Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6561,2,Mod(1,6561)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6561, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6561.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6561 = 3^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6561.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: | \(52.3898487662\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | no (minimal twist has level 81) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6561.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.27431 | −1.60818 | −0.804089 | − | 0.594509i | \(-0.797346\pi\) | ||||
−0.804089 | + | 0.594509i | \(0.797346\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.17247 | 1.58624 | ||||||||
\(5\) | 0.586876 | 0.262459 | 0.131230 | − | 0.991352i | \(-0.458108\pi\) | ||||
0.131230 | + | 0.991352i | \(0.458108\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.80961 | 1.43990 | 0.719948 | − | 0.694028i | \(-0.244166\pi\) | ||||
0.719948 | + | 0.694028i | \(0.244166\pi\) | |||||||
\(8\) | −2.66656 | −0.942773 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.33474 | −0.422081 | ||||||||
\(11\) | 4.98958 | 1.50441 | 0.752207 | − | 0.658927i | \(-0.228989\pi\) | ||||
0.752207 | + | 0.658927i | \(0.228989\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.48589 | −0.689461 | −0.344731 | − | 0.938702i | \(-0.612030\pi\) | ||||
−0.344731 | + | 0.938702i | \(0.612030\pi\) | |||||||
\(14\) | −8.66421 | −2.31561 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.280361 | −0.0700902 | ||||||||
\(17\) | 2.85693 | 0.692908 | 0.346454 | − | 0.938067i | \(-0.387386\pi\) | ||||
0.346454 | + | 0.938067i | \(0.387386\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.417601 | 0.0958042 | 0.0479021 | − | 0.998852i | \(-0.484746\pi\) | ||||
0.0479021 | + | 0.998852i | \(0.484746\pi\) | |||||||
\(20\) | 1.86185 | 0.416322 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.3478 | −2.41936 | ||||||||
\(23\) | 7.35642 | 1.53392 | 0.766960 | − | 0.641695i | \(-0.221769\pi\) | ||||
0.766960 | + | 0.641695i | \(0.221769\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65558 | −0.931115 | ||||||||
\(26\) | 5.65367 | 1.10878 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 12.0859 | 2.28401 | ||||||||
\(29\) | 5.28268 | 0.980968 | 0.490484 | − | 0.871450i | \(-0.336820\pi\) | ||||
0.490484 | + | 0.871450i | \(0.336820\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.93826 | 0.527727 | 0.263863 | − | 0.964560i | \(-0.415003\pi\) | ||||
0.263863 | + | 0.964560i | \(0.415003\pi\) | |||||||
\(32\) | 5.97075 | 1.05549 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.49755 | −1.11432 | ||||||||
\(35\) | 2.23577 | 0.377914 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.29234 | −1.03445 | −0.517227 | − | 0.855848i | \(-0.673036\pi\) | ||||
−0.517227 | + | 0.855848i | \(0.673036\pi\) | |||||||
\(38\) | −0.949753 | −0.154070 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.56494 | −0.247439 | ||||||||
\(41\) | 3.65040 | 0.570097 | 0.285049 | − | 0.958513i | \(-0.407990\pi\) | ||||
0.285049 | + | 0.958513i | \(0.407990\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.01707 | −0.917595 | −0.458797 | − | 0.888541i | \(-0.651720\pi\) | ||||
−0.458797 | + | 0.888541i | \(0.651720\pi\) | |||||||
\(44\) | 15.8293 | 2.38636 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −16.7308 | −2.46682 | ||||||||
\(47\) | −6.58406 | −0.960385 | −0.480192 | − | 0.877163i | \(-0.659433\pi\) | ||||
−0.480192 | + | 0.877163i | \(0.659433\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.51309 | 1.07330 | ||||||||
\(50\) | 10.5882 | 1.49740 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.88641 | −1.09365 | ||||||||
\(53\) | 2.47763 | 0.340329 | 0.170165 | − | 0.985416i | \(-0.445570\pi\) | ||||
0.170165 | + | 0.985416i | \(0.445570\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.92826 | 0.394847 | ||||||||
\(56\) | −10.1586 | −1.35749 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.0144 | −1.57757 | ||||||||
\(59\) | −4.63396 | −0.603290 | −0.301645 | − | 0.953420i | \(-0.597536\pi\) | ||||
−0.301645 | + | 0.953420i | \(0.597536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3950 | 1.45899 | 0.729493 | − | 0.683988i | \(-0.239756\pi\) | ||||
0.729493 | + | 0.683988i | \(0.239756\pi\) | |||||||
\(62\) | −6.68250 | −0.848678 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0186 | −1.62733 | ||||||||
\(65\) | −1.45891 | −0.180955 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.94721 | 0.726568 | 0.363284 | − | 0.931679i | \(-0.381656\pi\) | ||||
0.363284 | + | 0.931679i | \(0.381656\pi\) | |||||||
\(68\) | 9.06355 | 1.09912 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.08482 | −0.607752 | ||||||||
\(71\) | 2.82531 | 0.335302 | 0.167651 | − | 0.985846i | \(-0.446382\pi\) | ||||
0.167651 | + | 0.985846i | \(0.446382\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.7368 | −1.60778 | −0.803888 | − | 0.594781i | \(-0.797239\pi\) | ||||
−0.803888 | + | 0.594781i | \(0.797239\pi\) | |||||||
\(74\) | 14.3107 | 1.66359 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.32483 | 0.151968 | ||||||||
\(77\) | 19.0083 | 2.16620 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5673 | 1.41393 | 0.706964 | − | 0.707250i | \(-0.250064\pi\) | ||||
0.706964 | + | 0.707250i | \(0.250064\pi\) | |||||||
\(80\) | −0.164537 | −0.0183958 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.30214 | −0.916818 | ||||||||
\(83\) | −2.09817 | −0.230305 | −0.115152 | − | 0.993348i | \(-0.536736\pi\) | ||||
−0.115152 | + | 0.993348i | \(0.536736\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.67667 | 0.181860 | ||||||||
\(86\) | 13.6847 | 1.47566 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13.3050 | −1.41832 | ||||||||
\(89\) | −0.345463 | −0.0366190 | −0.0183095 | − | 0.999832i | \(-0.505828\pi\) | ||||
−0.0183095 | + | 0.999832i | \(0.505828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.47025 | −0.992752 | ||||||||
\(92\) | 23.3380 | 2.43316 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.9742 | 1.54447 | ||||||||
\(95\) | 0.245080 | 0.0251447 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9705 | 1.11389 | 0.556944 | − | 0.830550i | \(-0.311974\pi\) | ||||
0.556944 | + | 0.830550i | \(0.311974\pi\) | |||||||
\(98\) | −17.0871 | −1.72606 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.7697 | −1.47697 | ||||||||
\(101\) | 1.77372 | 0.176492 | 0.0882458 | − | 0.996099i | \(-0.471874\pi\) | ||||
0.0882458 | + | 0.996099i | \(0.471874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.5976 | 1.73395 | 0.866974 | − | 0.498354i | \(-0.166062\pi\) | ||||
0.866974 | + | 0.498354i | \(0.166062\pi\) | |||||||
\(104\) | 6.62878 | 0.650005 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.63490 | −0.547310 | ||||||||
\(107\) | −4.53980 | −0.438879 | −0.219439 | − | 0.975626i | \(-0.570423\pi\) | ||||
−0.219439 | + | 0.975626i | \(0.570423\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.90189 | 0.373733 | 0.186866 | − | 0.982385i | \(-0.440167\pi\) | ||||
0.186866 | + | 0.982385i | \(0.440167\pi\) | |||||||
\(110\) | −6.65977 | −0.634984 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.06806 | −0.100923 | ||||||||
\(113\) | 13.0376 | 1.22647 | 0.613235 | − | 0.789900i | \(-0.289868\pi\) | ||||
0.613235 | + | 0.789900i | \(0.289868\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.31731 | 0.402591 | ||||||||
\(116\) | 16.7591 | 1.55605 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.5390 | 0.970198 | ||||||||
\(119\) | 10.8838 | 0.997716 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.8959 | 1.26326 | ||||||||
\(122\) | −25.9158 | −2.34631 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.32154 | 0.837099 | ||||||||
\(125\) | −5.66663 | −0.506839 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.19348 | −0.727054 | −0.363527 | − | 0.931584i | \(-0.618427\pi\) | ||||
−0.363527 | + | 0.931584i | \(0.618427\pi\) | |||||||
\(128\) | 17.6668 | 1.56154 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.31801 | 0.291009 | ||||||||
\(131\) | 1.73569 | 0.151648 | 0.0758238 | − | 0.997121i | \(-0.475841\pi\) | ||||
0.0758238 | + | 0.997121i | \(0.475841\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.59089 | 0.137948 | ||||||||
\(134\) | −13.5258 | −1.16845 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.61820 | −0.653255 | ||||||||
\(137\) | 2.74802 | 0.234780 | 0.117390 | − | 0.993086i | \(-0.462547\pi\) | ||||
0.117390 | + | 0.993086i | \(0.462547\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.65405 | 0.734027 | 0.367013 | − | 0.930216i | \(-0.380380\pi\) | ||||
0.367013 | + | 0.930216i | \(0.380380\pi\) | |||||||
\(140\) | 7.09291 | 0.599460 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.42561 | −0.539225 | ||||||||
\(143\) | −12.4035 | −1.03724 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.10028 | 0.257464 | ||||||||
\(146\) | 31.2418 | 2.58559 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.9623 | −1.64089 | ||||||||
\(149\) | −5.73323 | −0.469685 | −0.234842 | − | 0.972033i | \(-0.575457\pi\) | ||||
−0.234842 | + | 0.972033i | \(0.575457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.77462 | 0.144417 | 0.0722083 | − | 0.997390i | \(-0.476995\pi\) | ||||
0.0722083 | + | 0.997390i | \(0.476995\pi\) | |||||||
\(152\) | −1.11356 | −0.0903216 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −43.2307 | −3.48363 | ||||||||
\(155\) | 1.72439 | 0.138507 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.50907 | 0.758906 | 0.379453 | − | 0.925211i | \(-0.376112\pi\) | ||||
0.379453 | + | 0.925211i | \(0.376112\pi\) | |||||||
\(158\) | −28.5818 | −2.27385 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.50409 | 0.277023 | ||||||||
\(161\) | 28.0251 | 2.20868 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.38623 | 0.578534 | 0.289267 | − | 0.957248i | \(-0.406588\pi\) | ||||
0.289267 | + | 0.957248i | \(0.406588\pi\) | |||||||
\(164\) | 11.5808 | 0.904309 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.77189 | 0.370371 | ||||||||
\(167\) | 4.55339 | 0.352352 | 0.176176 | − | 0.984359i | \(-0.443627\pi\) | ||||
0.176176 | + | 0.984359i | \(0.443627\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.82036 | −0.524643 | ||||||||
\(170\) | −3.81326 | −0.292463 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −19.0890 | −1.45552 | ||||||||
\(173\) | −4.65432 | −0.353861 | −0.176931 | − | 0.984223i | \(-0.556617\pi\) | ||||
−0.176931 | + | 0.984223i | \(0.556617\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.7359 | −1.34071 | ||||||||
\(176\) | −1.39888 | −0.105445 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.785688 | 0.0588898 | ||||||||
\(179\) | 3.47274 | 0.259564 | 0.129782 | − | 0.991543i | \(-0.458572\pi\) | ||||
0.129782 | + | 0.991543i | \(0.458572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.2925 | −1.13668 | −0.568341 | − | 0.822793i | \(-0.692415\pi\) | ||||
−0.568341 | + | 0.822793i | \(0.692415\pi\) | |||||||
\(182\) | 21.5383 | 1.59652 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.6164 | −1.44614 | ||||||||
\(185\) | −3.69283 | −0.271502 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.2549 | 1.04242 | ||||||||
\(188\) | −20.8878 | −1.52340 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.557388 | −0.0404371 | ||||||||
\(191\) | −22.3873 | −1.61989 | −0.809945 | − | 0.586506i | \(-0.800503\pi\) | ||||
−0.809945 | + | 0.586506i | \(0.800503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.47290 | −0.465930 | −0.232965 | − | 0.972485i | \(-0.574843\pi\) | ||||
−0.232965 | + | 0.972485i | \(0.574843\pi\) | |||||||
\(194\) | −24.9504 | −1.79133 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 23.8351 | 1.70251 | ||||||||
\(197\) | −5.53590 | −0.394416 | −0.197208 | − | 0.980362i | \(-0.563187\pi\) | ||||
−0.197208 | + | 0.980362i | \(0.563187\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.8019 | −1.19106 | −0.595529 | − | 0.803334i | \(-0.703057\pi\) | ||||
−0.595529 | + | 0.803334i | \(0.703057\pi\) | |||||||
\(200\) | 12.4144 | 0.877830 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.03398 | −0.283830 | ||||||||
\(203\) | 20.1249 | 1.41249 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.14234 | 0.149627 | ||||||||
\(206\) | −40.0225 | −2.78850 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.696946 | 0.0483245 | ||||||||
\(209\) | 2.08365 | 0.144129 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.65013 | −0.526656 | −0.263328 | − | 0.964706i | \(-0.584820\pi\) | ||||
−0.263328 | + | 0.964706i | \(0.584820\pi\) | |||||||
\(212\) | 7.86022 | 0.539842 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.3249 | 0.705795 | ||||||||
\(215\) | −3.53128 | −0.240831 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.1936 | 0.759871 | ||||||||
\(218\) | −8.87409 | −0.601029 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.28984 | 0.626321 | ||||||||
\(221\) | −7.10202 | −0.477734 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.45766 | −0.566367 | −0.283183 | − | 0.959066i | \(-0.591390\pi\) | ||||
−0.283183 | + | 0.959066i | \(0.591390\pi\) | |||||||
\(224\) | 22.7462 | 1.51980 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −29.6514 | −1.97238 | ||||||||
\(227\) | −26.7392 | −1.77475 | −0.887373 | − | 0.461052i | \(-0.847472\pi\) | ||||
−0.887373 | + | 0.461052i | \(0.847472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.07865 | −0.203443 | −0.101722 | − | 0.994813i | \(-0.532435\pi\) | ||||
−0.101722 | + | 0.994813i | \(0.532435\pi\) | |||||||
\(230\) | −9.81889 | −0.647438 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.0866 | −0.924830 | ||||||||
\(233\) | 7.10490 | 0.465457 | 0.232729 | − | 0.972542i | \(-0.425235\pi\) | ||||
0.232729 | + | 0.972542i | \(0.425235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.86403 | −0.252062 | ||||||||
\(236\) | −14.7011 | −0.956961 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −24.7531 | −1.60450 | ||||||||
\(239\) | −4.58602 | −0.296645 | −0.148323 | − | 0.988939i | \(-0.547387\pi\) | ||||
−0.148323 | + | 0.988939i | \(0.547387\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.15729 | 0.396626 | 0.198313 | − | 0.980139i | \(-0.436454\pi\) | ||||
0.198313 | + | 0.980139i | \(0.436454\pi\) | |||||||
\(242\) | −31.6035 | −2.03155 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 36.1505 | 2.31430 | ||||||||
\(245\) | 4.40926 | 0.281697 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.03811 | −0.0660533 | ||||||||
\(248\) | −7.83505 | −0.497526 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.8877 | 0.815087 | ||||||||
\(251\) | 29.3779 | 1.85431 | 0.927157 | − | 0.374673i | \(-0.122245\pi\) | ||||
0.927157 | + | 0.374673i | \(0.122245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.7054 | 2.30765 | ||||||||
\(254\) | 18.6345 | 1.16923 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.1425 | −0.883908 | ||||||||
\(257\) | 18.9070 | 1.17938 | 0.589692 | − | 0.807628i | \(-0.299249\pi\) | ||||
0.589692 | + | 0.807628i | \(0.299249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.9713 | −1.48951 | ||||||||
\(260\) | −4.62835 | −0.287038 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.94748 | −0.243876 | ||||||||
\(263\) | 14.6501 | 0.903362 | 0.451681 | − | 0.892180i | \(-0.350825\pi\) | ||||
0.451681 | + | 0.892180i | \(0.350825\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.45406 | 0.0893224 | ||||||||
\(266\) | −3.61818 | −0.221845 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18.8674 | 1.15251 | ||||||||
\(269\) | −5.89036 | −0.359142 | −0.179571 | − | 0.983745i | \(-0.557471\pi\) | ||||
−0.179571 | + | 0.983745i | \(0.557471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.1929 | −1.40887 | −0.704435 | − | 0.709768i | \(-0.748800\pi\) | ||||
−0.704435 | + | 0.709768i | \(0.748800\pi\) | |||||||
\(272\) | −0.800973 | −0.0485661 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.24985 | −0.377567 | ||||||||
\(275\) | −23.2293 | −1.40078 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.4388 | −1.04780 | −0.523899 | − | 0.851780i | \(-0.675523\pi\) | ||||
−0.523899 | + | 0.851780i | \(0.675523\pi\) | |||||||
\(278\) | −19.6820 | −1.18045 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.96182 | −0.356287 | ||||||||
\(281\) | 28.5863 | 1.70532 | 0.852659 | − | 0.522467i | \(-0.174988\pi\) | ||||
0.852659 | + | 0.522467i | \(0.174988\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.8097 | 1.05868 | 0.529340 | − | 0.848410i | \(-0.322440\pi\) | ||||
0.529340 | + | 0.848410i | \(0.322440\pi\) | |||||||
\(284\) | 8.96321 | 0.531868 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 28.2094 | 1.66806 | ||||||||
\(287\) | 13.9066 | 0.820881 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.83792 | −0.519878 | ||||||||
\(290\) | −7.05098 | −0.414048 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −43.5798 | −2.55031 | ||||||||
\(293\) | −16.6353 | −0.971846 | −0.485923 | − | 0.874002i | \(-0.661516\pi\) | ||||
−0.485923 | + | 0.874002i | \(0.661516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.71956 | −0.158339 | ||||||||
\(296\) | 16.7789 | 0.975255 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.0391 | 0.755337 | ||||||||
\(299\) | −18.2872 | −1.05758 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.9227 | −1.32124 | ||||||||
\(302\) | −4.03604 | −0.232248 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.117079 | −0.00671494 | ||||||||
\(305\) | 6.68748 | 0.382924 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.1106 | −0.805335 | −0.402668 | − | 0.915346i | \(-0.631917\pi\) | ||||
−0.402668 | + | 0.915346i | \(0.631917\pi\) | |||||||
\(308\) | 60.3034 | 3.43610 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.92180 | −0.222743 | ||||||||
\(311\) | 23.6481 | 1.34096 | 0.670480 | − | 0.741928i | \(-0.266088\pi\) | ||||
0.670480 | + | 0.741928i | \(0.266088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.18392 | 0.462583 | 0.231291 | − | 0.972885i | \(-0.425705\pi\) | ||||
0.231291 | + | 0.972885i | \(0.425705\pi\) | |||||||
\(314\) | −21.6265 | −1.22046 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 39.8693 | 2.24282 | ||||||||
\(317\) | 4.09853 | 0.230196 | 0.115098 | − | 0.993354i | \(-0.463282\pi\) | ||||
0.115098 | + | 0.993354i | \(0.463282\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.3583 | 1.47578 | ||||||||
\(320\) | −7.64031 | −0.427106 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −63.7376 | −3.55196 | ||||||||
\(323\) | 1.19306 | 0.0663836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.5732 | 0.641968 | ||||||||
\(326\) | −16.7985 | −0.930385 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.73404 | −0.537472 | ||||||||
\(329\) | −25.0827 | −1.38285 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.7961 | −1.36292 | −0.681458 | − | 0.731857i | \(-0.738654\pi\) | ||||
−0.681458 | + | 0.731857i | \(0.738654\pi\) | |||||||
\(332\) | −6.65640 | −0.365318 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.3558 | −0.566645 | ||||||||
\(335\) | 3.49028 | 0.190694 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.1613 | 0.825890 | 0.412945 | − | 0.910756i | \(-0.364500\pi\) | ||||
0.412945 | + | 0.910756i | \(0.364500\pi\) | |||||||
\(338\) | 15.5116 | 0.843719 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.31918 | 0.288473 | ||||||||
\(341\) | 14.6607 | 0.793919 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.95468 | 0.105543 | ||||||||
\(344\) | 16.0449 | 0.865083 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5853 | 0.569072 | ||||||||
\(347\) | −25.1222 | −1.34863 | −0.674316 | − | 0.738443i | \(-0.735561\pi\) | ||||
−0.674316 | + | 0.738443i | \(0.735561\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.3457 | −0.928492 | −0.464246 | − | 0.885706i | \(-0.653675\pi\) | ||||
−0.464246 | + | 0.885706i | \(0.653675\pi\) | |||||||
\(350\) | 40.3369 | 2.15610 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 29.7915 | 1.58789 | ||||||||
\(353\) | 21.7225 | 1.15617 | 0.578086 | − | 0.815976i | \(-0.303800\pi\) | ||||
0.578086 | + | 0.815976i | \(0.303800\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.65811 | 0.0880031 | ||||||||
\(356\) | −1.09597 | −0.0580863 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.89807 | −0.417426 | ||||||||
\(359\) | −27.5292 | −1.45293 | −0.726467 | − | 0.687201i | \(-0.758839\pi\) | ||||
−0.726467 | + | 0.687201i | \(0.758839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8256 | −0.990822 | ||||||||
\(362\) | 34.7798 | 1.82799 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −30.0441 | −1.57474 | ||||||||
\(365\) | −8.06183 | −0.421975 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.3548 | −1.27131 | −0.635656 | − | 0.771972i | \(-0.719270\pi\) | ||||
−0.635656 | + | 0.771972i | \(0.719270\pi\) | |||||||
\(368\) | −2.06245 | −0.107513 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.39862 | 0.436624 | ||||||||
\(371\) | 9.43880 | 0.490038 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.6726 | 0.863275 | 0.431638 | − | 0.902047i | \(-0.357936\pi\) | ||||
0.431638 | + | 0.902047i | \(0.357936\pi\) | |||||||
\(374\) | −32.4200 | −1.67640 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.5568 | 0.905424 | ||||||||
\(377\) | −13.1321 | −0.676340 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.06537 | −0.106091 | −0.0530454 | − | 0.998592i | \(-0.516893\pi\) | ||||
−0.0530454 | + | 0.998592i | \(0.516893\pi\) | |||||||
\(380\) | 0.777510 | 0.0398854 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 50.9156 | 2.60507 | ||||||||
\(383\) | 14.4104 | 0.736339 | 0.368170 | − | 0.929759i | \(-0.379985\pi\) | ||||
0.368170 | + | 0.929759i | \(0.379985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.1555 | 0.568538 | ||||||||
\(386\) | 14.7214 | 0.749298 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 34.8037 | 1.76689 | ||||||||
\(389\) | 12.3423 | 0.625779 | 0.312890 | − | 0.949790i | \(-0.398703\pi\) | ||||
0.312890 | + | 0.949790i | \(0.398703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0168 | 1.06287 | ||||||||
\(392\) | −20.0341 | −1.01188 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.5903 | 0.634291 | ||||||||
\(395\) | 7.37543 | 0.371098 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.1683 | 0.962028 | 0.481014 | − | 0.876713i | \(-0.340269\pi\) | ||||
0.481014 | + | 0.876713i | \(0.340269\pi\) | |||||||
\(398\) | 38.2127 | 1.91543 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.30524 | 0.0652621 | ||||||||
\(401\) | −10.0840 | −0.503569 | −0.251784 | − | 0.967783i | \(-0.581017\pi\) | ||||
−0.251784 | + | 0.967783i | \(0.581017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.30418 | −0.363847 | ||||||||
\(404\) | 5.62708 | 0.279957 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −45.7702 | −2.27154 | ||||||||
\(407\) | −31.3961 | −1.55625 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.46034 | −0.171103 | −0.0855514 | − | 0.996334i | \(-0.527265\pi\) | ||||
−0.0855514 | + | 0.996334i | \(0.527265\pi\) | |||||||
\(410\) | −4.87233 | −0.240627 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 55.8281 | 2.75045 | ||||||||
\(413\) | −17.6536 | −0.868675 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.23137 | −0.0604455 | ||||||||
\(416\) | −14.8426 | −0.727720 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.73886 | −0.231785 | ||||||||
\(419\) | −5.82990 | −0.284809 | −0.142405 | − | 0.989809i | \(-0.545483\pi\) | ||||
−0.142405 | + | 0.989809i | \(0.545483\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.5555 | 1.87908 | 0.939541 | − | 0.342436i | \(-0.111252\pi\) | ||||
0.939541 | + | 0.342436i | \(0.111252\pi\) | |||||||
\(422\) | 17.3987 | 0.846957 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.60677 | −0.320853 | ||||||||
\(425\) | −13.3007 | −0.645178 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.4106 | 2.10079 | ||||||||
\(428\) | −14.4024 | −0.696165 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.03121 | 0.387299 | ||||||||
\(431\) | −0.202222 | −0.00974071 | −0.00487036 | − | 0.999988i | \(-0.501550\pi\) | ||||
−0.00487036 | + | 0.999988i | \(0.501550\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.06122 | −0.387398 | −0.193699 | − | 0.981061i | \(-0.562048\pi\) | ||||
−0.193699 | + | 0.981061i | \(0.562048\pi\) | |||||||
\(434\) | −25.4577 | −1.22201 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.3786 | 0.592829 | ||||||||
\(437\) | 3.07205 | 0.146956 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.18593 | −0.104329 | −0.0521645 | − | 0.998639i | \(-0.516612\pi\) | ||||
−0.0521645 | + | 0.998639i | \(0.516612\pi\) | |||||||
\(440\) | −7.80840 | −0.372251 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.1522 | 0.768281 | ||||||||
\(443\) | −32.3583 | −1.53739 | −0.768695 | − | 0.639616i | \(-0.779093\pi\) | ||||
−0.768695 | + | 0.639616i | \(0.779093\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.202744 | −0.00961098 | ||||||||
\(446\) | 19.2353 | 0.910818 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −49.5958 | −2.34318 | ||||||||
\(449\) | 38.8633 | 1.83407 | 0.917036 | − | 0.398805i | \(-0.130575\pi\) | ||||
0.917036 | + | 0.398805i | \(0.130575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.2140 | 0.857662 | ||||||||
\(452\) | 41.3613 | 1.94547 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 60.8132 | 2.85411 | ||||||||
\(455\) | −5.55787 | −0.260557 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.5254 | −1.38114 | −0.690571 | − | 0.723265i | \(-0.742641\pi\) | ||||
−0.690571 | + | 0.723265i | \(0.742641\pi\) | |||||||
\(458\) | 7.00181 | 0.327173 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.6965 | 0.638605 | ||||||||
\(461\) | 21.5243 | 1.00249 | 0.501244 | − | 0.865306i | \(-0.332876\pi\) | ||||
0.501244 | + | 0.865306i | \(0.332876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.9400 | −1.62380 | −0.811901 | − | 0.583795i | \(-0.801567\pi\) | ||||
−0.811901 | + | 0.583795i | \(0.801567\pi\) | |||||||
\(464\) | −1.48106 | −0.0687563 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.1587 | −0.748538 | ||||||||
\(467\) | −25.1115 | −1.16202 | −0.581011 | − | 0.813896i | \(-0.697343\pi\) | ||||
−0.581011 | + | 0.813896i | \(0.697343\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.6565 | 1.04618 | ||||||||
\(470\) | 8.78800 | 0.405360 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.3568 | 0.568766 | ||||||||
\(473\) | −30.0226 | −1.38044 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.94417 | −0.0892048 | ||||||||
\(476\) | 34.5285 | 1.58261 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.4300 | 0.477058 | ||||||||
\(479\) | −9.81192 | −0.448318 | −0.224159 | − | 0.974553i | \(-0.571964\pi\) | ||||
−0.224159 | + | 0.974553i | \(0.571964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.6421 | 0.713216 | ||||||||
\(482\) | −14.0036 | −0.637845 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 44.0843 | 2.00383 | ||||||||
\(485\) | 6.43835 | 0.292350 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.0318 | −0.771785 | −0.385892 | − | 0.922544i | \(-0.626106\pi\) | ||||
−0.385892 | + | 0.922544i | \(0.626106\pi\) | |||||||
\(488\) | −30.3856 | −1.37549 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.0280 | −0.453019 | ||||||||
\(491\) | −8.40937 | −0.379510 | −0.189755 | − | 0.981831i | \(-0.560769\pi\) | ||||
−0.189755 | + | 0.981831i | \(0.560769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0923 | 0.679721 | ||||||||
\(494\) | 2.36098 | 0.106225 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.823772 | −0.0369885 | ||||||||
\(497\) | 10.7633 | 0.482800 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.1628 | 1.08168 | 0.540838 | − | 0.841127i | \(-0.318107\pi\) | ||||
0.540838 | + | 0.841127i | \(0.318107\pi\) | |||||||
\(500\) | −17.9772 | −0.803966 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −66.8143 | −2.98207 | ||||||||
\(503\) | −3.67529 | −0.163873 | −0.0819366 | − | 0.996638i | \(-0.526111\pi\) | ||||
−0.0819366 | + | 0.996638i | \(0.526111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.04095 | 0.0463218 | ||||||||
\(506\) | −83.4794 | −3.71111 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −25.9936 | −1.15328 | ||||||||
\(509\) | −29.3717 | −1.30188 | −0.650939 | − | 0.759130i | \(-0.725625\pi\) | ||||
−0.650939 | + | 0.759130i | \(0.725625\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −52.3320 | −2.31503 | ||||||||
\(512\) | −3.16917 | −0.140059 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −43.0002 | −1.89666 | ||||||||
\(515\) | 10.3276 | 0.455090 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.8517 | −1.44482 | ||||||||
\(518\) | 54.5182 | 2.39539 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.89027 | 0.170600 | ||||||||
\(521\) | 34.6944 | 1.51999 | 0.759996 | − | 0.649928i | \(-0.225201\pi\) | ||||
0.759996 | + | 0.649928i | \(0.225201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.8835 | 1.26299 | 0.631493 | − | 0.775381i | \(-0.282442\pi\) | ||||
0.631493 | + | 0.775381i | \(0.282442\pi\) | |||||||
\(524\) | 5.50642 | 0.240549 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −33.3187 | −1.45277 | ||||||||
\(527\) | 8.39441 | 0.365666 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.1169 | 1.35291 | ||||||||
\(530\) | −3.30699 | −0.143646 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.04707 | 0.218818 | ||||||||
\(533\) | −9.07450 | −0.393060 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.66430 | −0.115188 | ||||||||
\(536\) | −15.8586 | −0.684988 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.3965 | 0.577564 | ||||||||
\(539\) | 37.4871 | 1.61469 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.57548 | −0.368689 | −0.184344 | − | 0.982862i | \(-0.559016\pi\) | ||||
−0.184344 | + | 0.982862i | \(0.559016\pi\) | |||||||
\(542\) | 52.7479 | 2.26571 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.0581 | 0.731358 | ||||||||
\(545\) | 2.28992 | 0.0980896 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.1821 | −1.07671 | −0.538355 | − | 0.842718i | \(-0.680954\pi\) | ||||
−0.538355 | + | 0.842718i | \(0.680954\pi\) | |||||||
\(548\) | 8.71803 | 0.372416 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 52.8307 | 2.25271 | ||||||||
\(551\) | 2.20605 | 0.0939809 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47.8763 | 2.03591 | ||||||||
\(554\) | 39.6613 | 1.68505 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.4547 | 1.16434 | ||||||||
\(557\) | −16.3019 | −0.690734 | −0.345367 | − | 0.938468i | \(-0.612246\pi\) | ||||
−0.345367 | + | 0.938468i | \(0.612246\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.9578 | 0.632646 | ||||||||
\(560\) | −0.626822 | −0.0264881 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −65.0141 | −2.74246 | ||||||||
\(563\) | 43.7482 | 1.84377 | 0.921884 | − | 0.387467i | \(-0.126650\pi\) | ||||
0.921884 | + | 0.387467i | \(0.126650\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.65143 | 0.321898 | ||||||||
\(566\) | −40.5048 | −1.70254 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.53386 | −0.316114 | ||||||||
\(569\) | 34.2317 | 1.43507 | 0.717533 | − | 0.696524i | \(-0.245271\pi\) | ||||
0.717533 | + | 0.696524i | \(0.245271\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.3804 | −1.35508 | −0.677540 | − | 0.735486i | \(-0.736954\pi\) | ||||
−0.677540 | + | 0.735486i | \(0.736954\pi\) | |||||||
\(572\) | −39.3499 | −1.64530 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −31.6279 | −1.32012 | ||||||||
\(575\) | −34.2484 | −1.42826 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.8114 | −1.90715 | −0.953576 | − | 0.301151i | \(-0.902629\pi\) | ||||
−0.953576 | + | 0.301151i | \(0.902629\pi\) | |||||||
\(578\) | 20.1002 | 0.836056 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.83555 | 0.408399 | ||||||||
\(581\) | −7.99322 | −0.331614 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.3623 | 0.511996 | ||||||||
\(584\) | 36.6302 | 1.51577 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 37.8338 | 1.56290 | ||||||||
\(587\) | 43.0407 | 1.77648 | 0.888240 | − | 0.459380i | \(-0.151928\pi\) | ||||
0.888240 | + | 0.459380i | \(0.151928\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.22702 | 0.0505584 | ||||||||
\(590\) | 6.18512 | 0.254637 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.76413 | 0.0725051 | ||||||||
\(593\) | 27.0758 | 1.11187 | 0.555935 | − | 0.831225i | \(-0.312360\pi\) | ||||
0.555935 | + | 0.831225i | \(0.312360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.38744 | 0.261860 | ||||||||
\(596\) | −18.1885 | −0.745031 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 41.5908 | 1.70077 | ||||||||
\(599\) | 2.02845 | 0.0828803 | 0.0414401 | − | 0.999141i | \(-0.486805\pi\) | ||||
0.0414401 | + | 0.999141i | \(0.486805\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.84512 | 0.320009 | 0.160005 | − | 0.987116i | \(-0.448849\pi\) | ||||
0.160005 | + | 0.987116i | \(0.448849\pi\) | |||||||
\(602\) | 52.1332 | 2.12479 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.62994 | 0.229079 | ||||||||
\(605\) | 8.15516 | 0.331554 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.5896 | −0.835704 | −0.417852 | − | 0.908515i | \(-0.637217\pi\) | ||||
−0.417852 | + | 0.908515i | \(0.637217\pi\) | |||||||
\(608\) | 2.49339 | 0.101120 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.2094 | −0.615810 | ||||||||
\(611\) | 16.3672 | 0.662148 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.44225 | −0.0582521 | −0.0291261 | − | 0.999576i | \(-0.509272\pi\) | ||||
−0.0291261 | + | 0.999576i | \(0.509272\pi\) | |||||||
\(614\) | 32.0919 | 1.29512 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −50.6869 | −2.04223 | ||||||||
\(617\) | −3.39364 | −0.136623 | −0.0683114 | − | 0.997664i | \(-0.521761\pi\) | ||||
−0.0683114 | + | 0.997664i | \(0.521761\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.9382 | 1.24351 | 0.621755 | − | 0.783212i | \(-0.286420\pi\) | ||||
0.621755 | + | 0.783212i | \(0.286420\pi\) | |||||||
\(620\) | 5.47059 | 0.219704 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −53.7830 | −2.15650 | ||||||||
\(623\) | −1.31608 | −0.0527275 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9523 | 0.798091 | ||||||||
\(626\) | −18.6128 | −0.743915 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 30.1673 | 1.20381 | ||||||||
\(629\) | −17.9768 | −0.716782 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.5776 | 1.33670 | 0.668352 | − | 0.743845i | \(-0.267000\pi\) | ||||
0.668352 | + | 0.743845i | \(0.267000\pi\) | |||||||
\(632\) | −33.5114 | −1.33301 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.32132 | −0.370197 | ||||||||
\(635\) | −4.80856 | −0.190822 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.6767 | −0.739998 | ||||||||
\(638\) | −59.9469 | −2.37332 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.3682 | 0.409840 | ||||||||
\(641\) | 16.1196 | 0.636687 | 0.318343 | − | 0.947975i | \(-0.396874\pi\) | ||||
0.318343 | + | 0.947975i | \(0.396874\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.50957 | 0.296149 | 0.148074 | − | 0.988976i | \(-0.452693\pi\) | ||||
0.148074 | + | 0.988976i | \(0.452693\pi\) | |||||||
\(644\) | 88.9087 | 3.50350 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.71338 | −0.106757 | ||||||||
\(647\) | −18.2475 | −0.717384 | −0.358692 | − | 0.933456i | \(-0.616777\pi\) | ||||
−0.358692 | + | 0.933456i | \(0.616777\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.1215 | −0.907598 | ||||||||
\(650\) | −26.3211 | −1.03240 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23.4326 | 0.917691 | ||||||||
\(653\) | 8.51042 | 0.333038 | 0.166519 | − | 0.986038i | \(-0.446747\pi\) | ||||
0.166519 | + | 0.986038i | \(0.446747\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.01863 | 0.0398013 | ||||||||
\(656\) | −1.02343 | −0.0399582 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 57.0457 | 2.22387 | ||||||||
\(659\) | 13.1603 | 0.512653 | 0.256326 | − | 0.966590i | \(-0.417488\pi\) | ||||
0.256326 | + | 0.966590i | \(0.417488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.6091 | −0.451542 | −0.225771 | − | 0.974180i | \(-0.572490\pi\) | ||||
−0.225771 | + | 0.974180i | \(0.572490\pi\) | |||||||
\(662\) | 56.3939 | 2.19181 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.59492 | 0.217125 | ||||||||
\(665\) | 0.933659 | 0.0362057 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.8616 | 1.50473 | ||||||||
\(668\) | 14.4455 | 0.558914 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.93797 | −0.306670 | ||||||||
\(671\) | 56.8565 | 2.19492 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.1759 | 1.54867 | 0.774333 | − | 0.632778i | \(-0.218086\pi\) | ||||
0.774333 | + | 0.632778i | \(0.218086\pi\) | |||||||
\(674\) | −34.4815 | −1.32818 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.6374 | −0.832208 | ||||||||
\(677\) | 13.6989 | 0.526491 | 0.263245 | − | 0.964729i | \(-0.415207\pi\) | ||||
0.263245 | + | 0.964729i | \(0.415207\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.7934 | 1.60388 | ||||||||
\(680\) | −4.47094 | −0.171453 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −33.3428 | −1.27676 | ||||||||
\(683\) | −19.7916 | −0.757304 | −0.378652 | − | 0.925539i | \(-0.623612\pi\) | ||||
−0.378652 | + | 0.925539i | \(0.623612\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.61275 | 0.0616200 | ||||||||
\(686\) | −4.44553 | −0.169731 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.68695 | 0.0643144 | ||||||||
\(689\) | −6.15912 | −0.234644 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.39957 | 0.357577 | 0.178788 | − | 0.983888i | \(-0.442782\pi\) | ||||
0.178788 | + | 0.983888i | \(0.442782\pi\) | |||||||
\(692\) | −14.7657 | −0.561307 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 57.1357 | 2.16884 | ||||||||
\(695\) | 5.07886 | 0.192652 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.4290 | 0.395025 | ||||||||
\(698\) | 39.4494 | 1.49318 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −56.2667 | −2.12668 | ||||||||
\(701\) | 19.3019 | 0.729024 | 0.364512 | − | 0.931199i | \(-0.381236\pi\) | ||||
0.364512 | + | 0.931199i | \(0.381236\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.62769 | −0.0991051 | ||||||||
\(704\) | −64.9573 | −2.44817 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −49.4036 | −1.85933 | ||||||||
\(707\) | 6.75717 | 0.254129 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.94291 | 0.373414 | 0.186707 | − | 0.982416i | \(-0.440219\pi\) | ||||
0.186707 | + | 0.982416i | \(0.440219\pi\) | |||||||
\(710\) | −3.77104 | −0.141525 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.921198 | 0.0345234 | ||||||||
\(713\) | 21.6151 | 0.809490 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.27934 | −0.272232 | ||||||||
\(716\) | 11.0172 | 0.411731 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 62.6098 | 2.33658 | ||||||||
\(719\) | 38.2949 | 1.42816 | 0.714080 | − | 0.700064i | \(-0.246845\pi\) | ||||
0.714080 | + | 0.700064i | \(0.246845\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 67.0401 | 2.49670 | ||||||||
\(722\) | 42.8152 | 1.59342 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −48.5150 | −1.80305 | ||||||||
\(725\) | −24.5939 | −0.913394 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.4738 | 0.870596 | 0.435298 | − | 0.900286i | \(-0.356643\pi\) | ||||
0.435298 | + | 0.900286i | \(0.356643\pi\) | |||||||
\(728\) | 25.2530 | 0.935940 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.3351 | 0.678612 | ||||||||
\(731\) | −17.1904 | −0.635809 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.7297 | −0.765670 | −0.382835 | − | 0.923817i | \(-0.625052\pi\) | ||||
−0.382835 | + | 0.923817i | \(0.625052\pi\) | |||||||
\(734\) | 55.3904 | 2.04450 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 43.9234 | 1.61904 | ||||||||
\(737\) | 29.6741 | 1.09306 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.7841 | 0.690984 | 0.345492 | − | 0.938422i | \(-0.387712\pi\) | ||||
0.345492 | + | 0.938422i | \(0.387712\pi\) | |||||||
\(740\) | −11.7154 | −0.430666 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −21.4667 | −0.788069 | ||||||||
\(743\) | −31.0779 | −1.14014 | −0.570068 | − | 0.821597i | \(-0.693083\pi\) | ||||
−0.570068 | + | 0.821597i | \(0.693083\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.36470 | −0.123273 | ||||||||
\(746\) | −37.9187 | −1.38830 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 45.2233 | 1.65353 | ||||||||
\(749\) | −17.2948 | −0.631939 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.1552 | −0.881435 | −0.440718 | − | 0.897646i | \(-0.645276\pi\) | ||||
−0.440718 | + | 0.897646i | \(0.645276\pi\) | |||||||
\(752\) | 1.84591 | 0.0673136 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 29.8665 | 1.08767 | ||||||||
\(755\) | 1.04148 | 0.0379035 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.915266 | −0.0332659 | −0.0166330 | − | 0.999862i | \(-0.505295\pi\) | ||||
−0.0166330 | + | 0.999862i | \(0.505295\pi\) | |||||||
\(758\) | 4.69728 | 0.170613 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.653522 | −0.0237057 | ||||||||
\(761\) | 20.3847 | 0.738946 | 0.369473 | − | 0.929241i | \(-0.379538\pi\) | ||||
0.369473 | + | 0.929241i | \(0.379538\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.8646 | 0.538136 | ||||||||
\(764\) | −71.0232 | −2.56953 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.7738 | −1.18416 | ||||||||
\(767\) | 11.5195 | 0.415945 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.5892 | 0.814589 | 0.407294 | − | 0.913297i | \(-0.366472\pi\) | ||||
0.407294 | + | 0.913297i | \(0.366472\pi\) | |||||||
\(770\) | −25.3711 | −0.914311 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.5351 | −0.739075 | ||||||||
\(773\) | 1.67594 | 0.0602793 | 0.0301396 | − | 0.999546i | \(-0.490405\pi\) | ||||
0.0301396 | + | 0.999546i | \(0.490405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.6793 | −0.491374 | ||||||||
\(776\) | −29.2536 | −1.05014 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.0702 | −1.00636 | ||||||||
\(779\) | 1.52441 | 0.0546177 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0971 | 0.504433 | ||||||||
\(782\) | −47.7987 | −1.70928 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.10638 | −0.0752277 | ||||||||
\(785\) | 5.58065 | 0.199182 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.3700 | −1.11822 | −0.559109 | − | 0.829094i | \(-0.688857\pi\) | ||||
−0.559109 | + | 0.829094i | \(0.688857\pi\) | |||||||
\(788\) | −17.5625 | −0.625637 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.7740 | −0.596792 | ||||||||
\(791\) | 49.6679 | 1.76599 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.3268 | −1.00591 | ||||||||
\(794\) | −43.5946 | −1.54711 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −53.3037 | −1.88930 | ||||||||
\(797\) | −47.2210 | −1.67265 | −0.836326 | − | 0.548232i | \(-0.815301\pi\) | ||||
−0.836326 | + | 0.548232i | \(0.815301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.8102 | −0.665459 | ||||||||
\(800\) | −27.7973 | −0.982783 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.9340 | 0.809828 | ||||||||
\(803\) | −68.5410 | −2.41876 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.4472 | 0.579689 | ||||||||
\(806\) | 16.6119 | 0.585131 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.72973 | −0.166391 | ||||||||
\(809\) | −15.1675 | −0.533260 | −0.266630 | − | 0.963799i | \(-0.585910\pi\) | ||||
−0.266630 | + | 0.963799i | \(0.585910\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.5509 | 1.24836 | 0.624181 | − | 0.781280i | \(-0.285433\pi\) | ||||
0.624181 | + | 0.781280i | \(0.285433\pi\) | |||||||
\(812\) | 63.8457 | 2.24055 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 71.4044 | 2.50272 | ||||||||
\(815\) | 4.33480 | 0.151841 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.51273 | −0.0879095 | ||||||||
\(818\) | 7.86987 | 0.275164 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.79650 | 0.237344 | ||||||||
\(821\) | 12.0520 | 0.420616 | 0.210308 | − | 0.977635i | \(-0.432553\pi\) | ||||
0.210308 | + | 0.977635i | \(0.432553\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.6728 | 1.27833 | 0.639167 | − | 0.769068i | \(-0.279279\pi\) | ||||
0.639167 | + | 0.769068i | \(0.279279\pi\) | |||||||
\(824\) | −46.9252 | −1.63472 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 40.1496 | 1.39698 | ||||||||
\(827\) | 46.7729 | 1.62645 | 0.813227 | − | 0.581946i | \(-0.197709\pi\) | ||||
0.813227 | + | 0.581946i | \(0.197709\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.600579 | 0.0208590 | 0.0104295 | − | 0.999946i | \(-0.496680\pi\) | ||||
0.0104295 | + | 0.999946i | \(0.496680\pi\) | |||||||
\(830\) | 2.80051 | 0.0972072 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 32.3628 | 1.12198 | ||||||||
\(833\) | 21.4644 | 0.743698 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.67228 | 0.0924780 | ||||||||
\(836\) | 6.61033 | 0.228623 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.2590 | 0.458024 | ||||||||
\(839\) | 43.3323 | 1.49600 | 0.747998 | − | 0.663701i | \(-0.231015\pi\) | ||||
0.747998 | + | 0.663701i | \(0.231015\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.09334 | −0.0377015 | ||||||||
\(842\) | −87.6871 | −3.02190 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.2698 | −0.835402 | ||||||||
\(845\) | −4.00271 | −0.137697 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 52.9378 | 1.81896 | ||||||||
\(848\) | −0.694631 | −0.0238537 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.2498 | 1.03756 | ||||||||
\(851\) | −46.2891 | −1.58677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.7838 | 0.437708 | 0.218854 | − | 0.975758i | \(-0.429768\pi\) | ||||
0.218854 | + | 0.975758i | \(0.429768\pi\) | |||||||
\(854\) | −98.7291 | −3.37844 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.1057 | 0.413763 | ||||||||
\(857\) | −19.3404 | −0.660655 | −0.330327 | − | 0.943866i | \(-0.607159\pi\) | ||||
−0.330327 | + | 0.943866i | \(0.607159\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.4521 | 0.902535 | 0.451268 | − | 0.892389i | \(-0.350972\pi\) | ||||
0.451268 | + | 0.892389i | \(0.350972\pi\) | |||||||
\(860\) | −11.2029 | −0.382015 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.459916 | 0.0156648 | ||||||||
\(863\) | −3.26295 | −0.111072 | −0.0555360 | − | 0.998457i | \(-0.517687\pi\) | ||||
−0.0555360 | + | 0.998457i | \(0.517687\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.73151 | −0.0928741 | ||||||||
\(866\) | 18.3337 | 0.623004 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 35.5114 | 1.20534 | ||||||||
\(869\) | 62.7053 | 2.12713 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.7841 | −0.500940 | ||||||||
\(872\) | −10.4046 | −0.352345 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.98678 | −0.236331 | ||||||||
\(875\) | −21.5876 | −0.729795 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.1459 | −1.35563 | −0.677815 | − | 0.735233i | \(-0.737073\pi\) | ||||
−0.677815 | + | 0.735233i | \(0.737073\pi\) | |||||||
\(878\) | 4.97149 | 0.167780 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.820971 | −0.0276749 | ||||||||
\(881\) | 45.4262 | 1.53045 | 0.765223 | − | 0.643765i | \(-0.222629\pi\) | ||||
0.765223 | + | 0.643765i | \(0.222629\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.8695 | −1.00519 | −0.502594 | − | 0.864523i | \(-0.667621\pi\) | ||||
−0.502594 | + | 0.864523i | \(0.667621\pi\) | |||||||
\(884\) | −22.5310 | −0.757798 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 73.5927 | 2.47240 | ||||||||
\(887\) | −27.8682 | −0.935722 | −0.467861 | − | 0.883802i | \(-0.654975\pi\) | ||||
−0.467861 | + | 0.883802i | \(0.654975\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.2139 | −1.04688 | ||||||||
\(890\) | 0.461102 | 0.0154562 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −26.8317 | −0.898391 | ||||||||
\(893\) | −2.74951 | −0.0920089 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.03807 | 0.0681250 | ||||||||
\(896\) | 67.3035 | 2.24845 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −88.3870 | −2.94951 | ||||||||
\(899\) | 15.5219 | 0.517683 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.07843 | 0.235817 | ||||||||
\(902\) | −41.4242 | −1.37927 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34.7655 | −1.15628 | ||||||||
\(905\) | −8.97480 | −0.298333 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.5554 | −0.914963 | −0.457481 | − | 0.889219i | \(-0.651248\pi\) | ||||
−0.457481 | + | 0.889219i | \(0.651248\pi\) | |||||||
\(908\) | −84.8295 | −2.81517 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.6403 | 0.419022 | ||||||||
\(911\) | 6.14871 | 0.203716 | 0.101858 | − | 0.994799i | \(-0.467521\pi\) | ||||
0.101858 | + | 0.994799i | \(0.467521\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.4690 | −0.346473 | ||||||||
\(914\) | 67.1499 | 2.22112 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.76695 | −0.322709 | ||||||||
\(917\) | 6.61228 | 0.218357 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.7617 | 0.552917 | 0.276459 | − | 0.961026i | \(-0.410839\pi\) | ||||
0.276459 | + | 0.961026i | \(0.410839\pi\) | |||||||
\(920\) | −11.5124 | −0.379552 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −48.9529 | −1.61218 | ||||||||
\(923\) | −7.02339 | −0.231178 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.2945 | 0.963196 | ||||||||
\(926\) | 79.4644 | 2.61136 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 31.5416 | 1.03540 | ||||||||
\(929\) | −54.8425 | −1.79933 | −0.899663 | − | 0.436586i | \(-0.856188\pi\) | ||||
−0.899663 | + | 0.436586i | \(0.856188\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.13747 | 0.102827 | ||||||||
\(932\) | 22.5401 | 0.738325 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 57.1113 | 1.86874 | ||||||||
\(935\) | 8.36586 | 0.273593 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.1436 | 0.494719 | 0.247359 | − | 0.968924i | \(-0.420437\pi\) | ||||
0.247359 | + | 0.968924i | \(0.420437\pi\) | |||||||
\(938\) | −51.5279 | −1.68245 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.2585 | −0.399829 | ||||||||
\(941\) | 20.8740 | 0.680473 | 0.340237 | − | 0.940340i | \(-0.389493\pi\) | ||||
0.340237 | + | 0.940340i | \(0.389493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.8539 | 0.874484 | ||||||||
\(944\) | 1.29918 | 0.0422847 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 68.2807 | 2.22000 | ||||||||
\(947\) | −50.6227 | −1.64502 | −0.822509 | − | 0.568752i | \(-0.807426\pi\) | ||||
−0.822509 | + | 0.568752i | \(0.807426\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.1483 | 1.10850 | ||||||||
\(950\) | 4.42165 | 0.143457 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29.0223 | −0.940619 | ||||||||
\(953\) | −54.4936 | −1.76522 | −0.882610 | − | 0.470107i | \(-0.844215\pi\) | ||||
−0.882610 | + | 0.470107i | \(0.844215\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.1386 | −0.425155 | ||||||||
\(956\) | −14.5490 | −0.470549 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.3153 | 0.720976 | ||||||||
\(959\) | 10.4689 | 0.338058 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.3666 | −0.721505 | ||||||||
\(962\) | −35.5748 | −1.14698 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.5338 | 0.629143 | ||||||||
\(965\) | −3.79879 | −0.122288 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.1758 | 1.32412 | 0.662062 | − | 0.749449i | \(-0.269682\pi\) | ||||
0.662062 | + | 0.749449i | \(0.269682\pi\) | |||||||
\(968\) | −37.0542 | −1.19097 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.6428 | −0.470151 | ||||||||
\(971\) | −9.59297 | −0.307853 | −0.153927 | − | 0.988082i | \(-0.549192\pi\) | ||||
−0.153927 | + | 0.988082i | \(0.549192\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.9685 | 1.05692 | ||||||||
\(974\) | 38.7355 | 1.24117 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.19473 | −0.102261 | ||||||||
\(977\) | 15.0831 | 0.482551 | 0.241276 | − | 0.970457i | \(-0.422434\pi\) | ||||
0.241276 | + | 0.970457i | \(0.422434\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.72371 | −0.0550901 | ||||||||
\(980\) | 13.9882 | 0.446838 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.1255 | 0.610319 | ||||||||
\(983\) | −56.0198 | −1.78675 | −0.893377 | − | 0.449307i | \(-0.851671\pi\) | ||||
−0.893377 | + | 0.449307i | \(0.851671\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.24889 | −0.103518 | ||||||||
\(986\) | −34.3244 | −1.09311 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.29337 | −0.104776 | ||||||||
\(989\) | −44.2641 | −1.40752 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.1880 | 0.609527 | 0.304763 | − | 0.952428i | \(-0.401423\pi\) | ||||
0.304763 | + | 0.952428i | \(0.401423\pi\) | |||||||
\(992\) | 17.5436 | 0.557010 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −24.4790 | −0.776428 | ||||||||
\(995\) | −9.86065 | −0.312604 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.1559 | 1.01839 | 0.509195 | − | 0.860651i | \(-0.329943\pi\) | ||||
0.509195 | + | 0.860651i | \(0.329943\pi\) | |||||||
\(998\) | −54.9537 | −1.73953 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6561.2.a.d.1.5 | 72 | ||
3.2 | odd | 2 | 6561.2.a.c.1.68 | 72 | |||
81.2 | odd | 54 | 81.2.g.a.4.1 | ✓ | 144 | ||
81.13 | even | 27 | 729.2.g.b.541.1 | 144 | |||
81.14 | odd | 54 | 729.2.g.d.55.8 | 144 | |||
81.25 | even | 27 | 729.2.g.b.190.1 | 144 | |||
81.29 | odd | 54 | 729.2.g.d.676.8 | 144 | |||
81.40 | even | 27 | 243.2.g.a.19.8 | 144 | |||
81.41 | odd | 54 | 81.2.g.a.61.1 | yes | 144 | ||
81.52 | even | 27 | 729.2.g.a.676.1 | 144 | |||
81.56 | odd | 54 | 729.2.g.c.190.8 | 144 | |||
81.67 | even | 27 | 729.2.g.a.55.1 | 144 | |||
81.68 | odd | 54 | 729.2.g.c.541.8 | 144 | |||
81.79 | even | 27 | 243.2.g.a.64.8 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.4.1 | ✓ | 144 | 81.2 | odd | 54 | ||
81.2.g.a.61.1 | yes | 144 | 81.41 | odd | 54 | ||
243.2.g.a.19.8 | 144 | 81.40 | even | 27 | |||
243.2.g.a.64.8 | 144 | 81.79 | even | 27 | |||
729.2.g.a.55.1 | 144 | 81.67 | even | 27 | |||
729.2.g.a.676.1 | 144 | 81.52 | even | 27 | |||
729.2.g.b.190.1 | 144 | 81.25 | even | 27 | |||
729.2.g.b.541.1 | 144 | 81.13 | even | 27 | |||
729.2.g.c.190.8 | 144 | 81.56 | odd | 54 | |||
729.2.g.c.541.8 | 144 | 81.68 | odd | 54 | |||
729.2.g.d.55.8 | 144 | 81.14 | odd | 54 | |||
729.2.g.d.676.8 | 144 | 81.29 | odd | 54 | |||
6561.2.a.c.1.68 | 72 | 3.2 | odd | 2 | |||
6561.2.a.d.1.5 | 72 | 1.1 | even | 1 | trivial |