Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,1,Mod(68,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(28))
chi = DirichletCharacter(H, H._module([14, 14, 23]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.68");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.bf (of order \(28\), degree \(12\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.998629090279\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{28})\) |
Coefficient field: | \(\Q(\zeta_{84})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{84}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{84} - \cdots)\) |
Embedding invariants
Embedding label | 206.2 | ||
Root | \(-0.563320 - 0.826239i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.206 |
Dual form | 2001.1.bf.c.68.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times\).
\(n\) | \(553\) | \(668\) | \(1132\) |
\(\chi(n)\) | \(e\left(\frac{5}{28}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0397866 | − | 0.0633201i | 0.0397866 | − | 0.0633201i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(4\) | 0.431457 | + | 0.895930i | 0.431457 | + | 0.895930i | ||||
\(5\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(6\) | −0.0487796 | + | 0.0566829i | −0.0487796 | + | 0.0566829i | ||||
\(7\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(8\) | 0.148209 | + | 0.0166991i | 0.148209 | + | 0.0166991i | ||||
\(9\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(12\) | −0.293107 | − | 0.950229i | −0.293107 | − | 0.950229i | ||||
\(13\) | 1.14625 | + | 0.914101i | 1.14625 | + | 0.914101i | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.613049 | + | 0.768739i | −0.613049 | + | 0.768739i | ||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | 0.0566829 | − | 0.0487796i | 0.0566829 | − | 0.0487796i | ||||
\(19\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.974928 | − | 0.222521i | −0.974928 | − | 0.222521i | ||||
\(24\) | −0.144065 | − | 0.0386020i | −0.144065 | − | 0.0386020i | ||||
\(25\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(26\) | 0.103486 | − | 0.0362114i | 0.103486 | − | 0.0362114i | ||||
\(27\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.563320 | − | 0.826239i | 0.563320 | − | 0.826239i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.438297 | + | 0.275400i | 0.438297 | + | 0.275400i | 0.733052 | − | 0.680173i | \(-0.238095\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(32\) | 0.0735454 | + | 0.210181i | 0.0735454 | + | 0.210181i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.148209 | + | 0.983301i | 0.148209 | + | 0.983301i | ||||
\(37\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.997204 | − | 1.07473i | −0.997204 | − | 1.07473i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.29621 | − | 1.29621i | 1.29621 | − | 1.29621i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.930874 | − | 0.365341i | \(-0.119048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.0528791 | + | 0.0528791i | −0.0528791 | + | 0.0528791i | ||||
\(47\) | 0.220025 | + | 1.95278i | 0.220025 | + | 1.95278i | 0.294755 | + | 0.955573i | \(0.404762\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(48\) | 0.720776 | − | 0.668783i | 0.720776 | − | 0.668783i | ||||
\(49\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(50\) | −0.00837297 | + | 0.0743122i | −0.00837297 | + | 0.0743122i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.324414 | + | 1.42135i | −0.324414 | + | 1.42135i | ||||
\(53\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(54\) | −0.0633201 | + | 0.0397866i | −0.0633201 | + | 0.0397866i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0299049 | − | 0.0685427i | −0.0299049 | − | 0.0685427i | ||||
\(59\) | 1.80194i | 1.80194i | 0.433884 | + | 0.900969i | \(0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(62\) | 0.0348767 | − | 0.0167957i | 0.0348767 | − | 0.0167957i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.942367 | − | 0.215089i | −0.942367 | − | 0.215089i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.930874 | + | 0.365341i | 0.930874 | + | 0.365341i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.367554 | + | 0.460898i | −0.367554 | + | 0.460898i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) |
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(72\) | 0.136702 | + | 0.0596425i | 0.136702 | + | 0.0596425i | ||||
\(73\) | −1.10462 | + | 0.694076i | −1.10462 | + | 0.694076i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.955573 | − | 0.294755i | 0.955573 | − | 0.294755i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.107727 | + | 0.0203831i | −0.107727 | + | 0.0203831i | ||||
\(79\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.826239 | + | 0.563320i | 0.826239 | + | 0.563320i | ||||
\(82\) | −0.0305044 | − | 0.133648i | −0.0305044 | − | 0.133648i | ||||
\(83\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.680173 | + | 0.733052i | −0.680173 | + | 0.733052i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.221277 | − | 0.969476i | −0.221277 | − | 0.969476i | ||||
\(93\) | −0.392355 | − | 0.337649i | −0.392355 | − | 0.337649i | ||||
\(94\) | 0.132404 | + | 0.0637624i | 0.132404 | + | 0.0637624i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.0413982 | − | 0.218795i | −0.0413982 | − | 0.218795i | ||||
\(97\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(98\) | 0.0743122 | − | 0.00837297i | 0.0743122 | − | 0.00837297i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.777459 | − | 0.620003i | −0.777459 | − | 0.620003i | ||||
\(101\) | 0.559311 | − | 0.351438i | 0.559311 | − | 0.351438i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(104\) | 0.154619 | + | 0.154619i | 0.154619 | + | 0.154619i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(108\) | − | 0.994408i | − | 0.994408i | ||||||
\(109\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.983301 | + | 0.148209i | 0.983301 | + | 0.148209i | ||||
\(117\) | 0.825886 | + | 1.21135i | 0.825886 | + | 1.21135i | ||||
\(118\) | 0.114099 | + | 0.0716930i | 0.114099 | + | 0.0716930i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.974928 | − | 0.222521i | 0.974928 | − | 0.222521i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.47493 | + | 1.08855i | −1.47493 | + | 1.08855i | ||||
\(124\) | −0.0576330 | + | 0.511507i | −0.0576330 | + | 0.511507i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.180173 | − | 1.59908i | −0.180173 | − | 1.59908i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(128\) | −0.208569 | + | 0.208569i | −0.208569 | + | 0.208569i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.06332 | − | 1.69226i | −1.06332 | − | 1.69226i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(138\) | 0.0601697 | − | 0.0444073i | 0.0601697 | − | 0.0444073i | ||||
\(139\) | −0.131178 | + | 0.574730i | −0.131178 | + | 0.574730i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0734787 | − | 1.96376i | 0.0734787 | − | 1.96376i | ||||
\(142\) | 0.0145603 | + | 0.0416111i | 0.0145603 | + | 0.0416111i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.812403 | + | 0.553887i | −0.812403 | + | 0.553887i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.0975592i | 0.0975592i | ||||||||
\(147\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(150\) | 0.0193551 | − | 0.0722342i | 0.0193551 | − | 0.0722342i | ||||
\(151\) | 0.974928 | + | 0.222521i | 0.974928 | + | 0.222521i | 0.680173 | − | 0.733052i | \(-0.261905\pi\) |
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.532632 | − | 1.35713i | 0.532632 | − | 1.35713i | ||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.0685427 | − | 0.0299049i | 0.0685427 | − | 0.0299049i | ||||
\(163\) | 1.95278 | − | 0.220025i | 1.95278 | − | 0.220025i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
0.997204 | + | 0.0747301i | \(0.0238095\pi\) | |||||||
\(164\) | 1.72058 | + | 0.602057i | 1.72058 | + | 0.602057i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.400969 | + | 0.193096i | 0.400969 | + | 0.193096i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.255779 | + | 1.12064i | 0.255779 | + | 1.12064i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.24698 | −1.24698 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(174\) | 0.0193551 | + | 0.0722342i | 0.0193551 | + | 0.0722342i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.268565 | − | 1.78181i | 0.268565 | − | 1.78181i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.440071 | − | 1.92808i | −0.440071 | − | 1.92808i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
−0.0747301 | − | 0.997204i | \(-0.523810\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.140777 | − | 0.0492600i | −0.140777 | − | 0.0492600i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0369904 | + | 0.0114100i | −0.0369904 | + | 0.0114100i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.65462 | + | 1.03967i | −1.65462 | + | 1.03967i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(192\) | 0.899784 | + | 0.353139i | 0.899784 | + | 0.353139i | ||||
\(193\) | 0.500684 | − | 1.43087i | 0.500684 | − | 1.43087i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.431457 | + | 0.895930i | −0.431457 | + | 0.895930i | ||||
\(197\) | −1.68862 | − | 0.385418i | −1.68862 | − | 0.385418i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(200\) | −0.140777 | + | 0.0492600i | −0.140777 | + | 0.0492600i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 0.0493981i | − | 0.0493981i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(208\) | −1.40541 | + | 0.320776i | −1.40541 | + | 0.320776i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.158342 | − | 1.40532i | 0.158342 | − | 1.40532i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
0.781831 | − | 0.623490i | \(-0.214286\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.432142 | − | 0.400969i | 0.432142 | − | 0.400969i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.126286 | − | 0.0793508i | −0.126286 | − | 0.0793508i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.19572 | − | 0.521689i | 1.19572 | − | 0.521689i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.777479 | − | 0.974928i | −0.777479 | − | 0.974928i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.988831 | + | 0.149042i | −0.988831 | + | 0.149042i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0972864 | − | 0.113049i | 0.0972864 | − | 0.113049i | ||||
\(233\) | 0.730682i | 0.730682i | 0.930874 | + | 0.365341i | \(0.119048\pi\) | ||||
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(234\) | 0.109562 | − | 0.00409952i | 0.109562 | − | 0.00409952i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.61441 | + | 0.777459i | −1.61441 | + | 0.777459i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.807782 | − | 1.67738i | 0.807782 | − | 1.67738i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
0.733052 | − | 0.680173i | \(-0.238095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(242\) | 0.0246991 | − | 0.0705858i | 0.0246991 | − | 0.0705858i | ||||
\(243\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0102444 | + | 0.136702i | 0.0102444 | + | 0.136702i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.0603605 | + | 0.0481359i | 0.0603605 | + | 0.0481359i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.108422 | − | 0.0522133i | −0.108422 | − | 0.0522133i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.210181 | − | 0.920862i | −0.210181 | − | 0.920862i | ||||
\(257\) | 0.488831 | + | 1.01507i | 0.488831 | + | 1.01507i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.781831 | − | 0.623490i | 0.781831 | − | 0.623490i | ||||
\(262\) | −0.149460 | −0.149460 | ||||||||
\(263\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.59908 | + | 0.180173i | 1.59908 | + | 0.180173i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00435 | − | 0.351438i | −1.00435 | − | 0.351438i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.0743122 | + | 0.991627i | 0.0743122 | + | 0.991627i | ||||
\(277\) | 1.19158 | − | 1.49419i | 1.19158 | − | 1.49419i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(278\) | 0.0311728 | + | 0.0311728i | 0.0311728 | + | 0.0311728i | ||||
\(279\) | 0.337649 | + | 0.392355i | 0.337649 | + | 0.392355i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(282\) | −0.121422 | − | 0.0827840i | −0.121422 | − | 0.0827840i | ||||
\(283\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(284\) | −0.571516 | − | 0.130445i | −0.571516 | − | 0.130445i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.00832615 | + | 0.222521i | 0.00832615 | + | 0.222521i | ||||
\(289\) | 1.00000i | 1.00000i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.09844 | − | 0.690194i | −1.09844 | − | 0.690194i | ||||
\(293\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(294\) | −0.0747301 | − | 0.00279620i | −0.0747301 | − | 0.00279620i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.914101 | − | 1.14625i | −0.914101 | − | 1.14625i | ||||
\(300\) | 0.676369 | + | 0.728952i | 0.676369 | + | 0.728952i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.0528791 | − | 0.0528791i | 0.0528791 | − | 0.0528791i | ||||
\(303\) | −0.605443 | + | 0.264152i | −0.605443 | + | 0.264152i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.33485 | − | 1.33485i | 1.33485 | − | 1.33485i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
0.900969 | − | 0.433884i | \(-0.142857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.197979 | + | 1.75711i | −0.197979 | + | 1.75711i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(312\) | −0.129847 | − | 0.175937i | −0.129847 | − | 0.175937i | ||||
\(313\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.43388 | − | 0.900969i | −1.43388 | − | 0.900969i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.148209 | + | 0.983301i | −0.148209 | + | 0.983301i | ||||
\(325\) | −1.42935 | − | 0.326239i | −1.42935 | − | 0.326239i | ||||
\(326\) | 0.0637624 | − | 0.132404i | 0.0637624 | − | 0.132404i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.213756 | − | 0.170465i | 0.213756 | − | 0.170465i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.839789 | − | 0.839789i | −0.839789 | − | 0.839789i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.0281801 | − | 0.0177067i | 0.0281801 | − | 0.0177067i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(338\) | 0.0811356 | + | 0.0283906i | 0.0811356 | + | 0.0283906i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0496131 | + | 0.0789588i | −0.0496131 | + | 0.0789588i | ||||
\(347\) | −1.56366 | −1.56366 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(348\) | −0.950229 | − | 0.293107i | −0.950229 | − | 0.293107i | ||||
\(349\) | 1.65248 | 1.65248 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.636119 | − | 1.32091i | −0.636119 | − | 1.32091i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.0663300 | + | 0.290611i | 0.0663300 | + | 0.290611i | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(354\) | −0.102139 | − | 0.0878978i | −0.102139 | − | 0.0878978i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.139595 | − | 0.0488464i | −0.139595 | − | 0.0488464i | ||||
\(359\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.781831 | − | 0.623490i | −0.781831 | − | 0.623490i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.997204 | + | 0.0747301i | −0.997204 | + | 0.0747301i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(368\) | 0.768739 | − | 0.613049i | 0.768739 | − | 0.613049i | ||||
\(369\) | 1.62069 | − | 0.856562i | 1.62069 | − | 0.856562i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.133225 | − | 0.497204i | 0.133225 | − | 0.497204i | ||||
\(373\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.293093i | 0.293093i | ||||||||
\(377\) | 1.40097 | − | 0.432142i | 1.40097 | − | 0.432142i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.0601697 | + | 1.60807i | −0.0601697 | + | 1.60807i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(384\) | 0.237325 | − | 0.175154i | 0.237325 | − | 0.175154i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.0706825 | − | 0.0886330i | −0.0706825 | − | 0.0886330i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.0793508 | + | 0.126286i | 0.0793508 | + | 0.126286i | ||||
\(393\) | 0.799225 | + | 1.83184i | 0.799225 | + | 1.83184i | ||||
\(394\) | −0.0915893 | + | 0.0915893i | −0.0915893 | + | 0.0915893i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.16078 | − | 1.45557i | −1.16078 | − | 1.45557i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.294755 | − | 0.955573i | \(-0.595238\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.218795 | − | 0.958602i | 0.218795 | − | 0.958602i | ||||
\(401\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.250652 | + | 0.716324i | 0.250652 | + | 0.716324i | ||||
\(404\) | 0.556183 | + | 0.349473i | 0.556183 | + | 0.349473i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.73026 | + | 0.605443i | −1.73026 | + | 0.605443i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.0661163 | + | 0.0349435i | −0.0661163 | + | 0.0349435i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.107825 | + | 0.308147i | −0.107825 | + | 0.308147i | ||||
\(417\) | 0.215372 | − | 0.548760i | 0.215372 | − | 0.548760i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(422\) | −0.0826851 | − | 0.0659392i | −0.0826851 | − | 0.0659392i | ||||
\(423\) | −0.365341 | + | 1.93087i | −0.365341 | + | 1.93087i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.00819591 | − | 0.0433164i | −0.00819591 | − | 0.0433164i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(432\) | 0.885881 | − | 0.426618i | 0.885881 | − | 0.426618i | ||||
\(433\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.0145404 | − | 0.0964696i | 0.0145404 | − | 0.0964696i | ||||
\(439\) | 0.807782 | + | 1.67738i | 0.807782 | + | 1.67738i | 0.733052 | + | 0.680173i | \(0.238095\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.50641 | + | 0.169732i | 1.50641 | + | 0.169732i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
0.680173 | + | 0.733052i | \(0.261905\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.0926658 | + | 0.0104409i | −0.0926658 | + | 0.0104409i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.900969 | + | 0.566116i | −0.900969 | + | 0.566116i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | −0.0299049 | + | 0.0685427i | −0.0299049 | + | 0.0685427i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.930874 | − | 0.365341i | −0.930874 | − | 0.365341i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.12099 | + | 0.392253i | −1.12099 | + | 0.392253i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.445042i | 0.445042i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(464\) | 0.289819 | + | 0.939571i | 0.289819 | + | 0.939571i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.0462668 | + | 0.0290714i | 0.0462668 | + | 0.0290714i | ||||
\(467\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(468\) | −0.728952 | + | 1.26258i | −0.728952 | + | 1.26258i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.0300908 | + | 0.267063i | −0.0300908 | + | 0.267063i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.0740727 | − | 0.117886i | −0.0740727 | − | 0.117886i | ||||
\(479\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.620003 | + | 0.777459i | 0.620003 | + | 0.777459i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.0722342 | + | 0.0193551i | −0.0722342 | + | 0.0193551i | ||||
\(487\) | 0.0663300 | − | 0.290611i | 0.0663300 | − | 0.290611i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) |
0.997204 | + | 0.0747301i | \(0.0238095\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.96376 | − | 0.0734787i | −1.96376 | − | 0.0734787i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.677197 | − | 0.425511i | −0.677197 | − | 0.425511i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(492\) | −1.61163 | − | 0.851771i | −1.61163 | − | 0.851771i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.480408 | + | 0.168102i | −0.480408 | + | 0.168102i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.61105 | + | 0.367711i | 1.61105 | + | 0.367711i | 0.930874 | − | 0.365341i | \(-0.119048\pi\) |
0.680173 | + | 0.733052i | \(0.261905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.367711 | − | 0.250701i | −0.367711 | − | 0.250701i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.0858993 | − | 1.14625i | −0.0858993 | − | 1.14625i | ||||
\(508\) | 1.35492 | − | 0.851356i | 1.35492 | − | 0.851356i | ||||
\(509\) | 1.55929 | + | 1.24349i | 1.55929 | + | 1.24349i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.345081 | − | 0.120749i | −0.345081 | − | 0.120749i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.0837231 | + | 0.00943332i | 0.0837231 | + | 0.00943332i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.23305 | + | 0.185853i | 1.23305 | + | 0.185853i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | −0.00837297 | − | 0.0743122i | −0.00837297 | − | 0.0743122i | ||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 1.05737 | − | 1.68280i | 1.05737 | − | 1.68280i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.900969 | + | 0.433884i | 0.900969 | + | 0.433884i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.531130 | + | 1.72188i | −0.531130 | + | 1.72188i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.67065 | − | 0.300910i | 2.67065 | − | 0.300910i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.147791 | + | 1.97213i | 0.147791 | + | 1.97213i | ||||
\(538\) | 0.0750304 | − | 0.0940852i | 0.0750304 | − | 0.0940852i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.122805 | − | 0.350958i | 0.122805 | − | 0.350958i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(542\) | −0.0622129 | + | 0.0496131i | −0.0622129 | + | 0.0496131i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.658322 | − | 0.317031i | 0.658322 | − | 0.317031i | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) |
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.131863 | + | 0.0696915i | 0.131863 | + | 0.0696915i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.0472035 | − | 0.134900i | −0.0472035 | − | 0.134900i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.571516 | + | 0.130445i | −0.571516 | + | 0.130445i | ||||
\(557\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(558\) | 0.0382779 | − | 0.00576946i | 0.0382779 | − | 0.00576946i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 1.79109 | − | 0.781446i | 1.79109 | − | 0.781446i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.0621713 | + | 0.0621713i | −0.0621713 | + | 0.0621713i | ||||
\(569\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.974928 | − | 0.222521i | 0.974928 | − | 0.222521i | ||||
\(576\) | −0.837102 | − | 0.483301i | −0.837102 | − | 0.483301i | ||||
\(577\) | −0.392253 | − | 1.12099i | −0.392253 | − | 1.12099i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.563320 | − | 0.826239i | \(-0.309524\pi\) | |||||||
\(578\) | 0.0633201 | + | 0.0397866i | 0.0633201 | + | 0.0397866i | ||||
\(579\) | −0.708353 | + | 1.34027i | −0.708353 | + | 1.34027i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.175304 | + | 0.0844220i | −0.175304 | + | 0.0844220i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.129334 | − | 0.268565i | 0.129334 | − | 0.268565i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(588\) | 0.560170 | − | 0.821618i | 0.560170 | − | 0.821618i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.61232 | + | 0.632789i | 1.61232 | + | 0.632789i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.974928 | − | 1.22252i | 0.974928 | − | 1.22252i | − | 1.00000i | \(-0.5\pi\) | |
0.974928 | − | 0.222521i | \(-0.0714286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.108949 | + | 0.0122756i | −0.108949 | + | 0.0122756i | ||||
\(599\) | 1.00435 | + | 0.351438i | 1.00435 | + | 0.351438i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(600\) | 0.146546 | − | 0.0277281i | 0.146546 | − | 0.0277281i | ||||
\(601\) | 1.91970 | + | 0.216299i | 1.91970 | + | 0.216299i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.221277 | + | 0.969476i | 0.221277 | + | 0.969476i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.00736241 | + | 0.0488464i | −0.00736241 | + | 0.0488464i | ||||
\(607\) | −1.05737 | + | 1.68280i | −1.05737 | + | 1.68280i | −0.433884 | + | 0.900969i | \(0.642857\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.53283 | + | 2.43949i | −1.53283 | + | 2.43949i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(614\) | −0.0314137 | − | 0.137632i | −0.0314137 | − | 0.137632i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.781831 | + | 0.623490i | 0.781831 | + | 0.623490i | ||||
\(622\) | 0.103384 | + | 0.0824456i | 0.103384 | + | 0.0824456i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.43752 | − | 0.107727i | 1.43752 | − | 0.107727i | ||||
\(625\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(634\) | −0.114099 | + | 0.0549471i | −0.114099 | + | 0.0549471i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.46610i | 1.46610i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.487076 | + | 0.332083i | −0.487076 | + | 0.332083i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.24349 | − | 1.55929i | −1.24349 | − | 1.55929i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
−0.563320 | − | 0.826239i | \(-0.690476\pi\) | |||||||
\(648\) | 0.113049 | + | 0.0972864i | 0.113049 | + | 0.0972864i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.0775263 | + | 0.0775263i | −0.0775263 | + | 0.0775263i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.03967 | + | 1.65462i | 1.03967 | + | 1.65462i | ||||
\(653\) | −1.02781 | − | 1.63575i | −1.02781 | − | 1.63575i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.294755 | − | 0.955573i | \(-0.595238\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.201808 | + | 1.79109i | 0.201808 | + | 1.79109i | ||||
\(657\) | −1.26012 | + | 0.337649i | −1.26012 | + | 0.337649i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(662\) | −0.0865878 | + | 0.0197631i | −0.0865878 | + | 0.0197631i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(668\) | 0.442553i | 0.442553i | ||||||||
\(669\) | 0.623490 | + | 1.07992i | 0.623490 | + | 1.07992i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.290611 | − | 0.0663300i | −0.290611 | − | 0.0663300i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 1.00000 | ||||||||
\(676\) | −0.893658 | + | 0.712669i | −0.893658 | + | 0.712669i | ||||
\(677\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.880843 | + | 0.702449i | 0.880843 | + | 0.702449i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.433884 | − | 1.90097i | −0.433884 | − | 1.90097i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(692\) | −0.538018 | − | 1.11721i | −0.538018 | − | 1.11721i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.0622129 | + | 0.0990112i | −0.0622129 | + | 0.0990112i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.113049 | + | 0.0972864i | −0.113049 | + | 0.0972864i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.0657465 | − | 0.104635i | 0.0657465 | − | 0.104635i | ||||
\(699\) | 0.108903 | − | 0.722521i | 0.108903 | − | 0.722521i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(702\) | −0.108949 | − | 0.0122756i | −0.108949 | − | 0.0122756i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.0210406 | + | 0.00736241i | 0.0210406 | + | 0.00736241i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.71225 | − | 0.528160i | 1.71225 | − | 0.528160i | ||||
\(709\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.366025 | − | 0.366025i | −0.366025 | − | 0.366025i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.53755 | − | 1.22616i | 1.53755 | − | 1.22616i | ||||
\(717\) | −1.04876 | + | 1.53825i | −1.04876 | + | 1.53825i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.90097 | + | 0.433884i | 1.90097 | + | 0.433884i | 1.00000 | \(0\) | ||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.0705858 | + | 0.0246991i | −0.0705858 | + | 0.0246991i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.149042 | + | 0.988831i | −0.149042 | + | 0.988831i | ||||
\(726\) | −0.0349435 | + | 0.0661163i | −0.0349435 | + | 0.0661163i | ||||
\(727\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.0249319 | − | 0.221277i | −0.0249319 | − | 0.221277i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.0102444 | − | 0.136702i | 0.0102444 | − | 0.136702i | ||||
\(739\) | −0.975281 | − | 1.55215i | −0.975281 | − | 1.55215i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
−0.149042 | − | 0.988831i | \(-0.547619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(744\) | −0.0525120 | − | 0.0565945i | −0.0525120 | − | 0.0565945i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(752\) | −1.63606 | − | 1.02801i | −1.63606 | − | 1.02801i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.0283766 | − | 0.105903i | 0.0283766 | − | 0.105903i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.829215 | − | 1.72188i | 0.829215 | − | 1.72188i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
0.680173 | − | 0.733052i | \(-0.261905\pi\) | |||||||
\(762\) | 0.0994292 | + | 0.0677896i | 0.0994292 | + | 0.0677896i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.64715 | + | 2.06546i | −1.64715 | + | 2.06546i | ||||
\(768\) | 0.0705858 | + | 0.941903i | 0.0705858 | + | 0.941903i | ||||
\(769\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.332083 | − | 1.07659i | −0.332083 | − | 1.07659i | ||||
\(772\) | 1.49799 | − | 0.168783i | 1.49799 | − | 0.168783i | ||||
\(773\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.514383 | − | 0.0579571i | −0.514383 | − | 0.0579571i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(784\) | −0.983254 | −0.983254 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.147791 | + | 0.0222759i | 0.147791 | + | 0.0222759i | ||||
\(787\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(788\) | −0.383262 | − | 1.67918i | −0.383262 | − | 1.67918i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.138351 | + | 0.0155884i | −0.138351 | + | 0.0155884i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.157456 | − | 0.157456i | −0.157456 | − | 0.157456i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.0553303 | + | 0.0126288i | 0.0553303 | + | 0.0126288i | ||||
\(807\) | −1.55436 | − | 0.416490i | −1.55436 | − | 0.416490i | ||||
\(808\) | 0.0887634 | − | 0.0427462i | 0.0887634 | − | 0.0427462i | ||||
\(809\) | −1.87590 | + | 0.656405i | −1.87590 | + | 0.656405i | −0.900969 | + | 0.433884i | \(0.857143\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.940755 | + | 0.497204i | 0.940755 | + | 0.497204i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.0305044 | + | 0.133648i | −0.0305044 | + | 0.133648i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.541044 | − | 0.678448i | −0.541044 | − | 0.678448i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0895474 | + | 0.794755i | 0.0895474 | + | 0.794755i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(828\) | 0.0743122 | − | 0.991627i | 0.0743122 | − | 0.991627i | ||||
\(829\) | −1.19745 | + | 1.19745i | −1.19745 | + | 1.19745i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.40097 | + | 1.29991i | −1.40097 | + | 1.29991i | ||||
\(832\) | −0.883571 | − | 1.10796i | −0.883571 | − | 1.10796i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.0261786 | − | 0.0354707i | −0.0261786 | − | 0.0354707i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.275400 | − | 0.438297i | −0.275400 | − | 0.438297i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.365341 | − | 0.930874i | −0.365341 | − | 0.930874i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.32739 | − | 0.464473i | 1.32739 | − | 0.464473i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.107727 | + | 0.0999564i | 0.107727 | + | 0.0999564i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0.545691 | + | 0.214168i | 0.545691 | + | 0.214168i | ||||
\(853\) | 0.467085 | + | 0.467085i | 0.467085 | + | 0.467085i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.781831 | + | 0.623490i | 0.781831 | + | 0.623490i | 0.930874 | − | 0.365341i | \(-0.119048\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.794755 | + | 0.0895474i | −0.794755 | + | 0.0895474i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.900969 | + | 0.433884i | 0.900969 | + | 0.433884i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(864\) | 0.0249319 | − | 0.221277i | 0.0249319 | − | 0.221277i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.149042 | − | 0.988831i | 0.149042 | − | 0.988831i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.983301 | + | 0.846199i | 0.983301 | + | 0.846199i | ||||
\(877\) | −0.781831 | − | 0.376510i | −0.781831 | − | 0.376510i | − | 1.00000i | \(-0.5\pi\) | |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(878\) | 0.138351 | + | 0.0155884i | 0.138351 | + | 0.0155884i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(882\) | 0.0734787 | + | 0.0139029i | 0.0734787 | + | 0.0139029i | ||||
\(883\) | −1.40881 | − | 1.12349i | −1.40881 | − | 1.12349i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.433884 | − | 0.900969i | \(-0.642857\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.0706825 | − | 0.0886330i | 0.0706825 | − | 0.0886330i | ||||
\(887\) | 1.13787 | + | 1.13787i | 1.13787 | + | 1.13787i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.538018 | − | 1.11721i | 0.538018 | − | 1.11721i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.733052 | + | 1.26968i | 0.733052 | + | 1.26968i | ||||
\(898\) | 0.0795733i | 0.0795733i | ||||||||
\(899\) | 0.474448 | − | 0.206999i | 0.474448 | − | 0.206999i | ||||
\(900\) | −0.560170 | − | 0.821618i | −0.560170 | − | 0.821618i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.0601697 | + | 0.0444073i | −0.0601697 | + | 0.0444073i | ||||
\(907\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.638050 | − | 0.170965i | 0.638050 | − | 0.170965i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.51889 | + | 1.12099i | −1.51889 | + | 1.12099i | ||||
\(922\) | −0.0197631 | + | 0.0865878i | −0.0197631 | + | 0.0865878i | ||||
\(923\) | −0.842614 | + | 0.192321i | −0.842614 | + | 0.192321i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.0281801 | + | 0.0177067i | 0.0281801 | + | 0.0177067i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.215089 | + | 0.0576330i | 0.215089 | + | 0.0576330i | ||||
\(929\) | 1.46610i | 1.46610i | 0.680173 | + | 0.733052i | \(0.261905\pi\) | ||||
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.654640 | + | 0.315258i | −0.654640 | + | 0.315258i | ||||
\(933\) | 0.457652 | − | 1.70798i | 0.457652 | − | 1.70798i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.102175 | + | 0.193325i | 0.102175 | + | 0.193325i | ||||
\(937\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.55215 | + | 0.975281i | −1.55215 | + | 0.975281i | ||||
\(944\) | −1.38522 | − | 1.10468i | −1.38522 | − | 1.10468i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.51889 | + | 0.531484i | 1.51889 | + | 0.531484i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.90062 | − | 0.214148i | −1.90062 | − | 0.214148i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.28359 | + | 1.10462i | 1.28359 | + | 1.10462i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.85134 | 1.85134 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.317625 | − | 0.659555i | −0.317625 | − | 0.659555i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.43087 | + | 0.500684i | 1.43087 | + | 0.500684i | 0.930874 | − | 0.365341i | \(-0.119048\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(968\) | 0.148209 | − | 0.0166991i | 0.148209 | − | 0.0166991i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(972\) | 0.293107 | − | 0.950229i | 0.293107 | − | 0.950229i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.0157625 | − | 0.0157625i | −0.0157625 | − | 0.0157625i | ||||
\(975\) | 1.36476 | + | 0.535628i | 1.36476 | + | 0.535628i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(978\) | −0.0827840 | + | 0.121422i | −0.0827840 | + | 0.121422i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.0538867 | + | 0.0259505i | −0.0538867 | + | 0.0259505i | ||||
\(983\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(984\) | −0.236775 | + | 0.136702i | −0.236775 | + | 0.136702i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.52446 | + | 0.347948i | −1.52446 | + | 0.347948i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(992\) | −0.0256491 | + | 0.112376i | −0.0256491 | + | 0.112376i | ||||
\(993\) | 0.705245 | + | 0.955573i | 0.705245 | + | 0.955573i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.119137 | − | 1.05737i | −0.119137 | − | 1.05737i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.781831 | − | 0.623490i | \(-0.214286\pi\) | |||||||
\(998\) | 0.0873816 | − | 0.0873816i | 0.0873816 | − | 0.0873816i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2001.1.bf.c.206.2 | yes | 24 | |
3.2 | odd | 2 | 2001.1.bf.d.206.1 | yes | 24 | ||
23.22 | odd | 2 | CM | 2001.1.bf.c.206.2 | yes | 24 | |
29.10 | odd | 28 | 2001.1.bf.d.68.1 | yes | 24 | ||
69.68 | even | 2 | 2001.1.bf.d.206.1 | yes | 24 | ||
87.68 | even | 28 | inner | 2001.1.bf.c.68.2 | ✓ | 24 | |
667.68 | even | 28 | 2001.1.bf.d.68.1 | yes | 24 | ||
2001.68 | odd | 28 | inner | 2001.1.bf.c.68.2 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.1.bf.c.68.2 | ✓ | 24 | 87.68 | even | 28 | inner | |
2001.1.bf.c.68.2 | ✓ | 24 | 2001.68 | odd | 28 | inner | |
2001.1.bf.c.206.2 | yes | 24 | 1.1 | even | 1 | trivial | |
2001.1.bf.c.206.2 | yes | 24 | 23.22 | odd | 2 | CM | |
2001.1.bf.d.68.1 | yes | 24 | 29.10 | odd | 28 | ||
2001.1.bf.d.68.1 | yes | 24 | 667.68 | even | 28 | ||
2001.1.bf.d.206.1 | yes | 24 | 3.2 | odd | 2 | ||
2001.1.bf.d.206.1 | yes | 24 | 69.68 | even | 2 |