Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,1,Mod(143,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, base_ring=CyclotomicField(84))
chi = DirichletCharacter(H, H._module([42, 63, 62]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3675.143");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.cy (of order \(84\), degree \(24\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.83406392143\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{84})\) |
Coefficient field: | \(\Q(\zeta_{168})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{48} + x^{44} - x^{36} - x^{32} + x^{24} - x^{16} - x^{12} + x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{42}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{42} + \cdots)\) |
Embedding invariants
Embedding label | 143.2 | ||
Root | \(0.185912 + 0.982566i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.143 |
Dual form | 3675.1.cy.a.257.2 |
$q$-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 \(\left(\mathbb{Z}/3675\mathbb{Z}\right)^\times\).
\(n\) | \(1177\) | \(1226\) | \(2551\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{31}{42}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.982566 | − | 0.185912i | \(-0.0595238\pi\) | ||||
−0.982566 | + | 0.185912i | \(0.940476\pi\) | |||||||
\(3\) | 0.999301 | − | 0.0373912i | 0.999301 | − | 0.0373912i | ||||
\(4\) | 0.930874 | − | 0.365341i | 0.930874 | − | 0.365341i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.757972 | + | 0.652287i | −0.757972 | + | 0.652287i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.997204 | − | 0.0747301i | 0.997204 | − | 0.0747301i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(12\) | 0.916562 | − | 0.399892i | 0.916562 | − | 0.399892i | ||||
\(13\) | −0.631211 | + | 1.80390i | −0.631211 | + | 1.80390i | −0.0373912 | + | 0.999301i | \(0.511905\pi\) |
−0.593820 | + | 0.804598i | \(0.702381\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.733052 | − | 0.680173i | 0.733052 | − | 0.680173i | ||||
\(17\) | 0 | 0 | −0.804598 | − | 0.593820i | \(-0.797619\pi\) | ||||
0.804598 | + | 0.593820i | \(0.202381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.997204 | + | 1.72721i | 0.997204 | + | 1.72721i | 0.563320 | + | 0.826239i | \(0.309524\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.593820 | − | 0.804598i | \(-0.702381\pi\) | ||||
0.593820 | + | 0.804598i | \(0.297619\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.993712 | − | 0.111964i | 0.993712 | − | 0.111964i | ||||
\(28\) | −0.467269 | + | 0.884115i | −0.467269 | + | 0.884115i | ||||
\(29\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.35417 | − | 0.781831i | −1.35417 | − | 0.781831i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(37\) | −0.119202 | − | 0.273213i | −0.119202 | − | 0.273213i | 0.846724 | − | 0.532032i | \(-0.178571\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.563320 | + | 1.82624i | −0.563320 | + | 1.82624i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.461680 | − | 0.734760i | 0.461680 | − | 0.734760i | −0.532032 | − | 0.846724i | \(-0.678571\pi\) |
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.185912 | − | 0.982566i | \(-0.559524\pi\) | ||||
0.185912 | + | 0.982566i | \(0.440476\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(49\) | 0.149042 | − | 0.988831i | 0.149042 | − | 0.988831i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0714600 | + | 1.90981i | 0.0714600 | + | 1.90981i | ||||
\(53\) | 0 | 0 | 0.399892 | − | 0.916562i | \(-0.369048\pi\) | ||||
−0.399892 | + | 0.916562i | \(0.630952\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.06109 | + | 1.68871i | 1.06109 | + | 1.68871i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.73305 | − | 0.680173i | −1.73305 | − | 0.680173i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(64\) | 0.433884 | − | 0.900969i | 0.433884 | − | 0.900969i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.352083 | − | 1.31399i | −0.352083 | − | 1.31399i | −0.884115 | − | 0.467269i | \(-0.845238\pi\) |
0.532032 | − | 0.846724i | \(-0.321429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.367670 | − | 1.94318i | 0.367670 | − | 1.94318i | 0.0373912 | − | 0.999301i | \(-0.488095\pi\) |
0.330279 | − | 0.943883i | \(-0.392857\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.55929 | + | 1.24349i | 1.55929 | + | 1.24349i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.632789 | − | 0.365341i | 0.632789 | − | 0.365341i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.988831 | − | 0.149042i | 0.988831 | − | 0.149042i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(84\) | −0.433884 | + | 0.900969i | −0.433884 | + | 0.900969i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.698220 | − | 1.77904i | −0.698220 | − | 1.77904i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.38246 | − | 0.730651i | −1.38246 | − | 0.730651i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.16848 | + | 1.16848i | 1.16848 | + | 1.16848i | 0.982566 | + | 0.185912i | \(0.0595238\pi\) |
0.185912 | + | 0.982566i | \(0.440476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.680173 | − | 0.733052i | \(-0.261905\pi\) | ||||
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.0698381 | − | 0.132140i | 0.0698381 | − | 0.132140i | −0.846724 | − | 0.532032i | \(-0.821429\pi\) |
0.916562 | + | 0.399892i | \(0.130952\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.757972 | − | 0.652287i | \(-0.773810\pi\) | ||||
0.757972 | + | 0.652287i | \(0.226190\pi\) | |||||||
\(108\) | 0.884115 | − | 0.467269i | 0.884115 | − | 0.467269i | ||||
\(109\) | 1.46200 | + | 0.109562i | 1.46200 | + | 0.109562i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
0.680173 | + | 0.733052i | \(0.261905\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.129334 | − | 0.268565i | −0.129334 | − | 0.268565i | ||||
\(112\) | −0.111964 | + | 0.993712i | −0.111964 | + | 0.993712i | ||||
\(113\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.494641 | + | 1.84602i | −0.494641 | + | 1.84602i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.54620 | − | 0.233052i | −1.54620 | − | 0.233052i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.11956 | − | 0.126144i | −1.11956 | − | 0.126144i | −0.467269 | − | 0.884115i | \(-0.654762\pi\) |
−0.652287 | + | 0.757972i | \(0.726190\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.433884 | − | 0.751509i | 0.433884 | − | 0.751509i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.680173 | − | 0.733052i | \(-0.738095\pi\) | ||||
0.680173 | + | 0.733052i | \(0.261905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.88249 | − | 0.658711i | −1.88249 | − | 0.658711i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.884115 | − | 0.467269i | \(-0.154762\pi\) | ||||
−0.884115 | + | 0.467269i | \(0.845238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −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 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.680173 | − | 0.733052i | 0.680173 | − | 0.733052i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.111964 | − | 0.993712i | 0.111964 | − | 0.993712i | ||||
\(148\) | −0.210778 | − | 0.210778i | −0.210778 | − | 0.210778i | ||||
\(149\) | 0 | 0 | 0.563320 | − | 0.826239i | \(-0.309524\pi\) | ||||
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0546039 | + | 0.139129i | 0.0546039 | + | 0.139129i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.142820 | + | 1.90580i | 0.142820 | + | 1.90580i | ||||
\(157\) | −0.685064 | − | 1.29620i | −0.685064 | − | 1.29620i | −0.943883 | − | 0.330279i | \(-0.892857\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.589098 | − | 0.0220425i | −0.589098 | − | 0.0220425i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.07379 | − | 1.65379i | −2.07379 | − | 1.65379i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.12349 | + | 1.64786i | 1.12349 | + | 1.64786i | ||||
\(172\) | 0.161328 | − | 0.852639i | 0.161328 | − | 0.852639i | ||||
\(173\) | 0 | 0 | 0.804598 | − | 0.593820i | \(-0.202381\pi\) | ||||
−0.804598 | + | 0.593820i | \(0.797619\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.149042 | − | 0.988831i | \(-0.547619\pi\) | ||||
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.846011 | − | 1.75676i | 0.846011 | − | 1.75676i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.75727 | − | 0.614896i | −1.75727 | − | 0.614896i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.680173 | + | 0.733052i | −0.680173 | + | 0.733052i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(192\) | 0.399892 | − | 0.916562i | 0.399892 | − | 0.916562i | ||||
\(193\) | 0.0729074 | + | 1.94849i | 0.0729074 | + | 1.94849i | 0.258819 | + | 0.965926i | \(0.416667\pi\) |
−0.185912 | + | 0.982566i | \(0.559524\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(197\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.825886 | + | 0.766310i | 0.825886 | + | 0.766310i | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.400969 | − | 1.29991i | −0.400969 | − | 1.29991i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.764252 | + | 1.75168i | 0.764252 | + | 1.75168i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.78181 | − | 0.858075i | −1.78181 | − | 0.858075i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
−0.826239 | − | 0.563320i | \(-0.809524\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.53640 | − | 0.290703i | 1.53640 | − | 0.290703i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.294755 | − | 1.95557i | 0.294755 | − | 1.95557i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.0818104 | + | 0.726088i | 0.0818104 | + | 0.726088i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.884115 | + | 0.467269i | \(0.845238\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(228\) | 1.60470 | + | 1.18432i | 1.60470 | + | 1.18432i | ||||
\(229\) | −0.825886 | + | 0.766310i | −0.825886 | + | 0.766310i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.916562 | − | 0.399892i | \(-0.130952\pi\) | ||||
−0.916562 | + | 0.399892i | \(0.869048\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.618686 | − | 0.388746i | 0.618686 | − | 0.388746i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.26631 | − | 0.496990i | 1.26631 | − | 0.496990i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.982566 | − | 0.185912i | 0.982566 | − | 0.185912i | ||||
\(244\) | −1.86175 | −1.86175 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.74515 | + | 0.708621i | −3.74515 | + | 0.708621i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(252\) | −0.399892 | + | 0.916562i | −0.399892 | + | 0.916562i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.0747301 | − | 0.997204i | 0.0747301 | − | 0.997204i | ||||
\(257\) | 0 | 0 | 0.916562 | − | 0.399892i | \(-0.130952\pi\) | ||||
−0.916562 | + | 0.399892i | \(0.869048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.268565 | + | 0.129334i | 0.268565 | + | 0.129334i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.807801 | − | 1.09453i | −0.807801 | − | 1.09453i | ||||
\(269\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.290611 | + | 1.92808i | −0.290611 | + | 1.92808i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.764252 | − | 1.75168i | −0.764252 | − | 1.75168i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.350063 | − | 0.474319i | 0.350063 | − | 0.474319i | −0.593820 | − | 0.804598i | \(-0.702381\pi\) |
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.40881 | − | 0.678448i | −1.40881 | − | 0.678448i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.476615 | − | 0.553836i | −0.476615 | − | 0.553836i | 0.467269 | − | 0.884115i | \(-0.345238\pi\) |
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.294755 | + | 0.955573i | 0.294755 | + | 0.955573i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.21135 | + | 1.12397i | 1.21135 | + | 1.12397i | ||||
\(292\) | −0.367670 | − | 1.94318i | −0.367670 | − | 1.94318i | ||||
\(293\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.129334 | + | 0.858075i | 0.129334 | + | 0.858075i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.90580 | + | 0.587862i | 1.90580 | + | 0.587862i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.70082 | − | 0.595142i | −1.70082 | − | 0.595142i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0648483 | − | 0.134659i | 0.0648483 | − | 0.134659i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.149042 | − | 0.988831i | \(-0.547619\pi\) | ||||
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.20449 | + | 0.322742i | 1.20449 | + | 0.322742i | 0.804598 | − | 0.593820i | \(-0.202381\pi\) |
0.399892 | + | 0.916562i | \(0.369048\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.455573 | − | 0.571270i | 0.455573 | − | 0.571270i | ||||
\(317\) | 0 | 0 | 0.804598 | − | 0.593820i | \(-0.202381\pi\) | ||||
−0.804598 | + | 0.593820i | \(0.797619\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.46508 | + | 0.0548194i | 1.46508 | + | 0.0548194i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.603718 | + | 1.53825i | −0.603718 | + | 1.53825i | 0.222521 | + | 0.974928i | \(0.428571\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.139286 | − | 0.263541i | −0.139286 | − | 0.263541i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.0747301 | + | 0.997204i | −0.0747301 | + | 0.997204i | ||||
\(337\) | 1.65099 | + | 1.03739i | 1.65099 | + | 1.03739i | 0.943883 | + | 0.330279i | \(0.107143\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.532032 | + | 0.846724i | 0.532032 | + | 0.846724i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.916562 | − | 0.399892i | \(-0.869048\pi\) | ||||
0.916562 | + | 0.399892i | \(0.130952\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.193096 | + | 0.846011i | 0.193096 | + | 0.846011i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.425270 | + | 1.86323i | −0.425270 | + | 1.86323i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.884115 | − | 0.467269i | \(-0.154762\pi\) | ||||
−0.884115 | + | 0.467269i | \(0.845238\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.680173 | − | 0.733052i | \(-0.738095\pi\) | ||||
0.680173 | + | 0.733052i | \(0.261905\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.48883 | + | 2.57873i | −1.48883 | + | 2.57873i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.993712 | − | 0.111964i | −0.993712 | − | 0.111964i | ||||
\(364\) | −1.29991 | − | 1.40097i | −1.29991 | − | 1.40097i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.437283 | − | 0.0827384i | −0.437283 | − | 0.0827384i | −0.0373912 | − | 0.999301i | \(-0.511905\pi\) |
−0.399892 | + | 0.916562i | \(0.630952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.55383 | − | 0.175075i | −1.55383 | − | 0.175075i | ||||
\(373\) | 0.291596 | − | 1.08825i | 0.291596 | − | 1.08825i | −0.652287 | − | 0.757972i | \(-0.726190\pi\) |
0.943883 | − | 0.330279i | \(-0.107143\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.0648483 | − | 0.134659i | −0.0648483 | − | 0.134659i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.12349 | − | 0.0841939i | −1.12349 | − | 0.0841939i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.757972 | − | 0.652287i | \(-0.773810\pi\) | ||||
0.757972 | + | 0.652287i | \(0.226190\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.405481 | − | 0.767207i | 0.405481 | − | 0.767207i | ||||
\(388\) | 1.51460 | + | 0.660813i | 1.51460 | + | 0.660813i | ||||
\(389\) | 0 | 0 | 0.680173 | − | 0.733052i | \(-0.261905\pi\) | ||||
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.10247 | − | 0.582674i | −1.10247 | − | 0.582674i | −0.185912 | − | 0.982566i | \(-0.559524\pi\) |
−0.916562 | + | 0.399892i | \(0.869048\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.90580 | − | 0.587862i | −1.90580 | − | 0.587862i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.26511 | − | 1.94929i | 2.26511 | − | 1.94929i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.294755 | − | 0.0444272i | 0.294755 | − | 0.0444272i | − | 1.00000i | \(-0.5\pi\) | |
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.0167342 | − | 0.148520i | 0.0167342 | − | 0.148520i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.109597 | + | 0.579233i | −0.109597 | + | 0.579233i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.914101 | + | 1.14625i | 0.914101 | + | 1.14625i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.75727 | − | 0.614896i | 1.75727 | − | 0.614896i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(432\) | 0.652287 | − | 0.757972i | 0.652287 | − | 0.757972i | ||||
\(433\) | 0.958689 | + | 1.52574i | 0.958689 | + | 1.52574i | 0.846724 | + | 0.532032i | \(0.178571\pi\) |
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.40097 | − | 0.432142i | 1.40097 | − | 0.432142i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.487076 | − | 0.332083i | −0.487076 | − | 0.332083i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0747301 | − | 0.997204i | 0.0747301 | − | 0.997204i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.185912 | − | 0.982566i | \(-0.559524\pi\) | ||||
0.185912 | + | 0.982566i | \(0.440476\pi\) | |||||||
\(444\) | −0.218511 | − | 0.202749i | −0.218511 | − | 0.202749i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(449\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.0597679 | + | 0.136990i | 0.0597679 | + | 0.136990i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0696130 | − | 1.86045i | 0.0696130 | − | 1.86045i | −0.330279 | − | 0.943883i | \(-0.607143\pi\) |
0.399892 | − | 0.916562i | \(-0.369048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.585804 | − | 0.0660042i | 0.585804 | − | 0.0660042i | 0.185912 | − | 0.982566i | \(-0.440476\pi\) |
0.399892 | + | 0.916562i | \(0.369048\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.593820 | − | 0.804598i | \(-0.702381\pi\) | ||||
0.593820 | + | 0.804598i | \(0.297619\pi\) | |||||||
\(468\) | 0.213980 | + | 1.89913i | 0.213980 | + | 1.89913i | ||||
\(469\) | 1.12397 | + | 0.766310i | 1.12397 | + | 0.766310i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.733052 | − | 1.26968i | −0.733052 | − | 1.26968i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.568090 | − | 0.0425725i | 0.568090 | − | 0.0425725i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.974928 | + | 0.222521i | −0.974928 | + | 0.222521i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.56257 | − | 0.0584672i | 1.56257 | − | 0.0584672i | 0.757972 | − | 0.652287i | \(-0.226190\pi\) |
0.804598 | + | 0.593820i | \(0.202381\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.589510 | −0.589510 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.52446 | + | 0.347948i | −1.52446 | + | 0.347948i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.97213 | + | 0.147791i | −1.97213 | + | 0.147791i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | −2.13418 | − | 1.57509i | −2.13418 | − | 1.57509i | ||||
\(508\) | −1.08825 | + | 0.291596i | −1.08825 | + | 0.291596i | ||||
\(509\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.988831 | + | 1.71271i | 0.988831 | + | 1.71271i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.18432 | + | 1.60470i | 1.18432 | + | 1.60470i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.129334 | − | 0.858075i | 0.129334 | − | 0.858075i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.0466261 | + | 1.24611i | −0.0466261 | + | 1.24611i | 0.757972 | + | 0.652287i | \(0.226190\pi\) |
−0.804598 | + | 0.593820i | \(0.797619\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.294755 | + | 0.955573i | −0.294755 | + | 0.955573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.99301 | + | 0.0745733i | −1.99301 | + | 0.0745733i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.123490 | + | 0.0841939i | 0.123490 | + | 0.0841939i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.779732 | − | 1.78716i | 0.779732 | − | 1.78716i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.831919 | − | 1.32399i | −0.831919 | − | 1.32399i | −0.943883 | − | 0.330279i | \(-0.892857\pi\) |
0.111964 | − | 0.993712i | \(-0.464286\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.77904 | − | 0.548760i | −1.77904 | − | 0.548760i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.241329 | + | 0.689679i | −0.241329 | + | 0.689679i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.0878620 | + | 0.582926i | 0.0878620 | + | 0.582926i | ||||
\(557\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.03401 | + | 1.29661i | 1.03401 | + | 1.29661i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.185912 | − | 0.982566i | \(-0.440476\pi\) | ||||
−0.185912 | + | 0.982566i | \(0.559524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.652287 | + | 0.757972i | −0.652287 | + | 0.757972i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.722521 | + | 0.108903i | −0.722521 | + | 0.108903i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(577\) | 0.337329 | − | 0.290295i | 0.337329 | − | 0.290295i | −0.467269 | − | 0.884115i | \(-0.654762\pi\) |
0.804598 | + | 0.593820i | \(0.202381\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.145713 | + | 1.94440i | 0.145713 | + | 1.94440i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(589\) | − | 3.11858i | − | 3.11858i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.273213 | − | 0.119202i | −0.273213 | − | 0.119202i | ||||
\(593\) | 0 | 0 | 0.467269 | − | 0.884115i | \(-0.345238\pi\) | ||||
−0.467269 | + | 0.884115i | \(0.654762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.853961 | + | 0.734893i | 0.853961 | + | 0.734893i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) | ||||
0.997204 | + | 0.0747301i | \(0.0238095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.751509 | − | 1.56052i | −0.751509 | − | 1.56052i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
0.0747301 | − | 0.997204i | \(-0.476190\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.449294 | − | 1.28401i | −0.449294 | − | 1.28401i | ||||
\(604\) | 0.101659 | + | 0.109562i | 0.101659 | + | 0.109562i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.53640 | + | 0.290703i | 1.53640 | + | 0.290703i | 0.884115 | − | 0.467269i | \(-0.154762\pi\) |
0.652287 | + | 0.757972i | \(0.273810\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 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 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.829215 | + | 1.72188i | 0.829215 | + | 1.72188i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.11127 | − | 0.956321i | −1.11127 | − | 0.956321i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.162592 | − | 0.712362i | −0.162592 | − | 0.712362i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.81265 | − | 0.790851i | −1.81265 | − | 0.790851i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.68967 | + | 0.893018i | 1.68967 | + | 0.893018i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.24139 | − | 0.780014i | −1.24139 | − | 0.780014i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.982566 | + | 0.185912i | \(0.940476\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.467269 | − | 0.884115i | \(-0.654762\pi\) | ||||
0.467269 | + | 0.884115i | \(0.345238\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.52446 | − | 0.347948i | 1.52446 | − | 0.347948i | ||||
\(652\) | −0.556429 | + | 0.194703i | −0.556429 | + | 0.194703i | ||||
\(653\) | 0 | 0 | −0.999301 | − | 0.0373912i | \(-0.988095\pi\) | ||||
0.999301 | + | 0.0373912i | \(0.0119048\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.221428 | − | 1.96523i | 0.221428 | − | 1.96523i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.975699 | − | 1.43109i | −0.975699 | − | 1.43109i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
−0.0747301 | − | 0.997204i | \(-0.523810\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.108903 | + | 0.722521i | 0.108903 | + | 0.722521i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.28401 | − | 0.449294i | −1.28401 | − | 0.449294i | −0.399892 | − | 0.916562i | \(-0.630952\pi\) |
−0.884115 | + | 0.467269i | \(0.845238\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.53464 | − | 0.781831i | −2.53464 | − | 0.781831i | ||||
\(677\) | 0 | 0 | 0.652287 | − | 0.757972i | \(-0.273810\pi\) | ||||
−0.652287 | + | 0.757972i | \(0.726190\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.64786 | − | 0.123490i | −1.64786 | − | 0.123490i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.0373912 | − | 0.999301i | \(-0.511905\pi\) | ||||
0.0373912 | + | 0.999301i | \(0.488095\pi\) | |||||||
\(684\) | 1.64786 | + | 1.12349i | 1.64786 | + | 1.12349i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.796655 | + | 0.796655i | −0.796655 | + | 0.796655i | ||||
\(688\) | −0.161328 | − | 0.852639i | −0.161328 | − | 0.852639i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.510531 | + | 1.65510i | 0.510531 | + | 1.65510i | 0.733052 | + | 0.680173i | \(0.238095\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.353027 | − | 0.478335i | 0.353027 | − | 0.478335i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.246289 | − | 1.63402i | 0.246289 | − | 1.63402i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.680173 | − | 0.733052i | \(-0.261905\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.603718 | − | 0.411608i | 0.603718 | − | 0.411608i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0332580 | + | 0.145713i | 0.0332580 | + | 0.145713i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.24684 | − | 0.543991i | 1.24684 | − | 0.543991i | ||||
\(724\) | 0.145713 | − | 1.94440i | 0.145713 | − | 1.94440i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.846724 | + | 0.532032i | −0.846724 | + | 0.532032i | −0.884115 | − | 0.467269i | \(-0.845238\pi\) |
0.0373912 | + | 0.999301i | \(0.488095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.974928 | − | 0.222521i | 0.974928 | − | 0.222521i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.86045 | + | 0.0696130i | −1.86045 | + | 0.0696130i | ||||
\(733\) | −1.62367 | + | 0.307215i | −1.62367 | + | 0.307215i | −0.916562 | − | 0.399892i | \(-0.869048\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.36476 | + | 0.535628i | −1.36476 | + | 0.535628i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.71604 | + | 0.848162i | −3.71604 | + | 0.848162i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.109562 | + | 0.101659i | −0.109562 | + | 0.101659i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.365341 | + | 0.930874i | −0.365341 | + | 0.930874i | ||||
\(757\) | −0.152310 | − | 1.35179i | −0.152310 | − | 1.35179i | −0.804598 | − | 0.593820i | \(-0.797619\pi\) |
0.652287 | − | 0.757972i | \(-0.273810\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.149042 | − | 0.988831i | \(-0.452381\pi\) | ||||
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.17962 | + | 0.870602i | −1.17962 | + | 0.870602i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.0373912 | − | 0.999301i | 0.0373912 | − | 0.999301i | ||||
\(769\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.779732 | + | 1.78716i | 0.779732 | + | 1.78716i | ||||
\(773\) | 0 | 0 | −0.652287 | − | 0.757972i | \(-0.726190\pi\) | ||||
0.652287 | + | 0.757972i | \(0.273810\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.273213 | + | 0.119202i | 0.273213 | + | 0.119202i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.563320 | − | 0.826239i | −0.563320 | − | 0.826239i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.0739471 | − | 1.97628i | −0.0739471 | − | 1.97628i | −0.185912 | − | 0.982566i | \(-0.559524\pi\) |
0.111964 | − | 0.993712i | \(-0.464286\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.32088 | − | 2.69692i | 2.32088 | − | 2.69692i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.04876 | + | 0.411608i | 1.04876 | + | 0.411608i | ||||
\(797\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.848162 | − | 1.06356i | −0.848162 | − | 1.06356i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.563320 | − | 0.826239i | \(-0.690476\pi\) | ||||
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.06356 | + | 0.848162i | 1.06356 | + | 0.848162i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.218315 | + | 1.93760i | −0.218315 | + | 1.93760i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.72947 | + | 0.0647123i | 1.72947 | + | 0.0647123i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.829215 | − | 1.72188i | −0.829215 | − | 1.72188i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.931924 | − | 1.76329i | −0.931924 | − | 1.76329i | −0.532032 | − | 0.846724i | \(-0.678571\pi\) |
−0.399892 | − | 0.916562i | \(-0.630952\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.680173 | + | 1.73305i | 0.680173 | + | 1.73305i | 0.680173 | + | 0.733052i | \(0.261905\pi\) |
1.00000i | \(0.500000\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.332083 | − | 0.487076i | 0.332083 | − | 0.487076i | ||||
\(832\) | 1.35138 | + | 1.35138i | 1.35138 | + | 1.35138i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.43319 | − | 0.625296i | −1.43319 | − | 0.625296i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.222521 | − | 0.974928i | 0.222521 | − | 0.974928i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.97213 | − | 0.147791i | −1.97213 | − | 0.147791i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.846724 | − | 0.532032i | 0.846724 | − | 0.532032i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.496990 | − | 0.535628i | −0.496990 | − | 0.535628i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.79061 | − | 0.201753i | −1.79061 | − | 0.201753i | −0.846724 | − | 0.532032i | \(-0.821429\pi\) |
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.982566 | − | 0.185912i | \(-0.940476\pi\) | ||||
0.982566 | + | 0.185912i | \(0.0595238\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.858075 | − | 0.129334i | −0.858075 | − | 0.129334i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.330279 | + | 0.943883i | 0.330279 | + | 0.943883i | ||||
\(868\) | 1.32399 | − | 0.831919i | 1.32399 | − | 0.831919i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.59255 | + | 0.194285i | 2.59255 | + | 0.194285i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.25253 | + | 1.07789i | 1.25253 | + | 1.07789i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.440071 | − | 1.92808i | −0.440071 | − | 1.92808i | ||||
\(877\) | −0.931924 | + | 1.76329i | −0.931924 | + | 1.76329i | −0.399892 | + | 0.916562i | \(0.630952\pi\) |
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.416847 | + | 0.416847i | 0.416847 | + | 0.416847i | 0.884115 | − | 0.467269i | \(-0.154762\pi\) |
−0.467269 | + | 0.884115i | \(0.654762\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.884115 | − | 0.467269i | \(-0.845238\pi\) | ||||
0.884115 | + | 0.467269i | \(0.154762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.930874 | − | 0.634659i | 0.930874 | − | 0.634659i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.341425 | + | 0.646007i | 0.341425 | + | 0.646007i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.161328 | + | 0.852639i | 0.161328 | + | 0.852639i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.252904 | + | 1.33663i | −0.252904 | + | 1.33663i | 0.593820 | + | 0.804598i | \(0.297619\pi\) |
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(912\) | 1.92645 | + | 0.516191i | 1.92645 | + | 0.516191i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.488831 | + | 1.01507i | −0.488831 | + | 1.01507i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.414278 | − | 0.162592i | −0.414278 | − | 0.162592i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.72188 | − | 0.531130i | −1.72188 | − | 0.531130i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0597679 | − | 0.136990i | 0.0597679 | − | 0.136990i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.85654 | − | 0.728639i | 1.85654 | − | 0.728639i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.958689 | + | 1.52574i | −0.958689 | + | 1.52574i | −0.111964 | + | 0.993712i | \(0.535714\pi\) |
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.21572 | + | 0.277479i | 1.21572 | + | 0.277479i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.294755 | − | 0.955573i | \(-0.404762\pi\) | ||||
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.0373912 | − | 0.999301i | \(-0.488095\pi\) | ||||
−0.0373912 | + | 0.999301i | \(0.511905\pi\) | |||||||
\(948\) | 0.433894 | − | 0.587905i | 0.433894 | − | 0.587905i | ||||
\(949\) | 3.27323 | + | 1.88980i | 3.27323 | + | 1.88980i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.722521 | + | 1.25144i | 0.722521 | + | 1.25144i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.997204 | − | 0.925270i | 0.997204 | − | 0.925270i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.658711 | + | 1.88249i | −0.658711 | + | 1.88249i | −0.258819 | + | 0.965926i | \(0.583333\pi\) |
−0.399892 | + | 0.916562i | \(0.630952\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | ||||
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(972\) | 0.846724 | − | 0.532032i | 0.846724 | − | 0.532032i | ||||
\(973\) | −0.275460 | − | 0.521195i | −0.275460 | − | 0.521195i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.73305 | + | 0.680173i | −1.73305 | + | 0.680173i | ||||
\(977\) | 0 | 0 | 0.999301 | − | 0.0373912i | \(-0.0119048\pi\) | ||||
−0.999301 | + | 0.0373912i | \(0.988095\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.46610 | 1.46610 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.999301 | − | 0.0373912i | \(-0.0119048\pi\) | ||||
−0.999301 | + | 0.0373912i | \(0.988095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.22738 | + | 2.02790i | −3.22738 | + | 2.02790i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.134659 | − | 1.79690i | 0.134659 | − | 1.79690i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.545779 | + | 1.55975i | −0.545779 | + | 1.55975i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.804598 | + | 0.593820i | 0.804598 | + | 0.593820i | 0.916562 | − | 0.399892i | \(-0.130952\pi\) |
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.149042 | − | 0.258149i | −0.149042 | − | 0.258149i |
(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 | 3675.1.cy.a.143.2 | yes | 48 | |
3.2 | odd | 2 | CM | 3675.1.cy.a.143.2 | yes | 48 | |
5.2 | odd | 4 | inner | 3675.1.cy.a.1907.1 | yes | 48 | |
5.3 | odd | 4 | inner | 3675.1.cy.a.1907.2 | yes | 48 | |
5.4 | even | 2 | inner | 3675.1.cy.a.143.1 | ✓ | 48 | |
15.2 | even | 4 | inner | 3675.1.cy.a.1907.1 | yes | 48 | |
15.8 | even | 4 | inner | 3675.1.cy.a.1907.2 | yes | 48 | |
15.14 | odd | 2 | inner | 3675.1.cy.a.143.1 | ✓ | 48 | |
49.12 | odd | 42 | inner | 3675.1.cy.a.2168.1 | yes | 48 | |
147.110 | even | 42 | inner | 3675.1.cy.a.2168.1 | yes | 48 | |
245.12 | even | 84 | inner | 3675.1.cy.a.257.2 | yes | 48 | |
245.159 | odd | 42 | inner | 3675.1.cy.a.2168.2 | yes | 48 | |
245.208 | even | 84 | inner | 3675.1.cy.a.257.1 | yes | 48 | |
735.257 | odd | 84 | inner | 3675.1.cy.a.257.2 | yes | 48 | |
735.404 | even | 42 | inner | 3675.1.cy.a.2168.2 | yes | 48 | |
735.698 | odd | 84 | inner | 3675.1.cy.a.257.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3675.1.cy.a.143.1 | ✓ | 48 | 5.4 | even | 2 | inner | |
3675.1.cy.a.143.1 | ✓ | 48 | 15.14 | odd | 2 | inner | |
3675.1.cy.a.143.2 | yes | 48 | 1.1 | even | 1 | trivial | |
3675.1.cy.a.143.2 | yes | 48 | 3.2 | odd | 2 | CM | |
3675.1.cy.a.257.1 | yes | 48 | 245.208 | even | 84 | inner | |
3675.1.cy.a.257.1 | yes | 48 | 735.698 | odd | 84 | inner | |
3675.1.cy.a.257.2 | yes | 48 | 245.12 | even | 84 | inner | |
3675.1.cy.a.257.2 | yes | 48 | 735.257 | odd | 84 | inner | |
3675.1.cy.a.1907.1 | yes | 48 | 5.2 | odd | 4 | inner | |
3675.1.cy.a.1907.1 | yes | 48 | 15.2 | even | 4 | inner | |
3675.1.cy.a.1907.2 | yes | 48 | 5.3 | odd | 4 | inner | |
3675.1.cy.a.1907.2 | yes | 48 | 15.8 | even | 4 | inner | |
3675.1.cy.a.2168.1 | yes | 48 | 49.12 | odd | 42 | inner | |
3675.1.cy.a.2168.1 | yes | 48 | 147.110 | even | 42 | inner | |
3675.1.cy.a.2168.2 | yes | 48 | 245.159 | odd | 42 | inner | |
3675.1.cy.a.2168.2 | yes | 48 | 735.404 | even | 42 | inner |