Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, 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("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.17009 | −0.827376 | −0.413688 | − | 0.910419i | \(-0.635760\pi\) | ||||
−0.413688 | + | 0.910419i | \(0.635760\pi\) | |||||||
\(3\) | 0.539189 | 0.311301 | 0.155650 | − | 0.987812i | \(-0.450253\pi\) | ||||
0.155650 | + | 0.987812i | \(0.450253\pi\) | |||||||
\(4\) | −0.630898 | −0.315449 | ||||||||
\(5\) | 0.460811 | 0.206081 | 0.103041 | − | 0.994677i | \(-0.467143\pi\) | ||||
0.103041 | + | 0.994677i | \(0.467143\pi\) | |||||||
\(6\) | −0.630898 | −0.257563 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.07838 | 1.08837 | ||||||||
\(9\) | −2.70928 | −0.903092 | ||||||||
\(10\) | −0.539189 | −0.170506 | ||||||||
\(11\) | 0.829914 | 0.250228 | 0.125114 | − | 0.992142i | \(-0.460070\pi\) | ||||
0.125114 | + | 0.992142i | \(0.460070\pi\) | |||||||
\(12\) | −0.340173 | −0.0981995 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.17009 | 0.312719 | ||||||||
\(15\) | 0.248464 | 0.0641532 | ||||||||
\(16\) | −2.34017 | −0.585043 | ||||||||
\(17\) | −2.87936 | −0.698348 | −0.349174 | − | 0.937058i | \(-0.613538\pi\) | ||||
−0.349174 | + | 0.937058i | \(0.613538\pi\) | |||||||
\(18\) | 3.17009 | 0.747197 | ||||||||
\(19\) | 4.32684 | 0.992646 | 0.496323 | − | 0.868138i | \(-0.334683\pi\) | ||||
0.496323 | + | 0.868138i | \(0.334683\pi\) | |||||||
\(20\) | −0.290725 | −0.0650080 | ||||||||
\(21\) | −0.539189 | −0.117661 | ||||||||
\(22\) | −0.971071 | −0.207033 | ||||||||
\(23\) | 5.04945 | 1.05288 | 0.526441 | − | 0.850211i | \(-0.323526\pi\) | ||||
0.526441 | + | 0.850211i | \(0.323526\pi\) | |||||||
\(24\) | 1.65983 | 0.338811 | ||||||||
\(25\) | −4.78765 | −0.957531 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.07838 | −0.592434 | ||||||||
\(28\) | 0.630898 | 0.119228 | ||||||||
\(29\) | 0.261795 | 0.0486142 | 0.0243071 | − | 0.999705i | \(-0.492262\pi\) | ||||
0.0243071 | + | 0.999705i | \(0.492262\pi\) | |||||||
\(30\) | −0.290725 | −0.0530788 | ||||||||
\(31\) | 6.80098 | 1.22149 | 0.610746 | − | 0.791826i | \(-0.290869\pi\) | ||||
0.610746 | + | 0.791826i | \(0.290869\pi\) | |||||||
\(32\) | −3.41855 | −0.604320 | ||||||||
\(33\) | 0.447480 | 0.0778963 | ||||||||
\(34\) | 3.36910 | 0.577796 | ||||||||
\(35\) | −0.460811 | −0.0778913 | ||||||||
\(36\) | 1.70928 | 0.284879 | ||||||||
\(37\) | 9.51026 | 1.56348 | 0.781739 | − | 0.623606i | \(-0.214333\pi\) | ||||
0.781739 | + | 0.623606i | \(0.214333\pi\) | |||||||
\(38\) | −5.06278 | −0.821291 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.41855 | 0.224293 | ||||||||
\(41\) | −6.68035 | −1.04329 | −0.521647 | − | 0.853161i | \(-0.674682\pi\) | ||||
−0.521647 | + | 0.853161i | \(0.674682\pi\) | |||||||
\(42\) | 0.630898 | 0.0973496 | ||||||||
\(43\) | −0.418551 | −0.0638284 | −0.0319142 | − | 0.999491i | \(-0.510160\pi\) | ||||
−0.0319142 | + | 0.999491i | \(0.510160\pi\) | |||||||
\(44\) | −0.523590 | −0.0789342 | ||||||||
\(45\) | −1.24846 | −0.186110 | ||||||||
\(46\) | −5.90829 | −0.871130 | ||||||||
\(47\) | 9.24846 | 1.34903 | 0.674514 | − | 0.738262i | \(-0.264353\pi\) | ||||
0.674514 | + | 0.738262i | \(0.264353\pi\) | |||||||
\(48\) | −1.26180 | −0.182124 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.60197 | 0.792238 | ||||||||
\(51\) | −1.55252 | −0.217396 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.63090 | 0.224021 | 0.112011 | − | 0.993707i | \(-0.464271\pi\) | ||||
0.112011 | + | 0.993707i | \(0.464271\pi\) | |||||||
\(54\) | 3.60197 | 0.490166 | ||||||||
\(55\) | 0.382433 | 0.0515673 | ||||||||
\(56\) | −3.07838 | −0.411366 | ||||||||
\(57\) | 2.33299 | 0.309011 | ||||||||
\(58\) | −0.306323 | −0.0402222 | ||||||||
\(59\) | −2.78765 | −0.362922 | −0.181461 | − | 0.983398i | \(-0.558083\pi\) | ||||
−0.181461 | + | 0.983398i | \(0.558083\pi\) | |||||||
\(60\) | −0.156755 | −0.0202370 | ||||||||
\(61\) | 7.26180 | 0.929778 | 0.464889 | − | 0.885369i | \(-0.346094\pi\) | ||||
0.464889 | + | 0.885369i | \(0.346094\pi\) | |||||||
\(62\) | −7.95774 | −1.01063 | ||||||||
\(63\) | 2.70928 | 0.341337 | ||||||||
\(64\) | 8.68035 | 1.08504 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.523590 | −0.0644495 | ||||||||
\(67\) | −5.07838 | −0.620423 | −0.310211 | − | 0.950668i | \(-0.600400\pi\) | ||||
−0.310211 | + | 0.950668i | \(0.600400\pi\) | |||||||
\(68\) | 1.81658 | 0.220293 | ||||||||
\(69\) | 2.72261 | 0.327763 | ||||||||
\(70\) | 0.539189 | 0.0644454 | ||||||||
\(71\) | 12.7721 | 1.51576 | 0.757882 | − | 0.652392i | \(-0.226234\pi\) | ||||
0.757882 | + | 0.652392i | \(0.226234\pi\) | |||||||
\(72\) | −8.34017 | −0.982899 | ||||||||
\(73\) | 0.353504 | 0.0413745 | 0.0206873 | − | 0.999786i | \(-0.493415\pi\) | ||||
0.0206873 | + | 0.999786i | \(0.493415\pi\) | |||||||
\(74\) | −11.1278 | −1.29358 | ||||||||
\(75\) | −2.58145 | −0.298080 | ||||||||
\(76\) | −2.72979 | −0.313129 | ||||||||
\(77\) | −0.829914 | −0.0945774 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.81658 | 0.316890 | 0.158445 | − | 0.987368i | \(-0.449352\pi\) | ||||
0.158445 | + | 0.987368i | \(0.449352\pi\) | |||||||
\(80\) | −1.07838 | −0.120566 | ||||||||
\(81\) | 6.46800 | 0.718667 | ||||||||
\(82\) | 7.81658 | 0.863197 | ||||||||
\(83\) | 10.3763 | 1.13895 | 0.569473 | − | 0.822010i | \(-0.307147\pi\) | ||||
0.569473 | + | 0.822010i | \(0.307147\pi\) | |||||||
\(84\) | 0.340173 | 0.0371159 | ||||||||
\(85\) | −1.32684 | −0.143916 | ||||||||
\(86\) | 0.489741 | 0.0528101 | ||||||||
\(87\) | 0.141157 | 0.0151336 | ||||||||
\(88\) | 2.55479 | 0.272341 | ||||||||
\(89\) | 5.43188 | 0.575778 | 0.287889 | − | 0.957664i | \(-0.407047\pi\) | ||||
0.287889 | + | 0.957664i | \(0.407047\pi\) | |||||||
\(90\) | 1.46081 | 0.153983 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.18568 | −0.332131 | ||||||||
\(93\) | 3.66701 | 0.380252 | ||||||||
\(94\) | −10.8215 | −1.11615 | ||||||||
\(95\) | 1.99386 | 0.204565 | ||||||||
\(96\) | −1.84324 | −0.188125 | ||||||||
\(97\) | −12.6092 | −1.28027 | −0.640133 | − | 0.768264i | \(-0.721121\pi\) | ||||
−0.640133 | + | 0.768264i | \(0.721121\pi\) | |||||||
\(98\) | −1.17009 | −0.118197 | ||||||||
\(99\) | −2.24846 | −0.225979 | ||||||||
\(100\) | 3.02052 | 0.302052 | ||||||||
\(101\) | 3.64423 | 0.362614 | 0.181307 | − | 0.983427i | \(-0.441967\pi\) | ||||
0.181307 | + | 0.983427i | \(0.441967\pi\) | |||||||
\(102\) | 1.81658 | 0.179868 | ||||||||
\(103\) | 17.9421 | 1.76789 | 0.883946 | − | 0.467589i | \(-0.154877\pi\) | ||||
0.883946 | + | 0.467589i | \(0.154877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.248464 | −0.0242476 | ||||||||
\(106\) | −1.90829 | −0.185350 | ||||||||
\(107\) | 2.94441 | 0.284647 | 0.142323 | − | 0.989820i | \(-0.454543\pi\) | ||||
0.142323 | + | 0.989820i | \(0.454543\pi\) | |||||||
\(108\) | 1.94214 | 0.186883 | ||||||||
\(109\) | 8.43188 | 0.807628 | 0.403814 | − | 0.914841i | \(-0.367684\pi\) | ||||
0.403814 | + | 0.914841i | \(0.367684\pi\) | |||||||
\(110\) | −0.447480 | −0.0426656 | ||||||||
\(111\) | 5.12783 | 0.486712 | ||||||||
\(112\) | 2.34017 | 0.221126 | ||||||||
\(113\) | 12.8082 | 1.20489 | 0.602446 | − | 0.798160i | \(-0.294193\pi\) | ||||
0.602446 | + | 0.798160i | \(0.294193\pi\) | |||||||
\(114\) | −2.72979 | −0.255669 | ||||||||
\(115\) | 2.32684 | 0.216979 | ||||||||
\(116\) | −0.165166 | −0.0153353 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.26180 | 0.300273 | ||||||||
\(119\) | 2.87936 | 0.263951 | ||||||||
\(120\) | 0.764867 | 0.0698225 | ||||||||
\(121\) | −10.3112 | −0.937386 | ||||||||
\(122\) | −8.49693 | −0.769276 | ||||||||
\(123\) | −3.60197 | −0.324779 | ||||||||
\(124\) | −4.29072 | −0.385318 | ||||||||
\(125\) | −4.51026 | −0.403410 | ||||||||
\(126\) | −3.17009 | −0.282414 | ||||||||
\(127\) | −13.4680 | −1.19509 | −0.597546 | − | 0.801835i | \(-0.703857\pi\) | ||||
−0.597546 | + | 0.801835i | \(0.703857\pi\) | |||||||
\(128\) | −3.31965 | −0.293419 | ||||||||
\(129\) | −0.225678 | −0.0198698 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.4391 | −1.26155 | −0.630774 | − | 0.775967i | \(-0.717262\pi\) | ||||
−0.630774 | + | 0.775967i | \(0.717262\pi\) | |||||||
\(132\) | −0.282314 | −0.0245723 | ||||||||
\(133\) | −4.32684 | −0.375185 | ||||||||
\(134\) | 5.94214 | 0.513323 | ||||||||
\(135\) | −1.41855 | −0.122089 | ||||||||
\(136\) | −8.86376 | −0.760061 | ||||||||
\(137\) | 16.4319 | 1.40387 | 0.701935 | − | 0.712241i | \(-0.252320\pi\) | ||||
0.701935 | + | 0.712241i | \(0.252320\pi\) | |||||||
\(138\) | −3.18568 | −0.271184 | ||||||||
\(139\) | 13.2195 | 1.12127 | 0.560633 | − | 0.828064i | \(-0.310558\pi\) | ||||
0.560633 | + | 0.828064i | \(0.310558\pi\) | |||||||
\(140\) | 0.290725 | 0.0245707 | ||||||||
\(141\) | 4.98667 | 0.419953 | ||||||||
\(142\) | −14.9444 | −1.25411 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.34017 | 0.528348 | ||||||||
\(145\) | 0.120638 | 0.0100185 | ||||||||
\(146\) | −0.413630 | −0.0342323 | ||||||||
\(147\) | 0.539189 | 0.0444715 | ||||||||
\(148\) | −6.00000 | −0.493197 | ||||||||
\(149\) | 20.5041 | 1.67976 | 0.839881 | − | 0.542770i | \(-0.182624\pi\) | ||||
0.839881 | + | 0.542770i | \(0.182624\pi\) | |||||||
\(150\) | 3.02052 | 0.246624 | ||||||||
\(151\) | −1.59478 | −0.129781 | −0.0648907 | − | 0.997892i | \(-0.520670\pi\) | ||||
−0.0648907 | + | 0.997892i | \(0.520670\pi\) | |||||||
\(152\) | 13.3197 | 1.08037 | ||||||||
\(153\) | 7.80098 | 0.630672 | ||||||||
\(154\) | 0.971071 | 0.0782511 | ||||||||
\(155\) | 3.13397 | 0.251726 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.29791 | −0.662246 | −0.331123 | − | 0.943588i | \(-0.607427\pi\) | ||||
−0.331123 | + | 0.943588i | \(0.607427\pi\) | |||||||
\(158\) | −3.29565 | −0.262187 | ||||||||
\(159\) | 0.879362 | 0.0697379 | ||||||||
\(160\) | −1.57531 | −0.124539 | ||||||||
\(161\) | −5.04945 | −0.397952 | ||||||||
\(162\) | −7.56812 | −0.594608 | ||||||||
\(163\) | 0.398032 | 0.0311763 | 0.0155881 | − | 0.999878i | \(-0.495038\pi\) | ||||
0.0155881 | + | 0.999878i | \(0.495038\pi\) | |||||||
\(164\) | 4.21461 | 0.329106 | ||||||||
\(165\) | 0.206204 | 0.0160529 | ||||||||
\(166\) | −12.1412 | −0.942337 | ||||||||
\(167\) | −23.8710 | −1.84719 | −0.923595 | − | 0.383370i | \(-0.874763\pi\) | ||||
−0.923595 | + | 0.383370i | \(0.874763\pi\) | |||||||
\(168\) | −1.65983 | −0.128058 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.55252 | 0.119073 | ||||||||
\(171\) | −11.7226 | −0.896450 | ||||||||
\(172\) | 0.264063 | 0.0201346 | ||||||||
\(173\) | 25.8999 | 1.96913 | 0.984566 | − | 0.175015i | \(-0.0559975\pi\) | ||||
0.984566 | + | 0.175015i | \(0.0559975\pi\) | |||||||
\(174\) | −0.165166 | −0.0125212 | ||||||||
\(175\) | 4.78765 | 0.361913 | ||||||||
\(176\) | −1.94214 | −0.146394 | ||||||||
\(177\) | −1.50307 | −0.112978 | ||||||||
\(178\) | −6.35577 | −0.476385 | ||||||||
\(179\) | 20.6742 | 1.54526 | 0.772631 | − | 0.634855i | \(-0.218940\pi\) | ||||
0.772631 | + | 0.634855i | \(0.218940\pi\) | |||||||
\(180\) | 0.787653 | 0.0587082 | ||||||||
\(181\) | 15.7165 | 1.16820 | 0.584098 | − | 0.811683i | \(-0.301448\pi\) | ||||
0.584098 | + | 0.811683i | \(0.301448\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.91548 | 0.289441 | ||||||||
\(184\) | 15.5441 | 1.14593 | ||||||||
\(185\) | 4.38243 | 0.322203 | ||||||||
\(186\) | −4.29072 | −0.314611 | ||||||||
\(187\) | −2.38962 | −0.174746 | ||||||||
\(188\) | −5.83483 | −0.425549 | ||||||||
\(189\) | 3.07838 | 0.223919 | ||||||||
\(190\) | −2.33299 | −0.169253 | ||||||||
\(191\) | −16.7877 | −1.21471 | −0.607356 | − | 0.794430i | \(-0.707770\pi\) | ||||
−0.607356 | + | 0.794430i | \(0.707770\pi\) | |||||||
\(192\) | 4.68035 | 0.337775 | ||||||||
\(193\) | −20.0144 | −1.44067 | −0.720333 | − | 0.693628i | \(-0.756011\pi\) | ||||
−0.720333 | + | 0.693628i | \(0.756011\pi\) | |||||||
\(194\) | 14.7538 | 1.05926 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.630898 | −0.0450641 | ||||||||
\(197\) | 17.5174 | 1.24807 | 0.624033 | − | 0.781398i | \(-0.285493\pi\) | ||||
0.624033 | + | 0.781398i | \(0.285493\pi\) | |||||||
\(198\) | 2.63090 | 0.186970 | ||||||||
\(199\) | −16.2979 | −1.15533 | −0.577664 | − | 0.816275i | \(-0.696036\pi\) | ||||
−0.577664 | + | 0.816275i | \(0.696036\pi\) | |||||||
\(200\) | −14.7382 | −1.04215 | ||||||||
\(201\) | −2.73820 | −0.193138 | ||||||||
\(202\) | −4.26406 | −0.300018 | ||||||||
\(203\) | −0.261795 | −0.0183744 | ||||||||
\(204\) | 0.979481 | 0.0685774 | ||||||||
\(205\) | −3.07838 | −0.215003 | ||||||||
\(206\) | −20.9939 | −1.46271 | ||||||||
\(207\) | −13.6803 | −0.950850 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.59090 | 0.248388 | ||||||||
\(210\) | 0.290725 | 0.0200619 | ||||||||
\(211\) | 2.70928 | 0.186514 | 0.0932571 | − | 0.995642i | \(-0.470272\pi\) | ||||
0.0932571 | + | 0.995642i | \(0.470272\pi\) | |||||||
\(212\) | −1.02893 | −0.0706672 | ||||||||
\(213\) | 6.88655 | 0.471859 | ||||||||
\(214\) | −3.44521 | −0.235510 | ||||||||
\(215\) | −0.192873 | −0.0131538 | ||||||||
\(216\) | −9.47641 | −0.644788 | ||||||||
\(217\) | −6.80098 | −0.461681 | ||||||||
\(218\) | −9.86603 | −0.668212 | ||||||||
\(219\) | 0.190605 | 0.0128799 | ||||||||
\(220\) | −0.241276 | −0.0162668 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.00000 | −0.402694 | ||||||||
\(223\) | −19.7948 | −1.32556 | −0.662780 | − | 0.748814i | \(-0.730624\pi\) | ||||
−0.662780 | + | 0.748814i | \(0.730624\pi\) | |||||||
\(224\) | 3.41855 | 0.228412 | ||||||||
\(225\) | 12.9711 | 0.864738 | ||||||||
\(226\) | −14.9867 | −0.996898 | ||||||||
\(227\) | 13.2618 | 0.880216 | 0.440108 | − | 0.897945i | \(-0.354940\pi\) | ||||
0.440108 | + | 0.897945i | \(0.354940\pi\) | |||||||
\(228\) | −1.47187 | −0.0974773 | ||||||||
\(229\) | −27.8082 | −1.83762 | −0.918808 | − | 0.394705i | \(-0.870847\pi\) | ||||
−0.918808 | + | 0.394705i | \(0.870847\pi\) | |||||||
\(230\) | −2.72261 | −0.179523 | ||||||||
\(231\) | −0.447480 | −0.0294420 | ||||||||
\(232\) | 0.805905 | 0.0529102 | ||||||||
\(233\) | −13.3668 | −0.875690 | −0.437845 | − | 0.899050i | \(-0.644258\pi\) | ||||
−0.437845 | + | 0.899050i | \(0.644258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.26180 | 0.278009 | ||||||||
\(236\) | 1.75872 | 0.114483 | ||||||||
\(237\) | 1.51867 | 0.0986482 | ||||||||
\(238\) | −3.36910 | −0.218386 | ||||||||
\(239\) | −8.70701 | −0.563210 | −0.281605 | − | 0.959530i | \(-0.590867\pi\) | ||||
−0.281605 | + | 0.959530i | \(0.590867\pi\) | |||||||
\(240\) | −0.581449 | −0.0375324 | ||||||||
\(241\) | 16.9311 | 1.09063 | 0.545313 | − | 0.838232i | \(-0.316411\pi\) | ||||
0.545313 | + | 0.838232i | \(0.316411\pi\) | |||||||
\(242\) | 12.0650 | 0.775571 | ||||||||
\(243\) | 12.7226 | 0.816156 | ||||||||
\(244\) | −4.58145 | −0.293297 | ||||||||
\(245\) | 0.460811 | 0.0294401 | ||||||||
\(246\) | 4.21461 | 0.268714 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 20.9360 | 1.32944 | ||||||||
\(249\) | 5.59478 | 0.354555 | ||||||||
\(250\) | 5.27739 | 0.333772 | ||||||||
\(251\) | −8.82150 | −0.556808 | −0.278404 | − | 0.960464i | \(-0.589805\pi\) | ||||
−0.278404 | + | 0.960464i | \(0.589805\pi\) | |||||||
\(252\) | −1.70928 | −0.107674 | ||||||||
\(253\) | 4.19061 | 0.263461 | ||||||||
\(254\) | 15.7587 | 0.988790 | ||||||||
\(255\) | −0.715418 | −0.0448012 | ||||||||
\(256\) | −13.4764 | −0.842276 | ||||||||
\(257\) | −13.6442 | −0.851104 | −0.425552 | − | 0.904934i | \(-0.639920\pi\) | ||||
−0.425552 | + | 0.904934i | \(0.639920\pi\) | |||||||
\(258\) | 0.264063 | 0.0164398 | ||||||||
\(259\) | −9.51026 | −0.590939 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.709275 | −0.0439030 | ||||||||
\(262\) | 16.8950 | 1.04377 | ||||||||
\(263\) | −12.1773 | −0.750883 | −0.375441 | − | 0.926846i | \(-0.622509\pi\) | ||||
−0.375441 | + | 0.926846i | \(0.622509\pi\) | |||||||
\(264\) | 1.37751 | 0.0847801 | ||||||||
\(265\) | 0.751536 | 0.0461665 | ||||||||
\(266\) | 5.06278 | 0.310419 | ||||||||
\(267\) | 2.92881 | 0.179240 | ||||||||
\(268\) | 3.20394 | 0.195712 | ||||||||
\(269\) | −11.0472 | −0.673559 | −0.336779 | − | 0.941584i | \(-0.609338\pi\) | ||||
−0.336779 | + | 0.941584i | \(0.609338\pi\) | |||||||
\(270\) | 1.65983 | 0.101014 | ||||||||
\(271\) | 10.9360 | 0.664315 | 0.332157 | − | 0.943224i | \(-0.392224\pi\) | ||||
0.332157 | + | 0.943224i | \(0.392224\pi\) | |||||||
\(272\) | 6.73820 | 0.408564 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.2267 | −1.16153 | ||||||||
\(275\) | −3.97334 | −0.239601 | ||||||||
\(276\) | −1.71769 | −0.103393 | ||||||||
\(277\) | −26.1194 | −1.56936 | −0.784682 | − | 0.619899i | \(-0.787174\pi\) | ||||
−0.784682 | + | 0.619899i | \(0.787174\pi\) | |||||||
\(278\) | −15.4680 | −0.927709 | ||||||||
\(279\) | −18.4257 | −1.10312 | ||||||||
\(280\) | −1.41855 | −0.0847746 | ||||||||
\(281\) | −4.80325 | −0.286538 | −0.143269 | − | 0.989684i | \(-0.545761\pi\) | ||||
−0.143269 | + | 0.989684i | \(0.545761\pi\) | |||||||
\(282\) | −5.83483 | −0.347459 | ||||||||
\(283\) | 0.979481 | 0.0582241 | 0.0291121 | − | 0.999576i | \(-0.490732\pi\) | ||||
0.0291121 | + | 0.999576i | \(0.490732\pi\) | |||||||
\(284\) | −8.05786 | −0.478146 | ||||||||
\(285\) | 1.07507 | 0.0636814 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.68035 | 0.394328 | ||||||||
\(288\) | 9.26180 | 0.545757 | ||||||||
\(289\) | −8.70928 | −0.512310 | ||||||||
\(290\) | −0.141157 | −0.00828903 | ||||||||
\(291\) | −6.79872 | −0.398548 | ||||||||
\(292\) | −0.223025 | −0.0130515 | ||||||||
\(293\) | 24.3268 | 1.42119 | 0.710595 | − | 0.703602i | \(-0.248426\pi\) | ||||
0.710595 | + | 0.703602i | \(0.248426\pi\) | |||||||
\(294\) | −0.630898 | −0.0367947 | ||||||||
\(295\) | −1.28458 | −0.0747912 | ||||||||
\(296\) | 29.2762 | 1.70164 | ||||||||
\(297\) | −2.55479 | −0.148244 | ||||||||
\(298\) | −23.9916 | −1.38980 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.62863 | 0.0940290 | ||||||||
\(301\) | 0.418551 | 0.0241249 | ||||||||
\(302\) | 1.86603 | 0.107378 | ||||||||
\(303\) | 1.96493 | 0.112882 | ||||||||
\(304\) | −10.1256 | −0.580741 | ||||||||
\(305\) | 3.34632 | 0.191609 | ||||||||
\(306\) | −9.12783 | −0.521803 | ||||||||
\(307\) | −6.21953 | −0.354968 | −0.177484 | − | 0.984124i | \(-0.556796\pi\) | ||||
−0.177484 | + | 0.984124i | \(0.556796\pi\) | |||||||
\(308\) | 0.523590 | 0.0298343 | ||||||||
\(309\) | 9.67420 | 0.550346 | ||||||||
\(310\) | −3.66701 | −0.208272 | ||||||||
\(311\) | −25.1084 | −1.42376 | −0.711882 | − | 0.702299i | \(-0.752157\pi\) | ||||
−0.711882 | + | 0.702299i | \(0.752157\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.24005 | 0.126615 | 0.0633077 | − | 0.997994i | \(-0.479835\pi\) | ||||
0.0633077 | + | 0.997994i | \(0.479835\pi\) | |||||||
\(314\) | 9.70928 | 0.547926 | ||||||||
\(315\) | 1.24846 | 0.0703430 | ||||||||
\(316\) | −1.77698 | −0.0999627 | ||||||||
\(317\) | −2.89496 | −0.162597 | −0.0812986 | − | 0.996690i | \(-0.525907\pi\) | ||||
−0.0812986 | + | 0.996690i | \(0.525907\pi\) | |||||||
\(318\) | −1.02893 | −0.0576995 | ||||||||
\(319\) | 0.217267 | 0.0121646 | ||||||||
\(320\) | 4.00000 | 0.223607 | ||||||||
\(321\) | 1.58759 | 0.0886108 | ||||||||
\(322\) | 5.90829 | 0.329256 | ||||||||
\(323\) | −12.4585 | −0.693212 | ||||||||
\(324\) | −4.08065 | −0.226703 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.465732 | −0.0257945 | ||||||||
\(327\) | 4.54638 | 0.251415 | ||||||||
\(328\) | −20.5646 | −1.13549 | ||||||||
\(329\) | −9.24846 | −0.509884 | ||||||||
\(330\) | −0.241276 | −0.0132818 | ||||||||
\(331\) | −4.25565 | −0.233912 | −0.116956 | − | 0.993137i | \(-0.537314\pi\) | ||||
−0.116956 | + | 0.993137i | \(0.537314\pi\) | |||||||
\(332\) | −6.54638 | −0.359279 | ||||||||
\(333\) | −25.7659 | −1.41196 | ||||||||
\(334\) | 27.9311 | 1.52832 | ||||||||
\(335\) | −2.34017 | −0.127857 | ||||||||
\(336\) | 1.26180 | 0.0688366 | ||||||||
\(337\) | 15.5464 | 0.846865 | 0.423433 | − | 0.905928i | \(-0.360825\pi\) | ||||
0.423433 | + | 0.905928i | \(0.360825\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.90602 | 0.375084 | ||||||||
\(340\) | 0.837101 | 0.0453982 | ||||||||
\(341\) | 5.64423 | 0.305652 | ||||||||
\(342\) | 13.7165 | 0.741701 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.28846 | −0.0694690 | ||||||||
\(345\) | 1.25461 | 0.0675458 | ||||||||
\(346\) | −30.3051 | −1.62921 | ||||||||
\(347\) | −20.3812 | −1.09412 | −0.547060 | − | 0.837093i | \(-0.684253\pi\) | ||||
−0.547060 | + | 0.837093i | \(0.684253\pi\) | |||||||
\(348\) | −0.0890557 | −0.00477388 | ||||||||
\(349\) | −7.16394 | −0.383477 | −0.191739 | − | 0.981446i | \(-0.561413\pi\) | ||||
−0.191739 | + | 0.981446i | \(0.561413\pi\) | |||||||
\(350\) | −5.60197 | −0.299438 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.83710 | −0.151218 | ||||||||
\(353\) | −5.38348 | −0.286534 | −0.143267 | − | 0.989684i | \(-0.545761\pi\) | ||||
−0.143267 | + | 0.989684i | \(0.545761\pi\) | |||||||
\(354\) | 1.75872 | 0.0934751 | ||||||||
\(355\) | 5.88550 | 0.312370 | ||||||||
\(356\) | −3.42696 | −0.181629 | ||||||||
\(357\) | 1.55252 | 0.0821681 | ||||||||
\(358\) | −24.1906 | −1.27851 | ||||||||
\(359\) | 15.6937 | 0.828281 | 0.414140 | − | 0.910213i | \(-0.364082\pi\) | ||||
0.414140 | + | 0.910213i | \(0.364082\pi\) | |||||||
\(360\) | −3.84324 | −0.202557 | ||||||||
\(361\) | −0.278438 | −0.0146547 | ||||||||
\(362\) | −18.3896 | −0.966537 | ||||||||
\(363\) | −5.55971 | −0.291809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.162899 | 0.00852650 | ||||||||
\(366\) | −4.58145 | −0.239476 | ||||||||
\(367\) | 0.324575 | 0.0169427 | 0.00847133 | − | 0.999964i | \(-0.497303\pi\) | ||||
0.00847133 | + | 0.999964i | \(0.497303\pi\) | |||||||
\(368\) | −11.8166 | −0.615982 | ||||||||
\(369\) | 18.0989 | 0.942191 | ||||||||
\(370\) | −5.12783 | −0.266583 | ||||||||
\(371\) | −1.63090 | −0.0846720 | ||||||||
\(372\) | −2.31351 | −0.119950 | ||||||||
\(373\) | −25.3112 | −1.31057 | −0.655283 | − | 0.755383i | \(-0.727451\pi\) | ||||
−0.655283 | + | 0.755383i | \(0.727451\pi\) | |||||||
\(374\) | 2.79606 | 0.144581 | ||||||||
\(375\) | −2.43188 | −0.125582 | ||||||||
\(376\) | 28.4703 | 1.46824 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.60197 | −0.185265 | ||||||||
\(379\) | −16.7187 | −0.858784 | −0.429392 | − | 0.903118i | \(-0.641272\pi\) | ||||
−0.429392 | + | 0.903118i | \(0.641272\pi\) | |||||||
\(380\) | −1.25792 | −0.0645299 | ||||||||
\(381\) | −7.26180 | −0.372033 | ||||||||
\(382\) | 19.6430 | 1.00502 | ||||||||
\(383\) | 13.1629 | 0.672593 | 0.336296 | − | 0.941756i | \(-0.390826\pi\) | ||||
0.336296 | + | 0.941756i | \(0.390826\pi\) | |||||||
\(384\) | −1.78992 | −0.0913415 | ||||||||
\(385\) | −0.382433 | −0.0194906 | ||||||||
\(386\) | 23.4186 | 1.19197 | ||||||||
\(387\) | 1.13397 | 0.0576429 | ||||||||
\(388\) | 7.95509 | 0.403858 | ||||||||
\(389\) | −10.0761 | −0.510879 | −0.255440 | − | 0.966825i | \(-0.582220\pi\) | ||||
−0.255440 | + | 0.966825i | \(0.582220\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.5392 | −0.735278 | ||||||||
\(392\) | 3.07838 | 0.155482 | ||||||||
\(393\) | −7.78539 | −0.392721 | ||||||||
\(394\) | −20.4969 | −1.03262 | ||||||||
\(395\) | 1.29791 | 0.0653051 | ||||||||
\(396\) | 1.41855 | 0.0712849 | ||||||||
\(397\) | 8.07119 | 0.405081 | 0.202541 | − | 0.979274i | \(-0.435080\pi\) | ||||
0.202541 | + | 0.979274i | \(0.435080\pi\) | |||||||
\(398\) | 19.0700 | 0.955891 | ||||||||
\(399\) | −2.33299 | −0.116795 | ||||||||
\(400\) | 11.2039 | 0.560197 | ||||||||
\(401\) | 12.8371 | 0.641054 | 0.320527 | − | 0.947239i | \(-0.396140\pi\) | ||||
0.320527 | + | 0.947239i | \(0.396140\pi\) | |||||||
\(402\) | 3.20394 | 0.159798 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2.29914 | −0.114386 | ||||||||
\(405\) | 2.98053 | 0.148104 | ||||||||
\(406\) | 0.306323 | 0.0152026 | ||||||||
\(407\) | 7.89269 | 0.391226 | ||||||||
\(408\) | −4.77924 | −0.236608 | ||||||||
\(409\) | −18.7515 | −0.927204 | −0.463602 | − | 0.886044i | \(-0.653443\pi\) | ||||
−0.463602 | + | 0.886044i | \(0.653443\pi\) | |||||||
\(410\) | 3.60197 | 0.177889 | ||||||||
\(411\) | 8.85989 | 0.437026 | ||||||||
\(412\) | −11.3197 | −0.557679 | ||||||||
\(413\) | 2.78765 | 0.137171 | ||||||||
\(414\) | 16.0072 | 0.786710 | ||||||||
\(415\) | 4.78151 | 0.234715 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.12783 | 0.349051 | ||||||||
\(418\) | −4.20167 | −0.205510 | ||||||||
\(419\) | 23.6319 | 1.15450 | 0.577248 | − | 0.816569i | \(-0.304127\pi\) | ||||
0.577248 | + | 0.816569i | \(0.304127\pi\) | |||||||
\(420\) | 0.156755 | 0.00764888 | ||||||||
\(421\) | −19.4524 | −0.948052 | −0.474026 | − | 0.880511i | \(-0.657200\pi\) | ||||
−0.474026 | + | 0.880511i | \(0.657200\pi\) | |||||||
\(422\) | −3.17009 | −0.154317 | ||||||||
\(423\) | −25.0566 | −1.21830 | ||||||||
\(424\) | 5.02052 | 0.243818 | ||||||||
\(425\) | 13.7854 | 0.668689 | ||||||||
\(426\) | −8.05786 | −0.390405 | ||||||||
\(427\) | −7.26180 | −0.351423 | ||||||||
\(428\) | −1.85762 | −0.0897915 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.225678 | 0.0108832 | ||||||||
\(431\) | −18.0989 | −0.871793 | −0.435897 | − | 0.899997i | \(-0.643569\pi\) | ||||
−0.435897 | + | 0.899997i | \(0.643569\pi\) | |||||||
\(432\) | 7.20394 | 0.346600 | ||||||||
\(433\) | 20.5380 | 0.986992 | 0.493496 | − | 0.869748i | \(-0.335719\pi\) | ||||
0.493496 | + | 0.869748i | \(0.335719\pi\) | |||||||
\(434\) | 7.95774 | 0.381984 | ||||||||
\(435\) | 0.0650468 | 0.00311875 | ||||||||
\(436\) | −5.31965 | −0.254765 | ||||||||
\(437\) | 21.8482 | 1.04514 | ||||||||
\(438\) | −0.223025 | −0.0106565 | ||||||||
\(439\) | −26.9627 | −1.28686 | −0.643429 | − | 0.765506i | \(-0.722489\pi\) | ||||
−0.643429 | + | 0.765506i | \(0.722489\pi\) | |||||||
\(440\) | 1.17727 | 0.0561244 | ||||||||
\(441\) | −2.70928 | −0.129013 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.4101 | 1.25478 | 0.627392 | − | 0.778704i | \(-0.284122\pi\) | ||||
0.627392 | + | 0.778704i | \(0.284122\pi\) | |||||||
\(444\) | −3.23513 | −0.153533 | ||||||||
\(445\) | 2.50307 | 0.118657 | ||||||||
\(446\) | 23.1617 | 1.09674 | ||||||||
\(447\) | 11.0556 | 0.522912 | ||||||||
\(448\) | −8.68035 | −0.410108 | ||||||||
\(449\) | 31.4329 | 1.48341 | 0.741706 | − | 0.670725i | \(-0.234017\pi\) | ||||
0.741706 | + | 0.670725i | \(0.234017\pi\) | |||||||
\(450\) | −15.1773 | −0.715464 | ||||||||
\(451\) | −5.54411 | −0.261062 | ||||||||
\(452\) | −8.08065 | −0.380082 | ||||||||
\(453\) | −0.859888 | −0.0404011 | ||||||||
\(454\) | −15.5174 | −0.728270 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.18181 | 0.336319 | ||||||||
\(457\) | 18.0650 | 0.845047 | 0.422524 | − | 0.906352i | \(-0.361144\pi\) | ||||
0.422524 | + | 0.906352i | \(0.361144\pi\) | |||||||
\(458\) | 32.5380 | 1.52040 | ||||||||
\(459\) | 8.86376 | 0.413725 | ||||||||
\(460\) | −1.46800 | −0.0684458 | ||||||||
\(461\) | 23.0784 | 1.07487 | 0.537434 | − | 0.843306i | \(-0.319394\pi\) | ||||
0.537434 | + | 0.843306i | \(0.319394\pi\) | |||||||
\(462\) | 0.523590 | 0.0243596 | ||||||||
\(463\) | 4.54760 | 0.211345 | 0.105672 | − | 0.994401i | \(-0.466301\pi\) | ||||
0.105672 | + | 0.994401i | \(0.466301\pi\) | |||||||
\(464\) | −0.612646 | −0.0284414 | ||||||||
\(465\) | 1.68980 | 0.0783627 | ||||||||
\(466\) | 15.6404 | 0.724525 | ||||||||
\(467\) | 37.8154 | 1.74989 | 0.874943 | − | 0.484226i | \(-0.160899\pi\) | ||||
0.874943 | + | 0.484226i | \(0.160899\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.07838 | 0.234498 | ||||||||
\(470\) | −4.98667 | −0.230018 | ||||||||
\(471\) | −4.47414 | −0.206158 | ||||||||
\(472\) | −8.58145 | −0.394993 | ||||||||
\(473\) | −0.347361 | −0.0159717 | ||||||||
\(474\) | −1.77698 | −0.0816192 | ||||||||
\(475\) | −20.7154 | −0.950489 | ||||||||
\(476\) | −1.81658 | −0.0832629 | ||||||||
\(477\) | −4.41855 | −0.202312 | ||||||||
\(478\) | 10.1880 | 0.465986 | ||||||||
\(479\) | 9.24005 | 0.422189 | 0.211094 | − | 0.977466i | \(-0.432297\pi\) | ||||
0.211094 | + | 0.977466i | \(0.432297\pi\) | |||||||
\(480\) | −0.849388 | −0.0387691 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −19.8108 | −0.902358 | ||||||||
\(483\) | −2.72261 | −0.123883 | ||||||||
\(484\) | 6.50534 | 0.295697 | ||||||||
\(485\) | −5.81044 | −0.263838 | ||||||||
\(486\) | −14.8865 | −0.675268 | ||||||||
\(487\) | −13.6598 | −0.618986 | −0.309493 | − | 0.950902i | \(-0.600159\pi\) | ||||
−0.309493 | + | 0.950902i | \(0.600159\pi\) | |||||||
\(488\) | 22.3545 | 1.01194 | ||||||||
\(489\) | 0.214614 | 0.00970519 | ||||||||
\(490\) | −0.539189 | −0.0243581 | ||||||||
\(491\) | −29.6514 | −1.33815 | −0.669075 | − | 0.743195i | \(-0.733309\pi\) | ||||
−0.669075 | + | 0.743195i | \(0.733309\pi\) | |||||||
\(492\) | 2.27247 | 0.102451 | ||||||||
\(493\) | −0.753803 | −0.0339496 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.03612 | −0.0465700 | ||||||||
\(496\) | −15.9155 | −0.714626 | ||||||||
\(497\) | −12.7721 | −0.572905 | ||||||||
\(498\) | −6.54638 | −0.293350 | ||||||||
\(499\) | 35.5246 | 1.59030 | 0.795151 | − | 0.606412i | \(-0.207392\pi\) | ||||
0.795151 | + | 0.606412i | \(0.207392\pi\) | |||||||
\(500\) | 2.84551 | 0.127255 | ||||||||
\(501\) | −12.8710 | −0.575032 | ||||||||
\(502\) | 10.3219 | 0.460690 | ||||||||
\(503\) | 34.4124 | 1.53437 | 0.767187 | − | 0.641424i | \(-0.221656\pi\) | ||||
0.767187 | + | 0.641424i | \(0.221656\pi\) | |||||||
\(504\) | 8.34017 | 0.371501 | ||||||||
\(505\) | 1.67930 | 0.0747279 | ||||||||
\(506\) | −4.90337 | −0.217981 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.49693 | 0.376990 | ||||||||
\(509\) | 11.1184 | 0.492813 | 0.246407 | − | 0.969167i | \(-0.420750\pi\) | ||||
0.246407 | + | 0.969167i | \(0.420750\pi\) | |||||||
\(510\) | 0.837101 | 0.0370675 | ||||||||
\(511\) | −0.353504 | −0.0156381 | ||||||||
\(512\) | 22.4079 | 0.990297 | ||||||||
\(513\) | −13.3197 | −0.588077 | ||||||||
\(514\) | 15.9649 | 0.704183 | ||||||||
\(515\) | 8.26794 | 0.364329 | ||||||||
\(516\) | 0.142380 | 0.00626791 | ||||||||
\(517\) | 7.67543 | 0.337565 | ||||||||
\(518\) | 11.1278 | 0.488929 | ||||||||
\(519\) | 13.9649 | 0.612992 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.8888 | −0.783723 | −0.391862 | − | 0.920024i | \(-0.628169\pi\) | ||||
−0.391862 | + | 0.920024i | \(0.628169\pi\) | |||||||
\(522\) | 0.829914 | 0.0363243 | ||||||||
\(523\) | −23.9877 | −1.04891 | −0.524455 | − | 0.851438i | \(-0.675731\pi\) | ||||
−0.524455 | + | 0.851438i | \(0.675731\pi\) | |||||||
\(524\) | 9.10957 | 0.397954 | ||||||||
\(525\) | 2.58145 | 0.112664 | ||||||||
\(526\) | 14.2485 | 0.621263 | ||||||||
\(527\) | −19.5825 | −0.853027 | ||||||||
\(528\) | −1.04718 | −0.0455727 | ||||||||
\(529\) | 2.49693 | 0.108562 | ||||||||
\(530\) | −0.879362 | −0.0381970 | ||||||||
\(531\) | 7.55252 | 0.327751 | ||||||||
\(532\) | 2.72979 | 0.118352 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.42696 | −0.148299 | ||||||||
\(535\) | 1.35682 | 0.0586603 | ||||||||
\(536\) | −15.6332 | −0.675250 | ||||||||
\(537\) | 11.1473 | 0.481042 | ||||||||
\(538\) | 12.9262 | 0.557286 | ||||||||
\(539\) | 0.829914 | 0.0357469 | ||||||||
\(540\) | 0.894960 | 0.0385130 | ||||||||
\(541\) | −19.4114 | −0.834560 | −0.417280 | − | 0.908778i | \(-0.637017\pi\) | ||||
−0.417280 | + | 0.908778i | \(0.637017\pi\) | |||||||
\(542\) | −12.7961 | −0.549638 | ||||||||
\(543\) | 8.47414 | 0.363660 | ||||||||
\(544\) | 9.84324 | 0.422026 | ||||||||
\(545\) | 3.88550 | 0.166437 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.81432 | −0.0775745 | −0.0387873 | − | 0.999247i | \(-0.512349\pi\) | ||||
−0.0387873 | + | 0.999247i | \(0.512349\pi\) | |||||||
\(548\) | −10.3668 | −0.442849 | ||||||||
\(549\) | −19.6742 | −0.839675 | ||||||||
\(550\) | 4.64915 | 0.198240 | ||||||||
\(551\) | 1.13275 | 0.0482566 | ||||||||
\(552\) | 8.38121 | 0.356728 | ||||||||
\(553\) | −2.81658 | −0.119773 | ||||||||
\(554\) | 30.5620 | 1.29845 | ||||||||
\(555\) | 2.36296 | 0.100302 | ||||||||
\(556\) | −8.34017 | −0.353702 | ||||||||
\(557\) | 23.4186 | 0.992276 | 0.496138 | − | 0.868244i | \(-0.334751\pi\) | ||||
0.496138 | + | 0.868244i | \(0.334751\pi\) | |||||||
\(558\) | 21.5597 | 0.912695 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.07838 | 0.0455698 | ||||||||
\(561\) | −1.28846 | −0.0543987 | ||||||||
\(562\) | 5.62022 | 0.237075 | ||||||||
\(563\) | 26.6947 | 1.12505 | 0.562524 | − | 0.826781i | \(-0.309830\pi\) | ||||
0.562524 | + | 0.826781i | \(0.309830\pi\) | |||||||
\(564\) | −3.14608 | −0.132474 | ||||||||
\(565\) | 5.90215 | 0.248305 | ||||||||
\(566\) | −1.14608 | −0.0481732 | ||||||||
\(567\) | −6.46800 | −0.271630 | ||||||||
\(568\) | 39.3172 | 1.64971 | ||||||||
\(569\) | −26.5897 | −1.11470 | −0.557349 | − | 0.830279i | \(-0.688181\pi\) | ||||
−0.557349 | + | 0.830279i | \(0.688181\pi\) | |||||||
\(570\) | −1.25792 | −0.0526885 | ||||||||
\(571\) | −3.43310 | −0.143671 | −0.0718355 | − | 0.997416i | \(-0.522886\pi\) | ||||
−0.0718355 | + | 0.997416i | \(0.522886\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.05172 | −0.378141 | ||||||||
\(574\) | −7.81658 | −0.326258 | ||||||||
\(575\) | −24.1750 | −1.00817 | ||||||||
\(576\) | −23.5174 | −0.979894 | ||||||||
\(577\) | 30.4657 | 1.26831 | 0.634153 | − | 0.773208i | \(-0.281349\pi\) | ||||
0.634153 | + | 0.773208i | \(0.281349\pi\) | |||||||
\(578\) | 10.1906 | 0.423873 | ||||||||
\(579\) | −10.7915 | −0.448481 | ||||||||
\(580\) | −0.0761103 | −0.00316031 | ||||||||
\(581\) | −10.3763 | −0.430481 | ||||||||
\(582\) | 7.95509 | 0.329749 | ||||||||
\(583\) | 1.35350 | 0.0560564 | ||||||||
\(584\) | 1.08822 | 0.0450308 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.4645 | −1.17586 | ||||||||
\(587\) | 26.2606 | 1.08389 | 0.541945 | − | 0.840414i | \(-0.317688\pi\) | ||||
0.541945 | + | 0.840414i | \(0.317688\pi\) | |||||||
\(588\) | −0.340173 | −0.0140285 | ||||||||
\(589\) | 29.4268 | 1.21251 | ||||||||
\(590\) | 1.50307 | 0.0618805 | ||||||||
\(591\) | 9.44521 | 0.388524 | ||||||||
\(592\) | −22.2557 | −0.914702 | ||||||||
\(593\) | 40.8420 | 1.67718 | 0.838590 | − | 0.544762i | \(-0.183380\pi\) | ||||
0.838590 | + | 0.544762i | \(0.183380\pi\) | |||||||
\(594\) | 2.98932 | 0.122653 | ||||||||
\(595\) | 1.32684 | 0.0543952 | ||||||||
\(596\) | −12.9360 | −0.529879 | ||||||||
\(597\) | −8.78765 | −0.359655 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.3545 | −1.11768 | −0.558838 | − | 0.829277i | \(-0.688753\pi\) | ||||
−0.558838 | + | 0.829277i | \(0.688753\pi\) | |||||||
\(600\) | −7.94668 | −0.324422 | ||||||||
\(601\) | 25.4908 | 1.03979 | 0.519895 | − | 0.854230i | \(-0.325971\pi\) | ||||
0.519895 | + | 0.854230i | \(0.325971\pi\) | |||||||
\(602\) | −0.489741 | −0.0199603 | ||||||||
\(603\) | 13.7587 | 0.560299 | ||||||||
\(604\) | 1.00614 | 0.0409394 | ||||||||
\(605\) | −4.75154 | −0.193177 | ||||||||
\(606\) | −2.29914 | −0.0933960 | ||||||||
\(607\) | 19.9311 | 0.808977 | 0.404489 | − | 0.914543i | \(-0.367449\pi\) | ||||
0.404489 | + | 0.914543i | \(0.367449\pi\) | |||||||
\(608\) | −14.7915 | −0.599876 | ||||||||
\(609\) | −0.141157 | −0.00571997 | ||||||||
\(610\) | −3.91548 | −0.158533 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.92162 | −0.198945 | ||||||||
\(613\) | 22.7214 | 0.917708 | 0.458854 | − | 0.888512i | \(-0.348260\pi\) | ||||
0.458854 | + | 0.888512i | \(0.348260\pi\) | |||||||
\(614\) | 7.27739 | 0.293692 | ||||||||
\(615\) | −1.65983 | −0.0669307 | ||||||||
\(616\) | −2.55479 | −0.102935 | ||||||||
\(617\) | −14.3545 | −0.577892 | −0.288946 | − | 0.957345i | \(-0.593305\pi\) | ||||
−0.288946 | + | 0.957345i | \(0.593305\pi\) | |||||||
\(618\) | −11.3197 | −0.455343 | ||||||||
\(619\) | 27.9832 | 1.12474 | 0.562369 | − | 0.826886i | \(-0.309890\pi\) | ||||
0.562369 | + | 0.826886i | \(0.309890\pi\) | |||||||
\(620\) | −1.97721 | −0.0794068 | ||||||||
\(621\) | −15.5441 | −0.623764 | ||||||||
\(622\) | 29.3789 | 1.17799 | ||||||||
\(623\) | −5.43188 | −0.217624 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.8599 | 0.874396 | ||||||||
\(626\) | −2.62106 | −0.104758 | ||||||||
\(627\) | 1.93618 | 0.0773234 | ||||||||
\(628\) | 5.23513 | 0.208905 | ||||||||
\(629\) | −27.3835 | −1.09185 | ||||||||
\(630\) | −1.46081 | −0.0582001 | ||||||||
\(631\) | −21.4186 | −0.852659 | −0.426330 | − | 0.904568i | \(-0.640194\pi\) | ||||
−0.426330 | + | 0.904568i | \(0.640194\pi\) | |||||||
\(632\) | 8.67050 | 0.344894 | ||||||||
\(633\) | 1.46081 | 0.0580620 | ||||||||
\(634\) | 3.38735 | 0.134529 | ||||||||
\(635\) | −6.20620 | −0.246286 | ||||||||
\(636\) | −0.554787 | −0.0219987 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.254222 | −0.0100647 | ||||||||
\(639\) | −34.6030 | −1.36887 | ||||||||
\(640\) | −1.52973 | −0.0604680 | ||||||||
\(641\) | −37.9360 | −1.49838 | −0.749191 | − | 0.662354i | \(-0.769557\pi\) | ||||
−0.749191 | + | 0.662354i | \(0.769557\pi\) | |||||||
\(642\) | −1.85762 | −0.0733144 | ||||||||
\(643\) | 36.2122 | 1.42807 | 0.714034 | − | 0.700111i | \(-0.246866\pi\) | ||||
0.714034 | + | 0.700111i | \(0.246866\pi\) | |||||||
\(644\) | 3.18568 | 0.125534 | ||||||||
\(645\) | −0.103995 | −0.00409479 | ||||||||
\(646\) | 14.5776 | 0.573547 | ||||||||
\(647\) | 42.7948 | 1.68244 | 0.841219 | − | 0.540694i | \(-0.181838\pi\) | ||||
0.841219 | + | 0.540694i | \(0.181838\pi\) | |||||||
\(648\) | 19.9109 | 0.782176 | ||||||||
\(649\) | −2.31351 | −0.0908132 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.66701 | −0.143722 | ||||||||
\(652\) | −0.251117 | −0.00983451 | ||||||||
\(653\) | 5.54864 | 0.217135 | 0.108568 | − | 0.994089i | \(-0.465374\pi\) | ||||
0.108568 | + | 0.994089i | \(0.465374\pi\) | |||||||
\(654\) | −5.31965 | −0.208015 | ||||||||
\(655\) | −6.65368 | −0.259981 | ||||||||
\(656\) | 15.6332 | 0.610373 | ||||||||
\(657\) | −0.957740 | −0.0373650 | ||||||||
\(658\) | 10.8215 | 0.421866 | ||||||||
\(659\) | −23.1529 | −0.901908 | −0.450954 | − | 0.892547i | \(-0.648916\pi\) | ||||
−0.450954 | + | 0.892547i | \(0.648916\pi\) | |||||||
\(660\) | −0.130094 | −0.00506388 | ||||||||
\(661\) | 47.2544 | 1.83798 | 0.918992 | − | 0.394276i | \(-0.129005\pi\) | ||||
0.918992 | + | 0.394276i | \(0.129005\pi\) | |||||||
\(662\) | 4.97948 | 0.193533 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.9421 | 1.23960 | ||||||||
\(665\) | −1.99386 | −0.0773185 | ||||||||
\(666\) | 30.1483 | 1.16822 | ||||||||
\(667\) | 1.32192 | 0.0511850 | ||||||||
\(668\) | 15.0601 | 0.582694 | ||||||||
\(669\) | −10.6732 | −0.412648 | ||||||||
\(670\) | 2.73820 | 0.105786 | ||||||||
\(671\) | 6.02666 | 0.232657 | ||||||||
\(672\) | 1.84324 | 0.0711047 | ||||||||
\(673\) | −3.42082 | −0.131863 | −0.0659314 | − | 0.997824i | \(-0.521002\pi\) | ||||
−0.0659314 | + | 0.997824i | \(0.521002\pi\) | |||||||
\(674\) | −18.1906 | −0.700676 | ||||||||
\(675\) | 14.7382 | 0.567274 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.6959 | 0.411079 | 0.205539 | − | 0.978649i | \(-0.434105\pi\) | ||||
0.205539 | + | 0.978649i | \(0.434105\pi\) | |||||||
\(678\) | −8.08065 | −0.310335 | ||||||||
\(679\) | 12.6092 | 0.483895 | ||||||||
\(680\) | −4.08452 | −0.156634 | ||||||||
\(681\) | 7.15061 | 0.274012 | ||||||||
\(682\) | −6.60424 | −0.252889 | ||||||||
\(683\) | 6.59583 | 0.252382 | 0.126191 | − | 0.992006i | \(-0.459725\pi\) | ||||
0.126191 | + | 0.992006i | \(0.459725\pi\) | |||||||
\(684\) | 7.39576 | 0.282784 | ||||||||
\(685\) | 7.57199 | 0.289311 | ||||||||
\(686\) | 1.17009 | 0.0446741 | ||||||||
\(687\) | −14.9939 | −0.572051 | ||||||||
\(688\) | 0.979481 | 0.0373424 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.46800 | −0.0558858 | ||||||||
\(691\) | −49.4729 | −1.88204 | −0.941019 | − | 0.338353i | \(-0.890130\pi\) | ||||
−0.941019 | + | 0.338353i | \(0.890130\pi\) | |||||||
\(692\) | −16.3402 | −0.621160 | ||||||||
\(693\) | 2.24846 | 0.0854121 | ||||||||
\(694\) | 23.8478 | 0.905249 | ||||||||
\(695\) | 6.09171 | 0.231072 | ||||||||
\(696\) | 0.434535 | 0.0164710 | ||||||||
\(697\) | 19.2351 | 0.728583 | ||||||||
\(698\) | 8.38243 | 0.317280 | ||||||||
\(699\) | −7.20725 | −0.272603 | ||||||||
\(700\) | −3.02052 | −0.114165 | ||||||||
\(701\) | 20.8166 | 0.786231 | 0.393116 | − | 0.919489i | \(-0.371397\pi\) | ||||
0.393116 | + | 0.919489i | \(0.371397\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.1494 | 1.55198 | ||||||||
\(704\) | 7.20394 | 0.271509 | ||||||||
\(705\) | 2.29791 | 0.0865444 | ||||||||
\(706\) | 6.29914 | 0.237071 | ||||||||
\(707\) | −3.64423 | −0.137055 | ||||||||
\(708\) | 0.948284 | 0.0356387 | ||||||||
\(709\) | 5.95386 | 0.223602 | 0.111801 | − | 0.993731i | \(-0.464338\pi\) | ||||
0.111801 | + | 0.993731i | \(0.464338\pi\) | |||||||
\(710\) | −6.88655 | −0.258448 | ||||||||
\(711\) | −7.63090 | −0.286181 | ||||||||
\(712\) | 16.7214 | 0.626660 | ||||||||
\(713\) | 34.3412 | 1.28609 | ||||||||
\(714\) | −1.81658 | −0.0679839 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.0433 | −0.487451 | ||||||||
\(717\) | −4.69472 | −0.175328 | ||||||||
\(718\) | −18.3630 | −0.685300 | ||||||||
\(719\) | −1.68980 | −0.0630190 | −0.0315095 | − | 0.999503i | \(-0.510031\pi\) | ||||
−0.0315095 | + | 0.999503i | \(0.510031\pi\) | |||||||
\(720\) | 2.92162 | 0.108882 | ||||||||
\(721\) | −17.9421 | −0.668200 | ||||||||
\(722\) | 0.325797 | 0.0121249 | ||||||||
\(723\) | 9.12905 | 0.339513 | ||||||||
\(724\) | −9.91548 | −0.368506 | ||||||||
\(725\) | −1.25338 | −0.0465495 | ||||||||
\(726\) | 6.50534 | 0.241436 | ||||||||
\(727\) | 14.0722 | 0.521910 | 0.260955 | − | 0.965351i | \(-0.415963\pi\) | ||||
0.260955 | + | 0.965351i | \(0.415963\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.5441 | −0.464597 | ||||||||
\(730\) | −0.190605 | −0.00705462 | ||||||||
\(731\) | 1.20516 | 0.0445744 | ||||||||
\(732\) | −2.47027 | −0.0913037 | ||||||||
\(733\) | −10.9311 | −0.403749 | −0.201874 | − | 0.979411i | \(-0.564703\pi\) | ||||
−0.201874 | + | 0.979411i | \(0.564703\pi\) | |||||||
\(734\) | −0.379780 | −0.0140179 | ||||||||
\(735\) | 0.248464 | 0.00916474 | ||||||||
\(736\) | −17.2618 | −0.636278 | ||||||||
\(737\) | −4.21461 | −0.155247 | ||||||||
\(738\) | −21.1773 | −0.779546 | ||||||||
\(739\) | −3.17009 | −0.116614 | −0.0583068 | − | 0.998299i | \(-0.518570\pi\) | ||||
−0.0583068 | + | 0.998299i | \(0.518570\pi\) | |||||||
\(740\) | −2.76487 | −0.101639 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.90829 | 0.0700556 | ||||||||
\(743\) | 9.73206 | 0.357035 | 0.178517 | − | 0.983937i | \(-0.442870\pi\) | ||||
0.178517 | + | 0.983937i | \(0.442870\pi\) | |||||||
\(744\) | 11.2885 | 0.413855 | ||||||||
\(745\) | 9.44852 | 0.346167 | ||||||||
\(746\) | 29.6163 | 1.08433 | ||||||||
\(747\) | −28.1122 | −1.02857 | ||||||||
\(748\) | 1.50761 | 0.0551235 | ||||||||
\(749\) | −2.94441 | −0.107586 | ||||||||
\(750\) | 2.84551 | 0.103903 | ||||||||
\(751\) | 7.77924 | 0.283869 | 0.141934 | − | 0.989876i | \(-0.454668\pi\) | ||||
0.141934 | + | 0.989876i | \(0.454668\pi\) | |||||||
\(752\) | −21.6430 | −0.789239 | ||||||||
\(753\) | −4.75646 | −0.173335 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.734892 | −0.0267455 | ||||||||
\(756\) | −1.94214 | −0.0706350 | ||||||||
\(757\) | 10.8576 | 0.394627 | 0.197313 | − | 0.980340i | \(-0.436778\pi\) | ||||
0.197313 | + | 0.980340i | \(0.436778\pi\) | |||||||
\(758\) | 19.5624 | 0.710537 | ||||||||
\(759\) | 2.25953 | 0.0820157 | ||||||||
\(760\) | 6.13784 | 0.222643 | ||||||||
\(761\) | 1.82150 | 0.0660294 | 0.0330147 | − | 0.999455i | \(-0.489489\pi\) | ||||
0.0330147 | + | 0.999455i | \(0.489489\pi\) | |||||||
\(762\) | 8.49693 | 0.307811 | ||||||||
\(763\) | −8.43188 | −0.305255 | ||||||||
\(764\) | 10.5913 | 0.383179 | ||||||||
\(765\) | 3.59478 | 0.129970 | ||||||||
\(766\) | −15.4017 | −0.556487 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −7.26633 | −0.262201 | ||||||||
\(769\) | 39.7948 | 1.43504 | 0.717519 | − | 0.696539i | \(-0.245277\pi\) | ||||
0.717519 | + | 0.696539i | \(0.245277\pi\) | |||||||
\(770\) | 0.447480 | 0.0161261 | ||||||||
\(771\) | −7.35682 | −0.264949 | ||||||||
\(772\) | 12.6270 | 0.454456 | ||||||||
\(773\) | 18.3135 | 0.658691 | 0.329346 | − | 0.944209i | \(-0.393172\pi\) | ||||
0.329346 | + | 0.944209i | \(0.393172\pi\) | |||||||
\(774\) | −1.32684 | −0.0476924 | ||||||||
\(775\) | −32.5608 | −1.16962 | ||||||||
\(776\) | −38.8157 | −1.39340 | ||||||||
\(777\) | −5.12783 | −0.183960 | ||||||||
\(778\) | 11.7899 | 0.422689 | ||||||||
\(779\) | −28.9048 | −1.03562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5997 | 0.379287 | ||||||||
\(782\) | 17.0121 | 0.608352 | ||||||||
\(783\) | −0.805905 | −0.0288007 | ||||||||
\(784\) | −2.34017 | −0.0835776 | ||||||||
\(785\) | −3.82377 | −0.136476 | ||||||||
\(786\) | 9.10957 | 0.324928 | ||||||||
\(787\) | −26.2606 | −0.936088 | −0.468044 | − | 0.883705i | \(-0.655041\pi\) | ||||
−0.468044 | + | 0.883705i | \(0.655041\pi\) | |||||||
\(788\) | −11.0517 | −0.393701 | ||||||||
\(789\) | −6.56585 | −0.233750 | ||||||||
\(790\) | −1.51867 | −0.0540319 | ||||||||
\(791\) | −12.8082 | −0.455406 | ||||||||
\(792\) | −6.92162 | −0.245949 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9.44399 | −0.335155 | ||||||||
\(795\) | 0.405220 | 0.0143717 | ||||||||
\(796\) | 10.2823 | 0.364447 | ||||||||
\(797\) | −44.0677 | −1.56096 | −0.780479 | − | 0.625182i | \(-0.785025\pi\) | ||||
−0.780479 | + | 0.625182i | \(0.785025\pi\) | |||||||
\(798\) | 2.72979 | 0.0966337 | ||||||||
\(799\) | −26.6297 | −0.942090 | ||||||||
\(800\) | 16.3668 | 0.578655 | ||||||||
\(801\) | −14.7165 | −0.519981 | ||||||||
\(802\) | −15.0205 | −0.530393 | ||||||||
\(803\) | 0.293378 | 0.0103531 | ||||||||
\(804\) | 1.72753 | 0.0609252 | ||||||||
\(805\) | −2.32684 | −0.0820104 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.95652 | −0.209679 | ||||||||
\(808\) | 11.2183 | 0.394659 | ||||||||
\(809\) | −8.07838 | −0.284021 | −0.142010 | − | 0.989865i | \(-0.545357\pi\) | ||||
−0.142010 | + | 0.989865i | \(0.545357\pi\) | |||||||
\(810\) | −3.48747 | −0.122537 | ||||||||
\(811\) | −38.0098 | −1.33471 | −0.667353 | − | 0.744742i | \(-0.732573\pi\) | ||||
−0.667353 | + | 0.744742i | \(0.732573\pi\) | |||||||
\(812\) | 0.165166 | 0.00579619 | ||||||||
\(813\) | 5.89657 | 0.206802 | ||||||||
\(814\) | −9.23513 | −0.323691 | ||||||||
\(815\) | 0.183417 | 0.00642483 | ||||||||
\(816\) | 3.63317 | 0.127186 | ||||||||
\(817\) | −1.81100 | −0.0633590 | ||||||||
\(818\) | 21.9409 | 0.767146 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.94214 | 0.0678225 | ||||||||
\(821\) | −13.7542 | −0.480025 | −0.240012 | − | 0.970770i | \(-0.577151\pi\) | ||||
−0.240012 | + | 0.970770i | \(0.577151\pi\) | |||||||
\(822\) | −10.3668 | −0.361585 | ||||||||
\(823\) | 9.91935 | 0.345767 | 0.172883 | − | 0.984942i | \(-0.444692\pi\) | ||||
0.172883 | + | 0.984942i | \(0.444692\pi\) | |||||||
\(824\) | 55.2327 | 1.92412 | ||||||||
\(825\) | −2.14238 | −0.0745881 | ||||||||
\(826\) | −3.26180 | −0.113492 | ||||||||
\(827\) | 3.77101 | 0.131131 | 0.0655654 | − | 0.997848i | \(-0.479115\pi\) | ||||
0.0655654 | + | 0.997848i | \(0.479115\pi\) | |||||||
\(828\) | 8.63090 | 0.299944 | ||||||||
\(829\) | −11.5187 | −0.400060 | −0.200030 | − | 0.979790i | \(-0.564104\pi\) | ||||
−0.200030 | + | 0.979790i | \(0.564104\pi\) | |||||||
\(830\) | −5.59478 | −0.194198 | ||||||||
\(831\) | −14.0833 | −0.488544 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.87936 | −0.0997640 | ||||||||
\(834\) | −8.34017 | −0.288797 | ||||||||
\(835\) | −11.0000 | −0.380671 | ||||||||
\(836\) | −2.26549 | −0.0783537 | ||||||||
\(837\) | −20.9360 | −0.723654 | ||||||||
\(838\) | −27.6514 | −0.955202 | ||||||||
\(839\) | −43.6475 | −1.50688 | −0.753440 | − | 0.657516i | \(-0.771607\pi\) | ||||
−0.753440 | + | 0.657516i | \(0.771607\pi\) | |||||||
\(840\) | −0.764867 | −0.0263904 | ||||||||
\(841\) | −28.9315 | −0.997637 | ||||||||
\(842\) | 22.7610 | 0.784396 | ||||||||
\(843\) | −2.58986 | −0.0891995 | ||||||||
\(844\) | −1.70928 | −0.0588357 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 29.3184 | 1.00799 | ||||||||
\(847\) | 10.3112 | 0.354299 | ||||||||
\(848\) | −3.81658 | −0.131062 | ||||||||
\(849\) | 0.528125 | 0.0181252 | ||||||||
\(850\) | −16.1301 | −0.553258 | ||||||||
\(851\) | 48.0216 | 1.64616 | ||||||||
\(852\) | −4.34471 | −0.148847 | ||||||||
\(853\) | −10.0940 | −0.345611 | −0.172806 | − | 0.984956i | \(-0.555283\pi\) | ||||
−0.172806 | + | 0.984956i | \(0.555283\pi\) | |||||||
\(854\) | 8.49693 | 0.290759 | ||||||||
\(855\) | −5.40191 | −0.184741 | ||||||||
\(856\) | 9.06400 | 0.309801 | ||||||||
\(857\) | −24.0267 | −0.820735 | −0.410368 | − | 0.911920i | \(-0.634600\pi\) | ||||
−0.410368 | + | 0.911920i | \(0.634600\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.65983 | −0.0566326 | −0.0283163 | − | 0.999599i | \(-0.509015\pi\) | ||||
−0.0283163 | + | 0.999599i | \(0.509015\pi\) | |||||||
\(860\) | 0.121683 | 0.00414936 | ||||||||
\(861\) | 3.60197 | 0.122755 | ||||||||
\(862\) | 21.1773 | 0.721301 | ||||||||
\(863\) | −28.6270 | −0.974475 | −0.487238 | − | 0.873269i | \(-0.661995\pi\) | ||||
−0.487238 | + | 0.873269i | \(0.661995\pi\) | |||||||
\(864\) | 10.5236 | 0.358020 | ||||||||
\(865\) | 11.9350 | 0.405801 | ||||||||
\(866\) | −24.0312 | −0.816613 | ||||||||
\(867\) | −4.69594 | −0.159483 | ||||||||
\(868\) | 4.29072 | 0.145637 | ||||||||
\(869\) | 2.33752 | 0.0792949 | ||||||||
\(870\) | −0.0761103 | −0.00258038 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 25.9565 | 0.878999 | ||||||||
\(873\) | 34.1617 | 1.15620 | ||||||||
\(874\) | −25.5642 | −0.864723 | ||||||||
\(875\) | 4.51026 | 0.152475 | ||||||||
\(876\) | −0.120252 | −0.00406296 | ||||||||
\(877\) | −40.8587 | −1.37970 | −0.689850 | − | 0.723953i | \(-0.742323\pi\) | ||||
−0.689850 | + | 0.723953i | \(0.742323\pi\) | |||||||
\(878\) | 31.5486 | 1.06472 | ||||||||
\(879\) | 13.1168 | 0.442417 | ||||||||
\(880\) | −0.894960 | −0.0301691 | ||||||||
\(881\) | 48.5835 | 1.63682 | 0.818411 | − | 0.574634i | \(-0.194856\pi\) | ||||
0.818411 | + | 0.574634i | \(0.194856\pi\) | |||||||
\(882\) | 3.17009 | 0.106742 | ||||||||
\(883\) | −49.2456 | −1.65725 | −0.828624 | − | 0.559806i | \(-0.810876\pi\) | ||||
−0.828624 | + | 0.559806i | \(0.810876\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.692632 | −0.0232826 | ||||||||
\(886\) | −30.9021 | −1.03818 | ||||||||
\(887\) | −13.1773 | −0.442450 | −0.221225 | − | 0.975223i | \(-0.571005\pi\) | ||||
−0.221225 | + | 0.975223i | \(0.571005\pi\) | |||||||
\(888\) | 15.7854 | 0.529723 | ||||||||
\(889\) | 13.4680 | 0.451702 | ||||||||
\(890\) | −2.92881 | −0.0981739 | ||||||||
\(891\) | 5.36788 | 0.179831 | ||||||||
\(892\) | 12.4885 | 0.418147 | ||||||||
\(893\) | 40.0166 | 1.33911 | ||||||||
\(894\) | −12.9360 | −0.432644 | ||||||||
\(895\) | 9.52690 | 0.318449 | ||||||||
\(896\) | 3.31965 | 0.110902 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.7792 | −1.22734 | ||||||||
\(899\) | 1.78047 | 0.0593818 | ||||||||
\(900\) | −8.18342 | −0.272781 | ||||||||
\(901\) | −4.69594 | −0.156445 | ||||||||
\(902\) | 6.48709 | 0.215996 | ||||||||
\(903\) | 0.225678 | 0.00751009 | ||||||||
\(904\) | 39.4284 | 1.31137 | ||||||||
\(905\) | 7.24232 | 0.240743 | ||||||||
\(906\) | 1.00614 | 0.0334269 | ||||||||
\(907\) | 15.3051 | 0.508198 | 0.254099 | − | 0.967178i | \(-0.418221\pi\) | ||||
0.254099 | + | 0.967178i | \(0.418221\pi\) | |||||||
\(908\) | −8.36683 | −0.277663 | ||||||||
\(909\) | −9.87322 | −0.327474 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.07223 | −0.168051 | −0.0840253 | − | 0.996464i | \(-0.526778\pi\) | ||||
−0.0840253 | + | 0.996464i | \(0.526778\pi\) | |||||||
\(912\) | −5.45959 | −0.180785 | ||||||||
\(913\) | 8.61142 | 0.284997 | ||||||||
\(914\) | −21.1377 | −0.699172 | ||||||||
\(915\) | 1.80430 | 0.0596482 | ||||||||
\(916\) | 17.5441 | 0.579674 | ||||||||
\(917\) | 14.4391 | 0.476820 | ||||||||
\(918\) | −10.3714 | −0.342306 | ||||||||
\(919\) | −46.3689 | −1.52957 | −0.764785 | − | 0.644286i | \(-0.777155\pi\) | ||||
−0.764785 | + | 0.644286i | \(0.777155\pi\) | |||||||
\(920\) | 7.16290 | 0.236154 | ||||||||
\(921\) | −3.35350 | −0.110502 | ||||||||
\(922\) | −27.0037 | −0.889319 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.282314 | 0.00928745 | ||||||||
\(925\) | −45.5318 | −1.49708 | ||||||||
\(926\) | −5.32108 | −0.174862 | ||||||||
\(927\) | −48.6102 | −1.59657 | ||||||||
\(928\) | −0.894960 | −0.0293785 | ||||||||
\(929\) | −23.4547 | −0.769523 | −0.384761 | − | 0.923016i | \(-0.625716\pi\) | ||||
−0.384761 | + | 0.923016i | \(0.625716\pi\) | |||||||
\(930\) | −1.97721 | −0.0648354 | ||||||||
\(931\) | 4.32684 | 0.141807 | ||||||||
\(932\) | 8.43310 | 0.276236 | ||||||||
\(933\) | −13.5381 | −0.443219 | ||||||||
\(934\) | −44.2472 | −1.44781 | ||||||||
\(935\) | −1.10116 | −0.0360119 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.0156 | −0.588544 | −0.294272 | − | 0.955722i | \(-0.595077\pi\) | ||||
−0.294272 | + | 0.955722i | \(0.595077\pi\) | |||||||
\(938\) | −5.94214 | −0.194018 | ||||||||
\(939\) | 1.20781 | 0.0394155 | ||||||||
\(940\) | −2.68876 | −0.0876976 | ||||||||
\(941\) | −31.7805 | −1.03601 | −0.518007 | − | 0.855377i | \(-0.673326\pi\) | ||||
−0.518007 | + | 0.855377i | \(0.673326\pi\) | |||||||
\(942\) | 5.23513 | 0.170570 | ||||||||
\(943\) | −33.7321 | −1.09847 | ||||||||
\(944\) | 6.52359 | 0.212325 | ||||||||
\(945\) | 1.41855 | 0.0461455 | ||||||||
\(946\) | 0.406442 | 0.0132146 | ||||||||
\(947\) | −46.3812 | −1.50719 | −0.753593 | − | 0.657341i | \(-0.771681\pi\) | ||||
−0.753593 | + | 0.657341i | \(0.771681\pi\) | |||||||
\(948\) | −0.958125 | −0.0311185 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 24.2388 | 0.786412 | ||||||||
\(951\) | −1.56093 | −0.0506166 | ||||||||
\(952\) | 8.86376 | 0.287276 | ||||||||
\(953\) | −27.2511 | −0.882750 | −0.441375 | − | 0.897323i | \(-0.645509\pi\) | ||||
−0.441375 | + | 0.897323i | \(0.645509\pi\) | |||||||
\(954\) | 5.17009 | 0.167388 | ||||||||
\(955\) | −7.73594 | −0.250329 | ||||||||
\(956\) | 5.49323 | 0.177664 | ||||||||
\(957\) | 0.117148 | 0.00378686 | ||||||||
\(958\) | −10.8117 | −0.349309 | ||||||||
\(959\) | −16.4319 | −0.530613 | ||||||||
\(960\) | 2.15676 | 0.0696090 | ||||||||
\(961\) | 15.2534 | 0.492045 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.97721 | −0.257062 | ||||||||
\(964\) | −10.6818 | −0.344037 | ||||||||
\(965\) | −9.22285 | −0.296894 | ||||||||
\(966\) | 3.18568 | 0.102498 | ||||||||
\(967\) | −9.77045 | −0.314196 | −0.157098 | − | 0.987583i | \(-0.550214\pi\) | ||||
−0.157098 | + | 0.987583i | \(0.550214\pi\) | |||||||
\(968\) | −31.7419 | −1.02022 | ||||||||
\(969\) | −6.71751 | −0.215797 | ||||||||
\(970\) | 6.79872 | 0.218294 | ||||||||
\(971\) | −13.9856 | −0.448820 | −0.224410 | − | 0.974495i | \(-0.572045\pi\) | ||||
−0.224410 | + | 0.974495i | \(0.572045\pi\) | |||||||
\(972\) | −8.02666 | −0.257455 | ||||||||
\(973\) | −13.2195 | −0.423799 | ||||||||
\(974\) | 15.9832 | 0.512134 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.9939 | −0.543960 | ||||||||
\(977\) | 54.7454 | 1.75146 | 0.875730 | − | 0.482801i | \(-0.160381\pi\) | ||||
0.875730 | + | 0.482801i | \(0.160381\pi\) | |||||||
\(978\) | −0.251117 | −0.00802985 | ||||||||
\(979\) | 4.50799 | 0.144076 | ||||||||
\(980\) | −0.290725 | −0.00928686 | ||||||||
\(981\) | −22.8443 | −0.729362 | ||||||||
\(982\) | 34.6947 | 1.10715 | ||||||||
\(983\) | −0.0399930 | −0.00127558 | −0.000637789 | − | 1.00000i | \(-0.500203\pi\) | ||||
−0.000637789 | 1.00000i | \(0.500203\pi\) | ||||||||
\(984\) | −11.0882 | −0.353480 | ||||||||
\(985\) | 8.07223 | 0.257203 | ||||||||
\(986\) | 0.882015 | 0.0280891 | ||||||||
\(987\) | −4.98667 | −0.158727 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.11345 | −0.0672038 | ||||||||
\(990\) | 1.21235 | 0.0385309 | ||||||||
\(991\) | 53.9481 | 1.71372 | 0.856859 | − | 0.515551i | \(-0.172413\pi\) | ||||
0.856859 | + | 0.515551i | \(0.172413\pi\) | |||||||
\(992\) | −23.2495 | −0.738173 | ||||||||
\(993\) | −2.29460 | −0.0728169 | ||||||||
\(994\) | 14.9444 | 0.474008 | ||||||||
\(995\) | −7.51026 | −0.238091 | ||||||||
\(996\) | −3.52973 | −0.111844 | ||||||||
\(997\) | 42.0554 | 1.33191 | 0.665954 | − | 0.745993i | \(-0.268025\pi\) | ||||
0.665954 | + | 0.745993i | \(0.268025\pi\) | |||||||
\(998\) | −41.5669 | −1.31578 | ||||||||
\(999\) | −29.2762 | −0.926257 |
(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 | 1183.2.a.j.1.1 | 3 | ||
7.6 | odd | 2 | 8281.2.a.bi.1.1 | 3 | |||
13.5 | odd | 4 | 91.2.c.a.64.5 | yes | 6 | ||
13.8 | odd | 4 | 91.2.c.a.64.2 | ✓ | 6 | ||
13.12 | even | 2 | 1183.2.a.h.1.3 | 3 | |||
39.5 | even | 4 | 819.2.c.b.64.2 | 6 | |||
39.8 | even | 4 | 819.2.c.b.64.5 | 6 | |||
52.31 | even | 4 | 1456.2.k.c.337.3 | 6 | |||
52.47 | even | 4 | 1456.2.k.c.337.4 | 6 | |||
91.5 | even | 12 | 637.2.r.d.116.5 | 12 | |||
91.18 | odd | 12 | 637.2.r.e.324.2 | 12 | |||
91.31 | even | 12 | 637.2.r.d.324.2 | 12 | |||
91.34 | even | 4 | 637.2.c.d.246.2 | 6 | |||
91.44 | odd | 12 | 637.2.r.e.116.5 | 12 | |||
91.47 | even | 12 | 637.2.r.d.116.2 | 12 | |||
91.60 | odd | 12 | 637.2.r.e.324.5 | 12 | |||
91.73 | even | 12 | 637.2.r.d.324.5 | 12 | |||
91.83 | even | 4 | 637.2.c.d.246.5 | 6 | |||
91.86 | odd | 12 | 637.2.r.e.116.2 | 12 | |||
91.90 | odd | 2 | 8281.2.a.be.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.c.a.64.2 | ✓ | 6 | 13.8 | odd | 4 | ||
91.2.c.a.64.5 | yes | 6 | 13.5 | odd | 4 | ||
637.2.c.d.246.2 | 6 | 91.34 | even | 4 | |||
637.2.c.d.246.5 | 6 | 91.83 | even | 4 | |||
637.2.r.d.116.2 | 12 | 91.47 | even | 12 | |||
637.2.r.d.116.5 | 12 | 91.5 | even | 12 | |||
637.2.r.d.324.2 | 12 | 91.31 | even | 12 | |||
637.2.r.d.324.5 | 12 | 91.73 | even | 12 | |||
637.2.r.e.116.2 | 12 | 91.86 | odd | 12 | |||
637.2.r.e.116.5 | 12 | 91.44 | odd | 12 | |||
637.2.r.e.324.2 | 12 | 91.18 | odd | 12 | |||
637.2.r.e.324.5 | 12 | 91.60 | odd | 12 | |||
819.2.c.b.64.2 | 6 | 39.5 | even | 4 | |||
819.2.c.b.64.5 | 6 | 39.8 | even | 4 | |||
1183.2.a.h.1.3 | 3 | 13.12 | even | 2 | |||
1183.2.a.j.1.1 | 3 | 1.1 | even | 1 | trivial | ||
1456.2.k.c.337.3 | 6 | 52.31 | even | 4 | |||
1456.2.k.c.337.4 | 6 | 52.47 | even | 4 | |||
8281.2.a.be.1.3 | 3 | 91.90 | odd | 2 | |||
8281.2.a.bi.1.1 | 3 | 7.6 | odd | 2 |