Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.94436 | −1.37487 | −0.687434 | − | 0.726247i | \(-0.741263\pi\) | ||||
−0.687434 | + | 0.726247i | \(0.741263\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.78053 | 0.890263 | ||||||||
\(5\) | −1.34248 | −0.600374 | −0.300187 | − | 0.953880i | \(-0.597049\pi\) | ||||
−0.300187 | + | 0.953880i | \(0.597049\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.426737 | 0.150874 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.61025 | 0.825435 | ||||||||
\(11\) | 0.671920 | 0.202591 | 0.101296 | − | 0.994856i | \(-0.467701\pi\) | ||||
0.101296 | + | 0.994856i | \(0.467701\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.12397 | −0.589084 | −0.294542 | − | 0.955639i | \(-0.595167\pi\) | ||||
−0.294542 | + | 0.955639i | \(0.595167\pi\) | |||||||
\(14\) | −1.94436 | −0.519651 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.39078 | −1.09769 | ||||||||
\(17\) | −1.91283 | −0.463930 | −0.231965 | − | 0.972724i | \(-0.574515\pi\) | ||||
−0.231965 | + | 0.972724i | \(0.574515\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.48056 | −1.02791 | −0.513956 | − | 0.857817i | \(-0.671821\pi\) | ||||
−0.513956 | + | 0.857817i | \(0.671821\pi\) | |||||||
\(20\) | −2.39031 | −0.534490 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.30645 | −0.278537 | ||||||||
\(23\) | 4.40373 | 0.918241 | 0.459121 | − | 0.888374i | \(-0.348165\pi\) | ||||
0.459121 | + | 0.888374i | \(0.348165\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.19776 | −0.639551 | ||||||||
\(26\) | 4.12976 | 0.809913 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.78053 | 0.336488 | ||||||||
\(29\) | 2.36148 | 0.438516 | 0.219258 | − | 0.975667i | \(-0.429636\pi\) | ||||
0.219258 | + | 0.975667i | \(0.429636\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.43789 | 0.258253 | 0.129126 | − | 0.991628i | \(-0.458783\pi\) | ||||
0.129126 | + | 0.991628i | \(0.458783\pi\) | |||||||
\(32\) | 7.68377 | 1.35831 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.71923 | 0.637842 | ||||||||
\(35\) | −1.34248 | −0.226920 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.60291 | 0.921113 | 0.460556 | − | 0.887630i | \(-0.347650\pi\) | ||||
0.460556 | + | 0.887630i | \(0.347650\pi\) | |||||||
\(38\) | 8.71182 | 1.41324 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.572884 | −0.0905809 | ||||||||
\(41\) | 4.45855 | 0.696308 | 0.348154 | − | 0.937437i | \(-0.386809\pi\) | ||||
0.348154 | + | 0.937437i | \(0.386809\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.18323 | −1.24793 | −0.623965 | − | 0.781452i | \(-0.714479\pi\) | ||||
−0.623965 | + | 0.781452i | \(0.714479\pi\) | |||||||
\(44\) | 1.19637 | 0.180360 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.56242 | −1.26246 | ||||||||
\(47\) | 13.1888 | 1.92378 | 0.961889 | − | 0.273440i | \(-0.0881614\pi\) | ||||
0.961889 | + | 0.273440i | \(0.0881614\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.21758 | 0.879299 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.78179 | −0.524439 | ||||||||
\(53\) | −11.7277 | −1.61093 | −0.805464 | − | 0.592644i | \(-0.798084\pi\) | ||||
−0.805464 | + | 0.592644i | \(0.798084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.902037 | −0.121631 | ||||||||
\(56\) | 0.426737 | 0.0570251 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.59157 | −0.602902 | ||||||||
\(59\) | 7.06826 | 0.920209 | 0.460104 | − | 0.887865i | \(-0.347812\pi\) | ||||
0.460104 | + | 0.887865i | \(0.347812\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.58432 | 0.458925 | 0.229462 | − | 0.973318i | \(-0.426303\pi\) | ||||
0.229462 | + | 0.973318i | \(0.426303\pi\) | |||||||
\(62\) | −2.79577 | −0.355063 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.15844 | −0.769805 | ||||||||
\(65\) | 2.85138 | 0.353671 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.70366 | 0.208135 | 0.104068 | − | 0.994570i | \(-0.466814\pi\) | ||||
0.104068 | + | 0.994570i | \(0.466814\pi\) | |||||||
\(68\) | −3.40584 | −0.413019 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.61025 | 0.311985 | ||||||||
\(71\) | 5.36282 | 0.636450 | 0.318225 | − | 0.948015i | \(-0.396913\pi\) | ||||
0.318225 | + | 0.948015i | \(0.396913\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.516847 | −0.0604924 | −0.0302462 | − | 0.999542i | \(-0.509629\pi\) | ||||
−0.0302462 | + | 0.999542i | \(0.509629\pi\) | |||||||
\(74\) | −10.8941 | −1.26641 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.97776 | −0.915112 | ||||||||
\(77\) | 0.671920 | 0.0765724 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.93892 | −0.780689 | −0.390345 | − | 0.920669i | \(-0.627644\pi\) | ||||
−0.390345 | + | 0.920669i | \(0.627644\pi\) | |||||||
\(80\) | 5.89452 | 0.659027 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.66901 | −0.957332 | ||||||||
\(83\) | 8.45270 | 0.927805 | 0.463902 | − | 0.885886i | \(-0.346449\pi\) | ||||
0.463902 | + | 0.885886i | \(0.346449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.56793 | 0.278531 | ||||||||
\(86\) | 15.9111 | 1.71574 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.286733 | 0.0305658 | ||||||||
\(89\) | −13.3759 | −1.41784 | −0.708922 | − | 0.705287i | \(-0.750818\pi\) | ||||
−0.708922 | + | 0.705287i | \(0.750818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.12397 | −0.222653 | ||||||||
\(92\) | 7.84095 | 0.817476 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −25.6437 | −2.64494 | ||||||||
\(95\) | 6.01505 | 0.617131 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9250 | −1.31233 | −0.656166 | − | 0.754617i | \(-0.727823\pi\) | ||||
−0.656166 | + | 0.754617i | \(0.727823\pi\) | |||||||
\(98\) | −1.94436 | −0.196410 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.69369 | −0.569369 | ||||||||
\(101\) | −3.29760 | −0.328123 | −0.164062 | − | 0.986450i | \(-0.552460\pi\) | ||||
−0.164062 | + | 0.986450i | \(0.552460\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.91791 | −0.780175 | −0.390088 | − | 0.920778i | \(-0.627555\pi\) | ||||
−0.390088 | + | 0.920778i | \(0.627555\pi\) | |||||||
\(104\) | −0.906377 | −0.0888776 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.8029 | 2.21481 | ||||||||
\(107\) | −1.84047 | −0.177925 | −0.0889626 | − | 0.996035i | \(-0.528355\pi\) | ||||
−0.0889626 | + | 0.996035i | \(0.528355\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.4450 | 1.47936 | 0.739680 | − | 0.672959i | \(-0.234977\pi\) | ||||
0.739680 | + | 0.672959i | \(0.234977\pi\) | |||||||
\(110\) | 1.75388 | 0.167226 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.39078 | −0.414890 | ||||||||
\(113\) | −10.5350 | −0.991053 | −0.495527 | − | 0.868593i | \(-0.665025\pi\) | ||||
−0.495527 | + | 0.868593i | \(0.665025\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.91190 | −0.551288 | ||||||||
\(116\) | 4.20468 | 0.390395 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.7432 | −1.26517 | ||||||||
\(119\) | −1.91283 | −0.175349 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5485 | −0.958957 | ||||||||
\(122\) | −6.96919 | −0.630961 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.56020 | 0.229913 | ||||||||
\(125\) | 11.0053 | 0.984344 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −3.39334 | −0.299932 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.54411 | −0.486250 | ||||||||
\(131\) | −21.6997 | −1.89591 | −0.947957 | − | 0.318398i | \(-0.896855\pi\) | ||||
−0.947957 | + | 0.318398i | \(0.896855\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.48056 | −0.388514 | ||||||||
\(134\) | −3.31253 | −0.286159 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.816275 | −0.0699950 | ||||||||
\(137\) | 8.54803 | 0.730307 | 0.365154 | − | 0.930947i | \(-0.381016\pi\) | ||||
0.365154 | + | 0.930947i | \(0.381016\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.4438 | −0.970651 | −0.485326 | − | 0.874334i | \(-0.661299\pi\) | ||||
−0.485326 | + | 0.874334i | \(0.661299\pi\) | |||||||
\(140\) | −2.39031 | −0.202018 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.4272 | −0.875035 | ||||||||
\(143\) | −1.42714 | −0.119343 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.17024 | −0.263274 | ||||||||
\(146\) | 1.00494 | 0.0831690 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.97613 | 0.820033 | ||||||||
\(149\) | 6.76371 | 0.554104 | 0.277052 | − | 0.960855i | \(-0.410642\pi\) | ||||
0.277052 | + | 0.960855i | \(0.410642\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0326 | 0.979196 | 0.489598 | − | 0.871948i | \(-0.337144\pi\) | ||||
0.489598 | + | 0.871948i | \(0.337144\pi\) | |||||||
\(152\) | −1.91202 | −0.155085 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.30645 | −0.105277 | ||||||||
\(155\) | −1.93033 | −0.155048 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.4980 | 1.55611 | 0.778055 | − | 0.628196i | \(-0.216207\pi\) | ||||
0.778055 | + | 0.628196i | \(0.216207\pi\) | |||||||
\(158\) | 13.4917 | 1.07334 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.3153 | −0.815495 | ||||||||
\(161\) | 4.40373 | 0.347063 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.06631 | −0.475150 | −0.237575 | − | 0.971369i | \(-0.576353\pi\) | ||||
−0.237575 | + | 0.971369i | \(0.576353\pi\) | |||||||
\(164\) | 7.93855 | 0.619897 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.4351 | −1.27561 | ||||||||
\(167\) | 6.63895 | 0.513738 | 0.256869 | − | 0.966446i | \(-0.417309\pi\) | ||||
0.256869 | + | 0.966446i | \(0.417309\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.48874 | −0.652980 | ||||||||
\(170\) | −4.99297 | −0.382944 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.5704 | −1.11099 | ||||||||
\(173\) | 0.951266 | 0.0723234 | 0.0361617 | − | 0.999346i | \(-0.488487\pi\) | ||||
0.0361617 | + | 0.999346i | \(0.488487\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.19776 | −0.241728 | ||||||||
\(176\) | −2.95025 | −0.222384 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 26.0076 | 1.94935 | ||||||||
\(179\) | 13.7723 | 1.02939 | 0.514696 | − | 0.857373i | \(-0.327905\pi\) | ||||
0.514696 | + | 0.857373i | \(0.327905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3370 | 0.768345 | 0.384173 | − | 0.923261i | \(-0.374487\pi\) | ||||
0.384173 | + | 0.923261i | \(0.374487\pi\) | |||||||
\(182\) | 4.12976 | 0.306118 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.87923 | 0.138539 | ||||||||
\(185\) | −7.52178 | −0.553012 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.28527 | −0.0939882 | ||||||||
\(188\) | 23.4829 | 1.71267 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.6954 | −0.848474 | ||||||||
\(191\) | 19.1142 | 1.38306 | 0.691528 | − | 0.722350i | \(-0.256938\pi\) | ||||
0.691528 | + | 0.722350i | \(0.256938\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.102612 | −0.00738619 | −0.00369309 | − | 0.999993i | \(-0.501176\pi\) | ||||
−0.00369309 | + | 0.999993i | \(0.501176\pi\) | |||||||
\(194\) | 25.1308 | 1.80428 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.78053 | 0.127180 | ||||||||
\(197\) | 3.80038 | 0.270766 | 0.135383 | − | 0.990793i | \(-0.456774\pi\) | ||||
0.135383 | + | 0.990793i | \(0.456774\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2697 | 1.08244 | 0.541219 | − | 0.840881i | \(-0.317963\pi\) | ||||
0.541219 | + | 0.840881i | \(0.317963\pi\) | |||||||
\(200\) | −1.36460 | −0.0964918 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.41171 | 0.451126 | ||||||||
\(203\) | 2.36148 | 0.165744 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.98549 | −0.418045 | ||||||||
\(206\) | 15.3953 | 1.07264 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.32589 | 0.646634 | ||||||||
\(209\) | −3.01058 | −0.208246 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5104 | −1.34315 | −0.671577 | − | 0.740934i | \(-0.734383\pi\) | ||||
−0.671577 | + | 0.740934i | \(0.734383\pi\) | |||||||
\(212\) | −20.8815 | −1.43415 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.57853 | 0.244624 | ||||||||
\(215\) | 10.9858 | 0.749225 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.43789 | 0.0976103 | ||||||||
\(218\) | −30.0305 | −2.03393 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.60610 | −0.108283 | ||||||||
\(221\) | 4.06280 | 0.273293 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.8049 | 1.72802 | 0.864012 | − | 0.503472i | \(-0.167944\pi\) | ||||
0.864012 | + | 0.503472i | \(0.167944\pi\) | |||||||
\(224\) | 7.68377 | 0.513394 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.4839 | 1.36257 | ||||||||
\(227\) | 19.9150 | 1.32181 | 0.660904 | − | 0.750471i | \(-0.270173\pi\) | ||||
0.660904 | + | 0.750471i | \(0.270173\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2646 | −1.14088 | −0.570440 | − | 0.821339i | \(-0.693227\pi\) | ||||
−0.570440 | + | 0.821339i | \(0.693227\pi\) | |||||||
\(230\) | 11.4949 | 0.757948 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00773 | 0.0661608 | ||||||||
\(233\) | −29.8061 | −1.95267 | −0.976333 | − | 0.216275i | \(-0.930609\pi\) | ||||
−0.976333 | + | 0.216275i | \(0.930609\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.7056 | −1.15499 | ||||||||
\(236\) | 12.5852 | 0.819228 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.71923 | 0.241082 | ||||||||
\(239\) | −8.83517 | −0.571500 | −0.285750 | − | 0.958304i | \(-0.592243\pi\) | ||||
−0.285750 | + | 0.958304i | \(0.592243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.377401 | 0.0243106 | 0.0121553 | − | 0.999926i | \(-0.496131\pi\) | ||||
0.0121553 | + | 0.999926i | \(0.496131\pi\) | |||||||
\(242\) | 20.5101 | 1.31844 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.38197 | 0.408564 | ||||||||
\(245\) | −1.34248 | −0.0857677 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.51659 | 0.605526 | ||||||||
\(248\) | 0.613600 | 0.0389637 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −21.3982 | −1.35334 | ||||||||
\(251\) | 11.8270 | 0.746512 | 0.373256 | − | 0.927728i | \(-0.378241\pi\) | ||||
0.373256 | + | 0.927728i | \(0.378241\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.95895 | 0.186028 | ||||||||
\(254\) | −1.94436 | −0.122000 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.9147 | 1.18217 | ||||||||
\(257\) | −23.0339 | −1.43682 | −0.718409 | − | 0.695621i | \(-0.755129\pi\) | ||||
−0.718409 | + | 0.695621i | \(0.755129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.60291 | 0.348148 | ||||||||
\(260\) | 5.07696 | 0.314860 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 42.1920 | 2.60663 | ||||||||
\(263\) | −24.6731 | −1.52141 | −0.760704 | − | 0.649098i | \(-0.775146\pi\) | ||||
−0.760704 | + | 0.649098i | \(0.775146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.7442 | 0.967159 | ||||||||
\(266\) | 8.71182 | 0.534156 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.03341 | 0.185295 | ||||||||
\(269\) | 14.9956 | 0.914298 | 0.457149 | − | 0.889390i | \(-0.348871\pi\) | ||||
0.457149 | + | 0.889390i | \(0.348871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.69915 | 0.589182 | 0.294591 | − | 0.955623i | \(-0.404817\pi\) | ||||
0.294591 | + | 0.955623i | \(0.404817\pi\) | |||||||
\(272\) | 8.39882 | 0.509253 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.6204 | −1.00408 | ||||||||
\(275\) | −2.14864 | −0.129568 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.0320 | −0.722935 | −0.361468 | − | 0.932385i | \(-0.617724\pi\) | ||||
−0.361468 | + | 0.932385i | \(0.617724\pi\) | |||||||
\(278\) | 22.2509 | 1.33452 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.572884 | −0.0342364 | ||||||||
\(281\) | 8.05023 | 0.480237 | 0.240118 | − | 0.970744i | \(-0.422814\pi\) | ||||
0.240118 | + | 0.970744i | \(0.422814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.4524 | 1.33466 | 0.667329 | − | 0.744763i | \(-0.267438\pi\) | ||||
0.667329 | + | 0.744763i | \(0.267438\pi\) | |||||||
\(284\) | 9.54864 | 0.566608 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.77487 | 0.164081 | ||||||||
\(287\) | 4.45855 | 0.263180 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3411 | −0.784769 | ||||||||
\(290\) | 6.16407 | 0.361967 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.920259 | −0.0538541 | ||||||||
\(293\) | −11.9622 | −0.698842 | −0.349421 | − | 0.936966i | \(-0.613622\pi\) | ||||
−0.349421 | + | 0.936966i | \(0.613622\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.48897 | −0.552469 | ||||||||
\(296\) | 2.39097 | 0.138972 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.1511 | −0.761821 | ||||||||
\(299\) | −9.35340 | −0.540921 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.18323 | −0.471674 | ||||||||
\(302\) | −23.3956 | −1.34627 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 19.6732 | 1.12833 | ||||||||
\(305\) | −4.81186 | −0.275526 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.9768 | −1.25428 | −0.627140 | − | 0.778906i | \(-0.715775\pi\) | ||||
−0.627140 | + | 0.778906i | \(0.715775\pi\) | |||||||
\(308\) | 1.19637 | 0.0681695 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.75326 | 0.213171 | ||||||||
\(311\) | −28.3108 | −1.60536 | −0.802678 | − | 0.596413i | \(-0.796592\pi\) | ||||
−0.802678 | + | 0.596413i | \(0.796592\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.01192 | −0.170244 | −0.0851219 | − | 0.996371i | \(-0.527128\pi\) | ||||
−0.0851219 | + | 0.996371i | \(0.527128\pi\) | |||||||
\(314\) | −37.9111 | −2.13945 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.3549 | −0.695019 | ||||||||
\(317\) | −3.65038 | −0.205026 | −0.102513 | − | 0.994732i | \(-0.532688\pi\) | ||||
−0.102513 | + | 0.994732i | \(0.532688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.58673 | 0.0888397 | ||||||||
\(320\) | 8.26756 | 0.462171 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.56242 | −0.477165 | ||||||||
\(323\) | 8.57056 | 0.476879 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.79195 | 0.376749 | ||||||||
\(326\) | 11.7951 | 0.653269 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.90263 | 0.105055 | ||||||||
\(329\) | 13.1888 | 0.727120 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.6291 | −1.46367 | −0.731834 | − | 0.681483i | \(-0.761335\pi\) | ||||
−0.731834 | + | 0.681483i | \(0.761335\pi\) | |||||||
\(332\) | 15.0503 | 0.825990 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.9085 | −0.706322 | ||||||||
\(335\) | −2.28713 | −0.124959 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.2796 | −1.81286 | −0.906429 | − | 0.422359i | \(-0.861202\pi\) | ||||
−0.906429 | + | 0.422359i | \(0.861202\pi\) | |||||||
\(338\) | 16.5051 | 0.897762 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.57227 | 0.247966 | ||||||||
\(341\) | 0.966146 | 0.0523198 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.49208 | −0.188281 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.84960 | −0.0994351 | ||||||||
\(347\) | 30.1843 | 1.62038 | 0.810189 | − | 0.586168i | \(-0.199364\pi\) | ||||
0.810189 | + | 0.586168i | \(0.199364\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0746 | 0.967511 | 0.483756 | − | 0.875203i | \(-0.339272\pi\) | ||||
0.483756 | + | 0.875203i | \(0.339272\pi\) | |||||||
\(350\) | 6.21758 | 0.332344 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.16288 | 0.275182 | ||||||||
\(353\) | 16.5042 | 0.878431 | 0.439216 | − | 0.898382i | \(-0.355256\pi\) | ||||
0.439216 | + | 0.898382i | \(0.355256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.19946 | −0.382108 | ||||||||
\(356\) | −23.8162 | −1.26225 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.7783 | −1.41528 | ||||||||
\(359\) | 10.1195 | 0.534088 | 0.267044 | − | 0.963684i | \(-0.413953\pi\) | ||||
0.267044 | + | 0.963684i | \(0.413953\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.07546 | 0.0566030 | ||||||||
\(362\) | −20.0989 | −1.05637 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.78179 | −0.198219 | ||||||||
\(365\) | 0.693855 | 0.0363180 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.6629 | −1.39179 | −0.695896 | − | 0.718142i | \(-0.744993\pi\) | ||||
−0.695896 | + | 0.718142i | \(0.744993\pi\) | |||||||
\(368\) | −19.3358 | −1.00795 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14.6250 | 0.760319 | ||||||||
\(371\) | −11.7277 | −0.608874 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.4276 | −1.26481 | −0.632406 | − | 0.774637i | \(-0.717932\pi\) | ||||
−0.632406 | + | 0.774637i | \(0.717932\pi\) | |||||||
\(374\) | 2.49902 | 0.129221 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.62813 | 0.290249 | ||||||||
\(377\) | −5.01572 | −0.258323 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.7301 | 1.42440 | 0.712200 | − | 0.701976i | \(-0.247699\pi\) | ||||
0.712200 | + | 0.701976i | \(0.247699\pi\) | |||||||
\(380\) | 10.7100 | 0.549409 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −37.1648 | −1.90152 | ||||||||
\(383\) | 8.00622 | 0.409099 | 0.204549 | − | 0.978856i | \(-0.434427\pi\) | ||||
0.204549 | + | 0.978856i | \(0.434427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.902037 | −0.0459720 | ||||||||
\(386\) | 0.199515 | 0.0101550 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −23.0132 | −1.16832 | ||||||||
\(389\) | 21.3761 | 1.08381 | 0.541906 | − | 0.840439i | \(-0.317703\pi\) | ||||
0.541906 | + | 0.840439i | \(0.317703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.42359 | −0.425999 | ||||||||
\(392\) | 0.426737 | 0.0215535 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.38930 | −0.372268 | ||||||||
\(395\) | 9.31533 | 0.468705 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.45298 | −0.424243 | −0.212122 | − | 0.977243i | \(-0.568037\pi\) | ||||
−0.212122 | + | 0.977243i | \(0.568037\pi\) | |||||||
\(398\) | −29.6897 | −1.48821 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.0406 | 0.702032 | ||||||||
\(401\) | −23.5609 | −1.17657 | −0.588287 | − | 0.808652i | \(-0.700197\pi\) | ||||
−0.588287 | + | 0.808652i | \(0.700197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.05404 | −0.152132 | ||||||||
\(404\) | −5.87146 | −0.292116 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.59157 | −0.227876 | ||||||||
\(407\) | 3.76471 | 0.186610 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.81664 | −0.435955 | −0.217977 | − | 0.975954i | \(-0.569946\pi\) | ||||
−0.217977 | + | 0.975954i | \(0.569946\pi\) | |||||||
\(410\) | 11.6379 | 0.574757 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.0980 | −0.694561 | ||||||||
\(413\) | 7.06826 | 0.347806 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.3476 | −0.557030 | ||||||||
\(416\) | −16.3201 | −0.800160 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.85364 | 0.286311 | ||||||||
\(419\) | −33.1820 | −1.62104 | −0.810522 | − | 0.585708i | \(-0.800817\pi\) | ||||
−0.810522 | + | 0.585708i | \(0.800817\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.0973 | −1.51559 | −0.757795 | − | 0.652493i | \(-0.773723\pi\) | ||||
−0.757795 | + | 0.652493i | \(0.773723\pi\) | |||||||
\(422\) | 37.9353 | 1.84666 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.00466 | −0.243048 | ||||||||
\(425\) | 6.11677 | 0.296707 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.58432 | 0.173457 | ||||||||
\(428\) | −3.27701 | −0.158400 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.3603 | −1.03009 | ||||||||
\(431\) | −28.9047 | −1.39229 | −0.696145 | − | 0.717901i | \(-0.745103\pi\) | ||||
−0.696145 | + | 0.717901i | \(0.745103\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.4141 | 1.46161 | 0.730803 | − | 0.682588i | \(-0.239146\pi\) | ||||
0.730803 | + | 0.682588i | \(0.239146\pi\) | |||||||
\(434\) | −2.79577 | −0.134201 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 27.5002 | 1.31702 | ||||||||
\(437\) | −19.7312 | −0.943871 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.4997 | 0.644303 | 0.322152 | − | 0.946688i | \(-0.395594\pi\) | ||||
0.322152 | + | 0.946688i | \(0.395594\pi\) | |||||||
\(440\) | −0.384932 | −0.0183509 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.89953 | −0.375743 | ||||||||
\(443\) | −18.1731 | −0.863432 | −0.431716 | − | 0.902010i | \(-0.642092\pi\) | ||||
−0.431716 | + | 0.902010i | \(0.642092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.9569 | 0.851237 | ||||||||
\(446\) | −50.1739 | −2.37580 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.15844 | −0.290959 | ||||||||
\(449\) | −4.42578 | −0.208865 | −0.104433 | − | 0.994532i | \(-0.533303\pi\) | ||||
−0.104433 | + | 0.994532i | \(0.533303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.99579 | 0.141066 | ||||||||
\(452\) | −18.7579 | −0.882298 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −38.7219 | −1.81731 | ||||||||
\(455\) | 2.85138 | 0.133675 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.9525 | 0.980116 | 0.490058 | − | 0.871690i | \(-0.336976\pi\) | ||||
0.490058 | + | 0.871690i | \(0.336976\pi\) | |||||||
\(458\) | 33.5686 | 1.56856 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.5263 | −0.490791 | ||||||||
\(461\) | 30.2835 | 1.41044 | 0.705222 | − | 0.708986i | \(-0.250847\pi\) | ||||
0.705222 | + | 0.708986i | \(0.250847\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2977 | 1.12921 | 0.564606 | − | 0.825361i | \(-0.309028\pi\) | ||||
0.564606 | + | 0.825361i | \(0.309028\pi\) | |||||||
\(464\) | −10.3688 | −0.481357 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 57.9538 | 2.68466 | ||||||||
\(467\) | −1.83190 | −0.0847703 | −0.0423852 | − | 0.999101i | \(-0.513496\pi\) | ||||
−0.0423852 | + | 0.999101i | \(0.513496\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.70366 | 0.0786678 | ||||||||
\(470\) | 34.4260 | 1.58795 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.01629 | 0.138836 | ||||||||
\(473\) | −5.49847 | −0.252820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.3278 | 0.657402 | ||||||||
\(476\) | −3.40584 | −0.156107 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.1787 | 0.785737 | ||||||||
\(479\) | −30.4527 | −1.39142 | −0.695711 | − | 0.718322i | \(-0.744910\pi\) | ||||
−0.695711 | + | 0.718322i | \(0.744910\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.9004 | −0.542613 | ||||||||
\(482\) | −0.733803 | −0.0334238 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.7819 | −0.853723 | ||||||||
\(485\) | 17.3515 | 0.787890 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.6116 | −1.16057 | −0.580286 | − | 0.814413i | \(-0.697059\pi\) | ||||
−0.580286 | + | 0.814413i | \(0.697059\pi\) | |||||||
\(488\) | 1.52956 | 0.0692399 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.61025 | 0.117919 | ||||||||
\(491\) | −25.2765 | −1.14071 | −0.570356 | − | 0.821398i | \(-0.693195\pi\) | ||||
−0.570356 | + | 0.821398i | \(0.693195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.51712 | −0.203441 | ||||||||
\(494\) | −18.5037 | −0.832519 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.31346 | −0.283483 | ||||||||
\(497\) | 5.36282 | 0.240555 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.6164 | −0.699088 | −0.349544 | − | 0.936920i | \(-0.613663\pi\) | ||||
−0.349544 | + | 0.936920i | \(0.613663\pi\) | |||||||
\(500\) | 19.5952 | 0.876325 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.9959 | −1.02636 | ||||||||
\(503\) | 6.09933 | 0.271956 | 0.135978 | − | 0.990712i | \(-0.456582\pi\) | ||||
0.135978 | + | 0.990712i | \(0.456582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.42695 | 0.196997 | ||||||||
\(506\) | −5.75326 | −0.255764 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.78053 | 0.0789980 | ||||||||
\(509\) | 0.424702 | 0.0188246 | 0.00941230 | − | 0.999956i | \(-0.497004\pi\) | ||||
0.00941230 | + | 0.999956i | \(0.497004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.516847 | −0.0228640 | ||||||||
\(512\) | −29.9903 | −1.32540 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 44.7862 | 1.97543 | ||||||||
\(515\) | 10.6296 | 0.468397 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.86179 | 0.389741 | ||||||||
\(518\) | −10.8941 | −0.478658 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.21679 | 0.0533598 | ||||||||
\(521\) | 32.4537 | 1.42182 | 0.710912 | − | 0.703281i | \(-0.248282\pi\) | ||||
0.710912 | + | 0.703281i | \(0.248282\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.7148 | −1.91151 | −0.955757 | − | 0.294156i | \(-0.904961\pi\) | ||||
−0.955757 | + | 0.294156i | \(0.904961\pi\) | |||||||
\(524\) | −38.6369 | −1.68786 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 47.9733 | 2.09174 | ||||||||
\(527\) | −2.75044 | −0.119811 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.60717 | −0.156833 | ||||||||
\(530\) | −30.6124 | −1.32972 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.97776 | −0.345880 | ||||||||
\(533\) | −9.46983 | −0.410184 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.47079 | 0.106822 | ||||||||
\(536\) | 0.727015 | 0.0314023 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.1568 | −1.25704 | ||||||||
\(539\) | 0.671920 | 0.0289416 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.6352 | −1.23113 | −0.615563 | − | 0.788088i | \(-0.711071\pi\) | ||||
−0.615563 | + | 0.788088i | \(0.711071\pi\) | |||||||
\(542\) | −18.8586 | −0.810047 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.6978 | −0.630161 | ||||||||
\(545\) | −20.7345 | −0.888169 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1793 | 1.33313 | 0.666565 | − | 0.745447i | \(-0.267764\pi\) | ||||
0.666565 | + | 0.745447i | \(0.267764\pi\) | |||||||
\(548\) | 15.2200 | 0.650165 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.17772 | 0.178138 | ||||||||
\(551\) | −10.5808 | −0.450756 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.93892 | −0.295073 | ||||||||
\(554\) | 23.3946 | 0.993941 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.3760 | −0.864134 | ||||||||
\(557\) | 21.4442 | 0.908618 | 0.454309 | − | 0.890844i | \(-0.349886\pi\) | ||||
0.454309 | + | 0.890844i | \(0.349886\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.3810 | 0.735136 | ||||||||
\(560\) | 5.89452 | 0.249089 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.6525 | −0.660262 | ||||||||
\(563\) | −3.29577 | −0.138900 | −0.0694500 | − | 0.997585i | \(-0.522124\pi\) | ||||
−0.0694500 | + | 0.997585i | \(0.522124\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.1430 | 0.595002 | ||||||||
\(566\) | −43.6555 | −1.83498 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.28851 | 0.0960239 | ||||||||
\(569\) | 8.46859 | 0.355022 | 0.177511 | − | 0.984119i | \(-0.443195\pi\) | ||||
0.177511 | + | 0.984119i | \(0.443195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.9586 | −1.17003 | −0.585016 | − | 0.811021i | \(-0.698912\pi\) | ||||
−0.585016 | + | 0.811021i | \(0.698912\pi\) | |||||||
\(572\) | −2.54106 | −0.106247 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.66901 | −0.361837 | ||||||||
\(575\) | −14.0821 | −0.587262 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.0599 | −0.668583 | −0.334292 | − | 0.942470i | \(-0.608497\pi\) | ||||
−0.334292 | + | 0.942470i | \(0.608497\pi\) | |||||||
\(578\) | 25.9398 | 1.07895 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.64469 | −0.234383 | ||||||||
\(581\) | 8.45270 | 0.350677 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.88010 | −0.326360 | ||||||||
\(584\) | −0.220558 | −0.00912674 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.2589 | 0.960816 | ||||||||
\(587\) | 41.1062 | 1.69664 | 0.848318 | − | 0.529487i | \(-0.177616\pi\) | ||||
0.848318 | + | 0.529487i | \(0.177616\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.44256 | −0.265461 | ||||||||
\(590\) | 18.4500 | 0.759573 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.6012 | −1.01110 | ||||||||
\(593\) | −35.2860 | −1.44902 | −0.724511 | − | 0.689263i | \(-0.757934\pi\) | ||||
−0.724511 | + | 0.689263i | \(0.757934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.56793 | 0.105275 | ||||||||
\(596\) | 12.0430 | 0.493299 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 18.1863 | 0.743695 | ||||||||
\(599\) | 19.8649 | 0.811656 | 0.405828 | − | 0.913949i | \(-0.366983\pi\) | ||||
0.405828 | + | 0.913949i | \(0.366983\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.83491 | −0.197220 | −0.0986101 | − | 0.995126i | \(-0.531440\pi\) | ||||
−0.0986101 | + | 0.995126i | \(0.531440\pi\) | |||||||
\(602\) | 15.9111 | 0.648489 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.4243 | 0.871742 | ||||||||
\(605\) | 14.1611 | 0.575732 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.91972 | −0.402629 | −0.201315 | − | 0.979527i | \(-0.564521\pi\) | ||||
−0.201315 | + | 0.979527i | \(0.564521\pi\) | |||||||
\(608\) | −34.4276 | −1.39622 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.35598 | 0.378812 | ||||||||
\(611\) | −28.0126 | −1.13327 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.74214 | −0.191533 | −0.0957666 | − | 0.995404i | \(-0.530530\pi\) | ||||
−0.0957666 | + | 0.995404i | \(0.530530\pi\) | |||||||
\(614\) | 42.7307 | 1.72447 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.286733 | 0.0115528 | ||||||||
\(617\) | −21.7621 | −0.876109 | −0.438055 | − | 0.898948i | \(-0.644332\pi\) | ||||
−0.438055 | + | 0.898948i | \(0.644332\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.52363 | 0.382787 | 0.191394 | − | 0.981513i | \(-0.438699\pi\) | ||||
0.191394 | + | 0.981513i | \(0.438699\pi\) | |||||||
\(620\) | −3.43701 | −0.138034 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 55.0462 | 2.20715 | ||||||||
\(623\) | −13.3759 | −0.535895 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.21443 | 0.0485772 | ||||||||
\(626\) | 5.85625 | 0.234063 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 34.7167 | 1.38535 | ||||||||
\(629\) | −10.7174 | −0.427332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.7939 | −0.907412 | −0.453706 | − | 0.891151i | \(-0.649898\pi\) | ||||
−0.453706 | + | 0.891151i | \(0.649898\pi\) | |||||||
\(632\) | −2.96109 | −0.117786 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.09765 | 0.281884 | ||||||||
\(635\) | −1.34248 | −0.0532746 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.12397 | −0.0841548 | ||||||||
\(638\) | −3.08517 | −0.122143 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.55548 | 0.180071 | ||||||||
\(641\) | −26.6372 | −1.05211 | −0.526053 | − | 0.850452i | \(-0.676329\pi\) | ||||
−0.526053 | + | 0.850452i | \(0.676329\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.6748 | 0.618155 | 0.309077 | − | 0.951037i | \(-0.399980\pi\) | ||||
0.309077 | + | 0.951037i | \(0.399980\pi\) | |||||||
\(644\) | 7.84095 | 0.308977 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.6642 | −0.655646 | ||||||||
\(647\) | −27.0353 | −1.06287 | −0.531433 | − | 0.847100i | \(-0.678346\pi\) | ||||
−0.531433 | + | 0.847100i | \(0.678346\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.74930 | 0.186426 | ||||||||
\(650\) | −13.2060 | −0.517981 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.8012 | −0.423009 | ||||||||
\(653\) | −13.7013 | −0.536174 | −0.268087 | − | 0.963395i | \(-0.586391\pi\) | ||||
−0.268087 | + | 0.963395i | \(0.586391\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.1314 | 1.13826 | ||||||||
\(656\) | −19.5765 | −0.764334 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −25.6437 | −0.999694 | ||||||||
\(659\) | 5.11654 | 0.199312 | 0.0996560 | − | 0.995022i | \(-0.468226\pi\) | ||||
0.0996560 | + | 0.995022i | \(0.468226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.8743 | −0.773022 | −0.386511 | − | 0.922285i | \(-0.626320\pi\) | ||||
−0.386511 | + | 0.922285i | \(0.626320\pi\) | |||||||
\(662\) | 51.7765 | 2.01235 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.60708 | 0.139982 | ||||||||
\(665\) | 6.01505 | 0.233254 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.3993 | 0.402664 | ||||||||
\(668\) | 11.8208 | 0.457361 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.44699 | 0.171802 | ||||||||
\(671\) | 2.40837 | 0.0929742 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.6067 | −0.485951 | −0.242975 | − | 0.970032i | \(-0.578123\pi\) | ||||
−0.242975 | + | 0.970032i | \(0.578123\pi\) | |||||||
\(674\) | 64.7075 | 2.49244 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.1144 | −0.581324 | ||||||||
\(677\) | −44.6723 | −1.71690 | −0.858449 | − | 0.512899i | \(-0.828571\pi\) | ||||
−0.858449 | + | 0.512899i | \(0.828571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.9250 | −0.496015 | ||||||||
\(680\) | 1.09583 | 0.0420232 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.87853 | −0.0719328 | ||||||||
\(683\) | 38.3924 | 1.46905 | 0.734523 | − | 0.678584i | \(-0.237406\pi\) | ||||
0.734523 | + | 0.678584i | \(0.237406\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.4755 | −0.438457 | ||||||||
\(686\) | −1.94436 | −0.0742359 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 35.9308 | 1.36985 | ||||||||
\(689\) | 24.9094 | 0.948972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.4516 | 1.38668 | 0.693342 | − | 0.720608i | \(-0.256137\pi\) | ||||
0.693342 | + | 0.720608i | \(0.256137\pi\) | |||||||
\(692\) | 1.69375 | 0.0643868 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −58.6891 | −2.22781 | ||||||||
\(695\) | 15.3630 | 0.582753 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.52844 | −0.323038 | ||||||||
\(698\) | −35.1435 | −1.33020 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.69369 | −0.215201 | ||||||||
\(701\) | −37.4865 | −1.41585 | −0.707923 | − | 0.706289i | \(-0.750368\pi\) | ||||
−0.707923 | + | 0.706289i | \(0.750368\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.1042 | −0.946823 | ||||||||
\(704\) | −4.13798 | −0.155956 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −32.0901 | −1.20773 | ||||||||
\(707\) | −3.29760 | −0.124019 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.0970 | 1.69365 | 0.846827 | − | 0.531869i | \(-0.178510\pi\) | ||||
0.846827 | + | 0.531869i | \(0.178510\pi\) | |||||||
\(710\) | 13.9983 | 0.525348 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.70800 | −0.213916 | ||||||||
\(713\) | 6.33208 | 0.237138 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.91590 | 0.0716506 | ||||||||
\(716\) | 24.5220 | 0.916429 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.6760 | −0.734300 | ||||||||
\(719\) | −39.5236 | −1.47398 | −0.736991 | − | 0.675903i | \(-0.763754\pi\) | ||||
−0.736991 | + | 0.675903i | \(0.763754\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.91791 | −0.294878 | ||||||||
\(722\) | −2.09107 | −0.0778217 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.4053 | 0.684029 | ||||||||
\(725\) | −7.55145 | −0.280454 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.1237 | 0.375466 | 0.187733 | − | 0.982220i | \(-0.439886\pi\) | ||||
0.187733 | + | 0.982220i | \(0.439886\pi\) | |||||||
\(728\) | −0.906377 | −0.0335926 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.34910 | −0.0499325 | ||||||||
\(731\) | 15.6531 | 0.578952 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.2111 | 0.709579 | 0.354789 | − | 0.934946i | \(-0.384553\pi\) | ||||
0.354789 | + | 0.934946i | \(0.384553\pi\) | |||||||
\(734\) | 51.8422 | 1.91353 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33.8373 | 1.24726 | ||||||||
\(737\) | 1.14472 | 0.0421665 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.1795 | −1.62517 | −0.812585 | − | 0.582843i | \(-0.801940\pi\) | ||||
−0.812585 | + | 0.582843i | \(0.801940\pi\) | |||||||
\(740\) | −13.3927 | −0.492326 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.8029 | 0.837121 | ||||||||
\(743\) | −10.6927 | −0.392278 | −0.196139 | − | 0.980576i | \(-0.562840\pi\) | ||||
−0.196139 | + | 0.980576i | \(0.562840\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.08012 | −0.332670 | ||||||||
\(746\) | 47.4959 | 1.73895 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.28845 | −0.0836742 | ||||||||
\(749\) | −1.84047 | −0.0672494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.0632 | −0.403703 | −0.201852 | − | 0.979416i | \(-0.564696\pi\) | ||||
−0.201852 | + | 0.979416i | \(0.564696\pi\) | |||||||
\(752\) | −57.9089 | −2.11172 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.75236 | 0.355160 | ||||||||
\(755\) | −16.1534 | −0.587884 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.6535 | −1.95007 | −0.975034 | − | 0.222055i | \(-0.928724\pi\) | ||||
−0.975034 | + | 0.222055i | \(0.928724\pi\) | |||||||
\(758\) | −53.9173 | −1.95836 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.56684 | 0.0931092 | ||||||||
\(761\) | −40.9670 | −1.48505 | −0.742526 | − | 0.669818i | \(-0.766372\pi\) | ||||
−0.742526 | + | 0.669818i | \(0.766372\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.4450 | 0.559146 | ||||||||
\(764\) | 34.0333 | 1.23128 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.5670 | −0.562457 | ||||||||
\(767\) | −15.0128 | −0.542080 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.83517 | −0.138300 | −0.0691499 | − | 0.997606i | \(-0.522029\pi\) | ||||
−0.0691499 | + | 0.997606i | \(0.522029\pi\) | |||||||
\(770\) | 1.75388 | 0.0632055 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.182704 | −0.00657565 | ||||||||
\(773\) | 21.2549 | 0.764487 | 0.382243 | − | 0.924062i | \(-0.375152\pi\) | ||||
0.382243 | + | 0.924062i | \(0.375152\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.59802 | −0.165166 | ||||||||
\(776\) | −5.51556 | −0.197997 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.5628 | −1.49010 | ||||||||
\(779\) | −19.9768 | −0.715743 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.60339 | 0.128939 | ||||||||
\(782\) | 16.3785 | 0.585693 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.39078 | −0.156814 | ||||||||
\(785\) | −26.1756 | −0.934247 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.4079 | 0.477938 | 0.238969 | − | 0.971027i | \(-0.423191\pi\) | ||||
0.238969 | + | 0.971027i | \(0.423191\pi\) | |||||||
\(788\) | 6.76668 | 0.241053 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18.1123 | −0.644408 | ||||||||
\(791\) | −10.5350 | −0.374583 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.61299 | −0.270345 | ||||||||
\(794\) | 16.4356 | 0.583278 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.1881 | 0.963655 | ||||||||
\(797\) | −10.0542 | −0.356137 | −0.178069 | − | 0.984018i | \(-0.556985\pi\) | ||||
−0.178069 | + | 0.984018i | \(0.556985\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.2279 | −0.892498 | ||||||||
\(800\) | −24.5708 | −0.868710 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 45.8108 | 1.61763 | ||||||||
\(803\) | −0.347280 | −0.0122552 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.91190 | −0.208367 | ||||||||
\(806\) | 5.93814 | 0.209162 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.40721 | −0.0495053 | ||||||||
\(809\) | 25.4204 | 0.893733 | 0.446867 | − | 0.894601i | \(-0.352540\pi\) | ||||
0.446867 | + | 0.894601i | \(0.352540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.2864 | 1.13373 | 0.566865 | − | 0.823811i | \(-0.308156\pi\) | ||||
0.566865 | + | 0.823811i | \(0.308156\pi\) | |||||||
\(812\) | 4.20468 | 0.147555 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.31994 | −0.256564 | ||||||||
\(815\) | 8.14388 | 0.285268 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.6655 | 1.28276 | ||||||||
\(818\) | 17.1427 | 0.599380 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.6573 | −0.372170 | ||||||||
\(821\) | −2.38698 | −0.0833062 | −0.0416531 | − | 0.999132i | \(-0.513262\pi\) | ||||
−0.0416531 | + | 0.999132i | \(0.513262\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.37746 | −0.257162 | −0.128581 | − | 0.991699i | \(-0.541042\pi\) | ||||
−0.128581 | + | 0.991699i | \(0.541042\pi\) | |||||||
\(824\) | −3.37886 | −0.117708 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.7432 | −0.478188 | ||||||||
\(827\) | −10.1241 | −0.352051 | −0.176025 | − | 0.984386i | \(-0.556324\pi\) | ||||
−0.176025 | + | 0.984386i | \(0.556324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.9788 | 0.971743 | 0.485871 | − | 0.874030i | \(-0.338502\pi\) | ||||
0.485871 | + | 0.874030i | \(0.338502\pi\) | |||||||
\(830\) | 22.0637 | 0.765842 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.0804 | 0.453480 | ||||||||
\(833\) | −1.91283 | −0.0662757 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.91264 | −0.308435 | ||||||||
\(836\) | −5.36041 | −0.185394 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 64.5176 | 2.22872 | ||||||||
\(839\) | 20.3383 | 0.702154 | 0.351077 | − | 0.936347i | \(-0.385815\pi\) | ||||
0.351077 | + | 0.936347i | \(0.385815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4234 | −0.807703 | ||||||||
\(842\) | 60.4643 | 2.08374 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −34.7389 | −1.19576 | ||||||||
\(845\) | 11.3959 | 0.392032 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.5485 | −0.362452 | ||||||||
\(848\) | 51.4939 | 1.76831 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.8932 | −0.407933 | ||||||||
\(851\) | 24.6737 | 0.845804 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.2870 | 0.660376 | 0.330188 | − | 0.943915i | \(-0.392888\pi\) | ||||
0.330188 | + | 0.943915i | \(0.392888\pi\) | |||||||
\(854\) | −6.96919 | −0.238481 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.785397 | −0.0268443 | ||||||||
\(857\) | −22.4053 | −0.765350 | −0.382675 | − | 0.923883i | \(-0.624997\pi\) | ||||
−0.382675 | + | 0.923883i | \(0.624997\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.3277 | −0.966529 | −0.483265 | − | 0.875474i | \(-0.660549\pi\) | ||||
−0.483265 | + | 0.875474i | \(0.660549\pi\) | |||||||
\(860\) | 19.5605 | 0.667007 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 56.2010 | 1.91421 | ||||||||
\(863\) | −2.87085 | −0.0977248 | −0.0488624 | − | 0.998806i | \(-0.515560\pi\) | ||||
−0.0488624 | + | 0.998806i | \(0.515560\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.27705 | −0.0434211 | ||||||||
\(866\) | −59.1358 | −2.00952 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.56020 | 0.0868988 | ||||||||
\(869\) | −4.66240 | −0.158161 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.61853 | −0.122609 | ||||||||
\(872\) | 6.59094 | 0.223197 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 38.3645 | 1.29770 | ||||||||
\(875\) | 11.0053 | 0.372047 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.5296 | −0.456861 | −0.228430 | − | 0.973560i | \(-0.573359\pi\) | ||||
−0.228430 | + | 0.973560i | \(0.573359\pi\) | |||||||
\(878\) | −26.2481 | −0.885832 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.96064 | 0.133513 | ||||||||
\(881\) | −31.4414 | −1.05929 | −0.529644 | − | 0.848220i | \(-0.677675\pi\) | ||||
−0.529644 | + | 0.848220i | \(0.677675\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.1820 | 1.62145 | 0.810727 | − | 0.585424i | \(-0.199072\pi\) | ||||
0.810727 | + | 0.585424i | \(0.199072\pi\) | |||||||
\(884\) | 7.23392 | 0.243303 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.3351 | 1.18711 | ||||||||
\(887\) | 21.8868 | 0.734887 | 0.367443 | − | 0.930046i | \(-0.380233\pi\) | ||||
0.367443 | + | 0.930046i | \(0.380233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −34.9145 | −1.17034 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 45.9463 | 1.53840 | ||||||||
\(893\) | −59.0931 | −1.97747 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.4890 | −0.618019 | ||||||||
\(896\) | −3.39334 | −0.113363 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.60529 | 0.287162 | ||||||||
\(899\) | 3.39555 | 0.113248 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.4332 | 0.747357 | ||||||||
\(902\) | −5.82488 | −0.193947 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.49569 | −0.149524 | ||||||||
\(905\) | −13.8772 | −0.461294 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.2138 | 0.571575 | 0.285788 | − | 0.958293i | \(-0.407745\pi\) | ||||
0.285788 | + | 0.958293i | \(0.407745\pi\) | |||||||
\(908\) | 35.4592 | 1.17676 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.54411 | −0.183785 | ||||||||
\(911\) | −48.6408 | −1.61154 | −0.805770 | − | 0.592228i | \(-0.798248\pi\) | ||||
−0.805770 | + | 0.592228i | \(0.798248\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.67954 | 0.187965 | ||||||||
\(914\) | −40.7391 | −1.34753 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −30.7401 | −1.01568 | ||||||||
\(917\) | −21.6997 | −0.716588 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.3448 | 0.539165 | 0.269583 | − | 0.962977i | \(-0.413114\pi\) | ||||
0.269583 | + | 0.962977i | \(0.413114\pi\) | |||||||
\(920\) | −2.52283 | −0.0831751 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −58.8820 | −1.93918 | ||||||||
\(923\) | −11.3905 | −0.374922 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.9167 | −0.589099 | ||||||||
\(926\) | −47.2435 | −1.55252 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 18.1451 | 0.595642 | ||||||||
\(929\) | −28.5730 | −0.937451 | −0.468725 | − | 0.883344i | \(-0.655287\pi\) | ||||
−0.468725 | + | 0.883344i | \(0.655287\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.48056 | −0.146845 | ||||||||
\(932\) | −53.0706 | −1.73839 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.56187 | 0.116548 | ||||||||
\(935\) | 1.72544 | 0.0564280 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5805 | −0.345650 | −0.172825 | − | 0.984953i | \(-0.555290\pi\) | ||||
−0.172825 | + | 0.984953i | \(0.555290\pi\) | |||||||
\(938\) | −3.31253 | −0.108158 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −31.5253 | −1.02824 | ||||||||
\(941\) | −16.7748 | −0.546842 | −0.273421 | − | 0.961894i | \(-0.588155\pi\) | ||||
−0.273421 | + | 0.961894i | \(0.588155\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.6342 | 0.639378 | ||||||||
\(944\) | −31.0352 | −1.01011 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.6910 | 0.347594 | ||||||||
\(947\) | 32.0250 | 1.04067 | 0.520336 | − | 0.853961i | \(-0.325807\pi\) | ||||
0.520336 | + | 0.853961i | \(0.325807\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.09777 | 0.0356351 | ||||||||
\(950\) | −27.8583 | −0.903842 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.816275 | −0.0264556 | ||||||||
\(953\) | −30.0313 | −0.972809 | −0.486405 | − | 0.873734i | \(-0.661692\pi\) | ||||
−0.486405 | + | 0.873734i | \(0.661692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.6604 | −0.830350 | ||||||||
\(956\) | −15.7312 | −0.508785 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 59.2110 | 1.91302 | ||||||||
\(959\) | 8.54803 | 0.276030 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9325 | −0.933306 | ||||||||
\(962\) | 23.1387 | 0.746021 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.671973 | 0.0216428 | ||||||||
\(965\) | 0.137754 | 0.00443447 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.7947 | −0.411451 | −0.205725 | − | 0.978610i | \(-0.565955\pi\) | ||||
−0.205725 | + | 0.978610i | \(0.565955\pi\) | |||||||
\(968\) | −4.50144 | −0.144682 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −33.7375 | −1.08324 | ||||||||
\(971\) | 30.9532 | 0.993334 | 0.496667 | − | 0.867941i | \(-0.334557\pi\) | ||||
0.496667 | + | 0.867941i | \(0.334557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.4438 | −0.366872 | ||||||||
\(974\) | 49.7981 | 1.59563 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.7379 | −0.503759 | ||||||||
\(977\) | 18.5496 | 0.593456 | 0.296728 | − | 0.954962i | \(-0.404105\pi\) | ||||
0.296728 | + | 0.954962i | \(0.404105\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.98754 | −0.287243 | ||||||||
\(980\) | −2.39031 | −0.0763558 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 49.1465 | 1.56833 | ||||||||
\(983\) | 9.51156 | 0.303372 | 0.151686 | − | 0.988429i | \(-0.451530\pi\) | ||||
0.151686 | + | 0.988429i | \(0.451530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.10192 | −0.162561 | ||||||||
\(986\) | 8.78289 | 0.279704 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.9445 | 0.539078 | ||||||||
\(989\) | −36.0367 | −1.14590 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.4713 | −1.47621 | −0.738105 | − | 0.674686i | \(-0.764279\pi\) | ||||
−0.738105 | + | 0.674686i | \(0.764279\pi\) | |||||||
\(992\) | 11.0484 | 0.350788 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.4272 | −0.330732 | ||||||||
\(995\) | −20.4992 | −0.649868 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.682471 | −0.0216141 | −0.0108070 | − | 0.999942i | \(-0.503440\pi\) | ||||
−0.0108070 | + | 0.999942i | \(0.503440\pi\) | |||||||
\(998\) | 30.3639 | 0.961153 | ||||||||
\(999\) | 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 | 8001.2.a.x.1.4 | ✓ | 22 | |
3.2 | odd | 2 | inner | 8001.2.a.x.1.19 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.x.1.4 | ✓ | 22 | 1.1 | even | 1 | trivial | |
8001.2.a.x.1.19 | yes | 22 | 3.2 | odd | 2 | inner |