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 | 827.2 | ||
Root | \(0.294755 + 0.955573i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.827 |
Dual form | 2001.1.bf.c.1655.2 |
$q$-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 \(\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times\).
\(n\) | \(553\) | \(668\) | \(1132\) |
\(\chi(n)\) | \(e\left(\frac{27}{28}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0895474 | − | 0.794755i | −0.0895474 | − | 0.794755i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(3\) | 0.0747301 | − | 0.997204i | 0.0747301 | − | 0.997204i | ||||
\(4\) | 0.351311 | − | 0.0801844i | 0.351311 | − | 0.0801844i | ||||
\(5\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(6\) | −0.799225 | + | 0.0299049i | −0.799225 | + | 0.0299049i | ||||
\(7\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(8\) | −0.359338 | − | 1.02693i | −0.359338 | − | 1.02693i | ||||
\(9\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(12\) | −0.0537067 | − | 0.356321i | −0.0537067 | − | 0.356321i | ||||
\(13\) | −0.317031 | − | 0.658322i | −0.317031 | − | 0.658322i | 0.680173 | − | 0.733052i | \(-0.261905\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.459319 | + | 0.221196i | −0.459319 | + | 0.221196i | ||||
\(17\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | −0.0299049 | + | 0.799225i | −0.0299049 | + | 0.799225i | ||||
\(19\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.781831 | − | 0.623490i | 0.781831 | − | 0.623490i | ||||
\(24\) | −1.05091 | + | 0.281591i | −1.05091 | + | 0.281591i | ||||
\(25\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(26\) | −0.494815 | + | 0.310913i | −0.494815 | + | 0.310913i | ||||
\(27\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.294755 | + | 0.955573i | −0.294755 | + | 0.955573i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.514383 | + | 0.0579571i | −0.514383 | + | 0.0579571i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(32\) | −0.361914 | − | 0.575983i | −0.361914 | − | 0.575983i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.359338 | + | 0.0269287i | −0.359338 | + | 0.0269287i | ||||
\(37\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.680173 | + | 0.266948i | −0.680173 | + | 0.266948i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.262919 | + | 0.262919i | 0.262919 | + | 0.262919i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.565533 | − | 0.565533i | −0.565533 | − | 0.565533i | ||||
\(47\) | 0.882094 | + | 0.308658i | 0.882094 | + | 0.308658i | 0.733052 | − | 0.680173i | \(-0.238095\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(48\) | 0.186253 | + | 0.474565i | 0.186253 | + | 0.474565i | ||||
\(49\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(50\) | −0.754903 | + | 0.264152i | −0.754903 | + | 0.264152i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.164164 | − | 0.205855i | −0.164164 | − | 0.205855i | ||||
\(53\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(54\) | 0.794755 | + | 0.0895474i | 0.794755 | + | 0.0895474i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.785841 | + | 0.148689i | 0.785841 | + | 0.148689i | ||||
\(59\) | − | 0.445042i | − | 0.445042i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||
0.974928 | − | 0.222521i | \(-0.0714286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(62\) | 0.0921234 | + | 0.403619i | 0.0921234 | + | 0.403619i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.823939 | + | 0.657069i | −0.823939 | + | 0.657069i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.563320 | − | 0.826239i | −0.563320 | − | 0.826239i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.268565 | − | 0.129334i | 0.268565 | − | 0.129334i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(72\) | 0.202269 | + | 1.06902i | 0.202269 | + | 1.06902i | ||||
\(73\) | 1.98603 | + | 0.223772i | 1.98603 | + | 0.223772i | 0.997204 | + | 0.0747301i | \(0.0238095\pi\) |
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.988831 | + | 0.149042i | −0.988831 | + | 0.149042i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.273066 | + | 0.516666i | 0.273066 | + | 0.516666i | ||||
\(79\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(82\) | 0.185412 | − | 0.232500i | 0.185412 | − | 0.232500i | ||||
\(83\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.930874 | + | 0.365341i | 0.930874 | + | 0.365341i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.224672 | − | 0.281729i | 0.224672 | − | 0.281729i | ||||
\(93\) | 0.0193551 | + | 0.517276i | 0.0193551 | + | 0.517276i | ||||
\(94\) | 0.166318 | − | 0.728688i | 0.166318 | − | 0.728688i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.601418 | + | 0.317859i | −0.601418 | + | 0.317859i | ||||
\(97\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(98\) | −0.264152 | + | 0.754903i | −0.264152 | + | 0.754903i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.156348 | − | 0.324660i | −0.156348 | − | 0.324660i | ||||
\(101\) | 1.05737 | + | 0.119137i | 1.05737 | + | 0.119137i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(104\) | −0.562128 | + | 0.562128i | −0.562128 | + | 0.562128i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(108\) | 0.360345i | 0.360345i | ||||||||
\(109\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0269287 | + | 0.359338i | −0.0269287 | + | 0.359338i | ||||
\(117\) | 0.215372 | + | 0.698220i | 0.215372 | + | 0.698220i | ||||
\(118\) | −0.353699 | + | 0.0398523i | −0.353699 | + | 0.0398523i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.781831 | − | 0.623490i | −0.781831 | − | 0.623490i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.281831 | − | 0.242536i | 0.281831 | − | 0.242536i | ||||
\(124\) | −0.176061 | + | 0.0616065i | −0.176061 | + | 0.0616065i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.43087 | + | 0.500684i | 1.43087 | + | 0.500684i | 0.930874 | − | 0.365341i | \(-0.119048\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(128\) | 0.114983 | + | 0.114983i | 0.114983 | + | 0.114983i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.205245 | + | 1.82160i | −0.205245 | + | 1.82160i | 0.294755 | + | 0.955573i | \(0.404762\pi\) |
−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 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(138\) | −0.606214 | + | 0.521689i | −0.606214 | + | 0.521689i | ||||
\(139\) | 0.185853 | + | 0.233052i | 0.185853 | + | 0.233052i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.373714 | − | 0.856562i | 0.373714 | − | 0.856562i | ||||
\(142\) | −0.126838 | − | 0.201862i | −0.126838 | − | 0.201862i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.487156 | − | 0.150268i | 0.487156 | − | 0.150268i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 1.59845i | − | 1.59845i | ||||||
\(147\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(150\) | 0.206999 | + | 0.772532i | 0.206999 | + | 0.772532i | ||||
\(151\) | −0.781831 | + | 0.623490i | −0.781831 | + | 0.623490i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.217547 | + | 0.148321i | −0.217547 | + | 0.148321i | ||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.148689 | − | 0.785841i | 0.148689 | − | 0.785841i | ||||
\(163\) | −0.308658 | + | 0.882094i | −0.308658 | + | 0.882094i | 0.680173 | + | 0.733052i | \(0.261905\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(164\) | 0.113448 | + | 0.0712842i | 0.113448 | + | 0.0712842i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.277479 | + | 1.21572i | −0.277479 | + | 1.21572i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.290611 | − | 0.364415i | 0.290611 | − | 0.364415i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.80194 | 1.80194 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(174\) | 0.206999 | − | 0.772532i | 0.206999 | − | 0.772532i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.443797 | − | 0.0332580i | −0.443797 | − | 0.0332580i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.0931869 | + | 0.116853i | −0.0931869 | + | 0.116853i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.921221 | − | 0.578842i | −0.921221 | − | 0.578842i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.409375 | − | 0.0617033i | 0.409375 | − | 0.0617033i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.334639 | + | 0.0377047i | 0.334639 | + | 0.0377047i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(192\) | 0.593659 | + | 0.870738i | 0.593659 | + | 0.870738i | ||||
\(193\) | 0.0397866 | − | 0.0633201i | 0.0397866 | − | 0.0633201i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.351311 | − | 0.0801844i | −0.351311 | − | 0.0801844i | ||||
\(197\) | 1.35417 | − | 1.07992i | 1.35417 | − | 1.07992i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.988831 | − | 0.149042i | \(-0.0476190\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(200\) | −0.921221 | + | 0.578842i | −0.921221 | + | 0.578842i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 0.851022i | − | 0.851022i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(208\) | 0.291237 | + | 0.232254i | 0.291237 | + | 0.232254i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.33485 | − | 0.467085i | 1.33485 | − | 0.467085i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.108903 | − | 0.277479i | −0.108903 | − | 0.277479i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.08114 | − | 0.121815i | 1.08114 | − | 0.121815i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.371563 | − | 1.96376i | 0.371563 | − | 1.96376i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.62349 | − | 0.781831i | −1.62349 | − | 0.781831i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.08722 | − | 0.0406810i | 1.08722 | − | 0.0406810i | ||||
\(233\) | − | 1.65248i | − | 1.65248i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) | ||
0.563320 | − | 0.826239i | \(-0.309524\pi\) | |||||||
\(234\) | 0.535628 | − | 0.233692i | 0.535628 | − | 0.233692i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.0356854 | − | 0.156348i | −0.0356854 | − | 0.156348i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.09839 | − | 0.250701i | −1.09839 | − | 0.250701i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(242\) | −0.425511 | + | 0.677197i | −0.425511 | + | 0.677197i | ||||
\(243\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.217994 | − | 0.202269i | −0.217994 | − | 0.202269i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.244355 | + | 0.507409i | 0.244355 | + | 0.507409i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.269790 | − | 1.18203i | 0.269790 | − | 1.18203i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.575983 | + | 0.722259i | −0.575983 | + | 0.722259i | ||||
\(257\) | −0.574730 | + | 0.131178i | −0.574730 | + | 0.131178i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.433884 | − | 0.900969i | 0.433884 | − | 0.900969i | ||||
\(262\) | 1.46610 | 1.46610 | ||||||||
\(263\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.500684 | + | 1.43087i | 0.500684 | + | 1.43087i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.189606 | + | 0.119137i | 0.189606 | + | 0.119137i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.264152 | − | 0.245097i | −0.264152 | − | 0.245097i | ||||
\(277\) | 1.78181 | − | 0.858075i | 1.78181 | − | 0.858075i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(278\) | 0.168577 | − | 0.168577i | 0.168577 | − | 0.168577i | ||||
\(279\) | 0.517276 | + | 0.0193551i | 0.517276 | + | 0.0193551i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(282\) | −0.714222 | − | 0.220308i | −0.714222 | − | 0.220308i | ||||
\(283\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(284\) | 0.0839792 | − | 0.0669712i | 0.0839792 | − | 0.0669712i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.272026 | + | 0.623490i | 0.272026 | + | 0.623490i | ||||
\(289\) | − | 1.00000i | − | 1.00000i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.715659 | − | 0.0806354i | 0.715659 | − | 0.0806354i | ||||
\(293\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(294\) | 0.733052 | + | 0.319827i | 0.733052 | + | 0.319827i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.658322 | − | 0.317031i | −0.658322 | − | 0.317031i | ||||
\(300\) | −0.335436 | + | 0.131649i | −0.335436 | + | 0.131649i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.565533 | + | 0.565533i | 0.565533 | + | 0.565533i | ||||
\(303\) | 0.197822 | − | 1.04551i | 0.197822 | − | 1.04551i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.19745 | + | 1.19745i | 1.19745 | + | 1.19745i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.12099 | − | 0.392253i | 1.12099 | − | 0.392253i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(312\) | 0.518549 | + | 0.602564i | 0.518549 | + | 0.602564i | ||||
\(313\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.97493 | + | 0.222521i | −1.97493 | + | 0.222521i | −0.974928 | + | 0.222521i | \(0.928571\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.359338 | + | 0.0269287i | 0.359338 | + | 0.0269287i | ||||
\(325\) | −0.571270 | + | 0.455573i | −0.571270 | + | 0.455573i | ||||
\(326\) | 0.728688 | + | 0.166318i | 0.728688 | + | 0.166318i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.175522 | − | 0.364475i | 0.175522 | − | 0.364475i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.922474 | + | 0.922474i | −0.922474 | + | 0.922474i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.991043 | + | 0.111664i | 0.991043 | + | 0.111664i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(338\) | −0.315644 | − | 0.198332i | −0.315644 | − | 0.198332i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.161359 | − | 1.43210i | −0.161359 | − | 1.43210i | ||||
\(347\) | −0.867767 | −0.867767 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(348\) | 0.356321 | + | 0.0537067i | 0.356321 | + | 0.0537067i | ||||
\(349\) | 1.91115 | 1.91115 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.712362 | − | 0.162592i | 0.712362 | − | 0.162592i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.24349 | − | 1.55929i | 1.24349 | − | 1.55929i | 0.563320 | − | 0.826239i | \(-0.309524\pi\) |
0.680173 | − | 0.733052i | \(-0.261905\pi\) | |||||||
\(354\) | 0.0133089 | + | 0.355688i | 0.0133089 | + | 0.355688i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.101214 | + | 0.0635969i | 0.101214 | + | 0.0635969i | ||||
\(359\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.433884 | − | 0.900969i | −0.433884 | − | 0.900969i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.680173 | + | 0.733052i | −0.680173 | + | 0.733052i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(368\) | −0.221196 | + | 0.459319i | −0.221196 | + | 0.459319i | ||||
\(369\) | −0.220796 | − | 0.299168i | −0.220796 | − | 0.299168i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.0482771 | + | 0.180173i | 0.0482771 | + | 0.180173i | ||||
\(373\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 1.01676i | − | 1.01676i | ||||||
\(377\) | 0.722521 | − | 0.108903i | 0.722521 | − | 0.108903i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.606214 | − | 1.38946i | 0.606214 | − | 1.38946i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(384\) | 0.123254 | − | 0.106069i | 0.123254 | − | 0.106069i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.0538867 | − | 0.0259505i | −0.0538867 | − | 0.0259505i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.121815 | + | 1.08114i | −0.121815 | + | 1.08114i | ||||
\(393\) | 1.80117 | + | 0.340799i | 1.80117 | + | 0.340799i | ||||
\(394\) | −0.979531 | − | 0.979531i | −0.979531 | − | 0.979531i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.01507 | − | 0.488831i | −1.01507 | − | 0.488831i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.317859 | + | 0.398582i | 0.317859 | + | 0.398582i | ||||
\(401\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.201230 | + | 0.320256i | 0.201230 | + | 0.320256i | ||||
\(404\) | 0.381020 | − | 0.0429306i | 0.381020 | − | 0.0429306i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.314832 | + | 0.197822i | −0.314832 | + | 0.197822i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.474928 | + | 0.643504i | 0.474928 | + | 0.643504i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.264444 | + | 0.420860i | −0.264444 | + | 0.420860i | ||||
\(417\) | 0.246289 | − | 0.167917i | 0.246289 | − | 0.167917i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(422\) | −0.490751 | − | 1.01905i | −0.490751 | − | 1.01905i | ||||
\(423\) | −0.826239 | − | 0.436680i | −0.826239 | − | 0.436680i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.210776 | + | 0.111398i | −0.210776 | + | 0.111398i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(432\) | −0.113442 | − | 0.497024i | −0.113442 | − | 0.497024i | ||||
\(433\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.59398 | − | 0.119452i | −1.59398 | − | 0.119452i | ||||
\(439\) | −1.09839 | + | 0.250701i | −1.09839 | + | 0.250701i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.826239 | + | 0.563320i | 0.826239 | + | 0.563320i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0246991 | + | 0.0705858i | 0.0246991 | + | 0.0705858i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.475985 | + | 1.36029i | −0.475985 | + | 1.36029i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.222521 | − | 0.0250721i | −0.222521 | − | 0.0250721i | − | 1.00000i | \(-0.5\pi\) | |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(450\) | 0.785841 | − | 0.148689i | 0.785841 | − | 0.148689i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.563320 | + | 0.826239i | 0.563320 | + | 0.826239i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.10462 | + | 0.694076i | −1.10462 | + | 0.694076i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.24698i | 1.24698i | 0.781831 | + | 0.623490i | \(0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(464\) | −0.0759826 | − | 0.504112i | −0.0759826 | − | 0.504112i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.31332 | + | 0.147975i | −1.31332 | + | 0.147975i | ||||
\(467\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(468\) | 0.131649 | + | 0.228023i | 0.131649 | + | 0.228023i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.457026 | + | 0.159920i | −0.457026 | + | 0.159920i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.100888 | + | 0.895403i | −0.100888 | + | 0.895403i | ||||
\(479\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.324660 | − | 0.156348i | −0.324660 | − | 0.156348i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.772532 | − | 0.206999i | −0.772532 | − | 0.206999i | ||||
\(487\) | 1.24349 | + | 1.55929i | 1.24349 | + | 1.55929i | 0.680173 | + | 0.733052i | \(0.261905\pi\) |
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.856562 | + | 0.373714i | 0.856562 | + | 0.373714i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.95278 | + | 0.220025i | −1.95278 | + | 0.220025i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(492\) | 0.0795629 | − | 0.107804i | 0.0795629 | − | 0.107804i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.223446 | − | 0.140401i | 0.223446 | − | 0.140401i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.49419 | + | 1.19158i | −1.49419 | + | 1.19158i | −0.563320 | + | 0.826239i | \(0.690476\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.19158 | + | 0.367554i | 1.19158 | + | 0.367554i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.341678 | − | 0.317031i | −0.341678 | − | 0.317031i | ||||
\(508\) | 0.542829 | + | 0.0611621i | 0.542829 | + | 0.0611621i | ||||
\(509\) | 0.590232 | + | 1.22563i | 0.590232 | + | 1.22563i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.763283 | + | 0.479602i | 0.763283 | + | 0.479602i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.155720 | + | 0.445023i | 0.155720 | + | 0.445023i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.134659 | − | 1.79690i | 0.134659 | − | 1.79690i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | −0.754903 | − | 0.264152i | −0.754903 | − | 0.264152i | ||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0.0739590 | + | 0.656405i | 0.0739590 | + | 0.656405i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.222521 | − | 0.974928i | 0.222521 | − | 0.974928i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0663300 | + | 0.440071i | −0.0663300 | + | 0.440071i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0897317 | − | 0.256439i | 0.0897317 | − | 0.256439i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.109562 | + | 0.101659i | 0.109562 | + | 0.101659i | ||||
\(538\) | 1.09236 | − | 0.526053i | 1.09236 | − | 0.526053i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.940755 | + | 1.49720i | −0.940755 | + | 1.49720i | −0.0747301 | + | 0.997204i | \(0.523810\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(542\) | 0.0777063 | − | 0.161359i | 0.0777063 | − | 0.161359i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.367711 | + | 1.61105i | 0.367711 | + | 1.61105i | 0.733052 | + | 0.680173i | \(0.238095\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.646066 | + | 0.875388i | −0.646066 | + | 0.875388i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.841516 | − | 1.33927i | −0.841516 | − | 1.33927i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.0839792 | + | 0.0669712i | 0.0839792 | + | 0.0669712i | ||||
\(557\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(558\) | −0.0309382 | − | 0.412841i | −0.0309382 | − | 0.412841i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 0.0626069 | − | 0.330885i | 0.0626069 | − | 0.330885i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.229322 | − | 0.229322i | −0.229322 | − | 0.229322i | ||||
\(569\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.781831 | − | 0.623490i | −0.781831 | − | 0.623490i | ||||
\(576\) | 0.912667 | − | 0.526929i | 0.912667 | − | 0.526929i | ||||
\(577\) | 0.694076 | + | 1.10462i | 0.694076 | + | 1.10462i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(578\) | −0.794755 | + | 0.0895474i | −0.794755 | + | 0.0895474i | ||||
\(579\) | −0.0601697 | − | 0.0444073i | −0.0601697 | − | 0.0444073i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.483859 | − | 2.11993i | −0.483859 | − | 2.11993i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.94440 | − | 0.443797i | −1.94440 | − | 0.443797i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.955573 | − | 0.294755i | \(-0.904762\pi\) | |||||||
\(588\) | −0.106214 | + | 0.344336i | −0.106214 | + | 0.344336i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.975699 | − | 1.43109i | −0.975699 | − | 1.43109i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.781831 | + | 0.376510i | −0.781831 | + | 0.376510i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.193011 | + | 0.551594i | −0.193011 | + | 0.551594i | ||||
\(599\) | −0.189606 | − | 0.119137i | −0.189606 | − | 0.119137i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(600\) | 0.508380 | + | 0.961902i | 0.508380 | + | 0.961902i | ||||
\(601\) | −0.638050 | − | 1.82344i | −0.638050 | − | 1.82344i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) |
−0.0747301 | − | 0.997204i | \(-0.523810\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.224672 | + | 0.281729i | −0.224672 | + | 0.281729i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.848642 | − | 0.0635969i | −0.848642 | − | 0.0635969i | ||||
\(607\) | −0.0739590 | − | 0.656405i | −0.0739590 | − | 0.656405i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
0.900969 | − | 0.433884i | \(-0.142857\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0764549 | − | 0.678556i | −0.0764549 | − | 0.678556i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(614\) | 0.844450 | − | 1.05891i | 0.844450 | − | 1.05891i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.433884 | + | 0.900969i | 0.433884 | + | 0.900969i | ||||
\(622\) | −0.412127 | − | 0.855791i | −0.412127 | − | 0.855791i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.253368 | − | 0.273066i | 0.253368 | − | 0.273066i | ||||
\(625\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(634\) | 0.353699 | + | 1.54966i | 0.353699 | + | 1.54966i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.730682i | 0.730682i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.284841 | + | 0.0878620i | −0.284841 | + | 0.0878620i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.22563 | + | 0.590232i | 1.22563 | + | 0.590232i | 0.930874 | − | 0.365341i | \(-0.119048\pi\) |
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(648\) | −0.0406810 | − | 1.08722i | −0.0406810 | − | 1.08722i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.413225 | + | 0.413225i | 0.413225 | + | 0.413225i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.0377047 | + | 0.334639i | −0.0377047 | + | 0.334639i | ||||
\(653\) | 0.216299 | − | 1.91970i | 0.216299 | − | 1.91970i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.178920 | − | 0.0626069i | −0.178920 | − | 0.0626069i | ||||
\(657\) | −1.93050 | − | 0.517276i | −1.93050 | − | 0.517276i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(662\) | 0.815746 | + | 0.650536i | 0.815746 | + | 0.650536i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | ||||
\(668\) | 0.449343i | 0.449343i | ||||||||
\(669\) | −0.900969 | + | 1.56052i | −0.900969 | + | 1.56052i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.55929 | + | 1.24349i | −1.55929 | + | 1.24349i | −0.733052 | + | 0.680173i | \(0.761905\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 1.00000 | ||||||||
\(676\) | 0.0728744 | − | 0.151325i | 0.0728744 | − | 0.151325i | ||||
\(677\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.255779 | − | 0.531130i | −0.255779 | − | 0.531130i | 0.733052 | − | 0.680173i | \(-0.238095\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.974928 | + | 1.22252i | −0.974928 | + | 1.22252i | 1.00000i | \(0.5\pi\) | ||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(692\) | 0.633040 | − | 0.144487i | 0.633040 | − | 0.144487i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.0777063 | + | 0.689663i | 0.0777063 | + | 0.689663i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.0406810 | − | 1.08722i | 0.0406810 | − | 1.08722i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −0.171138 | − | 1.51889i | −0.171138 | − | 1.51889i | ||||
\(699\) | −1.64786 | − | 0.123490i | −1.64786 | − | 0.123490i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(702\) | −0.193011 | − | 0.551594i | −0.193011 | − | 0.551594i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.35061 | − | 0.848642i | −1.35061 | − | 0.848642i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.158578 | + | 0.0239017i | −0.158578 | + | 0.0239017i | ||||
\(709\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.366025 | + | 0.366025i | −0.366025 | + | 0.366025i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.0233678 | + | 0.0485238i | −0.0233678 | + | 0.0485238i | ||||
\(717\) | −0.332083 | + | 1.07659i | −0.332083 | + | 1.07659i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.22252 | − | 0.974928i | 1.22252 | − | 0.974928i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
1.00000 | \(0\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.677197 | + | 0.425511i | −0.677197 | + | 0.425511i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.997204 | + | 0.0747301i | 0.997204 | + | 0.0747301i | ||||
\(726\) | 0.643504 | + | 0.474928i | 0.643504 | + | 0.474928i | ||||
\(727\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.642075 | − | 0.224672i | −0.642075 | − | 0.224672i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.217994 | + | 0.202269i | −0.217994 | + | 0.202269i | ||||
\(739\) | 0.0416310 | − | 0.369485i | 0.0416310 | − | 0.369485i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(744\) | 0.524251 | − | 0.205753i | 0.524251 | − | 0.205753i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(752\) | −0.473437 | + | 0.0533435i | −0.473437 | + | 0.0533435i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.151251 | − | 0.564475i | −0.151251 | − | 0.564475i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.92808 | − | 0.440071i | −1.92808 | − | 0.440071i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) |
−0.930874 | − | 0.365341i | \(-0.880952\pi\) | |||||||
\(762\) | −1.15856 | − | 0.357369i | −1.15856 | − | 0.357369i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.292981 | + | 0.141092i | −0.292981 | + | 0.141092i | ||||
\(768\) | 0.677197 | + | 0.628347i | 0.677197 | + | 0.628347i | ||||
\(769\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.0878620 | + | 0.582926i | 0.0878620 | + | 0.582926i | ||||
\(772\) | 0.00890019 | − | 0.0254353i | 0.00890019 | − | 0.0254353i | ||||
\(773\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.170965 | + | 0.488590i | 0.170965 | + | 0.488590i | ||||
\(776\) | 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 | ||||
\(784\) | 0.509806 | 0.509806 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.109562 | − | 1.46200i | 0.109562 | − | 1.46200i | ||||
\(787\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(788\) | 0.389143 | − | 0.487970i | 0.389143 | − | 0.487970i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.297604 | + | 0.850504i | −0.297604 | + | 0.850504i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.481008 | + | 0.481008i | −0.481008 | + | 0.481008i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.236505 | − | 0.188607i | 0.236505 | − | 0.188607i | ||||
\(807\) | 1.46429 | − | 0.392355i | 1.46429 | − | 0.392355i | ||||
\(808\) | −0.257609 | − | 1.12866i | −0.257609 | − | 1.12866i | ||||
\(809\) | 0.559311 | − | 0.351438i | 0.559311 | − | 0.351438i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.73205i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.132974 | − | 0.180173i | 0.132974 | − | 0.180173i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.185412 | + | 0.232500i | 0.185412 | + | 0.232500i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.75676 | + | 0.846011i | 1.75676 | + | 0.846011i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.85486 | − | 0.649042i | −1.85486 | − | 0.649042i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.866025 | − | 0.500000i | \(-0.833333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(828\) | −0.264152 | + | 0.245097i | −0.264152 | + | 0.245097i | ||||
\(829\) | 1.40532 | + | 1.40532i | 1.40532 | + | 1.40532i | 0.781831 | + | 0.623490i | \(0.214286\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.722521 | − | 1.84095i | −0.722521 | − | 1.84095i | ||||
\(832\) | 0.693777 | + | 0.334105i | 0.693777 | + | 0.334105i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.155507 | − | 0.180703i | −0.155507 | − | 0.180703i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.0579571 | − | 0.514383i | 0.0579571 | − | 0.514383i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.826239 | − | 0.563320i | −0.826239 | − | 0.563320i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.431495 | − | 0.271126i | 0.431495 | − | 0.271126i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.273066 | + | 0.695761i | −0.273066 | + | 0.695761i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.0605081 | − | 0.0887491i | −0.0605081 | − | 0.0887491i | ||||
\(853\) | −0.752407 | + | 0.752407i | −0.752407 | + | 0.752407i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.433884 | + | 0.900969i | 0.433884 | + | 0.900969i | 0.997204 | + | 0.0747301i | \(0.0238095\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.649042 | + | 1.85486i | −0.649042 | + | 1.85486i | −0.149042 | + | 0.988831i | \(0.547619\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.222521 | − | 0.974928i | 0.222521 | − | 0.974928i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(864\) | 0.642075 | − | 0.224672i | 0.642075 | − | 0.224672i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.997204 | − | 0.0747301i | −0.997204 | − | 0.0747301i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0269287 | − | 0.719683i | −0.0269287 | − | 0.719683i | ||||
\(877\) | −0.433884 | + | 1.90097i | −0.433884 | + | 1.90097i | 1.00000i | \(0.5\pi\) | ||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(878\) | 0.297604 | + | 0.850504i | 0.297604 | + | 0.850504i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(882\) | 0.373714 | − | 0.707101i | 0.373714 | − | 0.707101i | ||||
\(883\) | −0.193096 | − | 0.400969i | −0.193096 | − | 0.400969i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.0538867 | − | 0.0259505i | 0.0538867 | − | 0.0259505i | ||||
\(887\) | −1.07193 | + | 1.07193i | −1.07193 | + | 1.07193i | −0.0747301 | + | 0.997204i | \(0.523810\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.633040 | − | 0.144487i | −0.633040 | − | 0.144487i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.365341 | + | 0.632789i | −0.365341 | + | 0.632789i | ||||
\(898\) | 0.179095i | 0.179095i | ||||||||
\(899\) | 0.0962349 | − | 0.508614i | 0.0962349 | − | 0.508614i | ||||
\(900\) | 0.106214 | + | 0.344336i | 0.106214 | + | 0.344336i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.606214 | − | 0.521689i | 0.606214 | − | 0.521689i | ||||
\(907\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.02781 | − | 0.275400i | −1.02781 | − | 0.275400i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.28359 | − | 1.10462i | 1.28359 | − | 1.10462i | ||||
\(922\) | 0.650536 | + | 0.815746i | 0.650536 | + | 0.815746i | ||||
\(923\) | −0.170287 | − | 0.135799i | −0.170287 | − | 0.135799i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.991043 | − | 0.111664i | 0.991043 | − | 0.111664i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.657069 | − | 0.176061i | 0.657069 | − | 0.176061i | ||||
\(929\) | 0.730682i | 0.730682i | 0.930874 | + | 0.365341i | \(0.119048\pi\) | ||||
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.132503 | − | 0.580533i | −0.132503 | − | 0.580533i | ||||
\(933\) | −0.307384 | − | 1.14717i | −0.307384 | − | 1.14717i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.639631 | − | 0.472069i | 0.639631 | − | 0.472069i | ||||
\(937\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.369485 | + | 0.0416310i | 0.369485 | + | 0.0416310i | ||||
\(944\) | 0.0984417 | + | 0.204416i | 0.0984417 | + | 0.204416i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.28359 | − | 0.806531i | −1.28359 | − | 0.806531i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.482320 | − | 1.37839i | −0.482320 | − | 1.37839i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.0743122 | + | 1.98603i | 0.0743122 | + | 1.98603i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.405980 | −0.405980 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.713697 | + | 0.162897i | −0.713697 | + | 0.162897i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.0633201 | − | 0.0397866i | −0.0633201 | − | 0.0397866i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(968\) | −0.359338 | + | 1.02693i | −0.359338 | + | 1.02693i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(972\) | 0.0537067 | − | 0.356321i | 0.0537067 | − | 0.356321i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.12790 | − | 1.12790i | 1.12790 | − | 1.12790i | ||||
\(975\) | 0.411608 | + | 0.603718i | 0.411608 | + | 0.603718i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(978\) | 0.220308 | − | 0.714222i | 0.220308 | − | 0.714222i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.349732 | + | 1.53228i | 0.349732 | + | 1.53228i | ||||
\(983\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(984\) | −0.350339 | − | 0.202269i | −0.350339 | − | 0.202269i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.678448 | + | 0.541044i | 0.678448 | + | 0.541044i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(992\) | 0.219545 | + | 0.275300i | 0.219545 | + | 0.275300i | ||||
\(993\) | 0.850958 | + | 0.988831i | 0.850958 | + | 0.988831i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.211363 | + | 0.0739590i | 0.211363 | + | 0.0739590i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(998\) | 1.08082 | + | 1.08082i | 1.08082 | + | 1.08082i | ||||
\(999\) | 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.827.2 | ✓ | 24 | |
3.2 | odd | 2 | 2001.1.bf.d.827.1 | yes | 24 | ||
23.22 | odd | 2 | CM | 2001.1.bf.c.827.2 | ✓ | 24 | |
29.2 | odd | 28 | 2001.1.bf.d.1655.1 | yes | 24 | ||
69.68 | even | 2 | 2001.1.bf.d.827.1 | yes | 24 | ||
87.2 | even | 28 | inner | 2001.1.bf.c.1655.2 | yes | 24 | |
667.321 | even | 28 | 2001.1.bf.d.1655.1 | yes | 24 | ||
2001.1655 | odd | 28 | inner | 2001.1.bf.c.1655.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.1.bf.c.827.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2001.1.bf.c.827.2 | ✓ | 24 | 23.22 | odd | 2 | CM | |
2001.1.bf.c.1655.2 | yes | 24 | 87.2 | even | 28 | inner | |
2001.1.bf.c.1655.2 | yes | 24 | 2001.1655 | odd | 28 | inner | |
2001.1.bf.d.827.1 | yes | 24 | 3.2 | odd | 2 | ||
2001.1.bf.d.827.1 | yes | 24 | 69.68 | even | 2 | ||
2001.1.bf.d.1655.1 | yes | 24 | 29.2 | odd | 28 | ||
2001.1.bf.d.1655.1 | yes | 24 | 667.321 | even | 28 |