Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 27 x^{18} + 52 x^{17} + 302 x^{16} - 552 x^{15} - 1820 x^{14} + 3090 x^{13} + 6449 x^{12} - 9852 x^{11} - 13797 x^{10} + 18080 x^{9} + 17721 x^{8} - 18446 x^{7} + \cdots + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-0.463326\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.463326 | 0.327621 | 0.163811 | − | 0.986492i | \(-0.447621\pi\) | ||||
0.163811 | + | 0.986492i | \(0.447621\pi\) | |||||||
\(3\) | 0.981674 | 0.566770 | 0.283385 | − | 0.959006i | \(-0.408543\pi\) | ||||
0.283385 | + | 0.959006i | \(0.408543\pi\) | |||||||
\(4\) | −1.78533 | −0.892664 | ||||||||
\(5\) | −3.31637 | −1.48313 | −0.741563 | − | 0.670884i | \(-0.765915\pi\) | ||||
−0.741563 | + | 0.670884i | \(0.765915\pi\) | |||||||
\(6\) | 0.454835 | 0.185686 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.75384 | −0.620077 | ||||||||
\(9\) | −2.03632 | −0.678772 | ||||||||
\(10\) | −1.53656 | −0.485903 | ||||||||
\(11\) | −2.89859 | −0.873958 | −0.436979 | − | 0.899472i | \(-0.643952\pi\) | ||||
−0.436979 | + | 0.899472i | \(0.643952\pi\) | |||||||
\(12\) | −1.75261 | −0.505935 | ||||||||
\(13\) | −6.95519 | −1.92902 | −0.964512 | − | 0.264040i | \(-0.914945\pi\) | ||||
−0.964512 | + | 0.264040i | \(0.914945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.25559 | −0.840590 | ||||||||
\(16\) | 2.75806 | 0.689514 | ||||||||
\(17\) | 7.66901 | 1.86001 | 0.930004 | − | 0.367550i | \(-0.119803\pi\) | ||||
0.930004 | + | 0.367550i | \(0.119803\pi\) | |||||||
\(18\) | −0.943479 | −0.222380 | ||||||||
\(19\) | 1.90411 | 0.436833 | 0.218416 | − | 0.975856i | \(-0.429911\pi\) | ||||
0.218416 | + | 0.975856i | \(0.429911\pi\) | |||||||
\(20\) | 5.92081 | 1.32393 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.34299 | −0.286327 | ||||||||
\(23\) | 3.76800 | 0.785682 | 0.392841 | − | 0.919606i | \(-0.371492\pi\) | ||||
0.392841 | + | 0.919606i | \(0.371492\pi\) | |||||||
\(24\) | −1.72170 | −0.351441 | ||||||||
\(25\) | 5.99830 | 1.19966 | ||||||||
\(26\) | −3.22252 | −0.631989 | ||||||||
\(27\) | −4.94402 | −0.951477 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.58717 | −0.666120 | −0.333060 | − | 0.942906i | \(-0.608081\pi\) | ||||
−0.333060 | + | 0.942906i | \(0.608081\pi\) | |||||||
\(30\) | −1.50840 | −0.275395 | ||||||||
\(31\) | 8.42330 | 1.51287 | 0.756435 | − | 0.654069i | \(-0.226940\pi\) | ||||
0.756435 | + | 0.654069i | \(0.226940\pi\) | |||||||
\(32\) | 4.78557 | 0.845976 | ||||||||
\(33\) | −2.84547 | −0.495333 | ||||||||
\(34\) | 3.55325 | 0.609378 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.63549 | 0.605916 | ||||||||
\(37\) | −3.65525 | −0.600920 | −0.300460 | − | 0.953794i | \(-0.597140\pi\) | ||||
−0.300460 | + | 0.953794i | \(0.597140\pi\) | |||||||
\(38\) | 0.882224 | 0.143116 | ||||||||
\(39\) | −6.82773 | −1.09331 | ||||||||
\(40\) | 5.81639 | 0.919652 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.24584 | −0.189989 | −0.0949944 | − | 0.995478i | \(-0.530283\pi\) | ||||
−0.0949944 | + | 0.995478i | \(0.530283\pi\) | |||||||
\(44\) | 5.17494 | 0.780151 | ||||||||
\(45\) | 6.75318 | 1.00670 | ||||||||
\(46\) | 1.74581 | 0.257406 | ||||||||
\(47\) | 8.86125 | 1.29255 | 0.646273 | − | 0.763106i | \(-0.276327\pi\) | ||||
0.646273 | + | 0.763106i | \(0.276327\pi\) | |||||||
\(48\) | 2.70751 | 0.390796 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.77917 | 0.393034 | ||||||||
\(51\) | 7.52846 | 1.05420 | ||||||||
\(52\) | 12.4173 | 1.72197 | ||||||||
\(53\) | 4.12816 | 0.567047 | 0.283523 | − | 0.958965i | \(-0.408497\pi\) | ||||
0.283523 | + | 0.958965i | \(0.408497\pi\) | |||||||
\(54\) | −2.29070 | −0.311724 | ||||||||
\(55\) | 9.61280 | 1.29619 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.86922 | 0.247584 | ||||||||
\(58\) | −1.66203 | −0.218235 | ||||||||
\(59\) | −10.5998 | −1.37997 | −0.689987 | − | 0.723822i | \(-0.742384\pi\) | ||||
−0.689987 | + | 0.723822i | \(0.742384\pi\) | |||||||
\(60\) | 5.81230 | 0.750365 | ||||||||
\(61\) | 8.56444 | 1.09656 | 0.548282 | − | 0.836293i | \(-0.315282\pi\) | ||||
0.548282 | + | 0.836293i | \(0.315282\pi\) | |||||||
\(62\) | 3.90274 | 0.495648 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.29883 | −0.412354 | ||||||||
\(65\) | 23.0660 | 2.86098 | ||||||||
\(66\) | −1.31838 | −0.162282 | ||||||||
\(67\) | −4.56055 | −0.557160 | −0.278580 | − | 0.960413i | \(-0.589864\pi\) | ||||
−0.278580 | + | 0.960413i | \(0.589864\pi\) | |||||||
\(68\) | −13.6917 | −1.66036 | ||||||||
\(69\) | 3.69895 | 0.445301 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.16682 | 0.257154 | 0.128577 | − | 0.991700i | \(-0.458959\pi\) | ||||
0.128577 | + | 0.991700i | \(0.458959\pi\) | |||||||
\(72\) | 3.57138 | 0.420891 | ||||||||
\(73\) | 3.80196 | 0.444985 | 0.222493 | − | 0.974934i | \(-0.428581\pi\) | ||||
0.222493 | + | 0.974934i | \(0.428581\pi\) | |||||||
\(74\) | −1.69358 | −0.196874 | ||||||||
\(75\) | 5.88838 | 0.679931 | ||||||||
\(76\) | −3.39946 | −0.389945 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.16347 | −0.358192 | ||||||||
\(79\) | −11.0070 | −1.23838 | −0.619191 | − | 0.785240i | \(-0.712539\pi\) | ||||
−0.619191 | + | 0.785240i | \(0.712539\pi\) | |||||||
\(80\) | −9.14673 | −1.02264 | ||||||||
\(81\) | 1.25553 | 0.139504 | ||||||||
\(82\) | 0.463326 | 0.0511658 | ||||||||
\(83\) | 12.5558 | 1.37818 | 0.689089 | − | 0.724677i | \(-0.258011\pi\) | ||||
0.689089 | + | 0.724677i | \(0.258011\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.4333 | −2.75862 | ||||||||
\(86\) | −0.577230 | −0.0622443 | ||||||||
\(87\) | −3.52143 | −0.377537 | ||||||||
\(88\) | 5.08367 | 0.541921 | ||||||||
\(89\) | −7.65506 | −0.811435 | −0.405717 | − | 0.913999i | \(-0.632978\pi\) | ||||
−0.405717 | + | 0.913999i | \(0.632978\pi\) | |||||||
\(90\) | 3.12892 | 0.329818 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.72712 | −0.701350 | ||||||||
\(93\) | 8.26893 | 0.857449 | ||||||||
\(94\) | 4.10565 | 0.423465 | ||||||||
\(95\) | −6.31473 | −0.647878 | ||||||||
\(96\) | 4.69786 | 0.479474 | ||||||||
\(97\) | −0.742199 | −0.0753589 | −0.0376795 | − | 0.999290i | \(-0.511997\pi\) | ||||
−0.0376795 | + | 0.999290i | \(0.511997\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.90245 | 0.593218 | ||||||||
\(100\) | −10.7089 | −1.07089 | ||||||||
\(101\) | −3.22970 | −0.321367 | −0.160683 | − | 0.987006i | \(-0.551370\pi\) | ||||
−0.160683 | + | 0.987006i | \(0.551370\pi\) | |||||||
\(102\) | 3.48814 | 0.345377 | ||||||||
\(103\) | 9.82813 | 0.968394 | 0.484197 | − | 0.874959i | \(-0.339112\pi\) | ||||
0.484197 | + | 0.874959i | \(0.339112\pi\) | |||||||
\(104\) | 12.1983 | 1.19614 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.91269 | 0.185777 | ||||||||
\(107\) | −18.3990 | −1.77870 | −0.889350 | − | 0.457226i | \(-0.848843\pi\) | ||||
−0.889350 | + | 0.457226i | \(0.848843\pi\) | |||||||
\(108\) | 8.82670 | 0.849350 | ||||||||
\(109\) | 6.43698 | 0.616551 | 0.308276 | − | 0.951297i | \(-0.400248\pi\) | ||||
0.308276 | + | 0.951297i | \(0.400248\pi\) | |||||||
\(110\) | 4.45386 | 0.424659 | ||||||||
\(111\) | −3.58827 | −0.340583 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.3856 | −1.25921 | −0.629605 | − | 0.776915i | \(-0.716783\pi\) | ||||
−0.629605 | + | 0.776915i | \(0.716783\pi\) | |||||||
\(114\) | 0.866057 | 0.0811137 | ||||||||
\(115\) | −12.4961 | −1.16527 | ||||||||
\(116\) | 6.40427 | 0.594622 | ||||||||
\(117\) | 14.1630 | 1.30937 | ||||||||
\(118\) | −4.91116 | −0.452109 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.70980 | 0.521231 | ||||||||
\(121\) | −2.59817 | −0.236198 | ||||||||
\(122\) | 3.96813 | 0.359258 | ||||||||
\(123\) | 0.981674 | 0.0885146 | ||||||||
\(124\) | −15.0384 | −1.35048 | ||||||||
\(125\) | −3.31074 | −0.296121 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.62684 | −0.588037 | −0.294018 | − | 0.955800i | \(-0.594993\pi\) | ||||
−0.294018 | + | 0.955800i | \(0.594993\pi\) | |||||||
\(128\) | −11.0996 | −0.981072 | ||||||||
\(129\) | −1.22301 | −0.107680 | ||||||||
\(130\) | 10.6871 | 0.937319 | ||||||||
\(131\) | 15.7977 | 1.38025 | 0.690124 | − | 0.723692i | \(-0.257556\pi\) | ||||
0.690124 | + | 0.723692i | \(0.257556\pi\) | |||||||
\(132\) | 5.08010 | 0.442166 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.11302 | −0.182537 | ||||||||
\(135\) | 16.3962 | 1.41116 | ||||||||
\(136\) | −13.4502 | −1.15335 | ||||||||
\(137\) | 4.59477 | 0.392558 | 0.196279 | − | 0.980548i | \(-0.437114\pi\) | ||||
0.196279 | + | 0.980548i | \(0.437114\pi\) | |||||||
\(138\) | 1.71382 | 0.145890 | ||||||||
\(139\) | −2.72020 | −0.230724 | −0.115362 | − | 0.993324i | \(-0.536803\pi\) | ||||
−0.115362 | + | 0.993324i | \(0.536803\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.69886 | 0.732576 | ||||||||
\(142\) | 1.00394 | 0.0842490 | ||||||||
\(143\) | 20.1603 | 1.68589 | ||||||||
\(144\) | −5.61627 | −0.468023 | ||||||||
\(145\) | 11.8964 | 0.987939 | ||||||||
\(146\) | 1.76155 | 0.145787 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.52583 | 0.536420 | ||||||||
\(149\) | 8.74660 | 0.716549 | 0.358275 | − | 0.933616i | \(-0.383365\pi\) | ||||
0.358275 | + | 0.933616i | \(0.383365\pi\) | |||||||
\(150\) | 2.72824 | 0.222760 | ||||||||
\(151\) | 19.9371 | 1.62246 | 0.811228 | − | 0.584730i | \(-0.198799\pi\) | ||||
0.811228 | + | 0.584730i | \(0.198799\pi\) | |||||||
\(152\) | −3.33951 | −0.270870 | ||||||||
\(153\) | −15.6165 | −1.26252 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −27.9348 | −2.24377 | ||||||||
\(156\) | 12.1897 | 0.975961 | ||||||||
\(157\) | 18.4568 | 1.47301 | 0.736505 | − | 0.676432i | \(-0.236475\pi\) | ||||
0.736505 | + | 0.676432i | \(0.236475\pi\) | |||||||
\(158\) | −5.09982 | −0.405720 | ||||||||
\(159\) | 4.05251 | 0.321385 | ||||||||
\(160\) | −15.8707 | −1.25469 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.581721 | 0.0457043 | ||||||||
\(163\) | −7.80147 | −0.611058 | −0.305529 | − | 0.952183i | \(-0.598833\pi\) | ||||
−0.305529 | + | 0.952183i | \(0.598833\pi\) | |||||||
\(164\) | −1.78533 | −0.139411 | ||||||||
\(165\) | 9.43663 | 0.734641 | ||||||||
\(166\) | 5.81743 | 0.451520 | ||||||||
\(167\) | −5.52402 | −0.427461 | −0.213731 | − | 0.976893i | \(-0.568561\pi\) | ||||
−0.213731 | + | 0.976893i | \(0.568561\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.3747 | 2.72113 | ||||||||
\(170\) | −11.7839 | −0.903784 | ||||||||
\(171\) | −3.87737 | −0.296510 | ||||||||
\(172\) | 2.22423 | 0.169596 | ||||||||
\(173\) | −8.52314 | −0.648002 | −0.324001 | − | 0.946057i | \(-0.605028\pi\) | ||||
−0.324001 | + | 0.946057i | \(0.605028\pi\) | |||||||
\(174\) | −1.63157 | −0.123689 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.99447 | −0.602606 | ||||||||
\(177\) | −10.4055 | −0.782127 | ||||||||
\(178\) | −3.54679 | −0.265843 | ||||||||
\(179\) | −11.1040 | −0.829950 | −0.414975 | − | 0.909833i | \(-0.636210\pi\) | ||||
−0.414975 | + | 0.909833i | \(0.636210\pi\) | |||||||
\(180\) | −12.0566 | −0.898649 | ||||||||
\(181\) | 25.7288 | 1.91241 | 0.956203 | − | 0.292704i | \(-0.0945552\pi\) | ||||
0.956203 | + | 0.292704i | \(0.0945552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.40749 | 0.621499 | ||||||||
\(184\) | −6.60848 | −0.487183 | ||||||||
\(185\) | 12.1222 | 0.891239 | ||||||||
\(186\) | 3.83122 | 0.280918 | ||||||||
\(187\) | −22.2293 | −1.62557 | ||||||||
\(188\) | −15.8202 | −1.15381 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.92578 | −0.212259 | ||||||||
\(191\) | 11.4290 | 0.826975 | 0.413487 | − | 0.910510i | \(-0.364311\pi\) | ||||
0.413487 | + | 0.910510i | \(0.364311\pi\) | |||||||
\(192\) | −3.23838 | −0.233710 | ||||||||
\(193\) | 14.0055 | 1.00814 | 0.504068 | − | 0.863664i | \(-0.331836\pi\) | ||||
0.504068 | + | 0.863664i | \(0.331836\pi\) | |||||||
\(194\) | −0.343881 | −0.0246892 | ||||||||
\(195\) | 22.6433 | 1.62152 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.0830 | 1.07462 | 0.537310 | − | 0.843385i | \(-0.319440\pi\) | ||||
0.537310 | + | 0.843385i | \(0.319440\pi\) | |||||||
\(198\) | 2.73476 | 0.194351 | ||||||||
\(199\) | 18.4669 | 1.30909 | 0.654543 | − | 0.756025i | \(-0.272861\pi\) | ||||
0.654543 | + | 0.756025i | \(0.272861\pi\) | |||||||
\(200\) | −10.5201 | −0.743882 | ||||||||
\(201\) | −4.47697 | −0.315781 | ||||||||
\(202\) | −1.49640 | −0.105287 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −13.4408 | −0.941043 | ||||||||
\(205\) | −3.31637 | −0.231625 | ||||||||
\(206\) | 4.55363 | 0.317266 | ||||||||
\(207\) | −7.67284 | −0.533299 | ||||||||
\(208\) | −19.1828 | −1.33009 | ||||||||
\(209\) | −5.51924 | −0.381774 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8693 | −0.954805 | −0.477402 | − | 0.878685i | \(-0.658422\pi\) | ||||
−0.477402 | + | 0.878685i | \(0.658422\pi\) | |||||||
\(212\) | −7.37013 | −0.506182 | ||||||||
\(213\) | 2.12711 | 0.145747 | ||||||||
\(214\) | −8.52475 | −0.582740 | ||||||||
\(215\) | 4.13166 | 0.281777 | ||||||||
\(216\) | 8.67103 | 0.589989 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.98242 | 0.201995 | ||||||||
\(219\) | 3.73228 | 0.252204 | ||||||||
\(220\) | −17.1620 | −1.15706 | ||||||||
\(221\) | −53.3394 | −3.58800 | ||||||||
\(222\) | −1.66254 | −0.111582 | ||||||||
\(223\) | 25.2567 | 1.69132 | 0.845658 | − | 0.533725i | \(-0.179208\pi\) | ||||
0.845658 | + | 0.533725i | \(0.179208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.2144 | −0.814296 | ||||||||
\(226\) | −6.20190 | −0.412544 | ||||||||
\(227\) | 6.76044 | 0.448706 | 0.224353 | − | 0.974508i | \(-0.427973\pi\) | ||||
0.224353 | + | 0.974508i | \(0.427973\pi\) | |||||||
\(228\) | −3.33716 | −0.221009 | ||||||||
\(229\) | −13.6311 | −0.900771 | −0.450385 | − | 0.892834i | \(-0.648713\pi\) | ||||
−0.450385 | + | 0.892834i | \(0.648713\pi\) | |||||||
\(230\) | −5.78976 | −0.381766 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.29132 | 0.413046 | ||||||||
\(233\) | 0.294047 | 0.0192637 | 0.00963183 | − | 0.999954i | \(-0.496934\pi\) | ||||
0.00963183 | + | 0.999954i | \(0.496934\pi\) | |||||||
\(234\) | 6.56208 | 0.428977 | ||||||||
\(235\) | −29.3872 | −1.91701 | ||||||||
\(236\) | 18.9241 | 1.23185 | ||||||||
\(237\) | −10.8053 | −0.701877 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.90226 | −0.575839 | −0.287920 | − | 0.957655i | \(-0.592964\pi\) | ||||
−0.287920 | + | 0.957655i | \(0.592964\pi\) | |||||||
\(240\) | −8.97911 | −0.579599 | ||||||||
\(241\) | −9.51807 | −0.613113 | −0.306556 | − | 0.951853i | \(-0.599177\pi\) | ||||
−0.306556 | + | 0.951853i | \(0.599177\pi\) | |||||||
\(242\) | −1.20380 | −0.0773833 | ||||||||
\(243\) | 16.0646 | 1.03054 | ||||||||
\(244\) | −15.2903 | −0.978864 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.454835 | 0.0289992 | ||||||||
\(247\) | −13.2435 | −0.842661 | ||||||||
\(248\) | −14.7731 | −0.938095 | ||||||||
\(249\) | 12.3257 | 0.781109 | ||||||||
\(250\) | −1.53395 | −0.0970156 | ||||||||
\(251\) | −28.4152 | −1.79355 | −0.896774 | − | 0.442488i | \(-0.854096\pi\) | ||||
−0.896774 | + | 0.442488i | \(0.854096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.9219 | −0.686653 | ||||||||
\(254\) | −3.07039 | −0.192653 | ||||||||
\(255\) | −24.9672 | −1.56350 | ||||||||
\(256\) | 1.45494 | 0.0909340 | ||||||||
\(257\) | −14.2422 | −0.888403 | −0.444202 | − | 0.895927i | \(-0.646513\pi\) | ||||
−0.444202 | + | 0.895927i | \(0.646513\pi\) | |||||||
\(258\) | −0.566652 | −0.0352782 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −41.1804 | −2.55390 | ||||||||
\(261\) | 7.30460 | 0.452144 | ||||||||
\(262\) | 7.31947 | 0.452198 | ||||||||
\(263\) | 25.1201 | 1.54897 | 0.774487 | − | 0.632590i | \(-0.218008\pi\) | ||||
0.774487 | + | 0.632590i | \(0.218008\pi\) | |||||||
\(264\) | 4.99051 | 0.307145 | ||||||||
\(265\) | −13.6905 | −0.841001 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.51478 | −0.459897 | ||||||||
\(268\) | 8.14208 | 0.497357 | ||||||||
\(269\) | 8.45011 | 0.515212 | 0.257606 | − | 0.966250i | \(-0.417066\pi\) | ||||
0.257606 | + | 0.966250i | \(0.417066\pi\) | |||||||
\(270\) | 7.59679 | 0.462326 | ||||||||
\(271\) | −2.52722 | −0.153518 | −0.0767588 | − | 0.997050i | \(-0.524457\pi\) | ||||
−0.0767588 | + | 0.997050i | \(0.524457\pi\) | |||||||
\(272\) | 21.1515 | 1.28250 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.12888 | 0.128610 | ||||||||
\(275\) | −17.3866 | −1.04845 | ||||||||
\(276\) | −6.60384 | −0.397504 | ||||||||
\(277\) | 19.9949 | 1.20138 | 0.600689 | − | 0.799482i | \(-0.294893\pi\) | ||||
0.600689 | + | 0.799482i | \(0.294893\pi\) | |||||||
\(278\) | −1.26034 | −0.0755901 | ||||||||
\(279\) | −17.1525 | −1.02689 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.76965 | 0.403843 | 0.201922 | − | 0.979402i | \(-0.435281\pi\) | ||||
0.201922 | + | 0.979402i | \(0.435281\pi\) | |||||||
\(282\) | 4.03041 | 0.240007 | ||||||||
\(283\) | 6.32699 | 0.376101 | 0.188050 | − | 0.982159i | \(-0.439783\pi\) | ||||
0.188050 | + | 0.982159i | \(0.439783\pi\) | |||||||
\(284\) | −3.86848 | −0.229552 | ||||||||
\(285\) | −6.19901 | −0.367198 | ||||||||
\(286\) | 9.34078 | 0.552332 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −9.74492 | −0.574225 | ||||||||
\(289\) | 41.8137 | 2.45963 | ||||||||
\(290\) | 5.51190 | 0.323670 | ||||||||
\(291\) | −0.728598 | −0.0427112 | ||||||||
\(292\) | −6.78774 | −0.397223 | ||||||||
\(293\) | −27.0292 | −1.57906 | −0.789530 | − | 0.613712i | \(-0.789676\pi\) | ||||
−0.789530 | + | 0.613712i | \(0.789676\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.1528 | 2.04667 | ||||||||
\(296\) | 6.41074 | 0.372617 | ||||||||
\(297\) | 14.3307 | 0.831551 | ||||||||
\(298\) | 4.05253 | 0.234757 | ||||||||
\(299\) | −26.2072 | −1.51560 | ||||||||
\(300\) | −10.5127 | −0.606950 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.23737 | 0.531551 | ||||||||
\(303\) | −3.17051 | −0.182141 | ||||||||
\(304\) | 5.25164 | 0.301202 | ||||||||
\(305\) | −28.4028 | −1.62634 | ||||||||
\(306\) | −7.23555 | −0.413629 | ||||||||
\(307\) | 5.48187 | 0.312867 | 0.156433 | − | 0.987689i | \(-0.450000\pi\) | ||||
0.156433 | + | 0.987689i | \(0.450000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.64802 | 0.548856 | ||||||||
\(310\) | −12.9429 | −0.735108 | ||||||||
\(311\) | 7.22580 | 0.409737 | 0.204869 | − | 0.978789i | \(-0.434323\pi\) | ||||
0.204869 | + | 0.978789i | \(0.434323\pi\) | |||||||
\(312\) | 11.9748 | 0.677938 | ||||||||
\(313\) | 18.5794 | 1.05017 | 0.525086 | − | 0.851049i | \(-0.324033\pi\) | ||||
0.525086 | + | 0.851049i | \(0.324033\pi\) | |||||||
\(314\) | 8.55151 | 0.482589 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.6511 | 1.10546 | ||||||||
\(317\) | 29.0493 | 1.63157 | 0.815786 | − | 0.578353i | \(-0.196305\pi\) | ||||
0.815786 | + | 0.578353i | \(0.196305\pi\) | |||||||
\(318\) | 1.87763 | 0.105293 | ||||||||
\(319\) | 10.3977 | 0.582161 | ||||||||
\(320\) | 10.9401 | 0.611573 | ||||||||
\(321\) | −18.0618 | −1.00811 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.6026 | 0.812512 | ||||||||
\(324\) | −2.24154 | −0.124530 | ||||||||
\(325\) | −41.7194 | −2.31417 | ||||||||
\(326\) | −3.61463 | −0.200196 | ||||||||
\(327\) | 6.31902 | 0.349443 | ||||||||
\(328\) | −1.75384 | −0.0968398 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.37224 | 0.240684 | ||||||||
\(331\) | 4.58876 | 0.252221 | 0.126111 | − | 0.992016i | \(-0.459751\pi\) | ||||
0.126111 | + | 0.992016i | \(0.459751\pi\) | |||||||
\(332\) | −22.4162 | −1.23025 | ||||||||
\(333\) | 7.44325 | 0.407888 | ||||||||
\(334\) | −2.55942 | −0.140045 | ||||||||
\(335\) | 15.1245 | 0.826338 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.2998 | 1.75948 | 0.879742 | − | 0.475451i | \(-0.157715\pi\) | ||||
0.879742 | + | 0.475451i | \(0.157715\pi\) | |||||||
\(338\) | 16.3900 | 0.891501 | ||||||||
\(339\) | −13.1403 | −0.713683 | ||||||||
\(340\) | 45.4067 | 2.46253 | ||||||||
\(341\) | −24.4157 | −1.32218 | ||||||||
\(342\) | −1.79649 | −0.0971429 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.18501 | 0.117808 | ||||||||
\(345\) | −12.2671 | −0.660437 | ||||||||
\(346\) | −3.94899 | −0.212299 | ||||||||
\(347\) | −13.6395 | −0.732207 | −0.366103 | − | 0.930574i | \(-0.619308\pi\) | ||||
−0.366103 | + | 0.930574i | \(0.619308\pi\) | |||||||
\(348\) | 6.28691 | 0.337014 | ||||||||
\(349\) | −15.2222 | −0.814824 | −0.407412 | − | 0.913244i | \(-0.633569\pi\) | ||||
−0.407412 | + | 0.913244i | \(0.633569\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 34.3866 | 1.83542 | ||||||||
\(352\) | −13.8714 | −0.739348 | ||||||||
\(353\) | −10.9932 | −0.585106 | −0.292553 | − | 0.956249i | \(-0.594505\pi\) | ||||
−0.292553 | + | 0.956249i | \(0.594505\pi\) | |||||||
\(354\) | −4.82115 | −0.256241 | ||||||||
\(355\) | −7.18596 | −0.381391 | ||||||||
\(356\) | 13.6668 | 0.724339 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.14476 | −0.271909 | ||||||||
\(359\) | −2.33360 | −0.123163 | −0.0615814 | − | 0.998102i | \(-0.519614\pi\) | ||||
−0.0615814 | + | 0.998102i | \(0.519614\pi\) | |||||||
\(360\) | −11.8440 | −0.624234 | ||||||||
\(361\) | −15.3744 | −0.809177 | ||||||||
\(362\) | 11.9208 | 0.626545 | ||||||||
\(363\) | −2.55056 | −0.133870 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.6087 | −0.659969 | ||||||||
\(366\) | 3.89541 | 0.203616 | ||||||||
\(367\) | −27.5423 | −1.43770 | −0.718849 | − | 0.695166i | \(-0.755331\pi\) | ||||
−0.718849 | + | 0.695166i | \(0.755331\pi\) | |||||||
\(368\) | 10.3924 | 0.541739 | ||||||||
\(369\) | −2.03632 | −0.106006 | ||||||||
\(370\) | 5.61652 | 0.291989 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −14.7628 | −0.765414 | ||||||||
\(373\) | −0.841692 | −0.0435811 | −0.0217906 | − | 0.999763i | \(-0.506937\pi\) | ||||
−0.0217906 | + | 0.999763i | \(0.506937\pi\) | |||||||
\(374\) | −10.2994 | −0.532571 | ||||||||
\(375\) | −3.25006 | −0.167833 | ||||||||
\(376\) | −15.5412 | −0.801478 | ||||||||
\(377\) | 24.9494 | 1.28496 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.8659 | 0.660875 | 0.330437 | − | 0.943828i | \(-0.392804\pi\) | ||||
0.330437 | + | 0.943828i | \(0.392804\pi\) | |||||||
\(380\) | 11.2739 | 0.578337 | ||||||||
\(381\) | −6.50540 | −0.333282 | ||||||||
\(382\) | 5.29537 | 0.270935 | ||||||||
\(383\) | −23.4028 | −1.19583 | −0.597914 | − | 0.801560i | \(-0.704004\pi\) | ||||
−0.597914 | + | 0.801560i | \(0.704004\pi\) | |||||||
\(384\) | −10.8962 | −0.556042 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.48910 | 0.330287 | ||||||||
\(387\) | 2.53692 | 0.128959 | ||||||||
\(388\) | 1.32507 | 0.0672702 | ||||||||
\(389\) | 4.88275 | 0.247565 | 0.123783 | − | 0.992309i | \(-0.460497\pi\) | ||||
0.123783 | + | 0.992309i | \(0.460497\pi\) | |||||||
\(390\) | 10.4912 | 0.531244 | ||||||||
\(391\) | 28.8968 | 1.46137 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.5081 | 0.782282 | ||||||||
\(394\) | 6.98836 | 0.352068 | ||||||||
\(395\) | 36.5032 | 1.83668 | ||||||||
\(396\) | −10.5378 | −0.529545 | ||||||||
\(397\) | 25.0538 | 1.25741 | 0.628707 | − | 0.777642i | \(-0.283585\pi\) | ||||
0.628707 | + | 0.777642i | \(0.283585\pi\) | |||||||
\(398\) | 8.55621 | 0.428884 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.5437 | 0.827183 | ||||||||
\(401\) | −9.10250 | −0.454557 | −0.227279 | − | 0.973830i | \(-0.572983\pi\) | ||||
−0.227279 | + | 0.973830i | \(0.572983\pi\) | |||||||
\(402\) | −2.07430 | −0.103457 | ||||||||
\(403\) | −58.5857 | −2.91836 | ||||||||
\(404\) | 5.76607 | 0.286873 | ||||||||
\(405\) | −4.16381 | −0.206901 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.5951 | 0.525179 | ||||||||
\(408\) | −13.2037 | −0.653683 | ||||||||
\(409\) | 4.42310 | 0.218708 | 0.109354 | − | 0.994003i | \(-0.465122\pi\) | ||||
0.109354 | + | 0.994003i | \(0.465122\pi\) | |||||||
\(410\) | −1.53656 | −0.0758853 | ||||||||
\(411\) | 4.51057 | 0.222490 | ||||||||
\(412\) | −17.5464 | −0.864451 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.55503 | −0.174720 | ||||||||
\(415\) | −41.6396 | −2.04401 | ||||||||
\(416\) | −33.2845 | −1.63191 | ||||||||
\(417\) | −2.67035 | −0.130767 | ||||||||
\(418\) | −2.55721 | −0.125077 | ||||||||
\(419\) | −1.58417 | −0.0773919 | −0.0386959 | − | 0.999251i | \(-0.512320\pi\) | ||||
−0.0386959 | + | 0.999251i | \(0.512320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.6911 | 1.05716 | 0.528579 | − | 0.848884i | \(-0.322725\pi\) | ||||
0.528579 | + | 0.848884i | \(0.322725\pi\) | |||||||
\(422\) | −6.42603 | −0.312814 | ||||||||
\(423\) | −18.0443 | −0.877344 | ||||||||
\(424\) | −7.24015 | −0.351613 | ||||||||
\(425\) | 46.0010 | 2.23138 | ||||||||
\(426\) | 0.985544 | 0.0477498 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 32.8483 | 1.58778 | ||||||||
\(429\) | 19.7908 | 0.955509 | ||||||||
\(430\) | 1.91431 | 0.0923162 | ||||||||
\(431\) | −4.06913 | −0.196003 | −0.0980015 | − | 0.995186i | \(-0.531245\pi\) | ||||
−0.0980015 | + | 0.995186i | \(0.531245\pi\) | |||||||
\(432\) | −13.6359 | −0.656057 | ||||||||
\(433\) | 24.6813 | 1.18611 | 0.593055 | − | 0.805162i | \(-0.297922\pi\) | ||||
0.593055 | + | 0.805162i | \(0.297922\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.6784 | 0.559934 | ||||||||
\(436\) | −11.4921 | −0.550373 | ||||||||
\(437\) | 7.17469 | 0.343212 | ||||||||
\(438\) | 1.72926 | 0.0826275 | ||||||||
\(439\) | −24.9536 | −1.19097 | −0.595484 | − | 0.803367i | \(-0.703040\pi\) | ||||
−0.595484 | + | 0.803367i | \(0.703040\pi\) | |||||||
\(440\) | −16.8593 | −0.803737 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.7136 | −1.17550 | ||||||||
\(443\) | −15.1895 | −0.721676 | −0.360838 | − | 0.932629i | \(-0.617509\pi\) | ||||
−0.360838 | + | 0.932629i | \(0.617509\pi\) | |||||||
\(444\) | 6.40624 | 0.304026 | ||||||||
\(445\) | 25.3870 | 1.20346 | ||||||||
\(446\) | 11.7021 | 0.554111 | ||||||||
\(447\) | 8.58631 | 0.406118 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.42027 | −0.0670267 | −0.0335134 | − | 0.999438i | \(-0.510670\pi\) | ||||
−0.0335134 | + | 0.999438i | \(0.510670\pi\) | |||||||
\(450\) | −5.65927 | −0.266781 | ||||||||
\(451\) | −2.89859 | −0.136489 | ||||||||
\(452\) | 23.8977 | 1.12405 | ||||||||
\(453\) | 19.5717 | 0.919559 | ||||||||
\(454\) | 3.13229 | 0.147006 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.27831 | −0.153521 | ||||||||
\(457\) | 13.0274 | 0.609396 | 0.304698 | − | 0.952449i | \(-0.401445\pi\) | ||||
0.304698 | + | 0.952449i | \(0.401445\pi\) | |||||||
\(458\) | −6.31566 | −0.295112 | ||||||||
\(459\) | −37.9157 | −1.76975 | ||||||||
\(460\) | 22.3096 | 1.04019 | ||||||||
\(461\) | 32.4046 | 1.50923 | 0.754617 | − | 0.656165i | \(-0.227823\pi\) | ||||
0.754617 | + | 0.656165i | \(0.227823\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.32911 | 0.154717 | 0.0773584 | − | 0.997003i | \(-0.475351\pi\) | ||||
0.0773584 | + | 0.997003i | \(0.475351\pi\) | |||||||
\(464\) | −9.89360 | −0.459299 | ||||||||
\(465\) | −27.4228 | −1.27170 | ||||||||
\(466\) | 0.136240 | 0.00631118 | ||||||||
\(467\) | 11.3449 | 0.524979 | 0.262490 | − | 0.964935i | \(-0.415456\pi\) | ||||
0.262490 | + | 0.964935i | \(0.415456\pi\) | |||||||
\(468\) | −25.2856 | −1.16883 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −13.6158 | −0.628052 | ||||||||
\(471\) | 18.1185 | 0.834858 | ||||||||
\(472\) | 18.5903 | 0.855690 | ||||||||
\(473\) | 3.61118 | 0.166042 | ||||||||
\(474\) | −5.00636 | −0.229950 | ||||||||
\(475\) | 11.4214 | 0.524051 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.40625 | −0.384896 | ||||||||
\(478\) | −4.12465 | −0.188657 | ||||||||
\(479\) | −17.9451 | −0.819931 | −0.409965 | − | 0.912101i | \(-0.634459\pi\) | ||||
−0.409965 | + | 0.912101i | \(0.634459\pi\) | |||||||
\(480\) | −15.5799 | −0.711120 | ||||||||
\(481\) | 25.4230 | 1.15919 | ||||||||
\(482\) | −4.40997 | −0.200869 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.63859 | 0.210845 | ||||||||
\(485\) | 2.46141 | 0.111767 | ||||||||
\(486\) | 7.44315 | 0.337628 | ||||||||
\(487\) | 5.37906 | 0.243748 | 0.121874 | − | 0.992546i | \(-0.461110\pi\) | ||||
0.121874 | + | 0.992546i | \(0.461110\pi\) | |||||||
\(488\) | −15.0207 | −0.679954 | ||||||||
\(489\) | −7.65850 | −0.346329 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.1637 | 0.774586 | 0.387293 | − | 0.921957i | \(-0.373410\pi\) | ||||
0.387293 | + | 0.921957i | \(0.373410\pi\) | |||||||
\(492\) | −1.75261 | −0.0790138 | ||||||||
\(493\) | −27.5100 | −1.23899 | ||||||||
\(494\) | −6.13604 | −0.276074 | ||||||||
\(495\) | −19.5747 | −0.879817 | ||||||||
\(496\) | 23.2319 | 1.04314 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.71082 | 0.255908 | ||||||||
\(499\) | −24.0541 | −1.07681 | −0.538405 | − | 0.842686i | \(-0.680973\pi\) | ||||
−0.538405 | + | 0.842686i | \(0.680973\pi\) | |||||||
\(500\) | 5.91075 | 0.264337 | ||||||||
\(501\) | −5.42278 | −0.242272 | ||||||||
\(502\) | −13.1655 | −0.587605 | ||||||||
\(503\) | −34.1088 | −1.52084 | −0.760418 | − | 0.649434i | \(-0.775006\pi\) | ||||
−0.760418 | + | 0.649434i | \(0.775006\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.7109 | 0.476627 | ||||||||
\(506\) | −5.06040 | −0.224962 | ||||||||
\(507\) | 34.7264 | 1.54226 | ||||||||
\(508\) | 11.8311 | 0.524920 | ||||||||
\(509\) | −21.1292 | −0.936534 | −0.468267 | − | 0.883587i | \(-0.655122\pi\) | ||||
−0.468267 | + | 0.883587i | \(0.655122\pi\) | |||||||
\(510\) | −11.5679 | −0.512237 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.8732 | 1.01086 | ||||||||
\(513\) | −9.41396 | −0.415636 | ||||||||
\(514\) | −6.59878 | −0.291060 | ||||||||
\(515\) | −32.5937 | −1.43625 | ||||||||
\(516\) | 2.18347 | 0.0961220 | ||||||||
\(517\) | −25.6851 | −1.12963 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.36694 | −0.367268 | ||||||||
\(520\) | −40.4541 | −1.77403 | ||||||||
\(521\) | 21.1323 | 0.925822 | 0.462911 | − | 0.886405i | \(-0.346805\pi\) | ||||
0.462911 | + | 0.886405i | \(0.346805\pi\) | |||||||
\(522\) | 3.38442 | 0.148132 | ||||||||
\(523\) | −20.8085 | −0.909890 | −0.454945 | − | 0.890519i | \(-0.650341\pi\) | ||||
−0.454945 | + | 0.890519i | \(0.650341\pi\) | |||||||
\(524\) | −28.2040 | −1.23210 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.6388 | 0.507477 | ||||||||
\(527\) | 64.5983 | 2.81395 | ||||||||
\(528\) | −7.84797 | −0.341539 | ||||||||
\(529\) | −8.80218 | −0.382704 | ||||||||
\(530\) | −6.34318 | −0.275530 | ||||||||
\(531\) | 21.5845 | 0.936687 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.95519 | −0.301263 | ||||||||
\(534\) | −3.48179 | −0.150672 | ||||||||
\(535\) | 61.0179 | 2.63804 | ||||||||
\(536\) | 7.99849 | 0.345482 | ||||||||
\(537\) | −10.9005 | −0.470390 | ||||||||
\(538\) | 3.91516 | 0.168794 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −29.2726 | −1.25969 | ||||||||
\(541\) | 6.38057 | 0.274322 | 0.137161 | − | 0.990549i | \(-0.456202\pi\) | ||||
0.137161 | + | 0.990549i | \(0.456202\pi\) | |||||||
\(542\) | −1.17093 | −0.0502956 | ||||||||
\(543\) | 25.2573 | 1.08389 | ||||||||
\(544\) | 36.7005 | 1.57352 | ||||||||
\(545\) | −21.3474 | −0.914422 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.3335 | −1.46799 | −0.733997 | − | 0.679152i | \(-0.762347\pi\) | ||||
−0.733997 | + | 0.679152i | \(0.762347\pi\) | |||||||
\(548\) | −8.20318 | −0.350423 | ||||||||
\(549\) | −17.4399 | −0.744317 | ||||||||
\(550\) | −8.05568 | −0.343495 | ||||||||
\(551\) | −6.83036 | −0.290983 | ||||||||
\(552\) | −6.48737 | −0.276121 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.26418 | 0.393597 | ||||||||
\(555\) | 11.9000 | 0.505128 | ||||||||
\(556\) | 4.85645 | 0.205959 | ||||||||
\(557\) | 3.13283 | 0.132742 | 0.0663712 | − | 0.997795i | \(-0.478858\pi\) | ||||
0.0663712 | + | 0.997795i | \(0.478858\pi\) | |||||||
\(558\) | −7.94721 | −0.336432 | ||||||||
\(559\) | 8.66506 | 0.366493 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.8219 | −0.921323 | ||||||||
\(562\) | 3.13656 | 0.132308 | ||||||||
\(563\) | 4.81748 | 0.203032 | 0.101516 | − | 0.994834i | \(-0.467631\pi\) | ||||
0.101516 | + | 0.994834i | \(0.467631\pi\) | |||||||
\(564\) | −15.5303 | −0.653944 | ||||||||
\(565\) | 44.3916 | 1.86757 | ||||||||
\(566\) | 2.93146 | 0.123219 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.80025 | −0.159455 | ||||||||
\(569\) | −17.7546 | −0.744310 | −0.372155 | − | 0.928171i | \(-0.621381\pi\) | ||||
−0.372155 | + | 0.928171i | \(0.621381\pi\) | |||||||
\(570\) | −2.87216 | −0.120302 | ||||||||
\(571\) | −27.2787 | −1.14158 | −0.570788 | − | 0.821097i | \(-0.693362\pi\) | ||||
−0.570788 | + | 0.821097i | \(0.693362\pi\) | |||||||
\(572\) | −35.9927 | −1.50493 | ||||||||
\(573\) | 11.2196 | 0.468704 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.6016 | 0.942552 | ||||||||
\(576\) | 6.71747 | 0.279894 | ||||||||
\(577\) | −23.2141 | −0.966415 | −0.483207 | − | 0.875506i | \(-0.660528\pi\) | ||||
−0.483207 | + | 0.875506i | \(0.660528\pi\) | |||||||
\(578\) | 19.3734 | 0.805826 | ||||||||
\(579\) | 13.7488 | 0.571381 | ||||||||
\(580\) | −21.2389 | −0.881898 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.337579 | −0.0139931 | ||||||||
\(583\) | −11.9659 | −0.495575 | ||||||||
\(584\) | −6.66803 | −0.275925 | ||||||||
\(585\) | −46.9696 | −1.94196 | ||||||||
\(586\) | −12.5233 | −0.517334 | ||||||||
\(587\) | 11.8476 | 0.489001 | 0.244501 | − | 0.969649i | \(-0.421376\pi\) | ||||
0.244501 | + | 0.969649i | \(0.421376\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0389 | 0.660871 | ||||||||
\(590\) | 16.2872 | 0.670534 | ||||||||
\(591\) | 14.8066 | 0.609062 | ||||||||
\(592\) | −10.0814 | −0.414343 | ||||||||
\(593\) | 42.6426 | 1.75112 | 0.875562 | − | 0.483106i | \(-0.160492\pi\) | ||||
0.875562 | + | 0.483106i | \(0.160492\pi\) | |||||||
\(594\) | 6.63979 | 0.272434 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.6155 | −0.639638 | ||||||||
\(597\) | 18.1285 | 0.741950 | ||||||||
\(598\) | −12.1425 | −0.496543 | ||||||||
\(599\) | 41.4555 | 1.69383 | 0.846913 | − | 0.531732i | \(-0.178459\pi\) | ||||
0.846913 | + | 0.531732i | \(0.178459\pi\) | |||||||
\(600\) | −10.3273 | −0.421610 | ||||||||
\(601\) | −18.5531 | −0.756799 | −0.378399 | − | 0.925642i | \(-0.623525\pi\) | ||||
−0.378399 | + | 0.925642i | \(0.623525\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.28672 | 0.378185 | ||||||||
\(604\) | −35.5942 | −1.44831 | ||||||||
\(605\) | 8.61650 | 0.350311 | ||||||||
\(606\) | −1.46898 | −0.0596732 | ||||||||
\(607\) | 17.5428 | 0.712039 | 0.356019 | − | 0.934479i | \(-0.384134\pi\) | ||||
0.356019 | + | 0.934479i | \(0.384134\pi\) | |||||||
\(608\) | 9.11224 | 0.369550 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.1598 | −0.532824 | ||||||||
\(611\) | −61.6317 | −2.49335 | ||||||||
\(612\) | 27.8806 | 1.12701 | ||||||||
\(613\) | 5.18107 | 0.209262 | 0.104631 | − | 0.994511i | \(-0.466634\pi\) | ||||
0.104631 | + | 0.994511i | \(0.466634\pi\) | |||||||
\(614\) | 2.53990 | 0.102502 | ||||||||
\(615\) | −3.25559 | −0.131278 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.7278 | 0.673434 | 0.336717 | − | 0.941606i | \(-0.390683\pi\) | ||||
0.336717 | + | 0.941606i | \(0.390683\pi\) | |||||||
\(618\) | 4.47018 | 0.179817 | ||||||||
\(619\) | 18.0170 | 0.724164 | 0.362082 | − | 0.932146i | \(-0.382066\pi\) | ||||
0.362082 | + | 0.932146i | \(0.382066\pi\) | |||||||
\(620\) | 49.8727 | 2.00294 | ||||||||
\(621\) | −18.6291 | −0.747559 | ||||||||
\(622\) | 3.34790 | 0.134239 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −18.8313 | −0.753854 | ||||||||
\(625\) | −19.0119 | −0.760475 | ||||||||
\(626\) | 8.60835 | 0.344059 | ||||||||
\(627\) | −5.41809 | −0.216378 | ||||||||
\(628\) | −32.9514 | −1.31490 | ||||||||
\(629\) | −28.0322 | −1.11772 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.604726 | −0.0240738 | −0.0120369 | − | 0.999928i | \(-0.503832\pi\) | ||||
−0.0120369 | + | 0.999928i | \(0.503832\pi\) | |||||||
\(632\) | 19.3045 | 0.767892 | ||||||||
\(633\) | −13.6152 | −0.541154 | ||||||||
\(634\) | 13.4593 | 0.534538 | ||||||||
\(635\) | 21.9770 | 0.872132 | ||||||||
\(636\) | −7.23506 | −0.286889 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.81754 | 0.190728 | ||||||||
\(639\) | −4.41232 | −0.174549 | ||||||||
\(640\) | 36.8103 | 1.45505 | ||||||||
\(641\) | −28.2472 | −1.11570 | −0.557848 | − | 0.829943i | \(-0.688373\pi\) | ||||
−0.557848 | + | 0.829943i | \(0.688373\pi\) | |||||||
\(642\) | −8.36853 | −0.330279 | ||||||||
\(643\) | 22.1196 | 0.872312 | 0.436156 | − | 0.899871i | \(-0.356340\pi\) | ||||
0.436156 | + | 0.899871i | \(0.356340\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.05595 | 0.159703 | ||||||||
\(646\) | 6.76579 | 0.266196 | ||||||||
\(647\) | −12.8921 | −0.506843 | −0.253421 | − | 0.967356i | \(-0.581556\pi\) | ||||
−0.253421 | + | 0.967356i | \(0.581556\pi\) | |||||||
\(648\) | −2.20201 | −0.0865030 | ||||||||
\(649\) | 30.7244 | 1.20604 | ||||||||
\(650\) | −19.3297 | −0.758172 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.9282 | 0.545470 | ||||||||
\(653\) | −9.61112 | −0.376112 | −0.188056 | − | 0.982158i | \(-0.560219\pi\) | ||||
−0.188056 | + | 0.982158i | \(0.560219\pi\) | |||||||
\(654\) | 2.92777 | 0.114485 | ||||||||
\(655\) | −52.3908 | −2.04708 | ||||||||
\(656\) | 2.75806 | 0.107684 | ||||||||
\(657\) | −7.74199 | −0.302044 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.0986 | 1.52307 | 0.761533 | − | 0.648126i | \(-0.224447\pi\) | ||||
0.761533 | + | 0.648126i | \(0.224447\pi\) | |||||||
\(660\) | −16.8475 | −0.655788 | ||||||||
\(661\) | 14.0488 | 0.546436 | 0.273218 | − | 0.961952i | \(-0.411912\pi\) | ||||
0.273218 | + | 0.961952i | \(0.411912\pi\) | |||||||
\(662\) | 2.12610 | 0.0826331 | ||||||||
\(663\) | −52.3619 | −2.03357 | ||||||||
\(664\) | −22.0209 | −0.854576 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.44865 | 0.133633 | ||||||||
\(667\) | −13.5164 | −0.523359 | ||||||||
\(668\) | 9.86219 | 0.381580 | ||||||||
\(669\) | 24.7939 | 0.958587 | ||||||||
\(670\) | 7.00757 | 0.270726 | ||||||||
\(671\) | −24.8248 | −0.958351 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.9310 | −1.23085 | −0.615426 | − | 0.788195i | \(-0.711016\pi\) | ||||
−0.615426 | + | 0.788195i | \(0.711016\pi\) | |||||||
\(674\) | 14.9654 | 0.576444 | ||||||||
\(675\) | −29.6557 | −1.14145 | ||||||||
\(676\) | −63.1555 | −2.42906 | ||||||||
\(677\) | 29.5898 | 1.13723 | 0.568614 | − | 0.822604i | \(-0.307480\pi\) | ||||
0.568614 | + | 0.822604i | \(0.307480\pi\) | |||||||
\(678\) | −6.08824 | −0.233818 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 44.6059 | 1.71056 | ||||||||
\(681\) | 6.63655 | 0.254313 | ||||||||
\(682\) | −11.3124 | −0.433176 | ||||||||
\(683\) | 4.62301 | 0.176895 | 0.0884473 | − | 0.996081i | \(-0.471810\pi\) | ||||
0.0884473 | + | 0.996081i | \(0.471810\pi\) | |||||||
\(684\) | 6.92238 | 0.264684 | ||||||||
\(685\) | −15.2380 | −0.582213 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.3813 | −0.510530 | ||||||||
\(688\) | −3.43610 | −0.131000 | ||||||||
\(689\) | −28.7122 | −1.09385 | ||||||||
\(690\) | −5.68366 | −0.216373 | ||||||||
\(691\) | 19.5317 | 0.743021 | 0.371511 | − | 0.928429i | \(-0.378840\pi\) | ||||
0.371511 | + | 0.928429i | \(0.378840\pi\) | |||||||
\(692\) | 15.2166 | 0.578448 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.31954 | −0.239886 | ||||||||
\(695\) | 9.02118 | 0.342193 | ||||||||
\(696\) | 6.17603 | 0.234102 | ||||||||
\(697\) | 7.66901 | 0.290484 | ||||||||
\(698\) | −7.05284 | −0.266954 | ||||||||
\(699\) | 0.288658 | 0.0109181 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.2862 | −0.803968 | −0.401984 | − | 0.915647i | \(-0.631679\pi\) | ||||
−0.401984 | + | 0.915647i | \(0.631679\pi\) | |||||||
\(702\) | 15.9322 | 0.601323 | ||||||||
\(703\) | −6.96000 | −0.262502 | ||||||||
\(704\) | 9.56197 | 0.360380 | ||||||||
\(705\) | −28.8486 | −1.08650 | ||||||||
\(706\) | −5.09342 | −0.191693 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.5773 | 0.698177 | ||||||||
\(709\) | 19.7977 | 0.743520 | 0.371760 | − | 0.928329i | \(-0.378754\pi\) | ||||
0.371760 | + | 0.928329i | \(0.378754\pi\) | |||||||
\(710\) | −3.32944 | −0.124952 | ||||||||
\(711\) | 22.4137 | 0.840579 | ||||||||
\(712\) | 13.4258 | 0.503152 | ||||||||
\(713\) | 31.7390 | 1.18863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −66.8589 | −2.50038 | ||||||||
\(716\) | 19.8242 | 0.740866 | ||||||||
\(717\) | −8.73911 | −0.326368 | ||||||||
\(718\) | −1.08122 | −0.0403508 | ||||||||
\(719\) | 9.67617 | 0.360860 | 0.180430 | − | 0.983588i | \(-0.442251\pi\) | ||||
0.180430 | + | 0.983588i | \(0.442251\pi\) | |||||||
\(720\) | 18.6256 | 0.694136 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.12335 | −0.265104 | ||||||||
\(723\) | −9.34364 | −0.347494 | ||||||||
\(724\) | −45.9343 | −1.70714 | ||||||||
\(725\) | −21.5169 | −0.799118 | ||||||||
\(726\) | −1.18174 | −0.0438585 | ||||||||
\(727\) | 28.6421 | 1.06228 | 0.531138 | − | 0.847285i | \(-0.321764\pi\) | ||||
0.531138 | + | 0.847285i | \(0.321764\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.0036 | 0.444577 | ||||||||
\(730\) | −5.84194 | −0.216220 | ||||||||
\(731\) | −9.55435 | −0.353380 | ||||||||
\(732\) | −15.0101 | −0.554790 | ||||||||
\(733\) | −42.4156 | −1.56666 | −0.783328 | − | 0.621608i | \(-0.786480\pi\) | ||||
−0.783328 | + | 0.621608i | \(0.786480\pi\) | |||||||
\(734\) | −12.7611 | −0.471021 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.0320 | 0.664669 | ||||||||
\(737\) | 13.2192 | 0.486934 | ||||||||
\(738\) | −0.943479 | −0.0347299 | ||||||||
\(739\) | 47.5757 | 1.75010 | 0.875051 | − | 0.484031i | \(-0.160828\pi\) | ||||
0.875051 | + | 0.484031i | \(0.160828\pi\) | |||||||
\(740\) | −21.6421 | −0.795578 | ||||||||
\(741\) | −13.0008 | −0.477595 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.7704 | −1.64247 | −0.821234 | − | 0.570591i | \(-0.806714\pi\) | ||||
−0.821234 | + | 0.570591i | \(0.806714\pi\) | |||||||
\(744\) | −14.5024 | −0.531684 | ||||||||
\(745\) | −29.0069 | −1.06273 | ||||||||
\(746\) | −0.389978 | −0.0142781 | ||||||||
\(747\) | −25.5676 | −0.935468 | ||||||||
\(748\) | 39.6866 | 1.45109 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.50584 | −0.0549855 | ||||||||
\(751\) | −17.6077 | −0.642513 | −0.321256 | − | 0.946992i | \(-0.604105\pi\) | ||||
−0.321256 | + | 0.946992i | \(0.604105\pi\) | |||||||
\(752\) | 24.4398 | 0.891228 | ||||||||
\(753\) | −27.8944 | −1.01653 | ||||||||
\(754\) | 11.5597 | 0.420981 | ||||||||
\(755\) | −66.1187 | −2.40631 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.6213 | −0.894876 | −0.447438 | − | 0.894315i | \(-0.647663\pi\) | ||||
−0.447438 | + | 0.894315i | \(0.647663\pi\) | |||||||
\(758\) | 5.96109 | 0.216517 | ||||||||
\(759\) | −10.7217 | −0.389174 | ||||||||
\(760\) | 11.0750 | 0.401734 | ||||||||
\(761\) | 5.91079 | 0.214266 | 0.107133 | − | 0.994245i | \(-0.465833\pi\) | ||||
0.107133 | + | 0.994245i | \(0.465833\pi\) | |||||||
\(762\) | −3.01412 | −0.109190 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.4046 | −0.738211 | ||||||||
\(765\) | 51.7902 | 1.87248 | ||||||||
\(766\) | −10.8431 | −0.391779 | ||||||||
\(767\) | 73.7235 | 2.66200 | ||||||||
\(768\) | 1.42828 | 0.0515386 | ||||||||
\(769\) | −10.0471 | −0.362308 | −0.181154 | − | 0.983455i | \(-0.557983\pi\) | ||||
−0.181154 | + | 0.983455i | \(0.557983\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.9812 | −0.503520 | ||||||||
\(772\) | −25.0044 | −0.899927 | ||||||||
\(773\) | −23.6963 | −0.852297 | −0.426148 | − | 0.904653i | \(-0.640130\pi\) | ||||
−0.426148 | + | 0.904653i | \(0.640130\pi\) | |||||||
\(774\) | 1.17542 | 0.0422497 | ||||||||
\(775\) | 50.5255 | 1.81493 | ||||||||
\(776\) | 1.30170 | 0.0467283 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.26231 | 0.0811076 | ||||||||
\(779\) | 1.90411 | 0.0682218 | ||||||||
\(780\) | −40.4257 | −1.44747 | ||||||||
\(781\) | −6.28071 | −0.224741 | ||||||||
\(782\) | 13.3887 | 0.478777 | ||||||||
\(783\) | 17.7350 | 0.633798 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −61.2094 | −2.18466 | ||||||||
\(786\) | 7.18533 | 0.256292 | ||||||||
\(787\) | 29.2904 | 1.04409 | 0.522045 | − | 0.852918i | \(-0.325169\pi\) | ||||
0.522045 | + | 0.852918i | \(0.325169\pi\) | |||||||
\(788\) | −26.9281 | −0.959275 | ||||||||
\(789\) | 24.6598 | 0.877912 | ||||||||
\(790\) | 16.9129 | 0.601734 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.3520 | −0.367841 | ||||||||
\(793\) | −59.5673 | −2.11530 | ||||||||
\(794\) | 11.6081 | 0.411955 | ||||||||
\(795\) | −13.4396 | −0.476654 | ||||||||
\(796\) | −32.9695 | −1.16857 | ||||||||
\(797\) | 16.9100 | 0.598983 | 0.299491 | − | 0.954099i | \(-0.403183\pi\) | ||||
0.299491 | + | 0.954099i | \(0.403183\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.9570 | 2.40415 | ||||||||
\(800\) | 28.7053 | 1.01488 | ||||||||
\(801\) | 15.5881 | 0.550779 | ||||||||
\(802\) | −4.21743 | −0.148923 | ||||||||
\(803\) | −11.0203 | −0.388899 | ||||||||
\(804\) | 7.99287 | 0.281887 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27.1443 | −0.956117 | ||||||||
\(807\) | 8.29525 | 0.292007 | ||||||||
\(808\) | 5.66438 | 0.199272 | ||||||||
\(809\) | 4.00253 | 0.140721 | 0.0703607 | − | 0.997522i | \(-0.477585\pi\) | ||||
0.0703607 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(810\) | −1.92920 | −0.0677852 | ||||||||
\(811\) | 18.9202 | 0.664380 | 0.332190 | − | 0.943213i | \(-0.392213\pi\) | ||||
0.332190 | + | 0.943213i | \(0.392213\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.48091 | −0.0870092 | ||||||||
\(814\) | 4.90898 | 0.172060 | ||||||||
\(815\) | 25.8725 | 0.906276 | ||||||||
\(816\) | 20.7639 | 0.726883 | ||||||||
\(817\) | −2.37222 | −0.0829933 | ||||||||
\(818\) | 2.04934 | 0.0716535 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.92081 | 0.206764 | ||||||||
\(821\) | −1.63520 | −0.0570688 | −0.0285344 | − | 0.999593i | \(-0.509084\pi\) | ||||
−0.0285344 | + | 0.999593i | \(0.509084\pi\) | |||||||
\(822\) | 2.08987 | 0.0728925 | ||||||||
\(823\) | 33.2336 | 1.15845 | 0.579225 | − | 0.815168i | \(-0.303355\pi\) | ||||
0.579225 | + | 0.815168i | \(0.303355\pi\) | |||||||
\(824\) | −17.2370 | −0.600479 | ||||||||
\(825\) | −17.0680 | −0.594231 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.0333819 | −0.00116080 | −0.000580400 | − | 1.00000i | \(-0.500185\pi\) | ||||
−0.000580400 | 1.00000i | \(0.500185\pi\) | ||||||||
\(828\) | 13.6985 | 0.476057 | ||||||||
\(829\) | 52.9231 | 1.83810 | 0.919048 | − | 0.394147i | \(-0.128960\pi\) | ||||
0.919048 | + | 0.394147i | \(0.128960\pi\) | |||||||
\(830\) | −19.2927 | −0.669661 | ||||||||
\(831\) | 19.6285 | 0.680905 | ||||||||
\(832\) | 22.9440 | 0.795441 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.23724 | −0.0428422 | ||||||||
\(835\) | 18.3197 | 0.633979 | ||||||||
\(836\) | 9.85365 | 0.340796 | ||||||||
\(837\) | −41.6450 | −1.43946 | ||||||||
\(838\) | −0.733989 | −0.0253552 | ||||||||
\(839\) | 10.1155 | 0.349227 | 0.174613 | − | 0.984637i | \(-0.444132\pi\) | ||||
0.174613 | + | 0.984637i | \(0.444132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.1322 | −0.556284 | ||||||||
\(842\) | 10.0500 | 0.346347 | ||||||||
\(843\) | 6.64558 | 0.228886 | ||||||||
\(844\) | 24.7613 | 0.852320 | ||||||||
\(845\) | −117.316 | −4.03578 | ||||||||
\(846\) | −8.36040 | −0.287437 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.3857 | 0.390987 | ||||||||
\(849\) | 6.21104 | 0.213162 | ||||||||
\(850\) | 21.3135 | 0.731047 | ||||||||
\(851\) | −13.7730 | −0.472132 | ||||||||
\(852\) | −3.79758 | −0.130103 | ||||||||
\(853\) | 33.0103 | 1.13025 | 0.565126 | − | 0.825005i | \(-0.308828\pi\) | ||||
0.565126 | + | 0.825005i | \(0.308828\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.8588 | 0.439761 | ||||||||
\(856\) | 32.2690 | 1.10293 | ||||||||
\(857\) | 24.4904 | 0.836576 | 0.418288 | − | 0.908315i | \(-0.362630\pi\) | ||||
0.418288 | + | 0.908315i | \(0.362630\pi\) | |||||||
\(858\) | 9.16960 | 0.313045 | ||||||||
\(859\) | 36.0524 | 1.23009 | 0.615045 | − | 0.788492i | \(-0.289138\pi\) | ||||
0.615045 | + | 0.788492i | \(0.289138\pi\) | |||||||
\(860\) | −7.37638 | −0.251532 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.88533 | −0.0642147 | ||||||||
\(863\) | 12.4612 | 0.424183 | 0.212091 | − | 0.977250i | \(-0.431973\pi\) | ||||
0.212091 | + | 0.977250i | \(0.431973\pi\) | |||||||
\(864\) | −23.6599 | −0.804927 | ||||||||
\(865\) | 28.2659 | 0.961068 | ||||||||
\(866\) | 11.4355 | 0.388595 | ||||||||
\(867\) | 41.0474 | 1.39404 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.9047 | 1.08229 | ||||||||
\(870\) | 5.41089 | 0.183446 | ||||||||
\(871\) | 31.7195 | 1.07477 | ||||||||
\(872\) | −11.2895 | −0.382309 | ||||||||
\(873\) | 1.51135 | 0.0511515 | ||||||||
\(874\) | 3.32422 | 0.112443 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.66335 | −0.225134 | ||||||||
\(877\) | 36.5137 | 1.23298 | 0.616490 | − | 0.787363i | \(-0.288554\pi\) | ||||
0.616490 | + | 0.787363i | \(0.288554\pi\) | |||||||
\(878\) | −11.5616 | −0.390187 | ||||||||
\(879\) | −26.5338 | −0.894963 | ||||||||
\(880\) | 26.5126 | 0.893740 | ||||||||
\(881\) | −9.53691 | −0.321307 | −0.160653 | − | 0.987011i | \(-0.551360\pi\) | ||||
−0.160653 | + | 0.987011i | \(0.551360\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.2983 | 1.72633 | 0.863163 | − | 0.504925i | \(-0.168480\pi\) | ||||
0.863163 | + | 0.504925i | \(0.168480\pi\) | |||||||
\(884\) | 95.2284 | 3.20288 | ||||||||
\(885\) | 34.5086 | 1.15999 | ||||||||
\(886\) | −7.03770 | −0.236436 | ||||||||
\(887\) | 50.8458 | 1.70723 | 0.853617 | − | 0.520901i | \(-0.174404\pi\) | ||||
0.853617 | + | 0.520901i | \(0.174404\pi\) | |||||||
\(888\) | 6.29326 | 0.211188 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11.7625 | 0.394279 | ||||||||
\(891\) | −3.63927 | −0.121920 | ||||||||
\(892\) | −45.0916 | −1.50978 | ||||||||
\(893\) | 16.8728 | 0.564626 | ||||||||
\(894\) | 3.97826 | 0.133053 | ||||||||
\(895\) | 36.8249 | 1.23092 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.7269 | −0.858996 | ||||||||
\(898\) | −0.658049 | −0.0219594 | ||||||||
\(899\) | −30.2158 | −1.00775 | ||||||||
\(900\) | 21.8068 | 0.726893 | ||||||||
\(901\) | 31.6589 | 1.05471 | ||||||||
\(902\) | −1.34299 | −0.0447168 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23.4762 | 0.780808 | ||||||||
\(905\) | −85.3262 | −2.83634 | ||||||||
\(906\) | 9.06809 | 0.301267 | ||||||||
\(907\) | 45.7791 | 1.52007 | 0.760034 | − | 0.649883i | \(-0.225182\pi\) | ||||
0.760034 | + | 0.649883i | \(0.225182\pi\) | |||||||
\(908\) | −12.0696 | −0.400544 | ||||||||
\(909\) | 6.57668 | 0.218135 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.0642 | −1.55931 | −0.779653 | − | 0.626212i | \(-0.784605\pi\) | ||||
−0.779653 | + | 0.626212i | \(0.784605\pi\) | |||||||
\(912\) | 5.15540 | 0.170712 | ||||||||
\(913\) | −36.3941 | −1.20447 | ||||||||
\(914\) | 6.03593 | 0.199651 | ||||||||
\(915\) | −27.8823 | −0.921761 | ||||||||
\(916\) | 24.3361 | 0.804086 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −17.5674 | −0.579809 | ||||||||
\(919\) | 39.0485 | 1.28809 | 0.644045 | − | 0.764987i | \(-0.277255\pi\) | ||||
0.644045 | + | 0.764987i | \(0.277255\pi\) | |||||||
\(920\) | 21.9161 | 0.722554 | ||||||||
\(921\) | 5.38141 | 0.177323 | ||||||||
\(922\) | 15.0139 | 0.494457 | ||||||||
\(923\) | −15.0706 | −0.496055 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.9253 | −0.720900 | ||||||||
\(926\) | 1.54246 | 0.0506885 | ||||||||
\(927\) | −20.0132 | −0.657319 | ||||||||
\(928\) | −17.1666 | −0.563522 | ||||||||
\(929\) | −23.8926 | −0.783891 | −0.391945 | − | 0.919988i | \(-0.628198\pi\) | ||||
−0.391945 | + | 0.919988i | \(0.628198\pi\) | |||||||
\(930\) | −12.7057 | −0.416637 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.524971 | −0.0171960 | ||||||||
\(933\) | 7.09338 | 0.232227 | ||||||||
\(934\) | 5.25639 | 0.171994 | ||||||||
\(935\) | 73.7206 | 2.41092 | ||||||||
\(936\) | −24.8396 | −0.811909 | ||||||||
\(937\) | −36.1258 | −1.18018 | −0.590090 | − | 0.807338i | \(-0.700908\pi\) | ||||
−0.590090 | + | 0.807338i | \(0.700908\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.2390 | 0.595206 | ||||||||
\(940\) | 52.4658 | 1.71124 | ||||||||
\(941\) | 22.9141 | 0.746980 | 0.373490 | − | 0.927634i | \(-0.378161\pi\) | ||||
0.373490 | + | 0.927634i | \(0.378161\pi\) | |||||||
\(942\) | 8.39479 | 0.273517 | ||||||||
\(943\) | 3.76800 | 0.122703 | ||||||||
\(944\) | −29.2348 | −0.951511 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.67315 | 0.0543989 | ||||||||
\(947\) | 17.4074 | 0.565664 | 0.282832 | − | 0.959170i | \(-0.408726\pi\) | ||||
0.282832 | + | 0.959170i | \(0.408726\pi\) | |||||||
\(948\) | 19.2909 | 0.626541 | ||||||||
\(949\) | −26.4434 | −0.858387 | ||||||||
\(950\) | 5.29185 | 0.171690 | ||||||||
\(951\) | 28.5170 | 0.924726 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.6396 | −0.668583 | −0.334292 | − | 0.942470i | \(-0.608497\pi\) | ||||
−0.334292 | + | 0.942470i | \(0.608497\pi\) | |||||||
\(954\) | −3.89484 | −0.126100 | ||||||||
\(955\) | −37.9028 | −1.22651 | ||||||||
\(956\) | 15.8935 | 0.514031 | ||||||||
\(957\) | 10.2072 | 0.329951 | ||||||||
\(958\) | −8.31442 | −0.268627 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 10.7397 | 0.346621 | ||||||||
\(961\) | 39.9520 | 1.28877 | ||||||||
\(962\) | 11.7791 | 0.379775 | ||||||||
\(963\) | 37.4662 | 1.20733 | ||||||||
\(964\) | 16.9929 | 0.547304 | ||||||||
\(965\) | −46.4473 | −1.49519 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.77753 | −0.0893193 | −0.0446597 | − | 0.999002i | \(-0.514220\pi\) | ||||
−0.0446597 | + | 0.999002i | \(0.514220\pi\) | |||||||
\(968\) | 4.55679 | 0.146461 | ||||||||
\(969\) | 14.3350 | 0.460507 | ||||||||
\(970\) | 1.14043 | 0.0366172 | ||||||||
\(971\) | −18.3051 | −0.587438 | −0.293719 | − | 0.955892i | \(-0.594893\pi\) | ||||
−0.293719 | + | 0.955892i | \(0.594893\pi\) | |||||||
\(972\) | −28.6806 | −0.919930 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.49226 | 0.0798571 | ||||||||
\(975\) | −40.9548 | −1.31160 | ||||||||
\(976\) | 23.6212 | 0.756096 | ||||||||
\(977\) | 3.18355 | 0.101851 | 0.0509253 | − | 0.998702i | \(-0.483783\pi\) | ||||
0.0509253 | + | 0.998702i | \(0.483783\pi\) | |||||||
\(978\) | −3.54838 | −0.113465 | ||||||||
\(979\) | 22.1889 | 0.709160 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.1077 | −0.418498 | ||||||||
\(982\) | 7.95239 | 0.253771 | ||||||||
\(983\) | −19.8284 | −0.632426 | −0.316213 | − | 0.948688i | \(-0.602412\pi\) | ||||
−0.316213 | + | 0.948688i | \(0.602412\pi\) | |||||||
\(984\) | −1.72170 | −0.0548858 | ||||||||
\(985\) | −50.0208 | −1.59380 | ||||||||
\(986\) | −12.7461 | −0.405919 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.6439 | 0.752213 | ||||||||
\(989\) | −4.69432 | −0.149271 | ||||||||
\(990\) | −9.06947 | −0.288247 | ||||||||
\(991\) | −29.6097 | −0.940583 | −0.470292 | − | 0.882511i | \(-0.655851\pi\) | ||||
−0.470292 | + | 0.882511i | \(0.655851\pi\) | |||||||
\(992\) | 40.3103 | 1.27985 | ||||||||
\(993\) | 4.50467 | 0.142951 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −61.2431 | −1.94154 | ||||||||
\(996\) | −22.0054 | −0.697268 | ||||||||
\(997\) | 34.8793 | 1.10464 | 0.552319 | − | 0.833633i | \(-0.313743\pi\) | ||||
0.552319 | + | 0.833633i | \(0.313743\pi\) | |||||||
\(998\) | −11.1449 | −0.352786 | ||||||||
\(999\) | 18.0716 | 0.571762 |
(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 | 2009.2.a.u.1.12 | yes | 20 | |
7.6 | odd | 2 | 2009.2.a.t.1.12 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2009.2.a.t.1.12 | ✓ | 20 | 7.6 | odd | 2 | ||
2009.2.a.u.1.12 | yes | 20 | 1.1 | even | 1 | trivial |