Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(881,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.f (of order \(2\), degree \(1\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.8 | ||
Root | \(-0.923880 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.881 |
Dual form | 1764.2.f.b.881.7 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.84776 | 0.826343 | 0.413171 | − | 0.910653i | \(-0.364421\pi\) | ||||
0.413171 | + | 0.910653i | \(0.364421\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.46088i | 1.23723i | 0.785695 | + | 0.618613i | \(0.212305\pi\) | ||||
−0.785695 | + | 0.618613i | \(0.787695\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.29610 | −0.556886 | −0.278443 | − | 0.960453i | \(-0.589818\pi\) | ||||
−0.278443 | + | 0.960453i | \(0.589818\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.53073i | − 0.351174i | −0.984464 | − | 0.175587i | \(-0.943818\pi\) | ||||
0.984464 | − | 0.175587i | \(-0.0561824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.82843i | 1.84085i | 0.390914 | + | 0.920427i | \(0.372159\pi\) | ||||
−0.390914 | + | 0.920427i | \(0.627841\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.58579 | −0.317157 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.17157i | − 0.217556i | −0.994066 | − | 0.108778i | \(-0.965306\pi\) | ||||
0.994066 | − | 0.108778i | \(-0.0346937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.86030i | 1.05254i | 0.850317 | + | 0.526271i | \(0.176410\pi\) | ||||
−0.850317 | + | 0.526271i | \(0.823590\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24264 | 1.35508 | 0.677541 | − | 0.735485i | \(-0.263046\pi\) | ||||
0.677541 | + | 0.735485i | \(0.263046\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.8519 | −1.85096 | −0.925480 | − | 0.378798i | \(-0.876338\pi\) | ||||
−0.925480 | + | 0.378798i | \(0.876338\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.17157 | 0.178663 | 0.0893316 | − | 0.996002i | \(-0.471527\pi\) | ||||
0.0893316 | + | 0.996002i | \(0.471527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.02509 | 1.17058 | 0.585290 | − | 0.810824i | \(-0.300981\pi\) | ||||
0.585290 | + | 0.810824i | \(0.300981\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.75736i | 0.516113i | 0.966130 | + | 0.258056i | \(0.0830821\pi\) | ||||
−0.966130 | + | 0.258056i | \(0.916918\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.69552i | 0.498304i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.81845 | −1.27825 | −0.639127 | − | 0.769101i | \(-0.720704\pi\) | ||||
−0.639127 | + | 0.769101i | \(0.720704\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 12.3003i | − 1.57489i | −0.616387 | − | 0.787444i | \(-0.711404\pi\) | ||||
0.616387 | − | 0.787444i | \(-0.288596\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.24264i | 1.02237i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4853 | 1.52532 | 0.762660 | − | 0.646800i | \(-0.223893\pi\) | ||||
0.762660 | + | 0.646800i | \(0.223893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3137i | 1.58005i | 0.613077 | + | 0.790023i | \(0.289932\pi\) | ||||
−0.613077 | + | 0.790023i | \(0.710068\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 2.74444i | − 0.321213i | −0.987019 | − | 0.160606i | \(-0.948655\pi\) | ||||
0.987019 | − | 0.160606i | \(-0.0513450\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.4525 | −1.14731 | −0.573656 | − | 0.819097i | \(-0.694475\pi\) | ||||
−0.573656 | + | 0.819097i | \(0.694475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.24264 | −0.460179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.4650 | 1.53329 | 0.766646 | − | 0.642070i | \(-0.221924\pi\) | ||||
0.766646 | + | 0.642070i | \(0.221924\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 2.82843i | − 0.290191i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.74444i | 0.278656i | 0.990246 | + | 0.139328i | \(0.0444942\pi\) | ||||
−0.990246 | + | 0.139328i | \(0.955506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.74444 | −0.273082 | −0.136541 | − | 0.990634i | \(-0.543599\pi\) | ||||
−0.136541 | + | 0.990634i | \(0.543599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.634051i | 0.0624749i | 0.999512 | + | 0.0312374i | \(0.00994480\pi\) | ||||
−0.999512 | + | 0.0312374i | \(0.990055\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8284i | 1.24017i | 0.784534 | + | 0.620085i | \(0.212902\pi\) | ||||
−0.784534 | + | 0.620085i | \(0.787098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.07107 | 0.294155 | 0.147077 | − | 0.989125i | \(-0.453013\pi\) | ||||
0.147077 | + | 0.989125i | \(0.453013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 13.4142i | − 1.26190i | −0.775822 | − | 0.630952i | \(-0.782665\pi\) | ||||
0.775822 | − | 0.630952i | \(-0.217335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.3128i | 1.52118i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1689 | −1.08842 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.82843 | 0.605925 | 0.302962 | − | 0.953002i | \(-0.402024\pi\) | ||||
0.302962 | + | 0.953002i | \(0.402024\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3492 | −0.991583 | −0.495792 | − | 0.868442i | \(-0.665122\pi\) | ||||
−0.495792 | + | 0.868442i | \(0.665122\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.17157i | 0.441837i | 0.975292 | + | 0.220919i | \(0.0709055\pi\) | ||||
−0.975292 | + | 0.220919i | \(0.929094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.49435i | 0.550844i | 0.961323 | + | 0.275422i | \(0.0888176\pi\) | ||||
−0.961323 | + | 0.275422i | \(0.911182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.92177 | −0.746076 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 2.16478i | − 0.179776i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.07107i | 0.579284i | 0.957135 | + | 0.289642i | \(0.0935363\pi\) | ||||
−0.957135 | + | 0.289642i | \(0.906464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1421 | −1.47639 | −0.738193 | − | 0.674590i | \(-0.764321\pi\) | ||||
−0.738193 | + | 0.674590i | \(0.764321\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.8284i | 0.869760i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 11.2179i | − 0.895284i | −0.894213 | − | 0.447642i | \(-0.852264\pi\) | ||||
0.894213 | − | 0.447642i | \(-0.147736\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.82843 | −0.221540 | −0.110770 | − | 0.993846i | \(-0.535332\pi\) | ||||
−0.110770 | + | 0.993846i | \(0.535332\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.3128 | 1.26232 | 0.631161 | − | 0.775652i | \(-0.282579\pi\) | ||||
0.631161 | + | 0.775652i | \(0.282579\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.89949 | −0.530730 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.1146 | 0.921052 | 0.460526 | − | 0.887646i | \(-0.347661\pi\) | ||||
0.460526 | + | 0.887646i | \(0.347661\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.3137i | 0.995113i | 0.867431 | + | 0.497557i | \(0.165769\pi\) | ||||
−0.867431 | + | 0.497557i | \(0.834231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.4650i | 1.07518i | 0.843207 | + | 0.537589i | \(0.180665\pi\) | ||||
−0.843207 | + | 0.537589i | \(0.819335\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.2304 | 1.11976 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4.59220i | − 0.335815i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 5.31371i | − 0.384486i | −0.981347 | − | 0.192243i | \(-0.938424\pi\) | ||||
0.981347 | − | 0.192243i | \(-0.0615763\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.65685 | 0.119263 | 0.0596315 | − | 0.998220i | \(-0.481007\pi\) | ||||
0.0596315 | + | 0.998220i | \(0.481007\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 11.0711i | − 0.788781i | −0.918943 | − | 0.394390i | \(-0.870956\pi\) | ||||
0.918943 | − | 0.394390i | \(-0.129044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.06147i | 0.217022i | 0.994095 | + | 0.108511i | \(0.0346082\pi\) | ||||
−0.994095 | + | 0.108511i | \(0.965392\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.8995 | −1.52953 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.06147 | 0.211766 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.6274 | 1.83311 | 0.916553 | − | 0.399912i | \(-0.130959\pi\) | ||||
0.916553 | + | 0.399912i | \(0.130959\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.16478 | 0.147637 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 10.2426i | − 0.688995i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 21.2764i | − 1.42477i | −0.701786 | − | 0.712387i | \(-0.747614\pi\) | ||||
0.701786 | − | 0.712387i | \(-0.252386\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.86030 | −0.388962 | −0.194481 | − | 0.980906i | \(-0.562302\pi\) | ||||
−0.194481 | + | 0.980906i | \(0.562302\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.1969i | 0.872079i | 0.899928 | + | 0.436039i | \(0.143619\pi\) | ||||
−0.899928 | + | 0.436039i | \(0.856381\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 20.8284i | − 1.36452i | −0.731112 | − | 0.682258i | \(-0.760998\pi\) | ||||
0.731112 | − | 0.682258i | \(-0.239002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.8284 | 0.967300 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.17157i | 0.205152i | 0.994725 | + | 0.102576i | \(0.0327085\pi\) | ||||
−0.994725 | + | 0.102576i | \(0.967292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.25425i | 0.402872i | 0.979502 | + | 0.201436i | \(0.0645608\pi\) | ||||
−0.979502 | + | 0.201436i | \(0.935439\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.82843 | 0.434482 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.7457 | 1.24634 | 0.623169 | − | 0.782088i | \(-0.285845\pi\) | ||||
0.623169 | + | 0.782088i | \(0.285845\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.6569 | −1.11008 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.1200 | −0.818405 | −0.409202 | − | 0.912444i | \(-0.634193\pi\) | ||||
−0.409202 | + | 0.912444i | \(0.634193\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 8.34315i | − 0.514460i | −0.966350 | − | 0.257230i | \(-0.917190\pi\) | ||||
0.966350 | − | 0.257230i | \(-0.0828099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.94269i | 0.426486i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.7318 | 1.50793 | 0.753964 | − | 0.656916i | \(-0.228140\pi\) | ||||
0.753964 | + | 0.656916i | \(0.228140\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.7038i | 1.43991i | 0.694023 | + | 0.719953i | \(0.255837\pi\) | ||||
−0.694023 | + | 0.719953i | \(0.744163\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 3.17157i | − 0.191253i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.9706 | −1.26000 | −0.630000 | − | 0.776596i | \(-0.716945\pi\) | ||||
−0.630000 | + | 0.776596i | \(0.716945\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 6.48528i | − 0.386879i | −0.981112 | − | 0.193440i | \(-0.938036\pi\) | ||||
0.981112 | − | 0.193440i | \(-0.0619644\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 31.9916i | − 1.90170i | −0.309650 | − | 0.950850i | \(-0.600212\pi\) | ||||
0.309650 | − | 0.950850i | \(-0.399788\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.7279 | −0.689878 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.34211 | −0.487351 | −0.243676 | − | 0.969857i | \(-0.578353\pi\) | ||||
−0.243676 | + | 0.969857i | \(0.578353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.1421 | −1.05628 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −39.3826 | −2.27755 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 22.7279i | − 1.30140i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 28.5587i | − 1.62993i | −0.579510 | − | 0.814965i | \(-0.696756\pi\) | ||||
0.579510 | − | 0.814965i | \(-0.303244\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.9105 | −1.24243 | −0.621215 | − | 0.783641i | \(-0.713360\pi\) | ||||
−0.621215 | + | 0.783641i | \(0.713360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 22.6758i | − 1.28171i | −0.767660 | − | 0.640857i | \(-0.778579\pi\) | ||||
0.767660 | − | 0.640857i | \(-0.221421\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 24.2426i | − 1.36160i | −0.732468 | − | 0.680801i | \(-0.761632\pi\) | ||||
0.732468 | − | 0.680801i | \(-0.238368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.34315 | 0.131191 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.51472i | 0.195564i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 7.07401i | − 0.392396i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.68629 | −0.257582 | −0.128791 | − | 0.991672i | \(-0.541110\pi\) | ||||
−0.128791 | + | 0.991672i | \(0.541110\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23.0698 | 1.26044 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9289 | −0.704284 | −0.352142 | − | 0.935947i | \(-0.614547\pi\) | ||||
−0.352142 | + | 0.935947i | \(0.614547\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.7206 | −0.634706 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.79899i | 0.526037i | 0.964791 | + | 0.263019i | \(0.0847181\pi\) | ||||
−0.964791 | + | 0.263019i | \(0.915282\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 30.0669i | − 1.60944i | −0.593652 | − | 0.804722i | \(-0.702315\pi\) | ||||
0.593652 | − | 0.804722i | \(-0.297685\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.5712 | 1.73359 | 0.866796 | − | 0.498664i | \(-0.166176\pi\) | ||||
0.866796 | + | 0.498664i | \(0.166176\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.6005i | 1.30566i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 31.4558i | − 1.66018i | −0.557632 | − | 0.830088i | \(-0.688290\pi\) | ||||
0.557632 | − | 0.830088i | \(-0.311710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.6569 | 0.876677 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.07107i | − 0.265432i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.9246i | 1.45765i | 0.684698 | + | 0.728827i | \(0.259934\pi\) | ||||
−0.684698 | + | 0.728827i | \(0.740066\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.6274 | −0.757379 | −0.378689 | − | 0.925524i | \(-0.623625\pi\) | ||||
−0.378689 | + | 0.925524i | \(0.623625\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.22625 | 0.269166 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.2843 | 1.04193 | 0.520967 | − | 0.853577i | \(-0.325572\pi\) | ||||
0.520967 | + | 0.853577i | \(0.325572\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.12293 | 0.312867 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6.82843i | − 0.346215i | −0.984903 | − | 0.173107i | \(-0.944619\pi\) | ||||
0.984903 | − | 0.173107i | \(-0.0553808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 20.2710i | − 1.02515i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.9050 | 1.05185 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.97069i | 0.400038i | 0.979792 | + | 0.200019i | \(0.0641003\pi\) | ||||
−0.979792 | + | 0.200019i | \(0.935900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 22.4853i | − 1.12286i | −0.827524 | − | 0.561431i | \(-0.810251\pi\) | ||||
0.827524 | − | 0.561431i | \(-0.189749\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.1421 | −1.30223 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.4853i | 0.817145i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 28.6131i | − 1.41483i | −0.706801 | − | 0.707413i | \(-0.749862\pi\) | ||||
0.706801 | − | 0.707413i | \(-0.250138\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.3137 | −0.948073 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.5194 | 0.709321 | 0.354661 | − | 0.934995i | \(-0.384596\pi\) | ||||
0.354661 | + | 0.934995i | \(0.384596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.31371 | −0.356448 | −0.178224 | − | 0.983990i | \(-0.557035\pi\) | ||||
−0.178224 | + | 0.983990i | \(0.557035\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.64113 | 0.176621 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 10.6863i | − 0.514741i | −0.966313 | − | 0.257370i | \(-0.917144\pi\) | ||||
0.966313 | − | 0.257370i | \(-0.0828560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.6913i | 0.946303i | 0.880981 | + | 0.473152i | \(0.156884\pi\) | ||||
−0.880981 | + | 0.473152i | \(0.843116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.5140 | 0.646461 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 18.7402i | − 0.894422i | −0.894428 | − | 0.447211i | \(-0.852417\pi\) | ||||
0.894428 | − | 0.447211i | \(-0.147583\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.68629i | − 0.317675i | −0.987305 | − | 0.158838i | \(-0.949225\pi\) | ||||
0.987305 | − | 0.158838i | \(-0.0507746\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.7279 | 1.26703 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 19.5563i | − 0.922921i | −0.887161 | − | 0.461461i | \(-0.847326\pi\) | ||||
0.887161 | − | 0.461461i | \(-0.152674\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 23.7038i | − 1.11617i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.1647 | 1.31176 | 0.655881 | − | 0.754864i | \(-0.272297\pi\) | ||||
0.655881 | + | 0.754864i | \(0.272297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.82843 | 0.131448 | 0.0657241 | − | 0.997838i | \(-0.479064\pi\) | ||||
0.0657241 | + | 0.997838i | \(0.479064\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.2178 | −1.72224 | −0.861118 | − | 0.508406i | \(-0.830235\pi\) | ||||
−0.861118 | + | 0.508406i | \(0.830235\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.34315i | 0.107738i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.42742i | 0.111378i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.9719 | −1.14100 | −0.570499 | − | 0.821299i | \(-0.693250\pi\) | ||||
−0.570499 | + | 0.821299i | \(0.693250\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36.7695i | 1.67654i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.07107i | 0.230265i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.7990 | −0.897178 | −0.448589 | − | 0.893738i | \(-0.648073\pi\) | ||||
−0.448589 | + | 0.893738i | \(0.648073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.5147i | 0.790428i | 0.918589 | + | 0.395214i | \(0.129330\pi\) | ||||
−0.918589 | + | 0.395214i | \(0.870670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.69005i | 0.121154i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.14214 | −0.0958952 | −0.0479476 | − | 0.998850i | \(-0.515268\pi\) | ||||
−0.0479476 | + | 0.998850i | \(0.515268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2459 | 0.546016 | 0.273008 | − | 0.962012i | \(-0.411981\pi\) | ||||
0.273008 | + | 0.962012i | \(0.411981\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.07107 | −0.225660 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.35757 | 0.237470 | 0.118735 | − | 0.992926i | \(-0.462116\pi\) | ||||
0.118735 | + | 0.992926i | \(0.462116\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.17157i | 0.0516257i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0502i | 0.705886i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.9958 | −0.700788 | −0.350394 | − | 0.936602i | \(-0.613952\pi\) | ||||
−0.350394 | + | 0.936602i | \(0.613952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.1927i | 1.27651i | 0.769826 | + | 0.638254i | \(0.220343\pi\) | ||||
−0.769826 | + | 0.638254i | \(0.779657\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 13.4558i | − 0.586146i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −54.9411 | −2.38874 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 52.8701i | − 2.29006i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.7038i | 1.02481i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.6569 | 0.845114 | 0.422557 | − | 0.906336i | \(-0.361133\pi\) | ||||
0.422557 | + | 0.906336i | \(0.361133\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.67459 | 0.243073 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0000 | 0.684111 | 0.342055 | − | 0.939680i | \(-0.388877\pi\) | ||||
0.342055 | + | 0.939680i | \(0.388877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.79337 | −0.0764000 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.72792i | 0.369814i | 0.982756 | + | 0.184907i | \(0.0591984\pi\) | ||||
−0.982756 | + | 0.184907i | \(0.940802\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.22625i | 0.221047i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.8155 | 1.80446 | 0.902229 | − | 0.431258i | \(-0.141930\pi\) | ||||
0.902229 | + | 0.431258i | \(0.141930\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 24.7862i | − 1.04276i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.4853i | 0.691099i | 0.938401 | + | 0.345549i | \(0.112307\pi\) | ||||
−0.938401 | + | 0.345549i | \(0.887693\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.6274 | 1.78390 | 0.891951 | − | 0.452132i | \(-0.149336\pi\) | ||||
0.891951 | + | 0.452132i | \(0.149336\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 14.0000i | − 0.583840i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 14.7277i | − 0.613121i | −0.951851 | − | 0.306561i | \(-0.900822\pi\) | ||||
0.951851 | − | 0.306561i | \(-0.0991782\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.51472 | −0.311228 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.9414 | −0.657971 | −0.328986 | − | 0.944335i | \(-0.606707\pi\) | ||||
−0.328986 | + | 0.944335i | \(0.606707\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.97056 | 0.369626 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.08947 | 0.167934 | 0.0839671 | − | 0.996469i | \(-0.473241\pi\) | ||||
0.0839671 | + | 0.996469i | \(0.473241\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 13.3137i | − 0.543983i | −0.962300 | − | 0.271992i | \(-0.912318\pi\) | ||||
0.962300 | − | 0.271992i | \(-0.0876823\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 42.0501i | − 1.71526i | −0.514267 | − | 0.857630i | \(-0.671936\pi\) | ||||
0.514267 | − | 0.857630i | \(-0.328064\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.9343 | 0.525855 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 0.896683i | − 0.0363952i | −0.999834 | − | 0.0181976i | \(-0.994207\pi\) | ||||
0.999834 | − | 0.0181976i | \(-0.00579280\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.7990i | 1.44827i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.78680 | −0.112558 | −0.0562788 | − | 0.998415i | \(-0.517924\pi\) | ||||
−0.0562788 | + | 0.998415i | \(0.517924\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4558i | 1.34688i | 0.739241 | + | 0.673441i | \(0.235184\pi\) | ||||
−0.739241 | + | 0.673441i | \(0.764816\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.2346i | 1.01426i | 0.861869 | + | 0.507132i | \(0.169294\pi\) | ||||
−0.861869 | + | 0.507132i | \(0.830706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.5563 | −0.582254 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.9259 | −0.754626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.48528 | 0.178556 | 0.0892781 | − | 0.996007i | \(-0.471544\pi\) | ||||
0.0892781 | + | 0.996007i | \(0.471544\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.6173 | 0.500702 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.4558i | 1.08444i | 0.840236 | + | 0.542220i | \(0.182416\pi\) | ||||
−0.840236 | + | 0.542220i | \(0.817584\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.1451i | 1.85922i | 0.368546 | + | 0.929610i | \(0.379856\pi\) | ||||
−0.368546 | + | 0.929610i | \(0.620144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.3211 | −1.42793 | −0.713965 | − | 0.700181i | \(-0.753103\pi\) | ||||
−0.713965 | + | 0.700181i | \(0.753103\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 19.6369i | − 0.770816i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 34.1421i | − 1.33609i | −0.744123 | − | 0.668043i | \(-0.767132\pi\) | ||||
0.744123 | − | 0.668043i | \(-0.232868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.9706 | −0.819388 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.9706i | 1.20644i | 0.797574 | + | 0.603221i | \(0.206116\pi\) | ||||
−0.797574 | + | 0.603221i | \(0.793884\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1.02800i | − 0.0399845i | −0.999800 | − | 0.0199923i | \(-0.993636\pi\) | ||||
0.999800 | − | 0.0199923i | \(-0.00636416\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.3431 | 0.400488 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.6005 | 0.949693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0416 | −1.08093 | −0.540463 | − | 0.841368i | \(-0.681751\pi\) | ||||
−0.540463 | + | 0.841368i | \(0.681751\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.0586 | 0.386582 | 0.193291 | − | 0.981142i | \(-0.438084\pi\) | ||||
0.193291 | + | 0.981142i | \(0.438084\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.0294i | 0.498558i | 0.968432 | + | 0.249279i | \(0.0801935\pi\) | ||||
−0.968432 | + | 0.249279i | \(0.919806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.55582i | 0.365109i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.7611 | −0.638549 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 32.2542i | − 1.22701i | −0.789692 | − | 0.613504i | \(-0.789760\pi\) | ||||
0.789692 | − | 0.613504i | \(-0.210240\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0000i | 0.455186i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.2132 | 1.03077 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.4558i | 1.33915i | 0.742745 | + | 0.669574i | \(0.233523\pi\) | ||||
−0.742745 | + | 0.669574i | \(0.766477\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 12.6173i | − 0.475870i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8701 | 0.858903 | 0.429452 | − | 0.903090i | \(-0.358707\pi\) | ||||
0.429452 | + | 0.903090i | \(0.358707\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −51.7373 | −1.93758 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.4853 | −0.616515 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.5027 | 0.988383 | 0.494192 | − | 0.869353i | \(-0.335464\pi\) | ||||
0.494192 | + | 0.869353i | \(0.335464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.85786i | 0.0689994i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 25.3434i | − 0.939933i | −0.882684 | − | 0.469967i | \(-0.844266\pi\) | ||||
0.882684 | − | 0.469967i | \(-0.155734\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.69005 | −0.0994951 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.58513i | − 0.0585480i | −0.999571 | − | 0.0292740i | \(-0.990680\pi\) | ||||
0.999571 | − | 0.0292740i | \(-0.00931953\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.9706i | 0.919803i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 53.4558 | 1.96641 | 0.983203 | − | 0.182518i | \(-0.0584248\pi\) | ||||
0.983203 | + | 0.182518i | \(0.0584248\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 32.3431i | − 1.18655i | −0.804998 | − | 0.593277i | \(-0.797834\pi\) | ||||
0.804998 | − | 0.593277i | \(-0.202166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.0656i | 0.478688i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.2843 | 0.740184 | 0.370092 | − | 0.928995i | \(-0.379326\pi\) | ||||
0.370092 | + | 0.928995i | \(0.379326\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.5223 | −1.22000 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.8995 | 1.37748 | 0.688740 | − | 0.725008i | \(-0.258164\pi\) | ||||
0.688740 | + | 0.725008i | \(0.258164\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.5738 | 0.528301 | 0.264151 | − | 0.964481i | \(-0.414908\pi\) | ||||
0.264151 | + | 0.964481i | \(0.414908\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 43.7990i | − 1.58149i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.5684i | 0.489288i | 0.969613 | + | 0.244644i | \(0.0786710\pi\) | ||||
−0.969613 | + | 0.244644i | \(0.921329\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.2375 | −0.655957 | −0.327978 | − | 0.944685i | \(-0.606367\pi\) | ||||
−0.327978 | + | 0.944685i | \(0.606367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 9.29319i | − 0.333821i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.1421i | 0.650009i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.6274 | −0.952804 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 20.7279i | − 0.739811i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 3.58673i | − 0.127853i | −0.997955 | − | 0.0639266i | \(-0.979638\pi\) | ||||
0.997955 | − | 0.0639266i | \(-0.0203624\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.8701 | 1.94849 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.4064 | −1.07705 | −0.538526 | − | 0.842609i | \(-0.681018\pi\) | ||||
−0.538526 | + | 0.842609i | \(0.681018\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.4264 | −0.651879 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.48888 | 0.193699 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 21.2132i | − 0.745817i | −0.927868 | − | 0.372908i | \(-0.878361\pi\) | ||||
0.927868 | − | 0.372908i | \(-0.121639\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 13.1426i | − 0.461497i | −0.973013 | − | 0.230749i | \(-0.925882\pi\) | ||||
0.973013 | − | 0.230749i | \(-0.0741175\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.22625 | −0.183068 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.79337i | − 0.0627419i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.9289i | 1.28883i | 0.764677 | + | 0.644414i | \(0.222899\pi\) | ||||
−0.764677 | + | 0.644414i | \(0.777101\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.2843 | 0.567634 | 0.283817 | − | 0.958878i | \(-0.408399\pi\) | ||||
0.283817 | + | 0.958878i | \(0.408399\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.51472i | 0.0526719i | 0.999653 | + | 0.0263360i | \(0.00838397\pi\) | ||||
−0.999653 | + | 0.0263360i | \(0.991616\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.99709i | 0.243019i | 0.992590 | + | 0.121509i | \(0.0387735\pi\) | ||||
−0.992590 | + | 0.121509i | \(0.961227\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.1421 | 1.04311 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.6842 | −0.576003 | −0.288002 | − | 0.957630i | \(-0.592991\pi\) | ||||
−0.288002 | + | 0.957630i | \(0.592991\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.6274 | 0.952670 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.7486 | −0.438565 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 72.7696i | 2.49451i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.7264i | 0.812376i | 0.913790 | + | 0.406188i | \(0.133142\pi\) | ||||
−0.913790 | + | 0.406188i | \(0.866858\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.2249 | −1.37406 | −0.687028 | − | 0.726631i | \(-0.741085\pi\) | ||||
−0.687028 | + | 0.726631i | \(0.741085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.2597i | 1.13481i | 0.823441 | + | 0.567403i | \(0.192052\pi\) | ||||
−0.823441 | + | 0.567403i | \(0.807948\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.1127i | 1.26333i | 0.775241 | + | 0.631665i | \(0.217628\pi\) | ||||
−0.775241 | + | 0.631665i | \(0.782372\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.3848 | 0.761105 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.6274i | 0.767583i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.6954i | 1.88717i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.0711 | 0.508914 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.8155 | 0.566530 | 0.283265 | − | 0.959042i | \(-0.408582\pi\) | ||||
0.283265 | + | 0.959042i | \(0.408582\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.1421 | −1.68742 | −0.843709 | − | 0.536801i | \(-0.819632\pi\) | ||||
−0.843709 | + | 0.536801i | \(0.819632\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.0417 | 1.61308 | 0.806542 | − | 0.591177i | \(-0.201337\pi\) | ||||
0.806542 | + | 0.591177i | \(0.201337\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 12.2843i | − 0.411077i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.6005i | 0.822305i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.86577 | 0.228986 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 8.62727i | − 0.287416i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.7279i | 0.888466i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.5147 | −0.515158 | −0.257579 | − | 0.966257i | \(-0.582925\pi\) | ||||
−0.257579 | + | 0.966257i | \(0.582925\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.2843i | 0.473259i | 0.971600 | + | 0.236630i | \(0.0760428\pi\) | ||||
−0.971600 | + | 0.236630i | \(0.923957\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 20.9050i | − 0.691855i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.4853 | −1.07159 | −0.535795 | − | 0.844348i | \(-0.679988\pi\) | ||||
−0.535795 | + | 0.844348i | \(0.679988\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −59.3909 | −1.95488 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.0711 | −0.429774 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.58513 | 0.0520063 | 0.0260032 | − | 0.999662i | \(-0.491722\pi\) | ||||
0.0260032 | + | 0.999662i | \(0.491722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 8.48528i | − 0.277498i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.1116i | 1.47373i | 0.676039 | + | 0.736866i | \(0.263695\pi\) | ||||
−0.676039 | + | 0.736866i | \(0.736305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.3127 | −1.37936 | −0.689678 | − | 0.724116i | \(-0.742248\pi\) | ||||
−0.689678 | + | 0.724116i | \(0.742248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 104.634i | − 3.40735i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.17157i | 0.103062i | 0.998671 | + | 0.0515311i | \(0.0164101\pi\) | ||||
−0.998671 | + | 0.0515311i | \(0.983590\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.2426 | 0.397413 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 5.12994i | − 0.166175i | −0.996542 | − | 0.0830876i | \(-0.973522\pi\) | ||||
0.996542 | − | 0.0830876i | \(-0.0264781\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 9.81845i | − 0.317718i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.34315 | −0.107843 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.06147 | 0.0985521 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.4853 | 1.04466 | 0.522328 | − | 0.852745i | \(-0.325064\pi\) | ||||
0.522328 | + | 0.852745i | \(0.325064\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.79337 | −0.0575519 | −0.0287759 | − | 0.999586i | \(-0.509161\pi\) | ||||
−0.0287759 | + | 0.999586i | \(0.509161\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.4853i | 0.527411i | 0.964603 | + | 0.263705i | \(0.0849447\pi\) | ||||
−0.964603 | + | 0.263705i | \(0.915055\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.9301i | 0.924610i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.3994 | 0.873904 | 0.436952 | − | 0.899485i | \(-0.356058\pi\) | ||||
0.436952 | + | 0.899485i | \(0.356058\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 20.4567i | − 0.651804i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.3431i | 0.328893i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.1421 | −1.21162 | −0.605812 | − | 0.795608i | \(-0.707152\pi\) | ||||
−0.605812 | + | 0.795608i | \(0.707152\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.65685i | 0.179334i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.0446i | 1.29990i | 0.759978 | + | 0.649949i | \(0.225210\pi\) | ||||
−0.759978 | + | 0.649949i | \(0.774790\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1764.2.f.b.881.8 | yes | 8 | |
3.2 | odd | 2 | inner | 1764.2.f.b.881.1 | ✓ | 8 | |
4.3 | odd | 2 | 7056.2.k.e.881.7 | 8 | |||
7.2 | even | 3 | 1764.2.t.c.521.1 | 16 | |||
7.3 | odd | 6 | 1764.2.t.c.1097.8 | 16 | |||
7.4 | even | 3 | 1764.2.t.c.1097.2 | 16 | |||
7.5 | odd | 6 | 1764.2.t.c.521.7 | 16 | |||
7.6 | odd | 2 | inner | 1764.2.f.b.881.2 | yes | 8 | |
12.11 | even | 2 | 7056.2.k.e.881.2 | 8 | |||
21.2 | odd | 6 | 1764.2.t.c.521.8 | 16 | |||
21.5 | even | 6 | 1764.2.t.c.521.2 | 16 | |||
21.11 | odd | 6 | 1764.2.t.c.1097.7 | 16 | |||
21.17 | even | 6 | 1764.2.t.c.1097.1 | 16 | |||
21.20 | even | 2 | inner | 1764.2.f.b.881.7 | yes | 8 | |
28.27 | even | 2 | 7056.2.k.e.881.1 | 8 | |||
84.83 | odd | 2 | 7056.2.k.e.881.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.f.b.881.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
1764.2.f.b.881.2 | yes | 8 | 7.6 | odd | 2 | inner | |
1764.2.f.b.881.7 | yes | 8 | 21.20 | even | 2 | inner | |
1764.2.f.b.881.8 | yes | 8 | 1.1 | even | 1 | trivial | |
1764.2.t.c.521.1 | 16 | 7.2 | even | 3 | |||
1764.2.t.c.521.2 | 16 | 21.5 | even | 6 | |||
1764.2.t.c.521.7 | 16 | 7.5 | odd | 6 | |||
1764.2.t.c.521.8 | 16 | 21.2 | odd | 6 | |||
1764.2.t.c.1097.1 | 16 | 21.17 | even | 6 | |||
1764.2.t.c.1097.2 | 16 | 7.4 | even | 3 | |||
1764.2.t.c.1097.7 | 16 | 21.11 | odd | 6 | |||
1764.2.t.c.1097.8 | 16 | 7.3 | odd | 6 | |||
7056.2.k.e.881.1 | 8 | 28.27 | even | 2 | |||
7056.2.k.e.881.2 | 8 | 12.11 | even | 2 | |||
7056.2.k.e.881.7 | 8 | 4.3 | odd | 2 | |||
7056.2.k.e.881.8 | 8 | 84.83 | odd | 2 |