Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} - 4673 x^{11} - 15053 x^{10} + 16875 x^{9} + 20141 x^{8} - 28019 x^{7} - 11589 x^{6} + \cdots - 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 671) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.488177\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.488177 | −0.345194 | −0.172597 | − | 0.984993i | \(-0.555216\pi\) | ||||
−0.172597 | + | 0.984993i | \(0.555216\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.76168 | −0.880841 | ||||||||
\(5\) | −1.92726 | −0.861899 | −0.430949 | − | 0.902376i | \(-0.641821\pi\) | ||||
−0.430949 | + | 0.902376i | \(0.641821\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.259128 | 0.0979411 | 0.0489706 | − | 0.998800i | \(-0.484406\pi\) | ||||
0.0489706 | + | 0.998800i | \(0.484406\pi\) | |||||||
\(8\) | 1.83637 | 0.649254 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.940847 | 0.297522 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.14915 | −0.596067 | −0.298033 | − | 0.954555i | \(-0.596331\pi\) | ||||
−0.298033 | + | 0.954555i | \(0.596331\pi\) | |||||||
\(14\) | −0.126500 | −0.0338086 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.62689 | 0.656723 | ||||||||
\(17\) | −4.30678 | −1.04455 | −0.522274 | − | 0.852778i | \(-0.674916\pi\) | ||||
−0.522274 | + | 0.852778i | \(0.674916\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.44254 | 1.70744 | 0.853718 | − | 0.520736i | \(-0.174342\pi\) | ||||
0.853718 | + | 0.520736i | \(0.174342\pi\) | |||||||
\(20\) | 3.39523 | 0.759196 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.488177 | 0.104080 | ||||||||
\(23\) | −3.82807 | −0.798208 | −0.399104 | − | 0.916906i | \(-0.630679\pi\) | ||||
−0.399104 | + | 0.916906i | \(0.630679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.28565 | −0.257130 | ||||||||
\(26\) | 1.04917 | 0.205758 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.456501 | −0.0862706 | ||||||||
\(29\) | 3.58210 | 0.665179 | 0.332589 | − | 0.943072i | \(-0.392078\pi\) | ||||
0.332589 | + | 0.943072i | \(0.392078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.02405 | −1.44116 | −0.720581 | − | 0.693371i | \(-0.756125\pi\) | ||||
−0.720581 | + | 0.693371i | \(0.756125\pi\) | |||||||
\(32\) | −4.95513 | −0.875951 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.10248 | 0.360571 | ||||||||
\(35\) | −0.499408 | −0.0844153 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.82822 | −1.12255 | −0.561276 | − | 0.827628i | \(-0.689690\pi\) | ||||
−0.561276 | + | 0.827628i | \(0.689690\pi\) | |||||||
\(38\) | −3.63328 | −0.589396 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.53917 | −0.559592 | ||||||||
\(41\) | −5.88081 | −0.918429 | −0.459214 | − | 0.888326i | \(-0.651869\pi\) | ||||
−0.459214 | + | 0.888326i | \(0.651869\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.55874 | 1.15270 | 0.576348 | − | 0.817204i | \(-0.304477\pi\) | ||||
0.576348 | + | 0.817204i | \(0.304477\pi\) | |||||||
\(44\) | 1.76168 | 0.265584 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.86878 | 0.275536 | ||||||||
\(47\) | 13.1755 | 1.92184 | 0.960922 | − | 0.276820i | \(-0.0892807\pi\) | ||||
0.960922 | + | 0.276820i | \(0.0892807\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.93285 | −0.990408 | ||||||||
\(50\) | 0.627626 | 0.0887597 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.78612 | 0.525040 | ||||||||
\(53\) | 10.1230 | 1.39050 | 0.695249 | − | 0.718769i | \(-0.255294\pi\) | ||||
0.695249 | + | 0.718769i | \(0.255294\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.92726 | 0.259872 | ||||||||
\(56\) | 0.475854 | 0.0635887 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.74870 | −0.229616 | ||||||||
\(59\) | −5.99815 | −0.780892 | −0.390446 | − | 0.920626i | \(-0.627679\pi\) | ||||
−0.390446 | + | 0.920626i | \(0.627679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 3.91716 | 0.497480 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.83480 | −0.354350 | ||||||||
\(65\) | 4.14198 | 0.513749 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73926 | −0.212484 | −0.106242 | − | 0.994340i | \(-0.533882\pi\) | ||||
−0.106242 | + | 0.994340i | \(0.533882\pi\) | |||||||
\(68\) | 7.58719 | 0.920082 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.243800 | 0.0291396 | ||||||||
\(71\) | −11.3363 | −1.34537 | −0.672687 | − | 0.739927i | \(-0.734860\pi\) | ||||
−0.672687 | + | 0.739927i | \(0.734860\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.24305 | −0.145488 | −0.0727440 | − | 0.997351i | \(-0.523176\pi\) | ||||
−0.0727440 | + | 0.997351i | \(0.523176\pi\) | |||||||
\(74\) | 3.33338 | 0.387498 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.1114 | −1.50398 | ||||||||
\(77\) | −0.259128 | −0.0295304 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.01217 | −1.01395 | −0.506974 | − | 0.861961i | \(-0.669236\pi\) | ||||
−0.506974 | + | 0.861961i | \(0.669236\pi\) | |||||||
\(80\) | −5.06272 | −0.566029 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.87088 | 0.317036 | ||||||||
\(83\) | 13.5489 | 1.48719 | 0.743595 | − | 0.668631i | \(-0.233119\pi\) | ||||
0.743595 | + | 0.668631i | \(0.233119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.30031 | 0.900295 | ||||||||
\(86\) | −3.69001 | −0.397903 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.83637 | −0.195758 | ||||||||
\(89\) | −5.65666 | −0.599605 | −0.299803 | − | 0.954001i | \(-0.596921\pi\) | ||||
−0.299803 | + | 0.954001i | \(0.596921\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.556904 | −0.0583794 | ||||||||
\(92\) | 6.74385 | 0.703095 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.43198 | −0.663408 | ||||||||
\(95\) | −14.3437 | −1.47164 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.0543 | −1.73161 | −0.865803 | − | 0.500385i | \(-0.833192\pi\) | ||||
−0.865803 | + | 0.500385i | \(0.833192\pi\) | |||||||
\(98\) | 3.38446 | 0.341882 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.26491 | 0.226491 | ||||||||
\(101\) | −17.3123 | −1.72264 | −0.861321 | − | 0.508062i | \(-0.830362\pi\) | ||||
−0.861321 | + | 0.508062i | \(0.830362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.07195 | 0.105622 | 0.0528112 | − | 0.998605i | \(-0.483182\pi\) | ||||
0.0528112 | + | 0.998605i | \(0.483182\pi\) | |||||||
\(104\) | −3.94663 | −0.386999 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.94181 | −0.479991 | ||||||||
\(107\) | 7.23733 | 0.699660 | 0.349830 | − | 0.936813i | \(-0.386239\pi\) | ||||
0.349830 | + | 0.936813i | \(0.386239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0213 | 1.15143 | 0.575714 | − | 0.817651i | \(-0.304724\pi\) | ||||
0.575714 | + | 0.817651i | \(0.304724\pi\) | |||||||
\(110\) | −0.940847 | −0.0897063 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.680701 | 0.0643202 | ||||||||
\(113\) | −18.4118 | −1.73204 | −0.866018 | − | 0.500012i | \(-0.833329\pi\) | ||||
−0.866018 | + | 0.500012i | \(0.833329\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.37770 | 0.687975 | ||||||||
\(116\) | −6.31052 | −0.585917 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.92816 | 0.269559 | ||||||||
\(119\) | −1.11601 | −0.102304 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.488177 | 0.0441975 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.1358 | 1.26943 | ||||||||
\(125\) | 12.1141 | 1.08352 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.91532 | −0.702371 | −0.351185 | − | 0.936306i | \(-0.614221\pi\) | ||||
−0.351185 | + | 0.936306i | \(0.614221\pi\) | |||||||
\(128\) | 11.2941 | 0.998270 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.02202 | −0.177343 | ||||||||
\(131\) | 13.2420 | 1.15695 | 0.578477 | − | 0.815698i | \(-0.303647\pi\) | ||||
0.578477 | + | 0.815698i | \(0.303647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.92857 | 0.167228 | ||||||||
\(134\) | 0.849067 | 0.0733482 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.90884 | −0.678178 | ||||||||
\(137\) | −7.41315 | −0.633349 | −0.316674 | − | 0.948534i | \(-0.602566\pi\) | ||||
−0.316674 | + | 0.948534i | \(0.602566\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.45579 | −0.293116 | −0.146558 | − | 0.989202i | \(-0.546819\pi\) | ||||
−0.146558 | + | 0.989202i | \(0.546819\pi\) | |||||||
\(140\) | 0.879798 | 0.0743565 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.53414 | 0.464414 | ||||||||
\(143\) | 2.14915 | 0.179721 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.90365 | −0.573317 | ||||||||
\(146\) | 0.606829 | 0.0502215 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.0292 | 0.988791 | ||||||||
\(149\) | 8.16171 | 0.668634 | 0.334317 | − | 0.942461i | \(-0.391494\pi\) | ||||
0.334317 | + | 0.942461i | \(0.391494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.09846 | 0.414906 | 0.207453 | − | 0.978245i | \(-0.433483\pi\) | ||||
0.207453 | + | 0.978245i | \(0.433483\pi\) | |||||||
\(152\) | 13.6672 | 1.10856 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.126500 | 0.0101937 | ||||||||
\(155\) | 15.4645 | 1.24214 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.46388 | 0.595682 | 0.297841 | − | 0.954615i | \(-0.403733\pi\) | ||||
0.297841 | + | 0.954615i | \(0.403733\pi\) | |||||||
\(158\) | 4.39954 | 0.350009 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.54984 | 0.754981 | ||||||||
\(161\) | −0.991960 | −0.0781774 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6957 | 0.916077 | 0.458038 | − | 0.888932i | \(-0.348552\pi\) | ||||
0.458038 | + | 0.888932i | \(0.348552\pi\) | |||||||
\(164\) | 10.3601 | 0.808990 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.61429 | −0.513368 | ||||||||
\(167\) | −10.6559 | −0.824581 | −0.412291 | − | 0.911052i | \(-0.635271\pi\) | ||||
−0.412291 | + | 0.911052i | \(0.635271\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.38116 | −0.644705 | ||||||||
\(170\) | −4.05203 | −0.310776 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.3161 | −1.01534 | ||||||||
\(173\) | 2.15144 | 0.163571 | 0.0817855 | − | 0.996650i | \(-0.473938\pi\) | ||||
0.0817855 | + | 0.996650i | \(0.473938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.333148 | −0.0251836 | ||||||||
\(176\) | −2.62689 | −0.198009 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.76146 | 0.206980 | ||||||||
\(179\) | 10.1067 | 0.755414 | 0.377707 | − | 0.925925i | \(-0.376713\pi\) | ||||
0.377707 | + | 0.925925i | \(0.376713\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.277428 | 0.0206211 | 0.0103105 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103105 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(182\) | 0.271868 | 0.0201522 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.02975 | −0.518240 | ||||||||
\(185\) | 13.1598 | 0.967527 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.30678 | 0.314943 | ||||||||
\(188\) | −23.2110 | −1.69284 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.00229 | 0.508000 | ||||||||
\(191\) | 6.09681 | 0.441150 | 0.220575 | − | 0.975370i | \(-0.429207\pi\) | ||||
0.220575 | + | 0.975370i | \(0.429207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.45136 | 0.680323 | 0.340162 | − | 0.940367i | \(-0.389518\pi\) | ||||
0.340162 | + | 0.940367i | \(0.389518\pi\) | |||||||
\(194\) | 8.32555 | 0.597739 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.2135 | 0.872392 | ||||||||
\(197\) | 18.3986 | 1.31085 | 0.655425 | − | 0.755261i | \(-0.272490\pi\) | ||||
0.655425 | + | 0.755261i | \(0.272490\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.30293 | 0.517691 | 0.258846 | − | 0.965919i | \(-0.416658\pi\) | ||||
0.258846 | + | 0.965919i | \(0.416658\pi\) | |||||||
\(200\) | −2.36093 | −0.166943 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.45149 | 0.594645 | ||||||||
\(203\) | 0.928221 | 0.0651484 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.3339 | 0.791593 | ||||||||
\(206\) | −0.523302 | −0.0364601 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.64558 | −0.391451 | ||||||||
\(209\) | −7.44254 | −0.514811 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0652 | 1.24366 | 0.621828 | − | 0.783154i | \(-0.286390\pi\) | ||||
0.621828 | + | 0.783154i | \(0.286390\pi\) | |||||||
\(212\) | −17.8335 | −1.22481 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.53310 | −0.241518 | ||||||||
\(215\) | −14.5677 | −0.993508 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.07925 | −0.141149 | ||||||||
\(218\) | −5.86851 | −0.397466 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.39523 | −0.228906 | ||||||||
\(221\) | 9.25592 | 0.622621 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.04349 | 0.605597 | 0.302799 | − | 0.953055i | \(-0.402079\pi\) | ||||
0.302799 | + | 0.953055i | \(0.402079\pi\) | |||||||
\(224\) | −1.28401 | −0.0857916 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.98823 | 0.597888 | ||||||||
\(227\) | 13.3724 | 0.887560 | 0.443780 | − | 0.896136i | \(-0.353637\pi\) | ||||
0.443780 | + | 0.896136i | \(0.353637\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.6227 | 1.09846 | 0.549228 | − | 0.835672i | \(-0.314922\pi\) | ||||
0.549228 | + | 0.835672i | \(0.314922\pi\) | |||||||
\(230\) | −3.60163 | −0.237484 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.57805 | 0.431870 | ||||||||
\(233\) | 0.993972 | 0.0651173 | 0.0325586 | − | 0.999470i | \(-0.489634\pi\) | ||||
0.0325586 | + | 0.999470i | \(0.489634\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.3927 | −1.65643 | ||||||||
\(236\) | 10.5668 | 0.687842 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.544810 | 0.0353148 | ||||||||
\(239\) | 7.06734 | 0.457148 | 0.228574 | − | 0.973527i | \(-0.426594\pi\) | ||||
0.228574 | + | 0.973527i | \(0.426594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5749 | −1.26093 | −0.630467 | − | 0.776216i | \(-0.717136\pi\) | ||||
−0.630467 | + | 0.776216i | \(0.717136\pi\) | |||||||
\(242\) | −0.488177 | −0.0313812 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.76168 | 0.112780 | ||||||||
\(245\) | 13.3614 | 0.853631 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.9951 | −1.01775 | ||||||||
\(248\) | −14.7351 | −0.935680 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.91384 | −0.374024 | ||||||||
\(251\) | 1.82154 | 0.114974 | 0.0574872 | − | 0.998346i | \(-0.481691\pi\) | ||||
0.0574872 | + | 0.998346i | \(0.481691\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.82807 | 0.240669 | ||||||||
\(254\) | 3.86408 | 0.242454 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.156059 | 0.00975369 | ||||||||
\(257\) | 1.98706 | 0.123949 | 0.0619747 | − | 0.998078i | \(-0.480260\pi\) | ||||
0.0619747 | + | 0.998078i | \(0.480260\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.76938 | −0.109944 | ||||||||
\(260\) | −7.29685 | −0.452532 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.46442 | −0.399373 | ||||||||
\(263\) | −8.50019 | −0.524144 | −0.262072 | − | 0.965048i | \(-0.584406\pi\) | ||||
−0.262072 | + | 0.965048i | \(0.584406\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.5097 | −1.19847 | ||||||||
\(266\) | −0.941484 | −0.0577261 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.06402 | 0.187165 | ||||||||
\(269\) | −19.4329 | −1.18485 | −0.592423 | − | 0.805627i | \(-0.701829\pi\) | ||||
−0.592423 | + | 0.805627i | \(0.701829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.6791 | 1.19542 | 0.597710 | − | 0.801712i | \(-0.296077\pi\) | ||||
0.597710 | + | 0.801712i | \(0.296077\pi\) | |||||||
\(272\) | −11.3135 | −0.685979 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.61893 | 0.218628 | ||||||||
\(275\) | 1.28565 | 0.0775277 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.0557 | −1.08486 | −0.542430 | − | 0.840101i | \(-0.682496\pi\) | ||||
−0.542430 | + | 0.840101i | \(0.682496\pi\) | |||||||
\(278\) | 1.68704 | 0.101182 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.917097 | −0.0548070 | ||||||||
\(281\) | 20.0260 | 1.19465 | 0.597326 | − | 0.801999i | \(-0.296230\pi\) | ||||
0.597326 | + | 0.801999i | \(0.296230\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.7189 | 1.82605 | 0.913026 | − | 0.407902i | \(-0.133739\pi\) | ||||
0.913026 | + | 0.407902i | \(0.133739\pi\) | |||||||
\(284\) | 19.9710 | 1.18506 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.04917 | −0.0620385 | ||||||||
\(287\) | −1.52388 | −0.0899519 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.54839 | 0.0910818 | ||||||||
\(290\) | 3.37021 | 0.197905 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.18986 | 0.128152 | ||||||||
\(293\) | −30.1972 | −1.76414 | −0.882069 | − | 0.471121i | \(-0.843850\pi\) | ||||
−0.882069 | + | 0.471121i | \(0.843850\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.5600 | 0.673050 | ||||||||
\(296\) | −12.5391 | −0.728822 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.98436 | −0.230808 | ||||||||
\(299\) | 8.22709 | 0.475785 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.95868 | 0.112896 | ||||||||
\(302\) | −2.48895 | −0.143223 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 19.5507 | 1.12131 | ||||||||
\(305\) | 1.92726 | 0.110355 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.02731 | 0.343997 | 0.171998 | − | 0.985097i | \(-0.444978\pi\) | ||||
0.171998 | + | 0.985097i | \(0.444978\pi\) | |||||||
\(308\) | 0.456501 | 0.0260116 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.54940 | −0.428777 | ||||||||
\(311\) | 15.9585 | 0.904922 | 0.452461 | − | 0.891784i | \(-0.350546\pi\) | ||||
0.452461 | + | 0.891784i | \(0.350546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.72668 | 0.210644 | 0.105322 | − | 0.994438i | \(-0.466413\pi\) | ||||
0.105322 | + | 0.994438i | \(0.466413\pi\) | |||||||
\(314\) | −3.64370 | −0.205626 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.8766 | 0.893128 | ||||||||
\(317\) | 12.4598 | 0.699811 | 0.349905 | − | 0.936785i | \(-0.386214\pi\) | ||||
0.349905 | + | 0.936785i | \(0.386214\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.58210 | −0.200559 | ||||||||
\(320\) | 5.46341 | 0.305414 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.484252 | 0.0269863 | ||||||||
\(323\) | −32.0534 | −1.78350 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.76306 | 0.153267 | ||||||||
\(326\) | −5.70957 | −0.316224 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.7993 | −0.596294 | ||||||||
\(329\) | 3.41414 | 0.188227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.4673 | 1.39981 | 0.699905 | − | 0.714236i | \(-0.253226\pi\) | ||||
0.699905 | + | 0.714236i | \(0.253226\pi\) | |||||||
\(332\) | −23.8689 | −1.30998 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.20199 | 0.284640 | ||||||||
\(335\) | 3.35201 | 0.183140 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.8147 | 1.73306 | 0.866529 | − | 0.499126i | \(-0.166346\pi\) | ||||
0.866529 | + | 0.499126i | \(0.166346\pi\) | |||||||
\(338\) | 4.09149 | 0.222548 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.6225 | −0.793017 | ||||||||
\(341\) | 8.02405 | 0.434526 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.61039 | −0.194943 | ||||||||
\(344\) | 13.8806 | 0.748393 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.05028 | −0.0564636 | ||||||||
\(347\) | 17.9415 | 0.963149 | 0.481575 | − | 0.876405i | \(-0.340065\pi\) | ||||
0.481575 | + | 0.876405i | \(0.340065\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.8428 | 1.86509 | 0.932547 | − | 0.361049i | \(-0.117581\pi\) | ||||
0.932547 | + | 0.361049i | \(0.117581\pi\) | |||||||
\(350\) | 0.162635 | 0.00869323 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.95513 | 0.264109 | ||||||||
\(353\) | −21.0412 | −1.11991 | −0.559955 | − | 0.828523i | \(-0.689182\pi\) | ||||
−0.559955 | + | 0.828523i | \(0.689182\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.8481 | 1.15958 | ||||||||
\(356\) | 9.96525 | 0.528157 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.93389 | −0.260764 | ||||||||
\(359\) | 7.15114 | 0.377423 | 0.188711 | − | 0.982033i | \(-0.439569\pi\) | ||||
0.188711 | + | 0.982033i | \(0.439569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.3914 | 1.91534 | ||||||||
\(362\) | −0.135434 | −0.00711826 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.981089 | 0.0514230 | ||||||||
\(365\) | 2.39569 | 0.125396 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.4282 | 0.544348 | 0.272174 | − | 0.962248i | \(-0.412257\pi\) | ||||
0.272174 | + | 0.962248i | \(0.412257\pi\) | |||||||
\(368\) | −10.0559 | −0.524201 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.42431 | −0.333984 | ||||||||
\(371\) | 2.62315 | 0.136187 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.18290 | 0.423694 | 0.211847 | − | 0.977303i | \(-0.432052\pi\) | ||||
0.211847 | + | 0.977303i | \(0.432052\pi\) | |||||||
\(374\) | −2.10248 | −0.108716 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.1951 | 1.24777 | ||||||||
\(377\) | −7.69846 | −0.396491 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.8456 | −1.12213 | −0.561067 | − | 0.827770i | \(-0.689609\pi\) | ||||
−0.561067 | + | 0.827770i | \(0.689609\pi\) | |||||||
\(380\) | 25.2691 | 1.29628 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.97633 | −0.152282 | ||||||||
\(383\) | 11.7434 | 0.600058 | 0.300029 | − | 0.953930i | \(-0.403004\pi\) | ||||
0.300029 | + | 0.953930i | \(0.403004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.499408 | 0.0254522 | ||||||||
\(386\) | −4.61394 | −0.234843 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 30.0443 | 1.52527 | ||||||||
\(389\) | −1.07865 | −0.0546896 | −0.0273448 | − | 0.999626i | \(-0.508705\pi\) | ||||
−0.0273448 | + | 0.999626i | \(0.508705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.4867 | 0.833767 | ||||||||
\(392\) | −12.7313 | −0.643026 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.98180 | −0.452497 | ||||||||
\(395\) | 17.3688 | 0.873921 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.649240 | −0.0325844 | −0.0162922 | − | 0.999867i | \(-0.505186\pi\) | ||||
−0.0162922 | + | 0.999867i | \(0.505186\pi\) | |||||||
\(398\) | −3.56513 | −0.178704 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.37727 | −0.168863 | ||||||||
\(401\) | −8.09547 | −0.404269 | −0.202134 | − | 0.979358i | \(-0.564788\pi\) | ||||
−0.202134 | + | 0.979358i | \(0.564788\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.2449 | 0.859028 | ||||||||
\(404\) | 30.4988 | 1.51737 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.453137 | −0.0224888 | ||||||||
\(407\) | 6.82822 | 0.338462 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.5573 | 1.46152 | 0.730758 | − | 0.682636i | \(-0.239167\pi\) | ||||
0.730758 | + | 0.682636i | \(0.239167\pi\) | |||||||
\(410\) | −5.53295 | −0.273253 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.88843 | −0.0930365 | ||||||||
\(413\) | −1.55429 | −0.0764814 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.1124 | −1.28181 | ||||||||
\(416\) | 10.6493 | 0.522125 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.63328 | 0.177710 | ||||||||
\(419\) | 17.0334 | 0.832134 | 0.416067 | − | 0.909334i | \(-0.363408\pi\) | ||||
0.416067 | + | 0.909334i | \(0.363408\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.2184 | −0.839172 | −0.419586 | − | 0.907716i | \(-0.637825\pi\) | ||||
−0.419586 | + | 0.907716i | \(0.637825\pi\) | |||||||
\(422\) | −8.81900 | −0.429302 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.5895 | 0.902787 | ||||||||
\(425\) | 5.53702 | 0.268585 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.259128 | −0.0125401 | ||||||||
\(428\) | −12.7499 | −0.616289 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.11162 | 0.342953 | ||||||||
\(431\) | 6.62757 | 0.319239 | 0.159619 | − | 0.987179i | \(-0.448973\pi\) | ||||
0.159619 | + | 0.987179i | \(0.448973\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.5499 | 1.51619 | 0.758095 | − | 0.652144i | \(-0.226130\pi\) | ||||
0.758095 | + | 0.652144i | \(0.226130\pi\) | |||||||
\(434\) | 1.01504 | 0.0487237 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.1776 | −1.01423 | ||||||||
\(437\) | −28.4906 | −1.36289 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.99975 | 0.0954430 | 0.0477215 | − | 0.998861i | \(-0.484804\pi\) | ||||
0.0477215 | + | 0.998861i | \(0.484804\pi\) | |||||||
\(440\) | 3.53917 | 0.168723 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.51853 | −0.214925 | ||||||||
\(443\) | −34.0277 | −1.61670 | −0.808352 | − | 0.588700i | \(-0.799640\pi\) | ||||
−0.808352 | + | 0.588700i | \(0.799640\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.9019 | 0.516799 | ||||||||
\(446\) | −4.41483 | −0.209048 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.734576 | −0.0347055 | ||||||||
\(449\) | −15.5859 | −0.735544 | −0.367772 | − | 0.929916i | \(-0.619879\pi\) | ||||
−0.367772 | + | 0.929916i | \(0.619879\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.88081 | 0.276917 | ||||||||
\(452\) | 32.4358 | 1.52565 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.52812 | −0.306380 | ||||||||
\(455\) | 1.07330 | 0.0503172 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.87791 | −0.368513 | −0.184257 | − | 0.982878i | \(-0.558988\pi\) | ||||
−0.184257 | + | 0.982878i | \(0.558988\pi\) | |||||||
\(458\) | −8.11481 | −0.379180 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.9972 | −0.605996 | ||||||||
\(461\) | −28.7163 | −1.33745 | −0.668725 | − | 0.743510i | \(-0.733160\pi\) | ||||
−0.668725 | + | 0.743510i | \(0.733160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.92149 | 0.228721 | 0.114360 | − | 0.993439i | \(-0.463518\pi\) | ||||
0.114360 | + | 0.993439i | \(0.463518\pi\) | |||||||
\(464\) | 9.40978 | 0.436838 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.485235 | −0.0224781 | ||||||||
\(467\) | 18.6313 | 0.862152 | 0.431076 | − | 0.902316i | \(-0.358134\pi\) | ||||
0.431076 | + | 0.902316i | \(0.358134\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.450690 | −0.0208110 | ||||||||
\(470\) | 12.3961 | 0.571791 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.0148 | −0.506998 | ||||||||
\(473\) | −7.55874 | −0.347551 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.56851 | −0.439033 | ||||||||
\(476\) | 1.96605 | 0.0901138 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.45011 | −0.157805 | ||||||||
\(479\) | 18.3125 | 0.836720 | 0.418360 | − | 0.908281i | \(-0.362605\pi\) | ||||
0.418360 | + | 0.908281i | \(0.362605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.6749 | 0.669116 | ||||||||
\(482\) | 9.55605 | 0.435266 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.76168 | −0.0800765 | ||||||||
\(485\) | 32.8682 | 1.49247 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.8841 | −1.39949 | −0.699745 | − | 0.714393i | \(-0.746703\pi\) | ||||
−0.699745 | + | 0.714393i | \(0.746703\pi\) | |||||||
\(488\) | −1.83637 | −0.0831285 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.52275 | −0.294668 | ||||||||
\(491\) | 7.76148 | 0.350271 | 0.175135 | − | 0.984544i | \(-0.443964\pi\) | ||||
0.175135 | + | 0.984544i | \(0.443964\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.4273 | −0.694812 | ||||||||
\(494\) | 7.80846 | 0.351319 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.0783 | −0.946443 | ||||||||
\(497\) | −2.93756 | −0.131767 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.8210 | 0.573947 | 0.286973 | − | 0.957939i | \(-0.407351\pi\) | ||||
0.286973 | + | 0.957939i | \(0.407351\pi\) | |||||||
\(500\) | −21.3412 | −0.954409 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.889234 | −0.0396884 | ||||||||
\(503\) | 14.4507 | 0.644325 | 0.322162 | − | 0.946684i | \(-0.395590\pi\) | ||||
0.322162 | + | 0.946684i | \(0.395590\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.3654 | 1.48474 | ||||||||
\(506\) | −1.86878 | −0.0830773 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.9443 | 0.618677 | ||||||||
\(509\) | −35.2748 | −1.56353 | −0.781764 | − | 0.623574i | \(-0.785680\pi\) | ||||
−0.781764 | + | 0.623574i | \(0.785680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.322109 | −0.0142493 | ||||||||
\(512\) | −22.6645 | −1.00164 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.970037 | −0.0427865 | ||||||||
\(515\) | −2.06593 | −0.0910357 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.1755 | −0.579458 | ||||||||
\(518\) | 0.863772 | 0.0379520 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.60620 | 0.333554 | ||||||||
\(521\) | 4.52876 | 0.198408 | 0.0992042 | − | 0.995067i | \(-0.468370\pi\) | ||||
0.0992042 | + | 0.995067i | \(0.468370\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.1945 | −1.01422 | −0.507112 | − | 0.861880i | \(-0.669287\pi\) | ||||
−0.507112 | + | 0.861880i | \(0.669287\pi\) | |||||||
\(524\) | −23.3281 | −1.01909 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.14960 | 0.180931 | ||||||||
\(527\) | 34.5578 | 1.50536 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.34588 | −0.362864 | ||||||||
\(530\) | 9.52418 | 0.413704 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.39753 | −0.147301 | ||||||||
\(533\) | 12.6387 | 0.547445 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.9483 | −0.603036 | ||||||||
\(536\) | −3.19392 | −0.137956 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.48671 | 0.409001 | ||||||||
\(539\) | 6.93285 | 0.298619 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.64556 | 0.199728 | 0.0998641 | − | 0.995001i | \(-0.468159\pi\) | ||||
0.0998641 | + | 0.995001i | \(0.468159\pi\) | |||||||
\(542\) | −9.60690 | −0.412652 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.3407 | 0.914973 | ||||||||
\(545\) | −23.1682 | −0.992415 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.9951 | 1.41077 | 0.705384 | − | 0.708825i | \(-0.250774\pi\) | ||||
0.705384 | + | 0.708825i | \(0.250774\pi\) | |||||||
\(548\) | 13.0596 | 0.557880 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.627626 | −0.0267621 | ||||||||
\(551\) | 26.6599 | 1.13575 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.33530 | −0.0993073 | ||||||||
\(554\) | 8.81438 | 0.374487 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.08800 | 0.258189 | ||||||||
\(557\) | 39.8211 | 1.68727 | 0.843637 | − | 0.536914i | \(-0.180410\pi\) | ||||
0.843637 | + | 0.536914i | \(0.180410\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.2449 | −0.687084 | ||||||||
\(560\) | −1.31189 | −0.0554375 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.77624 | −0.412386 | ||||||||
\(563\) | −26.0693 | −1.09869 | −0.549345 | − | 0.835596i | \(-0.685123\pi\) | ||||
−0.549345 | + | 0.835596i | \(0.685123\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.4844 | 1.49284 | ||||||||
\(566\) | −14.9963 | −0.630341 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.8177 | −0.873490 | ||||||||
\(569\) | 34.9916 | 1.46692 | 0.733462 | − | 0.679730i | \(-0.237903\pi\) | ||||
0.733462 | + | 0.679730i | \(0.237903\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.45551 | 0.144609 | 0.0723043 | − | 0.997383i | \(-0.476965\pi\) | ||||
0.0723043 | + | 0.997383i | \(0.476965\pi\) | |||||||
\(572\) | −3.78612 | −0.158306 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.743925 | 0.0310508 | ||||||||
\(575\) | 4.92156 | 0.205243 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.1331 | −0.629998 | −0.314999 | − | 0.949092i | \(-0.602004\pi\) | ||||
−0.314999 | + | 0.949092i | \(0.602004\pi\) | |||||||
\(578\) | −0.755889 | −0.0314409 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.1620 | 0.505001 | ||||||||
\(581\) | 3.51091 | 0.145657 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.1230 | −0.419251 | ||||||||
\(584\) | −2.28270 | −0.0944587 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.7416 | 0.608969 | ||||||||
\(587\) | −18.7095 | −0.772224 | −0.386112 | − | 0.922452i | \(-0.626182\pi\) | ||||
−0.386112 | + | 0.922452i | \(0.626182\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −59.7193 | −2.46069 | ||||||||
\(590\) | −5.64334 | −0.232333 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.9370 | −0.737206 | ||||||||
\(593\) | 14.5930 | 0.599262 | 0.299631 | − | 0.954055i | \(-0.403137\pi\) | ||||
0.299631 | + | 0.954055i | \(0.403137\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.15084 | 0.0881759 | ||||||||
\(596\) | −14.3783 | −0.588960 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.01628 | −0.164238 | ||||||||
\(599\) | 39.2459 | 1.60354 | 0.801771 | − | 0.597631i | \(-0.203891\pi\) | ||||
0.801771 | + | 0.597631i | \(0.203891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.52750 | 0.143890 | 0.0719449 | − | 0.997409i | \(-0.477079\pi\) | ||||
0.0719449 | + | 0.997409i | \(0.477079\pi\) | |||||||
\(602\) | −0.956183 | −0.0389711 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.98186 | −0.365467 | ||||||||
\(605\) | −1.92726 | −0.0783544 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.496801 | −0.0201645 | −0.0100823 | − | 0.999949i | \(-0.503209\pi\) | ||||
−0.0100823 | + | 0.999949i | \(0.503209\pi\) | |||||||
\(608\) | −36.8787 | −1.49563 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.940847 | −0.0380938 | ||||||||
\(611\) | −28.3161 | −1.14555 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.8350 | −0.720349 | −0.360174 | − | 0.932885i | \(-0.617283\pi\) | ||||
−0.360174 | + | 0.932885i | \(0.617283\pi\) | |||||||
\(614\) | −2.94240 | −0.118746 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.475854 | −0.0191727 | ||||||||
\(617\) | −30.2909 | −1.21946 | −0.609732 | − | 0.792608i | \(-0.708723\pi\) | ||||
−0.609732 | + | 0.792608i | \(0.708723\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.8595 | −0.637448 | −0.318724 | − | 0.947847i | \(-0.603254\pi\) | ||||
−0.318724 | + | 0.947847i | \(0.603254\pi\) | |||||||
\(620\) | −27.2435 | −1.09412 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.79057 | −0.312373 | ||||||||
\(623\) | −1.46580 | −0.0587260 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.9188 | −0.676754 | ||||||||
\(626\) | −1.81928 | −0.0727131 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.1490 | −0.524701 | ||||||||
\(629\) | 29.4077 | 1.17256 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.1448 | −0.961188 | −0.480594 | − | 0.876943i | \(-0.659579\pi\) | ||||
−0.480594 | + | 0.876943i | \(0.659579\pi\) | |||||||
\(632\) | −16.5497 | −0.658311 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.08258 | −0.241570 | ||||||||
\(635\) | 15.2549 | 0.605373 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.8997 | 0.590349 | ||||||||
\(638\) | 1.74870 | 0.0692317 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.7668 | −0.860408 | ||||||||
\(641\) | 11.9751 | 0.472987 | 0.236493 | − | 0.971633i | \(-0.424002\pi\) | ||||
0.236493 | + | 0.971633i | \(0.424002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −49.2315 | −1.94150 | −0.970750 | − | 0.240094i | \(-0.922822\pi\) | ||||
−0.970750 | + | 0.240094i | \(0.922822\pi\) | |||||||
\(644\) | 1.74752 | 0.0688619 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.6478 | 0.615653 | ||||||||
\(647\) | 19.8119 | 0.778886 | 0.389443 | − | 0.921050i | \(-0.372667\pi\) | ||||
0.389443 | + | 0.921050i | \(0.372667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.99815 | 0.235448 | ||||||||
\(650\) | −1.34886 | −0.0529067 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.6041 | −0.806918 | ||||||||
\(653\) | −3.15323 | −0.123395 | −0.0616976 | − | 0.998095i | \(-0.519651\pi\) | ||||
−0.0616976 | + | 0.998095i | \(0.519651\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.5207 | −0.997178 | ||||||||
\(656\) | −15.4483 | −0.603153 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.66670 | −0.0649749 | ||||||||
\(659\) | 5.25903 | 0.204863 | 0.102431 | − | 0.994740i | \(-0.467338\pi\) | ||||
0.102431 | + | 0.994740i | \(0.467338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.7574 | 1.62417 | 0.812087 | − | 0.583537i | \(-0.198332\pi\) | ||||
0.812087 | + | 0.583537i | \(0.198332\pi\) | |||||||
\(662\) | −12.4326 | −0.483205 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24.8808 | 0.965564 | ||||||||
\(665\) | −3.71686 | −0.144134 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.7125 | −0.530951 | ||||||||
\(668\) | 18.7724 | 0.726325 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.63638 | −0.0632188 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.4335 | 1.67424 | 0.837118 | − | 0.547022i | \(-0.184238\pi\) | ||||
0.837118 | + | 0.547022i | \(0.184238\pi\) | |||||||
\(674\) | −15.5312 | −0.598241 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.7649 | 0.567882 | ||||||||
\(677\) | −35.0164 | −1.34579 | −0.672894 | − | 0.739739i | \(-0.734949\pi\) | ||||
−0.672894 | + | 0.739739i | \(0.734949\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.41926 | −0.169595 | ||||||||
\(680\) | 15.2424 | 0.584521 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.91716 | −0.149996 | ||||||||
\(683\) | 41.6290 | 1.59289 | 0.796445 | − | 0.604711i | \(-0.206711\pi\) | ||||
0.796445 | + | 0.604711i | \(0.206711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.2871 | 0.545882 | ||||||||
\(686\) | 1.76251 | 0.0672930 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.8560 | 0.757002 | ||||||||
\(689\) | −21.7558 | −0.828830 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.8432 | 0.792912 | 0.396456 | − | 0.918054i | \(-0.370240\pi\) | ||||
0.396456 | + | 0.918054i | \(0.370240\pi\) | |||||||
\(692\) | −3.79015 | −0.144080 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.75863 | −0.332473 | ||||||||
\(695\) | 6.66021 | 0.252636 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.3274 | 0.959343 | ||||||||
\(698\) | −17.0095 | −0.643819 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.586901 | 0.0221828 | ||||||||
\(701\) | −33.5579 | −1.26747 | −0.633733 | − | 0.773552i | \(-0.718478\pi\) | ||||
−0.633733 | + | 0.773552i | \(0.718478\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −50.8193 | −1.91669 | ||||||||
\(704\) | 2.83480 | 0.106841 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.2718 | 0.386586 | ||||||||
\(707\) | −4.48611 | −0.168717 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.6060 | 1.37477 | 0.687384 | − | 0.726294i | \(-0.258759\pi\) | ||||
0.687384 | + | 0.726294i | \(0.258759\pi\) | |||||||
\(710\) | −10.6657 | −0.400278 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.3877 | −0.389296 | ||||||||
\(713\) | 30.7166 | 1.15035 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.14198 | −0.154901 | ||||||||
\(716\) | −17.8049 | −0.665400 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.49102 | −0.130284 | ||||||||
\(719\) | 18.2060 | 0.678970 | 0.339485 | − | 0.940611i | \(-0.389747\pi\) | ||||
0.339485 | + | 0.940611i | \(0.389747\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.277772 | 0.0103448 | ||||||||
\(722\) | −17.7655 | −0.661162 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.488740 | −0.0181639 | ||||||||
\(725\) | −4.60533 | −0.171038 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.2387 | 0.602259 | 0.301130 | − | 0.953583i | \(-0.402636\pi\) | ||||
0.301130 | + | 0.953583i | \(0.402636\pi\) | |||||||
\(728\) | −1.02268 | −0.0379031 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.16952 | −0.0432859 | ||||||||
\(731\) | −32.5538 | −1.20405 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.3708 | −1.08483 | −0.542417 | − | 0.840109i | \(-0.682491\pi\) | ||||
−0.542417 | + | 0.840109i | \(0.682491\pi\) | |||||||
\(734\) | −5.09082 | −0.187906 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.9686 | 0.699191 | ||||||||
\(737\) | 1.73926 | 0.0640664 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.4179 | 0.787872 | 0.393936 | − | 0.919138i | \(-0.371113\pi\) | ||||
0.393936 | + | 0.919138i | \(0.371113\pi\) | |||||||
\(740\) | −23.1834 | −0.852238 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.28056 | −0.0470109 | ||||||||
\(743\) | −32.8143 | −1.20384 | −0.601921 | − | 0.798556i | \(-0.705598\pi\) | ||||
−0.601921 | + | 0.798556i | \(0.705598\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.7298 | −0.576295 | ||||||||
\(746\) | −3.99471 | −0.146257 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.58719 | −0.277415 | ||||||||
\(749\) | 1.87539 | 0.0685254 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.9406 | −1.56693 | −0.783463 | − | 0.621439i | \(-0.786548\pi\) | ||||
−0.783463 | + | 0.621439i | \(0.786548\pi\) | |||||||
\(752\) | 34.6106 | 1.26212 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.75822 | 0.136866 | ||||||||
\(755\) | −9.82607 | −0.357607 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.8797 | −1.26772 | −0.633861 | − | 0.773447i | \(-0.718531\pi\) | ||||
−0.633861 | + | 0.773447i | \(0.718531\pi\) | |||||||
\(758\) | 10.6645 | 0.387354 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −26.3404 | −0.955467 | ||||||||
\(761\) | 42.2729 | 1.53239 | 0.766196 | − | 0.642607i | \(-0.222147\pi\) | ||||
0.766196 | + | 0.642607i | \(0.222147\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.11504 | 0.112772 | ||||||||
\(764\) | −10.7407 | −0.388583 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.73285 | −0.207136 | ||||||||
\(767\) | 12.8909 | 0.465464 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.3299 | 0.805238 | 0.402619 | − | 0.915368i | \(-0.368100\pi\) | ||||
0.402619 | + | 0.915368i | \(0.368100\pi\) | |||||||
\(770\) | −0.243800 | −0.00878593 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.6503 | −0.599257 | ||||||||
\(773\) | −34.1247 | −1.22738 | −0.613689 | − | 0.789548i | \(-0.710315\pi\) | ||||
−0.613689 | + | 0.789548i | \(0.710315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3161 | 0.370566 | ||||||||
\(776\) | −31.3181 | −1.12425 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.526571 | 0.0188785 | ||||||||
\(779\) | −43.7682 | −1.56816 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3363 | 0.405645 | ||||||||
\(782\) | −8.04842 | −0.287811 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.2119 | −0.650423 | ||||||||
\(785\) | −14.3849 | −0.513418 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.69963 | 0.131878 | 0.0659388 | − | 0.997824i | \(-0.478996\pi\) | ||||
0.0659388 | + | 0.997824i | \(0.478996\pi\) | |||||||
\(788\) | −32.4126 | −1.15465 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.47908 | −0.301672 | ||||||||
\(791\) | −4.77101 | −0.169638 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.14915 | 0.0763185 | ||||||||
\(794\) | 0.316944 | 0.0112479 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.8655 | −0.456004 | ||||||||
\(797\) | −15.0310 | −0.532426 | −0.266213 | − | 0.963914i | \(-0.585773\pi\) | ||||
−0.266213 | + | 0.963914i | \(0.585773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −56.7440 | −2.00746 | ||||||||
\(800\) | 6.37057 | 0.225234 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.95203 | 0.139551 | ||||||||
\(803\) | 1.24305 | 0.0438663 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.91177 | 0.0673810 | ||||||||
\(806\) | −8.41856 | −0.296531 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −31.7918 | −1.11843 | ||||||||
\(809\) | 0.622132 | 0.0218730 | 0.0109365 | − | 0.999940i | \(-0.496519\pi\) | ||||
0.0109365 | + | 0.999940i | \(0.496519\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.8338 | 0.626230 | 0.313115 | − | 0.949715i | \(-0.398628\pi\) | ||||
0.313115 | + | 0.949715i | \(0.398628\pi\) | |||||||
\(812\) | −1.63523 | −0.0573854 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.33338 | −0.116835 | ||||||||
\(815\) | −22.5407 | −0.789566 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.2562 | 1.96816 | ||||||||
\(818\) | −14.4292 | −0.504506 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.9667 | −0.697268 | ||||||||
\(821\) | −3.48246 | −0.121539 | −0.0607694 | − | 0.998152i | \(-0.519355\pi\) | ||||
−0.0607694 | + | 0.998152i | \(0.519355\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.6086 | −0.369793 | −0.184897 | − | 0.982758i | \(-0.559195\pi\) | ||||
−0.184897 | + | 0.982758i | \(0.559195\pi\) | |||||||
\(824\) | 1.96849 | 0.0685757 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.758768 | 0.0264009 | ||||||||
\(827\) | 18.3993 | 0.639805 | 0.319902 | − | 0.947451i | \(-0.396350\pi\) | ||||
0.319902 | + | 0.947451i | \(0.396350\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.1655 | −0.526720 | −0.263360 | − | 0.964698i | \(-0.584831\pi\) | ||||
−0.263360 | + | 0.964698i | \(0.584831\pi\) | |||||||
\(830\) | 12.7475 | 0.442472 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.09241 | 0.211216 | ||||||||
\(833\) | 29.8583 | 1.03453 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.5368 | 0.710706 | ||||||||
\(836\) | 13.1114 | 0.453467 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.31530 | −0.287247 | ||||||||
\(839\) | 17.5973 | 0.607528 | 0.303764 | − | 0.952747i | \(-0.401757\pi\) | ||||
0.303764 | + | 0.952747i | \(0.401757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.1686 | −0.557537 | ||||||||
\(842\) | 8.40562 | 0.289677 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −31.8251 | −1.09546 | ||||||||
\(845\) | 16.1527 | 0.555670 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.259128 | 0.00890374 | ||||||||
\(848\) | 26.5920 | 0.913172 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.70305 | −0.0927138 | ||||||||
\(851\) | 26.1389 | 0.896030 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −57.7984 | −1.97898 | −0.989490 | − | 0.144602i | \(-0.953810\pi\) | ||||
−0.989490 | + | 0.144602i | \(0.953810\pi\) | |||||||
\(854\) | 0.126500 | 0.00432875 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.2904 | 0.454257 | ||||||||
\(857\) | 12.5542 | 0.428844 | 0.214422 | − | 0.976741i | \(-0.431213\pi\) | ||||
0.214422 | + | 0.976741i | \(0.431213\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.2175 | −1.23573 | −0.617863 | − | 0.786286i | \(-0.712001\pi\) | ||||
−0.617863 | + | 0.786286i | \(0.712001\pi\) | |||||||
\(860\) | 25.6636 | 0.875123 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.23543 | −0.110199 | ||||||||
\(863\) | −13.9997 | −0.476554 | −0.238277 | − | 0.971197i | \(-0.576583\pi\) | ||||
−0.238277 | + | 0.971197i | \(0.576583\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.14639 | −0.140982 | ||||||||
\(866\) | −15.4019 | −0.523379 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.66298 | 0.124330 | ||||||||
\(869\) | 9.01217 | 0.305717 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.73793 | 0.126655 | ||||||||
\(872\) | 22.0755 | 0.747570 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.9085 | 0.470460 | ||||||||
\(875\) | 3.13910 | 0.106121 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.3773 | 1.26214 | 0.631071 | − | 0.775725i | \(-0.282616\pi\) | ||||
0.631071 | + | 0.775725i | \(0.282616\pi\) | |||||||
\(878\) | −0.976235 | −0.0329463 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.06272 | 0.170664 | ||||||||
\(881\) | −20.9400 | −0.705485 | −0.352743 | − | 0.935720i | \(-0.614751\pi\) | ||||
−0.352743 | + | 0.935720i | \(0.614751\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.8733 | 1.17358 | 0.586789 | − | 0.809740i | \(-0.300392\pi\) | ||||
0.586789 | + | 0.809740i | \(0.300392\pi\) | |||||||
\(884\) | −16.3060 | −0.548430 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.6115 | 0.558076 | ||||||||
\(887\) | 1.28356 | 0.0430978 | 0.0215489 | − | 0.999768i | \(-0.493140\pi\) | ||||
0.0215489 | + | 0.999768i | \(0.493140\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.05108 | −0.0687910 | ||||||||
\(890\) | −5.32206 | −0.178396 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.9318 | −0.533435 | ||||||||
\(893\) | 98.0591 | 3.28142 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.4784 | −0.651090 | ||||||||
\(896\) | 2.92663 | 0.0977717 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.60869 | 0.253905 | ||||||||
\(899\) | −28.7429 | −0.958630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.5975 | −1.45244 | ||||||||
\(902\) | −2.87088 | −0.0955899 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33.8109 | −1.12453 | ||||||||
\(905\) | −0.534677 | −0.0177733 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.99757 | 0.199146 | 0.0995730 | − | 0.995030i | \(-0.468252\pi\) | ||||
0.0995730 | + | 0.995030i | \(0.468252\pi\) | |||||||
\(908\) | −23.5580 | −0.781799 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.523962 | −0.0173692 | ||||||||
\(911\) | 36.5132 | 1.20974 | 0.604869 | − | 0.796325i | \(-0.293226\pi\) | ||||
0.604869 | + | 0.796325i | \(0.293226\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5489 | −0.448404 | ||||||||
\(914\) | 3.84582 | 0.127208 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29.2839 | −0.967566 | ||||||||
\(917\) | 3.43136 | 0.113313 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.2375 | 1.09640 | 0.548201 | − | 0.836346i | \(-0.315313\pi\) | ||||
0.548201 | + | 0.836346i | \(0.315313\pi\) | |||||||
\(920\) | 13.5482 | 0.446670 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.0186 | 0.461679 | ||||||||
\(923\) | 24.3634 | 0.801932 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.77871 | 0.288642 | ||||||||
\(926\) | −2.40256 | −0.0789530 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.7498 | −0.582664 | ||||||||
\(929\) | −41.6156 | −1.36537 | −0.682683 | − | 0.730715i | \(-0.739187\pi\) | ||||
−0.682683 | + | 0.730715i | \(0.739187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −51.5980 | −1.69106 | ||||||||
\(932\) | −1.75106 | −0.0573580 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.09536 | −0.297609 | ||||||||
\(935\) | −8.30031 | −0.271449 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.3565 | 0.501674 | 0.250837 | − | 0.968029i | \(-0.419294\pi\) | ||||
0.250837 | + | 0.968029i | \(0.419294\pi\) | |||||||
\(938\) | 0.220017 | 0.00718381 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 44.7338 | 1.45906 | ||||||||
\(941\) | 34.5345 | 1.12579 | 0.562897 | − | 0.826527i | \(-0.309687\pi\) | ||||
0.562897 | + | 0.826527i | \(0.309687\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.5122 | 0.733097 | ||||||||
\(944\) | −15.7565 | −0.512830 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.69001 | 0.119972 | ||||||||
\(947\) | 41.3303 | 1.34305 | 0.671527 | − | 0.740980i | \(-0.265639\pi\) | ||||
0.671527 | + | 0.740980i | \(0.265639\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.67150 | 0.0867205 | ||||||||
\(950\) | 4.67113 | 0.151552 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.04940 | −0.0664215 | ||||||||
\(953\) | −23.2336 | −0.752610 | −0.376305 | − | 0.926496i | \(-0.622805\pi\) | ||||
−0.376305 | + | 0.926496i | \(0.622805\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.7502 | −0.380227 | ||||||||
\(956\) | −12.4504 | −0.402675 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.93975 | −0.288830 | ||||||||
\(959\) | −1.92095 | −0.0620309 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.3853 | 1.07695 | ||||||||
\(962\) | −7.16394 | −0.230975 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 34.4848 | 1.11068 | ||||||||
\(965\) | −18.2153 | −0.586370 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.466832 | 0.0150123 | 0.00750615 | − | 0.999972i | \(-0.497611\pi\) | ||||
0.00750615 | + | 0.999972i | \(0.497611\pi\) | |||||||
\(968\) | 1.83637 | 0.0590231 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16.0455 | −0.515191 | ||||||||
\(971\) | −4.43549 | −0.142342 | −0.0711709 | − | 0.997464i | \(-0.522674\pi\) | ||||
−0.0711709 | + | 0.997464i | \(0.522674\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.895490 | −0.0287081 | ||||||||
\(974\) | 15.0769 | 0.483095 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.62689 | −0.0840848 | ||||||||
\(977\) | −15.5007 | −0.495912 | −0.247956 | − | 0.968771i | \(-0.579759\pi\) | ||||
−0.247956 | + | 0.968771i | \(0.579759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.65666 | 0.180788 | ||||||||
\(980\) | −23.5386 | −0.751914 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.78898 | −0.120911 | ||||||||
\(983\) | 36.2887 | 1.15743 | 0.578715 | − | 0.815530i | \(-0.303554\pi\) | ||||
0.578715 | + | 0.815530i | \(0.303554\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.4591 | −1.12982 | ||||||||
\(986\) | 7.53127 | 0.239845 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 28.1783 | 0.896472 | ||||||||
\(989\) | −28.9354 | −0.920092 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.8702 | 0.980625 | 0.490313 | − | 0.871547i | \(-0.336883\pi\) | ||||
0.490313 | + | 0.871547i | \(0.336883\pi\) | |||||||
\(992\) | 39.7602 | 1.26239 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.43405 | 0.0454853 | ||||||||
\(995\) | −14.0747 | −0.446198 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.22245 | 0.0703857 | 0.0351929 | − | 0.999381i | \(-0.488795\pi\) | ||||
0.0351929 | + | 0.999381i | \(0.488795\pi\) | |||||||
\(998\) | −6.25893 | −0.198123 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.k.1.10 | 19 | ||
3.2 | odd | 2 | 671.2.a.c.1.10 | ✓ | 19 | ||
33.32 | even | 2 | 7381.2.a.i.1.10 | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.c.1.10 | ✓ | 19 | 3.2 | odd | 2 | ||
6039.2.a.k.1.10 | 19 | 1.1 | even | 1 | trivial | ||
7381.2.a.i.1.10 | 19 | 33.32 | even | 2 |