Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 23x^{8} + 44x^{7} + 167x^{6} - 266x^{5} - 491x^{4} + 460x^{3} + 546x^{2} + 56x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.0787429\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 3.30364 | 1.90736 | 0.953680 | − | 0.300824i | \(-0.0972616\pi\) | ||||
0.953680 | + | 0.300824i | \(0.0972616\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.55295 | 1.14171 | 0.570857 | − | 0.821049i | \(-0.306611\pi\) | ||||
0.570857 | + | 0.821049i | \(0.306611\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32515 | 0.500858 | 0.250429 | − | 0.968135i | \(-0.419428\pi\) | ||||
0.250429 | + | 0.968135i | \(0.419428\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.91406 | 2.63802 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.51756 | 0.759072 | 0.379536 | − | 0.925177i | \(-0.376084\pi\) | ||||
0.379536 | + | 0.925177i | \(0.376084\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.22781 | −0.340532 | −0.170266 | − | 0.985398i | \(-0.554463\pi\) | ||||
−0.170266 | + | 0.985398i | \(0.554463\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.43404 | 2.17766 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.210784 | 0.0511227 | 0.0255614 | − | 0.999673i | \(-0.491863\pi\) | ||||
0.0255614 | + | 0.999673i | \(0.491863\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.37781 | 0.955316 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.11631 | −1.69237 | −0.846184 | − | 0.532891i | \(-0.821105\pi\) | ||||
−0.846184 | + | 0.532891i | \(0.821105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.51756 | 0.303512 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.2343 | 3.12429 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.97458 | 1.10945 | 0.554726 | − | 0.832033i | \(-0.312823\pi\) | ||||
0.554726 | + | 0.832033i | \(0.312823\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.01598 | 1.08050 | 0.540251 | − | 0.841504i | \(-0.318329\pi\) | ||||
0.540251 | + | 0.841504i | \(0.318329\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.31712 | 1.44782 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.38303 | 0.571837 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.2625 | −1.85154 | −0.925769 | − | 0.378089i | \(-0.876581\pi\) | ||||
−0.925769 | + | 0.378089i | \(0.876581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.05623 | −0.649517 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.996870 | 0.155685 | 0.0778424 | − | 0.996966i | \(-0.475197\pi\) | ||||
0.0778424 | + | 0.996966i | \(0.475197\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.83781 | −1.19525 | −0.597627 | − | 0.801774i | \(-0.703890\pi\) | ||||
−0.597627 | + | 0.801774i | \(0.703890\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 20.2042 | 3.01187 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.910938 | −0.132874 | −0.0664369 | − | 0.997791i | \(-0.521163\pi\) | ||||
−0.0664369 | + | 0.997791i | \(0.521163\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.24399 | −0.749141 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.696356 | 0.0975094 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.32429 | −0.456627 | −0.228313 | − | 0.973588i | \(-0.573321\pi\) | ||||
−0.228313 | + | 0.973588i | \(0.573321\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.42720 | 0.866644 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.30364 | 0.437578 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.04859 | −0.266704 | −0.133352 | − | 0.991069i | \(-0.542574\pi\) | ||||
−0.133352 | + | 0.991069i | \(0.542574\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0769 | −1.29022 | −0.645108 | − | 0.764091i | \(-0.723188\pi\) | ||||
−0.645108 | + | 0.764091i | \(0.723188\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.4873 | 1.32127 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.13453 | −0.388790 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7584 | 1.43652 | 0.718260 | − | 0.695775i | \(-0.244939\pi\) | ||||
0.718260 | + | 0.695775i | \(0.244939\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −26.8134 | −3.22795 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9944 | −1.42347 | −0.711737 | − | 0.702446i | \(-0.752091\pi\) | ||||
−0.711737 | + | 0.702446i | \(0.752091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.0038 | 1.52198 | 0.760989 | − | 0.648764i | \(-0.224714\pi\) | ||||
0.760989 | + | 0.648764i | \(0.224714\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.01347 | 0.578906 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.33613 | 0.380187 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0761 | 1.35866 | 0.679332 | − | 0.733831i | \(-0.262270\pi\) | ||||
0.679332 | + | 0.733831i | \(0.262270\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.8902 | 3.32113 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.50788 | −0.494804 | −0.247402 | − | 0.968913i | \(-0.579577\pi\) | ||||
−0.247402 | + | 0.968913i | \(0.579577\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.538122 | 0.0583675 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.7379 | 2.11612 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.64553 | −0.704425 | −0.352213 | − | 0.935920i | \(-0.614571\pi\) | ||||
−0.352213 | + | 0.935920i | \(0.614571\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.62702 | −0.170558 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.8746 | 2.06090 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.55295 | 0.261927 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.92753 | 1.00799 | 0.503994 | − | 0.863707i | \(-0.331863\pi\) | ||||
0.503994 | + | 0.863707i | \(0.331863\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.9241 | 2.00245 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.26920 | 0.126290 | 0.0631450 | − | 0.998004i | \(-0.479887\pi\) | ||||
0.0631450 | + | 0.998004i | \(0.479887\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.4500 | −1.42380 | −0.711901 | − | 0.702280i | \(-0.752166\pi\) | ||||
−0.711901 | + | 0.702280i | \(0.752166\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.1763 | 1.09070 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3868 | −1.00413 | −0.502066 | − | 0.864829i | \(-0.667427\pi\) | ||||
−0.502066 | + | 0.864829i | \(0.667427\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.3639 | −1.47160 | −0.735799 | − | 0.677200i | \(-0.763193\pi\) | ||||
−0.735799 | + | 0.677200i | \(0.763193\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −37.2072 | −3.53155 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.2509 | 1.52876 | 0.764379 | − | 0.644768i | \(-0.223046\pi\) | ||||
0.764379 | + | 0.644768i | \(0.223046\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.7205 | −1.93220 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.71693 | −0.898331 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.279320 | 0.0256052 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.66190 | −0.423809 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.29330 | 0.296947 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.89050 | −0.795191 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.56693 | −0.582721 | −0.291360 | − | 0.956613i | \(-0.594108\pi\) | ||||
−0.291360 | + | 0.956613i | \(0.594108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −25.8933 | −2.27978 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.0235 | −0.875759 | −0.437880 | − | 0.899034i | \(-0.644270\pi\) | ||||
−0.437880 | + | 0.899034i | \(0.644270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.32515 | 0.114905 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 41.4454 | 3.56705 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.01005 | −0.598909 | −0.299455 | − | 0.954111i | \(-0.596805\pi\) | ||||
−0.299455 | + | 0.954111i | \(0.596805\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.13111 | −0.265577 | −0.132789 | − | 0.991144i | \(-0.542393\pi\) | ||||
−0.132789 | + | 0.991144i | \(0.542393\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00941 | −0.253438 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.09107 | −0.258489 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.2528 | 1.26668 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.3243 | −1.42888 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.47186 | 0.612119 | 0.306059 | − | 0.952012i | \(-0.400989\pi\) | ||||
0.306059 | + | 0.952012i | \(0.400989\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.1373 | 1.47599 | 0.737995 | − | 0.674806i | \(-0.235773\pi\) | ||||
0.737995 | + | 0.674806i | \(0.235773\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.66816 | 0.134863 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.3585 | 1.23362 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.69383 | 0.534225 | 0.267113 | − | 0.963665i | \(-0.413930\pi\) | ||||
0.267113 | + | 0.963665i | \(0.413930\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.9823 | −0.870952 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.7553 | −0.847635 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6424 | 1.22521 | 0.612604 | − | 0.790390i | \(-0.290122\pi\) | ||||
0.612604 | + | 0.790390i | \(0.290122\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21.2332 | 1.65300 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.23338 | −0.327588 | −0.163794 | − | 0.986495i | \(-0.552373\pi\) | ||||
−0.163794 | + | 0.986495i | \(0.552373\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4925 | −0.884038 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.91406 | 0.605203 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.25476 | 0.323483 | 0.161742 | − | 0.986833i | \(-0.448289\pi\) | ||||
0.161742 | + | 0.986833i | \(0.448289\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.01099 | 0.152016 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.76781 | −0.508700 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.3171 | 1.51857 | 0.759286 | − | 0.650757i | \(-0.225548\pi\) | ||||
0.759286 | + | 0.650757i | \(0.225548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6430 | 1.23706 | 0.618532 | − | 0.785760i | \(-0.287728\pi\) | ||||
0.618532 | + | 0.785760i | \(0.287728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −33.2905 | −2.46091 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −28.7525 | −2.11393 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.530662 | 0.0388058 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21.5128 | 1.56483 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.9246 | 1.15226 | 0.576132 | − | 0.817357i | \(-0.304561\pi\) | ||||
0.576132 | + | 0.817357i | \(0.304561\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.8762 | −1.86261 | −0.931304 | − | 0.364242i | \(-0.881328\pi\) | ||||
−0.931304 | + | 0.364242i | \(0.881328\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.3554 | −0.741563 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.2850 | −1.30275 | −0.651376 | − | 0.758755i | \(-0.725808\pi\) | ||||
−0.651376 | + | 0.758755i | \(0.725808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0808 | −0.714606 | −0.357303 | − | 0.933989i | \(-0.616304\pi\) | ||||
−0.357303 | + | 0.933989i | \(0.616304\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 38.8456 | 2.73996 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.91719 | 0.555678 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.54496 | 0.177748 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −64.2330 | −4.46450 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.51756 | 0.174143 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8127 | 1.08859 | 0.544297 | − | 0.838893i | \(-0.316796\pi\) | ||||
0.544297 | + | 0.838893i | \(0.316796\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −39.6252 | −2.71508 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.0095 | −1.36464 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.97204 | 0.541178 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 42.9599 | 2.90296 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.258802 | −0.0174089 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.15828 | −0.278459 | −0.139229 | − | 0.990260i | \(-0.544463\pi\) | ||||
−0.139229 | + | 0.990260i | \(0.544463\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.0101 | 0.800670 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.7714 | 1.11315 | 0.556577 | − | 0.830796i | \(-0.312114\pi\) | ||||
0.556577 | + | 0.830796i | \(0.312114\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.32899 | −0.0878220 | −0.0439110 | − | 0.999035i | \(-0.513982\pi\) | ||||
−0.0439110 | + | 0.999035i | \(0.513982\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.0214 | 0.725154 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.4631 | 1.01302 | 0.506510 | − | 0.862234i | \(-0.330935\pi\) | ||||
0.506510 | + | 0.862234i | \(0.330935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.32558 | −0.151704 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 39.8950 | 2.59146 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4564 | −0.999794 | −0.499897 | − | 0.866085i | \(-0.666629\pi\) | ||||
−0.499897 | + | 0.866085i | \(0.666629\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0126 | −0.902632 | −0.451316 | − | 0.892364i | \(-0.649045\pi\) | ||||
−0.451316 | + | 0.892364i | \(0.649045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 50.0436 | 3.21030 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.3877 | −0.855306 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.22781 | −0.0781234 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.8924 | −0.943769 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.36102 | 0.275265 | 0.137632 | − | 0.990483i | \(-0.456051\pi\) | ||||
0.137632 | + | 0.990483i | \(0.456051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.4333 | −1.28463 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.77776 | 0.111328 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.4237 | 1.33637 | 0.668186 | − | 0.743994i | \(-0.267071\pi\) | ||||
0.668186 | + | 0.743994i | \(0.267071\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.9244 | −0.927357 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 47.2832 | 2.92676 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.37369 | 0.331356 | 0.165678 | − | 0.986180i | \(-0.447019\pi\) | ||||
0.165678 | + | 0.986180i | \(0.447019\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.48676 | −0.521338 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.9545 | −1.34359 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0684 | 0.613879 | 0.306940 | − | 0.951729i | \(-0.400695\pi\) | ||||
0.306940 | + | 0.951729i | \(0.400695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.6347 | 1.67869 | 0.839344 | − | 0.543601i | \(-0.182940\pi\) | ||||
0.839344 | + | 0.543601i | \(0.182940\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.37510 | −0.325316 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.82054 | 0.230387 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.52596 | −0.572360 | −0.286180 | − | 0.958176i | \(-0.592385\pi\) | ||||
−0.286180 | + | 0.958176i | \(0.592385\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 47.6108 | 2.85038 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.6168 | −1.64748 | −0.823739 | − | 0.566969i | \(-0.808116\pi\) | ||||
−0.823739 | + | 0.566969i | \(0.808116\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0192 | 1.01168 | 0.505842 | − | 0.862626i | \(-0.331182\pi\) | ||||
0.505842 | + | 0.862626i | \(0.331182\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.43404 | 0.499589 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.32100 | 0.0779760 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9556 | −0.997386 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.7970 | 1.92260 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.8952 | −0.811767 | −0.405884 | − | 0.913925i | \(-0.633036\pi\) | ||||
−0.405884 | + | 0.913925i | \(0.633036\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.22995 | −0.304499 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 40.8708 | 2.37157 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.96525 | 0.576305 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3862 | −0.598652 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.19298 | 0.240880 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −25.7259 | −1.47306 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.57307 | −0.489291 | −0.244645 | − | 0.969613i | \(-0.578672\pi\) | ||||
−0.244645 | + | 0.969613i | \(0.578672\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −47.7377 | −2.71570 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.7442 | 1.06288 | 0.531442 | − | 0.847094i | \(-0.321650\pi\) | ||||
0.531442 | + | 0.847094i | \(0.321650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.267307 | −0.0151091 | −0.00755454 | − | 0.999971i | \(-0.502405\pi\) | ||||
−0.00755454 | + | 0.999971i | \(0.502405\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.7735 | 1.50852 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.3865 | −1.36968 | −0.684841 | − | 0.728693i | \(-0.740128\pi\) | ||||
−0.684841 | + | 0.728693i | \(0.740128\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.0414 | 0.842155 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −34.3144 | −1.91524 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.210784 | 0.0117284 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.86327 | −0.103355 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −50.7570 | −2.80687 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.20712 | −0.0665509 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.8978 | 0.873824 | 0.436912 | − | 0.899504i | \(-0.356072\pi\) | ||||
0.436912 | + | 0.899504i | \(0.356072\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −89.1319 | −4.88440 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 30.0187 | 1.64009 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.4174 | −1.27563 | −0.637814 | − | 0.770190i | \(-0.720161\pi\) | ||||
−0.637814 | + | 0.770190i | \(0.720161\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 53.6872 | 2.91589 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.1456 | 0.820179 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.2251 | −0.876071 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −68.4533 | −3.68540 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.166224 | −0.00892336 | −0.00446168 | − | 0.999990i | \(-0.501420\pi\) | ||||
−0.00446168 | + | 0.999990i | \(0.501420\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.92636 | −0.210173 | −0.105087 | − | 0.994463i | \(-0.533512\pi\) | ||||
−0.105087 | + | 0.994463i | \(0.533512\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.9326 | −1.06392 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.45111 | 0.503032 | 0.251516 | − | 0.967853i | \(-0.419071\pi\) | ||||
0.251516 | + | 0.967853i | \(0.419071\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.6211 | −1.62520 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.922773 | 0.0488383 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.81041 | 0.412218 | 0.206109 | − | 0.978529i | \(-0.433920\pi\) | ||||
0.206109 | + | 0.978529i | \(0.433920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.4013 | −0.808356 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 33.1980 | 1.73766 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.3412 | 1.79260 | 0.896298 | − | 0.443452i | \(-0.146246\pi\) | ||||
0.896298 | + | 0.443452i | \(0.146246\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.88929 | 0.410700 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.40517 | −0.228705 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.9919 | 1.76004 | 0.880018 | − | 0.474941i | \(-0.157531\pi\) | ||||
0.880018 | + | 0.474941i | \(0.157531\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −29.3711 | −1.51671 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.33563 | −0.377804 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.11882 | −0.211570 | −0.105785 | − | 0.994389i | \(-0.533735\pi\) | ||||
−0.105785 | + | 0.994389i | \(0.533735\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.6948 | −1.11146 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.5442 | 0.896467 | 0.448233 | − | 0.893917i | \(-0.352053\pi\) | ||||
0.448233 | + | 0.893917i | \(0.352053\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.51698 | 0.434065 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −62.0289 | −3.15310 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.23423 | 0.113280 | 0.0566399 | − | 0.998395i | \(-0.481961\pi\) | ||||
0.0566399 | + | 0.998395i | \(0.481961\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.71079 | −0.0865184 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −33.1142 | −1.67039 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.8296 | 1.55121 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.4349 | 0.774655 | 0.387327 | − | 0.921942i | \(-0.373398\pi\) | ||||
0.387327 | + | 0.921942i | \(0.373398\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.37781 | 0.219164 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.3503 | −1.11612 | −0.558061 | − | 0.829800i | \(-0.688454\pi\) | ||||
−0.558061 | + | 0.829800i | \(0.688454\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.38645 | −0.367945 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 76.3082 | 3.79178 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.3539 | −1.40545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.58617 | −0.424559 | −0.212279 | − | 0.977209i | \(-0.568089\pi\) | ||||
−0.212279 | + | 0.977209i | \(0.568089\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.1587 | −1.14234 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.71468 | −0.133581 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.5084 | −0.564925 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.3441 | −0.506551 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.9670 | 1.07316 | 0.536579 | − | 0.843850i | \(-0.319716\pi\) | ||||
0.536579 | + | 0.843850i | \(0.319716\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3942 | 1.09143 | 0.545713 | − | 0.837972i | \(-0.316259\pi\) | ||||
0.545713 | + | 0.837972i | \(0.316259\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.20922 | −0.350524 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.319878 | 0.0155163 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.3534 | −0.646215 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.2118 | −0.493031 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.39422 | −0.356167 | −0.178084 | − | 0.984015i | \(-0.556990\pi\) | ||||
−0.178084 | + | 0.984015i | \(0.556990\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.0766 | −1.44539 | −0.722694 | − | 0.691168i | \(-0.757097\pi\) | ||||
−0.722694 | + | 0.691168i | \(0.757097\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 50.3899 | 2.41601 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.11631 | −0.388256 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.3397 | 0.779850 | 0.389925 | − | 0.920847i | \(-0.372501\pi\) | ||||
0.389925 | + | 0.920847i | \(0.372501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −41.5013 | −1.97625 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.07589 | 0.193651 | 0.0968256 | − | 0.995301i | \(-0.469131\pi\) | ||||
0.0968256 | + | 0.995301i | \(0.469131\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.9657 | −0.804252 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 24.6844 | 1.16753 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.21892 | 0.199103 | 0.0995517 | − | 0.995032i | \(-0.468259\pi\) | ||||
0.0995517 | + | 0.995032i | \(0.468259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.50968 | 0.118176 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 59.9191 | 2.81525 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.15370 | −0.194729 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.8382 | −1.34899 | −0.674496 | − | 0.738278i | \(-0.735639\pi\) | ||||
−0.674496 | + | 0.738278i | \(0.735639\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.42194 | 0.159722 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.0261 | 1.44503 | 0.722514 | − | 0.691356i | \(-0.242986\pi\) | ||||
0.722514 | + | 0.691356i | \(0.242986\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5849 | 0.584870 | 0.292435 | − | 0.956285i | \(-0.405535\pi\) | ||||
0.292435 | + | 0.956285i | \(0.405535\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 50.7390 | 2.35296 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.8849 | −1.29036 | −0.645179 | − | 0.764032i | \(-0.723217\pi\) | ||||
−0.645179 | + | 0.764032i | \(0.723217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.5816 | 0.719492 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.1140 | 1.01896 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.7321 | −0.907284 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.51756 | 0.0696304 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.3087 | −1.20459 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.7138 | −0.535217 | −0.267608 | − | 0.963528i | \(-0.586233\pi\) | ||||
−0.267608 | + | 0.963528i | \(0.586233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.8281 | 0.630508 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −35.5316 | −1.61675 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.3445 | 1.15083 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.07492 | 0.365909 | 0.182955 | − | 0.983121i | \(-0.441434\pi\) | ||||
0.182955 | + | 0.983121i | \(0.441434\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 51.6769 | 2.33691 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0953 | −0.681240 | −0.340620 | − | 0.940201i | \(-0.610637\pi\) | ||||
−0.340620 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.25935 | 0.0567182 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 50.8653 | 2.28622 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.8943 | −0.712958 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.2381 | 1.39841 | 0.699205 | − | 0.714922i | \(-0.253538\pi\) | ||||
0.699205 | + | 0.714922i | \(0.253538\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.9856 | −0.624829 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.7755 | −0.970920 | −0.485460 | − | 0.874259i | \(-0.661348\pi\) | ||||
−0.485460 | + | 0.874259i | \(0.661348\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.24020 | 0.144187 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.9671 | −1.68618 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.88080 | 0.216338 | 0.108169 | − | 0.994133i | \(-0.465501\pi\) | ||||
0.108169 | + | 0.994133i | \(0.465501\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.2319 | 0.762295 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.2343 | 0.716762 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.8902 | −1.62558 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.29334 | −0.100861 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.0562 | 0.616998 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8112 | −0.473645 | −0.236823 | − | 0.971553i | \(-0.576106\pi\) | ||||
−0.236823 | + | 0.971553i | \(0.576106\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.1722 | −0.925798 | −0.462899 | − | 0.886411i | \(-0.653191\pi\) | ||||
−0.462899 | + | 0.886411i | \(0.653191\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.64358 | 0.289950 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.26807 | 0.0552382 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 42.8745 | 1.86411 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.2127 | −0.703570 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.22396 | −0.0530157 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.5170 | −1.14643 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 67.1205 | 2.89646 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.2021 | −0.568653 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.1179 | 0.649969 | 0.324984 | − | 0.945719i | \(-0.394641\pi\) | ||||
0.324984 | + | 0.945719i | \(0.394641\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 54.9825 | 2.35952 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −39.2234 | −1.68014 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.51960 | 0.236001 | 0.118001 | − | 0.993014i | \(-0.462352\pi\) | ||||
0.118001 | + | 0.993014i | \(0.462352\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −79.7493 | −3.40362 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.97458 | 0.254526 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0025 | 0.680497 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −94.9881 | −4.03202 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.9708 | −0.803820 | −0.401910 | − | 0.915679i | \(-0.631654\pi\) | ||||
−0.401910 | + | 0.915679i | \(0.631654\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.62330 | 0.407022 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.75312 | 0.0740167 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.5505 | 0.655374 | 0.327687 | − | 0.944786i | \(-0.393731\pi\) | ||||
0.327687 | + | 0.944786i | \(0.393731\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 41.4878 | 1.74540 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 39.6088 | 1.66341 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.32025 | 0.139192 | 0.0695960 | − | 0.997575i | \(-0.477829\pi\) | ||||
0.0695960 | + | 0.997575i | \(0.477829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.41420 | 0.352123 | 0.176062 | − | 0.984379i | \(-0.443664\pi\) | ||||
0.176062 | + | 0.984379i | \(0.443664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 52.6092 | 2.19778 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.3170 | −0.513653 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.94857 | 0.247642 | 0.123821 | − | 0.992305i | \(-0.460485\pi\) | ||||
0.123821 | + | 0.992305i | \(0.460485\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −85.4857 | −3.55266 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.97359 | −0.247826 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.36911 | −0.346613 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.8068 | −1.02564 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.1449 | 1.12039 | 0.560196 | − | 0.828360i | \(-0.310726\pi\) | ||||
0.560196 | + | 0.828360i | \(0.310726\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.01598 | 0.247884 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −60.4071 | −2.48482 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.3801 | −1.00117 | −0.500585 | − | 0.865687i | \(-0.666882\pi\) | ||||
−0.500585 | + | 0.865687i | \(0.666882\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.713090 | 0.0292338 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −33.3032 | −1.36301 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.7108 | −0.764502 | −0.382251 | − | 0.924059i | \(-0.624851\pi\) | ||||
−0.382251 | + | 0.924059i | \(0.624851\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.2967 | −1.80690 | −0.903451 | − | 0.428692i | \(-0.858975\pi\) | ||||
−0.903451 | + | 0.428692i | \(0.858975\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 93.0568 | 3.78957 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.9016 | −0.483869 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.5153 | 1.23858 | 0.619290 | − | 0.785163i | \(-0.287421\pi\) | ||||
0.619290 | + | 0.785163i | \(0.287421\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.1556 | 1.05988 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.11845 | 0.0452478 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3377 | 0.861822 | 0.430911 | − | 0.902395i | \(-0.358192\pi\) | ||||
0.430911 | + | 0.902395i | \(0.358192\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.40764 | 0.339029 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.5271 | 0.947163 | 0.473582 | − | 0.880750i | \(-0.342961\pi\) | ||||
0.473582 | + | 0.880750i | \(0.342961\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.0716 | 0.726357 | 0.363179 | − | 0.931720i | \(-0.381692\pi\) | ||||
0.363179 | + | 0.931720i | \(0.381692\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −131.763 | −5.28745 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.80630 | −0.352817 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.2848 | −1.21139 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.31712 | 0.332154 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.37395 | −0.0946557 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.2280 | 0.526600 | 0.263300 | − | 0.964714i | \(-0.415189\pi\) | ||||
0.263300 | + | 0.964714i | \(0.415189\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 52.2397 | 2.07634 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.7650 | −0.665301 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.43860 | 0.255107 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −94.9245 | −3.75515 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.1208 | −1.18970 | −0.594851 | − | 0.803836i | \(-0.702789\pi\) | ||||
−0.594851 | + | 0.803836i | \(0.702789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.7964 | −0.977876 | −0.488938 | − | 0.872319i | \(-0.662616\pi\) | ||||
−0.488938 | + | 0.872319i | \(0.662616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −66.1044 | −2.60286 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.8386 | 0.897880 | 0.448940 | − | 0.893562i | \(-0.351802\pi\) | ||||
0.448940 | + | 0.893562i | \(0.351802\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.15744 | −0.202447 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.3368 | 1.03222 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.4823 | 1.27113 | 0.635565 | − | 0.772048i | \(-0.280767\pi\) | ||||
0.635565 | + | 0.772048i | \(0.280767\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.5896 | −0.999867 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 102.913 | 4.01501 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.2055 | 0.670229 | 0.335115 | − | 0.942177i | \(-0.391225\pi\) | ||||
0.335115 | + | 0.942177i | \(0.391225\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.0942 | 0.509305 | 0.254653 | − | 0.967033i | \(-0.418039\pi\) | ||||
0.254653 | + | 0.967033i | \(0.418039\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.854990 | −0.0332051 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.38303 | 0.131188 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.4916 | −1.87760 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.7375 | −0.531121 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.3692 | −0.979368 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.3396 | −0.437110 | −0.218555 | − | 0.975825i | \(-0.570134\pi\) | ||||
−0.218555 | + | 0.975825i | \(0.570134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.6365 | 0.948260 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.2663 | −1.66286 | −0.831429 | − | 0.555631i | \(-0.812477\pi\) | ||||
−0.831429 | + | 0.555631i | \(0.812477\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.1554 | 0.504859 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 55.4066 | 2.12319 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.63100 | −0.291992 | −0.145996 | − | 0.989285i | \(-0.546639\pi\) | ||||
−0.145996 | + | 0.989285i | \(0.546639\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.8963 | −0.683783 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.39051 | −0.167508 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.08159 | 0.155496 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.2177 | −0.769117 | −0.384558 | − | 0.923101i | \(-0.625646\pi\) | ||||
−0.384558 | + | 0.923101i | \(0.625646\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26.4023 | 1.00294 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.99356 | −0.303213 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.210124 | 0.00795903 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 51.0845 | 1.93219 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3108 | 0.502743 | 0.251372 | − | 0.967891i | \(-0.419118\pi\) | ||||
0.251372 | + | 0.967891i | \(0.419118\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.2625 | −0.424772 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.68288 | −0.289354 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.68187 | 0.0632533 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.7864 | 0.893319 | 0.446659 | − | 0.894704i | \(-0.352614\pi\) | ||||
0.446659 | + | 0.894704i | \(0.352614\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 95.5707 | 3.58418 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48.8275 | −1.82861 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.89136 | −0.295120 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −51.0626 | −1.90697 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.77476 | 0.327243 | 0.163622 | − | 0.986523i | \(-0.447682\pi\) | ||||
0.163622 | + | 0.986523i | \(0.447682\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.1484 | −0.713123 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46.2927 | −1.72164 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.06678 | 0.336732 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.1826 | 1.52738 | 0.763689 | − | 0.645584i | \(-0.223386\pi\) | ||||
0.763689 | + | 0.645584i | \(0.223386\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 75.6557 | 2.80206 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.65209 | −0.0611046 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.2810 | −1.78330 | −0.891649 | − | 0.452727i | \(-0.850451\pi\) | ||||
−0.891649 | + | 0.452727i | \(0.850451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −44.2280 | −1.63138 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.6025 | 1.09042 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.7479 | 0.910366 | 0.455183 | − | 0.890398i | \(-0.349574\pi\) | ||||
0.455183 | + | 0.890398i | \(0.349574\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.05623 | −0.149009 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.1141 | −1.47164 | −0.735822 | − | 0.677175i | \(-0.763204\pi\) | ||||
−0.735822 | + | 0.677175i | \(0.763204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.0753 | 0.698865 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.6756 | −1.30530 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.7640 | −0.502927 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.9595 | −1.16622 | −0.583110 | − | 0.812393i | \(-0.698164\pi\) | ||||
−0.583110 | + | 0.812393i | \(0.698164\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.4072 | 0.525029 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46.3036 | 1.68516 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.7492 | 0.935870 | 0.467935 | − | 0.883763i | \(-0.344998\pi\) | ||||
0.467935 | + | 0.883763i | \(0.344998\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −67.5043 | −2.45025 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.4825 | 0.778740 | 0.389370 | − | 0.921082i | \(-0.372693\pi\) | ||||
0.389370 | + | 0.921082i | \(0.372693\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.3594 | −0.737061 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.25873 | 0.153975 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.51527 | 0.0908211 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.9749 | 0.503949 | 0.251975 | − | 0.967734i | \(-0.418920\pi\) | ||||
0.251975 | + | 0.967734i | \(0.418920\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 70.7762 | 2.54894 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.8238 | 0.569143 | 0.284572 | − | 0.958655i | \(-0.408149\pi\) | ||||
0.284572 | + | 0.958655i | \(0.408149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.12960 | 0.327945 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −49.3049 | −1.76880 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.996870 | 0.0357166 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.1966 | −1.08052 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 96.9933 | 3.46626 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.0890 | 0.609933 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.5418 | −0.874820 | −0.437410 | − | 0.899262i | \(-0.644104\pi\) | ||||
−0.437410 | + | 0.899262i | \(0.644104\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.7528 | 0.632015 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.5348 | 0.765690 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3725 | 0.439360 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −28.0372 | −0.994378 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.3819 | 1.71377 | 0.856887 | − | 0.515505i | \(-0.172396\pi\) | ||||
0.856887 | + | 0.515505i | \(0.172396\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.192011 | −0.00679287 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −52.5932 | −1.85829 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.7378 | 1.15529 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.4577 | −0.967758 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.2623 | 1.17089 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.1294 | 0.461604 | 0.230802 | − | 0.973001i | \(-0.425865\pi\) | ||||
0.230802 | + | 0.973001i | \(0.425865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.76569 | −0.132231 | −0.0661157 | − | 0.997812i | \(-0.521061\pi\) | ||||
−0.0661157 | + | 0.997812i | \(0.521061\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 91.2951 | 3.20186 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.9343 | 1.39884 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.83781 | −0.274210 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.8763 | −0.449936 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.5291 | 1.41447 | 0.707237 | − | 0.706977i | \(-0.249941\pi\) | ||||
0.707237 | + | 0.706977i | \(0.249941\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.7979 | 0.480964 | 0.240482 | − | 0.970654i | \(-0.422695\pi\) | ||||
0.240482 | + | 0.970654i | \(0.422695\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.6217 | 0.439432 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.3483 | 1.64646 | 0.823230 | − | 0.567708i | \(-0.192170\pi\) | ||||
0.823230 | + | 0.567708i | \(0.192170\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.49303 | 0.0865865 | 0.0432933 | − | 0.999062i | \(-0.486215\pi\) | ||||
0.0432933 | + | 0.999062i | \(0.486215\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.4704 | −1.09170 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.10535 | −0.0382981 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.8076 | −0.374012 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 97.6652 | 3.37580 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.94935 | 0.136347 | 0.0681733 | − | 0.997673i | \(-0.478283\pi\) | ||||
0.0681733 | + | 0.997673i | \(0.478283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.69567 | 0.230885 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −91.2360 | −3.14233 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.3398 | −1.00932 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.17769 | −0.212268 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 56.2253 | 1.92965 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 91.4097 | 3.13348 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.6335 | −1.63094 | −0.815470 | − | 0.578799i | \(-0.803521\pi\) | ||||
−0.815470 | + | 0.578799i | \(0.803521\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.2042 | 0.690969 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.1888 | 1.71442 | 0.857209 | − | 0.514969i | \(-0.172196\pi\) | ||||
0.857209 | + | 0.514969i | \(0.172196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0894 | 0.378366 | 0.189183 | − | 0.981942i | \(-0.439416\pi\) | ||||
0.189183 | + | 0.981942i | \(0.439416\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.36410 | 0.148728 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.7550 | −1.28520 | −0.642598 | − | 0.766204i | \(-0.722143\pi\) | ||||
−0.642598 | + | 0.766204i | \(0.722143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8622 | 0.369325 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −56.0152 | −1.90237 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.4022 | 1.03132 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4371 | −0.489181 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 78.5671 | 2.65909 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.7812 | −0.398277 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.6274 | −1.47319 | −0.736596 | − | 0.676333i | \(-0.763568\pi\) | ||||
−0.736596 | + | 0.676333i | \(0.763568\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −45.9049 | −1.54833 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.5145 | −0.522698 | −0.261349 | − | 0.965244i | \(-0.584167\pi\) | ||||
−0.261349 | + | 0.965244i | \(0.584167\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.166224 | 0.00559388 | 0.00279694 | − | 0.999996i | \(-0.499110\pi\) | ||||
0.00279694 | + | 0.999996i | \(0.499110\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.2779 | −0.580790 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.04708 | 0.303771 | 0.151886 | − | 0.988398i | \(-0.451465\pi\) | ||||
0.151886 | + | 0.988398i | \(0.451465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.70213 | −0.291860 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 75.2503 | 2.52098 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.910938 | −0.0304834 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 51.8686 | 1.73378 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.9216 | 1.09922 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.9430 | 1.19877 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.700709 | −0.0233440 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −34.3124 | −1.14185 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 42.4887 | 1.41237 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.2748 | −0.540395 | −0.270198 | − | 0.962805i | \(-0.587089\pi\) | ||||
−0.270198 | + | 0.962805i | \(0.587089\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.0445 | 0.333155 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.6990 | −0.387604 | −0.193802 | − | 0.981041i | \(-0.562082\pi\) | ||||
−0.193802 | + | 0.981041i | \(0.562082\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.3488 | −0.375592 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −84.9891 | −2.80965 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.2826 | −0.438631 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0697 | 0.793987 | 0.396994 | − | 0.917821i | \(-0.370053\pi\) | ||||
0.396994 | + | 0.917821i | \(0.370053\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.3224 | −0.933254 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.7268 | 0.484739 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.0915 | −0.561964 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −114.358 | −3.75602 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.5910 | 1.46298 | 0.731491 | − | 0.681851i | \(-0.238825\pi\) | ||||
0.731491 | + | 0.681851i | \(0.238825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.24399 | −0.171865 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 61.9241 | 2.02730 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.35475 | 0.0443052 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.6674 | −1.52456 | −0.762278 | − | 0.647250i | \(-0.775919\pi\) | ||||
−0.762278 | + | 0.647250i | \(0.775919\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.883087 | −0.0288185 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.4624 | 1.25384 | 0.626919 | − | 0.779085i | \(-0.284316\pi\) | ||||
0.626919 | + | 0.779085i | \(0.284316\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.09090 | −0.263476 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 54.9212 | 1.78659 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.6521 | −0.931068 | −0.465534 | − | 0.885030i | \(-0.654138\pi\) | ||||
−0.465534 | + | 0.885030i | \(0.654138\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.9661 | −0.518282 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −80.5642 | −2.61247 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55.7585 | −1.80619 | −0.903097 | − | 0.429437i | \(-0.858712\pi\) | ||||
−0.903097 | + | 0.429437i | \(0.858712\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.6547 | 1.31556 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 49.6913 | 1.60629 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.28934 | −0.299968 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.19198 | 0.167483 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −82.2019 | −2.64892 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −66.0606 | −2.12657 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.84686 | −0.0593909 | −0.0296954 | − | 0.999559i | \(-0.509454\pi\) | ||||
−0.0296954 | + | 0.999559i | \(0.509454\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.696356 | 0.0223702 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.95804 | 0.223294 | 0.111647 | − | 0.993748i | \(-0.464387\pi\) | ||||
0.111647 | + | 0.993748i | \(0.464387\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.14917 | −0.133016 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.15557 | −0.197136 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.75699 | −0.0882039 | −0.0441020 | − | 0.999027i | \(-0.514043\pi\) | ||||
−0.0441020 | + | 0.999027i | \(0.514043\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.7305 | −0.534710 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −121.591 | −3.88211 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.9562 | 1.37009 | 0.685045 | − | 0.728500i | \(-0.259782\pi\) | ||||
0.685045 | + | 0.728500i | \(0.259782\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −46.6807 | −1.48737 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.98791 | −0.126937 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 63.6141 | 2.02281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.1884 | −1.43546 | −0.717729 | − | 0.696323i | \(-0.754818\pi\) | ||||
−0.717729 | + | 0.696323i | \(0.754818\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 52.5208 | 1.66670 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.7357 | −0.815876 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.7095 | 1.06759 | 0.533795 | − | 0.845614i | \(-0.320766\pi\) | ||||
0.533795 | + | 0.845614i | \(0.320766\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −182.838 | −5.78475 |
(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 | 4864.2.a.bt.1.10 | 10 | ||
4.3 | odd | 2 | 4864.2.a.bs.1.2 | 10 | |||
8.3 | odd | 2 | inner | 4864.2.a.bt.1.9 | 10 | ||
8.5 | even | 2 | 4864.2.a.bs.1.1 | 10 | |||
16.3 | odd | 4 | 2432.2.c.j.1217.1 | ✓ | 20 | ||
16.5 | even | 4 | 2432.2.c.j.1217.2 | yes | 20 | ||
16.11 | odd | 4 | 2432.2.c.j.1217.20 | yes | 20 | ||
16.13 | even | 4 | 2432.2.c.j.1217.19 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.j.1217.1 | ✓ | 20 | 16.3 | odd | 4 | ||
2432.2.c.j.1217.2 | yes | 20 | 16.5 | even | 4 | ||
2432.2.c.j.1217.19 | yes | 20 | 16.13 | even | 4 | ||
2432.2.c.j.1217.20 | yes | 20 | 16.11 | odd | 4 | ||
4864.2.a.bs.1.1 | 10 | 8.5 | even | 2 | |||
4864.2.a.bs.1.2 | 10 | 4.3 | odd | 2 | |||
4864.2.a.bt.1.9 | 10 | 8.3 | odd | 2 | inner | ||
4864.2.a.bt.1.10 | 10 | 1.1 | even | 1 | trivial |