Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
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: | \( x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.58984\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58984 | −1.12419 | −0.562095 | − | 0.827073i | \(-0.690004\pi\) | ||||
−0.562095 | + | 0.827073i | \(0.690004\pi\) | |||||||
\(3\) | 1.33784 | 0.772404 | 0.386202 | − | 0.922414i | \(-0.373787\pi\) | ||||
0.386202 | + | 0.922414i | \(0.373787\pi\) | |||||||
\(4\) | 0.527606 | 0.263803 | ||||||||
\(5\) | 0.921074 | 0.411917 | 0.205958 | − | 0.978561i | \(-0.433969\pi\) | ||||
0.205958 | + | 0.978561i | \(0.433969\pi\) | |||||||
\(6\) | −2.12696 | −0.868329 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.34088 | 0.827625 | ||||||||
\(9\) | −1.21017 | −0.403391 | ||||||||
\(10\) | −1.46436 | −0.463073 | ||||||||
\(11\) | −4.89445 | −1.47573 | −0.737865 | − | 0.674948i | \(-0.764166\pi\) | ||||
−0.737865 | + | 0.674948i | \(0.764166\pi\) | |||||||
\(12\) | 0.705855 | 0.203763 | ||||||||
\(13\) | 2.00945 | 0.557321 | 0.278660 | − | 0.960390i | \(-0.410110\pi\) | ||||
0.278660 | + | 0.960390i | \(0.410110\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.23225 | 0.318166 | ||||||||
\(16\) | −4.77684 | −1.19421 | ||||||||
\(17\) | −4.36499 | −1.05866 | −0.529332 | − | 0.848415i | \(-0.677558\pi\) | ||||
−0.529332 | + | 0.848415i | \(0.677558\pi\) | |||||||
\(18\) | 1.92399 | 0.453489 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.485964 | 0.108665 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.78141 | 1.65900 | ||||||||
\(23\) | −2.75694 | −0.574862 | −0.287431 | − | 0.957801i | \(-0.592801\pi\) | ||||
−0.287431 | + | 0.957801i | \(0.592801\pi\) | |||||||
\(24\) | 3.13173 | 0.639261 | ||||||||
\(25\) | −4.15162 | −0.830325 | ||||||||
\(26\) | −3.19471 | −0.626534 | ||||||||
\(27\) | −5.63256 | −1.08399 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.04504 | −0.194059 | −0.0970296 | − | 0.995281i | \(-0.530934\pi\) | ||||
−0.0970296 | + | 0.995281i | \(0.530934\pi\) | |||||||
\(30\) | −1.95909 | −0.357679 | ||||||||
\(31\) | 7.63918 | 1.37204 | 0.686019 | − | 0.727584i | \(-0.259357\pi\) | ||||
0.686019 | + | 0.727584i | \(0.259357\pi\) | |||||||
\(32\) | 2.91269 | 0.514895 | ||||||||
\(33\) | −6.54800 | −1.13986 | ||||||||
\(34\) | 6.93965 | 1.19014 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.638496 | −0.106416 | ||||||||
\(37\) | −4.59760 | −0.755841 | −0.377920 | − | 0.925838i | \(-0.623361\pi\) | ||||
−0.377920 | + | 0.925838i | \(0.623361\pi\) | |||||||
\(38\) | 1.58984 | 0.257907 | ||||||||
\(39\) | 2.68833 | 0.430477 | ||||||||
\(40\) | 2.15612 | 0.340913 | ||||||||
\(41\) | 1.06899 | 0.166948 | 0.0834742 | − | 0.996510i | \(-0.473398\pi\) | ||||
0.0834742 | + | 0.996510i | \(0.473398\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.09076 | −0.471337 | −0.235668 | − | 0.971834i | \(-0.575728\pi\) | ||||
−0.235668 | + | 0.971834i | \(0.575728\pi\) | |||||||
\(44\) | −2.58234 | −0.389303 | ||||||||
\(45\) | −1.11466 | −0.166164 | ||||||||
\(46\) | 4.38311 | 0.646254 | ||||||||
\(47\) | −2.37859 | −0.346953 | −0.173477 | − | 0.984838i | \(-0.555500\pi\) | ||||
−0.173477 | + | 0.984838i | \(0.555500\pi\) | |||||||
\(48\) | −6.39067 | −0.922414 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.60044 | 0.933443 | ||||||||
\(51\) | −5.83967 | −0.817717 | ||||||||
\(52\) | 1.06020 | 0.147023 | ||||||||
\(53\) | 11.3241 | 1.55549 | 0.777745 | − | 0.628579i | \(-0.216363\pi\) | ||||
0.777745 | + | 0.628579i | \(0.216363\pi\) | |||||||
\(54\) | 8.95489 | 1.21861 | ||||||||
\(55\) | −4.50815 | −0.607878 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.33784 | −0.177202 | ||||||||
\(58\) | 1.66145 | 0.218159 | ||||||||
\(59\) | −8.49491 | −1.10594 | −0.552972 | − | 0.833200i | \(-0.686506\pi\) | ||||
−0.552972 | + | 0.833200i | \(0.686506\pi\) | |||||||
\(60\) | 0.650145 | 0.0839333 | ||||||||
\(61\) | −9.80934 | −1.25596 | −0.627979 | − | 0.778230i | \(-0.716118\pi\) | ||||
−0.627979 | + | 0.778230i | \(0.716118\pi\) | |||||||
\(62\) | −12.1451 | −1.54243 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.92297 | 0.615371 | ||||||||
\(65\) | 1.85085 | 0.229570 | ||||||||
\(66\) | 10.4103 | 1.28142 | ||||||||
\(67\) | −1.77700 | −0.217095 | −0.108548 | − | 0.994091i | \(-0.534620\pi\) | ||||
−0.108548 | + | 0.994091i | \(0.534620\pi\) | |||||||
\(68\) | −2.30300 | −0.279279 | ||||||||
\(69\) | −3.68836 | −0.444026 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.03345 | 0.478683 | 0.239341 | − | 0.970935i | \(-0.423068\pi\) | ||||
0.239341 | + | 0.970935i | \(0.423068\pi\) | |||||||
\(72\) | −2.83287 | −0.333857 | ||||||||
\(73\) | −8.39827 | −0.982943 | −0.491472 | − | 0.870894i | \(-0.663541\pi\) | ||||
−0.491472 | + | 0.870894i | \(0.663541\pi\) | |||||||
\(74\) | 7.30947 | 0.849709 | ||||||||
\(75\) | −5.55422 | −0.641346 | ||||||||
\(76\) | −0.527606 | −0.0605206 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.27402 | −0.483938 | ||||||||
\(79\) | 12.0311 | 1.35361 | 0.676804 | − | 0.736163i | \(-0.263364\pi\) | ||||
0.676804 | + | 0.736163i | \(0.263364\pi\) | |||||||
\(80\) | −4.39983 | −0.491916 | ||||||||
\(81\) | −3.90496 | −0.433884 | ||||||||
\(82\) | −1.69953 | −0.187682 | ||||||||
\(83\) | −5.56817 | −0.611186 | −0.305593 | − | 0.952162i | \(-0.598855\pi\) | ||||
−0.305593 | + | 0.952162i | \(0.598855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.02048 | −0.436082 | ||||||||
\(86\) | 4.91383 | 0.529872 | ||||||||
\(87\) | −1.39810 | −0.149892 | ||||||||
\(88\) | −11.4573 | −1.22135 | ||||||||
\(89\) | −5.54181 | −0.587431 | −0.293715 | − | 0.955893i | \(-0.594892\pi\) | ||||
−0.293715 | + | 0.955893i | \(0.594892\pi\) | |||||||
\(90\) | 1.77214 | 0.186800 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.45458 | −0.151650 | ||||||||
\(93\) | 10.2200 | 1.05977 | ||||||||
\(94\) | 3.78159 | 0.390041 | ||||||||
\(95\) | −0.921074 | −0.0945002 | ||||||||
\(96\) | 3.89672 | 0.397707 | ||||||||
\(97\) | −3.89678 | −0.395658 | −0.197829 | − | 0.980237i | \(-0.563389\pi\) | ||||
−0.197829 | + | 0.980237i | \(0.563389\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.92313 | 0.595297 | ||||||||
\(100\) | −2.19042 | −0.219042 | ||||||||
\(101\) | −13.7798 | −1.37114 | −0.685569 | − | 0.728008i | \(-0.740446\pi\) | ||||
−0.685569 | + | 0.728008i | \(0.740446\pi\) | |||||||
\(102\) | 9.28417 | 0.919270 | ||||||||
\(103\) | 15.4644 | 1.52375 | 0.761876 | − | 0.647723i | \(-0.224279\pi\) | ||||
0.761876 | + | 0.647723i | \(0.224279\pi\) | |||||||
\(104\) | 4.70387 | 0.461252 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.0036 | −1.74867 | ||||||||
\(107\) | −5.43108 | −0.525043 | −0.262521 | − | 0.964926i | \(-0.584554\pi\) | ||||
−0.262521 | + | 0.964926i | \(0.584554\pi\) | |||||||
\(108\) | −2.97177 | −0.285959 | ||||||||
\(109\) | 5.66759 | 0.542856 | 0.271428 | − | 0.962459i | \(-0.412504\pi\) | ||||
0.271428 | + | 0.962459i | \(0.412504\pi\) | |||||||
\(110\) | 7.16725 | 0.683371 | ||||||||
\(111\) | −6.15087 | −0.583815 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.4755 | −1.54988 | −0.774941 | − | 0.632034i | \(-0.782220\pi\) | ||||
−0.774941 | + | 0.632034i | \(0.782220\pi\) | |||||||
\(114\) | 2.12696 | 0.199208 | ||||||||
\(115\) | −2.53935 | −0.236795 | ||||||||
\(116\) | −0.551370 | −0.0511934 | ||||||||
\(117\) | −2.43178 | −0.224818 | ||||||||
\(118\) | 13.5056 | 1.24329 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.88455 | 0.263322 | ||||||||
\(121\) | 12.9556 | 1.17778 | ||||||||
\(122\) | 15.5953 | 1.41194 | ||||||||
\(123\) | 1.43014 | 0.128952 | ||||||||
\(124\) | 4.03048 | 0.361948 | ||||||||
\(125\) | −8.42932 | −0.753941 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.6318 | −1.47583 | −0.737916 | − | 0.674893i | \(-0.764190\pi\) | ||||
−0.737916 | + | 0.674893i | \(0.764190\pi\) | |||||||
\(128\) | −13.6521 | −1.20669 | ||||||||
\(129\) | −4.13496 | −0.364063 | ||||||||
\(130\) | −2.94256 | −0.258080 | ||||||||
\(131\) | −19.2102 | −1.67840 | −0.839201 | − | 0.543821i | \(-0.816977\pi\) | ||||
−0.839201 | + | 0.543821i | \(0.816977\pi\) | |||||||
\(132\) | −3.45477 | −0.300699 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.82515 | 0.244056 | ||||||||
\(135\) | −5.18800 | −0.446512 | ||||||||
\(136\) | −10.2179 | −0.876178 | ||||||||
\(137\) | −13.7573 | −1.17537 | −0.587685 | − | 0.809090i | \(-0.699960\pi\) | ||||
−0.587685 | + | 0.809090i | \(0.699960\pi\) | |||||||
\(138\) | 5.86391 | 0.499170 | ||||||||
\(139\) | 14.4092 | 1.22217 | 0.611085 | − | 0.791565i | \(-0.290733\pi\) | ||||
0.611085 | + | 0.791565i | \(0.290733\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.18218 | −0.267988 | ||||||||
\(142\) | −6.41256 | −0.538130 | ||||||||
\(143\) | −9.83513 | −0.822455 | ||||||||
\(144\) | 5.78081 | 0.481734 | ||||||||
\(145\) | −0.962560 | −0.0799362 | ||||||||
\(146\) | 13.3519 | 1.10502 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.42572 | −0.199393 | ||||||||
\(149\) | 16.6987 | 1.36801 | 0.684004 | − | 0.729478i | \(-0.260237\pi\) | ||||
0.684004 | + | 0.729478i | \(0.260237\pi\) | |||||||
\(150\) | 8.83035 | 0.720995 | ||||||||
\(151\) | 15.0737 | 1.22668 | 0.613339 | − | 0.789820i | \(-0.289826\pi\) | ||||
0.613339 | + | 0.789820i | \(0.289826\pi\) | |||||||
\(152\) | −2.34088 | −0.189870 | ||||||||
\(153\) | 5.28239 | 0.427056 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.03625 | 0.565165 | ||||||||
\(156\) | 1.41838 | 0.113561 | ||||||||
\(157\) | 0.866746 | 0.0691739 | 0.0345869 | − | 0.999402i | \(-0.488988\pi\) | ||||
0.0345869 | + | 0.999402i | \(0.488988\pi\) | |||||||
\(158\) | −19.1276 | −1.52171 | ||||||||
\(159\) | 15.1499 | 1.20147 | ||||||||
\(160\) | 2.68280 | 0.212094 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 6.20827 | 0.487768 | ||||||||
\(163\) | 21.5909 | 1.69113 | 0.845563 | − | 0.533876i | \(-0.179265\pi\) | ||||
0.845563 | + | 0.533876i | \(0.179265\pi\) | |||||||
\(164\) | 0.564007 | 0.0440415 | ||||||||
\(165\) | −6.03119 | −0.469528 | ||||||||
\(166\) | 8.85253 | 0.687090 | ||||||||
\(167\) | 1.10594 | 0.0855800 | 0.0427900 | − | 0.999084i | \(-0.486375\pi\) | ||||
0.0427900 | + | 0.999084i | \(0.486375\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.96212 | −0.689394 | ||||||||
\(170\) | 6.39193 | 0.490239 | ||||||||
\(171\) | 1.21017 | 0.0925443 | ||||||||
\(172\) | −1.63071 | −0.124340 | ||||||||
\(173\) | −19.9412 | −1.51610 | −0.758051 | − | 0.652195i | \(-0.773848\pi\) | ||||
−0.758051 | + | 0.652195i | \(0.773848\pi\) | |||||||
\(174\) | 2.22276 | 0.168507 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.3800 | 1.76233 | ||||||||
\(177\) | −11.3649 | −0.854235 | ||||||||
\(178\) | 8.81062 | 0.660384 | ||||||||
\(179\) | −6.83473 | −0.510852 | −0.255426 | − | 0.966829i | \(-0.582216\pi\) | ||||
−0.255426 | + | 0.966829i | \(0.582216\pi\) | |||||||
\(180\) | −0.588102 | −0.0438345 | ||||||||
\(181\) | 11.4381 | 0.850190 | 0.425095 | − | 0.905149i | \(-0.360241\pi\) | ||||
0.425095 | + | 0.905149i | \(0.360241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.1234 | −0.970107 | ||||||||
\(184\) | −6.45366 | −0.475770 | ||||||||
\(185\) | −4.23473 | −0.311343 | ||||||||
\(186\) | −16.2483 | −1.19138 | ||||||||
\(187\) | 21.3642 | 1.56230 | ||||||||
\(188\) | −1.25496 | −0.0915274 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.46436 | 0.106236 | ||||||||
\(191\) | −7.66755 | −0.554804 | −0.277402 | − | 0.960754i | \(-0.589473\pi\) | ||||
−0.277402 | + | 0.960754i | \(0.589473\pi\) | |||||||
\(192\) | 6.58616 | 0.475315 | ||||||||
\(193\) | 10.4449 | 0.751837 | 0.375919 | − | 0.926653i | \(-0.377327\pi\) | ||||
0.375919 | + | 0.926653i | \(0.377327\pi\) | |||||||
\(194\) | 6.19527 | 0.444794 | ||||||||
\(195\) | 2.47615 | 0.177321 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.5993 | 1.75263 | 0.876313 | − | 0.481743i | \(-0.159996\pi\) | ||||
0.876313 | + | 0.481743i | \(0.159996\pi\) | |||||||
\(198\) | −9.41686 | −0.669227 | ||||||||
\(199\) | 1.73370 | 0.122899 | 0.0614494 | − | 0.998110i | \(-0.480428\pi\) | ||||
0.0614494 | + | 0.998110i | \(0.480428\pi\) | |||||||
\(200\) | −9.71844 | −0.687197 | ||||||||
\(201\) | −2.37735 | −0.167685 | ||||||||
\(202\) | 21.9077 | 1.54142 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.08105 | −0.215716 | ||||||||
\(205\) | 0.984620 | 0.0687688 | ||||||||
\(206\) | −24.5860 | −1.71299 | ||||||||
\(207\) | 3.33638 | 0.231894 | ||||||||
\(208\) | −9.59882 | −0.665558 | ||||||||
\(209\) | 4.89445 | 0.338556 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5700 | −1.00304 | −0.501522 | − | 0.865145i | \(-0.667226\pi\) | ||||
−0.501522 | + | 0.865145i | \(0.667226\pi\) | |||||||
\(212\) | 5.97469 | 0.410343 | ||||||||
\(213\) | 5.39613 | 0.369737 | ||||||||
\(214\) | 8.63458 | 0.590248 | ||||||||
\(215\) | −2.84682 | −0.194152 | ||||||||
\(216\) | −13.1851 | −0.897134 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.01058 | −0.610274 | ||||||||
\(219\) | −11.2356 | −0.759230 | ||||||||
\(220\) | −2.37853 | −0.160360 | ||||||||
\(221\) | −8.77121 | −0.590016 | ||||||||
\(222\) | 9.77893 | 0.656319 | ||||||||
\(223\) | 11.0288 | 0.738546 | 0.369273 | − | 0.929321i | \(-0.379607\pi\) | ||||
0.369273 | + | 0.929321i | \(0.379607\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.02419 | 0.334946 | ||||||||
\(226\) | 26.1934 | 1.74236 | ||||||||
\(227\) | 23.9276 | 1.58813 | 0.794064 | − | 0.607834i | \(-0.207961\pi\) | ||||
0.794064 | + | 0.607834i | \(0.207961\pi\) | |||||||
\(228\) | −0.705855 | −0.0467464 | ||||||||
\(229\) | 25.2326 | 1.66741 | 0.833707 | − | 0.552207i | \(-0.186214\pi\) | ||||
0.833707 | + | 0.552207i | \(0.186214\pi\) | |||||||
\(230\) | 4.03717 | 0.266203 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.44631 | −0.160608 | ||||||||
\(233\) | 17.5991 | 1.15296 | 0.576478 | − | 0.817113i | \(-0.304427\pi\) | ||||
0.576478 | + | 0.817113i | \(0.304427\pi\) | |||||||
\(234\) | 3.86616 | 0.252739 | ||||||||
\(235\) | −2.19086 | −0.142916 | ||||||||
\(236\) | −4.48197 | −0.291751 | ||||||||
\(237\) | 16.0958 | 1.04553 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.01140 | −0.324160 | −0.162080 | − | 0.986778i | \(-0.551820\pi\) | ||||
−0.162080 | + | 0.986778i | \(0.551820\pi\) | |||||||
\(240\) | −5.88628 | −0.379958 | ||||||||
\(241\) | −3.06702 | −0.197564 | −0.0987819 | − | 0.995109i | \(-0.531495\pi\) | ||||
−0.0987819 | + | 0.995109i | \(0.531495\pi\) | |||||||
\(242\) | −20.5974 | −1.32405 | ||||||||
\(243\) | 11.6734 | 0.748852 | ||||||||
\(244\) | −5.17547 | −0.331326 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.27371 | −0.144966 | ||||||||
\(247\) | −2.00945 | −0.127858 | ||||||||
\(248\) | 17.8824 | 1.13553 | ||||||||
\(249\) | −7.44934 | −0.472083 | ||||||||
\(250\) | 13.4013 | 0.847573 | ||||||||
\(251\) | −24.4585 | −1.54381 | −0.771903 | − | 0.635740i | \(-0.780695\pi\) | ||||
−0.771903 | + | 0.635740i | \(0.780695\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.4937 | 0.848342 | ||||||||
\(254\) | 26.4419 | 1.65912 | ||||||||
\(255\) | −5.37877 | −0.336831 | ||||||||
\(256\) | 11.8588 | 0.741177 | ||||||||
\(257\) | 23.1609 | 1.44474 | 0.722369 | − | 0.691507i | \(-0.243053\pi\) | ||||
0.722369 | + | 0.691507i | \(0.243053\pi\) | |||||||
\(258\) | 6.57394 | 0.409276 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.976520 | 0.0605612 | ||||||||
\(261\) | 1.26468 | 0.0782818 | ||||||||
\(262\) | 30.5412 | 1.88684 | ||||||||
\(263\) | 20.2172 | 1.24664 | 0.623322 | − | 0.781965i | \(-0.285783\pi\) | ||||
0.623322 | + | 0.781965i | \(0.285783\pi\) | |||||||
\(264\) | −15.3281 | −0.943377 | ||||||||
\(265\) | 10.4304 | 0.640733 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.41408 | −0.453734 | ||||||||
\(268\) | −0.937557 | −0.0572704 | ||||||||
\(269\) | 11.0749 | 0.675248 | 0.337624 | − | 0.941281i | \(-0.390377\pi\) | ||||
0.337624 | + | 0.941281i | \(0.390377\pi\) | |||||||
\(270\) | 8.24811 | 0.501964 | ||||||||
\(271\) | 16.7966 | 1.02032 | 0.510160 | − | 0.860079i | \(-0.329586\pi\) | ||||
0.510160 | + | 0.860079i | \(0.329586\pi\) | |||||||
\(272\) | 20.8509 | 1.26427 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.8720 | 1.32134 | ||||||||
\(275\) | 20.3199 | 1.22534 | ||||||||
\(276\) | −1.94600 | −0.117135 | ||||||||
\(277\) | 2.97484 | 0.178741 | 0.0893704 | − | 0.995998i | \(-0.471515\pi\) | ||||
0.0893704 | + | 0.995998i | \(0.471515\pi\) | |||||||
\(278\) | −22.9084 | −1.37395 | ||||||||
\(279\) | −9.24474 | −0.553468 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.4781 | 1.22162 | 0.610810 | − | 0.791777i | \(-0.290844\pi\) | ||||
0.610810 | + | 0.791777i | \(0.290844\pi\) | |||||||
\(282\) | 5.05918 | 0.301270 | ||||||||
\(283\) | 15.3609 | 0.913113 | 0.456557 | − | 0.889694i | \(-0.349083\pi\) | ||||
0.456557 | + | 0.889694i | \(0.349083\pi\) | |||||||
\(284\) | 2.12808 | 0.126278 | ||||||||
\(285\) | −1.23225 | −0.0729924 | ||||||||
\(286\) | 15.6363 | 0.924596 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.52486 | −0.207704 | ||||||||
\(289\) | 2.05311 | 0.120771 | ||||||||
\(290\) | 1.53032 | 0.0898635 | ||||||||
\(291\) | −5.21328 | −0.305608 | ||||||||
\(292\) | −4.43098 | −0.259304 | ||||||||
\(293\) | 0.713696 | 0.0416946 | 0.0208473 | − | 0.999783i | \(-0.493364\pi\) | ||||
0.0208473 | + | 0.999783i | \(0.493364\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.82444 | −0.455556 | ||||||||
\(296\) | −10.7624 | −0.625553 | ||||||||
\(297\) | 27.5682 | 1.59967 | ||||||||
\(298\) | −26.5483 | −1.53790 | ||||||||
\(299\) | −5.53993 | −0.320382 | ||||||||
\(300\) | −2.93044 | −0.169189 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −23.9648 | −1.37902 | ||||||||
\(303\) | −18.4352 | −1.05907 | ||||||||
\(304\) | 4.77684 | 0.273971 | ||||||||
\(305\) | −9.03513 | −0.517350 | ||||||||
\(306\) | −8.39819 | −0.480092 | ||||||||
\(307\) | −26.2825 | −1.50002 | −0.750012 | − | 0.661425i | \(-0.769952\pi\) | ||||
−0.750012 | + | 0.661425i | \(0.769952\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.6889 | 1.17695 | ||||||||
\(310\) | −11.1865 | −0.635353 | ||||||||
\(311\) | −15.7868 | −0.895189 | −0.447594 | − | 0.894237i | \(-0.647719\pi\) | ||||
−0.447594 | + | 0.894237i | \(0.647719\pi\) | |||||||
\(312\) | 6.29304 | 0.356273 | ||||||||
\(313\) | −28.8711 | −1.63189 | −0.815946 | − | 0.578128i | \(-0.803783\pi\) | ||||
−0.815946 | + | 0.578128i | \(0.803783\pi\) | |||||||
\(314\) | −1.37799 | −0.0777646 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.34771 | 0.357086 | ||||||||
\(317\) | −28.9077 | −1.62362 | −0.811809 | − | 0.583922i | \(-0.801517\pi\) | ||||
−0.811809 | + | 0.583922i | \(0.801517\pi\) | |||||||
\(318\) | −24.0860 | −1.35068 | ||||||||
\(319\) | 5.11489 | 0.286379 | ||||||||
\(320\) | 4.53442 | 0.253482 | ||||||||
\(321\) | −7.26594 | −0.405545 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.36499 | 0.242874 | ||||||||
\(324\) | −2.06028 | −0.114460 | ||||||||
\(325\) | −8.34247 | −0.462757 | ||||||||
\(326\) | −34.3261 | −1.90115 | ||||||||
\(327\) | 7.58234 | 0.419305 | ||||||||
\(328\) | 2.50238 | 0.138171 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.58866 | 0.527838 | ||||||||
\(331\) | 16.3394 | 0.898096 | 0.449048 | − | 0.893508i | \(-0.351763\pi\) | ||||
0.449048 | + | 0.893508i | \(0.351763\pi\) | |||||||
\(332\) | −2.93780 | −0.161233 | ||||||||
\(333\) | 5.56390 | 0.304900 | ||||||||
\(334\) | −1.75827 | −0.0962082 | ||||||||
\(335\) | −1.63675 | −0.0894251 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.75609 | −0.422501 | −0.211251 | − | 0.977432i | \(-0.567754\pi\) | ||||
−0.211251 | + | 0.977432i | \(0.567754\pi\) | |||||||
\(338\) | 14.2484 | 0.775010 | ||||||||
\(339\) | −22.0416 | −1.19713 | ||||||||
\(340\) | −2.12123 | −0.115040 | ||||||||
\(341\) | −37.3895 | −2.02476 | ||||||||
\(342\) | −1.92399 | −0.104037 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.23510 | −0.390090 | ||||||||
\(345\) | −3.39725 | −0.182902 | ||||||||
\(346\) | 31.7034 | 1.70439 | ||||||||
\(347\) | 24.5341 | 1.31706 | 0.658530 | − | 0.752554i | \(-0.271178\pi\) | ||||
0.658530 | + | 0.752554i | \(0.271178\pi\) | |||||||
\(348\) | −0.737647 | −0.0395420 | ||||||||
\(349\) | −30.5639 | −1.63605 | −0.818023 | − | 0.575185i | \(-0.804930\pi\) | ||||
−0.818023 | + | 0.575185i | \(0.804930\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.3183 | −0.604128 | ||||||||
\(352\) | −14.2560 | −0.759847 | ||||||||
\(353\) | −16.2887 | −0.866960 | −0.433480 | − | 0.901163i | \(-0.642715\pi\) | ||||
−0.433480 | + | 0.901163i | \(0.642715\pi\) | |||||||
\(354\) | 18.0684 | 0.960323 | ||||||||
\(355\) | 3.71511 | 0.197177 | ||||||||
\(356\) | −2.92390 | −0.154966 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.8662 | 0.574295 | ||||||||
\(359\) | −9.90106 | −0.522558 | −0.261279 | − | 0.965263i | \(-0.584144\pi\) | ||||
−0.261279 | + | 0.965263i | \(0.584144\pi\) | |||||||
\(360\) | −2.60928 | −0.137521 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −18.1849 | −0.955775 | ||||||||
\(363\) | 17.3326 | 0.909723 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.73543 | −0.404891 | ||||||||
\(366\) | 20.8641 | 1.09058 | ||||||||
\(367\) | 11.7221 | 0.611888 | 0.305944 | − | 0.952050i | \(-0.401028\pi\) | ||||
0.305944 | + | 0.952050i | \(0.401028\pi\) | |||||||
\(368\) | 13.1695 | 0.686507 | ||||||||
\(369\) | −1.29367 | −0.0673455 | ||||||||
\(370\) | 6.73256 | 0.350009 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.39215 | 0.279570 | ||||||||
\(373\) | 18.7553 | 0.971114 | 0.485557 | − | 0.874205i | \(-0.338617\pi\) | ||||
0.485557 | + | 0.874205i | \(0.338617\pi\) | |||||||
\(374\) | −33.9657 | −1.75633 | ||||||||
\(375\) | −11.2771 | −0.582348 | ||||||||
\(376\) | −5.56799 | −0.287147 | ||||||||
\(377\) | −2.09996 | −0.108153 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.9305 | −1.94836 | −0.974179 | − | 0.225779i | \(-0.927507\pi\) | ||||
−0.974179 | + | 0.225779i | \(0.927507\pi\) | |||||||
\(380\) | −0.485964 | −0.0249295 | ||||||||
\(381\) | −22.2507 | −1.13994 | ||||||||
\(382\) | 12.1902 | 0.623705 | ||||||||
\(383\) | 23.0865 | 1.17966 | 0.589832 | − | 0.807526i | \(-0.299194\pi\) | ||||
0.589832 | + | 0.807526i | \(0.299194\pi\) | |||||||
\(384\) | −18.2644 | −0.932052 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.6057 | −0.845208 | ||||||||
\(387\) | 3.74036 | 0.190133 | ||||||||
\(388\) | −2.05596 | −0.104376 | ||||||||
\(389\) | −6.18005 | −0.313341 | −0.156670 | − | 0.987651i | \(-0.550076\pi\) | ||||
−0.156670 | + | 0.987651i | \(0.550076\pi\) | |||||||
\(390\) | −3.93669 | −0.199342 | ||||||||
\(391\) | 12.0340 | 0.608586 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −25.7002 | −1.29641 | ||||||||
\(394\) | −39.1090 | −1.97028 | ||||||||
\(395\) | 11.0816 | 0.557574 | ||||||||
\(396\) | 3.12508 | 0.157041 | ||||||||
\(397\) | 6.16132 | 0.309228 | 0.154614 | − | 0.987975i | \(-0.450587\pi\) | ||||
0.154614 | + | 0.987975i | \(0.450587\pi\) | |||||||
\(398\) | −2.75631 | −0.138162 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.8317 | 0.991583 | ||||||||
\(401\) | −11.9645 | −0.597478 | −0.298739 | − | 0.954335i | \(-0.596566\pi\) | ||||
−0.298739 | + | 0.954335i | \(0.596566\pi\) | |||||||
\(402\) | 3.77961 | 0.188510 | ||||||||
\(403\) | 15.3505 | 0.764664 | ||||||||
\(404\) | −7.27029 | −0.361711 | ||||||||
\(405\) | −3.59675 | −0.178724 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.5027 | 1.11542 | ||||||||
\(408\) | −13.6700 | −0.676763 | ||||||||
\(409\) | −36.0597 | −1.78304 | −0.891518 | − | 0.452986i | \(-0.850359\pi\) | ||||
−0.891518 | + | 0.452986i | \(0.850359\pi\) | |||||||
\(410\) | −1.56539 | −0.0773092 | ||||||||
\(411\) | −18.4052 | −0.907860 | ||||||||
\(412\) | 8.15911 | 0.401971 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.30433 | −0.260693 | ||||||||
\(415\) | −5.12870 | −0.251758 | ||||||||
\(416\) | 5.85289 | 0.286962 | ||||||||
\(417\) | 19.2772 | 0.944010 | ||||||||
\(418\) | −7.78141 | −0.380601 | ||||||||
\(419\) | −26.6207 | −1.30051 | −0.650253 | − | 0.759717i | \(-0.725337\pi\) | ||||
−0.650253 | + | 0.759717i | \(0.725337\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.3357 | 1.33226 | 0.666130 | − | 0.745836i | \(-0.267950\pi\) | ||||
0.666130 | + | 0.745836i | \(0.267950\pi\) | |||||||
\(422\) | 23.1641 | 1.12761 | ||||||||
\(423\) | 2.87851 | 0.139958 | ||||||||
\(424\) | 26.5084 | 1.28736 | ||||||||
\(425\) | 18.1218 | 0.879035 | ||||||||
\(426\) | −8.57901 | −0.415654 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.86547 | −0.138508 | ||||||||
\(429\) | −13.1579 | −0.635268 | ||||||||
\(430\) | 4.52600 | 0.218263 | ||||||||
\(431\) | −18.5449 | −0.893276 | −0.446638 | − | 0.894715i | \(-0.647379\pi\) | ||||
−0.446638 | + | 0.894715i | \(0.647379\pi\) | |||||||
\(432\) | 26.9058 | 1.29451 | ||||||||
\(433\) | −16.8498 | −0.809748 | −0.404874 | − | 0.914372i | \(-0.632685\pi\) | ||||
−0.404874 | + | 0.914372i | \(0.632685\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.28775 | −0.0617431 | ||||||||
\(436\) | 2.99026 | 0.143207 | ||||||||
\(437\) | 2.75694 | 0.131882 | ||||||||
\(438\) | 17.8628 | 0.853518 | ||||||||
\(439\) | 19.6943 | 0.939959 | 0.469980 | − | 0.882677i | \(-0.344261\pi\) | ||||
0.469980 | + | 0.882677i | \(0.344261\pi\) | |||||||
\(440\) | −10.5530 | −0.503095 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.9449 | 0.663290 | ||||||||
\(443\) | −25.0222 | −1.18884 | −0.594421 | − | 0.804154i | \(-0.702619\pi\) | ||||
−0.594421 | + | 0.804154i | \(0.702619\pi\) | |||||||
\(444\) | −3.24524 | −0.154012 | ||||||||
\(445\) | −5.10442 | −0.241973 | ||||||||
\(446\) | −17.5341 | −0.830266 | ||||||||
\(447\) | 22.3402 | 1.05666 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.86818 | 0.135358 | 0.0676788 | − | 0.997707i | \(-0.478441\pi\) | ||||
0.0676788 | + | 0.997707i | \(0.478441\pi\) | |||||||
\(450\) | −7.98768 | −0.376543 | ||||||||
\(451\) | −5.23212 | −0.246371 | ||||||||
\(452\) | −8.69256 | −0.408864 | ||||||||
\(453\) | 20.1662 | 0.947491 | ||||||||
\(454\) | −38.0411 | −1.78536 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.13173 | −0.146657 | ||||||||
\(457\) | −0.343243 | −0.0160562 | −0.00802811 | − | 0.999968i | \(-0.502555\pi\) | ||||
−0.00802811 | + | 0.999968i | \(0.502555\pi\) | |||||||
\(458\) | −40.1158 | −1.87449 | ||||||||
\(459\) | 24.5860 | 1.14758 | ||||||||
\(460\) | −1.33978 | −0.0624674 | ||||||||
\(461\) | −14.4944 | −0.675072 | −0.337536 | − | 0.941313i | \(-0.609593\pi\) | ||||
−0.337536 | + | 0.941313i | \(0.609593\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.0295 | −1.39559 | −0.697795 | − | 0.716297i | \(-0.745835\pi\) | ||||
−0.697795 | + | 0.716297i | \(0.745835\pi\) | |||||||
\(464\) | 4.99200 | 0.231748 | ||||||||
\(465\) | 9.41340 | 0.436536 | ||||||||
\(466\) | −27.9798 | −1.29614 | ||||||||
\(467\) | 13.2015 | 0.610894 | 0.305447 | − | 0.952209i | \(-0.401194\pi\) | ||||
0.305447 | + | 0.952209i | \(0.401194\pi\) | |||||||
\(468\) | −1.28302 | −0.0593078 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.48312 | 0.160665 | ||||||||
\(471\) | 1.15957 | 0.0534302 | ||||||||
\(472\) | −19.8855 | −0.915306 | ||||||||
\(473\) | 15.1276 | 0.695566 | ||||||||
\(474\) | −25.5898 | −1.17538 | ||||||||
\(475\) | 4.15162 | 0.190490 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.7042 | −0.627472 | ||||||||
\(478\) | 7.96735 | 0.364418 | ||||||||
\(479\) | 17.0291 | 0.778080 | 0.389040 | − | 0.921221i | \(-0.372807\pi\) | ||||
0.389040 | + | 0.921221i | \(0.372807\pi\) | |||||||
\(480\) | 3.58917 | 0.163822 | ||||||||
\(481\) | −9.23864 | −0.421246 | ||||||||
\(482\) | 4.87608 | 0.222099 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.83545 | 0.310702 | ||||||||
\(485\) | −3.58922 | −0.162978 | ||||||||
\(486\) | −18.5590 | −0.841852 | ||||||||
\(487\) | 11.0041 | 0.498644 | 0.249322 | − | 0.968421i | \(-0.419792\pi\) | ||||
0.249322 | + | 0.968421i | \(0.419792\pi\) | |||||||
\(488\) | −22.9625 | −1.03946 | ||||||||
\(489\) | 28.8852 | 1.30623 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.1415 | 1.45053 | 0.725264 | − | 0.688471i | \(-0.241718\pi\) | ||||
0.725264 | + | 0.688471i | \(0.241718\pi\) | |||||||
\(492\) | 0.754553 | 0.0340179 | ||||||||
\(493\) | 4.56159 | 0.205444 | ||||||||
\(494\) | 3.19471 | 0.143737 | ||||||||
\(495\) | 5.45564 | 0.245213 | ||||||||
\(496\) | −36.4912 | −1.63850 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.8433 | 0.530711 | ||||||||
\(499\) | 10.0670 | 0.450659 | 0.225329 | − | 0.974283i | \(-0.427654\pi\) | ||||
0.225329 | + | 0.974283i | \(0.427654\pi\) | |||||||
\(500\) | −4.44736 | −0.198892 | ||||||||
\(501\) | 1.47957 | 0.0661024 | ||||||||
\(502\) | 38.8852 | 1.73553 | ||||||||
\(503\) | −12.2667 | −0.546944 | −0.273472 | − | 0.961880i | \(-0.588172\pi\) | ||||
−0.273472 | + | 0.961880i | \(0.588172\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.6922 | −0.564794 | ||||||||
\(506\) | −21.4529 | −0.953697 | ||||||||
\(507\) | −11.9899 | −0.532491 | ||||||||
\(508\) | −8.77503 | −0.389329 | ||||||||
\(509\) | −41.5323 | −1.84089 | −0.920444 | − | 0.390874i | \(-0.872173\pi\) | ||||
−0.920444 | + | 0.390874i | \(0.872173\pi\) | |||||||
\(510\) | 8.55141 | 0.378663 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.45056 | 0.373466 | ||||||||
\(513\) | 5.63256 | 0.248683 | ||||||||
\(514\) | −36.8223 | −1.62416 | ||||||||
\(515\) | 14.2438 | 0.627659 | ||||||||
\(516\) | −2.18163 | −0.0960409 | ||||||||
\(517\) | 11.6419 | 0.512009 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.6782 | −1.17104 | ||||||||
\(520\) | 4.33261 | 0.189998 | ||||||||
\(521\) | −16.5432 | −0.724773 | −0.362386 | − | 0.932028i | \(-0.618038\pi\) | ||||
−0.362386 | + | 0.932028i | \(0.618038\pi\) | |||||||
\(522\) | −2.01065 | −0.0880036 | ||||||||
\(523\) | 16.5511 | 0.723728 | 0.361864 | − | 0.932231i | \(-0.382141\pi\) | ||||
0.361864 | + | 0.932231i | \(0.382141\pi\) | |||||||
\(524\) | −10.1354 | −0.442768 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −32.1422 | −1.40147 | ||||||||
\(527\) | −33.3449 | −1.45253 | ||||||||
\(528\) | 31.2788 | 1.36123 | ||||||||
\(529\) | −15.3993 | −0.669534 | ||||||||
\(530\) | −16.5827 | −0.720305 | ||||||||
\(531\) | 10.2803 | 0.446128 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.14808 | 0.0930438 | ||||||||
\(534\) | 11.7872 | 0.510084 | ||||||||
\(535\) | −5.00243 | −0.216274 | ||||||||
\(536\) | −4.15974 | −0.179673 | ||||||||
\(537\) | −9.14380 | −0.394584 | ||||||||
\(538\) | −17.6074 | −0.759107 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.73722 | −0.117791 | ||||||||
\(541\) | −23.2230 | −0.998435 | −0.499217 | − | 0.866477i | \(-0.666379\pi\) | ||||
−0.499217 | + | 0.866477i | \(0.666379\pi\) | |||||||
\(542\) | −26.7040 | −1.14703 | ||||||||
\(543\) | 15.3024 | 0.656691 | ||||||||
\(544\) | −12.7138 | −0.545101 | ||||||||
\(545\) | 5.22027 | 0.223612 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.8730 | 0.806953 | 0.403476 | − | 0.914990i | \(-0.367802\pi\) | ||||
0.403476 | + | 0.914990i | \(0.367802\pi\) | |||||||
\(548\) | −7.25846 | −0.310066 | ||||||||
\(549\) | 11.8710 | 0.506643 | ||||||||
\(550\) | −32.3055 | −1.37751 | ||||||||
\(551\) | 1.04504 | 0.0445202 | ||||||||
\(552\) | −8.63399 | −0.367487 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.72954 | −0.200939 | ||||||||
\(555\) | −5.66541 | −0.240483 | ||||||||
\(556\) | 7.60238 | 0.322413 | ||||||||
\(557\) | −25.0658 | −1.06207 | −0.531037 | − | 0.847349i | \(-0.678197\pi\) | ||||
−0.531037 | + | 0.847349i | \(0.678197\pi\) | |||||||
\(558\) | 14.6977 | 0.622203 | ||||||||
\(559\) | −6.21073 | −0.262686 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.5819 | 1.20673 | ||||||||
\(562\) | −32.5570 | −1.37333 | ||||||||
\(563\) | 38.5050 | 1.62279 | 0.811396 | − | 0.584497i | \(-0.198708\pi\) | ||||
0.811396 | + | 0.584497i | \(0.198708\pi\) | |||||||
\(564\) | −1.67894 | −0.0706961 | ||||||||
\(565\) | −15.1751 | −0.638422 | ||||||||
\(566\) | −24.4215 | −1.02651 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.44182 | 0.396170 | ||||||||
\(569\) | 38.6595 | 1.62069 | 0.810345 | − | 0.585953i | \(-0.199280\pi\) | ||||
0.810345 | + | 0.585953i | \(0.199280\pi\) | |||||||
\(570\) | 1.95909 | 0.0820573 | ||||||||
\(571\) | −10.0910 | −0.422295 | −0.211147 | − | 0.977454i | \(-0.567720\pi\) | ||||
−0.211147 | + | 0.977454i | \(0.567720\pi\) | |||||||
\(572\) | −5.18908 | −0.216966 | ||||||||
\(573\) | −10.2580 | −0.428533 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.4458 | 0.477322 | ||||||||
\(576\) | −5.95765 | −0.248235 | ||||||||
\(577\) | 31.9815 | 1.33141 | 0.665705 | − | 0.746215i | \(-0.268131\pi\) | ||||
0.665705 | + | 0.746215i | \(0.268131\pi\) | |||||||
\(578\) | −3.26413 | −0.135770 | ||||||||
\(579\) | 13.9736 | 0.580722 | ||||||||
\(580\) | −0.507853 | −0.0210874 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.28830 | 0.343561 | ||||||||
\(583\) | −55.4254 | −2.29549 | ||||||||
\(584\) | −19.6593 | −0.813508 | ||||||||
\(585\) | −2.23985 | −0.0926064 | ||||||||
\(586\) | −1.13467 | −0.0468726 | ||||||||
\(587\) | 20.3512 | 0.839984 | 0.419992 | − | 0.907528i | \(-0.362033\pi\) | ||||
0.419992 | + | 0.907528i | \(0.362033\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.63918 | −0.314767 | ||||||||
\(590\) | 12.4396 | 0.512132 | ||||||||
\(591\) | 32.9100 | 1.35374 | ||||||||
\(592\) | 21.9620 | 0.902633 | ||||||||
\(593\) | −32.2562 | −1.32460 | −0.662302 | − | 0.749237i | \(-0.730420\pi\) | ||||
−0.662302 | + | 0.749237i | \(0.730420\pi\) | |||||||
\(594\) | −43.8292 | −1.79833 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.81032 | 0.360885 | ||||||||
\(597\) | 2.31942 | 0.0949275 | ||||||||
\(598\) | 8.80763 | 0.360171 | ||||||||
\(599\) | 17.7020 | 0.723285 | 0.361643 | − | 0.932317i | \(-0.382216\pi\) | ||||
0.361643 | + | 0.932317i | \(0.382216\pi\) | |||||||
\(600\) | −13.0018 | −0.530794 | ||||||||
\(601\) | 17.5840 | 0.717266 | 0.358633 | − | 0.933479i | \(-0.383243\pi\) | ||||
0.358633 | + | 0.933479i | \(0.383243\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.15048 | 0.0875743 | ||||||||
\(604\) | 7.95296 | 0.323601 | ||||||||
\(605\) | 11.9331 | 0.485148 | ||||||||
\(606\) | 29.3091 | 1.19060 | ||||||||
\(607\) | −38.2578 | −1.55284 | −0.776418 | − | 0.630218i | \(-0.782966\pi\) | ||||
−0.776418 | + | 0.630218i | \(0.782966\pi\) | |||||||
\(608\) | −2.91269 | −0.118125 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.3645 | 0.581600 | ||||||||
\(611\) | −4.77965 | −0.193364 | ||||||||
\(612\) | 2.78703 | 0.112659 | ||||||||
\(613\) | 8.36322 | 0.337787 | 0.168894 | − | 0.985634i | \(-0.445981\pi\) | ||||
0.168894 | + | 0.985634i | \(0.445981\pi\) | |||||||
\(614\) | 41.7851 | 1.68631 | ||||||||
\(615\) | 1.31727 | 0.0531173 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.16193 | −0.248070 | −0.124035 | − | 0.992278i | \(-0.539584\pi\) | ||||
−0.124035 | + | 0.992278i | \(0.539584\pi\) | |||||||
\(618\) | −32.8922 | −1.32312 | ||||||||
\(619\) | 20.0432 | 0.805603 | 0.402801 | − | 0.915287i | \(-0.368037\pi\) | ||||
0.402801 | + | 0.915287i | \(0.368037\pi\) | |||||||
\(620\) | 3.71237 | 0.149092 | ||||||||
\(621\) | 15.5286 | 0.623142 | ||||||||
\(622\) | 25.0986 | 1.00636 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −12.8417 | −0.514080 | ||||||||
\(625\) | 12.9941 | 0.519764 | ||||||||
\(626\) | 45.9006 | 1.83456 | ||||||||
\(627\) | 6.54800 | 0.261502 | ||||||||
\(628\) | 0.457301 | 0.0182483 | ||||||||
\(629\) | 20.0685 | 0.800182 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.98034 | 0.277883 | 0.138941 | − | 0.990301i | \(-0.455630\pi\) | ||||
0.138941 | + | 0.990301i | \(0.455630\pi\) | |||||||
\(632\) | 28.1634 | 1.12028 | ||||||||
\(633\) | −19.4924 | −0.774755 | ||||||||
\(634\) | 45.9588 | 1.82526 | ||||||||
\(635\) | −15.3191 | −0.607920 | ||||||||
\(636\) | 7.99320 | 0.316951 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.13189 | −0.321945 | ||||||||
\(639\) | −4.88118 | −0.193097 | ||||||||
\(640\) | −12.5746 | −0.497055 | ||||||||
\(641\) | −27.4849 | −1.08559 | −0.542794 | − | 0.839866i | \(-0.682634\pi\) | ||||
−0.542794 | + | 0.839866i | \(0.682634\pi\) | |||||||
\(642\) | 11.5517 | 0.455910 | ||||||||
\(643\) | −34.2026 | −1.34882 | −0.674409 | − | 0.738358i | \(-0.735602\pi\) | ||||
−0.674409 | + | 0.738358i | \(0.735602\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.80860 | −0.149964 | ||||||||
\(646\) | −6.93965 | −0.273037 | ||||||||
\(647\) | −6.01536 | −0.236488 | −0.118244 | − | 0.992985i | \(-0.537727\pi\) | ||||
−0.118244 | + | 0.992985i | \(0.537727\pi\) | |||||||
\(648\) | −9.14102 | −0.359093 | ||||||||
\(649\) | 41.5779 | 1.63207 | ||||||||
\(650\) | 13.2632 | 0.520227 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.3915 | 0.446125 | ||||||||
\(653\) | −2.90207 | −0.113567 | −0.0567833 | − | 0.998387i | \(-0.518084\pi\) | ||||
−0.0567833 | + | 0.998387i | \(0.518084\pi\) | |||||||
\(654\) | −12.0548 | −0.471378 | ||||||||
\(655\) | −17.6940 | −0.691362 | ||||||||
\(656\) | −5.10640 | −0.199372 | ||||||||
\(657\) | 10.1634 | 0.396511 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.29792 | 0.284287 | 0.142143 | − | 0.989846i | \(-0.454601\pi\) | ||||
0.142143 | + | 0.989846i | \(0.454601\pi\) | |||||||
\(660\) | −3.18210 | −0.123863 | ||||||||
\(661\) | −49.1630 | −1.91222 | −0.956110 | − | 0.293008i | \(-0.905344\pi\) | ||||
−0.956110 | + | 0.293008i | \(0.905344\pi\) | |||||||
\(662\) | −25.9771 | −1.00963 | ||||||||
\(663\) | −11.7345 | −0.455731 | ||||||||
\(664\) | −13.0344 | −0.505833 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.84573 | −0.342765 | ||||||||
\(667\) | 2.88112 | 0.111557 | ||||||||
\(668\) | 0.583500 | 0.0225763 | ||||||||
\(669\) | 14.7549 | 0.570456 | ||||||||
\(670\) | 2.60218 | 0.100531 | ||||||||
\(671\) | 48.0113 | 1.85346 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.3470 | 0.977054 | 0.488527 | − | 0.872549i | \(-0.337534\pi\) | ||||
0.488527 | + | 0.872549i | \(0.337534\pi\) | |||||||
\(674\) | 12.3310 | 0.474971 | ||||||||
\(675\) | 23.3842 | 0.900060 | ||||||||
\(676\) | −4.72847 | −0.181864 | ||||||||
\(677\) | 12.4843 | 0.479809 | 0.239905 | − | 0.970796i | \(-0.422884\pi\) | ||||
0.239905 | + | 0.970796i | \(0.422884\pi\) | |||||||
\(678\) | 35.0427 | 1.34581 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.41144 | −0.360912 | ||||||||
\(681\) | 32.0114 | 1.22668 | ||||||||
\(682\) | 59.4436 | 2.27621 | ||||||||
\(683\) | −27.9149 | −1.06813 | −0.534066 | − | 0.845443i | \(-0.679337\pi\) | ||||
−0.534066 | + | 0.845443i | \(0.679337\pi\) | |||||||
\(684\) | 0.638496 | 0.0244135 | ||||||||
\(685\) | −12.6715 | −0.484154 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.7572 | 1.28792 | ||||||||
\(688\) | 14.7641 | 0.562876 | ||||||||
\(689\) | 22.7553 | 0.866907 | ||||||||
\(690\) | 5.40110 | 0.205616 | ||||||||
\(691\) | −42.3271 | −1.61020 | −0.805100 | − | 0.593140i | \(-0.797888\pi\) | ||||
−0.805100 | + | 0.593140i | \(0.797888\pi\) | |||||||
\(692\) | −10.5211 | −0.399953 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −39.0054 | −1.48063 | ||||||||
\(695\) | 13.2719 | 0.503433 | ||||||||
\(696\) | −3.27278 | −0.124055 | ||||||||
\(697\) | −4.66613 | −0.176742 | ||||||||
\(698\) | 48.5918 | 1.83923 | ||||||||
\(699\) | 23.5448 | 0.890548 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.3827 | 0.920921 | 0.460460 | − | 0.887680i | \(-0.347684\pi\) | ||||
0.460460 | + | 0.887680i | \(0.347684\pi\) | |||||||
\(702\) | 17.9944 | 0.679154 | ||||||||
\(703\) | 4.59760 | 0.173402 | ||||||||
\(704\) | −24.0952 | −0.908122 | ||||||||
\(705\) | −2.93103 | −0.110389 | ||||||||
\(706\) | 25.8965 | 0.974628 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.99617 | −0.225350 | ||||||||
\(709\) | −1.94001 | −0.0728588 | −0.0364294 | − | 0.999336i | \(-0.511598\pi\) | ||||
−0.0364294 | + | 0.999336i | \(0.511598\pi\) | |||||||
\(710\) | −5.90645 | −0.221665 | ||||||||
\(711\) | −14.5598 | −0.546034 | ||||||||
\(712\) | −12.9727 | −0.486173 | ||||||||
\(713\) | −21.0608 | −0.788732 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.05888 | −0.338783 | ||||||||
\(716\) | −3.60605 | −0.134764 | ||||||||
\(717\) | −6.70447 | −0.250383 | ||||||||
\(718\) | 15.7411 | 0.587454 | ||||||||
\(719\) | 27.4622 | 1.02417 | 0.512084 | − | 0.858935i | \(-0.328874\pi\) | ||||
0.512084 | + | 0.858935i | \(0.328874\pi\) | |||||||
\(720\) | 5.32456 | 0.198434 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.58984 | −0.0591679 | ||||||||
\(723\) | −4.10319 | −0.152599 | ||||||||
\(724\) | 6.03484 | 0.224283 | ||||||||
\(725\) | 4.33862 | 0.161132 | ||||||||
\(726\) | −27.5561 | −1.02270 | ||||||||
\(727\) | 18.7684 | 0.696081 | 0.348041 | − | 0.937479i | \(-0.386847\pi\) | ||||
0.348041 | + | 0.937479i | \(0.386847\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.3321 | 1.01230 | ||||||||
\(730\) | 12.2981 | 0.455174 | ||||||||
\(731\) | 13.4911 | 0.498988 | ||||||||
\(732\) | −6.92397 | −0.255917 | ||||||||
\(733\) | −38.2534 | −1.41292 | −0.706461 | − | 0.707752i | \(-0.749710\pi\) | ||||
−0.706461 | + | 0.707752i | \(0.749710\pi\) | |||||||
\(734\) | −18.6363 | −0.687878 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.03011 | −0.295994 | ||||||||
\(737\) | 8.69743 | 0.320374 | ||||||||
\(738\) | 2.05673 | 0.0757092 | ||||||||
\(739\) | 43.0751 | 1.58454 | 0.792272 | − | 0.610168i | \(-0.208898\pi\) | ||||
0.792272 | + | 0.610168i | \(0.208898\pi\) | |||||||
\(740\) | −2.23427 | −0.0821334 | ||||||||
\(741\) | −2.68833 | −0.0987582 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.03951 | 0.111509 | 0.0557545 | − | 0.998445i | \(-0.482244\pi\) | ||||
0.0557545 | + | 0.998445i | \(0.482244\pi\) | |||||||
\(744\) | 23.9238 | 0.877090 | ||||||||
\(745\) | 15.3807 | 0.563505 | ||||||||
\(746\) | −29.8181 | −1.09172 | ||||||||
\(747\) | 6.73846 | 0.246547 | ||||||||
\(748\) | 11.2719 | 0.412141 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17.9289 | 0.654669 | ||||||||
\(751\) | −16.8163 | −0.613634 | −0.306817 | − | 0.951768i | \(-0.599264\pi\) | ||||
−0.306817 | + | 0.951768i | \(0.599264\pi\) | |||||||
\(752\) | 11.3622 | 0.414335 | ||||||||
\(753\) | −32.7216 | −1.19244 | ||||||||
\(754\) | 3.33860 | 0.121585 | ||||||||
\(755\) | 13.8840 | 0.505289 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.98576 | 0.326593 | 0.163296 | − | 0.986577i | \(-0.447787\pi\) | ||||
0.163296 | + | 0.986577i | \(0.447787\pi\) | |||||||
\(758\) | 60.3036 | 2.19032 | ||||||||
\(759\) | 18.0525 | 0.655263 | ||||||||
\(760\) | −2.15612 | −0.0782107 | ||||||||
\(761\) | 15.5631 | 0.564161 | 0.282081 | − | 0.959391i | \(-0.408975\pi\) | ||||
0.282081 | + | 0.959391i | \(0.408975\pi\) | |||||||
\(762\) | 35.3752 | 1.28151 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.04545 | −0.146359 | ||||||||
\(765\) | 4.86548 | 0.175912 | ||||||||
\(766\) | −36.7039 | −1.32617 | ||||||||
\(767\) | −17.0701 | −0.616365 | ||||||||
\(768\) | 15.8653 | 0.572488 | ||||||||
\(769\) | −51.5950 | −1.86056 | −0.930282 | − | 0.366844i | \(-0.880438\pi\) | ||||
−0.930282 | + | 0.366844i | \(0.880438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.9857 | 1.11592 | ||||||||
\(772\) | 5.51077 | 0.198337 | ||||||||
\(773\) | −5.73561 | −0.206295 | −0.103148 | − | 0.994666i | \(-0.532891\pi\) | ||||
−0.103148 | + | 0.994666i | \(0.532891\pi\) | |||||||
\(774\) | −5.94660 | −0.213746 | ||||||||
\(775\) | −31.7150 | −1.13924 | ||||||||
\(776\) | −9.12187 | −0.327456 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.82531 | 0.352255 | ||||||||
\(779\) | −1.06899 | −0.0383006 | ||||||||
\(780\) | 1.30643 | 0.0467778 | ||||||||
\(781\) | −19.7415 | −0.706407 | ||||||||
\(782\) | −19.1322 | −0.684167 | ||||||||
\(783\) | 5.88625 | 0.210357 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.798337 | 0.0284939 | ||||||||
\(786\) | 40.8594 | 1.45741 | ||||||||
\(787\) | 5.15928 | 0.183909 | 0.0919543 | − | 0.995763i | \(-0.470689\pi\) | ||||
0.0919543 | + | 0.995763i | \(0.470689\pi\) | |||||||
\(788\) | 12.9787 | 0.462348 | ||||||||
\(789\) | 27.0474 | 0.962914 | ||||||||
\(790\) | −17.6180 | −0.626819 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 13.8653 | 0.492683 | ||||||||
\(793\) | −19.7114 | −0.699971 | ||||||||
\(794\) | −9.79554 | −0.347631 | ||||||||
\(795\) | 13.9542 | 0.494905 | ||||||||
\(796\) | 0.914711 | 0.0324211 | ||||||||
\(797\) | 3.73501 | 0.132301 | 0.0661505 | − | 0.997810i | \(-0.478928\pi\) | ||||
0.0661505 | + | 0.997810i | \(0.478928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.3825 | 0.367307 | ||||||||
\(800\) | −12.0924 | −0.427530 | ||||||||
\(801\) | 6.70656 | 0.236965 | ||||||||
\(802\) | 19.0217 | 0.671679 | ||||||||
\(803\) | 41.1049 | 1.45056 | ||||||||
\(804\) | −1.25430 | −0.0442359 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.4050 | −0.859628 | ||||||||
\(807\) | 14.8165 | 0.521565 | ||||||||
\(808\) | −32.2567 | −1.13479 | ||||||||
\(809\) | −37.9348 | −1.33372 | −0.666858 | − | 0.745185i | \(-0.732361\pi\) | ||||
−0.666858 | + | 0.745185i | \(0.732361\pi\) | |||||||
\(810\) | 5.71828 | 0.200920 | ||||||||
\(811\) | 38.2521 | 1.34321 | 0.671606 | − | 0.740908i | \(-0.265605\pi\) | ||||
0.671606 | + | 0.740908i | \(0.265605\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.4712 | 0.788100 | ||||||||
\(814\) | −35.7758 | −1.25394 | ||||||||
\(815\) | 19.8868 | 0.696603 | ||||||||
\(816\) | 27.8952 | 0.976527 | ||||||||
\(817\) | 3.09076 | 0.108132 | ||||||||
\(818\) | 57.3293 | 2.00447 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.519492 | 0.0181414 | ||||||||
\(821\) | −7.72337 | −0.269547 | −0.134774 | − | 0.990876i | \(-0.543031\pi\) | ||||
−0.134774 | + | 0.990876i | \(0.543031\pi\) | |||||||
\(822\) | 29.2614 | 1.02061 | ||||||||
\(823\) | −20.4419 | −0.712561 | −0.356281 | − | 0.934379i | \(-0.615955\pi\) | ||||
−0.356281 | + | 0.934379i | \(0.615955\pi\) | |||||||
\(824\) | 36.2002 | 1.26110 | ||||||||
\(825\) | 27.1848 | 0.946455 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.63691 | −0.126468 | −0.0632340 | − | 0.997999i | \(-0.520141\pi\) | ||||
−0.0632340 | + | 0.997999i | \(0.520141\pi\) | |||||||
\(828\) | 1.76030 | 0.0611745 | ||||||||
\(829\) | −33.4020 | −1.16010 | −0.580049 | − | 0.814582i | \(-0.696967\pi\) | ||||
−0.580049 | + | 0.814582i | \(0.696967\pi\) | |||||||
\(830\) | 8.15383 | 0.283024 | ||||||||
\(831\) | 3.97987 | 0.138060 | ||||||||
\(832\) | 9.89245 | 0.342959 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −30.6478 | −1.06125 | ||||||||
\(835\) | 1.01865 | 0.0352518 | ||||||||
\(836\) | 2.58234 | 0.0893121 | ||||||||
\(837\) | −43.0281 | −1.48727 | ||||||||
\(838\) | 42.3228 | 1.46202 | ||||||||
\(839\) | 7.32368 | 0.252842 | 0.126421 | − | 0.991977i | \(-0.459651\pi\) | ||||
0.126421 | + | 0.991977i | \(0.459651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9079 | −0.962341 | ||||||||
\(842\) | −43.4595 | −1.49771 | ||||||||
\(843\) | 27.3965 | 0.943585 | ||||||||
\(844\) | −7.68725 | −0.264606 | ||||||||
\(845\) | −8.25477 | −0.283973 | ||||||||
\(846\) | −4.57638 | −0.157339 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −54.0937 | −1.85758 | ||||||||
\(849\) | 20.5505 | 0.705293 | ||||||||
\(850\) | −28.8108 | −0.988203 | ||||||||
\(851\) | 12.6753 | 0.434504 | ||||||||
\(852\) | 2.84703 | 0.0975377 | ||||||||
\(853\) | −11.8322 | −0.405127 | −0.202563 | − | 0.979269i | \(-0.564927\pi\) | ||||
−0.202563 | + | 0.979269i | \(0.564927\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.11466 | 0.0381206 | ||||||||
\(856\) | −12.7135 | −0.434538 | ||||||||
\(857\) | 32.6270 | 1.11452 | 0.557258 | − | 0.830340i | \(-0.311854\pi\) | ||||
0.557258 | + | 0.830340i | \(0.311854\pi\) | |||||||
\(858\) | 20.9190 | 0.714162 | ||||||||
\(859\) | 26.2072 | 0.894180 | 0.447090 | − | 0.894489i | \(-0.352460\pi\) | ||||
0.447090 | + | 0.894489i | \(0.352460\pi\) | |||||||
\(860\) | −1.50200 | −0.0512178 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.4835 | 1.00421 | ||||||||
\(863\) | −2.83616 | −0.0965440 | −0.0482720 | − | 0.998834i | \(-0.515371\pi\) | ||||
−0.0482720 | + | 0.998834i | \(0.515371\pi\) | |||||||
\(864\) | −16.4059 | −0.558139 | ||||||||
\(865\) | −18.3673 | −0.624508 | ||||||||
\(866\) | 26.7885 | 0.910311 | ||||||||
\(867\) | 2.74674 | 0.0932842 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −58.8857 | −1.99756 | ||||||||
\(870\) | 2.04733 | 0.0694110 | ||||||||
\(871\) | −3.57079 | −0.120992 | ||||||||
\(872\) | 13.2671 | 0.449281 | ||||||||
\(873\) | 4.71578 | 0.159605 | ||||||||
\(874\) | −4.38311 | −0.148261 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.92796 | −0.200287 | ||||||||
\(877\) | −12.6963 | −0.428725 | −0.214363 | − | 0.976754i | \(-0.568767\pi\) | ||||
−0.214363 | + | 0.976754i | \(0.568767\pi\) | |||||||
\(878\) | −31.3109 | −1.05669 | ||||||||
\(879\) | 0.954814 | 0.0322051 | ||||||||
\(880\) | 21.5347 | 0.725935 | ||||||||
\(881\) | −23.3775 | −0.787607 | −0.393804 | − | 0.919195i | \(-0.628841\pi\) | ||||
−0.393804 | + | 0.919195i | \(0.628841\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.5254 | −0.589777 | −0.294889 | − | 0.955532i | \(-0.595283\pi\) | ||||
−0.294889 | + | 0.955532i | \(0.595283\pi\) | |||||||
\(884\) | −4.62775 | −0.155648 | ||||||||
\(885\) | −10.4679 | −0.351874 | ||||||||
\(886\) | 39.7814 | 1.33648 | ||||||||
\(887\) | 21.3712 | 0.717575 | 0.358787 | − | 0.933419i | \(-0.383190\pi\) | ||||
0.358787 | + | 0.933419i | \(0.383190\pi\) | |||||||
\(888\) | −14.3984 | −0.483180 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.11523 | 0.272023 | ||||||||
\(891\) | 19.1126 | 0.640296 | ||||||||
\(892\) | 5.81889 | 0.194831 | ||||||||
\(893\) | 2.37859 | 0.0795965 | ||||||||
\(894\) | −35.5175 | −1.18788 | ||||||||
\(895\) | −6.29529 | −0.210428 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.41156 | −0.247465 | ||||||||
\(898\) | −4.55995 | −0.152168 | ||||||||
\(899\) | −7.98325 | −0.266256 | ||||||||
\(900\) | 2.65079 | 0.0883598 | ||||||||
\(901\) | −49.4297 | −1.64674 | ||||||||
\(902\) | 8.31826 | 0.276968 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −38.5670 | −1.28272 | ||||||||
\(905\) | 10.5354 | 0.350208 | ||||||||
\(906\) | −32.0611 | −1.06516 | ||||||||
\(907\) | 4.73336 | 0.157169 | 0.0785844 | − | 0.996907i | \(-0.474960\pi\) | ||||
0.0785844 | + | 0.996907i | \(0.474960\pi\) | |||||||
\(908\) | 12.6243 | 0.418954 | ||||||||
\(909\) | 16.6759 | 0.553105 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.71101 | 0.288609 | 0.144304 | − | 0.989533i | \(-0.453906\pi\) | ||||
0.144304 | + | 0.989533i | \(0.453906\pi\) | |||||||
\(912\) | 6.39067 | 0.211616 | ||||||||
\(913\) | 27.2531 | 0.901946 | ||||||||
\(914\) | 0.545703 | 0.0180502 | ||||||||
\(915\) | −12.0876 | −0.399603 | ||||||||
\(916\) | 13.3129 | 0.439869 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −39.0880 | −1.29010 | ||||||||
\(919\) | 26.5863 | 0.877001 | 0.438501 | − | 0.898731i | \(-0.355510\pi\) | ||||
0.438501 | + | 0.898731i | \(0.355510\pi\) | |||||||
\(920\) | −5.94430 | −0.195978 | ||||||||
\(921\) | −35.1619 | −1.15862 | ||||||||
\(922\) | 23.0439 | 0.758909 | ||||||||
\(923\) | 8.10501 | 0.266780 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.0875 | 0.627593 | ||||||||
\(926\) | 47.7423 | 1.56891 | ||||||||
\(927\) | −18.7146 | −0.614668 | ||||||||
\(928\) | −3.04388 | −0.0999201 | ||||||||
\(929\) | −31.3999 | −1.03020 | −0.515098 | − | 0.857131i | \(-0.672244\pi\) | ||||
−0.515098 | + | 0.857131i | \(0.672244\pi\) | |||||||
\(930\) | −14.9658 | −0.490749 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.28540 | 0.304153 | ||||||||
\(933\) | −21.1203 | −0.691448 | ||||||||
\(934\) | −20.9884 | −0.686761 | ||||||||
\(935\) | 19.6780 | 0.643539 | ||||||||
\(936\) | −5.69250 | −0.186065 | ||||||||
\(937\) | −13.6016 | −0.444346 | −0.222173 | − | 0.975007i | \(-0.571315\pi\) | ||||
−0.222173 | + | 0.975007i | \(0.571315\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.6250 | −1.26048 | ||||||||
\(940\) | −1.15591 | −0.0377017 | ||||||||
\(941\) | −31.8478 | −1.03821 | −0.519105 | − | 0.854710i | \(-0.673735\pi\) | ||||
−0.519105 | + | 0.854710i | \(0.673735\pi\) | |||||||
\(942\) | −1.84354 | −0.0600657 | ||||||||
\(943\) | −2.94715 | −0.0959723 | ||||||||
\(944\) | 40.5789 | 1.32073 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.0505 | −0.781949 | ||||||||
\(947\) | −32.2423 | −1.04774 | −0.523868 | − | 0.851800i | \(-0.675511\pi\) | ||||
−0.523868 | + | 0.851800i | \(0.675511\pi\) | |||||||
\(948\) | 8.49224 | 0.275815 | ||||||||
\(949\) | −16.8759 | −0.547815 | ||||||||
\(950\) | −6.60044 | −0.214146 | ||||||||
\(951\) | −38.6740 | −1.25409 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.4552 | −0.954146 | −0.477073 | − | 0.878864i | \(-0.658302\pi\) | ||||
−0.477073 | + | 0.878864i | \(0.658302\pi\) | |||||||
\(954\) | 21.7875 | 0.705397 | ||||||||
\(955\) | −7.06238 | −0.228533 | ||||||||
\(956\) | −2.64405 | −0.0855146 | ||||||||
\(957\) | 6.84293 | 0.221201 | ||||||||
\(958\) | −27.0737 | −0.874710 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.06634 | 0.195790 | ||||||||
\(961\) | 27.3571 | 0.882486 | ||||||||
\(962\) | 14.6880 | 0.473560 | ||||||||
\(963\) | 6.57256 | 0.211798 | ||||||||
\(964\) | −1.61818 | −0.0521180 | ||||||||
\(965\) | 9.62048 | 0.309694 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.6199 | 1.43488 | 0.717440 | − | 0.696621i | \(-0.245314\pi\) | ||||
0.717440 | + | 0.696621i | \(0.245314\pi\) | |||||||
\(968\) | 30.3275 | 0.974761 | ||||||||
\(969\) | 5.83967 | 0.187597 | ||||||||
\(970\) | 5.70630 | 0.183218 | ||||||||
\(971\) | −25.7414 | −0.826082 | −0.413041 | − | 0.910712i | \(-0.635533\pi\) | ||||
−0.413041 | + | 0.910712i | \(0.635533\pi\) | |||||||
\(972\) | 6.15898 | 0.197550 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.4948 | −0.560570 | ||||||||
\(975\) | −11.1609 | −0.357436 | ||||||||
\(976\) | 46.8577 | 1.49988 | ||||||||
\(977\) | 16.8590 | 0.539366 | 0.269683 | − | 0.962949i | \(-0.413081\pi\) | ||||
0.269683 | + | 0.962949i | \(0.413081\pi\) | |||||||
\(978\) | −45.9230 | −1.46845 | ||||||||
\(979\) | 27.1241 | 0.866890 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.85877 | −0.218984 | ||||||||
\(982\) | −51.1001 | −1.63067 | ||||||||
\(983\) | −53.4576 | −1.70503 | −0.852516 | − | 0.522700i | \(-0.824925\pi\) | ||||
−0.852516 | + | 0.522700i | \(0.824925\pi\) | |||||||
\(984\) | 3.34779 | 0.106724 | ||||||||
\(985\) | 22.6577 | 0.721936 | ||||||||
\(986\) | −7.25222 | −0.230958 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.06020 | −0.0337294 | ||||||||
\(989\) | 8.52105 | 0.270954 | ||||||||
\(990\) | −8.67362 | −0.275666 | ||||||||
\(991\) | 4.94618 | 0.157120 | 0.0785602 | − | 0.996909i | \(-0.474968\pi\) | ||||
0.0785602 | + | 0.996909i | \(0.474968\pi\) | |||||||
\(992\) | 22.2505 | 0.706455 | ||||||||
\(993\) | 21.8596 | 0.693693 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.59687 | 0.0506240 | ||||||||
\(996\) | −3.93032 | −0.124537 | ||||||||
\(997\) | 17.2528 | 0.546402 | 0.273201 | − | 0.961957i | \(-0.411918\pi\) | ||||
0.273201 | + | 0.961957i | \(0.411918\pi\) | |||||||
\(998\) | −16.0049 | −0.506626 | ||||||||
\(999\) | 25.8962 | 0.819321 |
(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 | 931.2.a.p.1.3 | ✓ | 10 | |
3.2 | odd | 2 | 8379.2.a.ct.1.8 | 10 | |||
7.2 | even | 3 | 931.2.f.r.704.8 | 20 | |||
7.3 | odd | 6 | 931.2.f.q.324.8 | 20 | |||
7.4 | even | 3 | 931.2.f.r.324.8 | 20 | |||
7.5 | odd | 6 | 931.2.f.q.704.8 | 20 | |||
7.6 | odd | 2 | 931.2.a.q.1.3 | yes | 10 | ||
21.20 | even | 2 | 8379.2.a.cs.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
931.2.a.p.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
931.2.a.q.1.3 | yes | 10 | 7.6 | odd | 2 | ||
931.2.f.q.324.8 | 20 | 7.3 | odd | 6 | |||
931.2.f.q.704.8 | 20 | 7.5 | odd | 6 | |||
931.2.f.r.324.8 | 20 | 7.4 | even | 3 | |||
931.2.f.r.704.8 | 20 | 7.2 | even | 3 | |||
8379.2.a.cs.1.8 | 10 | 21.20 | even | 2 | |||
8379.2.a.ct.1.8 | 10 | 3.2 | odd | 2 |