Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 110x^{6} - 154x^{5} - 282x^{4} + 256x^{3} + 253x^{2} - 126x - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.73395\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73395 | 1.00110 | 0.500549 | − | 0.865708i | \(-0.333132\pi\) | ||||
0.500549 | + | 0.865708i | \(0.333132\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.41343 | 1.52653 | 0.763266 | − | 0.646085i | \(-0.223595\pi\) | ||||
0.763266 | + | 0.646085i | \(0.223595\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.00658743 | 0.00219581 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.67665 | 0.505530 | 0.252765 | − | 0.967528i | \(-0.418660\pi\) | ||||
0.252765 | + | 0.967528i | \(0.418660\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.13889 | −1.70262 | −0.851311 | − | 0.524661i | \(-0.824192\pi\) | ||||
−0.851311 | + | 0.524661i | \(0.824192\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.91872 | 1.52821 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.78979 | −0.919159 | −0.459580 | − | 0.888137i | \(-0.652000\pi\) | ||||
−0.459580 | + | 0.888137i | \(0.652000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.86873 | −0.887547 | −0.443774 | − | 0.896139i | \(-0.646361\pi\) | ||||
−0.443774 | + | 0.896139i | \(0.646361\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.49935 | −1.14669 | −0.573347 | − | 0.819312i | \(-0.694355\pi\) | ||||
−0.573347 | + | 0.819312i | \(0.694355\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65149 | 1.33030 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19043 | −0.998899 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.172699 | −0.0320695 | −0.0160347 | − | 0.999871i | \(-0.505104\pi\) | ||||
−0.0160347 | + | 0.999871i | \(0.505104\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.15470 | −1.28502 | −0.642511 | − | 0.766276i | \(-0.722107\pi\) | ||||
−0.642511 | + | 0.766276i | \(0.722107\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.90724 | 0.506085 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.80199 | −0.789443 | −0.394721 | − | 0.918801i | \(-0.629159\pi\) | ||||
−0.394721 | + | 0.918801i | \(0.629159\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.6445 | −1.70449 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.845176 | 0.128888 | 0.0644441 | − | 0.997921i | \(-0.479473\pi\) | ||||
0.0644441 | + | 0.997921i | \(0.479473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0224857 | 0.00335197 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.65792 | −0.679428 | −0.339714 | − | 0.940529i | \(-0.610330\pi\) | ||||
−0.339714 | + | 0.940529i | \(0.610330\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.57131 | −0.920168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.46567 | 0.613407 | 0.306703 | − | 0.951805i | \(-0.400774\pi\) | ||||
0.306703 | + | 0.951805i | \(0.400774\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.72314 | 0.771708 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.70819 | −0.888521 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.38395 | 0.440553 | 0.220276 | − | 0.975437i | \(-0.429304\pi\) | ||||
0.220276 | + | 0.975437i | \(0.429304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.643064 | −0.0823359 | −0.0411679 | − | 0.999152i | \(-0.513108\pi\) | ||||
−0.0411679 | + | 0.999152i | \(0.513108\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −20.9547 | −2.59911 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.25183 | −0.275105 | −0.137553 | − | 0.990494i | \(-0.543924\pi\) | ||||
−0.137553 | + | 0.990494i | \(0.543924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.53561 | −1.14795 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.77826 | −0.567076 | −0.283538 | − | 0.958961i | \(-0.591508\pi\) | ||||
−0.283538 | + | 0.958961i | \(0.591508\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.42378 | −1.10297 | −0.551485 | − | 0.834185i | \(-0.685939\pi\) | ||||
−0.551485 | + | 0.834185i | \(0.685939\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.5334 | 1.33176 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.64751 | 0.410377 | 0.205189 | − | 0.978722i | \(-0.434219\pi\) | ||||
0.205189 | + | 0.978722i | \(0.434219\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.01972 | −1.00219 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.7027 | 1.39430 | 0.697149 | − | 0.716926i | \(-0.254452\pi\) | ||||
0.697149 | + | 0.716926i | \(0.254452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.9362 | −1.40313 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.299452 | −0.0321046 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.83667 | −0.724685 | −0.362343 | − | 0.932045i | \(-0.618023\pi\) | ||||
−0.362343 | + | 0.932045i | \(0.618023\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.4059 | −1.28643 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.2056 | −1.35487 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.615292 | 0.0624734 | 0.0312367 | − | 0.999512i | \(-0.490055\pi\) | ||||
0.0312367 | + | 0.999512i | \(0.490055\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0110448 | 0.00111005 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.55350 | 0.652098 | 0.326049 | − | 0.945353i | \(-0.394283\pi\) | ||||
0.326049 | + | 0.945353i | \(0.394283\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.40980 | 0.927175 | 0.463588 | − | 0.886051i | \(-0.346562\pi\) | ||||
0.463588 | + | 0.886051i | \(0.346562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.66303 | 0.354119 | 0.177059 | − | 0.984200i | \(-0.443342\pi\) | ||||
0.177059 | + | 0.984200i | \(0.443342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1194 | 0.969263 | 0.484632 | − | 0.874718i | \(-0.338954\pi\) | ||||
0.484632 | + | 0.874718i | \(0.338954\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.32642 | −0.790309 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.0216 | −1.03683 | −0.518413 | − | 0.855131i | \(-0.673477\pi\) | ||||
−0.518413 | + | 0.855131i | \(0.673477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.7717 | −1.75047 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0404395 | −0.00373863 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.18883 | −0.744439 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.73395 | −0.156345 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.63724 | 0.504210 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1077 | 1.34059 | 0.670296 | − | 0.742094i | \(-0.266167\pi\) | ||||
0.670296 | + | 0.742094i | \(0.266167\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.46549 | 0.129030 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.99133 | −0.523465 | −0.261732 | − | 0.965140i | \(-0.584294\pi\) | ||||
−0.261732 | + | 0.965140i | \(0.584294\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.7172 | −1.52485 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.1656 | −1.03938 | −0.519688 | − | 0.854356i | \(-0.673952\pi\) | ||||
−0.519688 | + | 0.854356i | \(0.673952\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.02141 | 0.425910 | 0.212955 | − | 0.977062i | \(-0.431691\pi\) | ||||
0.212955 | + | 0.977062i | \(0.431691\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.07661 | −0.680173 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.2928 | −0.860728 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.589497 | −0.0489550 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.7546 | 0.881055 | 0.440528 | − | 0.897739i | \(-0.354791\pi\) | ||||
0.440528 | + | 0.897739i | \(0.354791\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.3236 | −1.16564 | −0.582818 | − | 0.812602i | \(-0.698050\pi\) | ||||
−0.582818 | + | 0.812602i | \(0.698050\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0249650 | −0.00201830 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.4221 | −1.96163 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9304 | 1.35119 | 0.675596 | − | 0.737272i | \(-0.263886\pi\) | ||||
0.675596 | + | 0.737272i | \(0.263886\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.74325 | 0.614080 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.72220 | −0.448197 | −0.224099 | − | 0.974566i | \(-0.571944\pi\) | ||||
−0.224099 | + | 0.974566i | \(0.571944\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.92365 | 0.772555 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.3051 | −0.874812 | −0.437406 | − | 0.899264i | \(-0.644103\pi\) | ||||
−0.437406 | + | 0.899264i | \(0.644103\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.6860 | 1.89892 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0254850 | −0.00194888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.4786 | 1.48093 | 0.740465 | − | 0.672095i | \(-0.234605\pi\) | ||||
0.740465 | + | 0.672095i | \(0.234605\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.86761 | 0.441036 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.59474 | 0.119197 | 0.0595983 | − | 0.998222i | \(-0.481018\pi\) | ||||
0.0595983 | + | 0.998222i | \(0.481018\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.25966 | −0.539607 | −0.269803 | − | 0.962915i | \(-0.586959\pi\) | ||||
−0.269803 | + | 0.962915i | \(0.586959\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.11504 | −0.0824262 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.3913 | −1.20511 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.35417 | −0.464663 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.7348 | 1.71739 | 0.858694 | − | 0.512488i | \(-0.171276\pi\) | ||||
0.858694 | + | 0.512488i | \(0.171276\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.2501 | 1.45763 | 0.728817 | − | 0.684709i | \(-0.240071\pi\) | ||||
0.728817 | + | 0.684709i | \(0.240071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −36.3344 | −2.60196 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.4401 | −1.17131 | −0.585654 | − | 0.810561i | \(-0.699162\pi\) | ||||
−0.585654 | + | 0.810561i | \(0.699162\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.2785 | 0.941291 | 0.470646 | − | 0.882322i | \(-0.344021\pi\) | ||||
0.470646 | + | 0.882322i | \(0.344021\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.90457 | −0.275407 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.41343 | −0.238404 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0362266 | −0.00251792 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.48652 | −0.448682 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.73436 | 0.119398 | 0.0596991 | − | 0.998216i | \(-0.480986\pi\) | ||||
0.0596991 | + | 0.998216i | \(0.480986\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.28528 | −0.567698 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.88495 | 0.196752 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.3404 | −1.10418 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.2651 | 1.56498 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.4764 | −1.77299 | −0.886496 | − | 0.462737i | \(-0.846868\pi\) | ||||
−0.886496 | + | 0.462737i | \(0.846868\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0438162 | 0.00292108 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.7320 | −1.11054 | −0.555271 | − | 0.831669i | \(-0.687386\pi\) | ||||
−0.555271 | + | 0.831669i | \(0.687386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.74483 | −0.445711 | −0.222855 | − | 0.974852i | \(-0.571538\pi\) | ||||
−0.222855 | + | 0.974852i | \(0.571538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7713 | 0.967697 | 0.483849 | − | 0.875152i | \(-0.339239\pi\) | ||||
0.483849 | + | 0.875152i | \(0.339239\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.8995 | −1.03717 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.32461 | 0.410828 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.2994 | −1.05432 | −0.527161 | − | 0.849766i | \(-0.676743\pi\) | ||||
−0.527161 | + | 0.849766i | \(0.676743\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.34464 | −0.537526 | −0.268763 | − | 0.963206i | \(-0.586615\pi\) | ||||
−0.268763 | + | 0.963206i | \(0.586615\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.0684584 | −0.00439161 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.7497 | 1.51116 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.0258 | 1.39583 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.21866 | 0.140041 | 0.0700204 | − | 0.997546i | \(-0.477694\pi\) | ||||
0.0700204 | + | 0.997546i | \(0.477694\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.22052 | −0.579689 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −22.4307 | −1.40467 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.4944 | 1.52792 | 0.763961 | − | 0.645263i | \(-0.223252\pi\) | ||||
0.763961 | + | 0.645263i | \(0.223252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.00113764 | −7.04184e−5 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.53312 | −0.464512 | −0.232256 | − | 0.972655i | \(-0.574611\pi\) | ||||
−0.232256 | + | 0.972655i | \(0.574611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.2432 | 0.936385 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.8544 | −0.725480 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.0410 | −1.34386 | −0.671931 | − | 0.740614i | \(-0.734535\pi\) | ||||
−0.671931 | + | 0.740614i | \(0.734535\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.4621 | 1.30373 | 0.651864 | − | 0.758336i | \(-0.273987\pi\) | ||||
0.651864 | + | 0.758336i | \(0.273987\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.1523 | 0.672506 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.7745 | 1.90915 | 0.954573 | − | 0.297977i | \(-0.0963119\pi\) | ||||
0.954573 | + | 0.297977i | \(0.0963119\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.0471311 | −0.00282166 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.66405 | −0.337889 | −0.168944 | − | 0.985626i | \(-0.554036\pi\) | ||||
−0.168944 | + | 0.985626i | \(0.554036\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.1824 | −1.31860 | −0.659302 | − | 0.751878i | \(-0.729148\pi\) | ||||
−0.659302 | + | 0.751878i | \(0.729148\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.8979 | −1.35636 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.63748 | −0.155146 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.06689 | 0.0625419 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.662844 | 0.0387238 | 0.0193619 | − | 0.999813i | \(-0.493837\pi\) | ||||
0.0193619 | + | 0.999813i | \(0.493837\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.5509 | 0.672518 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.70256 | −0.504974 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 33.7599 | 1.95239 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.3635 | 0.652813 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.19505 | −0.125688 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.6945 | −0.667438 | −0.333719 | − | 0.942673i | \(-0.608304\pi\) | ||||
−0.333719 | + | 0.942673i | \(0.608304\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.3161 | 0.928193 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.1939 | 0.578044 | 0.289022 | − | 0.957322i | \(-0.406670\pi\) | ||||
0.289022 | + | 0.957322i | \(0.406670\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.90892 | −0.220945 | −0.110473 | − | 0.993879i | \(-0.535236\pi\) | ||||
−0.110473 | + | 0.993879i | \(0.535236\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.2084 | 1.07885 | 0.539427 | − | 0.842033i | \(-0.318641\pi\) | ||||
0.539427 | + | 0.842033i | \(0.318641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.289557 | −0.0162121 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.35152 | 0.354507 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.6617 | 0.815798 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −40.8328 | −2.26500 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.5466 | 0.970327 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.3104 | 1.39119 | 0.695594 | − | 0.718435i | \(-0.255141\pi\) | ||||
0.695594 | + | 0.718435i | \(0.255141\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0316328 | −0.00173346 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.68647 | −0.419957 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.5103 | 1.87990 | 0.939948 | − | 0.341319i | \(-0.110873\pi\) | ||||
0.939948 | + | 0.341319i | \(0.110873\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.1109 | −1.03796 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.9960 | −0.649618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −32.5491 | −1.75239 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.5932 | 1.05182 | 0.525910 | − | 0.850540i | \(-0.323725\pi\) | ||||
0.525910 | + | 0.850540i | \(0.323725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.0415 | −1.44750 | −0.723750 | − | 0.690063i | \(-0.757583\pi\) | ||||
−0.723750 | + | 0.690063i | \(0.757583\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 31.8635 | 1.70075 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.6917 | −1.52711 | −0.763553 | − | 0.645745i | \(-0.776547\pi\) | ||||
−0.763553 | + | 0.645745i | \(0.776547\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.3103 | −0.865659 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.4429 | −1.50116 | −0.750578 | − | 0.660782i | \(-0.770225\pi\) | ||||
−0.750578 | + | 0.660782i | \(0.770225\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.03293 | −0.212260 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.1990 | −0.745256 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.1674 | −1.68372 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.2393 | 1.42188 | 0.710939 | − | 0.703254i | \(-0.248270\pi\) | ||||
0.710939 | + | 0.703254i | \(0.248270\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.00658743 | −0.000342928 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0603 | 0.624461 | 0.312230 | − | 0.950006i | \(-0.398924\pi\) | ||||
0.312230 | + | 0.950006i | \(0.398924\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.77471 | 0.504764 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.06018 | 0.0546022 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8577 | 1.48232 | 0.741160 | − | 0.671329i | \(-0.234276\pi\) | ||||
0.741160 | + | 0.671329i | \(0.234276\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.1960 | 1.34206 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.6206 | 0.695982 | 0.347991 | − | 0.937498i | \(-0.386864\pi\) | ||||
0.347991 | + | 0.937498i | \(0.386864\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.00556753 | 0.000283014 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.1436 | −0.615704 | −0.307852 | − | 0.951434i | \(-0.599610\pi\) | ||||
−0.307852 | + | 0.951434i | \(0.599610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.8414 | 1.05400 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.3887 | −0.524039 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.4505 | 0.626454 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.1841 | 1.21376 | 0.606882 | − | 0.794792i | \(-0.292420\pi\) | ||||
0.606882 | + | 0.794792i | \(0.292420\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.87866 | −0.343504 | −0.171752 | − | 0.985140i | \(-0.554943\pi\) | ||||
−0.171752 | + | 0.985140i | \(0.554943\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 43.9220 | 2.18791 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −30.7882 | −1.52988 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.05128 | −0.399087 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.83930 | −0.437075 | −0.218538 | − | 0.975829i | \(-0.570129\pi\) | ||||
−0.218538 | + | 0.975829i | \(0.570129\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.0945 | −1.04052 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 43.3596 | 2.12844 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.70687 | 0.426377 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.1974 | −0.889000 | −0.444500 | − | 0.895779i | \(-0.646619\pi\) | ||||
−0.444500 | + | 0.895779i | \(0.646619\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7003 | −0.667711 | −0.333856 | − | 0.942624i | \(-0.608350\pi\) | ||||
−0.333856 | + | 0.942624i | \(0.608350\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.0306837 | −0.00149189 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.2078 | −1.22276 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.8472 | −0.861672 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.1190 | −1.40261 | −0.701307 | − | 0.712859i | \(-0.747400\pi\) | ||||
−0.701307 | + | 0.712859i | \(0.747400\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.49135 | −0.263897 | −0.131949 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131949 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.02216 | −0.0490087 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.2755 | 1.01775 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.58453 | 0.409717 | 0.204859 | − | 0.978792i | \(-0.434327\pi\) | ||||
0.204859 | + | 0.978792i | \(0.434327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.1993 | 1.57734 | 0.788672 | − | 0.614814i | \(-0.210769\pi\) | ||||
0.788672 | + | 0.614814i | \(0.210769\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.3365 | −1.10625 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.6480 | 0.882022 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.3746 | 0.819960 | 0.409980 | − | 0.912094i | \(-0.365536\pi\) | ||||
0.409980 | + | 0.912094i | \(0.365536\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.67665 | −0.0789506 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.8364 | −1.16692 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.33864 | −0.343287 | −0.171644 | − | 0.985159i | \(-0.554908\pi\) | ||||
−0.171644 | + | 0.985159i | \(0.554908\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.6707 | 0.918148 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.46073 | −0.114608 | −0.0573038 | − | 0.998357i | \(-0.518250\pi\) | ||||
−0.0573038 | + | 0.998357i | \(0.518250\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.1206 | −1.63219 | −0.816097 | − | 0.577915i | \(-0.803866\pi\) | ||||
−0.816097 | + | 0.577915i | \(0.803866\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −42.3467 | −1.96378 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.4411 | −0.529433 | −0.264716 | − | 0.964326i | \(-0.585278\pi\) | ||||
−0.264716 | + | 0.964326i | \(0.585278\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.3565 | 1.35268 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.41707 | 0.0651569 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.7328 | −1.18070 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.0294173 | 0.00134692 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.8860 | 0.588778 | 0.294389 | − | 0.955686i | \(-0.404884\pi\) | ||||
0.294389 | + | 0.955686i | \(0.404884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.4789 | 1.34412 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.10025 | 0.0953676 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.5691 | −1.33990 | −0.669952 | − | 0.742405i | \(-0.733685\pi\) | ||||
−0.669952 | + | 0.742405i | \(0.733685\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.92201 | −0.448689 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.3180 | −1.27797 | −0.638986 | − | 0.769218i | \(-0.720646\pi\) | ||||
−0.638986 | + | 0.769218i | \(0.720646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.654494 | 0.0294769 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0377008 | 0.00169452 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.71814 | −0.435044 | −0.217522 | − | 0.976055i | \(-0.569797\pi\) | ||||
−0.217522 | + | 0.976055i | \(0.569797\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.6024 | −0.875772 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.2237 | −1.21385 | −0.606923 | − | 0.794760i | \(-0.707597\pi\) | ||||
−0.606923 | + | 0.794760i | \(0.707597\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.3699 | 0.995448 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 42.8043 | 1.90101 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.2038 | −1.51606 | −0.758028 | − | 0.652222i | \(-0.773837\pi\) | ||||
−0.758028 | + | 0.652222i | \(0.773837\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.0804 | 0.886570 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.1197 | 1.41536 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.80973 | −0.343471 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 33.7749 | 1.48255 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.2153 | −1.63043 | −0.815216 | − | 0.579157i | \(-0.803382\pi\) | ||||
−0.815216 | + | 0.579157i | \(0.803382\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.9891 | 0.480519 | 0.240259 | − | 0.970709i | \(-0.422767\pi\) | ||||
0.240259 | + | 0.970709i | \(0.422767\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.1148 | 1.18114 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.24290 | 0.314909 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0222915 | 0.000967370 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.13889 | 0.265905 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5035 | 0.540573 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.76520 | 0.119327 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.7378 | −0.547643 | −0.273821 | − | 0.961781i | \(-0.588288\pi\) | ||||
−0.273821 | + | 0.961781i | \(0.588288\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.5879 | −0.540199 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34.5419 | 1.47961 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0176 | 0.684865 | 0.342432 | − | 0.939542i | \(-0.388749\pi\) | ||||
0.342432 | + | 0.939542i | \(0.388749\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.00423614 | −0.000180794 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.668127 | 0.0284632 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −28.4216 | −1.20643 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.0799 | −1.65587 | −0.827935 | − | 0.560824i | \(-0.810484\pi\) | ||||
−0.827935 | + | 0.560824i | \(0.810484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.18845 | −0.219448 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0178 | −0.465173 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.1641 | 1.22912 | 0.614561 | − | 0.788869i | \(-0.289333\pi\) | ||||
0.614561 | + | 0.788869i | \(0.289333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.6215 | −1.58275 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.6973 | −0.448453 | −0.224226 | − | 0.974537i | \(-0.571986\pi\) | ||||
−0.224226 | + | 0.974537i | \(0.571986\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.67889 | −0.279503 | −0.139751 | − | 0.990187i | \(-0.544630\pi\) | ||||
−0.139751 | + | 0.990187i | \(0.544630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 41.1550 | 1.71927 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −36.5789 | −1.52545 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.7440 | −0.905213 | −0.452607 | − | 0.891710i | \(-0.649506\pi\) | ||||
−0.452607 | + | 0.891710i | \(0.649506\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.1127 | 1.45923 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.48739 | 0.310096 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.138037 | −0.00570714 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.7691 | 1.26998 | 0.634988 | − | 0.772522i | \(-0.281005\pi\) | ||||
0.634988 | + | 0.772522i | \(0.281005\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.6796 | 1.14052 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.5063 | −1.17259 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.2968 | 1.12095 | 0.560473 | − | 0.828173i | \(-0.310619\pi\) | ||||
0.560473 | + | 0.828173i | \(0.310619\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.0244 | 0.942324 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.15083 | −0.128739 | −0.0643697 | − | 0.997926i | \(-0.520504\pi\) | ||||
−0.0643697 | + | 0.997926i | \(0.520504\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.4377 | −1.73107 | −0.865534 | − | 0.500850i | \(-0.833021\pi\) | ||||
−0.865534 | + | 0.500850i | \(0.833021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0148338 | −0.000604079 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.9520 | −1.13641 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.1857 | 1.26579 | 0.632894 | − | 0.774239i | \(-0.281867\pi\) | ||||
0.632894 | + | 0.774239i | \(0.281867\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.5945 | 1.15681 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.9343 | 1.49176 | 0.745880 | − | 0.666080i | \(-0.232029\pi\) | ||||
0.745880 | + | 0.666080i | \(0.232029\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.91872 | −0.238666 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.8487 | −0.638045 | −0.319023 | − | 0.947747i | \(-0.603355\pi\) | ||||
−0.319023 | + | 0.947747i | \(0.603355\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.2914 | 0.936159 | 0.468080 | − | 0.883686i | \(-0.344946\pi\) | ||||
0.468080 | + | 0.883686i | \(0.344946\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.5440 | 1.14543 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.0151 | −0.560605 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.2473 | −0.449175 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.1985 | 0.725624 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.4445 | 0.694453 | 0.347227 | − | 0.937781i | \(-0.387123\pi\) | ||||
0.347227 | + | 0.937781i | \(0.387123\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.00730 | 0.119529 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 51.5690 | 2.04646 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0314765 | −0.00124519 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.8551 | −1.13971 | −0.569855 | − | 0.821746i | \(-0.693000\pi\) | ||||
−0.569855 | + | 0.821746i | \(0.693000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.4989 | −0.690090 | −0.345045 | − | 0.938586i | \(-0.612136\pi\) | ||||
−0.345045 | + | 0.938586i | \(0.612136\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.00236 | 0.196968 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.7880 | −0.895887 | −0.447944 | − | 0.894062i | \(-0.647843\pi\) | ||||
−0.447944 | + | 0.894062i | \(0.647843\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.67372 | 0.222713 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.1360 | 1.68804 | 0.844021 | − | 0.536311i | \(-0.180182\pi\) | ||||
0.844021 | + | 0.536311i | \(0.180182\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.4510 | −0.799086 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.0620785 | −0.00242191 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.9211 | 0.425424 | 0.212712 | − | 0.977115i | \(-0.431770\pi\) | ||||
0.212712 | + | 0.977115i | \(0.431770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.4575 | 1.10687 | 0.553434 | − | 0.832893i | \(-0.313317\pi\) | ||||
0.553434 | + | 0.832893i | \(0.313317\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 40.3406 | 1.56670 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.949735 | 0.0367739 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −45.9088 | −1.77494 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.07820 | −0.0416233 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.3470 | −1.43962 | −0.719810 | − | 0.694171i | \(-0.755771\pi\) | ||||
−0.719810 | + | 0.694171i | \(0.755771\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −34.5241 | −1.32883 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.5079 | −0.749748 | −0.374874 | − | 0.927076i | \(-0.622314\pi\) | ||||
−0.374874 | + | 0.927076i | \(0.622314\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.0125 | −1.11176 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −46.3804 | −1.77469 | −0.887347 | − | 0.461101i | \(-0.847454\pi\) | ||||
−0.887347 | + | 0.461101i | \(0.847454\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41.5264 | −1.58664 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.6952 | −0.446200 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.4143 | −1.04440 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.07303 | 0.154945 | 0.0774726 | − | 0.996994i | \(-0.475315\pi\) | ||||
0.0774726 | + | 0.996994i | \(0.475315\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.1402 | 0.650165 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.78979 | 0.143549 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.6126 | 0.968759 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.2407 | 1.78426 | 0.892128 | − | 0.451783i | \(-0.149212\pi\) | ||||
0.892128 | + | 0.451783i | \(0.149212\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5776 | 0.700668 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.5689 | −1.03831 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.8445 | −0.595053 | −0.297526 | − | 0.954714i | \(-0.596162\pi\) | ||||
−0.297526 | + | 0.954714i | \(0.596162\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0240277 | 0.000901110 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.3462 | 1.47353 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35.1337 | −1.31393 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.2624 | −1.05548 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.2097 | −1.72333 | −0.861665 | − | 0.507478i | \(-0.830578\pi\) | ||||
−0.861665 | + | 0.507478i | \(0.830578\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.4692 | −0.538115 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.14871 | −0.0426619 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.2962 | 1.71703 | 0.858515 | − | 0.512788i | \(-0.171387\pi\) | ||||
0.858515 | + | 0.512788i | \(0.171387\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9405 | 0.997795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.20304 | −0.118469 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.3823 | −0.531222 | −0.265611 | − | 0.964080i | \(-0.585574\pi\) | ||||
−0.265611 | + | 0.964080i | \(0.585574\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.77555 | −0.139074 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.1656 | −0.852161 | −0.426080 | − | 0.904685i | \(-0.640106\pi\) | ||||
−0.426080 | + | 0.904685i | \(0.640106\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 41.1808 | 1.51282 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.59555 | 0.315340 | 0.157670 | − | 0.987492i | \(-0.449602\pi\) | ||||
0.157670 | + | 0.987492i | \(0.449602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.7102 | 1.34496 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0836778 | 0.00306161 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.6291 | 1.26363 | 0.631817 | − | 0.775118i | \(-0.282310\pi\) | ||||
0.631817 | + | 0.775118i | \(0.282310\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.84706 | 0.140194 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −48.8925 | −1.77938 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.3458 | 1.28467 | 0.642333 | − | 0.766426i | \(-0.277967\pi\) | ||||
0.642333 | + | 0.766426i | \(0.277967\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.9879 | −0.580325 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.9971 | −0.833645 | −0.416823 | − | 0.908988i | \(-0.636856\pi\) | ||||
−0.416823 | + | 0.908988i | \(0.636856\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0852161 | −0.00308100 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.7737 | −0.750095 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.5231 | −0.559776 | −0.279888 | − | 0.960033i | \(-0.590297\pi\) | ||||
−0.279888 | + | 0.960033i | \(0.590297\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.4722 | 1.52960 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.7953 | −1.46731 | −0.733653 | − | 0.679524i | \(-0.762186\pi\) | ||||
−0.733653 | + | 0.679524i | \(0.762186\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.5894 | −1.70946 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.86873 | 0.138612 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.01150 | −0.286674 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.896384 | 0.0320341 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 57.7907 | 2.06264 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.2880 | −0.509313 | −0.254656 | − | 0.967032i | \(-0.581962\pi\) | ||||
−0.254656 | + | 0.967032i | \(0.581962\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.0621 | −0.465022 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.94770 | 0.140187 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 26.4310 | 0.937412 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.9428 | −1.59196 | −0.795978 | − | 0.605326i | \(-0.793043\pi\) | ||||
−0.795978 | + | 0.605326i | \(0.793043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.6526 | 0.624502 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0450360 | −0.00159127 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.8004 | −0.557585 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.2180 | −1.34534 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.8169 | −1.78663 | −0.893314 | − | 0.449432i | \(-0.851626\pi\) | ||||
−0.893314 | + | 0.449432i | \(0.851626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.6587 | −0.830769 | −0.415385 | − | 0.909646i | \(-0.636353\pi\) | ||||
−0.415385 | + | 0.909646i | \(0.636353\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.2142 | 1.30516 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.5323 | −0.684187 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.26976 | −0.114394 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.0297 | −1.01314 | −0.506572 | − | 0.862198i | \(-0.669087\pi\) | ||||
−0.506572 | + | 0.862198i | \(0.669087\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.7149 | −1.87238 | −0.936192 | − | 0.351488i | \(-0.885676\pi\) | ||||
−0.936192 | + | 0.351488i | \(0.885676\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19.3375 | 0.673244 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.55779 | 0.228037 | 0.114018 | − | 0.993479i | \(-0.463628\pi\) | ||||
0.114018 | + | 0.993479i | \(0.463628\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.1994 | −1.84769 | −0.923847 | − | 0.382763i | \(-0.874973\pi\) | ||||
−0.923847 | + | 0.382763i | \(0.874973\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 55.0955 | 1.91124 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.5890 | −1.33543 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37.1360 | 1.28361 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.3780 | −0.772574 | −0.386287 | − | 0.922379i | \(-0.626242\pi\) | ||||
−0.386287 | + | 0.922379i | \(0.626242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9702 | −0.998972 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.82119 | −0.338260 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 84.2639 | 2.89877 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38.4631 | −1.32005 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.4079 | 0.905250 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.5227 | −1.04508 | −0.522539 | − | 0.852615i | \(-0.675015\pi\) | ||||
−0.522539 | + | 0.852615i | \(0.675015\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0869911 | −0.00297503 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.8325 | 1.42897 | 0.714485 | − | 0.699651i | \(-0.246661\pi\) | ||||
0.714485 | + | 0.699651i | \(0.246661\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.8918 | −0.678699 | −0.339349 | − | 0.940660i | \(-0.610207\pi\) | ||||
−0.339349 | + | 0.940660i | \(0.610207\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.48686 | 0.0506134 | 0.0253067 | − | 0.999680i | \(-0.491944\pi\) | ||||
0.0253067 | + | 0.999680i | \(0.491944\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 66.4888 | 2.26069 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.57326 | −0.155316 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.11562 | 0.207458 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.8238 | 0.468400 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.00405319 | 0.000137180 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.8377 | −1.51406 | −0.757032 | − | 0.653378i | \(-0.773351\pi\) | ||||
−0.757032 | + | 0.653378i | \(0.773351\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.14934 | 0.0387663 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.5372 | −1.46681 | −0.733404 | − | 0.679794i | \(-0.762069\pi\) | ||||
−0.733404 | + | 0.679794i | \(0.762069\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.769970 | 0.0259116 | 0.0129558 | − | 0.999916i | \(-0.495876\pi\) | ||||
0.0129558 | + | 0.999916i | \(0.495876\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.0287 | 0.673256 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9096 | 0.567770 | 0.283885 | − | 0.958858i | \(-0.408377\pi\) | ||||
0.283885 | + | 0.958858i | \(0.408377\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.1230 | −0.506638 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.0202 | 0.603024 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.44354 | 0.181957 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 58.5381 | 1.95453 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.23561 | 0.0412100 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.9240 | −0.563819 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.7803 | −0.823726 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.6035 | 1.84628 | 0.923142 | − | 0.384459i | \(-0.125612\pi\) | ||||
0.923142 | + | 0.384459i | \(0.125612\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.0431707 | 0.00143188 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.1374 | 0.534655 | 0.267327 | − | 0.963606i | \(-0.413859\pi\) | ||||
0.267327 | + | 0.963606i | \(0.413859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.2980 | 0.704860 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.80611 | −0.125826 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.8317 | 0.918082 | 0.459041 | − | 0.888415i | \(-0.348193\pi\) | ||||
0.459041 | + | 0.888415i | \(0.348193\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.2776 | −0.668171 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.3333 | 0.965516 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31.9404 | −1.05019 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0619864 | 0.00203590 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.1727 | −0.924315 | −0.462157 | − | 0.886798i | \(-0.652925\pi\) | ||||
−0.462157 | + | 0.886798i | \(0.652925\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.6757 | 0.578678 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.6895 | −0.709323 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.3030 | −1.02262 | −0.511312 | − | 0.859395i | \(-0.670840\pi\) | ||||
−0.511312 | + | 0.859395i | \(0.670840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.77787 | −0.221187 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55.2328 | −1.80054 | −0.900270 | − | 0.435333i | \(-0.856631\pi\) | ||||
−0.900270 | + | 0.435333i | \(0.856631\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.49935 | 0.179084 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.7591 | −0.512101 | −0.256050 | − | 0.966663i | \(-0.582421\pi\) | ||||
−0.256050 | + | 0.966663i | \(0.582421\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.8516 | 1.87794 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.3065 | 1.08004 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49.2694 | −1.59599 | −0.797996 | − | 0.602662i | \(-0.794107\pi\) | ||||
−0.797996 | + | 0.602662i | \(0.794107\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 81.0170 | 2.62165 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.502078 | −0.0162299 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.1898 | 0.651283 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0241299 | 0.000777576 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 69.1223 | 2.22512 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.6867 | −0.826030 | −0.413015 | − | 0.910724i | \(-0.635524\pi\) | ||||
−0.413015 | + | 0.910724i | \(0.635524\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.4226 | 0.816693 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.0629 | 0.932672 | 0.466336 | − | 0.884608i | \(-0.345574\pi\) | ||||
0.466336 | + | 0.884608i | \(0.345574\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −70.8021 | −2.26748 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.0637 | 0.417946 | 0.208973 | − | 0.977921i | \(-0.432988\pi\) | ||||
0.208973 | + | 0.977921i | \(0.432988\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.4627 | −0.366350 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0666608 | 0.00212832 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.4830 | 0.940361 | 0.470180 | − | 0.882570i | \(-0.344189\pi\) | ||||
0.470180 | + | 0.882570i | \(0.344189\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −56.1171 | −1.78804 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.64792 | −0.147795 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.9953 | −1.17520 | −0.587598 | − | 0.809153i | \(-0.699926\pi\) | ||||
−0.587598 | + | 0.809153i | \(0.699926\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.8871 | 1.39271 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 45.3254 | 1.43691 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.6514 | −0.685707 | −0.342854 | − | 0.939389i | \(-0.611394\pi\) | ||||
−0.342854 | + | 0.939389i | \(0.611394\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.9244 | 0.788573 |
(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 | 8036.2.a.o.1.8 | ✓ | 10 | |
7.6 | odd | 2 | 8036.2.a.p.1.3 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.o.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8036.2.a.p.1.3 | yes | 10 | 7.6 | odd | 2 |