | − | 0.139129i | 0.0546039 | − | 0.139129i | ||||
\(292\) | 1.19158 | + | 0.367554i | 1.19158 | + | 0.367554i | ||||
\(293\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(294\) | 0.826239 | − | 0.563320i | 0.826239 | − | 0.563320i | ||||
\(295\) | 1.46610 | 1.46610 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.603718 | − | 1.53825i | 0.603718 | − | 1.53825i | ||||
\(298\) | 1.03030 | + | 0.702449i | 1.03030 | + | 0.702449i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.716677 | − | 0.898684i | 0.716677 | − | 0.898684i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | ||||
\(303\) | 1.32091 | + | 1.22563i | 1.32091 | + | 1.22563i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(308\) | 1.65248 | 1.65248 | ||||||||
\(309\) | 0.400969 | − | 1.75676i | 0.400969 | − | 1.75676i | ||||
\(310\) | −0.391374 | − | 0.997204i | −0.391374 | − | 0.997204i | ||||
\(311\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.988831 | − | 1.71271i | 0.988831 | − | 1.71271i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.07473 | + | 0.997204i | 1.07473 | + | 0.997204i | ||||
\(316\) | 1.78181 | − | 0.858075i | 1.78181 | − | 0.858075i | ||||
\(317\) | 0.0111692 | − | 0.149042i | 0.0111692 | − | 0.149042i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
1.00000 | \(0\) | |||||||||
\(318\) | −0.955573 | + | 0.294755i | −0.955573 | + | 0.294755i | ||||
\(319\) | 3.01782 | − | 0.930874i | 3.01782 | − | 0.930874i | ||||
\(320\) | −0.109562 | + | 1.46200i | −0.109562 | + | 1.46200i | ||||
\(321\) | 1.78181 | − | 0.858075i | 1.78181 | − | 0.858075i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.539102 | + | 2.36196i | 0.539102 | + | 2.36196i | ||||
\(331\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(332\) | −1.40097 | + | 1.29991i | −1.40097 | + | 1.29991i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(337\) | −0.623490 | + | 0.781831i | −0.623490 | + | 0.781831i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(338\) | −0.988831 | + | 0.149042i | −0.988831 | + | 0.149042i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.15379 | + | 0.355898i | 1.15379 | + | 0.355898i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.162592 | + | 0.414278i | −0.162592 | + | 0.414278i | ||||
\(347\) | −0.367711 | − | 0.250701i | −0.367711 | − | 0.250701i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(348\) | −1.88980 | + | 0.284841i | −1.88980 | + | 0.284841i | ||||
\(349\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(350\) | −1.13662 | − | 0.171318i | −1.13662 | − | 0.171318i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.21135 | − | 1.12397i | −1.21135 | − | 1.12397i | ||||
\(353\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(354\) | 0.733052 | − | 0.680173i | 0.733052 | − | 0.680173i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.0990311 | − | 0.433884i | 0.0990311 | − | 0.433884i | ||||
\(359\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(360\) | −0.109562 | − | 1.46200i | −0.109562 | − | 1.46200i | ||||
\(361\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.55929 | − | 0.750915i | −1.55929 | − | 0.750915i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.64715 | − | 0.793227i | 1.64715 | − | 0.793227i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.955573 | + | 0.294755i | −0.955573 | + | 0.294755i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.733052 | + | 0.680173i | 0.733052 | + | 0.680173i | ||||
\(372\) | −0.658322 | − | 0.317031i | −0.658322 | − | 0.317031i | ||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.0163752 | − | 0.218511i | −0.0163752 | − | 0.218511i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 1.00000 | ||||||||
\(379\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.535628 | + | 0.496990i | −0.535628 | + | 0.496990i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(384\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(385\) | 1.77597 | − | 1.64786i | 1.77597 | − | 1.64786i | ||||
\(386\) | −1.23305 | + | 1.54620i | −1.23305 | + | 1.54620i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.123490 | + | 0.0841939i | 0.123490 | + | 0.0841939i | ||||
\(389\) | −0.162592 | + | 0.414278i | −0.162592 | + | 0.414278i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | ||||
\(393\) | −1.97766 | −1.97766 | ||||||||
\(394\) | −1.72188 | − | 0.531130i | −1.72188 | − | 0.531130i | ||||
\(395\) | 1.05929 | − | 2.69903i | 1.05929 | − | 2.69903i | ||||
\(396\) | 1.36534 | + | 0.930874i | 1.36534 | + | 0.930874i | ||||
\(397\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(398\) | 0.777479 | − | 0.974928i | 0.777479 | − | 0.974928i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.716677 | + | 0.898684i | 0.716677 | + | 0.898684i | ||||
\(401\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.48883 | + | 1.01507i | −1.48883 | + | 1.01507i | ||||
\(405\) | 0.326239 | + | 1.42935i | 0.326239 | + | 1.42935i | ||||
\(406\) | 1.19158 | + | 1.49419i | 1.19158 | + | 1.49419i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.0747301 | − | 0.997204i | −0.0747301 | − | 0.997204i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.62349 | + | 0.781831i | 1.62349 | + | 0.781831i | ||||
\(413\) | −0.955573 | − | 0.294755i | −0.955573 | − | 0.294755i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.209389 | + | 2.79410i | −0.209389 | + | 2.79410i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.400969 | − | 0.193096i | 0.400969 | − | 0.193096i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(420\) | −1.21135 | + | 0.825886i | −1.21135 | + | 0.825886i | ||||
\(421\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.0747301 | − | 0.997204i | −0.0747301 | − | 0.997204i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.440071 | + | 1.92808i | 0.440071 | + | 1.92808i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(432\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(433\) | −0.277479 | − | 0.347948i | −0.277479 | − | 0.347948i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(434\) | 0.0546039 | + | 0.728639i | 0.0546039 | + | 0.728639i | ||||
\(435\) | −1.74698 | + | 2.19064i | −1.74698 | + | 2.19064i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.455573 | − | 1.16078i | 0.455573 | − | 1.16078i | ||||
\(439\) | 1.57906 | + | 0.487076i | 1.57906 | + | 0.487076i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(440\) | −2.42270 | −2.42270 | ||||||||
\(441\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.142820 | + | 0.0440542i | 0.142820 | + | 0.0440542i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.147791 | + | 0.0222759i | −0.147791 | + | 0.0222759i | ||||
\(447\) | 0.777479 | − | 0.974928i | 0.777479 | − | 0.974928i | ||||
\(448\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(449\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(450\) | −0.842614 | − | 0.781831i | −0.842614 | − | 0.781831i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.826239 | + | 0.563320i | −0.826239 | + | 0.563320i | ||||
\(454\) | −0.367711 | − | 1.61105i | −0.367711 | − | 1.61105i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.698220 | + | 1.77904i | 0.698220 | + | 1.77904i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.12349 | − | 0.541044i | −1.12349 | − | 0.541044i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(462\) | 0.123490 | − | 1.64786i | 0.123490 | − | 1.64786i | ||||
\(463\) | 0.400969 | − | 0.193096i | 0.400969 | − | 0.193096i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(464\) | 0.142820 | − | 1.90580i | 0.142820 | − | 1.90580i | ||||
\(465\) | −1.02366 | + | 0.315758i | −1.02366 | + | 0.315758i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.134659 | + | 1.79690i | −0.134659 | + | 1.79690i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.722521 | − | 1.84095i | −0.722521 | − | 1.84095i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(480\) | 1.44973 | + | 0.218511i | 1.44973 | + | 0.218511i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.19158 | + | 1.49419i | 1.19158 | + | 1.49419i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.07906 | − | 1.35310i | 1.07906 | − | 1.35310i | ||||
\(485\) | 0.216677 | − | 0.0326588i | 0.216677 | − | 0.0326588i | ||||
\(486\) | 0.826239 | + | 0.563320i | 0.826239 | + | 0.563320i | ||||
\(487\) | 0.266948 | − | 0.680173i | 0.266948 | − | 0.680173i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
1.00000 | \(0\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.32091 | + | 0.636119i | 1.32091 | + | 0.636119i | ||||
\(491\) | −1.46610 | −1.46610 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.39564 | − | 0.361085i | 2.39564 | − | 0.361085i | ||||
\(496\) | 0.455573 | − | 0.571270i | 0.455573 | − | 0.571270i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.19158 | + | 1.49419i | 1.19158 | + | 1.49419i | ||||
\(499\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(500\) | 0.216677 | + | 0.0326588i | 0.216677 | + | 0.0326588i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.603718 | − | 0.411608i | 0.603718 | − | 0.411608i | ||||
\(503\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(504\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(505\) | −0.587862 | + | 2.57559i | −0.587862 | + | 2.57559i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(508\) | −0.365341 | − | 0.632789i | −0.365341 | − | 0.632789i | ||||
\(509\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.23305 | + | 0.185853i | −1.23305 | + | 0.185853i | ||||
\(512\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.52446 | − | 0.778692i | 2.52446 | − | 0.778692i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.400969 | + | 0.193096i | 0.400969 | + | 0.193096i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0.142820 | + | 1.90580i | 0.142820 | + | 1.90580i | ||||
\(523\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(524\) | 0.440071 | − | 1.92808i | 0.440071 | − | 1.92808i | ||||
\(525\) | −0.255779 | + | 1.12064i | −0.255779 | + | 1.12064i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.21135 | + | 1.12397i | −1.21135 | + | 1.12397i | ||||
\(529\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(530\) | −1.07473 | − | 0.997204i | −1.07473 | − | 0.997204i | ||||
\(531\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.39564 | + | 1.63332i | 2.39564 | + | 1.63332i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.425270 | − | 0.131178i | −0.425270 | − | 0.131178i | ||||
\(538\) | 1.91115 | 1.91115 | ||||||||
\(539\) | −1.48883 | + | 0.716983i | −1.48883 | + | 0.716983i | ||||
\(540\) | −1.46610 | −1.46610 | ||||||||
\(541\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(542\) | 0.0546039 | − | 0.139129i | 0.0546039 | − | 0.139129i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.39240 | + | 1.29196i | −1.39240 | + | 1.29196i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.23305 | + | 1.54620i | −1.23305 | + | 1.54620i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.733052 | + | 1.26968i | 0.733052 | + | 1.26968i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(558\) | −0.365341 | + | 0.632789i | −0.365341 | + | 0.632789i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.535628 | − | 1.36476i | −0.535628 | − | 1.36476i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.88980 | + | 0.582926i | −1.88980 | + | 0.582926i | −0.900969 | + | 0.433884i | \(0.857143\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0747301 | − | 0.997204i | 0.0747301 | − | 0.997204i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.826239 | − | 0.563320i | 0.826239 | − | 0.563320i | ||||
\(577\) | −0.535628 | + | 0.496990i | −0.535628 | + | 0.496990i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(578\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(579\) | 1.44973 | + | 1.34515i | 1.44973 | + | 1.34515i | ||||
\(580\) | −1.74698 | − | 2.19064i | −1.74698 | − | 2.19064i | ||||
\(581\) | 0.698220 | − | 1.77904i | 0.698220 | − | 1.77904i | ||||
\(582\) | 0.0931869 | − | 0.116853i | 0.0931869 | − | 0.116853i | ||||
\(583\) | 1.63402 | − | 0.246289i | 1.63402 | − | 0.246289i | ||||
\(584\) | 1.03030 | + | 0.702449i | 1.03030 | + | 0.702449i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.142820 | + | 0.0440542i | 0.142820 | + | 0.0440542i | ||||
\(587\) | 1.65248 | 1.65248 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(588\) | 0.955573 | − | 0.294755i | 0.955573 | − | 0.294755i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.40097 | + | 0.432142i | 1.40097 | + | 0.432142i | ||||
\(591\) | −0.658322 | + | 1.67738i | −0.658322 | + | 1.67738i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(594\) | 1.03030 | − | 1.29196i | 1.03030 | − | 1.29196i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.777479 | + | 0.974928i | 0.777479 | + | 0.974928i | ||||
\(597\) | −0.914101 | − | 0.848162i | −0.914101 | − | 0.848162i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(600\) | 0.949729 | − | 0.647514i | 0.949729 | − | 0.647514i | ||||
\(601\) | −0.162592 | − | 0.712362i | −0.162592 | − | 0.712362i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.365341 | − | 0.930874i | −0.365341 | − | 0.930874i | ||||
\(605\) | −0.189617 | − | 2.53026i | −0.189617 | − | 2.53026i | ||||
\(606\) | 0.900969 | + | 1.56052i | 0.900969 | + | 1.56052i | ||||
\(607\) | −0.826239 | + | 1.43109i | −0.826239 | + | 1.43109i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.57906 | − | 1.07659i | 1.57906 | − | 1.07659i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.57906 | + | 0.487076i | 1.57906 | + | 0.487076i | ||||
\(617\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(618\) | 0.900969 | − | 1.56052i | 0.900969 | − | 1.56052i | ||||
\(619\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(620\) | −0.0800550 | − | 1.06826i | −0.0800550 | − | 1.06826i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.684292 | + | 0.466542i | −0.684292 | + | 0.466542i | ||||
\(626\) | 1.44973 | − | 1.34515i | 1.44973 | − | 1.34515i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.733052 | + | 1.26968i | 0.733052 | + | 1.26968i | ||||
\(631\) | 0.0931869 | − | 0.116853i | 0.0931869 | − | 0.116853i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(632\) | 1.95557 | − | 0.294755i | 1.95557 | − | 0.294755i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.0546039 | − | 0.139129i | 0.0546039 | − | 0.139129i | ||||
\(635\) | −1.02366 | − | 0.315758i | −1.02366 | − | 0.315758i | ||||
\(636\) | −1.00000 | −1.00000 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.15813 | 3.15813 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.535628 | + | 1.36476i | −0.535628 | + | 1.36476i | ||||
\(641\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(642\) | 1.95557 | − | 0.294755i | 1.95557 | − | 0.294755i | ||||
\(643\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(648\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(649\) | −1.36534 | + | 0.930874i | −1.36534 | + | 0.930874i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.730682 | 0.730682 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.535628 | − | 1.36476i | −0.535628 | − | 1.36476i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.44973 | − | 2.51100i | −1.44973 | − | 2.51100i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.12349 | − | 0.541044i | −1.12349 | − | 0.541044i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.62349 | − | 0.781831i | 1.62349 | − | 0.781831i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
1.00000 | \(0\) | |||||||||
\(660\) | −0.181049 | + | 2.41593i | −0.181049 | + | 2.41593i | ||||
\(661\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.72188 | + | 0.829215i | −1.72188 | + | 0.829215i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.0111692 | + | 0.149042i | 0.0111692 | + | 0.149042i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(673\) | −0.367711 | − | 1.61105i | −0.367711 | − | 1.61105i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(674\) | −0.826239 | + | 0.563320i | −0.826239 | + | 0.563320i | ||||
\(675\) | −0.842614 | + | 0.781831i | −0.842614 | + | 0.781831i | ||||
\(676\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(677\) | −1.21135 | − | 1.12397i | −1.21135 | − | 1.12397i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.147791 | − | 0.0222759i | −0.147791 | − | 0.0222759i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.63402 | + | 0.246289i | −1.63402 | + | 0.246289i | ||||
\(682\) | 0.997630 | + | 0.680173i | 0.997630 | + | 0.680173i | ||||
\(683\) | −0.535628 | + | 1.36476i | −0.535628 | + | 1.36476i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(692\) | −0.277479 | + | 0.347948i | −0.277479 | + | 0.347948i | ||||
\(693\) | −1.63402 | − | 0.246289i | −1.63402 | − | 0.246289i | ||||
\(694\) | −0.277479 | − | 0.347948i | −0.277479 | − | 0.347948i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.88980 | − | 0.284841i | −1.88980 | − | 0.284841i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.03563 | − | 0.498732i | −1.03563 | − | 0.498732i | ||||
\(701\) | −0.162592 | + | 0.712362i | −0.162592 | + | 0.712362i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.826239 | − | 1.43109i | −0.826239 | − | 1.43109i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.900969 | − | 1.56052i | 0.900969 | − | 1.56052i | ||||
\(708\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(709\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.88980 | + | 0.582926i | −1.88980 | + | 0.582926i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.222521 | − | 0.385418i | 0.222521 | − | 0.385418i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(720\) | 0.326239 | − | 1.42935i | 0.326239 | − | 1.42935i | ||||
\(721\) | −1.80194 | −1.80194 | ||||||||
\(722\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(723\) | 1.57906 | − | 1.07659i | 1.57906 | − | 1.07659i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.17225 | − | 0.327414i | −2.17225 | − | 0.327414i | ||||
\(726\) | −1.26868 | − | 1.17716i | −1.26868 | − | 1.17716i | ||||
\(727\) | 1.19158 | + | 1.49419i | 1.19158 | + | 1.49419i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(730\) | 1.80778 | − | 0.272479i | 1.80778 | − | 0.272479i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(734\) | −1.00000 | −1.00000 | ||||||||
\(735\) | 0.733052 | − | 1.26968i | 0.733052 | − | 1.26968i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(743\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(744\) | −0.535628 | − | 0.496990i | −0.535628 | − | 0.496990i | ||||
\(745\) | 1.80778 | + | 0.272479i | 1.80778 | + | 0.272479i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.57906 | − | 1.07659i | 1.57906 | − | 1.07659i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.23305 | − | 1.54620i | −1.23305 | − | 1.54620i | ||||
\(750\) | 0.0487597 | − | 0.213630i | 0.0487597 | − | 0.213630i | ||||
\(751\) | 0.603718 | + | 1.53825i | 0.603718 | + | 1.53825i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.365341 | − | 0.632789i | −0.365341 | − | 0.632789i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.32091 | − | 0.636119i | −1.32091 | − | 0.636119i | ||||
\(756\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(757\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(762\) | −0.658322 | + | 0.317031i | −0.658322 | + | 0.317031i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | ||||
\(769\) | 0.440071 | − | 1.92808i | 0.440071 | − | 1.92808i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(770\) | 2.18278 | − | 1.05117i | 2.18278 | − | 1.05117i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.63402 | + | 1.11406i | −1.63402 | + | 1.11406i | ||||
\(773\) | 1.32091 | − | 1.22563i | 1.32091 | − | 1.22563i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.615683 | − | 0.571270i | −0.615683 | − | 0.571270i | ||||
\(776\) | 0.0931869 | + | 0.116853i | 0.0931869 | + | 0.116853i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.277479 | + | 0.347948i | −0.277479 | + | 0.347948i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.91115 | 1.91115 | ||||||||
\(784\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.88980 | − | 0.582926i | −1.88980 | − | 0.582926i | ||||
\(787\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(788\) | −1.48883 | − | 1.01507i | −1.48883 | − | 1.01507i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.80778 | − | 2.26689i | 1.80778 | − | 2.26689i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.03030 | + | 1.29196i | 1.03030 | + | 1.29196i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.07473 | + | 0.997204i | −1.07473 | + | 0.997204i | ||||
\(796\) | 1.03030 | − | 0.702449i | 1.03030 | − | 0.702449i | ||||
\(797\) | −0.0332580 | − | 0.145713i | −0.0332580 | − | 0.145713i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.419945 | + | 1.07000i | 0.419945 | + | 1.07000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.03030 | + | 1.78454i | −1.03030 | + | 1.78454i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.142820 | − | 1.90580i | 0.142820 | − | 1.90580i | ||||
\(808\) | −1.72188 | + | 0.531130i | −1.72188 | + | 0.531130i | ||||
\(809\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(810\) | −0.109562 | + | 1.46200i | −0.109562 | + | 1.46200i | ||||
\(811\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(812\) | 0.698220 | + | 1.77904i | 0.698220 | + | 1.77904i | ||||
\(813\) | −0.134659 | − | 0.0648483i | −0.134659 | − | 0.0648483i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.222521 | − | 0.974928i | 0.222521 | − | 0.974928i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.63402 | + | 1.11406i | −1.63402 | + | 1.11406i | −0.733052 | + | 0.680173i | \(0.761905\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.23305 | − | 0.185853i | −1.23305 | − | 0.185853i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(824\) | 1.32091 | + | 1.22563i | 1.32091 | + | 1.22563i | ||||
\(825\) | 1.18429 | + | 1.48506i | 1.18429 | + | 1.48506i | ||||
\(826\) | −0.826239 | − | 0.563320i | −0.826239 | − | 0.563320i | ||||
\(827\) | −0.914101 | + | 1.14625i | −0.914101 | + | 1.14625i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(830\) | −1.02366 | + | 2.60825i | −1.02366 | + | 2.60825i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.603718 | + | 0.411608i | 0.603718 | + | 0.411608i | ||||
\(838\) | 0.440071 | − | 0.0663300i | 0.440071 | − | 0.0663300i | ||||
\(839\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(840\) | −1.40097 | + | 0.432142i | −1.40097 | + | 0.432142i | ||||
\(841\) | 1.65379 | + | 2.07379i | 1.65379 | + | 2.07379i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.21135 | + | 0.825886i | −1.21135 | + | 0.825886i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.385113 | + | 1.68729i | −0.385113 | + | 1.68729i | ||||
\(848\) | 0.222521 | − | 0.974928i | 0.222521 | − | 0.974928i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.147791 | + | 1.97213i | −0.147791 | + | 1.97213i | ||||
\(857\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(865\) | 0.0487597 | + | 0.650653i | 0.0487597 | + | 0.650653i | ||||
\(866\) | −0.162592 | − | 0.414278i | −0.162592 | − | 0.414278i | ||||
\(867\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(868\) | −0.162592 | + | 0.712362i | −0.162592 | + | 0.712362i | ||||
\(869\) | 0.727208 | + | 3.18610i | 0.727208 | + | 3.18610i | ||||
\(870\) | −2.31507 | + | 1.57839i | −2.31507 | + | 1.57839i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.109562 | − | 0.101659i | −0.109562 | − | 0.101659i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.209389 | + | 0.0645880i | −0.209389 | + | 0.0645880i | ||||
\(876\) | 0.777479 | − | 0.974928i | 0.777479 | − | 0.974928i | ||||
\(877\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(878\) | 1.36534 | + | 0.930874i | 1.36534 | + | 0.930874i | ||||
\(879\) | 0.0546039 | − | 0.139129i | 0.0546039 | − | 0.139129i | ||||
\(880\) | −2.31507 | − | 0.714104i | −2.31507 | − | 0.714104i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.535628 | − | 1.36476i | 0.535628 | − | 1.36476i | ||||
\(886\) | 0.123490 | + | 0.0841939i | 0.123490 | + | 0.0841939i | ||||
\(887\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.603718 | + | 0.411608i | 0.603718 | + | 0.411608i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.21135 | − | 1.12397i | −1.21135 | − | 1.12397i | ||||
\(892\) | −0.147791 | − | 0.0222759i | −0.147791 | − | 0.0222759i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 1.03030 | − | 0.702449i | 1.03030 | − | 0.702449i | ||||
\(895\) | −0.145190 | − | 0.636119i | −0.145190 | − | 0.636119i | ||||
\(896\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.104356 | + | 1.39254i | 0.104356 | + | 1.39254i | ||||
\(900\) | −0.574730 | − | 0.995462i | −0.574730 | − | 0.995462i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.955573 | + | 0.294755i | −0.955573 | + | 0.294755i | ||||
\(907\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(908\) | 0.123490 | − | 1.64786i | 0.123490 | − | 1.64786i | ||||
\(909\) | 1.62349 | − | 0.781831i | 1.62349 | − | 0.781831i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.57906 | − | 2.73502i | −1.57906 | − | 2.73502i | ||||
\(914\) | 0.142820 | + | 1.90580i | 0.142820 | + | 1.90580i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.440071 | + | 1.92808i | 0.440071 | + | 1.92808i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.48883 | + | 1.01507i | −1.48883 | + | 1.01507i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.914101 | − | 0.848162i | −0.914101 | − | 0.848162i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.603718 | − | 1.53825i | 0.603718 | − | 1.53825i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.440071 | − | 0.0663300i | 0.440071 | − | 0.0663300i | ||||
\(927\) | −1.48883 | − | 1.01507i | −1.48883 | − | 1.01507i | ||||
\(928\) | 0.698220 | − | 1.77904i | 0.698220 | − | 1.77904i | ||||
\(929\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(930\) | −1.07126 | −1.07126 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.658322 | + | 1.67738i | −0.658322 | + | 1.67738i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.455573 | − | 0.571270i | 0.455573 | − | 0.571270i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.23305 | − | 1.54620i | −1.23305 | − | 1.54620i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.147791 | − | 0.0222759i | −0.147791 | − | 0.0222759i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(945\) | 1.32091 | − | 0.636119i | 1.32091 | − | 0.636119i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.455573 | + | 1.16078i | 0.455573 | + | 1.16078i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | −0.147791 | − | 1.97213i | −0.147791 | − | 1.97213i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.134659 | − | 0.0648483i | −0.134659 | − | 0.0648483i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(954\) | −0.0747301 | + | 0.997204i | −0.0747301 | + | 0.997204i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.236007 | − | 3.14929i | 0.236007 | − | 3.14929i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.32091 | + | 0.636119i | 1.32091 | + | 0.636119i | ||||
\(961\) | 0.233052 | − | 0.403658i | 0.233052 | − | 0.403658i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.147791 | − | 1.97213i | −0.147791 | − | 1.97213i | ||||
\(964\) | 0.698220 | + | 1.77904i | 0.698220 | + | 1.77904i | ||||
\(965\) | −0.645190 | + | 2.82676i | −0.645190 | + | 2.82676i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.440071 | + | 1.92808i | 0.440071 | + | 1.92808i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(968\) | 1.42996 | − | 0.974928i | 1.42996 | − | 0.974928i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.216677 | + | 0.0326588i | 0.216677 | + | 0.0326588i | ||||
\(971\) | −0.535628 | − | 0.496990i | −0.535628 | − | 0.496990i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(972\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.455573 | − | 0.571270i | 0.455573 | − | 0.571270i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.07473 | + | 0.997204i | 1.07473 | + | 0.997204i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.40097 | − | 0.432142i | −1.40097 | − | 0.432142i | ||||
\(983\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.61232 | + | 0.393744i | −2.61232 | + | 0.393744i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 2.39564 | + | 0.361085i | 2.39564 | + | 0.361085i | ||||
\(991\) | −1.21135 | + | 1.12397i | −1.21135 | + | 1.12397i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(992\) | 0.603718 | − | 0.411608i | 0.603718 | − | 0.411608i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.406813 | − | 1.78236i | 0.406813 | − | 1.78236i | ||||
\(996\) | 0.698220 | + | 1.77904i | 0.698220 | + | 1.77904i | ||||
\(997\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(998\) | 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 | 1176.1.ck.b.149.1 | yes | 12 | |
3.2 | odd | 2 | 1176.1.ck.a.149.1 | ✓ | 12 | ||
8.5 | even | 2 | 1176.1.ck.a.149.1 | ✓ | 12 | ||
24.5 | odd | 2 | CM | 1176.1.ck.b.149.1 | yes | 12 | |
49.25 | even | 21 | inner | 1176.1.ck.b.221.1 | yes | 12 | |
147.74 | odd | 42 | 1176.1.ck.a.221.1 | yes | 12 | ||
392.221 | even | 42 | 1176.1.ck.a.221.1 | yes | 12 | ||
1176.221 | odd | 42 | inner | 1176.1.ck.b.221.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.1.ck.a.149.1 | ✓ | 12 | 3.2 | odd | 2 | ||
1176.1.ck.a.149.1 | ✓ | 12 | 8.5 | even | 2 | ||
1176.1.ck.a.221.1 | yes | 12 | 147.74 | odd | 42 | ||
1176.1.ck.a.221.1 | yes | 12 | 392.221 | even | 42 | ||
1176.1.ck.b.149.1 | yes | 12 | 1.1 | even | 1 | trivial | |
1176.1.ck.b.149.1 | yes | 12 | 24.5 | odd | 2 | CM | |
1176.1.ck.b.221.1 | yes | 12 | 49.25 | even | 21 | inner | |
1176.1.ck.b.221.1 | yes | 12 | 1176.221 | odd | 42 | inner |