Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.737640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45589 | 1.73657 | 0.868287 | − | 0.496062i | \(-0.165221\pi\) | ||||
0.868287 | + | 0.496062i | \(0.165221\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.03138 | 2.01569 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.45589 | 1.00261 | ||||||||
\(7\) | 3.28684 | 1.24231 | 0.621155 | − | 0.783688i | \(-0.286664\pi\) | ||||
0.621155 | + | 0.783688i | \(0.286664\pi\) | |||||||
\(8\) | 4.98884 | 1.76382 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.45589 | −0.776620 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 4.03138 | 1.16376 | ||||||||
\(13\) | −0.313133 | −0.0868476 | −0.0434238 | − | 0.999057i | \(-0.513827\pi\) | ||||
−0.0434238 | + | 0.999057i | \(0.513827\pi\) | |||||||
\(14\) | 8.07211 | 2.15736 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 4.18926 | 1.04732 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 2.45589 | 0.578858 | ||||||||
\(19\) | −7.45408 | −1.71008 | −0.855041 | − | 0.518560i | \(-0.826468\pi\) | ||||
−0.855041 | + | 0.518560i | \(0.826468\pi\) | |||||||
\(20\) | −4.03138 | −0.901444 | ||||||||
\(21\) | 3.28684 | 0.717248 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.07392 | 0.223928 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(24\) | 4.98884 | 1.01834 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.769020 | −0.150817 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 13.2505 | 2.50411 | ||||||||
\(29\) | −5.03647 | −0.935249 | −0.467624 | − | 0.883927i | \(-0.654890\pi\) | ||||
−0.467624 | + | 0.883927i | \(0.654890\pi\) | |||||||
\(30\) | −2.45589 | −0.448382 | ||||||||
\(31\) | 3.44899 | 0.619457 | 0.309728 | − | 0.950825i | \(-0.399762\pi\) | ||||
0.309728 | + | 0.950825i | \(0.399762\pi\) | |||||||
\(32\) | 0.310680 | 0.0549210 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.2794 | 2.10591 | ||||||||
\(35\) | −3.28684 | −0.555578 | ||||||||
\(36\) | 4.03138 | 0.671897 | ||||||||
\(37\) | 2.63428 | 0.433073 | 0.216537 | − | 0.976274i | \(-0.430524\pi\) | ||||
0.216537 | + | 0.976274i | \(0.430524\pi\) | |||||||
\(38\) | −18.3064 | −2.96969 | ||||||||
\(39\) | −0.313133 | −0.0501415 | ||||||||
\(40\) | −4.98884 | −0.788805 | ||||||||
\(41\) | 10.8472 | 1.69405 | 0.847024 | − | 0.531554i | \(-0.178392\pi\) | ||||
0.847024 | + | 0.531554i | \(0.178392\pi\) | |||||||
\(42\) | 8.07211 | 1.24555 | ||||||||
\(43\) | −5.51468 | −0.840980 | −0.420490 | − | 0.907297i | \(-0.638142\pi\) | ||||
−0.420490 | + | 0.907297i | \(0.638142\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 2.63743 | 0.388868 | ||||||||
\(47\) | −11.9982 | −1.75012 | −0.875058 | − | 0.484018i | \(-0.839177\pi\) | ||||
−0.875058 | + | 0.484018i | \(0.839177\pi\) | |||||||
\(48\) | 4.18926 | 0.604668 | ||||||||
\(49\) | 3.80333 | 0.543333 | ||||||||
\(50\) | 2.45589 | 0.347315 | ||||||||
\(51\) | 5.00000 | 0.700140 | ||||||||
\(52\) | −1.26236 | −0.175058 | ||||||||
\(53\) | 4.93543 | 0.677934 | 0.338967 | − | 0.940798i | \(-0.389923\pi\) | ||||
0.338967 | + | 0.940798i | \(0.389923\pi\) | |||||||
\(54\) | 2.45589 | 0.334204 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 16.3975 | 2.19121 | ||||||||
\(57\) | −7.45408 | −0.987317 | ||||||||
\(58\) | −12.3690 | −1.62413 | ||||||||
\(59\) | −9.16409 | −1.19306 | −0.596531 | − | 0.802590i | \(-0.703455\pi\) | ||||
−0.596531 | + | 0.802590i | \(0.703455\pi\) | |||||||
\(60\) | −4.03138 | −0.520449 | ||||||||
\(61\) | 9.18431 | 1.17593 | 0.587965 | − | 0.808886i | \(-0.299929\pi\) | ||||
0.587965 | + | 0.808886i | \(0.299929\pi\) | |||||||
\(62\) | 8.47033 | 1.07573 | ||||||||
\(63\) | 3.28684 | 0.414103 | ||||||||
\(64\) | −7.61553 | −0.951942 | ||||||||
\(65\) | 0.313133 | 0.0388394 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.2739 | −1.86600 | −0.933000 | − | 0.359876i | \(-0.882819\pi\) | ||||
−0.933000 | + | 0.359876i | \(0.882819\pi\) | |||||||
\(68\) | 20.1569 | 2.44438 | ||||||||
\(69\) | 1.07392 | 0.129285 | ||||||||
\(70\) | −8.07211 | −0.964802 | ||||||||
\(71\) | 3.07211 | 0.364593 | 0.182296 | − | 0.983244i | \(-0.441647\pi\) | ||||
0.182296 | + | 0.983244i | \(0.441647\pi\) | |||||||
\(72\) | 4.98884 | 0.587940 | ||||||||
\(73\) | −8.65269 | −1.01272 | −0.506361 | − | 0.862322i | \(-0.669009\pi\) | ||||
−0.506361 | + | 0.862322i | \(0.669009\pi\) | |||||||
\(74\) | 6.46950 | 0.752064 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −30.0502 | −3.44700 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.769020 | −0.0870744 | ||||||||
\(79\) | 5.41446 | 0.609175 | 0.304587 | − | 0.952484i | \(-0.401481\pi\) | ||||
0.304587 | + | 0.952484i | \(0.401481\pi\) | |||||||
\(80\) | −4.18926 | −0.468374 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 26.6395 | 2.94184 | ||||||||
\(83\) | 16.2454 | 1.78317 | 0.891583 | − | 0.452857i | \(-0.149595\pi\) | ||||
0.891583 | + | 0.452857i | \(0.149595\pi\) | |||||||
\(84\) | 13.2505 | 1.44575 | ||||||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | −13.5434 | −1.46042 | ||||||||
\(87\) | −5.03647 | −0.539966 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.62118 | 0.171845 | 0.0859223 | − | 0.996302i | \(-0.472616\pi\) | ||||
0.0859223 | + | 0.996302i | \(0.472616\pi\) | |||||||
\(90\) | −2.45589 | −0.258873 | ||||||||
\(91\) | −1.02922 | −0.107892 | ||||||||
\(92\) | 4.32938 | 0.451369 | ||||||||
\(93\) | 3.44899 | 0.357643 | ||||||||
\(94\) | −29.4662 | −3.03921 | ||||||||
\(95\) | 7.45408 | 0.764772 | ||||||||
\(96\) | 0.310680 | 0.0317086 | ||||||||
\(97\) | 0.224082 | 0.0227521 | 0.0113760 | − | 0.999935i | \(-0.496379\pi\) | ||||
0.0113760 | + | 0.999935i | \(0.496379\pi\) | |||||||
\(98\) | 9.34054 | 0.943537 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.03138 | 0.403138 | ||||||||
\(101\) | −0.505326 | −0.0502818 | −0.0251409 | − | 0.999684i | \(-0.508003\pi\) | ||||
−0.0251409 | + | 0.999684i | \(0.508003\pi\) | |||||||
\(102\) | 12.2794 | 1.21585 | ||||||||
\(103\) | −6.40197 | −0.630805 | −0.315402 | − | 0.948958i | \(-0.602139\pi\) | ||||
−0.315402 | + | 0.948958i | \(0.602139\pi\) | |||||||
\(104\) | −1.56217 | −0.153184 | ||||||||
\(105\) | −3.28684 | −0.320763 | ||||||||
\(106\) | 12.1209 | 1.17728 | ||||||||
\(107\) | 2.09249 | 0.202289 | 0.101144 | − | 0.994872i | \(-0.467750\pi\) | ||||
0.101144 | + | 0.994872i | \(0.467750\pi\) | |||||||
\(108\) | 4.03138 | 0.387920 | ||||||||
\(109\) | −6.69278 | −0.641052 | −0.320526 | − | 0.947240i | \(-0.603860\pi\) | ||||
−0.320526 | + | 0.947240i | \(0.603860\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.63428 | 0.250035 | ||||||||
\(112\) | 13.7694 | 1.30109 | ||||||||
\(113\) | −10.7941 | −1.01542 | −0.507712 | − | 0.861527i | \(-0.669509\pi\) | ||||
−0.507712 | + | 0.861527i | \(0.669509\pi\) | |||||||
\(114\) | −18.3064 | −1.71455 | ||||||||
\(115\) | −1.07392 | −0.100144 | ||||||||
\(116\) | −20.3039 | −1.88517 | ||||||||
\(117\) | −0.313133 | −0.0289492 | ||||||||
\(118\) | −22.5060 | −2.07184 | ||||||||
\(119\) | 16.4342 | 1.50652 | ||||||||
\(120\) | −4.98884 | −0.455417 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 22.5556 | 2.04209 | ||||||||
\(123\) | 10.8472 | 0.978059 | ||||||||
\(124\) | 13.9042 | 1.24863 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 8.07211 | 0.719121 | ||||||||
\(127\) | −17.0033 | −1.50880 | −0.754398 | − | 0.656417i | \(-0.772071\pi\) | ||||
−0.754398 | + | 0.656417i | \(0.772071\pi\) | |||||||
\(128\) | −19.3242 | −1.70804 | ||||||||
\(129\) | −5.51468 | −0.485540 | ||||||||
\(130\) | 0.769020 | 0.0674475 | ||||||||
\(131\) | −0.0430508 | −0.00376136 | −0.00188068 | − | 0.999998i | \(-0.500599\pi\) | ||||
−0.00188068 | + | 0.999998i | \(0.500599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.5004 | −2.12445 | ||||||||
\(134\) | −37.5109 | −3.24045 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 24.9442 | 2.13895 | ||||||||
\(137\) | 7.36257 | 0.629027 | 0.314513 | − | 0.949253i | \(-0.398159\pi\) | ||||
0.314513 | + | 0.949253i | \(0.398159\pi\) | |||||||
\(138\) | 2.63743 | 0.224513 | ||||||||
\(139\) | 13.2393 | 1.12295 | 0.561473 | − | 0.827495i | \(-0.310235\pi\) | ||||
0.561473 | + | 0.827495i | \(0.310235\pi\) | |||||||
\(140\) | −13.2505 | −1.11987 | ||||||||
\(141\) | −11.9982 | −1.01043 | ||||||||
\(142\) | 7.54476 | 0.633142 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.18926 | 0.349105 | ||||||||
\(145\) | 5.03647 | 0.418256 | ||||||||
\(146\) | −21.2500 | −1.75867 | ||||||||
\(147\) | 3.80333 | 0.313693 | ||||||||
\(148\) | 10.6198 | 0.872942 | ||||||||
\(149\) | −5.87858 | −0.481592 | −0.240796 | − | 0.970576i | \(-0.577409\pi\) | ||||
−0.240796 | + | 0.970576i | \(0.577409\pi\) | |||||||
\(150\) | 2.45589 | 0.200522 | ||||||||
\(151\) | 7.62821 | 0.620775 | 0.310387 | − | 0.950610i | \(-0.399541\pi\) | ||||
0.310387 | + | 0.950610i | \(0.399541\pi\) | |||||||
\(152\) | −37.1872 | −3.01628 | ||||||||
\(153\) | 5.00000 | 0.404226 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.44899 | −0.277029 | ||||||||
\(156\) | −1.26236 | −0.101070 | ||||||||
\(157\) | −10.1332 | −0.808719 | −0.404360 | − | 0.914600i | \(-0.632506\pi\) | ||||
−0.404360 | + | 0.914600i | \(0.632506\pi\) | |||||||
\(158\) | 13.2973 | 1.05788 | ||||||||
\(159\) | 4.93543 | 0.391405 | ||||||||
\(160\) | −0.310680 | −0.0245614 | ||||||||
\(161\) | 3.52981 | 0.278188 | ||||||||
\(162\) | 2.45589 | 0.192953 | ||||||||
\(163\) | −5.02906 | −0.393906 | −0.196953 | − | 0.980413i | \(-0.563105\pi\) | ||||
−0.196953 | + | 0.980413i | \(0.563105\pi\) | |||||||
\(164\) | 43.7292 | 3.41468 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 39.8969 | 3.09660 | ||||||||
\(167\) | 5.79105 | 0.448125 | 0.224062 | − | 0.974575i | \(-0.428068\pi\) | ||||
0.224062 | + | 0.974575i | \(0.428068\pi\) | |||||||
\(168\) | 16.3975 | 1.26510 | ||||||||
\(169\) | −12.9019 | −0.992457 | ||||||||
\(170\) | −12.2794 | −0.941790 | ||||||||
\(171\) | −7.45408 | −0.570028 | ||||||||
\(172\) | −22.2318 | −1.69516 | ||||||||
\(173\) | 16.0652 | 1.22142 | 0.610708 | − | 0.791856i | \(-0.290885\pi\) | ||||
0.610708 | + | 0.791856i | \(0.290885\pi\) | |||||||
\(174\) | −12.3690 | −0.937691 | ||||||||
\(175\) | 3.28684 | 0.248462 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.16409 | −0.688815 | ||||||||
\(178\) | 3.98143 | 0.298421 | ||||||||
\(179\) | −8.30309 | −0.620602 | −0.310301 | − | 0.950638i | \(-0.600430\pi\) | ||||
−0.310301 | + | 0.950638i | \(0.600430\pi\) | |||||||
\(180\) | −4.03138 | −0.300481 | ||||||||
\(181\) | −6.46425 | −0.480484 | −0.240242 | − | 0.970713i | \(-0.577227\pi\) | ||||
−0.240242 | + | 0.970713i | \(0.577227\pi\) | |||||||
\(182\) | −2.52765 | −0.187362 | ||||||||
\(183\) | 9.18431 | 0.678924 | ||||||||
\(184\) | 5.35762 | 0.394969 | ||||||||
\(185\) | −2.63428 | −0.193676 | ||||||||
\(186\) | 8.47033 | 0.621074 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −48.3693 | −3.52769 | ||||||||
\(189\) | 3.28684 | 0.239083 | ||||||||
\(190\) | 18.3064 | 1.32808 | ||||||||
\(191\) | 15.3693 | 1.11208 | 0.556041 | − | 0.831155i | \(-0.312320\pi\) | ||||
0.556041 | + | 0.831155i | \(0.312320\pi\) | |||||||
\(192\) | −7.61553 | −0.549604 | ||||||||
\(193\) | 15.7518 | 1.13384 | 0.566919 | − | 0.823773i | \(-0.308135\pi\) | ||||
0.566919 | + | 0.823773i | \(0.308135\pi\) | |||||||
\(194\) | 0.550320 | 0.0395107 | ||||||||
\(195\) | 0.313133 | 0.0224239 | ||||||||
\(196\) | 15.3327 | 1.09519 | ||||||||
\(197\) | 16.3940 | 1.16802 | 0.584010 | − | 0.811746i | \(-0.301483\pi\) | ||||
0.584010 | + | 0.811746i | \(0.301483\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.96500 | 0.493736 | 0.246868 | − | 0.969049i | \(-0.420599\pi\) | ||||
0.246868 | + | 0.969049i | \(0.420599\pi\) | |||||||
\(200\) | 4.98884 | 0.352764 | ||||||||
\(201\) | −15.2739 | −1.07734 | ||||||||
\(202\) | −1.24102 | −0.0873180 | ||||||||
\(203\) | −16.5541 | −1.16187 | ||||||||
\(204\) | 20.1569 | 1.41127 | ||||||||
\(205\) | −10.8472 | −0.757602 | ||||||||
\(206\) | −15.7225 | −1.09544 | ||||||||
\(207\) | 1.07392 | 0.0746427 | ||||||||
\(208\) | −1.31180 | −0.0909569 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −8.07211 | −0.557029 | ||||||||
\(211\) | −19.9531 | −1.37363 | −0.686814 | − | 0.726833i | \(-0.740992\pi\) | ||||
−0.686814 | + | 0.726833i | \(0.740992\pi\) | |||||||
\(212\) | 19.8966 | 1.36650 | ||||||||
\(213\) | 3.07211 | 0.210498 | ||||||||
\(214\) | 5.13892 | 0.351289 | ||||||||
\(215\) | 5.51468 | 0.376098 | ||||||||
\(216\) | 4.98884 | 0.339447 | ||||||||
\(217\) | 11.3363 | 0.769557 | ||||||||
\(218\) | −16.4367 | −1.11323 | ||||||||
\(219\) | −8.65269 | −0.584695 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.56567 | −0.105318 | ||||||||
\(222\) | 6.46950 | 0.434204 | ||||||||
\(223\) | −20.1466 | −1.34912 | −0.674559 | − | 0.738221i | \(-0.735666\pi\) | ||||
−0.674559 | + | 0.738221i | \(0.735666\pi\) | |||||||
\(224\) | 1.02116 | 0.0682289 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −26.5091 | −1.76336 | ||||||||
\(227\) | 0.533937 | 0.0354386 | 0.0177193 | − | 0.999843i | \(-0.494359\pi\) | ||||
0.0177193 | + | 0.999843i | \(0.494359\pi\) | |||||||
\(228\) | −30.0502 | −1.99012 | ||||||||
\(229\) | −22.1931 | −1.46656 | −0.733279 | − | 0.679928i | \(-0.762011\pi\) | ||||
−0.733279 | + | 0.679928i | \(0.762011\pi\) | |||||||
\(230\) | −2.63743 | −0.173907 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −25.1261 | −1.64961 | ||||||||
\(233\) | −4.56567 | −0.299107 | −0.149553 | − | 0.988754i | \(-0.547784\pi\) | ||||
−0.149553 | + | 0.988754i | \(0.547784\pi\) | |||||||
\(234\) | −0.769020 | −0.0502724 | ||||||||
\(235\) | 11.9982 | 0.782676 | ||||||||
\(236\) | −36.9439 | −2.40485 | ||||||||
\(237\) | 5.41446 | 0.351707 | ||||||||
\(238\) | 40.3606 | 2.61619 | ||||||||
\(239\) | −5.86053 | −0.379086 | −0.189543 | − | 0.981872i | \(-0.560701\pi\) | ||||
−0.189543 | + | 0.981872i | \(0.560701\pi\) | |||||||
\(240\) | −4.18926 | −0.270416 | ||||||||
\(241\) | 9.96074 | 0.641628 | 0.320814 | − | 0.947142i | \(-0.396044\pi\) | ||||
0.320814 | + | 0.947142i | \(0.396044\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 37.0254 | 2.37031 | ||||||||
\(245\) | −3.80333 | −0.242986 | ||||||||
\(246\) | 26.6395 | 1.69847 | ||||||||
\(247\) | 2.33412 | 0.148517 | ||||||||
\(248\) | 17.2065 | 1.09261 | ||||||||
\(249\) | 16.2454 | 1.02951 | ||||||||
\(250\) | −2.45589 | −0.155324 | ||||||||
\(251\) | −16.8788 | −1.06538 | −0.532690 | − | 0.846310i | \(-0.678819\pi\) | ||||
−0.532690 | + | 0.846310i | \(0.678819\pi\) | |||||||
\(252\) | 13.2505 | 0.834704 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −41.7581 | −2.62014 | ||||||||
\(255\) | −5.00000 | −0.313112 | ||||||||
\(256\) | −32.2271 | −2.01419 | ||||||||
\(257\) | 11.1436 | 0.695117 | 0.347559 | − | 0.937658i | \(-0.387011\pi\) | ||||
0.347559 | + | 0.937658i | \(0.387011\pi\) | |||||||
\(258\) | −13.5434 | −0.843177 | ||||||||
\(259\) | 8.65847 | 0.538011 | ||||||||
\(260\) | 1.26236 | 0.0782882 | ||||||||
\(261\) | −5.03647 | −0.311750 | ||||||||
\(262\) | −0.105728 | −0.00653189 | ||||||||
\(263\) | −26.8726 | −1.65704 | −0.828519 | − | 0.559961i | \(-0.810816\pi\) | ||||
−0.828519 | + | 0.559961i | \(0.810816\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.93543 | −0.303181 | ||||||||
\(266\) | −60.1701 | −3.68927 | ||||||||
\(267\) | 1.62118 | 0.0992145 | ||||||||
\(268\) | −61.5748 | −3.76128 | ||||||||
\(269\) | −10.0629 | −0.613545 | −0.306773 | − | 0.951783i | \(-0.599249\pi\) | ||||
−0.306773 | + | 0.951783i | \(0.599249\pi\) | |||||||
\(270\) | −2.45589 | −0.149461 | ||||||||
\(271\) | 10.5441 | 0.640509 | 0.320255 | − | 0.947331i | \(-0.396232\pi\) | ||||
0.320255 | + | 0.947331i | \(0.396232\pi\) | |||||||
\(272\) | 20.9463 | 1.27006 | ||||||||
\(273\) | −1.02922 | −0.0622912 | ||||||||
\(274\) | 18.0816 | 1.09235 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.32938 | 0.260598 | ||||||||
\(277\) | −17.9376 | −1.07777 | −0.538883 | − | 0.842381i | \(-0.681153\pi\) | ||||
−0.538883 | + | 0.842381i | \(0.681153\pi\) | |||||||
\(278\) | 32.5143 | 1.95008 | ||||||||
\(279\) | 3.44899 | 0.206486 | ||||||||
\(280\) | −16.3975 | −0.979939 | ||||||||
\(281\) | 7.41103 | 0.442105 | 0.221052 | − | 0.975262i | \(-0.429051\pi\) | ||||
0.221052 | + | 0.975262i | \(0.429051\pi\) | |||||||
\(282\) | −29.4662 | −1.75469 | ||||||||
\(283\) | 5.38684 | 0.320214 | 0.160107 | − | 0.987100i | \(-0.448816\pi\) | ||||
0.160107 | + | 0.987100i | \(0.448816\pi\) | |||||||
\(284\) | 12.3848 | 0.734905 | ||||||||
\(285\) | 7.45408 | 0.441541 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.6530 | 2.10453 | ||||||||
\(288\) | 0.310680 | 0.0183070 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 12.3690 | 0.726332 | ||||||||
\(291\) | 0.224082 | 0.0131359 | ||||||||
\(292\) | −34.8823 | −2.04133 | ||||||||
\(293\) | −1.74006 | −0.101655 | −0.0508277 | − | 0.998707i | \(-0.516186\pi\) | ||||
−0.0508277 | + | 0.998707i | \(0.516186\pi\) | |||||||
\(294\) | 9.34054 | 0.544752 | ||||||||
\(295\) | 9.16409 | 0.533554 | ||||||||
\(296\) | 13.1420 | 0.763864 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.4371 | −0.836321 | ||||||||
\(299\) | −0.336280 | −0.0194476 | ||||||||
\(300\) | 4.03138 | 0.232752 | ||||||||
\(301\) | −18.1259 | −1.04476 | ||||||||
\(302\) | 18.7340 | 1.07802 | ||||||||
\(303\) | −0.505326 | −0.0290302 | ||||||||
\(304\) | −31.2271 | −1.79100 | ||||||||
\(305\) | −9.18431 | −0.525892 | ||||||||
\(306\) | 12.2794 | 0.701969 | ||||||||
\(307\) | 21.3566 | 1.21889 | 0.609444 | − | 0.792829i | \(-0.291393\pi\) | ||||
0.609444 | + | 0.792829i | \(0.291393\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.40197 | −0.364195 | ||||||||
\(310\) | −8.47033 | −0.481082 | ||||||||
\(311\) | 32.8096 | 1.86046 | 0.930231 | − | 0.366975i | \(-0.119607\pi\) | ||||
0.930231 | + | 0.366975i | \(0.119607\pi\) | |||||||
\(312\) | −1.56217 | −0.0884406 | ||||||||
\(313\) | −3.45852 | −0.195487 | −0.0977436 | − | 0.995212i | \(-0.531163\pi\) | ||||
−0.0977436 | + | 0.995212i | \(0.531163\pi\) | |||||||
\(314\) | −24.8860 | −1.40440 | ||||||||
\(315\) | −3.28684 | −0.185193 | ||||||||
\(316\) | 21.8278 | 1.22791 | ||||||||
\(317\) | −2.87566 | −0.161513 | −0.0807565 | − | 0.996734i | \(-0.525734\pi\) | ||||
−0.0807565 | + | 0.996734i | \(0.525734\pi\) | |||||||
\(318\) | 12.1209 | 0.679704 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 7.61553 | 0.425721 | ||||||||
\(321\) | 2.09249 | 0.116791 | ||||||||
\(322\) | 8.66881 | 0.483094 | ||||||||
\(323\) | −37.2704 | −2.07378 | ||||||||
\(324\) | 4.03138 | 0.223966 | ||||||||
\(325\) | −0.313133 | −0.0173695 | ||||||||
\(326\) | −12.3508 | −0.684048 | ||||||||
\(327\) | −6.69278 | −0.370112 | ||||||||
\(328\) | 54.1150 | 2.98800 | ||||||||
\(329\) | −39.4362 | −2.17419 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.1221 | −0.776219 | −0.388109 | − | 0.921613i | \(-0.626872\pi\) | ||||
−0.388109 | + | 0.921613i | \(0.626872\pi\) | |||||||
\(332\) | 65.4915 | 3.59431 | ||||||||
\(333\) | 2.63428 | 0.144358 | ||||||||
\(334\) | 14.2222 | 0.778202 | ||||||||
\(335\) | 15.2739 | 0.834501 | ||||||||
\(336\) | 13.7694 | 0.751185 | ||||||||
\(337\) | 15.9490 | 0.868796 | 0.434398 | − | 0.900721i | \(-0.356961\pi\) | ||||
0.434398 | + | 0.900721i | \(0.356961\pi\) | |||||||
\(338\) | −31.6857 | −1.72348 | ||||||||
\(339\) | −10.7941 | −0.586256 | ||||||||
\(340\) | −20.1569 | −1.09316 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −18.3064 | −0.989895 | ||||||||
\(343\) | −10.5070 | −0.567322 | ||||||||
\(344\) | −27.5118 | −1.48334 | ||||||||
\(345\) | −1.07392 | −0.0578180 | ||||||||
\(346\) | 39.4543 | 2.12108 | ||||||||
\(347\) | 29.6801 | 1.59331 | 0.796656 | − | 0.604433i | \(-0.206600\pi\) | ||||
0.796656 | + | 0.604433i | \(0.206600\pi\) | |||||||
\(348\) | −20.3039 | −1.08840 | ||||||||
\(349\) | 31.6937 | 1.69653 | 0.848263 | − | 0.529574i | \(-0.177648\pi\) | ||||
0.848263 | + | 0.529574i | \(0.177648\pi\) | |||||||
\(350\) | 8.07211 | 0.431472 | ||||||||
\(351\) | −0.313133 | −0.0167138 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.20189 | 0.0639703 | 0.0319852 | − | 0.999488i | \(-0.489817\pi\) | ||||
0.0319852 | + | 0.999488i | \(0.489817\pi\) | |||||||
\(354\) | −22.5060 | −1.19618 | ||||||||
\(355\) | −3.07211 | −0.163051 | ||||||||
\(356\) | 6.53559 | 0.346385 | ||||||||
\(357\) | 16.4342 | 0.869791 | ||||||||
\(358\) | −20.3915 | −1.07772 | ||||||||
\(359\) | −11.6591 | −0.615343 | −0.307671 | − | 0.951493i | \(-0.599550\pi\) | ||||
−0.307671 | + | 0.951493i | \(0.599550\pi\) | |||||||
\(360\) | −4.98884 | −0.262935 | ||||||||
\(361\) | 36.5633 | 1.92438 | ||||||||
\(362\) | −15.8755 | −0.834396 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.14918 | −0.217476 | ||||||||
\(365\) | 8.65269 | 0.452903 | ||||||||
\(366\) | 22.5556 | 1.17900 | ||||||||
\(367\) | 15.9860 | 0.834465 | 0.417232 | − | 0.908800i | \(-0.363000\pi\) | ||||
0.417232 | + | 0.908800i | \(0.363000\pi\) | |||||||
\(368\) | 4.49894 | 0.234523 | ||||||||
\(369\) | 10.8472 | 0.564683 | ||||||||
\(370\) | −6.46950 | −0.336333 | ||||||||
\(371\) | 16.2220 | 0.842203 | ||||||||
\(372\) | 13.9042 | 0.720898 | ||||||||
\(373\) | 0.321975 | 0.0166712 | 0.00833561 | − | 0.999965i | \(-0.497347\pi\) | ||||
0.00833561 | + | 0.999965i | \(0.497347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −59.8570 | −3.08689 | ||||||||
\(377\) | 1.57709 | 0.0812241 | ||||||||
\(378\) | 8.07211 | 0.415185 | ||||||||
\(379\) | 11.4174 | 0.586475 | 0.293237 | − | 0.956040i | \(-0.405267\pi\) | ||||
0.293237 | + | 0.956040i | \(0.405267\pi\) | |||||||
\(380\) | 30.0502 | 1.54154 | ||||||||
\(381\) | −17.0033 | −0.871104 | ||||||||
\(382\) | 37.7452 | 1.93121 | ||||||||
\(383\) | 28.3673 | 1.44950 | 0.724750 | − | 0.689012i | \(-0.241955\pi\) | ||||
0.724750 | + | 0.689012i | \(0.241955\pi\) | |||||||
\(384\) | −19.3242 | −0.986136 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 38.6846 | 1.96899 | ||||||||
\(387\) | −5.51468 | −0.280327 | ||||||||
\(388\) | 0.903359 | 0.0458611 | ||||||||
\(389\) | 15.1802 | 0.769666 | 0.384833 | − | 0.922986i | \(-0.374259\pi\) | ||||
0.384833 | + | 0.922986i | \(0.374259\pi\) | |||||||
\(390\) | 0.769020 | 0.0389409 | ||||||||
\(391\) | 5.36960 | 0.271553 | ||||||||
\(392\) | 18.9742 | 0.958341 | ||||||||
\(393\) | −0.0430508 | −0.00217163 | ||||||||
\(394\) | 40.2617 | 2.02835 | ||||||||
\(395\) | −5.41446 | −0.272431 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.22461 | 0.262216 | 0.131108 | − | 0.991368i | \(-0.458147\pi\) | ||||
0.131108 | + | 0.991368i | \(0.458147\pi\) | |||||||
\(398\) | 17.1053 | 0.857409 | ||||||||
\(399\) | −24.5004 | −1.22655 | ||||||||
\(400\) | 4.18926 | 0.209463 | ||||||||
\(401\) | 14.0007 | 0.699160 | 0.349580 | − | 0.936907i | \(-0.386324\pi\) | ||||
0.349580 | + | 0.936907i | \(0.386324\pi\) | |||||||
\(402\) | −37.5109 | −1.87087 | ||||||||
\(403\) | −1.07999 | −0.0537983 | ||||||||
\(404\) | −2.03716 | −0.101352 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −40.6549 | −2.01767 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 24.9442 | 1.23492 | ||||||||
\(409\) | 33.3112 | 1.64713 | 0.823567 | − | 0.567218i | \(-0.191980\pi\) | ||||
0.823567 | + | 0.567218i | \(0.191980\pi\) | |||||||
\(410\) | −26.6395 | −1.31563 | ||||||||
\(411\) | 7.36257 | 0.363169 | ||||||||
\(412\) | −25.8088 | −1.27151 | ||||||||
\(413\) | −30.1209 | −1.48215 | ||||||||
\(414\) | 2.63743 | 0.129623 | ||||||||
\(415\) | −16.2454 | −0.797456 | ||||||||
\(416\) | −0.0972843 | −0.00476975 | ||||||||
\(417\) | 13.2393 | 0.648334 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.28460 | −0.258170 | −0.129085 | − | 0.991634i | \(-0.541204\pi\) | ||||
−0.129085 | + | 0.991634i | \(0.541204\pi\) | |||||||
\(420\) | −13.2505 | −0.646559 | ||||||||
\(421\) | −30.7810 | −1.50017 | −0.750087 | − | 0.661340i | \(-0.769988\pi\) | ||||
−0.750087 | + | 0.661340i | \(0.769988\pi\) | |||||||
\(422\) | −49.0026 | −2.38541 | ||||||||
\(423\) | −11.9982 | −0.583372 | ||||||||
\(424\) | 24.6221 | 1.19575 | ||||||||
\(425\) | 5.00000 | 0.242536 | ||||||||
\(426\) | 7.54476 | 0.365545 | ||||||||
\(427\) | 30.1874 | 1.46087 | ||||||||
\(428\) | 8.43562 | 0.407751 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.5434 | 0.653122 | ||||||||
\(431\) | 12.3506 | 0.594910 | 0.297455 | − | 0.954736i | \(-0.403862\pi\) | ||||
0.297455 | + | 0.954736i | \(0.403862\pi\) | |||||||
\(432\) | 4.18926 | 0.201556 | ||||||||
\(433\) | 1.41287 | 0.0678983 | 0.0339491 | − | 0.999424i | \(-0.489192\pi\) | ||||
0.0339491 | + | 0.999424i | \(0.489192\pi\) | |||||||
\(434\) | 27.8406 | 1.33639 | ||||||||
\(435\) | 5.03647 | 0.241480 | ||||||||
\(436\) | −26.9811 | −1.29216 | ||||||||
\(437\) | −8.00509 | −0.382935 | ||||||||
\(438\) | −21.2500 | −1.01537 | ||||||||
\(439\) | −7.58532 | −0.362028 | −0.181014 | − | 0.983481i | \(-0.557938\pi\) | ||||
−0.181014 | + | 0.983481i | \(0.557938\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.80333 | 0.181111 | ||||||||
\(442\) | −3.84510 | −0.182893 | ||||||||
\(443\) | 11.0662 | 0.525771 | 0.262885 | − | 0.964827i | \(-0.415326\pi\) | ||||
0.262885 | + | 0.964827i | \(0.415326\pi\) | |||||||
\(444\) | 10.6198 | 0.503993 | ||||||||
\(445\) | −1.62118 | −0.0768512 | ||||||||
\(446\) | −49.4779 | −2.34284 | ||||||||
\(447\) | −5.87858 | −0.278047 | ||||||||
\(448\) | −25.0311 | −1.18261 | ||||||||
\(449\) | 6.32856 | 0.298663 | 0.149332 | − | 0.988787i | \(-0.452288\pi\) | ||||
0.149332 | + | 0.988787i | \(0.452288\pi\) | |||||||
\(450\) | 2.45589 | 0.115772 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −43.5152 | −2.04678 | ||||||||
\(453\) | 7.62821 | 0.358405 | ||||||||
\(454\) | 1.31129 | 0.0615418 | ||||||||
\(455\) | 1.02922 | 0.0482506 | ||||||||
\(456\) | −37.1872 | −1.74145 | ||||||||
\(457\) | −0.189579 | −0.00886814 | −0.00443407 | − | 0.999990i | \(-0.501411\pi\) | ||||
−0.00443407 | + | 0.999990i | \(0.501411\pi\) | |||||||
\(458\) | −54.5036 | −2.54679 | ||||||||
\(459\) | 5.00000 | 0.233380 | ||||||||
\(460\) | −4.32938 | −0.201859 | ||||||||
\(461\) | −26.6198 | −1.23981 | −0.619904 | − | 0.784678i | \(-0.712828\pi\) | ||||
−0.619904 | + | 0.784678i | \(0.712828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.9935 | 0.975652 | 0.487826 | − | 0.872941i | \(-0.337790\pi\) | ||||
0.487826 | + | 0.872941i | \(0.337790\pi\) | |||||||
\(464\) | −21.0991 | −0.979501 | ||||||||
\(465\) | −3.44899 | −0.159943 | ||||||||
\(466\) | −11.2128 | −0.519421 | ||||||||
\(467\) | 7.89989 | 0.365563 | 0.182782 | − | 0.983154i | \(-0.441490\pi\) | ||||
0.182782 | + | 0.983154i | \(0.441490\pi\) | |||||||
\(468\) | −1.26236 | −0.0583526 | ||||||||
\(469\) | −50.2028 | −2.31815 | ||||||||
\(470\) | 29.4662 | 1.35917 | ||||||||
\(471\) | −10.1332 | −0.466914 | ||||||||
\(472\) | −45.7182 | −2.10435 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 13.2973 | 0.610766 | ||||||||
\(475\) | −7.45408 | −0.342017 | ||||||||
\(476\) | 66.2525 | 3.03668 | ||||||||
\(477\) | 4.93543 | 0.225978 | ||||||||
\(478\) | −14.3928 | −0.658311 | ||||||||
\(479\) | 39.9728 | 1.82640 | 0.913201 | − | 0.407509i | \(-0.133602\pi\) | ||||
0.913201 | + | 0.407509i | \(0.133602\pi\) | |||||||
\(480\) | −0.310680 | −0.0141805 | ||||||||
\(481\) | −0.824882 | −0.0376114 | ||||||||
\(482\) | 24.4624 | 1.11423 | ||||||||
\(483\) | 3.52981 | 0.160612 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.224082 | −0.0101750 | ||||||||
\(486\) | 2.45589 | 0.111401 | ||||||||
\(487\) | −9.93556 | −0.450223 | −0.225112 | − | 0.974333i | \(-0.572275\pi\) | ||||
−0.225112 | + | 0.974333i | \(0.572275\pi\) | |||||||
\(488\) | 45.8190 | 2.07413 | ||||||||
\(489\) | −5.02906 | −0.227422 | ||||||||
\(490\) | −9.34054 | −0.421963 | ||||||||
\(491\) | 4.97349 | 0.224451 | 0.112225 | − | 0.993683i | \(-0.464202\pi\) | ||||
0.112225 | + | 0.993683i | \(0.464202\pi\) | |||||||
\(492\) | 43.7292 | 1.97146 | ||||||||
\(493\) | −25.1823 | −1.13416 | ||||||||
\(494\) | 5.73234 | 0.257910 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.4487 | 0.648767 | ||||||||
\(497\) | 10.0975 | 0.452937 | ||||||||
\(498\) | 39.8969 | 1.78782 | ||||||||
\(499\) | 43.7757 | 1.95967 | 0.979834 | − | 0.199812i | \(-0.0640332\pi\) | ||||
0.979834 | + | 0.199812i | \(0.0640332\pi\) | |||||||
\(500\) | −4.03138 | −0.180289 | ||||||||
\(501\) | 5.79105 | 0.258725 | ||||||||
\(502\) | −41.4524 | −1.85011 | ||||||||
\(503\) | 6.28236 | 0.280117 | 0.140058 | − | 0.990143i | \(-0.455271\pi\) | ||||
0.140058 | + | 0.990143i | \(0.455271\pi\) | |||||||
\(504\) | 16.3975 | 0.730404 | ||||||||
\(505\) | 0.505326 | 0.0224867 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9019 | −0.572996 | ||||||||
\(508\) | −68.5467 | −3.04127 | ||||||||
\(509\) | 24.8381 | 1.10093 | 0.550465 | − | 0.834858i | \(-0.314450\pi\) | ||||
0.550465 | + | 0.834858i | \(0.314450\pi\) | |||||||
\(510\) | −12.2794 | −0.543742 | ||||||||
\(511\) | −28.4400 | −1.25811 | ||||||||
\(512\) | −40.4976 | −1.78976 | ||||||||
\(513\) | −7.45408 | −0.329106 | ||||||||
\(514\) | 27.3674 | 1.20712 | ||||||||
\(515\) | 6.40197 | 0.282104 | ||||||||
\(516\) | −22.2318 | −0.978699 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 21.2642 | 0.934296 | ||||||||
\(519\) | 16.0652 | 0.705185 | ||||||||
\(520\) | 1.56217 | 0.0685058 | ||||||||
\(521\) | −6.94869 | −0.304428 | −0.152214 | − | 0.988348i | \(-0.548640\pi\) | ||||
−0.152214 | + | 0.988348i | \(0.548640\pi\) | |||||||
\(522\) | −12.3690 | −0.541376 | ||||||||
\(523\) | −26.7510 | −1.16974 | −0.584869 | − | 0.811128i | \(-0.698854\pi\) | ||||
−0.584869 | + | 0.811128i | \(0.698854\pi\) | |||||||
\(524\) | −0.173554 | −0.00758175 | ||||||||
\(525\) | 3.28684 | 0.143450 | ||||||||
\(526\) | −65.9962 | −2.87757 | ||||||||
\(527\) | 17.2449 | 0.751202 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8467 | −0.949856 | ||||||||
\(530\) | −12.1209 | −0.526496 | ||||||||
\(531\) | −9.16409 | −0.397688 | ||||||||
\(532\) | −98.7703 | −4.28224 | ||||||||
\(533\) | −3.39662 | −0.147124 | ||||||||
\(534\) | 3.98143 | 0.172293 | ||||||||
\(535\) | −2.09249 | −0.0904662 | ||||||||
\(536\) | −76.1989 | −3.29129 | ||||||||
\(537\) | −8.30309 | −0.358305 | ||||||||
\(538\) | −24.7133 | −1.06547 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.03138 | −0.173483 | ||||||||
\(541\) | 14.5084 | 0.623767 | 0.311883 | − | 0.950120i | \(-0.399040\pi\) | ||||
0.311883 | + | 0.950120i | \(0.399040\pi\) | |||||||
\(542\) | 25.8951 | 1.11229 | ||||||||
\(543\) | −6.46425 | −0.277408 | ||||||||
\(544\) | 1.55340 | 0.0666015 | ||||||||
\(545\) | 6.69278 | 0.286687 | ||||||||
\(546\) | −2.52765 | −0.108173 | ||||||||
\(547\) | −26.7346 | −1.14309 | −0.571543 | − | 0.820572i | \(-0.693655\pi\) | ||||
−0.571543 | + | 0.820572i | \(0.693655\pi\) | |||||||
\(548\) | 29.6813 | 1.26792 | ||||||||
\(549\) | 9.18431 | 0.391977 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.5422 | 1.59935 | ||||||||
\(552\) | 5.35762 | 0.228035 | ||||||||
\(553\) | 17.7965 | 0.756784 | ||||||||
\(554\) | −44.0527 | −1.87162 | ||||||||
\(555\) | −2.63428 | −0.111819 | ||||||||
\(556\) | 53.3728 | 2.26351 | ||||||||
\(557\) | 17.2444 | 0.730670 | 0.365335 | − | 0.930876i | \(-0.380954\pi\) | ||||
0.365335 | + | 0.930876i | \(0.380954\pi\) | |||||||
\(558\) | 8.47033 | 0.358578 | ||||||||
\(559\) | 1.72683 | 0.0730371 | ||||||||
\(560\) | −13.7694 | −0.581865 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.2006 | 0.767748 | ||||||||
\(563\) | −0.831914 | −0.0350610 | −0.0175305 | − | 0.999846i | \(-0.505580\pi\) | ||||
−0.0175305 | + | 0.999846i | \(0.505580\pi\) | |||||||
\(564\) | −48.3693 | −2.03671 | ||||||||
\(565\) | 10.7941 | 0.454112 | ||||||||
\(566\) | 13.2295 | 0.556076 | ||||||||
\(567\) | 3.28684 | 0.138034 | ||||||||
\(568\) | 15.3263 | 0.643076 | ||||||||
\(569\) | 11.5961 | 0.486132 | 0.243066 | − | 0.970010i | \(-0.421847\pi\) | ||||
0.243066 | + | 0.970010i | \(0.421847\pi\) | |||||||
\(570\) | 18.3064 | 0.766769 | ||||||||
\(571\) | 21.8414 | 0.914034 | 0.457017 | − | 0.889458i | \(-0.348918\pi\) | ||||
0.457017 | + | 0.889458i | \(0.348918\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.3693 | 0.642061 | ||||||||
\(574\) | 87.5598 | 3.65468 | ||||||||
\(575\) | 1.07392 | 0.0447856 | ||||||||
\(576\) | −7.61553 | −0.317314 | ||||||||
\(577\) | 9.74587 | 0.405726 | 0.202863 | − | 0.979207i | \(-0.434975\pi\) | ||||
0.202863 | + | 0.979207i | \(0.434975\pi\) | |||||||
\(578\) | 19.6471 | 0.817211 | ||||||||
\(579\) | 15.7518 | 0.654622 | ||||||||
\(580\) | 20.3039 | 0.843074 | ||||||||
\(581\) | 53.3961 | 2.21524 | ||||||||
\(582\) | 0.550320 | 0.0228115 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −43.1669 | −1.78626 | ||||||||
\(585\) | 0.313133 | 0.0129465 | ||||||||
\(586\) | −4.27339 | −0.176532 | ||||||||
\(587\) | 22.9441 | 0.947005 | 0.473502 | − | 0.880793i | \(-0.342990\pi\) | ||||
0.473502 | + | 0.880793i | \(0.342990\pi\) | |||||||
\(588\) | 15.3327 | 0.632308 | ||||||||
\(589\) | −25.7090 | −1.05932 | ||||||||
\(590\) | 22.5060 | 0.926556 | ||||||||
\(591\) | 16.3940 | 0.674357 | ||||||||
\(592\) | 11.0357 | 0.453565 | ||||||||
\(593\) | 28.7819 | 1.18193 | 0.590965 | − | 0.806697i | \(-0.298747\pi\) | ||||
0.590965 | + | 0.806697i | \(0.298747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.4342 | −0.673737 | ||||||||
\(596\) | −23.6988 | −0.970741 | ||||||||
\(597\) | 6.96500 | 0.285059 | ||||||||
\(598\) | −0.825867 | −0.0337722 | ||||||||
\(599\) | −29.1951 | −1.19288 | −0.596440 | − | 0.802657i | \(-0.703419\pi\) | ||||
−0.596440 | + | 0.802657i | \(0.703419\pi\) | |||||||
\(600\) | 4.98884 | 0.203668 | ||||||||
\(601\) | −6.68087 | −0.272518 | −0.136259 | − | 0.990673i | \(-0.543508\pi\) | ||||
−0.136259 | + | 0.990673i | \(0.543508\pi\) | |||||||
\(602\) | −44.5151 | −1.81430 | ||||||||
\(603\) | −15.2739 | −0.622000 | ||||||||
\(604\) | 30.7522 | 1.25129 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.24102 | −0.0504131 | ||||||||
\(607\) | −42.6108 | −1.72952 | −0.864759 | − | 0.502188i | \(-0.832529\pi\) | ||||
−0.864759 | + | 0.502188i | \(0.832529\pi\) | |||||||
\(608\) | −2.31583 | −0.0939194 | ||||||||
\(609\) | −16.5541 | −0.670805 | ||||||||
\(610\) | −22.5556 | −0.913251 | ||||||||
\(611\) | 3.75703 | 0.151993 | ||||||||
\(612\) | 20.1569 | 0.814794 | ||||||||
\(613\) | −5.83156 | −0.235535 | −0.117767 | − | 0.993041i | \(-0.537574\pi\) | ||||
−0.117767 | + | 0.993041i | \(0.537574\pi\) | |||||||
\(614\) | 52.4495 | 2.11669 | ||||||||
\(615\) | −10.8472 | −0.437401 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.6386 | −1.35424 | −0.677119 | − | 0.735874i | \(-0.736772\pi\) | ||||
−0.677119 | + | 0.735874i | \(0.736772\pi\) | |||||||
\(618\) | −15.7225 | −0.632452 | ||||||||
\(619\) | 42.5616 | 1.71070 | 0.855349 | − | 0.518053i | \(-0.173343\pi\) | ||||
0.855349 | + | 0.518053i | \(0.173343\pi\) | |||||||
\(620\) | −13.9042 | −0.558405 | ||||||||
\(621\) | 1.07392 | 0.0430950 | ||||||||
\(622\) | 80.5766 | 3.23083 | ||||||||
\(623\) | 5.32856 | 0.213484 | ||||||||
\(624\) | −1.31180 | −0.0525140 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.49374 | −0.339478 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −40.8509 | −1.63013 | ||||||||
\(629\) | 13.1714 | 0.525179 | ||||||||
\(630\) | −8.07211 | −0.321601 | ||||||||
\(631\) | −8.89989 | −0.354299 | −0.177149 | − | 0.984184i | \(-0.556688\pi\) | ||||
−0.177149 | + | 0.984184i | \(0.556688\pi\) | |||||||
\(632\) | 27.0119 | 1.07448 | ||||||||
\(633\) | −19.9531 | −0.793065 | ||||||||
\(634\) | −7.06228 | −0.280479 | ||||||||
\(635\) | 17.0033 | 0.674755 | ||||||||
\(636\) | 19.8966 | 0.788951 | ||||||||
\(637\) | −1.19095 | −0.0471871 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.07211 | 0.121531 | ||||||||
\(640\) | 19.3242 | 0.763858 | ||||||||
\(641\) | −6.16806 | −0.243624 | −0.121812 | − | 0.992553i | \(-0.538870\pi\) | ||||
−0.121812 | + | 0.992553i | \(0.538870\pi\) | |||||||
\(642\) | 5.13892 | 0.202817 | ||||||||
\(643\) | 4.35335 | 0.171680 | 0.0858398 | − | 0.996309i | \(-0.472643\pi\) | ||||
0.0858398 | + | 0.996309i | \(0.472643\pi\) | |||||||
\(644\) | 14.2300 | 0.560740 | ||||||||
\(645\) | 5.51468 | 0.217140 | ||||||||
\(646\) | −91.5318 | −3.60127 | ||||||||
\(647\) | 13.4933 | 0.530478 | 0.265239 | − | 0.964183i | \(-0.414549\pi\) | ||||
0.265239 | + | 0.964183i | \(0.414549\pi\) | |||||||
\(648\) | 4.98884 | 0.195980 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.769020 | −0.0301635 | ||||||||
\(651\) | 11.3363 | 0.444304 | ||||||||
\(652\) | −20.2741 | −0.793993 | ||||||||
\(653\) | 27.4481 | 1.07413 | 0.537064 | − | 0.843541i | \(-0.319533\pi\) | ||||
0.537064 | + | 0.843541i | \(0.319533\pi\) | |||||||
\(654\) | −16.4367 | −0.642726 | ||||||||
\(655\) | 0.0430508 | 0.00168213 | ||||||||
\(656\) | 45.4418 | 1.77420 | ||||||||
\(657\) | −8.65269 | −0.337574 | ||||||||
\(658\) | −96.8507 | −3.77563 | ||||||||
\(659\) | −18.7768 | −0.731441 | −0.365721 | − | 0.930725i | \(-0.619177\pi\) | ||||
−0.365721 | + | 0.930725i | \(0.619177\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.6525 | −0.842184 | −0.421092 | − | 0.907018i | \(-0.638353\pi\) | ||||
−0.421092 | + | 0.907018i | \(0.638353\pi\) | |||||||
\(662\) | −34.6822 | −1.34796 | ||||||||
\(663\) | −1.56567 | −0.0608055 | ||||||||
\(664\) | 81.0458 | 3.14519 | ||||||||
\(665\) | 24.5004 | 0.950084 | ||||||||
\(666\) | 6.46950 | 0.250688 | ||||||||
\(667\) | −5.40877 | −0.209428 | ||||||||
\(668\) | 23.3459 | 0.903281 | ||||||||
\(669\) | −20.1466 | −0.778914 | ||||||||
\(670\) | 37.5109 | 1.44917 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.02116 | 0.0393919 | ||||||||
\(673\) | 23.3021 | 0.898232 | 0.449116 | − | 0.893474i | \(-0.351739\pi\) | ||||
0.449116 | + | 0.893474i | \(0.351739\pi\) | |||||||
\(674\) | 39.1689 | 1.50873 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −52.0127 | −2.00049 | ||||||||
\(677\) | 33.2808 | 1.27909 | 0.639543 | − | 0.768756i | \(-0.279124\pi\) | ||||
0.639543 | + | 0.768756i | \(0.279124\pi\) | |||||||
\(678\) | −26.5091 | −1.01808 | ||||||||
\(679\) | 0.736522 | 0.0282651 | ||||||||
\(680\) | −24.9442 | −0.956566 | ||||||||
\(681\) | 0.533937 | 0.0204605 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.9244 | 0.647593 | 0.323796 | − | 0.946127i | \(-0.395041\pi\) | ||||
0.323796 | + | 0.946127i | \(0.395041\pi\) | |||||||
\(684\) | −30.0502 | −1.14900 | ||||||||
\(685\) | −7.36257 | −0.281309 | ||||||||
\(686\) | −25.8039 | −0.985197 | ||||||||
\(687\) | −22.1931 | −0.846718 | ||||||||
\(688\) | −23.1024 | −0.880772 | ||||||||
\(689\) | −1.54545 | −0.0588769 | ||||||||
\(690\) | −2.63743 | −0.100405 | ||||||||
\(691\) | −48.4335 | −1.84250 | −0.921249 | − | 0.388973i | \(-0.872830\pi\) | ||||
−0.921249 | + | 0.388973i | \(0.872830\pi\) | |||||||
\(692\) | 64.7650 | 2.46200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 72.8910 | 2.76690 | ||||||||
\(695\) | −13.2393 | −0.502197 | ||||||||
\(696\) | −25.1261 | −0.952403 | ||||||||
\(697\) | 54.2360 | 2.05434 | ||||||||
\(698\) | 77.8362 | 2.94614 | ||||||||
\(699\) | −4.56567 | −0.172689 | ||||||||
\(700\) | 13.2505 | 0.500822 | ||||||||
\(701\) | −45.4161 | −1.71534 | −0.857672 | − | 0.514197i | \(-0.828090\pi\) | ||||
−0.857672 | + | 0.514197i | \(0.828090\pi\) | |||||||
\(702\) | −0.769020 | −0.0290248 | ||||||||
\(703\) | −19.6361 | −0.740591 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.9982 | 0.451878 | ||||||||
\(706\) | 2.95171 | 0.111089 | ||||||||
\(707\) | −1.66093 | −0.0624655 | ||||||||
\(708\) | −36.9439 | −1.38844 | ||||||||
\(709\) | −1.76497 | −0.0662848 | −0.0331424 | − | 0.999451i | \(-0.510551\pi\) | ||||
−0.0331424 | + | 0.999451i | \(0.510551\pi\) | |||||||
\(710\) | −7.54476 | −0.283150 | ||||||||
\(711\) | 5.41446 | 0.203058 | ||||||||
\(712\) | 8.08780 | 0.303103 | ||||||||
\(713\) | 3.70394 | 0.138714 | ||||||||
\(714\) | 40.3606 | 1.51046 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −33.4729 | −1.25094 | ||||||||
\(717\) | −5.86053 | −0.218865 | ||||||||
\(718\) | −28.6334 | −1.06859 | ||||||||
\(719\) | −3.29998 | −0.123069 | −0.0615343 | − | 0.998105i | \(-0.519599\pi\) | ||||
−0.0615343 | + | 0.998105i | \(0.519599\pi\) | |||||||
\(720\) | −4.18926 | −0.156125 | ||||||||
\(721\) | −21.0423 | −0.783655 | ||||||||
\(722\) | 89.7952 | 3.34183 | ||||||||
\(723\) | 9.96074 | 0.370444 | ||||||||
\(724\) | −26.0599 | −0.968507 | ||||||||
\(725\) | −5.03647 | −0.187050 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.7838 | 0.437037 | 0.218519 | − | 0.975833i | \(-0.429878\pi\) | ||||
0.218519 | + | 0.975833i | \(0.429878\pi\) | |||||||
\(728\) | −5.13461 | −0.190301 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.2500 | 0.786499 | ||||||||
\(731\) | −27.5734 | −1.01984 | ||||||||
\(732\) | 37.0254 | 1.36850 | ||||||||
\(733\) | 5.73108 | 0.211682 | 0.105841 | − | 0.994383i | \(-0.466246\pi\) | ||||
0.105841 | + | 0.994383i | \(0.466246\pi\) | |||||||
\(734\) | 39.2599 | 1.44911 | ||||||||
\(735\) | −3.80333 | −0.140288 | ||||||||
\(736\) | 0.333646 | 0.0122983 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 26.6395 | 0.980614 | ||||||||
\(739\) | −21.0551 | −0.774524 | −0.387262 | − | 0.921970i | \(-0.626579\pi\) | ||||
−0.387262 | + | 0.921970i | \(0.626579\pi\) | |||||||
\(740\) | −10.6198 | −0.390391 | ||||||||
\(741\) | 2.33412 | 0.0857461 | ||||||||
\(742\) | 39.8393 | 1.46255 | ||||||||
\(743\) | 13.1283 | 0.481630 | 0.240815 | − | 0.970571i | \(-0.422585\pi\) | ||||
0.240815 | + | 0.970571i | \(0.422585\pi\) | |||||||
\(744\) | 17.2065 | 0.630819 | ||||||||
\(745\) | 5.87858 | 0.215375 | ||||||||
\(746\) | 0.790734 | 0.0289508 | ||||||||
\(747\) | 16.2454 | 0.594389 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.87768 | 0.251305 | ||||||||
\(750\) | −2.45589 | −0.0896763 | ||||||||
\(751\) | 25.6251 | 0.935073 | 0.467537 | − | 0.883974i | \(-0.345142\pi\) | ||||
0.467537 | + | 0.883974i | \(0.345142\pi\) | |||||||
\(752\) | −50.2636 | −1.83292 | ||||||||
\(753\) | −16.8788 | −0.615098 | ||||||||
\(754\) | 3.87315 | 0.141052 | ||||||||
\(755\) | −7.62821 | −0.277619 | ||||||||
\(756\) | 13.2505 | 0.481916 | ||||||||
\(757\) | 31.1970 | 1.13387 | 0.566936 | − | 0.823762i | \(-0.308129\pi\) | ||||
0.566936 | + | 0.823762i | \(0.308129\pi\) | |||||||
\(758\) | 28.0400 | 1.01846 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 37.1872 | 1.34892 | ||||||||
\(761\) | 11.3761 | 0.412382 | 0.206191 | − | 0.978512i | \(-0.433893\pi\) | ||||
0.206191 | + | 0.978512i | \(0.433893\pi\) | |||||||
\(762\) | −41.7581 | −1.51274 | ||||||||
\(763\) | −21.9981 | −0.796385 | ||||||||
\(764\) | 61.9594 | 2.24161 | ||||||||
\(765\) | −5.00000 | −0.180775 | ||||||||
\(766\) | 69.6668 | 2.51717 | ||||||||
\(767\) | 2.86958 | 0.103615 | ||||||||
\(768\) | −32.2271 | −1.16290 | ||||||||
\(769\) | 10.3938 | 0.374811 | 0.187405 | − | 0.982283i | \(-0.439992\pi\) | ||||
0.187405 | + | 0.982283i | \(0.439992\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.1436 | 0.401326 | ||||||||
\(772\) | 63.5014 | 2.28547 | ||||||||
\(773\) | 14.0348 | 0.504796 | 0.252398 | − | 0.967623i | \(-0.418781\pi\) | ||||
0.252398 | + | 0.967623i | \(0.418781\pi\) | |||||||
\(774\) | −13.5434 | −0.486808 | ||||||||
\(775\) | 3.44899 | 0.123891 | ||||||||
\(776\) | 1.11791 | 0.0401306 | ||||||||
\(777\) | 8.65847 | 0.310621 | ||||||||
\(778\) | 37.2808 | 1.33658 | ||||||||
\(779\) | −80.8559 | −2.89696 | ||||||||
\(780\) | 1.26236 | 0.0451997 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 13.1871 | 0.471571 | ||||||||
\(783\) | −5.03647 | −0.179989 | ||||||||
\(784\) | 15.9331 | 0.569041 | ||||||||
\(785\) | 10.1332 | 0.361670 | ||||||||
\(786\) | −0.105728 | −0.00377119 | ||||||||
\(787\) | −13.8176 | −0.492545 | −0.246273 | − | 0.969201i | \(-0.579206\pi\) | ||||
−0.246273 | + | 0.969201i | \(0.579206\pi\) | |||||||
\(788\) | 66.0902 | 2.35437 | ||||||||
\(789\) | −26.8726 | −0.956691 | ||||||||
\(790\) | −13.2973 | −0.473097 | ||||||||
\(791\) | −35.4785 | −1.26147 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.87591 | −0.102127 | ||||||||
\(794\) | 12.8311 | 0.455357 | ||||||||
\(795\) | −4.93543 | −0.175042 | ||||||||
\(796\) | 28.0786 | 0.995218 | ||||||||
\(797\) | −5.38594 | −0.190780 | −0.0953898 | − | 0.995440i | \(-0.530410\pi\) | ||||
−0.0953898 | + | 0.995440i | \(0.530410\pi\) | |||||||
\(798\) | −60.1701 | −2.13000 | ||||||||
\(799\) | −59.9910 | −2.12233 | ||||||||
\(800\) | 0.310680 | 0.0109842 | ||||||||
\(801\) | 1.62118 | 0.0572815 | ||||||||
\(802\) | 34.3840 | 1.21414 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −61.5748 | −2.17157 | ||||||||
\(805\) | −3.52981 | −0.124409 | ||||||||
\(806\) | −2.65234 | −0.0934248 | ||||||||
\(807\) | −10.0629 | −0.354231 | ||||||||
\(808\) | −2.52099 | −0.0886880 | ||||||||
\(809\) | 23.7748 | 0.835876 | 0.417938 | − | 0.908476i | \(-0.362753\pi\) | ||||
0.417938 | + | 0.908476i | \(0.362753\pi\) | |||||||
\(810\) | −2.45589 | −0.0862911 | ||||||||
\(811\) | 9.46335 | 0.332303 | 0.166152 | − | 0.986100i | \(-0.446866\pi\) | ||||
0.166152 | + | 0.986100i | \(0.446866\pi\) | |||||||
\(812\) | −66.7358 | −2.34197 | ||||||||
\(813\) | 10.5441 | 0.369798 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.02906 | 0.176160 | ||||||||
\(816\) | 20.9463 | 0.733268 | ||||||||
\(817\) | 41.1068 | 1.43815 | ||||||||
\(818\) | 81.8086 | 2.86037 | ||||||||
\(819\) | −1.02922 | −0.0359639 | ||||||||
\(820\) | −43.7292 | −1.52709 | ||||||||
\(821\) | −10.4189 | −0.363622 | −0.181811 | − | 0.983334i | \(-0.558196\pi\) | ||||
−0.181811 | + | 0.983334i | \(0.558196\pi\) | |||||||
\(822\) | 18.0816 | 0.630670 | ||||||||
\(823\) | 24.3540 | 0.848928 | 0.424464 | − | 0.905445i | \(-0.360463\pi\) | ||||
0.424464 | + | 0.905445i | \(0.360463\pi\) | |||||||
\(824\) | −31.9384 | −1.11263 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −73.9736 | −2.57387 | ||||||||
\(827\) | −22.0006 | −0.765037 | −0.382519 | − | 0.923948i | \(-0.624943\pi\) | ||||
−0.382519 | + | 0.923948i | \(0.624943\pi\) | |||||||
\(828\) | 4.32938 | 0.150456 | ||||||||
\(829\) | 3.03289 | 0.105337 | 0.0526683 | − | 0.998612i | \(-0.483227\pi\) | ||||
0.0526683 | + | 0.998612i | \(0.483227\pi\) | |||||||
\(830\) | −39.8969 | −1.38484 | ||||||||
\(831\) | −17.9376 | −0.622248 | ||||||||
\(832\) | 2.38468 | 0.0826738 | ||||||||
\(833\) | 19.0166 | 0.658888 | ||||||||
\(834\) | 32.5143 | 1.12588 | ||||||||
\(835\) | −5.79105 | −0.200408 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.44899 | 0.119214 | ||||||||
\(838\) | −12.9784 | −0.448331 | ||||||||
\(839\) | −48.5383 | −1.67573 | −0.837864 | − | 0.545879i | \(-0.816196\pi\) | ||||
−0.837864 | + | 0.545879i | \(0.816196\pi\) | |||||||
\(840\) | −16.3975 | −0.565768 | ||||||||
\(841\) | −3.63399 | −0.125310 | ||||||||
\(842\) | −75.5946 | −2.60516 | ||||||||
\(843\) | 7.41103 | 0.255249 | ||||||||
\(844\) | −80.4386 | −2.76881 | ||||||||
\(845\) | 12.9019 | 0.443840 | ||||||||
\(846\) | −29.4662 | −1.01307 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20.6758 | 0.710011 | ||||||||
\(849\) | 5.38684 | 0.184876 | ||||||||
\(850\) | 12.2794 | 0.421181 | ||||||||
\(851\) | 2.82901 | 0.0969773 | ||||||||
\(852\) | 12.3848 | 0.424298 | ||||||||
\(853\) | −11.7632 | −0.402766 | −0.201383 | − | 0.979513i | \(-0.564544\pi\) | ||||
−0.201383 | + | 0.979513i | \(0.564544\pi\) | |||||||
\(854\) | 74.1368 | 2.53691 | ||||||||
\(855\) | 7.45408 | 0.254924 | ||||||||
\(856\) | 10.4391 | 0.356801 | ||||||||
\(857\) | 1.61311 | 0.0551026 | 0.0275513 | − | 0.999620i | \(-0.491229\pi\) | ||||
0.0275513 | + | 0.999620i | \(0.491229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.3263 | 1.61475 | 0.807376 | − | 0.590038i | \(-0.200887\pi\) | ||||
0.807376 | + | 0.590038i | \(0.200887\pi\) | |||||||
\(860\) | 22.2318 | 0.758097 | ||||||||
\(861\) | 35.6530 | 1.21505 | ||||||||
\(862\) | 30.3318 | 1.03310 | ||||||||
\(863\) | −9.97233 | −0.339462 | −0.169731 | − | 0.985490i | \(-0.554290\pi\) | ||||
−0.169731 | + | 0.985490i | \(0.554290\pi\) | |||||||
\(864\) | 0.310680 | 0.0105695 | ||||||||
\(865\) | −16.0652 | −0.546234 | ||||||||
\(866\) | 3.46985 | 0.117910 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 45.7009 | 1.55119 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 12.3690 | 0.419348 | ||||||||
\(871\) | 4.78276 | 0.162058 | ||||||||
\(872\) | −33.3892 | −1.13070 | ||||||||
\(873\) | 0.224082 | 0.00758402 | ||||||||
\(874\) | −19.6596 | −0.664996 | ||||||||
\(875\) | −3.28684 | −0.111116 | ||||||||
\(876\) | −34.8823 | −1.17856 | ||||||||
\(877\) | 26.0057 | 0.878151 | 0.439076 | − | 0.898450i | \(-0.355306\pi\) | ||||
0.439076 | + | 0.898450i | \(0.355306\pi\) | |||||||
\(878\) | −18.6287 | −0.628688 | ||||||||
\(879\) | −1.74006 | −0.0586907 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.4081 | 0.350657 | 0.175329 | − | 0.984510i | \(-0.443901\pi\) | ||||
0.175329 | + | 0.984510i | \(0.443901\pi\) | |||||||
\(882\) | 9.34054 | 0.314512 | ||||||||
\(883\) | −53.7283 | −1.80810 | −0.904051 | − | 0.427424i | \(-0.859421\pi\) | ||||
−0.904051 | + | 0.427424i | \(0.859421\pi\) | |||||||
\(884\) | −6.31180 | −0.212289 | ||||||||
\(885\) | 9.16409 | 0.308048 | ||||||||
\(886\) | 27.1773 | 0.913040 | ||||||||
\(887\) | −40.6246 | −1.36404 | −0.682021 | − | 0.731333i | \(-0.738899\pi\) | ||||
−0.682021 | + | 0.731333i | \(0.738899\pi\) | |||||||
\(888\) | 13.1420 | 0.441017 | ||||||||
\(889\) | −55.8871 | −1.87439 | ||||||||
\(890\) | −3.98143 | −0.133458 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −81.2188 | −2.71941 | ||||||||
\(893\) | 89.4354 | 2.99284 | ||||||||
\(894\) | −14.4371 | −0.482850 | ||||||||
\(895\) | 8.30309 | 0.277542 | ||||||||
\(896\) | −63.5157 | −2.12191 | ||||||||
\(897\) | −0.336280 | −0.0112281 | ||||||||
\(898\) | 15.5422 | 0.518651 | ||||||||
\(899\) | −17.3707 | −0.579346 | ||||||||
\(900\) | 4.03138 | 0.134379 | ||||||||
\(901\) | 24.6772 | 0.822115 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.1259 | −0.603191 | ||||||||
\(904\) | −53.8501 | −1.79103 | ||||||||
\(905\) | 6.46425 | 0.214879 | ||||||||
\(906\) | 18.7340 | 0.622396 | ||||||||
\(907\) | −19.4070 | −0.644398 | −0.322199 | − | 0.946672i | \(-0.604422\pi\) | ||||
−0.322199 | + | 0.946672i | \(0.604422\pi\) | |||||||
\(908\) | 2.15250 | 0.0714333 | ||||||||
\(909\) | −0.505326 | −0.0167606 | ||||||||
\(910\) | 2.52765 | 0.0837907 | ||||||||
\(911\) | 10.7208 | 0.355195 | 0.177597 | − | 0.984103i | \(-0.443168\pi\) | ||||
0.177597 | + | 0.984103i | \(0.443168\pi\) | |||||||
\(912\) | −31.2271 | −1.03403 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.465585 | −0.0154002 | ||||||||
\(915\) | −9.18431 | −0.303624 | ||||||||
\(916\) | −89.4686 | −2.95613 | ||||||||
\(917\) | −0.141501 | −0.00467278 | ||||||||
\(918\) | 12.2794 | 0.405282 | ||||||||
\(919\) | −23.1310 | −0.763021 | −0.381511 | − | 0.924364i | \(-0.624596\pi\) | ||||
−0.381511 | + | 0.924364i | \(0.624596\pi\) | |||||||
\(920\) | −5.35762 | −0.176635 | ||||||||
\(921\) | 21.3566 | 0.703725 | ||||||||
\(922\) | −65.3752 | −2.15302 | ||||||||
\(923\) | −0.961981 | −0.0316640 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.63428 | 0.0866147 | ||||||||
\(926\) | 51.5577 | 1.69429 | ||||||||
\(927\) | −6.40197 | −0.210268 | ||||||||
\(928\) | −1.56473 | −0.0513648 | ||||||||
\(929\) | 26.2273 | 0.860489 | 0.430245 | − | 0.902712i | \(-0.358427\pi\) | ||||
0.430245 | + | 0.902712i | \(0.358427\pi\) | |||||||
\(930\) | −8.47033 | −0.277753 | ||||||||
\(931\) | −28.3503 | −0.929144 | ||||||||
\(932\) | −18.4059 | −0.602907 | ||||||||
\(933\) | 32.8096 | 1.07414 | ||||||||
\(934\) | 19.4012 | 0.634828 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.56217 | −0.0510612 | ||||||||
\(937\) | 23.4011 | 0.764480 | 0.382240 | − | 0.924063i | \(-0.375153\pi\) | ||||
0.382240 | + | 0.924063i | \(0.375153\pi\) | |||||||
\(938\) | −123.292 | −4.02564 | ||||||||
\(939\) | −3.45852 | −0.112865 | ||||||||
\(940\) | 48.3693 | 1.57763 | ||||||||
\(941\) | −10.9687 | −0.357570 | −0.178785 | − | 0.983888i | \(-0.557217\pi\) | ||||
−0.178785 | + | 0.983888i | \(0.557217\pi\) | |||||||
\(942\) | −24.8860 | −0.810831 | ||||||||
\(943\) | 11.6490 | 0.379345 | ||||||||
\(944\) | −38.3908 | −1.24951 | ||||||||
\(945\) | −3.28684 | −0.106921 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.3652 | −0.434310 | −0.217155 | − | 0.976137i | \(-0.569678\pi\) | ||||
−0.217155 | + | 0.976137i | \(0.569678\pi\) | |||||||
\(948\) | 21.8278 | 0.708933 | ||||||||
\(949\) | 2.70945 | 0.0879524 | ||||||||
\(950\) | −18.3064 | −0.593937 | ||||||||
\(951\) | −2.87566 | −0.0932495 | ||||||||
\(952\) | 81.9876 | 2.65723 | ||||||||
\(953\) | −21.8242 | −0.706956 | −0.353478 | − | 0.935443i | \(-0.615001\pi\) | ||||
−0.353478 | + | 0.935443i | \(0.615001\pi\) | |||||||
\(954\) | 12.1209 | 0.392427 | ||||||||
\(955\) | −15.3693 | −0.497339 | ||||||||
\(956\) | −23.6260 | −0.764120 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 98.1686 | 3.17168 | ||||||||
\(959\) | 24.1996 | 0.781446 | ||||||||
\(960\) | 7.61553 | 0.245790 | ||||||||
\(961\) | −19.1045 | −0.616273 | ||||||||
\(962\) | −2.02582 | −0.0653150 | ||||||||
\(963\) | 2.09249 | 0.0674295 | ||||||||
\(964\) | 40.1555 | 1.29332 | ||||||||
\(965\) | −15.7518 | −0.507068 | ||||||||
\(966\) | 8.66881 | 0.278914 | ||||||||
\(967\) | 16.6600 | 0.535750 | 0.267875 | − | 0.963454i | \(-0.413679\pi\) | ||||
0.267875 | + | 0.963454i | \(0.413679\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −37.2704 | −1.19730 | ||||||||
\(970\) | −0.550320 | −0.0176697 | ||||||||
\(971\) | 11.1032 | 0.356320 | 0.178160 | − | 0.984002i | \(-0.442986\pi\) | ||||
0.178160 | + | 0.984002i | \(0.442986\pi\) | |||||||
\(972\) | 4.03138 | 0.129307 | ||||||||
\(973\) | 43.5156 | 1.39505 | ||||||||
\(974\) | −24.4006 | −0.781846 | ||||||||
\(975\) | −0.313133 | −0.0100283 | ||||||||
\(976\) | 38.4755 | 1.23157 | ||||||||
\(977\) | 18.8144 | 0.601926 | 0.300963 | − | 0.953636i | \(-0.402692\pi\) | ||||
0.300963 | + | 0.953636i | \(0.402692\pi\) | |||||||
\(978\) | −12.3508 | −0.394935 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −15.3327 | −0.489784 | ||||||||
\(981\) | −6.69278 | −0.213684 | ||||||||
\(982\) | 12.2143 | 0.389775 | ||||||||
\(983\) | −1.37848 | −0.0439667 | −0.0219833 | − | 0.999758i | \(-0.506998\pi\) | ||||
−0.0219833 | + | 0.999758i | \(0.506998\pi\) | |||||||
\(984\) | 54.1150 | 1.72512 | ||||||||
\(985\) | −16.3940 | −0.522355 | ||||||||
\(986\) | −61.8450 | −1.96955 | ||||||||
\(987\) | −39.4362 | −1.25527 | ||||||||
\(988\) | 9.40973 | 0.299363 | ||||||||
\(989\) | −5.92233 | −0.188319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.3186 | −1.47136 | −0.735680 | − | 0.677329i | \(-0.763137\pi\) | ||||
−0.735680 | + | 0.677329i | \(0.763137\pi\) | |||||||
\(992\) | 1.07153 | 0.0340212 | ||||||||
\(993\) | −14.1221 | −0.448150 | ||||||||
\(994\) | 24.7984 | 0.786558 | ||||||||
\(995\) | −6.96500 | −0.220805 | ||||||||
\(996\) | 65.4915 | 2.07518 | ||||||||
\(997\) | 14.5470 | 0.460709 | 0.230355 | − | 0.973107i | \(-0.426011\pi\) | ||||
0.230355 | + | 0.973107i | \(0.426011\pi\) | |||||||
\(998\) | 107.508 | 3.40311 | ||||||||
\(999\) | 2.63428 | 0.0833450 |
(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 | 1815.2.a.x.1.3 | 4 | ||
3.2 | odd | 2 | 5445.2.a.be.1.2 | 4 | |||
5.4 | even | 2 | 9075.2.a.cl.1.2 | 4 | |||
11.3 | even | 5 | 165.2.m.a.31.2 | yes | 8 | ||
11.4 | even | 5 | 165.2.m.a.16.2 | ✓ | 8 | ||
11.10 | odd | 2 | 1815.2.a.o.1.2 | 4 | |||
33.14 | odd | 10 | 495.2.n.d.361.1 | 8 | |||
33.26 | odd | 10 | 495.2.n.d.181.1 | 8 | |||
33.32 | even | 2 | 5445.2.a.bv.1.3 | 4 | |||
55.3 | odd | 20 | 825.2.bx.h.724.1 | 16 | |||
55.4 | even | 10 | 825.2.n.k.676.1 | 8 | |||
55.14 | even | 10 | 825.2.n.k.526.1 | 8 | |||
55.37 | odd | 20 | 825.2.bx.h.49.1 | 16 | |||
55.47 | odd | 20 | 825.2.bx.h.724.4 | 16 | |||
55.48 | odd | 20 | 825.2.bx.h.49.4 | 16 | |||
55.54 | odd | 2 | 9075.2.a.dj.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.a.16.2 | ✓ | 8 | 11.4 | even | 5 | ||
165.2.m.a.31.2 | yes | 8 | 11.3 | even | 5 | ||
495.2.n.d.181.1 | 8 | 33.26 | odd | 10 | |||
495.2.n.d.361.1 | 8 | 33.14 | odd | 10 | |||
825.2.n.k.526.1 | 8 | 55.14 | even | 10 | |||
825.2.n.k.676.1 | 8 | 55.4 | even | 10 | |||
825.2.bx.h.49.1 | 16 | 55.37 | odd | 20 | |||
825.2.bx.h.49.4 | 16 | 55.48 | odd | 20 | |||
825.2.bx.h.724.1 | 16 | 55.3 | odd | 20 | |||
825.2.bx.h.724.4 | 16 | 55.47 | odd | 20 | |||
1815.2.a.o.1.2 | 4 | 11.10 | odd | 2 | |||
1815.2.a.x.1.3 | 4 | 1.1 | even | 1 | trivial | ||
5445.2.a.be.1.2 | 4 | 3.2 | odd | 2 | |||
5445.2.a.bv.1.3 | 4 | 33.32 | even | 2 | |||
9075.2.a.cl.1.2 | 4 | 5.4 | even | 2 | |||
9075.2.a.dj.1.3 | 4 | 55.54 | odd | 2 |