Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.258228.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 12x^{2} + 6x + 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.63927\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.639273 | −0.369085 | −0.184542 | − | 0.982825i | \(-0.559080\pi\) | ||||
−0.184542 | + | 0.982825i | \(0.559080\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.63927 | −0.733105 | −0.366553 | − | 0.930397i | \(-0.619462\pi\) | ||||
−0.366553 | + | 0.930397i | \(0.619462\pi\) | |||||||
\(6\) | −0.639273 | −0.260982 | ||||||||
\(7\) | 1.54956 | 0.585679 | 0.292839 | − | 0.956162i | \(-0.405400\pi\) | ||||
0.292839 | + | 0.956162i | \(0.405400\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.59133 | −0.863776 | ||||||||
\(10\) | −1.63927 | −0.518384 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.639273 | −0.184542 | ||||||||
\(13\) | 6.04177 | 1.67569 | 0.837843 | − | 0.545912i | \(-0.183817\pi\) | ||||
0.837843 | + | 0.545912i | \(0.183817\pi\) | |||||||
\(14\) | 1.54956 | 0.414137 | ||||||||
\(15\) | 1.04794 | 0.270578 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.54956 | −0.618359 | −0.309180 | − | 0.951004i | \(-0.600054\pi\) | ||||
−0.309180 | + | 0.951004i | \(0.600054\pi\) | |||||||
\(18\) | −2.59133 | −0.610782 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −1.63927 | −0.366553 | ||||||||
\(21\) | −0.990593 | −0.216165 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.04177 | −1.46831 | −0.734155 | − | 0.678982i | \(-0.762422\pi\) | ||||
−0.734155 | + | 0.678982i | \(0.762422\pi\) | |||||||
\(24\) | −0.639273 | −0.130491 | ||||||||
\(25\) | −2.31278 | −0.462557 | ||||||||
\(26\) | 6.04177 | 1.18489 | ||||||||
\(27\) | 3.57439 | 0.687891 | ||||||||
\(28\) | 1.54956 | 0.292839 | ||||||||
\(29\) | 1.95206 | 0.362488 | 0.181244 | − | 0.983438i | \(-0.441988\pi\) | ||||
0.181244 | + | 0.983438i | \(0.441988\pi\) | |||||||
\(30\) | 1.04794 | 0.191328 | ||||||||
\(31\) | −1.27855 | −0.229634 | −0.114817 | − | 0.993387i | \(-0.536628\pi\) | ||||
−0.114817 | + | 0.993387i | \(0.536628\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.54956 | −0.437246 | ||||||||
\(35\) | −2.54015 | −0.429364 | ||||||||
\(36\) | −2.59133 | −0.431888 | ||||||||
\(37\) | 5.73839 | 0.943386 | 0.471693 | − | 0.881763i | \(-0.343643\pi\) | ||||
0.471693 | + | 0.881763i | \(0.343643\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −3.86234 | −0.618470 | ||||||||
\(40\) | −1.63927 | −0.259192 | ||||||||
\(41\) | 9.13148 | 1.42610 | 0.713049 | − | 0.701114i | \(-0.247314\pi\) | ||||
0.713049 | + | 0.701114i | \(0.247314\pi\) | |||||||
\(42\) | −0.990593 | −0.152852 | ||||||||
\(43\) | 12.8050 | 1.95274 | 0.976371 | − | 0.216099i | \(-0.0693334\pi\) | ||||
0.976371 | + | 0.216099i | \(0.0693334\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.24790 | 0.633239 | ||||||||
\(46\) | −7.04177 | −1.03825 | ||||||||
\(47\) | 3.59133 | 0.523849 | 0.261925 | − | 0.965088i | \(-0.415643\pi\) | ||||
0.261925 | + | 0.965088i | \(0.415643\pi\) | |||||||
\(48\) | −0.639273 | −0.0922712 | ||||||||
\(49\) | −4.59886 | −0.656980 | ||||||||
\(50\) | −2.31278 | −0.327077 | ||||||||
\(51\) | 1.62987 | 0.228227 | ||||||||
\(52\) | 6.04177 | 0.837843 | ||||||||
\(53\) | −7.95206 | −1.09230 | −0.546149 | − | 0.837688i | \(-0.683907\pi\) | ||||
−0.546149 | + | 0.837688i | \(0.683907\pi\) | |||||||
\(54\) | 3.57439 | 0.486413 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.54956 | 0.207069 | ||||||||
\(57\) | −0.639273 | −0.0846738 | ||||||||
\(58\) | 1.95206 | 0.256318 | ||||||||
\(59\) | 5.40250 | 0.703345 | 0.351673 | − | 0.936123i | \(-0.385613\pi\) | ||||
0.351673 | + | 0.936123i | \(0.385613\pi\) | |||||||
\(60\) | 1.04794 | 0.135289 | ||||||||
\(61\) | 13.5434 | 1.73405 | 0.867026 | − | 0.498262i | \(-0.166028\pi\) | ||||
0.867026 | + | 0.498262i | \(0.166028\pi\) | |||||||
\(62\) | −1.27855 | −0.162376 | ||||||||
\(63\) | −4.01542 | −0.505896 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.90411 | −1.22845 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.2212 | 1.24872 | 0.624359 | − | 0.781138i | \(-0.285360\pi\) | ||||
0.624359 | + | 0.781138i | \(0.285360\pi\) | |||||||
\(68\) | −2.54956 | −0.309180 | ||||||||
\(69\) | 4.50162 | 0.541931 | ||||||||
\(70\) | −2.54015 | −0.303606 | ||||||||
\(71\) | −12.4100 | −1.47280 | −0.736400 | − | 0.676547i | \(-0.763476\pi\) | ||||
−0.736400 | + | 0.676547i | \(0.763476\pi\) | |||||||
\(72\) | −2.59133 | −0.305391 | ||||||||
\(73\) | −1.45044 | −0.169761 | −0.0848806 | − | 0.996391i | \(-0.527051\pi\) | ||||
−0.0848806 | + | 0.996391i | \(0.527051\pi\) | |||||||
\(74\) | 5.73839 | 0.667075 | ||||||||
\(75\) | 1.47850 | 0.170723 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.86234 | −0.437324 | ||||||||
\(79\) | −1.13148 | −0.127302 | −0.0636509 | − | 0.997972i | \(-0.520274\pi\) | ||||
−0.0636509 | + | 0.997972i | \(0.520274\pi\) | |||||||
\(80\) | −1.63927 | −0.183276 | ||||||||
\(81\) | 5.48898 | 0.609886 | ||||||||
\(82\) | 9.13148 | 1.00840 | ||||||||
\(83\) | −4.36073 | −0.478652 | −0.239326 | − | 0.970939i | \(-0.576926\pi\) | ||||
−0.239326 | + | 0.970939i | \(0.576926\pi\) | |||||||
\(84\) | −0.990593 | −0.108083 | ||||||||
\(85\) | 4.17943 | 0.453322 | ||||||||
\(86\) | 12.8050 | 1.38080 | ||||||||
\(87\) | −1.24790 | −0.133789 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.85294 | −0.620410 | −0.310205 | − | 0.950670i | \(-0.600398\pi\) | ||||
−0.310205 | + | 0.950670i | \(0.600398\pi\) | |||||||
\(90\) | 4.24790 | 0.447768 | ||||||||
\(91\) | 9.36209 | 0.981413 | ||||||||
\(92\) | −7.04177 | −0.734155 | ||||||||
\(93\) | 0.817341 | 0.0847543 | ||||||||
\(94\) | 3.59133 | 0.370417 | ||||||||
\(95\) | −1.63927 | −0.168186 | ||||||||
\(96\) | −0.639273 | −0.0652456 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | −4.59886 | −0.464555 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.31278 | −0.231278 | ||||||||
\(101\) | −8.26484 | −0.822382 | −0.411191 | − | 0.911549i | \(-0.634887\pi\) | ||||
−0.411191 | + | 0.911549i | \(0.634887\pi\) | |||||||
\(102\) | 1.62987 | 0.161381 | ||||||||
\(103\) | 8.14706 | 0.802754 | 0.401377 | − | 0.915913i | \(-0.368532\pi\) | ||||
0.401377 | + | 0.915913i | \(0.368532\pi\) | |||||||
\(104\) | 6.04177 | 0.592444 | ||||||||
\(105\) | 1.62385 | 0.158472 | ||||||||
\(106\) | −7.95206 | −0.772372 | ||||||||
\(107\) | 12.5509 | 1.21334 | 0.606672 | − | 0.794953i | \(-0.292504\pi\) | ||||
0.606672 | + | 0.794953i | \(0.292504\pi\) | |||||||
\(108\) | 3.57439 | 0.343946 | ||||||||
\(109\) | −3.40250 | −0.325900 | −0.162950 | − | 0.986634i | \(-0.552101\pi\) | ||||
−0.162950 | + | 0.986634i | \(0.552101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.66840 | −0.348189 | ||||||||
\(112\) | 1.54956 | 0.146420 | ||||||||
\(113\) | −3.13148 | −0.294585 | −0.147293 | − | 0.989093i | \(-0.547056\pi\) | ||||
−0.147293 | + | 0.989093i | \(0.547056\pi\) | |||||||
\(114\) | −0.639273 | −0.0598734 | ||||||||
\(115\) | 11.5434 | 1.07643 | ||||||||
\(116\) | 1.95206 | 0.181244 | ||||||||
\(117\) | −15.6562 | −1.44742 | ||||||||
\(118\) | 5.40250 | 0.497340 | ||||||||
\(119\) | −3.95070 | −0.362160 | ||||||||
\(120\) | 1.04794 | 0.0956638 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 13.5434 | 1.22616 | ||||||||
\(123\) | −5.83751 | −0.526351 | ||||||||
\(124\) | −1.27855 | −0.114817 | ||||||||
\(125\) | 11.9877 | 1.07221 | ||||||||
\(126\) | −4.01542 | −0.357722 | ||||||||
\(127\) | −5.82057 | −0.516492 | −0.258246 | − | 0.966079i | \(-0.583145\pi\) | ||||
−0.258246 | + | 0.966079i | \(0.583145\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.18589 | −0.720728 | ||||||||
\(130\) | −9.90411 | −0.868648 | ||||||||
\(131\) | 14.9844 | 1.30919 | 0.654597 | − | 0.755978i | \(-0.272838\pi\) | ||||
0.654597 | + | 0.755978i | \(0.272838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.54956 | 0.134364 | ||||||||
\(134\) | 10.2212 | 0.882977 | ||||||||
\(135\) | −5.85940 | −0.504297 | ||||||||
\(136\) | −2.54956 | −0.218623 | ||||||||
\(137\) | 19.3546 | 1.65357 | 0.826785 | − | 0.562517i | \(-0.190167\pi\) | ||||
0.826785 | + | 0.562517i | \(0.190167\pi\) | |||||||
\(138\) | 4.50162 | 0.383203 | ||||||||
\(139\) | 15.7398 | 1.33503 | 0.667514 | − | 0.744597i | \(-0.267358\pi\) | ||||
0.667514 | + | 0.744597i | \(0.267358\pi\) | |||||||
\(140\) | −2.54015 | −0.214682 | ||||||||
\(141\) | −2.29584 | −0.193345 | ||||||||
\(142\) | −12.4100 | −1.04143 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.59133 | −0.215944 | ||||||||
\(145\) | −3.19995 | −0.265742 | ||||||||
\(146\) | −1.45044 | −0.120039 | ||||||||
\(147\) | 2.93993 | 0.242481 | ||||||||
\(148\) | 5.73839 | 0.471693 | ||||||||
\(149\) | 19.4456 | 1.59305 | 0.796524 | − | 0.604607i | \(-0.206670\pi\) | ||||
0.796524 | + | 0.604607i | \(0.206670\pi\) | |||||||
\(150\) | 1.47850 | 0.120719 | ||||||||
\(151\) | −12.2306 | −0.995312 | −0.497656 | − | 0.867374i | \(-0.665806\pi\) | ||||
−0.497656 | + | 0.867374i | \(0.665806\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 6.60675 | 0.534124 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.09589 | 0.168346 | ||||||||
\(156\) | −3.86234 | −0.309235 | ||||||||
\(157\) | 24.6425 | 1.96669 | 0.983343 | − | 0.181759i | \(-0.0581792\pi\) | ||||
0.983343 | + | 0.181759i | \(0.0581792\pi\) | |||||||
\(158\) | −1.13148 | −0.0900159 | ||||||||
\(159\) | 5.08354 | 0.403151 | ||||||||
\(160\) | −1.63927 | −0.129596 | ||||||||
\(161\) | −10.9116 | −0.859958 | ||||||||
\(162\) | 5.48898 | 0.431255 | ||||||||
\(163\) | −19.0032 | −1.48845 | −0.744224 | − | 0.667930i | \(-0.767181\pi\) | ||||
−0.744224 | + | 0.667930i | \(0.767181\pi\) | |||||||
\(164\) | 9.13148 | 0.713049 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.36073 | −0.338458 | ||||||||
\(167\) | −1.82057 | −0.140880 | −0.0704401 | − | 0.997516i | \(-0.522440\pi\) | ||||
−0.0704401 | + | 0.997516i | \(0.522440\pi\) | |||||||
\(168\) | −0.990593 | −0.0764259 | ||||||||
\(169\) | 23.5030 | 1.80792 | ||||||||
\(170\) | 4.17943 | 0.320547 | ||||||||
\(171\) | −2.59133 | −0.198164 | ||||||||
\(172\) | 12.8050 | 0.976371 | ||||||||
\(173\) | 10.3109 | 0.783924 | 0.391962 | − | 0.919981i | \(-0.371796\pi\) | ||||
0.391962 | + | 0.919981i | \(0.371796\pi\) | |||||||
\(174\) | −1.24790 | −0.0946029 | ||||||||
\(175\) | −3.58380 | −0.270909 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.45367 | −0.259594 | ||||||||
\(178\) | −5.85294 | −0.438696 | ||||||||
\(179\) | 5.78770 | 0.432593 | 0.216296 | − | 0.976328i | \(-0.430602\pi\) | ||||
0.216296 | + | 0.976328i | \(0.430602\pi\) | |||||||
\(180\) | 4.24790 | 0.316620 | ||||||||
\(181\) | 15.4768 | 1.15038 | 0.575190 | − | 0.818020i | \(-0.304928\pi\) | ||||
0.575190 | + | 0.818020i | \(0.304928\pi\) | |||||||
\(182\) | 9.36209 | 0.693964 | ||||||||
\(183\) | −8.65793 | −0.640012 | ||||||||
\(184\) | −7.04177 | −0.519126 | ||||||||
\(185\) | −9.40680 | −0.691601 | ||||||||
\(186\) | 0.817341 | 0.0599304 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.59133 | 0.261925 | ||||||||
\(189\) | 5.53873 | 0.402883 | ||||||||
\(190\) | −1.63927 | −0.118925 | ||||||||
\(191\) | 15.4537 | 1.11819 | 0.559094 | − | 0.829104i | \(-0.311149\pi\) | ||||
0.559094 | + | 0.829104i | \(0.311149\pi\) | |||||||
\(192\) | −0.639273 | −0.0461356 | ||||||||
\(193\) | 8.00000 | 0.575853 | 0.287926 | − | 0.957653i | \(-0.407034\pi\) | ||||
0.287926 | + | 0.957653i | \(0.407034\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | 6.33144 | 0.453404 | ||||||||
\(196\) | −4.59886 | −0.328490 | ||||||||
\(197\) | 5.72469 | 0.407867 | 0.203933 | − | 0.978985i | \(-0.434627\pi\) | ||||
0.203933 | + | 0.978985i | \(0.434627\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.18696 | 0.296806 | 0.148403 | − | 0.988927i | \(-0.452587\pi\) | ||||
0.148403 | + | 0.988927i | \(0.452587\pi\) | |||||||
\(200\) | −2.31278 | −0.163538 | ||||||||
\(201\) | −6.53414 | −0.460883 | ||||||||
\(202\) | −8.26484 | −0.581512 | ||||||||
\(203\) | 3.02483 | 0.212301 | ||||||||
\(204\) | 1.62987 | 0.114113 | ||||||||
\(205\) | −14.9690 | −1.04548 | ||||||||
\(206\) | 8.14706 | 0.567633 | ||||||||
\(207\) | 18.2475 | 1.26829 | ||||||||
\(208\) | 6.04177 | 0.418921 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.62385 | 0.112056 | ||||||||
\(211\) | 12.9022 | 0.888227 | 0.444113 | − | 0.895971i | \(-0.353519\pi\) | ||||
0.444113 | + | 0.895971i | \(0.353519\pi\) | |||||||
\(212\) | −7.95206 | −0.546149 | ||||||||
\(213\) | 7.93340 | 0.543588 | ||||||||
\(214\) | 12.5509 | 0.857963 | ||||||||
\(215\) | −20.9909 | −1.43157 | ||||||||
\(216\) | 3.57439 | 0.243206 | ||||||||
\(217\) | −1.98119 | −0.134492 | ||||||||
\(218\) | −3.40250 | −0.230446 | ||||||||
\(219\) | 0.927228 | 0.0626562 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.4039 | −1.03618 | ||||||||
\(222\) | −3.66840 | −0.246207 | ||||||||
\(223\) | 21.3109 | 1.42708 | 0.713542 | − | 0.700612i | \(-0.247090\pi\) | ||||
0.713542 | + | 0.700612i | \(0.247090\pi\) | |||||||
\(224\) | 1.54956 | 0.103534 | ||||||||
\(225\) | 5.99318 | 0.399545 | ||||||||
\(226\) | −3.13148 | −0.208303 | ||||||||
\(227\) | −20.5030 | −1.36083 | −0.680415 | − | 0.732827i | \(-0.738201\pi\) | ||||
−0.680415 | + | 0.732827i | \(0.738201\pi\) | |||||||
\(228\) | −0.639273 | −0.0423369 | ||||||||
\(229\) | 16.6406 | 1.09964 | 0.549822 | − | 0.835282i | \(-0.314696\pi\) | ||||
0.549822 | + | 0.835282i | \(0.314696\pi\) | |||||||
\(230\) | 11.5434 | 0.761148 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.95206 | 0.128159 | ||||||||
\(233\) | 6.57575 | 0.430792 | 0.215396 | − | 0.976527i | \(-0.430896\pi\) | ||||
0.215396 | + | 0.976527i | \(0.430896\pi\) | |||||||
\(234\) | −15.6562 | −1.02348 | ||||||||
\(235\) | −5.88717 | −0.384037 | ||||||||
\(236\) | 5.40250 | 0.351673 | ||||||||
\(237\) | 0.723327 | 0.0469851 | ||||||||
\(238\) | −3.95070 | −0.256086 | ||||||||
\(239\) | 3.63791 | 0.235317 | 0.117659 | − | 0.993054i | \(-0.462461\pi\) | ||||
0.117659 | + | 0.993054i | \(0.462461\pi\) | |||||||
\(240\) | 1.04794 | 0.0676445 | ||||||||
\(241\) | 28.1498 | 1.81329 | 0.906643 | − | 0.421898i | \(-0.138636\pi\) | ||||
0.906643 | + | 0.421898i | \(0.138636\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.2321 | −0.912991 | ||||||||
\(244\) | 13.5434 | 0.867026 | ||||||||
\(245\) | 7.53879 | 0.481636 | ||||||||
\(246\) | −5.83751 | −0.372186 | ||||||||
\(247\) | 6.04177 | 0.384429 | ||||||||
\(248\) | −1.27855 | −0.0811878 | ||||||||
\(249\) | 2.78770 | 0.176663 | ||||||||
\(250\) | 11.9877 | 0.758166 | ||||||||
\(251\) | −10.8050 | −0.682005 | −0.341003 | − | 0.940062i | \(-0.610766\pi\) | ||||
−0.341003 | + | 0.940062i | \(0.610766\pi\) | |||||||
\(252\) | −4.01542 | −0.252948 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.82057 | −0.365215 | ||||||||
\(255\) | −2.67180 | −0.167314 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.0032 | −0.935876 | −0.467938 | − | 0.883761i | \(-0.655003\pi\) | ||||
−0.467938 | + | 0.883761i | \(0.655003\pi\) | |||||||
\(258\) | −8.18589 | −0.509631 | ||||||||
\(259\) | 8.89199 | 0.552521 | ||||||||
\(260\) | −9.90411 | −0.614227 | ||||||||
\(261\) | −5.05842 | −0.313108 | ||||||||
\(262\) | 14.9844 | 0.925740 | ||||||||
\(263\) | −3.57575 | −0.220490 | −0.110245 | − | 0.993904i | \(-0.535164\pi\) | ||||
−0.110245 | + | 0.993904i | \(0.535164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.0356 | 0.800770 | ||||||||
\(266\) | 1.54956 | 0.0950096 | ||||||||
\(267\) | 3.74163 | 0.228984 | ||||||||
\(268\) | 10.2212 | 0.624359 | ||||||||
\(269\) | −25.5895 | −1.56022 | −0.780108 | − | 0.625644i | \(-0.784836\pi\) | ||||
−0.780108 | + | 0.625644i | \(0.784836\pi\) | |||||||
\(270\) | −5.85940 | −0.356592 | ||||||||
\(271\) | 10.8125 | 0.656814 | 0.328407 | − | 0.944536i | \(-0.393488\pi\) | ||||
0.328407 | + | 0.944536i | \(0.393488\pi\) | |||||||
\(272\) | −2.54956 | −0.154590 | ||||||||
\(273\) | −5.98493 | −0.362225 | ||||||||
\(274\) | 19.3546 | 1.16925 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.50162 | 0.270965 | ||||||||
\(277\) | −0.277188 | −0.0166546 | −0.00832731 | − | 0.999965i | \(-0.502651\pi\) | ||||
−0.00832731 | + | 0.999965i | \(0.502651\pi\) | |||||||
\(278\) | 15.7398 | 0.944008 | ||||||||
\(279\) | 3.31314 | 0.198352 | ||||||||
\(280\) | −2.54015 | −0.151803 | ||||||||
\(281\) | −8.23060 | −0.490997 | −0.245498 | − | 0.969397i | \(-0.578952\pi\) | ||||
−0.245498 | + | 0.969397i | \(0.578952\pi\) | |||||||
\(282\) | −2.29584 | −0.136715 | ||||||||
\(283\) | −20.4612 | −1.21629 | −0.608146 | − | 0.793825i | \(-0.708087\pi\) | ||||
−0.608146 | + | 0.793825i | \(0.708087\pi\) | |||||||
\(284\) | −12.4100 | −0.736400 | ||||||||
\(285\) | 1.04794 | 0.0620748 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.1498 | 0.835235 | ||||||||
\(288\) | −2.59133 | −0.152696 | ||||||||
\(289\) | −10.4997 | −0.617632 | ||||||||
\(290\) | −3.19995 | −0.187908 | ||||||||
\(291\) | 6.39273 | 0.374749 | ||||||||
\(292\) | −1.45044 | −0.0848806 | ||||||||
\(293\) | 11.5402 | 0.674183 | 0.337091 | − | 0.941472i | \(-0.390557\pi\) | ||||
0.337091 | + | 0.941472i | \(0.390557\pi\) | |||||||
\(294\) | 2.93993 | 0.171460 | ||||||||
\(295\) | −8.85617 | −0.515626 | ||||||||
\(296\) | 5.73839 | 0.333537 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.4456 | 1.12645 | ||||||||
\(299\) | −42.5447 | −2.46043 | ||||||||
\(300\) | 1.47850 | 0.0853613 | ||||||||
\(301\) | 19.8421 | 1.14368 | ||||||||
\(302\) | −12.2306 | −0.703792 | ||||||||
\(303\) | 5.28349 | 0.303529 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −22.2013 | −1.27124 | ||||||||
\(306\) | 6.60675 | 0.377683 | ||||||||
\(307\) | −1.75382 | −0.100096 | −0.0500478 | − | 0.998747i | \(-0.515937\pi\) | ||||
−0.0500478 | + | 0.998747i | \(0.515937\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.20820 | −0.296284 | ||||||||
\(310\) | 2.09589 | 0.119038 | ||||||||
\(311\) | −17.7473 | −1.00636 | −0.503178 | − | 0.864183i | \(-0.667836\pi\) | ||||
−0.503178 | + | 0.864183i | \(0.667836\pi\) | |||||||
\(312\) | −3.86234 | −0.218662 | ||||||||
\(313\) | −16.4381 | −0.929136 | −0.464568 | − | 0.885538i | \(-0.653790\pi\) | ||||
−0.464568 | + | 0.885538i | \(0.653790\pi\) | |||||||
\(314\) | 24.6425 | 1.39066 | ||||||||
\(315\) | 6.58237 | 0.370875 | ||||||||
\(316\) | −1.13148 | −0.0636509 | ||||||||
\(317\) | 6.78204 | 0.380917 | 0.190459 | − | 0.981695i | \(-0.439003\pi\) | ||||
0.190459 | + | 0.981695i | \(0.439003\pi\) | |||||||
\(318\) | 5.08354 | 0.285071 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.63927 | −0.0916382 | ||||||||
\(321\) | −8.02347 | −0.447826 | ||||||||
\(322\) | −10.9116 | −0.608082 | ||||||||
\(323\) | −2.54956 | −0.141861 | ||||||||
\(324\) | 5.48898 | 0.304943 | ||||||||
\(325\) | −13.9733 | −0.775099 | ||||||||
\(326\) | −19.0032 | −1.05249 | ||||||||
\(327\) | 2.17513 | 0.120285 | ||||||||
\(328\) | 9.13148 | 0.504202 | ||||||||
\(329\) | 5.56498 | 0.306807 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.61616 | −0.418622 | −0.209311 | − | 0.977849i | \(-0.567122\pi\) | ||||
−0.209311 | + | 0.977849i | \(0.567122\pi\) | |||||||
\(332\) | −4.36073 | −0.239326 | ||||||||
\(333\) | −14.8701 | −0.814875 | ||||||||
\(334\) | −1.82057 | −0.0996174 | ||||||||
\(335\) | −16.7553 | −0.915442 | ||||||||
\(336\) | −0.990593 | −0.0540413 | ||||||||
\(337\) | −20.0200 | −1.09056 | −0.545280 | − | 0.838254i | \(-0.683577\pi\) | ||||
−0.545280 | + | 0.838254i | \(0.683577\pi\) | |||||||
\(338\) | 23.5030 | 1.27839 | ||||||||
\(339\) | 2.00187 | 0.108727 | ||||||||
\(340\) | 4.17943 | 0.226661 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.59133 | −0.140123 | ||||||||
\(343\) | −17.9731 | −0.970458 | ||||||||
\(344\) | 12.8050 | 0.690399 | ||||||||
\(345\) | −7.37938 | −0.397292 | ||||||||
\(346\) | 10.3109 | 0.554318 | ||||||||
\(347\) | −16.3296 | −0.876617 | −0.438308 | − | 0.898825i | \(-0.644422\pi\) | ||||
−0.438308 | + | 0.898825i | \(0.644422\pi\) | |||||||
\(348\) | −1.24790 | −0.0668943 | ||||||||
\(349\) | −26.9995 | −1.44525 | −0.722625 | − | 0.691241i | \(-0.757064\pi\) | ||||
−0.722625 | + | 0.691241i | \(0.757064\pi\) | |||||||
\(350\) | −3.58380 | −0.191562 | ||||||||
\(351\) | 21.5956 | 1.15269 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.0525 | 0.747941 | 0.373970 | − | 0.927441i | \(-0.377996\pi\) | ||||
0.373970 | + | 0.927441i | \(0.377996\pi\) | |||||||
\(354\) | −3.45367 | −0.183561 | ||||||||
\(355\) | 20.3434 | 1.07972 | ||||||||
\(356\) | −5.85294 | −0.310205 | ||||||||
\(357\) | 2.52558 | 0.133668 | ||||||||
\(358\) | 5.78770 | 0.305889 | ||||||||
\(359\) | 25.3546 | 1.33816 | 0.669081 | − | 0.743189i | \(-0.266688\pi\) | ||||
0.669081 | + | 0.743189i | \(0.266688\pi\) | |||||||
\(360\) | 4.24790 | 0.223884 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 15.4768 | 0.813442 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.36209 | 0.490707 | ||||||||
\(365\) | 2.37767 | 0.124453 | ||||||||
\(366\) | −8.65793 | −0.452557 | ||||||||
\(367\) | 19.3931 | 1.01231 | 0.506155 | − | 0.862442i | \(-0.331066\pi\) | ||||
0.506155 | + | 0.862442i | \(0.331066\pi\) | |||||||
\(368\) | −7.04177 | −0.367078 | ||||||||
\(369\) | −23.6627 | −1.23183 | ||||||||
\(370\) | −9.40680 | −0.489036 | ||||||||
\(371\) | −12.3222 | −0.639736 | ||||||||
\(372\) | 0.817341 | 0.0423772 | ||||||||
\(373\) | −35.3018 | −1.82786 | −0.913929 | − | 0.405875i | \(-0.866967\pi\) | ||||
−0.913929 | + | 0.405875i | \(0.866967\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.66339 | −0.395736 | ||||||||
\(376\) | 3.59133 | 0.185209 | ||||||||
\(377\) | 11.7939 | 0.607415 | ||||||||
\(378\) | 5.53873 | 0.284882 | ||||||||
\(379\) | −5.17002 | −0.265566 | −0.132783 | − | 0.991145i | \(-0.542391\pi\) | ||||
−0.132783 | + | 0.991145i | \(0.542391\pi\) | |||||||
\(380\) | −1.63927 | −0.0840930 | ||||||||
\(381\) | 3.72094 | 0.190629 | ||||||||
\(382\) | 15.4537 | 0.790679 | ||||||||
\(383\) | −5.16759 | −0.264052 | −0.132026 | − | 0.991246i | \(-0.542148\pi\) | ||||
−0.132026 | + | 0.991246i | \(0.542148\pi\) | |||||||
\(384\) | −0.639273 | −0.0326228 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | −33.1820 | −1.68673 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | 4.91782 | 0.249343 | 0.124672 | − | 0.992198i | \(-0.460212\pi\) | ||||
0.124672 | + | 0.992198i | \(0.460212\pi\) | |||||||
\(390\) | 6.33144 | 0.320605 | ||||||||
\(391\) | 17.9534 | 0.907943 | ||||||||
\(392\) | −4.59886 | −0.232278 | ||||||||
\(393\) | −9.57914 | −0.483204 | ||||||||
\(394\) | 5.72469 | 0.288405 | ||||||||
\(395\) | 1.85481 | 0.0933256 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.54151 | −0.378498 | −0.189249 | − | 0.981929i | \(-0.560605\pi\) | ||||
−0.189249 | + | 0.981929i | \(0.560605\pi\) | |||||||
\(398\) | 4.18696 | 0.209873 | ||||||||
\(399\) | −0.990593 | −0.0495917 | ||||||||
\(400\) | −2.31278 | −0.115639 | ||||||||
\(401\) | 4.03236 | 0.201367 | 0.100683 | − | 0.994919i | \(-0.467897\pi\) | ||||
0.100683 | + | 0.994919i | \(0.467897\pi\) | |||||||
\(402\) | −6.53414 | −0.325893 | ||||||||
\(403\) | −7.72469 | −0.384794 | ||||||||
\(404\) | −8.26484 | −0.411191 | ||||||||
\(405\) | −8.99793 | −0.447111 | ||||||||
\(406\) | 3.02483 | 0.150120 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.62987 | 0.0806904 | ||||||||
\(409\) | −0.358853 | −0.0177441 | −0.00887207 | − | 0.999961i | \(-0.502824\pi\) | ||||
−0.00887207 | + | 0.999961i | \(0.502824\pi\) | |||||||
\(410\) | −14.9690 | −0.739266 | ||||||||
\(411\) | −12.3729 | −0.610308 | ||||||||
\(412\) | 8.14706 | 0.401377 | ||||||||
\(413\) | 8.37149 | 0.411934 | ||||||||
\(414\) | 18.2475 | 0.896818 | ||||||||
\(415\) | 7.14842 | 0.350902 | ||||||||
\(416\) | 6.04177 | 0.296222 | ||||||||
\(417\) | −10.0620 | −0.492739 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.2643 | 1.52736 | 0.763681 | − | 0.645594i | \(-0.223390\pi\) | ||||
0.763681 | + | 0.645594i | \(0.223390\pi\) | |||||||
\(420\) | 1.62385 | 0.0792359 | ||||||||
\(421\) | 18.7303 | 0.912861 | 0.456431 | − | 0.889759i | \(-0.349128\pi\) | ||||
0.456431 | + | 0.889759i | \(0.349128\pi\) | |||||||
\(422\) | 12.9022 | 0.628071 | ||||||||
\(423\) | −9.30632 | −0.452489 | ||||||||
\(424\) | −7.95206 | −0.386186 | ||||||||
\(425\) | 5.89658 | 0.286026 | ||||||||
\(426\) | 7.93340 | 0.384375 | ||||||||
\(427\) | 20.9863 | 1.01560 | ||||||||
\(428\) | 12.5509 | 0.606672 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20.9909 | −1.01227 | ||||||||
\(431\) | −7.03559 | −0.338893 | −0.169446 | − | 0.985539i | \(-0.554198\pi\) | ||||
−0.169446 | + | 0.985539i | \(0.554198\pi\) | |||||||
\(432\) | 3.57439 | 0.171973 | ||||||||
\(433\) | 11.2785 | 0.542012 | 0.271006 | − | 0.962578i | \(-0.412644\pi\) | ||||
0.271006 | + | 0.962578i | \(0.412644\pi\) | |||||||
\(434\) | −1.98119 | −0.0950999 | ||||||||
\(435\) | 2.04565 | 0.0980812 | ||||||||
\(436\) | −3.40250 | −0.162950 | ||||||||
\(437\) | −7.04177 | −0.336854 | ||||||||
\(438\) | 0.927228 | 0.0443047 | ||||||||
\(439\) | −2.47356 | −0.118056 | −0.0590282 | − | 0.998256i | \(-0.518800\pi\) | ||||
−0.0590282 | + | 0.998256i | \(0.518800\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.9172 | 0.567484 | ||||||||
\(442\) | −15.4039 | −0.732687 | ||||||||
\(443\) | 23.0680 | 1.09599 | 0.547996 | − | 0.836481i | \(-0.315391\pi\) | ||||
0.547996 | + | 0.836481i | \(0.315391\pi\) | |||||||
\(444\) | −3.66840 | −0.174095 | ||||||||
\(445\) | 9.59456 | 0.454826 | ||||||||
\(446\) | 21.3109 | 1.00910 | ||||||||
\(447\) | −12.4311 | −0.587969 | ||||||||
\(448\) | 1.54956 | 0.0732098 | ||||||||
\(449\) | −22.8050 | −1.07623 | −0.538117 | − | 0.842870i | \(-0.680864\pi\) | ||||
−0.538117 | + | 0.842870i | \(0.680864\pi\) | |||||||
\(450\) | 5.99318 | 0.282521 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.13148 | −0.147293 | ||||||||
\(453\) | 7.81870 | 0.367355 | ||||||||
\(454\) | −20.5030 | −0.962252 | ||||||||
\(455\) | −15.3470 | −0.719479 | ||||||||
\(456\) | −0.639273 | −0.0299367 | ||||||||
\(457\) | −19.1253 | −0.894644 | −0.447322 | − | 0.894373i | \(-0.647622\pi\) | ||||
−0.447322 | + | 0.894373i | \(0.647622\pi\) | |||||||
\(458\) | 16.6406 | 0.777566 | ||||||||
\(459\) | −9.11312 | −0.425364 | ||||||||
\(460\) | 11.5434 | 0.538213 | ||||||||
\(461\) | −16.2799 | −0.758231 | −0.379115 | − | 0.925349i | \(-0.623772\pi\) | ||||
−0.379115 | + | 0.925349i | \(0.623772\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0525 | −0.978394 | −0.489197 | − | 0.872173i | \(-0.662710\pi\) | ||||
−0.489197 | + | 0.872173i | \(0.662710\pi\) | |||||||
\(464\) | 1.95206 | 0.0906219 | ||||||||
\(465\) | −1.33985 | −0.0621339 | ||||||||
\(466\) | 6.57575 | 0.304616 | ||||||||
\(467\) | −32.9909 | −1.52664 | −0.763318 | − | 0.646023i | \(-0.776431\pi\) | ||||
−0.763318 | + | 0.646023i | \(0.776431\pi\) | |||||||
\(468\) | −15.6562 | −0.723709 | ||||||||
\(469\) | 15.8384 | 0.731347 | ||||||||
\(470\) | −5.88717 | −0.271555 | ||||||||
\(471\) | −15.7533 | −0.725874 | ||||||||
\(472\) | 5.40250 | 0.248670 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.723327 | 0.0332235 | ||||||||
\(475\) | −2.31278 | −0.106118 | ||||||||
\(476\) | −3.95070 | −0.181080 | ||||||||
\(477\) | 20.6064 | 0.943502 | ||||||||
\(478\) | 3.63791 | 0.166394 | ||||||||
\(479\) | −21.2630 | −0.971530 | −0.485765 | − | 0.874090i | \(-0.661459\pi\) | ||||
−0.485765 | + | 0.874090i | \(0.661459\pi\) | |||||||
\(480\) | 1.04794 | 0.0478319 | ||||||||
\(481\) | 34.6701 | 1.58082 | ||||||||
\(482\) | 28.1498 | 1.28219 | ||||||||
\(483\) | 6.97553 | 0.317397 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.3927 | 0.744356 | ||||||||
\(486\) | −14.2321 | −0.645582 | ||||||||
\(487\) | 19.4306 | 0.880483 | 0.440241 | − | 0.897880i | \(-0.354893\pi\) | ||||
0.440241 | + | 0.897880i | \(0.354893\pi\) | |||||||
\(488\) | 13.5434 | 0.613080 | ||||||||
\(489\) | 12.1483 | 0.549363 | ||||||||
\(490\) | 7.53879 | 0.340568 | ||||||||
\(491\) | 32.2968 | 1.45754 | 0.728768 | − | 0.684761i | \(-0.240093\pi\) | ||||
0.728768 | + | 0.684761i | \(0.240093\pi\) | |||||||
\(492\) | −5.83751 | −0.263175 | ||||||||
\(493\) | −4.97688 | −0.224148 | ||||||||
\(494\) | 6.04177 | 0.271832 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.27855 | −0.0574085 | ||||||||
\(497\) | −19.2301 | −0.862587 | ||||||||
\(498\) | 2.78770 | 0.124920 | ||||||||
\(499\) | 4.26484 | 0.190920 | 0.0954602 | − | 0.995433i | \(-0.469568\pi\) | ||||
0.0954602 | + | 0.995433i | \(0.469568\pi\) | |||||||
\(500\) | 11.9877 | 0.536104 | ||||||||
\(501\) | 1.16384 | 0.0519967 | ||||||||
\(502\) | −10.8050 | −0.482250 | ||||||||
\(503\) | 22.0108 | 0.981412 | 0.490706 | − | 0.871325i | \(-0.336739\pi\) | ||||
0.490706 | + | 0.871325i | \(0.336739\pi\) | |||||||
\(504\) | −4.01542 | −0.178861 | ||||||||
\(505\) | 13.5483 | 0.602893 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.0248 | −0.667276 | ||||||||
\(508\) | −5.82057 | −0.258246 | ||||||||
\(509\) | −7.31107 | −0.324057 | −0.162029 | − | 0.986786i | \(-0.551804\pi\) | ||||
−0.162029 | + | 0.986786i | \(0.551804\pi\) | |||||||
\(510\) | −2.67180 | −0.118309 | ||||||||
\(511\) | −2.24754 | −0.0994255 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.57439 | 0.157813 | ||||||||
\(514\) | −15.0032 | −0.661764 | ||||||||
\(515\) | −13.3553 | −0.588503 | ||||||||
\(516\) | −8.18589 | −0.360364 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.89199 | 0.390691 | ||||||||
\(519\) | −6.59149 | −0.289334 | ||||||||
\(520\) | −9.90411 | −0.434324 | ||||||||
\(521\) | −31.4644 | −1.37848 | −0.689241 | − | 0.724532i | \(-0.742056\pi\) | ||||
−0.689241 | + | 0.724532i | \(0.742056\pi\) | |||||||
\(522\) | −5.05842 | −0.221401 | ||||||||
\(523\) | −4.01264 | −0.175460 | −0.0877302 | − | 0.996144i | \(-0.527961\pi\) | ||||
−0.0877302 | + | 0.996144i | \(0.527961\pi\) | |||||||
\(524\) | 14.9844 | 0.654597 | ||||||||
\(525\) | 2.29103 | 0.0999886 | ||||||||
\(526\) | −3.57575 | −0.155910 | ||||||||
\(527\) | 3.25973 | 0.141996 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26.5865 | 1.15594 | ||||||||
\(530\) | 13.0356 | 0.566230 | ||||||||
\(531\) | −13.9996 | −0.607533 | ||||||||
\(532\) | 1.54956 | 0.0671820 | ||||||||
\(533\) | 55.1703 | 2.38969 | ||||||||
\(534\) | 3.74163 | 0.161916 | ||||||||
\(535\) | −20.5744 | −0.889508 | ||||||||
\(536\) | 10.2212 | 0.441488 | ||||||||
\(537\) | −3.69992 | −0.159663 | ||||||||
\(538\) | −25.5895 | −1.10324 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.85940 | −0.252148 | ||||||||
\(541\) | −6.65298 | −0.286034 | −0.143017 | − | 0.989720i | \(-0.545680\pi\) | ||||
−0.143017 | + | 0.989720i | \(0.545680\pi\) | |||||||
\(542\) | 10.8125 | 0.464438 | ||||||||
\(543\) | −9.89390 | −0.424588 | ||||||||
\(544\) | −2.54956 | −0.109311 | ||||||||
\(545\) | 5.57762 | 0.238919 | ||||||||
\(546\) | −5.98493 | −0.256131 | ||||||||
\(547\) | 22.5622 | 0.964690 | 0.482345 | − | 0.875981i | \(-0.339785\pi\) | ||||
0.482345 | + | 0.875981i | \(0.339785\pi\) | |||||||
\(548\) | 19.3546 | 0.826785 | ||||||||
\(549\) | −35.0954 | −1.49783 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.95206 | 0.0831604 | ||||||||
\(552\) | 4.50162 | 0.191602 | ||||||||
\(553\) | −1.75330 | −0.0745579 | ||||||||
\(554\) | −0.277188 | −0.0117766 | ||||||||
\(555\) | 6.01352 | 0.255260 | ||||||||
\(556\) | 15.7398 | 0.667514 | ||||||||
\(557\) | 25.8270 | 1.09433 | 0.547163 | − | 0.837026i | \(-0.315708\pi\) | ||||
0.547163 | + | 0.837026i | \(0.315708\pi\) | |||||||
\(558\) | 3.31314 | 0.140256 | ||||||||
\(559\) | 77.3648 | 3.27218 | ||||||||
\(560\) | −2.54015 | −0.107341 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.23060 | −0.347187 | ||||||||
\(563\) | 22.0698 | 0.930132 | 0.465066 | − | 0.885276i | \(-0.346031\pi\) | ||||
0.465066 | + | 0.885276i | \(0.346031\pi\) | |||||||
\(564\) | −2.29584 | −0.0966724 | ||||||||
\(565\) | 5.13336 | 0.215962 | ||||||||
\(566\) | −20.4612 | −0.860049 | ||||||||
\(567\) | 8.50550 | 0.357197 | ||||||||
\(568\) | −12.4100 | −0.520713 | ||||||||
\(569\) | −0.275315 | −0.0115418 | −0.00577089 | − | 0.999983i | \(-0.501837\pi\) | ||||
−0.00577089 | + | 0.999983i | \(0.501837\pi\) | |||||||
\(570\) | 1.04794 | 0.0438935 | ||||||||
\(571\) | −37.4287 | −1.56634 | −0.783171 | − | 0.621807i | \(-0.786399\pi\) | ||||
−0.783171 | + | 0.621807i | \(0.786399\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.87912 | −0.412706 | ||||||||
\(574\) | 14.1498 | 0.590600 | ||||||||
\(575\) | 16.2861 | 0.679177 | ||||||||
\(576\) | −2.59133 | −0.107972 | ||||||||
\(577\) | −14.2893 | −0.594872 | −0.297436 | − | 0.954742i | \(-0.596131\pi\) | ||||
−0.297436 | + | 0.954742i | \(0.596131\pi\) | |||||||
\(578\) | −10.4997 | −0.436732 | ||||||||
\(579\) | −5.11419 | −0.212538 | ||||||||
\(580\) | −3.19995 | −0.132871 | ||||||||
\(581\) | −6.75721 | −0.280336 | ||||||||
\(582\) | 6.39273 | 0.264987 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.45044 | −0.0600196 | ||||||||
\(585\) | 25.6648 | 1.06111 | ||||||||
\(586\) | 11.5402 | 0.476719 | ||||||||
\(587\) | 0.100479 | 0.00414722 | 0.00207361 | − | 0.999998i | \(-0.499340\pi\) | ||||
0.00207361 | + | 0.999998i | \(0.499340\pi\) | |||||||
\(588\) | 2.93993 | 0.121241 | ||||||||
\(589\) | −1.27855 | −0.0526816 | ||||||||
\(590\) | −8.85617 | −0.364603 | ||||||||
\(591\) | −3.65964 | −0.150537 | ||||||||
\(592\) | 5.73839 | 0.235847 | ||||||||
\(593\) | −19.4270 | −0.797770 | −0.398885 | − | 0.917001i | \(-0.630603\pi\) | ||||
−0.398885 | + | 0.917001i | \(0.630603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.47627 | 0.265501 | ||||||||
\(596\) | 19.4456 | 0.796524 | ||||||||
\(597\) | −2.67661 | −0.109546 | ||||||||
\(598\) | −42.5447 | −1.73978 | ||||||||
\(599\) | −36.8389 | −1.50520 | −0.752598 | − | 0.658481i | \(-0.771199\pi\) | ||||
−0.752598 | + | 0.658481i | \(0.771199\pi\) | |||||||
\(600\) | 1.47850 | 0.0603595 | ||||||||
\(601\) | 2.98170 | 0.121626 | 0.0608130 | − | 0.998149i | \(-0.480631\pi\) | ||||
0.0608130 | + | 0.998149i | \(0.480631\pi\) | |||||||
\(602\) | 19.8421 | 0.808704 | ||||||||
\(603\) | −26.4865 | −1.07861 | ||||||||
\(604\) | −12.2306 | −0.497656 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.28349 | 0.214627 | ||||||||
\(607\) | 28.2118 | 1.14508 | 0.572541 | − | 0.819876i | \(-0.305958\pi\) | ||||
0.572541 | + | 0.819876i | \(0.305958\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −1.93369 | −0.0783572 | ||||||||
\(610\) | −22.2013 | −0.898905 | ||||||||
\(611\) | 21.6980 | 0.877806 | ||||||||
\(612\) | 6.60675 | 0.267062 | ||||||||
\(613\) | −33.8872 | −1.36869 | −0.684345 | − | 0.729158i | \(-0.739912\pi\) | ||||
−0.684345 | + | 0.729158i | \(0.739912\pi\) | |||||||
\(614\) | −1.75382 | −0.0707782 | ||||||||
\(615\) | 9.56928 | 0.385871 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.9346 | −0.601244 | −0.300622 | − | 0.953743i | \(-0.597194\pi\) | ||||
−0.300622 | + | 0.953743i | \(0.597194\pi\) | |||||||
\(618\) | −5.20820 | −0.209505 | ||||||||
\(619\) | −30.9909 | −1.24563 | −0.622814 | − | 0.782370i | \(-0.714011\pi\) | ||||
−0.622814 | + | 0.782370i | \(0.714011\pi\) | |||||||
\(620\) | 2.09589 | 0.0841729 | ||||||||
\(621\) | −25.1700 | −1.01004 | ||||||||
\(622\) | −17.7473 | −0.711601 | ||||||||
\(623\) | −9.06948 | −0.363361 | ||||||||
\(624\) | −3.86234 | −0.154617 | ||||||||
\(625\) | −8.08712 | −0.323485 | ||||||||
\(626\) | −16.4381 | −0.656998 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.6425 | 0.983343 | ||||||||
\(629\) | −14.6304 | −0.583351 | ||||||||
\(630\) | 6.58237 | 0.262248 | ||||||||
\(631\) | −8.54526 | −0.340181 | −0.170091 | − | 0.985428i | \(-0.554406\pi\) | ||||
−0.170091 | + | 0.985428i | \(0.554406\pi\) | |||||||
\(632\) | −1.13148 | −0.0450080 | ||||||||
\(633\) | −8.24806 | −0.327831 | ||||||||
\(634\) | 6.78204 | 0.269349 | ||||||||
\(635\) | 9.54151 | 0.378643 | ||||||||
\(636\) | 5.08354 | 0.201575 | ||||||||
\(637\) | −27.7853 | −1.10089 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32.1585 | 1.27217 | ||||||||
\(640\) | −1.63927 | −0.0647980 | ||||||||
\(641\) | −41.5776 | −1.64222 | −0.821109 | − | 0.570772i | \(-0.806644\pi\) | ||||
−0.821109 | + | 0.570772i | \(0.806644\pi\) | |||||||
\(642\) | −8.02347 | −0.316661 | ||||||||
\(643\) | −9.38090 | −0.369947 | −0.184973 | − | 0.982744i | \(-0.559220\pi\) | ||||
−0.184973 | + | 0.982744i | \(0.559220\pi\) | |||||||
\(644\) | −10.9116 | −0.429979 | ||||||||
\(645\) | 13.4189 | 0.528369 | ||||||||
\(646\) | −2.54956 | −0.100311 | ||||||||
\(647\) | −44.9256 | −1.76621 | −0.883105 | − | 0.469176i | \(-0.844551\pi\) | ||||
−0.883105 | + | 0.469176i | \(0.844551\pi\) | |||||||
\(648\) | 5.48898 | 0.215627 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −13.9733 | −0.548078 | ||||||||
\(651\) | 1.26652 | 0.0496388 | ||||||||
\(652\) | −19.0032 | −0.744224 | ||||||||
\(653\) | 4.78618 | 0.187298 | 0.0936488 | − | 0.995605i | \(-0.470147\pi\) | ||||
0.0936488 | + | 0.995605i | \(0.470147\pi\) | |||||||
\(654\) | 2.17513 | 0.0850541 | ||||||||
\(655\) | −24.5636 | −0.959778 | ||||||||
\(656\) | 9.13148 | 0.356524 | ||||||||
\(657\) | 3.75857 | 0.146636 | ||||||||
\(658\) | 5.56498 | 0.216946 | ||||||||
\(659\) | 32.1934 | 1.25408 | 0.627039 | − | 0.778988i | \(-0.284267\pi\) | ||||
0.627039 | + | 0.778988i | \(0.284267\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.1684 | −1.64016 | −0.820081 | − | 0.572247i | \(-0.806072\pi\) | ||||
−0.820081 | + | 0.572247i | \(0.806072\pi\) | |||||||
\(662\) | −7.61616 | −0.296010 | ||||||||
\(663\) | 9.84728 | 0.382436 | ||||||||
\(664\) | −4.36073 | −0.169229 | ||||||||
\(665\) | −2.54015 | −0.0985029 | ||||||||
\(666\) | −14.8701 | −0.576203 | ||||||||
\(667\) | −13.7459 | −0.532244 | ||||||||
\(668\) | −1.82057 | −0.0704401 | ||||||||
\(669\) | −13.6235 | −0.526715 | ||||||||
\(670\) | −16.7553 | −0.647315 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.990593 | −0.0382129 | ||||||||
\(673\) | −37.4009 | −1.44170 | −0.720850 | − | 0.693092i | \(-0.756248\pi\) | ||||
−0.720850 | + | 0.693092i | \(0.756248\pi\) | |||||||
\(674\) | −20.0200 | −0.771142 | ||||||||
\(675\) | −8.26678 | −0.318189 | ||||||||
\(676\) | 23.5030 | 0.903961 | ||||||||
\(677\) | −40.3742 | −1.55171 | −0.775853 | − | 0.630913i | \(-0.782680\pi\) | ||||
−0.775853 | + | 0.630913i | \(0.782680\pi\) | |||||||
\(678\) | 2.00187 | 0.0768815 | ||||||||
\(679\) | −15.4956 | −0.594667 | ||||||||
\(680\) | 4.17943 | 0.160274 | ||||||||
\(681\) | 13.1070 | 0.502262 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.06472 | −0.308588 | −0.154294 | − | 0.988025i | \(-0.549310\pi\) | ||||
−0.154294 | + | 0.988025i | \(0.549310\pi\) | |||||||
\(684\) | −2.59133 | −0.0990820 | ||||||||
\(685\) | −31.7274 | −1.21224 | ||||||||
\(686\) | −17.9731 | −0.686218 | ||||||||
\(687\) | −10.6379 | −0.405862 | ||||||||
\(688\) | 12.8050 | 0.488186 | ||||||||
\(689\) | −48.0445 | −1.83035 | ||||||||
\(690\) | −7.37938 | −0.280928 | ||||||||
\(691\) | 27.8402 | 1.05909 | 0.529546 | − | 0.848281i | \(-0.322362\pi\) | ||||
0.529546 | + | 0.848281i | \(0.322362\pi\) | |||||||
\(692\) | 10.3109 | 0.391962 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.3296 | −0.619862 | ||||||||
\(695\) | −25.8018 | −0.978717 | ||||||||
\(696\) | −1.24790 | −0.0473014 | ||||||||
\(697\) | −23.2813 | −0.881841 | ||||||||
\(698\) | −26.9995 | −1.02195 | ||||||||
\(699\) | −4.20370 | −0.158999 | ||||||||
\(700\) | −3.58380 | −0.135455 | ||||||||
\(701\) | −36.2010 | −1.36729 | −0.683646 | − | 0.729814i | \(-0.739607\pi\) | ||||
−0.683646 | + | 0.729814i | \(0.739607\pi\) | |||||||
\(702\) | 21.5956 | 0.815075 | ||||||||
\(703\) | 5.73839 | 0.216428 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.76351 | 0.141742 | ||||||||
\(706\) | 14.0525 | 0.528874 | ||||||||
\(707\) | −12.8069 | −0.481652 | ||||||||
\(708\) | −3.45367 | −0.129797 | ||||||||
\(709\) | 22.7091 | 0.852858 | 0.426429 | − | 0.904521i | \(-0.359771\pi\) | ||||
0.426429 | + | 0.904521i | \(0.359771\pi\) | |||||||
\(710\) | 20.3434 | 0.763475 | ||||||||
\(711\) | 2.93204 | 0.109960 | ||||||||
\(712\) | −5.85294 | −0.219348 | ||||||||
\(713\) | 9.00323 | 0.337174 | ||||||||
\(714\) | 2.52558 | 0.0945173 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.78770 | 0.216296 | ||||||||
\(717\) | −2.32562 | −0.0868520 | ||||||||
\(718\) | 25.3546 | 0.946223 | ||||||||
\(719\) | 22.2859 | 0.831125 | 0.415562 | − | 0.909565i | \(-0.363585\pi\) | ||||
0.415562 | + | 0.909565i | \(0.363585\pi\) | |||||||
\(720\) | 4.24790 | 0.158310 | ||||||||
\(721\) | 12.6244 | 0.470156 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −17.9954 | −0.669256 | ||||||||
\(724\) | 15.4768 | 0.575190 | ||||||||
\(725\) | −4.51468 | −0.167671 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.03100 | −0.149502 | −0.0747508 | − | 0.997202i | \(-0.523816\pi\) | ||||
−0.0747508 | + | 0.997202i | \(0.523816\pi\) | |||||||
\(728\) | 9.36209 | 0.346982 | ||||||||
\(729\) | −7.36871 | −0.272915 | ||||||||
\(730\) | 2.37767 | 0.0880014 | ||||||||
\(731\) | −32.6471 | −1.20750 | ||||||||
\(732\) | −8.65793 | −0.320006 | ||||||||
\(733\) | −36.0712 | −1.33232 | −0.666160 | − | 0.745809i | \(-0.732063\pi\) | ||||
−0.666160 | + | 0.745809i | \(0.732063\pi\) | |||||||
\(734\) | 19.3931 | 0.715812 | ||||||||
\(735\) | −4.81935 | −0.177764 | ||||||||
\(736\) | −7.04177 | −0.259563 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −23.6627 | −0.871035 | ||||||||
\(739\) | 38.6388 | 1.42135 | 0.710675 | − | 0.703521i | \(-0.248390\pi\) | ||||
0.710675 | + | 0.703521i | \(0.248390\pi\) | |||||||
\(740\) | −9.40680 | −0.345801 | ||||||||
\(741\) | −3.86234 | −0.141887 | ||||||||
\(742\) | −12.3222 | −0.452362 | ||||||||
\(743\) | 50.8416 | 1.86520 | 0.932599 | − | 0.360915i | \(-0.117536\pi\) | ||||
0.932599 | + | 0.360915i | \(0.117536\pi\) | |||||||
\(744\) | 0.817341 | 0.0299652 | ||||||||
\(745\) | −31.8767 | −1.16787 | ||||||||
\(746\) | −35.3018 | −1.29249 | ||||||||
\(747\) | 11.3001 | 0.413448 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.4484 | 0.710629 | ||||||||
\(750\) | −7.66339 | −0.279827 | ||||||||
\(751\) | 39.4521 | 1.43963 | 0.719814 | − | 0.694167i | \(-0.244227\pi\) | ||||
0.719814 | + | 0.694167i | \(0.244227\pi\) | |||||||
\(752\) | 3.59133 | 0.130962 | ||||||||
\(753\) | 6.90734 | 0.251718 | ||||||||
\(754\) | 11.7939 | 0.429507 | ||||||||
\(755\) | 20.0493 | 0.729669 | ||||||||
\(756\) | 5.53873 | 0.201442 | ||||||||
\(757\) | 16.5402 | 0.601162 | 0.300581 | − | 0.953756i | \(-0.402819\pi\) | ||||
0.300581 | + | 0.953756i | \(0.402819\pi\) | |||||||
\(758\) | −5.17002 | −0.187784 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.63927 | −0.0594627 | ||||||||
\(761\) | −23.5341 | −0.853112 | −0.426556 | − | 0.904461i | \(-0.640273\pi\) | ||||
−0.426556 | + | 0.904461i | \(0.640273\pi\) | |||||||
\(762\) | 3.72094 | 0.134795 | ||||||||
\(763\) | −5.27237 | −0.190873 | ||||||||
\(764\) | 15.4537 | 0.559094 | ||||||||
\(765\) | −10.8303 | −0.391569 | ||||||||
\(766\) | −5.16759 | −0.186713 | ||||||||
\(767\) | 32.6406 | 1.17858 | ||||||||
\(768\) | −0.639273 | −0.0230678 | ||||||||
\(769\) | −0.0803060 | −0.00289591 | −0.00144795 | − | 0.999999i | \(-0.500461\pi\) | ||||
−0.00144795 | + | 0.999999i | \(0.500461\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.59117 | 0.345417 | ||||||||
\(772\) | 8.00000 | 0.287926 | ||||||||
\(773\) | 16.2541 | 0.584618 | 0.292309 | − | 0.956324i | \(-0.405576\pi\) | ||||
0.292309 | + | 0.956324i | \(0.405576\pi\) | |||||||
\(774\) | −33.1820 | −1.19270 | ||||||||
\(775\) | 2.95700 | 0.106219 | ||||||||
\(776\) | −10.0000 | −0.358979 | ||||||||
\(777\) | −5.68441 | −0.203927 | ||||||||
\(778\) | 4.91782 | 0.176312 | ||||||||
\(779\) | 9.13148 | 0.327169 | ||||||||
\(780\) | 6.33144 | 0.226702 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 17.9534 | 0.642013 | ||||||||
\(783\) | 6.97741 | 0.249352 | ||||||||
\(784\) | −4.59886 | −0.164245 | ||||||||
\(785\) | −40.3958 | −1.44179 | ||||||||
\(786\) | −9.57914 | −0.341677 | ||||||||
\(787\) | 11.7726 | 0.419649 | 0.209824 | − | 0.977739i | \(-0.432711\pi\) | ||||
0.209824 | + | 0.977739i | \(0.432711\pi\) | |||||||
\(788\) | 5.72469 | 0.203933 | ||||||||
\(789\) | 2.28588 | 0.0813795 | ||||||||
\(790\) | 1.85481 | 0.0659911 | ||||||||
\(791\) | −4.85242 | −0.172532 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 81.8260 | 2.90573 | ||||||||
\(794\) | −7.54151 | −0.267638 | ||||||||
\(795\) | −8.33331 | −0.295552 | ||||||||
\(796\) | 4.18696 | 0.148403 | ||||||||
\(797\) | 12.5003 | 0.442782 | 0.221391 | − | 0.975185i | \(-0.428940\pi\) | ||||
0.221391 | + | 0.975185i | \(0.428940\pi\) | |||||||
\(798\) | −0.990593 | −0.0350666 | ||||||||
\(799\) | −9.15631 | −0.323927 | ||||||||
\(800\) | −2.31278 | −0.0817692 | ||||||||
\(801\) | 15.1669 | 0.535895 | ||||||||
\(802\) | 4.03236 | 0.142388 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −6.53414 | −0.230441 | ||||||||
\(805\) | 17.8872 | 0.630440 | ||||||||
\(806\) | −7.72469 | −0.272090 | ||||||||
\(807\) | 16.3587 | 0.575852 | ||||||||
\(808\) | −8.26484 | −0.290756 | ||||||||
\(809\) | −6.86988 | −0.241532 | −0.120766 | − | 0.992681i | \(-0.538535\pi\) | ||||
−0.120766 | + | 0.992681i | \(0.538535\pi\) | |||||||
\(810\) | −8.99793 | −0.316155 | ||||||||
\(811\) | −34.8255 | −1.22289 | −0.611445 | − | 0.791287i | \(-0.709411\pi\) | ||||
−0.611445 | + | 0.791287i | \(0.709411\pi\) | |||||||
\(812\) | 3.02483 | 0.106151 | ||||||||
\(813\) | −6.91216 | −0.242420 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.1515 | 1.09119 | ||||||||
\(816\) | 1.62987 | 0.0570567 | ||||||||
\(817\) | 12.8050 | 0.447990 | ||||||||
\(818\) | −0.358853 | −0.0125470 | ||||||||
\(819\) | −24.2602 | −0.847722 | ||||||||
\(820\) | −14.9690 | −0.522740 | ||||||||
\(821\) | −8.45933 | −0.295233 | −0.147616 | − | 0.989045i | \(-0.547160\pi\) | ||||
−0.147616 | + | 0.989045i | \(0.547160\pi\) | |||||||
\(822\) | −12.3729 | −0.431553 | ||||||||
\(823\) | −7.47627 | −0.260606 | −0.130303 | − | 0.991474i | \(-0.541595\pi\) | ||||
−0.130303 | + | 0.991474i | \(0.541595\pi\) | |||||||
\(824\) | 8.14706 | 0.283816 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.37149 | 0.291281 | ||||||||
\(827\) | 16.4386 | 0.571626 | 0.285813 | − | 0.958285i | \(-0.407736\pi\) | ||||
0.285813 | + | 0.958285i | \(0.407736\pi\) | |||||||
\(828\) | 18.2475 | 0.634146 | ||||||||
\(829\) | 7.49974 | 0.260477 | 0.130238 | − | 0.991483i | \(-0.458426\pi\) | ||||
0.130238 | + | 0.991483i | \(0.458426\pi\) | |||||||
\(830\) | 7.14842 | 0.248125 | ||||||||
\(831\) | 0.177199 | 0.00614697 | ||||||||
\(832\) | 6.04177 | 0.209461 | ||||||||
\(833\) | 11.7251 | 0.406250 | ||||||||
\(834\) | −10.0620 | −0.348419 | ||||||||
\(835\) | 2.98442 | 0.103280 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.57002 | −0.157963 | ||||||||
\(838\) | 31.2643 | 1.08001 | ||||||||
\(839\) | 5.60879 | 0.193637 | 0.0968184 | − | 0.995302i | \(-0.469133\pi\) | ||||
0.0968184 | + | 0.995302i | \(0.469133\pi\) | |||||||
\(840\) | 1.62385 | 0.0560282 | ||||||||
\(841\) | −25.1895 | −0.868603 | ||||||||
\(842\) | 18.7303 | 0.645490 | ||||||||
\(843\) | 5.26161 | 0.181219 | ||||||||
\(844\) | 12.9022 | 0.444113 | ||||||||
\(845\) | −38.5278 | −1.32540 | ||||||||
\(846\) | −9.30632 | −0.319958 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.95206 | −0.273075 | ||||||||
\(849\) | 13.0803 | 0.448915 | ||||||||
\(850\) | 5.89658 | 0.202251 | ||||||||
\(851\) | −40.4084 | −1.38518 | ||||||||
\(852\) | 7.93340 | 0.271794 | ||||||||
\(853\) | −5.80176 | −0.198648 | −0.0993242 | − | 0.995055i | \(-0.531668\pi\) | ||||
−0.0993242 | + | 0.995055i | \(0.531668\pi\) | |||||||
\(854\) | 20.9863 | 0.718136 | ||||||||
\(855\) | 4.24790 | 0.145275 | ||||||||
\(856\) | 12.5509 | 0.428982 | ||||||||
\(857\) | −18.6444 | −0.636880 | −0.318440 | − | 0.947943i | \(-0.603159\pi\) | ||||
−0.318440 | + | 0.947943i | \(0.603159\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.4502 | −1.14131 | −0.570653 | − | 0.821191i | \(-0.693310\pi\) | ||||
−0.570653 | + | 0.821191i | \(0.693310\pi\) | |||||||
\(860\) | −20.9909 | −0.715783 | ||||||||
\(861\) | −9.04558 | −0.308273 | ||||||||
\(862\) | −7.03559 | −0.239633 | ||||||||
\(863\) | −29.9256 | −1.01868 | −0.509340 | − | 0.860565i | \(-0.670111\pi\) | ||||
−0.509340 | + | 0.860565i | \(0.670111\pi\) | |||||||
\(864\) | 3.57439 | 0.121603 | ||||||||
\(865\) | −16.9024 | −0.574699 | ||||||||
\(866\) | 11.2785 | 0.383261 | ||||||||
\(867\) | 6.71221 | 0.227958 | ||||||||
\(868\) | −1.98119 | −0.0672458 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 2.04565 | 0.0693539 | ||||||||
\(871\) | 61.7541 | 2.09246 | ||||||||
\(872\) | −3.40250 | −0.115223 | ||||||||
\(873\) | 25.9133 | 0.877032 | ||||||||
\(874\) | −7.04177 | −0.238191 | ||||||||
\(875\) | 18.5756 | 0.627969 | ||||||||
\(876\) | 0.927228 | 0.0313281 | ||||||||
\(877\) | −15.6024 | −0.526857 | −0.263429 | − | 0.964679i | \(-0.584853\pi\) | ||||
−0.263429 | + | 0.964679i | \(0.584853\pi\) | |||||||
\(878\) | −2.47356 | −0.0834785 | ||||||||
\(879\) | −7.37731 | −0.248831 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.93799 | −0.301129 | −0.150564 | − | 0.988600i | \(-0.548109\pi\) | ||||
−0.150564 | + | 0.988600i | \(0.548109\pi\) | |||||||
\(882\) | 11.9172 | 0.401272 | ||||||||
\(883\) | 32.7196 | 1.10110 | 0.550551 | − | 0.834802i | \(-0.314418\pi\) | ||||
0.550551 | + | 0.834802i | \(0.314418\pi\) | |||||||
\(884\) | −15.4039 | −0.518088 | ||||||||
\(885\) | 5.66151 | 0.190310 | ||||||||
\(886\) | 23.0680 | 0.774983 | ||||||||
\(887\) | 56.4812 | 1.89645 | 0.948227 | − | 0.317594i | \(-0.102875\pi\) | ||||
0.948227 | + | 0.317594i | \(0.102875\pi\) | |||||||
\(888\) | −3.66840 | −0.123104 | ||||||||
\(889\) | −9.01933 | −0.302499 | ||||||||
\(890\) | 9.59456 | 0.321610 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.3109 | 0.713542 | ||||||||
\(893\) | 3.59133 | 0.120179 | ||||||||
\(894\) | −12.4311 | −0.415757 | ||||||||
\(895\) | −9.48762 | −0.317136 | ||||||||
\(896\) | 1.54956 | 0.0517672 | ||||||||
\(897\) | 27.1977 | 0.908106 | ||||||||
\(898\) | −22.8050 | −0.761012 | ||||||||
\(899\) | −2.49580 | −0.0832394 | ||||||||
\(900\) | 5.99318 | 0.199773 | ||||||||
\(901\) | 20.2742 | 0.675433 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.6845 | −0.422115 | ||||||||
\(904\) | −3.13148 | −0.104152 | ||||||||
\(905\) | −25.3707 | −0.843350 | ||||||||
\(906\) | 7.81870 | 0.259759 | ||||||||
\(907\) | −5.76135 | −0.191302 | −0.0956512 | − | 0.995415i | \(-0.530493\pi\) | ||||
−0.0956512 | + | 0.995415i | \(0.530493\pi\) | |||||||
\(908\) | −20.5030 | −0.680415 | ||||||||
\(909\) | 21.4169 | 0.710354 | ||||||||
\(910\) | −15.3470 | −0.508749 | ||||||||
\(911\) | 9.78821 | 0.324298 | 0.162149 | − | 0.986766i | \(-0.448157\pi\) | ||||
0.162149 | + | 0.986766i | \(0.448157\pi\) | |||||||
\(912\) | −0.639273 | −0.0211685 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −19.1253 | −0.632609 | ||||||||
\(915\) | 14.1927 | 0.469197 | ||||||||
\(916\) | 16.6406 | 0.549822 | ||||||||
\(917\) | 23.2193 | 0.766767 | ||||||||
\(918\) | −9.11312 | −0.300778 | ||||||||
\(919\) | −33.1748 | −1.09433 | −0.547167 | − | 0.837023i | \(-0.684294\pi\) | ||||
−0.547167 | + | 0.837023i | \(0.684294\pi\) | |||||||
\(920\) | 11.5434 | 0.380574 | ||||||||
\(921\) | 1.12117 | 0.0369437 | ||||||||
\(922\) | −16.2799 | −0.536150 | ||||||||
\(923\) | −74.9785 | −2.46795 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.2717 | −0.436369 | ||||||||
\(926\) | −21.0525 | −0.691829 | ||||||||
\(927\) | −21.1117 | −0.693400 | ||||||||
\(928\) | 1.95206 | 0.0640794 | ||||||||
\(929\) | −12.5415 | −0.411474 | −0.205737 | − | 0.978607i | \(-0.565959\pi\) | ||||
−0.205737 | + | 0.978607i | \(0.565959\pi\) | |||||||
\(930\) | −1.33985 | −0.0439353 | ||||||||
\(931\) | −4.59886 | −0.150722 | ||||||||
\(932\) | 6.57575 | 0.215396 | ||||||||
\(933\) | 11.3454 | 0.371431 | ||||||||
\(934\) | −32.9909 | −1.07949 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.6562 | −0.511739 | ||||||||
\(937\) | 52.2470 | 1.70684 | 0.853418 | − | 0.521227i | \(-0.174526\pi\) | ||||
0.853418 | + | 0.521227i | \(0.174526\pi\) | |||||||
\(938\) | 15.8384 | 0.517141 | ||||||||
\(939\) | 10.5084 | 0.342930 | ||||||||
\(940\) | −5.88717 | −0.192018 | ||||||||
\(941\) | 29.4189 | 0.959029 | 0.479515 | − | 0.877534i | \(-0.340813\pi\) | ||||
0.479515 | + | 0.877534i | \(0.340813\pi\) | |||||||
\(942\) | −15.7533 | −0.513270 | ||||||||
\(943\) | −64.3018 | −2.09395 | ||||||||
\(944\) | 5.40250 | 0.175836 | ||||||||
\(945\) | −9.07949 | −0.295356 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.4370 | −1.54150 | −0.770748 | − | 0.637140i | \(-0.780117\pi\) | ||||
−0.770748 | + | 0.637140i | \(0.780117\pi\) | |||||||
\(948\) | 0.723327 | 0.0234926 | ||||||||
\(949\) | −8.76322 | −0.284466 | ||||||||
\(950\) | −2.31278 | −0.0750366 | ||||||||
\(951\) | −4.33558 | −0.140591 | ||||||||
\(952\) | −3.95070 | −0.128043 | ||||||||
\(953\) | 42.4785 | 1.37601 | 0.688007 | − | 0.725704i | \(-0.258486\pi\) | ||||
0.688007 | + | 0.725704i | \(0.258486\pi\) | |||||||
\(954\) | 20.6064 | 0.667157 | ||||||||
\(955\) | −25.3328 | −0.819750 | ||||||||
\(956\) | 3.63791 | 0.117659 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.2630 | −0.686975 | ||||||||
\(959\) | 29.9910 | 0.968461 | ||||||||
\(960\) | 1.04794 | 0.0338222 | ||||||||
\(961\) | −29.3653 | −0.947268 | ||||||||
\(962\) | 34.6701 | 1.11781 | ||||||||
\(963\) | −32.5236 | −1.04806 | ||||||||
\(964\) | 28.1498 | 0.906643 | ||||||||
\(965\) | −13.1142 | −0.422161 | ||||||||
\(966\) | 6.97553 | 0.224434 | ||||||||
\(967\) | 40.6096 | 1.30592 | 0.652959 | − | 0.757393i | \(-0.273527\pi\) | ||||
0.652959 | + | 0.757393i | \(0.273527\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.62987 | 0.0523588 | ||||||||
\(970\) | 16.3927 | 0.526339 | ||||||||
\(971\) | 35.5000 | 1.13925 | 0.569625 | − | 0.821905i | \(-0.307088\pi\) | ||||
0.569625 | + | 0.821905i | \(0.307088\pi\) | |||||||
\(972\) | −14.2321 | −0.456496 | ||||||||
\(973\) | 24.3897 | 0.781898 | ||||||||
\(974\) | 19.4306 | 0.622595 | ||||||||
\(975\) | 8.93276 | 0.286077 | ||||||||
\(976\) | 13.5434 | 0.433513 | ||||||||
\(977\) | 22.0986 | 0.706997 | 0.353499 | − | 0.935435i | \(-0.384992\pi\) | ||||
0.353499 | + | 0.935435i | \(0.384992\pi\) | |||||||
\(978\) | 12.1483 | 0.388459 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 7.53879 | 0.240818 | ||||||||
\(981\) | 8.81699 | 0.281505 | ||||||||
\(982\) | 32.2968 | 1.03063 | ||||||||
\(983\) | −26.1310 | −0.833448 | −0.416724 | − | 0.909033i | \(-0.636822\pi\) | ||||
−0.416724 | + | 0.909033i | \(0.636822\pi\) | |||||||
\(984\) | −5.83751 | −0.186093 | ||||||||
\(985\) | −9.38433 | −0.299009 | ||||||||
\(986\) | −4.97688 | −0.158496 | ||||||||
\(987\) | −3.55754 | −0.113238 | ||||||||
\(988\) | 6.04177 | 0.192214 | ||||||||
\(989\) | −90.1698 | −2.86723 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.0168 | −0.349960 | −0.174980 | − | 0.984572i | \(-0.555986\pi\) | ||||
−0.174980 | + | 0.984572i | \(0.555986\pi\) | |||||||
\(992\) | −1.27855 | −0.0405939 | ||||||||
\(993\) | 4.86881 | 0.154507 | ||||||||
\(994\) | −19.2301 | −0.609941 | ||||||||
\(995\) | −6.86357 | −0.217590 | ||||||||
\(996\) | 2.78770 | 0.0883316 | ||||||||
\(997\) | −11.0945 | −0.351367 | −0.175684 | − | 0.984447i | \(-0.556214\pi\) | ||||
−0.175684 | + | 0.984447i | \(0.556214\pi\) | |||||||
\(998\) | 4.26484 | 0.135001 | ||||||||
\(999\) | 20.5112 | 0.648947 |
(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 | 4598.2.a.bv.1.2 | yes | 4 | |
11.10 | odd | 2 | 4598.2.a.bs.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.bs.1.2 | ✓ | 4 | 11.10 | odd | 2 | ||
4598.2.a.bv.1.2 | yes | 4 | 1.1 | even | 1 | trivial |