Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, 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("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 100x^{5} + 26x^{4} + 108x^{3} - 33x^{2} - 36x + 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.46930\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.46930 | 1.03895 | 0.519474 | − | 0.854486i | \(-0.326128\pi\) | ||||
0.519474 | + | 0.854486i | \(0.326128\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.158829 | 0.0794147 | ||||||||
\(5\) | −2.14842 | −0.960801 | −0.480400 | − | 0.877049i | \(-0.659509\pi\) | ||||
−0.480400 | + | 0.877049i | \(0.659509\pi\) | |||||||
\(6\) | 1.46930 | 0.599837 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.70522 | −0.956441 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.15666 | −0.998223 | ||||||||
\(11\) | 2.16247 | 0.652011 | 0.326005 | − | 0.945368i | \(-0.394297\pi\) | ||||
0.326005 | + | 0.945368i | \(0.394297\pi\) | |||||||
\(12\) | 0.158829 | 0.0458501 | ||||||||
\(13\) | 3.08320 | 0.855127 | 0.427563 | − | 0.903985i | \(-0.359372\pi\) | ||||
0.427563 | + | 0.903985i | \(0.359372\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.14842 | −0.554719 | ||||||||
\(16\) | −4.29243 | −1.07311 | ||||||||
\(17\) | 0.354774 | 0.0860453 | 0.0430227 | − | 0.999074i | \(-0.486301\pi\) | ||||
0.0430227 | + | 0.999074i | \(0.486301\pi\) | |||||||
\(18\) | 1.46930 | 0.346316 | ||||||||
\(19\) | 4.96083 | 1.13809 | 0.569046 | − | 0.822306i | \(-0.307313\pi\) | ||||
0.569046 | + | 0.822306i | \(0.307313\pi\) | |||||||
\(20\) | −0.341232 | −0.0763017 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.17731 | 0.677406 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −2.70522 | −0.552201 | ||||||||
\(25\) | −0.384310 | −0.0768621 | ||||||||
\(26\) | 4.53014 | 0.888433 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.50055 | −0.464340 | −0.232170 | − | 0.972675i | \(-0.574583\pi\) | ||||
−0.232170 | + | 0.972675i | \(0.574583\pi\) | |||||||
\(30\) | −3.15666 | −0.576324 | ||||||||
\(31\) | −1.83663 | −0.329869 | −0.164934 | − | 0.986305i | \(-0.552741\pi\) | ||||
−0.164934 | + | 0.986305i | \(0.552741\pi\) | |||||||
\(32\) | −0.896404 | −0.158463 | ||||||||
\(33\) | 2.16247 | 0.376438 | ||||||||
\(34\) | 0.521268 | 0.0893967 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.158829 | 0.0264716 | ||||||||
\(37\) | −4.50032 | −0.739847 | −0.369924 | − | 0.929062i | \(-0.620616\pi\) | ||||
−0.369924 | + | 0.929062i | \(0.620616\pi\) | |||||||
\(38\) | 7.28892 | 1.18242 | ||||||||
\(39\) | 3.08320 | 0.493708 | ||||||||
\(40\) | 5.81195 | 0.918949 | ||||||||
\(41\) | 10.5155 | 1.64225 | 0.821124 | − | 0.570749i | \(-0.193347\pi\) | ||||
0.821124 | + | 0.570749i | \(0.193347\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.96942 | 1.21533 | 0.607663 | − | 0.794195i | \(-0.292107\pi\) | ||||
0.607663 | + | 0.794195i | \(0.292107\pi\) | |||||||
\(44\) | 0.343465 | 0.0517792 | ||||||||
\(45\) | −2.14842 | −0.320267 | ||||||||
\(46\) | −1.46930 | −0.216636 | ||||||||
\(47\) | 7.83688 | 1.14313 | 0.571564 | − | 0.820558i | \(-0.306337\pi\) | ||||
0.571564 | + | 0.820558i | \(0.306337\pi\) | |||||||
\(48\) | −4.29243 | −0.619559 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.564665 | −0.0798557 | ||||||||
\(51\) | 0.354774 | 0.0496783 | ||||||||
\(52\) | 0.489703 | 0.0679096 | ||||||||
\(53\) | 8.86015 | 1.21703 | 0.608517 | − | 0.793541i | \(-0.291765\pi\) | ||||
0.608517 | + | 0.793541i | \(0.291765\pi\) | |||||||
\(54\) | 1.46930 | 0.199946 | ||||||||
\(55\) | −4.64589 | −0.626452 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.96083 | 0.657078 | ||||||||
\(58\) | −3.67404 | −0.482425 | ||||||||
\(59\) | 6.79270 | 0.884334 | 0.442167 | − | 0.896933i | \(-0.354210\pi\) | ||||
0.442167 | + | 0.896933i | \(0.354210\pi\) | |||||||
\(60\) | −0.341232 | −0.0440528 | ||||||||
\(61\) | −2.35137 | −0.301062 | −0.150531 | − | 0.988605i | \(-0.548098\pi\) | ||||
−0.150531 | + | 0.988605i | \(0.548098\pi\) | |||||||
\(62\) | −2.69856 | −0.342717 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.26778 | 0.908473 | ||||||||
\(65\) | −6.62400 | −0.821606 | ||||||||
\(66\) | 3.17731 | 0.391100 | ||||||||
\(67\) | −2.20673 | −0.269595 | −0.134798 | − | 0.990873i | \(-0.543038\pi\) | ||||
−0.134798 | + | 0.990873i | \(0.543038\pi\) | |||||||
\(68\) | 0.0563485 | 0.00683326 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.08130 | 0.365683 | 0.182841 | − | 0.983142i | \(-0.441471\pi\) | ||||
0.182841 | + | 0.983142i | \(0.441471\pi\) | |||||||
\(72\) | −2.70522 | −0.318814 | ||||||||
\(73\) | 3.33525 | 0.390362 | 0.195181 | − | 0.980767i | \(-0.437471\pi\) | ||||
0.195181 | + | 0.980767i | \(0.437471\pi\) | |||||||
\(74\) | −6.61229 | −0.768664 | ||||||||
\(75\) | −0.384310 | −0.0443763 | ||||||||
\(76\) | 0.787926 | 0.0903813 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.53014 | 0.512937 | ||||||||
\(79\) | −5.15275 | −0.579729 | −0.289865 | − | 0.957068i | \(-0.593610\pi\) | ||||
−0.289865 | + | 0.957068i | \(0.593610\pi\) | |||||||
\(80\) | 9.22193 | 1.03104 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 15.4504 | 1.70621 | ||||||||
\(83\) | 4.70908 | 0.516889 | 0.258445 | − | 0.966026i | \(-0.416790\pi\) | ||||
0.258445 | + | 0.966026i | \(0.416790\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.762202 | −0.0826724 | ||||||||
\(86\) | 11.7094 | 1.26266 | ||||||||
\(87\) | −2.50055 | −0.268087 | ||||||||
\(88\) | −5.84998 | −0.623610 | ||||||||
\(89\) | 1.87944 | 0.199220 | 0.0996101 | − | 0.995027i | \(-0.468240\pi\) | ||||
0.0996101 | + | 0.995027i | \(0.468240\pi\) | |||||||
\(90\) | −3.15666 | −0.332741 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.158829 | −0.0165591 | ||||||||
\(93\) | −1.83663 | −0.190450 | ||||||||
\(94\) | 11.5147 | 1.18765 | ||||||||
\(95\) | −10.6579 | −1.09348 | ||||||||
\(96\) | −0.896404 | −0.0914888 | ||||||||
\(97\) | 8.12795 | 0.825268 | 0.412634 | − | 0.910897i | \(-0.364609\pi\) | ||||
0.412634 | + | 0.910897i | \(0.364609\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.16247 | 0.217337 | ||||||||
\(100\) | −0.0610398 | −0.00610398 | ||||||||
\(101\) | 18.1335 | 1.80435 | 0.902174 | − | 0.431371i | \(-0.141970\pi\) | ||||
0.902174 | + | 0.431371i | \(0.141970\pi\) | |||||||
\(102\) | 0.521268 | 0.0516132 | ||||||||
\(103\) | 3.90946 | 0.385210 | 0.192605 | − | 0.981276i | \(-0.438306\pi\) | ||||
0.192605 | + | 0.981276i | \(0.438306\pi\) | |||||||
\(104\) | −8.34076 | −0.817878 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.0182 | 1.26444 | ||||||||
\(107\) | −5.42225 | −0.524188 | −0.262094 | − | 0.965042i | \(-0.584413\pi\) | ||||
−0.262094 | + | 0.965042i | \(0.584413\pi\) | |||||||
\(108\) | 0.158829 | 0.0152834 | ||||||||
\(109\) | 15.2859 | 1.46412 | 0.732060 | − | 0.681240i | \(-0.238559\pi\) | ||||
0.732060 | + | 0.681240i | \(0.238559\pi\) | |||||||
\(110\) | −6.82619 | −0.650852 | ||||||||
\(111\) | −4.50032 | −0.427151 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.97105 | 0.561709 | 0.280854 | − | 0.959750i | \(-0.409382\pi\) | ||||
0.280854 | + | 0.959750i | \(0.409382\pi\) | |||||||
\(114\) | 7.28892 | 0.682670 | ||||||||
\(115\) | 2.14842 | 0.200341 | ||||||||
\(116\) | −0.397160 | −0.0368754 | ||||||||
\(117\) | 3.08320 | 0.285042 | ||||||||
\(118\) | 9.98048 | 0.918778 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.81195 | 0.530556 | ||||||||
\(121\) | −6.32370 | −0.574882 | ||||||||
\(122\) | −3.45486 | −0.312788 | ||||||||
\(123\) | 10.5155 | 0.948153 | ||||||||
\(124\) | −0.291711 | −0.0261964 | ||||||||
\(125\) | 11.5677 | 1.03465 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.84667 | −0.696279 | −0.348140 | − | 0.937443i | \(-0.613186\pi\) | ||||
−0.348140 | + | 0.937443i | \(0.613186\pi\) | |||||||
\(128\) | 12.4713 | 1.10232 | ||||||||
\(129\) | 7.96942 | 0.701669 | ||||||||
\(130\) | −9.73262 | −0.853607 | ||||||||
\(131\) | −5.14450 | −0.449477 | −0.224738 | − | 0.974419i | \(-0.572153\pi\) | ||||
−0.224738 | + | 0.974419i | \(0.572153\pi\) | |||||||
\(132\) | 0.343465 | 0.0298948 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.24234 | −0.280096 | ||||||||
\(135\) | −2.14842 | −0.184906 | ||||||||
\(136\) | −0.959743 | −0.0822973 | ||||||||
\(137\) | 11.7090 | 1.00037 | 0.500183 | − | 0.865920i | \(-0.333266\pi\) | ||||
0.500183 | + | 0.865920i | \(0.333266\pi\) | |||||||
\(138\) | −1.46930 | −0.125075 | ||||||||
\(139\) | −3.57676 | −0.303377 | −0.151688 | − | 0.988428i | \(-0.548471\pi\) | ||||
−0.151688 | + | 0.988428i | \(0.548471\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.83688 | 0.659985 | ||||||||
\(142\) | 4.52734 | 0.379926 | ||||||||
\(143\) | 6.66735 | 0.557552 | ||||||||
\(144\) | −4.29243 | −0.357703 | ||||||||
\(145\) | 5.37221 | 0.446138 | ||||||||
\(146\) | 4.90047 | 0.405566 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.714783 | −0.0587548 | ||||||||
\(149\) | −9.49709 | −0.778032 | −0.389016 | − | 0.921231i | \(-0.627185\pi\) | ||||
−0.389016 | + | 0.921231i | \(0.627185\pi\) | |||||||
\(150\) | −0.564665 | −0.0461047 | ||||||||
\(151\) | −12.8737 | −1.04765 | −0.523825 | − | 0.851826i | \(-0.675496\pi\) | ||||
−0.523825 | + | 0.851826i | \(0.675496\pi\) | |||||||
\(152\) | −13.4202 | −1.08852 | ||||||||
\(153\) | 0.354774 | 0.0286818 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.94585 | 0.316938 | ||||||||
\(156\) | 0.489703 | 0.0392077 | ||||||||
\(157\) | −7.53352 | −0.601241 | −0.300620 | − | 0.953744i | \(-0.597194\pi\) | ||||
−0.300620 | + | 0.953744i | \(0.597194\pi\) | |||||||
\(158\) | −7.57091 | −0.602309 | ||||||||
\(159\) | 8.86015 | 0.702655 | ||||||||
\(160\) | 1.92585 | 0.152252 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.46930 | 0.115439 | ||||||||
\(163\) | −18.0136 | −1.41094 | −0.705468 | − | 0.708742i | \(-0.749263\pi\) | ||||
−0.705468 | + | 0.708742i | \(0.749263\pi\) | |||||||
\(164\) | 1.67017 | 0.130419 | ||||||||
\(165\) | −4.64589 | −0.361682 | ||||||||
\(166\) | 6.91904 | 0.537021 | ||||||||
\(167\) | 16.8365 | 1.30285 | 0.651425 | − | 0.758713i | \(-0.274171\pi\) | ||||
0.651425 | + | 0.758713i | \(0.274171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.49385 | −0.268758 | ||||||||
\(170\) | −1.11990 | −0.0858924 | ||||||||
\(171\) | 4.96083 | 0.379364 | ||||||||
\(172\) | 1.26578 | 0.0965147 | ||||||||
\(173\) | −16.8181 | −1.27865 | −0.639327 | − | 0.768935i | \(-0.720787\pi\) | ||||
−0.639327 | + | 0.768935i | \(0.720787\pi\) | |||||||
\(174\) | −3.67404 | −0.278528 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.28227 | −0.699678 | ||||||||
\(177\) | 6.79270 | 0.510571 | ||||||||
\(178\) | 2.76145 | 0.206980 | ||||||||
\(179\) | 3.16675 | 0.236694 | 0.118347 | − | 0.992972i | \(-0.462241\pi\) | ||||
0.118347 | + | 0.992972i | \(0.462241\pi\) | |||||||
\(180\) | −0.341232 | −0.0254339 | ||||||||
\(181\) | −23.1662 | −1.72193 | −0.860965 | − | 0.508664i | \(-0.830139\pi\) | ||||
−0.860965 | + | 0.508664i | \(0.830139\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.35137 | −0.173818 | ||||||||
\(184\) | 2.70522 | 0.199432 | ||||||||
\(185\) | 9.66855 | 0.710846 | ||||||||
\(186\) | −2.69856 | −0.197868 | ||||||||
\(187\) | 0.767190 | 0.0561025 | ||||||||
\(188\) | 1.24473 | 0.0907811 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.6596 | −1.13607 | ||||||||
\(191\) | −4.73960 | −0.342945 | −0.171473 | − | 0.985189i | \(-0.554853\pi\) | ||||
−0.171473 | + | 0.985189i | \(0.554853\pi\) | |||||||
\(192\) | 7.26778 | 0.524507 | ||||||||
\(193\) | 20.9142 | 1.50544 | 0.752720 | − | 0.658341i | \(-0.228742\pi\) | ||||
0.752720 | + | 0.658341i | \(0.228742\pi\) | |||||||
\(194\) | 11.9424 | 0.857411 | ||||||||
\(195\) | −6.62400 | −0.474355 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.8120 | −1.41155 | −0.705773 | − | 0.708438i | \(-0.749400\pi\) | ||||
−0.705773 | + | 0.708438i | \(0.749400\pi\) | |||||||
\(198\) | 3.17731 | 0.225802 | ||||||||
\(199\) | 12.7673 | 0.905051 | 0.452525 | − | 0.891751i | \(-0.350523\pi\) | ||||
0.452525 | + | 0.891751i | \(0.350523\pi\) | |||||||
\(200\) | 1.03965 | 0.0735140 | ||||||||
\(201\) | −2.20673 | −0.155651 | ||||||||
\(202\) | 26.6434 | 1.87463 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.0563485 | 0.00394519 | ||||||||
\(205\) | −22.5917 | −1.57787 | ||||||||
\(206\) | 5.74415 | 0.400214 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −13.2344 | −0.917644 | ||||||||
\(209\) | 10.7277 | 0.742048 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.77646 | 0.259983 | 0.129991 | − | 0.991515i | \(-0.458505\pi\) | ||||
0.129991 | + | 0.991515i | \(0.458505\pi\) | |||||||
\(212\) | 1.40725 | 0.0966504 | ||||||||
\(213\) | 3.08130 | 0.211127 | ||||||||
\(214\) | −7.96688 | −0.544605 | ||||||||
\(215\) | −17.1216 | −1.16769 | ||||||||
\(216\) | −2.70522 | −0.184067 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 22.4594 | 1.52115 | ||||||||
\(219\) | 3.33525 | 0.225376 | ||||||||
\(220\) | −0.737905 | −0.0497495 | ||||||||
\(221\) | 1.09384 | 0.0735797 | ||||||||
\(222\) | −6.61229 | −0.443788 | ||||||||
\(223\) | 3.14153 | 0.210373 | 0.105186 | − | 0.994453i | \(-0.466456\pi\) | ||||
0.105186 | + | 0.994453i | \(0.466456\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.384310 | −0.0256207 | ||||||||
\(226\) | 8.77323 | 0.583587 | ||||||||
\(227\) | 19.6642 | 1.30516 | 0.652579 | − | 0.757721i | \(-0.273687\pi\) | ||||
0.652579 | + | 0.757721i | \(0.273687\pi\) | |||||||
\(228\) | 0.787926 | 0.0521816 | ||||||||
\(229\) | −3.40015 | −0.224688 | −0.112344 | − | 0.993669i | \(-0.535836\pi\) | ||||
−0.112344 | + | 0.993669i | \(0.535836\pi\) | |||||||
\(230\) | 3.15666 | 0.208144 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.76454 | 0.444114 | ||||||||
\(233\) | −19.1227 | −1.25277 | −0.626385 | − | 0.779514i | \(-0.715466\pi\) | ||||
−0.626385 | + | 0.779514i | \(0.715466\pi\) | |||||||
\(234\) | 4.53014 | 0.296144 | ||||||||
\(235\) | −16.8369 | −1.09832 | ||||||||
\(236\) | 1.07888 | 0.0702291 | ||||||||
\(237\) | −5.15275 | −0.334707 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.10915 | 0.201114 | 0.100557 | − | 0.994931i | \(-0.467937\pi\) | ||||
0.100557 | + | 0.994931i | \(0.467937\pi\) | |||||||
\(240\) | 9.22193 | 0.595273 | ||||||||
\(241\) | −20.0711 | −1.29289 | −0.646445 | − | 0.762961i | \(-0.723745\pi\) | ||||
−0.646445 | + | 0.762961i | \(0.723745\pi\) | |||||||
\(242\) | −9.29139 | −0.597273 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.373467 | −0.0239088 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.4504 | 0.985082 | ||||||||
\(247\) | 15.2952 | 0.973213 | ||||||||
\(248\) | 4.96850 | 0.315500 | ||||||||
\(249\) | 4.70908 | 0.298426 | ||||||||
\(250\) | 16.9964 | 1.07495 | ||||||||
\(251\) | −4.73370 | −0.298788 | −0.149394 | − | 0.988778i | \(-0.547732\pi\) | ||||
−0.149394 | + | 0.988778i | \(0.547732\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.16247 | −0.135954 | ||||||||
\(254\) | −11.5291 | −0.723398 | ||||||||
\(255\) | −0.762202 | −0.0477309 | ||||||||
\(256\) | 3.78850 | 0.236781 | ||||||||
\(257\) | −3.68563 | −0.229903 | −0.114952 | − | 0.993371i | \(-0.536671\pi\) | ||||
−0.114952 | + | 0.993371i | \(0.536671\pi\) | |||||||
\(258\) | 11.7094 | 0.728998 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.05209 | −0.0652476 | ||||||||
\(261\) | −2.50055 | −0.154780 | ||||||||
\(262\) | −7.55879 | −0.466983 | ||||||||
\(263\) | −4.58029 | −0.282433 | −0.141216 | − | 0.989979i | \(-0.545101\pi\) | ||||
−0.141216 | + | 0.989979i | \(0.545101\pi\) | |||||||
\(264\) | −5.84998 | −0.360041 | ||||||||
\(265\) | −19.0353 | −1.16933 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.87944 | 0.115020 | ||||||||
\(268\) | −0.350494 | −0.0214098 | ||||||||
\(269\) | −18.9657 | −1.15636 | −0.578181 | − | 0.815909i | \(-0.696237\pi\) | ||||
−0.578181 | + | 0.815909i | \(0.696237\pi\) | |||||||
\(270\) | −3.15666 | −0.192108 | ||||||||
\(271\) | 5.77817 | 0.350999 | 0.175499 | − | 0.984480i | \(-0.443846\pi\) | ||||
0.175499 | + | 0.984480i | \(0.443846\pi\) | |||||||
\(272\) | −1.52284 | −0.0923359 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.2040 | 1.03933 | ||||||||
\(275\) | −0.831061 | −0.0501149 | ||||||||
\(276\) | −0.158829 | −0.00956041 | ||||||||
\(277\) | −15.5279 | −0.932981 | −0.466490 | − | 0.884526i | \(-0.654482\pi\) | ||||
−0.466490 | + | 0.884526i | \(0.654482\pi\) | |||||||
\(278\) | −5.25532 | −0.315193 | ||||||||
\(279\) | −1.83663 | −0.109956 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5853 | 1.34733 | 0.673664 | − | 0.739038i | \(-0.264720\pi\) | ||||
0.673664 | + | 0.739038i | \(0.264720\pi\) | |||||||
\(282\) | 11.5147 | 0.685690 | ||||||||
\(283\) | −22.4715 | −1.33579 | −0.667897 | − | 0.744254i | \(-0.732805\pi\) | ||||
−0.667897 | + | 0.744254i | \(0.732805\pi\) | |||||||
\(284\) | 0.489401 | 0.0290406 | ||||||||
\(285\) | −10.6579 | −0.631321 | ||||||||
\(286\) | 9.79631 | 0.579268 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.896404 | −0.0528211 | ||||||||
\(289\) | −16.8741 | −0.992596 | ||||||||
\(290\) | 7.89337 | 0.463514 | ||||||||
\(291\) | 8.12795 | 0.476469 | ||||||||
\(292\) | 0.529736 | 0.0310005 | ||||||||
\(293\) | 5.71918 | 0.334118 | 0.167059 | − | 0.985947i | \(-0.446573\pi\) | ||||
0.167059 | + | 0.985947i | \(0.446573\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.5935 | −0.849669 | ||||||||
\(296\) | 12.1744 | 0.707620 | ||||||||
\(297\) | 2.16247 | 0.125479 | ||||||||
\(298\) | −13.9540 | −0.808335 | ||||||||
\(299\) | −3.08320 | −0.178306 | ||||||||
\(300\) | −0.0610398 | −0.00352413 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −18.9153 | −1.08846 | ||||||||
\(303\) | 18.1335 | 1.04174 | ||||||||
\(304\) | −21.2940 | −1.22130 | ||||||||
\(305\) | 5.05173 | 0.289261 | ||||||||
\(306\) | 0.521268 | 0.0297989 | ||||||||
\(307\) | 9.95544 | 0.568187 | 0.284093 | − | 0.958797i | \(-0.408307\pi\) | ||||
0.284093 | + | 0.958797i | \(0.408307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.90946 | 0.222401 | ||||||||
\(310\) | 5.79762 | 0.329283 | ||||||||
\(311\) | −17.6774 | −1.00239 | −0.501197 | − | 0.865333i | \(-0.667107\pi\) | ||||
−0.501197 | + | 0.865333i | \(0.667107\pi\) | |||||||
\(312\) | −8.34076 | −0.472202 | ||||||||
\(313\) | −17.1317 | −0.968339 | −0.484169 | − | 0.874974i | \(-0.660878\pi\) | ||||
−0.484169 | + | 0.874974i | \(0.660878\pi\) | |||||||
\(314\) | −11.0690 | −0.624658 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.818408 | −0.0460390 | ||||||||
\(317\) | 6.44673 | 0.362084 | 0.181042 | − | 0.983475i | \(-0.442053\pi\) | ||||
0.181042 | + | 0.983475i | \(0.442053\pi\) | |||||||
\(318\) | 13.0182 | 0.730023 | ||||||||
\(319\) | −5.40737 | −0.302754 | ||||||||
\(320\) | −15.6142 | −0.872861 | ||||||||
\(321\) | −5.42225 | −0.302640 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.75997 | 0.0979275 | ||||||||
\(324\) | 0.158829 | 0.00882386 | ||||||||
\(325\) | −1.18491 | −0.0657268 | ||||||||
\(326\) | −26.4673 | −1.46589 | ||||||||
\(327\) | 15.2859 | 0.845310 | ||||||||
\(328\) | −28.4468 | −1.57071 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.82619 | −0.375769 | ||||||||
\(331\) | −6.58020 | −0.361681 | −0.180840 | − | 0.983512i | \(-0.557882\pi\) | ||||
−0.180840 | + | 0.983512i | \(0.557882\pi\) | |||||||
\(332\) | 0.747941 | 0.0410486 | ||||||||
\(333\) | −4.50032 | −0.246616 | ||||||||
\(334\) | 24.7378 | 1.35359 | ||||||||
\(335\) | 4.74098 | 0.259028 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.4661 | 1.87749 | 0.938744 | − | 0.344615i | \(-0.111990\pi\) | ||||
0.938744 | + | 0.344615i | \(0.111990\pi\) | |||||||
\(338\) | −5.13350 | −0.279226 | ||||||||
\(339\) | 5.97105 | 0.324303 | ||||||||
\(340\) | −0.121060 | −0.00656540 | ||||||||
\(341\) | −3.97167 | −0.215078 | ||||||||
\(342\) | 7.28892 | 0.394140 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −21.5591 | −1.16239 | ||||||||
\(345\) | 2.14842 | 0.115667 | ||||||||
\(346\) | −24.7107 | −1.32846 | ||||||||
\(347\) | −23.6184 | −1.26790 | −0.633950 | − | 0.773374i | \(-0.718567\pi\) | ||||
−0.633950 | + | 0.773374i | \(0.718567\pi\) | |||||||
\(348\) | −0.397160 | −0.0212900 | ||||||||
\(349\) | 14.7497 | 0.789536 | 0.394768 | − | 0.918781i | \(-0.370825\pi\) | ||||
0.394768 | + | 0.918781i | \(0.370825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.08320 | 0.164569 | ||||||||
\(352\) | −1.93845 | −0.103320 | ||||||||
\(353\) | −20.6050 | −1.09669 | −0.548346 | − | 0.836252i | \(-0.684742\pi\) | ||||
−0.548346 | + | 0.836252i | \(0.684742\pi\) | |||||||
\(354\) | 9.98048 | 0.530457 | ||||||||
\(355\) | −6.61991 | −0.351348 | ||||||||
\(356\) | 0.298510 | 0.0158210 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.65289 | 0.245913 | ||||||||
\(359\) | −26.7302 | −1.41077 | −0.705383 | − | 0.708826i | \(-0.749225\pi\) | ||||
−0.705383 | + | 0.708826i | \(0.749225\pi\) | |||||||
\(360\) | 5.81195 | 0.306316 | ||||||||
\(361\) | 5.60983 | 0.295254 | ||||||||
\(362\) | −34.0380 | −1.78900 | ||||||||
\(363\) | −6.32370 | −0.331908 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.16551 | −0.375060 | ||||||||
\(366\) | −3.45486 | −0.180589 | ||||||||
\(367\) | −33.4515 | −1.74616 | −0.873078 | − | 0.487580i | \(-0.837880\pi\) | ||||
−0.873078 | + | 0.487580i | \(0.837880\pi\) | |||||||
\(368\) | 4.29243 | 0.223758 | ||||||||
\(369\) | 10.5155 | 0.547416 | ||||||||
\(370\) | 14.2060 | 0.738533 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.291711 | −0.0151245 | ||||||||
\(373\) | 26.3427 | 1.36397 | 0.681985 | − | 0.731366i | \(-0.261117\pi\) | ||||
0.681985 | + | 0.731366i | \(0.261117\pi\) | |||||||
\(374\) | 1.12723 | 0.0582876 | ||||||||
\(375\) | 11.5677 | 0.597355 | ||||||||
\(376\) | −21.2005 | −1.09333 | ||||||||
\(377\) | −7.70969 | −0.397069 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.2340 | 0.987984 | 0.493992 | − | 0.869466i | \(-0.335537\pi\) | ||||
0.493992 | + | 0.869466i | \(0.335537\pi\) | |||||||
\(380\) | −1.69279 | −0.0868384 | ||||||||
\(381\) | −7.84667 | −0.401997 | ||||||||
\(382\) | −6.96387 | −0.356303 | ||||||||
\(383\) | −16.3969 | −0.837842 | −0.418921 | − | 0.908023i | \(-0.637592\pi\) | ||||
−0.418921 | + | 0.908023i | \(0.637592\pi\) | |||||||
\(384\) | 12.4713 | 0.636425 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 30.7292 | 1.56407 | ||||||||
\(387\) | 7.96942 | 0.405109 | ||||||||
\(388\) | 1.29096 | 0.0655384 | ||||||||
\(389\) | 22.6519 | 1.14849 | 0.574247 | − | 0.818682i | \(-0.305295\pi\) | ||||
0.574247 | + | 0.818682i | \(0.305295\pi\) | |||||||
\(390\) | −9.73262 | −0.492830 | ||||||||
\(391\) | −0.354774 | −0.0179417 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.14450 | −0.259506 | ||||||||
\(394\) | −29.1097 | −1.46652 | ||||||||
\(395\) | 11.0702 | 0.557004 | ||||||||
\(396\) | 0.343465 | 0.0172597 | ||||||||
\(397\) | 15.2035 | 0.763040 | 0.381520 | − | 0.924361i | \(-0.375401\pi\) | ||||
0.381520 | + | 0.924361i | \(0.375401\pi\) | |||||||
\(398\) | 18.7590 | 0.940302 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.64963 | 0.0824813 | ||||||||
\(401\) | 7.05495 | 0.352307 | 0.176154 | − | 0.984363i | \(-0.443634\pi\) | ||||
0.176154 | + | 0.984363i | \(0.443634\pi\) | |||||||
\(402\) | −3.24234 | −0.161713 | ||||||||
\(403\) | −5.66271 | −0.282080 | ||||||||
\(404\) | 2.88013 | 0.143292 | ||||||||
\(405\) | −2.14842 | −0.106756 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.73182 | −0.482388 | ||||||||
\(408\) | −0.959743 | −0.0475144 | ||||||||
\(409\) | 27.4335 | 1.35650 | 0.678249 | − | 0.734832i | \(-0.262739\pi\) | ||||
0.678249 | + | 0.734832i | \(0.262739\pi\) | |||||||
\(410\) | −33.1939 | −1.63933 | ||||||||
\(411\) | 11.7090 | 0.577561 | ||||||||
\(412\) | 0.620937 | 0.0305913 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.46930 | −0.0722119 | ||||||||
\(415\) | −10.1171 | −0.496627 | ||||||||
\(416\) | −2.76380 | −0.135506 | ||||||||
\(417\) | −3.57676 | −0.175155 | ||||||||
\(418\) | 15.7621 | 0.770950 | ||||||||
\(419\) | 8.06199 | 0.393854 | 0.196927 | − | 0.980418i | \(-0.436904\pi\) | ||||
0.196927 | + | 0.980418i | \(0.436904\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.26503 | −0.159128 | −0.0795640 | − | 0.996830i | \(-0.525353\pi\) | ||||
−0.0795640 | + | 0.996830i | \(0.525353\pi\) | |||||||
\(422\) | 5.54874 | 0.270109 | ||||||||
\(423\) | 7.83688 | 0.381042 | ||||||||
\(424\) | −23.9687 | −1.16402 | ||||||||
\(425\) | −0.136343 | −0.00661362 | ||||||||
\(426\) | 4.52734 | 0.219350 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.861212 | −0.0416283 | ||||||||
\(429\) | 6.66735 | 0.321903 | ||||||||
\(430\) | −25.1567 | −1.21317 | ||||||||
\(431\) | 18.7612 | 0.903697 | 0.451848 | − | 0.892095i | \(-0.350765\pi\) | ||||
0.451848 | + | 0.892095i | \(0.350765\pi\) | |||||||
\(432\) | −4.29243 | −0.206520 | ||||||||
\(433\) | 4.07674 | 0.195915 | 0.0979577 | − | 0.995191i | \(-0.468769\pi\) | ||||
0.0979577 | + | 0.995191i | \(0.468769\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.37221 | 0.257578 | ||||||||
\(436\) | 2.42784 | 0.116273 | ||||||||
\(437\) | −4.96083 | −0.237309 | ||||||||
\(438\) | 4.90047 | 0.234154 | ||||||||
\(439\) | 20.0760 | 0.958173 | 0.479087 | − | 0.877768i | \(-0.340968\pi\) | ||||
0.479087 | + | 0.877768i | \(0.340968\pi\) | |||||||
\(440\) | 12.5682 | 0.599165 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.60717 | 0.0764455 | ||||||||
\(443\) | 18.1100 | 0.860433 | 0.430216 | − | 0.902726i | \(-0.358437\pi\) | ||||
0.430216 | + | 0.902726i | \(0.358437\pi\) | |||||||
\(444\) | −0.714783 | −0.0339221 | ||||||||
\(445\) | −4.03782 | −0.191411 | ||||||||
\(446\) | 4.61584 | 0.218566 | ||||||||
\(447\) | −9.49709 | −0.449197 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.9396 | 1.03539 | 0.517697 | − | 0.855564i | \(-0.326790\pi\) | ||||
0.517697 | + | 0.855564i | \(0.326790\pi\) | |||||||
\(450\) | −0.564665 | −0.0266186 | ||||||||
\(451\) | 22.7396 | 1.07076 | ||||||||
\(452\) | 0.948378 | 0.0446079 | ||||||||
\(453\) | −12.8737 | −0.604861 | ||||||||
\(454\) | 28.8925 | 1.35599 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.4202 | −0.628456 | ||||||||
\(457\) | 25.7102 | 1.20267 | 0.601336 | − | 0.798997i | \(-0.294636\pi\) | ||||
0.601336 | + | 0.798997i | \(0.294636\pi\) | |||||||
\(458\) | −4.99583 | −0.233440 | ||||||||
\(459\) | 0.354774 | 0.0165594 | ||||||||
\(460\) | 0.341232 | 0.0159100 | ||||||||
\(461\) | −29.6004 | −1.37863 | −0.689313 | − | 0.724464i | \(-0.742088\pi\) | ||||
−0.689313 | + | 0.724464i | \(0.742088\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.00166 | 0.325395 | 0.162697 | − | 0.986676i | \(-0.447981\pi\) | ||||
0.162697 | + | 0.986676i | \(0.447981\pi\) | |||||||
\(464\) | 10.7334 | 0.498287 | ||||||||
\(465\) | 3.94585 | 0.182984 | ||||||||
\(466\) | −28.0969 | −1.30156 | ||||||||
\(467\) | 21.5522 | 0.997317 | 0.498659 | − | 0.866798i | \(-0.333826\pi\) | ||||
0.498659 | + | 0.866798i | \(0.333826\pi\) | |||||||
\(468\) | 0.489703 | 0.0226365 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −24.7384 | −1.14110 | ||||||||
\(471\) | −7.53352 | −0.347126 | ||||||||
\(472\) | −18.3758 | −0.845813 | ||||||||
\(473\) | 17.2337 | 0.792405 | ||||||||
\(474\) | −7.57091 | −0.347743 | ||||||||
\(475\) | −1.90650 | −0.0874761 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.86015 | 0.405678 | ||||||||
\(478\) | 4.56826 | 0.208947 | ||||||||
\(479\) | 1.45000 | 0.0662524 | 0.0331262 | − | 0.999451i | \(-0.489454\pi\) | ||||
0.0331262 | + | 0.999451i | \(0.489454\pi\) | |||||||
\(480\) | 1.92585 | 0.0879025 | ||||||||
\(481\) | −13.8754 | −0.632663 | ||||||||
\(482\) | −29.4903 | −1.34325 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.00439 | −0.0456541 | ||||||||
\(485\) | −17.4622 | −0.792918 | ||||||||
\(486\) | 1.46930 | 0.0666486 | ||||||||
\(487\) | −29.3715 | −1.33095 | −0.665474 | − | 0.746421i | \(-0.731770\pi\) | ||||
−0.665474 | + | 0.746421i | \(0.731770\pi\) | |||||||
\(488\) | 6.36099 | 0.287948 | ||||||||
\(489\) | −18.0136 | −0.814605 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.0308 | −0.994235 | −0.497117 | − | 0.867683i | \(-0.665608\pi\) | ||||
−0.497117 | + | 0.867683i | \(0.665608\pi\) | |||||||
\(492\) | 1.67017 | 0.0752973 | ||||||||
\(493\) | −0.887129 | −0.0399543 | ||||||||
\(494\) | 22.4732 | 1.01112 | ||||||||
\(495\) | −4.64589 | −0.208817 | ||||||||
\(496\) | 7.88362 | 0.353985 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.91904 | 0.310049 | ||||||||
\(499\) | −13.0025 | −0.582074 | −0.291037 | − | 0.956712i | \(-0.594000\pi\) | ||||
−0.291037 | + | 0.956712i | \(0.594000\pi\) | |||||||
\(500\) | 1.83730 | 0.0821664 | ||||||||
\(501\) | 16.8365 | 0.752201 | ||||||||
\(502\) | −6.95520 | −0.310426 | ||||||||
\(503\) | −27.4378 | −1.22339 | −0.611695 | − | 0.791094i | \(-0.709512\pi\) | ||||
−0.611695 | + | 0.791094i | \(0.709512\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.9583 | −1.73362 | ||||||||
\(506\) | −3.17731 | −0.141249 | ||||||||
\(507\) | −3.49385 | −0.155168 | ||||||||
\(508\) | −1.24628 | −0.0552948 | ||||||||
\(509\) | 10.7217 | 0.475231 | 0.237615 | − | 0.971359i | \(-0.423634\pi\) | ||||
0.237615 | + | 0.971359i | \(0.423634\pi\) | |||||||
\(510\) | −1.11990 | −0.0495900 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −19.3762 | −0.856316 | ||||||||
\(513\) | 4.96083 | 0.219026 | ||||||||
\(514\) | −5.41528 | −0.238858 | ||||||||
\(515\) | −8.39914 | −0.370110 | ||||||||
\(516\) | 1.26578 | 0.0557228 | ||||||||
\(517\) | 16.9471 | 0.745331 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.8181 | −0.738231 | ||||||||
\(520\) | 17.9194 | 0.785818 | ||||||||
\(521\) | 35.8465 | 1.57046 | 0.785232 | − | 0.619202i | \(-0.212544\pi\) | ||||
0.785232 | + | 0.619202i | \(0.212544\pi\) | |||||||
\(522\) | −3.67404 | −0.160808 | ||||||||
\(523\) | 17.0049 | 0.743573 | 0.371787 | − | 0.928318i | \(-0.378745\pi\) | ||||
0.371787 | + | 0.928318i | \(0.378745\pi\) | |||||||
\(524\) | −0.817097 | −0.0356951 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.72980 | −0.293433 | ||||||||
\(527\) | −0.651589 | −0.0283837 | ||||||||
\(528\) | −9.28227 | −0.403959 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −27.9684 | −1.21487 | ||||||||
\(531\) | 6.79270 | 0.294778 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.4215 | 1.40433 | ||||||||
\(534\) | 2.76145 | 0.119500 | ||||||||
\(535\) | 11.6492 | 0.503641 | ||||||||
\(536\) | 5.96971 | 0.257852 | ||||||||
\(537\) | 3.16675 | 0.136655 | ||||||||
\(538\) | −27.8663 | −1.20140 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.341232 | −0.0146843 | ||||||||
\(541\) | −34.8174 | −1.49692 | −0.748459 | − | 0.663181i | \(-0.769206\pi\) | ||||
−0.748459 | + | 0.663181i | \(0.769206\pi\) | |||||||
\(542\) | 8.48983 | 0.364670 | ||||||||
\(543\) | −23.1662 | −0.994157 | ||||||||
\(544\) | −0.318021 | −0.0136350 | ||||||||
\(545\) | −32.8404 | −1.40673 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.3988 | −1.42803 | −0.714015 | − | 0.700130i | \(-0.753125\pi\) | ||||
−0.714015 | + | 0.700130i | \(0.753125\pi\) | |||||||
\(548\) | 1.85973 | 0.0794437 | ||||||||
\(549\) | −2.35137 | −0.100354 | ||||||||
\(550\) | −1.22107 | −0.0520668 | ||||||||
\(551\) | −12.4048 | −0.528461 | ||||||||
\(552\) | 2.70522 | 0.115142 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −22.8151 | −0.969319 | ||||||||
\(555\) | 9.66855 | 0.410407 | ||||||||
\(556\) | −0.568095 | −0.0240926 | ||||||||
\(557\) | 39.5811 | 1.67711 | 0.838553 | − | 0.544820i | \(-0.183402\pi\) | ||||
0.838553 | + | 0.544820i | \(0.183402\pi\) | |||||||
\(558\) | −2.69856 | −0.114239 | ||||||||
\(559\) | 24.5714 | 1.03926 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.767190 | 0.0323908 | ||||||||
\(562\) | 33.1845 | 1.39980 | ||||||||
\(563\) | 15.5253 | 0.654314 | 0.327157 | − | 0.944970i | \(-0.393909\pi\) | ||||
0.327157 | + | 0.944970i | \(0.393909\pi\) | |||||||
\(564\) | 1.24473 | 0.0524125 | ||||||||
\(565\) | −12.8283 | −0.539690 | ||||||||
\(566\) | −33.0173 | −1.38782 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.33560 | −0.349754 | ||||||||
\(569\) | 34.0553 | 1.42767 | 0.713836 | − | 0.700313i | \(-0.246956\pi\) | ||||
0.713836 | + | 0.700313i | \(0.246956\pi\) | |||||||
\(570\) | −15.6596 | −0.655910 | ||||||||
\(571\) | 29.7572 | 1.24530 | 0.622650 | − | 0.782500i | \(-0.286056\pi\) | ||||
0.622650 | + | 0.782500i | \(0.286056\pi\) | |||||||
\(572\) | 1.05897 | 0.0442778 | ||||||||
\(573\) | −4.73960 | −0.198000 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.384310 | 0.0160268 | ||||||||
\(576\) | 7.26778 | 0.302824 | ||||||||
\(577\) | −2.09294 | −0.0871304 | −0.0435652 | − | 0.999051i | \(-0.513872\pi\) | ||||
−0.0435652 | + | 0.999051i | \(0.513872\pi\) | |||||||
\(578\) | −24.7931 | −1.03126 | ||||||||
\(579\) | 20.9142 | 0.869166 | ||||||||
\(580\) | 0.853265 | 0.0354299 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 11.9424 | 0.495026 | ||||||||
\(583\) | 19.1598 | 0.793519 | ||||||||
\(584\) | −9.02261 | −0.373358 | ||||||||
\(585\) | −6.62400 | −0.273869 | ||||||||
\(586\) | 8.40317 | 0.347132 | ||||||||
\(587\) | −35.6427 | −1.47113 | −0.735565 | − | 0.677454i | \(-0.763083\pi\) | ||||
−0.735565 | + | 0.677454i | \(0.763083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.11122 | −0.375421 | ||||||||
\(590\) | −21.4422 | −0.882762 | ||||||||
\(591\) | −19.8120 | −0.814956 | ||||||||
\(592\) | 19.3173 | 0.793936 | ||||||||
\(593\) | −24.5094 | −1.00648 | −0.503240 | − | 0.864147i | \(-0.667859\pi\) | ||||
−0.503240 | + | 0.864147i | \(0.667859\pi\) | |||||||
\(594\) | 3.17731 | 0.130367 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.50842 | −0.0617871 | ||||||||
\(597\) | 12.7673 | 0.522531 | ||||||||
\(598\) | −4.53014 | −0.185251 | ||||||||
\(599\) | 5.61551 | 0.229443 | 0.114722 | − | 0.993398i | \(-0.463402\pi\) | ||||
0.114722 | + | 0.993398i | \(0.463402\pi\) | |||||||
\(600\) | 1.03965 | 0.0424433 | ||||||||
\(601\) | 13.1302 | 0.535594 | 0.267797 | − | 0.963475i | \(-0.413704\pi\) | ||||
0.267797 | + | 0.963475i | \(0.413704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.20673 | −0.0898652 | ||||||||
\(604\) | −2.04473 | −0.0831989 | ||||||||
\(605\) | 13.5859 | 0.552347 | ||||||||
\(606\) | 26.6434 | 1.08232 | ||||||||
\(607\) | 0.0961849 | 0.00390403 | 0.00195201 | − | 0.999998i | \(-0.499379\pi\) | ||||
0.00195201 | + | 0.999998i | \(0.499379\pi\) | |||||||
\(608\) | −4.44691 | −0.180346 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.42248 | 0.300527 | ||||||||
\(611\) | 24.1627 | 0.977519 | ||||||||
\(612\) | 0.0563485 | 0.00227775 | ||||||||
\(613\) | 2.52392 | 0.101940 | 0.0509701 | − | 0.998700i | \(-0.483769\pi\) | ||||
0.0509701 | + | 0.998700i | \(0.483769\pi\) | |||||||
\(614\) | 14.6275 | 0.590317 | ||||||||
\(615\) | −22.5917 | −0.910986 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.7394 | 0.915453 | 0.457727 | − | 0.889093i | \(-0.348664\pi\) | ||||
0.457727 | + | 0.889093i | \(0.348664\pi\) | |||||||
\(618\) | 5.74415 | 0.231063 | ||||||||
\(619\) | −23.8721 | −0.959500 | −0.479750 | − | 0.877405i | \(-0.659273\pi\) | ||||
−0.479750 | + | 0.877405i | \(0.659273\pi\) | |||||||
\(620\) | 0.626717 | 0.0251696 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −25.9734 | −1.04144 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −13.2344 | −0.529802 | ||||||||
\(625\) | −22.9308 | −0.917230 | ||||||||
\(626\) | −25.1715 | −1.00605 | ||||||||
\(627\) | 10.7277 | 0.428422 | ||||||||
\(628\) | −1.19654 | −0.0477473 | ||||||||
\(629\) | −1.59659 | −0.0636604 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5166 | 0.538086 | 0.269043 | − | 0.963128i | \(-0.413293\pi\) | ||||
0.269043 | + | 0.963128i | \(0.413293\pi\) | |||||||
\(632\) | 13.9393 | 0.554477 | ||||||||
\(633\) | 3.77646 | 0.150101 | ||||||||
\(634\) | 9.47215 | 0.376187 | ||||||||
\(635\) | 16.8579 | 0.668985 | ||||||||
\(636\) | 1.40725 | 0.0558012 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.94502 | −0.314546 | ||||||||
\(639\) | 3.08130 | 0.121894 | ||||||||
\(640\) | −26.7936 | −1.05911 | ||||||||
\(641\) | 17.3683 | 0.686005 | 0.343002 | − | 0.939335i | \(-0.388556\pi\) | ||||
0.343002 | + | 0.939335i | \(0.388556\pi\) | |||||||
\(642\) | −7.96688 | −0.314428 | ||||||||
\(643\) | 10.2840 | 0.405561 | 0.202780 | − | 0.979224i | \(-0.435002\pi\) | ||||
0.202780 | + | 0.979224i | \(0.435002\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.1216 | −0.674164 | ||||||||
\(646\) | 2.58592 | 0.101742 | ||||||||
\(647\) | −43.6516 | −1.71612 | −0.858060 | − | 0.513550i | \(-0.828330\pi\) | ||||
−0.858060 | + | 0.513550i | \(0.828330\pi\) | |||||||
\(648\) | −2.70522 | −0.106271 | ||||||||
\(649\) | 14.6890 | 0.576595 | ||||||||
\(650\) | −1.74098 | −0.0682868 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.86109 | −0.112049 | ||||||||
\(653\) | 5.79970 | 0.226960 | 0.113480 | − | 0.993540i | \(-0.463800\pi\) | ||||
0.113480 | + | 0.993540i | \(0.463800\pi\) | |||||||
\(654\) | 22.4594 | 0.878234 | ||||||||
\(655\) | 11.0525 | 0.431858 | ||||||||
\(656\) | −45.1372 | −1.76231 | ||||||||
\(657\) | 3.33525 | 0.130121 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.50649 | 0.175548 | 0.0877740 | − | 0.996140i | \(-0.472025\pi\) | ||||
0.0877740 | + | 0.996140i | \(0.472025\pi\) | |||||||
\(660\) | −0.737905 | −0.0287229 | ||||||||
\(661\) | −19.2687 | −0.749467 | −0.374734 | − | 0.927133i | \(-0.622266\pi\) | ||||
−0.374734 | + | 0.927133i | \(0.622266\pi\) | |||||||
\(662\) | −9.66826 | −0.375768 | ||||||||
\(663\) | 1.09384 | 0.0424812 | ||||||||
\(664\) | −12.7391 | −0.494374 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.61229 | −0.256221 | ||||||||
\(667\) | 2.50055 | 0.0968215 | ||||||||
\(668\) | 2.67414 | 0.103465 | ||||||||
\(669\) | 3.14153 | 0.121459 | ||||||||
\(670\) | 6.96590 | 0.269116 | ||||||||
\(671\) | −5.08478 | −0.196296 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.9683 | −1.57921 | −0.789606 | − | 0.613615i | \(-0.789715\pi\) | ||||
−0.789606 | + | 0.613615i | \(0.789715\pi\) | |||||||
\(674\) | 50.6409 | 1.95061 | ||||||||
\(675\) | −0.384310 | −0.0147921 | ||||||||
\(676\) | −0.554927 | −0.0213433 | ||||||||
\(677\) | 20.8977 | 0.803165 | 0.401582 | − | 0.915823i | \(-0.368460\pi\) | ||||
0.401582 | + | 0.915823i | \(0.368460\pi\) | |||||||
\(678\) | 8.77323 | 0.336934 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.06193 | 0.0790713 | ||||||||
\(681\) | 19.6642 | 0.753533 | ||||||||
\(682\) | −5.83556 | −0.223455 | ||||||||
\(683\) | 50.4475 | 1.93032 | 0.965159 | − | 0.261663i | \(-0.0842709\pi\) | ||||
0.965159 | + | 0.261663i | \(0.0842709\pi\) | |||||||
\(684\) | 0.787926 | 0.0301271 | ||||||||
\(685\) | −25.1558 | −0.961152 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.40015 | −0.129724 | ||||||||
\(688\) | −34.2082 | −1.30418 | ||||||||
\(689\) | 27.3176 | 1.04072 | ||||||||
\(690\) | 3.15666 | 0.120172 | ||||||||
\(691\) | 21.7766 | 0.828422 | 0.414211 | − | 0.910181i | \(-0.364057\pi\) | ||||
0.414211 | + | 0.910181i | \(0.364057\pi\) | |||||||
\(692\) | −2.67120 | −0.101544 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.7023 | −1.31728 | ||||||||
\(695\) | 7.68437 | 0.291485 | ||||||||
\(696\) | 6.76454 | 0.256409 | ||||||||
\(697\) | 3.73063 | 0.141308 | ||||||||
\(698\) | 21.6717 | 0.820287 | ||||||||
\(699\) | −19.1227 | −0.723287 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.05307 | 0.190852 | 0.0954259 | − | 0.995437i | \(-0.469579\pi\) | ||||
0.0954259 | + | 0.995437i | \(0.469579\pi\) | |||||||
\(702\) | 4.53014 | 0.170979 | ||||||||
\(703\) | −22.3253 | −0.842015 | ||||||||
\(704\) | 15.7164 | 0.592334 | ||||||||
\(705\) | −16.8369 | −0.634114 | ||||||||
\(706\) | −30.2748 | −1.13941 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.07888 | 0.0405468 | ||||||||
\(709\) | −19.4725 | −0.731304 | −0.365652 | − | 0.930752i | \(-0.619154\pi\) | ||||
−0.365652 | + | 0.930752i | \(0.619154\pi\) | |||||||
\(710\) | −9.72660 | −0.365033 | ||||||||
\(711\) | −5.15275 | −0.193243 | ||||||||
\(712\) | −5.08431 | −0.190542 | ||||||||
\(713\) | 1.83663 | 0.0687824 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.3242 | −0.535696 | ||||||||
\(716\) | 0.502973 | 0.0187970 | ||||||||
\(717\) | 3.10915 | 0.116113 | ||||||||
\(718\) | −39.2746 | −1.46571 | ||||||||
\(719\) | 21.1483 | 0.788698 | 0.394349 | − | 0.918961i | \(-0.370970\pi\) | ||||
0.394349 | + | 0.918961i | \(0.370970\pi\) | |||||||
\(720\) | 9.22193 | 0.343681 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.24249 | 0.306754 | ||||||||
\(723\) | −20.0711 | −0.746450 | ||||||||
\(724\) | −3.67947 | −0.136747 | ||||||||
\(725\) | 0.960985 | 0.0356901 | ||||||||
\(726\) | −9.29139 | −0.344836 | ||||||||
\(727\) | 36.0941 | 1.33866 | 0.669328 | − | 0.742967i | \(-0.266582\pi\) | ||||
0.669328 | + | 0.742967i | \(0.266582\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.5283 | −0.389668 | ||||||||
\(731\) | 2.82734 | 0.104573 | ||||||||
\(732\) | −0.373467 | −0.0138037 | ||||||||
\(733\) | −12.5279 | −0.462728 | −0.231364 | − | 0.972867i | \(-0.574319\pi\) | ||||
−0.231364 | + | 0.972867i | \(0.574319\pi\) | |||||||
\(734\) | −49.1502 | −1.81417 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.896404 | 0.0330419 | ||||||||
\(737\) | −4.77201 | −0.175779 | ||||||||
\(738\) | 15.4504 | 0.568738 | ||||||||
\(739\) | 28.8783 | 1.06230 | 0.531152 | − | 0.847276i | \(-0.321759\pi\) | ||||
0.531152 | + | 0.847276i | \(0.321759\pi\) | |||||||
\(740\) | 1.53565 | 0.0564516 | ||||||||
\(741\) | 15.2952 | 0.561885 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.69965 | 0.172413 | 0.0862066 | − | 0.996277i | \(-0.472525\pi\) | ||||
0.0862066 | + | 0.996277i | \(0.472525\pi\) | |||||||
\(744\) | 4.96850 | 0.182154 | ||||||||
\(745\) | 20.4037 | 0.747533 | ||||||||
\(746\) | 38.7051 | 1.41710 | ||||||||
\(747\) | 4.70908 | 0.172296 | ||||||||
\(748\) | 0.121852 | 0.00445536 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 16.9964 | 0.620622 | ||||||||
\(751\) | −49.0318 | −1.78920 | −0.894598 | − | 0.446871i | \(-0.852538\pi\) | ||||
−0.894598 | + | 0.446871i | \(0.852538\pi\) | |||||||
\(752\) | −33.6393 | −1.22670 | ||||||||
\(753\) | −4.73370 | −0.172505 | ||||||||
\(754\) | −11.3278 | −0.412535 | ||||||||
\(755\) | 27.6582 | 1.00658 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.25720 | −0.336459 | −0.168229 | − | 0.985748i | \(-0.553805\pi\) | ||||
−0.168229 | + | 0.985748i | \(0.553805\pi\) | |||||||
\(758\) | 28.2604 | 1.02646 | ||||||||
\(759\) | −2.16247 | −0.0784929 | ||||||||
\(760\) | 28.8321 | 1.04585 | ||||||||
\(761\) | 9.75714 | 0.353696 | 0.176848 | − | 0.984238i | \(-0.443410\pi\) | ||||
0.176848 | + | 0.984238i | \(0.443410\pi\) | |||||||
\(762\) | −11.5291 | −0.417654 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.752788 | −0.0272349 | ||||||||
\(765\) | −0.762202 | −0.0275575 | ||||||||
\(766\) | −24.0919 | −0.870475 | ||||||||
\(767\) | 20.9433 | 0.756218 | ||||||||
\(768\) | 3.78850 | 0.136706 | ||||||||
\(769\) | −3.88254 | −0.140008 | −0.0700041 | − | 0.997547i | \(-0.522301\pi\) | ||||
−0.0700041 | + | 0.997547i | \(0.522301\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.68563 | −0.132735 | ||||||||
\(772\) | 3.32180 | 0.119554 | ||||||||
\(773\) | −32.6917 | −1.17584 | −0.587919 | − | 0.808920i | \(-0.700053\pi\) | ||||
−0.587919 | + | 0.808920i | \(0.700053\pi\) | |||||||
\(774\) | 11.7094 | 0.420887 | ||||||||
\(775\) | 0.705836 | 0.0253544 | ||||||||
\(776\) | −21.9879 | −0.789320 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.2823 | 1.19323 | ||||||||
\(779\) | 52.1657 | 1.86903 | ||||||||
\(780\) | −1.05209 | −0.0376707 | ||||||||
\(781\) | 6.66323 | 0.238429 | ||||||||
\(782\) | −0.521268 | −0.0186405 | ||||||||
\(783\) | −2.50055 | −0.0893622 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.1851 | 0.577672 | ||||||||
\(786\) | −7.55879 | −0.269613 | ||||||||
\(787\) | 29.4878 | 1.05113 | 0.525563 | − | 0.850755i | \(-0.323855\pi\) | ||||
0.525563 | + | 0.850755i | \(0.323855\pi\) | |||||||
\(788\) | −3.14673 | −0.112097 | ||||||||
\(789\) | −4.58029 | −0.163063 | ||||||||
\(790\) | 16.2655 | 0.578699 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.84998 | −0.207870 | ||||||||
\(793\) | −7.24976 | −0.257447 | ||||||||
\(794\) | 22.3384 | 0.792759 | ||||||||
\(795\) | −19.0353 | −0.675112 | ||||||||
\(796\) | 2.02783 | 0.0718744 | ||||||||
\(797\) | 31.2478 | 1.10685 | 0.553427 | − | 0.832897i | \(-0.313320\pi\) | ||||
0.553427 | + | 0.832897i | \(0.313320\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.78032 | 0.0983607 | ||||||||
\(800\) | 0.344497 | 0.0121798 | ||||||||
\(801\) | 1.87944 | 0.0664068 | ||||||||
\(802\) | 10.3658 | 0.366029 | ||||||||
\(803\) | 7.21240 | 0.254520 | ||||||||
\(804\) | −0.350494 | −0.0123610 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.32020 | −0.293066 | ||||||||
\(807\) | −18.9657 | −0.667626 | ||||||||
\(808\) | −49.0551 | −1.72575 | ||||||||
\(809\) | −6.47854 | −0.227773 | −0.113887 | − | 0.993494i | \(-0.536330\pi\) | ||||
−0.113887 | + | 0.993494i | \(0.536330\pi\) | |||||||
\(810\) | −3.15666 | −0.110914 | ||||||||
\(811\) | −16.2398 | −0.570257 | −0.285128 | − | 0.958489i | \(-0.592036\pi\) | ||||
−0.285128 | + | 0.958489i | \(0.592036\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.77817 | 0.202649 | ||||||||
\(814\) | −14.2989 | −0.501177 | ||||||||
\(815\) | 38.7008 | 1.35563 | ||||||||
\(816\) | −1.52284 | −0.0533102 | ||||||||
\(817\) | 39.5349 | 1.38315 | ||||||||
\(818\) | 40.3079 | 1.40933 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.58823 | −0.125306 | ||||||||
\(821\) | −39.9374 | −1.39382 | −0.696912 | − | 0.717157i | \(-0.745443\pi\) | ||||
−0.696912 | + | 0.717157i | \(0.745443\pi\) | |||||||
\(822\) | 17.2040 | 0.600057 | ||||||||
\(823\) | 51.5045 | 1.79533 | 0.897667 | − | 0.440675i | \(-0.145261\pi\) | ||||
0.897667 | + | 0.440675i | \(0.145261\pi\) | |||||||
\(824\) | −10.5760 | −0.368431 | ||||||||
\(825\) | −0.831061 | −0.0289338 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.0594 | −0.384571 | −0.192286 | − | 0.981339i | \(-0.561590\pi\) | ||||
−0.192286 | + | 0.981339i | \(0.561590\pi\) | |||||||
\(828\) | −0.158829 | −0.00551970 | ||||||||
\(829\) | 9.76537 | 0.339165 | 0.169583 | − | 0.985516i | \(-0.445758\pi\) | ||||
0.169583 | + | 0.985516i | \(0.445758\pi\) | |||||||
\(830\) | −14.8650 | −0.515971 | ||||||||
\(831\) | −15.5279 | −0.538657 | ||||||||
\(832\) | 22.4081 | 0.776859 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.25532 | −0.181977 | ||||||||
\(835\) | −36.1719 | −1.25178 | ||||||||
\(836\) | 1.70387 | 0.0589295 | ||||||||
\(837\) | −1.83663 | −0.0634833 | ||||||||
\(838\) | 11.8454 | 0.409194 | ||||||||
\(839\) | 27.3798 | 0.945254 | 0.472627 | − | 0.881262i | \(-0.343306\pi\) | ||||
0.472627 | + | 0.881262i | \(0.343306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.7473 | −0.784389 | ||||||||
\(842\) | −4.79730 | −0.165326 | ||||||||
\(843\) | 22.5853 | 0.777880 | ||||||||
\(844\) | 0.599814 | 0.0206464 | ||||||||
\(845\) | 7.50625 | 0.258223 | ||||||||
\(846\) | 11.5147 | 0.395884 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −38.0316 | −1.30601 | ||||||||
\(849\) | −22.4715 | −0.771221 | ||||||||
\(850\) | −0.200329 | −0.00687121 | ||||||||
\(851\) | 4.50032 | 0.154269 | ||||||||
\(852\) | 0.489401 | 0.0167666 | ||||||||
\(853\) | −29.0973 | −0.996274 | −0.498137 | − | 0.867098i | \(-0.665982\pi\) | ||||
−0.498137 | + | 0.867098i | \(0.665982\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.6579 | −0.364493 | ||||||||
\(856\) | 14.6684 | 0.501355 | ||||||||
\(857\) | −44.9912 | −1.53687 | −0.768435 | − | 0.639928i | \(-0.778964\pi\) | ||||
−0.768435 | + | 0.639928i | \(0.778964\pi\) | |||||||
\(858\) | 9.79631 | 0.334440 | ||||||||
\(859\) | −9.64929 | −0.329230 | −0.164615 | − | 0.986358i | \(-0.552638\pi\) | ||||
−0.164615 | + | 0.986358i | \(0.552638\pi\) | |||||||
\(860\) | −2.71942 | −0.0927314 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.5658 | 0.938895 | ||||||||
\(863\) | 12.9216 | 0.439856 | 0.219928 | − | 0.975516i | \(-0.429418\pi\) | ||||
0.219928 | + | 0.975516i | \(0.429418\pi\) | |||||||
\(864\) | −0.896404 | −0.0304963 | ||||||||
\(865\) | 36.1322 | 1.22853 | ||||||||
\(866\) | 5.98993 | 0.203546 | ||||||||
\(867\) | −16.8741 | −0.573076 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.1427 | −0.377990 | ||||||||
\(870\) | 7.89337 | 0.267610 | ||||||||
\(871\) | −6.80381 | −0.230538 | ||||||||
\(872\) | −41.3517 | −1.40034 | ||||||||
\(873\) | 8.12795 | 0.275089 | ||||||||
\(874\) | −7.28892 | −0.246552 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.529736 | 0.0178981 | ||||||||
\(877\) | 32.3173 | 1.09128 | 0.545639 | − | 0.838020i | \(-0.316287\pi\) | ||||
0.545639 | + | 0.838020i | \(0.316287\pi\) | |||||||
\(878\) | 29.4975 | 0.995493 | ||||||||
\(879\) | 5.71918 | 0.192903 | ||||||||
\(880\) | 19.9422 | 0.672251 | ||||||||
\(881\) | 46.4011 | 1.56329 | 0.781647 | − | 0.623721i | \(-0.214380\pi\) | ||||
0.781647 | + | 0.623721i | \(0.214380\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.37111 | −0.147100 | −0.0735498 | − | 0.997292i | \(-0.523433\pi\) | ||||
−0.0735498 | + | 0.997292i | \(0.523433\pi\) | |||||||
\(884\) | 0.173734 | 0.00584331 | ||||||||
\(885\) | −14.5935 | −0.490557 | ||||||||
\(886\) | 26.6090 | 0.893946 | ||||||||
\(887\) | 25.3672 | 0.851749 | 0.425874 | − | 0.904782i | \(-0.359967\pi\) | ||||
0.425874 | + | 0.904782i | \(0.359967\pi\) | |||||||
\(888\) | 12.1744 | 0.408545 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.93275 | −0.198866 | ||||||||
\(891\) | 2.16247 | 0.0724456 | ||||||||
\(892\) | 0.498968 | 0.0167067 | ||||||||
\(893\) | 38.8774 | 1.30098 | ||||||||
\(894\) | −13.9540 | −0.466692 | ||||||||
\(895\) | −6.80349 | −0.227416 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.08320 | −0.102945 | ||||||||
\(898\) | 32.2358 | 1.07572 | ||||||||
\(899\) | 4.59258 | 0.153171 | ||||||||
\(900\) | −0.0610398 | −0.00203466 | ||||||||
\(901\) | 3.14335 | 0.104720 | ||||||||
\(902\) | 33.4111 | 1.11247 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.1530 | −0.537241 | ||||||||
\(905\) | 49.7706 | 1.65443 | ||||||||
\(906\) | −18.9153 | −0.628420 | ||||||||
\(907\) | −50.6441 | −1.68161 | −0.840804 | − | 0.541340i | \(-0.817917\pi\) | ||||
−0.840804 | + | 0.541340i | \(0.817917\pi\) | |||||||
\(908\) | 3.12325 | 0.103649 | ||||||||
\(909\) | 18.1335 | 0.601450 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.29108 | −0.208433 | −0.104216 | − | 0.994555i | \(-0.533233\pi\) | ||||
−0.104216 | + | 0.994555i | \(0.533233\pi\) | |||||||
\(912\) | −21.2940 | −0.705116 | ||||||||
\(913\) | 10.1833 | 0.337017 | ||||||||
\(914\) | 37.7758 | 1.24951 | ||||||||
\(915\) | 5.05173 | 0.167005 | ||||||||
\(916\) | −0.540044 | −0.0178436 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.521268 | 0.0172044 | ||||||||
\(919\) | 26.3435 | 0.868991 | 0.434496 | − | 0.900674i | \(-0.356927\pi\) | ||||
0.434496 | + | 0.900674i | \(0.356927\pi\) | |||||||
\(920\) | −5.81195 | −0.191614 | ||||||||
\(921\) | 9.95544 | 0.328043 | ||||||||
\(922\) | −43.4917 | −1.43232 | ||||||||
\(923\) | 9.50027 | 0.312705 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.72952 | 0.0568662 | ||||||||
\(926\) | 10.2875 | 0.338069 | ||||||||
\(927\) | 3.90946 | 0.128403 | ||||||||
\(928\) | 2.24150 | 0.0735808 | ||||||||
\(929\) | 51.3944 | 1.68619 | 0.843097 | − | 0.537762i | \(-0.180730\pi\) | ||||
0.843097 | + | 0.537762i | \(0.180730\pi\) | |||||||
\(930\) | 5.79762 | 0.190111 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.03725 | −0.0994884 | ||||||||
\(933\) | −17.6774 | −0.578733 | ||||||||
\(934\) | 31.6666 | 1.03616 | ||||||||
\(935\) | −1.64824 | −0.0539033 | ||||||||
\(936\) | −8.34076 | −0.272626 | ||||||||
\(937\) | −9.83635 | −0.321339 | −0.160670 | − | 0.987008i | \(-0.551365\pi\) | ||||
−0.160670 | + | 0.987008i | \(0.551365\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.1317 | −0.559071 | ||||||||
\(940\) | −2.67419 | −0.0872225 | ||||||||
\(941\) | 43.7737 | 1.42698 | 0.713491 | − | 0.700664i | \(-0.247113\pi\) | ||||
0.713491 | + | 0.700664i | \(0.247113\pi\) | |||||||
\(942\) | −11.0690 | −0.360647 | ||||||||
\(943\) | −10.5155 | −0.342433 | ||||||||
\(944\) | −29.1572 | −0.948986 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.3214 | 0.823268 | ||||||||
\(947\) | −29.6306 | −0.962865 | −0.481432 | − | 0.876483i | \(-0.659883\pi\) | ||||
−0.481432 | + | 0.876483i | \(0.659883\pi\) | |||||||
\(948\) | −0.818408 | −0.0265806 | ||||||||
\(949\) | 10.2833 | 0.333809 | ||||||||
\(950\) | −2.80121 | −0.0908832 | ||||||||
\(951\) | 6.44673 | 0.209049 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.6354 | 1.25152 | 0.625762 | − | 0.780014i | \(-0.284788\pi\) | ||||
0.625762 | + | 0.780014i | \(0.284788\pi\) | |||||||
\(954\) | 13.0182 | 0.421479 | ||||||||
\(955\) | 10.1826 | 0.329502 | ||||||||
\(956\) | 0.493825 | 0.0159714 | ||||||||
\(957\) | −5.40737 | −0.174795 | ||||||||
\(958\) | 2.13048 | 0.0688328 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −15.6142 | −0.503947 | ||||||||
\(961\) | −27.6268 | −0.891187 | ||||||||
\(962\) | −20.3871 | −0.657305 | ||||||||
\(963\) | −5.42225 | −0.174729 | ||||||||
\(964\) | −3.18787 | −0.102674 | ||||||||
\(965\) | −44.9325 | −1.44643 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.5223 | −1.49606 | −0.748028 | − | 0.663668i | \(-0.768999\pi\) | ||||
−0.748028 | + | 0.663668i | \(0.768999\pi\) | |||||||
\(968\) | 17.1070 | 0.549841 | ||||||||
\(969\) | 1.75997 | 0.0565385 | ||||||||
\(970\) | −25.6571 | −0.823801 | ||||||||
\(971\) | −5.98111 | −0.191943 | −0.0959715 | − | 0.995384i | \(-0.530596\pi\) | ||||
−0.0959715 | + | 0.995384i | \(0.530596\pi\) | |||||||
\(972\) | 0.158829 | 0.00509446 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −43.1553 | −1.38279 | ||||||||
\(975\) | −1.18491 | −0.0379474 | ||||||||
\(976\) | 10.0931 | 0.323073 | ||||||||
\(977\) | −10.9369 | −0.349901 | −0.174950 | − | 0.984577i | \(-0.555977\pi\) | ||||
−0.174950 | + | 0.984577i | \(0.555977\pi\) | |||||||
\(978\) | −26.4673 | −0.846332 | ||||||||
\(979\) | 4.06424 | 0.129894 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.2859 | 0.488040 | ||||||||
\(982\) | −32.3697 | −1.03296 | ||||||||
\(983\) | −56.6707 | −1.80751 | −0.903757 | − | 0.428045i | \(-0.859202\pi\) | ||||
−0.903757 | + | 0.428045i | \(0.859202\pi\) | |||||||
\(984\) | −28.4468 | −0.906852 | ||||||||
\(985\) | 42.5644 | 1.35621 | ||||||||
\(986\) | −1.30345 | −0.0415104 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.42934 | 0.0772874 | ||||||||
\(989\) | −7.96942 | −0.253413 | ||||||||
\(990\) | −6.82619 | −0.216951 | ||||||||
\(991\) | 9.57119 | 0.304039 | 0.152019 | − | 0.988378i | \(-0.451422\pi\) | ||||
0.152019 | + | 0.988378i | \(0.451422\pi\) | |||||||
\(992\) | 1.64636 | 0.0522721 | ||||||||
\(993\) | −6.58020 | −0.208816 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.4295 | −0.869574 | ||||||||
\(996\) | 0.747941 | 0.0236994 | ||||||||
\(997\) | −56.0202 | −1.77418 | −0.887089 | − | 0.461598i | \(-0.847276\pi\) | ||||
−0.887089 | + | 0.461598i | \(0.847276\pi\) | |||||||
\(998\) | −19.1046 | −0.604745 | ||||||||
\(999\) | −4.50032 | −0.142384 |
(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 | 3381.2.a.bl.1.7 | yes | 10 | |
7.6 | odd | 2 | 3381.2.a.bk.1.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3381.2.a.bk.1.7 | ✓ | 10 | 7.6 | odd | 2 | ||
3381.2.a.bl.1.7 | yes | 10 | 1.1 | even | 1 | trivial |