Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 16x^{6} + 69x^{4} - 10x^{3} - 70x^{2} + 10x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.90474\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.90474 | −1.67705 | −0.838526 | − | 0.544861i | \(-0.816582\pi\) | ||||
−0.838526 | + | 0.544861i | \(0.816582\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.90474 | −1.18586 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.43751 | 1.81250 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.90474 | −0.838526 | ||||||||
\(13\) | −6.51020 | −1.80560 | −0.902802 | − | 0.430056i | \(-0.858494\pi\) | ||||
−0.902802 | + | 0.430056i | \(0.858494\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.90474 | 0.750001 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.07831 | 1.71674 | 0.858371 | − | 0.513030i | \(-0.171477\pi\) | ||||
0.858371 | + | 0.513030i | \(0.171477\pi\) | |||||||
\(18\) | 5.43751 | 1.28163 | ||||||||
\(19\) | 3.97479 | 0.911879 | 0.455940 | − | 0.890011i | \(-0.349303\pi\) | ||||
0.455940 | + | 0.890011i | \(0.349303\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.90474 | 0.633866 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.39994 | 1.96002 | 0.980011 | − | 0.198943i | \(-0.0637509\pi\) | ||||
0.980011 | + | 0.198943i | \(0.0637509\pi\) | |||||||
\(24\) | −2.90474 | −0.592928 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.51020 | −1.27676 | ||||||||
\(27\) | −7.08034 | −1.36261 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 1.17923 | 0.218977 | 0.109489 | − | 0.993988i | \(-0.465079\pi\) | ||||
0.109489 | + | 0.993988i | \(0.465079\pi\) | |||||||
\(30\) | 2.90474 | 0.530331 | ||||||||
\(31\) | −1.28349 | −0.230522 | −0.115261 | − | 0.993335i | \(-0.536770\pi\) | ||||
−0.115261 | + | 0.993335i | \(0.536770\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.07831 | 1.21392 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 5.43751 | 0.906252 | ||||||||
\(37\) | −1.00807 | −0.165726 | −0.0828630 | − | 0.996561i | \(-0.526406\pi\) | ||||
−0.0828630 | + | 0.996561i | \(0.526406\pi\) | |||||||
\(38\) | 3.97479 | 0.644796 | ||||||||
\(39\) | 18.9104 | 3.02809 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.43144 | −0.848248 | −0.424124 | − | 0.905604i | \(-0.639418\pi\) | ||||
−0.424124 | + | 0.905604i | \(0.639418\pi\) | |||||||
\(42\) | 2.90474 | 0.448211 | ||||||||
\(43\) | −11.2003 | −1.70803 | −0.854013 | − | 0.520251i | \(-0.825838\pi\) | ||||
−0.854013 | + | 0.520251i | \(0.825838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.43751 | −0.810577 | ||||||||
\(46\) | 9.39994 | 1.38594 | ||||||||
\(47\) | −11.3915 | −1.66161 | −0.830807 | − | 0.556561i | \(-0.812121\pi\) | ||||
−0.830807 | + | 0.556561i | \(0.812121\pi\) | |||||||
\(48\) | −2.90474 | −0.419263 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −20.5606 | −2.87907 | ||||||||
\(52\) | −6.51020 | −0.902802 | ||||||||
\(53\) | −7.75606 | −1.06538 | −0.532688 | − | 0.846311i | \(-0.678818\pi\) | ||||
−0.532688 | + | 0.846311i | \(0.678818\pi\) | |||||||
\(54\) | −7.08034 | −0.963513 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −11.5457 | −1.52927 | ||||||||
\(58\) | 1.17923 | 0.154840 | ||||||||
\(59\) | −5.64597 | −0.735042 | −0.367521 | − | 0.930015i | \(-0.619793\pi\) | ||||
−0.367521 | + | 0.930015i | \(0.619793\pi\) | |||||||
\(60\) | 2.90474 | 0.375000 | ||||||||
\(61\) | 6.33662 | 0.811321 | 0.405660 | − | 0.914024i | \(-0.367042\pi\) | ||||
0.405660 | + | 0.914024i | \(0.367042\pi\) | |||||||
\(62\) | −1.28349 | −0.163004 | ||||||||
\(63\) | −5.43751 | −0.685062 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.51020 | 0.807491 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.88122 | 0.474166 | 0.237083 | − | 0.971489i | \(-0.423809\pi\) | ||||
0.237083 | + | 0.971489i | \(0.423809\pi\) | |||||||
\(68\) | 7.07831 | 0.858371 | ||||||||
\(69\) | −27.3044 | −3.28706 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −0.259926 | −0.0308475 | −0.0154238 | − | 0.999881i | \(-0.504910\pi\) | ||||
−0.0154238 | + | 0.999881i | \(0.504910\pi\) | |||||||
\(72\) | 5.43751 | 0.640817 | ||||||||
\(73\) | 4.82486 | 0.564707 | 0.282354 | − | 0.959310i | \(-0.408885\pi\) | ||||
0.282354 | + | 0.959310i | \(0.408885\pi\) | |||||||
\(74\) | −1.00807 | −0.117186 | ||||||||
\(75\) | −2.90474 | −0.335410 | ||||||||
\(76\) | 3.97479 | 0.455940 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 18.9104 | 2.14119 | ||||||||
\(79\) | 14.3428 | 1.61369 | 0.806843 | − | 0.590765i | \(-0.201174\pi\) | ||||
0.806843 | + | 0.590765i | \(0.201174\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 4.25401 | 0.472668 | ||||||||
\(82\) | −5.43144 | −0.599802 | ||||||||
\(83\) | 4.59502 | 0.504368 | 0.252184 | − | 0.967679i | \(-0.418851\pi\) | ||||
0.252184 | + | 0.967679i | \(0.418851\pi\) | |||||||
\(84\) | 2.90474 | 0.316933 | ||||||||
\(85\) | −7.07831 | −0.767750 | ||||||||
\(86\) | −11.2003 | −1.20776 | ||||||||
\(87\) | −3.42535 | −0.367236 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.43088 | −0.151673 | −0.0758366 | − | 0.997120i | \(-0.524163\pi\) | ||||
−0.0758366 | + | 0.997120i | \(0.524163\pi\) | |||||||
\(90\) | −5.43751 | −0.573164 | ||||||||
\(91\) | 6.51020 | 0.682454 | ||||||||
\(92\) | 9.39994 | 0.980011 | ||||||||
\(93\) | 3.72822 | 0.386598 | ||||||||
\(94\) | −11.3915 | −1.17494 | ||||||||
\(95\) | −3.97479 | −0.407805 | ||||||||
\(96\) | −2.90474 | −0.296464 | ||||||||
\(97\) | −8.60695 | −0.873903 | −0.436952 | − | 0.899485i | \(-0.643942\pi\) | ||||
−0.436952 | + | 0.899485i | \(0.643942\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −7.14255 | −0.710710 | −0.355355 | − | 0.934731i | \(-0.615640\pi\) | ||||
−0.355355 | + | 0.934731i | \(0.615640\pi\) | |||||||
\(102\) | −20.5606 | −2.03581 | ||||||||
\(103\) | 3.12129 | 0.307550 | 0.153775 | − | 0.988106i | \(-0.450857\pi\) | ||||
0.153775 | + | 0.988106i | \(0.450857\pi\) | |||||||
\(104\) | −6.51020 | −0.638378 | ||||||||
\(105\) | −2.90474 | −0.283474 | ||||||||
\(106\) | −7.75606 | −0.753335 | ||||||||
\(107\) | −3.29188 | −0.318238 | −0.159119 | − | 0.987259i | \(-0.550865\pi\) | ||||
−0.159119 | + | 0.987259i | \(0.550865\pi\) | |||||||
\(108\) | −7.08034 | −0.681306 | ||||||||
\(109\) | 12.5855 | 1.20547 | 0.602736 | − | 0.797941i | \(-0.294077\pi\) | ||||
0.602736 | + | 0.797941i | \(0.294077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.92819 | 0.277931 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 1.20490 | 0.113347 | 0.0566737 | − | 0.998393i | \(-0.481951\pi\) | ||||
0.0566737 | + | 0.998393i | \(0.481951\pi\) | |||||||
\(114\) | −11.5457 | −1.08136 | ||||||||
\(115\) | −9.39994 | −0.876549 | ||||||||
\(116\) | 1.17923 | 0.109489 | ||||||||
\(117\) | −35.3993 | −3.27267 | ||||||||
\(118\) | −5.64597 | −0.519753 | ||||||||
\(119\) | −7.07831 | −0.648867 | ||||||||
\(120\) | 2.90474 | 0.265165 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.33662 | 0.573690 | ||||||||
\(123\) | 15.7769 | 1.42256 | ||||||||
\(124\) | −1.28349 | −0.115261 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.43751 | −0.484412 | ||||||||
\(127\) | −16.0026 | −1.42000 | −0.710000 | − | 0.704202i | \(-0.751305\pi\) | ||||
−0.710000 | + | 0.704202i | \(0.751305\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 32.5339 | 2.86445 | ||||||||
\(130\) | 6.51020 | 0.570982 | ||||||||
\(131\) | 14.6019 | 1.27577 | 0.637887 | − | 0.770130i | \(-0.279809\pi\) | ||||
0.637887 | + | 0.770130i | \(0.279809\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.97479 | −0.344658 | ||||||||
\(134\) | 3.88122 | 0.335286 | ||||||||
\(135\) | 7.08034 | 0.609379 | ||||||||
\(136\) | 7.07831 | 0.606960 | ||||||||
\(137\) | 10.0996 | 0.862871 | 0.431435 | − | 0.902144i | \(-0.358007\pi\) | ||||
0.431435 | + | 0.902144i | \(0.358007\pi\) | |||||||
\(138\) | −27.3044 | −2.32430 | ||||||||
\(139\) | −18.5110 | −1.57009 | −0.785043 | − | 0.619442i | \(-0.787359\pi\) | ||||
−0.785043 | + | 0.619442i | \(0.787359\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 33.0892 | 2.78661 | ||||||||
\(142\) | −0.259926 | −0.0218125 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.43751 | 0.453126 | ||||||||
\(145\) | −1.17923 | −0.0979296 | ||||||||
\(146\) | 4.82486 | 0.399308 | ||||||||
\(147\) | −2.90474 | −0.239579 | ||||||||
\(148\) | −1.00807 | −0.0828630 | ||||||||
\(149\) | 11.5126 | 0.943152 | 0.471576 | − | 0.881826i | \(-0.343685\pi\) | ||||
0.471576 | + | 0.881826i | \(0.343685\pi\) | |||||||
\(150\) | −2.90474 | −0.237171 | ||||||||
\(151\) | 5.43407 | 0.442218 | 0.221109 | − | 0.975249i | \(-0.429032\pi\) | ||||
0.221109 | + | 0.975249i | \(0.429032\pi\) | |||||||
\(152\) | 3.97479 | 0.322398 | ||||||||
\(153\) | 38.4884 | 3.11160 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.28349 | 0.103093 | ||||||||
\(156\) | 18.9104 | 1.51405 | ||||||||
\(157\) | 7.97651 | 0.636595 | 0.318297 | − | 0.947991i | \(-0.396889\pi\) | ||||
0.318297 | + | 0.947991i | \(0.396889\pi\) | |||||||
\(158\) | 14.3428 | 1.14105 | ||||||||
\(159\) | 22.5293 | 1.78669 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −9.39994 | −0.740819 | ||||||||
\(162\) | 4.25401 | 0.334227 | ||||||||
\(163\) | 14.3432 | 1.12345 | 0.561723 | − | 0.827326i | \(-0.310139\pi\) | ||||
0.561723 | + | 0.827326i | \(0.310139\pi\) | |||||||
\(164\) | −5.43144 | −0.424124 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.59502 | 0.356642 | ||||||||
\(167\) | −1.91040 | −0.147831 | −0.0739155 | − | 0.997265i | \(-0.523550\pi\) | ||||
−0.0739155 | + | 0.997265i | \(0.523550\pi\) | |||||||
\(168\) | 2.90474 | 0.224106 | ||||||||
\(169\) | 29.3827 | 2.26021 | ||||||||
\(170\) | −7.07831 | −0.542881 | ||||||||
\(171\) | 21.6130 | 1.65279 | ||||||||
\(172\) | −11.2003 | −0.854013 | ||||||||
\(173\) | −14.5926 | −1.10945 | −0.554726 | − | 0.832033i | \(-0.687177\pi\) | ||||
−0.554726 | + | 0.832033i | \(0.687177\pi\) | |||||||
\(174\) | −3.42535 | −0.259675 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.4001 | 1.23270 | ||||||||
\(178\) | −1.43088 | −0.107249 | ||||||||
\(179\) | −3.15693 | −0.235960 | −0.117980 | − | 0.993016i | \(-0.537642\pi\) | ||||
−0.117980 | + | 0.993016i | \(0.537642\pi\) | |||||||
\(180\) | −5.43751 | −0.405288 | ||||||||
\(181\) | −7.09045 | −0.527029 | −0.263514 | − | 0.964655i | \(-0.584882\pi\) | ||||
−0.263514 | + | 0.964655i | \(0.584882\pi\) | |||||||
\(182\) | 6.51020 | 0.482568 | ||||||||
\(183\) | −18.4062 | −1.36063 | ||||||||
\(184\) | 9.39994 | 0.692972 | ||||||||
\(185\) | 1.00807 | 0.0741149 | ||||||||
\(186\) | 3.72822 | 0.273366 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −11.3915 | −0.830807 | ||||||||
\(189\) | 7.08034 | 0.515019 | ||||||||
\(190\) | −3.97479 | −0.288362 | ||||||||
\(191\) | 7.61496 | 0.550999 | 0.275500 | − | 0.961301i | \(-0.411157\pi\) | ||||
0.275500 | + | 0.961301i | \(0.411157\pi\) | |||||||
\(192\) | −2.90474 | −0.209632 | ||||||||
\(193\) | −8.55503 | −0.615804 | −0.307902 | − | 0.951418i | \(-0.599627\pi\) | ||||
−0.307902 | + | 0.951418i | \(0.599627\pi\) | |||||||
\(194\) | −8.60695 | −0.617943 | ||||||||
\(195\) | −18.9104 | −1.35420 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 5.30318 | 0.377836 | 0.188918 | − | 0.981993i | \(-0.439502\pi\) | ||||
0.188918 | + | 0.981993i | \(0.439502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.8463 | 1.97397 | 0.986987 | − | 0.160798i | \(-0.0514068\pi\) | ||||
0.986987 | + | 0.160798i | \(0.0514068\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −11.2739 | −0.795201 | ||||||||
\(202\) | −7.14255 | −0.502548 | ||||||||
\(203\) | −1.17923 | −0.0827656 | ||||||||
\(204\) | −20.5606 | −1.43953 | ||||||||
\(205\) | 5.43144 | 0.379348 | ||||||||
\(206\) | 3.12129 | 0.217470 | ||||||||
\(207\) | 51.1123 | 3.55255 | ||||||||
\(208\) | −6.51020 | −0.451401 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.90474 | −0.200446 | ||||||||
\(211\) | 9.26733 | 0.637989 | 0.318995 | − | 0.947757i | \(-0.396655\pi\) | ||||
0.318995 | + | 0.947757i | \(0.396655\pi\) | |||||||
\(212\) | −7.75606 | −0.532688 | ||||||||
\(213\) | 0.755017 | 0.0517329 | ||||||||
\(214\) | −3.29188 | −0.225028 | ||||||||
\(215\) | 11.2003 | 0.763853 | ||||||||
\(216\) | −7.08034 | −0.481756 | ||||||||
\(217\) | 1.28349 | 0.0871293 | ||||||||
\(218\) | 12.5855 | 0.852397 | ||||||||
\(219\) | −14.0150 | −0.947044 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −46.0812 | −3.09976 | ||||||||
\(222\) | 2.92819 | 0.196527 | ||||||||
\(223\) | 26.0134 | 1.74198 | 0.870992 | − | 0.491297i | \(-0.163477\pi\) | ||||
0.870992 | + | 0.491297i | \(0.163477\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 5.43751 | 0.362501 | ||||||||
\(226\) | 1.20490 | 0.0801487 | ||||||||
\(227\) | −0.293119 | −0.0194550 | −0.00972750 | − | 0.999953i | \(-0.503096\pi\) | ||||
−0.00972750 | + | 0.999953i | \(0.503096\pi\) | |||||||
\(228\) | −11.5457 | −0.764635 | ||||||||
\(229\) | −19.9552 | −1.31867 | −0.659337 | − | 0.751847i | \(-0.729163\pi\) | ||||
−0.659337 | + | 0.751847i | \(0.729163\pi\) | |||||||
\(230\) | −9.39994 | −0.619813 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.17923 | 0.0774202 | ||||||||
\(233\) | 0.201558 | 0.0132045 | 0.00660225 | − | 0.999978i | \(-0.497898\pi\) | ||||
0.00660225 | + | 0.999978i | \(0.497898\pi\) | |||||||
\(234\) | −35.3993 | −2.31412 | ||||||||
\(235\) | 11.3915 | 0.743096 | ||||||||
\(236\) | −5.64597 | −0.367521 | ||||||||
\(237\) | −41.6620 | −2.70624 | ||||||||
\(238\) | −7.07831 | −0.458819 | ||||||||
\(239\) | 23.9193 | 1.54721 | 0.773604 | − | 0.633669i | \(-0.218452\pi\) | ||||
0.773604 | + | 0.633669i | \(0.218452\pi\) | |||||||
\(240\) | 2.90474 | 0.187500 | ||||||||
\(241\) | −18.5851 | −1.19717 | −0.598586 | − | 0.801059i | \(-0.704270\pi\) | ||||
−0.598586 | + | 0.801059i | \(0.704270\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.88423 | 0.569924 | ||||||||
\(244\) | 6.33662 | 0.405660 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 15.7769 | 1.00590 | ||||||||
\(247\) | −25.8767 | −1.64649 | ||||||||
\(248\) | −1.28349 | −0.0815020 | ||||||||
\(249\) | −13.3473 | −0.845852 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −10.0947 | −0.637174 | −0.318587 | − | 0.947894i | \(-0.603208\pi\) | ||||
−0.318587 | + | 0.947894i | \(0.603208\pi\) | |||||||
\(252\) | −5.43751 | −0.342531 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.0026 | −1.00409 | ||||||||
\(255\) | 20.5606 | 1.28756 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.47320 | −0.341409 | −0.170704 | − | 0.985322i | \(-0.554604\pi\) | ||||
−0.170704 | + | 0.985322i | \(0.554604\pi\) | |||||||
\(258\) | 32.5339 | 2.02547 | ||||||||
\(259\) | 1.00807 | 0.0626385 | ||||||||
\(260\) | 6.51020 | 0.403745 | ||||||||
\(261\) | 6.41207 | 0.396897 | ||||||||
\(262\) | 14.6019 | 0.902109 | ||||||||
\(263\) | −12.8440 | −0.791998 | −0.395999 | − | 0.918251i | \(-0.629602\pi\) | ||||
−0.395999 | + | 0.918251i | \(0.629602\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.75606 | 0.476451 | ||||||||
\(266\) | −3.97479 | −0.243710 | ||||||||
\(267\) | 4.15634 | 0.254364 | ||||||||
\(268\) | 3.88122 | 0.237083 | ||||||||
\(269\) | 7.87541 | 0.480172 | 0.240086 | − | 0.970752i | \(-0.422824\pi\) | ||||
0.240086 | + | 0.970752i | \(0.422824\pi\) | |||||||
\(270\) | 7.08034 | 0.430896 | ||||||||
\(271\) | 9.87947 | 0.600135 | 0.300068 | − | 0.953918i | \(-0.402991\pi\) | ||||
0.300068 | + | 0.953918i | \(0.402991\pi\) | |||||||
\(272\) | 7.07831 | 0.429185 | ||||||||
\(273\) | −18.9104 | −1.14451 | ||||||||
\(274\) | 10.0996 | 0.610142 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −27.3044 | −1.64353 | ||||||||
\(277\) | 27.0289 | 1.62401 | 0.812006 | − | 0.583649i | \(-0.198376\pi\) | ||||
0.812006 | + | 0.583649i | \(0.198376\pi\) | |||||||
\(278\) | −18.5110 | −1.11022 | ||||||||
\(279\) | −6.97902 | −0.417823 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 13.6419 | 0.813806 | 0.406903 | − | 0.913471i | \(-0.366609\pi\) | ||||
0.406903 | + | 0.913471i | \(0.366609\pi\) | |||||||
\(282\) | 33.0892 | 1.97043 | ||||||||
\(283\) | 18.3850 | 1.09287 | 0.546437 | − | 0.837500i | \(-0.315984\pi\) | ||||
0.546437 | + | 0.837500i | \(0.315984\pi\) | |||||||
\(284\) | −0.259926 | −0.0154238 | ||||||||
\(285\) | 11.5457 | 0.683910 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.43144 | 0.320608 | ||||||||
\(288\) | 5.43751 | 0.320409 | ||||||||
\(289\) | 33.1024 | 1.94720 | ||||||||
\(290\) | −1.17923 | −0.0692467 | ||||||||
\(291\) | 25.0009 | 1.46558 | ||||||||
\(292\) | 4.82486 | 0.282354 | ||||||||
\(293\) | 9.87445 | 0.576871 | 0.288436 | − | 0.957499i | \(-0.406865\pi\) | ||||
0.288436 | + | 0.957499i | \(0.406865\pi\) | |||||||
\(294\) | −2.90474 | −0.169408 | ||||||||
\(295\) | 5.64597 | 0.328721 | ||||||||
\(296\) | −1.00807 | −0.0585930 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.5126 | 0.666909 | ||||||||
\(299\) | −61.1955 | −3.53902 | ||||||||
\(300\) | −2.90474 | −0.167705 | ||||||||
\(301\) | 11.2003 | 0.645573 | ||||||||
\(302\) | 5.43407 | 0.312696 | ||||||||
\(303\) | 20.7473 | 1.19190 | ||||||||
\(304\) | 3.97479 | 0.227970 | ||||||||
\(305\) | −6.33662 | −0.362834 | ||||||||
\(306\) | 38.4884 | 2.20023 | ||||||||
\(307\) | 6.50344 | 0.371171 | 0.185585 | − | 0.982628i | \(-0.440582\pi\) | ||||
0.185585 | + | 0.982628i | \(0.440582\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.06653 | −0.515777 | ||||||||
\(310\) | 1.28349 | 0.0728976 | ||||||||
\(311\) | 3.36996 | 0.191093 | 0.0955464 | − | 0.995425i | \(-0.469540\pi\) | ||||
0.0955464 | + | 0.995425i | \(0.469540\pi\) | |||||||
\(312\) | 18.9104 | 1.07059 | ||||||||
\(313\) | −5.42220 | −0.306481 | −0.153240 | − | 0.988189i | \(-0.548971\pi\) | ||||
−0.153240 | + | 0.988189i | \(0.548971\pi\) | |||||||
\(314\) | 7.97651 | 0.450141 | ||||||||
\(315\) | 5.43751 | 0.306369 | ||||||||
\(316\) | 14.3428 | 0.806843 | ||||||||
\(317\) | −7.15998 | −0.402145 | −0.201072 | − | 0.979576i | \(-0.564443\pi\) | ||||
−0.201072 | + | 0.979576i | \(0.564443\pi\) | |||||||
\(318\) | 22.5293 | 1.26338 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 9.56205 | 0.533702 | ||||||||
\(322\) | −9.39994 | −0.523838 | ||||||||
\(323\) | 28.1348 | 1.56546 | ||||||||
\(324\) | 4.25401 | 0.236334 | ||||||||
\(325\) | −6.51020 | −0.361121 | ||||||||
\(326\) | 14.3432 | 0.794396 | ||||||||
\(327\) | −36.5576 | −2.02164 | ||||||||
\(328\) | −5.43144 | −0.299901 | ||||||||
\(329\) | 11.3915 | 0.628031 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.6983 | 1.13768 | 0.568842 | − | 0.822447i | \(-0.307392\pi\) | ||||
0.568842 | + | 0.822447i | \(0.307392\pi\) | |||||||
\(332\) | 4.59502 | 0.252184 | ||||||||
\(333\) | −5.48140 | −0.300379 | ||||||||
\(334\) | −1.91040 | −0.104532 | ||||||||
\(335\) | −3.88122 | −0.212053 | ||||||||
\(336\) | 2.90474 | 0.158467 | ||||||||
\(337\) | −7.81093 | −0.425488 | −0.212744 | − | 0.977108i | \(-0.568240\pi\) | ||||
−0.212744 | + | 0.977108i | \(0.568240\pi\) | |||||||
\(338\) | 29.3827 | 1.59821 | ||||||||
\(339\) | −3.49992 | −0.190090 | ||||||||
\(340\) | −7.07831 | −0.383875 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 21.6130 | 1.16870 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −11.2003 | −0.603879 | ||||||||
\(345\) | 27.3044 | 1.47002 | ||||||||
\(346\) | −14.5926 | −0.784502 | ||||||||
\(347\) | −27.9220 | −1.49893 | −0.749465 | − | 0.662044i | \(-0.769689\pi\) | ||||
−0.749465 | + | 0.662044i | \(0.769689\pi\) | |||||||
\(348\) | −3.42535 | −0.183618 | ||||||||
\(349\) | 20.5937 | 1.10236 | 0.551178 | − | 0.834387i | \(-0.314178\pi\) | ||||
0.551178 | + | 0.834387i | \(0.314178\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 46.0944 | 2.46034 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.61133 | −0.298661 | −0.149330 | − | 0.988787i | \(-0.547712\pi\) | ||||
−0.149330 | + | 0.988787i | \(0.547712\pi\) | |||||||
\(354\) | 16.4001 | 0.871653 | ||||||||
\(355\) | 0.259926 | 0.0137954 | ||||||||
\(356\) | −1.43088 | −0.0758366 | ||||||||
\(357\) | 20.5606 | 1.08818 | ||||||||
\(358\) | −3.15693 | −0.166849 | ||||||||
\(359\) | 8.24264 | 0.435030 | 0.217515 | − | 0.976057i | \(-0.430205\pi\) | ||||
0.217515 | + | 0.976057i | \(0.430205\pi\) | |||||||
\(360\) | −5.43751 | −0.286582 | ||||||||
\(361\) | −3.20104 | −0.168476 | ||||||||
\(362\) | −7.09045 | −0.372666 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.51020 | 0.341227 | ||||||||
\(365\) | −4.82486 | −0.252545 | ||||||||
\(366\) | −18.4062 | −0.962109 | ||||||||
\(367\) | −4.10818 | −0.214445 | −0.107223 | − | 0.994235i | \(-0.534196\pi\) | ||||
−0.107223 | + | 0.994235i | \(0.534196\pi\) | |||||||
\(368\) | 9.39994 | 0.490006 | ||||||||
\(369\) | −29.5335 | −1.53745 | ||||||||
\(370\) | 1.00807 | 0.0524071 | ||||||||
\(371\) | 7.75606 | 0.402675 | ||||||||
\(372\) | 3.72822 | 0.193299 | ||||||||
\(373\) | −26.2182 | −1.35753 | −0.678764 | − | 0.734356i | \(-0.737484\pi\) | ||||
−0.678764 | + | 0.734356i | \(0.737484\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.90474 | 0.150000 | ||||||||
\(376\) | −11.3915 | −0.587469 | ||||||||
\(377\) | −7.67702 | −0.395386 | ||||||||
\(378\) | 7.08034 | 0.364174 | ||||||||
\(379\) | 19.7398 | 1.01397 | 0.506983 | − | 0.861956i | \(-0.330761\pi\) | ||||
0.506983 | + | 0.861956i | \(0.330761\pi\) | |||||||
\(380\) | −3.97479 | −0.203902 | ||||||||
\(381\) | 46.4834 | 2.38141 | ||||||||
\(382\) | 7.61496 | 0.389615 | ||||||||
\(383\) | 35.8040 | 1.82950 | 0.914749 | − | 0.404022i | \(-0.132388\pi\) | ||||
0.914749 | + | 0.404022i | \(0.132388\pi\) | |||||||
\(384\) | −2.90474 | −0.148232 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.55503 | −0.435439 | ||||||||
\(387\) | −60.9017 | −3.09581 | ||||||||
\(388\) | −8.60695 | −0.436952 | ||||||||
\(389\) | −28.8835 | −1.46445 | −0.732226 | − | 0.681062i | \(-0.761518\pi\) | ||||
−0.732226 | + | 0.681062i | \(0.761518\pi\) | |||||||
\(390\) | −18.9104 | −0.957567 | ||||||||
\(391\) | 66.5356 | 3.36485 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −42.4147 | −2.13954 | ||||||||
\(394\) | 5.30318 | 0.267171 | ||||||||
\(395\) | −14.3428 | −0.721663 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.7117 | −1.59156 | −0.795782 | − | 0.605583i | \(-0.792940\pi\) | ||||
−0.795782 | + | 0.605583i | \(0.792940\pi\) | |||||||
\(398\) | 27.8463 | 1.39581 | ||||||||
\(399\) | 11.5457 | 0.578010 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −24.8442 | −1.24066 | −0.620331 | − | 0.784340i | \(-0.713002\pi\) | ||||
−0.620331 | + | 0.784340i | \(0.713002\pi\) | |||||||
\(402\) | −11.2739 | −0.562292 | ||||||||
\(403\) | 8.35580 | 0.416232 | ||||||||
\(404\) | −7.14255 | −0.355355 | ||||||||
\(405\) | −4.25401 | −0.211384 | ||||||||
\(406\) | −1.17923 | −0.0585242 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −20.5606 | −1.01790 | ||||||||
\(409\) | 17.6373 | 0.872107 | 0.436054 | − | 0.899921i | \(-0.356376\pi\) | ||||
0.436054 | + | 0.899921i | \(0.356376\pi\) | |||||||
\(410\) | 5.43144 | 0.268240 | ||||||||
\(411\) | −29.3368 | −1.44708 | ||||||||
\(412\) | 3.12129 | 0.153775 | ||||||||
\(413\) | 5.64597 | 0.277820 | ||||||||
\(414\) | 51.1123 | 2.51203 | ||||||||
\(415\) | −4.59502 | −0.225560 | ||||||||
\(416\) | −6.51020 | −0.319189 | ||||||||
\(417\) | 53.7697 | 2.63312 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.70771 | 0.327693 | 0.163847 | − | 0.986486i | \(-0.447610\pi\) | ||||
0.163847 | + | 0.986486i | \(0.447610\pi\) | |||||||
\(420\) | −2.90474 | −0.141737 | ||||||||
\(421\) | 16.0438 | 0.781925 | 0.390962 | − | 0.920407i | \(-0.372142\pi\) | ||||
0.390962 | + | 0.920407i | \(0.372142\pi\) | |||||||
\(422\) | 9.26733 | 0.451126 | ||||||||
\(423\) | −61.9412 | −3.01168 | ||||||||
\(424\) | −7.75606 | −0.376668 | ||||||||
\(425\) | 7.07831 | 0.343348 | ||||||||
\(426\) | 0.755017 | 0.0365807 | ||||||||
\(427\) | −6.33662 | −0.306650 | ||||||||
\(428\) | −3.29188 | −0.159119 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.2003 | 0.540125 | ||||||||
\(431\) | 31.5480 | 1.51961 | 0.759807 | − | 0.650148i | \(-0.225293\pi\) | ||||
0.759807 | + | 0.650148i | \(0.225293\pi\) | |||||||
\(432\) | −7.08034 | −0.340653 | ||||||||
\(433\) | −8.26911 | −0.397388 | −0.198694 | − | 0.980062i | \(-0.563670\pi\) | ||||
−0.198694 | + | 0.980062i | \(0.563670\pi\) | |||||||
\(434\) | 1.28349 | 0.0616097 | ||||||||
\(435\) | 3.42535 | 0.164233 | ||||||||
\(436\) | 12.5855 | 0.602736 | ||||||||
\(437\) | 37.3628 | 1.78730 | ||||||||
\(438\) | −14.0150 | −0.669661 | ||||||||
\(439\) | 11.1008 | 0.529814 | 0.264907 | − | 0.964274i | \(-0.414659\pi\) | ||||
0.264907 | + | 0.964274i | \(0.414659\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.43751 | 0.258929 | ||||||||
\(442\) | −46.0812 | −2.19186 | ||||||||
\(443\) | 4.53871 | 0.215641 | 0.107820 | − | 0.994170i | \(-0.465613\pi\) | ||||
0.107820 | + | 0.994170i | \(0.465613\pi\) | |||||||
\(444\) | 2.92819 | 0.138966 | ||||||||
\(445\) | 1.43088 | 0.0678303 | ||||||||
\(446\) | 26.0134 | 1.23177 | ||||||||
\(447\) | −33.4412 | −1.58171 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −9.71975 | −0.458703 | −0.229352 | − | 0.973344i | \(-0.573661\pi\) | ||||
−0.229352 | + | 0.973344i | \(0.573661\pi\) | |||||||
\(450\) | 5.43751 | 0.256327 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.20490 | 0.0566737 | ||||||||
\(453\) | −15.7846 | −0.741623 | ||||||||
\(454\) | −0.293119 | −0.0137568 | ||||||||
\(455\) | −6.51020 | −0.305203 | ||||||||
\(456\) | −11.5457 | −0.540678 | ||||||||
\(457\) | 21.1478 | 0.989251 | 0.494626 | − | 0.869106i | \(-0.335305\pi\) | ||||
0.494626 | + | 0.869106i | \(0.335305\pi\) | |||||||
\(458\) | −19.9552 | −0.932444 | ||||||||
\(459\) | −50.1168 | −2.33925 | ||||||||
\(460\) | −9.39994 | −0.438274 | ||||||||
\(461\) | 20.5158 | 0.955516 | 0.477758 | − | 0.878492i | \(-0.341450\pi\) | ||||
0.477758 | + | 0.878492i | \(0.341450\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.06175 | −0.235239 | −0.117620 | − | 0.993059i | \(-0.537526\pi\) | ||||
−0.117620 | + | 0.993059i | \(0.537526\pi\) | |||||||
\(464\) | 1.17923 | 0.0547443 | ||||||||
\(465\) | −3.72822 | −0.172892 | ||||||||
\(466\) | 0.201558 | 0.00933699 | ||||||||
\(467\) | −7.48743 | −0.346477 | −0.173239 | − | 0.984880i | \(-0.555423\pi\) | ||||
−0.173239 | + | 0.984880i | \(0.555423\pi\) | |||||||
\(468\) | −35.3993 | −1.63633 | ||||||||
\(469\) | −3.88122 | −0.179218 | ||||||||
\(470\) | 11.3915 | 0.525448 | ||||||||
\(471\) | −23.1697 | −1.06760 | ||||||||
\(472\) | −5.64597 | −0.259877 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −41.6620 | −1.91360 | ||||||||
\(475\) | 3.97479 | 0.182376 | ||||||||
\(476\) | −7.07831 | −0.324434 | ||||||||
\(477\) | −42.1737 | −1.93100 | ||||||||
\(478\) | 23.9193 | 1.09404 | ||||||||
\(479\) | −0.414174 | −0.0189241 | −0.00946206 | − | 0.999955i | \(-0.503012\pi\) | ||||
−0.00946206 | + | 0.999955i | \(0.503012\pi\) | |||||||
\(480\) | 2.90474 | 0.132583 | ||||||||
\(481\) | 6.56275 | 0.299235 | ||||||||
\(482\) | −18.5851 | −0.846528 | ||||||||
\(483\) | 27.3044 | 1.24239 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.60695 | 0.390821 | ||||||||
\(486\) | 8.88423 | 0.402997 | ||||||||
\(487\) | −23.7328 | −1.07544 | −0.537718 | − | 0.843125i | \(-0.680714\pi\) | ||||
−0.537718 | + | 0.843125i | \(0.680714\pi\) | |||||||
\(488\) | 6.33662 | 0.286845 | ||||||||
\(489\) | −41.6632 | −1.88408 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 32.2162 | 1.45390 | 0.726949 | − | 0.686691i | \(-0.240937\pi\) | ||||
0.726949 | + | 0.686691i | \(0.240937\pi\) | |||||||
\(492\) | 15.7769 | 0.711278 | ||||||||
\(493\) | 8.34695 | 0.375928 | ||||||||
\(494\) | −25.8767 | −1.16425 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.28349 | −0.0576306 | ||||||||
\(497\) | 0.259926 | 0.0116593 | ||||||||
\(498\) | −13.3473 | −0.598108 | ||||||||
\(499\) | −4.48988 | −0.200995 | −0.100497 | − | 0.994937i | \(-0.532043\pi\) | ||||
−0.100497 | + | 0.994937i | \(0.532043\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 5.54921 | 0.247920 | ||||||||
\(502\) | −10.0947 | −0.450550 | ||||||||
\(503\) | 30.8299 | 1.37464 | 0.687319 | − | 0.726355i | \(-0.258787\pi\) | ||||
0.687319 | + | 0.726355i | \(0.258787\pi\) | |||||||
\(504\) | −5.43751 | −0.242206 | ||||||||
\(505\) | 7.14255 | 0.317839 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −85.3491 | −3.79049 | ||||||||
\(508\) | −16.0026 | −0.710000 | ||||||||
\(509\) | −2.65682 | −0.117762 | −0.0588808 | − | 0.998265i | \(-0.518753\pi\) | ||||
−0.0588808 | + | 0.998265i | \(0.518753\pi\) | |||||||
\(510\) | 20.5606 | 0.910440 | ||||||||
\(511\) | −4.82486 | −0.213439 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −28.1429 | −1.24254 | ||||||||
\(514\) | −5.47320 | −0.241412 | ||||||||
\(515\) | −3.12129 | −0.137540 | ||||||||
\(516\) | 32.5339 | 1.43222 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.00807 | 0.0442921 | ||||||||
\(519\) | 42.3876 | 1.86061 | ||||||||
\(520\) | 6.51020 | 0.285491 | ||||||||
\(521\) | 5.98594 | 0.262249 | 0.131124 | − | 0.991366i | \(-0.458141\pi\) | ||||
0.131124 | + | 0.991366i | \(0.458141\pi\) | |||||||
\(522\) | 6.41207 | 0.280649 | ||||||||
\(523\) | 0.966746 | 0.0422728 | 0.0211364 | − | 0.999777i | \(-0.493272\pi\) | ||||
0.0211364 | + | 0.999777i | \(0.493272\pi\) | |||||||
\(524\) | 14.6019 | 0.637887 | ||||||||
\(525\) | 2.90474 | 0.126773 | ||||||||
\(526\) | −12.8440 | −0.560027 | ||||||||
\(527\) | −9.08497 | −0.395747 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 65.3588 | 2.84169 | ||||||||
\(530\) | 7.75606 | 0.336902 | ||||||||
\(531\) | −30.7000 | −1.33227 | ||||||||
\(532\) | −3.97479 | −0.172329 | ||||||||
\(533\) | 35.3597 | 1.53160 | ||||||||
\(534\) | 4.15634 | 0.179862 | ||||||||
\(535\) | 3.29188 | 0.142320 | ||||||||
\(536\) | 3.88122 | 0.167643 | ||||||||
\(537\) | 9.17005 | 0.395717 | ||||||||
\(538\) | 7.87541 | 0.339533 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.08034 | 0.304689 | ||||||||
\(541\) | −1.56401 | −0.0672420 | −0.0336210 | − | 0.999435i | \(-0.510704\pi\) | ||||
−0.0336210 | + | 0.999435i | \(0.510704\pi\) | |||||||
\(542\) | 9.87947 | 0.424360 | ||||||||
\(543\) | 20.5959 | 0.883855 | ||||||||
\(544\) | 7.07831 | 0.303480 | ||||||||
\(545\) | −12.5855 | −0.539103 | ||||||||
\(546\) | −18.9104 | −0.809292 | ||||||||
\(547\) | −14.5413 | −0.621741 | −0.310870 | − | 0.950452i | \(-0.600620\pi\) | ||||
−0.310870 | + | 0.950452i | \(0.600620\pi\) | |||||||
\(548\) | 10.0996 | 0.431435 | ||||||||
\(549\) | 34.4554 | 1.47052 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.68719 | 0.199681 | ||||||||
\(552\) | −27.3044 | −1.16215 | ||||||||
\(553\) | −14.3428 | −0.609916 | ||||||||
\(554\) | 27.0289 | 1.14835 | ||||||||
\(555\) | −2.92819 | −0.124295 | ||||||||
\(556\) | −18.5110 | −0.785043 | ||||||||
\(557\) | −37.0040 | −1.56791 | −0.783956 | − | 0.620817i | \(-0.786801\pi\) | ||||
−0.783956 | + | 0.620817i | \(0.786801\pi\) | |||||||
\(558\) | −6.97902 | −0.295445 | ||||||||
\(559\) | 72.9160 | 3.08402 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.6419 | 0.575448 | ||||||||
\(563\) | 23.9389 | 1.00890 | 0.504452 | − | 0.863440i | \(-0.331694\pi\) | ||||
0.504452 | + | 0.863440i | \(0.331694\pi\) | |||||||
\(564\) | 33.0892 | 1.39331 | ||||||||
\(565\) | −1.20490 | −0.0506905 | ||||||||
\(566\) | 18.3850 | 0.772779 | ||||||||
\(567\) | −4.25401 | −0.178652 | ||||||||
\(568\) | −0.259926 | −0.0109063 | ||||||||
\(569\) | −26.6076 | −1.11545 | −0.557725 | − | 0.830026i | \(-0.688326\pi\) | ||||
−0.557725 | + | 0.830026i | \(0.688326\pi\) | |||||||
\(570\) | 11.5457 | 0.483597 | ||||||||
\(571\) | 17.4823 | 0.731610 | 0.365805 | − | 0.930692i | \(-0.380794\pi\) | ||||
0.365805 | + | 0.930692i | \(0.380794\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.1195 | −0.924055 | ||||||||
\(574\) | 5.43144 | 0.226704 | ||||||||
\(575\) | 9.39994 | 0.392004 | ||||||||
\(576\) | 5.43751 | 0.226563 | ||||||||
\(577\) | 31.3194 | 1.30385 | 0.651923 | − | 0.758285i | \(-0.273963\pi\) | ||||
0.651923 | + | 0.758285i | \(0.273963\pi\) | |||||||
\(578\) | 33.1024 | 1.37688 | ||||||||
\(579\) | 24.8501 | 1.03274 | ||||||||
\(580\) | −1.17923 | −0.0489648 | ||||||||
\(581\) | −4.59502 | −0.190633 | ||||||||
\(582\) | 25.0009 | 1.03632 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.82486 | 0.199654 | ||||||||
\(585\) | 35.3993 | 1.46358 | ||||||||
\(586\) | 9.87445 | 0.407910 | ||||||||
\(587\) | 4.04656 | 0.167019 | 0.0835097 | − | 0.996507i | \(-0.473387\pi\) | ||||
0.0835097 | + | 0.996507i | \(0.473387\pi\) | |||||||
\(588\) | −2.90474 | −0.119789 | ||||||||
\(589\) | −5.10162 | −0.210209 | ||||||||
\(590\) | 5.64597 | 0.232441 | ||||||||
\(591\) | −15.4044 | −0.633651 | ||||||||
\(592\) | −1.00807 | −0.0414315 | ||||||||
\(593\) | 23.7125 | 0.973756 | 0.486878 | − | 0.873470i | \(-0.338136\pi\) | ||||
0.486878 | + | 0.873470i | \(0.338136\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.07831 | 0.290182 | ||||||||
\(596\) | 11.5126 | 0.471576 | ||||||||
\(597\) | −80.8864 | −3.31046 | ||||||||
\(598\) | −61.1955 | −2.50247 | ||||||||
\(599\) | −10.4237 | −0.425900 | −0.212950 | − | 0.977063i | \(-0.568307\pi\) | ||||
−0.212950 | + | 0.977063i | \(0.568307\pi\) | |||||||
\(600\) | −2.90474 | −0.118586 | ||||||||
\(601\) | −15.5929 | −0.636049 | −0.318025 | − | 0.948082i | \(-0.603019\pi\) | ||||
−0.318025 | + | 0.948082i | \(0.603019\pi\) | |||||||
\(602\) | 11.2003 | 0.456489 | ||||||||
\(603\) | 21.1042 | 0.859428 | ||||||||
\(604\) | 5.43407 | 0.221109 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 20.7473 | 0.842799 | ||||||||
\(607\) | −3.06966 | −0.124594 | −0.0622968 | − | 0.998058i | \(-0.519843\pi\) | ||||
−0.0622968 | + | 0.998058i | \(0.519843\pi\) | |||||||
\(608\) | 3.97479 | 0.161199 | ||||||||
\(609\) | 3.42535 | 0.138802 | ||||||||
\(610\) | −6.33662 | −0.256562 | ||||||||
\(611\) | 74.1606 | 3.00022 | ||||||||
\(612\) | 38.4884 | 1.55580 | ||||||||
\(613\) | 25.5273 | 1.03104 | 0.515520 | − | 0.856878i | \(-0.327599\pi\) | ||||
0.515520 | + | 0.856878i | \(0.327599\pi\) | |||||||
\(614\) | 6.50344 | 0.262457 | ||||||||
\(615\) | −15.7769 | −0.636187 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.4437 | −0.581483 | −0.290741 | − | 0.956802i | \(-0.593902\pi\) | ||||
−0.290741 | + | 0.956802i | \(0.593902\pi\) | |||||||
\(618\) | −9.06653 | −0.364709 | ||||||||
\(619\) | 1.76790 | 0.0710578 | 0.0355289 | − | 0.999369i | \(-0.488688\pi\) | ||||
0.0355289 | + | 0.999369i | \(0.488688\pi\) | |||||||
\(620\) | 1.28349 | 0.0515464 | ||||||||
\(621\) | −66.5548 | −2.67075 | ||||||||
\(622\) | 3.36996 | 0.135123 | ||||||||
\(623\) | 1.43088 | 0.0573270 | ||||||||
\(624\) | 18.9104 | 0.757023 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.42220 | −0.216715 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.97651 | 0.318297 | ||||||||
\(629\) | −7.13544 | −0.284509 | ||||||||
\(630\) | 5.43751 | 0.216636 | ||||||||
\(631\) | 21.3564 | 0.850185 | 0.425093 | − | 0.905150i | \(-0.360242\pi\) | ||||
0.425093 | + | 0.905150i | \(0.360242\pi\) | |||||||
\(632\) | 14.3428 | 0.570524 | ||||||||
\(633\) | −26.9192 | −1.06994 | ||||||||
\(634\) | −7.15998 | −0.284359 | ||||||||
\(635\) | 16.0026 | 0.635043 | ||||||||
\(636\) | 22.5293 | 0.893346 | ||||||||
\(637\) | −6.51020 | −0.257943 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.41335 | −0.0559113 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 46.1398 | 1.82241 | 0.911205 | − | 0.411952i | \(-0.135153\pi\) | ||||
0.911205 | + | 0.411952i | \(0.135153\pi\) | |||||||
\(642\) | 9.56205 | 0.377384 | ||||||||
\(643\) | 18.4699 | 0.728383 | 0.364191 | − | 0.931324i | \(-0.381345\pi\) | ||||
0.364191 | + | 0.931324i | \(0.381345\pi\) | |||||||
\(644\) | −9.39994 | −0.370409 | ||||||||
\(645\) | −32.5339 | −1.28102 | ||||||||
\(646\) | 28.1348 | 1.10695 | ||||||||
\(647\) | 36.3807 | 1.43027 | 0.715137 | − | 0.698984i | \(-0.246364\pi\) | ||||
0.715137 | + | 0.698984i | \(0.246364\pi\) | |||||||
\(648\) | 4.25401 | 0.167113 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −6.51020 | −0.255351 | ||||||||
\(651\) | −3.72822 | −0.146120 | ||||||||
\(652\) | 14.3432 | 0.561723 | ||||||||
\(653\) | −2.89414 | −0.113256 | −0.0566281 | − | 0.998395i | \(-0.518035\pi\) | ||||
−0.0566281 | + | 0.998395i | \(0.518035\pi\) | |||||||
\(654\) | −36.5576 | −1.42951 | ||||||||
\(655\) | −14.6019 | −0.570544 | ||||||||
\(656\) | −5.43144 | −0.212062 | ||||||||
\(657\) | 26.2352 | 1.02353 | ||||||||
\(658\) | 11.3915 | 0.444085 | ||||||||
\(659\) | 19.1764 | 0.747008 | 0.373504 | − | 0.927629i | \(-0.378156\pi\) | ||||
0.373504 | + | 0.927629i | \(0.378156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.9234 | −0.969406 | −0.484703 | − | 0.874679i | \(-0.661072\pi\) | ||||
−0.484703 | + | 0.874679i | \(0.661072\pi\) | |||||||
\(662\) | 20.6983 | 0.804463 | ||||||||
\(663\) | 133.854 | 5.19845 | ||||||||
\(664\) | 4.59502 | 0.178321 | ||||||||
\(665\) | 3.97479 | 0.154136 | ||||||||
\(666\) | −5.48140 | −0.212400 | ||||||||
\(667\) | 11.0847 | 0.429200 | ||||||||
\(668\) | −1.91040 | −0.0739155 | ||||||||
\(669\) | −75.5621 | −2.92140 | ||||||||
\(670\) | −3.88122 | −0.149944 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.90474 | 0.112053 | ||||||||
\(673\) | 13.3066 | 0.512932 | 0.256466 | − | 0.966553i | \(-0.417442\pi\) | ||||
0.256466 | + | 0.966553i | \(0.417442\pi\) | |||||||
\(674\) | −7.81093 | −0.300866 | ||||||||
\(675\) | −7.08034 | −0.272523 | ||||||||
\(676\) | 29.3827 | 1.13010 | ||||||||
\(677\) | 28.2748 | 1.08669 | 0.543344 | − | 0.839510i | \(-0.317158\pi\) | ||||
0.543344 | + | 0.839510i | \(0.317158\pi\) | |||||||
\(678\) | −3.49992 | −0.134414 | ||||||||
\(679\) | 8.60695 | 0.330304 | ||||||||
\(680\) | −7.07831 | −0.271441 | ||||||||
\(681\) | 0.851435 | 0.0326271 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.1040 | −0.769259 | −0.384629 | − | 0.923071i | \(-0.625671\pi\) | ||||
−0.384629 | + | 0.923071i | \(0.625671\pi\) | |||||||
\(684\) | 21.6130 | 0.826393 | ||||||||
\(685\) | −10.0996 | −0.385887 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 57.9646 | 2.21149 | ||||||||
\(688\) | −11.2003 | −0.427007 | ||||||||
\(689\) | 50.4935 | 1.92365 | ||||||||
\(690\) | 27.3044 | 1.03946 | ||||||||
\(691\) | −1.68862 | −0.0642382 | −0.0321191 | − | 0.999484i | \(-0.510226\pi\) | ||||
−0.0321191 | + | 0.999484i | \(0.510226\pi\) | |||||||
\(692\) | −14.5926 | −0.554726 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.9220 | −1.05990 | ||||||||
\(695\) | 18.5110 | 0.702164 | ||||||||
\(696\) | −3.42535 | −0.129838 | ||||||||
\(697\) | −38.4454 | −1.45622 | ||||||||
\(698\) | 20.5937 | 0.779484 | ||||||||
\(699\) | −0.585473 | −0.0221446 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 2.04142 | 0.0771035 | 0.0385517 | − | 0.999257i | \(-0.487726\pi\) | ||||
0.0385517 | + | 0.999257i | \(0.487726\pi\) | |||||||
\(702\) | 46.0944 | 1.73972 | ||||||||
\(703\) | −4.00687 | −0.151122 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.0892 | −1.24621 | ||||||||
\(706\) | −5.61133 | −0.211185 | ||||||||
\(707\) | 7.14255 | 0.268623 | ||||||||
\(708\) | 16.4001 | 0.616352 | ||||||||
\(709\) | 4.99388 | 0.187549 | 0.0937745 | − | 0.995593i | \(-0.470107\pi\) | ||||
0.0937745 | + | 0.995593i | \(0.470107\pi\) | |||||||
\(710\) | 0.259926 | 0.00975485 | ||||||||
\(711\) | 77.9890 | 2.92481 | ||||||||
\(712\) | −1.43088 | −0.0536245 | ||||||||
\(713\) | −12.0648 | −0.451829 | ||||||||
\(714\) | 20.5606 | 0.769463 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.15693 | −0.117980 | ||||||||
\(717\) | −69.4792 | −2.59475 | ||||||||
\(718\) | 8.24264 | 0.307613 | ||||||||
\(719\) | 34.3305 | 1.28031 | 0.640156 | − | 0.768245i | \(-0.278870\pi\) | ||||
0.640156 | + | 0.768245i | \(0.278870\pi\) | |||||||
\(720\) | −5.43751 | −0.202644 | ||||||||
\(721\) | −3.12129 | −0.116243 | ||||||||
\(722\) | −3.20104 | −0.119130 | ||||||||
\(723\) | 53.9849 | 2.00772 | ||||||||
\(724\) | −7.09045 | −0.263514 | ||||||||
\(725\) | 1.17923 | 0.0437955 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.6447 | 0.988196 | 0.494098 | − | 0.869406i | \(-0.335498\pi\) | ||||
0.494098 | + | 0.869406i | \(0.335498\pi\) | |||||||
\(728\) | 6.51020 | 0.241284 | ||||||||
\(729\) | −38.5684 | −1.42846 | ||||||||
\(730\) | −4.82486 | −0.178576 | ||||||||
\(731\) | −79.2790 | −2.93224 | ||||||||
\(732\) | −18.4062 | −0.680314 | ||||||||
\(733\) | 14.1335 | 0.522032 | 0.261016 | − | 0.965334i | \(-0.415942\pi\) | ||||
0.261016 | + | 0.965334i | \(0.415942\pi\) | |||||||
\(734\) | −4.10818 | −0.151636 | ||||||||
\(735\) | 2.90474 | 0.107143 | ||||||||
\(736\) | 9.39994 | 0.346486 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −29.5335 | −1.08714 | ||||||||
\(739\) | 36.0918 | 1.32766 | 0.663829 | − | 0.747884i | \(-0.268930\pi\) | ||||
0.663829 | + | 0.747884i | \(0.268930\pi\) | |||||||
\(740\) | 1.00807 | 0.0370574 | ||||||||
\(741\) | 75.1650 | 2.76126 | ||||||||
\(742\) | 7.75606 | 0.284734 | ||||||||
\(743\) | −29.3508 | −1.07678 | −0.538389 | − | 0.842697i | \(-0.680967\pi\) | ||||
−0.538389 | + | 0.842697i | \(0.680967\pi\) | |||||||
\(744\) | 3.72822 | 0.136683 | ||||||||
\(745\) | −11.5126 | −0.421790 | ||||||||
\(746\) | −26.2182 | −0.959917 | ||||||||
\(747\) | 24.9855 | 0.914170 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.29188 | 0.120283 | ||||||||
\(750\) | 2.90474 | 0.106066 | ||||||||
\(751\) | 36.8418 | 1.34438 | 0.672189 | − | 0.740380i | \(-0.265354\pi\) | ||||
0.672189 | + | 0.740380i | \(0.265354\pi\) | |||||||
\(752\) | −11.3915 | −0.415404 | ||||||||
\(753\) | 29.3226 | 1.06857 | ||||||||
\(754\) | −7.67702 | −0.279580 | ||||||||
\(755\) | −5.43407 | −0.197766 | ||||||||
\(756\) | 7.08034 | 0.257510 | ||||||||
\(757\) | −36.7671 | −1.33632 | −0.668161 | − | 0.744016i | \(-0.732918\pi\) | ||||
−0.668161 | + | 0.744016i | \(0.732918\pi\) | |||||||
\(758\) | 19.7398 | 0.716982 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.97479 | −0.144181 | ||||||||
\(761\) | 35.6456 | 1.29215 | 0.646075 | − | 0.763274i | \(-0.276409\pi\) | ||||
0.646075 | + | 0.763274i | \(0.276409\pi\) | |||||||
\(762\) | 46.4834 | 1.68391 | ||||||||
\(763\) | −12.5855 | −0.455625 | ||||||||
\(764\) | 7.61496 | 0.275500 | ||||||||
\(765\) | −38.4884 | −1.39155 | ||||||||
\(766\) | 35.8040 | 1.29365 | ||||||||
\(767\) | 36.7564 | 1.32720 | ||||||||
\(768\) | −2.90474 | −0.104816 | ||||||||
\(769\) | 30.6264 | 1.10442 | 0.552209 | − | 0.833706i | \(-0.313785\pi\) | ||||
0.552209 | + | 0.833706i | \(0.313785\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.8982 | 0.572560 | ||||||||
\(772\) | −8.55503 | −0.307902 | ||||||||
\(773\) | −10.7328 | −0.386033 | −0.193017 | − | 0.981195i | \(-0.561827\pi\) | ||||
−0.193017 | + | 0.981195i | \(0.561827\pi\) | |||||||
\(774\) | −60.9017 | −2.18907 | ||||||||
\(775\) | −1.28349 | −0.0461045 | ||||||||
\(776\) | −8.60695 | −0.308971 | ||||||||
\(777\) | −2.92819 | −0.105048 | ||||||||
\(778\) | −28.8835 | −1.03552 | ||||||||
\(779\) | −21.5888 | −0.773500 | ||||||||
\(780\) | −18.9104 | −0.677102 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 66.5356 | 2.37931 | ||||||||
\(783\) | −8.34934 | −0.298381 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −7.97651 | −0.284694 | ||||||||
\(786\) | −42.4147 | −1.51288 | ||||||||
\(787\) | −18.2605 | −0.650917 | −0.325459 | − | 0.945556i | \(-0.605519\pi\) | ||||
−0.325459 | + | 0.945556i | \(0.605519\pi\) | |||||||
\(788\) | 5.30318 | 0.188918 | ||||||||
\(789\) | 37.3086 | 1.32822 | ||||||||
\(790\) | −14.3428 | −0.510293 | ||||||||
\(791\) | −1.20490 | −0.0428413 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.2526 | −1.46492 | ||||||||
\(794\) | −31.7117 | −1.12541 | ||||||||
\(795\) | −22.5293 | −0.799033 | ||||||||
\(796\) | 27.8463 | 0.986987 | ||||||||
\(797\) | −29.4786 | −1.04418 | −0.522092 | − | 0.852889i | \(-0.674848\pi\) | ||||
−0.522092 | + | 0.852889i | \(0.674848\pi\) | |||||||
\(798\) | 11.5457 | 0.408714 | ||||||||
\(799\) | −80.6322 | −2.85256 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −7.78044 | −0.274908 | ||||||||
\(802\) | −24.8442 | −0.877281 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −11.2739 | −0.397601 | ||||||||
\(805\) | 9.39994 | 0.331304 | ||||||||
\(806\) | 8.35580 | 0.294321 | ||||||||
\(807\) | −22.8760 | −0.805274 | ||||||||
\(808\) | −7.14255 | −0.251274 | ||||||||
\(809\) | −22.3819 | −0.786904 | −0.393452 | − | 0.919345i | \(-0.628719\pi\) | ||||
−0.393452 | + | 0.919345i | \(0.628719\pi\) | |||||||
\(810\) | −4.25401 | −0.149471 | ||||||||
\(811\) | −27.0318 | −0.949214 | −0.474607 | − | 0.880198i | \(-0.657410\pi\) | ||||
−0.474607 | + | 0.880198i | \(0.657410\pi\) | |||||||
\(812\) | −1.17923 | −0.0413828 | ||||||||
\(813\) | −28.6973 | −1.00646 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.3432 | −0.502420 | ||||||||
\(816\) | −20.5606 | −0.719766 | ||||||||
\(817\) | −44.5188 | −1.55751 | ||||||||
\(818\) | 17.6373 | 0.616673 | ||||||||
\(819\) | 35.3993 | 1.23695 | ||||||||
\(820\) | 5.43144 | 0.189674 | ||||||||
\(821\) | −14.4241 | −0.503404 | −0.251702 | − | 0.967805i | \(-0.580990\pi\) | ||||
−0.251702 | + | 0.967805i | \(0.580990\pi\) | |||||||
\(822\) | −29.3368 | −1.02324 | ||||||||
\(823\) | −15.3358 | −0.534572 | −0.267286 | − | 0.963617i | \(-0.586127\pi\) | ||||
−0.267286 | + | 0.963617i | \(0.586127\pi\) | |||||||
\(824\) | 3.12129 | 0.108735 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.64597 | 0.196448 | ||||||||
\(827\) | 44.2084 | 1.53728 | 0.768638 | − | 0.639685i | \(-0.220935\pi\) | ||||
0.768638 | + | 0.639685i | \(0.220935\pi\) | |||||||
\(828\) | 51.1123 | 1.77627 | ||||||||
\(829\) | −27.9599 | −0.971087 | −0.485544 | − | 0.874212i | \(-0.661378\pi\) | ||||
−0.485544 | + | 0.874212i | \(0.661378\pi\) | |||||||
\(830\) | −4.59502 | −0.159495 | ||||||||
\(831\) | −78.5120 | −2.72355 | ||||||||
\(832\) | −6.51020 | −0.225701 | ||||||||
\(833\) | 7.07831 | 0.245249 | ||||||||
\(834\) | 53.7697 | 1.86189 | ||||||||
\(835\) | 1.91040 | 0.0661120 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.08758 | 0.314113 | ||||||||
\(838\) | 6.70771 | 0.231714 | ||||||||
\(839\) | −4.45002 | −0.153632 | −0.0768159 | − | 0.997045i | \(-0.524475\pi\) | ||||
−0.0768159 | + | 0.997045i | \(0.524475\pi\) | |||||||
\(840\) | −2.90474 | −0.100223 | ||||||||
\(841\) | −27.6094 | −0.952049 | ||||||||
\(842\) | 16.0438 | 0.552904 | ||||||||
\(843\) | −39.6261 | −1.36480 | ||||||||
\(844\) | 9.26733 | 0.318995 | ||||||||
\(845\) | −29.3827 | −1.01080 | ||||||||
\(846\) | −61.9412 | −2.12958 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.75606 | −0.266344 | ||||||||
\(849\) | −53.4036 | −1.83281 | ||||||||
\(850\) | 7.07831 | 0.242784 | ||||||||
\(851\) | −9.47581 | −0.324826 | ||||||||
\(852\) | 0.755017 | 0.0258665 | ||||||||
\(853\) | 2.31141 | 0.0791411 | 0.0395705 | − | 0.999217i | \(-0.487401\pi\) | ||||
0.0395705 | + | 0.999217i | \(0.487401\pi\) | |||||||
\(854\) | −6.33662 | −0.216835 | ||||||||
\(855\) | −21.6130 | −0.739148 | ||||||||
\(856\) | −3.29188 | −0.112514 | ||||||||
\(857\) | 2.10357 | 0.0718566 | 0.0359283 | − | 0.999354i | \(-0.488561\pi\) | ||||
0.0359283 | + | 0.999354i | \(0.488561\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.91941 | −0.236087 | −0.118044 | − | 0.993008i | \(-0.537662\pi\) | ||||
−0.118044 | + | 0.993008i | \(0.537662\pi\) | |||||||
\(860\) | 11.2003 | 0.381926 | ||||||||
\(861\) | −15.7769 | −0.537676 | ||||||||
\(862\) | 31.5480 | 1.07453 | ||||||||
\(863\) | −37.5821 | −1.27931 | −0.639655 | − | 0.768662i | \(-0.720923\pi\) | ||||
−0.639655 | + | 0.768662i | \(0.720923\pi\) | |||||||
\(864\) | −7.08034 | −0.240878 | ||||||||
\(865\) | 14.5926 | 0.496162 | ||||||||
\(866\) | −8.26911 | −0.280996 | ||||||||
\(867\) | −96.1540 | −3.26556 | ||||||||
\(868\) | 1.28349 | 0.0435646 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.42535 | 0.116130 | ||||||||
\(871\) | −25.2675 | −0.856156 | ||||||||
\(872\) | 12.5855 | 0.426199 | ||||||||
\(873\) | −46.8004 | −1.58395 | ||||||||
\(874\) | 37.3628 | 1.26381 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −14.0150 | −0.473522 | ||||||||
\(877\) | 34.1431 | 1.15293 | 0.576465 | − | 0.817122i | \(-0.304432\pi\) | ||||
0.576465 | + | 0.817122i | \(0.304432\pi\) | |||||||
\(878\) | 11.1008 | 0.374635 | ||||||||
\(879\) | −28.6827 | −0.967443 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.7897 | 1.30686 | 0.653429 | − | 0.756987i | \(-0.273330\pi\) | ||||
0.653429 | + | 0.756987i | \(0.273330\pi\) | |||||||
\(882\) | 5.43751 | 0.183091 | ||||||||
\(883\) | 1.29604 | 0.0436152 | 0.0218076 | − | 0.999762i | \(-0.493058\pi\) | ||||
0.0218076 | + | 0.999762i | \(0.493058\pi\) | |||||||
\(884\) | −46.0812 | −1.54988 | ||||||||
\(885\) | −16.4001 | −0.551282 | ||||||||
\(886\) | 4.53871 | 0.152481 | ||||||||
\(887\) | 6.44111 | 0.216271 | 0.108136 | − | 0.994136i | \(-0.465512\pi\) | ||||
0.108136 | + | 0.994136i | \(0.465512\pi\) | |||||||
\(888\) | 2.92819 | 0.0982635 | ||||||||
\(889\) | 16.0026 | 0.536710 | ||||||||
\(890\) | 1.43088 | 0.0479633 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.0134 | 0.870992 | ||||||||
\(893\) | −45.2786 | −1.51519 | ||||||||
\(894\) | −33.4412 | −1.11844 | ||||||||
\(895\) | 3.15693 | 0.105524 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 177.757 | 5.93513 | ||||||||
\(898\) | −9.71975 | −0.324352 | ||||||||
\(899\) | −1.51353 | −0.0504792 | ||||||||
\(900\) | 5.43751 | 0.181250 | ||||||||
\(901\) | −54.8998 | −1.82898 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −32.5339 | −1.08266 | ||||||||
\(904\) | 1.20490 | 0.0400744 | ||||||||
\(905\) | 7.09045 | 0.235694 | ||||||||
\(906\) | −15.7846 | −0.524407 | ||||||||
\(907\) | 35.2975 | 1.17203 | 0.586017 | − | 0.810299i | \(-0.300695\pi\) | ||||
0.586017 | + | 0.810299i | \(0.300695\pi\) | |||||||
\(908\) | −0.293119 | −0.00972750 | ||||||||
\(909\) | −38.8377 | −1.28817 | ||||||||
\(910\) | −6.51020 | −0.215811 | ||||||||
\(911\) | −36.9287 | −1.22350 | −0.611752 | − | 0.791050i | \(-0.709535\pi\) | ||||
−0.611752 | + | 0.791050i | \(0.709535\pi\) | |||||||
\(912\) | −11.5457 | −0.382317 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 21.1478 | 0.699506 | ||||||||
\(915\) | 18.4062 | 0.608491 | ||||||||
\(916\) | −19.9552 | −0.659337 | ||||||||
\(917\) | −14.6019 | −0.482197 | ||||||||
\(918\) | −50.1168 | −1.65410 | ||||||||
\(919\) | −35.4760 | −1.17025 | −0.585123 | − | 0.810945i | \(-0.698954\pi\) | ||||
−0.585123 | + | 0.810945i | \(0.698954\pi\) | |||||||
\(920\) | −9.39994 | −0.309907 | ||||||||
\(921\) | −18.8908 | −0.622473 | ||||||||
\(922\) | 20.5158 | 0.675652 | ||||||||
\(923\) | 1.69217 | 0.0556984 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00807 | −0.0331452 | ||||||||
\(926\) | −5.06175 | −0.166339 | ||||||||
\(927\) | 16.9720 | 0.557435 | ||||||||
\(928\) | 1.17923 | 0.0387101 | ||||||||
\(929\) | −17.7706 | −0.583034 | −0.291517 | − | 0.956566i | \(-0.594160\pi\) | ||||
−0.291517 | + | 0.956566i | \(0.594160\pi\) | |||||||
\(930\) | −3.72822 | −0.122253 | ||||||||
\(931\) | 3.97479 | 0.130268 | ||||||||
\(932\) | 0.201558 | 0.00660225 | ||||||||
\(933\) | −9.78885 | −0.320473 | ||||||||
\(934\) | −7.48743 | −0.244996 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −35.3993 | −1.15706 | ||||||||
\(937\) | 6.01550 | 0.196518 | 0.0982589 | − | 0.995161i | \(-0.468673\pi\) | ||||
0.0982589 | + | 0.995161i | \(0.468673\pi\) | |||||||
\(938\) | −3.88122 | −0.126726 | ||||||||
\(939\) | 15.7501 | 0.513985 | ||||||||
\(940\) | 11.3915 | 0.371548 | ||||||||
\(941\) | 30.6883 | 1.00041 | 0.500205 | − | 0.865907i | \(-0.333258\pi\) | ||||
0.500205 | + | 0.865907i | \(0.333258\pi\) | |||||||
\(942\) | −23.1697 | −0.754909 | ||||||||
\(943\) | −51.0552 | −1.66258 | ||||||||
\(944\) | −5.64597 | −0.183761 | ||||||||
\(945\) | −7.08034 | −0.230324 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.3767 | 1.05210 | 0.526051 | − | 0.850453i | \(-0.323672\pi\) | ||||
0.526051 | + | 0.850453i | \(0.323672\pi\) | |||||||
\(948\) | −41.6620 | −1.35312 | ||||||||
\(949\) | −31.4108 | −1.01964 | ||||||||
\(950\) | 3.97479 | 0.128959 | ||||||||
\(951\) | 20.7979 | 0.674417 | ||||||||
\(952\) | −7.07831 | −0.229409 | ||||||||
\(953\) | 11.8836 | 0.384948 | 0.192474 | − | 0.981302i | \(-0.438349\pi\) | ||||
0.192474 | + | 0.981302i | \(0.438349\pi\) | |||||||
\(954\) | −42.1737 | −1.36542 | ||||||||
\(955\) | −7.61496 | −0.246414 | ||||||||
\(956\) | 23.9193 | 0.773604 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.414174 | −0.0133814 | ||||||||
\(959\) | −10.0996 | −0.326134 | ||||||||
\(960\) | 2.90474 | 0.0937501 | ||||||||
\(961\) | −29.3526 | −0.946859 | ||||||||
\(962\) | 6.56275 | 0.211591 | ||||||||
\(963\) | −17.8996 | −0.576808 | ||||||||
\(964\) | −18.5851 | −0.598586 | ||||||||
\(965\) | 8.55503 | 0.275396 | ||||||||
\(966\) | 27.3044 | 0.878504 | ||||||||
\(967\) | 24.0988 | 0.774965 | 0.387483 | − | 0.921877i | \(-0.373345\pi\) | ||||
0.387483 | + | 0.921877i | \(0.373345\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −81.7242 | −2.62536 | ||||||||
\(970\) | 8.60695 | 0.276352 | ||||||||
\(971\) | −2.52446 | −0.0810139 | −0.0405069 | − | 0.999179i | \(-0.512897\pi\) | ||||
−0.0405069 | + | 0.999179i | \(0.512897\pi\) | |||||||
\(972\) | 8.88423 | 0.284962 | ||||||||
\(973\) | 18.5110 | 0.593437 | ||||||||
\(974\) | −23.7328 | −0.760448 | ||||||||
\(975\) | 18.9104 | 0.605619 | ||||||||
\(976\) | 6.33662 | 0.202830 | ||||||||
\(977\) | −25.8513 | −0.827056 | −0.413528 | − | 0.910491i | \(-0.635704\pi\) | ||||
−0.413528 | + | 0.910491i | \(0.635704\pi\) | |||||||
\(978\) | −41.6632 | −1.33224 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 68.4338 | 2.18492 | ||||||||
\(982\) | 32.2162 | 1.02806 | ||||||||
\(983\) | −0.975472 | −0.0311127 | −0.0155564 | − | 0.999879i | \(-0.504952\pi\) | ||||
−0.0155564 | + | 0.999879i | \(0.504952\pi\) | |||||||
\(984\) | 15.7769 | 0.502950 | ||||||||
\(985\) | −5.30318 | −0.168973 | ||||||||
\(986\) | 8.34695 | 0.265821 | ||||||||
\(987\) | −33.0892 | −1.05324 | ||||||||
\(988\) | −25.8767 | −0.823247 | ||||||||
\(989\) | −105.282 | −3.34777 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.48309 | 0.110644 | 0.0553220 | − | 0.998469i | \(-0.482381\pi\) | ||||
0.0553220 | + | 0.998469i | \(0.482381\pi\) | |||||||
\(992\) | −1.28349 | −0.0407510 | ||||||||
\(993\) | −60.1233 | −1.90795 | ||||||||
\(994\) | 0.259926 | 0.00824435 | ||||||||
\(995\) | −27.8463 | −0.882788 | ||||||||
\(996\) | −13.3473 | −0.422926 | ||||||||
\(997\) | 43.0019 | 1.36188 | 0.680942 | − | 0.732337i | \(-0.261570\pi\) | ||||
0.680942 | + | 0.732337i | \(0.261570\pi\) | |||||||
\(998\) | −4.48988 | −0.142125 | ||||||||
\(999\) | 7.13749 | 0.225820 |
(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 | 8470.2.a.dh.1.1 | 8 | ||
11.5 | even | 5 | 770.2.n.k.421.1 | ✓ | 16 | ||
11.9 | even | 5 | 770.2.n.k.631.1 | yes | 16 | ||
11.10 | odd | 2 | 8470.2.a.dg.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.k.421.1 | ✓ | 16 | 11.5 | even | 5 | ||
770.2.n.k.631.1 | yes | 16 | 11.9 | even | 5 | ||
8470.2.a.dg.1.1 | 8 | 11.10 | odd | 2 | |||
8470.2.a.dh.1.1 | 8 | 1.1 | even | 1 | trivial |