Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.a (trivial) |
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: | yes |
Analytic conductor: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −1.61532 | −0.932603 | −0.466302 | − | 0.884626i | \(-0.654414\pi\) | ||||
−0.466302 | + | 0.884626i | \(0.654414\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.18505 | 0.529972 | 0.264986 | − | 0.964252i | \(-0.414633\pi\) | ||||
0.264986 | + | 0.964252i | \(0.414633\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.44544 | 1.30225 | 0.651127 | − | 0.758968i | \(-0.274296\pi\) | ||||
0.651127 | + | 0.758968i | \(0.274296\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.390754 | −0.130251 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.43776 | −1.63955 | −0.819773 | − | 0.572688i | \(-0.805900\pi\) | ||||
−0.819773 | + | 0.572688i | \(0.805900\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.64341 | 1.28785 | 0.643926 | − | 0.765088i | \(-0.277305\pi\) | ||||
0.643926 | + | 0.765088i | \(0.277305\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.91424 | −0.494253 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.71018 | 0.414780 | 0.207390 | − | 0.978258i | \(-0.433503\pi\) | ||||
0.207390 | + | 0.978258i | \(0.433503\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.56548 | −1.21449 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.61889 | −0.546076 | −0.273038 | − | 0.962003i | \(-0.588029\pi\) | ||||
−0.273038 | + | 0.962003i | \(0.588029\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.59565 | −0.719130 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.47714 | 1.05408 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.806736 | −0.149807 | −0.0749036 | − | 0.997191i | \(-0.523865\pi\) | ||||
−0.0749036 | + | 0.997191i | \(0.523865\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.06235 | 0.190803 | 0.0954014 | − | 0.995439i | \(-0.469587\pi\) | ||||
0.0954014 | + | 0.995439i | \(0.469587\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.78370 | 1.52905 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.08303 | 0.690159 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.55276 | −0.912868 | −0.456434 | − | 0.889757i | \(-0.650874\pi\) | ||||
−0.456434 | + | 0.889757i | \(0.650874\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.50058 | −1.20105 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.63256 | −1.34818 | −0.674090 | − | 0.738649i | \(-0.735464\pi\) | ||||
−0.674090 | + | 0.738649i | \(0.735464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.18814 | 0.333688 | 0.166844 | − | 0.985983i | \(-0.446642\pi\) | ||||
0.166844 | + | 0.985983i | \(0.446642\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.463065 | −0.0690296 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.20135 | 1.34216 | 0.671078 | − | 0.741387i | \(-0.265832\pi\) | ||||
0.671078 | + | 0.741387i | \(0.265832\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.87108 | 0.695868 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.76248 | −0.386825 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.3427 | −1.69539 | −0.847697 | − | 0.530480i | \(-0.822012\pi\) | ||||
−0.847697 | + | 0.530480i | \(0.822012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.44403 | −0.868914 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.61532 | 0.213954 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.65530 | 0.736257 | 0.368128 | − | 0.929775i | \(-0.379999\pi\) | ||||
0.368128 | + | 0.929775i | \(0.379999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.83852 | −0.747546 | −0.373773 | − | 0.927520i | \(-0.621936\pi\) | ||||
−0.373773 | + | 0.927520i | \(0.621936\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.34632 | −0.169621 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.50269 | 0.682525 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.38626 | 0.535867 | 0.267934 | − | 0.963437i | \(-0.413659\pi\) | ||||
0.267934 | + | 0.963437i | \(0.413659\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.23034 | 0.509273 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.01663 | −0.358008 | −0.179004 | − | 0.983848i | \(-0.557287\pi\) | ||||
−0.179004 | + | 0.983848i | \(0.557287\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.48547 | −0.524985 | −0.262492 | − | 0.964934i | \(-0.584544\pi\) | ||||
−0.262492 | + | 0.964934i | \(0.584544\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.80811 | 0.670663 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.7355 | −2.13511 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.67505 | −0.852783 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.91424 | −0.758936 | −0.379468 | − | 0.925205i | \(-0.623893\pi\) | ||||
−0.379468 | + | 0.925205i | \(0.623893\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.02666 | 0.219822 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.30313 | 0.139711 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.30790 | −0.562636 | −0.281318 | − | 0.959615i | \(-0.590772\pi\) | ||||
−0.281318 | + | 0.959615i | \(0.590772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.9986 | 1.67711 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.71602 | −0.177943 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.18505 | −0.121584 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.2074 | −1.74715 | −0.873575 | − | 0.486689i | \(-0.838204\pi\) | ||||
−0.873575 | + | 0.486689i | \(0.838204\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.12483 | 0.213553 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.60632 | 0.657353 | 0.328677 | − | 0.944443i | \(-0.393397\pi\) | ||||
0.328677 | + | 0.944443i | \(0.393397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.1905 | −1.59530 | −0.797650 | − | 0.603121i | \(-0.793924\pi\) | ||||
−0.797650 | + | 0.603121i | \(0.793924\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.59539 | −0.643644 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.6560 | 1.22350 | 0.611752 | − | 0.791050i | \(-0.290465\pi\) | ||||
0.611752 | + | 0.791050i | \(0.290465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.9436 | 1.33555 | 0.667776 | − | 0.744362i | \(-0.267246\pi\) | ||||
0.667776 | + | 0.744362i | \(0.267246\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.96946 | 0.851344 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.02361 | −0.660726 | −0.330363 | − | 0.943854i | \(-0.607171\pi\) | ||||
−0.330363 | + | 0.943854i | \(0.607171\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.10352 | −0.289405 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.81443 | −0.167745 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.89233 | 0.540149 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.5692 | 1.68811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.9443 | 1.25732 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.1863 | −0.911091 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.7459 | −1.30848 | −0.654242 | − | 0.756285i | \(-0.727012\pi\) | ||||
−0.654242 | + | 0.756285i | \(0.727012\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.53454 | −0.311199 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.39829 | 0.384280 | 0.192140 | − | 0.981368i | \(-0.438457\pi\) | ||||
0.192140 | + | 0.981368i | \(0.438457\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.44544 | −0.298758 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.49070 | 0.558631 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.9832 | 1.28010 | 0.640052 | − | 0.768332i | \(-0.278913\pi\) | ||||
0.640052 | + | 0.768332i | \(0.278913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.5566 | −0.895395 | −0.447698 | − | 0.894185i | \(-0.647756\pi\) | ||||
−0.447698 | + | 0.894185i | \(0.647756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.8631 | −1.25170 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.2498 | −2.11149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.956025 | −0.0793936 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.86833 | −0.648969 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.7617 | −1.53702 | −0.768508 | − | 0.639840i | \(-0.779001\pi\) | ||||
−0.768508 | + | 0.639840i | \(0.779001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4683 | 1.66569 | 0.832844 | − | 0.553508i | \(-0.186711\pi\) | ||||
0.832844 | + | 0.553508i | \(0.186711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.668261 | −0.0540257 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.25894 | 0.101120 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.3142 | 1.54144 | 0.770721 | − | 0.637173i | \(-0.219896\pi\) | ||||
0.770721 | + | 0.637173i | \(0.219896\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.9373 | 1.58113 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.02324 | −0.711131 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00618 | 0.627093 | 0.313546 | − | 0.949573i | \(-0.398483\pi\) | ||||
0.313546 | + | 0.949573i | \(0.398483\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.4092 | 0.810351 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.4783 | 1.12037 | 0.560183 | − | 0.828369i | \(-0.310731\pi\) | ||||
0.560183 | + | 0.828369i | \(0.310731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.56130 | 0.658562 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.390754 | 0.0298817 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.0694 | −1.67791 | −0.838954 | − | 0.544203i | \(-0.816832\pi\) | ||||
−0.838954 | + | 0.544203i | \(0.816832\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.3886 | −0.936490 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.13509 | −0.686635 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.7105 | −1.54797 | −0.773986 | − | 0.633202i | \(-0.781740\pi\) | ||||
−0.773986 | + | 0.633202i | \(0.781740\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.3283 | 1.06502 | 0.532509 | − | 0.846425i | \(-0.321249\pi\) | ||||
0.532509 | + | 0.846425i | \(0.321249\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.43105 | 0.697164 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.58032 | −0.483795 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.29955 | −0.680051 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.8712 | 1.37268 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.05380 | 0.148608 | 0.0743040 | − | 0.997236i | \(-0.476326\pi\) | ||||
0.0743040 | + | 0.997236i | \(0.476326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.81409 | −0.274544 | −0.137272 | − | 0.990533i | \(-0.543833\pi\) | ||||
−0.137272 | + | 0.990533i | \(0.543833\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.88859 | −0.636525 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.30212 | 0.520255 | 0.260127 | − | 0.965574i | \(-0.416235\pi\) | ||||
0.260127 | + | 0.965574i | \(0.416235\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.0024 | 1.63060 | 0.815299 | − | 0.579040i | \(-0.196573\pi\) | ||||
0.815299 | + | 0.579040i | \(0.196573\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.08520 | −0.499752 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.77956 | −0.195087 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.2300 | −0.714497 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.02334 | 0.0711272 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.43776 | 0.376138 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3860 | 0.921531 | 0.460766 | − | 0.887522i | \(-0.347575\pi\) | ||||
0.460766 | + | 0.887522i | \(0.347575\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.87281 | 0.333879 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.59306 | 0.176845 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.66025 | 0.248474 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.24545 | 0.489602 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.94108 | 0.534175 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.23905 | −0.484762 | −0.242381 | − | 0.970181i | \(-0.577928\pi\) | ||||
−0.242381 | + | 0.970181i | \(0.577928\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.40502 | 0.0936677 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.9688 | 0.927144 | 0.463572 | − | 0.886059i | \(-0.346568\pi\) | ||||
0.463572 | + | 0.886059i | \(0.346568\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.7269 | −1.76616 | −0.883081 | − | 0.469220i | \(-0.844535\pi\) | ||||
−0.883081 | + | 0.469220i | \(0.844535\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 30.2637 | 1.99121 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.8449 | −1.62764 | −0.813822 | − | 0.581114i | \(-0.802617\pi\) | ||||
−0.813822 | + | 0.581114i | \(0.802617\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.9041 | 0.711305 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.61532 | −0.104926 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.2227 | −1.63152 | −0.815759 | − | 0.578392i | \(-0.803681\pi\) | ||||
−0.815759 | + | 0.578392i | \(0.803681\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.81067 | −0.567545 | −0.283773 | − | 0.958892i | \(-0.591586\pi\) | ||||
−0.283773 | + | 0.958892i | \(0.591586\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.03379 | −0.258768 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.77249 | 0.368791 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.64341 | −0.295453 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.1687 | 0.707786 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.4408 | −1.66893 | −0.834466 | − | 0.551060i | \(-0.814224\pi\) | ||||
−0.834466 | + | 0.551060i | \(0.814224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.2409 | 0.895318 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.27369 | −0.205006 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.4631 | −1.27645 | −0.638227 | − | 0.769848i | \(-0.720332\pi\) | ||||
−0.638227 | + | 0.769848i | \(0.720332\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.1317 | −1.18879 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.315236 | 0.0195126 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.8588 | −1.22455 | −0.612274 | − | 0.790645i | \(-0.709745\pi\) | ||||
−0.612274 | + | 0.790645i | \(0.709745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.6267 | −0.898512 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.57394 | 0.524716 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.9660 | 1.94900 | 0.974502 | − | 0.224379i | \(-0.0720354\pi\) | ||||
0.974502 | + | 0.224379i | \(0.0720354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.80839 | 0.292089 | 0.146044 | − | 0.989278i | \(-0.453346\pi\) | ||||
0.146044 | + | 0.989278i | \(0.453346\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.8428 | −1.56408 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.5523 | 1.17905 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.28103 | 0.0769696 | 0.0384848 | − | 0.999259i | \(-0.487747\pi\) | ||||
0.0384848 | + | 0.999259i | \(0.487747\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.415116 | −0.0248524 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.4228 | −1.51660 | −0.758298 | − | 0.651908i | \(-0.773969\pi\) | ||||
−0.758298 | + | 0.651908i | \(0.773969\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.2196 | −0.904711 | −0.452356 | − | 0.891838i | \(-0.649416\pi\) | ||||
−0.452356 | + | 0.891838i | \(0.649416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.91424 | 0.113390 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.7430 | −1.75567 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0753 | −0.827958 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 27.7954 | 1.62940 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.04597 | 0.177948 | 0.0889738 | − | 0.996034i | \(-0.471641\pi\) | ||||
0.0889738 | + | 0.996034i | \(0.471641\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.70183 | 0.390196 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −29.7834 | −1.72821 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.1606 | −0.703265 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.53911 | 0.434547 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.6713 | −0.613050 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.91896 | −0.396178 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.53950 | −0.144937 | −0.0724685 | − | 0.997371i | \(-0.523088\pi\) | ||||
−0.0724685 | + | 0.997371i | \(0.523088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.1528 | 1.48778 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.6382 | 0.603236 | 0.301618 | − | 0.953429i | \(-0.402473\pi\) | ||||
0.301618 | + | 0.953429i | \(0.402473\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.8186 | −0.894121 | −0.447061 | − | 0.894504i | \(-0.647529\pi\) | ||||
−0.447061 | + | 0.894504i | \(0.647529\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.59546 | −0.0898942 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.0648254 | −0.00364096 | −0.00182048 | − | 0.999998i | \(-0.500579\pi\) | ||||
−0.00182048 | + | 0.999998i | \(0.500579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.38684 | 0.245616 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.4435 | −1.14104 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.71018 | −0.0951570 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.6961 | −0.926132 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.5233 | −1.24554 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.7027 | 1.74783 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.9946 | 1.75858 | 0.879292 | − | 0.476282i | \(-0.158016\pi\) | ||||
0.879292 | + | 0.476282i | \(0.158016\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.16977 | 0.118902 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.19796 | 0.283995 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.7643 | 1.51242 | 0.756208 | − | 0.654331i | \(-0.227050\pi\) | ||||
0.756208 | + | 0.654331i | \(0.227050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.3454 | 0.616195 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.77678 | −0.312830 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.33508 | −0.396057 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.01317 | 0.269900 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.5438 | −1.10285 | −0.551425 | − | 0.834225i | \(-0.685916\pi\) | ||||
−0.551425 | + | 0.834225i | \(0.685916\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.7986 | 0.792149 | 0.396075 | − | 0.918218i | \(-0.370372\pi\) | ||||
0.396075 | + | 0.918218i | \(0.370372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.4326 | 1.35749 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.9461 | 0.582600 | 0.291300 | − | 0.956632i | \(-0.405912\pi\) | ||||
0.291300 | + | 0.956632i | \(0.405912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.57486 | −0.189734 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.51797 | −0.503745 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3680 | −1.18054 | −0.590269 | − | 0.807207i | \(-0.700978\pi\) | ||||
−0.590269 | + | 0.807207i | \(0.700978\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −29.9952 | −1.57434 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.31552 | −0.278227 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.32448 | −0.486734 | −0.243367 | − | 0.969934i | \(-0.578252\pi\) | ||||
−0.243367 | + | 0.969934i | \(0.578252\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.37321 | 0.175602 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −42.5259 | −2.20784 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.4335 | −0.695559 | −0.347779 | − | 0.937576i | \(-0.613064\pi\) | ||||
−0.347779 | + | 0.937576i | \(0.613064\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.4541 | 0.849686 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.74601 | −0.192929 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.8773 | 1.58606 | 0.793029 | − | 0.609184i | \(-0.208503\pi\) | ||||
0.793029 | + | 0.609184i | \(0.208503\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.8192 | 1.22030 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.44439 | −0.176000 | −0.0880001 | − | 0.996120i | \(-0.528048\pi\) | ||||
−0.0880001 | + | 0.996120i | \(0.528048\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.2026 | −1.13155 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.855025 | −0.0434634 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.9939 | −0.658815 | −0.329408 | − | 0.944188i | \(-0.606849\pi\) | ||||
−0.329408 | + | 0.944188i | \(0.606849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.47878 | −0.226501 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.10462 | −0.358381 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.18505 | 0.0596265 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.0856 | −1.66052 | −0.830260 | − | 0.557377i | \(-0.811808\pi\) | ||||
−0.830260 | + | 0.557377i | \(0.811808\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.56548 | 0.278622 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5689 | −0.677598 | −0.338799 | − | 0.940859i | \(-0.610021\pi\) | ||||
−0.338799 | + | 0.940859i | \(0.610021\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.93291 | 0.245726 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.09534 | −0.451951 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.1946 | 1.49669 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.6595 | −0.922655 | −0.461327 | − | 0.887230i | \(-0.652627\pi\) | ||||
−0.461327 | + | 0.887230i | \(0.652627\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.2026 | −1.19383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.4850 | 0.958794 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.19374 | −0.402215 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.0522 | 0.835049 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.5635 | −1.68854 | −0.844269 | − | 0.535920i | \(-0.819965\pi\) | ||||
−0.844269 | + | 0.535920i | \(0.819965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.7325 | 1.69276 | 0.846379 | − | 0.532581i | \(-0.178778\pi\) | ||||
0.846379 | + | 0.532581i | \(0.178778\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.59547 | −0.174818 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.14921 | −0.298280 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.1163 | −0.973495 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 40.7864 | 1.96918 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.49379 | −0.360963 | −0.180482 | − | 0.983578i | \(-0.557766\pi\) | ||||
−0.180482 | + | 0.983578i | \(0.557766\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.2912 | 0.638733 | 0.319366 | − | 0.947631i | \(-0.396530\pi\) | ||||
0.319366 | + | 0.947631i | \(0.396530\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.54428 | 0.0740427 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.61889 | 0.125279 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.4598 | 0.737855 | 0.368928 | − | 0.929458i | \(-0.379725\pi\) | ||||
0.368928 | + | 0.929458i | \(0.379725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.90339 | −0.0906378 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.2671 | −1.24799 | −0.623995 | − | 0.781428i | \(-0.714491\pi\) | ||||
−0.623995 | + | 0.781428i | \(0.714491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.29014 | −0.298181 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.3060 | 1.43343 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.7091 | −1.21329 | −0.606643 | − | 0.794975i | \(-0.707484\pi\) | ||||
−0.606643 | + | 0.794975i | \(0.707484\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 46.9418 | 2.21040 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.0628 | −1.55343 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.9592 | 0.888822 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.3717 | 1.04650 | 0.523251 | − | 0.852179i | \(-0.324719\pi\) | ||||
0.523251 | + | 0.852179i | \(0.324719\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.36690 | 0.437209 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.0230 | 0.932566 | 0.466283 | − | 0.884636i | \(-0.345593\pi\) | ||||
0.466283 | + | 0.884636i | \(0.345593\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.76680 | −0.175058 | −0.0875291 | − | 0.996162i | \(-0.527897\pi\) | ||||
−0.0875291 | + | 0.996162i | \(0.527897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.03358 | −0.0943050 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.4190 | −0.944880 | −0.472440 | − | 0.881363i | \(-0.656627\pi\) | ||||
−0.472440 | + | 0.881363i | \(0.656627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.1126 | 0.697836 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.1986 | −1.43755 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.8986 | −0.547097 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.59565 | 0.164980 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.82295 | 0.220828 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2513 | −0.468393 | −0.234197 | − | 0.972189i | \(-0.575246\pi\) | ||||
−0.234197 | + | 0.972189i | \(0.575246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.7838 | −1.17564 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.5754 | 0.663203 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.3917 | −0.925941 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.0510 | −1.49769 | −0.748843 | − | 0.662747i | \(-0.769390\pi\) | ||||
−0.748843 | + | 0.662747i | \(0.769390\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.9325 | −0.584829 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.6519 | −0.841750 | −0.420875 | − | 0.907119i | \(-0.638277\pi\) | ||||
−0.420875 | + | 0.907119i | \(0.638277\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.37966 | −0.0621370 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.51803 | 0.113177 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.3936 | −0.466217 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.5250 | 0.605462 | 0.302731 | − | 0.953076i | \(-0.402102\pi\) | ||||
0.302731 | + | 0.953076i | \(0.402102\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.3871 | −1.04486 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.73467 | 0.389459 | 0.194730 | − | 0.980857i | \(-0.437617\pi\) | ||||
0.194730 | + | 0.980857i | \(0.437617\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.82884 | 0.348379 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.8292 | −0.614177 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.560197 | −0.0248303 | −0.0124151 | − | 0.999923i | \(-0.503952\pi\) | ||||
−0.0124151 | + | 0.999923i | \(0.503952\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.4544 | −0.683664 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.47714 | −0.241822 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.1866 | −0.845464 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −50.0348 | −2.20053 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 35.6491 | 1.56482 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.4651 | −0.896591 | −0.448295 | − | 0.893886i | \(-0.647969\pi\) | ||||
−0.448295 | + | 0.893886i | \(0.647969\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.3411 | −1.28300 | −0.641499 | − | 0.767124i | \(-0.721687\pi\) | ||||
−0.641499 | + | 0.767124i | \(0.721687\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.0115 | 0.873374 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.81680 | 0.0791412 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1414 | −0.701801 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.20983 | −0.0958985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.0846 | −1.73626 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.9981 | 0.648423 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.4539 | 1.44364 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.4877 | −1.14091 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.77071 | −0.377082 | −0.188541 | − | 0.982065i | \(-0.560376\pi\) | ||||
−0.188541 | + | 0.982065i | \(0.560376\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.1448 | −0.993238 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.5239 | 0.707805 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.9124 | −1.02242 | −0.511210 | − | 0.859456i | \(-0.670802\pi\) | ||||
−0.511210 | + | 0.859456i | \(0.670802\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.28143 | 0.0973689 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.806736 | 0.0343681 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.44544 | 0.146515 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.6293 | 0.451188 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.45034 | 0.400424 | 0.200212 | − | 0.979753i | \(-0.435837\pi\) | ||||
0.200212 | + | 0.979753i | \(0.435837\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.1604 | 0.429741 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.0217 | 0.634217 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.80189 | 0.244521 | 0.122260 | − | 0.992498i | \(-0.460986\pi\) | ||||
0.122260 | + | 0.992498i | \(0.460986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.32336 | −0.350166 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −26.4439 | −1.11054 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.7152 | 0.700738 | 0.350369 | − | 0.936612i | \(-0.386056\pi\) | ||||
0.350369 | + | 0.936612i | \(0.386056\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.51700 | −0.147182 | −0.0735908 | − | 0.997289i | \(-0.523446\pi\) | ||||
−0.0735908 | + | 0.997289i | \(0.523446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.31754 | −0.138592 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.41661 | 0.392700 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.6755 | −1.31867 | −0.659335 | − | 0.751850i | \(-0.729162\pi\) | ||||
−0.659335 | + | 0.751850i | \(0.729162\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.16095 | 0.256041 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.8226 | −0.988328 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 67.1164 | 2.77968 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.15020 | −0.0888999 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.4349 | −1.13236 | −0.566181 | − | 0.824281i | \(-0.691579\pi\) | ||||
−0.566181 | + | 0.824281i | \(0.691579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.06235 | −0.0437732 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.7952 | −0.485191 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −46.6882 | −1.91725 | −0.958627 | − | 0.284664i | \(-0.908118\pi\) | ||||
−0.958627 | + | 0.284664i | \(0.908118\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.98272 | 0.286264 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −37.1562 | −1.52070 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.5787 | 1.20855 | 0.604277 | − | 0.796774i | \(-0.293462\pi\) | ||||
0.604277 | + | 0.796774i | \(0.293462\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.7745 | −1.41848 | −0.709240 | − | 0.704967i | \(-0.750962\pi\) | ||||
−0.709240 | + | 0.704967i | \(0.750962\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.71395 | −0.0697975 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.0055 | 0.894652 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.9130 | −1.33590 | −0.667949 | − | 0.744207i | \(-0.732828\pi\) | ||||
−0.667949 | + | 0.744207i | \(0.732828\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.48987 | 0.181939 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.7257 | 1.72850 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5859 | 0.791068 | 0.395534 | − | 0.918451i | \(-0.370560\pi\) | ||||
0.395534 | + | 0.918451i | \(0.370560\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.5248 | 0.666342 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.3887 | 0.981854 | 0.490927 | − | 0.871201i | \(-0.336658\pi\) | ||||
0.490927 | + | 0.871201i | \(0.336658\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.8558 | −1.80291 | −0.901453 | − | 0.432877i | \(-0.857499\pi\) | ||||
−0.901453 | + | 0.432877i | \(0.857499\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.3440 | −0.575606 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.2881 | −0.732696 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.90693 | 0.236277 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.78370 | −0.350787 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.49622 | −0.378639 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.0615 | 1.55501 | 0.777507 | − | 0.628874i | \(-0.216484\pi\) | ||||
0.777507 | + | 0.628874i | \(0.216484\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.6226 | −0.859423 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.4746 | −0.693460 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.6184 | 0.896175 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.17876 | 0.0466310 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.4718 | −0.966579 | −0.483290 | − | 0.875461i | \(-0.660558\pi\) | ||||
−0.483290 | + | 0.875461i | \(0.660558\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.37313 | 0.369640 | 0.184820 | − | 0.982772i | \(-0.440830\pi\) | ||||
0.184820 | + | 0.982772i | \(0.440830\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.18861 | −0.164927 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.81761 | 0.385970 | 0.192985 | − | 0.981202i | \(-0.438183\pi\) | ||||
0.192985 | + | 0.981202i | \(0.438183\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.7521 | −1.20713 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.91246 | −0.231728 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.0034 | −0.508863 | −0.254431 | − | 0.967091i | \(-0.581888\pi\) | ||||
−0.254431 | + | 0.967091i | \(0.581888\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.21220 | 0.203658 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.75272 | 0.0683800 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.7289 | −1.39180 | −0.695901 | − | 0.718138i | \(-0.744995\pi\) | ||||
−0.695901 | + | 0.718138i | \(0.744995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.2807 | −0.944410 | −0.472205 | − | 0.881489i | \(-0.656542\pi\) | ||||
−0.472205 | + | 0.881489i | \(0.656542\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.8274 | −0.498173 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.08303 | −0.158333 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.11275 | 0.0818062 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.6933 | 0.452091 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.7485 | 1.22564 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.92837 | −0.0743333 | −0.0371666 | − | 0.999309i | \(-0.511833\pi\) | ||||
−0.0371666 | + | 0.999309i | \(0.511833\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.6939 | −0.758017 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.3731 | 0.590836 | 0.295418 | − | 0.955368i | \(-0.404541\pi\) | ||||
0.295418 | + | 0.955368i | \(0.404541\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −59.2872 | −2.27524 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.5641 | −0.864657 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.0393 | 1.79991 | 0.899955 | − | 0.435984i | \(-0.143599\pi\) | ||||
0.899955 | + | 0.435984i | \(0.143599\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.7559 | 0.678419 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 43.1724 | 1.64713 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −57.3121 | −2.18342 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.4209 | −0.776848 | −0.388424 | − | 0.921481i | \(-0.626980\pi\) | ||||
−0.388424 | + | 0.921481i | \(0.626980\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.32097 | 0.278101 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.5101 | −0.474534 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.7632 | −0.559198 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 40.1324 | 1.51795 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.2673 | 0.916563 | 0.458281 | − | 0.888807i | \(-0.348465\pi\) | ||||
0.458281 | + | 0.888807i | \(0.348465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.55276 | 0.209426 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.6136 | −0.663365 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.7617 | 0.856041 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.40771 | −0.240647 | −0.120323 | − | 0.992735i | \(-0.538393\pi\) | ||||
−0.120323 | + | 0.992735i | \(0.538393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.390754 | −0.0146544 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.78217 | −0.104193 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.9223 | −1.11903 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40.7426 | 1.52156 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.9142 | 1.30208 | 0.651040 | − | 0.759044i | \(-0.274333\pi\) | ||||
0.651040 | + | 0.759044i | \(0.274333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −55.7835 | −2.07749 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.2320 | 0.529294 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.90074 | 0.107731 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.3193 | 1.08739 | 0.543697 | − | 0.839282i | \(-0.317024\pi\) | ||||
0.543697 | + | 0.839282i | \(0.317024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.5410 | 1.09411 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.74211 | 0.138407 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.6082 | 1.38909 | 0.694546 | − | 0.719449i | \(-0.255605\pi\) | ||||
0.694546 | + | 0.719449i | \(0.255605\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.32439 | −0.343935 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.8514 | −0.878579 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.9972 | 1.21382 | 0.606912 | − | 0.794769i | \(-0.292408\pi\) | ||||
0.606912 | + | 0.794769i | \(0.292408\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.50058 | 0.275541 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.6773 | 1.52899 | 0.764496 | − | 0.644628i | \(-0.222988\pi\) | ||||
0.764496 | + | 0.644628i | \(0.222988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.2336 | −0.814576 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.70177 | 0.0988525 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.6056 | 1.59331 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.711656 | 0.0259687 | 0.0129843 | − | 0.999916i | \(-0.495867\pi\) | ||||
0.0129843 | + | 0.999916i | \(0.495867\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 42.7103 | 1.55645 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.2560 | 0.882768 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.3888 | 0.777390 | 0.388695 | − | 0.921367i | \(-0.372926\pi\) | ||||
0.388695 | + | 0.921367i | \(0.372926\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.0035 | −0.834976 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.2328 | 0.805938 | 0.402969 | − | 0.915214i | \(-0.367978\pi\) | ||||
0.402969 | + | 0.915214i | \(0.367978\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.0418 | 1.73923 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.791924 | −0.0286321 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.2599 | 0.948190 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.49512 | 0.270281 | 0.135140 | − | 0.990826i | \(-0.456851\pi\) | ||||
0.135140 | + | 0.990826i | \(0.456851\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.0544 | 1.19042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.8860 | 0.895087 | 0.447543 | − | 0.894262i | \(-0.352299\pi\) | ||||
0.447543 | + | 0.894262i | \(0.352299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.81982 | −0.137212 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.9038 | 1.10867 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.63256 | 0.309294 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.4037 | 0.586970 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.41861 | −0.157908 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.8884 | 0.816921 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.5288 | 1.37340 | 0.686702 | − | 0.726939i | \(-0.259058\pi\) | ||||
0.686702 | + | 0.726939i | \(0.259058\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.0783 | 1.14202 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.1995 | −0.860434 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.1107 | −0.962728 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.6268 | 0.837955 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.5646 | 0.657593 | 0.328796 | − | 0.944401i | \(-0.393357\pi\) | ||||
0.328796 | + | 0.944401i | \(0.393357\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.7360 | 0.556699 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.07409 | 0.0732842 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.3909 | 0.860737 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.6930 | −0.376879 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −51.6353 | −1.81765 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 54.8809 | 1.92951 | 0.964755 | − | 0.263151i | \(-0.0847619\pi\) | ||||
0.964755 | + | 0.263151i | \(0.0847619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.8437 | 1.11818 | 0.559092 | − | 0.829106i | \(-0.311150\pi\) | ||||
0.559092 | + | 0.829106i | \(0.311150\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.76707 | −0.272403 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.48775 | 0.332342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.18814 | −0.0765533 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.25153 | −0.218446 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.357647 | −0.0124820 | −0.00624099 | − | 0.999981i | \(-0.501987\pi\) | ||||
−0.00624099 | + | 0.999981i | \(0.501987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.87566 | −0.274528 | −0.137264 | − | 0.990534i | \(-0.543831\pi\) | ||||
−0.137264 | + | 0.990534i | \(0.543831\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −31.5831 | −1.09958 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.44374 | −0.0849771 | −0.0424885 | − | 0.999097i | \(-0.513529\pi\) | ||||
−0.0424885 | + | 0.999097i | \(0.513529\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.57494 | −0.193626 | −0.0968128 | − | 0.995303i | \(-0.530865\pi\) | ||||
−0.0968128 | + | 0.995303i | \(0.530865\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.06927 | −0.0717821 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.33042 | 0.288632 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.1576 | 0.593763 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.81862 | 0.201121 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.8433 | −0.719590 | −0.359795 | − | 0.933031i | \(-0.617153\pi\) | ||||
−0.359795 | + | 0.933031i | \(0.617153\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3492 | −0.977558 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 41.0658 | 1.41438 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.1456 | 0.349019 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 63.9792 | 2.19835 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.5845 | 0.843737 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.5421 | 0.498496 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.4904 | 1.35212 | 0.676062 | − | 0.736844i | \(-0.263685\pi\) | ||||
0.676062 | + | 0.736844i | \(0.263685\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.463065 | 0.0158365 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.5217 | −0.803484 | −0.401742 | − | 0.915753i | \(-0.631595\pi\) | ||||
−0.401742 | + | 0.915753i | \(0.631595\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.2488 | −0.725001 | −0.362500 | − | 0.931984i | \(-0.618077\pi\) | ||||
−0.362500 | + | 0.931984i | \(0.618077\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 48.0443 | 1.63735 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.4284 | 0.865591 | 0.432796 | − | 0.901492i | \(-0.357527\pi\) | ||||
0.432796 | + | 0.901492i | \(0.357527\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.1535 | −0.889244 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.7360 | 0.772156 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.43776 | −0.184463 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.3672 | 0.690118 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.72388 | 0.227569 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35.0963 | −1.18647 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.1523 | 1.15324 | 0.576621 | − | 0.817012i | \(-0.304371\pi\) | ||||
0.576621 | + | 0.817012i | \(0.304371\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.92021 | −0.165954 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.9438 | −1.58158 | −0.790788 | − | 0.612090i | \(-0.790329\pi\) | ||||
−0.790788 | + | 0.612090i | \(0.790329\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.84520 | −0.129401 | −0.0647007 | − | 0.997905i | \(-0.520609\pi\) | ||||
−0.0647007 | + | 0.997905i | \(0.520609\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.8256 | −0.363898 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.4085 | −1.15532 | −0.577661 | − | 0.816276i | \(-0.696035\pi\) | ||||
−0.577661 | + | 0.816276i | \(0.696035\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.8060 | −1.70398 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 41.7351 | 1.39818 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.20135 | −0.307912 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.5430 | −0.820382 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.6432 | 0.655867 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.857033 | −0.0285836 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.1082 | −0.703215 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.1780 | −0.405260 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.9798 | 0.564429 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.2956 | 1.70324 | 0.851621 | − | 0.524158i | \(-0.175620\pi\) | ||||
0.851621 | + | 0.524158i | \(0.175620\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.58145 | −0.0856212 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.03426 | −0.133661 | −0.0668305 | − | 0.997764i | \(-0.521289\pi\) | ||||
−0.0668305 | + | 0.997764i | \(0.521289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.5980 | 1.24431 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.1763 | 0.369477 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.1540 | 0.500431 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.1394 | −0.532389 | −0.266195 | − | 0.963919i | \(-0.585766\pi\) | ||||
−0.266195 | + | 0.963919i | \(0.585766\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.10210 | 0.135169 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.0075 | −0.461061 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.9658 | 0.656471 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.32652 | 0.207790 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.5862 | −0.937884 | −0.468942 | − | 0.883229i | \(-0.655365\pi\) | ||||
−0.468942 | + | 0.883229i | \(0.655365\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.87108 | −0.159643 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.1840 | −0.562580 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.0205 | −0.360408 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.7196 | −1.26491 | −0.632457 | − | 0.774595i | \(-0.717954\pi\) | ||||
−0.632457 | + | 0.774595i | \(0.717954\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.5521 | 0.833860 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −57.3448 | −1.86939 | −0.934694 | − | 0.355453i | \(-0.884326\pi\) | ||||
−0.934694 | + | 0.355453i | \(0.884326\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.6077 | 0.736209 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 22.3633 | 0.727480 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.7156 | 0.673165 | 0.336582 | − | 0.941654i | \(-0.390729\pi\) | ||||
0.336582 | + | 0.941654i | \(0.390729\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.8279 | −0.676102 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.104714 | 0.00339557 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.8695 | 0.676029 | 0.338014 | − | 0.941141i | \(-0.390245\pi\) | ||||
0.338014 | + | 0.941141i | \(0.390245\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.43387 | 0.0787581 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.08613 | −0.229062 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 51.6238 | 1.66702 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8714 | −0.963594 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.94539 | −0.159363 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.51990 | −0.145501 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.36701 | 0.204749 | 0.102375 | − | 0.994746i | \(-0.467356\pi\) | ||||
0.102375 | + | 0.994746i | \(0.467356\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.76248 | 0.0887437 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.5899 | 1.71978 | 0.859890 | − | 0.510479i | \(-0.170532\pi\) | ||||
0.859890 | + | 0.510479i | \(0.170532\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.3720 | −1.16603 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.9695 | 0.863714 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.45811 | 0.174620 | 0.0873102 | − | 0.996181i | \(-0.472173\pi\) | ||||
0.0873102 | + | 0.996181i | \(0.472173\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.8631 | 0.922468 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.44851 | −0.173958 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.20849 | 0.134230 | 0.0671150 | − | 0.997745i | \(-0.478621\pi\) | ||||
0.0671150 | + | 0.997745i | \(0.478621\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.65340 | 0.275720 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −51.2099 | −1.63003 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.73050 | −0.182219 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.6760 | 1.83214 | 0.916069 | − | 0.401021i | \(-0.131344\pi\) | ||||
0.916069 | + | 0.401021i | \(0.131344\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −51.6815 | −1.64006 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.2591 | 0.864171 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.8984 | −1.26359 | −0.631797 | − | 0.775134i | \(-0.717682\pi\) | ||||
−0.631797 | + | 0.775134i | \(0.717682\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.4132 | −0.962233 |
(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 | 6004.2.a.f.1.5 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.f.1.5 | ✓ | 25 | 1.1 | even | 1 | trivial |