Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.18890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.456850 | 0.323042 | 0.161521 | − | 0.986869i | \(-0.448360\pi\) | ||||
0.161521 | + | 0.986869i | \(0.448360\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.79129 | −0.895644 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.456850 | 0.186508 | ||||||||
\(7\) | −2.18890 | −0.827327 | −0.413663 | − | 0.910430i | \(-0.635751\pi\) | ||||
−0.413663 | + | 0.910430i | \(0.635751\pi\) | |||||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.79129 | −0.517100 | ||||||||
\(13\) | −0.456850 | −0.126707 | −0.0633537 | − | 0.997991i | \(-0.520180\pi\) | ||||
−0.0633537 | + | 0.997991i | \(0.520180\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.79129 | 0.697822 | ||||||||
\(17\) | 1.73205 | 0.420084 | 0.210042 | − | 0.977692i | \(-0.432640\pi\) | ||||
0.210042 | + | 0.977692i | \(0.432640\pi\) | |||||||
\(18\) | 0.456850 | 0.107681 | ||||||||
\(19\) | 1.73205 | 0.397360 | 0.198680 | − | 0.980064i | \(-0.436335\pi\) | ||||
0.198680 | + | 0.980064i | \(0.436335\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.18890 | −0.477657 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.20871 | −0.252034 | −0.126017 | − | 0.992028i | \(-0.540219\pi\) | ||||
−0.126017 | + | 0.992028i | \(0.540219\pi\) | |||||||
\(24\) | −1.73205 | −0.353553 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.208712 | −0.0409318 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.92095 | 0.740990 | ||||||||
\(29\) | 1.73205 | 0.321634 | 0.160817 | − | 0.986984i | \(-0.448587\pi\) | ||||
0.160817 | + | 0.986984i | \(0.448587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.20871 | −0.576302 | −0.288151 | − | 0.957585i | \(-0.593040\pi\) | ||||
−0.288151 | + | 0.957585i | \(0.593040\pi\) | |||||||
\(32\) | 4.73930 | 0.837798 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.791288 | 0.135705 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.79129 | −0.298548 | ||||||||
\(37\) | 1.58258 | 0.260174 | 0.130087 | − | 0.991503i | \(-0.458474\pi\) | ||||
0.130087 | + | 0.991503i | \(0.458474\pi\) | |||||||
\(38\) | 0.791288 | 0.128364 | ||||||||
\(39\) | −0.456850 | −0.0731546 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.10260 | −0.484545 | −0.242272 | − | 0.970208i | \(-0.577893\pi\) | ||||
−0.242272 | + | 0.970208i | \(0.577893\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 3.46410 | 0.528271 | 0.264135 | − | 0.964486i | \(-0.414913\pi\) | ||||
0.264135 | + | 0.964486i | \(0.414913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.552200 | −0.0814175 | ||||||||
\(47\) | −5.58258 | −0.814302 | −0.407151 | − | 0.913361i | \(-0.633478\pi\) | ||||
−0.407151 | + | 0.913361i | \(0.633478\pi\) | |||||||
\(48\) | 2.79129 | 0.402888 | ||||||||
\(49\) | −2.20871 | −0.315530 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.73205 | 0.242536 | ||||||||
\(52\) | 0.818350 | 0.113485 | ||||||||
\(53\) | 6.79129 | 0.932855 | 0.466428 | − | 0.884559i | \(-0.345541\pi\) | ||||
0.466428 | + | 0.884559i | \(0.345541\pi\) | |||||||
\(54\) | 0.456850 | 0.0621694 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.79129 | 0.506632 | ||||||||
\(57\) | 1.73205 | 0.229416 | ||||||||
\(58\) | 0.791288 | 0.103901 | ||||||||
\(59\) | −12.1652 | −1.58377 | −0.791884 | − | 0.610672i | \(-0.790900\pi\) | ||||
−0.791884 | + | 0.610672i | \(0.790900\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.11890 | 0.911482 | 0.455741 | − | 0.890112i | \(-0.349374\pi\) | ||||
0.455741 | + | 0.890112i | \(0.349374\pi\) | |||||||
\(62\) | −1.46590 | −0.186170 | ||||||||
\(63\) | −2.18890 | −0.275776 | ||||||||
\(64\) | −3.41742 | −0.427178 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.16515 | −1.11970 | −0.559851 | − | 0.828593i | \(-0.689142\pi\) | ||||
−0.559851 | + | 0.828593i | \(0.689142\pi\) | |||||||
\(68\) | −3.10260 | −0.376246 | ||||||||
\(69\) | −1.20871 | −0.145512 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.7477 | 1.86891 | 0.934456 | − | 0.356079i | \(-0.115887\pi\) | ||||
0.934456 | + | 0.356079i | \(0.115887\pi\) | |||||||
\(72\) | −1.73205 | −0.204124 | ||||||||
\(73\) | 9.21245 | 1.07824 | 0.539118 | − | 0.842230i | \(-0.318758\pi\) | ||||
0.539118 | + | 0.842230i | \(0.318758\pi\) | |||||||
\(74\) | 0.723000 | 0.0840471 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.10260 | −0.355893 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.208712 | −0.0236320 | ||||||||
\(79\) | −14.7701 | −1.66177 | −0.830883 | − | 0.556447i | \(-0.812164\pi\) | ||||
−0.830883 | + | 0.556447i | \(0.812164\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.41742 | −0.156528 | ||||||||
\(83\) | 14.5040 | 1.59202 | 0.796008 | − | 0.605286i | \(-0.206941\pi\) | ||||
0.796008 | + | 0.605286i | \(0.206941\pi\) | |||||||
\(84\) | 3.92095 | 0.427811 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.58258 | 0.170654 | ||||||||
\(87\) | 1.73205 | 0.185695 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.62614 | −0.278370 | −0.139185 | − | 0.990266i | \(-0.544448\pi\) | ||||
−0.139185 | + | 0.990266i | \(0.544448\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 2.16515 | 0.225733 | ||||||||
\(93\) | −3.20871 | −0.332728 | ||||||||
\(94\) | −2.55040 | −0.263054 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.73930 | 0.483703 | ||||||||
\(97\) | −13.5826 | −1.37910 | −0.689551 | − | 0.724237i | \(-0.742192\pi\) | ||||
−0.689551 | + | 0.724237i | \(0.742192\pi\) | |||||||
\(98\) | −1.00905 | −0.101930 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.4177 | −1.53411 | −0.767057 | − | 0.641579i | \(-0.778280\pi\) | ||||
−0.767057 | + | 0.641579i | \(0.778280\pi\) | |||||||
\(102\) | 0.791288 | 0.0783492 | ||||||||
\(103\) | 7.16515 | 0.706003 | 0.353002 | − | 0.935623i | \(-0.385161\pi\) | ||||
0.353002 | + | 0.935623i | \(0.385161\pi\) | |||||||
\(104\) | 0.791288 | 0.0775922 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.10260 | 0.301351 | ||||||||
\(107\) | 11.8582 | 1.14638 | 0.573188 | − | 0.819424i | \(-0.305706\pi\) | ||||
0.573188 | + | 0.819424i | \(0.305706\pi\) | |||||||
\(108\) | −1.79129 | −0.172367 | ||||||||
\(109\) | 11.4014 | 1.09205 | 0.546026 | − | 0.837768i | \(-0.316140\pi\) | ||||
0.546026 | + | 0.837768i | \(0.316140\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.58258 | 0.150211 | ||||||||
\(112\) | −6.10985 | −0.577327 | ||||||||
\(113\) | −10.7477 | −1.01106 | −0.505531 | − | 0.862809i | \(-0.668703\pi\) | ||||
−0.505531 | + | 0.862809i | \(0.668703\pi\) | |||||||
\(114\) | 0.791288 | 0.0741109 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.10260 | −0.288069 | ||||||||
\(117\) | −0.456850 | −0.0422358 | ||||||||
\(118\) | −5.55765 | −0.511623 | ||||||||
\(119\) | −3.79129 | −0.347547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.25227 | 0.294447 | ||||||||
\(123\) | −3.10260 | −0.279752 | ||||||||
\(124\) | 5.74773 | 0.516161 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −13.2288 | −1.17386 | −0.586931 | − | 0.809637i | \(-0.699664\pi\) | ||||
−0.586931 | + | 0.809637i | \(0.699664\pi\) | |||||||
\(128\) | −11.0399 | −0.975795 | ||||||||
\(129\) | 3.46410 | 0.304997 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.27520 | 0.111415 | 0.0557074 | − | 0.998447i | \(-0.482259\pi\) | ||||
0.0557074 | + | 0.998447i | \(0.482259\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.79129 | −0.328746 | ||||||||
\(134\) | −4.18710 | −0.361710 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | 0.417424 | 0.0356630 | 0.0178315 | − | 0.999841i | \(-0.494324\pi\) | ||||
0.0178315 | + | 0.999841i | \(0.494324\pi\) | |||||||
\(138\) | −0.552200 | −0.0470064 | ||||||||
\(139\) | 6.66205 | 0.565068 | 0.282534 | − | 0.959257i | \(-0.408825\pi\) | ||||
0.282534 | + | 0.959257i | \(0.408825\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.58258 | −0.470138 | ||||||||
\(142\) | 7.19435 | 0.603737 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.79129 | 0.232607 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.20871 | 0.348315 | ||||||||
\(147\) | −2.20871 | −0.182172 | ||||||||
\(148\) | −2.83485 | −0.233023 | ||||||||
\(149\) | −9.02175 | −0.739091 | −0.369545 | − | 0.929213i | \(-0.620487\pi\) | ||||
−0.369545 | + | 0.929213i | \(0.620487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8582 | 0.965007 | 0.482504 | − | 0.875894i | \(-0.339728\pi\) | ||||
0.482504 | + | 0.875894i | \(0.339728\pi\) | |||||||
\(152\) | −3.00000 | −0.243332 | ||||||||
\(153\) | 1.73205 | 0.140028 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.818350 | 0.0655205 | ||||||||
\(157\) | −7.74773 | −0.618336 | −0.309168 | − | 0.951007i | \(-0.600051\pi\) | ||||
−0.309168 | + | 0.951007i | \(0.600051\pi\) | |||||||
\(158\) | −6.74773 | −0.536820 | ||||||||
\(159\) | 6.79129 | 0.538584 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.64575 | 0.208514 | ||||||||
\(162\) | 0.456850 | 0.0358935 | ||||||||
\(163\) | 16.3739 | 1.28250 | 0.641250 | − | 0.767332i | \(-0.278416\pi\) | ||||
0.641250 | + | 0.767332i | \(0.278416\pi\) | |||||||
\(164\) | 5.55765 | 0.433980 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.62614 | 0.514288 | ||||||||
\(167\) | −17.9681 | −1.39041 | −0.695205 | − | 0.718811i | \(-0.744686\pi\) | ||||
−0.695205 | + | 0.718811i | \(0.744686\pi\) | |||||||
\(168\) | 3.79129 | 0.292504 | ||||||||
\(169\) | −12.7913 | −0.983945 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.73205 | 0.132453 | ||||||||
\(172\) | −6.20520 | −0.473142 | ||||||||
\(173\) | −22.5167 | −1.71191 | −0.855955 | − | 0.517050i | \(-0.827030\pi\) | ||||
−0.855955 | + | 0.517050i | \(0.827030\pi\) | |||||||
\(174\) | 0.791288 | 0.0599874 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.1652 | −0.914389 | ||||||||
\(178\) | −1.19975 | −0.0899251 | ||||||||
\(179\) | −24.1652 | −1.80619 | −0.903094 | − | 0.429443i | \(-0.858710\pi\) | ||||
−0.903094 | + | 0.429443i | \(0.858710\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.41742 | −0.477003 | −0.238502 | − | 0.971142i | \(-0.576656\pi\) | ||||
−0.238502 | + | 0.971142i | \(0.576656\pi\) | |||||||
\(182\) | 0.456850 | 0.0338640 | ||||||||
\(183\) | 7.11890 | 0.526244 | ||||||||
\(184\) | 2.09355 | 0.154339 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.46590 | −0.107485 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.0000 | 0.729325 | ||||||||
\(189\) | −2.18890 | −0.159219 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.62614 | −0.696523 | −0.348261 | − | 0.937397i | \(-0.613228\pi\) | ||||
−0.348261 | + | 0.937397i | \(0.613228\pi\) | |||||||
\(192\) | −3.41742 | −0.246631 | ||||||||
\(193\) | −1.63670 | −0.117812 | −0.0589061 | − | 0.998264i | \(-0.518761\pi\) | ||||
−0.0589061 | + | 0.998264i | \(0.518761\pi\) | |||||||
\(194\) | −6.20520 | −0.445508 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.95644 | 0.282603 | ||||||||
\(197\) | −16.2360 | −1.15677 | −0.578384 | − | 0.815765i | \(-0.696316\pi\) | ||||
−0.578384 | + | 0.815765i | \(0.696316\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | 0.708881 | 0.354441 | − | 0.935079i | \(-0.384671\pi\) | ||||
0.354441 | + | 0.935079i | \(0.384671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.16515 | −0.646460 | ||||||||
\(202\) | −7.04356 | −0.495583 | ||||||||
\(203\) | −3.79129 | −0.266096 | ||||||||
\(204\) | −3.10260 | −0.217226 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.27340 | 0.228069 | ||||||||
\(207\) | −1.20871 | −0.0840113 | ||||||||
\(208\) | −1.27520 | −0.0884192 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.7792 | −1.08628 | −0.543141 | − | 0.839641i | \(-0.682765\pi\) | ||||
−0.543141 | + | 0.839641i | \(0.682765\pi\) | |||||||
\(212\) | −12.1652 | −0.835506 | ||||||||
\(213\) | 15.7477 | 1.07902 | ||||||||
\(214\) | 5.41742 | 0.370328 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.73205 | −0.117851 | ||||||||
\(217\) | 7.02355 | 0.476790 | ||||||||
\(218\) | 5.20871 | 0.352779 | ||||||||
\(219\) | 9.21245 | 0.622520 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.791288 | −0.0532278 | ||||||||
\(222\) | 0.723000 | 0.0485246 | ||||||||
\(223\) | −3.83485 | −0.256800 | −0.128400 | − | 0.991722i | \(-0.540984\pi\) | ||||
−0.128400 | + | 0.991722i | \(0.540984\pi\) | |||||||
\(224\) | −10.3739 | −0.693133 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.91010 | −0.326615 | ||||||||
\(227\) | 16.5022 | 1.09529 | 0.547643 | − | 0.836712i | \(-0.315525\pi\) | ||||
0.547643 | + | 0.836712i | \(0.315525\pi\) | |||||||
\(228\) | −3.10260 | −0.205475 | ||||||||
\(229\) | −21.3739 | −1.41242 | −0.706212 | − | 0.708000i | \(-0.749598\pi\) | ||||
−0.706212 | + | 0.708000i | \(0.749598\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | 8.29875 | 0.543669 | 0.271835 | − | 0.962344i | \(-0.412370\pi\) | ||||
0.271835 | + | 0.962344i | \(0.412370\pi\) | |||||||
\(234\) | −0.208712 | −0.0136439 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 21.7913 | 1.41849 | ||||||||
\(237\) | −14.7701 | −0.959422 | ||||||||
\(238\) | −1.73205 | −0.112272 | ||||||||
\(239\) | 16.5975 | 1.07360 | 0.536802 | − | 0.843708i | \(-0.319632\pi\) | ||||
0.536802 | + | 0.843708i | \(0.319632\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.64575 | −0.170428 | −0.0852139 | − | 0.996363i | \(-0.527157\pi\) | ||||
−0.0852139 | + | 0.996363i | \(0.527157\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −12.7520 | −0.816364 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.41742 | −0.0903717 | ||||||||
\(247\) | −0.791288 | −0.0503484 | ||||||||
\(248\) | 5.55765 | 0.352911 | ||||||||
\(249\) | 14.5040 | 0.919151 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.41742 | 0.215706 | 0.107853 | − | 0.994167i | \(-0.465602\pi\) | ||||
0.107853 | + | 0.994167i | \(0.465602\pi\) | |||||||
\(252\) | 3.92095 | 0.246997 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.04356 | −0.379207 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.79129 | 0.111955 | ||||||||
\(257\) | −21.7913 | −1.35930 | −0.679652 | − | 0.733535i | \(-0.737869\pi\) | ||||
−0.679652 | + | 0.733535i | \(0.737869\pi\) | |||||||
\(258\) | 1.58258 | 0.0985269 | ||||||||
\(259\) | −3.46410 | −0.215249 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.73205 | 0.107211 | ||||||||
\(262\) | 0.582576 | 0.0359916 | ||||||||
\(263\) | −14.1425 | −0.872061 | −0.436031 | − | 0.899932i | \(-0.643616\pi\) | ||||
−0.436031 | + | 0.899932i | \(0.643616\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.73205 | −0.106199 | ||||||||
\(267\) | −2.62614 | −0.160717 | ||||||||
\(268\) | 16.4174 | 1.00285 | ||||||||
\(269\) | −9.95644 | −0.607055 | −0.303527 | − | 0.952823i | \(-0.598164\pi\) | ||||
−0.303527 | + | 0.952823i | \(0.598164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.48945 | −0.515698 | −0.257849 | − | 0.966185i | \(-0.583014\pi\) | ||||
−0.257849 | + | 0.966185i | \(0.583014\pi\) | |||||||
\(272\) | 4.83465 | 0.293144 | ||||||||
\(273\) | 1.00000 | 0.0605228 | ||||||||
\(274\) | 0.190700 | 0.0115206 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.16515 | 0.130327 | ||||||||
\(277\) | −9.76465 | −0.586701 | −0.293351 | − | 0.956005i | \(-0.594770\pi\) | ||||
−0.293351 | + | 0.956005i | \(0.594770\pi\) | |||||||
\(278\) | 3.04356 | 0.182541 | ||||||||
\(279\) | −3.20871 | −0.192101 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.6947 | −0.876610 | −0.438305 | − | 0.898826i | \(-0.644421\pi\) | ||||
−0.438305 | + | 0.898826i | \(0.644421\pi\) | |||||||
\(282\) | −2.55040 | −0.151874 | ||||||||
\(283\) | −11.5722 | −0.687893 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(284\) | −28.2087 | −1.67388 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.79129 | 0.400877 | ||||||||
\(288\) | 4.73930 | 0.279266 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.5826 | −0.796225 | ||||||||
\(292\) | −16.5022 | −0.965716 | ||||||||
\(293\) | −8.94630 | −0.522649 | −0.261324 | − | 0.965251i | \(-0.584159\pi\) | ||||
−0.261324 | + | 0.965251i | \(0.584159\pi\) | |||||||
\(294\) | −1.00905 | −0.0588490 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.74110 | −0.159323 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.12159 | −0.238757 | ||||||||
\(299\) | 0.552200 | 0.0319346 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.58258 | −0.437052 | ||||||||
\(302\) | 5.41742 | 0.311738 | ||||||||
\(303\) | −15.4177 | −0.885721 | ||||||||
\(304\) | 4.83465 | 0.277286 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.791288 | 0.0452349 | ||||||||
\(307\) | −13.3241 | −0.760447 | −0.380223 | − | 0.924895i | \(-0.624153\pi\) | ||||
−0.380223 | + | 0.924895i | \(0.624153\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.16515 | 0.407611 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.208712 | −0.0118350 | −0.00591749 | − | 0.999982i | \(-0.501884\pi\) | ||||
−0.00591749 | + | 0.999982i | \(0.501884\pi\) | |||||||
\(312\) | 0.791288 | 0.0447979 | ||||||||
\(313\) | −8.16515 | −0.461522 | −0.230761 | − | 0.973011i | \(-0.574121\pi\) | ||||
−0.230761 | + | 0.973011i | \(0.574121\pi\) | |||||||
\(314\) | −3.53955 | −0.199748 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.4575 | 1.48835 | ||||||||
\(317\) | 0.165151 | 0.00927583 | 0.00463791 | − | 0.999989i | \(-0.498524\pi\) | ||||
0.00463791 | + | 0.999989i | \(0.498524\pi\) | |||||||
\(318\) | 3.10260 | 0.173985 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8582 | 0.661861 | ||||||||
\(322\) | 1.20871 | 0.0673589 | ||||||||
\(323\) | 3.00000 | 0.166924 | ||||||||
\(324\) | −1.79129 | −0.0995160 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.48040 | 0.414301 | ||||||||
\(327\) | 11.4014 | 0.630496 | ||||||||
\(328\) | 5.37386 | 0.296722 | ||||||||
\(329\) | 12.2197 | 0.673694 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.4955 | −1.56625 | −0.783126 | − | 0.621863i | \(-0.786376\pi\) | ||||
−0.783126 | + | 0.621863i | \(0.786376\pi\) | |||||||
\(332\) | −25.9808 | −1.42588 | ||||||||
\(333\) | 1.58258 | 0.0867246 | ||||||||
\(334\) | −8.20871 | −0.449161 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.10985 | −0.333320 | ||||||||
\(337\) | 2.64575 | 0.144123 | 0.0720616 | − | 0.997400i | \(-0.477042\pi\) | ||||
0.0720616 | + | 0.997400i | \(0.477042\pi\) | |||||||
\(338\) | −5.84370 | −0.317856 | ||||||||
\(339\) | −10.7477 | −0.583736 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.791288 | 0.0427879 | ||||||||
\(343\) | 20.1570 | 1.08837 | ||||||||
\(344\) | −6.00000 | −0.323498 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.2867 | −0.553019 | ||||||||
\(347\) | 23.3549 | 1.25376 | 0.626879 | − | 0.779117i | \(-0.284332\pi\) | ||||
0.626879 | + | 0.779117i | \(0.284332\pi\) | |||||||
\(348\) | −3.10260 | −0.166317 | ||||||||
\(349\) | 35.5746 | 1.90427 | 0.952133 | − | 0.305685i | \(-0.0988853\pi\) | ||||
0.952133 | + | 0.305685i | \(0.0988853\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.456850 | −0.0243849 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.58258 | 0.243906 | 0.121953 | − | 0.992536i | \(-0.461084\pi\) | ||||
0.121953 | + | 0.992536i | \(0.461084\pi\) | |||||||
\(354\) | −5.55765 | −0.295386 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.70417 | 0.249320 | ||||||||
\(357\) | −3.79129 | −0.200656 | ||||||||
\(358\) | −11.0399 | −0.583474 | ||||||||
\(359\) | −19.9663 | −1.05378 | −0.526889 | − | 0.849934i | \(-0.676642\pi\) | ||||
−0.526889 | + | 0.849934i | \(0.676642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0000 | −0.842105 | ||||||||
\(362\) | −2.93180 | −0.154092 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.79129 | −0.0938890 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.25227 | 0.169999 | ||||||||
\(367\) | −4.25227 | −0.221967 | −0.110983 | − | 0.993822i | \(-0.535400\pi\) | ||||
−0.110983 | + | 0.993822i | \(0.535400\pi\) | |||||||
\(368\) | −3.37386 | −0.175875 | ||||||||
\(369\) | −3.10260 | −0.161515 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.8655 | −0.771776 | ||||||||
\(372\) | 5.74773 | 0.298006 | ||||||||
\(373\) | 0.647551 | 0.0335289 | 0.0167645 | − | 0.999859i | \(-0.494663\pi\) | ||||
0.0167645 | + | 0.999859i | \(0.494663\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.66930 | 0.498656 | ||||||||
\(377\) | −0.791288 | −0.0407534 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 10.6261 | 0.545828 | 0.272914 | − | 0.962038i | \(-0.412013\pi\) | ||||
0.272914 | + | 0.962038i | \(0.412013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.2288 | −0.677730 | ||||||||
\(382\) | −4.39770 | −0.225006 | ||||||||
\(383\) | 11.2087 | 0.572738 | 0.286369 | − | 0.958119i | \(-0.407552\pi\) | ||||
0.286369 | + | 0.958119i | \(0.407552\pi\) | |||||||
\(384\) | −11.0399 | −0.563375 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.747727 | −0.0380583 | ||||||||
\(387\) | 3.46410 | 0.176090 | ||||||||
\(388\) | 24.3303 | 1.23518 | ||||||||
\(389\) | −28.7477 | −1.45757 | −0.728784 | − | 0.684744i | \(-0.759914\pi\) | ||||
−0.728784 | + | 0.684744i | \(0.759914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.09355 | −0.105875 | ||||||||
\(392\) | 3.82560 | 0.193222 | ||||||||
\(393\) | 1.27520 | 0.0643254 | ||||||||
\(394\) | −7.41742 | −0.373684 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.3303 | 0.568652 | 0.284326 | − | 0.958728i | \(-0.408230\pi\) | ||||
0.284326 | + | 0.958728i | \(0.408230\pi\) | |||||||
\(398\) | 4.56850 | 0.228998 | ||||||||
\(399\) | −3.79129 | −0.189802 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.4174 | −0.570159 | −0.285079 | − | 0.958504i | \(-0.592020\pi\) | ||||
−0.285079 | + | 0.958504i | \(0.592020\pi\) | |||||||
\(402\) | −4.18710 | −0.208834 | ||||||||
\(403\) | 1.46590 | 0.0730217 | ||||||||
\(404\) | 27.6175 | 1.37402 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.73205 | −0.0859602 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3.00000 | −0.148522 | ||||||||
\(409\) | −21.3368 | −1.05504 | −0.527519 | − | 0.849543i | \(-0.676878\pi\) | ||||
−0.527519 | + | 0.849543i | \(0.676878\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.417424 | 0.0205900 | ||||||||
\(412\) | −12.8348 | −0.632328 | ||||||||
\(413\) | 26.6283 | 1.31029 | ||||||||
\(414\) | −0.552200 | −0.0271392 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.16515 | −0.106155 | ||||||||
\(417\) | 6.66205 | 0.326242 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.79129 | 0.136363 | 0.0681817 | − | 0.997673i | \(-0.478280\pi\) | ||||
0.0681817 | + | 0.997673i | \(0.478280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.8348 | −0.576795 | −0.288398 | − | 0.957511i | \(-0.593122\pi\) | ||||
−0.288398 | + | 0.957511i | \(0.593122\pi\) | |||||||
\(422\) | −7.20871 | −0.350915 | ||||||||
\(423\) | −5.58258 | −0.271434 | ||||||||
\(424\) | −11.7629 | −0.571255 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.19435 | 0.348568 | ||||||||
\(427\) | −15.5826 | −0.754094 | ||||||||
\(428\) | −21.2415 | −1.02674 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.9717 | −1.20285 | −0.601423 | − | 0.798931i | \(-0.705399\pi\) | ||||
−0.601423 | + | 0.798931i | \(0.705399\pi\) | |||||||
\(432\) | 2.79129 | 0.134296 | ||||||||
\(433\) | 23.5390 | 1.13121 | 0.565606 | − | 0.824675i | \(-0.308642\pi\) | ||||
0.565606 | + | 0.824675i | \(0.308642\pi\) | |||||||
\(434\) | 3.20871 | 0.154023 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.4231 | −0.978090 | ||||||||
\(437\) | −2.09355 | −0.100148 | ||||||||
\(438\) | 4.20871 | 0.201100 | ||||||||
\(439\) | 21.6983 | 1.03560 | 0.517802 | − | 0.855501i | \(-0.326750\pi\) | ||||
0.517802 | + | 0.855501i | \(0.326750\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.20871 | −0.105177 | ||||||||
\(442\) | −0.361500 | −0.0171948 | ||||||||
\(443\) | −9.91288 | −0.470975 | −0.235488 | − | 0.971877i | \(-0.575669\pi\) | ||||
−0.235488 | + | 0.971877i | \(0.575669\pi\) | |||||||
\(444\) | −2.83485 | −0.134536 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.75195 | −0.0829573 | ||||||||
\(447\) | −9.02175 | −0.426714 | ||||||||
\(448\) | 7.48040 | 0.353416 | ||||||||
\(449\) | −21.3303 | −1.00664 | −0.503320 | − | 0.864100i | \(-0.667888\pi\) | ||||
−0.503320 | + | 0.864100i | \(0.667888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 19.2523 | 0.905551 | ||||||||
\(453\) | 11.8582 | 0.557147 | ||||||||
\(454\) | 7.53901 | 0.353824 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | −19.2433 | −0.900162 | −0.450081 | − | 0.892988i | \(-0.648605\pi\) | ||||
−0.450081 | + | 0.892988i | \(0.648605\pi\) | |||||||
\(458\) | −9.76465 | −0.456272 | ||||||||
\(459\) | 1.73205 | 0.0808452 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.4877 | 0.488459 | 0.244229 | − | 0.969717i | \(-0.421465\pi\) | ||||
0.244229 | + | 0.969717i | \(0.421465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.7477 | −1.28955 | −0.644773 | − | 0.764374i | \(-0.723048\pi\) | ||||
−0.644773 | + | 0.764374i | \(0.723048\pi\) | |||||||
\(464\) | 4.83465 | 0.224443 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.79129 | 0.175628 | ||||||||
\(467\) | 34.1652 | 1.58097 | 0.790487 | − | 0.612478i | \(-0.209827\pi\) | ||||
0.790487 | + | 0.612478i | \(0.209827\pi\) | |||||||
\(468\) | 0.818350 | 0.0378283 | ||||||||
\(469\) | 20.0616 | 0.926359 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.74773 | −0.356996 | ||||||||
\(472\) | 21.0707 | 0.969856 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.74773 | −0.309933 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.79129 | 0.311278 | ||||||||
\(477\) | 6.79129 | 0.310952 | ||||||||
\(478\) | 7.58258 | 0.346819 | ||||||||
\(479\) | −38.4865 | −1.75849 | −0.879247 | − | 0.476366i | \(-0.841954\pi\) | ||||
−0.879247 | + | 0.476366i | \(0.841954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.723000 | −0.0329660 | ||||||||
\(482\) | −1.20871 | −0.0550553 | ||||||||
\(483\) | 2.64575 | 0.120386 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.456850 | 0.0207231 | ||||||||
\(487\) | −2.58258 | −0.117028 | −0.0585138 | − | 0.998287i | \(-0.518636\pi\) | ||||
−0.0585138 | + | 0.998287i | \(0.518636\pi\) | |||||||
\(488\) | −12.3303 | −0.558167 | ||||||||
\(489\) | 16.3739 | 0.740452 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.2705 | 1.50148 | 0.750738 | − | 0.660601i | \(-0.229698\pi\) | ||||
0.750738 | + | 0.660601i | \(0.229698\pi\) | |||||||
\(492\) | 5.55765 | 0.250558 | ||||||||
\(493\) | 3.00000 | 0.135113 | ||||||||
\(494\) | −0.361500 | −0.0162647 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.95644 | −0.402156 | ||||||||
\(497\) | −34.4702 | −1.54620 | ||||||||
\(498\) | 6.62614 | 0.296924 | ||||||||
\(499\) | −6.83485 | −0.305970 | −0.152985 | − | 0.988229i | \(-0.548889\pi\) | ||||
−0.152985 | + | 0.988229i | \(0.548889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.9681 | −0.802754 | ||||||||
\(502\) | 1.56125 | 0.0696820 | ||||||||
\(503\) | −8.56490 | −0.381890 | −0.190945 | − | 0.981601i | \(-0.561155\pi\) | ||||
−0.190945 | + | 0.981601i | \(0.561155\pi\) | |||||||
\(504\) | 3.79129 | 0.168877 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7913 | −0.568081 | ||||||||
\(508\) | 23.6965 | 1.05136 | ||||||||
\(509\) | 6.25227 | 0.277127 | 0.138564 | − | 0.990354i | \(-0.455751\pi\) | ||||
0.138564 | + | 0.990354i | \(0.455751\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.1652 | −0.892054 | ||||||||
\(512\) | 22.8981 | 1.01196 | ||||||||
\(513\) | 1.73205 | 0.0764719 | ||||||||
\(514\) | −9.95536 | −0.439112 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.20520 | −0.273169 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.58258 | −0.0695344 | ||||||||
\(519\) | −22.5167 | −0.988372 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.00000 | −0.175243 | −0.0876216 | − | 0.996154i | \(-0.527927\pi\) | ||||
−0.0876216 | + | 0.996154i | \(0.527927\pi\) | |||||||
\(522\) | 0.791288 | 0.0346337 | ||||||||
\(523\) | 21.3368 | 0.932994 | 0.466497 | − | 0.884523i | \(-0.345516\pi\) | ||||
0.466497 | + | 0.884523i | \(0.345516\pi\) | |||||||
\(524\) | −2.28425 | −0.0997880 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.46099 | −0.281712 | ||||||||
\(527\) | −5.55765 | −0.242095 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5390 | −0.936479 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.1652 | −0.527923 | ||||||||
\(532\) | 6.79129 | 0.294440 | ||||||||
\(533\) | 1.41742 | 0.0613955 | ||||||||
\(534\) | −1.19975 | −0.0519183 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.8745 | 0.685674 | ||||||||
\(537\) | −24.1652 | −1.04280 | ||||||||
\(538\) | −4.54860 | −0.196104 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.0634 | 0.776607 | 0.388303 | − | 0.921532i | \(-0.373061\pi\) | ||||
0.388303 | + | 0.921532i | \(0.373061\pi\) | |||||||
\(542\) | −3.87841 | −0.166592 | ||||||||
\(543\) | −6.41742 | −0.275398 | ||||||||
\(544\) | 8.20871 | 0.351946 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.456850 | 0.0195514 | ||||||||
\(547\) | 40.7509 | 1.74238 | 0.871191 | − | 0.490945i | \(-0.163348\pi\) | ||||
0.871191 | + | 0.490945i | \(0.163348\pi\) | |||||||
\(548\) | −0.747727 | −0.0319413 | ||||||||
\(549\) | 7.11890 | 0.303827 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | 0.127804 | ||||||||
\(552\) | 2.09355 | 0.0891074 | ||||||||
\(553\) | 32.3303 | 1.37482 | ||||||||
\(554\) | −4.46099 | −0.189529 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.9337 | −0.506100 | ||||||||
\(557\) | 29.2741 | 1.24038 | 0.620191 | − | 0.784451i | \(-0.287055\pi\) | ||||
0.620191 | + | 0.784451i | \(0.287055\pi\) | |||||||
\(558\) | −1.46590 | −0.0620565 | ||||||||
\(559\) | −1.58258 | −0.0669358 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.71326 | −0.283182 | ||||||||
\(563\) | 23.1642 | 0.976255 | 0.488128 | − | 0.872772i | \(-0.337680\pi\) | ||||
0.488128 | + | 0.872772i | \(0.337680\pi\) | |||||||
\(564\) | 10.0000 | 0.421076 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.28674 | −0.222218 | ||||||||
\(567\) | −2.18890 | −0.0919252 | ||||||||
\(568\) | −27.2759 | −1.14447 | ||||||||
\(569\) | 30.7400 | 1.28869 | 0.644343 | − | 0.764736i | \(-0.277131\pi\) | ||||
0.644343 | + | 0.764736i | \(0.277131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.3139 | 1.68709 | 0.843543 | − | 0.537062i | \(-0.180466\pi\) | ||||
0.843543 | + | 0.537062i | \(0.180466\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.62614 | −0.402138 | ||||||||
\(574\) | 3.10260 | 0.129500 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.41742 | −0.142393 | ||||||||
\(577\) | 27.1216 | 1.12909 | 0.564543 | − | 0.825403i | \(-0.309052\pi\) | ||||
0.564543 | + | 0.825403i | \(0.309052\pi\) | |||||||
\(578\) | −6.39590 | −0.266035 | ||||||||
\(579\) | −1.63670 | −0.0680190 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.7477 | −1.31712 | ||||||||
\(582\) | −6.20520 | −0.257214 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −15.9564 | −0.660282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.08712 | −0.168837 | ||||||||
\(587\) | −29.8693 | −1.23284 | −0.616419 | − | 0.787418i | \(-0.711417\pi\) | ||||
−0.616419 | + | 0.787418i | \(0.711417\pi\) | |||||||
\(588\) | 3.95644 | 0.163161 | ||||||||
\(589\) | −5.55765 | −0.228999 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.2360 | −0.667860 | ||||||||
\(592\) | 4.41742 | 0.181555 | ||||||||
\(593\) | −3.38865 | −0.139155 | −0.0695776 | − | 0.997577i | \(-0.522165\pi\) | ||||
−0.0695776 | + | 0.997577i | \(0.522165\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.1606 | 0.661962 | ||||||||
\(597\) | 10.0000 | 0.409273 | ||||||||
\(598\) | 0.252273 | 0.0103162 | ||||||||
\(599\) | −41.1216 | −1.68018 | −0.840091 | − | 0.542445i | \(-0.817499\pi\) | ||||
−0.840091 | + | 0.542445i | \(0.817499\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.01270 | 0.326845 | 0.163422 | − | 0.986556i | \(-0.447747\pi\) | ||||
0.163422 | + | 0.986556i | \(0.447747\pi\) | |||||||
\(602\) | −3.46410 | −0.141186 | ||||||||
\(603\) | −9.16515 | −0.373234 | ||||||||
\(604\) | −21.2415 | −0.864303 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.04356 | −0.286125 | ||||||||
\(607\) | 19.7756 | 0.802665 | 0.401333 | − | 0.915932i | \(-0.368547\pi\) | ||||
0.401333 | + | 0.915932i | \(0.368547\pi\) | |||||||
\(608\) | 8.20871 | 0.332907 | ||||||||
\(609\) | −3.79129 | −0.153631 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.55040 | 0.103178 | ||||||||
\(612\) | −3.10260 | −0.125415 | ||||||||
\(613\) | 7.30960 | 0.295232 | 0.147616 | − | 0.989045i | \(-0.452840\pi\) | ||||
0.147616 | + | 0.989045i | \(0.452840\pi\) | |||||||
\(614\) | −6.08712 | −0.245656 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.1216 | 1.37368 | 0.686842 | − | 0.726807i | \(-0.258997\pi\) | ||||
0.686842 | + | 0.726807i | \(0.258997\pi\) | |||||||
\(618\) | 3.27340 | 0.131676 | ||||||||
\(619\) | −5.00000 | −0.200967 | −0.100483 | − | 0.994939i | \(-0.532039\pi\) | ||||
−0.100483 | + | 0.994939i | \(0.532039\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.20871 | −0.0485039 | ||||||||
\(622\) | −0.0953502 | −0.00382319 | ||||||||
\(623\) | 5.74835 | 0.230303 | ||||||||
\(624\) | −1.27520 | −0.0510489 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.73025 | −0.149091 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.8784 | 0.553809 | ||||||||
\(629\) | 2.74110 | 0.109295 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.5390 | −0.538980 | −0.269490 | − | 0.963003i | \(-0.586855\pi\) | ||||
−0.269490 | + | 0.963003i | \(0.586855\pi\) | |||||||
\(632\) | 25.5826 | 1.01762 | ||||||||
\(633\) | −15.7792 | −0.627165 | ||||||||
\(634\) | 0.0754495 | 0.00299648 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.1652 | −0.482380 | ||||||||
\(637\) | 1.00905 | 0.0399800 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.7477 | 0.622970 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.3739 | −1.12070 | −0.560350 | − | 0.828256i | \(-0.689333\pi\) | ||||
−0.560350 | + | 0.828256i | \(0.689333\pi\) | |||||||
\(642\) | 5.41742 | 0.213809 | ||||||||
\(643\) | −27.4955 | −1.08431 | −0.542157 | − | 0.840277i | \(-0.682392\pi\) | ||||
−0.542157 | + | 0.840277i | \(0.682392\pi\) | |||||||
\(644\) | −4.73930 | −0.186755 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.37055 | 0.0539236 | ||||||||
\(647\) | 7.00000 | 0.275198 | 0.137599 | − | 0.990488i | \(-0.456061\pi\) | ||||
0.137599 | + | 0.990488i | \(0.456061\pi\) | |||||||
\(648\) | −1.73205 | −0.0680414 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.02355 | 0.275275 | ||||||||
\(652\) | −29.3303 | −1.14866 | ||||||||
\(653\) | 38.4955 | 1.50644 | 0.753222 | − | 0.657767i | \(-0.228499\pi\) | ||||
0.753222 | + | 0.657767i | \(0.228499\pi\) | |||||||
\(654\) | 5.20871 | 0.203677 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.66025 | −0.338126 | ||||||||
\(657\) | 9.21245 | 0.359412 | ||||||||
\(658\) | 5.58258 | 0.217631 | ||||||||
\(659\) | −6.94810 | −0.270660 | −0.135330 | − | 0.990801i | \(-0.543209\pi\) | ||||
−0.135330 | + | 0.990801i | \(0.543209\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.8693 | −1.47295 | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(662\) | −13.0182 | −0.505965 | ||||||||
\(663\) | −0.791288 | −0.0307311 | ||||||||
\(664\) | −25.1216 | −0.974907 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.723000 | 0.0280157 | ||||||||
\(667\) | −2.09355 | −0.0810626 | ||||||||
\(668\) | 32.1860 | 1.24531 | ||||||||
\(669\) | −3.83485 | −0.148264 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −10.3739 | −0.400180 | ||||||||
\(673\) | −0.170800 | −0.00658384 | −0.00329192 | − | 0.999995i | \(-0.501048\pi\) | ||||
−0.00329192 | + | 0.999995i | \(0.501048\pi\) | |||||||
\(674\) | 1.20871 | 0.0465579 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.9129 | 0.881265 | ||||||||
\(677\) | 22.9735 | 0.882944 | 0.441472 | − | 0.897275i | \(-0.354456\pi\) | ||||
0.441472 | + | 0.897275i | \(0.354456\pi\) | |||||||
\(678\) | −4.91010 | −0.188571 | ||||||||
\(679\) | 29.7309 | 1.14097 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.5022 | 0.632364 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.3303 | 0.510070 | 0.255035 | − | 0.966932i | \(-0.417913\pi\) | ||||
0.255035 | + | 0.966932i | \(0.417913\pi\) | |||||||
\(684\) | −3.10260 | −0.118631 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.20871 | 0.351590 | ||||||||
\(687\) | −21.3739 | −0.815464 | ||||||||
\(688\) | 9.66930 | 0.368639 | ||||||||
\(689\) | −3.10260 | −0.118200 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.79129 | 0.296395 | 0.148197 | − | 0.988958i | \(-0.452653\pi\) | ||||
0.148197 | + | 0.988958i | \(0.452653\pi\) | |||||||
\(692\) | 40.3338 | 1.53326 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.6697 | 0.405016 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.00000 | −0.113715 | ||||||||
\(697\) | −5.37386 | −0.203550 | ||||||||
\(698\) | 16.2523 | 0.615158 | ||||||||
\(699\) | 8.29875 | 0.313888 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.6929 | −0.630481 | −0.315240 | − | 0.949012i | \(-0.602085\pi\) | ||||
−0.315240 | + | 0.949012i | \(0.602085\pi\) | |||||||
\(702\) | −0.208712 | −0.00787733 | ||||||||
\(703\) | 2.74110 | 0.103383 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.09355 | 0.0787918 | ||||||||
\(707\) | 33.7477 | 1.26921 | ||||||||
\(708\) | 21.7913 | 0.818967 | ||||||||
\(709\) | 22.1216 | 0.830794 | 0.415397 | − | 0.909640i | \(-0.363643\pi\) | ||||
0.415397 | + | 0.909640i | \(0.363643\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.7701 | −0.553922 | ||||||||
\(712\) | 4.54860 | 0.170466 | ||||||||
\(713\) | 3.87841 | 0.145248 | ||||||||
\(714\) | −1.73205 | −0.0648204 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 43.2867 | 1.61770 | ||||||||
\(717\) | 16.5975 | 0.619845 | ||||||||
\(718\) | −9.12159 | −0.340415 | ||||||||
\(719\) | 11.1652 | 0.416390 | 0.208195 | − | 0.978087i | \(-0.433241\pi\) | ||||
0.208195 | + | 0.978087i | \(0.433241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.6838 | −0.584096 | ||||||||
\(722\) | −7.30960 | −0.272035 | ||||||||
\(723\) | −2.64575 | −0.0983965 | ||||||||
\(724\) | 11.4955 | 0.427225 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.7913 | −0.771106 | −0.385553 | − | 0.922686i | \(-0.625989\pi\) | ||||
−0.385553 | + | 0.922686i | \(0.625989\pi\) | |||||||
\(728\) | −1.73205 | −0.0641941 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | 0.221918 | ||||||||
\(732\) | −12.7520 | −0.471328 | ||||||||
\(733\) | −0.532300 | −0.0196609 | −0.00983047 | − | 0.999952i | \(-0.503129\pi\) | ||||
−0.00983047 | + | 0.999952i | \(0.503129\pi\) | |||||||
\(734\) | −1.94265 | −0.0717046 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.72845 | −0.211154 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.41742 | −0.0521761 | ||||||||
\(739\) | −17.0743 | −0.628087 | −0.314043 | − | 0.949409i | \(-0.601684\pi\) | ||||
−0.314043 | + | 0.949409i | \(0.601684\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.791288 | −0.0290687 | ||||||||
\(742\) | −6.79129 | −0.249316 | ||||||||
\(743\) | 37.9343 | 1.39168 | 0.695838 | − | 0.718199i | \(-0.255033\pi\) | ||||
0.695838 | + | 0.718199i | \(0.255033\pi\) | |||||||
\(744\) | 5.55765 | 0.203753 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.295834 | 0.0108312 | ||||||||
\(747\) | 14.5040 | 0.530672 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.9564 | −0.948428 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.04356 | −0.293514 | −0.146757 | − | 0.989173i | \(-0.546883\pi\) | ||||
−0.146757 | + | 0.989173i | \(0.546883\pi\) | |||||||
\(752\) | −15.5826 | −0.568238 | ||||||||
\(753\) | 3.41742 | 0.124538 | ||||||||
\(754\) | −0.361500 | −0.0131651 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.92095 | 0.142604 | ||||||||
\(757\) | −54.2867 | −1.97309 | −0.986543 | − | 0.163504i | \(-0.947720\pi\) | ||||
−0.986543 | + | 0.163504i | \(0.947720\pi\) | |||||||
\(758\) | 4.85455 | 0.176325 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.1287 | −1.63591 | −0.817957 | − | 0.575280i | \(-0.804893\pi\) | ||||
−0.817957 | + | 0.575280i | \(0.804893\pi\) | |||||||
\(762\) | −6.04356 | −0.218935 | ||||||||
\(763\) | −24.9564 | −0.903484 | ||||||||
\(764\) | 17.2432 | 0.623836 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.12070 | 0.185019 | ||||||||
\(767\) | 5.55765 | 0.200675 | ||||||||
\(768\) | 1.79129 | 0.0646375 | ||||||||
\(769\) | −15.2469 | −0.549816 | −0.274908 | − | 0.961471i | \(-0.588647\pi\) | ||||
−0.274908 | + | 0.961471i | \(0.588647\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.7913 | −0.784794 | ||||||||
\(772\) | 2.93180 | 0.105518 | ||||||||
\(773\) | 5.37386 | 0.193284 | 0.0966422 | − | 0.995319i | \(-0.469190\pi\) | ||||
0.0966422 | + | 0.995319i | \(0.469190\pi\) | |||||||
\(774\) | 1.58258 | 0.0568845 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 23.5257 | 0.844524 | ||||||||
\(777\) | −3.46410 | −0.124274 | ||||||||
\(778\) | −13.1334 | −0.470855 | ||||||||
\(779\) | −5.37386 | −0.192539 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.956439 | −0.0342022 | ||||||||
\(783\) | 1.73205 | 0.0618984 | ||||||||
\(784\) | −6.16515 | −0.220184 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.582576 | 0.0207798 | ||||||||
\(787\) | −12.0290 | −0.428788 | −0.214394 | − | 0.976747i | \(-0.568778\pi\) | ||||
−0.214394 | + | 0.976747i | \(0.568778\pi\) | |||||||
\(788\) | 29.0834 | 1.03605 | ||||||||
\(789\) | −14.1425 | −0.503485 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.5257 | 0.836478 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.25227 | −0.115492 | ||||||||
\(794\) | 5.17625 | 0.183698 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.9129 | −0.634905 | ||||||||
\(797\) | 53.1652 | 1.88321 | 0.941603 | − | 0.336725i | \(-0.109319\pi\) | ||||
0.941603 | + | 0.336725i | \(0.109319\pi\) | |||||||
\(798\) | −1.73205 | −0.0613139 | ||||||||
\(799\) | −9.66930 | −0.342075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.62614 | −0.0927900 | ||||||||
\(802\) | −5.21605 | −0.184185 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 16.4174 | 0.578998 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.669697 | 0.0235891 | ||||||||
\(807\) | −9.95644 | −0.350483 | ||||||||
\(808\) | 26.7042 | 0.939449 | ||||||||
\(809\) | −20.5185 | −0.721391 | −0.360695 | − | 0.932684i | \(-0.617461\pi\) | ||||
−0.360695 | + | 0.932684i | \(0.617461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.18530 | −0.217195 | −0.108598 | − | 0.994086i | \(-0.534636\pi\) | ||||
−0.108598 | + | 0.994086i | \(0.534636\pi\) | |||||||
\(812\) | 6.79129 | 0.238327 | ||||||||
\(813\) | −8.48945 | −0.297738 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.83465 | 0.169247 | ||||||||
\(817\) | 6.00000 | 0.209913 | ||||||||
\(818\) | −9.74773 | −0.340821 | ||||||||
\(819\) | 1.00000 | 0.0349428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0308 | 0.350078 | 0.175039 | − | 0.984562i | \(-0.443995\pi\) | ||||
0.175039 | + | 0.984562i | \(0.443995\pi\) | |||||||
\(822\) | 0.190700 | 0.00665144 | ||||||||
\(823\) | −23.4174 | −0.816280 | −0.408140 | − | 0.912919i | \(-0.633822\pi\) | ||||
−0.408140 | + | 0.912919i | \(0.633822\pi\) | |||||||
\(824\) | −12.4104 | −0.432337 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.1652 | 0.423280 | ||||||||
\(827\) | −22.0598 | −0.767095 | −0.383547 | − | 0.923521i | \(-0.625298\pi\) | ||||
−0.383547 | + | 0.923521i | \(0.625298\pi\) | |||||||
\(828\) | 2.16515 | 0.0752442 | ||||||||
\(829\) | −3.87841 | −0.134703 | −0.0673514 | − | 0.997729i | \(-0.521455\pi\) | ||||
−0.0673514 | + | 0.997729i | \(0.521455\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.76465 | −0.338732 | ||||||||
\(832\) | 1.56125 | 0.0541266 | ||||||||
\(833\) | −3.82560 | −0.132549 | ||||||||
\(834\) | 3.04356 | 0.105390 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.20871 | −0.110909 | ||||||||
\(838\) | 1.27520 | 0.0440511 | ||||||||
\(839\) | −12.6261 | −0.435903 | −0.217951 | − | 0.975960i | \(-0.569937\pi\) | ||||
−0.217951 | + | 0.975960i | \(0.569937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | −5.40675 | −0.186329 | ||||||||
\(843\) | −14.6947 | −0.506111 | ||||||||
\(844\) | 28.2650 | 0.972922 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.55040 | −0.0876846 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 18.9564 | 0.650967 | ||||||||
\(849\) | −11.5722 | −0.397155 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.91288 | −0.0655726 | ||||||||
\(852\) | −28.2087 | −0.966415 | ||||||||
\(853\) | −33.6320 | −1.15154 | −0.575768 | − | 0.817613i | \(-0.695297\pi\) | ||||
−0.575768 | + | 0.817613i | \(0.695297\pi\) | |||||||
\(854\) | −7.11890 | −0.243604 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.5390 | −0.702009 | ||||||||
\(857\) | −18.3097 | −0.625446 | −0.312723 | − | 0.949844i | \(-0.601241\pi\) | ||||
−0.312723 | + | 0.949844i | \(0.601241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.7913 | 0.743509 | 0.371755 | − | 0.928331i | \(-0.378756\pi\) | ||||
0.371755 | + | 0.928331i | \(0.378756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.79129 | 0.231446 | ||||||||
\(862\) | −11.4083 | −0.388569 | ||||||||
\(863\) | 7.25227 | 0.246870 | 0.123435 | − | 0.992353i | \(-0.460609\pi\) | ||||
0.123435 | + | 0.992353i | \(0.460609\pi\) | |||||||
\(864\) | 4.73930 | 0.161234 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.7538 | 0.365429 | ||||||||
\(867\) | −14.0000 | −0.475465 | ||||||||
\(868\) | −12.5812 | −0.427034 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.18710 | 0.141875 | ||||||||
\(872\) | −19.7477 | −0.668742 | ||||||||
\(873\) | −13.5826 | −0.459701 | ||||||||
\(874\) | −0.956439 | −0.0323520 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.5022 | −0.557556 | ||||||||
\(877\) | −19.7955 | −0.668445 | −0.334223 | − | 0.942494i | \(-0.608474\pi\) | ||||
−0.334223 | + | 0.942494i | \(0.608474\pi\) | |||||||
\(878\) | 9.91288 | 0.334543 | ||||||||
\(879\) | −8.94630 | −0.301751 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.2432 | 1.22106 | 0.610532 | − | 0.791992i | \(-0.290956\pi\) | ||||
0.610532 | + | 0.791992i | \(0.290956\pi\) | |||||||
\(882\) | −1.00905 | −0.0339765 | ||||||||
\(883\) | 22.8693 | 0.769614 | 0.384807 | − | 0.922997i | \(-0.374268\pi\) | ||||
0.384807 | + | 0.922997i | \(0.374268\pi\) | |||||||
\(884\) | 1.41742 | 0.0476731 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.52870 | −0.152145 | ||||||||
\(887\) | −19.7756 | −0.663998 | −0.331999 | − | 0.943280i | \(-0.607723\pi\) | ||||
−0.331999 | + | 0.943280i | \(0.607723\pi\) | |||||||
\(888\) | −2.74110 | −0.0919853 | ||||||||
\(889\) | 28.9564 | 0.971168 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.86932 | 0.230002 | ||||||||
\(893\) | −9.66930 | −0.323571 | ||||||||
\(894\) | −4.12159 | −0.137847 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24.1652 | 0.807301 | ||||||||
\(897\) | 0.552200 | 0.0184374 | ||||||||
\(898\) | −9.74475 | −0.325187 | ||||||||
\(899\) | −5.55765 | −0.185358 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.7629 | 0.391878 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.58258 | −0.252332 | ||||||||
\(904\) | 18.6156 | 0.619146 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.41742 | 0.179982 | ||||||||
\(907\) | −29.2867 | −0.972450 | −0.486225 | − | 0.873834i | \(-0.661627\pi\) | ||||
−0.486225 | + | 0.873834i | \(0.661627\pi\) | |||||||
\(908\) | −29.5601 | −0.980987 | ||||||||
\(909\) | −15.4177 | −0.511371 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.8693 | 1.05588 | 0.527939 | − | 0.849282i | \(-0.322965\pi\) | ||||
0.527939 | + | 0.849282i | \(0.322965\pi\) | |||||||
\(912\) | 4.83465 | 0.160091 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −8.79129 | −0.290790 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 38.2867 | 1.26503 | ||||||||
\(917\) | −2.79129 | −0.0921764 | ||||||||
\(918\) | 0.791288 | 0.0261164 | ||||||||
\(919\) | 6.39590 | 0.210981 | 0.105491 | − | 0.994420i | \(-0.466359\pi\) | ||||
0.105491 | + | 0.994420i | \(0.466359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.3241 | −0.439044 | ||||||||
\(922\) | 4.79129 | 0.157793 | ||||||||
\(923\) | −7.19435 | −0.236805 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.6766 | −0.416577 | ||||||||
\(927\) | 7.16515 | 0.235334 | ||||||||
\(928\) | 8.20871 | 0.269464 | ||||||||
\(929\) | −32.2867 | −1.05929 | −0.529647 | − | 0.848218i | \(-0.677676\pi\) | ||||
−0.529647 | + | 0.848218i | \(0.677676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.82560 | −0.125379 | ||||||||
\(932\) | −14.8655 | −0.486934 | ||||||||
\(933\) | −0.208712 | −0.00683293 | ||||||||
\(934\) | 15.6084 | 0.510721 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.791288 | 0.0258641 | ||||||||
\(937\) | 58.5680 | 1.91333 | 0.956667 | − | 0.291184i | \(-0.0940492\pi\) | ||||
0.956667 | + | 0.291184i | \(0.0940492\pi\) | |||||||
\(938\) | 9.16515 | 0.299253 | ||||||||
\(939\) | −8.16515 | −0.266460 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.0659 | 1.72990 | 0.864950 | − | 0.501858i | \(-0.167350\pi\) | ||||
0.864950 | + | 0.501858i | \(0.167350\pi\) | |||||||
\(942\) | −3.53955 | −0.115325 | ||||||||
\(943\) | 3.75015 | 0.122122 | ||||||||
\(944\) | −33.9564 | −1.10519 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.7042 | 1.68016 | 0.840080 | − | 0.542463i | \(-0.182508\pi\) | ||||
0.840080 | + | 0.542463i | \(0.182508\pi\) | |||||||
\(948\) | 26.4575 | 0.859300 | ||||||||
\(949\) | −4.20871 | −0.136621 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.165151 | 0.00535540 | ||||||||
\(952\) | 6.56670 | 0.212828 | ||||||||
\(953\) | 30.6645 | 0.993321 | 0.496661 | − | 0.867945i | \(-0.334559\pi\) | ||||
0.496661 | + | 0.867945i | \(0.334559\pi\) | |||||||
\(954\) | 3.10260 | 0.100450 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −29.7309 | −0.961566 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.5826 | −0.568067 | ||||||||
\(959\) | −0.913701 | −0.0295049 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7042 | −0.667876 | ||||||||
\(962\) | −0.330303 | −0.0106494 | ||||||||
\(963\) | 11.8582 | 0.382125 | ||||||||
\(964\) | 4.73930 | 0.152643 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.20871 | 0.0388897 | ||||||||
\(967\) | 7.04345 | 0.226502 | 0.113251 | − | 0.993566i | \(-0.463874\pi\) | ||||
0.113251 | + | 0.993566i | \(0.463874\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.00000 | 0.0963739 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.1652 | −0.582947 | −0.291474 | − | 0.956579i | \(-0.594146\pi\) | ||||
−0.291474 | + | 0.956579i | \(0.594146\pi\) | |||||||
\(972\) | −1.79129 | −0.0574556 | ||||||||
\(973\) | −14.5826 | −0.467496 | ||||||||
\(974\) | −1.17985 | −0.0378048 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.8709 | 0.636052 | ||||||||
\(977\) | 21.7913 | 0.697165 | 0.348583 | − | 0.937278i | \(-0.386663\pi\) | ||||
0.348583 | + | 0.937278i | \(0.386663\pi\) | |||||||
\(978\) | 7.48040 | 0.239197 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.4014 | 0.364017 | ||||||||
\(982\) | 15.1996 | 0.485039 | ||||||||
\(983\) | 20.6606 | 0.658971 | 0.329485 | − | 0.944161i | \(-0.393125\pi\) | ||||
0.329485 | + | 0.944161i | \(0.393125\pi\) | |||||||
\(984\) | 5.37386 | 0.171313 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.37055 | 0.0436472 | ||||||||
\(987\) | 12.2197 | 0.388958 | ||||||||
\(988\) | 1.41742 | 0.0450943 | ||||||||
\(989\) | −4.18710 | −0.133142 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.62614 | −0.178720 | −0.0893601 | − | 0.995999i | \(-0.528482\pi\) | ||||
−0.0893601 | + | 0.995999i | \(0.528482\pi\) | |||||||
\(992\) | −15.2071 | −0.482825 | ||||||||
\(993\) | −28.4955 | −0.904276 | ||||||||
\(994\) | −15.7477 | −0.499488 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25.9808 | −0.823232 | ||||||||
\(997\) | −4.75920 | −0.150725 | −0.0753627 | − | 0.997156i | \(-0.524011\pi\) | ||||
−0.0753627 | + | 0.997156i | \(0.524011\pi\) | |||||||
\(998\) | −3.12250 | −0.0988411 | ||||||||
\(999\) | 1.58258 | 0.0500705 |
(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 | 9075.2.a.da.1.3 | yes | 4 | |
5.4 | even | 2 | 9075.2.a.ct.1.2 | ✓ | 4 | ||
11.10 | odd | 2 | inner | 9075.2.a.da.1.2 | yes | 4 | |
55.54 | odd | 2 | 9075.2.a.ct.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9075.2.a.ct.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
9075.2.a.ct.1.3 | yes | 4 | 55.54 | odd | 2 | ||
9075.2.a.da.1.2 | yes | 4 | 11.10 | odd | 2 | inner | |
9075.2.a.da.1.3 | yes | 4 | 1.1 | even | 1 | trivial |