Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6044,2,Mod(1,6044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6044, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6044 = 2^{2} \cdot 1511 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6044.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: | \(48.2615829817\) |
Analytic rank: | \(0\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6044.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.38781 | −1.37860 | −0.689302 | − | 0.724474i | \(-0.742083\pi\) | ||||
−0.689302 | + | 0.724474i | \(0.742083\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.32923 | 1.04166 | 0.520831 | − | 0.853660i | \(-0.325622\pi\) | ||||
0.520831 | + | 0.853660i | \(0.325622\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.907839 | 0.343131 | 0.171565 | − | 0.985173i | \(-0.445118\pi\) | ||||
0.171565 | + | 0.985173i | \(0.445118\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.70165 | 0.900549 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.04154 | −0.314036 | −0.157018 | − | 0.987596i | \(-0.550188\pi\) | ||||
−0.157018 | + | 0.987596i | \(0.550188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.23918 | 1.17574 | 0.587868 | − | 0.808957i | \(-0.299967\pi\) | ||||
0.587868 | + | 0.808957i | \(0.299967\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.56176 | −1.43604 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.62050 | −1.60571 | −0.802853 | − | 0.596177i | \(-0.796686\pi\) | ||||
−0.802853 | + | 0.596177i | \(0.796686\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.90051 | 0.436008 | 0.218004 | − | 0.975948i | \(-0.430045\pi\) | ||||
0.218004 | + | 0.975948i | \(0.430045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.16775 | −0.473042 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.80035 | 0.583913 | 0.291956 | − | 0.956432i | \(-0.405694\pi\) | ||||
0.291956 | + | 0.956432i | \(0.405694\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.425308 | 0.0850617 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.712408 | 0.137103 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.30952 | 0.428867 | 0.214433 | − | 0.976739i | \(-0.431210\pi\) | ||||
0.214433 | + | 0.976739i | \(0.431210\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.25461 | 1.12336 | 0.561680 | − | 0.827354i | \(-0.310155\pi\) | ||||
0.561680 | + | 0.827354i | \(0.310155\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.48700 | 0.432931 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.11456 | 0.357427 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0624 | −1.65425 | −0.827125 | − | 0.562018i | \(-0.810025\pi\) | ||||
−0.827125 | + | 0.562018i | \(0.810025\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.1224 | −1.62087 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.97060 | 0.620103 | 0.310052 | − | 0.950720i | \(-0.399654\pi\) | ||||
0.310052 | + | 0.950720i | \(0.399654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.68322 | −0.866684 | −0.433342 | − | 0.901230i | \(-0.642666\pi\) | ||||
−0.433342 | + | 0.901230i | \(0.642666\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.29276 | 0.938069 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.35422 | 1.07272 | 0.536362 | − | 0.843988i | \(-0.319798\pi\) | ||||
0.536362 | + | 0.843988i | \(0.319798\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.17583 | −0.882261 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.8085 | 2.21363 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.38380 | −0.602162 | −0.301081 | − | 0.953599i | \(-0.597347\pi\) | ||||
−0.301081 | + | 0.953599i | \(0.597347\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.42598 | −0.327119 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.53807 | −0.601082 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.1332 | 1.44942 | 0.724710 | − | 0.689054i | \(-0.241974\pi\) | ||||
0.724710 | + | 0.689054i | \(0.241974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.35639 | 1.06993 | 0.534963 | − | 0.844875i | \(-0.320325\pi\) | ||||
0.534963 | + | 0.844875i | \(0.320325\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.45266 | 0.309006 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.87401 | 1.22472 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.6964 | 1.55111 | 0.775557 | − | 0.631277i | \(-0.217469\pi\) | ||||
0.775557 | + | 0.631277i | \(0.217469\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.68670 | −0.804985 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0778 | 1.31469 | 0.657345 | − | 0.753590i | \(-0.271680\pi\) | ||||
0.657345 | + | 0.753590i | \(0.271680\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.989184 | −0.115775 | −0.0578876 | − | 0.998323i | \(-0.518437\pi\) | ||||
−0.0578876 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.01556 | −0.117266 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.945549 | −0.107755 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.07763 | 1.02131 | 0.510656 | − | 0.859785i | \(-0.329402\pi\) | ||||
0.510656 | + | 0.859785i | \(0.329402\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.80604 | −1.08956 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.8401 | −1.84844 | −0.924219 | − | 0.381863i | \(-0.875283\pi\) | ||||
−0.924219 | + | 0.381863i | \(0.875283\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.4207 | −1.67261 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.51470 | −0.591238 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.38252 | −0.252547 | −0.126273 | − | 0.991995i | \(-0.540302\pi\) | ||||
−0.126273 | + | 0.991995i | \(0.540302\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.84849 | 0.403431 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.9348 | −1.54867 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.42673 | 0.454173 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.71850 | 0.479091 | 0.239545 | − | 0.970885i | \(-0.423002\pi\) | ||||
0.239545 | + | 0.970885i | \(0.423002\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.81387 | −0.282805 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.75643 | −0.572786 | −0.286393 | − | 0.958112i | \(-0.592456\pi\) | ||||
−0.286393 | + | 0.958112i | \(0.592456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.952242 | −0.0938272 | −0.0469136 | − | 0.998899i | \(-0.514939\pi\) | ||||
−0.0469136 | + | 0.998899i | \(0.514939\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.04918 | −0.492750 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.85561 | −0.662757 | −0.331378 | − | 0.943498i | \(-0.607514\pi\) | ||||
−0.331378 | + | 0.943498i | \(0.607514\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.85367 | 0.369114 | 0.184557 | − | 0.982822i | \(-0.440915\pi\) | ||||
0.184557 | + | 0.982822i | \(0.440915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.0272 | 2.28056 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.79313 | 0.827188 | 0.413594 | − | 0.910461i | \(-0.364273\pi\) | ||||
0.413594 | + | 0.910461i | \(0.364273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.52265 | 0.608240 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.4528 | 1.05881 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.01035 | −0.550967 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.91520 | −0.901382 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.48105 | −0.854877 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.6555 | −0.953057 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2679 | 1.17734 | 0.588668 | − | 0.808375i | \(-0.299652\pi\) | ||||
0.588668 | + | 0.808375i | \(0.299652\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.5705 | 1.19481 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2514 | 0.983042 | 0.491521 | − | 0.870866i | \(-0.336441\pi\) | ||||
0.491521 | + | 0.870866i | \(0.336441\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.72536 | 0.149608 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.65936 | 0.142815 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.5519 | −1.67043 | −0.835214 | − | 0.549925i | \(-0.814656\pi\) | ||||
−0.835214 | + | 0.549925i | \(0.814656\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.88490 | −0.753608 | −0.376804 | − | 0.926293i | \(-0.622977\pi\) | ||||
−0.376804 | + | 0.926293i | \(0.622977\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.5605 | −1.47886 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.41527 | −0.369223 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.37940 | 0.446735 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.7467 | 1.21629 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.71713 | 0.632212 | 0.316106 | − | 0.948724i | \(-0.397624\pi\) | ||||
0.316106 | + | 0.948724i | \(0.397624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.262069 | −0.0213269 | −0.0106635 | − | 0.999943i | \(-0.503394\pi\) | ||||
−0.0106635 | + | 0.999943i | \(0.503394\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.8863 | −1.44602 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.5684 | 1.17016 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.4092 | 1.62883 | 0.814417 | − | 0.580279i | \(-0.197057\pi\) | ||||
0.814417 | + | 0.580279i | \(0.197057\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.4677 | 0.830143 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.54226 | 0.200358 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.68148 | −0.366682 | −0.183341 | − | 0.983049i | \(-0.558691\pi\) | ||||
−0.183341 | + | 0.983049i | \(0.558691\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.79279 | 0.450968 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.37414 | −0.183716 | −0.0918581 | − | 0.995772i | \(-0.529281\pi\) | ||||
−0.0918581 | + | 0.995772i | \(0.529281\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.97062 | 0.382356 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.13452 | 0.392646 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.2464 | 0.779019 | 0.389509 | − | 0.921022i | \(-0.372645\pi\) | ||||
0.389509 | + | 0.921022i | \(0.372645\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.386112 | 0.0291873 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −26.5840 | −1.99818 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.70716 | −0.127599 | −0.0637996 | − | 0.997963i | \(-0.520322\pi\) | ||||
−0.0637996 | + | 0.997963i | \(0.520322\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.414455 | 0.0308062 | 0.0154031 | − | 0.999881i | \(-0.495097\pi\) | ||||
0.0154031 | + | 0.999881i | \(0.495097\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.9535 | −1.47501 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.4377 | −1.72317 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.89550 | 0.504249 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.646752 | 0.0470443 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.36045 | 0.243154 | 0.121577 | − | 0.992582i | \(-0.461205\pi\) | ||||
0.121577 | + | 0.992582i | \(0.461205\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.99526 | 0.431548 | 0.215774 | − | 0.976443i | \(-0.430773\pi\) | ||||
0.215774 | + | 0.976443i | \(0.430773\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −23.5773 | −1.68841 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.26356 | −0.303766 | −0.151883 | − | 0.988398i | \(-0.548534\pi\) | ||||
−0.151883 | + | 0.988398i | \(0.548534\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.91534 | 0.348439 | 0.174220 | − | 0.984707i | \(-0.444260\pi\) | ||||
0.174220 | + | 0.984707i | \(0.444260\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −30.3167 | −2.13837 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.09667 | 0.147157 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.24844 | 0.645939 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.56555 | 0.525842 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.97946 | −0.136922 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.8714 | −1.02379 | −0.511893 | − | 0.859049i | \(-0.671056\pi\) | ||||
−0.511893 | + | 0.859049i | \(0.671056\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −26.4516 | −1.81244 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.2375 | −0.902792 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.67817 | 0.385460 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.36199 | 0.159608 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.0655 | −1.88789 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.91359 | −0.128143 | −0.0640717 | − | 0.997945i | \(-0.520409\pi\) | ||||
−0.0640717 | + | 0.997945i | \(0.520409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.14903 | 0.0766023 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00054 | −0.398270 | −0.199135 | − | 0.979972i | \(-0.563813\pi\) | ||||
−0.199135 | + | 0.979972i | \(0.563813\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.8457 | −0.981033 | −0.490516 | − | 0.871432i | \(-0.663192\pi\) | ||||
−0.490516 | + | 0.871432i | \(0.663192\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.25779 | 0.148552 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.11518 | −0.400618 | −0.200309 | − | 0.979733i | \(-0.564195\pi\) | ||||
−0.200309 | + | 0.979733i | \(0.564195\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.1297 | 1.11742 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.6757 | −1.40799 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.0980 | −1.68814 | −0.844070 | − | 0.536233i | \(-0.819847\pi\) | ||||
−0.844070 | + | 0.536233i | \(0.819847\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.4414 | 1.83207 | 0.916037 | − | 0.401094i | \(-0.131370\pi\) | ||||
0.916037 | + | 0.401094i | \(0.131370\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.2778 | 1.36497 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.3849 | −0.919019 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.05661 | 0.512630 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 40.2109 | 2.54826 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.2672 | 0.900540 | 0.450270 | − | 0.892893i | \(-0.351328\pi\) | ||||
0.450270 | + | 0.892893i | \(0.351328\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.91667 | −0.183369 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 36.8216 | 2.30586 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.5326 | 1.34317 | 0.671583 | − | 0.740930i | \(-0.265615\pi\) | ||||
0.671583 | + | 0.740930i | \(0.265615\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.13505 | −0.567624 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.23951 | 0.386216 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.7282 | 1.03151 | 0.515753 | − | 0.856737i | \(-0.327512\pi\) | ||||
0.515753 | + | 0.856737i | \(0.327512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.2109 | −0.627250 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.68901 | 0.348162 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.3618 | 1.11954 | 0.559770 | − | 0.828648i | \(-0.310890\pi\) | ||||
0.559770 | + | 0.828648i | \(0.310890\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.817864 | 0.0496817 | 0.0248409 | − | 0.999691i | \(-0.492092\pi\) | ||||
0.0248409 | + | 0.999691i | \(0.492092\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.18947 | −0.556172 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.442975 | −0.0267124 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.48038 | 0.209116 | 0.104558 | − | 0.994519i | \(-0.466657\pi\) | ||||
0.104558 | + | 0.994519i | \(0.466657\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.8977 | 1.01164 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.227107 | 0.0135481 | 0.00677405 | − | 0.999977i | \(-0.497844\pi\) | ||||
0.00677405 | + | 0.999977i | \(0.497844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0300 | 1.01233 | 0.506164 | − | 0.862437i | \(-0.331063\pi\) | ||||
0.506164 | + | 0.862437i | \(0.331063\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.5702 | −0.626125 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.60466 | 0.212777 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.8310 | 1.57829 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.2669 | −0.660477 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.04606 | −0.411635 | −0.205818 | − | 0.978590i | \(-0.565985\pi\) | ||||
−0.205818 | + | 0.978590i | \(0.565985\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.9318 | 1.50981 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.742001 | −0.0430553 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.8712 | 0.686527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.15945 | −0.297386 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.7453 | 0.789646 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.4640 | 1.11450 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.6994 | 1.29552 | 0.647761 | − | 0.761844i | \(-0.275706\pi\) | ||||
0.647761 | + | 0.761844i | \(0.275706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.27378 | 0.129351 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.954336 | −0.0541154 | −0.0270577 | − | 0.999634i | \(-0.508614\pi\) | ||||
−0.0270577 | + | 0.999634i | \(0.508614\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0245 | 1.24490 | 0.622448 | − | 0.782661i | \(-0.286138\pi\) | ||||
0.622448 | + | 0.782661i | \(0.286138\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.71281 | 0.321880 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.3676 | −0.975460 | −0.487730 | − | 0.872995i | \(-0.662175\pi\) | ||||
−0.487730 | + | 0.872995i | \(0.662175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.40545 | −0.134680 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.3699 | 0.913679 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.5823 | −0.700100 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.80296 | 0.100010 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.20183 | −0.508862 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.67645 | 0.368085 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0016 | 0.659668 | 0.329834 | − | 0.944039i | \(-0.393007\pi\) | ||||
0.329834 | + | 0.944039i | \(0.393007\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.1851 | −1.48973 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 29.5729 | 1.61574 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.88456 | −0.483973 | −0.241987 | − | 0.970280i | \(-0.577799\pi\) | ||||
−0.241987 | + | 0.970280i | \(0.577799\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.9963 | −1.14036 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.51441 | −0.352775 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.9615 | −0.645862 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.5749 | −0.838523 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.2220 | 1.08558 | 0.542788 | − | 0.839870i | \(-0.317369\pi\) | ||||
0.542788 | + | 0.839870i | \(0.317369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.4699 | 1.36337 | 0.681687 | − | 0.731644i | \(-0.261247\pi\) | ||||
0.681687 | + | 0.731644i | \(0.261247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.02003 | 0.161197 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.90681 | −0.101489 | −0.0507446 | − | 0.998712i | \(-0.516159\pi\) | ||||
−0.0507446 | + | 0.998712i | \(0.516159\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.8027 | 1.36946 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.3516 | 0.759566 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.7172 | −0.618409 | −0.309205 | − | 0.950996i | \(-0.600063\pi\) | ||||
−0.309205 | + | 0.950996i | \(0.600063\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3881 | −0.809897 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 23.6756 | 1.24265 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.30404 | −0.120599 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.0286 | 0.993284 | 0.496642 | − | 0.867955i | \(-0.334566\pi\) | ||||
0.496642 | + | 0.867955i | \(0.334566\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.7272 | 0.558434 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.97979 | −0.206620 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.4686 | 1.52583 | 0.762914 | − | 0.646500i | \(-0.223768\pi\) | ||||
0.762914 | + | 0.646500i | \(0.223768\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.4433 | 1.31389 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.79046 | 0.504234 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.1939 | 0.985924 | 0.492962 | − | 0.870051i | \(-0.335914\pi\) | ||||
0.492962 | + | 0.870051i | \(0.335914\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −31.6813 | −1.62308 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.5482 | −0.743379 | −0.371690 | − | 0.928357i | \(-0.621221\pi\) | ||||
−0.371690 | + | 0.928357i | \(0.621221\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.20240 | −0.112245 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.3541 | −0.780491 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.1354 | 1.73073 | 0.865367 | − | 0.501139i | \(-0.167085\pi\) | ||||
0.865367 | + | 0.501139i | \(0.167085\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.5397 | −0.937593 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.8663 | −1.35523 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.1439 | 1.06386 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.4105 | −0.823618 | −0.411809 | − | 0.911270i | \(-0.635103\pi\) | ||||
−0.411809 | + | 0.911270i | \(0.635103\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.11983 | −0.206250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.8862 | 1.74213 | 0.871066 | − | 0.491167i | \(-0.163429\pi\) | ||||
0.871066 | + | 0.491167i | \(0.163429\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.5144 | 1.32078 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.8405 | −1.13495 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.4804 | 0.519494 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.9642 | 1.38274 | 0.691369 | − | 0.722502i | \(-0.257008\pi\) | ||||
0.691369 | + | 0.722502i | \(0.257008\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 46.6862 | 2.30286 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.1072 | 0.497341 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39.2244 | −1.92545 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.2155 | 1.03893 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.1868 | −0.595363 | −0.297682 | − | 0.954665i | \(-0.596213\pi\) | ||||
−0.297682 | + | 0.954665i | \(0.596213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0228 | −0.829639 | −0.414820 | − | 0.909904i | \(-0.636155\pi\) | ||||
−0.414820 | + | 0.909904i | \(0.636155\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.8685 | 0.966041 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.81575 | −0.136584 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.58626 | 0.367125 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.5428 | 0.509013 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.216822 | −0.0104439 | −0.00522196 | − | 0.999986i | \(-0.501662\pi\) | ||||
−0.00522196 | + | 0.999986i | \(0.501662\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.3426 | 1.55429 | 0.777144 | − | 0.629323i | \(-0.216668\pi\) | ||||
0.777144 | + | 0.629323i | \(0.216668\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.8450 | −0.615870 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.32210 | 0.254590 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.7034 | 1.41767 | 0.708833 | − | 0.705377i | \(-0.249222\pi\) | ||||
0.708833 | + | 0.705377i | \(0.249222\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.6849 | −0.794520 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.2347 | 1.48401 | 0.742003 | − | 0.670397i | \(-0.233876\pi\) | ||||
0.742003 | + | 0.670397i | \(0.233876\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.54944 | −0.263069 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.4271 | −0.871571 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.4936 | −1.67505 | −0.837523 | − | 0.546402i | \(-0.815997\pi\) | ||||
−0.837523 | + | 0.546402i | \(0.815997\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.13553 | −0.194735 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.625773 | 0.0294014 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.96401 | 0.420239 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7043 | 0.687836 | 0.343918 | − | 0.939000i | \(-0.388246\pi\) | ||||
0.343918 | + | 0.939000i | \(0.388246\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.71650 | −0.220147 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.6079 | 1.37898 | 0.689488 | − | 0.724297i | \(-0.257836\pi\) | ||||
0.689488 | + | 0.724297i | \(0.257836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.6639 | −1.28565 | −0.642825 | − | 0.766013i | \(-0.722238\pi\) | ||||
−0.642825 | + | 0.766013i | \(0.722238\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −34.7866 | −1.61319 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.9157 | −0.597670 | −0.298835 | − | 0.954305i | \(-0.596598\pi\) | ||||
−0.298835 | + | 0.954305i | \(0.596598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.5263 | 0.532235 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −48.7334 | −2.24552 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.91930 | 0.272170 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.808304 | 0.0370875 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.8435 | −0.542277 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.0944 | 1.05521 | 0.527606 | − | 0.849489i | \(-0.323090\pi\) | ||||
0.527606 | + | 0.849489i | \(0.323090\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.6563 | −1.94496 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.07045 | −0.276215 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.9905 | 0.499051 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.2435 | 0.464178 | 0.232089 | − | 0.972695i | \(-0.425444\pi\) | ||||
0.232089 | + | 0.972695i | \(0.425444\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.1785 | 0.505509 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.2520 | −1.04935 | −0.524675 | − | 0.851303i | \(-0.675813\pi\) | ||||
−0.524675 | + | 0.851303i | \(0.675813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.2902 | −0.688634 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.55415 | −0.294587 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.0568 | 0.451110 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.835053 | −0.0373821 | −0.0186910 | − | 0.999825i | \(-0.505950\pi\) | ||||
−0.0186910 | + | 0.999825i | \(0.505950\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.66900 | 0.253272 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.9918 | 0.935979 | 0.467990 | − | 0.883734i | \(-0.344978\pi\) | ||||
0.467990 | + | 0.883734i | \(0.344978\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.4080 | −0.596650 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.8689 | −0.527117 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.6336 | 0.559975 | 0.279988 | − | 0.960004i | \(-0.409670\pi\) | ||||
0.279988 | + | 0.960004i | \(0.409670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.898020 | −0.0397261 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.35394 | 0.0597780 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.21799 | −0.0977364 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.65971 | −0.336874 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.4665 | −1.07396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.1830 | 0.752802 | 0.376401 | − | 0.926457i | \(-0.377162\pi\) | ||||
0.376401 | + | 0.926457i | \(0.377162\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.2317 | 1.14703 | 0.573515 | − | 0.819195i | \(-0.305579\pi\) | ||||
0.573515 | + | 0.819195i | \(0.305579\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.921962 | −0.0402377 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −41.4086 | −1.80379 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.1581 | −0.659046 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.0780 | 1.30527 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.8321 | 0.729078 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.9683 | −0.690369 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.07638 | 0.175909 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.43236 | 0.277062 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.3807 | 1.26318 | 0.631588 | − | 0.775304i | \(-0.282403\pi\) | ||||
0.631588 | + | 0.775304i | \(0.282403\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.989641 | −0.0424695 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.97607 | 0.384493 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.55830 | −0.0666282 | −0.0333141 | − | 0.999445i | \(-0.510606\pi\) | ||||
−0.0333141 | + | 0.999445i | \(0.510606\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22.5760 | 0.963522 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.38927 | 0.186989 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.24102 | 0.350444 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 55.9647 | 2.37557 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.2761 | 1.32521 | 0.662606 | − | 0.748968i | \(-0.269450\pi\) | ||||
0.662606 | + | 0.748968i | \(0.269450\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.0922 | −1.01899 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.4652 | −0.695160 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.4821 | 0.863216 | 0.431608 | − | 0.902061i | \(-0.357946\pi\) | ||||
0.431608 | + | 0.902061i | \(0.357946\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.4812 | 0.861651 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.90231 | −0.373862 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.2733 | −0.472601 | −0.236301 | − | 0.971680i | \(-0.575935\pi\) | ||||
−0.236301 | + | 0.971680i | \(0.575935\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.8440 | −1.29078 | −0.645390 | − | 0.763853i | \(-0.723305\pi\) | ||||
−0.645390 | + | 0.763853i | \(0.723305\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.02413 | −0.335213 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.19101 | 0.0496686 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.2626 | −1.09333 | −0.546663 | − | 0.837353i | \(-0.684102\pi\) | ||||
−0.546663 | + | 0.837353i | \(0.684102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.3155 | −0.594934 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.2881 | −0.634256 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.56590 | 0.189100 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 26.6761 | 1.10292 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.1067 | −1.03627 | −0.518133 | − | 0.855300i | \(-0.673373\pi\) | ||||
−0.518133 | + | 0.855300i | \(0.673373\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.8870 | 0.489794 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.1806 | 0.418774 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −46.4128 | −1.90594 | −0.952972 | − | 0.303059i | \(-0.901992\pi\) | ||||
−0.952972 | + | 0.303059i | \(0.901992\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.9995 | −0.573922 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.7369 | −0.480360 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.61988 | −0.311340 | −0.155670 | − | 0.987809i | \(-0.549754\pi\) | ||||
−0.155670 | + | 0.987809i | \(0.549754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.8210 | −0.604561 | −0.302280 | − | 0.953219i | \(-0.597748\pi\) | ||||
−0.302280 | + | 0.953219i | \(0.597748\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 34.3013 | 1.39686 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.0948 | −0.938936 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.02153 | −0.366173 | −0.183086 | − | 0.983097i | \(-0.558609\pi\) | ||||
−0.183086 | + | 0.983097i | \(0.558609\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.00646 | −0.202872 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.1759 | 1.26124 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.9957 | −0.767229 | −0.383615 | − | 0.923493i | \(-0.625321\pi\) | ||||
−0.383615 | + | 0.923493i | \(0.625321\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.0835 | −0.890494 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.6433 | 1.71675 | 0.858377 | − | 0.513020i | \(-0.171473\pi\) | ||||
0.858377 | + | 0.513020i | \(0.171473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.1388 | −0.487900 | −0.243950 | − | 0.969788i | \(-0.578443\pi\) | ||||
−0.243950 | + | 0.969788i | \(0.578443\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.99499 | 0.0800562 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.16295 | −0.0866566 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.9457 | −1.07783 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.72657 | 0.188761 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 66.6182 | 2.65624 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.63292 | −0.264052 | −0.132026 | − | 0.991246i | \(-0.542148\pi\) | ||||
−0.132026 | + | 0.991246i | \(0.542148\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 35.5100 | 1.41140 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.9040 | 1.22639 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.1804 | −1.03731 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.9282 | 1.18394 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.9095 | 1.61583 | 0.807914 | − | 0.589301i | \(-0.200597\pi\) | ||||
0.807914 | + | 0.589301i | \(0.200597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.35908 | 0.132469 | 0.0662346 | − | 0.997804i | \(-0.478901\pi\) | ||||
0.0662346 | + | 0.997804i | \(0.478901\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.6087 | 1.24459 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.2191 | −0.873522 | −0.436761 | − | 0.899577i | \(-0.643875\pi\) | ||||
−0.436761 | + | 0.899577i | \(0.643875\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.5957 | −0.455170 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.5584 | −0.531396 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.9752 | 1.44695 | 0.723477 | − | 0.690349i | \(-0.242543\pi\) | ||||
0.723477 | + | 0.690349i | \(0.242543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.2072 | 1.02400 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.67243 | −0.104261 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.7712 | 1.00390 | 0.501952 | − | 0.864896i | \(-0.332616\pi\) | ||||
0.501952 | + | 0.864896i | \(0.332616\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.19415 | −0.0464469 | −0.0232235 | − | 0.999730i | \(-0.507393\pi\) | ||||
−0.0232235 | + | 0.999730i | \(0.507393\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 67.0151 | 2.60265 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.01876 | 0.155841 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.46745 | 0.250421 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.56929 | 0.176659 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.70351 | −0.335995 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.1419 | 0.506585 | 0.253292 | − | 0.967390i | \(-0.418487\pi\) | ||||
0.253292 | + | 0.967390i | \(0.418487\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.302993 | 0.0116622 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.1967 | −1.31428 | −0.657142 | − | 0.753766i | \(-0.728235\pi\) | ||||
−0.657142 | + | 0.753766i | \(0.728235\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.28364 | 0.164391 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.3282 | 0.549057 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.9776 | −1.22359 | −0.611794 | − | 0.791017i | \(-0.709552\pi\) | ||||
−0.611794 | + | 0.791017i | \(0.709552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −45.5408 | −1.74002 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 35.4488 | 1.35246 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.5837 | −0.707984 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.4414 | 0.625461 | 0.312730 | − | 0.949842i | \(-0.398756\pi\) | ||||
0.312730 | + | 0.949842i | \(0.398756\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.55454 | −0.0970390 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.6950 | −0.785005 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.2873 | −0.995704 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.6019 | 0.552294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.74986 | −0.179400 | −0.0896998 | − | 0.995969i | \(-0.528591\pi\) | ||||
−0.0896998 | + | 0.995969i | \(0.528591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.1237 | −0.721266 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −40.9025 | −1.54048 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.22591 | −0.196541 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.65939 | 0.0623197 | 0.0311599 | − | 0.999514i | \(-0.490080\pi\) | ||||
0.0311599 | + | 0.999514i | \(0.490080\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.5246 | 0.919742 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.5151 | 0.655944 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.2842 | −0.384606 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 62.3171 | 2.32728 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −47.6457 | −1.77689 | −0.888443 | − | 0.458987i | \(-0.848213\pi\) | ||||
−0.888443 | + | 0.458987i | \(0.848213\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.864483 | −0.0321950 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −67.9128 | −2.52571 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.982258 | 0.0364801 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.4611 | −0.870125 | −0.435063 | − | 0.900400i | \(-0.643274\pi\) | ||||
−0.435063 | + | 0.900400i | \(0.643274\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.3892 | −0.792192 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.6258 | 1.39164 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.8143 | 0.953471 | 0.476736 | − | 0.879047i | \(-0.341820\pi\) | ||||
0.476736 | + | 0.879047i | \(0.341820\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 34.3485 | 1.26696 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.2238 | −0.487105 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.5668 | 0.719778 | 0.359889 | − | 0.932995i | \(-0.382815\pi\) | ||||
0.359889 | + | 0.932995i | \(0.382815\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.2377 | −0.706714 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.4757 | −1.48491 | −0.742455 | − | 0.669896i | \(-0.766339\pi\) | ||||
−0.742455 | + | 0.669896i | \(0.766339\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.9750 | 0.658552 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.4960 | −1.66461 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.22379 | −0.227412 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.4753 | 1.11206 | 0.556030 | − | 0.831162i | \(-0.312324\pi\) | ||||
0.556030 | + | 0.831162i | \(0.312324\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −34.0675 | −1.24149 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.610420 | −0.0222154 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.6072 | −1.33051 | −0.665256 | − | 0.746616i | \(-0.731678\pi\) | ||||
−0.665256 | + | 0.746616i | \(0.731678\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.96446 | 0.252794 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.7453 | −1.11452 | −0.557258 | − | 0.830339i | \(-0.688147\pi\) | ||||
−0.557258 | + | 0.830339i | \(0.688147\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.49851 | 0.126654 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −41.6612 | −1.50626 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47.1956 | 1.70414 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.9218 | 1.11507 | 0.557534 | − | 0.830154i | \(-0.311748\pi\) | ||||
0.557534 | + | 0.830154i | \(0.311748\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −51.4157 | −1.85169 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.4626 | −1.34744 | −0.673719 | − | 0.738988i | \(-0.735304\pi\) | ||||
−0.673719 | + | 0.738988i | \(0.735304\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.66014 | 0.0955549 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.8128 | 0.782529 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.54617 | 0.270370 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.5379 | −0.412859 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.64532 | 0.0587990 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 47.5378 | 1.69670 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.62500 | −0.164863 | −0.0824317 | − | 0.996597i | \(-0.526269\pi\) | ||||
−0.0824317 | + | 0.996597i | \(0.526269\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −39.9439 | −1.42204 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.98274 | 0.283834 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.4242 | 1.25795 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24.3817 | 0.864729 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.6947 | −1.44148 | −0.720739 | − | 0.693206i | \(-0.756198\pi\) | ||||
−0.720739 | + | 0.693206i | \(0.756198\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.6886 | −1.72248 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.43673 | −0.227431 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.03027 | 0.0363576 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.92152 | 0.208706 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −43.8446 | −1.54340 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.45930 | −0.121622 | −0.0608112 | − | 0.998149i | \(-0.519369\pi\) | ||||
−0.0608112 | + | 0.998149i | \(0.519369\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.91960 | 0.172750 | 0.0863752 | − | 0.996263i | \(-0.472472\pi\) | ||||
0.0863752 | + | 0.996263i | \(0.472472\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.95291 | −0.0684914 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.9042 | −0.381959 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.8010 | −0.377881 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.3973 | 0.363310 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.42588 | 0.0846637 | 0.0423319 | − | 0.999104i | \(-0.486521\pi\) | ||||
0.0423319 | + | 0.999104i | \(0.486521\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.29374 | 0.184528 | 0.0922642 | − | 0.995735i | \(-0.470590\pi\) | ||||
0.0922642 | + | 0.995735i | \(0.470590\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.05774 | 0.0368258 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.4382 | 1.16276 | 0.581381 | − | 0.813632i | \(-0.302513\pi\) | ||||
0.581381 | + | 0.813632i | \(0.302513\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.4602 | −1.33578 | −0.667889 | − | 0.744260i | \(-0.732802\pi\) | ||||
−0.667889 | + | 0.744260i | \(0.732802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.31050 | −0.288288 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 40.8871 | 1.41665 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.52991 | −0.191370 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.45583 | 0.154016 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.88565 | 0.0996236 | 0.0498118 | − | 0.998759i | \(-0.484138\pi\) | ||||
0.0498118 | + | 0.998759i | \(0.484138\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.6661 | −0.816073 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.542290 | −0.0186775 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.5777 | 0.398286 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.00140 | −0.309292 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40.6645 | −1.39560 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.1782 | −0.965938 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.8701 | −1.05697 | −0.528486 | − | 0.848942i | \(-0.677240\pi\) | ||||
−0.528486 | + | 0.848942i | \(0.677240\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.9595 | 0.409005 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.29361 | 0.0441888 | 0.0220944 | − | 0.999756i | \(-0.492967\pi\) | ||||
0.0220944 | + | 0.999756i | \(0.492967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.8946 | 1.94122 | 0.970610 | − | 0.240660i | \(-0.0773637\pi\) | ||||
0.970610 | + | 0.240660i | \(0.0773637\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.60726 | −0.293335 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.5502 | 0.631457 | 0.315729 | − | 0.948849i | \(-0.397751\pi\) | ||||
0.315729 | + | 0.948849i | \(0.397751\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.8662 | 0.811475 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −64.0674 | −2.17584 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.45470 | −0.320729 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53.8224 | 1.82370 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.7477 | 0.431445 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.67348 | −0.327023 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.3743 | 0.924363 | 0.462181 | − | 0.886785i | \(-0.347067\pi\) | ||||
0.462181 | + | 0.886785i | \(0.347067\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.8247 | 0.567482 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.5996 | 1.03093 | 0.515464 | − | 0.856911i | \(-0.327620\pi\) | ||||
0.515464 | + | 0.856911i | \(0.327620\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.5888 | −1.39958 | −0.699788 | − | 0.714351i | \(-0.746722\pi\) | ||||
−0.699788 | + | 0.714351i | \(0.746722\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −61.9202 | −2.08143 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.7938 | −1.36972 | −0.684861 | − | 0.728674i | \(-0.740137\pi\) | ||||
−0.684861 | + | 0.728674i | \(0.740137\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.0451 | 0.403980 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.2134 | 0.342161 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.9768 | 0.467716 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.97637 | −0.132915 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.3461 | −0.946449 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.4451 | 0.481772 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.0230 | 0.966895 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.3198 | 0.409977 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.965360 | 0.0320897 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.3558 | 1.14076 | 0.570382 | − | 0.821380i | \(-0.306795\pi\) | ||||
0.570382 | + | 0.821380i | \(0.306795\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.5519 | −0.515822 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.79316 | 0.0594099 | 0.0297049 | − | 0.999559i | \(-0.490543\pi\) | ||||
0.0297049 | + | 0.999559i | \(0.490543\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.5396 | 0.580476 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −46.4763 | −1.53646 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.2145 | 0.337312 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.4890 | 0.576908 | 0.288454 | − | 0.957494i | \(-0.406859\pi\) | ||||
0.288454 | + | 0.957494i | \(0.406859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −54.2018 | −1.78601 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.9606 | 1.54573 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.27963 | −0.140713 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.57262 | −0.0844961 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.7977 | 0.485498 | 0.242749 | − | 0.970089i | \(-0.421951\pi\) | ||||
0.242749 | + | 0.970089i | \(0.421951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.7372 | −0.384673 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.27878 | 0.0746038 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.0612 | 0.525258 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.9510 | −1.37048 | −0.685239 | − | 0.728318i | \(-0.740302\pi\) | ||||
−0.685239 | + | 0.728318i | \(0.740302\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −52.5903 | −1.71622 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.5890 | −0.736381 | −0.368190 | − | 0.929750i | \(-0.620022\pi\) | ||||
−0.368190 | + | 0.929750i | \(0.620022\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.1191 | 0.362086 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.50643 | 0.0490043 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.3420 | 1.27844 | 0.639222 | − | 0.769023i | \(-0.279257\pi\) | ||||
0.639222 | + | 0.769023i | \(0.279257\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.19333 | −0.136121 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 41.4705 | 1.34477 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.9239 | −1.32565 | −0.662827 | − | 0.748772i | \(-0.730644\pi\) | ||||
−0.662827 | + | 0.748772i | \(0.730644\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.82727 | 0.253284 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.74377 | 0.185670 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.7499 | −0.573175 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.12009 | 0.261938 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.5214 | −0.596845 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.9643 | 0.449528 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.79331 | −0.218458 | −0.109229 | − | 0.994017i | \(-0.534838\pi\) | ||||
−0.109229 | + | 0.994017i | \(0.534838\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.0443 | 0.965161 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.9929 | 1.28343 | 0.641717 | − | 0.766941i | \(-0.278222\pi\) | ||||
0.641717 | + | 0.766941i | \(0.278222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.06606 | −0.258586 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.30513 | −0.137874 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.9994 | −0.415887 | −0.207943 | − | 0.978141i | \(-0.566677\pi\) | ||||
−0.207943 | + | 0.978141i | \(0.566677\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.48149 | 0.0793087 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4112 | 0.332406 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.9226 | 0.635433 | 0.317716 | − | 0.948186i | \(-0.397084\pi\) | ||||
0.317716 | + | 0.948186i | \(0.397084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.93082 | −0.316422 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.9421 | −0.507443 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.9150 | −0.506068 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.6986 | −1.70579 | −0.852896 | − | 0.522082i | \(-0.825156\pi\) | ||||
−0.852896 | + | 0.522082i | \(0.825156\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.6576 | −0.909421 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.4490 | 0.362956 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.0105 | 1.01378 | 0.506891 | − | 0.862010i | \(-0.330795\pi\) | ||||
0.506891 | + | 0.862010i | \(0.330795\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.16855 | −0.226803 |
(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 | 6044.2.a.b.1.10 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6044.2.a.b.1.10 | ✓ | 63 | 1.1 | even | 1 | trivial |