Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | 1.28191 | 0.740113 | 0.370056 | − | 0.929009i | \(-0.379338\pi\) | ||||
0.370056 | + | 0.929009i | \(0.379338\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.791593 | −0.299194 | −0.149597 | − | 0.988747i | \(-0.547798\pi\) | ||||
−0.149597 | + | 0.988747i | \(0.547798\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.35670 | −0.452233 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.58550 | 1.68409 | 0.842046 | − | 0.539406i | \(-0.181351\pi\) | ||||
0.842046 | + | 0.539406i | \(0.181351\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.759032 | 0.210517 | 0.105259 | − | 0.994445i | \(-0.466433\pi\) | ||||
0.105259 | + | 0.994445i | \(0.466433\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.28191 | −0.330989 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.02370 | −1.70350 | −0.851749 | − | 0.523950i | \(-0.824458\pi\) | ||||
−0.851749 | + | 0.523950i | \(0.824458\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.40429 | 1.01041 | 0.505207 | − | 0.862998i | \(-0.331416\pi\) | ||||
0.505207 | + | 0.862998i | \(0.331416\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.01475 | −0.221437 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.48752 | 0.727197 | 0.363599 | − | 0.931556i | \(-0.381548\pi\) | ||||
0.363599 | + | 0.931556i | \(0.381548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.58491 | −1.07482 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.93092 | −0.915648 | −0.457824 | − | 0.889043i | \(-0.651371\pi\) | ||||
−0.457824 | + | 0.889043i | \(0.651371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.65417 | −1.01552 | −0.507759 | − | 0.861499i | \(-0.669526\pi\) | ||||
−0.507759 | + | 0.861499i | \(0.669526\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.16013 | 1.24642 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.791593 | 0.133804 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.56419 | 0.421550 | 0.210775 | − | 0.977535i | \(-0.432401\pi\) | ||||
0.210775 | + | 0.977535i | \(0.432401\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.973013 | 0.155807 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.22911 | −0.191955 | −0.0959774 | − | 0.995384i | \(-0.530598\pi\) | ||||
−0.0959774 | + | 0.995384i | \(0.530598\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.23743 | −0.951199 | −0.475600 | − | 0.879662i | \(-0.657769\pi\) | ||||
−0.475600 | + | 0.879662i | \(0.657769\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.35670 | 0.202245 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.02172 | −0.878359 | −0.439179 | − | 0.898399i | \(-0.644731\pi\) | ||||
−0.439179 | + | 0.898399i | \(0.644731\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.37338 | −0.910483 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.00378 | −1.26078 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.35453 | −1.14758 | −0.573792 | − | 0.819001i | \(-0.694528\pi\) | ||||
−0.573792 | + | 0.819001i | \(0.694528\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.58550 | −0.753149 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.64592 | 0.747820 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.38937 | −1.22239 | −0.611196 | − | 0.791479i | \(-0.709311\pi\) | ||||
−0.611196 | + | 0.791479i | \(0.709311\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5580 | 1.60788 | 0.803942 | − | 0.594707i | \(-0.202732\pi\) | ||||
0.803942 | + | 0.594707i | \(0.202732\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.07395 | 0.135305 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.759032 | −0.0941463 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.07506 | 0.742186 | 0.371093 | − | 0.928596i | \(-0.378983\pi\) | ||||
0.371093 | + | 0.928596i | \(0.378983\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.47069 | 0.538208 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00385 | 0.356491 | 0.178246 | − | 0.983986i | \(-0.442958\pi\) | ||||
0.178246 | + | 0.983986i | \(0.442958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.9513 | 1.63288 | 0.816439 | − | 0.577431i | \(-0.195945\pi\) | ||||
0.816439 | + | 0.577431i | \(0.195945\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.28191 | 0.148023 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.42144 | −0.503870 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.59616 | −0.967144 | −0.483572 | − | 0.875305i | \(-0.660661\pi\) | ||||
−0.483572 | + | 0.875305i | \(0.660661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.08927 | −0.343253 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.43565 | 0.706405 | 0.353202 | − | 0.935547i | \(-0.385093\pi\) | ||||
0.353202 | + | 0.935547i | \(0.385093\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.02370 | 0.761828 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.32101 | −0.677683 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.5424 | −1.96549 | −0.982746 | − | 0.184961i | \(-0.940784\pi\) | ||||
−0.982746 | + | 0.184961i | \(0.940784\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.600844 | −0.0629856 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.24815 | −0.751598 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.40429 | −0.451871 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.63228 | 0.267268 | 0.133634 | − | 0.991031i | \(-0.457335\pi\) | ||||
0.133634 | + | 0.991031i | \(0.457335\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.57784 | −0.761602 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.89067 | 0.984159 | 0.492079 | − | 0.870550i | \(-0.336237\pi\) | ||||
0.492079 | + | 0.870550i | \(0.336237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.81090 | 0.966696 | 0.483348 | − | 0.875428i | \(-0.339421\pi\) | ||||
0.483348 | + | 0.875428i | \(0.339421\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.01475 | 0.0990298 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.28328 | −0.897449 | −0.448724 | − | 0.893670i | \(-0.648122\pi\) | ||||
−0.448724 | + | 0.893670i | \(0.648122\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.20596 | 0.881772 | 0.440886 | − | 0.897563i | \(-0.354664\pi\) | ||||
0.440886 | + | 0.897563i | \(0.354664\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.28707 | 0.311995 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.17329 | −0.674806 | −0.337403 | − | 0.941360i | \(-0.609548\pi\) | ||||
−0.337403 | + | 0.941360i | \(0.609548\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.48752 | −0.325213 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.02978 | −0.0952029 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.55991 | 0.509676 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.1978 | 1.83617 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.57561 | −0.142068 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.87506 | −0.787534 | −0.393767 | − | 0.919210i | \(-0.628828\pi\) | ||||
−0.393767 | + | 0.919210i | \(0.628828\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.99584 | −0.703995 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.6250 | −1.10306 | −0.551528 | − | 0.834157i | \(-0.685955\pi\) | ||||
−0.551528 | + | 0.834157i | \(0.685955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.48640 | −0.302310 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.58491 | 0.480672 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.3741 | 1.82611 | 0.913057 | − | 0.407831i | \(-0.133715\pi\) | ||||
0.913057 | + | 0.407831i | \(0.133715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.4161 | −1.39240 | −0.696198 | − | 0.717850i | \(-0.745126\pi\) | ||||
−0.696198 | + | 0.717850i | \(0.745126\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.71933 | −0.650085 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.23957 | 0.354531 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.93092 | 0.409490 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.17012 | −0.673860 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.30611 | −0.270847 | −0.135424 | − | 0.990788i | \(-0.543240\pi\) | ||||
−0.135424 | + | 0.990788i | \(0.543240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.1331 | −1.80116 | −0.900582 | − | 0.434687i | \(-0.856859\pi\) | ||||
−0.900582 | + | 0.434687i | \(0.856859\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.52905 | 0.770378 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.65417 | 0.454154 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.997668 | 0.0796226 | 0.0398113 | − | 0.999207i | \(-0.487324\pi\) | ||||
0.0398113 | + | 0.999207i | \(0.487324\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.7098 | −0.849341 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.76069 | −0.217573 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.31518 | −0.651295 | −0.325647 | − | 0.945491i | \(-0.605582\pi\) | ||||
−0.325647 | + | 0.945491i | \(0.605582\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.16013 | −0.557415 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.7035 | 1.36993 | 0.684967 | − | 0.728574i | \(-0.259816\pi\) | ||||
0.684967 | + | 0.728574i | \(0.259816\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4239 | −0.955682 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.97529 | −0.456942 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.70744 | 0.357900 | 0.178950 | − | 0.983858i | \(-0.442730\pi\) | ||||
0.178950 | + | 0.983858i | \(0.442730\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.791593 | −0.0598388 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0364 | −0.904708 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.46430 | 0.333678 | 0.166839 | − | 0.985984i | \(-0.446644\pi\) | ||||
0.166839 | + | 0.985984i | \(0.446644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.70629 | −0.349816 | −0.174908 | − | 0.984585i | \(-0.555963\pi\) | ||||
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.0982 | 1.19002 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.56419 | −0.188523 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −39.2309 | −2.86885 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.42097 | 0.321579 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.7071 | −1.06417 | −0.532083 | − | 0.846692i | \(-0.678591\pi\) | ||||
−0.532083 | + | 0.846692i | \(0.678591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.6718 | 0.768176 | 0.384088 | − | 0.923297i | \(-0.374516\pi\) | ||||
0.384088 | + | 0.923297i | \(0.374516\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.973013 | −0.0696789 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.5613 | −1.39368 | −0.696842 | − | 0.717224i | \(-0.745412\pi\) | ||||
−0.696842 | + | 0.717224i | \(0.745412\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.1618 | −0.933013 | −0.466507 | − | 0.884518i | \(-0.654488\pi\) | ||||
−0.466507 | + | 0.884518i | \(0.654488\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.78770 | 0.549302 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.90328 | 0.273957 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.22911 | 0.0858448 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.73151 | −0.328863 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.6002 | 1.70163 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1961 | 0.701929 | 0.350964 | − | 0.936389i | \(-0.385854\pi\) | ||||
0.350964 | + | 0.936389i | \(0.385854\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.85067 | 0.263844 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.23743 | 0.425389 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.47580 | 0.303837 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.8844 | 1.20851 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.33121 | −0.358616 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.3836 | −1.49891 | −0.749457 | − | 0.662053i | \(-0.769685\pi\) | ||||
−0.749457 | + | 0.662053i | \(0.769685\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.35670 | −0.0904466 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.54471 | 0.633504 | 0.316752 | − | 0.948508i | \(-0.397408\pi\) | ||||
0.316752 | + | 0.948508i | \(0.397408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.6539 | −1.82742 | −0.913709 | − | 0.406369i | \(-0.866795\pi\) | ||||
−0.913709 | + | 0.406369i | \(0.866795\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.66791 | −0.372921 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.9698 | 1.11173 | 0.555866 | − | 0.831272i | \(-0.312387\pi\) | ||||
0.555866 | + | 0.831272i | \(0.312387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.02172 | 0.392814 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.0195 | −0.715796 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.1623 | −1.56293 | −0.781465 | − | 0.623949i | \(-0.785527\pi\) | ||||
−0.781465 | + | 0.623949i | \(0.785527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4656 | −1.38272 | −0.691361 | − | 0.722510i | \(-0.742988\pi\) | ||||
−0.691361 | + | 0.722510i | \(0.742988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.7945 | 0.820771 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.37338 | 0.407180 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.34300 | 0.212710 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.24995 | 0.522819 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.8183 | 0.872204 | 0.436102 | − | 0.899897i | \(-0.356359\pi\) | ||||
0.436102 | + | 0.899897i | \(0.356359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.4795 | 1.22467 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.00378 | 0.563838 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.0558 | 1.50056 | 0.750279 | − | 0.661122i | \(-0.229919\pi\) | ||||
0.750279 | + | 0.661122i | \(0.229919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.02979 | −0.126125 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.68977 | 0.414086 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.2776 | 0.818730 | 0.409365 | − | 0.912371i | \(-0.365750\pi\) | ||||
0.409365 | + | 0.912371i | \(0.365750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.35453 | 0.513215 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.7698 | −1.45469 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.6447 | −1.68553 | −0.842764 | − | 0.538284i | \(-0.819073\pi\) | ||||
−0.842764 | + | 0.538284i | \(0.819073\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.92757 | −0.299329 | −0.149664 | − | 0.988737i | \(-0.547819\pi\) | ||||
−0.149664 | + | 0.988737i | \(0.547819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.770230 | −0.0466164 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.58550 | 0.336818 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.7921 | −0.948856 | −0.474428 | − | 0.880294i | \(-0.657345\pi\) | ||||
−0.474428 | + | 0.880294i | \(0.657345\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.67100 | 0.459251 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.3943 | −1.45524 | −0.727622 | − | 0.685978i | \(-0.759375\pi\) | ||||
−0.727622 | + | 0.685978i | \(0.759375\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.4748 | 0.741552 | 0.370776 | − | 0.928722i | \(-0.379092\pi\) | ||||
0.370776 | + | 0.928722i | \(0.379092\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.64592 | −0.334435 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.972955 | 0.0574317 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.3324 | 1.90191 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.37436 | 0.197808 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.4210 | −1.07617 | −0.538084 | − | 0.842891i | \(-0.680852\pi\) | ||||
−0.538084 | + | 0.842891i | \(0.680852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.38937 | 0.546670 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −31.1945 | −1.81009 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.64713 | 0.153088 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.93751 | 0.284593 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.6790 | 0.728388 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.5580 | −0.719068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4379 | −0.709869 | −0.354934 | − | 0.934891i | \(-0.615497\pi\) | ||||
−0.354934 | + | 0.934891i | \(0.615497\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.5767 | 0.715465 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.5287 | −0.993962 | −0.496981 | − | 0.867761i | \(-0.665558\pi\) | ||||
−0.496981 | + | 0.867761i | \(0.665558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4878 | −0.988470 | −0.494235 | − | 0.869328i | \(-0.664552\pi\) | ||||
−0.494235 | + | 0.869328i | \(0.664552\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.07395 | −0.0605104 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.1071 | −1.18549 | −0.592747 | − | 0.805389i | \(-0.701957\pi\) | ||||
−0.592747 | + | 0.805389i | \(0.701957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.5416 | −1.54204 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.9004 | −0.664213 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −30.9344 | −1.72124 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.759032 | 0.0421035 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.8012 | 0.652610 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.76675 | 0.262800 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.411971 | −0.0226440 | −0.0113220 | − | 0.999936i | \(-0.503604\pi\) | ||||
−0.0113220 | + | 0.999936i | \(0.503604\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.47883 | −0.190639 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.07506 | −0.331916 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.8128 | −1.24269 | −0.621346 | − | 0.783537i | \(-0.713414\pi\) | ||||
−0.621346 | + | 0.783537i | \(0.713414\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.19553 | −0.499433 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.5814 | −1.71023 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.5863 | 0.571605 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.47069 | −0.240694 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.05568 | −0.164037 | −0.0820186 | − | 0.996631i | \(-0.526137\pi\) | ||||
−0.0820186 | + | 0.996631i | \(0.526137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.7216 | 0.680973 | 0.340487 | − | 0.940249i | \(-0.389408\pi\) | ||||
0.340487 | + | 0.940249i | \(0.389408\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.23912 | −0.226268 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.7134 | −0.996013 | −0.498006 | − | 0.867173i | \(-0.665934\pi\) | ||||
−0.498006 | + | 0.867173i | \(0.665934\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.00385 | −0.159428 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.12733 | 0.377218 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.73606 | −0.408294 | −0.204147 | − | 0.978940i | \(-0.565442\pi\) | ||||
−0.204147 | + | 0.978940i | \(0.565442\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.397772 | 0.0209354 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.8919 | 1.35897 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.9513 | −0.730246 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.9271 | 0.935785 | 0.467893 | − | 0.883785i | \(-0.345013\pi\) | ||||
0.467893 | + | 0.883785i | \(0.345013\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.66753 | 0.0868082 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.61339 | 0.343350 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.9192 | −1.75627 | −0.878136 | − | 0.478411i | \(-0.841213\pi\) | ||||
−0.878136 | + | 0.478411i | \(0.841213\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.28191 | −0.0661977 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.74272 | −0.192760 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.55881 | 0.336903 | 0.168452 | − | 0.985710i | \(-0.446123\pi\) | ||||
0.168452 | + | 0.985710i | \(0.446123\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3771 | −0.582864 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.9749 | −1.58274 | −0.791372 | − | 0.611335i | \(-0.790633\pi\) | ||||
−0.791372 | + | 0.611335i | \(0.790633\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.42144 | 0.225338 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.46231 | 0.430163 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.9747 | −0.962055 | −0.481028 | − | 0.876705i | \(-0.659736\pi\) | ||||
−0.481028 | + | 0.876705i | \(0.659736\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.4953 | −1.23878 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.1842 | −0.816385 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.59616 | 0.432520 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.4745 | −1.07778 | −0.538888 | − | 0.842378i | \(-0.681155\pi\) | ||||
−0.538888 | + | 0.842378i | \(0.681155\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.46927 | −0.223743 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.29169 | −0.213784 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.08927 | 0.153507 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.3223 | 0.709929 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.9821 | 1.72975 | 0.864876 | − | 0.501986i | \(-0.167397\pi\) | ||||
0.864876 | + | 0.501986i | \(0.167397\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.3998 | 1.35153 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.43256 | 0.365732 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.43565 | −0.315914 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.0440 | −1.03053 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.72757 | −0.230957 | −0.115479 | − | 0.993310i | \(-0.536840\pi\) | ||||
−0.115479 | + | 0.993310i | \(0.536840\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.955720 | −0.0465790 | −0.0232895 | − | 0.999729i | \(-0.507414\pi\) | ||||
−0.0232895 | + | 0.999729i | \(0.507414\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.16966 | 0.397223 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.02370 | −0.340700 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.94081 | −0.481069 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.43476 | 0.262393 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.32988 | −0.112226 | −0.0561132 | − | 0.998424i | \(-0.517871\pi\) | ||||
−0.0561132 | + | 0.998424i | \(0.517871\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.3584 | 0.641962 | 0.320981 | − | 0.947086i | \(-0.395987\pi\) | ||||
0.320981 | + | 0.947086i | \(0.395987\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.32101 | 0.303069 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.3600 | 0.734770 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.0726 | 1.10119 | 0.550597 | − | 0.834771i | \(-0.314400\pi\) | ||||
0.550597 | + | 0.834771i | \(0.314400\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.64676 | 0.411750 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.7515 | 1.41354 | 0.706769 | − | 0.707444i | \(-0.250152\pi\) | ||||
0.706769 | + | 0.707444i | \(0.250152\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.5424 | 0.878995 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.23815 | −0.200458 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5472 | 0.497752 | 0.248876 | − | 0.968535i | \(-0.419939\pi\) | ||||
0.248876 | + | 0.968535i | \(0.419939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.86519 | −0.323269 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −28.3727 | −1.33306 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.600844 | 0.0281680 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.1375 | 1.59688 | 0.798442 | − | 0.602071i | \(-0.205658\pi\) | ||||
0.798442 | + | 0.602071i | \(0.205658\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 39.2267 | 1.83095 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.24097 | −0.430395 | −0.215198 | − | 0.976571i | \(-0.569040\pi\) | ||||
−0.215198 | + | 0.976571i | \(0.569040\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.5872 | 1.60740 | 0.803702 | − | 0.595032i | \(-0.202860\pi\) | ||||
0.803702 | + | 0.595032i | \(0.202860\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.24815 | 0.336125 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.1999 | −0.471995 | −0.235998 | − | 0.971754i | \(-0.575836\pi\) | ||||
−0.235998 | + | 0.971754i | \(0.575836\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.80897 | −0.222058 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.27892 | 0.0589297 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34.8392 | −1.60191 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.40429 | 0.202083 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.3346 | 0.518975 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.9899 | 1.82718 | 0.913592 | − | 0.406633i | \(-0.133297\pi\) | ||||
0.913592 | + | 0.406633i | \(0.133297\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.94630 | 0.0887437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.53897 | −0.161029 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.63228 | −0.119526 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.3277 | −0.558621 | −0.279310 | − | 0.960201i | \(-0.590106\pi\) | ||||
−0.279310 | + | 0.960201i | \(0.590106\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.6593 | −0.482032 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.2443 | −1.63568 | −0.817841 | − | 0.575445i | \(-0.804829\pi\) | ||||
−0.817841 | + | 0.575445i | \(0.804829\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.6333 | 1.55981 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.57784 | 0.340599 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.37782 | −0.106660 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.39149 | −0.241356 | −0.120678 | − | 0.992692i | \(-0.538507\pi\) | ||||
−0.120678 | + | 0.992692i | \(0.538507\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.6943 | 1.01391 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.0782 | −0.806066 | −0.403033 | − | 0.915185i | \(-0.632044\pi\) | ||||
−0.403033 | + | 0.915185i | \(0.632044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.89067 | −0.440129 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.9263 | −0.707313 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.14418 | 0.0507148 | 0.0253574 | − | 0.999678i | \(-0.491928\pi\) | ||||
0.0253574 | + | 0.999678i | \(0.491928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0438 | −0.488548 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.5976 | −1.08601 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.81090 | −0.432320 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.6343 | −1.47924 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.03453 | 0.264887 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.4115 | 1.28854 | 0.644272 | − | 0.764797i | \(-0.277161\pi\) | ||||
0.644272 | + | 0.764797i | \(0.277161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.60715 | 0.332637 | 0.166319 | − | 0.986072i | \(-0.446812\pi\) | ||||
0.166319 | + | 0.986072i | \(0.446812\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.01475 | −0.0442875 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.7132 | 1.72993 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.8372 | −0.471184 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.7385 | 0.552806 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.932933 | −0.0404098 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.28328 | 0.401351 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.72285 | 0.246959 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −35.5985 | −1.53334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6971 | −0.459906 | −0.229953 | − | 0.973202i | \(-0.573857\pi\) | ||||
−0.229953 | + | 0.973202i | \(0.573857\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.03306 | −0.258903 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.20596 | −0.394340 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.1493 | −1.16082 | −0.580409 | − | 0.814325i | \(-0.697107\pi\) | ||||
−0.580409 | + | 0.814325i | \(0.697107\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.0374 | −0.727138 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.7172 | −0.925184 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.80466 | 0.289364 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.28707 | −0.139528 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.9739 | 1.56663 | 0.783317 | − | 0.621622i | \(-0.213526\pi\) | ||||
0.783317 | + | 0.621622i | \(0.213526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.73441 | −0.200244 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −50.2906 | −2.12327 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.4559 | 0.651389 | 0.325694 | − | 0.945475i | \(-0.394402\pi\) | ||||
0.325694 | + | 0.945475i | \(0.394402\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.17329 | 0.301782 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.44545 | 0.102699 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.7069 | 1.07769 | 0.538845 | − | 0.842405i | \(-0.318861\pi\) | ||||
0.538845 | + | 0.842405i | \(0.318861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7020 | 1.11744 | 0.558721 | − | 0.829356i | \(-0.311292\pi\) | ||||
0.558721 | + | 0.829356i | \(0.311292\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.8532 | −0.787604 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.48752 | 0.145439 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.386790 | −0.0161023 | −0.00805113 | − | 0.999968i | \(-0.502563\pi\) | ||||
−0.00805113 | + | 0.999968i | \(0.502563\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.6804 | 0.568537 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.09442 | −0.211352 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −46.6643 | −1.93264 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.02978 | 0.0425760 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.34300 | −0.261803 | −0.130902 | − | 0.991395i | \(-0.541787\pi\) | ||||
−0.130902 | + | 0.991395i | \(0.541787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.9026 | −1.02609 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.0759 | −1.03148 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.4452 | 1.04491 | 0.522455 | − | 0.852667i | \(-0.325016\pi\) | ||||
0.522455 | + | 0.852667i | \(0.325016\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.55991 | −0.227934 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.8722 | −0.690535 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.4800 | 0.428201 | 0.214101 | − | 0.976812i | \(-0.431318\pi\) | ||||
0.214101 | + | 0.976812i | \(0.431318\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.6484 | 1.82125 | 0.910624 | − | 0.413236i | \(-0.135601\pi\) | ||||
0.910624 | + | 0.413236i | \(0.135601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.24202 | −0.335641 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.1978 | −0.821158 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.66242 | −0.351597 | −0.175798 | − | 0.984426i | \(-0.556251\pi\) | ||||
−0.175798 | + | 0.984426i | \(0.556251\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.00367 | 0.202759 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.57068 | −0.184910 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.7969 | 1.32465 | 0.662327 | − | 0.749215i | \(-0.269569\pi\) | ||||
0.662327 | + | 0.749215i | \(0.269569\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.57561 | 0.0635348 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.6878 | −1.03415 | −0.517075 | − | 0.855940i | \(-0.672979\pi\) | ||||
−0.517075 | + | 0.855940i | \(0.672979\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.8144 | −0.756216 | −0.378108 | − | 0.925762i | \(-0.623425\pi\) | ||||
−0.378108 | + | 0.925762i | \(0.623425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.4775 | −0.781604 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.6780 | 0.588063 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 31.5353 | 1.25940 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.0101 | −0.718110 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8709 | 0.552190 | 0.276095 | − | 0.961130i | \(-0.410959\pi\) | ||||
0.276095 | + | 0.961130i | \(0.410959\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.0705 | 0.519506 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.87506 | 0.352196 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.83760 | −0.191673 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.07532 | −0.161217 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.1293 | 0.755562 | 0.377781 | − | 0.925895i | \(-0.376687\pi\) | ||||
0.377781 | + | 0.925895i | \(0.376687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.9557 | 0.905286 | 0.452643 | − | 0.891692i | \(-0.350481\pi\) | ||||
0.452643 | + | 0.891692i | \(0.350481\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.99584 | 0.314836 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.3306 | 1.42830 | 0.714151 | − | 0.699992i | \(-0.246813\pi\) | ||||
0.714151 | + | 0.699992i | \(0.246813\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −52.4444 | −2.05862 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.73759 | 0.224874 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.16730 | −0.123946 | −0.0619730 | − | 0.998078i | \(-0.519739\pi\) | ||||
−0.0619730 | + | 0.998078i | \(0.519739\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.6250 | 0.493301 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.9277 | −0.738441 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.1463 | −0.784790 | −0.392395 | − | 0.919797i | \(-0.628353\pi\) | ||||
−0.392395 | + | 0.919797i | \(0.628353\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.3936 | 1.45444 | 0.727221 | − | 0.686404i | \(-0.240812\pi\) | ||||
0.727221 | + | 0.686404i | \(0.240812\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.83415 | −0.265416 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.48640 | 0.135197 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.1967 | −0.665857 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.6938 | −1.10937 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 70.1426 | 2.70783 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.3817 | 1.28677 | 0.643384 | − | 0.765543i | \(-0.277530\pi\) | ||||
0.643384 | + | 0.765543i | \(0.277530\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.58491 | −0.214963 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.02763 | 0.270094 | 0.135047 | − | 0.990839i | \(-0.456881\pi\) | ||||
0.135047 | + | 0.990839i | \(0.456881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.08370 | −0.0799650 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.2355 | 0.468865 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.4854 | −1.47260 | −0.736301 | − | 0.676655i | \(-0.763429\pi\) | ||||
−0.736301 | + | 0.676655i | \(0.763429\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.3741 | −0.816663 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.4498 | −1.35250 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.34135 | −0.241586 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.4073 | 0.395912 | 0.197956 | − | 0.980211i | \(-0.436570\pi\) | ||||
0.197956 | + | 0.980211i | \(0.436570\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.99857 | 0.227867 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.4161 | 0.622698 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.63290 | 0.326994 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.7539 | 0.822807 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.1405 | 0.949543 | 0.474772 | − | 0.880109i | \(-0.342531\pi\) | ||||
0.474772 | + | 0.880109i | \(0.342531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.2934 | 0.425940 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.71933 | 0.290727 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.82938 | −0.294454 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.9132 | 1.23608 | 0.618041 | − | 0.786146i | \(-0.287927\pi\) | ||||
0.618041 | + | 0.786146i | \(0.287927\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.6624 | 0.437374 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.7190 | −0.738482 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.23957 | −0.158551 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.9740 | −1.15675 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.27997 | −0.234203 | −0.117102 | − | 0.993120i | \(-0.537360\pi\) | ||||
−0.117102 | + | 0.993120i | \(0.537360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.76624 | −0.289230 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.5170 | −1.02337 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.93092 | −0.183130 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.1103 | 1.52470 | 0.762348 | − | 0.647167i | \(-0.224046\pi\) | ||||
0.762348 | + | 0.647167i | \(0.224046\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.6693 | 0.950716 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43.8098 | 1.62037 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.73963 | 0.175062 | 0.0875311 | − | 0.996162i | \(-0.472102\pi\) | ||||
0.0875311 | + | 0.996162i | \(0.472102\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.17012 | 0.301359 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.9322 | 1.24991 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3329 | 0.527245 | 0.263622 | − | 0.964626i | \(-0.415083\pi\) | ||||
0.263622 | + | 0.964626i | \(0.415083\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.28543 | 0.157429 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.6197 | −0.573031 | −0.286516 | − | 0.958076i | \(-0.592497\pi\) | ||||
−0.286516 | + | 0.958076i | \(0.592497\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.30611 | 0.121127 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.73124 | −0.319459 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.34858 | 0.268511 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.9051 | 0.835819 | 0.417910 | − | 0.908489i | \(-0.362763\pi\) | ||||
0.417910 | + | 0.908489i | \(0.362763\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.7139 | 0.645529 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.1331 | 0.805505 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.6277 | −1.51298 | −0.756492 | − | 0.654003i | \(-0.773088\pi\) | ||||
−0.756492 | + | 0.654003i | \(0.773088\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.9711 | 0.906392 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.4121 | −0.449938 | −0.224969 | − | 0.974366i | \(-0.572228\pi\) | ||||
−0.224969 | + | 0.974366i | \(0.572228\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.28738 | −0.263821 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.52905 | −0.344523 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.12683 | −0.257335 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.2853 | 1.09212 | 0.546058 | − | 0.837747i | \(-0.316128\pi\) | ||||
0.546058 | + | 0.837747i | \(0.316128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.8374 | 1.11058 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.6168 | −1.42492 | −0.712459 | − | 0.701714i | \(-0.752419\pi\) | ||||
−0.712459 | + | 0.701714i | \(0.752419\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.65417 | −0.203104 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.60202 | −0.0933469 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.41336 | −0.193954 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.7780 | 0.600364 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.5387 | 0.984154 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.997668 | −0.0356083 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.3828 | 0.726567 | 0.363283 | − | 0.931679i | \(-0.381656\pi\) | ||||
0.363283 | + | 0.931679i | \(0.381656\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.0207 | 0.605952 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.67832 | 0.201898 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.53190 | 0.338488 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.7098 | 0.379837 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.2831 | 0.860151 | 0.430076 | − | 0.902793i | \(-0.358487\pi\) | ||||
0.430076 | + | 0.902793i | \(0.358487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.2948 | 1.49628 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.1565 | 0.888860 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 77.9251 | 2.74992 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.76069 | 0.0973016 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35.4381 | −1.24748 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.2630 | 1.66168 | 0.830839 | − | 0.556513i | \(-0.187861\pi\) | ||||
0.830839 | + | 0.556513i | \(0.187861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.23784 | 0.324385 | 0.162192 | − | 0.986759i | \(-0.448144\pi\) | ||||
0.162192 | + | 0.986759i | \(0.448144\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.31672 | −0.221537 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.31518 | 0.291268 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.4714 | −0.961104 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.815164 | 0.0284841 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.8556 | −1.73997 | −0.869986 | − | 0.493076i | \(-0.835872\pi\) | ||||
−0.869986 | + | 0.493076i | \(0.835872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.7530 | −0.758261 | −0.379131 | − | 0.925343i | \(-0.623777\pi\) | ||||
−0.379131 | + | 0.925343i | \(0.623777\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.16013 | 0.249284 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.1960 | −1.60639 | −0.803196 | − | 0.595714i | \(-0.796869\pi\) | ||||
−0.803196 | + | 0.595714i | \(0.796869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.0599 | −1.73865 | −0.869326 | − | 0.494239i | \(-0.835447\pi\) | ||||
−0.869326 | + | 0.494239i | \(0.835447\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.2441 | −0.702261 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 44.7647 | 1.55101 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.7035 | −0.612653 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.5780 | 1.09150 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.2881 | 0.803996 | 0.401998 | − | 0.915641i | \(-0.368316\pi\) | ||||
0.401998 | + | 0.915641i | \(0.368316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.68605 | −0.161588 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31.2714 | −1.07705 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4239 | 0.427394 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.9885 | −0.549370 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.9917 | 0.548832 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.94265 | 0.306550 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.79715 | 0.198491 | 0.0992453 | − | 0.995063i | \(-0.468357\pi\) | ||||
0.0992453 | + | 0.995063i | \(0.468357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.97529 | 0.204351 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.4699 | −1.17747 | −0.588734 | − | 0.808327i | \(-0.700373\pi\) | ||||
−0.588734 | + | 0.808327i | \(0.700373\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.65715 | 0.261258 | 0.130629 | − | 0.991431i | \(-0.458300\pi\) | ||||
0.130629 | + | 0.991431i | \(0.458300\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.24724 | 0.0425059 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.3622 | −1.20374 | −0.601871 | − | 0.798593i | \(-0.705578\pi\) | ||||
−0.601871 | + | 0.798593i | \(0.705578\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.70744 | −0.160058 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.4473 | 1.40763 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.0139 | −1.62876 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.61116 | 0.156243 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.57122 | −0.120867 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.791593 | 0.0267607 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.27554 | −0.178142 | −0.0890711 | − | 0.996025i | \(-0.528390\pi\) | ||||
−0.0890711 | + | 0.996025i | \(0.528390\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.6142 | −0.796486 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.5257 | 0.961055 | 0.480527 | − | 0.876980i | \(-0.340445\pi\) | ||||
0.480527 | + | 0.876980i | \(0.340445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.0960 | −1.85413 | −0.927064 | − | 0.374903i | \(-0.877676\pi\) | ||||
−0.927064 | + | 0.374903i | \(0.877676\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0364 | 0.404598 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.25850 | −0.310870 | −0.155435 | − | 0.987846i | \(-0.549678\pi\) | ||||
−0.155435 | + | 0.987846i | \(0.549678\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.02544 | 0.235626 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.2551 | −0.578069 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.5214 | −0.887505 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.46430 | −0.149225 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.39340 | 0.113302 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.8802 | 0.929858 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.6798 | 1.95491 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.32945 | 0.210631 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.70629 | 0.156443 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.0748 | 0.965414 | 0.482707 | − | 0.875782i | \(-0.339654\pi\) | ||||
0.482707 | + | 0.875782i | \(0.339654\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.4187 | −0.445069 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.4138 | 0.345026 | 0.172513 | − | 0.985007i | \(-0.444811\pi\) | ||||
0.172513 | + | 0.985007i | \(0.444811\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.9464 | 1.18965 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.0982 | −0.532191 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.99389 | 0.330027 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.399541 | 0.0131796 | 0.00658982 | − | 0.999978i | \(-0.497902\pi\) | ||||
0.00658982 | + | 0.999978i | \(0.497902\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.9443 | −0.525383 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.28002 | 0.0750476 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.56419 | 0.0843100 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.3104 | −0.437172 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.16684 | −0.103901 | −0.0519504 | − | 0.998650i | \(-0.516544\pi\) | ||||
−0.0519504 | + | 0.998650i | \(0.516544\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.0702 | −0.919964 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.4703 | −0.735644 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39.2309 | 1.28299 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.6327 | 0.837384 | 0.418692 | − | 0.908128i | \(-0.362489\pi\) | ||||
0.418692 | + | 0.908128i | \(0.362489\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.4179 | −0.731579 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.947081 | −0.0308740 | −0.0154370 | − | 0.999881i | \(-0.504914\pi\) | ||||
−0.0154370 | + | 0.999881i | \(0.504914\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.28654 | −0.139589 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.42097 | −0.143814 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.1998 | 1.30632 | 0.653159 | − | 0.757220i | \(-0.273443\pi\) | ||||
0.653159 | + | 0.757220i | \(0.273443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.5895 | 0.343750 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.0575 | −0.877400 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.6009 | 1.47716 | 0.738578 | − | 0.674168i | \(-0.235497\pi\) | ||||
0.738578 | + | 0.674168i | \(0.235497\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.7071 | 0.475910 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −35.3060 | −1.14128 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.9196 | −0.546363 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.969612 | 0.0312778 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.5946 | 0.405856 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.6718 | −0.343539 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.6396 | 1.21041 | 0.605204 | − | 0.796071i | \(-0.293092\pi\) | ||||
0.605204 | + | 0.796071i | \(0.293092\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −39.6552 | −1.27391 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.5218 | −0.401845 | −0.200923 | − | 0.979607i | \(-0.564394\pi\) | ||||
−0.200923 | + | 0.979607i | \(0.564394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.9949 | 0.416596 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.973013 | 0.0311613 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 61.2046 | 1.95811 | 0.979054 | − | 0.203599i | \(-0.0652638\pi\) | ||||
0.979054 | + | 0.203599i | \(0.0652638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −103.569 | −3.31007 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.4897 | −0.398766 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.2931 | 0.966200 | 0.483100 | − | 0.875565i | \(-0.339511\pi\) | ||||
0.483100 | + | 0.875565i | \(0.339511\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.5613 | 0.623275 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.11057 | 0.194501 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.7531 | −0.691709 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.3839 | −1.31460 | −0.657301 | − | 0.753628i | \(-0.728302\pi\) | ||||
−0.657301 | + | 0.753628i | \(0.728302\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.528111 | −0.0167591 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.1618 | 0.417256 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.09602 | 0.224733 | 0.112367 | − | 0.993667i | \(-0.464157\pi\) | ||||
0.112367 | + | 0.993667i | \(0.464157\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.3208 | −0.453089 |
(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 | 8020.2.a.c.1.19 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.19 | ✓ | 28 | 1.1 | even | 1 | trivial |