Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + 4553 x^{7} - 6393 x^{6} - 6785 x^{5} + 7806 x^{4} + 4632 x^{3} - 3811 x^{2} + \cdots + 281 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(1.86754\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.86754 | 1.32055 | 0.660274 | − | 0.751025i | \(-0.270440\pi\) | ||||
0.660274 | + | 0.751025i | \(0.270440\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.48770 | 0.743849 | ||||||||
\(5\) | −4.30941 | −1.92723 | −0.963613 | − | 0.267301i | \(-0.913868\pi\) | ||||
−0.963613 | + | 0.267301i | \(0.913868\pi\) | |||||||
\(6\) | 1.86754 | 0.762419 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −0.956744 | −0.338260 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −8.04798 | −2.54500 | ||||||||
\(11\) | −3.88982 | −1.17282 | −0.586412 | − | 0.810013i | \(-0.699460\pi\) | ||||
−0.586412 | + | 0.810013i | \(0.699460\pi\) | |||||||
\(12\) | 1.48770 | 0.429461 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.86754 | −0.499120 | ||||||||
\(15\) | −4.30941 | −1.11268 | ||||||||
\(16\) | −4.76215 | −1.19054 | ||||||||
\(17\) | 6.82373 | 1.65500 | 0.827498 | − | 0.561468i | \(-0.189763\pi\) | ||||
0.827498 | + | 0.561468i | \(0.189763\pi\) | |||||||
\(18\) | 1.86754 | 0.440183 | ||||||||
\(19\) | 5.88962 | 1.35117 | 0.675586 | − | 0.737282i | \(-0.263891\pi\) | ||||
0.675586 | + | 0.737282i | \(0.263891\pi\) | |||||||
\(20\) | −6.41110 | −1.43356 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −7.26438 | −1.54877 | ||||||||
\(23\) | −1.28080 | −0.267066 | −0.133533 | − | 0.991044i | \(-0.542632\pi\) | ||||
−0.133533 | + | 0.991044i | \(0.542632\pi\) | |||||||
\(24\) | −0.956744 | −0.195295 | ||||||||
\(25\) | 13.5710 | 2.71420 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.48770 | −0.281148 | ||||||||
\(29\) | 1.83066 | 0.339945 | 0.169973 | − | 0.985449i | \(-0.445632\pi\) | ||||
0.169973 | + | 0.985449i | \(0.445632\pi\) | |||||||
\(30\) | −8.04798 | −1.46935 | ||||||||
\(31\) | 1.37027 | 0.246108 | 0.123054 | − | 0.992400i | \(-0.460731\pi\) | ||||
0.123054 | + | 0.992400i | \(0.460731\pi\) | |||||||
\(32\) | −6.98001 | −1.23390 | ||||||||
\(33\) | −3.88982 | −0.677130 | ||||||||
\(34\) | 12.7436 | 2.18550 | ||||||||
\(35\) | 4.30941 | 0.728423 | ||||||||
\(36\) | 1.48770 | 0.247950 | ||||||||
\(37\) | 10.7371 | 1.76516 | 0.882580 | − | 0.470162i | \(-0.155804\pi\) | ||||
0.882580 | + | 0.470162i | \(0.155804\pi\) | |||||||
\(38\) | 10.9991 | 1.78429 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.12300 | 0.651904 | ||||||||
\(41\) | 6.71425 | 1.04859 | 0.524295 | − | 0.851537i | \(-0.324329\pi\) | ||||
0.524295 | + | 0.851537i | \(0.324329\pi\) | |||||||
\(42\) | −1.86754 | −0.288167 | ||||||||
\(43\) | 9.00507 | 1.37326 | 0.686630 | − | 0.727007i | \(-0.259089\pi\) | ||||
0.686630 | + | 0.727007i | \(0.259089\pi\) | |||||||
\(44\) | −5.78687 | −0.872404 | ||||||||
\(45\) | −4.30941 | −0.642409 | ||||||||
\(46\) | −2.39195 | −0.352674 | ||||||||
\(47\) | −9.83977 | −1.43528 | −0.717639 | − | 0.696416i | \(-0.754777\pi\) | ||||
−0.717639 | + | 0.696416i | \(0.754777\pi\) | |||||||
\(48\) | −4.76215 | −0.687357 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 25.3444 | 3.58423 | ||||||||
\(51\) | 6.82373 | 0.955513 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.63020 | 0.361285 | 0.180643 | − | 0.983549i | \(-0.442182\pi\) | ||||
0.180643 | + | 0.983549i | \(0.442182\pi\) | |||||||
\(54\) | 1.86754 | 0.254140 | ||||||||
\(55\) | 16.7628 | 2.26030 | ||||||||
\(56\) | 0.956744 | 0.127850 | ||||||||
\(57\) | 5.88962 | 0.780099 | ||||||||
\(58\) | 3.41883 | 0.448914 | ||||||||
\(59\) | 3.34355 | 0.435293 | 0.217647 | − | 0.976028i | \(-0.430162\pi\) | ||||
0.217647 | + | 0.976028i | \(0.430162\pi\) | |||||||
\(60\) | −6.41110 | −0.827669 | ||||||||
\(61\) | −10.4539 | −1.33848 | −0.669241 | − | 0.743045i | \(-0.733381\pi\) | ||||
−0.669241 | + | 0.743045i | \(0.733381\pi\) | |||||||
\(62\) | 2.55904 | 0.324998 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −3.51113 | −0.438891 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.26438 | −0.894184 | ||||||||
\(67\) | −7.48179 | −0.914046 | −0.457023 | − | 0.889455i | \(-0.651084\pi\) | ||||
−0.457023 | + | 0.889455i | \(0.651084\pi\) | |||||||
\(68\) | 10.1516 | 1.23107 | ||||||||
\(69\) | −1.28080 | −0.154191 | ||||||||
\(70\) | 8.04798 | 0.961918 | ||||||||
\(71\) | 4.78383 | 0.567736 | 0.283868 | − | 0.958863i | \(-0.408382\pi\) | ||||
0.283868 | + | 0.958863i | \(0.408382\pi\) | |||||||
\(72\) | −0.956744 | −0.112753 | ||||||||
\(73\) | −7.13412 | −0.834986 | −0.417493 | − | 0.908680i | \(-0.637091\pi\) | ||||
−0.417493 | + | 0.908680i | \(0.637091\pi\) | |||||||
\(74\) | 20.0519 | 2.33098 | ||||||||
\(75\) | 13.5710 | 1.56704 | ||||||||
\(76\) | 8.76197 | 1.00507 | ||||||||
\(77\) | 3.88982 | 0.443286 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.77176 | 0.424356 | 0.212178 | − | 0.977231i | \(-0.431944\pi\) | ||||
0.212178 | + | 0.977231i | \(0.431944\pi\) | |||||||
\(80\) | 20.5221 | 2.29444 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.5391 | 1.38471 | ||||||||
\(83\) | 3.87193 | 0.425000 | 0.212500 | − | 0.977161i | \(-0.431840\pi\) | ||||
0.212500 | + | 0.977161i | \(0.431840\pi\) | |||||||
\(84\) | −1.48770 | −0.162321 | ||||||||
\(85\) | −29.4062 | −3.18955 | ||||||||
\(86\) | 16.8173 | 1.81346 | ||||||||
\(87\) | 1.83066 | 0.196268 | ||||||||
\(88\) | 3.72156 | 0.396720 | ||||||||
\(89\) | −9.71508 | −1.02980 | −0.514898 | − | 0.857251i | \(-0.672170\pi\) | ||||
−0.514898 | + | 0.857251i | \(0.672170\pi\) | |||||||
\(90\) | −8.04798 | −0.848332 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.90545 | −0.198657 | ||||||||
\(93\) | 1.37027 | 0.142091 | ||||||||
\(94\) | −18.3761 | −1.89535 | ||||||||
\(95\) | −25.3808 | −2.60401 | ||||||||
\(96\) | −6.98001 | −0.712394 | ||||||||
\(97\) | 1.63979 | 0.166495 | 0.0832475 | − | 0.996529i | \(-0.473471\pi\) | ||||
0.0832475 | + | 0.996529i | \(0.473471\pi\) | |||||||
\(98\) | 1.86754 | 0.188650 | ||||||||
\(99\) | −3.88982 | −0.390941 | ||||||||
\(100\) | 20.1895 | 2.01895 | ||||||||
\(101\) | −4.24015 | −0.421910 | −0.210955 | − | 0.977496i | \(-0.567657\pi\) | ||||
−0.210955 | + | 0.977496i | \(0.567657\pi\) | |||||||
\(102\) | 12.7436 | 1.26180 | ||||||||
\(103\) | 6.12865 | 0.603874 | 0.301937 | − | 0.953328i | \(-0.402367\pi\) | ||||
0.301937 | + | 0.953328i | \(0.402367\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.30941 | 0.420555 | ||||||||
\(106\) | 4.91199 | 0.477095 | ||||||||
\(107\) | 3.75644 | 0.363149 | 0.181574 | − | 0.983377i | \(-0.441881\pi\) | ||||
0.181574 | + | 0.983377i | \(0.441881\pi\) | |||||||
\(108\) | 1.48770 | 0.143154 | ||||||||
\(109\) | 18.2430 | 1.74736 | 0.873681 | − | 0.486499i | \(-0.161726\pi\) | ||||
0.873681 | + | 0.486499i | \(0.161726\pi\) | |||||||
\(110\) | 31.3052 | 2.98483 | ||||||||
\(111\) | 10.7371 | 1.01912 | ||||||||
\(112\) | 4.76215 | 0.449981 | ||||||||
\(113\) | −10.1730 | −0.957000 | −0.478500 | − | 0.878088i | \(-0.658819\pi\) | ||||
−0.478500 | + | 0.878088i | \(0.658819\pi\) | |||||||
\(114\) | 10.9991 | 1.03016 | ||||||||
\(115\) | 5.51951 | 0.514697 | ||||||||
\(116\) | 2.72347 | 0.252868 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.24421 | 0.574826 | ||||||||
\(119\) | −6.82373 | −0.625530 | ||||||||
\(120\) | 4.12300 | 0.376377 | ||||||||
\(121\) | 4.13068 | 0.375517 | ||||||||
\(122\) | −19.5230 | −1.76753 | ||||||||
\(123\) | 6.71425 | 0.605404 | ||||||||
\(124\) | 2.03855 | 0.183067 | ||||||||
\(125\) | −36.9359 | −3.30365 | ||||||||
\(126\) | −1.86754 | −0.166373 | ||||||||
\(127\) | 0.713456 | 0.0633090 | 0.0316545 | − | 0.999499i | \(-0.489922\pi\) | ||||
0.0316545 | + | 0.999499i | \(0.489922\pi\) | |||||||
\(128\) | 7.40285 | 0.654326 | ||||||||
\(129\) | 9.00507 | 0.792852 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.47549 | −0.303655 | −0.151828 | − | 0.988407i | \(-0.548516\pi\) | ||||
−0.151828 | + | 0.988407i | \(0.548516\pi\) | |||||||
\(132\) | −5.78687 | −0.503683 | ||||||||
\(133\) | −5.88962 | −0.510695 | ||||||||
\(134\) | −13.9725 | −1.20704 | ||||||||
\(135\) | −4.30941 | −0.370895 | ||||||||
\(136\) | −6.52856 | −0.559819 | ||||||||
\(137\) | 6.49365 | 0.554790 | 0.277395 | − | 0.960756i | \(-0.410529\pi\) | ||||
0.277395 | + | 0.960756i | \(0.410529\pi\) | |||||||
\(138\) | −2.39195 | −0.203616 | ||||||||
\(139\) | 9.71185 | 0.823749 | 0.411874 | − | 0.911241i | \(-0.364874\pi\) | ||||
0.411874 | + | 0.911241i | \(0.364874\pi\) | |||||||
\(140\) | 6.41110 | 0.541836 | ||||||||
\(141\) | −9.83977 | −0.828658 | ||||||||
\(142\) | 8.93398 | 0.749723 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.76215 | −0.396846 | ||||||||
\(145\) | −7.88907 | −0.655151 | ||||||||
\(146\) | −13.3232 | −1.10264 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 15.9735 | 1.31301 | ||||||||
\(149\) | 7.63897 | 0.625808 | 0.312904 | − | 0.949785i | \(-0.398698\pi\) | ||||
0.312904 | + | 0.949785i | \(0.398698\pi\) | |||||||
\(150\) | 25.3444 | 2.06936 | ||||||||
\(151\) | 0.596432 | 0.0485369 | 0.0242685 | − | 0.999705i | \(-0.492274\pi\) | ||||
0.0242685 | + | 0.999705i | \(0.492274\pi\) | |||||||
\(152\) | −5.63486 | −0.457047 | ||||||||
\(153\) | 6.82373 | 0.551665 | ||||||||
\(154\) | 7.26438 | 0.585381 | ||||||||
\(155\) | −5.90507 | −0.474306 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8594 | −1.26572 | −0.632858 | − | 0.774268i | \(-0.718118\pi\) | ||||
−0.632858 | + | 0.774268i | \(0.718118\pi\) | |||||||
\(158\) | 7.04390 | 0.560383 | ||||||||
\(159\) | 2.63020 | 0.208588 | ||||||||
\(160\) | 30.0797 | 2.37801 | ||||||||
\(161\) | 1.28080 | 0.100942 | ||||||||
\(162\) | 1.86754 | 0.146728 | ||||||||
\(163\) | 14.9533 | 1.17123 | 0.585617 | − | 0.810588i | \(-0.300852\pi\) | ||||
0.585617 | + | 0.810588i | \(0.300852\pi\) | |||||||
\(164\) | 9.98878 | 0.779992 | ||||||||
\(165\) | 16.7628 | 1.30498 | ||||||||
\(166\) | 7.23098 | 0.561233 | ||||||||
\(167\) | −2.49975 | −0.193436 | −0.0967182 | − | 0.995312i | \(-0.530835\pi\) | ||||
−0.0967182 | + | 0.995312i | \(0.530835\pi\) | |||||||
\(168\) | 0.956744 | 0.0738144 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −54.9172 | −4.21196 | ||||||||
\(171\) | 5.88962 | 0.450390 | ||||||||
\(172\) | 13.3968 | 1.02150 | ||||||||
\(173\) | 2.05122 | 0.155952 | 0.0779758 | − | 0.996955i | \(-0.475154\pi\) | ||||
0.0779758 | + | 0.996955i | \(0.475154\pi\) | |||||||
\(174\) | 3.41883 | 0.259181 | ||||||||
\(175\) | −13.5710 | −1.02587 | ||||||||
\(176\) | 18.5239 | 1.39629 | ||||||||
\(177\) | 3.34355 | 0.251317 | ||||||||
\(178\) | −18.1433 | −1.35990 | ||||||||
\(179\) | 12.4319 | 0.929206 | 0.464603 | − | 0.885519i | \(-0.346197\pi\) | ||||
0.464603 | + | 0.885519i | \(0.346197\pi\) | |||||||
\(180\) | −6.41110 | −0.477855 | ||||||||
\(181\) | −11.3497 | −0.843617 | −0.421808 | − | 0.906685i | \(-0.638605\pi\) | ||||
−0.421808 | + | 0.906685i | \(0.638605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.4539 | −0.772773 | ||||||||
\(184\) | 1.22540 | 0.0903378 | ||||||||
\(185\) | −46.2703 | −3.40186 | ||||||||
\(186\) | 2.55904 | 0.187638 | ||||||||
\(187\) | −26.5430 | −1.94102 | ||||||||
\(188\) | −14.6386 | −1.06763 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −47.3996 | −3.43872 | ||||||||
\(191\) | −3.73903 | −0.270547 | −0.135273 | − | 0.990808i | \(-0.543191\pi\) | ||||
−0.135273 | + | 0.990808i | \(0.543191\pi\) | |||||||
\(192\) | −3.51113 | −0.253394 | ||||||||
\(193\) | 9.51514 | 0.684915 | 0.342457 | − | 0.939533i | \(-0.388741\pi\) | ||||
0.342457 | + | 0.939533i | \(0.388741\pi\) | |||||||
\(194\) | 3.06236 | 0.219865 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.48770 | 0.106264 | ||||||||
\(197\) | 15.0989 | 1.07575 | 0.537877 | − | 0.843023i | \(-0.319226\pi\) | ||||
0.537877 | + | 0.843023i | \(0.319226\pi\) | |||||||
\(198\) | −7.26438 | −0.516257 | ||||||||
\(199\) | 4.23261 | 0.300042 | 0.150021 | − | 0.988683i | \(-0.452066\pi\) | ||||
0.150021 | + | 0.988683i | \(0.452066\pi\) | |||||||
\(200\) | −12.9840 | −0.918106 | ||||||||
\(201\) | −7.48179 | −0.527725 | ||||||||
\(202\) | −7.91863 | −0.557153 | ||||||||
\(203\) | −1.83066 | −0.128487 | ||||||||
\(204\) | 10.1516 | 0.710757 | ||||||||
\(205\) | −28.9345 | −2.02087 | ||||||||
\(206\) | 11.4455 | 0.797444 | ||||||||
\(207\) | −1.28080 | −0.0890220 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.9095 | −1.58469 | ||||||||
\(210\) | 8.04798 | 0.555364 | ||||||||
\(211\) | 12.5911 | 0.866805 | 0.433403 | − | 0.901200i | \(-0.357313\pi\) | ||||
0.433403 | + | 0.901200i | \(0.357313\pi\) | |||||||
\(212\) | 3.91294 | 0.268741 | ||||||||
\(213\) | 4.78383 | 0.327783 | ||||||||
\(214\) | 7.01529 | 0.479556 | ||||||||
\(215\) | −38.8065 | −2.64658 | ||||||||
\(216\) | −0.956744 | −0.0650982 | ||||||||
\(217\) | −1.37027 | −0.0930202 | ||||||||
\(218\) | 34.0695 | 2.30748 | ||||||||
\(219\) | −7.13412 | −0.482079 | ||||||||
\(220\) | 24.9380 | 1.68132 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 20.0519 | 1.34579 | ||||||||
\(223\) | 17.9666 | 1.20313 | 0.601565 | − | 0.798824i | \(-0.294544\pi\) | ||||
0.601565 | + | 0.798824i | \(0.294544\pi\) | |||||||
\(224\) | 6.98001 | 0.466371 | ||||||||
\(225\) | 13.5710 | 0.904733 | ||||||||
\(226\) | −18.9986 | −1.26377 | ||||||||
\(227\) | 7.72887 | 0.512983 | 0.256491 | − | 0.966547i | \(-0.417433\pi\) | ||||
0.256491 | + | 0.966547i | \(0.417433\pi\) | |||||||
\(228\) | 8.76197 | 0.580276 | ||||||||
\(229\) | 21.7426 | 1.43679 | 0.718396 | − | 0.695635i | \(-0.244877\pi\) | ||||
0.718396 | + | 0.695635i | \(0.244877\pi\) | |||||||
\(230\) | 10.3079 | 0.679682 | ||||||||
\(231\) | 3.88982 | 0.255931 | ||||||||
\(232\) | −1.75148 | −0.114990 | ||||||||
\(233\) | −16.1360 | −1.05711 | −0.528553 | − | 0.848900i | \(-0.677265\pi\) | ||||
−0.528553 | + | 0.848900i | \(0.677265\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 42.4036 | 2.76610 | ||||||||
\(236\) | 4.97419 | 0.323792 | ||||||||
\(237\) | 3.77176 | 0.245002 | ||||||||
\(238\) | −12.7436 | −0.826043 | ||||||||
\(239\) | 19.3434 | 1.25122 | 0.625611 | − | 0.780135i | \(-0.284850\pi\) | ||||
0.625611 | + | 0.780135i | \(0.284850\pi\) | |||||||
\(240\) | 20.5221 | 1.32469 | ||||||||
\(241\) | −10.2012 | −0.657119 | −0.328560 | − | 0.944483i | \(-0.606563\pi\) | ||||
−0.328560 | + | 0.944483i | \(0.606563\pi\) | |||||||
\(242\) | 7.71421 | 0.495888 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.5522 | −0.995628 | ||||||||
\(245\) | −4.30941 | −0.275318 | ||||||||
\(246\) | 12.5391 | 0.799465 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.31100 | −0.0832487 | ||||||||
\(249\) | 3.87193 | 0.245374 | ||||||||
\(250\) | −68.9792 | −4.36263 | ||||||||
\(251\) | 18.1674 | 1.14671 | 0.573357 | − | 0.819306i | \(-0.305641\pi\) | ||||
0.573357 | + | 0.819306i | \(0.305641\pi\) | |||||||
\(252\) | −1.48770 | −0.0937161 | ||||||||
\(253\) | 4.98209 | 0.313222 | ||||||||
\(254\) | 1.33241 | 0.0836026 | ||||||||
\(255\) | −29.4062 | −1.84149 | ||||||||
\(256\) | 20.8474 | 1.30296 | ||||||||
\(257\) | −12.2798 | −0.765991 | −0.382995 | − | 0.923750i | \(-0.625107\pi\) | ||||
−0.382995 | + | 0.923750i | \(0.625107\pi\) | |||||||
\(258\) | 16.8173 | 1.04700 | ||||||||
\(259\) | −10.7371 | −0.667168 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.83066 | 0.113315 | ||||||||
\(262\) | −6.49061 | −0.400991 | ||||||||
\(263\) | 11.5962 | 0.715053 | 0.357527 | − | 0.933903i | \(-0.383620\pi\) | ||||
0.357527 | + | 0.933903i | \(0.383620\pi\) | |||||||
\(264\) | 3.72156 | 0.229046 | ||||||||
\(265\) | −11.3346 | −0.696278 | ||||||||
\(266\) | −10.9991 | −0.674397 | ||||||||
\(267\) | −9.71508 | −0.594554 | ||||||||
\(268\) | −11.1306 | −0.679912 | ||||||||
\(269\) | −6.89939 | −0.420664 | −0.210332 | − | 0.977630i | \(-0.567454\pi\) | ||||
−0.210332 | + | 0.977630i | \(0.567454\pi\) | |||||||
\(270\) | −8.04798 | −0.489785 | ||||||||
\(271\) | −4.69868 | −0.285424 | −0.142712 | − | 0.989764i | \(-0.545582\pi\) | ||||
−0.142712 | + | 0.989764i | \(0.545582\pi\) | |||||||
\(272\) | −32.4956 | −1.97034 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.1271 | 0.732627 | ||||||||
\(275\) | −52.7887 | −3.18328 | ||||||||
\(276\) | −1.90545 | −0.114695 | ||||||||
\(277\) | 12.9421 | 0.777618 | 0.388809 | − | 0.921318i | \(-0.372887\pi\) | ||||
0.388809 | + | 0.921318i | \(0.372887\pi\) | |||||||
\(278\) | 18.1373 | 1.08780 | ||||||||
\(279\) | 1.37027 | 0.0820361 | ||||||||
\(280\) | −4.12300 | −0.246396 | ||||||||
\(281\) | 30.0052 | 1.78996 | 0.894981 | − | 0.446104i | \(-0.147189\pi\) | ||||
0.894981 | + | 0.446104i | \(0.147189\pi\) | |||||||
\(282\) | −18.3761 | −1.09428 | ||||||||
\(283\) | 25.8570 | 1.53704 | 0.768521 | − | 0.639825i | \(-0.220993\pi\) | ||||
0.768521 | + | 0.639825i | \(0.220993\pi\) | |||||||
\(284\) | 7.11689 | 0.422310 | ||||||||
\(285\) | −25.3808 | −1.50343 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.71425 | −0.396330 | ||||||||
\(288\) | −6.98001 | −0.411301 | ||||||||
\(289\) | 29.5632 | 1.73901 | ||||||||
\(290\) | −14.7331 | −0.865159 | ||||||||
\(291\) | 1.63979 | 0.0961259 | ||||||||
\(292\) | −10.6134 | −0.621103 | ||||||||
\(293\) | −30.7151 | −1.79440 | −0.897199 | − | 0.441627i | \(-0.854401\pi\) | ||||
−0.897199 | + | 0.441627i | \(0.854401\pi\) | |||||||
\(294\) | 1.86754 | 0.108917 | ||||||||
\(295\) | −14.4087 | −0.838909 | ||||||||
\(296\) | −10.2726 | −0.597084 | ||||||||
\(297\) | −3.88982 | −0.225710 | ||||||||
\(298\) | 14.2661 | 0.826410 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 20.1895 | 1.16564 | ||||||||
\(301\) | −9.00507 | −0.519044 | ||||||||
\(302\) | 1.11386 | 0.0640954 | ||||||||
\(303\) | −4.24015 | −0.243590 | ||||||||
\(304\) | −28.0473 | −1.60862 | ||||||||
\(305\) | 45.0500 | 2.57956 | ||||||||
\(306\) | 12.7436 | 0.728501 | ||||||||
\(307\) | 13.1810 | 0.752277 | 0.376138 | − | 0.926564i | \(-0.377252\pi\) | ||||
0.376138 | + | 0.926564i | \(0.377252\pi\) | |||||||
\(308\) | 5.78687 | 0.329738 | ||||||||
\(309\) | 6.12865 | 0.348647 | ||||||||
\(310\) | −11.0279 | −0.626345 | ||||||||
\(311\) | −22.3404 | −1.26681 | −0.633404 | − | 0.773821i | \(-0.718343\pi\) | ||||
−0.633404 | + | 0.773821i | \(0.718343\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.5372 | 1.49997 | 0.749985 | − | 0.661455i | \(-0.230061\pi\) | ||||
0.749985 | + | 0.661455i | \(0.230061\pi\) | |||||||
\(314\) | −29.6180 | −1.67144 | ||||||||
\(315\) | 4.30941 | 0.242808 | ||||||||
\(316\) | 5.61124 | 0.315657 | ||||||||
\(317\) | −4.21944 | −0.236987 | −0.118494 | − | 0.992955i | \(-0.537807\pi\) | ||||
−0.118494 | + | 0.992955i | \(0.537807\pi\) | |||||||
\(318\) | 4.91199 | 0.275451 | ||||||||
\(319\) | −7.12094 | −0.398696 | ||||||||
\(320\) | 15.1309 | 0.845842 | ||||||||
\(321\) | 3.75644 | 0.209664 | ||||||||
\(322\) | 2.39195 | 0.133298 | ||||||||
\(323\) | 40.1891 | 2.23618 | ||||||||
\(324\) | 1.48770 | 0.0826499 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 27.9259 | 1.54667 | ||||||||
\(327\) | 18.2430 | 1.00884 | ||||||||
\(328\) | −6.42382 | −0.354696 | ||||||||
\(329\) | 9.83977 | 0.542484 | ||||||||
\(330\) | 31.3052 | 1.72329 | ||||||||
\(331\) | −16.1732 | −0.888960 | −0.444480 | − | 0.895789i | \(-0.646612\pi\) | ||||
−0.444480 | + | 0.895789i | \(0.646612\pi\) | |||||||
\(332\) | 5.76026 | 0.316135 | ||||||||
\(333\) | 10.7371 | 0.588387 | ||||||||
\(334\) | −4.66837 | −0.255442 | ||||||||
\(335\) | 32.2421 | 1.76157 | ||||||||
\(336\) | 4.76215 | 0.259797 | ||||||||
\(337\) | −10.2533 | −0.558534 | −0.279267 | − | 0.960214i | \(-0.590091\pi\) | ||||
−0.279267 | + | 0.960214i | \(0.590091\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.1730 | −0.552524 | ||||||||
\(340\) | −43.7476 | −2.37254 | ||||||||
\(341\) | −5.33011 | −0.288642 | ||||||||
\(342\) | 10.9991 | 0.594762 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −8.61555 | −0.464519 | ||||||||
\(345\) | 5.51951 | 0.297160 | ||||||||
\(346\) | 3.83073 | 0.205942 | ||||||||
\(347\) | 26.5008 | 1.42264 | 0.711318 | − | 0.702871i | \(-0.248099\pi\) | ||||
0.711318 | + | 0.702871i | \(0.248099\pi\) | |||||||
\(348\) | 2.72347 | 0.145993 | ||||||||
\(349\) | 17.4402 | 0.933555 | 0.466778 | − | 0.884375i | \(-0.345415\pi\) | ||||
0.466778 | + | 0.884375i | \(0.345415\pi\) | |||||||
\(350\) | −25.3444 | −1.35471 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 27.1510 | 1.44715 | ||||||||
\(353\) | 5.00425 | 0.266349 | 0.133175 | − | 0.991093i | \(-0.457483\pi\) | ||||
0.133175 | + | 0.991093i | \(0.457483\pi\) | |||||||
\(354\) | 6.24421 | 0.331876 | ||||||||
\(355\) | −20.6155 | −1.09416 | ||||||||
\(356\) | −14.4531 | −0.766013 | ||||||||
\(357\) | −6.82373 | −0.361150 | ||||||||
\(358\) | 23.2171 | 1.22706 | ||||||||
\(359\) | 4.95366 | 0.261444 | 0.130722 | − | 0.991419i | \(-0.458270\pi\) | ||||
0.130722 | + | 0.991419i | \(0.458270\pi\) | |||||||
\(360\) | 4.12300 | 0.217301 | ||||||||
\(361\) | 15.6876 | 0.825664 | ||||||||
\(362\) | −21.1960 | −1.11404 | ||||||||
\(363\) | 4.13068 | 0.216805 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.7438 | 1.60921 | ||||||||
\(366\) | −19.5230 | −1.02048 | ||||||||
\(367\) | 12.3603 | 0.645201 | 0.322601 | − | 0.946535i | \(-0.395443\pi\) | ||||
0.322601 | + | 0.946535i | \(0.395443\pi\) | |||||||
\(368\) | 6.09938 | 0.317952 | ||||||||
\(369\) | 6.71425 | 0.349530 | ||||||||
\(370\) | −86.4116 | −4.49233 | ||||||||
\(371\) | −2.63020 | −0.136553 | ||||||||
\(372\) | 2.03855 | 0.105694 | ||||||||
\(373\) | −16.5053 | −0.854613 | −0.427307 | − | 0.904107i | \(-0.640537\pi\) | ||||
−0.427307 | + | 0.904107i | \(0.640537\pi\) | |||||||
\(374\) | −49.5701 | −2.56321 | ||||||||
\(375\) | −36.9359 | −1.90736 | ||||||||
\(376\) | 9.41414 | 0.485497 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.86754 | −0.0960558 | ||||||||
\(379\) | −26.1674 | −1.34413 | −0.672066 | − | 0.740492i | \(-0.734593\pi\) | ||||
−0.672066 | + | 0.740492i | \(0.734593\pi\) | |||||||
\(380\) | −37.7589 | −1.93699 | ||||||||
\(381\) | 0.713456 | 0.0365515 | ||||||||
\(382\) | −6.98278 | −0.357270 | ||||||||
\(383\) | −27.8933 | −1.42528 | −0.712640 | − | 0.701530i | \(-0.752500\pi\) | ||||
−0.712640 | + | 0.701530i | \(0.752500\pi\) | |||||||
\(384\) | 7.40285 | 0.377775 | ||||||||
\(385\) | −16.7628 | −0.854312 | ||||||||
\(386\) | 17.7699 | 0.904463 | ||||||||
\(387\) | 9.00507 | 0.457753 | ||||||||
\(388\) | 2.43950 | 0.123847 | ||||||||
\(389\) | 0.413312 | 0.0209557 | 0.0104779 | − | 0.999945i | \(-0.496665\pi\) | ||||
0.0104779 | + | 0.999945i | \(0.496665\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.73986 | −0.441993 | ||||||||
\(392\) | −0.956744 | −0.0483229 | ||||||||
\(393\) | −3.47549 | −0.175315 | ||||||||
\(394\) | 28.1978 | 1.42059 | ||||||||
\(395\) | −16.2540 | −0.817830 | ||||||||
\(396\) | −5.78687 | −0.290801 | ||||||||
\(397\) | −10.3705 | −0.520482 | −0.260241 | − | 0.965544i | \(-0.583802\pi\) | ||||
−0.260241 | + | 0.965544i | \(0.583802\pi\) | |||||||
\(398\) | 7.90457 | 0.396220 | ||||||||
\(399\) | −5.88962 | −0.294850 | ||||||||
\(400\) | −64.6271 | −3.23136 | ||||||||
\(401\) | −16.6369 | −0.830806 | −0.415403 | − | 0.909638i | \(-0.636359\pi\) | ||||
−0.415403 | + | 0.909638i | \(0.636359\pi\) | |||||||
\(402\) | −13.9725 | −0.696886 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.30806 | −0.313837 | ||||||||
\(405\) | −4.30941 | −0.214136 | ||||||||
\(406\) | −3.41883 | −0.169674 | ||||||||
\(407\) | −41.7652 | −2.07022 | ||||||||
\(408\) | −6.52856 | −0.323212 | ||||||||
\(409\) | 7.05450 | 0.348822 | 0.174411 | − | 0.984673i | \(-0.444198\pi\) | ||||
0.174411 | + | 0.984673i | \(0.444198\pi\) | |||||||
\(410\) | −54.0362 | −2.66866 | ||||||||
\(411\) | 6.49365 | 0.320308 | ||||||||
\(412\) | 9.11757 | 0.449191 | ||||||||
\(413\) | −3.34355 | −0.164525 | ||||||||
\(414\) | −2.39195 | −0.117558 | ||||||||
\(415\) | −16.6857 | −0.819070 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.71185 | 0.475592 | ||||||||
\(418\) | −42.7844 | −2.09266 | ||||||||
\(419\) | 35.8189 | 1.74987 | 0.874934 | − | 0.484242i | \(-0.160904\pi\) | ||||
0.874934 | + | 0.484242i | \(0.160904\pi\) | |||||||
\(420\) | 6.41110 | 0.312829 | ||||||||
\(421\) | −20.5380 | −1.00096 | −0.500479 | − | 0.865748i | \(-0.666843\pi\) | ||||
−0.500479 | + | 0.865748i | \(0.666843\pi\) | |||||||
\(422\) | 23.5143 | 1.14466 | ||||||||
\(423\) | −9.83977 | −0.478426 | ||||||||
\(424\) | −2.51642 | −0.122208 | ||||||||
\(425\) | 92.6048 | 4.49199 | ||||||||
\(426\) | 8.93398 | 0.432853 | ||||||||
\(427\) | 10.4539 | 0.505899 | ||||||||
\(428\) | 5.58845 | 0.270128 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −72.4727 | −3.49494 | ||||||||
\(431\) | 13.1827 | 0.634987 | 0.317493 | − | 0.948261i | \(-0.397159\pi\) | ||||
0.317493 | + | 0.948261i | \(0.397159\pi\) | |||||||
\(432\) | −4.76215 | −0.229119 | ||||||||
\(433\) | 5.34891 | 0.257052 | 0.128526 | − | 0.991706i | \(-0.458975\pi\) | ||||
0.128526 | + | 0.991706i | \(0.458975\pi\) | |||||||
\(434\) | −2.55904 | −0.122838 | ||||||||
\(435\) | −7.88907 | −0.378252 | ||||||||
\(436\) | 27.1401 | 1.29977 | ||||||||
\(437\) | −7.54345 | −0.360852 | ||||||||
\(438\) | −13.3232 | −0.636609 | ||||||||
\(439\) | −32.3209 | −1.54259 | −0.771296 | − | 0.636476i | \(-0.780391\pi\) | ||||
−0.771296 | + | 0.636476i | \(0.780391\pi\) | |||||||
\(440\) | −16.0377 | −0.764569 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.3799 | 0.920769 | 0.460385 | − | 0.887720i | \(-0.347712\pi\) | ||||
0.460385 | + | 0.887720i | \(0.347712\pi\) | |||||||
\(444\) | 15.9735 | 0.758068 | ||||||||
\(445\) | 41.8663 | 1.98465 | ||||||||
\(446\) | 33.5533 | 1.58879 | ||||||||
\(447\) | 7.63897 | 0.361311 | ||||||||
\(448\) | 3.51113 | 0.165885 | ||||||||
\(449\) | −36.3017 | −1.71318 | −0.856592 | − | 0.515995i | \(-0.827422\pi\) | ||||
−0.856592 | + | 0.515995i | \(0.827422\pi\) | |||||||
\(450\) | 25.3444 | 1.19474 | ||||||||
\(451\) | −26.1172 | −1.22981 | ||||||||
\(452\) | −15.1344 | −0.711863 | ||||||||
\(453\) | 0.596432 | 0.0280228 | ||||||||
\(454\) | 14.4339 | 0.677419 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.63486 | −0.263876 | ||||||||
\(457\) | 2.08528 | 0.0975454 | 0.0487727 | − | 0.998810i | \(-0.484469\pi\) | ||||
0.0487727 | + | 0.998810i | \(0.484469\pi\) | |||||||
\(458\) | 40.6051 | 1.89735 | ||||||||
\(459\) | 6.82373 | 0.318504 | ||||||||
\(460\) | 8.21136 | 0.382857 | ||||||||
\(461\) | 28.1146 | 1.30943 | 0.654714 | − | 0.755877i | \(-0.272789\pi\) | ||||
0.654714 | + | 0.755877i | \(0.272789\pi\) | |||||||
\(462\) | 7.26438 | 0.337970 | ||||||||
\(463\) | 10.3933 | 0.483017 | 0.241509 | − | 0.970399i | \(-0.422358\pi\) | ||||
0.241509 | + | 0.970399i | \(0.422358\pi\) | |||||||
\(464\) | −8.71789 | −0.404718 | ||||||||
\(465\) | −5.90507 | −0.273841 | ||||||||
\(466\) | −30.1346 | −1.39596 | ||||||||
\(467\) | 4.78281 | 0.221322 | 0.110661 | − | 0.993858i | \(-0.464703\pi\) | ||||
0.110661 | + | 0.993858i | \(0.464703\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.48179 | 0.345477 | ||||||||
\(470\) | 79.1903 | 3.65277 | ||||||||
\(471\) | −15.8594 | −0.730761 | ||||||||
\(472\) | −3.19892 | −0.147242 | ||||||||
\(473\) | −35.0281 | −1.61059 | ||||||||
\(474\) | 7.04390 | 0.323537 | ||||||||
\(475\) | 79.9280 | 3.66735 | ||||||||
\(476\) | −10.1516 | −0.465300 | ||||||||
\(477\) | 2.63020 | 0.120428 | ||||||||
\(478\) | 36.1246 | 1.65230 | ||||||||
\(479\) | −8.07411 | −0.368916 | −0.184458 | − | 0.982840i | \(-0.559053\pi\) | ||||
−0.184458 | + | 0.982840i | \(0.559053\pi\) | |||||||
\(480\) | 30.0797 | 1.37294 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −19.0512 | −0.867758 | ||||||||
\(483\) | 1.28080 | 0.0582786 | ||||||||
\(484\) | 6.14521 | 0.279328 | ||||||||
\(485\) | −7.06650 | −0.320873 | ||||||||
\(486\) | 1.86754 | 0.0847132 | ||||||||
\(487\) | −11.1535 | −0.505412 | −0.252706 | − | 0.967543i | \(-0.581321\pi\) | ||||
−0.252706 | + | 0.967543i | \(0.581321\pi\) | |||||||
\(488\) | 10.0017 | 0.452755 | ||||||||
\(489\) | 14.9533 | 0.676213 | ||||||||
\(490\) | −8.04798 | −0.363571 | ||||||||
\(491\) | −5.11302 | −0.230747 | −0.115374 | − | 0.993322i | \(-0.536807\pi\) | ||||
−0.115374 | + | 0.993322i | \(0.536807\pi\) | |||||||
\(492\) | 9.98878 | 0.450329 | ||||||||
\(493\) | 12.4919 | 0.562608 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.7628 | 0.753432 | ||||||||
\(496\) | −6.52545 | −0.293001 | ||||||||
\(497\) | −4.78383 | −0.214584 | ||||||||
\(498\) | 7.23098 | 0.324028 | ||||||||
\(499\) | −38.6257 | −1.72912 | −0.864561 | − | 0.502528i | \(-0.832403\pi\) | ||||
−0.864561 | + | 0.502528i | \(0.832403\pi\) | |||||||
\(500\) | −54.9495 | −2.45742 | ||||||||
\(501\) | −2.49975 | −0.111681 | ||||||||
\(502\) | 33.9283 | 1.51429 | ||||||||
\(503\) | −43.5039 | −1.93974 | −0.969871 | − | 0.243620i | \(-0.921665\pi\) | ||||
−0.969871 | + | 0.243620i | \(0.921665\pi\) | |||||||
\(504\) | 0.956744 | 0.0426168 | ||||||||
\(505\) | 18.2725 | 0.813117 | ||||||||
\(506\) | 9.30425 | 0.413624 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.06141 | 0.0470923 | ||||||||
\(509\) | −19.3651 | −0.858344 | −0.429172 | − | 0.903223i | \(-0.641195\pi\) | ||||
−0.429172 | + | 0.903223i | \(0.641195\pi\) | |||||||
\(510\) | −54.9172 | −2.43178 | ||||||||
\(511\) | 7.13412 | 0.315595 | ||||||||
\(512\) | 24.1275 | 1.06630 | ||||||||
\(513\) | 5.88962 | 0.260033 | ||||||||
\(514\) | −22.9329 | −1.01153 | ||||||||
\(515\) | −26.4108 | −1.16380 | ||||||||
\(516\) | 13.3968 | 0.589762 | ||||||||
\(517\) | 38.2749 | 1.68333 | ||||||||
\(518\) | −20.0519 | −0.881028 | ||||||||
\(519\) | 2.05122 | 0.0900386 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.69912 | 0.205872 | 0.102936 | − | 0.994688i | \(-0.467176\pi\) | ||||
0.102936 | + | 0.994688i | \(0.467176\pi\) | |||||||
\(522\) | 3.41883 | 0.149638 | ||||||||
\(523\) | −11.7149 | −0.512256 | −0.256128 | − | 0.966643i | \(-0.582447\pi\) | ||||
−0.256128 | + | 0.966643i | \(0.582447\pi\) | |||||||
\(524\) | −5.17048 | −0.225874 | ||||||||
\(525\) | −13.5710 | −0.592287 | ||||||||
\(526\) | 21.6564 | 0.944263 | ||||||||
\(527\) | 9.35037 | 0.407309 | ||||||||
\(528\) | 18.5239 | 0.806149 | ||||||||
\(529\) | −21.3595 | −0.928676 | ||||||||
\(530\) | −21.1678 | −0.919469 | ||||||||
\(531\) | 3.34355 | 0.145098 | ||||||||
\(532\) | −8.76197 | −0.379880 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −18.1433 | −0.785137 | ||||||||
\(535\) | −16.1880 | −0.699870 | ||||||||
\(536\) | 7.15816 | 0.309185 | ||||||||
\(537\) | 12.4319 | 0.536477 | ||||||||
\(538\) | −12.8849 | −0.555507 | ||||||||
\(539\) | −3.88982 | −0.167546 | ||||||||
\(540\) | −6.41110 | −0.275890 | ||||||||
\(541\) | −12.0409 | −0.517677 | −0.258838 | − | 0.965921i | \(-0.583340\pi\) | ||||
−0.258838 | + | 0.965921i | \(0.583340\pi\) | |||||||
\(542\) | −8.77495 | −0.376917 | ||||||||
\(543\) | −11.3497 | −0.487062 | ||||||||
\(544\) | −47.6297 | −2.04210 | ||||||||
\(545\) | −78.6165 | −3.36756 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.9904 | −1.79538 | −0.897690 | − | 0.440628i | \(-0.854756\pi\) | ||||
−0.897690 | + | 0.440628i | \(0.854756\pi\) | |||||||
\(548\) | 9.66059 | 0.412680 | ||||||||
\(549\) | −10.4539 | −0.446161 | ||||||||
\(550\) | −98.5849 | −4.20368 | ||||||||
\(551\) | 10.7819 | 0.459324 | ||||||||
\(552\) | 1.22540 | 0.0521566 | ||||||||
\(553\) | −3.77176 | −0.160392 | ||||||||
\(554\) | 24.1699 | 1.02688 | ||||||||
\(555\) | −46.2703 | −1.96407 | ||||||||
\(556\) | 14.4483 | 0.612744 | ||||||||
\(557\) | −11.1177 | −0.471072 | −0.235536 | − | 0.971866i | \(-0.575685\pi\) | ||||
−0.235536 | + | 0.971866i | \(0.575685\pi\) | |||||||
\(558\) | 2.55904 | 0.108333 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −20.5221 | −0.867215 | ||||||||
\(561\) | −26.5430 | −1.12065 | ||||||||
\(562\) | 56.0359 | 2.36373 | ||||||||
\(563\) | 4.88687 | 0.205957 | 0.102979 | − | 0.994684i | \(-0.467163\pi\) | ||||
0.102979 | + | 0.994684i | \(0.467163\pi\) | |||||||
\(564\) | −14.6386 | −0.616396 | ||||||||
\(565\) | 43.8398 | 1.84436 | ||||||||
\(566\) | 48.2890 | 2.02974 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −4.57690 | −0.192043 | ||||||||
\(569\) | 23.5596 | 0.987669 | 0.493835 | − | 0.869556i | \(-0.335595\pi\) | ||||
0.493835 | + | 0.869556i | \(0.335595\pi\) | |||||||
\(570\) | −47.3996 | −1.98535 | ||||||||
\(571\) | 17.6931 | 0.740432 | 0.370216 | − | 0.928946i | \(-0.379284\pi\) | ||||
0.370216 | + | 0.928946i | \(0.379284\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.73903 | −0.156200 | ||||||||
\(574\) | −12.5391 | −0.523373 | ||||||||
\(575\) | −17.3818 | −0.724871 | ||||||||
\(576\) | −3.51113 | −0.146297 | ||||||||
\(577\) | 43.4059 | 1.80701 | 0.903507 | − | 0.428574i | \(-0.140984\pi\) | ||||
0.903507 | + | 0.428574i | \(0.140984\pi\) | |||||||
\(578\) | 55.2104 | 2.29645 | ||||||||
\(579\) | 9.51514 | 0.395436 | ||||||||
\(580\) | −11.7365 | −0.487334 | ||||||||
\(581\) | −3.87193 | −0.160635 | ||||||||
\(582\) | 3.06236 | 0.126939 | ||||||||
\(583\) | −10.2310 | −0.423724 | ||||||||
\(584\) | 6.82553 | 0.282442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −57.3617 | −2.36959 | ||||||||
\(587\) | 20.6405 | 0.851923 | 0.425962 | − | 0.904741i | \(-0.359936\pi\) | ||||
0.425962 | + | 0.904741i | \(0.359936\pi\) | |||||||
\(588\) | 1.48770 | 0.0613516 | ||||||||
\(589\) | 8.07039 | 0.332535 | ||||||||
\(590\) | −26.9088 | −1.10782 | ||||||||
\(591\) | 15.0989 | 0.621087 | ||||||||
\(592\) | −51.1315 | −2.10149 | ||||||||
\(593\) | 36.5043 | 1.49905 | 0.749526 | − | 0.661974i | \(-0.230281\pi\) | ||||
0.749526 | + | 0.661974i | \(0.230281\pi\) | |||||||
\(594\) | −7.26438 | −0.298061 | ||||||||
\(595\) | 29.4062 | 1.20554 | ||||||||
\(596\) | 11.3645 | 0.465507 | ||||||||
\(597\) | 4.23261 | 0.173229 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.7221 | 0.764962 | 0.382481 | − | 0.923963i | \(-0.375070\pi\) | ||||
0.382481 | + | 0.923963i | \(0.375070\pi\) | |||||||
\(600\) | −12.9840 | −0.530069 | ||||||||
\(601\) | −38.4712 | −1.56927 | −0.784636 | − | 0.619956i | \(-0.787150\pi\) | ||||
−0.784636 | + | 0.619956i | \(0.787150\pi\) | |||||||
\(602\) | −16.8173 | −0.685422 | ||||||||
\(603\) | −7.48179 | −0.304682 | ||||||||
\(604\) | 0.887310 | 0.0361041 | ||||||||
\(605\) | −17.8008 | −0.723705 | ||||||||
\(606\) | −7.91863 | −0.321673 | ||||||||
\(607\) | 34.0718 | 1.38293 | 0.691466 | − | 0.722409i | \(-0.256965\pi\) | ||||
0.691466 | + | 0.722409i | \(0.256965\pi\) | |||||||
\(608\) | −41.1096 | −1.66721 | ||||||||
\(609\) | −1.83066 | −0.0741822 | ||||||||
\(610\) | 84.1327 | 3.40643 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 10.1516 | 0.410356 | ||||||||
\(613\) | −14.9448 | −0.603616 | −0.301808 | − | 0.953369i | \(-0.597590\pi\) | ||||
−0.301808 | + | 0.953369i | \(0.597590\pi\) | |||||||
\(614\) | 24.6159 | 0.993418 | ||||||||
\(615\) | −28.9345 | −1.16675 | ||||||||
\(616\) | −3.72156 | −0.149946 | ||||||||
\(617\) | −30.6354 | −1.23334 | −0.616668 | − | 0.787223i | \(-0.711518\pi\) | ||||
−0.616668 | + | 0.787223i | \(0.711518\pi\) | |||||||
\(618\) | 11.4455 | 0.460405 | ||||||||
\(619\) | −44.8329 | −1.80198 | −0.900992 | − | 0.433835i | \(-0.857160\pi\) | ||||
−0.900992 | + | 0.433835i | \(0.857160\pi\) | |||||||
\(620\) | −8.78495 | −0.352812 | ||||||||
\(621\) | −1.28080 | −0.0513969 | ||||||||
\(622\) | −41.7215 | −1.67288 | ||||||||
\(623\) | 9.71508 | 0.389227 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 91.3170 | 3.65268 | ||||||||
\(626\) | 49.5592 | 1.98078 | ||||||||
\(627\) | −22.9095 | −0.914919 | ||||||||
\(628\) | −23.5939 | −0.941500 | ||||||||
\(629\) | 73.2667 | 2.92133 | ||||||||
\(630\) | 8.04798 | 0.320639 | ||||||||
\(631\) | 39.4759 | 1.57151 | 0.785756 | − | 0.618536i | \(-0.212274\pi\) | ||||
0.785756 | + | 0.618536i | \(0.212274\pi\) | |||||||
\(632\) | −3.60861 | −0.143543 | ||||||||
\(633\) | 12.5911 | 0.500450 | ||||||||
\(634\) | −7.87997 | −0.312953 | ||||||||
\(635\) | −3.07457 | −0.122011 | ||||||||
\(636\) | 3.91294 | 0.155158 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.2986 | −0.526498 | ||||||||
\(639\) | 4.78383 | 0.189245 | ||||||||
\(640\) | −31.9019 | −1.26103 | ||||||||
\(641\) | −26.1610 | −1.03330 | −0.516649 | − | 0.856197i | \(-0.672821\pi\) | ||||
−0.516649 | + | 0.856197i | \(0.672821\pi\) | |||||||
\(642\) | 7.01529 | 0.276872 | ||||||||
\(643\) | −12.8679 | −0.507460 | −0.253730 | − | 0.967275i | \(-0.581657\pi\) | ||||
−0.253730 | + | 0.967275i | \(0.581657\pi\) | |||||||
\(644\) | 1.90545 | 0.0750852 | ||||||||
\(645\) | −38.8065 | −1.52801 | ||||||||
\(646\) | 75.0547 | 2.95299 | ||||||||
\(647\) | 9.13149 | 0.358996 | 0.179498 | − | 0.983758i | \(-0.442553\pi\) | ||||
0.179498 | + | 0.983758i | \(0.442553\pi\) | |||||||
\(648\) | −0.956744 | −0.0375845 | ||||||||
\(649\) | −13.0058 | −0.510523 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.37027 | −0.0537053 | ||||||||
\(652\) | 22.2460 | 0.871222 | ||||||||
\(653\) | 21.3744 | 0.836445 | 0.418222 | − | 0.908345i | \(-0.362653\pi\) | ||||
0.418222 | + | 0.908345i | \(0.362653\pi\) | |||||||
\(654\) | 34.0695 | 1.33222 | ||||||||
\(655\) | 14.9773 | 0.585212 | ||||||||
\(656\) | −31.9743 | −1.24839 | ||||||||
\(657\) | −7.13412 | −0.278329 | ||||||||
\(658\) | 18.3761 | 0.716376 | ||||||||
\(659\) | −31.1995 | −1.21536 | −0.607679 | − | 0.794183i | \(-0.707899\pi\) | ||||
−0.607679 | + | 0.794183i | \(0.707899\pi\) | |||||||
\(660\) | 24.9380 | 0.970710 | ||||||||
\(661\) | 13.1927 | 0.513135 | 0.256568 | − | 0.966526i | \(-0.417408\pi\) | ||||
0.256568 | + | 0.966526i | \(0.417408\pi\) | |||||||
\(662\) | −30.2041 | −1.17392 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.70445 | −0.143760 | ||||||||
\(665\) | 25.3808 | 0.984224 | ||||||||
\(666\) | 20.0519 | 0.776993 | ||||||||
\(667\) | −2.34472 | −0.0907879 | ||||||||
\(668\) | −3.71887 | −0.143887 | ||||||||
\(669\) | 17.9666 | 0.694628 | ||||||||
\(670\) | 60.2133 | 2.32624 | ||||||||
\(671\) | 40.6637 | 1.56980 | ||||||||
\(672\) | 6.98001 | 0.269260 | ||||||||
\(673\) | 24.0900 | 0.928600 | 0.464300 | − | 0.885678i | \(-0.346306\pi\) | ||||
0.464300 | + | 0.885678i | \(0.346306\pi\) | |||||||
\(674\) | −19.1485 | −0.737571 | ||||||||
\(675\) | 13.5710 | 0.522348 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.3251 | −1.12705 | −0.563527 | − | 0.826097i | \(-0.690556\pi\) | ||||
−0.563527 | + | 0.826097i | \(0.690556\pi\) | |||||||
\(678\) | −18.9986 | −0.729635 | ||||||||
\(679\) | −1.63979 | −0.0629292 | ||||||||
\(680\) | 28.1342 | 1.07890 | ||||||||
\(681\) | 7.72887 | 0.296171 | ||||||||
\(682\) | −9.95419 | −0.381166 | ||||||||
\(683\) | 48.4183 | 1.85267 | 0.926337 | − | 0.376697i | \(-0.122940\pi\) | ||||
0.926337 | + | 0.376697i | \(0.122940\pi\) | |||||||
\(684\) | 8.76197 | 0.335022 | ||||||||
\(685\) | −27.9838 | −1.06921 | ||||||||
\(686\) | −1.86754 | −0.0713029 | ||||||||
\(687\) | 21.7426 | 0.829532 | ||||||||
\(688\) | −42.8835 | −1.63492 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 10.3079 | 0.392415 | ||||||||
\(691\) | 20.4556 | 0.778168 | 0.389084 | − | 0.921202i | \(-0.372792\pi\) | ||||
0.389084 | + | 0.921202i | \(0.372792\pi\) | |||||||
\(692\) | 3.05160 | 0.116004 | ||||||||
\(693\) | 3.88982 | 0.147762 | ||||||||
\(694\) | 49.4912 | 1.87866 | ||||||||
\(695\) | −41.8523 | −1.58755 | ||||||||
\(696\) | −1.75148 | −0.0663895 | ||||||||
\(697\) | 45.8162 | 1.73541 | ||||||||
\(698\) | 32.5703 | 1.23280 | ||||||||
\(699\) | −16.1360 | −0.610320 | ||||||||
\(700\) | −20.1895 | −0.763093 | ||||||||
\(701\) | 22.4924 | 0.849527 | 0.424763 | − | 0.905304i | \(-0.360357\pi\) | ||||
0.424763 | + | 0.905304i | \(0.360357\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 63.2371 | 2.38503 | ||||||||
\(704\) | 13.6576 | 0.514742 | ||||||||
\(705\) | 42.4036 | 1.59701 | ||||||||
\(706\) | 9.34563 | 0.351727 | ||||||||
\(707\) | 4.24015 | 0.159467 | ||||||||
\(708\) | 4.97419 | 0.186942 | ||||||||
\(709\) | 9.36836 | 0.351836 | 0.175918 | − | 0.984405i | \(-0.443711\pi\) | ||||
0.175918 | + | 0.984405i | \(0.443711\pi\) | |||||||
\(710\) | −38.5002 | −1.44489 | ||||||||
\(711\) | 3.77176 | 0.141452 | ||||||||
\(712\) | 9.29485 | 0.348339 | ||||||||
\(713\) | −1.75505 | −0.0657272 | ||||||||
\(714\) | −12.7436 | −0.476916 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.4950 | 0.691189 | ||||||||
\(717\) | 19.3434 | 0.722394 | ||||||||
\(718\) | 9.25115 | 0.345250 | ||||||||
\(719\) | −26.0078 | −0.969929 | −0.484965 | − | 0.874534i | \(-0.661167\pi\) | ||||
−0.484965 | + | 0.874534i | \(0.661167\pi\) | |||||||
\(720\) | 20.5221 | 0.764812 | ||||||||
\(721\) | −6.12865 | −0.228243 | ||||||||
\(722\) | 29.2972 | 1.09033 | ||||||||
\(723\) | −10.2012 | −0.379388 | ||||||||
\(724\) | −16.8849 | −0.627523 | ||||||||
\(725\) | 24.8439 | 0.922680 | ||||||||
\(726\) | 7.71421 | 0.286301 | ||||||||
\(727\) | −45.4636 | −1.68615 | −0.843076 | − | 0.537795i | \(-0.819258\pi\) | ||||
−0.843076 | + | 0.537795i | \(0.819258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 57.4153 | 2.12503 | ||||||||
\(731\) | 61.4481 | 2.27274 | ||||||||
\(732\) | −15.5522 | −0.574826 | ||||||||
\(733\) | −37.7796 | −1.39542 | −0.697711 | − | 0.716380i | \(-0.745798\pi\) | ||||
−0.697711 | + | 0.716380i | \(0.745798\pi\) | |||||||
\(734\) | 23.0833 | 0.852020 | ||||||||
\(735\) | −4.30941 | −0.158955 | ||||||||
\(736\) | 8.94002 | 0.329534 | ||||||||
\(737\) | 29.1028 | 1.07202 | ||||||||
\(738\) | 12.5391 | 0.461571 | ||||||||
\(739\) | 1.34453 | 0.0494595 | 0.0247297 | − | 0.999694i | \(-0.492127\pi\) | ||||
0.0247297 | + | 0.999694i | \(0.492127\pi\) | |||||||
\(740\) | −68.8363 | −2.53047 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.91199 | −0.180325 | ||||||||
\(743\) | 13.2274 | 0.485265 | 0.242633 | − | 0.970118i | \(-0.421989\pi\) | ||||
0.242633 | + | 0.970118i | \(0.421989\pi\) | |||||||
\(744\) | −1.31100 | −0.0480636 | ||||||||
\(745\) | −32.9194 | −1.20607 | ||||||||
\(746\) | −30.8243 | −1.12856 | ||||||||
\(747\) | 3.87193 | 0.141667 | ||||||||
\(748\) | −39.4880 | −1.44383 | ||||||||
\(749\) | −3.75644 | −0.137257 | ||||||||
\(750\) | −68.9792 | −2.51877 | ||||||||
\(751\) | −3.03878 | −0.110887 | −0.0554433 | − | 0.998462i | \(-0.517657\pi\) | ||||
−0.0554433 | + | 0.998462i | \(0.517657\pi\) | |||||||
\(752\) | 46.8585 | 1.70875 | ||||||||
\(753\) | 18.1674 | 0.662056 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.57027 | −0.0935417 | ||||||||
\(756\) | −1.48770 | −0.0541070 | ||||||||
\(757\) | 28.1535 | 1.02326 | 0.511628 | − | 0.859207i | \(-0.329043\pi\) | ||||
0.511628 | + | 0.859207i | \(0.329043\pi\) | |||||||
\(758\) | −48.8687 | −1.77499 | ||||||||
\(759\) | 4.98209 | 0.180839 | ||||||||
\(760\) | 24.2829 | 0.880834 | ||||||||
\(761\) | −21.5087 | −0.779691 | −0.389845 | − | 0.920880i | \(-0.627472\pi\) | ||||
−0.389845 | + | 0.920880i | \(0.627472\pi\) | |||||||
\(762\) | 1.33241 | 0.0482680 | ||||||||
\(763\) | −18.2430 | −0.660441 | ||||||||
\(764\) | −5.56255 | −0.201246 | ||||||||
\(765\) | −29.4062 | −1.06318 | ||||||||
\(766\) | −52.0917 | −1.88215 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 20.8474 | 0.752264 | ||||||||
\(769\) | 28.7707 | 1.03750 | 0.518749 | − | 0.854927i | \(-0.326398\pi\) | ||||
0.518749 | + | 0.854927i | \(0.326398\pi\) | |||||||
\(770\) | −31.3052 | −1.12816 | ||||||||
\(771\) | −12.2798 | −0.442245 | ||||||||
\(772\) | 14.1556 | 0.509473 | ||||||||
\(773\) | −28.8915 | −1.03916 | −0.519578 | − | 0.854423i | \(-0.673911\pi\) | ||||
−0.519578 | + | 0.854423i | \(0.673911\pi\) | |||||||
\(774\) | 16.8173 | 0.604486 | ||||||||
\(775\) | 18.5960 | 0.667987 | ||||||||
\(776\) | −1.56886 | −0.0563186 | ||||||||
\(777\) | −10.7371 | −0.385190 | ||||||||
\(778\) | 0.771876 | 0.0276731 | ||||||||
\(779\) | 39.5444 | 1.41682 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.6082 | −0.665855 | ||||||||
\(782\) | −16.3220 | −0.583674 | ||||||||
\(783\) | 1.83066 | 0.0654225 | ||||||||
\(784\) | −4.76215 | −0.170077 | ||||||||
\(785\) | 68.3445 | 2.43932 | ||||||||
\(786\) | −6.49061 | −0.231512 | ||||||||
\(787\) | 46.3190 | 1.65109 | 0.825547 | − | 0.564333i | \(-0.190866\pi\) | ||||
0.825547 | + | 0.564333i | \(0.190866\pi\) | |||||||
\(788\) | 22.4626 | 0.800198 | ||||||||
\(789\) | 11.5962 | 0.412836 | ||||||||
\(790\) | −30.3551 | −1.07998 | ||||||||
\(791\) | 10.1730 | 0.361712 | ||||||||
\(792\) | 3.72156 | 0.132240 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −19.3674 | −0.687322 | ||||||||
\(795\) | −11.3346 | −0.401996 | ||||||||
\(796\) | 6.29685 | 0.223186 | ||||||||
\(797\) | −7.09265 | −0.251235 | −0.125617 | − | 0.992079i | \(-0.540091\pi\) | ||||
−0.125617 | + | 0.992079i | \(0.540091\pi\) | |||||||
\(798\) | −10.9991 | −0.389363 | ||||||||
\(799\) | −67.1439 | −2.37538 | ||||||||
\(800\) | −94.7257 | −3.34906 | ||||||||
\(801\) | −9.71508 | −0.343266 | ||||||||
\(802\) | −31.0700 | −1.09712 | ||||||||
\(803\) | 27.7504 | 0.979291 | ||||||||
\(804\) | −11.1306 | −0.392547 | ||||||||
\(805\) | −5.51951 | −0.194537 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.89939 | −0.242870 | ||||||||
\(808\) | 4.05674 | 0.142715 | ||||||||
\(809\) | 26.8422 | 0.943721 | 0.471861 | − | 0.881673i | \(-0.343583\pi\) | ||||
0.471861 | + | 0.881673i | \(0.343583\pi\) | |||||||
\(810\) | −8.04798 | −0.282777 | ||||||||
\(811\) | 6.59151 | 0.231459 | 0.115730 | − | 0.993281i | \(-0.463079\pi\) | ||||
0.115730 | + | 0.993281i | \(0.463079\pi\) | |||||||
\(812\) | −2.72347 | −0.0955751 | ||||||||
\(813\) | −4.69868 | −0.164790 | ||||||||
\(814\) | −77.9981 | −2.73383 | ||||||||
\(815\) | −64.4400 | −2.25723 | ||||||||
\(816\) | −32.4956 | −1.13757 | ||||||||
\(817\) | 53.0364 | 1.85551 | ||||||||
\(818\) | 13.1745 | 0.460637 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −43.0457 | −1.50322 | ||||||||
\(821\) | −16.9329 | −0.590961 | −0.295481 | − | 0.955349i | \(-0.595480\pi\) | ||||
−0.295481 | + | 0.955349i | \(0.595480\pi\) | |||||||
\(822\) | 12.1271 | 0.422983 | ||||||||
\(823\) | −15.7875 | −0.550318 | −0.275159 | − | 0.961399i | \(-0.588730\pi\) | ||||
−0.275159 | + | 0.961399i | \(0.588730\pi\) | |||||||
\(824\) | −5.86355 | −0.204266 | ||||||||
\(825\) | −52.7887 | −1.83787 | ||||||||
\(826\) | −6.24421 | −0.217264 | ||||||||
\(827\) | −20.9917 | −0.729954 | −0.364977 | − | 0.931016i | \(-0.618923\pi\) | ||||
−0.364977 | + | 0.931016i | \(0.618923\pi\) | |||||||
\(828\) | −1.90545 | −0.0662189 | ||||||||
\(829\) | 27.4341 | 0.952827 | 0.476414 | − | 0.879221i | \(-0.341937\pi\) | ||||
0.476414 | + | 0.879221i | \(0.341937\pi\) | |||||||
\(830\) | −31.1612 | −1.08162 | ||||||||
\(831\) | 12.9421 | 0.448958 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.82373 | 0.236428 | ||||||||
\(834\) | 18.1373 | 0.628042 | ||||||||
\(835\) | 10.7724 | 0.372796 | ||||||||
\(836\) | −34.0825 | −1.17877 | ||||||||
\(837\) | 1.37027 | 0.0473636 | ||||||||
\(838\) | 66.8932 | 2.31079 | ||||||||
\(839\) | −44.6389 | −1.54111 | −0.770553 | − | 0.637376i | \(-0.780020\pi\) | ||||
−0.770553 | + | 0.637376i | \(0.780020\pi\) | |||||||
\(840\) | −4.12300 | −0.142257 | ||||||||
\(841\) | −25.6487 | −0.884437 | ||||||||
\(842\) | −38.3554 | −1.32181 | ||||||||
\(843\) | 30.0052 | 1.03344 | ||||||||
\(844\) | 18.7317 | 0.644772 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.3761 | −0.631785 | ||||||||
\(847\) | −4.13068 | −0.141932 | ||||||||
\(848\) | −12.5254 | −0.430124 | ||||||||
\(849\) | 25.8570 | 0.887411 | ||||||||
\(850\) | 172.943 | 5.93189 | ||||||||
\(851\) | −13.7521 | −0.471415 | ||||||||
\(852\) | 7.11689 | 0.243821 | ||||||||
\(853\) | −5.62125 | −0.192468 | −0.0962340 | − | 0.995359i | \(-0.530680\pi\) | ||||
−0.0962340 | + | 0.995359i | \(0.530680\pi\) | |||||||
\(854\) | 19.5230 | 0.668064 | ||||||||
\(855\) | −25.3808 | −0.868004 | ||||||||
\(856\) | −3.59395 | −0.122839 | ||||||||
\(857\) | −33.0059 | −1.12746 | −0.563729 | − | 0.825960i | \(-0.690634\pi\) | ||||
−0.563729 | + | 0.825960i | \(0.690634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.61943 | −0.123493 | −0.0617467 | − | 0.998092i | \(-0.519667\pi\) | ||||
−0.0617467 | + | 0.998092i | \(0.519667\pi\) | |||||||
\(860\) | −57.7324 | −1.96866 | ||||||||
\(861\) | −6.71425 | −0.228821 | ||||||||
\(862\) | 24.6191 | 0.838531 | ||||||||
\(863\) | 38.2126 | 1.30077 | 0.650386 | − | 0.759604i | \(-0.274607\pi\) | ||||
0.650386 | + | 0.759604i | \(0.274607\pi\) | |||||||
\(864\) | −6.98001 | −0.237465 | ||||||||
\(865\) | −8.83955 | −0.300554 | ||||||||
\(866\) | 9.98929 | 0.339450 | ||||||||
\(867\) | 29.5632 | 1.00402 | ||||||||
\(868\) | −2.03855 | −0.0691930 | ||||||||
\(869\) | −14.6715 | −0.497695 | ||||||||
\(870\) | −14.7331 | −0.499500 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17.4539 | −0.591063 | ||||||||
\(873\) | 1.63979 | 0.0554983 | ||||||||
\(874\) | −14.0877 | −0.476523 | ||||||||
\(875\) | 36.9359 | 1.24866 | ||||||||
\(876\) | −10.6134 | −0.358594 | ||||||||
\(877\) | −3.37408 | −0.113935 | −0.0569673 | − | 0.998376i | \(-0.518143\pi\) | ||||
−0.0569673 | + | 0.998376i | \(0.518143\pi\) | |||||||
\(878\) | −60.3605 | −2.03707 | ||||||||
\(879\) | −30.7151 | −1.03600 | ||||||||
\(880\) | −79.8270 | −2.69097 | ||||||||
\(881\) | 22.2190 | 0.748578 | 0.374289 | − | 0.927312i | \(-0.377887\pi\) | ||||
0.374289 | + | 0.927312i | \(0.377887\pi\) | |||||||
\(882\) | 1.86754 | 0.0628833 | ||||||||
\(883\) | 12.9182 | 0.434733 | 0.217367 | − | 0.976090i | \(-0.430253\pi\) | ||||
0.217367 | + | 0.976090i | \(0.430253\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.4087 | −0.484344 | ||||||||
\(886\) | 36.1928 | 1.21592 | ||||||||
\(887\) | 8.88838 | 0.298443 | 0.149221 | − | 0.988804i | \(-0.452323\pi\) | ||||
0.149221 | + | 0.988804i | \(0.452323\pi\) | |||||||
\(888\) | −10.2726 | −0.344726 | ||||||||
\(889\) | −0.713456 | −0.0239285 | ||||||||
\(890\) | 78.1868 | 2.62083 | ||||||||
\(891\) | −3.88982 | −0.130314 | ||||||||
\(892\) | 26.7288 | 0.894947 | ||||||||
\(893\) | −57.9525 | −1.93931 | ||||||||
\(894\) | 14.2661 | 0.477128 | ||||||||
\(895\) | −53.5743 | −1.79079 | ||||||||
\(896\) | −7.40285 | −0.247312 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −67.7948 | −2.26234 | ||||||||
\(899\) | 2.50851 | 0.0836634 | ||||||||
\(900\) | 20.1895 | 0.672985 | ||||||||
\(901\) | 17.9477 | 0.597926 | ||||||||
\(902\) | −48.7749 | −1.62403 | ||||||||
\(903\) | −9.00507 | −0.299670 | ||||||||
\(904\) | 9.73301 | 0.323715 | ||||||||
\(905\) | 48.9105 | 1.62584 | ||||||||
\(906\) | 1.11386 | 0.0370055 | ||||||||
\(907\) | 2.04682 | 0.0679636 | 0.0339818 | − | 0.999422i | \(-0.489181\pi\) | ||||
0.0339818 | + | 0.999422i | \(0.489181\pi\) | |||||||
\(908\) | 11.4982 | 0.381582 | ||||||||
\(909\) | −4.24015 | −0.140637 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2742 | −1.40061 | −0.700303 | − | 0.713846i | \(-0.746952\pi\) | ||||
−0.700303 | + | 0.713846i | \(0.746952\pi\) | |||||||
\(912\) | −28.0473 | −0.928737 | ||||||||
\(913\) | −15.0611 | −0.498450 | ||||||||
\(914\) | 3.89435 | 0.128814 | ||||||||
\(915\) | 45.0500 | 1.48931 | ||||||||
\(916\) | 32.3464 | 1.06876 | ||||||||
\(917\) | 3.47549 | 0.114771 | ||||||||
\(918\) | 12.7436 | 0.420600 | ||||||||
\(919\) | 21.0914 | 0.695743 | 0.347871 | − | 0.937542i | \(-0.386905\pi\) | ||||
0.347871 | + | 0.937542i | \(0.386905\pi\) | |||||||
\(920\) | −5.28076 | −0.174101 | ||||||||
\(921\) | 13.1810 | 0.434327 | ||||||||
\(922\) | 52.5051 | 1.72916 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 5.78687 | 0.190374 | ||||||||
\(925\) | 145.713 | 4.79100 | ||||||||
\(926\) | 19.4099 | 0.637847 | ||||||||
\(927\) | 6.12865 | 0.201291 | ||||||||
\(928\) | −12.7780 | −0.419460 | ||||||||
\(929\) | −14.2296 | −0.466859 | −0.233430 | − | 0.972374i | \(-0.574995\pi\) | ||||
−0.233430 | + | 0.972374i | \(0.574995\pi\) | |||||||
\(930\) | −11.0279 | −0.361620 | ||||||||
\(931\) | 5.88962 | 0.193024 | ||||||||
\(932\) | −24.0055 | −0.786327 | ||||||||
\(933\) | −22.3404 | −0.731392 | ||||||||
\(934\) | 8.93208 | 0.292267 | ||||||||
\(935\) | 114.385 | 3.74078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.73924 | 0.0568186 | 0.0284093 | − | 0.999596i | \(-0.490956\pi\) | ||||
0.0284093 | + | 0.999596i | \(0.490956\pi\) | |||||||
\(938\) | 13.9725 | 0.456219 | ||||||||
\(939\) | 26.5372 | 0.866008 | ||||||||
\(940\) | 63.0837 | 2.05756 | ||||||||
\(941\) | −9.02109 | −0.294079 | −0.147040 | − | 0.989131i | \(-0.546974\pi\) | ||||
−0.147040 | + | 0.989131i | \(0.546974\pi\) | |||||||
\(942\) | −29.6180 | −0.965005 | ||||||||
\(943\) | −8.59964 | −0.280043 | ||||||||
\(944\) | −15.9225 | −0.518233 | ||||||||
\(945\) | 4.30941 | 0.140185 | ||||||||
\(946\) | −65.4163 | −2.12687 | ||||||||
\(947\) | −18.8346 | −0.612041 | −0.306020 | − | 0.952025i | \(-0.598998\pi\) | ||||
−0.306020 | + | 0.952025i | \(0.598998\pi\) | |||||||
\(948\) | 5.61124 | 0.182244 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 149.269 | 4.84291 | ||||||||
\(951\) | −4.21944 | −0.136825 | ||||||||
\(952\) | 6.52856 | 0.211592 | ||||||||
\(953\) | −39.3935 | −1.27608 | −0.638040 | − | 0.770003i | \(-0.720254\pi\) | ||||
−0.638040 | + | 0.770003i | \(0.720254\pi\) | |||||||
\(954\) | 4.91199 | 0.159032 | ||||||||
\(955\) | 16.1130 | 0.521405 | ||||||||
\(956\) | 28.7772 | 0.930720 | ||||||||
\(957\) | −7.12094 | −0.230187 | ||||||||
\(958\) | −15.0787 | −0.487171 | ||||||||
\(959\) | −6.49365 | −0.209691 | ||||||||
\(960\) | 15.1309 | 0.488347 | ||||||||
\(961\) | −29.1224 | −0.939431 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.75644 | 0.121050 | ||||||||
\(964\) | −15.1763 | −0.488797 | ||||||||
\(965\) | −41.0046 | −1.31998 | ||||||||
\(966\) | 2.39195 | 0.0769597 | ||||||||
\(967\) | −20.0823 | −0.645804 | −0.322902 | − | 0.946432i | \(-0.604658\pi\) | ||||
−0.322902 | + | 0.946432i | \(0.604658\pi\) | |||||||
\(968\) | −3.95201 | −0.127022 | ||||||||
\(969\) | 40.1891 | 1.29106 | ||||||||
\(970\) | −13.1970 | −0.423729 | ||||||||
\(971\) | −28.4437 | −0.912803 | −0.456401 | − | 0.889774i | \(-0.650862\pi\) | ||||
−0.456401 | + | 0.889774i | \(0.650862\pi\) | |||||||
\(972\) | 1.48770 | 0.0477179 | ||||||||
\(973\) | −9.71185 | −0.311348 | ||||||||
\(974\) | −20.8295 | −0.667421 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 49.7830 | 1.59351 | ||||||||
\(977\) | −36.8889 | −1.18018 | −0.590091 | − | 0.807337i | \(-0.700908\pi\) | ||||
−0.590091 | + | 0.807337i | \(0.700908\pi\) | |||||||
\(978\) | 27.9259 | 0.892972 | ||||||||
\(979\) | 37.7899 | 1.20777 | ||||||||
\(980\) | −6.41110 | −0.204795 | ||||||||
\(981\) | 18.2430 | 0.582454 | ||||||||
\(982\) | −9.54875 | −0.304713 | ||||||||
\(983\) | −17.9973 | −0.574026 | −0.287013 | − | 0.957927i | \(-0.592662\pi\) | ||||
−0.287013 | + | 0.957927i | \(0.592662\pi\) | |||||||
\(984\) | −6.42382 | −0.204784 | ||||||||
\(985\) | −65.0674 | −2.07322 | ||||||||
\(986\) | 23.3292 | 0.742952 | ||||||||
\(987\) | 9.83977 | 0.313203 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.5337 | −0.366751 | ||||||||
\(990\) | 31.3052 | 0.994944 | ||||||||
\(991\) | −46.5528 | −1.47880 | −0.739400 | − | 0.673267i | \(-0.764891\pi\) | ||||
−0.739400 | + | 0.673267i | \(0.764891\pi\) | |||||||
\(992\) | −9.56452 | −0.303674 | ||||||||
\(993\) | −16.1732 | −0.513241 | ||||||||
\(994\) | −8.93398 | −0.283369 | ||||||||
\(995\) | −18.2401 | −0.578249 | ||||||||
\(996\) | 5.76026 | 0.182521 | ||||||||
\(997\) | 41.4216 | 1.31183 | 0.655917 | − | 0.754833i | \(-0.272282\pi\) | ||||
0.655917 | + | 0.754833i | \(0.272282\pi\) | |||||||
\(998\) | −72.1349 | −2.28339 | ||||||||
\(999\) | 10.7371 | 0.339705 |
(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 | 3549.2.a.bh.1.11 | yes | 15 | |
13.12 | even | 2 | 3549.2.a.bg.1.5 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.bg.1.5 | ✓ | 15 | 13.12 | even | 2 | ||
3549.2.a.bh.1.11 | yes | 15 | 1.1 | even | 1 | trivial |