Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.45 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.93661 | 1.69545 | 0.847727 | − | 0.530434i | \(-0.177971\pi\) | ||||
0.847727 | + | 0.530434i | \(0.177971\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.50463 | 1.56732 | 0.783659 | − | 0.621191i | \(-0.213351\pi\) | ||||
0.783659 | + | 0.621191i | \(0.213351\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.59612 | 1.35921 | 0.679603 | − | 0.733580i | \(-0.262152\pi\) | ||||
0.679603 | + | 0.733580i | \(0.262152\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.62368 | 1.87456 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.69390 | 0.812241 | 0.406121 | − | 0.913819i | \(-0.366881\pi\) | ||||
0.406121 | + | 0.913819i | \(0.366881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.54493 | −0.705837 | −0.352919 | − | 0.935654i | \(-0.614811\pi\) | ||||
−0.352919 | + | 0.935654i | \(0.614811\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.2917 | 2.65731 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.23138 | 0.541189 | 0.270595 | − | 0.962693i | \(-0.412780\pi\) | ||||
0.270595 | + | 0.962693i | \(0.412780\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.67199 | −1.76007 | −0.880037 | − | 0.474905i | \(-0.842482\pi\) | ||||
−0.880037 | + | 0.474905i | \(0.842482\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.5604 | 2.30447 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.01256 | −0.211134 | −0.105567 | − | 0.994412i | \(-0.533666\pi\) | ||||
−0.105567 | + | 0.994412i | \(0.533666\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.28243 | 1.45649 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.70474 | 1.48278 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.38015 | 0.999070 | 0.499535 | − | 0.866294i | \(-0.333504\pi\) | ||||
0.499535 | + | 0.866294i | \(0.333504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.95587 | −0.530890 | −0.265445 | − | 0.964126i | \(-0.585519\pi\) | ||||
−0.265445 | + | 0.964126i | \(0.585519\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.91094 | 1.37712 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.6031 | 2.13031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.73071 | −0.448926 | −0.224463 | − | 0.974483i | \(-0.572063\pi\) | ||||
−0.224463 | + | 0.974483i | \(0.572063\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.47347 | −1.19671 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.58852 | 0.560432 | 0.280216 | − | 0.959937i | \(-0.409594\pi\) | ||||
0.280216 | + | 0.959937i | \(0.409594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.3625 | −1.73277 | −0.866385 | − | 0.499377i | \(-0.833562\pi\) | ||||
−0.866385 | + | 0.499377i | \(0.833562\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 19.7089 | 2.93803 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.21067 | −0.176594 | −0.0882968 | − | 0.996094i | \(-0.528142\pi\) | ||||
−0.0882968 | + | 0.996094i | \(0.528142\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.93210 | 0.847443 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.55270 | 0.917561 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6872 | −1.60535 | −0.802677 | − | 0.596414i | \(-0.796592\pi\) | ||||
−0.802677 | + | 0.596414i | \(0.796592\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.44112 | 1.27304 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −22.5296 | −2.98412 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.51792 | −0.457994 | −0.228997 | − | 0.973427i | \(-0.573545\pi\) | ||||
−0.228997 | + | 0.973427i | \(0.573545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.42170 | −0.182030 | −0.0910152 | − | 0.995850i | \(-0.529011\pi\) | ||||
−0.0910152 | + | 0.995850i | \(0.529011\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.2235 | 2.54792 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.91905 | −1.10627 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.46876 | −0.179438 | −0.0897188 | − | 0.995967i | \(-0.528597\pi\) | ||||
−0.0897188 | + | 0.995967i | \(0.528597\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.97351 | −0.357968 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.41321 | −0.998464 | −0.499232 | − | 0.866468i | \(-0.666384\pi\) | ||||
−0.499232 | + | 0.866468i | \(0.666384\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1092 | −1.30023 | −0.650114 | − | 0.759837i | \(-0.725279\pi\) | ||||
−0.650114 | + | 0.759837i | \(0.725279\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 21.3857 | 2.46941 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.68759 | 1.10400 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.93478 | 0.892732 | 0.446366 | − | 0.894850i | \(-0.352718\pi\) | ||||
0.446366 | + | 0.894850i | \(0.352718\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.75476 | 0.639418 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.7358 | 1.17840 | 0.589201 | − | 0.807986i | \(-0.299443\pi\) | ||||
0.589201 | + | 0.807986i | \(0.299443\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.82016 | 0.848216 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.7994 | 1.69388 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.2270 | 1.50806 | 0.754029 | − | 0.656841i | \(-0.228108\pi\) | ||||
0.754029 | + | 0.656841i | \(0.228108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.15189 | −0.959378 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.68024 | −0.900099 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26.8875 | −2.75860 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.71302 | −0.783138 | −0.391569 | − | 0.920149i | \(-0.628068\pi\) | ||||
−0.391569 | + | 0.920149i | \(0.628068\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.1496 | 1.52260 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.18955 | −0.317372 | −0.158686 | − | 0.987329i | \(-0.550726\pi\) | ||||
−0.158686 | + | 0.987329i | \(0.550726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.1045 | 1.38976 | 0.694878 | − | 0.719128i | \(-0.255459\pi\) | ||||
0.694878 | + | 0.719128i | \(0.255459\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 37.0103 | 3.61184 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3289 | 1.48190 | 0.740948 | − | 0.671562i | \(-0.234376\pi\) | ||||
0.740948 | + | 0.671562i | \(0.234376\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.80717 | −0.173096 | −0.0865478 | − | 0.996248i | \(-0.527584\pi\) | ||||
−0.0865478 | + | 0.996248i | \(0.527584\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.01903 | −0.761133 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.98652 | 0.939453 | 0.469726 | − | 0.882812i | \(-0.344353\pi\) | ||||
0.469726 | + | 0.882812i | \(0.344353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.54866 | −0.330914 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.3119 | −1.32313 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.02432 | 0.735588 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.74290 | −0.340264 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.5381 | 0.950186 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.99909 | 0.715460 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.22182 | −0.729568 | −0.364784 | − | 0.931092i | \(-0.618857\pi\) | ||||
−0.364784 | + | 0.931092i | \(0.618857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −33.3673 | −2.93783 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.39359 | 0.209129 | 0.104564 | − | 0.994518i | \(-0.466655\pi\) | ||||
0.104564 | + | 0.994518i | \(0.466655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.5894 | −2.39230 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 27.0023 | 2.32398 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.26489 | −0.108067 | −0.0540336 | − | 0.998539i | \(-0.517208\pi\) | ||||
−0.0540336 | + | 0.998539i | \(0.517208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3386 | −1.13137 | −0.565684 | − | 0.824622i | \(-0.691388\pi\) | ||||
−0.565684 | + | 0.824622i | \(0.691388\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.55525 | −0.299406 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.85579 | −0.573310 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.8555 | 1.56586 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.4203 | 1.43680 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.2709 | 0.841428 | 0.420714 | − | 0.907193i | \(-0.361780\pi\) | ||||
0.420714 | + | 0.907193i | \(0.361780\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.1035 | −1.55462 | −0.777310 | − | 0.629118i | \(-0.783416\pi\) | ||||
−0.777310 | + | 0.629118i | \(0.783416\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.5486 | 1.01449 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.3592 | −0.832074 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2678 | −0.899268 | −0.449634 | − | 0.893213i | \(-0.648446\pi\) | ||||
−0.449634 | + | 0.893213i | \(0.648446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −34.3206 | −2.72180 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.64130 | −0.286975 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.86346 | −0.224283 | −0.112142 | − | 0.993692i | \(-0.535771\pi\) | ||||
−0.112142 | + | 0.993692i | \(0.535771\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 27.7249 | 2.15838 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.8434 | −1.14861 | −0.574307 | − | 0.818640i | \(-0.694728\pi\) | ||||
−0.574307 | + | 0.818640i | \(0.694728\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.52332 | −0.501794 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −43.1448 | −3.29937 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.4449 | 1.40234 | 0.701171 | − | 0.712993i | \(-0.252661\pi\) | ||||
0.701171 | + | 0.712993i | \(0.252661\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26.1885 | 1.97967 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.3308 | −0.776508 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.9032 | 1.26340 | 0.631701 | − | 0.775212i | \(-0.282357\pi\) | ||||
0.631701 | + | 0.775212i | \(0.282357\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9920 | 1.11434 | 0.557171 | − | 0.830397i | \(-0.311887\pi\) | ||||
0.557171 | + | 0.830397i | \(0.311887\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.17499 | −0.308624 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.57013 | −0.703610 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.01112 | 0.439576 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.7072 | 2.01540 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.588291 | −0.0425673 | −0.0212836 | − | 0.999773i | \(-0.506775\pi\) | ||||
−0.0212836 | + | 0.999773i | \(0.506775\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.57048 | −0.400972 | −0.200486 | − | 0.979697i | \(-0.564252\pi\) | ||||
−0.200486 | + | 0.979697i | \(0.564252\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −26.1918 | −1.87563 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.2860 | 1.87280 | 0.936401 | − | 0.350931i | \(-0.114135\pi\) | ||||
0.936401 | + | 0.350931i | \(0.114135\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.30553 | −0.163435 | −0.0817175 | − | 0.996656i | \(-0.526041\pi\) | ||||
−0.0817175 | + | 0.996656i | \(0.526041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.31318 | −0.304228 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.3477 | 1.35794 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.5764 | 0.878376 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.69434 | −0.395784 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.6676 | −1.42960 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5911 | −0.935651 | −0.467825 | − | 0.883821i | \(-0.654962\pi\) | ||||
−0.467825 | + | 0.883821i | \(0.654962\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.7063 | −1.69285 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −39.8215 | −2.71580 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.6297 | −0.721589 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −32.6233 | −2.20448 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.67871 | −0.381991 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.85854 | −0.392317 | −0.196158 | − | 0.980572i | \(-0.562847\pi\) | ||||
−0.196158 | + | 0.980572i | \(0.562847\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 40.9541 | 2.73027 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9583 | 1.12556 | 0.562781 | − | 0.826606i | \(-0.309731\pi\) | ||||
0.562781 | + | 0.826606i | \(0.309731\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.70965 | 0.641631 | 0.320816 | − | 0.947142i | \(-0.396043\pi\) | ||||
0.320816 | + | 0.947142i | \(0.396043\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 28.4487 | 1.87179 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.4730 | −1.93084 | −0.965420 | − | 0.260701i | \(-0.916046\pi\) | ||||
−0.965420 | + | 0.260701i | \(0.916046\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.24293 | −0.276779 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.3014 | 1.51359 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.18187 | 0.529241 | 0.264621 | − | 0.964353i | \(-0.414753\pi\) | ||||
0.264621 | + | 0.964353i | \(0.414753\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.2420 | −1.23948 | −0.619742 | − | 0.784806i | \(-0.712763\pi\) | ||||
−0.619742 | + | 0.784806i | \(0.712763\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.21471 | −0.398674 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.7898 | 1.32821 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.5247 | 1.24233 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 31.5267 | 1.99793 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.42671 | −0.153173 | −0.0765864 | − | 0.997063i | \(-0.524402\pi\) | ||||
−0.0765864 | + | 0.997063i | \(0.524402\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.72775 | −0.171492 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 22.9648 | 1.43811 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.5109 | −0.967544 | −0.483772 | − | 0.875194i | \(-0.660734\pi\) | ||||
−0.483772 | + | 0.875194i | \(0.660734\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.81997 | −0.610183 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 30.2563 | 1.87282 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.35072 | −0.0832891 | −0.0416446 | − | 0.999132i | \(-0.513260\pi\) | ||||
−0.0416446 | + | 0.999132i | \(0.513260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −40.9591 | −2.51610 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 41.7791 | 2.55684 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.53476 | −0.337460 | −0.168730 | − | 0.985662i | \(-0.553967\pi\) | ||||
−0.168730 | + | 0.985662i | \(0.553967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.07472 | −0.186776 | −0.0933881 | − | 0.995630i | \(-0.529770\pi\) | ||||
−0.0933881 | + | 0.995630i | \(0.529770\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26.8755 | −1.62658 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.6181 | 1.18302 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.965160 | 0.0579908 | 0.0289954 | − | 0.999580i | \(-0.490769\pi\) | ||||
0.0289954 | + | 0.999580i | \(0.490769\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.6229 | −0.995186 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.1746 | 0.666623 | 0.333311 | − | 0.942817i | \(-0.391834\pi\) | ||||
0.333311 | + | 0.942817i | \(0.391834\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.17440 | 0.0698110 | 0.0349055 | − | 0.999391i | \(-0.488887\pi\) | ||||
0.0349055 | + | 0.999391i | \(0.488887\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −78.9580 | −4.67707 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.9047 | 0.761743 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0209 | −0.707114 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.6501 | −1.32777 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.19135 | −0.420123 | −0.210062 | − | 0.977688i | \(-0.567366\pi\) | ||||
−0.210062 | + | 0.977688i | \(0.567366\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.3290 | −0.717823 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.7558 | 1.20437 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.57691 | 0.149026 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −40.8611 | −2.35519 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.36647 | −0.538090 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.98254 | −0.285300 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3913 | −0.650138 | −0.325069 | − | 0.945690i | \(-0.605388\pi\) | ||||
−0.325069 | + | 0.945690i | \(0.605388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 41.4193 | 2.35626 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.8473 | −1.29555 | −0.647776 | − | 0.761831i | \(-0.724301\pi\) | ||||
−0.647776 | + | 0.761831i | \(0.724301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.9858 | 1.24271 | 0.621356 | − | 0.783528i | \(-0.286582\pi\) | ||||
0.621356 | + | 0.783528i | \(0.286582\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 70.8757 | 3.99340 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.3667 | 1.08774 | 0.543871 | − | 0.839169i | \(-0.316958\pi\) | ||||
0.543871 | + | 0.839169i | \(0.316958\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.4936 | 0.811486 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.0149 | 2.51249 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.1191 | −0.952533 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.5333 | −1.02804 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.30696 | −0.293476 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.35370 | −0.240027 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0381 | 1.43118 | 0.715592 | − | 0.698519i | \(-0.246157\pi\) | ||||
0.715592 | + | 0.698519i | \(0.246157\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.3567 | −0.841539 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.14746 | −0.281236 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.4605 | 0.569820 | 0.284910 | − | 0.958554i | \(-0.408036\pi\) | ||||
0.284910 | + | 0.958554i | \(0.408036\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.3265 | 1.59280 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.96282 | −0.431211 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.84031 | −0.207357 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.4210 | −0.561050 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.17453 | −0.438832 | −0.219416 | − | 0.975631i | \(-0.570415\pi\) | ||||
−0.219416 | + | 0.975631i | \(0.570415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.22532 | −0.333234 | −0.166617 | − | 0.986022i | \(-0.553284\pi\) | ||||
−0.166617 | + | 0.986022i | \(0.553284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.6080 | −1.04660 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.8340 | 1.80080 | 0.900402 | − | 0.435060i | \(-0.143273\pi\) | ||||
0.900402 | + | 0.435060i | \(0.143273\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.4852 | −1.56491 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.5643 | 1.24716 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.15995 | 0.219554 | 0.109777 | − | 0.993956i | \(-0.464986\pi\) | ||||
0.109777 | + | 0.993956i | \(0.464986\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.8594 | 2.09786 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.9915 | −0.576902 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −38.9335 | −2.03787 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.0208 | 1.51488 | 0.757438 | − | 0.652907i | \(-0.226451\pi\) | ||||
0.757438 | + | 0.652907i | \(0.226451\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.1807 | 1.05056 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −42.0284 | −2.18201 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.5934 | 1.42873 | 0.714366 | − | 0.699773i | \(-0.246715\pi\) | ||||
0.714366 | + | 0.699773i | \(0.246715\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 23.4902 | 1.21303 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.6921 | −0.705180 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.1132 | 1.23861 | 0.619306 | − | 0.785150i | \(-0.287414\pi\) | ||||
0.619306 | + | 0.785150i | \(0.287414\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.1443 | −1.23695 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.50697 | −0.485783 | −0.242892 | − | 0.970053i | \(-0.578096\pi\) | ||||
−0.242892 | + | 0.970053i | \(0.578096\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 33.9514 | 1.73033 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −63.8993 | −3.24818 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.43073 | 0.173945 | 0.0869724 | − | 0.996211i | \(-0.472281\pi\) | ||||
0.0869724 | + | 0.996211i | \(0.472281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.25942 | −0.114264 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.02904 | 0.354568 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.8085 | 1.39920 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.4129 | 1.92789 | 0.963944 | − | 0.266105i | \(-0.0857367\pi\) | ||||
0.963944 | + | 0.266105i | \(0.0857367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −81.0193 | −4.05604 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.64454 | 0.281875 | 0.140938 | − | 0.990018i | \(-0.454988\pi\) | ||||
0.140938 | + | 0.990018i | \(0.454988\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.52249 | 0.374722 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.1683 | 1.00217 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.35626 | −0.364636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.46598 | −0.418616 | −0.209308 | − | 0.977850i | \(-0.567121\pi\) | ||||
−0.209308 | + | 0.977850i | \(0.567121\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.71450 | −0.183223 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.6509 | −0.622509 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37.6249 | 1.84693 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −39.1704 | −1.91818 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.309716 | 0.0151306 | 0.00756532 | − | 0.999971i | \(-0.497592\pi\) | ||||
0.00756532 | + | 0.999971i | \(0.497592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2903 | 0.891417 | 0.445709 | − | 0.895178i | \(-0.352952\pi\) | ||||
0.445709 | + | 0.895178i | \(0.352952\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.80840 | −0.331036 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.2499 | 0.788235 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.11262 | −0.247417 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.1328 | −0.972020 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.2770 | 1.69923 | 0.849616 | − | 0.527402i | \(-0.176834\pi\) | ||||
0.849616 | + | 0.527402i | \(0.176834\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.6692 | −0.704957 | −0.352478 | − | 0.935820i | \(-0.614661\pi\) | ||||
−0.352478 | + | 0.935820i | \(0.614661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 55.3711 | 2.65484 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.76838 | 0.371612 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1285 | 0.578862 | 0.289431 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289431 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 33.3602 | 1.58858 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.5872 | −0.740568 | −0.370284 | − | 0.928919i | \(-0.620740\pi\) | ||||
−0.370284 | + | 0.928919i | \(0.620740\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 49.8603 | 2.36361 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.1618 | 1.42660 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.3759 | −0.961597 | −0.480799 | − | 0.876831i | \(-0.659653\pi\) | ||||
−0.480799 | + | 0.876831i | \(0.659653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.66710 | 0.455206 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −56.0995 | −2.63578 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −32.0740 | −1.50365 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.3165 | 1.41815 | 0.709073 | − | 0.705136i | \(-0.249114\pi\) | ||||
0.709073 | + | 0.705136i | \(0.249114\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.1922 | 0.802463 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.7107 | −1.80294 | −0.901468 | − | 0.432846i | \(-0.857509\pi\) | ||||
−0.901468 | + | 0.432846i | \(0.857509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.39874 | 0.390323 | 0.195161 | − | 0.980771i | \(-0.437477\pi\) | ||||
0.195161 | + | 0.980771i | \(0.437477\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −30.4210 | −1.41074 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.32431 | 0.0612819 | 0.0306410 | − | 0.999530i | \(-0.490245\pi\) | ||||
0.0306410 | + | 0.999530i | \(0.490245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.28184 | −0.243893 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −33.0891 | −1.52467 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.6095 | −1.40743 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −55.8707 | −2.56352 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −65.7248 | −3.00933 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.4732 | −0.478531 | −0.239265 | − | 0.970954i | \(-0.576907\pi\) | ||||
−0.239265 | + | 0.970954i | \(0.576907\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.94947 | 0.316869 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.6931 | −0.486553 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −27.0313 | −1.22743 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.4707 | −1.47139 | −0.735693 | − | 0.677315i | \(-0.763144\pi\) | ||||
−0.735693 | + | 0.677315i | \(0.763144\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.40886 | −0.380262 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.6299 | 0.615108 | 0.307554 | − | 0.951531i | \(-0.400490\pi\) | ||||
0.307554 | + | 0.951531i | \(0.400490\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0052 | 0.540686 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 53.0939 | 2.38639 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.2549 | −1.35712 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.8315 | −1.33544 | −0.667720 | − | 0.744413i | \(-0.732730\pi\) | ||||
−0.667720 | + | 0.744413i | \(0.732730\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −43.5891 | −1.94742 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.4135 | 0.865605 | 0.432802 | − | 0.901489i | \(-0.357525\pi\) | ||||
0.432802 | + | 0.901489i | \(0.357525\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.1782 | −0.497423 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.1565 | −0.850768 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.7324 | 1.58381 | 0.791905 | − | 0.610644i | \(-0.209089\pi\) | ||||
0.791905 | + | 0.610644i | \(0.209089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.9499 | −1.76728 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −59.1106 | −2.60980 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 49.4310 | 2.17819 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.26141 | −0.143437 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 54.1656 | 2.37760 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.2806 | 1.19518 | 0.597592 | − | 0.801800i | \(-0.296124\pi\) | ||||
0.597592 | + | 0.801800i | \(0.296124\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.84286 | −0.299217 | −0.149609 | − | 0.988745i | \(-0.547801\pi\) | ||||
−0.149609 | + | 0.988745i | \(0.547801\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 76.9055 | 3.35643 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.59567 | −0.287312 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9747 | −0.955422 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.7837 | −0.858538 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.13253 | −0.395574 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 53.7220 | 2.32260 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 49.6380 | 2.14204 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.9805 | 0.688328 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.60345 | 0.240911 | 0.120455 | − | 0.992719i | \(-0.461564\pi\) | ||||
0.120455 | + | 0.992719i | \(0.461564\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 44.0255 | 1.88932 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.33347 | −0.271296 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.4025 | −1.12889 | −0.564445 | − | 0.825471i | \(-0.690910\pi\) | ||||
−0.564445 | + | 0.825471i | \(0.690910\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.99521 | −0.341227 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −41.2765 | −1.75844 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.5344 | 1.21341 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −28.1038 | −1.19294 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.85798 | −0.248211 | −0.124105 | − | 0.992269i | \(-0.539606\pi\) | ||||
−0.124105 | + | 0.992269i | \(0.539606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.9169 | 1.22305 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.6523 | 0.745281 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.1862 | 0.640022 | 0.320011 | − | 0.947414i | \(-0.396313\pi\) | ||||
0.320011 | + | 0.947414i | \(0.396313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.9991 | 1.47242 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.6948 | 0.869101 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.0977 | 0.465238 | 0.232619 | − | 0.972568i | \(-0.425270\pi\) | ||||
0.232619 | + | 0.972568i | \(0.425270\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.6029 | −1.74103 | −0.870515 | − | 0.492143i | \(-0.836214\pi\) | ||||
−0.870515 | + | 0.492143i | \(0.836214\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.72758 | −0.0721708 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.37393 | −0.307514 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.0854 | 1.33573 | 0.667867 | − | 0.744281i | \(-0.267208\pi\) | ||||
0.667867 | + | 0.744281i | \(0.267208\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.3583 | −0.679829 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.6071 | 1.60169 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.4840 | −1.30393 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −50.1579 | −2.07377 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.5966 | 1.75815 | 0.879074 | − | 0.476685i | \(-0.158162\pi\) | ||||
0.879074 | + | 0.476685i | \(0.158162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.6774 | 0.934406 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 77.1919 | 3.17525 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.7371 | −1.63181 | −0.815903 | − | 0.578189i | \(-0.803760\pi\) | ||||
−0.815903 | + | 0.578189i | \(0.803760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.1223 | 1.15290 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.77046 | −0.277096 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.5024 | 1.28715 | 0.643577 | − | 0.765381i | \(-0.277450\pi\) | ||||
0.643577 | + | 0.765381i | \(0.277450\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.6780 | −1.90404 | −0.952019 | − | 0.306040i | \(-0.900996\pi\) | ||||
−0.952019 | + | 0.306040i | \(0.900996\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.25984 | −0.336367 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.1175 | −0.533302 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.68374 | −0.190107 | −0.0950535 | − | 0.995472i | \(-0.530302\pi\) | ||||
−0.0950535 | + | 0.995472i | \(0.530302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 56.8166 | 2.30233 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.08106 | 0.124646 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2593 | 0.777874 | 0.388937 | − | 0.921264i | \(-0.372842\pi\) | ||||
0.388937 | + | 0.921264i | \(0.372842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 36.9321 | 1.48924 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.6116 | 1.43367 | 0.716834 | − | 0.697244i | \(-0.245591\pi\) | ||||
0.716834 | + | 0.697244i | \(0.245591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 48.6921 | 1.95710 | 0.978550 | − | 0.206012i | \(-0.0660485\pi\) | ||||
0.978550 | + | 0.206012i | \(0.0660485\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.80154 | −0.313065 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 51.1620 | 2.04976 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.37832 | −0.335133 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −60.6926 | −2.42383 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.09326 | −0.242954 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.5674 | −1.53534 | −0.767672 | − | 0.640843i | \(-0.778585\pi\) | ||||
−0.767672 | + | 0.640843i | \(0.778585\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39.9118 | −1.58635 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.8144 | −1.14347 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0968 | −0.598156 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −47.3132 | −1.87168 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 49.6921 | 1.96272 | 0.981360 | − | 0.192177i | \(-0.0615547\pi\) | ||||
0.981360 | + | 0.192177i | \(0.0615547\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.3290 | 1.03832 | 0.519158 | − | 0.854678i | \(-0.326246\pi\) | ||||
0.519158 | + | 0.854678i | \(0.326246\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −116.940 | −4.60451 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.8724 | −1.29235 | −0.646174 | − | 0.763190i | \(-0.723632\pi\) | ||||
−0.646174 | + | 0.763190i | \(0.723632\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.47693 | −0.372002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.2152 | −1.22342 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.5574 | 1.86107 | 0.930533 | − | 0.366208i | \(-0.119344\pi\) | ||||
0.930533 | + | 0.366208i | \(0.119344\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.38865 | 0.327772 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −62.4744 | −2.43736 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.5009 | 1.14919 | 0.574596 | − | 0.818437i | \(-0.305159\pi\) | ||||
0.574596 | + | 0.818437i | \(0.305159\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.1619 | 1.44543 | 0.722715 | − | 0.691146i | \(-0.242894\pi\) | ||||
0.722715 | + | 0.691146i | \(0.242894\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.6762 | −0.647649 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −96.6906 | −3.74950 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.44775 | −0.210938 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.2043 | −0.665155 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.82993 | −0.147853 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.7232 | 0.413350 | 0.206675 | − | 0.978410i | \(-0.433736\pi\) | ||||
0.206675 | + | 0.978410i | \(0.433736\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 56.1092 | 2.15965 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.0109611 | 0.000421268 0 | 0.000210634 | − | 1.00000i | \(-0.499933\pi\) | ||||
0.000210634 | 1.00000i | \(0.499933\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.7370 | −1.06445 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 49.7999 | 1.90834 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.0223 | −1.34009 | −0.670045 | − | 0.742320i | \(-0.733725\pi\) | ||||
−0.670045 | + | 0.742320i | \(0.733725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.43298 | −0.169376 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.5135 | 1.08786 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.7430 | 1.13312 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.6743 | −0.406068 | −0.203034 | − | 0.979172i | \(-0.565080\pi\) | ||||
−0.203034 | + | 0.979172i | \(0.565080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 54.4800 | 2.06952 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −46.7470 | −1.77321 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00735 | 0.303300 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −86.5507 | −3.27365 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.72867 | −0.178599 | −0.0892997 | − | 0.996005i | \(-0.528463\pi\) | ||||
−0.0892997 | + | 0.996005i | \(0.528463\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.9500 | 0.790143 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.4598 | −0.469265 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.4700 | −0.431375 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.31840 | 0.349960 | 0.174980 | − | 0.984572i | \(-0.444014\pi\) | ||||
0.174980 | + | 0.984572i | \(0.444014\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 44.6227 | 1.67348 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.99301 | 0.112089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0270 | −0.898559 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.0270 | 0.897303 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.7922 | 1.14836 | 0.574178 | − | 0.818730i | \(-0.305322\pi\) | ||||
0.574178 | + | 0.818730i | \(0.305322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.7214 | 1.88896 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −56.5062 | −2.10149 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.1806 | 1.45513 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.59936 | −0.356021 | −0.178010 | − | 0.984029i | \(-0.556966\pi\) | ||||
−0.178010 | + | 0.984029i | \(0.556966\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.5145 | −1.31535 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.3541 | −0.937757 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.09657 | −0.0405028 | −0.0202514 | − | 0.999795i | \(-0.506447\pi\) | ||||
−0.0202514 | + | 0.999795i | \(0.506447\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 61.0516 | 2.25192 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.95669 | −0.145747 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.7130 | −1.90229 | −0.951147 | − | 0.308738i | \(-0.900093\pi\) | ||||
−0.951147 | + | 0.308738i | \(0.900093\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 57.3364 | 2.10630 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.2172 | 1.10856 | 0.554280 | − | 0.832330i | \(-0.312994\pi\) | ||||
0.554280 | + | 0.832330i | \(0.312994\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.9958 | 1.31879 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 60.3745 | 2.20899 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 55.1244 | 2.01420 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.12632 | −0.259697 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −66.9507 | −2.43658 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.78653 | 0.319352 | 0.159676 | − | 0.987169i | \(-0.448955\pi\) | ||||
0.159676 | + | 0.987169i | \(0.448955\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.01033 | −0.290756 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.5283 | 0.562900 | 0.281450 | − | 0.959576i | \(-0.409185\pi\) | ||||
0.281450 | + | 0.959576i | \(0.409185\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.49881 | −0.235273 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 43.9781 | 1.59003 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.95287 | 0.323269 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.3925 | 0.699311 | 0.349655 | − | 0.936878i | \(-0.386299\pi\) | ||||
0.349655 | + | 0.936878i | \(0.386299\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.5495 | −1.64042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.4611 | −1.16755 | −0.583773 | − | 0.811917i | \(-0.698424\pi\) | ||||
−0.583773 | + | 0.811917i | \(0.698424\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.5259 | −0.773234 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.8374 | −1.03454 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.5310 | −0.986402 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.6643 | −0.810994 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 41.4527 | 1.48140 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.4895 | −1.40944 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −54.2967 | −1.93547 | −0.967734 | − | 0.251974i | \(-0.918920\pi\) | ||||
−0.967734 | + | 0.251974i | \(0.918920\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.96655 | −0.141213 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.9127 | 1.27691 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.61814 | 0.128484 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −120.281 | −4.26593 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.4918 | 1.57598 | 0.787990 | − | 0.615688i | \(-0.211122\pi\) | ||||
0.787990 | + | 0.615688i | \(0.211122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.70146 | −0.0955706 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 80.0081 | 2.82695 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29.9269 | −1.05610 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.7614 | −0.449781 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.2534 | −0.572148 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.2194 | −0.886665 | −0.443333 | − | 0.896357i | \(-0.646204\pi\) | ||||
−0.443333 | + | 0.896357i | \(0.646204\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.9521 | −0.630383 | −0.315191 | − | 0.949028i | \(-0.602069\pi\) | ||||
−0.315191 | + | 0.949028i | \(0.602069\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.02927 | −0.316670 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.0354 | −0.351523 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 87.1732 | 3.04980 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −51.4673 | −1.79841 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.8491 | 0.902139 | 0.451069 | − | 0.892489i | \(-0.351043\pi\) | ||||
0.451069 | + | 0.892489i | \(0.351043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.656538 | −0.0228855 | −0.0114427 | − | 0.999935i | \(-0.503642\pi\) | ||||
−0.0114427 | + | 0.999935i | \(0.503642\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 57.6109 | 2.00575 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.37285 | −0.152059 | −0.0760295 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760295 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.371007 | 0.0128856 | 0.00644280 | − | 0.999979i | \(-0.497949\pi\) | ||||
0.00644280 | + | 0.999979i | \(0.497949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.83430 | 0.0983207 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.2368 | 0.458627 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.0205 | −1.80024 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.7742 | −0.787192 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.9574 | −0.827100 | −0.413550 | − | 0.910481i | \(-0.635711\pi\) | ||||
−0.413550 | + | 0.910481i | \(0.635711\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.0539434 | −0.00186012 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.8155 | 1.13023 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.8618 | −0.786471 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.4599 | −0.462489 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.44876 | 0.118361 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.76502 | 0.0947836 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.2099 | 1.13708 | 0.568542 | − | 0.822654i | \(-0.307508\pi\) | ||||
0.568542 | + | 0.822654i | \(0.307508\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −151.207 | −5.17116 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.7486 | 0.367165 | 0.183582 | − | 0.983004i | \(-0.441231\pi\) | ||||
0.183582 | + | 0.983004i | \(0.441231\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2265 | 0.553643 | 0.276821 | − | 0.960921i | \(-0.410719\pi\) | ||||
0.276821 | + | 0.960921i | \(0.410719\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.8962 | 1.29150 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.4940 | 1.34439 | 0.672197 | − | 0.740373i | \(-0.265351\pi\) | ||||
0.672197 | + | 0.740373i | \(0.265351\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 64.6426 | 2.19792 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −35.3008 | −1.19888 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.3755 | 0.725114 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.73789 | 0.126654 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −43.3756 | −1.46804 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.7657 | 0.972458 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.12805 | −0.105627 | −0.0528134 | − | 0.998604i | \(-0.516819\pi\) | ||||
−0.0528134 | + | 0.998604i | \(0.516819\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.1182 | −0.712299 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.1801 | −0.679885 | −0.339942 | − | 0.940446i | \(-0.610408\pi\) | ||||
−0.339942 | + | 0.940446i | \(0.610408\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.9653 | −1.14302 | −0.571511 | − | 0.820594i | \(-0.693643\pi\) | ||||
−0.571511 | + | 0.820594i | \(0.693643\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −36.2055 | −1.21704 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.3478 | −0.683212 | −0.341606 | − | 0.939843i | \(-0.610971\pi\) | ||||
−0.341606 | + | 0.939843i | \(0.610971\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.5667 | −0.991634 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.5028 | 0.519362 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.28821 | 0.310818 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 59.2394 | 1.98015 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.56737 | 0.252667 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.9030 | −0.530396 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.0785 | −0.868800 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −119.993 | −3.99312 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 52.5412 | 1.74653 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.23956 | −0.207181 | −0.103591 | − | 0.994620i | \(-0.533033\pi\) | ||||
−0.103591 | + | 0.994620i | \(0.533033\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.9370 | −0.594934 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.34308 | 0.177024 | 0.0885120 | − | 0.996075i | \(-0.471789\pi\) | ||||
0.0885120 | + | 0.996075i | \(0.471789\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.9211 | 0.957147 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.6318 | −0.483712 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.60764 | 0.284249 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.09577 | 0.300042 | 0.150021 | − | 0.988683i | \(-0.452066\pi\) | ||||
0.150021 | + | 0.988683i | \(0.452066\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.4519 | −1.10228 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.4110 | 0.704753 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.8862 | −0.653855 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 79.3191 | 2.60518 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.7796 | 0.386477 | 0.193238 | − | 0.981152i | \(-0.438101\pi\) | ||||
0.193238 | + | 0.981152i | \(0.438101\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.5110 | −1.49156 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −67.0936 | −2.19655 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.0667 | 0.688956 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.4723 | −0.995487 | −0.497743 | − | 0.867324i | \(-0.665838\pi\) | ||||
−0.497743 | + | 0.867324i | \(0.665838\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 64.5638 | 2.10696 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.1624 | −0.331285 | −0.165642 | − | 0.986186i | \(-0.552970\pi\) | ||||
−0.165642 | + | 0.986186i | \(0.552970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.63360 | −0.118326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 97.1034 | 3.15877 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.7859 | 0.480476 | 0.240238 | − | 0.970714i | \(-0.422775\pi\) | ||||
0.240238 | + | 0.970714i | \(0.422775\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.2720 | 0.917749 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 56.8724 | 1.84421 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.8716 | −0.773277 | −0.386639 | − | 0.922231i | \(-0.626364\pi\) | ||||
−0.386639 | + | 0.922231i | \(0.626364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.06174 | −0.0667164 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 42.5620 | 1.37584 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.54871 | −0.146886 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2628 | −0.718156 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 86.2046 | 2.77790 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.5225 | −0.628451 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.7395 | −0.473990 | −0.236995 | − | 0.971511i | \(-0.576162\pi\) | ||||
−0.236995 | + | 0.971511i | \(0.576162\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −50.2722 | −1.61498 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.4852 | −1.58806 | −0.794028 | − | 0.607881i | \(-0.792020\pi\) | ||||
−0.794028 | + | 0.607881i | \(0.792020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −47.9674 | −1.53776 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −54.4251 | −1.74300 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.8293 | −1.62617 | −0.813087 | − | 0.582143i | \(-0.802215\pi\) | ||||
−0.813087 | + | 0.582143i | \(0.802215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.3261 | 1.22491 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.1630 | −0.324478 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.9347 | 0.890978 | 0.445489 | − | 0.895287i | \(-0.353030\pi\) | ||||
0.445489 | + | 0.895287i | \(0.353030\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 92.1228 | 2.93528 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.7851 | −0.406955 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.5053 | 0.365847 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.0473 | 1.04978 | 0.524891 | − | 0.851170i | \(-0.324106\pi\) | ||||
0.524891 | + | 0.851170i | \(0.324106\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 76.4637 | 2.42650 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.08005 | −0.256155 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.0785 | 1.01594 | 0.507968 | − | 0.861376i | \(-0.330397\pi\) | ||||
0.507968 | + | 0.861376i | \(0.330397\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.0394 | −0.665657 |
(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 | 6008.2.a.e.1.45 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.45 | ✓ | 50 | 1.1 | even | 1 | trivial |