Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6480,2,Mod(1,6480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6480, 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("6480.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6480 = 2^{4} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6480.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: | \(51.7430605098\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.08613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6480.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.08613 | −1.54441 | −0.772206 | − | 0.635372i | \(-0.780847\pi\) | ||||
−0.772206 | + | 0.635372i | \(0.780847\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.35194 | 0.407625 | 0.203813 | − | 0.979010i | \(-0.434667\pi\) | ||||
0.203813 | + | 0.979010i | \(0.434667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.648061 | 0.179740 | 0.0898699 | − | 0.995954i | \(-0.471355\pi\) | ||||
0.0898699 | + | 0.995954i | \(0.471355\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.35194 | −0.327893 | −0.163947 | − | 0.986469i | \(-0.552423\pi\) | ||||
−0.163947 | + | 0.986469i | \(0.552423\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.648061 | −0.148675 | −0.0743377 | − | 0.997233i | \(-0.523684\pi\) | ||||
−0.0743377 | + | 0.997233i | \(0.523684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.79001 | −0.998786 | −0.499393 | − | 0.866376i | \(-0.666444\pi\) | ||||
−0.499393 | + | 0.866376i | \(0.666444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.87614 | 0.719781 | 0.359890 | − | 0.932995i | \(-0.382814\pi\) | ||||
0.359890 | + | 0.932995i | \(0.382814\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.69646 | 1.38233 | 0.691163 | − | 0.722699i | \(-0.257099\pi\) | ||||
0.691163 | + | 0.722699i | \(0.257099\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.08613 | −0.690682 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.52420 | 1.23697 | 0.618485 | − | 0.785796i | \(-0.287747\pi\) | ||||
0.618485 | + | 0.785796i | \(0.287747\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.179679 | −0.0280611 | −0.0140306 | − | 0.999902i | \(-0.504466\pi\) | ||||
−0.0140306 | + | 0.999902i | \(0.504466\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.820321 | 0.125098 | 0.0625489 | − | 0.998042i | \(-0.480077\pi\) | ||||
0.0625489 | + | 0.998042i | \(0.480077\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.9065 | −1.59087 | −0.795435 | − | 0.606039i | \(-0.792757\pi\) | ||||
−0.795435 | + | 0.606039i | \(0.792757\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.69646 | 1.38521 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.17226 | 0.573104 | 0.286552 | − | 0.958065i | \(-0.407491\pi\) | ||||
0.286552 | + | 0.958065i | \(0.407491\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.35194 | 0.182295 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.17226 | −0.543182 | −0.271591 | − | 0.962413i | \(-0.587550\pi\) | ||||
−0.271591 | + | 0.962413i | \(0.587550\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.82032 | −0.489142 | −0.244571 | − | 0.969631i | \(-0.578647\pi\) | ||||
−0.244571 | + | 0.969631i | \(0.578647\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.648061 | 0.0803820 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.14195 | −0.994697 | −0.497349 | − | 0.867551i | \(-0.665693\pi\) | ||||
−0.497349 | + | 0.867551i | \(0.665693\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.11644 | 0.725888 | 0.362944 | − | 0.931811i | \(-0.381772\pi\) | ||||
0.362944 | + | 0.931811i | \(0.381772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3445 | −1.44482 | −0.722408 | − | 0.691467i | \(-0.756965\pi\) | ||||
−0.722408 | + | 0.691467i | \(0.756965\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.52420 | −0.629541 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.3445 | −1.16385 | −0.581925 | − | 0.813243i | \(-0.697700\pi\) | ||||
−0.581925 | + | 0.813243i | \(0.697700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2584 | 1.34553 | 0.672767 | − | 0.739855i | \(-0.265106\pi\) | ||||
0.672767 | + | 0.739855i | \(0.265106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.35194 | −0.146638 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.64806 | −0.277592 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.648061 | −0.0664896 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.5800 | −1.37884 | −0.689421 | − | 0.724361i | \(-0.742135\pi\) | ||||
−0.689421 | + | 0.724361i | \(0.742135\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.46838 | −0.146109 | −0.0730547 | − | 0.997328i | \(-0.523275\pi\) | ||||
−0.0730547 | + | 0.997328i | \(0.523275\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.52420 | −0.741381 | −0.370691 | − | 0.928756i | \(-0.620879\pi\) | ||||
−0.370691 | + | 0.928756i | \(0.620879\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.20999 | −0.116974 | −0.0584871 | − | 0.998288i | \(-0.518628\pi\) | ||||
−0.0584871 | + | 0.998288i | \(0.518628\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1042 | 1.35094 | 0.675469 | − | 0.737388i | \(-0.263941\pi\) | ||||
0.675469 | + | 0.737388i | \(0.263941\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9245 | −1.12177 | −0.560883 | − | 0.827895i | \(-0.689538\pi\) | ||||
−0.560883 | + | 0.827895i | \(0.689538\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.79001 | −0.446671 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.52420 | 0.506403 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.17226 | −0.833842 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.07871 | 0.628134 | 0.314067 | − | 0.949401i | \(-0.398308\pi\) | ||||
0.314067 | + | 0.949401i | \(0.398308\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.64806 | 0.229616 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.46838 | −0.638067 | −0.319033 | − | 0.947743i | \(-0.603358\pi\) | ||||
−0.319033 | + | 0.947743i | \(0.603358\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.876139 | 0.0732664 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.87614 | 0.321896 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5848 | −0.867143 | −0.433571 | − | 0.901119i | \(-0.642747\pi\) | ||||
−0.433571 | + | 0.901119i | \(0.642747\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.6965 | −1.44012 | −0.720059 | − | 0.693913i | \(-0.755885\pi\) | ||||
−0.720059 | + | 0.693913i | \(0.755885\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.69646 | 0.618195 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.53162 | −0.202045 | −0.101023 | − | 0.994884i | \(-0.532211\pi\) | ||||
−0.101023 | + | 0.994884i | \(0.532211\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.5726 | 1.54254 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.47580 | −0.663876 | −0.331938 | − | 0.943301i | \(-0.607702\pi\) | ||||
−0.331938 | + | 0.943301i | \(0.607702\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.7342 | −0.985401 | −0.492701 | − | 0.870199i | \(-0.663990\pi\) | ||||
−0.492701 | + | 0.870199i | \(0.663990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5800 | −0.967694 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.0484 | 1.75234 | 0.876169 | − | 0.482005i | \(-0.160091\pi\) | ||||
0.876169 | + | 0.482005i | \(0.160091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.08613 | −0.308882 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.22808 | −0.166534 | −0.0832672 | − | 0.996527i | \(-0.526535\pi\) | ||||
−0.0832672 | + | 0.996527i | \(0.526535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.468382 | 0.0348146 | 0.0174073 | − | 0.999848i | \(-0.494459\pi\) | ||||
0.0174073 | + | 0.999848i | \(0.494459\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.52420 | 0.553190 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.82774 | −0.133658 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.2281 | 1.46365 | 0.731826 | − | 0.681491i | \(-0.238668\pi\) | ||||
0.731826 | + | 0.681491i | \(0.238668\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.9293 | −1.43455 | −0.717273 | − | 0.696792i | \(-0.754610\pi\) | ||||
−0.717273 | + | 0.696792i | \(0.754610\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.5800 | −1.11003 | −0.555015 | − | 0.831840i | \(-0.687288\pi\) | ||||
−0.555015 | + | 0.831840i | \(0.687288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.58482 | −0.254121 | −0.127061 | − | 0.991895i | \(-0.540554\pi\) | ||||
−0.127061 | + | 0.991895i | \(0.540554\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.8384 | −1.11164 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.179679 | −0.0125493 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.876139 | −0.0606038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9926 | −1.03213 | −0.516066 | − | 0.856549i | \(-0.672604\pi\) | ||||
−0.516066 | + | 0.856549i | \(0.672604\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.820321 | 0.0559454 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.4487 | −2.13488 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.876139 | −0.0589355 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.8310 | 1.79674 | 0.898368 | − | 0.439244i | \(-0.144754\pi\) | ||||
0.898368 | + | 0.439244i | \(0.144754\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.35194 | −0.0897314 | −0.0448657 | − | 0.998993i | \(-0.514286\pi\) | ||||
−0.0448657 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.23550 | −0.544217 | −0.272108 | − | 0.962267i | \(-0.587721\pi\) | ||||
−0.272108 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.58744 | 0.562582 | 0.281291 | − | 0.959623i | \(-0.409237\pi\) | ||||
0.281291 | + | 0.959623i | \(0.409237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9065 | −0.711458 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.9245 | 1.54755 | 0.773775 | − | 0.633461i | \(-0.218366\pi\) | ||||
0.773775 | + | 0.633461i | \(0.218366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.24030 | −0.401973 | −0.200987 | − | 0.979594i | \(-0.564415\pi\) | ||||
−0.200987 | + | 0.979594i | \(0.564415\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.69646 | 0.619484 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.419983 | −0.0267229 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.5726 | 1.80349 | 0.901743 | − | 0.432272i | \(-0.142288\pi\) | ||||
0.901743 | + | 0.432272i | \(0.142288\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.47580 | −0.407130 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.0000 | −1.12281 | −0.561405 | − | 0.827541i | \(-0.689739\pi\) | ||||
−0.561405 | + | 0.827541i | \(0.689739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −30.7449 | −1.91039 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −31.8687 | −1.96511 | −0.982555 | − | 0.185974i | \(-0.940456\pi\) | ||||
−0.982555 | + | 0.185974i | \(0.940456\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.17226 | 0.256300 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.4971 | −1.92041 | −0.960207 | − | 0.279289i | \(-0.909901\pi\) | ||||
−0.960207 | + | 0.279289i | \(0.909901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.24030 | 0.196834 | 0.0984172 | − | 0.995145i | \(-0.468622\pi\) | ||||
0.0984172 | + | 0.995145i | \(0.468622\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.35194 | 0.0815250 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.58482 | −0.335560 | −0.167780 | − | 0.985824i | \(-0.553660\pi\) | ||||
−0.167780 | + | 0.985824i | \(0.553660\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.1042 | −1.43794 | −0.718969 | − | 0.695043i | \(-0.755385\pi\) | ||||
−0.718969 | + | 0.695043i | \(0.755385\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5423 | 0.626674 | 0.313337 | − | 0.949642i | \(-0.398553\pi\) | ||||
0.313337 | + | 0.949642i | \(0.398553\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.734191 | 0.0433379 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1723 | −0.892486 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.9926 | 1.10956 | 0.554779 | − | 0.831998i | \(-0.312803\pi\) | ||||
0.554779 | + | 0.831998i | \(0.312803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.17226 | −0.242918 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.10422 | −0.179521 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.35194 | −0.193203 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.82032 | −0.218751 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.4791 | −1.68246 | −0.841229 | − | 0.540679i | \(-0.818167\pi\) | ||||
−0.841229 | + | 0.540679i | \(0.818167\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.41256 | 0.533738 | 0.266869 | − | 0.963733i | \(-0.414011\pi\) | ||||
0.266869 | + | 0.963733i | \(0.414011\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6210 | 0.656858 | 0.328429 | − | 0.944529i | \(-0.393481\pi\) | ||||
0.328429 | + | 0.944529i | \(0.393481\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.17968 | −0.515582 | −0.257791 | − | 0.966201i | \(-0.582995\pi\) | ||||
−0.257791 | + | 0.966201i | \(0.582995\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.24030 | 0.293401 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.876139 | 0.0487497 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.648061 | 0.0359479 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 44.5652 | 2.45696 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.22066 | 0.396883 | 0.198442 | − | 0.980113i | \(-0.436412\pi\) | ||||
0.198442 | + | 0.980113i | \(0.436412\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.14195 | −0.444842 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.28390 | 0.124412 | 0.0622059 | − | 0.998063i | \(-0.480186\pi\) | ||||
0.0622059 | + | 0.998063i | \(0.480186\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4051 | 0.563470 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.0181 | −0.594921 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.708686 | 0.0380443 | 0.0190221 | − | 0.999819i | \(-0.493945\pi\) | ||||
0.0190221 | + | 0.999819i | \(0.493945\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.3445 | −1.14255 | −0.571273 | − | 0.820760i | \(-0.693550\pi\) | ||||
−0.571273 | + | 0.820760i | \(0.693550\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0968 | −0.537398 | −0.268699 | − | 0.963224i | \(-0.586594\pi\) | ||||
−0.268699 | + | 0.963224i | \(0.586594\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.11644 | 0.324627 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.5578 | −1.61278 | −0.806388 | − | 0.591386i | \(-0.798581\pi\) | ||||
−0.806388 | + | 0.591386i | \(0.798581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5800 | −0.977896 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.3445 | −0.646142 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.17968 | 0.374776 | 0.187388 | − | 0.982286i | \(-0.439998\pi\) | ||||
0.187388 | + | 0.982286i | \(0.439998\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.0484 | −0.885109 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.9245 | −1.13521 | −0.567605 | − | 0.823301i | \(-0.692130\pi\) | ||||
−0.567605 | + | 0.823301i | \(0.692130\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.51197 | 0.129373 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3929 | 0.893414 | 0.446707 | − | 0.894680i | \(-0.352597\pi\) | ||||
0.446707 | + | 0.894680i | \(0.352597\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.475800 | −0.0243123 | −0.0121561 | − | 0.999926i | \(-0.503870\pi\) | ||||
−0.0121561 | + | 0.999926i | \(0.503870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.52420 | −0.281539 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.58744 | −0.283294 | −0.141647 | − | 0.989917i | \(-0.545240\pi\) | ||||
−0.141647 | + | 0.989917i | \(0.545240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.47580 | 0.327495 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.3445 | −0.520489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.75228 | 0.188321 | 0.0941607 | − | 0.995557i | \(-0.469983\pi\) | ||||
0.0941607 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.5652 | 1.17679 | 0.588394 | − | 0.808574i | \(-0.299760\pi\) | ||||
0.588394 | + | 0.808574i | \(0.299760\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.98777 | 0.248459 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.1723 | 0.504220 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.04840 | 0.0518400 | 0.0259200 | − | 0.999664i | \(-0.491748\pi\) | ||||
0.0259200 | + | 0.999664i | \(0.491748\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.0484 | 0.838897 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.2584 | 0.601741 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.9197 | 1.26626 | 0.633131 | − | 0.774045i | \(-0.281769\pi\) | ||||
0.633131 | + | 0.774045i | \(0.281769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.64064 | 0.372382 | 0.186191 | − | 0.982514i | \(-0.440386\pi\) | ||||
0.186191 | + | 0.982514i | \(0.440386\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.35194 | −0.0655787 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.6103 | 0.755437 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.98516 | −0.384632 | −0.192316 | − | 0.981333i | \(-0.561600\pi\) | ||||
−0.192316 | + | 0.981333i | \(0.561600\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.5120 | −0.601287 | −0.300644 | − | 0.953737i | \(-0.597201\pi\) | ||||
−0.300644 | + | 0.953737i | \(0.597201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.10422 | 0.148495 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.76450 | 0.418307 | 0.209153 | − | 0.977883i | \(-0.432929\pi\) | ||||
0.209153 | + | 0.977883i | \(0.432929\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.67095 | −0.174412 | −0.0872062 | − | 0.996190i | \(-0.527794\pi\) | ||||
−0.0872062 | + | 0.996190i | \(0.527794\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | −0.142214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.1723 | 1.32953 | 0.664766 | − | 0.747052i | \(-0.268531\pi\) | ||||
0.664766 | + | 0.747052i | \(0.268531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.242915 | −0.0114384 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.64806 | −0.124143 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.2616 | 1.64947 | 0.824735 | − | 0.565519i | \(-0.191324\pi\) | ||||
0.824735 | + | 0.565519i | \(0.191324\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.6768 | 1.61506 | 0.807530 | − | 0.589826i | \(-0.200804\pi\) | ||||
0.807530 | + | 0.589826i | \(0.200804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.44874 | −0.346172 | −0.173086 | − | 0.984907i | \(-0.555374\pi\) | ||||
−0.173086 | + | 0.984907i | \(0.555374\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.9655 | −1.38664 | −0.693319 | − | 0.720630i | \(-0.743852\pi\) | ||||
−0.693319 | + | 0.720630i | \(0.743852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.2691 | 1.53622 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.10902 | 0.0509930 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.648061 | −0.0297351 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.98516 | 0.364851 | 0.182426 | − | 0.983220i | \(-0.441605\pi\) | ||||
0.182426 | + | 0.983220i | \(0.441605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.87614 | 0.222333 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.5800 | −0.616637 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9442 | 0.541243 | 0.270621 | − | 0.962686i | \(-0.412771\pi\) | ||||
0.270621 | + | 0.962686i | \(0.412771\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.22066 | 0.416123 | 0.208061 | − | 0.978116i | \(-0.433285\pi\) | ||||
0.208061 | + | 0.978116i | \(0.433285\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.24030 | −0.236011 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.9926 | −1.12107 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.1723 | −1.35070 | −0.675348 | − | 0.737499i | \(-0.736007\pi\) | ||||
−0.675348 | + | 0.737499i | \(0.736007\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.5981 | 0.472546 | 0.236273 | − | 0.971687i | \(-0.424074\pi\) | ||||
0.236273 | + | 0.971687i | \(0.424074\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.46838 | −0.0653421 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.7523 | 1.27442 | 0.637211 | − | 0.770689i | \(-0.280088\pi\) | ||||
0.637211 | + | 0.770689i | \(0.280088\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50.4413 | 2.23139 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.52420 | −0.331556 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.7449 | −0.648478 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.0942 | −1.58132 | −0.790658 | − | 0.612259i | \(-0.790261\pi\) | ||||
−0.790658 | + | 0.612259i | \(0.790261\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.1297 | −0.486669 | −0.243334 | − | 0.969942i | \(-0.578241\pi\) | ||||
−0.243334 | + | 0.969942i | \(0.578241\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.4051 | −0.453255 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.0558176 | −0.00242685 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.116443 | −0.00504370 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.20999 | −0.0523125 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.1090 | 0.564646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.7374 | −1.49348 | −0.746740 | − | 0.665116i | \(-0.768382\pi\) | ||||
−0.746740 | + | 0.665116i | \(0.768382\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.1042 | 0.604158 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.71455 | 0.116066 | 0.0580328 | − | 0.998315i | \(-0.481517\pi\) | ||||
0.0580328 | + | 0.998315i | \(0.481517\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.51197 | −0.107014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.2691 | 1.79746 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.93676 | −0.378663 | −0.189331 | − | 0.981913i | \(-0.560632\pi\) | ||||
−0.189331 | + | 0.981913i | \(0.560632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.531618 | 0.0224850 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.36261 | 0.394587 | 0.197293 | − | 0.980344i | \(-0.436785\pi\) | ||||
0.197293 | + | 0.980344i | \(0.436785\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.9245 | −0.501669 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.8735 | 1.50390 | 0.751948 | − | 0.659222i | \(-0.229114\pi\) | ||||
0.751948 | + | 0.659222i | \(0.229114\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.79001 | −0.199757 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.35675 | 0.0564821 | 0.0282411 | − | 0.999601i | \(-0.491009\pi\) | ||||
0.0282411 | + | 0.999601i | \(0.491009\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −50.0894 | −2.07806 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.64064 | 0.233612 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.7900 | −1.18829 | −0.594145 | − | 0.804358i | \(-0.702510\pi\) | ||||
−0.594145 | + | 0.804358i | \(0.702510\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.98777 | −0.205518 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.9171 | 1.26961 | 0.634807 | − | 0.772671i | \(-0.281080\pi\) | ||||
0.634807 | + | 0.772671i | \(0.281080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.52420 | 0.226470 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.39292 | −0.0569132 | −0.0284566 | − | 0.999595i | \(-0.509059\pi\) | ||||
−0.0284566 | + | 0.999595i | \(0.509059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.82513 | 0.359985 | 0.179992 | − | 0.983668i | \(-0.442393\pi\) | ||||
0.179992 | + | 0.983668i | \(0.442393\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.17226 | −0.372905 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.15678 | 0.0875412 | 0.0437706 | − | 0.999042i | \(-0.486063\pi\) | ||||
0.0437706 | + | 0.999042i | \(0.486063\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.06804 | −0.285942 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.57521 | −0.386739 | −0.193370 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193370 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.6768 | −1.51681 | −0.758406 | − | 0.651783i | \(-0.774021\pi\) | ||||
−0.758406 | + | 0.651783i | \(0.774021\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.1042 | −0.687477 | −0.343738 | − | 0.939065i | \(-0.611693\pi\) | ||||
−0.343738 | + | 0.939065i | \(0.611693\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.2584 | 0.491122 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.1723 | −0.405595 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.1090 | −1.31805 | −0.659025 | − | 0.752121i | \(-0.729031\pi\) | ||||
−0.659025 | + | 0.752121i | \(0.729031\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.07871 | 0.280910 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.28390 | 0.248977 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.1526 | −0.914473 | −0.457237 | − | 0.889345i | \(-0.651161\pi\) | ||||
−0.457237 | + | 0.889345i | \(0.651161\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.0639 | −1.69827 | −0.849137 | − | 0.528173i | \(-0.822877\pi\) | ||||
−0.849137 | + | 0.528173i | \(0.822877\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.6439 | 0.811595 | 0.405798 | − | 0.913963i | \(-0.366994\pi\) | ||||
0.405798 | + | 0.913963i | \(0.366994\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.64064 | −0.221415 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.83516 | 0.267480 | 0.133740 | − | 0.991016i | \(-0.457301\pi\) | ||||
0.133740 | + | 0.991016i | \(0.457301\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | 0.234439 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.8613 | 1.04637 | 0.523184 | − | 0.852220i | \(-0.324744\pi\) | ||||
0.523184 | + | 0.852220i | \(0.324744\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.12125 | −0.0825071 | −0.0412535 | − | 0.999149i | \(-0.513135\pi\) | ||||
−0.0412535 | + | 0.999149i | \(0.513135\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.64806 | 0.102687 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.5667 | −0.718907 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.16484 | −0.199387 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.8203 | 1.34222 | 0.671112 | − | 0.741356i | \(-0.265817\pi\) | ||||
0.671112 | + | 0.741356i | \(0.265817\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.6842 | −0.948692 | −0.474346 | − | 0.880338i | \(-0.657315\pi\) | ||||
−0.474346 | + | 0.880338i | \(0.657315\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 55.4897 | 2.12950 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.4610 | 1.47167 | 0.735834 | − | 0.677162i | \(-0.236790\pi\) | ||||
0.735834 | + | 0.677162i | \(0.236790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.46838 | −0.285352 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.70388 | 0.103010 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.480608 | −0.0182832 | −0.00914159 | − | 0.999958i | \(-0.502910\pi\) | ||||
−0.00914159 | + | 0.999958i | \(0.502910\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.00000 | −0.303457 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.242915 | 0.00920105 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.1797 | −0.686637 | −0.343318 | − | 0.939219i | \(-0.611551\pi\) | ||||
−0.343318 | + | 0.939219i | \(0.611551\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.87614 | −0.183907 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.18710 | 0.269917 | 0.134959 | − | 0.990851i | \(-0.456910\pi\) | ||||
0.134959 | + | 0.990851i | \(0.456910\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.8661 | −1.38065 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.876139 | 0.0327657 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.5168 | −0.466797 | −0.233399 | − | 0.972381i | \(-0.574985\pi\) | ||||
−0.233399 | + | 0.972381i | \(0.574985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.7449 | 1.14500 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.87614 | 0.143956 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.42584 | −0.312497 | −0.156249 | − | 0.987718i | \(-0.549940\pi\) | ||||
−0.156249 | + | 0.987718i | \(0.549940\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.10902 | −0.0410187 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.0074 | −0.405463 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.81290 | 0.0666887 | 0.0333444 | − | 0.999444i | \(-0.489384\pi\) | ||||
0.0333444 | + | 0.999444i | \(0.489384\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.1371 | −0.738760 | −0.369380 | − | 0.929278i | \(-0.620430\pi\) | ||||
−0.369380 | + | 0.929278i | \(0.620430\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5848 | −0.387798 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.94418 | 0.180656 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.2132 | −0.445668 | −0.222834 | − | 0.974856i | \(-0.571531\pi\) | ||||
−0.222834 | + | 0.974856i | \(0.571531\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.6965 | −0.644040 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.9533 | 1.92462 | 0.962310 | − | 0.271955i | \(-0.0876701\pi\) | ||||
0.962310 | + | 0.271955i | \(0.0876701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.4535 | −0.668940 | −0.334470 | − | 0.942406i | \(-0.608557\pi\) | ||||
−0.334470 | + | 0.942406i | \(0.608557\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −57.6317 | −2.08641 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.70388 | −0.0976314 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.45355 | −0.160599 | −0.0802995 | − | 0.996771i | \(-0.525588\pi\) | ||||
−0.0802995 | + | 0.996771i | \(0.525588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.9368 | 1.40046 | 0.700229 | − | 0.713918i | \(-0.253081\pi\) | ||||
0.700229 | + | 0.713918i | \(0.253081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.69646 | 0.276465 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.116443 | 0.00417200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.26906 | 0.295890 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.53162 | −0.0903573 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.2281 | −1.22010 | −0.610050 | − | 0.792363i | \(-0.708850\pi\) | ||||
−0.610050 | + | 0.792363i | \(0.708850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.7252 | 1.73247 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.47580 | −0.0879183 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.9655 | 0.848902 | 0.424451 | − | 0.905451i | \(-0.360467\pi\) | ||||
0.424451 | + | 0.905451i | \(0.360467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.7449 | 0.521636 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.6890 | −0.588943 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.5726 | 0.689843 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.283896 | −0.00998124 | −0.00499062 | − | 0.999988i | \(-0.501589\pi\) | ||||
−0.00499062 | + | 0.999988i | \(0.501589\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.4413 | −1.13917 | −0.569584 | − | 0.821933i | \(-0.692896\pi\) | ||||
−0.569584 | + | 0.821933i | \(0.692896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.47580 | −0.296894 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.531618 | −0.0185990 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.6694 | 1.45427 | 0.727136 | − | 0.686493i | \(-0.240851\pi\) | ||||
0.727136 | + | 0.686493i | \(0.240851\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.3626 | 0.674938 | 0.337469 | − | 0.941337i | \(-0.390429\pi\) | ||||
0.337469 | + | 0.941337i | \(0.390429\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.8097 | −0.654076 | −0.327038 | − | 0.945011i | \(-0.606050\pi\) | ||||
−0.327038 | + | 0.945011i | \(0.606050\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.1016 | −1.14967 | −0.574833 | − | 0.818271i | \(-0.694933\pi\) | ||||
−0.574833 | + | 0.818271i | \(0.694933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.1090 | −0.454201 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.7342 | −0.440685 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.6965 | 1.37047 | 0.685237 | − | 0.728320i | \(-0.259699\pi\) | ||||
0.685237 | + | 0.728320i | \(0.259699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9755 | −0.481915 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.5800 | −0.432766 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.4791 | 1.28780 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0410 | −1.23547 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.11644 | −0.140944 | −0.0704722 | − | 0.997514i | \(-0.522451\pi\) | ||||
−0.0704722 | + | 0.997514i | \(0.522451\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.7449 | 0.503675 | 0.251837 | − | 0.967770i | \(-0.418965\pi\) | ||||
0.251837 | + | 0.967770i | \(0.418965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.8539 | 1.29156 | 0.645779 | − | 0.763524i | \(-0.276533\pi\) | ||||
0.645779 | + | 0.763524i | \(0.276533\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.7704 | −0.911274 | −0.455637 | − | 0.890166i | \(-0.650588\pi\) | ||||
−0.455637 | + | 0.890166i | \(0.650588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.0484 | 0.783669 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.9852 | −0.474414 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.27648 | −0.178787 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.08613 | −0.138136 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.9681 | −1.58600 | −0.793001 | − | 0.609221i | \(-0.791482\pi\) | ||||
−0.793001 | + | 0.609221i | \(0.791482\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.8055 | −0.667264 | −0.333632 | − | 0.942703i | \(-0.608274\pi\) | ||||
−0.333632 | + | 0.942703i | \(0.608274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.20257 | 0.208733 | 0.104367 | − | 0.994539i | \(-0.466718\pi\) | ||||
0.104367 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.4274 | −0.450848 | −0.225424 | − | 0.974261i | \(-0.572377\pi\) | ||||
−0.225424 | + | 0.974261i | \(0.572377\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.9245 | −0.970098 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.06804 | 0.236523 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.22808 | −0.0744764 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.8325 | 0.994971 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.64064 | −0.187917 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.468382 | 0.0155695 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.673566 | −0.0223654 | −0.0111827 | − | 0.999937i | \(-0.503560\pi\) | ||||
−0.0111827 | + | 0.999937i | \(0.503560\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.90970 | 0.262060 | 0.131030 | − | 0.991378i | \(-0.458172\pi\) | ||||
0.131030 | + | 0.991378i | \(0.458172\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.5726 | 0.548473 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.5168 | −0.809615 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.58263 | 0.283115 | 0.141557 | − | 0.989930i | \(-0.454789\pi\) | ||||
0.141557 | + | 0.989930i | \(0.454789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.96383 | 0.130471 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.52420 | 0.247394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.6162 | 0.971676 | 0.485838 | − | 0.874049i | \(-0.338515\pi\) | ||||
0.485838 | + | 0.874049i | \(0.338515\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.28390 | −0.205946 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.82774 | −0.0597735 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.2058 | −0.496753 | −0.248376 | − | 0.968664i | \(-0.579897\pi\) | ||||
−0.248376 | + | 0.968664i | \(0.579897\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.65287 | 0.184278 | 0.0921391 | − | 0.995746i | \(-0.470630\pi\) | ||||
0.0921391 | + | 0.995746i | \(0.470630\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.860663 | 0.0280270 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.3962 | 1.31270 | 0.656350 | − | 0.754457i | \(-0.272100\pi\) | ||||
0.656350 | + | 0.754457i | \(0.272100\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00000 | −0.259691 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.9320 | −0.742839 | −0.371419 | − | 0.928465i | \(-0.621129\pi\) | ||||
−0.371419 | + | 0.928465i | \(0.621129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.2281 | 0.654565 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.5168 | 0.985438 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.2355 | 0.910822 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.9293 | −0.641548 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.3700 | −0.333478 | −0.166739 | − | 0.986001i | \(-0.553324\pi\) | ||||
−0.166739 | + | 0.986001i | \(0.553324\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.0410 | −1.54171 | −0.770854 | − | 0.637012i | \(-0.780170\pi\) | ||||
−0.770854 | + | 0.637012i | \(0.780170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.6890 | 1.04796 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.0532 | 0.865509 | 0.432754 | − | 0.901512i | \(-0.357542\pi\) | ||||
0.432754 | + | 0.901512i | \(0.357542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.05582 | −0.129624 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.4817 | 0.717054 | 0.358527 | − | 0.933519i | \(-0.383279\pi\) | ||||
0.358527 | + | 0.933519i | \(0.383279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.5800 | −0.496421 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.92935 | −0.124946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.5316 | 0.842805 | 0.421402 | − | 0.906874i | \(-0.361538\pi\) | ||||
0.421402 | + | 0.906874i | \(0.361538\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.58482 | −0.113647 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.3659 | −0.898356 | −0.449178 | − | 0.893442i | \(-0.648283\pi\) | ||||
−0.449178 | + | 0.893442i | \(0.648283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6480.2.a.bv.1.1 | 3 | ||
3.2 | odd | 2 | 6480.2.a.bs.1.1 | 3 | |||
4.3 | odd | 2 | 405.2.a.j.1.1 | 3 | |||
9.2 | odd | 6 | 2160.2.q.k.1441.3 | 6 | |||
9.4 | even | 3 | 720.2.q.i.241.3 | 6 | |||
9.5 | odd | 6 | 2160.2.q.k.721.3 | 6 | |||
9.7 | even | 3 | 720.2.q.i.481.3 | 6 | |||
12.11 | even | 2 | 405.2.a.i.1.3 | 3 | |||
20.3 | even | 4 | 2025.2.b.l.649.5 | 6 | |||
20.7 | even | 4 | 2025.2.b.l.649.2 | 6 | |||
20.19 | odd | 2 | 2025.2.a.n.1.3 | 3 | |||
36.7 | odd | 6 | 45.2.e.b.31.3 | yes | 6 | ||
36.11 | even | 6 | 135.2.e.b.91.1 | 6 | |||
36.23 | even | 6 | 135.2.e.b.46.1 | 6 | |||
36.31 | odd | 6 | 45.2.e.b.16.3 | ✓ | 6 | ||
60.23 | odd | 4 | 2025.2.b.m.649.2 | 6 | |||
60.47 | odd | 4 | 2025.2.b.m.649.5 | 6 | |||
60.59 | even | 2 | 2025.2.a.o.1.1 | 3 | |||
180.7 | even | 12 | 225.2.k.b.49.2 | 12 | |||
180.23 | odd | 12 | 675.2.k.b.424.5 | 12 | |||
180.43 | even | 12 | 225.2.k.b.49.5 | 12 | |||
180.47 | odd | 12 | 675.2.k.b.199.5 | 12 | |||
180.59 | even | 6 | 675.2.e.b.451.3 | 6 | |||
180.67 | even | 12 | 225.2.k.b.124.5 | 12 | |||
180.79 | odd | 6 | 225.2.e.b.76.1 | 6 | |||
180.83 | odd | 12 | 675.2.k.b.199.2 | 12 | |||
180.103 | even | 12 | 225.2.k.b.124.2 | 12 | |||
180.119 | even | 6 | 675.2.e.b.226.3 | 6 | |||
180.139 | odd | 6 | 225.2.e.b.151.1 | 6 | |||
180.167 | odd | 12 | 675.2.k.b.424.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.b.16.3 | ✓ | 6 | 36.31 | odd | 6 | ||
45.2.e.b.31.3 | yes | 6 | 36.7 | odd | 6 | ||
135.2.e.b.46.1 | 6 | 36.23 | even | 6 | |||
135.2.e.b.91.1 | 6 | 36.11 | even | 6 | |||
225.2.e.b.76.1 | 6 | 180.79 | odd | 6 | |||
225.2.e.b.151.1 | 6 | 180.139 | odd | 6 | |||
225.2.k.b.49.2 | 12 | 180.7 | even | 12 | |||
225.2.k.b.49.5 | 12 | 180.43 | even | 12 | |||
225.2.k.b.124.2 | 12 | 180.103 | even | 12 | |||
225.2.k.b.124.5 | 12 | 180.67 | even | 12 | |||
405.2.a.i.1.3 | 3 | 12.11 | even | 2 | |||
405.2.a.j.1.1 | 3 | 4.3 | odd | 2 | |||
675.2.e.b.226.3 | 6 | 180.119 | even | 6 | |||
675.2.e.b.451.3 | 6 | 180.59 | even | 6 | |||
675.2.k.b.199.2 | 12 | 180.83 | odd | 12 | |||
675.2.k.b.199.5 | 12 | 180.47 | odd | 12 | |||
675.2.k.b.424.2 | 12 | 180.167 | odd | 12 | |||
675.2.k.b.424.5 | 12 | 180.23 | odd | 12 | |||
720.2.q.i.241.3 | 6 | 9.4 | even | 3 | |||
720.2.q.i.481.3 | 6 | 9.7 | even | 3 | |||
2025.2.a.n.1.3 | 3 | 20.19 | odd | 2 | |||
2025.2.a.o.1.1 | 3 | 60.59 | even | 2 | |||
2025.2.b.l.649.2 | 6 | 20.7 | even | 4 | |||
2025.2.b.l.649.5 | 6 | 20.3 | even | 4 | |||
2025.2.b.m.649.2 | 6 | 60.23 | odd | 4 | |||
2025.2.b.m.649.5 | 6 | 60.47 | odd | 4 | |||
2160.2.q.k.721.3 | 6 | 9.5 | odd | 6 | |||
2160.2.q.k.1441.3 | 6 | 9.2 | odd | 6 | |||
6480.2.a.bs.1.1 | 3 | 3.2 | odd | 2 | |||
6480.2.a.bv.1.1 | 3 | 1.1 | even | 1 | trivial |