Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.76232 | −1.24615 | −0.623075 | − | 0.782162i | \(-0.714117\pi\) | ||||
−0.623075 | + | 0.782162i | \(0.714117\pi\) | |||||||
\(3\) | −3.28691 | −1.89770 | −0.948849 | − | 0.315731i | \(-0.897750\pi\) | ||||
−0.948849 | + | 0.315731i | \(0.897750\pi\) | |||||||
\(4\) | 1.10578 | 0.552891 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 5.79259 | 2.36482 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.57590 | 0.557165 | ||||||||
\(9\) | 7.80377 | 2.60126 | ||||||||
\(10\) | −1.76232 | −0.557295 | ||||||||
\(11\) | 4.40636 | 1.32857 | 0.664284 | − | 0.747480i | \(-0.268736\pi\) | ||||
0.664284 | + | 0.747480i | \(0.268736\pi\) | |||||||
\(12\) | −3.63460 | −1.04922 | ||||||||
\(13\) | 5.43044 | 1.50613 | 0.753066 | − | 0.657944i | \(-0.228574\pi\) | ||||
0.753066 | + | 0.657944i | \(0.228574\pi\) | |||||||
\(14\) | 1.76232 | 0.471001 | ||||||||
\(15\) | −3.28691 | −0.848676 | ||||||||
\(16\) | −4.98881 | −1.24720 | ||||||||
\(17\) | −1.03103 | −0.250061 | −0.125031 | − | 0.992153i | \(-0.539903\pi\) | ||||
−0.125031 | + | 0.992153i | \(0.539903\pi\) | |||||||
\(18\) | −13.7528 | −3.24156 | ||||||||
\(19\) | −5.58530 | −1.28136 | −0.640678 | − | 0.767810i | \(-0.721347\pi\) | ||||
−0.640678 | + | 0.767810i | \(0.721347\pi\) | |||||||
\(20\) | 1.10578 | 0.247260 | ||||||||
\(21\) | 3.28691 | 0.717262 | ||||||||
\(22\) | −7.76543 | −1.65560 | ||||||||
\(23\) | −5.83481 | −1.21664 | −0.608321 | − | 0.793691i | \(-0.708157\pi\) | ||||
−0.608321 | + | 0.793691i | \(0.708157\pi\) | |||||||
\(24\) | −5.17984 | −1.05733 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −9.57019 | −1.87687 | ||||||||
\(27\) | −15.7895 | −3.03870 | ||||||||
\(28\) | −1.10578 | −0.208973 | ||||||||
\(29\) | −2.55617 | −0.474669 | −0.237334 | − | 0.971428i | \(-0.576274\pi\) | ||||
−0.237334 | + | 0.971428i | \(0.576274\pi\) | |||||||
\(30\) | 5.79259 | 1.05758 | ||||||||
\(31\) | 6.32288 | 1.13562 | 0.567811 | − | 0.823159i | \(-0.307790\pi\) | ||||
0.567811 | + | 0.823159i | \(0.307790\pi\) | |||||||
\(32\) | 5.64009 | 0.997037 | ||||||||
\(33\) | −14.4833 | −2.52122 | ||||||||
\(34\) | 1.81701 | 0.311614 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 8.62926 | 1.43821 | ||||||||
\(37\) | 3.64651 | 0.599482 | 0.299741 | − | 0.954021i | \(-0.403100\pi\) | ||||
0.299741 | + | 0.954021i | \(0.403100\pi\) | |||||||
\(38\) | 9.84310 | 1.59676 | ||||||||
\(39\) | −17.8494 | −2.85818 | ||||||||
\(40\) | 1.57590 | 0.249172 | ||||||||
\(41\) | 5.95517 | 0.930041 | 0.465021 | − | 0.885300i | \(-0.346047\pi\) | ||||
0.465021 | + | 0.885300i | \(0.346047\pi\) | |||||||
\(42\) | −5.79259 | −0.893817 | ||||||||
\(43\) | −9.29106 | −1.41687 | −0.708436 | − | 0.705775i | \(-0.750599\pi\) | ||||
−0.708436 | + | 0.705775i | \(0.750599\pi\) | |||||||
\(44\) | 4.87248 | 0.734553 | ||||||||
\(45\) | 7.80377 | 1.16332 | ||||||||
\(46\) | 10.2828 | 1.51612 | ||||||||
\(47\) | −1.03700 | −0.151263 | −0.0756314 | − | 0.997136i | \(-0.524097\pi\) | ||||
−0.0756314 | + | 0.997136i | \(0.524097\pi\) | |||||||
\(48\) | 16.3978 | 2.36681 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.76232 | −0.249230 | ||||||||
\(51\) | 3.38890 | 0.474541 | ||||||||
\(52\) | 6.00488 | 0.832727 | ||||||||
\(53\) | 2.25858 | 0.310240 | 0.155120 | − | 0.987896i | \(-0.450424\pi\) | ||||
0.155120 | + | 0.987896i | \(0.450424\pi\) | |||||||
\(54\) | 27.8263 | 3.78667 | ||||||||
\(55\) | 4.40636 | 0.594154 | ||||||||
\(56\) | −1.57590 | −0.210589 | ||||||||
\(57\) | 18.3584 | 2.43163 | ||||||||
\(58\) | 4.50480 | 0.591509 | ||||||||
\(59\) | −3.22683 | −0.420097 | −0.210049 | − | 0.977691i | \(-0.567362\pi\) | ||||
−0.210049 | + | 0.977691i | \(0.567362\pi\) | |||||||
\(60\) | −3.63460 | −0.469225 | ||||||||
\(61\) | 11.7743 | 1.50754 | 0.753772 | − | 0.657136i | \(-0.228232\pi\) | ||||
0.753772 | + | 0.657136i | \(0.228232\pi\) | |||||||
\(62\) | −11.1430 | −1.41516 | ||||||||
\(63\) | −7.80377 | −0.983182 | ||||||||
\(64\) | 0.0379570 | 0.00474462 | ||||||||
\(65\) | 5.43044 | 0.673563 | ||||||||
\(66\) | 25.5243 | 3.14182 | ||||||||
\(67\) | 2.58147 | 0.315377 | 0.157689 | − | 0.987489i | \(-0.449596\pi\) | ||||
0.157689 | + | 0.987489i | \(0.449596\pi\) | |||||||
\(68\) | −1.14009 | −0.138257 | ||||||||
\(69\) | 19.1785 | 2.30882 | ||||||||
\(70\) | 1.76232 | 0.210638 | ||||||||
\(71\) | 7.64634 | 0.907454 | 0.453727 | − | 0.891141i | \(-0.350094\pi\) | ||||
0.453727 | + | 0.891141i | \(0.350094\pi\) | |||||||
\(72\) | 12.2980 | 1.44933 | ||||||||
\(73\) | 11.6989 | 1.36925 | 0.684624 | − | 0.728897i | \(-0.259967\pi\) | ||||
0.684624 | + | 0.728897i | \(0.259967\pi\) | |||||||
\(74\) | −6.42632 | −0.747045 | ||||||||
\(75\) | −3.28691 | −0.379539 | ||||||||
\(76\) | −6.17612 | −0.708450 | ||||||||
\(77\) | −4.40636 | −0.502152 | ||||||||
\(78\) | 31.4563 | 3.56173 | ||||||||
\(79\) | −1.20217 | −0.135255 | −0.0676276 | − | 0.997711i | \(-0.521543\pi\) | ||||
−0.0676276 | + | 0.997711i | \(0.521543\pi\) | |||||||
\(80\) | −4.98881 | −0.557766 | ||||||||
\(81\) | 28.4875 | 3.16527 | ||||||||
\(82\) | −10.4949 | −1.15897 | ||||||||
\(83\) | 1.63094 | 0.179019 | 0.0895093 | − | 0.995986i | \(-0.471470\pi\) | ||||
0.0895093 | + | 0.995986i | \(0.471470\pi\) | |||||||
\(84\) | 3.63460 | 0.396568 | ||||||||
\(85\) | −1.03103 | −0.111831 | ||||||||
\(86\) | 16.3738 | 1.76564 | ||||||||
\(87\) | 8.40189 | 0.900778 | ||||||||
\(88\) | 6.94399 | 0.740232 | ||||||||
\(89\) | 3.55742 | 0.377085 | 0.188543 | − | 0.982065i | \(-0.439624\pi\) | ||||
0.188543 | + | 0.982065i | \(0.439624\pi\) | |||||||
\(90\) | −13.7528 | −1.44967 | ||||||||
\(91\) | −5.43044 | −0.569265 | ||||||||
\(92\) | −6.45203 | −0.672670 | ||||||||
\(93\) | −20.7827 | −2.15507 | ||||||||
\(94\) | 1.82754 | 0.188496 | ||||||||
\(95\) | −5.58530 | −0.573040 | ||||||||
\(96\) | −18.5385 | −1.89207 | ||||||||
\(97\) | −15.7490 | −1.59907 | −0.799535 | − | 0.600620i | \(-0.794921\pi\) | ||||
−0.799535 | + | 0.600620i | \(0.794921\pi\) | |||||||
\(98\) | −1.76232 | −0.178021 | ||||||||
\(99\) | 34.3862 | 3.45595 | ||||||||
\(100\) | 1.10578 | 0.110578 | ||||||||
\(101\) | 16.7386 | 1.66555 | 0.832775 | − | 0.553611i | \(-0.186751\pi\) | ||||
0.832775 | + | 0.553611i | \(0.186751\pi\) | |||||||
\(102\) | −5.97233 | −0.591349 | ||||||||
\(103\) | −12.0463 | −1.18696 | −0.593480 | − | 0.804849i | \(-0.702246\pi\) | ||||
−0.593480 | + | 0.804849i | \(0.702246\pi\) | |||||||
\(104\) | 8.55783 | 0.839165 | ||||||||
\(105\) | 3.28691 | 0.320769 | ||||||||
\(106\) | −3.98035 | −0.386606 | ||||||||
\(107\) | −5.65632 | −0.546817 | −0.273408 | − | 0.961898i | \(-0.588151\pi\) | ||||
−0.273408 | + | 0.961898i | \(0.588151\pi\) | |||||||
\(108\) | −17.4598 | −1.68007 | ||||||||
\(109\) | −10.1238 | −0.969683 | −0.484842 | − | 0.874602i | \(-0.661123\pi\) | ||||
−0.484842 | + | 0.874602i | \(0.661123\pi\) | |||||||
\(110\) | −7.76543 | −0.740405 | ||||||||
\(111\) | −11.9857 | −1.13764 | ||||||||
\(112\) | 4.98881 | 0.471398 | ||||||||
\(113\) | −10.9738 | −1.03233 | −0.516163 | − | 0.856491i | \(-0.672640\pi\) | ||||
−0.516163 | + | 0.856491i | \(0.672640\pi\) | |||||||
\(114\) | −32.3534 | −3.03017 | ||||||||
\(115\) | −5.83481 | −0.544099 | ||||||||
\(116\) | −2.82657 | −0.262440 | ||||||||
\(117\) | 42.3779 | 3.91784 | ||||||||
\(118\) | 5.68672 | 0.523505 | ||||||||
\(119\) | 1.03103 | 0.0945143 | ||||||||
\(120\) | −5.17984 | −0.472853 | ||||||||
\(121\) | 8.41603 | 0.765094 | ||||||||
\(122\) | −20.7501 | −1.87863 | ||||||||
\(123\) | −19.5741 | −1.76494 | ||||||||
\(124\) | 6.99172 | 0.627875 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 13.7528 | 1.22519 | ||||||||
\(127\) | 17.3350 | 1.53823 | 0.769117 | − | 0.639108i | \(-0.220696\pi\) | ||||
0.769117 | + | 0.639108i | \(0.220696\pi\) | |||||||
\(128\) | −11.3471 | −1.00295 | ||||||||
\(129\) | 30.5389 | 2.68880 | ||||||||
\(130\) | −9.57019 | −0.839361 | ||||||||
\(131\) | −10.1945 | −0.890697 | −0.445348 | − | 0.895357i | \(-0.646920\pi\) | ||||
−0.445348 | + | 0.895357i | \(0.646920\pi\) | |||||||
\(132\) | −16.0154 | −1.39396 | ||||||||
\(133\) | 5.58530 | 0.484307 | ||||||||
\(134\) | −4.54939 | −0.393008 | ||||||||
\(135\) | −15.7895 | −1.35895 | ||||||||
\(136\) | −1.62480 | −0.139325 | ||||||||
\(137\) | 3.18481 | 0.272096 | 0.136048 | − | 0.990702i | \(-0.456560\pi\) | ||||
0.136048 | + | 0.990702i | \(0.456560\pi\) | |||||||
\(138\) | −33.7987 | −2.87714 | ||||||||
\(139\) | −12.3160 | −1.04463 | −0.522316 | − | 0.852752i | \(-0.674932\pi\) | ||||
−0.522316 | + | 0.852752i | \(0.674932\pi\) | |||||||
\(140\) | −1.10578 | −0.0934556 | ||||||||
\(141\) | 3.40854 | 0.287051 | ||||||||
\(142\) | −13.4753 | −1.13082 | ||||||||
\(143\) | 23.9285 | 2.00100 | ||||||||
\(144\) | −38.9315 | −3.24429 | ||||||||
\(145\) | −2.55617 | −0.212278 | ||||||||
\(146\) | −20.6172 | −1.70629 | ||||||||
\(147\) | −3.28691 | −0.271100 | ||||||||
\(148\) | 4.03224 | 0.331448 | ||||||||
\(149\) | 21.9670 | 1.79961 | 0.899805 | − | 0.436293i | \(-0.143709\pi\) | ||||
0.899805 | + | 0.436293i | \(0.143709\pi\) | |||||||
\(150\) | 5.79259 | 0.472963 | ||||||||
\(151\) | −9.44146 | −0.768335 | −0.384168 | − | 0.923263i | \(-0.625511\pi\) | ||||
−0.384168 | + | 0.923263i | \(0.625511\pi\) | |||||||
\(152\) | −8.80188 | −0.713927 | ||||||||
\(153\) | −8.04591 | −0.650473 | ||||||||
\(154\) | 7.76543 | 0.625756 | ||||||||
\(155\) | 6.32288 | 0.507866 | ||||||||
\(156\) | −19.7375 | −1.58026 | ||||||||
\(157\) | −17.4523 | −1.39285 | −0.696424 | − | 0.717630i | \(-0.745227\pi\) | ||||
−0.696424 | + | 0.717630i | \(0.745227\pi\) | |||||||
\(158\) | 2.11862 | 0.168548 | ||||||||
\(159\) | −7.42375 | −0.588742 | ||||||||
\(160\) | 5.64009 | 0.445888 | ||||||||
\(161\) | 5.83481 | 0.459848 | ||||||||
\(162\) | −50.2041 | −3.94441 | ||||||||
\(163\) | −0.502139 | −0.0393306 | −0.0196653 | − | 0.999807i | \(-0.506260\pi\) | ||||
−0.0196653 | + | 0.999807i | \(0.506260\pi\) | |||||||
\(164\) | 6.58512 | 0.514211 | ||||||||
\(165\) | −14.4833 | −1.12752 | ||||||||
\(166\) | −2.87424 | −0.223084 | ||||||||
\(167\) | 12.9429 | 1.00155 | 0.500776 | − | 0.865577i | \(-0.333048\pi\) | ||||
0.500776 | + | 0.865577i | \(0.333048\pi\) | |||||||
\(168\) | 5.17984 | 0.399633 | ||||||||
\(169\) | 16.4897 | 1.26844 | ||||||||
\(170\) | 1.81701 | 0.139358 | ||||||||
\(171\) | −43.5864 | −3.33313 | ||||||||
\(172\) | −10.2739 | −0.783376 | ||||||||
\(173\) | 4.06779 | 0.309268 | 0.154634 | − | 0.987972i | \(-0.450580\pi\) | ||||
0.154634 | + | 0.987972i | \(0.450580\pi\) | |||||||
\(174\) | −14.8068 | −1.12250 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −21.9825 | −1.65699 | ||||||||
\(177\) | 10.6063 | 0.797218 | ||||||||
\(178\) | −6.26932 | −0.469905 | ||||||||
\(179\) | 12.7406 | 0.952275 | 0.476137 | − | 0.879371i | \(-0.342037\pi\) | ||||
0.476137 | + | 0.879371i | \(0.342037\pi\) | |||||||
\(180\) | 8.62926 | 0.643187 | ||||||||
\(181\) | −6.87661 | −0.511134 | −0.255567 | − | 0.966791i | \(-0.582262\pi\) | ||||
−0.255567 | + | 0.966791i | \(0.582262\pi\) | |||||||
\(182\) | 9.57019 | 0.709389 | ||||||||
\(183\) | −38.7010 | −2.86086 | ||||||||
\(184\) | −9.19509 | −0.677871 | ||||||||
\(185\) | 3.64651 | 0.268097 | ||||||||
\(186\) | 36.6259 | 2.68554 | ||||||||
\(187\) | −4.54309 | −0.332224 | ||||||||
\(188\) | −1.14670 | −0.0836318 | ||||||||
\(189\) | 15.7895 | 1.14852 | ||||||||
\(190\) | 9.84310 | 0.714094 | ||||||||
\(191\) | 8.29513 | 0.600214 | 0.300107 | − | 0.953905i | \(-0.402978\pi\) | ||||
0.300107 | + | 0.953905i | \(0.402978\pi\) | |||||||
\(192\) | −0.124761 | −0.00900385 | ||||||||
\(193\) | 5.73607 | 0.412891 | 0.206446 | − | 0.978458i | \(-0.433810\pi\) | ||||
0.206446 | + | 0.978458i | \(0.433810\pi\) | |||||||
\(194\) | 27.7548 | 1.99268 | ||||||||
\(195\) | −17.8494 | −1.27822 | ||||||||
\(196\) | 1.10578 | 0.0789844 | ||||||||
\(197\) | 0.400857 | 0.0285599 | 0.0142800 | − | 0.999898i | \(-0.495454\pi\) | ||||
0.0142800 | + | 0.999898i | \(0.495454\pi\) | |||||||
\(198\) | −60.5996 | −4.30663 | ||||||||
\(199\) | 25.2282 | 1.78838 | 0.894191 | − | 0.447686i | \(-0.147752\pi\) | ||||
0.894191 | + | 0.447686i | \(0.147752\pi\) | |||||||
\(200\) | 1.57590 | 0.111433 | ||||||||
\(201\) | −8.48507 | −0.598491 | ||||||||
\(202\) | −29.4988 | −2.07553 | ||||||||
\(203\) | 2.55617 | 0.179408 | ||||||||
\(204\) | 3.74738 | 0.262369 | ||||||||
\(205\) | 5.95517 | 0.415927 | ||||||||
\(206\) | 21.2295 | 1.47913 | ||||||||
\(207\) | −45.5335 | −3.16480 | ||||||||
\(208\) | −27.0914 | −1.87845 | ||||||||
\(209\) | −24.6109 | −1.70237 | ||||||||
\(210\) | −5.79259 | −0.399727 | ||||||||
\(211\) | −2.40582 | −0.165623 | −0.0828116 | − | 0.996565i | \(-0.526390\pi\) | ||||
−0.0828116 | + | 0.996565i | \(0.526390\pi\) | |||||||
\(212\) | 2.49750 | 0.171529 | ||||||||
\(213\) | −25.1328 | −1.72207 | ||||||||
\(214\) | 9.96826 | 0.681416 | ||||||||
\(215\) | −9.29106 | −0.633645 | ||||||||
\(216\) | −24.8827 | −1.69306 | ||||||||
\(217\) | −6.32288 | −0.429225 | ||||||||
\(218\) | 17.8414 | 1.20837 | ||||||||
\(219\) | −38.4531 | −2.59842 | ||||||||
\(220\) | 4.87248 | 0.328502 | ||||||||
\(221\) | −5.59894 | −0.376626 | ||||||||
\(222\) | 21.1227 | 1.41767 | ||||||||
\(223\) | 19.8283 | 1.32780 | 0.663900 | − | 0.747821i | \(-0.268900\pi\) | ||||
0.663900 | + | 0.747821i | \(0.268900\pi\) | |||||||
\(224\) | −5.64009 | −0.376845 | ||||||||
\(225\) | 7.80377 | 0.520251 | ||||||||
\(226\) | 19.3393 | 1.28643 | ||||||||
\(227\) | 23.7096 | 1.57366 | 0.786831 | − | 0.617169i | \(-0.211720\pi\) | ||||
0.786831 | + | 0.617169i | \(0.211720\pi\) | |||||||
\(228\) | 20.3004 | 1.34442 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | 10.2828 | 0.678029 | ||||||||
\(231\) | 14.4833 | 0.952932 | ||||||||
\(232\) | −4.02827 | −0.264469 | ||||||||
\(233\) | −18.0360 | −1.18158 | −0.590789 | − | 0.806826i | \(-0.701183\pi\) | ||||
−0.590789 | + | 0.806826i | \(0.701183\pi\) | |||||||
\(234\) | −74.6835 | −4.88221 | ||||||||
\(235\) | −1.03700 | −0.0676467 | ||||||||
\(236\) | −3.56817 | −0.232268 | ||||||||
\(237\) | 3.95144 | 0.256673 | ||||||||
\(238\) | −1.81701 | −0.117779 | ||||||||
\(239\) | 16.3556 | 1.05795 | 0.528977 | − | 0.848636i | \(-0.322576\pi\) | ||||
0.528977 | + | 0.848636i | \(0.322576\pi\) | |||||||
\(240\) | 16.3978 | 1.05847 | ||||||||
\(241\) | 13.6237 | 0.877577 | 0.438788 | − | 0.898590i | \(-0.355408\pi\) | ||||
0.438788 | + | 0.898590i | \(0.355408\pi\) | |||||||
\(242\) | −14.8318 | −0.953422 | ||||||||
\(243\) | −46.2671 | −2.96803 | ||||||||
\(244\) | 13.0198 | 0.833508 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 34.4959 | 2.19938 | ||||||||
\(247\) | −30.3306 | −1.92989 | ||||||||
\(248\) | 9.96423 | 0.632729 | ||||||||
\(249\) | −5.36074 | −0.339723 | ||||||||
\(250\) | −1.76232 | −0.111459 | ||||||||
\(251\) | −0.876001 | −0.0552927 | −0.0276463 | − | 0.999618i | \(-0.508801\pi\) | ||||
−0.0276463 | + | 0.999618i | \(0.508801\pi\) | |||||||
\(252\) | −8.62926 | −0.543592 | ||||||||
\(253\) | −25.7103 | −1.61639 | ||||||||
\(254\) | −30.5499 | −1.91687 | ||||||||
\(255\) | 3.38890 | 0.212221 | ||||||||
\(256\) | 19.9213 | 1.24508 | ||||||||
\(257\) | −14.1919 | −0.885265 | −0.442633 | − | 0.896703i | \(-0.645955\pi\) | ||||
−0.442633 | + | 0.896703i | \(0.645955\pi\) | |||||||
\(258\) | −53.8193 | −3.35064 | ||||||||
\(259\) | −3.64651 | −0.226583 | ||||||||
\(260\) | 6.00488 | 0.372407 | ||||||||
\(261\) | −19.9477 | −1.23473 | ||||||||
\(262\) | 17.9660 | 1.10994 | ||||||||
\(263\) | −4.28934 | −0.264492 | −0.132246 | − | 0.991217i | \(-0.542219\pi\) | ||||
−0.132246 | + | 0.991217i | \(0.542219\pi\) | |||||||
\(264\) | −22.8243 | −1.40474 | ||||||||
\(265\) | 2.25858 | 0.138744 | ||||||||
\(266\) | −9.84310 | −0.603519 | ||||||||
\(267\) | −11.6929 | −0.715594 | ||||||||
\(268\) | 2.85455 | 0.174369 | ||||||||
\(269\) | 13.6871 | 0.834519 | 0.417259 | − | 0.908787i | \(-0.362991\pi\) | ||||
0.417259 | + | 0.908787i | \(0.362991\pi\) | |||||||
\(270\) | 27.8263 | 1.69345 | ||||||||
\(271\) | 9.10500 | 0.553089 | 0.276545 | − | 0.961001i | \(-0.410811\pi\) | ||||
0.276545 | + | 0.961001i | \(0.410811\pi\) | |||||||
\(272\) | 5.14361 | 0.311877 | ||||||||
\(273\) | 17.8494 | 1.08029 | ||||||||
\(274\) | −5.61266 | −0.339073 | ||||||||
\(275\) | 4.40636 | 0.265714 | ||||||||
\(276\) | 21.2072 | 1.27653 | ||||||||
\(277\) | −8.09876 | −0.486607 | −0.243304 | − | 0.969950i | \(-0.578231\pi\) | ||||
−0.243304 | + | 0.969950i | \(0.578231\pi\) | |||||||
\(278\) | 21.7048 | 1.30177 | ||||||||
\(279\) | 49.3423 | 2.95404 | ||||||||
\(280\) | −1.57590 | −0.0941781 | ||||||||
\(281\) | −28.4769 | −1.69879 | −0.849394 | − | 0.527759i | \(-0.823032\pi\) | ||||
−0.849394 | + | 0.527759i | \(0.823032\pi\) | |||||||
\(282\) | −6.00695 | −0.357709 | ||||||||
\(283\) | 24.8978 | 1.48002 | 0.740011 | − | 0.672595i | \(-0.234820\pi\) | ||||
0.740011 | + | 0.672595i | \(0.234820\pi\) | |||||||
\(284\) | 8.45519 | 0.501723 | ||||||||
\(285\) | 18.3584 | 1.08746 | ||||||||
\(286\) | −42.1697 | −2.49355 | ||||||||
\(287\) | −5.95517 | −0.351523 | ||||||||
\(288\) | 44.0140 | 2.59355 | ||||||||
\(289\) | −15.9370 | −0.937469 | ||||||||
\(290\) | 4.50480 | 0.264531 | ||||||||
\(291\) | 51.7656 | 3.03455 | ||||||||
\(292\) | 12.9364 | 0.757045 | ||||||||
\(293\) | 15.6565 | 0.914660 | 0.457330 | − | 0.889297i | \(-0.348806\pi\) | ||||
0.457330 | + | 0.889297i | \(0.348806\pi\) | |||||||
\(294\) | 5.79259 | 0.337831 | ||||||||
\(295\) | −3.22683 | −0.187873 | ||||||||
\(296\) | 5.74653 | 0.334011 | ||||||||
\(297\) | −69.5744 | −4.03712 | ||||||||
\(298\) | −38.7130 | −2.24258 | ||||||||
\(299\) | −31.6856 | −1.83242 | ||||||||
\(300\) | −3.63460 | −0.209844 | ||||||||
\(301\) | 9.29106 | 0.535528 | ||||||||
\(302\) | 16.6389 | 0.957461 | ||||||||
\(303\) | −55.0182 | −3.16071 | ||||||||
\(304\) | 27.8640 | 1.59811 | ||||||||
\(305\) | 11.7743 | 0.674194 | ||||||||
\(306\) | 14.1795 | 0.810588 | ||||||||
\(307\) | 9.28328 | 0.529825 | 0.264912 | − | 0.964272i | \(-0.414657\pi\) | ||||
0.264912 | + | 0.964272i | \(0.414657\pi\) | |||||||
\(308\) | −4.87248 | −0.277635 | ||||||||
\(309\) | 39.5952 | 2.25249 | ||||||||
\(310\) | −11.1430 | −0.632877 | ||||||||
\(311\) | 12.1809 | 0.690715 | 0.345358 | − | 0.938471i | \(-0.387758\pi\) | ||||
0.345358 | + | 0.938471i | \(0.387758\pi\) | |||||||
\(312\) | −28.1288 | −1.59248 | ||||||||
\(313\) | −14.0380 | −0.793477 | −0.396738 | − | 0.917932i | \(-0.629858\pi\) | ||||
−0.396738 | + | 0.917932i | \(0.629858\pi\) | |||||||
\(314\) | 30.7567 | 1.73570 | ||||||||
\(315\) | −7.80377 | −0.439692 | ||||||||
\(316\) | −1.32934 | −0.0747813 | ||||||||
\(317\) | −23.1156 | −1.29830 | −0.649151 | − | 0.760659i | \(-0.724876\pi\) | ||||
−0.649151 | + | 0.760659i | \(0.724876\pi\) | |||||||
\(318\) | 13.0830 | 0.733661 | ||||||||
\(319\) | −11.2634 | −0.630630 | ||||||||
\(320\) | 0.0379570 | 0.00212186 | ||||||||
\(321\) | 18.5918 | 1.03769 | ||||||||
\(322\) | −10.2828 | −0.573039 | ||||||||
\(323\) | 5.75861 | 0.320417 | ||||||||
\(324\) | 31.5009 | 1.75005 | ||||||||
\(325\) | 5.43044 | 0.301227 | ||||||||
\(326\) | 0.884932 | 0.0490118 | ||||||||
\(327\) | 33.2760 | 1.84017 | ||||||||
\(328\) | 9.38476 | 0.518187 | ||||||||
\(329\) | 1.03700 | 0.0571719 | ||||||||
\(330\) | 25.5243 | 1.40506 | ||||||||
\(331\) | 1.82351 | 0.100229 | 0.0501146 | − | 0.998743i | \(-0.484041\pi\) | ||||
0.0501146 | + | 0.998743i | \(0.484041\pi\) | |||||||
\(332\) | 1.80346 | 0.0989778 | ||||||||
\(333\) | 28.4565 | 1.55941 | ||||||||
\(334\) | −22.8096 | −1.24808 | ||||||||
\(335\) | 2.58147 | 0.141041 | ||||||||
\(336\) | −16.3978 | −0.894571 | ||||||||
\(337\) | 24.7765 | 1.34966 | 0.674831 | − | 0.737972i | \(-0.264217\pi\) | ||||
0.674831 | + | 0.737972i | \(0.264217\pi\) | |||||||
\(338\) | −29.0601 | −1.58066 | ||||||||
\(339\) | 36.0698 | 1.95904 | ||||||||
\(340\) | −1.14009 | −0.0618302 | ||||||||
\(341\) | 27.8609 | 1.50875 | ||||||||
\(342\) | 76.8133 | 4.15359 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −14.6418 | −0.789432 | ||||||||
\(345\) | 19.1785 | 1.03254 | ||||||||
\(346\) | −7.16876 | −0.385395 | ||||||||
\(347\) | 27.9134 | 1.49847 | 0.749235 | − | 0.662305i | \(-0.230422\pi\) | ||||
0.749235 | + | 0.662305i | \(0.230422\pi\) | |||||||
\(348\) | 9.29066 | 0.498032 | ||||||||
\(349\) | 19.7461 | 1.05698 | 0.528491 | − | 0.848939i | \(-0.322758\pi\) | ||||
0.528491 | + | 0.848939i | \(0.322758\pi\) | |||||||
\(350\) | 1.76232 | 0.0942001 | ||||||||
\(351\) | −85.7441 | −4.57668 | ||||||||
\(352\) | 24.8523 | 1.32463 | ||||||||
\(353\) | −9.08110 | −0.483338 | −0.241669 | − | 0.970359i | \(-0.577695\pi\) | ||||
−0.241669 | + | 0.970359i | \(0.577695\pi\) | |||||||
\(354\) | −18.6917 | −0.993453 | ||||||||
\(355\) | 7.64634 | 0.405826 | ||||||||
\(356\) | 3.93373 | 0.208487 | ||||||||
\(357\) | −3.38890 | −0.179360 | ||||||||
\(358\) | −22.4530 | −1.18668 | ||||||||
\(359\) | −24.7752 | −1.30758 | −0.653792 | − | 0.756674i | \(-0.726823\pi\) | ||||
−0.653792 | + | 0.756674i | \(0.726823\pi\) | |||||||
\(360\) | 12.2980 | 0.648160 | ||||||||
\(361\) | 12.1956 | 0.641872 | ||||||||
\(362\) | 12.1188 | 0.636950 | ||||||||
\(363\) | −27.6627 | −1.45192 | ||||||||
\(364\) | −6.00488 | −0.314741 | ||||||||
\(365\) | 11.6989 | 0.612346 | ||||||||
\(366\) | 68.2037 | 3.56507 | ||||||||
\(367\) | 20.6897 | 1.08000 | 0.539998 | − | 0.841666i | \(-0.318425\pi\) | ||||
0.539998 | + | 0.841666i | \(0.318425\pi\) | |||||||
\(368\) | 29.1088 | 1.51740 | ||||||||
\(369\) | 46.4727 | 2.41927 | ||||||||
\(370\) | −6.42632 | −0.334089 | ||||||||
\(371\) | −2.25858 | −0.117260 | ||||||||
\(372\) | −22.9812 | −1.19152 | ||||||||
\(373\) | −29.4653 | −1.52565 | −0.762827 | − | 0.646602i | \(-0.776189\pi\) | ||||
−0.762827 | + | 0.646602i | \(0.776189\pi\) | |||||||
\(374\) | 8.00639 | 0.414000 | ||||||||
\(375\) | −3.28691 | −0.169735 | ||||||||
\(376\) | −1.63422 | −0.0842783 | ||||||||
\(377\) | −13.8811 | −0.714914 | ||||||||
\(378\) | −27.8263 | −1.43123 | ||||||||
\(379\) | −34.1260 | −1.75294 | −0.876468 | − | 0.481461i | \(-0.840106\pi\) | ||||
−0.876468 | + | 0.481461i | \(0.840106\pi\) | |||||||
\(380\) | −6.17612 | −0.316828 | ||||||||
\(381\) | −56.9786 | −2.91910 | ||||||||
\(382\) | −14.6187 | −0.747958 | ||||||||
\(383\) | −14.3001 | −0.730703 | −0.365352 | − | 0.930870i | \(-0.619051\pi\) | ||||
−0.365352 | + | 0.930870i | \(0.619051\pi\) | |||||||
\(384\) | 37.2968 | 1.90329 | ||||||||
\(385\) | −4.40636 | −0.224569 | ||||||||
\(386\) | −10.1088 | −0.514524 | ||||||||
\(387\) | −72.5052 | −3.68565 | ||||||||
\(388\) | −17.4150 | −0.884111 | ||||||||
\(389\) | −0.477694 | −0.0242200 | −0.0121100 | − | 0.999927i | \(-0.503855\pi\) | ||||
−0.0121100 | + | 0.999927i | \(0.503855\pi\) | |||||||
\(390\) | 31.4563 | 1.59285 | ||||||||
\(391\) | 6.01586 | 0.304235 | ||||||||
\(392\) | 1.57590 | 0.0795950 | ||||||||
\(393\) | 33.5084 | 1.69027 | ||||||||
\(394\) | −0.706440 | −0.0355899 | ||||||||
\(395\) | −1.20217 | −0.0604879 | ||||||||
\(396\) | 38.0237 | 1.91076 | ||||||||
\(397\) | −27.5143 | −1.38090 | −0.690450 | − | 0.723380i | \(-0.742588\pi\) | ||||
−0.690450 | + | 0.723380i | \(0.742588\pi\) | |||||||
\(398\) | −44.4603 | −2.22859 | ||||||||
\(399\) | −18.3584 | −0.919068 | ||||||||
\(400\) | −4.98881 | −0.249441 | ||||||||
\(401\) | 1.78056 | 0.0889167 | 0.0444584 | − | 0.999011i | \(-0.485844\pi\) | ||||
0.0444584 | + | 0.999011i | \(0.485844\pi\) | |||||||
\(402\) | 14.9534 | 0.745810 | ||||||||
\(403\) | 34.3360 | 1.71040 | ||||||||
\(404\) | 18.5092 | 0.920868 | ||||||||
\(405\) | 28.4875 | 1.41555 | ||||||||
\(406\) | −4.50480 | −0.223569 | ||||||||
\(407\) | 16.0678 | 0.796453 | ||||||||
\(408\) | 5.34057 | 0.264398 | ||||||||
\(409\) | 21.2748 | 1.05197 | 0.525987 | − | 0.850493i | \(-0.323696\pi\) | ||||
0.525987 | + | 0.850493i | \(0.323696\pi\) | |||||||
\(410\) | −10.4949 | −0.518308 | ||||||||
\(411\) | −10.4682 | −0.516356 | ||||||||
\(412\) | −13.3206 | −0.656259 | ||||||||
\(413\) | 3.22683 | 0.158782 | ||||||||
\(414\) | 80.2447 | 3.94381 | ||||||||
\(415\) | 1.63094 | 0.0800596 | ||||||||
\(416\) | 30.6282 | 1.50167 | ||||||||
\(417\) | 40.4817 | 1.98240 | ||||||||
\(418\) | 43.3723 | 2.12141 | ||||||||
\(419\) | −36.6104 | −1.78853 | −0.894266 | − | 0.447535i | \(-0.852302\pi\) | ||||
−0.894266 | + | 0.447535i | \(0.852302\pi\) | |||||||
\(420\) | 3.63460 | 0.177350 | ||||||||
\(421\) | 20.5594 | 1.00200 | 0.501002 | − | 0.865446i | \(-0.332965\pi\) | ||||
0.501002 | + | 0.865446i | \(0.332965\pi\) | |||||||
\(422\) | 4.23983 | 0.206391 | ||||||||
\(423\) | −8.09254 | −0.393473 | ||||||||
\(424\) | 3.55930 | 0.172855 | ||||||||
\(425\) | −1.03103 | −0.0500123 | ||||||||
\(426\) | 44.2922 | 2.14596 | ||||||||
\(427\) | −11.7743 | −0.569798 | ||||||||
\(428\) | −6.25465 | −0.302330 | ||||||||
\(429\) | −78.6507 | −3.79729 | ||||||||
\(430\) | 16.3738 | 0.789617 | ||||||||
\(431\) | −32.6963 | −1.57493 | −0.787464 | − | 0.616361i | \(-0.788606\pi\) | ||||
−0.787464 | + | 0.616361i | \(0.788606\pi\) | |||||||
\(432\) | 78.7710 | 3.78987 | ||||||||
\(433\) | −18.0489 | −0.867376 | −0.433688 | − | 0.901063i | \(-0.642788\pi\) | ||||
−0.433688 | + | 0.901063i | \(0.642788\pi\) | |||||||
\(434\) | 11.1430 | 0.534879 | ||||||||
\(435\) | 8.40189 | 0.402840 | ||||||||
\(436\) | −11.1947 | −0.536129 | ||||||||
\(437\) | 32.5892 | 1.55895 | ||||||||
\(438\) | 67.7667 | 3.23802 | ||||||||
\(439\) | 5.09009 | 0.242937 | 0.121468 | − | 0.992595i | \(-0.461240\pi\) | ||||
0.121468 | + | 0.992595i | \(0.461240\pi\) | |||||||
\(440\) | 6.94399 | 0.331042 | ||||||||
\(441\) | 7.80377 | 0.371608 | ||||||||
\(442\) | 9.86714 | 0.469332 | ||||||||
\(443\) | 7.97576 | 0.378940 | 0.189470 | − | 0.981887i | \(-0.439323\pi\) | ||||
0.189470 | + | 0.981887i | \(0.439323\pi\) | |||||||
\(444\) | −13.2536 | −0.628988 | ||||||||
\(445\) | 3.55742 | 0.168638 | ||||||||
\(446\) | −34.9438 | −1.65464 | ||||||||
\(447\) | −72.2036 | −3.41511 | ||||||||
\(448\) | −0.0379570 | −0.00179330 | ||||||||
\(449\) | −33.1302 | −1.56351 | −0.781756 | − | 0.623584i | \(-0.785676\pi\) | ||||
−0.781756 | + | 0.623584i | \(0.785676\pi\) | |||||||
\(450\) | −13.7528 | −0.648311 | ||||||||
\(451\) | 26.2406 | 1.23562 | ||||||||
\(452\) | −12.1346 | −0.570763 | ||||||||
\(453\) | 31.0332 | 1.45807 | ||||||||
\(454\) | −41.7840 | −1.96102 | ||||||||
\(455\) | −5.43044 | −0.254583 | ||||||||
\(456\) | 28.9310 | 1.35482 | ||||||||
\(457\) | 9.21874 | 0.431234 | 0.215617 | − | 0.976478i | \(-0.430824\pi\) | ||||
0.215617 | + | 0.976478i | \(0.430824\pi\) | |||||||
\(458\) | 1.76232 | 0.0823479 | ||||||||
\(459\) | 16.2795 | 0.759861 | ||||||||
\(460\) | −6.45203 | −0.300827 | ||||||||
\(461\) | 19.1824 | 0.893413 | 0.446706 | − | 0.894681i | \(-0.352597\pi\) | ||||
0.446706 | + | 0.894681i | \(0.352597\pi\) | |||||||
\(462\) | −25.5243 | −1.18750 | ||||||||
\(463\) | 33.2009 | 1.54298 | 0.771489 | − | 0.636243i | \(-0.219512\pi\) | ||||
0.771489 | + | 0.636243i | \(0.219512\pi\) | |||||||
\(464\) | 12.7522 | 0.592008 | ||||||||
\(465\) | −20.7827 | −0.963776 | ||||||||
\(466\) | 31.7853 | 1.47242 | ||||||||
\(467\) | 2.69104 | 0.124527 | 0.0622633 | − | 0.998060i | \(-0.480168\pi\) | ||||
0.0622633 | + | 0.998060i | \(0.480168\pi\) | |||||||
\(468\) | 46.8607 | 2.16614 | ||||||||
\(469\) | −2.58147 | −0.119201 | ||||||||
\(470\) | 1.82754 | 0.0842980 | ||||||||
\(471\) | 57.3643 | 2.64321 | ||||||||
\(472\) | −5.08516 | −0.234064 | ||||||||
\(473\) | −40.9398 | −1.88241 | ||||||||
\(474\) | −6.96370 | −0.319854 | ||||||||
\(475\) | −5.58530 | −0.256271 | ||||||||
\(476\) | 1.14009 | 0.0522561 | ||||||||
\(477\) | 17.6254 | 0.807013 | ||||||||
\(478\) | −28.8238 | −1.31837 | ||||||||
\(479\) | −29.0584 | −1.32771 | −0.663857 | − | 0.747860i | \(-0.731082\pi\) | ||||
−0.663857 | + | 0.747860i | \(0.731082\pi\) | |||||||
\(480\) | −18.5385 | −0.846161 | ||||||||
\(481\) | 19.8021 | 0.902900 | ||||||||
\(482\) | −24.0093 | −1.09359 | ||||||||
\(483\) | −19.1785 | −0.872652 | ||||||||
\(484\) | 9.30630 | 0.423013 | ||||||||
\(485\) | −15.7490 | −0.715126 | ||||||||
\(486\) | 81.5375 | 3.69862 | ||||||||
\(487\) | 18.7216 | 0.848356 | 0.424178 | − | 0.905579i | \(-0.360563\pi\) | ||||
0.424178 | + | 0.905579i | \(0.360563\pi\) | |||||||
\(488\) | 18.5551 | 0.839951 | ||||||||
\(489\) | 1.65049 | 0.0746376 | ||||||||
\(490\) | −1.76232 | −0.0796136 | ||||||||
\(491\) | 5.02410 | 0.226735 | 0.113367 | − | 0.993553i | \(-0.463836\pi\) | ||||
0.113367 | + | 0.993553i | \(0.463836\pi\) | |||||||
\(492\) | −21.6447 | −0.975817 | ||||||||
\(493\) | 2.63548 | 0.118696 | ||||||||
\(494\) | 53.4524 | 2.40494 | ||||||||
\(495\) | 34.3862 | 1.54555 | ||||||||
\(496\) | −31.5436 | −1.41635 | ||||||||
\(497\) | −7.64634 | −0.342985 | ||||||||
\(498\) | 9.44736 | 0.423346 | ||||||||
\(499\) | 38.1903 | 1.70963 | 0.854816 | − | 0.518931i | \(-0.173670\pi\) | ||||
0.854816 | + | 0.518931i | \(0.173670\pi\) | |||||||
\(500\) | 1.10578 | 0.0494521 | ||||||||
\(501\) | −42.5421 | −1.90064 | ||||||||
\(502\) | 1.54380 | 0.0689030 | ||||||||
\(503\) | 24.6208 | 1.09779 | 0.548894 | − | 0.835892i | \(-0.315049\pi\) | ||||
0.548894 | + | 0.835892i | \(0.315049\pi\) | |||||||
\(504\) | −12.2980 | −0.547795 | ||||||||
\(505\) | 16.7386 | 0.744857 | ||||||||
\(506\) | 45.3098 | 2.01427 | ||||||||
\(507\) | −54.2000 | −2.40711 | ||||||||
\(508\) | 19.1688 | 0.850476 | ||||||||
\(509\) | 7.48466 | 0.331752 | 0.165876 | − | 0.986147i | \(-0.446955\pi\) | ||||
0.165876 | + | 0.986147i | \(0.446955\pi\) | |||||||
\(510\) | −5.97233 | −0.264459 | ||||||||
\(511\) | −11.6989 | −0.517527 | ||||||||
\(512\) | −12.4136 | −0.548609 | ||||||||
\(513\) | 88.1893 | 3.89365 | ||||||||
\(514\) | 25.0107 | 1.10317 | ||||||||
\(515\) | −12.0463 | −0.530825 | ||||||||
\(516\) | 33.7693 | 1.48661 | ||||||||
\(517\) | −4.56942 | −0.200963 | ||||||||
\(518\) | 6.42632 | 0.282356 | ||||||||
\(519\) | −13.3705 | −0.586898 | ||||||||
\(520\) | 8.55783 | 0.375286 | ||||||||
\(521\) | −8.08744 | −0.354317 | −0.177159 | − | 0.984182i | \(-0.556691\pi\) | ||||
−0.177159 | + | 0.984182i | \(0.556691\pi\) | |||||||
\(522\) | 35.1544 | 1.53866 | ||||||||
\(523\) | −12.8726 | −0.562881 | −0.281441 | − | 0.959579i | \(-0.590812\pi\) | ||||
−0.281441 | + | 0.959579i | \(0.590812\pi\) | |||||||
\(524\) | −11.2729 | −0.492458 | ||||||||
\(525\) | 3.28691 | 0.143452 | ||||||||
\(526\) | 7.55920 | 0.329597 | ||||||||
\(527\) | −6.51907 | −0.283975 | ||||||||
\(528\) | 72.2545 | 3.14447 | ||||||||
\(529\) | 11.0450 | 0.480218 | ||||||||
\(530\) | −3.98035 | −0.172895 | ||||||||
\(531\) | −25.1814 | −1.09278 | ||||||||
\(532\) | 6.17612 | 0.267769 | ||||||||
\(533\) | 32.3392 | 1.40077 | ||||||||
\(534\) | 20.6067 | 0.891738 | ||||||||
\(535\) | −5.65632 | −0.244544 | ||||||||
\(536\) | 4.06815 | 0.175717 | ||||||||
\(537\) | −41.8771 | −1.80713 | ||||||||
\(538\) | −24.1211 | −1.03994 | ||||||||
\(539\) | 4.40636 | 0.189795 | ||||||||
\(540\) | −17.4598 | −0.751350 | ||||||||
\(541\) | −37.0626 | −1.59345 | −0.796723 | − | 0.604344i | \(-0.793435\pi\) | ||||
−0.796723 | + | 0.604344i | \(0.793435\pi\) | |||||||
\(542\) | −16.0459 | −0.689232 | ||||||||
\(543\) | 22.6028 | 0.969978 | ||||||||
\(544\) | −5.81510 | −0.249320 | ||||||||
\(545\) | −10.1238 | −0.433656 | ||||||||
\(546\) | −31.4563 | −1.34621 | ||||||||
\(547\) | −22.2088 | −0.949579 | −0.474789 | − | 0.880099i | \(-0.657476\pi\) | ||||
−0.474789 | + | 0.880099i | \(0.657476\pi\) | |||||||
\(548\) | 3.52170 | 0.150440 | ||||||||
\(549\) | 91.8839 | 3.92151 | ||||||||
\(550\) | −7.76543 | −0.331119 | ||||||||
\(551\) | 14.2770 | 0.608219 | ||||||||
\(552\) | 30.2234 | 1.28639 | ||||||||
\(553\) | 1.20217 | 0.0511216 | ||||||||
\(554\) | 14.2726 | 0.606386 | ||||||||
\(555\) | −11.9857 | −0.508766 | ||||||||
\(556\) | −13.6188 | −0.577568 | ||||||||
\(557\) | −21.1021 | −0.894127 | −0.447063 | − | 0.894502i | \(-0.647530\pi\) | ||||
−0.447063 | + | 0.894502i | \(0.647530\pi\) | |||||||
\(558\) | −86.9570 | −3.68118 | ||||||||
\(559\) | −50.4545 | −2.13400 | ||||||||
\(560\) | 4.98881 | 0.210816 | ||||||||
\(561\) | 14.9327 | 0.630460 | ||||||||
\(562\) | 50.1855 | 2.11695 | ||||||||
\(563\) | −46.8024 | −1.97248 | −0.986242 | − | 0.165308i | \(-0.947138\pi\) | ||||
−0.986242 | + | 0.165308i | \(0.947138\pi\) | |||||||
\(564\) | 3.76910 | 0.158708 | ||||||||
\(565\) | −10.9738 | −0.461670 | ||||||||
\(566\) | −43.8780 | −1.84433 | ||||||||
\(567\) | −28.4875 | −1.19636 | ||||||||
\(568\) | 12.0499 | 0.505602 | ||||||||
\(569\) | −26.3851 | −1.10612 | −0.553061 | − | 0.833141i | \(-0.686540\pi\) | ||||
−0.553061 | + | 0.833141i | \(0.686540\pi\) | |||||||
\(570\) | −32.3534 | −1.35513 | ||||||||
\(571\) | −2.86020 | −0.119696 | −0.0598479 | − | 0.998208i | \(-0.519062\pi\) | ||||
−0.0598479 | + | 0.998208i | \(0.519062\pi\) | |||||||
\(572\) | 26.4597 | 1.10634 | ||||||||
\(573\) | −27.2653 | −1.13903 | ||||||||
\(574\) | 10.4949 | 0.438050 | ||||||||
\(575\) | −5.83481 | −0.243328 | ||||||||
\(576\) | 0.296207 | 0.0123420 | ||||||||
\(577\) | 2.32932 | 0.0969707 | 0.0484853 | − | 0.998824i | \(-0.484561\pi\) | ||||
0.0484853 | + | 0.998824i | \(0.484561\pi\) | |||||||
\(578\) | 28.0861 | 1.16823 | ||||||||
\(579\) | −18.8539 | −0.783542 | ||||||||
\(580\) | −2.82657 | −0.117367 | ||||||||
\(581\) | −1.63094 | −0.0676627 | ||||||||
\(582\) | −91.2276 | −3.78151 | ||||||||
\(583\) | 9.95213 | 0.412175 | ||||||||
\(584\) | 18.4362 | 0.762897 | ||||||||
\(585\) | 42.3779 | 1.75211 | ||||||||
\(586\) | −27.5917 | −1.13980 | ||||||||
\(587\) | 29.6281 | 1.22288 | 0.611441 | − | 0.791290i | \(-0.290590\pi\) | ||||
0.611441 | + | 0.791290i | \(0.290590\pi\) | |||||||
\(588\) | −3.63460 | −0.149889 | ||||||||
\(589\) | −35.3152 | −1.45514 | ||||||||
\(590\) | 5.68672 | 0.234118 | ||||||||
\(591\) | −1.31758 | −0.0541981 | ||||||||
\(592\) | −18.1917 | −0.747676 | ||||||||
\(593\) | 23.3009 | 0.956852 | 0.478426 | − | 0.878128i | \(-0.341207\pi\) | ||||
0.478426 | + | 0.878128i | \(0.341207\pi\) | |||||||
\(594\) | 122.613 | 5.03086 | ||||||||
\(595\) | 1.03103 | 0.0422681 | ||||||||
\(596\) | 24.2907 | 0.994988 | ||||||||
\(597\) | −82.9229 | −3.39381 | ||||||||
\(598\) | 55.8402 | 2.28348 | ||||||||
\(599\) | −43.9232 | −1.79465 | −0.897326 | − | 0.441369i | \(-0.854493\pi\) | ||||
−0.897326 | + | 0.441369i | \(0.854493\pi\) | |||||||
\(600\) | −5.17984 | −0.211466 | ||||||||
\(601\) | 41.8269 | 1.70615 | 0.853077 | − | 0.521785i | \(-0.174734\pi\) | ||||
0.853077 | + | 0.521785i | \(0.174734\pi\) | |||||||
\(602\) | −16.3738 | −0.667348 | ||||||||
\(603\) | 20.1452 | 0.820377 | ||||||||
\(604\) | −10.4402 | −0.424806 | ||||||||
\(605\) | 8.41603 | 0.342160 | ||||||||
\(606\) | 96.9598 | 3.93872 | ||||||||
\(607\) | −0.263730 | −0.0107045 | −0.00535223 | − | 0.999986i | \(-0.501704\pi\) | ||||
−0.00535223 | + | 0.999986i | \(0.501704\pi\) | |||||||
\(608\) | −31.5016 | −1.27756 | ||||||||
\(609\) | −8.40189 | −0.340462 | ||||||||
\(610\) | −20.7501 | −0.840147 | ||||||||
\(611\) | −5.63139 | −0.227822 | ||||||||
\(612\) | −8.89702 | −0.359641 | ||||||||
\(613\) | 35.6994 | 1.44189 | 0.720943 | − | 0.692994i | \(-0.243709\pi\) | ||||
0.720943 | + | 0.692994i | \(0.243709\pi\) | |||||||
\(614\) | −16.3601 | −0.660241 | ||||||||
\(615\) | −19.5741 | −0.789304 | ||||||||
\(616\) | −6.94399 | −0.279781 | ||||||||
\(617\) | −41.8226 | −1.68371 | −0.841857 | − | 0.539700i | \(-0.818538\pi\) | ||||
−0.841857 | + | 0.539700i | \(0.818538\pi\) | |||||||
\(618\) | −69.7795 | −2.80694 | ||||||||
\(619\) | −31.7655 | −1.27676 | −0.638381 | − | 0.769720i | \(-0.720396\pi\) | ||||
−0.638381 | + | 0.769720i | \(0.720396\pi\) | |||||||
\(620\) | 6.99172 | 0.280794 | ||||||||
\(621\) | 92.1290 | 3.69701 | ||||||||
\(622\) | −21.4667 | −0.860735 | ||||||||
\(623\) | −3.55742 | −0.142525 | ||||||||
\(624\) | 89.0470 | 3.56473 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 24.7396 | 0.988792 | ||||||||
\(627\) | 80.8936 | 3.23058 | ||||||||
\(628\) | −19.2985 | −0.770093 | ||||||||
\(629\) | −3.75965 | −0.149907 | ||||||||
\(630\) | 13.7528 | 0.547923 | ||||||||
\(631\) | 8.63712 | 0.343838 | 0.171919 | − | 0.985111i | \(-0.445003\pi\) | ||||
0.171919 | + | 0.985111i | \(0.445003\pi\) | |||||||
\(632\) | −1.89451 | −0.0753594 | ||||||||
\(633\) | 7.90770 | 0.314303 | ||||||||
\(634\) | 40.7372 | 1.61788 | ||||||||
\(635\) | 17.3350 | 0.687919 | ||||||||
\(636\) | −8.20905 | −0.325510 | ||||||||
\(637\) | 5.43044 | 0.215162 | ||||||||
\(638\) | 19.8498 | 0.785860 | ||||||||
\(639\) | 59.6703 | 2.36052 | ||||||||
\(640\) | −11.3471 | −0.448533 | ||||||||
\(641\) | −19.3749 | −0.765261 | −0.382631 | − | 0.923901i | \(-0.624982\pi\) | ||||
−0.382631 | + | 0.923901i | \(0.624982\pi\) | |||||||
\(642\) | −32.7647 | −1.29312 | ||||||||
\(643\) | −9.35555 | −0.368947 | −0.184473 | − | 0.982838i | \(-0.559058\pi\) | ||||
−0.184473 | + | 0.982838i | \(0.559058\pi\) | |||||||
\(644\) | 6.45203 | 0.254246 | ||||||||
\(645\) | 30.5389 | 1.20247 | ||||||||
\(646\) | −10.1485 | −0.399288 | ||||||||
\(647\) | −5.42711 | −0.213362 | −0.106681 | − | 0.994293i | \(-0.534022\pi\) | ||||
−0.106681 | + | 0.994293i | \(0.534022\pi\) | |||||||
\(648\) | 44.8934 | 1.76358 | ||||||||
\(649\) | −14.2186 | −0.558128 | ||||||||
\(650\) | −9.57019 | −0.375374 | ||||||||
\(651\) | 20.7827 | 0.814539 | ||||||||
\(652\) | −0.555257 | −0.0217455 | ||||||||
\(653\) | −39.5272 | −1.54682 | −0.773410 | − | 0.633906i | \(-0.781451\pi\) | ||||
−0.773410 | + | 0.633906i | \(0.781451\pi\) | |||||||
\(654\) | −58.6430 | −2.29312 | ||||||||
\(655\) | −10.1945 | −0.398332 | ||||||||
\(656\) | −29.7092 | −1.15995 | ||||||||
\(657\) | 91.2951 | 3.56176 | ||||||||
\(658\) | −1.82754 | −0.0712448 | ||||||||
\(659\) | 37.8741 | 1.47537 | 0.737683 | − | 0.675147i | \(-0.235920\pi\) | ||||
0.737683 | + | 0.675147i | \(0.235920\pi\) | |||||||
\(660\) | −16.0154 | −0.623398 | ||||||||
\(661\) | 29.4787 | 1.14659 | 0.573295 | − | 0.819349i | \(-0.305665\pi\) | ||||
0.573295 | + | 0.819349i | \(0.305665\pi\) | |||||||
\(662\) | −3.21361 | −0.124901 | ||||||||
\(663\) | 18.4032 | 0.714721 | ||||||||
\(664\) | 2.57020 | 0.0997430 | ||||||||
\(665\) | 5.58530 | 0.216589 | ||||||||
\(666\) | −50.1495 | −1.94325 | ||||||||
\(667\) | 14.9148 | 0.577502 | ||||||||
\(668\) | 14.3120 | 0.553749 | ||||||||
\(669\) | −65.1737 | −2.51976 | ||||||||
\(670\) | −4.54939 | −0.175758 | ||||||||
\(671\) | 51.8818 | 2.00288 | ||||||||
\(672\) | 18.5385 | 0.715137 | ||||||||
\(673\) | 14.0686 | 0.542304 | 0.271152 | − | 0.962537i | \(-0.412595\pi\) | ||||
0.271152 | + | 0.962537i | \(0.412595\pi\) | |||||||
\(674\) | −43.6642 | −1.68188 | ||||||||
\(675\) | −15.7895 | −0.607740 | ||||||||
\(676\) | 18.2340 | 0.701307 | ||||||||
\(677\) | 43.1973 | 1.66021 | 0.830103 | − | 0.557611i | \(-0.188282\pi\) | ||||
0.830103 | + | 0.557611i | \(0.188282\pi\) | |||||||
\(678\) | −63.5666 | −2.44126 | ||||||||
\(679\) | 15.7490 | 0.604392 | ||||||||
\(680\) | −1.62480 | −0.0623082 | ||||||||
\(681\) | −77.9313 | −2.98633 | ||||||||
\(682\) | −49.0999 | −1.88013 | ||||||||
\(683\) | 11.5041 | 0.440190 | 0.220095 | − | 0.975478i | \(-0.429363\pi\) | ||||
0.220095 | + | 0.975478i | \(0.429363\pi\) | |||||||
\(684\) | −48.1970 | −1.84286 | ||||||||
\(685\) | 3.18481 | 0.121685 | ||||||||
\(686\) | 1.76232 | 0.0672858 | ||||||||
\(687\) | 3.28691 | 0.125403 | ||||||||
\(688\) | 46.3513 | 1.76713 | ||||||||
\(689\) | 12.2651 | 0.467263 | ||||||||
\(690\) | −33.7987 | −1.28669 | ||||||||
\(691\) | 29.7992 | 1.13361 | 0.566807 | − | 0.823850i | \(-0.308178\pi\) | ||||
0.566807 | + | 0.823850i | \(0.308178\pi\) | |||||||
\(692\) | 4.49809 | 0.170992 | ||||||||
\(693\) | −34.3862 | −1.30622 | ||||||||
\(694\) | −49.1924 | −1.86732 | ||||||||
\(695\) | −12.3160 | −0.467174 | ||||||||
\(696\) | 13.2406 | 0.501882 | ||||||||
\(697\) | −6.13995 | −0.232567 | ||||||||
\(698\) | −34.7989 | −1.31716 | ||||||||
\(699\) | 59.2827 | 2.24228 | ||||||||
\(700\) | −1.10578 | −0.0417946 | ||||||||
\(701\) | 1.63907 | 0.0619069 | 0.0309535 | − | 0.999521i | \(-0.490146\pi\) | ||||
0.0309535 | + | 0.999521i | \(0.490146\pi\) | |||||||
\(702\) | 151.109 | 5.70324 | ||||||||
\(703\) | −20.3668 | −0.768150 | ||||||||
\(704\) | 0.167252 | 0.00630355 | ||||||||
\(705\) | 3.40854 | 0.128373 | ||||||||
\(706\) | 16.0038 | 0.602312 | ||||||||
\(707\) | −16.7386 | −0.629519 | ||||||||
\(708\) | 11.7282 | 0.440774 | ||||||||
\(709\) | 35.2610 | 1.32426 | 0.662128 | − | 0.749391i | \(-0.269654\pi\) | ||||
0.662128 | + | 0.749391i | \(0.269654\pi\) | |||||||
\(710\) | −13.4753 | −0.505720 | ||||||||
\(711\) | −9.38148 | −0.351833 | ||||||||
\(712\) | 5.60614 | 0.210099 | ||||||||
\(713\) | −36.8928 | −1.38165 | ||||||||
\(714\) | 5.97233 | 0.223509 | ||||||||
\(715\) | 23.9285 | 0.894875 | ||||||||
\(716\) | 14.0883 | 0.526504 | ||||||||
\(717\) | −53.7593 | −2.00768 | ||||||||
\(718\) | 43.6619 | 1.62945 | ||||||||
\(719\) | 20.4135 | 0.761295 | 0.380648 | − | 0.924720i | \(-0.375701\pi\) | ||||
0.380648 | + | 0.924720i | \(0.375701\pi\) | |||||||
\(720\) | −38.9315 | −1.45089 | ||||||||
\(721\) | 12.0463 | 0.448629 | ||||||||
\(722\) | −21.4925 | −0.799869 | ||||||||
\(723\) | −44.7797 | −1.66537 | ||||||||
\(724\) | −7.60403 | −0.282601 | ||||||||
\(725\) | −2.55617 | −0.0949337 | ||||||||
\(726\) | 48.7507 | 1.80931 | ||||||||
\(727\) | 13.4566 | 0.499078 | 0.249539 | − | 0.968365i | \(-0.419721\pi\) | ||||
0.249539 | + | 0.968365i | \(0.419721\pi\) | |||||||
\(728\) | −8.55783 | −0.317174 | ||||||||
\(729\) | 66.6132 | 2.46716 | ||||||||
\(730\) | −20.6172 | −0.763075 | ||||||||
\(731\) | 9.57935 | 0.354305 | ||||||||
\(732\) | −42.7949 | −1.58175 | ||||||||
\(733\) | 16.4925 | 0.609166 | 0.304583 | − | 0.952486i | \(-0.401483\pi\) | ||||
0.304583 | + | 0.952486i | \(0.401483\pi\) | |||||||
\(734\) | −36.4620 | −1.34584 | ||||||||
\(735\) | −3.28691 | −0.121239 | ||||||||
\(736\) | −32.9089 | −1.21304 | ||||||||
\(737\) | 11.3749 | 0.419000 | ||||||||
\(738\) | −81.9000 | −3.01478 | ||||||||
\(739\) | −23.1080 | −0.850040 | −0.425020 | − | 0.905184i | \(-0.639733\pi\) | ||||
−0.425020 | + | 0.905184i | \(0.639733\pi\) | |||||||
\(740\) | 4.03224 | 0.148228 | ||||||||
\(741\) | 99.6940 | 3.66235 | ||||||||
\(742\) | 3.98035 | 0.146123 | ||||||||
\(743\) | 18.9617 | 0.695636 | 0.347818 | − | 0.937562i | \(-0.386923\pi\) | ||||
0.347818 | + | 0.937562i | \(0.386923\pi\) | |||||||
\(744\) | −32.7515 | −1.20073 | ||||||||
\(745\) | 21.9670 | 0.804810 | ||||||||
\(746\) | 51.9273 | 1.90120 | ||||||||
\(747\) | 12.7275 | 0.465673 | ||||||||
\(748\) | −5.02366 | −0.183683 | ||||||||
\(749\) | 5.65632 | 0.206677 | ||||||||
\(750\) | 5.79259 | 0.211516 | ||||||||
\(751\) | 4.51863 | 0.164887 | 0.0824436 | − | 0.996596i | \(-0.473728\pi\) | ||||
0.0824436 | + | 0.996596i | \(0.473728\pi\) | |||||||
\(752\) | 5.17342 | 0.188655 | ||||||||
\(753\) | 2.87934 | 0.104929 | ||||||||
\(754\) | 24.4630 | 0.890891 | ||||||||
\(755\) | −9.44146 | −0.343610 | ||||||||
\(756\) | 17.4598 | 0.635006 | ||||||||
\(757\) | 40.2363 | 1.46241 | 0.731207 | − | 0.682156i | \(-0.238958\pi\) | ||||
0.731207 | + | 0.682156i | \(0.238958\pi\) | |||||||
\(758\) | 60.1410 | 2.18442 | ||||||||
\(759\) | 84.5074 | 3.06742 | ||||||||
\(760\) | −8.80188 | −0.319278 | ||||||||
\(761\) | −19.4041 | −0.703397 | −0.351699 | − | 0.936113i | \(-0.614396\pi\) | ||||
−0.351699 | + | 0.936113i | \(0.614396\pi\) | |||||||
\(762\) | 100.415 | 3.63764 | ||||||||
\(763\) | 10.1238 | 0.366506 | ||||||||
\(764\) | 9.17260 | 0.331853 | ||||||||
\(765\) | −8.04591 | −0.290900 | ||||||||
\(766\) | 25.2015 | 0.910566 | ||||||||
\(767\) | −17.5231 | −0.632722 | ||||||||
\(768\) | −65.4795 | −2.36279 | ||||||||
\(769\) | −43.3047 | −1.56161 | −0.780803 | − | 0.624777i | \(-0.785190\pi\) | ||||
−0.780803 | + | 0.624777i | \(0.785190\pi\) | |||||||
\(770\) | 7.76543 | 0.279847 | ||||||||
\(771\) | 46.6474 | 1.67997 | ||||||||
\(772\) | 6.34284 | 0.228284 | ||||||||
\(773\) | 12.7836 | 0.459795 | 0.229897 | − | 0.973215i | \(-0.426161\pi\) | ||||
0.229897 | + | 0.973215i | \(0.426161\pi\) | |||||||
\(774\) | 127.778 | 4.59287 | ||||||||
\(775\) | 6.32288 | 0.227124 | ||||||||
\(776\) | −24.8189 | −0.890946 | ||||||||
\(777\) | 11.9857 | 0.429986 | ||||||||
\(778\) | 0.841851 | 0.0301818 | ||||||||
\(779\) | −33.2614 | −1.19171 | ||||||||
\(780\) | −19.7375 | −0.706716 | ||||||||
\(781\) | 33.6926 | 1.20561 | ||||||||
\(782\) | −10.6019 | −0.379123 | ||||||||
\(783\) | 40.3607 | 1.44237 | ||||||||
\(784\) | −4.98881 | −0.178172 | ||||||||
\(785\) | −17.4523 | −0.622901 | ||||||||
\(786\) | −59.0526 | −2.10633 | ||||||||
\(787\) | −21.6351 | −0.771207 | −0.385604 | − | 0.922664i | \(-0.626007\pi\) | ||||
−0.385604 | + | 0.922664i | \(0.626007\pi\) | |||||||
\(788\) | 0.443261 | 0.0157905 | ||||||||
\(789\) | 14.0987 | 0.501926 | ||||||||
\(790\) | 2.11862 | 0.0753771 | ||||||||
\(791\) | 10.9738 | 0.390182 | ||||||||
\(792\) | 54.1893 | 1.92553 | ||||||||
\(793\) | 63.9396 | 2.27056 | ||||||||
\(794\) | 48.4890 | 1.72081 | ||||||||
\(795\) | −7.42375 | −0.263293 | ||||||||
\(796\) | 27.8969 | 0.988780 | ||||||||
\(797\) | −10.8565 | −0.384558 | −0.192279 | − | 0.981340i | \(-0.561588\pi\) | ||||
−0.192279 | + | 0.981340i | \(0.561588\pi\) | |||||||
\(798\) | 32.3534 | 1.14530 | ||||||||
\(799\) | 1.06918 | 0.0378249 | ||||||||
\(800\) | 5.64009 | 0.199407 | ||||||||
\(801\) | 27.7612 | 0.980895 | ||||||||
\(802\) | −3.13792 | −0.110804 | ||||||||
\(803\) | 51.5494 | 1.81914 | ||||||||
\(804\) | −9.38264 | −0.330900 | ||||||||
\(805\) | 5.83481 | 0.205650 | ||||||||
\(806\) | −60.5111 | −2.13141 | ||||||||
\(807\) | −44.9883 | −1.58366 | ||||||||
\(808\) | 26.3783 | 0.927987 | ||||||||
\(809\) | −30.5519 | −1.07415 | −0.537074 | − | 0.843535i | \(-0.680470\pi\) | ||||
−0.537074 | + | 0.843535i | \(0.680470\pi\) | |||||||
\(810\) | −50.2041 | −1.76399 | ||||||||
\(811\) | 20.9648 | 0.736175 | 0.368088 | − | 0.929791i | \(-0.380013\pi\) | ||||
0.368088 | + | 0.929791i | \(0.380013\pi\) | |||||||
\(812\) | 2.82657 | 0.0991930 | ||||||||
\(813\) | −29.9273 | −1.04960 | ||||||||
\(814\) | −28.3167 | −0.992500 | ||||||||
\(815\) | −0.502139 | −0.0175892 | ||||||||
\(816\) | −16.9066 | −0.591848 | ||||||||
\(817\) | 51.8933 | 1.81552 | ||||||||
\(818\) | −37.4931 | −1.31092 | ||||||||
\(819\) | −42.3779 | −1.48080 | ||||||||
\(820\) | 6.58512 | 0.229962 | ||||||||
\(821\) | 3.52819 | 0.123135 | 0.0615674 | − | 0.998103i | \(-0.480390\pi\) | ||||
0.0615674 | + | 0.998103i | \(0.480390\pi\) | |||||||
\(822\) | 18.4483 | 0.643458 | ||||||||
\(823\) | 4.95964 | 0.172882 | 0.0864410 | − | 0.996257i | \(-0.472451\pi\) | ||||
0.0864410 | + | 0.996257i | \(0.472451\pi\) | |||||||
\(824\) | −18.9838 | −0.661333 | ||||||||
\(825\) | −14.4833 | −0.504244 | ||||||||
\(826\) | −5.68672 | −0.197866 | ||||||||
\(827\) | −24.3741 | −0.847571 | −0.423785 | − | 0.905763i | \(-0.639299\pi\) | ||||
−0.423785 | + | 0.905763i | \(0.639299\pi\) | |||||||
\(828\) | −50.3501 | −1.74979 | ||||||||
\(829\) | 44.3078 | 1.53887 | 0.769437 | − | 0.638723i | \(-0.220537\pi\) | ||||
0.769437 | + | 0.638723i | \(0.220537\pi\) | |||||||
\(830\) | −2.87424 | −0.0997663 | ||||||||
\(831\) | 26.6199 | 0.923433 | ||||||||
\(832\) | 0.206123 | 0.00714603 | ||||||||
\(833\) | −1.03103 | −0.0357230 | ||||||||
\(834\) | −71.3418 | −2.47036 | ||||||||
\(835\) | 12.9429 | 0.447907 | ||||||||
\(836\) | −27.2142 | −0.941224 | ||||||||
\(837\) | −99.8353 | −3.45081 | ||||||||
\(838\) | 64.5193 | 2.22878 | ||||||||
\(839\) | −6.06520 | −0.209394 | −0.104697 | − | 0.994504i | \(-0.533387\pi\) | ||||
−0.104697 | + | 0.994504i | \(0.533387\pi\) | |||||||
\(840\) | 5.17984 | 0.178722 | ||||||||
\(841\) | −22.4660 | −0.774690 | ||||||||
\(842\) | −36.2323 | −1.24865 | ||||||||
\(843\) | 93.6009 | 3.22379 | ||||||||
\(844\) | −2.66031 | −0.0915716 | ||||||||
\(845\) | 16.4897 | 0.567262 | ||||||||
\(846\) | 14.2617 | 0.490326 | ||||||||
\(847\) | −8.41603 | −0.289178 | ||||||||
\(848\) | −11.2676 | −0.386932 | ||||||||
\(849\) | −81.8368 | −2.80863 | ||||||||
\(850\) | 1.81701 | 0.0623228 | ||||||||
\(851\) | −21.2767 | −0.729355 | ||||||||
\(852\) | −27.7914 | −0.952119 | ||||||||
\(853\) | 16.4050 | 0.561696 | 0.280848 | − | 0.959752i | \(-0.409384\pi\) | ||||
0.280848 | + | 0.959752i | \(0.409384\pi\) | |||||||
\(854\) | 20.7501 | 0.710054 | ||||||||
\(855\) | −43.5864 | −1.49062 | ||||||||
\(856\) | −8.91379 | −0.304667 | ||||||||
\(857\) | −26.5654 | −0.907456 | −0.453728 | − | 0.891140i | \(-0.649906\pi\) | ||||
−0.453728 | + | 0.891140i | \(0.649906\pi\) | |||||||
\(858\) | 138.608 | 4.73200 | ||||||||
\(859\) | −34.1507 | −1.16521 | −0.582603 | − | 0.812757i | \(-0.697966\pi\) | ||||
−0.582603 | + | 0.812757i | \(0.697966\pi\) | |||||||
\(860\) | −10.2739 | −0.350337 | ||||||||
\(861\) | 19.5741 | 0.667083 | ||||||||
\(862\) | 57.6215 | 1.96260 | ||||||||
\(863\) | 39.4616 | 1.34329 | 0.671644 | − | 0.740874i | \(-0.265589\pi\) | ||||
0.671644 | + | 0.740874i | \(0.265589\pi\) | |||||||
\(864\) | −89.0545 | −3.02969 | ||||||||
\(865\) | 4.06779 | 0.138309 | ||||||||
\(866\) | 31.8080 | 1.08088 | ||||||||
\(867\) | 52.3834 | 1.77903 | ||||||||
\(868\) | −6.99172 | −0.237315 | ||||||||
\(869\) | −5.29721 | −0.179696 | ||||||||
\(870\) | −14.8068 | −0.501999 | ||||||||
\(871\) | 14.0185 | 0.475000 | ||||||||
\(872\) | −15.9541 | −0.540274 | ||||||||
\(873\) | −122.902 | −4.15959 | ||||||||
\(874\) | −57.4326 | −1.94269 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −42.5207 | −1.43664 | ||||||||
\(877\) | 31.0030 | 1.04690 | 0.523448 | − | 0.852058i | \(-0.324645\pi\) | ||||
0.523448 | + | 0.852058i | \(0.324645\pi\) | |||||||
\(878\) | −8.97038 | −0.302736 | ||||||||
\(879\) | −51.4614 | −1.73575 | ||||||||
\(880\) | −21.9825 | −0.741030 | ||||||||
\(881\) | −12.7521 | −0.429628 | −0.214814 | − | 0.976655i | \(-0.568914\pi\) | ||||
−0.214814 | + | 0.976655i | \(0.568914\pi\) | |||||||
\(882\) | −13.7528 | −0.463079 | ||||||||
\(883\) | −35.9565 | −1.21003 | −0.605016 | − | 0.796213i | \(-0.706833\pi\) | ||||
−0.605016 | + | 0.796213i | \(0.706833\pi\) | |||||||
\(884\) | −6.19121 | −0.208233 | ||||||||
\(885\) | 10.6063 | 0.356527 | ||||||||
\(886\) | −14.0559 | −0.472216 | ||||||||
\(887\) | −10.6441 | −0.357392 | −0.178696 | − | 0.983904i | \(-0.557188\pi\) | ||||
−0.178696 | + | 0.983904i | \(0.557188\pi\) | |||||||
\(888\) | −18.8883 | −0.633851 | ||||||||
\(889\) | −17.3350 | −0.581398 | ||||||||
\(890\) | −6.26932 | −0.210148 | ||||||||
\(891\) | 125.526 | 4.20528 | ||||||||
\(892\) | 21.9258 | 0.734129 | ||||||||
\(893\) | 5.79198 | 0.193821 | ||||||||
\(894\) | 127.246 | 4.25575 | ||||||||
\(895\) | 12.7406 | 0.425870 | ||||||||
\(896\) | 11.3471 | 0.379079 | ||||||||
\(897\) | 104.148 | 3.47739 | ||||||||
\(898\) | 58.3862 | 1.94837 | ||||||||
\(899\) | −16.1623 | −0.539044 | ||||||||
\(900\) | 8.62926 | 0.287642 | ||||||||
\(901\) | −2.32866 | −0.0775790 | ||||||||
\(902\) | −46.2445 | −1.53977 | ||||||||
\(903\) | −30.5389 | −1.01627 | ||||||||
\(904\) | −17.2936 | −0.575176 | ||||||||
\(905\) | −6.87661 | −0.228586 | ||||||||
\(906\) | −54.6905 | −1.81697 | ||||||||
\(907\) | 37.7018 | 1.25187 | 0.625934 | − | 0.779876i | \(-0.284718\pi\) | ||||
0.625934 | + | 0.779876i | \(0.284718\pi\) | |||||||
\(908\) | 26.2176 | 0.870063 | ||||||||
\(909\) | 130.624 | 4.33252 | ||||||||
\(910\) | 9.57019 | 0.317249 | ||||||||
\(911\) | 3.78226 | 0.125312 | 0.0626559 | − | 0.998035i | \(-0.480043\pi\) | ||||
0.0626559 | + | 0.998035i | \(0.480043\pi\) | |||||||
\(912\) | −91.5864 | −3.03273 | ||||||||
\(913\) | 7.18650 | 0.237839 | ||||||||
\(914\) | −16.2464 | −0.537383 | ||||||||
\(915\) | −38.7010 | −1.27942 | ||||||||
\(916\) | −1.10578 | −0.0365361 | ||||||||
\(917\) | 10.1945 | 0.336652 | ||||||||
\(918\) | −28.6897 | −0.946901 | ||||||||
\(919\) | −25.0239 | −0.825463 | −0.412731 | − | 0.910853i | \(-0.635425\pi\) | ||||
−0.412731 | + | 0.910853i | \(0.635425\pi\) | |||||||
\(920\) | −9.19509 | −0.303153 | ||||||||
\(921\) | −30.5133 | −1.00545 | ||||||||
\(922\) | −33.8055 | −1.11333 | ||||||||
\(923\) | 41.5230 | 1.36675 | ||||||||
\(924\) | 16.0154 | 0.526867 | ||||||||
\(925\) | 3.64651 | 0.119896 | ||||||||
\(926\) | −58.5107 | −1.92278 | ||||||||
\(927\) | −94.0067 | −3.08759 | ||||||||
\(928\) | −14.4170 | −0.473262 | ||||||||
\(929\) | 29.7903 | 0.977388 | 0.488694 | − | 0.872455i | \(-0.337474\pi\) | ||||
0.488694 | + | 0.872455i | \(0.337474\pi\) | |||||||
\(930\) | 36.6259 | 1.20101 | ||||||||
\(931\) | −5.58530 | −0.183051 | ||||||||
\(932\) | −19.9439 | −0.653284 | ||||||||
\(933\) | −40.0375 | −1.31077 | ||||||||
\(934\) | −4.74249 | −0.155179 | ||||||||
\(935\) | −4.54309 | −0.148575 | ||||||||
\(936\) | 66.7833 | 2.18288 | ||||||||
\(937\) | 11.6512 | 0.380628 | 0.190314 | − | 0.981723i | \(-0.439049\pi\) | ||||
0.190314 | + | 0.981723i | \(0.439049\pi\) | |||||||
\(938\) | 4.54939 | 0.148543 | ||||||||
\(939\) | 46.1417 | 1.50578 | ||||||||
\(940\) | −1.14670 | −0.0374013 | ||||||||
\(941\) | 4.46755 | 0.145638 | 0.0728190 | − | 0.997345i | \(-0.476800\pi\) | ||||
0.0728190 | + | 0.997345i | \(0.476800\pi\) | |||||||
\(942\) | −101.094 | −3.29383 | ||||||||
\(943\) | −34.7473 | −1.13153 | ||||||||
\(944\) | 16.0980 | 0.523947 | ||||||||
\(945\) | 15.7895 | 0.513634 | ||||||||
\(946\) | 72.1491 | 2.34577 | ||||||||
\(947\) | −43.7087 | −1.42034 | −0.710172 | − | 0.704029i | \(-0.751383\pi\) | ||||
−0.710172 | + | 0.704029i | \(0.751383\pi\) | |||||||
\(948\) | 4.36943 | 0.141912 | ||||||||
\(949\) | 63.5299 | 2.06227 | ||||||||
\(950\) | 9.84310 | 0.319352 | ||||||||
\(951\) | 75.9789 | 2.46379 | ||||||||
\(952\) | 1.62480 | 0.0526601 | ||||||||
\(953\) | 55.8288 | 1.80847 | 0.904236 | − | 0.427032i | \(-0.140441\pi\) | ||||
0.904236 | + | 0.427032i | \(0.140441\pi\) | |||||||
\(954\) | −31.0617 | −1.00566 | ||||||||
\(955\) | 8.29513 | 0.268424 | ||||||||
\(956\) | 18.0857 | 0.584934 | ||||||||
\(957\) | 37.0218 | 1.19674 | ||||||||
\(958\) | 51.2103 | 1.65453 | ||||||||
\(959\) | −3.18481 | −0.102843 | ||||||||
\(960\) | −0.124761 | −0.00402665 | ||||||||
\(961\) | 8.97878 | 0.289638 | ||||||||
\(962\) | −34.8978 | −1.12515 | ||||||||
\(963\) | −44.1406 | −1.42241 | ||||||||
\(964\) | 15.0648 | 0.485204 | ||||||||
\(965\) | 5.73607 | 0.184650 | ||||||||
\(966\) | 33.7987 | 1.08746 | ||||||||
\(967\) | −22.4190 | −0.720947 | −0.360474 | − | 0.932769i | \(-0.617385\pi\) | ||||
−0.360474 | + | 0.932769i | \(0.617385\pi\) | |||||||
\(968\) | 13.2628 | 0.426284 | ||||||||
\(969\) | −18.9280 | −0.608055 | ||||||||
\(970\) | 27.7548 | 0.891154 | ||||||||
\(971\) | 28.2722 | 0.907297 | 0.453648 | − | 0.891181i | \(-0.350122\pi\) | ||||
0.453648 | + | 0.891181i | \(0.350122\pi\) | |||||||
\(972\) | −51.1613 | −1.64100 | ||||||||
\(973\) | 12.3160 | 0.394834 | ||||||||
\(974\) | −32.9935 | −1.05718 | ||||||||
\(975\) | −17.8494 | −0.571637 | ||||||||
\(976\) | −58.7397 | −1.88021 | ||||||||
\(977\) | 22.6727 | 0.725363 | 0.362681 | − | 0.931913i | \(-0.381861\pi\) | ||||
0.362681 | + | 0.931913i | \(0.381861\pi\) | |||||||
\(978\) | −2.90869 | −0.0930096 | ||||||||
\(979\) | 15.6753 | 0.500984 | ||||||||
\(980\) | 1.10578 | 0.0353229 | ||||||||
\(981\) | −79.0037 | −2.52239 | ||||||||
\(982\) | −8.85409 | −0.282545 | ||||||||
\(983\) | 26.0855 | 0.831998 | 0.415999 | − | 0.909365i | \(-0.363432\pi\) | ||||
0.415999 | + | 0.909365i | \(0.363432\pi\) | |||||||
\(984\) | −30.8468 | −0.983361 | ||||||||
\(985\) | 0.400857 | 0.0127724 | ||||||||
\(986\) | −4.64458 | −0.147913 | ||||||||
\(987\) | −3.40854 | −0.108495 | ||||||||
\(988\) | −33.5391 | −1.06702 | ||||||||
\(989\) | 54.2116 | 1.72383 | ||||||||
\(990\) | −60.5996 | −1.92598 | ||||||||
\(991\) | 50.8117 | 1.61409 | 0.807043 | − | 0.590492i | \(-0.201066\pi\) | ||||
0.807043 | + | 0.590492i | \(0.201066\pi\) | |||||||
\(992\) | 35.6616 | 1.13226 | ||||||||
\(993\) | −5.99371 | −0.190205 | ||||||||
\(994\) | 13.4753 | 0.427411 | ||||||||
\(995\) | 25.2282 | 0.799788 | ||||||||
\(996\) | −5.92781 | −0.187830 | ||||||||
\(997\) | −23.6891 | −0.750243 | −0.375121 | − | 0.926976i | \(-0.622399\pi\) | ||||
−0.375121 | + | 0.926976i | \(0.622399\pi\) | |||||||
\(998\) | −67.3036 | −2.13046 | ||||||||
\(999\) | −57.5767 | −1.82164 |
(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 | 8015.2.a.m.1.16 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.m.1.16 | ✓ | 67 | 1.1 | even | 1 | trivial |