Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.15021 | 1.24142 | 0.620712 | − | 0.784039i | \(-0.286844\pi\) | ||||
0.620712 | + | 0.784039i | \(0.286844\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.53922 | 0.688361 | 0.344180 | − | 0.938904i | \(-0.388157\pi\) | ||||
0.344180 | + | 0.938904i | \(0.388157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.745521 | −0.281781 | −0.140890 | − | 0.990025i | \(-0.544996\pi\) | ||||
−0.140890 | + | 0.990025i | \(0.544996\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.62340 | 0.541133 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.48378 | −1.35191 | −0.675955 | − | 0.736943i | \(-0.736269\pi\) | ||||
−0.675955 | + | 0.736943i | \(0.736269\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.05215 | 0.569164 | 0.284582 | − | 0.958652i | \(-0.408145\pi\) | ||||
0.284582 | + | 0.958652i | \(0.408145\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.30965 | 0.854547 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.76485 | −1.32255 | −0.661273 | − | 0.750145i | \(-0.729984\pi\) | ||||
−0.661273 | + | 0.750145i | \(0.729984\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.60303 | −0.349809 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.38388 | −0.914103 | −0.457052 | − | 0.889440i | \(-0.651095\pi\) | ||||
−0.457052 | + | 0.889440i | \(0.651095\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.63080 | −0.526160 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.95998 | −0.569649 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.97480 | 1.66658 | 0.833289 | − | 0.552838i | \(-0.186455\pi\) | ||||
0.833289 | + | 0.552838i | \(0.186455\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.172281 | −0.0309425 | −0.0154713 | − | 0.999880i | \(-0.504925\pi\) | ||||
−0.0154713 | + | 0.999880i | \(0.504925\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.64106 | −1.67829 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.14752 | −0.193967 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.69182 | 1.10013 | 0.550064 | − | 0.835122i | \(-0.314603\pi\) | ||||
0.550064 | + | 0.835122i | \(0.314603\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.41255 | 0.706574 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.53239 | 0.239319 | 0.119660 | − | 0.992815i | \(-0.461820\pi\) | ||||
0.119660 | + | 0.992815i | \(0.461820\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.47164 | −0.529420 | −0.264710 | − | 0.964328i | \(-0.585276\pi\) | ||||
−0.264710 | + | 0.964328i | \(0.585276\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.49877 | 0.372495 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.8212 | −1.57844 | −0.789219 | − | 0.614112i | \(-0.789514\pi\) | ||||
−0.789219 | + | 0.614112i | \(0.789514\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.44420 | −0.920600 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.15021 | −0.301089 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.84980 | 0.528811 | 0.264405 | − | 0.964412i | \(-0.414824\pi\) | ||||
0.264405 | + | 0.964412i | \(0.414824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.90153 | −0.930602 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.3956 | −1.64184 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9327 | 1.39979 | 0.699897 | − | 0.714244i | \(-0.253229\pi\) | ||||
0.699897 | + | 0.714244i | \(0.253229\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.21028 | −0.152481 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.15871 | 0.391790 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.23237 | −0.150558 | −0.0752791 | − | 0.997163i | \(-0.523985\pi\) | ||||
−0.0752791 | + | 0.997163i | \(0.523985\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.42627 | −1.13479 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.83196 | −0.454770 | −0.227385 | − | 0.973805i | \(-0.573018\pi\) | ||||
−0.227385 | + | 0.973805i | \(0.573018\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.18903 | −0.841413 | −0.420706 | − | 0.907197i | \(-0.638218\pi\) | ||||
−0.420706 | + | 0.907197i | \(0.638218\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.65677 | −0.653187 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.34275 | 0.380942 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.93308 | −1.11756 | −0.558779 | − | 0.829316i | \(-0.688730\pi\) | ||||
−0.558779 | + | 0.829316i | \(0.688730\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2348 | −1.24831 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.6903 | 1.61247 | 0.806237 | − | 0.591593i | \(-0.201501\pi\) | ||||
0.806237 | + | 0.591593i | \(0.201501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.53922 | −0.166952 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.2977 | 2.06893 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.6751 | −1.34356 | −0.671779 | − | 0.740752i | \(-0.734469\pi\) | ||||
−0.671779 | + | 0.740752i | \(0.734469\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.52992 | −0.160379 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.370439 | −0.0384128 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.87337 | −0.910389 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.6498 | 1.08133 | 0.540664 | − | 0.841238i | \(-0.318173\pi\) | ||||
0.540664 | + | 0.841238i | \(0.318173\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.27896 | −0.731563 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.365599 | 0.0363784 | 0.0181892 | − | 0.999835i | \(-0.494210\pi\) | ||||
0.0181892 | + | 0.999835i | \(0.494210\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.9762 | −1.47565 | −0.737824 | − | 0.674993i | \(-0.764147\pi\) | ||||
−0.737824 | + | 0.674993i | \(0.764147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.46741 | −0.240795 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.1951 | −1.75899 | −0.879495 | − | 0.475908i | \(-0.842119\pi\) | ||||
−0.879495 | + | 0.475908i | \(0.842119\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.75098 | −0.933975 | −0.466987 | − | 0.884264i | \(-0.654661\pi\) | ||||
−0.466987 | + | 0.884264i | \(0.654661\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.3888 | 1.36573 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.29832 | −0.780640 | −0.390320 | − | 0.920679i | \(-0.627636\pi\) | ||||
−0.390320 | + | 0.920679i | \(0.627636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.74777 | −0.629233 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.33146 | 0.307993 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.745521 | 0.0683418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.10427 | 0.827661 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.29496 | 0.297097 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7455 | −1.05055 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.99640 | 0.798301 | 0.399151 | − | 0.916885i | \(-0.369305\pi\) | ||||
0.399151 | + | 0.916885i | \(0.369305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.46475 | −0.657235 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.8641 | −1.47342 | −0.736710 | − | 0.676209i | \(-0.763622\pi\) | ||||
−0.736710 | + | 0.676209i | \(0.763622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.29782 | 0.372668 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.55606 | −0.392124 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.5922 | −1.41757 | −0.708783 | − | 0.705427i | \(-0.750755\pi\) | ||||
−0.708783 | + | 0.705427i | \(0.750755\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3366 | 1.38565 | 0.692827 | − | 0.721104i | \(-0.256365\pi\) | ||||
0.692827 | + | 0.721104i | \(0.256365\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −23.2679 | −1.95951 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.20139 | −0.769459 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.8142 | 1.14721 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.8564 | −1.14285 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.1693 | 1.65233 | 0.826167 | − | 0.563425i | \(-0.190517\pi\) | ||||
0.826167 | + | 0.563425i | \(0.190517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.2807 | −1.56904 | −0.784520 | − | 0.620104i | \(-0.787090\pi\) | ||||
−0.784520 | + | 0.620104i | \(0.787090\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.62340 | −0.131244 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.265178 | −0.0212996 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.6201 | 0.847577 | 0.423789 | − | 0.905761i | \(-0.360700\pi\) | ||||
0.423789 | + | 0.905761i | \(0.360700\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.27788 | 0.656478 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.26828 | 0.257577 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.00878 | −0.627296 | −0.313648 | − | 0.949539i | \(-0.601551\pi\) | ||||
−0.313648 | + | 0.949539i | \(0.601551\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.8397 | −1.15527 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.38685 | 0.184700 | 0.0923500 | − | 0.995727i | \(-0.470562\pi\) | ||||
0.0923500 | + | 0.995727i | \(0.470562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.78868 | −0.676052 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.35864 | −0.715673 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.38371 | 0.181230 | 0.0906152 | − | 0.995886i | \(-0.471117\pi\) | ||||
0.0906152 | + | 0.995886i | \(0.471117\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.96132 | 0.148262 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.15021 | −0.161620 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.62432 | 0.345638 | 0.172819 | − | 0.984954i | \(-0.444712\pi\) | ||||
0.172819 | + | 0.984954i | \(0.444712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.84379 | 0.137048 | 0.0685240 | − | 0.997649i | \(-0.478171\pi\) | ||||
0.0685240 | + | 0.997649i | \(0.478171\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.5077 | 1.73774 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.3002 | 0.757285 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.48378 | 0.327886 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.20673 | 0.160516 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.51470 | −0.254315 | −0.127157 | − | 0.991883i | \(-0.540585\pi\) | ||||
−0.127157 | + | 0.991883i | \(0.540585\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.663979 | 0.0477942 | 0.0238971 | − | 0.999714i | \(-0.492393\pi\) | ||||
0.0238971 | + | 0.999714i | \(0.492393\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.79189 | 0.486377 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.61133 | −0.328544 | −0.164272 | − | 0.986415i | \(-0.552527\pi\) | ||||
−0.164272 | + | 0.986415i | \(0.552527\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.07668 | −0.288988 | −0.144494 | − | 0.989506i | \(-0.546155\pi\) | ||||
−0.144494 | + | 0.989506i | \(0.546155\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.64986 | −0.186906 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.69090 | −0.469609 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.35869 | 0.164738 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.11679 | −0.494651 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.8483 | 1.78796 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.51118 | 0.241719 | 0.120860 | − | 0.992670i | \(-0.461435\pi\) | ||||
0.120860 | + | 0.992670i | \(0.461435\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.23951 | −0.564562 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.34362 | −0.364432 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.128439 | 0.00871900 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.4579 | −1.04455 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.05215 | −0.138043 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.0878155 | −0.00588056 | −0.00294028 | − | 0.999996i | \(-0.500936\pi\) | ||||
−0.00294028 | + | 0.999996i | \(0.500936\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.27083 | −0.284722 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.17378 | 0.608885 | 0.304443 | − | 0.952531i | \(-0.401530\pi\) | ||||
0.304443 | + | 0.952531i | \(0.401530\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.83455 | −0.385558 | −0.192779 | − | 0.981242i | \(-0.561750\pi\) | ||||
−0.192779 | + | 0.981242i | \(0.561750\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.18762 | 0.472911 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.99857 | −0.130931 | −0.0654653 | − | 0.997855i | \(-0.520853\pi\) | ||||
−0.0654653 | + | 0.997855i | \(0.520853\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.6563 | −1.08653 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.3582 | −1.38736 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.5793 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.2053 | −1.94570 | −0.972848 | − | 0.231447i | \(-0.925654\pi\) | ||||
−0.972848 | + | 0.231447i | \(0.925654\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2772 | −0.980031 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.91904 | −0.633705 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.8303 | −0.752746 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 31.5873 | 2.00176 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.2254 | 1.78157 | 0.890785 | − | 0.454425i | \(-0.150155\pi\) | ||||
0.890785 | + | 0.454425i | \(0.150155\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.6564 | 1.23579 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.30965 | −0.207258 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5690 | 0.659275 | 0.329637 | − | 0.944108i | \(-0.393073\pi\) | ||||
0.329637 | + | 0.944108i | \(0.393073\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.98890 | −0.309995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.5697 | 0.901840 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.1130 | 1.54853 | 0.774267 | − | 0.632859i | \(-0.218119\pi\) | ||||
0.774267 | + | 0.632859i | \(0.218119\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.92569 | 0.364013 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.2541 | −1.66792 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.32331 | −0.324568 | −0.162284 | − | 0.986744i | \(-0.551886\pi\) | ||||
−0.162284 | + | 0.986744i | \(0.551886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.1286 | 1.95167 | 0.975837 | − | 0.218498i | \(-0.0701158\pi\) | ||||
0.975837 | + | 0.218498i | \(0.0701158\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.28965 | −0.199099 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.7959 | 0.711321 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.4389 | −1.82890 | −0.914448 | − | 0.404704i | \(-0.867374\pi\) | ||||
−0.914448 | + | 0.404704i | \(0.867374\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.279680 | −0.0167440 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.4173 | −1.51627 | −0.758135 | − | 0.652098i | \(-0.773889\pi\) | ||||
−0.758135 | + | 0.652098i | \(0.773889\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.2985 | −1.50384 | −0.751920 | − | 0.659254i | \(-0.770872\pi\) | ||||
−0.751920 | + | 0.659254i | \(0.770872\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −19.0796 | −1.13018 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.14243 | −0.0674356 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.8994 | 1.34239 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.72136 | −0.509507 | −0.254754 | − | 0.967006i | \(-0.581994\pi\) | ||||
−0.254754 | + | 0.967006i | \(0.581994\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.53922 | −0.0896169 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.2719 | 0.770114 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.99639 | −0.520275 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.58818 | 0.149180 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.786113 | 0.0451610 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.8279 | 0.963563 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.7013 | 0.781974 | 0.390987 | − | 0.920396i | \(-0.372134\pi\) | ||||
0.390987 | + | 0.920396i | \(0.372134\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −32.2019 | −1.83190 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.8201 | −1.57753 | −0.788765 | − | 0.614695i | \(-0.789279\pi\) | ||||
−0.788765 | + | 0.614695i | \(0.789279\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.59213 | 0.146516 | 0.0732579 | − | 0.997313i | \(-0.476660\pi\) | ||||
0.0732579 | + | 0.997313i | \(0.476660\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.86289 | −0.104962 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.06614 | 0.0598803 | 0.0299402 | − | 0.999552i | \(-0.490468\pi\) | ||||
0.0299402 | + | 0.999552i | \(0.490468\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −40.2410 | −2.25306 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.1233 | −2.18365 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.76485 | 0.320765 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.39879 | −0.299471 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.9667 | −1.15946 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.06745 | 0.444773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.91407 | 0.434997 | 0.217498 | − | 0.976061i | \(-0.430210\pi\) | ||||
0.217498 | + | 0.976061i | \(0.430210\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.8635 | 0.595316 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.89689 | −0.103638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.500204 | −0.0272478 | −0.0136239 | − | 0.999907i | \(-0.504337\pi\) | ||||
−0.0136239 | + | 0.999907i | \(0.504337\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.8431 | −0.969105 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.772468 | 0.0418315 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0229 | 0.541188 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.5091 | −0.781144 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.4015 | 1.73940 | 0.869701 | − | 0.493578i | \(-0.164311\pi\) | ||||
0.869701 | + | 0.493578i | \(0.164311\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.20961 | −0.278864 | −0.139432 | − | 0.990232i | \(-0.544528\pi\) | ||||
−0.139432 | + | 0.990232i | \(0.544528\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.07432 | −0.324223 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.1004 | 0.697264 | 0.348632 | − | 0.937260i | \(-0.386646\pi\) | ||||
0.348632 | + | 0.937260i | \(0.386646\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.89823 | −0.313046 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.60303 | 0.0848412 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.0851 | 1.69339 | 0.846693 | − | 0.532081i | \(-0.178590\pi\) | ||||
0.846693 | + | 0.532081i | \(0.178590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.2335 | 0.749129 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.5761 | 1.02748 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.0655 | −0.579195 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.09787 | −0.318306 | −0.159153 | − | 0.987254i | \(-0.550876\pi\) | ||||
−0.159153 | + | 0.987254i | \(0.550876\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.48768 | 0.129504 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.87011 | −0.149009 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.9026 | −0.875185 | −0.437593 | − | 0.899173i | \(-0.644169\pi\) | ||||
−0.437593 | + | 0.899173i | \(0.644169\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.2552 | −1.30418 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.4176 | 0.948556 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.6925 | 0.754703 | 0.377352 | − | 0.926070i | \(-0.376835\pi\) | ||||
0.377352 | + | 0.926070i | \(0.376835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.3441 | 0.991030 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.9963 | 1.27725 | 0.638625 | − | 0.769518i | \(-0.279504\pi\) | ||||
0.638625 | + | 0.769518i | \(0.279504\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.14524 | 0.262226 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.63586 | −0.286487 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.4240 | −1.18764 | −0.593821 | − | 0.804597i | \(-0.702381\pi\) | ||||
−0.593821 | + | 0.804597i | \(0.702381\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.38388 | 0.221703 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −36.2612 | −1.82914 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.2892 | −0.769283 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.3666 | 1.52406 | 0.762028 | − | 0.647544i | \(-0.224204\pi\) | ||||
0.762028 | + | 0.647544i | \(0.224204\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.24120 | 0.462639 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.91678 | 0.445283 | 0.222641 | − | 0.974900i | \(-0.428532\pi\) | ||||
0.222641 | + | 0.974900i | \(0.428532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.353546 | −0.0176114 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.2928 | −0.859286 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −30.0046 | −1.48727 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.9501 | −0.788680 | −0.394340 | − | 0.918965i | \(-0.629027\pi\) | ||||
−0.394340 | + | 0.918965i | \(0.629027\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −35.6767 | −1.75980 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.745521 | 0.0366847 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.6117 | 1.10996 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.1272 | 1.72018 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −38.1632 | −1.86440 | −0.932198 | − | 0.361950i | \(-0.882111\pi\) | ||||
−0.932198 | + | 0.361950i | \(0.882111\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.3034 | 1.33069 | 0.665344 | − | 0.746537i | \(-0.268285\pi\) | ||||
0.665344 | + | 0.746537i | \(0.268285\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.5672 | −0.854144 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.63080 | 0.127612 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.15059 | −0.394435 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.7849 | −0.955224 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.7162 | 1.23870 | 0.619352 | − | 0.785114i | \(-0.287395\pi\) | ||||
0.619352 | + | 0.785114i | \(0.287395\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.6860 | 1.66690 | 0.833451 | − | 0.552593i | \(-0.186362\pi\) | ||||
0.833451 | + | 0.552593i | \(0.186362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 29.7034 | 1.42417 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.2724 | 1.20894 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.3155 | −1.63779 | −0.818895 | − | 0.573944i | \(-0.805413\pi\) | ||||
−0.818895 | + | 0.573944i | \(0.805413\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.4615 | −0.498167 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.95278 | 0.330337 | 0.165168 | − | 0.986265i | \(-0.447183\pi\) | ||||
0.165168 | + | 0.986265i | \(0.447183\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.5098 | −0.924852 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 43.3682 | 2.05125 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.94322 | −0.138899 | −0.0694496 | − | 0.997585i | \(-0.522124\pi\) | ||||
−0.0694496 | + | 0.997585i | \(0.522124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.87091 | −0.323538 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −41.4575 | −1.94784 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.35489 | −0.110399 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.2388 | 1.08706 | 0.543532 | − | 0.839389i | \(-0.317087\pi\) | ||||
0.543532 | + | 0.839389i | \(0.317087\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.95998 | 0.138160 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.54846 | −0.398141 | −0.199071 | − | 0.979985i | \(-0.563792\pi\) | ||||
−0.199071 | + | 0.979985i | \(0.563792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.03185 | 0.280324 | 0.140162 | − | 0.990129i | \(-0.455238\pi\) | ||||
0.140162 | + | 0.990129i | \(0.455238\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.570188 | −0.0264418 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.0998 | 1.02265 | 0.511327 | − | 0.859386i | \(-0.329154\pi\) | ||||
0.511327 | + | 0.859386i | \(0.329154\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.918760 | 0.0424244 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.8355 | 1.05220 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.5661 | 0.715728 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.1661 | 0.695871 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.24976 | 0.286157 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.0875 | −1.55750 | −0.778749 | − | 0.627335i | \(-0.784146\pi\) | ||||
−0.778749 | + | 0.627335i | \(0.784146\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.7326 | 0.626153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.02749 | 0.319762 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.3925 | 0.744344 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.2826 | −1.73475 | −0.867375 | − | 0.497655i | \(-0.834195\pi\) | ||||
−0.867375 | + | 0.497655i | \(0.834195\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.2206 | −0.778741 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.4833 | 1.01466 | 0.507328 | − | 0.861753i | \(-0.330633\pi\) | ||||
0.507328 | + | 0.861753i | \(0.330633\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.97480 | −0.404204 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.2039 | −0.503579 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.85681 | 0.128145 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.4971 | 1.94720 | 0.973599 | − | 0.228267i | \(-0.0733059\pi\) | ||||
0.973599 | + | 0.228267i | \(0.0733059\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.13223 | 0.229291 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.607269 | 0.0270768 | 0.0135384 | − | 0.999908i | \(-0.495690\pi\) | ||||
0.0135384 | + | 0.999908i | \(0.495690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.562737 | 0.0250415 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.8975 | −0.839267 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.0966872 | 0.00428559 | 0.00214279 | − | 0.999998i | \(-0.499318\pi\) | ||||
0.00214279 | + | 0.999998i | \(0.499318\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.35958 | 0.237094 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.0638 | 0.753387 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.0517 | −1.01578 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.5200 | 2.13391 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.12548 | 0.224984 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.07749 | 0.353881 | 0.176941 | − | 0.984222i | \(-0.443380\pi\) | ||||
0.176941 | + | 0.984222i | \(0.443380\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.6111 | −0.551447 | −0.275723 | − | 0.961237i | \(-0.588917\pi\) | ||||
−0.275723 | + | 0.961237i | \(0.588917\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.21724 | 0.184055 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.172281 | 0.00750466 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.78155 | −0.164415 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.62340 | −0.0704495 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.14470 | 0.136212 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.0063 | −1.21082 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.94325 | 0.429083 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.8944 | 1.24457 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.8815 | 1.88661 | 0.943306 | − | 0.331923i | \(-0.107698\pi\) | ||||
0.943306 | + | 0.331923i | \(0.107698\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.96454 | 0.170135 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.0089 | −0.642911 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.4073 | 1.47115 | 0.735576 | − | 0.677443i | \(-0.236912\pi\) | ||||
0.735576 | + | 0.677443i | \(0.236912\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.7482 | 0.757474 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.7383 | −2.20413 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.40532 | 0.314906 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.1476 | 0.940112 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.2200 | 0.475408 | 0.237704 | − | 0.971338i | \(-0.423605\pi\) | ||||
0.237704 | + | 0.971338i | \(0.423605\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.12433 | −0.301327 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.64106 | 0.407046 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.8439 | 0.499162 | 0.249581 | − | 0.968354i | \(-0.419707\pi\) | ||||
0.249581 | + | 0.968354i | \(0.419707\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.7729 | −0.537362 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.37576 | 0.351749 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.9566 | −1.29777 | −0.648883 | − | 0.760888i | \(-0.724764\pi\) | ||||
−0.648883 | + | 0.760888i | \(0.724764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.2197 | 1.55760 | 0.778799 | − | 0.627274i | \(-0.215829\pi\) | ||||
0.778799 | + | 0.627274i | \(0.215829\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.55734 | −0.315713 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.5331 | 0.480964 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.9600 | −0.789316 | −0.394658 | − | 0.918828i | \(-0.629137\pi\) | ||||
−0.394658 | + | 0.918828i | \(0.629137\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.42769 | 0.0593329 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9520 | −0.454364 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.2617 | −0.714905 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.12785 | 0.212010 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.3772 | 0.593413 | 0.296706 | − | 0.954969i | \(-0.404112\pi\) | ||||
0.296706 | + | 0.954969i | \(0.404112\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.993171 | 0.0409229 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.91532 | −0.407862 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.89753 | −0.283248 | −0.141624 | − | 0.989921i | \(-0.545232\pi\) | ||||
−0.141624 | + | 0.989921i | \(0.545232\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.14752 | 0.0470438 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.76571 | −0.358756 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0784 | −0.534370 | −0.267185 | − | 0.963645i | \(-0.586093\pi\) | ||||
−0.267185 | + | 0.963645i | \(0.586093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.7866 | −0.847902 | −0.423951 | − | 0.905685i | \(-0.639357\pi\) | ||||
−0.423951 | + | 0.905685i | \(0.639357\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.00063 | −0.0814720 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.0135 | 0.569729 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.6434 | 0.513181 | 0.256591 | − | 0.966520i | \(-0.417401\pi\) | ||||
0.256591 | + | 0.966520i | \(0.417401\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.3868 | −0.582984 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.2068 | −0.898390 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.0676 | −1.41637 | −0.708184 | − | 0.706028i | \(-0.750485\pi\) | ||||
−0.708184 | + | 0.706028i | \(0.750485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.07168 | 0.204510 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.63030 | −0.105892 | −0.0529460 | − | 0.998597i | \(-0.516861\pi\) | ||||
−0.0529460 | + | 0.998597i | \(0.516861\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.3842 | 1.18105 | 0.590526 | − | 0.807018i | \(-0.298920\pi\) | ||||
0.590526 | + | 0.807018i | \(0.298920\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.9762 | 0.520718 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.44956 | 0.378588 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.92491 | −0.196996 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 55.5792 | 2.21962 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.69182 | −0.266820 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.2093 | 1.16280 | 0.581401 | − | 0.813617i | \(-0.302505\pi\) | ||||
0.581401 | + | 0.813617i | \(0.302505\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.54976 | 0.300076 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.8474 | 0.549519 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.2245 | −0.523972 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.22080 | −0.246091 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.7856 | 1.61094 | 0.805468 | − | 0.592640i | \(-0.201914\pi\) | ||||
0.805468 | + | 0.592640i | \(0.201914\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.4632 | −0.688682 | −0.344341 | − | 0.938845i | \(-0.611898\pi\) | ||||
−0.344341 | + | 0.938845i | \(0.611898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.4899 | −0.452414 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.9904 | −0.746591 | −0.373296 | − | 0.927712i | \(-0.621772\pi\) | ||||
−0.373296 | + | 0.927712i | \(0.621772\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.48378 | 0.176004 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.276170 | 0.0108240 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.24228 | −0.244279 | −0.122140 | − | 0.992513i | \(-0.538976\pi\) | ||||
−0.122140 | + | 0.992513i | \(0.538976\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.9575 | −1.01424 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.6707 | −0.455316 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.4617 | −0.485441 | −0.242720 | − | 0.970096i | \(-0.578040\pi\) | ||||
−0.242720 | + | 0.970096i | \(0.578040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.1220 | −0.471492 | −0.235746 | − | 0.971815i | \(-0.575753\pi\) | ||||
−0.235746 | + | 0.971815i | \(0.575753\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.41255 | −0.171369 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.61529 | 0.256530 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −39.3445 | −1.52342 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.188822 | −0.00730027 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49.0200 | −1.89239 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.7932 | −1.03280 | −0.516402 | − | 0.856346i | \(-0.672729\pi\) | ||||
−0.516402 | + | 0.856346i | \(0.672729\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.78711 | 0.299726 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.3131 | 0.396366 | 0.198183 | − | 0.980165i | \(-0.436496\pi\) | ||||
0.198183 | + | 0.980165i | \(0.436496\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.93969 | −0.304697 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.7256 | 0.755885 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.09734 | −0.309836 | −0.154918 | − | 0.987927i | \(-0.549511\pi\) | ||||
−0.154918 | + | 0.987927i | \(0.549511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.5390 | −0.975796 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.5455 | −0.478641 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.90037 | 0.300980 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.3069 | 0.658386 | 0.329193 | − | 0.944263i | \(-0.393223\pi\) | ||||
0.329193 | + | 0.944263i | \(0.393223\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.42662 | 0.206140 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.1457 | 0.953830 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.53239 | −0.0580435 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.29734 | −0.162540 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.4252 | 0.620372 | 0.310186 | − | 0.950676i | \(-0.399609\pi\) | ||||
0.310186 | + | 0.950676i | \(0.399609\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.5773 | −1.45497 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −35.8144 | −1.34885 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.272562 | −0.0102507 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.2689 | 0.911438 | 0.455719 | − | 0.890124i | \(-0.349382\pi\) | ||||
0.455719 | + | 0.890124i | \(0.349382\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.1253 | −0.604748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.755258 | 0.0282846 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.1630 | −0.529665 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.4988 | 1.25103 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.7681 | 1.07287 | 0.536435 | − | 0.843942i | \(-0.319771\pi\) | ||||
0.536435 | + | 0.843942i | \(0.319771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.1651 | 0.415809 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −64.9477 | −2.41543 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.6109 | −0.876886 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.1298 | −0.449871 | −0.224935 | − | 0.974374i | \(-0.572217\pi\) | ||||
−0.224935 | + | 0.974374i | \(0.572217\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.855215 | 0.0316746 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.47164 | 0.128403 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.49693 | 0.0922264 | 0.0461132 | − | 0.998936i | \(-0.485317\pi\) | ||||
0.0461132 | + | 0.998936i | \(0.485317\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.3280 | −0.786696 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.52568 | 0.203541 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.6741 | −1.49622 | −0.748111 | − | 0.663574i | \(-0.769039\pi\) | ||||
−0.748111 | + | 0.663574i | \(0.769039\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.4377 | −0.934476 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.7646 | −0.725093 | −0.362546 | − | 0.931966i | \(-0.618093\pi\) | ||||
−0.362546 | + | 0.931966i | \(0.618093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.0450 | 1.13740 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.8483 | 0.872562 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.5649 | 0.495649 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3940 | 1.32804 | 0.664018 | − | 0.747717i | \(-0.268850\pi\) | ||||
0.664018 | + | 0.747717i | \(0.268850\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 60.6904 | 2.21168 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.6772 | −1.08007 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.4852 | −1.25339 | −0.626693 | − | 0.779267i | \(-0.715592\pi\) | ||||
−0.626693 | + | 0.779267i | \(0.715592\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 42.2653 | 1.53413 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.9649 | 0.723728 | 0.361864 | − | 0.932231i | \(-0.382140\pi\) | ||||
0.361864 | + | 0.932231i | \(0.382140\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.26957 | 0.263176 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.49877 | −0.0903432 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.05215 | −0.0740988 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.8906 | −0.789396 | −0.394698 | − | 0.918811i | \(-0.629151\pi\) | ||||
−0.394698 | + | 0.918811i | \(0.629151\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.7255 | 0.818439 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.3952 | −1.30904 | −0.654522 | − | 0.756043i | \(-0.727130\pi\) | ||||
−0.654522 | + | 0.756043i | \(0.727130\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.453236 | 0.0162807 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.7272 | −0.384835 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.83400 | −0.316511 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.1817 | 0.614808 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26.5652 | −0.949363 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.3467 | 0.583439 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.4675 | −1.19299 | −0.596494 | − | 0.802618i | \(-0.703440\pi\) | ||||
−0.596494 | + | 0.802618i | \(0.703440\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 53.9982 | 1.92239 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.18658 | 0.219969 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.4356 | 0.796712 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.7415 | 0.451894 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.7628 | 1.58558 | 0.792789 | − | 0.609496i | \(-0.208628\pi\) | ||||
0.792789 | + | 0.609496i | \(0.208628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.8212 | 0.382827 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.5767 | −0.727043 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.2340 | 1.13751 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.03061 | 0.177306 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.4462 | −0.402926 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.913247 | −0.0321081 | −0.0160540 | − | 0.999871i | \(-0.505110\pi\) | ||||
−0.0160540 | + | 0.999871i | \(0.505110\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.8076 | 0.660426 | 0.330213 | − | 0.943907i | \(-0.392879\pi\) | ||||
0.330213 | + | 0.943907i | \(0.392879\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 69.0832 | 2.42286 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.3273 | −0.431806 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.0135 | 0.700183 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.48367 | −0.0867866 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.2882 | 0.603361 | 0.301680 | − | 0.953409i | \(-0.402452\pi\) | ||||
0.301680 | + | 0.953409i | \(0.402452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.36213 | 0.326343 | 0.163172 | − | 0.986598i | \(-0.447828\pi\) | ||||
0.163172 | + | 0.986598i | \(0.447828\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.3637 | 0.883050 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.53918 | −0.192616 | −0.0963081 | − | 0.995352i | \(-0.530703\pi\) | ||||
−0.0963081 | + | 0.995352i | \(0.530703\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.5733 | −0.922929 | −0.461465 | − | 0.887159i | \(-0.652676\pi\) | ||||
−0.461465 | + | 0.887159i | \(0.652676\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −65.4500 | −2.27043 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.44420 | 0.223278 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.67389 | 0.127140 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.509947 | 0.0176264 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.1417 | 1.80013 | 0.900065 | − | 0.435755i | \(-0.143519\pi\) | ||||
0.900065 | + | 0.435755i | \(0.143519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.5469 | 1.77748 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −54.6525 | −1.88233 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.5277 | −0.465368 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.78743 | −0.233219 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54.3971 | −1.86690 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.3362 | −1.00563 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.2582 | −0.590910 | −0.295455 | − | 0.955357i | \(-0.595471\pi\) | ||||
−0.295455 | + | 0.955357i | \(0.595471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.4050 | −0.492641 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.4174 | −1.41479 | −0.707396 | − | 0.706818i | \(-0.750130\pi\) | ||||
−0.707396 | + | 0.706818i | \(0.750130\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.8381 | −0.642747 | −0.321374 | − | 0.946952i | \(-0.604145\pi\) | ||||
−0.321374 | + | 0.946952i | \(0.604145\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.45647 | −0.0837161 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.5843 | −1.34746 | −0.673732 | − | 0.738975i | \(-0.735310\pi\) | ||||
−0.673732 | + | 0.738975i | \(0.735310\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.66906 | 0.124752 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.15021 | 0.0730249 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.5377 | 1.51084 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.52901 | −0.0856923 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.2890 | 0.585142 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.75651 | 0.296024 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.1081 | −1.28682 | −0.643409 | − | 0.765522i | \(-0.722481\pi\) | ||||
−0.643409 | + | 0.765522i | \(0.722481\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.7527 | −0.632514 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.659310 | 0.0222127 | 0.0111064 | − | 0.999938i | \(-0.496465\pi\) | ||||
0.0111064 | + | 0.999938i | \(0.496465\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −58.8386 | −1.98008 | −0.990038 | − | 0.140801i | \(-0.955032\pi\) | ||||
−0.990038 | + | 0.140801i | \(0.955032\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.30965 | −0.111253 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.6915 | −0.459715 | −0.229857 | − | 0.973224i | \(-0.573826\pi\) | ||||
−0.229857 | + | 0.973224i | \(0.573826\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.70701 | −0.224946 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 50.3742 | 1.68760 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 62.3827 | 2.08756 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.11785 | 0.237923 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.3441 | −0.645881 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.54618 | −0.0515681 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.84980 | −0.128255 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.56513 | 0.185196 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.83800 | 0.0943384 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.6794 | 1.21792 | 0.608960 | − | 0.793201i | \(-0.291587\pi\) | ||||
0.608960 | + | 0.793201i | \(0.291587\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.593512 | 0.0196856 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.4068 | −1.67005 | −0.835026 | − | 0.550211i | \(-0.814547\pi\) | ||||
−0.835026 | + | 0.550211i | \(0.814547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −65.8682 | −2.17992 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.1835 | 1.19619 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.5725 | 0.415181 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.7697 | −0.850065 | −0.425033 | − | 0.905178i | \(-0.639737\pi\) | ||||
−0.425033 | + | 0.905178i | \(0.639737\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.4606 | 0.970761 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.86375 | −0.258839 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.6048 | −0.578843 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.3123 | −0.798522 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.1475 | −0.825061 | −0.412531 | − | 0.910944i | \(-0.635355\pi\) | ||||
−0.412531 | + | 0.910944i | \(0.635355\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.1498 | 1.21754 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −59.8189 | −1.95838 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.90153 | 0.225704 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.223784 | 0.00731069 | 0.00365534 | − | 0.999993i | \(-0.498836\pi\) | ||||
0.00365534 | + | 0.999993i | \(0.498836\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.57362 | 0.181888 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.0456 | 0.490474 | 0.245237 | − | 0.969463i | \(-0.421134\pi\) | ||||
0.245237 | + | 0.969463i | \(0.421134\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.71783 | −0.218763 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.39664 | 0.110493 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.5924 | 0.376701 | 0.188351 | − | 0.982102i | \(-0.439686\pi\) | ||||
0.188351 | + | 0.982102i | \(0.439686\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.7530 | −0.478902 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.29242 | 0.0743368 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.7820 | 1.51542 | 0.757709 | − | 0.652593i | \(-0.226319\pi\) | ||||
0.757709 | + | 0.652593i | \(0.226319\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.40990 | −0.175060 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −86.5265 | −2.79701 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.3698 | 0.399443 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9703 | −0.999043 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −29.5380 | −0.951847 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.02201 | 0.0328997 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.0468 | −0.773291 | −0.386646 | − | 0.922228i | \(-0.626366\pi\) | ||||
−0.386646 | + | 0.922228i | \(0.626366\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.3956 | 0.398205 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.6392 | −1.36836 | −0.684178 | − | 0.729315i | \(-0.739839\pi\) | ||||
−0.684178 | + | 0.729315i | \(0.739839\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.1793 | −0.390451 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.6085 | −0.371771 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.77838 | 0.184867 | 0.0924334 | − | 0.995719i | \(-0.470535\pi\) | ||||
0.0924334 | + | 0.995719i | \(0.470535\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.8323 | 1.81637 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.8297 | −0.505405 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0211 | 0.510993 | 0.255496 | − | 0.966810i | \(-0.417761\pi\) | ||||
0.255496 | + | 0.966810i | \(0.417761\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.09785 | −0.226156 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.3467 | 0.552152 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.2193 | 0.483945 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.3797 | −0.583851 | −0.291926 | − | 0.956441i | \(-0.594296\pi\) | ||||
−0.291926 | + | 0.956441i | \(0.594296\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.0169 | 0.540015 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.27491 | −0.198928 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.66918 | −0.147874 | −0.0739372 | − | 0.997263i | \(-0.523556\pi\) | ||||
−0.0739372 | + | 0.997263i | \(0.523556\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.8077 | −0.626687 |
(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 | 8024.2.a.y.1.19 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.y.1.19 | ✓ | 23 | 1.1 | even | 1 | trivial |