Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, 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("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 29 x^{17} + 165 x^{16} + 325 x^{15} - 2208 x^{14} - 1891 x^{13} + 15895 x^{12} + \cdots - 5628 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-0.435585\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-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 | ||||||||
\(3\) | 0.435585 | 0.251485 | 0.125742 | − | 0.992063i | \(-0.459869\pi\) | ||||
0.125742 | + | 0.992063i | \(0.459869\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.87898 | −1.08815 | −0.544076 | − | 0.839036i | \(-0.683120\pi\) | ||||
−0.544076 | + | 0.839036i | \(0.683120\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.81027 | −0.936755 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.29647 | −0.692413 | −0.346207 | − | 0.938158i | \(-0.612530\pi\) | ||||
−0.346207 | + | 0.938158i | \(0.612530\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0953190 | −0.0264367 | −0.0132184 | − | 0.999913i | \(-0.504208\pi\) | ||||
−0.0132184 | + | 0.999913i | \(0.504208\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.435585 | 0.112467 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.92440 | 0.951808 | 0.475904 | − | 0.879497i | \(-0.342121\pi\) | ||||
0.475904 | + | 0.879497i | \(0.342121\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.59133 | 1.51216 | 0.756078 | − | 0.654482i | \(-0.227113\pi\) | ||||
0.756078 | + | 0.654482i | \(0.227113\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.25404 | −0.273654 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.150319 | −0.0313438 | −0.0156719 | − | 0.999877i | \(-0.504989\pi\) | ||||
−0.0156719 | + | 0.999877i | \(0.504989\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.53086 | −0.487065 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.49904 | 0.464061 | 0.232030 | − | 0.972709i | \(-0.425463\pi\) | ||||
0.232030 | + | 0.972709i | \(0.425463\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.535578 | −0.0961926 | −0.0480963 | − | 0.998843i | \(-0.515315\pi\) | ||||
−0.0480963 | + | 0.998843i | \(0.515315\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00031 | −0.174132 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.87898 | −0.486636 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.7988 | −1.93971 | −0.969853 | − | 0.243691i | \(-0.921642\pi\) | ||||
−0.969853 | + | 0.243691i | \(0.921642\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0415195 | −0.00664844 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.05597 | 1.41430 | 0.707152 | − | 0.707061i | \(-0.249980\pi\) | ||||
0.707152 | + | 0.707061i | \(0.249980\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.32623 | 1.26974 | 0.634869 | − | 0.772619i | \(-0.281054\pi\) | ||||
0.634869 | + | 0.772619i | \(0.281054\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.81027 | −0.418930 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.88440 | −0.274869 | −0.137434 | − | 0.990511i | \(-0.543886\pi\) | ||||
−0.137434 | + | 0.990511i | \(0.543886\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.28851 | 0.184073 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.70941 | 0.239365 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4032 | 1.42899 | 0.714495 | − | 0.699641i | \(-0.246656\pi\) | ||||
0.714495 | + | 0.699641i | \(0.246656\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.29647 | −0.309657 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.87108 | 0.380284 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.46632 | −0.321088 | −0.160544 | − | 0.987029i | \(-0.551325\pi\) | ||||
−0.160544 | + | 0.987029i | \(0.551325\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0317 | −1.66854 | −0.834272 | − | 0.551353i | \(-0.814112\pi\) | ||||
−0.834272 | + | 0.551353i | \(0.814112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.09069 | 1.01933 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0953190 | −0.0118229 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.05767 | −0.495723 | −0.247862 | − | 0.968795i | \(-0.579728\pi\) | ||||
−0.247862 | + | 0.968795i | \(0.579728\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0654768 | −0.00788248 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0463 | −1.66699 | −0.833496 | − | 0.552526i | \(-0.813664\pi\) | ||||
−0.833496 | + | 0.552526i | \(0.813664\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.10385 | 0.597360 | 0.298680 | − | 0.954353i | \(-0.403454\pi\) | ||||
0.298680 | + | 0.954353i | \(0.403454\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.435585 | 0.0502970 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.61150 | 0.753450 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.1799 | −1.93290 | −0.966448 | − | 0.256864i | \(-0.917311\pi\) | ||||
−0.966448 | + | 0.256864i | \(0.917311\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.32839 | 0.814266 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.49380 | −0.932316 | −0.466158 | − | 0.884702i | \(-0.654362\pi\) | ||||
−0.466158 | + | 0.884702i | \(0.654362\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.92440 | 0.425661 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.08855 | 0.116704 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.92067 | −0.839590 | −0.419795 | − | 0.907619i | \(-0.637898\pi\) | ||||
−0.419795 | + | 0.907619i | \(0.637898\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.274421 | 0.0287672 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.233289 | −0.0241910 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.59133 | 0.676256 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3248 | 1.04833 | 0.524164 | − | 0.851617i | \(-0.324378\pi\) | ||||
0.524164 | + | 0.851617i | \(0.324378\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.45371 | 0.648622 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.8058 | 1.27422 | 0.637111 | − | 0.770772i | \(-0.280129\pi\) | ||||
0.637111 | + | 0.770772i | \(0.280129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.53362 | −0.939375 | −0.469688 | − | 0.882833i | \(-0.655633\pi\) | ||||
−0.469688 | + | 0.882833i | \(0.655633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.25404 | −0.122382 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.03299 | −0.776578 | −0.388289 | − | 0.921538i | \(-0.626934\pi\) | ||||
−0.388289 | + | 0.921538i | \(0.626934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.2799 | −1.55934 | −0.779668 | − | 0.626194i | \(-0.784612\pi\) | ||||
−0.779668 | + | 0.626194i | \(0.784612\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.13936 | −0.487807 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.2119 | −1.05473 | −0.527365 | − | 0.849639i | \(-0.676820\pi\) | ||||
−0.527365 | + | 0.849639i | \(0.676820\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.150319 | −0.0140174 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.267872 | 0.0247647 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.2983 | −1.03571 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.72620 | −0.520564 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.94464 | 0.355676 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.5298 | 1.20058 | 0.600288 | − | 0.799784i | \(-0.295053\pi\) | ||||
0.600288 | + | 0.799784i | \(0.295053\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.62678 | 0.319320 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.9965 | −1.22288 | −0.611440 | − | 0.791291i | \(-0.709410\pi\) | ||||
−0.611440 | + | 0.791291i | \(0.709410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.9763 | −1.64545 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.53086 | −0.217822 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.6311 | −1.16458 | −0.582290 | − | 0.812981i | \(-0.697843\pi\) | ||||
−0.582290 | + | 0.812981i | \(0.697843\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.05697 | 0.428927 | 0.214463 | − | 0.976732i | \(-0.431200\pi\) | ||||
0.214463 | + | 0.976732i | \(0.431200\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.820818 | −0.0691253 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.218898 | 0.0183051 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.49904 | 0.207534 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.561256 | 0.0462916 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.7804 | 0.883163 | 0.441582 | − | 0.897221i | \(-0.354418\pi\) | ||||
0.441582 | + | 0.897221i | \(0.354418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.0286 | −0.891611 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.535578 | −0.0430186 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.79705 | −0.542464 | −0.271232 | − | 0.962514i | \(-0.587431\pi\) | ||||
−0.271232 | + | 0.962514i | \(0.587431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.53148 | 0.359370 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.432766 | 0.0341068 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.9477 | −0.857490 | −0.428745 | − | 0.903426i | \(-0.641044\pi\) | ||||
−0.428745 | + | 0.903426i | \(0.641044\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.00031 | −0.0778740 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.1080 | −1.40124 | −0.700619 | − | 0.713536i | \(-0.747093\pi\) | ||||
−0.700619 | + | 0.713536i | \(0.747093\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9909 | −0.999301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.5234 | −1.41652 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.0264 | −0.762293 | −0.381147 | − | 0.924515i | \(-0.624471\pi\) | ||||
−0.381147 | + | 0.924515i | \(0.624471\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.87898 | −0.217630 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.07429 | −0.0807488 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.55432 | −0.489893 | −0.244946 | − | 0.969537i | \(-0.578770\pi\) | ||||
−0.244946 | + | 0.969537i | \(0.578770\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.98392 | −0.147464 | −0.0737319 | − | 0.997278i | \(-0.523491\pi\) | ||||
−0.0737319 | + | 0.997278i | \(0.523491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.67643 | −0.419614 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.7988 | −0.867463 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.01229 | −0.659044 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.28630 | 0.530000 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.2637 | −1.68331 | −0.841653 | − | 0.540019i | \(-0.818417\pi\) | ||||
−0.841653 | + | 0.540019i | \(0.818417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.70918 | −0.482937 | −0.241469 | − | 0.970409i | \(-0.577629\pi\) | ||||
−0.241469 | + | 0.970409i | \(0.577629\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0415195 | −0.00297327 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4808 | 0.817973 | 0.408987 | − | 0.912540i | \(-0.365882\pi\) | ||||
0.408987 | + | 0.912540i | \(0.365882\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.798470 | −0.0566021 | −0.0283010 | − | 0.999599i | \(-0.509010\pi\) | ||||
−0.0283010 | + | 0.999599i | \(0.509010\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.76746 | −0.124667 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.19469 | −0.504968 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.05597 | 0.632496 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.422438 | 0.0293614 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.1368 | −1.04704 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.44453 | −0.0994458 | −0.0497229 | − | 0.998763i | \(-0.515834\pi\) | ||||
−0.0497229 | + | 0.998763i | \(0.515834\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.11836 | −0.419223 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.32623 | 0.567844 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.54192 | 0.104672 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.22316 | 0.150227 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.374070 | −0.0251627 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.8447 | −1.79766 | −0.898829 | − | 0.438300i | \(-0.855581\pi\) | ||||
−0.898829 | + | 0.438300i | \(0.855581\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.81027 | −0.187351 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.8675 | −1.38503 | −0.692514 | − | 0.721404i | \(-0.743497\pi\) | ||||
−0.692514 | + | 0.721404i | \(0.743497\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.3475 | 1.14635 | 0.573177 | − | 0.819431i | \(-0.305711\pi\) | ||||
0.573177 | + | 0.819431i | \(0.305711\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.87987 | 0.189481 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.6111 | 0.891695 | 0.445848 | − | 0.895109i | \(-0.352902\pi\) | ||||
0.445848 | + | 0.895109i | \(0.352902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.88440 | −0.122925 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.48332 | −0.486094 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8966 | 0.963583 | 0.481792 | − | 0.876286i | \(-0.339986\pi\) | ||||
0.481792 | + | 0.876286i | \(0.339986\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0346 | 1.41937 | 0.709687 | − | 0.704517i | \(-0.248836\pi\) | ||||
0.709687 | + | 0.704517i | \(0.248836\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.7847 | 0.691840 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.28851 | 0.0823200 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.628279 | −0.0399764 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.69977 | −0.234463 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.9392 | 0.690474 | 0.345237 | − | 0.938515i | \(-0.387798\pi\) | ||||
0.345237 | + | 0.938515i | \(0.387798\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.345205 | 0.0217028 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.70941 | 0.107047 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.7485 | −0.795229 | −0.397615 | − | 0.917553i | \(-0.630162\pi\) | ||||
−0.397615 | + | 0.917553i | \(0.630162\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33.9684 | 2.11069 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.02298 | −0.434711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.7818 | 1.46645 | 0.733226 | − | 0.679986i | \(-0.238014\pi\) | ||||
0.733226 | + | 0.679986i | \(0.238014\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.4032 | 0.639064 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.45012 | −0.211144 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.5279 | 1.31258 | 0.656289 | − | 0.754509i | \(-0.272125\pi\) | ||||
0.656289 | + | 0.754509i | \(0.272125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.8224 | −0.961142 | −0.480571 | − | 0.876956i | \(-0.659571\pi\) | ||||
−0.480571 | + | 0.876956i | \(0.659571\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.119534 | 0.00723451 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.29647 | −0.138483 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7192 | 0.944473 | 0.472236 | − | 0.881472i | \(-0.343447\pi\) | ||||
0.472236 | + | 0.881472i | \(0.343447\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.50512 | 0.0901089 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.2396 | 1.50567 | 0.752836 | − | 0.658209i | \(-0.228686\pi\) | ||||
0.752836 | + | 0.658209i | \(0.228686\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.2312 | 1.20262 | 0.601309 | − | 0.799017i | \(-0.294646\pi\) | ||||
0.601309 | + | 0.799017i | \(0.294646\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.87108 | 0.170068 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.0719 | −1.53898 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.59906 | −0.0940621 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.49734 | 0.263639 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.18611 | 0.0692935 | 0.0346467 | − | 0.999400i | \(-0.488969\pi\) | ||||
0.0346467 | + | 0.999400i | \(0.488969\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.46632 | −0.143595 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.81206 | 0.337250 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0143283 | 0.000828627 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.9710 | −1.38167 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.57800 | 0.320448 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.0317 | −0.746195 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.8285 | 0.960452 | 0.480226 | − | 0.877145i | \(-0.340555\pi\) | ||||
0.480226 | + | 0.877145i | \(0.340555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.15270 | −0.236239 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.3198 | −1.37905 | −0.689524 | − | 0.724263i | \(-0.742180\pi\) | ||||
−0.689524 | + | 0.724263i | \(0.742180\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3054 | −0.639018 | −0.319509 | − | 0.947583i | \(-0.603518\pi\) | ||||
−0.319509 | + | 0.947583i | \(0.603518\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.09069 | 0.455859 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.1520 | −0.626358 | −0.313179 | − | 0.949694i | \(-0.601394\pi\) | ||||
−0.313179 | + | 0.949694i | \(0.601394\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.73899 | −0.321322 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.49905 | −0.195298 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.8670 | 1.43928 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0953190 | −0.00528735 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.09129 | −0.392149 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.42516 | 0.299099 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.4711 | −1.67484 | −0.837421 | − | 0.546558i | \(-0.815938\pi\) | ||||
−0.837421 | + | 0.546558i | \(0.815938\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 33.1577 | 1.81703 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.05767 | −0.221694 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.12539 | −0.388145 | −0.194072 | − | 0.980987i | \(-0.562170\pi\) | ||||
−0.194072 | + | 0.980987i | \(0.562170\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.88375 | −0.265249 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.22994 | 0.0666050 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4432 | 0.887852 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0654768 | −0.00352515 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.6155 | 0.891968 | 0.445984 | − | 0.895041i | \(-0.352854\pi\) | ||||
0.445984 | + | 0.895041i | \(0.352854\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.03464 | −0.108912 | −0.0544560 | − | 0.998516i | \(-0.517342\pi\) | ||||
−0.0544560 | + | 0.998516i | \(0.517342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.241239 | 0.0128764 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.89772 | −0.313904 | −0.156952 | − | 0.987606i | \(-0.550167\pi\) | ||||
−0.156952 | + | 0.987606i | \(0.550167\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.0463 | −0.745501 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.92135 | −0.260466 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.5127 | 1.82151 | 0.910755 | − | 0.412947i | \(-0.135501\pi\) | ||||
0.910755 | + | 0.412947i | \(0.135501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.4456 | 1.28661 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.49425 | −0.130914 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.10385 | 0.267148 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.4303 | 1.48405 | 0.742026 | − | 0.670372i | \(-0.233865\pi\) | ||||
0.742026 | + | 0.670372i | \(0.233865\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.4497 | −1.32486 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.9506 | −1.55496 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.71457 | 0.0887769 | 0.0443884 | − | 0.999014i | \(-0.485866\pi\) | ||||
0.0443884 | + | 0.999014i | \(0.485866\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.435585 | 0.0224935 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.238206 | −0.0122682 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4490 | 0.639462 | 0.319731 | − | 0.947508i | \(-0.396407\pi\) | ||||
0.319731 | + | 0.947508i | \(0.396407\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.89338 | 0.301927 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.31980 | 0.271829 | 0.135915 | − | 0.990721i | \(-0.456603\pi\) | ||||
0.135915 | + | 0.990721i | \(0.456603\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.61150 | 0.336953 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.3989 | −1.18943 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.9844 | 1.62167 | 0.810837 | − | 0.585272i | \(-0.199012\pi\) | ||||
0.810837 | + | 0.585272i | \(0.199012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.589914 | −0.0298332 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.09666 | −0.307536 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.1799 | −0.864417 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.29137 | 0.466320 | 0.233160 | − | 0.972438i | \(-0.425093\pi\) | ||||
0.233160 | + | 0.972438i | \(0.425093\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.26578 | −0.413807 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.7900 | −1.88714 | −0.943571 | − | 0.331170i | \(-0.892557\pi\) | ||||
−0.943571 | + | 0.331170i | \(0.892557\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0510507 | 0.00254302 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.32839 | 0.364151 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.0956 | 1.34308 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.84897 | −0.140873 | −0.0704363 | − | 0.997516i | \(-0.522439\pi\) | ||||
−0.0704363 | + | 0.997516i | \(0.522439\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.93748 | −0.292874 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.10049 | 0.349392 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.49380 | −0.416944 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.20274 | 0.107869 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.33413 | −0.162883 | −0.0814413 | − | 0.996678i | \(-0.525952\pi\) | ||||
−0.0814413 | + | 0.996678i | \(0.525952\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.6477 | −1.49368 | −0.746838 | − | 0.665006i | \(-0.768429\pi\) | ||||
−0.746838 | + | 0.665006i | \(0.768429\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.29568 | 0.257485 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.92440 | 0.190362 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.5181 | 1.81563 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0953485 | 0.00460347 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.7009 | −1.62332 | −0.811658 | − | 0.584133i | \(-0.801435\pi\) | ||||
−0.811658 | + | 0.584133i | \(0.801435\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.02391 | −0.241434 | −0.120717 | − | 0.992687i | \(-0.538519\pi\) | ||||
−0.120717 | + | 0.992687i | \(0.538519\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.08855 | 0.0521918 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.990805 | −0.0473966 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.1409 | −1.58173 | −0.790864 | − | 0.611992i | \(-0.790368\pi\) | ||||
−0.790864 | + | 0.611992i | \(0.790368\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.62106 | −0.172431 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.3387 | 0.871298 | 0.435649 | − | 0.900117i | \(-0.356519\pi\) | ||||
0.435649 | + | 0.900117i | \(0.356519\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.92067 | −0.375476 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.69577 | 0.222102 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.2443 | 1.52170 | 0.760852 | − | 0.648925i | \(-0.224781\pi\) | ||||
0.760852 | + | 0.648925i | \(0.224781\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.7968 | −0.979283 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.435585 | 0.0204656 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.274421 | 0.0128651 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.3685 | 1.56091 | 0.780457 | − | 0.625210i | \(-0.214987\pi\) | ||||
0.780457 | + | 0.625210i | \(0.214987\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.93213 | −0.463592 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.8368 | −0.877317 | −0.438659 | − | 0.898654i | \(-0.644546\pi\) | ||||
−0.438659 | + | 0.898654i | \(0.644546\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.5919 | −1.42173 | −0.710863 | − | 0.703330i | \(-0.751695\pi\) | ||||
−0.710863 | + | 0.703330i | \(0.751695\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.233289 | −0.0108185 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.66251 | −0.215755 | −0.107878 | − | 0.994164i | \(-0.534405\pi\) | ||||
−0.107878 | + | 0.994164i | \(0.534405\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.6819 | 0.539422 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.96069 | −0.136421 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.1210 | −0.879184 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.59133 | 0.302431 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.2358 | −1.33861 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.7934 | 1.54406 | 0.772030 | − | 0.635586i | \(-0.219241\pi\) | ||||
0.772030 | + | 0.635586i | \(0.219241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.12465 | 0.0512795 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.188506 | 0.00857734 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3248 | 0.468826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.3168 | −1.10190 | −0.550950 | − | 0.834538i | \(-0.685734\pi\) | ||||
−0.550950 | + | 0.834538i | \(0.685734\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.76865 | −0.215646 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.9100 | 0.808268 | 0.404134 | − | 0.914700i | \(-0.367573\pi\) | ||||
0.404134 | + | 0.914700i | \(0.367573\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.80726 | 0.441697 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.45371 | 0.290072 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.4390 | 1.81394 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.95485 | 0.221809 | 0.110905 | − | 0.993831i | \(-0.464625\pi\) | ||||
0.110905 | + | 0.993831i | \(0.464625\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.88756 | −0.352390 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.5787 | −0.694621 | −0.347311 | − | 0.937750i | \(-0.612905\pi\) | ||||
−0.347311 | + | 0.937750i | \(0.612905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.8058 | 0.569850 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.65864 | −0.251309 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −40.7094 | −1.80441 | −0.902207 | − | 0.431304i | \(-0.858054\pi\) | ||||
−0.902207 | + | 0.431304i | \(0.858054\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.6939 | −0.650018 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.6818 | −0.736518 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.53362 | −0.420101 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.32749 | 0.190323 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.36735 | −0.191705 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.4160 | 1.15731 | 0.578654 | − | 0.815573i | \(-0.303578\pi\) | ||||
0.578654 | + | 0.815573i | \(0.303578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.6940 | 0.861157 | 0.430578 | − | 0.902553i | \(-0.358310\pi\) | ||||
0.430578 | + | 0.902553i | \(0.358310\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.25404 | −0.0547307 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.10182 | −0.0915568 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9774 | −0.999018 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.93102 | 0.300781 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.863206 | −0.0373896 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.03299 | −0.347296 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.85496 | −0.123201 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.95903 | −0.127455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.9581 | −1.11603 | −0.558013 | − | 0.829832i | \(-0.688436\pi\) | ||||
−0.558013 | + | 0.829832i | \(0.688436\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.864166 | −0.0370849 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.2799 | −0.697356 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0398 | 0.685811 | 0.342905 | − | 0.939370i | \(-0.388589\pi\) | ||||
0.342905 | + | 0.939370i | \(0.388589\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.6227 | 1.56302 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.4720 | 0.701732 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 49.4607 | 2.10328 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.13936 | −0.218154 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.91035 | −0.165687 | −0.0828435 | − | 0.996563i | \(-0.526400\pi\) | ||||
−0.0828435 | + | 0.996563i | \(0.526400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.793648 | −0.0335677 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.92562 | −0.165740 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.3282 | −0.856729 | −0.428365 | − | 0.903606i | \(-0.640910\pi\) | ||||
−0.428365 | + | 0.903606i | \(0.640910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.2119 | −0.471690 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.0983 | −0.886044 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.2925 | −1.47954 | −0.739768 | − | 0.672862i | \(-0.765065\pi\) | ||||
−0.739768 | + | 0.672862i | \(0.765065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.6754 | −1.61852 | −0.809259 | − | 0.587453i | \(-0.800131\pi\) | ||||
−0.809259 | + | 0.587453i | \(0.800131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.1333 | −0.423326 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.150319 | −0.00626875 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.4030 | 0.807756 | 0.403878 | − | 0.914813i | \(-0.367662\pi\) | ||||
0.403878 | + | 0.914813i | \(0.367662\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.92242 | −0.121451 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.4535 | 1.01450 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.8907 | −0.989452 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.267872 | 0.0110751 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.30229 | 0.218849 | 0.109424 | − | 0.993995i | \(-0.465099\pi\) | ||||
0.109424 | + | 0.993995i | \(0.465099\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.53017 | −0.145458 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.00086 | 0.205708 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.1485 | 1.36125 | 0.680623 | − | 0.732634i | \(-0.261709\pi\) | ||||
0.680623 | + | 0.732634i | \(0.261709\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.2983 | −0.463184 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.347801 | −0.0142346 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.07126 | −0.0437704 | −0.0218852 | − | 0.999760i | \(-0.506967\pi\) | ||||
−0.0218852 | + | 0.999760i | \(0.506967\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.9381 | −1.87386 | −0.936928 | − | 0.349524i | \(-0.886343\pi\) | ||||
−0.936928 | + | 0.349524i | \(0.886343\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.4031 | 0.464371 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.72620 | −0.232803 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.3792 | 1.43600 | 0.717999 | − | 0.696044i | \(-0.245058\pi\) | ||||
0.717999 | + | 0.696044i | \(0.245058\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.13390 | −0.126992 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.179619 | 0.00726663 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.71728 | 0.392477 | 0.196239 | − | 0.980556i | \(-0.437127\pi\) | ||||
0.196239 | + | 0.980556i | \(0.437127\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.94464 | 0.159063 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.5619 | 1.06934 | 0.534670 | − | 0.845061i | \(-0.320436\pi\) | ||||
0.534670 | + | 0.845061i | \(0.320436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.6930 | −1.23366 | −0.616828 | − | 0.787098i | \(-0.711583\pi\) | ||||
−0.616828 | + | 0.787098i | \(0.711583\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.380438 | 0.0152664 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.8034 | 0.913601 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.59337 | −0.263314 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −46.3031 | −1.84623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.9175 | −0.434618 | −0.217309 | − | 0.976103i | \(-0.569728\pi\) | ||||
−0.217309 | + | 0.976103i | \(0.569728\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.629216 | −0.0250091 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.5298 | 0.536914 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.122820 | −0.00486629 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 39.4739 | 1.56156 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.0137 | −0.514011 | −0.257005 | − | 0.966410i | \(-0.582736\pi\) | ||||
−0.257005 | + | 0.966410i | \(0.582736\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.1789 | −1.46619 | −0.733096 | − | 0.680125i | \(-0.761925\pi\) | ||||
−0.733096 | + | 0.680125i | \(0.761925\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.62678 | 0.142804 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.7533 | −1.60218 | −0.801088 | − | 0.598547i | \(-0.795745\pi\) | ||||
−0.801088 | + | 0.598547i | \(0.795745\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.66385 | 0.222326 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.671635 | 0.0263234 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.45694 | 0.370079 | 0.185039 | − | 0.982731i | \(-0.440759\pi\) | ||||
0.185039 | + | 0.982731i | \(0.440759\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.9965 | −0.546889 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.3432 | −0.559580 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.9956 | −0.778917 | −0.389458 | − | 0.921044i | \(-0.627338\pi\) | ||||
−0.389458 | + | 0.921044i | \(0.627338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.6198 | 1.19097 | 0.595486 | − | 0.803366i | \(-0.296959\pi\) | ||||
0.595486 | + | 0.803366i | \(0.296959\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.162939 | −0.00632804 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.9763 | −0.735869 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.375655 | −0.0145454 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.6932 | −0.452084 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.9271 | 1.15532 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.4372 | 0.710700 | 0.355350 | − | 0.934733i | \(-0.384362\pi\) | ||||
0.355350 | + | 0.934733i | \(0.384362\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.53086 | −0.0974130 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.2683 | −1.20174 | −0.600870 | − | 0.799347i | \(-0.705179\pi\) | ||||
−0.600870 | + | 0.799347i | \(0.705179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.7250 | −1.14074 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.08959 | −0.348314 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.9300 | −0.800866 | −0.400433 | − | 0.916326i | \(-0.631140\pi\) | ||||
−0.400433 | + | 0.916326i | \(0.631140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.6311 | −0.520816 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.55630 | 0.288291 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.991623 | −0.0377778 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.0385 | 0.952510 | 0.476255 | − | 0.879307i | \(-0.341994\pi\) | ||||
0.476255 | + | 0.879307i | \(0.341994\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.5801 | −0.705799 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.05697 | 0.191822 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.5393 | 1.34615 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.92880 | 0.224248 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.6976 | 0.479583 | 0.239792 | − | 0.970824i | \(-0.422921\pi\) | ||||
0.239792 | + | 0.970824i | \(0.422921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −77.7696 | −2.93314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.820818 | −0.0309138 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −36.8676 | −1.38655 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.3293 | 1.32682 | 0.663410 | − | 0.748256i | \(-0.269109\pi\) | ||||
0.663410 | + | 0.748256i | \(0.269109\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 48.2802 | 1.81065 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.0805077 | 0.00301504 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.218898 | 0.00818631 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.48875 | 0.242327 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.63766 | 0.247543 | 0.123771 | − | 0.992311i | \(-0.460501\pi\) | ||||
0.123771 | + | 0.992311i | \(0.460501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.4471 | 1.02218 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.59794 | 0.356951 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.49904 | 0.0928122 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.6453 | −1.32201 | −0.661005 | − | 0.750381i | \(-0.729870\pi\) | ||||
−0.661005 | + | 0.750381i | \(0.729870\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.2875 | −0.640278 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.6755 | 1.20855 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.7386 | 1.02455 | 0.512275 | − | 0.858821i | \(-0.328803\pi\) | ||||
0.512275 | + | 0.858821i | \(0.328803\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.561256 | 0.0207022 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.31834 | 0.343245 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.7731 | −1.02165 | −0.510825 | − | 0.859685i | \(-0.670660\pi\) | ||||
−0.510825 | + | 0.859685i | \(0.670660\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.273669 | −0.0100535 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.2912 | −1.22133 | −0.610667 | − | 0.791887i | \(-0.709099\pi\) | ||||
−0.610667 | + | 0.791887i | \(0.709099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.7804 | 0.394963 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.8698 | 0.873352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.1268 | 0.845035 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.1238 | −0.697839 | −0.348919 | − | 0.937153i | \(-0.613451\pi\) | ||||
−0.348919 | + | 0.937153i | \(0.613451\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.76494 | 0.173644 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.8844 | 1.41328 | 0.706639 | − | 0.707574i | \(-0.250210\pi\) | ||||
0.706639 | + | 0.707574i | \(0.250210\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.150366 | 0.00545794 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.6053 | 1.03694 | 0.518471 | − | 0.855095i | \(-0.326501\pi\) | ||||
0.518471 | + | 0.855095i | \(0.326501\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.8696 | 1.69679 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.0286 | −0.398741 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.235087 | 0.00848851 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.10018 | −0.0396735 | −0.0198368 | − | 0.999803i | \(-0.506315\pi\) | ||||
−0.0198368 | + | 0.999803i | \(0.506315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.55305 | −0.199988 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.1611 | −0.725146 | −0.362573 | − | 0.931955i | \(-0.618102\pi\) | ||||
−0.362573 | + | 0.931955i | \(0.618102\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.535578 | −0.0192385 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.7961 | 0.530808 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 59.6909 | 2.13865 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.2570 | 1.15425 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.32474 | −0.226028 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.79705 | −0.242597 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.1630 | −1.28907 | −0.644537 | − | 0.764573i | \(-0.722950\pi\) | ||||
−0.644537 | + | 0.764573i | \(0.722950\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.3590 | 0.368790 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.2789 | 1.14771 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.24217 | 0.0441108 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.53148 | 0.160715 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.711463 | −0.0252013 | −0.0126007 | − | 0.999921i | \(-0.504011\pi\) | ||||
−0.0126007 | + | 0.999921i | \(0.504011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.39516 | −0.261622 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.2592 | 0.786490 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.7209 | −0.413620 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.432766 | 0.0152530 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.37722 | 0.330094 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.0952 | 1.16357 | 0.581783 | − | 0.813344i | \(-0.302355\pi\) | ||||
0.581783 | + | 0.813344i | \(0.302355\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.9967 | −0.596835 | −0.298418 | − | 0.954435i | \(-0.596459\pi\) | ||||
−0.298418 | + | 0.954435i | \(0.596459\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.89199 | −0.241713 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.9477 | −0.383481 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.8810 | 1.92004 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.771197 | −0.0269478 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.8714 | −1.42642 | −0.713211 | − | 0.700949i | \(-0.752760\pi\) | ||||
−0.713211 | + | 0.700949i | \(0.752760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.8495 | 0.482763 | 0.241382 | − | 0.970430i | \(-0.422399\pi\) | ||||
0.241382 | + | 0.970430i | \(0.422399\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.00031 | −0.0348263 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.02260 | −0.139879 | −0.0699397 | − | 0.997551i | \(-0.522281\pi\) | ||||
−0.0699397 | + | 0.997551i | \(0.522281\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −57.0302 | −1.98074 | −0.990371 | − | 0.138439i | \(-0.955791\pi\) | ||||
−0.990371 | + | 0.138439i | \(0.955791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.84703 | 0.237521 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.05664 | 0.175202 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.1080 | −0.626652 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.35547 | 0.0468520 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.4269 | −1.29212 | −0.646060 | − | 0.763286i | \(-0.723585\pi\) | ||||
−0.646060 | + | 0.763286i | \(0.723585\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.7548 | −0.784648 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.9940 | 0.378654 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.9909 | −0.446901 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.4856 | 0.566452 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.81238 | 0.302440 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.77358 | 0.0607977 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.50988 | −0.291373 | −0.145686 | − | 0.989331i | \(-0.546539\pi\) | ||||
−0.145686 | + | 0.989331i | \(0.546539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.5234 | −0.633487 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.12565 | −0.243407 | −0.121704 | − | 0.992566i | \(-0.538836\pi\) | ||||
−0.121704 | + | 0.992566i | \(0.538836\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.1830 | 0.756873 | 0.378437 | − | 0.925627i | \(-0.376462\pi\) | ||||
0.378437 | + | 0.925627i | \(0.376462\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.3565 | −0.387030 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.3622 | 0.931420 | 0.465710 | − | 0.884937i | \(-0.345799\pi\) | ||||
0.465710 | + | 0.884937i | \(0.345799\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0264 | −0.340908 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.696524 | −0.0236552 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.4533 | 1.33836 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.386773 | 0.0131053 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.0155 | −0.982027 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.87898 | −0.0973272 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6885 | 0.934973 | 0.467487 | − | 0.884000i | \(-0.345160\pi\) | ||||
0.467487 | + | 0.884000i | \(0.345160\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.516653 | 0.0174263 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.6743 | −1.16821 | −0.584103 | − | 0.811679i | \(-0.698554\pi\) | ||||
−0.584103 | + | 0.811679i | \(0.698554\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.3340 | 1.72753 | 0.863763 | − | 0.503898i | \(-0.168101\pi\) | ||||
0.863763 | + | 0.503898i | \(0.168101\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.07429 | −0.0361120 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.81524 | −0.0609498 | −0.0304749 | − | 0.999536i | \(-0.509702\pi\) | ||||
−0.0304749 | + | 0.999536i | \(0.509702\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.9520 | −1.30641 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.8295 | −0.563808 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.4207 | −0.415644 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.55432 | −0.219087 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.00624119 | 0.000208387 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.33843 | −0.0446392 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.8264 | 1.36012 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.4414 | −0.347469 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.98392 | −0.0659478 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.41840 | 0.146711 | 0.0733553 | − | 0.997306i | \(-0.476629\pi\) | ||||
0.0733553 | + | 0.997306i | \(0.476629\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −35.9876 | −1.19363 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.72012 | 0.156385 | 0.0781923 | − | 0.996938i | \(-0.475085\pi\) | ||||
0.0781923 | + | 0.996938i | \(0.475085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.5058 | 0.645548 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.67643 | −0.187657 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40.2956 | 1.33068 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.5048 | 1.13821 | 0.569105 | − | 0.822265i | \(-0.307290\pi\) | ||||
0.569105 | + | 0.822265i | \(0.307290\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.33023 | 0.241539 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.33888 | 0.0440698 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.7988 | −0.387941 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.7920 | 0.879965 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.8723 | 0.684799 | 0.342399 | − | 0.939555i | \(-0.388760\pi\) | ||||
0.342399 | + | 0.939555i | \(0.388760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.49301 | 0.278347 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.5933 | −0.346810 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.01229 | −0.294734 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.2913 | −0.728226 | −0.364113 | − | 0.931355i | \(-0.618628\pi\) | ||||
−0.364113 | + | 0.931355i | \(0.618628\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.92445 | −0.160703 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.8416 | −1.72259 | −0.861293 | − | 0.508109i | \(-0.830345\pi\) | ||||
−0.861293 | + | 0.508109i | \(0.830345\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.36129 | −0.0443296 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.28630 | 0.237023 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.6008 | 0.539454 | 0.269727 | − | 0.962937i | \(-0.413067\pi\) | ||||
0.269727 | + | 0.962937i | \(0.413067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.486494 | −0.0157923 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.85763 | −0.157520 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.7708 | 1.77420 | 0.887100 | − | 0.461577i | \(-0.152716\pi\) | ||||
0.887100 | + | 0.461577i | \(0.152716\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.2637 | −0.752797 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.49982 | −0.0808076 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.2435 | 1.26724 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7132 | −0.990747 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.5748 | 0.727464 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.70918 | −0.215976 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.82755 | −0.0909277 | −0.0454639 | − | 0.998966i | \(-0.514477\pi\) | ||||
−0.0454639 | + | 0.998966i | \(0.514477\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.2673 | 0.361957 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.4830 | −1.04243 | −0.521215 | − | 0.853425i | \(-0.674521\pi\) | ||||
−0.521215 | + | 0.853425i | \(0.674521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.5589 | −0.466737 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0415195 | −0.00132969 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.9936 | 0.543673 | 0.271837 | − | 0.962343i | \(-0.412369\pi\) | ||||
0.271837 | + | 0.962343i | \(0.412369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.1896 | 0.581343 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.7510 | 1.46072 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.9257 | −1.17775 | −0.588874 | − | 0.808225i | \(-0.700429\pi\) | ||||
−0.588874 | + | 0.808225i | \(0.700429\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.4808 | 0.365809 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.36312 | 0.0752188 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.25159 | −0.0397984 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.2820 | 0.930172 | 0.465086 | − | 0.885265i | \(-0.346023\pi\) | ||||
0.465086 | + | 0.885265i | \(0.346023\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.2727 | −0.421198 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.798470 | −0.0253132 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.3315 | 1.65736 | 0.828678 | − | 0.559726i | \(-0.189094\pi\) | ||||
0.828678 | + | 0.559726i | \(0.189094\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.8611 | 0.944763 |
(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 | 6040.2.a.p.1.11 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.p.1.11 | ✓ | 19 | 1.1 | even | 1 | trivial |