Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,2,Mod(2,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([33, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.2");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.p (of order \(66\), degree \(20\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.60499308063\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{66}]$ |
Embedding invariants
Embedding label | 44.1 | ||
Root | \(-0.786053 - 0.618159i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.44 |
Dual form | 201.2.p.a.32.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{61}{66}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.971812 | − | 0.235759i | \(-0.0757576\pi\) | ||||
−0.971812 | + | 0.235759i | \(0.924242\pi\) | |||||||
\(3\) | −1.71442 | − | 0.246497i | −0.989821 | − | 0.142315i | ||||
\(4\) | 1.77767 | − | 0.916453i | 0.888835 | − | 0.458227i | ||||
\(5\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.50336 | − | 3.67422i | −1.32415 | − | 1.38872i | −0.866162 | − | 0.499763i | \(-0.833421\pi\) |
−0.457983 | − | 0.888961i | \(-0.651428\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.87848 | + | 0.845198i | 0.959493 | + | 0.281733i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.0950560 | − | 0.995472i | \(-0.469697\pi\) | ||||
−0.0950560 | + | 0.995472i | \(0.530303\pi\) | |||||||
\(12\) | −3.27358 | + | 1.13300i | −0.945001 | + | 0.327068i | ||||
\(13\) | 0.687743 | − | 3.56835i | 0.190745 | − | 0.989681i | −0.752753 | − | 0.658303i | \(-0.771274\pi\) |
0.943498 | − | 0.331378i | \(-0.107514\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.32023 | − | 3.25830i | 0.580057 | − | 0.814576i | ||||
\(17\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.65758 | − | 1.58050i | −0.380276 | − | 0.362593i | 0.475700 | − | 0.879607i | \(-0.342195\pi\) |
−0.855976 | + | 0.517015i | \(0.827043\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.10055 | + | 7.16272i | 1.11303 | + | 1.56303i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.27430 | − | 3.77875i | 0.654861 | − | 0.755750i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.72659 | − | 2.15856i | −0.909632 | − | 0.415415i | ||||
\(28\) | −9.59507 | − | 3.32089i | −1.81330 | − | 0.627588i | ||||
\(29\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.88589 | + | 9.78494i | 0.338716 | + | 1.75743i | 0.607589 | + | 0.794252i | \(0.292137\pi\) |
−0.268872 | + | 0.963176i | \(0.586651\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.89157 | − | 1.13551i | 0.981929 | − | 0.189251i | ||||
\(37\) | 5.89230 | + | 10.2058i | 0.968688 | + | 1.67782i | 0.699363 | + | 0.714767i | \(0.253467\pi\) |
0.269325 | + | 0.963049i | \(0.413199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.05867 | + | 5.94812i | −0.329650 | + | 0.952462i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.24962 | + | 3.50047i | 0.343063 | + | 0.533817i | 0.969321 | − | 0.245800i | \(-0.0790505\pi\) |
−0.626258 | + | 0.779616i | \(0.715414\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(48\) | −4.78101 | + | 5.01418i | −0.690079 | + | 0.723734i | ||||
\(49\) | −0.893274 | + | 18.7521i | −0.127611 | + | 2.67888i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.04764 | − | 6.97363i | −0.283957 | − | 0.967069i | ||||
\(53\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.45221 | + | 3.11824i | 0.324803 | + | 0.413021i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.34031 | − | 14.0363i | −0.171609 | − | 1.79717i | −0.514188 | − | 0.857677i | \(-0.671907\pi\) |
0.342580 | − | 0.939489i | \(-0.388699\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.97891 | − | 13.5372i | −0.879259 | − | 1.70553i | ||||
\(64\) | 1.13852 | − | 7.91857i | 0.142315 | − | 0.989821i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.25333 | − | 6.99351i | −0.519627 | − | 0.854393i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.46168 | − | 0.521527i | 0.639242 | − | 0.0610402i | 0.229598 | − | 0.973286i | \(-0.426259\pi\) |
0.409644 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.54498 | + | 5.67126i | −0.755750 | + | 0.654861i | ||||
\(76\) | −4.39510 | − | 1.29052i | −0.504152 | − | 0.148032i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.3567 | − | 5.31502i | 1.72777 | − | 0.597986i | 0.731307 | − | 0.682048i | \(-0.238911\pi\) |
0.996461 | + | 0.0840621i | \(0.0267894\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.57128 | + | 4.86577i | 0.841254 | + | 0.540641i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(84\) | 15.6314 | + | 8.05855i | 1.70553 | + | 0.879259i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.5203 | + | 9.97429i | −1.62697 | + | 1.04559i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.821260 | − | 17.2404i | −0.0851607 | − | 1.78774i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.6466 | + | 9.03356i | −1.58867 | + | 0.917219i | −0.595143 | + | 0.803620i | \(0.702905\pi\) |
−0.993527 | + | 0.113599i | \(0.963762\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.35759 | − | 9.71812i | 0.235759 | − | 0.971812i | ||||
\(101\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.8014 | − | 3.81640i | 1.95109 | − | 0.376042i | 0.953998 | − | 0.299812i | \(-0.0969239\pi\) |
0.997090 | − | 0.0762298i | \(-0.0242882\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(108\) | −10.3805 | + | 0.494486i | −0.998867 | + | 0.0475819i | ||||
\(109\) | 7.88028 | + | 6.82830i | 0.754794 | + | 0.654033i | 0.944762 | − | 0.327758i | \(-0.106293\pi\) |
−0.189968 | + | 0.981790i | \(0.560838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.58619 | − | 18.9494i | −0.720050 | − | 1.79860i | ||||
\(112\) | −20.1003 | + | 2.88999i | −1.89930 | + | 0.273078i | ||||
\(113\) | 0 | 0 | 0.814576 | − | 0.580057i | \(-0.196970\pi\) | ||||
−0.814576 | + | 0.580057i | \(0.803030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.99561 | − | 9.69013i | 0.461844 | − | 0.895853i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8012 | − | 2.08176i | −0.981929 | − | 0.189251i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.3199 | + | 15.6661i | 1.10636 | + | 1.40686i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8418 | − | 11.2911i | 1.05079 | − | 1.00193i | 0.0507955 | − | 0.998709i | \(-0.483824\pi\) |
0.999995 | − | 0.00321749i | \(-0.00102416\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.99393 | − | 6.55580i | −0.263601 | − | 0.577206i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.6274i | 1.00822i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.21749 | + | 4.20949i | −0.781817 | + | 0.357044i | −0.766008 | − | 0.642831i | \(-0.777760\pi\) |
−0.0158092 | + | 0.999875i | \(0.505032\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 9.43264 | − | 7.41791i | 0.786053 | − | 0.618159i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.15379 | − | 31.9289i | 0.507556 | − | 2.63345i | ||||
\(148\) | 19.8277 | + | 12.7425i | 1.62982 | + | 1.04742i | ||||
\(149\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.58800 | − | 2.88081i | −0.454745 | − | 0.234437i | 0.215608 | − | 0.976480i | \(-0.430827\pi\) |
−0.670352 | + | 0.742043i | \(0.733857\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.79155 | + | 12.4605i | 0.143438 | + | 0.997636i | ||||
\(157\) | −7.03443 | + | 2.81616i | −0.561409 | + | 0.224754i | −0.634970 | − | 0.772537i | \(-0.718988\pi\) |
0.0735617 | + | 0.997291i | \(0.476563\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00036 | + | 3.46472i | −0.156680 | + | 0.271378i | −0.933670 | − | 0.358136i | \(-0.883413\pi\) |
0.776989 | + | 0.629514i | \(0.216746\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.191328 | − | 0.0765960i | −0.0147175 | − | 0.00589200i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.43549 | − | 5.95043i | −0.262718 | − | 0.455041i | ||||
\(172\) | 7.20709 | + | 4.16102i | 0.549536 | + | 0.317275i | ||||
\(173\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −25.3550 | + | 1.20781i | −1.91666 | + | 0.0913017i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.9975 | − | 16.5126i | −1.56073 | − | 1.22737i | −0.854599 | − | 0.519288i | \(-0.826197\pi\) |
−0.706129 | − | 0.708083i | \(-0.749560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.16205 | + | 24.3945i | −0.0859016 | + | 1.80330i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.62791 | + | 24.9287i | 0.627588 | + | 1.81330i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(192\) | −3.90380 | + | 13.2951i | −0.281733 | + | 0.959493i | ||||
\(193\) | 17.3277 | + | 19.9972i | 1.24727 | + | 1.43943i | 0.854216 | + | 0.519918i | \(0.174037\pi\) |
0.393058 | + | 0.919514i | \(0.371417\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.5975 | + | 34.1538i | 1.11411 | + | 2.43956i | ||||
\(197\) | 0 | 0 | −0.458227 | − | 0.888835i | \(-0.651515\pi\) | ||||
0.458227 | + | 0.888835i | \(0.348485\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.12987 | + | 4.65738i | 0.0800942 | + | 0.330153i | 0.997736 | − | 0.0672563i | \(-0.0214245\pi\) |
−0.917642 | + | 0.397409i | \(0.869909\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.56813 | + | 13.0382i | 0.392745 | + | 0.919647i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.0310 | − | 10.5203i | −0.695527 | − | 0.729448i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.8217 | + | 17.9472i | −1.57111 | + | 1.23554i | −0.763589 | + | 0.645703i | \(0.776565\pi\) |
−0.807524 | + | 0.589834i | \(0.799193\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 29.3450 | − | 41.2094i | 1.99207 | − | 2.79747i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.49218 | − | 0.452168i | −0.641422 | − | 0.0305547i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.14969 | + | 21.9066i | 0.210919 | + | 1.46697i | 0.770097 | + | 0.637927i | \(0.220208\pi\) |
−0.559178 | + | 0.829048i | \(0.688883\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.6188 | − | 8.10961i | 0.841254 | − | 0.540641i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(228\) | 7.21694 | + | 3.29587i | 0.477954 | + | 0.218274i | ||||
\(229\) | 23.2211 | + | 8.03689i | 1.53449 | + | 0.531093i | 0.958187 | − | 0.286143i | \(-0.0923732\pi\) |
0.576304 | + | 0.817235i | \(0.304494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.371662 | − | 0.928368i | \(-0.378788\pi\) | ||||
−0.371662 | + | 0.928368i | \(0.621212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.6380 | + | 5.32680i | −1.79528 | + | 0.346013i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.88943 | − | 17.2754i | 0.508203 | − | 1.11281i | −0.465512 | − | 0.885041i | \(-0.654130\pi\) |
0.973715 | − | 0.227768i | \(-0.0731428\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.7810 | − | 10.2083i | −0.755750 | − | 0.654861i | ||||
\(244\) | −15.2462 | − | 23.7236i | −0.976041 | − | 1.51875i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.77978 | + | 4.82786i | −0.431387 | + | 0.307189i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
−0.458227 | + | 0.888835i | \(0.651515\pi\) | |||||||
\(252\) | −24.8124 | − | 17.6688i | −1.56303 | − | 1.11303i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.23309 | − | 15.1200i | −0.327068 | − | 0.945001i | ||||
\(257\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.8553 | − | 57.4040i | 1.04734 | − | 3.56691i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.9702 | − | 8.53418i | −0.853369 | − | 0.521308i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.9757 | + | 4.45363i | 1.88164 | + | 0.270539i | 0.985042 | − | 0.172313i | \(-0.0551240\pi\) |
0.896595 | + | 0.442851i | \(0.146033\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 29.0669 | − | 13.2744i | 1.75921 | − | 0.803405i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0353 | − | 3.82752i | −0.783218 | − | 0.229974i | −0.134410 | − | 0.990926i | \(-0.542914\pi\) |
−0.648808 | + | 0.760952i | \(0.724732\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.84171 | + | 29.7597i | −0.170129 | + | 1.78167i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.8251 | + | 6.40842i | −1.29737 | + | 0.380941i | −0.856274 | − | 0.516522i | \(-0.827227\pi\) |
−0.441091 | + | 0.897462i | \(0.645408\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.86097 | + | 13.8478i | 0.580057 | + | 0.814576i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.0516 | − | 11.6305i | 1.70303 | − | 0.681792i | ||||
\(292\) | 9.23112 | − | 5.93248i | 0.540210 | − | 0.347172i | ||||
\(293\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −6.43738 | + | 16.0798i | −0.371662 | + | 0.928368i | ||||
\(301\) | 4.98028 | − | 20.5290i | 0.287058 | − | 1.18327i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.99574 | + | 1.73379i | −0.515941 | + | 0.0994395i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.93642 | + | 28.7094i | −0.567101 | + | 1.63853i | 0.187437 | + | 0.982277i | \(0.439982\pi\) |
−0.754539 | + | 0.656255i | \(0.772139\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.8886 | + | 1.66195i | −1.98475 | + | 0.0945451i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.1846 | + | 2.90210i | −1.14090 | + | 0.164037i | −0.686753 | − | 0.726891i | \(-0.740965\pi\) |
−0.454146 | + | 0.890927i | \(0.650056\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.4283 | − | 23.5221i | 1.26169 | − | 1.32322i | ||||
\(317\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 17.9185 | + | 1.71101i | 0.995472 | + | 0.0950560i | ||||
\(325\) | −11.2320 | − | 14.2827i | −0.623040 | − | 0.792259i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.8270 | − | 13.6490i | −0.654033 | − | 0.754794i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.82554 | + | 5.48078i | 0.155306 | + | 0.301251i | 0.953633 | − | 0.300973i | \(-0.0973116\pi\) |
−0.798327 | + | 0.602224i | \(0.794281\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.33497 | + | 34.3572i | 0.456754 | + | 1.88276i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 35.1728 | 1.91883 | ||||||||
\(337\) | −35.6286 | + | 8.64340i | −1.94081 | + | 0.470836i | −0.957730 | + | 0.287668i | \(0.907120\pi\) |
−0.983082 | + | 0.183168i | \(0.941365\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 45.1716 | − | 39.1414i | 2.43904 | − | 2.11344i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.945001 | − | 0.327068i | \(-0.106061\pi\) | ||||
−0.945001 | + | 0.327068i | \(0.893939\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.6340 | − | 18.4020i | −1.53274 | − | 0.985034i | −0.989350 | − | 0.145556i | \(-0.953503\pi\) |
−0.543394 | − | 0.839478i | \(-0.682861\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.9532 | + | 15.3816i | −0.584637 | + | 0.821007i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.998867 | − | 0.0475819i | \(-0.984848\pi\) | ||||
0.998867 | + | 0.0475819i | \(0.0151515\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.654462 | − | 13.7388i | −0.0344453 | − | 0.723097i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.0047 | + | 6.23148i | 0.945001 | + | 0.327068i | ||||
\(364\) | −18.4490 | + | 31.9546i | −0.966991 | + | 1.67488i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.23551 | − | 18.0734i | 0.377691 | − | 0.943426i | −0.610751 | − | 0.791823i | \(-0.709132\pi\) |
0.988441 | − | 0.151603i | \(-0.0484435\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −17.2599 | − | 29.8951i | −0.894886 | − | 1.54999i | ||||
\(373\) | 33.3959 | + | 19.2811i | 1.72917 | + | 0.998338i | 0.893400 | + | 0.449262i | \(0.148313\pi\) |
0.835773 | + | 0.549076i | \(0.185020\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.22836 | − | 15.5577i | −0.319929 | − | 0.799145i | −0.997944 | − | 0.0640964i | \(-0.979583\pi\) |
0.678014 | − | 0.735049i | \(-0.262841\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.0851 | + | 16.4388i | −1.18268 | + | 0.842185i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.690079 | − | 0.723734i | \(-0.257576\pi\) | ||||
−0.690079 | + | 0.723734i | \(0.742424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.51688 | + | 11.9774i | 0.178773 | + | 0.608845i | ||||
\(388\) | −19.5356 | + | 30.3981i | −0.991772 | + | 1.54323i | ||||
\(389\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.29651 | + | 20.3565i | 0.466579 | + | 1.02166i | 0.985938 | + | 0.167109i | \(0.0534431\pi\) |
−0.519360 | + | 0.854556i | \(0.673830\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.86611 | − | 19.9343i | 0.143485 | − | 0.997961i | ||||
\(400\) | −4.71518 | − | 19.4362i | −0.235759 | − | 0.971812i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.2131 | 1.80390 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.8255 | + | 29.1825i | 1.37588 | + | 1.44298i | 0.744869 | + | 0.667211i | \(0.232512\pi\) |
0.631013 | + | 0.775772i | \(0.282639\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 31.7028 | − | 24.9314i | 1.56188 | − | 1.22828i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.8403 | − | 4.94475i | 0.824672 | − | 0.242146i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.8996 | − | 27.5557i | −1.40848 | − | 1.34298i | −0.863323 | − | 0.504652i | \(-0.831621\pi\) |
−0.545159 | − | 0.838333i | \(-0.683531\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −46.8769 | + | 54.0988i | −2.26853 | + | 2.61803i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | −18.0000 | + | 10.3923i | −0.866025 | + | 0.500000i | ||||
\(433\) | −5.43786 | − | 28.2143i | −0.261327 | − | 1.35589i | −0.840996 | − | 0.541041i | \(-0.818030\pi\) |
0.579669 | − | 0.814852i | \(-0.303182\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.2664 | + | 4.91657i | 0.970583 | + | 0.235461i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.5867 | + | 33.9252i | 0.934824 | + | 1.61916i | 0.774947 | + | 0.632026i | \(0.217776\pi\) |
0.159877 | + | 0.987137i | \(0.448890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.4205 | + | 53.2226i | −0.877168 | + | 2.53441i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(444\) | −30.8520 | − | 26.7334i | −1.46417 | − | 1.26871i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −33.0832 | + | 23.5584i | −1.56303 | + | 1.11303i | ||||
\(449\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.87007 | + | 6.31635i | 0.416752 | + | 0.296768i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.01518 | − | 20.2690i | −0.328156 | − | 0.948146i | −0.981563 | − | 0.191139i | \(-0.938782\pi\) |
0.653407 | − | 0.757007i | \(-0.273339\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.01101 | + | 42.0052i | 0.186407 | + | 1.95215i | 0.288769 | + | 0.957399i | \(0.406754\pi\) |
−0.102362 | + | 0.994747i | \(0.532640\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(468\) | − | 21.8041i | − | 1.00790i | ||||||
\(469\) | −10.7947 | + | 40.1284i | −0.498454 | + | 1.85296i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.7541 | − | 3.09412i | 0.587680 | − | 0.142570i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.3998 | + | 1.08855i | −0.523057 | + | 0.0499459i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.4701 | − | 14.0068i | 1.84528 | − | 0.638656i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.1088 | + | 6.19812i | −0.959493 | + | 0.281733i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.0636 | + | 0.812840i | 0.773226 | + | 0.0368333i | 0.430486 | − | 0.902597i | \(-0.358342\pi\) |
0.342739 | + | 0.939430i | \(0.388645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.28350 | − | 5.44691i | 0.193707 | − | 0.246318i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.2580 | + | 16.5585i | 1.62803 | + | 0.743498i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.26271 | + | 1.88372i | −0.146059 | + | 0.0843271i | −0.571248 | − | 0.820777i | \(-0.693541\pi\) |
0.425190 | + | 0.905104i | \(0.360207\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.309135 | + | 0.178479i | 0.0137292 | + | 0.00792655i | ||||
\(508\) | 10.7030 | − | 30.9244i | 0.474870 | − | 1.37205i | ||||
\(509\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.0504 | − | 18.2403i | −0.931217 | − | 0.806904i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.42311 | + | 11.0484i | 0.195285 | + | 0.487798i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.3303 | − | 8.91026i | −0.498789 | − | 0.392252i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.92085 | − | 0.948415i | −0.215174 | − | 0.0414713i | 0.0805251 | − | 0.996753i | \(-0.474340\pi\) |
−0.295699 | + | 0.955281i | \(0.595552\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 43.7669 | + | 4.17923i | 1.91014 | + | 0.182397i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.6459 | − | 15.8718i | 0.723734 | − | 0.690079i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.6560 | + | 20.6697i | 0.461995 | + | 0.896145i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.7751 | + | 11.3144i | −1.06517 | + | 0.486445i | −0.869351 | − | 0.494195i | \(-0.835463\pi\) |
−0.195816 | + | 0.980641i | \(0.562736\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.9282 | + | 33.4853i | 1.37017 | + | 1.43699i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.306466 | − | 3.20945i | 0.0131035 | − | 0.137226i | −0.986553 | − | 0.163443i | \(-0.947740\pi\) |
0.999656 | + | 0.0262168i | \(0.00834602\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.00542 | − | 41.5361i | 0.341663 | − | 1.77272i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −73.3287 | − | 37.8036i | −3.11825 | − | 1.60757i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.5279 | + | 15.9305i | −0.531300 | + | 0.675603i | ||||
\(557\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.0380 | − | 5.61999i | 0.593746 | − | 0.237700i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.64703 | − | 44.8651i | −0.363141 | − | 1.88416i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.1677 | − | 5.67190i | −0.592901 | − | 0.237362i | 0.0557537 | − | 0.998445i | \(-0.482244\pi\) |
−0.648655 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.96996 | − | 21.8312i | 0.415415 | − | 0.909632i | ||||
\(577\) | −29.3997 | + | 1.40048i | −1.22392 | + | 0.0583027i | −0.649568 | − | 0.760303i | \(-0.725050\pi\) |
−0.574355 | + | 0.818606i | \(0.694747\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.7777 | − | 38.5549i | −1.02973 | − | 1.60229i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.814576 | − | 0.580057i | \(-0.803030\pi\) | ||||
0.814576 | + | 0.580057i | \(0.196970\pi\) | |||||||
\(588\) | −18.3219 | − | 62.3987i | −0.755583 | − | 2.57328i | ||||
\(589\) | 12.3391 | − | 19.2000i | 0.508424 | − | 0.791124i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 46.9249 | + | 4.48079i | 1.92860 | + | 0.184159i | ||||
\(593\) | 0 | 0 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.789042 | − | 8.26322i | −0.0322933 | − | 0.338191i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.458227 | − | 0.888835i | \(-0.651515\pi\) | ||||
0.458227 | + | 0.888835i | \(0.348485\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.03356 | + | 28.9927i | 0.286905 | + | 1.18264i | 0.914659 | + | 0.404226i | \(0.132459\pi\) |
−0.627754 | + | 0.778411i | \(0.716026\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.33223 | − | 23.7256i | −0.257868 | − | 0.966180i | ||||
\(604\) | −12.5737 | −0.511619 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.7079 | − | 17.8932i | 1.40875 | − | 0.726261i | 0.424897 | − | 0.905242i | \(-0.360310\pi\) |
0.983853 | + | 0.178981i | \(0.0572799\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.7044 | + | 29.6510i | −1.52286 | + | 1.19759i | −0.607930 | + | 0.793990i | \(0.708000\pi\) |
−0.914934 | + | 0.403603i | \(0.867758\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.3767 | + | 22.9979i | −0.658237 | + | 0.924364i | −0.999880 | − | 0.0154656i | \(-0.995077\pi\) |
0.341644 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 14.6042 | + | 20.5088i | 0.584637 | + | 0.821007i | ||||
\(625\) | −3.55787 | − | 24.7455i | −0.142315 | − | 0.989821i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.92402 | + | 11.4529i | −0.396012 | + | 0.457022i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.8957 | − | 13.1158i | −1.50860 | − | 0.522132i | −0.557279 | − | 0.830326i | \(-0.688154\pi\) |
−0.951324 | + | 0.308193i | \(0.900276\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 43.5500 | − | 25.1436i | 1.73096 | − | 0.999368i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 66.2998 | + | 16.0842i | 2.62689 | + | 0.637277i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.97674 | − | 15.2769i | 0.275136 | − | 0.602463i | −0.720738 | − | 0.693207i | \(-0.756197\pi\) |
0.995874 | + | 0.0907437i | \(0.0289244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.371662 | − | 0.928368i | \(-0.621212\pi\) | ||||
0.371662 | + | 0.928368i | \(0.378788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −60.4677 | + | 63.4167i | −2.36992 | + | 2.48550i | ||||
\(652\) | −0.380724 | + | 7.99238i | −0.0149103 | + | 0.313006i | ||||
\(653\) | 0 | 0 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
−0.458227 | + | 0.888835i | \(0.651515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.1621 | + | 3.11500i | 0.630545 | + | 0.121528i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.76889 | + | 12.8357i | −0.146593 | + | 0.499250i | −0.999749 | − | 0.0224061i | \(-0.992867\pi\) |
0.853156 | + | 0.521656i | \(0.174685\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 38.3335i | − | 1.48206i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.94884 | + | 1.28665i | 0.344952 | + | 0.0495967i | 0.312614 | − | 0.949880i | \(-0.398795\pi\) |
0.0323386 | + | 0.999477i | \(0.489705\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.6329 | + | 10.7928i | −0.909632 | + | 0.415415i | ||||
\(676\) | −0.410314 | + | 0.0391803i | −0.0157813 | + | 0.00150693i | ||||
\(677\) | 0 | 0 | −0.690079 | − | 0.723734i | \(-0.742424\pi\) | ||||
0.690079 | + | 0.723734i | \(0.257576\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 88.0069 | + | 25.8411i | 3.37739 | + | 0.991692i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(684\) | −11.5605 | − | 7.42945i | −0.442025 | − | 0.284072i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −37.8296 | − | 19.5025i | −1.44329 | − | 0.744068i | ||||
\(688\) | 16.6252 | + | 0.791957i | 0.633830 | + | 0.0301931i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.8176 | + | 36.2558i | 0.982149 | + | 1.37924i | 0.924620 | + | 0.380891i | \(0.124383\pi\) |
0.0575291 | + | 0.998344i | \(0.481678\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −43.9660 | + | 25.3838i | −1.66176 | + | 0.959416i | ||||
\(701\) | 0 | 0 | −0.189251 | − | 0.981929i | \(-0.560606\pi\) | ||||
0.189251 | + | 0.981929i | \(0.439394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.36326 | − | 26.2297i | 0.239995 | − | 0.989272i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.7245 | − | 48.3223i | 0.628103 | − | 1.81478i | 0.0501074 | − | 0.998744i | \(-0.484044\pi\) |
0.577995 | − | 0.816040i | \(-0.303835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 48.6963 | − | 2.31969i | 1.82625 | − | 0.0869952i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −83.3937 | − | 59.3844i | −3.10574 | − | 2.21159i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.7841 | + | 27.6727i | −0.661399 | + | 1.02916i | ||||
\(724\) | −52.4596 | − | 10.1108i | −1.94964 | − | 0.375763i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.2512 | + | 33.3811i | 0.973602 | + | 1.23804i | 0.971256 | + | 0.238039i | \(0.0765045\pi\) |
0.00234654 | + | 0.999997i | \(0.499253\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.6812 | + | 20.4052i | 0.654861 | + | 0.755750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 20.2907 | + | 44.4304i | 0.749966 | + | 1.64220i | ||||
\(733\) | −2.68340 | − | 5.20507i | −0.0991137 | − | 0.192254i | 0.834065 | − | 0.551666i | \(-0.186008\pi\) |
−0.933179 | + | 0.359412i | \(0.882977\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.9341 | + | 4.35077i | −0.659717 | + | 0.160046i | −0.551621 | − | 0.834095i | \(-0.685990\pi\) |
−0.108096 | + | 0.994140i | \(0.534475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.8134 | − | 6.60579i | 0.470714 | − | 0.242670i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.9231 | − | 18.5878i | −1.05542 | − | 0.678278i | −0.106667 | − | 0.994295i | \(-0.534018\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 38.1836 | + | 36.4080i | 1.38872 | + | 1.32415i | ||||
\(757\) | −31.3711 | + | 39.8916i | −1.14020 | + | 1.44989i | −0.266231 | + | 0.963909i | \(0.585778\pi\) |
−0.873972 | + | 0.485977i | \(0.838464\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.51879 | − | 52.8759i | −0.0911862 | − | 1.91423i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 5.24468 | + | 27.2120i | 0.189251 | + | 0.981929i | ||||
\(769\) | −7.43992 | + | 18.5840i | −0.268290 | + | 0.670157i | −0.999934 | − | 0.0115309i | \(-0.996330\pi\) |
0.731643 | + | 0.681688i | \(0.238754\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 49.1294 | + | 19.6685i | 1.76821 | + | 0.707883i | ||||
\(773\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.1498 | + | 24.9126i | 1.54999 | + | 0.894886i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −43.0470 | + | 94.2599i | −1.54430 | + | 3.38155i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 59.0276 | + | 46.4198i | 2.10813 | + | 1.65785i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.4325 | − | 39.6336i | 0.728341 | − | 1.41279i | −0.175309 | − | 0.984514i | \(-0.556092\pi\) |
0.903650 | − | 0.428272i | \(-0.140877\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51.0082 | − | 4.87070i | −1.81136 | − | 0.172963i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.27680 | + | 7.24382i | 0.222475 | + | 0.256750i | ||||
\(797\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 21.8472 | + | 18.0748i | 0.770493 | + | 0.637449i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.271593 | − | 0.284838i | −0.00953690 | − | 0.0100020i | 0.718948 | − | 0.695064i | \(-0.244624\pi\) |
−0.728485 | + | 0.685062i | \(0.759775\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −52.0075 | − | 15.2708i | −1.82398 | − | 0.535570i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.80358 | − | 9.35785i | 0.0630992 | − | 0.327390i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −53.1051 | + | 15.5931i | −1.85564 | + | 0.544866i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.18233 | − | 7.80184i | −0.285218 | − | 0.271955i | 0.533940 | − | 0.845522i | \(-0.320711\pi\) |
−0.819159 | + | 0.573567i | \(0.805559\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.1698 | − | 42.8962i | 1.29096 | − | 1.48985i | 0.518022 | − | 0.855367i | \(-0.326668\pi\) |
0.772939 | − | 0.634481i | \(-0.218786\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.4046 | + | 9.77515i | 0.742517 | + | 0.339096i | ||||
\(832\) | −27.4732 | − | 9.50857i | −0.952462 | − | 0.329650i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.2075 | − | 50.3202i | 0.421955 | − | 1.73932i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | − | 25.1147i | −0.500000 | − | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.1218 | + | 52.8193i | −0.830305 | + | 1.81811i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.1917 | + | 46.9792i | 1.03740 | + | 1.61422i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 38.9970 | − | 5.60692i | 1.33837 | − | 0.192429i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.21415 | − | 25.4882i | 0.0415718 | − | 0.872699i | −0.877732 | − | 0.479151i | \(-0.840945\pi\) |
0.919304 | − | 0.393548i | \(-0.128752\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.637099 | + | 1.84078i | 0.0217376 | + | 0.0628065i | 0.955348 | − | 0.295484i | \(-0.0954809\pi\) |
−0.933610 | + | 0.358291i | \(0.883360\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.4924 | − | 26.1716i | −0.458227 | − | 0.888835i | ||||
\(868\) | 14.3994 | − | 100.150i | 0.488747 | − | 3.39931i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.8805 | + | 10.3676i | −0.944693 | + | 0.351294i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −52.6735 | + | 12.7785i | −1.78273 | + | 0.432485i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.2884 | + | 7.89533i | −0.584120 | + | 0.266758i | ||||
\(877\) | 8.81998 | − | 0.842206i | 0.297829 | − | 0.0284393i | 0.0549283 | − | 0.998490i | \(-0.482507\pi\) |
0.242901 | + | 0.970051i | \(0.421901\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.4030 | − | 5.33103i | 0.518352 | − | 0.179403i | −0.0553507 | − | 0.998467i | \(-0.517628\pi\) |
0.573703 | + | 0.819064i | \(0.305506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −82.9722 | − | 3.95245i | −2.78280 | − | 0.132561i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.6755 | + | 36.0562i | 0.859679 | + | 1.20725i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 15.0000 | − | 25.9808i | 0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.5986 | + | 33.9677i | −0.452534 | + | 1.13037i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.9072 | − | 4.60773i | 0.793824 | − | 0.152997i | 0.223811 | − | 0.974633i | \(-0.428150\pi\) |
0.570013 | + | 0.821635i | \(0.306938\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(912\) | 15.8499 | − | 0.755022i | 0.524841 | − | 0.0250013i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 48.6448 | − | 6.99407i | 1.60727 | − | 0.231091i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.5788 | + | 43.6066i | −1.37156 | + | 1.43845i | −0.605110 | + | 0.796142i | \(0.706871\pi\) |
−0.766448 | + | 0.642307i | \(0.777978\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.1120 | − | 46.7707i | 0.794517 | − | 1.54115i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 57.8582 | + | 11.1512i | 1.90236 | + | 0.366651i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 60.2235 | + | 5.75065i | 1.97800 | + | 0.188876i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.1185 | − | 29.6714i | 1.01987 | − | 0.972442i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.6078i | 0.934576i | 0.884105 | + | 0.467288i | \(0.154769\pi\) | ||||
−0.884105 | + | 0.467288i | \(0.845231\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.3202 | 1.15263 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(948\) | −44.2496 | + | 34.7983i | −1.43716 | + | 1.13019i | ||||
\(949\) | 1.89524 | − | 19.8479i | 0.0615221 | − | 0.644289i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −63.4091 | + | 25.3852i | −2.04545 | + | 0.818877i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.80732 | − | 37.9403i | −0.0582099 | − | 1.22198i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.2272 | − | 35.0346i | 0.650464 | − | 1.12664i | −0.332547 | − | 0.943087i | \(-0.607908\pi\) |
0.983010 | − | 0.183550i | \(-0.0587588\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(972\) | −30.2981 | − | 7.35024i | −0.971812 | − | 0.235759i | ||||
\(973\) | 47.7587 | + | 19.1197i | 1.53107 | + | 0.612950i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.7358 | + | 27.2551i | 0.503948 | + | 0.872863i | ||||
\(976\) | −48.8444 | − | 28.2003i | −1.56347 | − | 0.902670i | ||||
\(977\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.9120 | + | 26.3155i | 0.539957 | + | 0.840190i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.62771 | + | 14.7957i | −0.242670 | + | 0.470714i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.5245 | + | 17.9324i | −0.366086 | + | 0.569642i | −0.974614 | − | 0.223891i | \(-0.928124\pi\) |
0.608528 | + | 0.793533i | \(0.291760\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.49317 | − | 10.0929i | −0.110852 | − | 0.320287i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.4855 | − | 45.5687i | −1.25052 | − | 1.44317i | −0.849912 | − | 0.526924i | \(-0.823345\pi\) |
−0.400606 | − | 0.916251i | \(-0.631200\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.82071 | − | 60.9573i | −0.184159 | − | 1.92860i |
(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 | 201.2.p.a.44.1 | yes | 20 | |
3.2 | odd | 2 | CM | 201.2.p.a.44.1 | yes | 20 | |
67.32 | odd | 66 | inner | 201.2.p.a.32.1 | ✓ | 20 | |
201.32 | even | 66 | inner | 201.2.p.a.32.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.2.p.a.32.1 | ✓ | 20 | 67.32 | odd | 66 | inner | |
201.2.p.a.32.1 | ✓ | 20 | 201.32 | even | 66 | inner | |
201.2.p.a.44.1 | yes | 20 | 1.1 | even | 1 | trivial | |
201.2.p.a.44.1 | yes | 20 | 3.2 | odd | 2 | CM |