Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25316 | −0.886118 | −0.443059 | − | 0.896492i | \(-0.646107\pi\) | ||||
−0.443059 | + | 0.896492i | \(0.646107\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.429590 | −0.214795 | ||||||||
\(5\) | 1.76265 | 0.788283 | 0.394142 | − | 0.919050i | \(-0.371042\pi\) | ||||
0.394142 | + | 0.919050i | \(0.371042\pi\) | |||||||
\(6\) | 1.25316 | 0.511600 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.04466 | 1.07645 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.20889 | −0.698512 | ||||||||
\(11\) | −4.84306 | −1.46024 | −0.730119 | − | 0.683320i | \(-0.760535\pi\) | ||||
−0.730119 | + | 0.683320i | \(0.760535\pi\) | |||||||
\(12\) | 0.429590 | 0.124012 | ||||||||
\(13\) | 3.18902 | 0.884475 | 0.442237 | − | 0.896898i | \(-0.354185\pi\) | ||||
0.442237 | + | 0.896898i | \(0.354185\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.76265 | −0.455115 | ||||||||
\(16\) | −2.95627 | −0.739068 | ||||||||
\(17\) | −6.61037 | −1.60325 | −0.801625 | − | 0.597827i | \(-0.796031\pi\) | ||||
−0.801625 | + | 0.597827i | \(0.796031\pi\) | |||||||
\(18\) | −1.25316 | −0.295373 | ||||||||
\(19\) | 8.31403 | 1.90737 | 0.953685 | − | 0.300808i | \(-0.0972564\pi\) | ||||
0.953685 | + | 0.300808i | \(0.0972564\pi\) | |||||||
\(20\) | −0.757219 | −0.169319 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.06913 | 1.29394 | ||||||||
\(23\) | −8.32423 | −1.73572 | −0.867861 | − | 0.496807i | \(-0.834506\pi\) | ||||
−0.867861 | + | 0.496807i | \(0.834506\pi\) | |||||||
\(24\) | −3.04466 | −0.621490 | ||||||||
\(25\) | −1.89305 | −0.378610 | ||||||||
\(26\) | −3.99635 | −0.783749 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.79558 | −1.44760 | −0.723802 | − | 0.690008i | \(-0.757607\pi\) | ||||
−0.723802 | + | 0.690008i | \(0.757607\pi\) | |||||||
\(30\) | 2.20889 | 0.403286 | ||||||||
\(31\) | 1.04110 | 0.186986 | 0.0934932 | − | 0.995620i | \(-0.470197\pi\) | ||||
0.0934932 | + | 0.995620i | \(0.470197\pi\) | |||||||
\(32\) | −2.38465 | −0.421550 | ||||||||
\(33\) | 4.84306 | 0.843068 | ||||||||
\(34\) | 8.28385 | 1.42067 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.429590 | −0.0715983 | ||||||||
\(37\) | 3.58658 | 0.589630 | 0.294815 | − | 0.955554i | \(-0.404742\pi\) | ||||
0.294815 | + | 0.955554i | \(0.404742\pi\) | |||||||
\(38\) | −10.4188 | −1.69015 | ||||||||
\(39\) | −3.18902 | −0.510652 | ||||||||
\(40\) | 5.36669 | 0.848549 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.05595 | 0.618527 | 0.309263 | − | 0.950976i | \(-0.399918\pi\) | ||||
0.309263 | + | 0.950976i | \(0.399918\pi\) | |||||||
\(44\) | 2.08053 | 0.313652 | ||||||||
\(45\) | 1.76265 | 0.262761 | ||||||||
\(46\) | 10.4316 | 1.53805 | ||||||||
\(47\) | −0.963735 | −0.140575 | −0.0702876 | − | 0.997527i | \(-0.522392\pi\) | ||||
−0.0702876 | + | 0.997527i | \(0.522392\pi\) | |||||||
\(48\) | 2.95627 | 0.426701 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.37229 | 0.335493 | ||||||||
\(51\) | 6.61037 | 0.925637 | ||||||||
\(52\) | −1.36997 | −0.189981 | ||||||||
\(53\) | 5.52023 | 0.758262 | 0.379131 | − | 0.925343i | \(-0.376223\pi\) | ||||
0.379131 | + | 0.925343i | \(0.376223\pi\) | |||||||
\(54\) | 1.25316 | 0.170533 | ||||||||
\(55\) | −8.53664 | −1.15108 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.31403 | −1.10122 | ||||||||
\(58\) | 9.76911 | 1.28275 | ||||||||
\(59\) | 9.28053 | 1.20822 | 0.604111 | − | 0.796900i | \(-0.293528\pi\) | ||||
0.604111 | + | 0.796900i | \(0.293528\pi\) | |||||||
\(60\) | 0.757219 | 0.0977565 | ||||||||
\(61\) | −11.2178 | −1.43629 | −0.718145 | − | 0.695893i | \(-0.755009\pi\) | ||||
−0.718145 | + | 0.695893i | \(0.755009\pi\) | |||||||
\(62\) | −1.30466 | −0.165692 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.90089 | 1.11261 | ||||||||
\(65\) | 5.62114 | 0.697217 | ||||||||
\(66\) | −6.06913 | −0.747058 | ||||||||
\(67\) | 6.04854 | 0.738946 | 0.369473 | − | 0.929241i | \(-0.379538\pi\) | ||||
0.369473 | + | 0.929241i | \(0.379538\pi\) | |||||||
\(68\) | 2.83975 | 0.344370 | ||||||||
\(69\) | 8.32423 | 1.00212 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.94007 | 1.17967 | 0.589834 | − | 0.807524i | \(-0.299193\pi\) | ||||
0.589834 | + | 0.807524i | \(0.299193\pi\) | |||||||
\(72\) | 3.04466 | 0.358817 | ||||||||
\(73\) | 3.75792 | 0.439832 | 0.219916 | − | 0.975519i | \(-0.429422\pi\) | ||||
0.219916 | + | 0.975519i | \(0.429422\pi\) | |||||||
\(74\) | −4.49456 | −0.522482 | ||||||||
\(75\) | 1.89305 | 0.218590 | ||||||||
\(76\) | −3.57162 | −0.409693 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.99635 | 0.452498 | ||||||||
\(79\) | −13.7937 | −1.55192 | −0.775958 | − | 0.630784i | \(-0.782733\pi\) | ||||
−0.775958 | + | 0.630784i | \(0.782733\pi\) | |||||||
\(80\) | −5.21089 | −0.582595 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.25316 | −0.138388 | ||||||||
\(83\) | −8.11111 | −0.890309 | −0.445155 | − | 0.895454i | \(-0.646851\pi\) | ||||
−0.445155 | + | 0.895454i | \(0.646851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.6518 | −1.26382 | ||||||||
\(86\) | −5.08276 | −0.548088 | ||||||||
\(87\) | 7.79558 | 0.835774 | ||||||||
\(88\) | −14.7455 | −1.57187 | ||||||||
\(89\) | 10.4911 | 1.11206 | 0.556029 | − | 0.831163i | \(-0.312324\pi\) | ||||
0.556029 | + | 0.831163i | \(0.312324\pi\) | |||||||
\(90\) | −2.20889 | −0.232837 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.57601 | 0.372824 | ||||||||
\(93\) | −1.04110 | −0.107957 | ||||||||
\(94\) | 1.20771 | 0.124566 | ||||||||
\(95\) | 14.6548 | 1.50355 | ||||||||
\(96\) | 2.38465 | 0.243382 | ||||||||
\(97\) | 11.2995 | 1.14729 | 0.573644 | − | 0.819104i | \(-0.305529\pi\) | ||||
0.573644 | + | 0.819104i | \(0.305529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.84306 | −0.486746 | ||||||||
\(100\) | 0.813234 | 0.0813234 | ||||||||
\(101\) | −16.1294 | −1.60494 | −0.802469 | − | 0.596694i | \(-0.796481\pi\) | ||||
−0.802469 | + | 0.596694i | \(0.796481\pi\) | |||||||
\(102\) | −8.28385 | −0.820224 | ||||||||
\(103\) | 14.9966 | 1.47766 | 0.738828 | − | 0.673894i | \(-0.235380\pi\) | ||||
0.738828 | + | 0.673894i | \(0.235380\pi\) | |||||||
\(104\) | 9.70950 | 0.952094 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.91773 | −0.671909 | ||||||||
\(107\) | −14.7499 | −1.42593 | −0.712963 | − | 0.701202i | \(-0.752647\pi\) | ||||
−0.712963 | + | 0.701202i | \(0.752647\pi\) | |||||||
\(108\) | 0.429590 | 0.0413373 | ||||||||
\(109\) | 6.63410 | 0.635432 | 0.317716 | − | 0.948186i | \(-0.397084\pi\) | ||||
0.317716 | + | 0.948186i | \(0.397084\pi\) | |||||||
\(110\) | 10.6978 | 1.01999 | ||||||||
\(111\) | −3.58658 | −0.340423 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.35078 | −0.127071 | −0.0635354 | − | 0.997980i | \(-0.520238\pi\) | ||||
−0.0635354 | + | 0.997980i | \(0.520238\pi\) | |||||||
\(114\) | 10.4188 | 0.975811 | ||||||||
\(115\) | −14.6727 | −1.36824 | ||||||||
\(116\) | 3.34890 | 0.310938 | ||||||||
\(117\) | 3.18902 | 0.294825 | ||||||||
\(118\) | −11.6300 | −1.07063 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.36669 | −0.489910 | ||||||||
\(121\) | 12.4552 | 1.13229 | ||||||||
\(122\) | 14.0577 | 1.27272 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −0.447244 | −0.0401637 | ||||||||
\(125\) | −12.1501 | −1.08673 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.16265 | −0.813054 | −0.406527 | − | 0.913639i | \(-0.633260\pi\) | ||||
−0.406527 | + | 0.913639i | \(0.633260\pi\) | |||||||
\(128\) | −6.38495 | −0.564355 | ||||||||
\(129\) | −4.05595 | −0.357107 | ||||||||
\(130\) | −7.04419 | −0.617816 | ||||||||
\(131\) | −5.34838 | −0.467291 | −0.233645 | − | 0.972322i | \(-0.575065\pi\) | ||||
−0.233645 | + | 0.972322i | \(0.575065\pi\) | |||||||
\(132\) | −2.08053 | −0.181087 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.57979 | −0.654794 | ||||||||
\(135\) | −1.76265 | −0.151705 | ||||||||
\(136\) | −20.1264 | −1.72582 | ||||||||
\(137\) | 20.2802 | 1.73266 | 0.866329 | − | 0.499474i | \(-0.166473\pi\) | ||||
0.866329 | + | 0.499474i | \(0.166473\pi\) | |||||||
\(138\) | −10.4316 | −0.887996 | ||||||||
\(139\) | −2.75452 | −0.233635 | −0.116818 | − | 0.993153i | \(-0.537269\pi\) | ||||
−0.116818 | + | 0.993153i | \(0.537269\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.963735 | 0.0811611 | ||||||||
\(142\) | −12.4565 | −1.04533 | ||||||||
\(143\) | −15.4446 | −1.29154 | ||||||||
\(144\) | −2.95627 | −0.246356 | ||||||||
\(145\) | −13.7409 | −1.14112 | ||||||||
\(146\) | −4.70928 | −0.389743 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.54076 | −0.126650 | ||||||||
\(149\) | 9.53225 | 0.780912 | 0.390456 | − | 0.920622i | \(-0.372317\pi\) | ||||
0.390456 | + | 0.920622i | \(0.372317\pi\) | |||||||
\(150\) | −2.37229 | −0.193697 | ||||||||
\(151\) | −5.68919 | −0.462979 | −0.231490 | − | 0.972837i | \(-0.574360\pi\) | ||||
−0.231490 | + | 0.972837i | \(0.574360\pi\) | |||||||
\(152\) | 25.3134 | 2.05319 | ||||||||
\(153\) | −6.61037 | −0.534417 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.83509 | 0.147398 | ||||||||
\(156\) | 1.36997 | 0.109685 | ||||||||
\(157\) | 10.9120 | 0.870869 | 0.435434 | − | 0.900221i | \(-0.356595\pi\) | ||||
0.435434 | + | 0.900221i | \(0.356595\pi\) | |||||||
\(158\) | 17.2858 | 1.37518 | ||||||||
\(159\) | −5.52023 | −0.437783 | ||||||||
\(160\) | −4.20331 | −0.332301 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.25316 | −0.0984576 | ||||||||
\(163\) | −2.69969 | −0.211456 | −0.105728 | − | 0.994395i | \(-0.533717\pi\) | ||||
−0.105728 | + | 0.994395i | \(0.533717\pi\) | |||||||
\(164\) | −0.429590 | −0.0335453 | ||||||||
\(165\) | 8.53664 | 0.664577 | ||||||||
\(166\) | 10.1645 | 0.788919 | ||||||||
\(167\) | 10.8810 | 0.841998 | 0.420999 | − | 0.907061i | \(-0.361680\pi\) | ||||
0.420999 | + | 0.907061i | \(0.361680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.83016 | −0.217704 | ||||||||
\(170\) | 14.6016 | 1.11989 | ||||||||
\(171\) | 8.31403 | 0.635790 | ||||||||
\(172\) | −1.74240 | −0.132856 | ||||||||
\(173\) | 14.5148 | 1.10354 | 0.551769 | − | 0.833997i | \(-0.313953\pi\) | ||||
0.551769 | + | 0.833997i | \(0.313953\pi\) | |||||||
\(174\) | −9.76911 | −0.740594 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.3174 | 1.07921 | ||||||||
\(177\) | −9.28053 | −0.697567 | ||||||||
\(178\) | −13.1471 | −0.985415 | ||||||||
\(179\) | 14.3925 | 1.07575 | 0.537873 | − | 0.843026i | \(-0.319228\pi\) | ||||
0.537873 | + | 0.843026i | \(0.319228\pi\) | |||||||
\(180\) | −0.757219 | −0.0564397 | ||||||||
\(181\) | 10.9137 | 0.811208 | 0.405604 | − | 0.914049i | \(-0.367061\pi\) | ||||
0.405604 | + | 0.914049i | \(0.367061\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2178 | 0.829243 | ||||||||
\(184\) | −25.3445 | −1.86842 | ||||||||
\(185\) | 6.32190 | 0.464795 | ||||||||
\(186\) | 1.30466 | 0.0956623 | ||||||||
\(187\) | 32.0144 | 2.34113 | ||||||||
\(188\) | 0.414011 | 0.0301948 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.3648 | −1.33232 | ||||||||
\(191\) | 2.59146 | 0.187512 | 0.0937558 | − | 0.995595i | \(-0.470113\pi\) | ||||
0.0937558 | + | 0.995595i | \(0.470113\pi\) | |||||||
\(192\) | −8.90089 | −0.642366 | ||||||||
\(193\) | −15.2810 | −1.09995 | −0.549977 | − | 0.835180i | \(-0.685363\pi\) | ||||
−0.549977 | + | 0.835180i | \(0.685363\pi\) | |||||||
\(194\) | −14.1601 | −1.01663 | ||||||||
\(195\) | −5.62114 | −0.402538 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.9063 | 1.06203 | 0.531013 | − | 0.847363i | \(-0.321811\pi\) | ||||
0.531013 | + | 0.847363i | \(0.321811\pi\) | |||||||
\(198\) | 6.06913 | 0.431314 | ||||||||
\(199\) | 3.57408 | 0.253360 | 0.126680 | − | 0.991944i | \(-0.459568\pi\) | ||||
0.126680 | + | 0.991944i | \(0.459568\pi\) | |||||||
\(200\) | −5.76370 | −0.407555 | ||||||||
\(201\) | −6.04854 | −0.426631 | ||||||||
\(202\) | 20.2128 | 1.42216 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.83975 | −0.198822 | ||||||||
\(205\) | 1.76265 | 0.123109 | ||||||||
\(206\) | −18.7931 | −1.30938 | ||||||||
\(207\) | −8.32423 | −0.578574 | ||||||||
\(208\) | −9.42761 | −0.653687 | ||||||||
\(209\) | −40.2653 | −2.78521 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.16912 | 0.0804857 | 0.0402428 | − | 0.999190i | \(-0.487187\pi\) | ||||
0.0402428 | + | 0.999190i | \(0.487187\pi\) | |||||||
\(212\) | −2.37143 | −0.162871 | ||||||||
\(213\) | −9.94007 | −0.681082 | ||||||||
\(214\) | 18.4840 | 1.26354 | ||||||||
\(215\) | 7.14924 | 0.487574 | ||||||||
\(216\) | −3.04466 | −0.207163 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.31359 | −0.563067 | ||||||||
\(219\) | −3.75792 | −0.253937 | ||||||||
\(220\) | 3.66725 | 0.247246 | ||||||||
\(221\) | −21.0806 | −1.41803 | ||||||||
\(222\) | 4.49456 | 0.301655 | ||||||||
\(223\) | 1.28838 | 0.0862763 | 0.0431382 | − | 0.999069i | \(-0.486264\pi\) | ||||
0.0431382 | + | 0.999069i | \(0.486264\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.89305 | −0.126203 | ||||||||
\(226\) | 1.69274 | 0.112600 | ||||||||
\(227\) | −24.1040 | −1.59984 | −0.799919 | − | 0.600108i | \(-0.795124\pi\) | ||||
−0.799919 | + | 0.600108i | \(0.795124\pi\) | |||||||
\(228\) | 3.57162 | 0.236537 | ||||||||
\(229\) | −0.361413 | −0.0238828 | −0.0119414 | − | 0.999929i | \(-0.503801\pi\) | ||||
−0.0119414 | + | 0.999929i | \(0.503801\pi\) | |||||||
\(230\) | 18.3873 | 1.21242 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −23.7349 | −1.55827 | ||||||||
\(233\) | 0.141975 | 0.00930108 | 0.00465054 | − | 0.999989i | \(-0.498520\pi\) | ||||
0.00465054 | + | 0.999989i | \(0.498520\pi\) | |||||||
\(234\) | −3.99635 | −0.261250 | ||||||||
\(235\) | −1.69873 | −0.110813 | ||||||||
\(236\) | −3.98682 | −0.259520 | ||||||||
\(237\) | 13.7937 | 0.896000 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.9975 | 0.776055 | 0.388027 | − | 0.921648i | \(-0.373157\pi\) | ||||
0.388027 | + | 0.921648i | \(0.373157\pi\) | |||||||
\(240\) | 5.21089 | 0.336361 | ||||||||
\(241\) | 1.49883 | 0.0965478 | 0.0482739 | − | 0.998834i | \(-0.484628\pi\) | ||||
0.0482739 | + | 0.998834i | \(0.484628\pi\) | |||||||
\(242\) | −15.6084 | −1.00335 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.81905 | 0.308508 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.25316 | 0.0798986 | ||||||||
\(247\) | 26.5136 | 1.68702 | ||||||||
\(248\) | 3.16979 | 0.201282 | ||||||||
\(249\) | 8.11111 | 0.514020 | ||||||||
\(250\) | 15.2260 | 0.962975 | ||||||||
\(251\) | −6.61735 | −0.417683 | −0.208842 | − | 0.977949i | \(-0.566969\pi\) | ||||
−0.208842 | + | 0.977949i | \(0.566969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.3147 | 2.53457 | ||||||||
\(254\) | 11.4823 | 0.720462 | ||||||||
\(255\) | 11.6518 | 0.729664 | ||||||||
\(256\) | −9.80042 | −0.612526 | ||||||||
\(257\) | −7.49560 | −0.467563 | −0.233781 | − | 0.972289i | \(-0.575110\pi\) | ||||
−0.233781 | + | 0.972289i | \(0.575110\pi\) | |||||||
\(258\) | 5.08276 | 0.316439 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.41479 | −0.149759 | ||||||||
\(261\) | −7.79558 | −0.482534 | ||||||||
\(262\) | 6.70238 | 0.414075 | ||||||||
\(263\) | −18.6115 | −1.14764 | −0.573818 | − | 0.818983i | \(-0.694538\pi\) | ||||
−0.573818 | + | 0.818983i | \(0.694538\pi\) | |||||||
\(264\) | 14.7455 | 0.907522 | ||||||||
\(265\) | 9.73025 | 0.597725 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.4911 | −0.642047 | ||||||||
\(268\) | −2.59839 | −0.158722 | ||||||||
\(269\) | −11.7570 | −0.716839 | −0.358419 | − | 0.933561i | \(-0.616684\pi\) | ||||
−0.358419 | + | 0.933561i | \(0.616684\pi\) | |||||||
\(270\) | 2.20889 | 0.134429 | ||||||||
\(271\) | −23.0447 | −1.39987 | −0.699933 | − | 0.714208i | \(-0.746787\pi\) | ||||
−0.699933 | + | 0.714208i | \(0.746787\pi\) | |||||||
\(272\) | 19.5421 | 1.18491 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.4144 | −1.53534 | ||||||||
\(275\) | 9.16814 | 0.552860 | ||||||||
\(276\) | −3.57601 | −0.215250 | ||||||||
\(277\) | 29.0686 | 1.74656 | 0.873282 | − | 0.487216i | \(-0.161987\pi\) | ||||
0.873282 | + | 0.487216i | \(0.161987\pi\) | |||||||
\(278\) | 3.45185 | 0.207028 | ||||||||
\(279\) | 1.04110 | 0.0623288 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.9373 | 0.891087 | 0.445543 | − | 0.895260i | \(-0.353010\pi\) | ||||
0.445543 | + | 0.895260i | \(0.353010\pi\) | |||||||
\(282\) | −1.20771 | −0.0719183 | ||||||||
\(283\) | 10.5976 | 0.629960 | 0.314980 | − | 0.949098i | \(-0.398002\pi\) | ||||
0.314980 | + | 0.949098i | \(0.398002\pi\) | |||||||
\(284\) | −4.27015 | −0.253387 | ||||||||
\(285\) | −14.6548 | −0.868073 | ||||||||
\(286\) | 19.3546 | 1.14446 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.38465 | −0.140517 | ||||||||
\(289\) | 26.6970 | 1.57041 | ||||||||
\(290\) | 17.2196 | 1.01117 | ||||||||
\(291\) | −11.2995 | −0.662388 | ||||||||
\(292\) | −1.61437 | −0.0944736 | ||||||||
\(293\) | −32.6469 | −1.90725 | −0.953625 | − | 0.300998i | \(-0.902680\pi\) | ||||
−0.953625 | + | 0.300998i | \(0.902680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.3584 | 0.952421 | ||||||||
\(296\) | 10.9199 | 0.634708 | ||||||||
\(297\) | 4.84306 | 0.281023 | ||||||||
\(298\) | −11.9454 | −0.691980 | ||||||||
\(299\) | −26.5461 | −1.53520 | ||||||||
\(300\) | −0.813234 | −0.0469521 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.12946 | 0.410254 | ||||||||
\(303\) | 16.1294 | 0.926611 | ||||||||
\(304\) | −24.5785 | −1.40968 | ||||||||
\(305\) | −19.7731 | −1.13220 | ||||||||
\(306\) | 8.28385 | 0.473556 | ||||||||
\(307\) | −14.5205 | −0.828728 | −0.414364 | − | 0.910111i | \(-0.635996\pi\) | ||||
−0.414364 | + | 0.910111i | \(0.635996\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.9966 | −0.853125 | ||||||||
\(310\) | −2.29967 | −0.130612 | ||||||||
\(311\) | 3.08406 | 0.174881 | 0.0874404 | − | 0.996170i | \(-0.472131\pi\) | ||||
0.0874404 | + | 0.996170i | \(0.472131\pi\) | |||||||
\(312\) | −9.70950 | −0.549692 | ||||||||
\(313\) | −8.36990 | −0.473094 | −0.236547 | − | 0.971620i | \(-0.576016\pi\) | ||||
−0.236547 | + | 0.971620i | \(0.576016\pi\) | |||||||
\(314\) | −13.6744 | −0.771692 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.92565 | 0.333344 | ||||||||
\(317\) | 24.4448 | 1.37295 | 0.686477 | − | 0.727151i | \(-0.259156\pi\) | ||||
0.686477 | + | 0.727151i | \(0.259156\pi\) | |||||||
\(318\) | 6.91773 | 0.387927 | ||||||||
\(319\) | 37.7545 | 2.11384 | ||||||||
\(320\) | 15.6892 | 0.877053 | ||||||||
\(321\) | 14.7499 | 0.823259 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −54.9588 | −3.05799 | ||||||||
\(324\) | −0.429590 | −0.0238661 | ||||||||
\(325\) | −6.03697 | −0.334871 | ||||||||
\(326\) | 3.38315 | 0.187375 | ||||||||
\(327\) | −6.63410 | −0.366867 | ||||||||
\(328\) | 3.04466 | 0.168114 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.6978 | −0.588893 | ||||||||
\(331\) | −17.2362 | −0.947390 | −0.473695 | − | 0.880689i | \(-0.657080\pi\) | ||||
−0.473695 | + | 0.880689i | \(0.657080\pi\) | |||||||
\(332\) | 3.48445 | 0.191234 | ||||||||
\(333\) | 3.58658 | 0.196543 | ||||||||
\(334\) | −13.6357 | −0.746110 | ||||||||
\(335\) | 10.6615 | 0.582499 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.2679 | −0.668274 | −0.334137 | − | 0.942525i | \(-0.608445\pi\) | ||||
−0.334137 | + | 0.942525i | \(0.608445\pi\) | |||||||
\(338\) | 3.54664 | 0.192912 | ||||||||
\(339\) | 1.35078 | 0.0733643 | ||||||||
\(340\) | 5.00550 | 0.271461 | ||||||||
\(341\) | −5.04209 | −0.273045 | ||||||||
\(342\) | −10.4188 | −0.563385 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.3490 | 0.665814 | ||||||||
\(345\) | 14.6727 | 0.789954 | ||||||||
\(346\) | −18.1893 | −0.977864 | ||||||||
\(347\) | −28.5063 | −1.53030 | −0.765149 | − | 0.643853i | \(-0.777335\pi\) | ||||
−0.765149 | + | 0.643853i | \(0.777335\pi\) | |||||||
\(348\) | −3.34890 | −0.179520 | ||||||||
\(349\) | 25.5334 | 1.36677 | 0.683385 | − | 0.730058i | \(-0.260507\pi\) | ||||
0.683385 | + | 0.730058i | \(0.260507\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.18902 | −0.170217 | ||||||||
\(352\) | 11.5490 | 0.615563 | ||||||||
\(353\) | 13.8669 | 0.738058 | 0.369029 | − | 0.929418i | \(-0.379690\pi\) | ||||
0.369029 | + | 0.929418i | \(0.379690\pi\) | |||||||
\(354\) | 11.6300 | 0.618127 | ||||||||
\(355\) | 17.5209 | 0.929913 | ||||||||
\(356\) | −4.50689 | −0.238865 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.0361 | −0.953237 | ||||||||
\(359\) | 31.5191 | 1.66352 | 0.831758 | − | 0.555139i | \(-0.187335\pi\) | ||||
0.831758 | + | 0.555139i | \(0.187335\pi\) | |||||||
\(360\) | 5.36669 | 0.282850 | ||||||||
\(361\) | 50.1231 | 2.63806 | ||||||||
\(362\) | −13.6766 | −0.718826 | ||||||||
\(363\) | −12.4552 | −0.653730 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.62392 | 0.346712 | ||||||||
\(366\) | −14.0577 | −0.734807 | ||||||||
\(367\) | −9.06523 | −0.473201 | −0.236601 | − | 0.971607i | \(-0.576033\pi\) | ||||
−0.236601 | + | 0.971607i | \(0.576033\pi\) | |||||||
\(368\) | 24.6087 | 1.28282 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −7.92235 | −0.411864 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.447244 | 0.0231885 | ||||||||
\(373\) | 8.28576 | 0.429021 | 0.214510 | − | 0.976722i | \(-0.431184\pi\) | ||||
0.214510 | + | 0.976722i | \(0.431184\pi\) | |||||||
\(374\) | −40.1192 | −2.07451 | ||||||||
\(375\) | 12.1501 | 0.627427 | ||||||||
\(376\) | −2.93425 | −0.151322 | ||||||||
\(377\) | −24.8603 | −1.28037 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.9123 | −1.07419 | −0.537096 | − | 0.843521i | \(-0.680479\pi\) | ||||
−0.537096 | + | 0.843521i | \(0.680479\pi\) | |||||||
\(380\) | −6.29554 | −0.322954 | ||||||||
\(381\) | 9.16265 | 0.469417 | ||||||||
\(382\) | −3.24752 | −0.166157 | ||||||||
\(383\) | 4.72176 | 0.241270 | 0.120635 | − | 0.992697i | \(-0.461507\pi\) | ||||
0.120635 | + | 0.992697i | \(0.461507\pi\) | |||||||
\(384\) | 6.38495 | 0.325830 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.1496 | 0.974688 | ||||||||
\(387\) | 4.05595 | 0.206176 | ||||||||
\(388\) | −4.85414 | −0.246432 | ||||||||
\(389\) | 27.0332 | 1.37064 | 0.685319 | − | 0.728243i | \(-0.259663\pi\) | ||||
0.685319 | + | 0.728243i | \(0.259663\pi\) | |||||||
\(390\) | 7.04419 | 0.356696 | ||||||||
\(391\) | 55.0263 | 2.78280 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.34838 | 0.269790 | ||||||||
\(394\) | −18.6799 | −0.941081 | ||||||||
\(395\) | −24.3136 | −1.22335 | ||||||||
\(396\) | 2.08053 | 0.104551 | ||||||||
\(397\) | 28.9049 | 1.45070 | 0.725348 | − | 0.688383i | \(-0.241679\pi\) | ||||
0.725348 | + | 0.688383i | \(0.241679\pi\) | |||||||
\(398\) | −4.47890 | −0.224507 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.59637 | 0.279818 | ||||||||
\(401\) | 35.6608 | 1.78082 | 0.890408 | − | 0.455163i | \(-0.150419\pi\) | ||||
0.890408 | + | 0.455163i | \(0.150419\pi\) | |||||||
\(402\) | 7.57979 | 0.378045 | ||||||||
\(403\) | 3.32008 | 0.165385 | ||||||||
\(404\) | 6.92904 | 0.344733 | ||||||||
\(405\) | 1.76265 | 0.0875870 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.3700 | −0.861000 | ||||||||
\(408\) | 20.1264 | 0.996404 | ||||||||
\(409\) | 1.70039 | 0.0840788 | 0.0420394 | − | 0.999116i | \(-0.486614\pi\) | ||||
0.0420394 | + | 0.999116i | \(0.486614\pi\) | |||||||
\(410\) | −2.20889 | −0.109089 | ||||||||
\(411\) | −20.2802 | −1.00035 | ||||||||
\(412\) | −6.44237 | −0.317393 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10.4316 | 0.512685 | ||||||||
\(415\) | −14.2971 | −0.701816 | ||||||||
\(416\) | −7.60469 | −0.372850 | ||||||||
\(417\) | 2.75452 | 0.134889 | ||||||||
\(418\) | 50.4589 | 2.46803 | ||||||||
\(419\) | 12.6493 | 0.617957 | 0.308978 | − | 0.951069i | \(-0.400013\pi\) | ||||
0.308978 | + | 0.951069i | \(0.400013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.5413 | 1.58597 | 0.792983 | − | 0.609244i | \(-0.208527\pi\) | ||||
0.792983 | + | 0.609244i | \(0.208527\pi\) | |||||||
\(422\) | −1.46510 | −0.0713198 | ||||||||
\(423\) | −0.963735 | −0.0468584 | ||||||||
\(424\) | 16.8072 | 0.816232 | ||||||||
\(425\) | 12.5138 | 0.607006 | ||||||||
\(426\) | 12.4565 | 0.603519 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.33640 | 0.306282 | ||||||||
\(429\) | 15.4446 | 0.745673 | ||||||||
\(430\) | −8.95914 | −0.432048 | ||||||||
\(431\) | −24.0660 | −1.15922 | −0.579609 | − | 0.814895i | \(-0.696795\pi\) | ||||
−0.579609 | + | 0.814895i | \(0.696795\pi\) | |||||||
\(432\) | 2.95627 | 0.142234 | ||||||||
\(433\) | 2.53991 | 0.122061 | 0.0610303 | − | 0.998136i | \(-0.480561\pi\) | ||||
0.0610303 | + | 0.998136i | \(0.480561\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.7409 | 0.658827 | ||||||||
\(436\) | −2.84994 | −0.136488 | ||||||||
\(437\) | −69.2079 | −3.31066 | ||||||||
\(438\) | 4.70928 | 0.225018 | ||||||||
\(439\) | 12.6793 | 0.605149 | 0.302575 | − | 0.953126i | \(-0.402154\pi\) | ||||
0.302575 | + | 0.953126i | \(0.402154\pi\) | |||||||
\(440\) | −25.9912 | −1.23908 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.4174 | 1.25655 | ||||||||
\(443\) | 10.4222 | 0.495175 | 0.247587 | − | 0.968866i | \(-0.420362\pi\) | ||||
0.247587 | + | 0.968866i | \(0.420362\pi\) | |||||||
\(444\) | 1.54076 | 0.0731212 | ||||||||
\(445\) | 18.4923 | 0.876617 | ||||||||
\(446\) | −1.61455 | −0.0764510 | ||||||||
\(447\) | −9.53225 | −0.450860 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.1665 | 1.70680 | 0.853401 | − | 0.521255i | \(-0.174536\pi\) | ||||
0.853401 | + | 0.521255i | \(0.174536\pi\) | |||||||
\(450\) | 2.37229 | 0.111831 | ||||||||
\(451\) | −4.84306 | −0.228051 | ||||||||
\(452\) | 0.580282 | 0.0272942 | ||||||||
\(453\) | 5.68919 | 0.267301 | ||||||||
\(454\) | 30.2061 | 1.41764 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −25.3134 | −1.18541 | ||||||||
\(457\) | −3.44773 | −0.161278 | −0.0806390 | − | 0.996743i | \(-0.525696\pi\) | ||||
−0.0806390 | + | 0.996743i | \(0.525696\pi\) | |||||||
\(458\) | 0.452908 | 0.0211630 | ||||||||
\(459\) | 6.61037 | 0.308546 | ||||||||
\(460\) | 6.30326 | 0.293891 | ||||||||
\(461\) | 39.2660 | 1.82880 | 0.914400 | − | 0.404811i | \(-0.132663\pi\) | ||||
0.914400 | + | 0.404811i | \(0.132663\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.1115 | 0.795240 | 0.397620 | − | 0.917550i | \(-0.369836\pi\) | ||||
0.397620 | + | 0.917550i | \(0.369836\pi\) | |||||||
\(464\) | 23.0459 | 1.06988 | ||||||||
\(465\) | −1.83509 | −0.0851004 | ||||||||
\(466\) | −0.177917 | −0.00824185 | ||||||||
\(467\) | 41.0229 | 1.89831 | 0.949157 | − | 0.314802i | \(-0.101938\pi\) | ||||
0.949157 | + | 0.314802i | \(0.101938\pi\) | |||||||
\(468\) | −1.36997 | −0.0633269 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.12878 | 0.0981934 | ||||||||
\(471\) | −10.9120 | −0.502796 | ||||||||
\(472\) | 28.2561 | 1.30059 | ||||||||
\(473\) | −19.6432 | −0.903196 | ||||||||
\(474\) | −17.2858 | −0.793961 | ||||||||
\(475\) | −15.7389 | −0.722148 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.52023 | 0.252754 | ||||||||
\(478\) | −15.0348 | −0.687676 | ||||||||
\(479\) | −1.39675 | −0.0638191 | −0.0319096 | − | 0.999491i | \(-0.510159\pi\) | ||||
−0.0319096 | + | 0.999491i | \(0.510159\pi\) | |||||||
\(480\) | 4.20331 | 0.191854 | ||||||||
\(481\) | 11.4377 | 0.521513 | ||||||||
\(482\) | −1.87827 | −0.0855527 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.35064 | −0.243211 | ||||||||
\(485\) | 19.9171 | 0.904388 | ||||||||
\(486\) | 1.25316 | 0.0568445 | ||||||||
\(487\) | 30.7325 | 1.39262 | 0.696312 | − | 0.717739i | \(-0.254823\pi\) | ||||
0.696312 | + | 0.717739i | \(0.254823\pi\) | |||||||
\(488\) | −34.1544 | −1.54610 | ||||||||
\(489\) | 2.69969 | 0.122084 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.7792 | 1.07314 | 0.536570 | − | 0.843856i | \(-0.319720\pi\) | ||||
0.536570 | + | 0.843856i | \(0.319720\pi\) | |||||||
\(492\) | 0.429590 | 0.0193674 | ||||||||
\(493\) | 51.5317 | 2.32087 | ||||||||
\(494\) | −33.2258 | −1.49490 | ||||||||
\(495\) | −8.53664 | −0.383693 | ||||||||
\(496\) | −3.07776 | −0.138196 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −10.1645 | −0.455483 | ||||||||
\(499\) | −8.09580 | −0.362418 | −0.181209 | − | 0.983445i | \(-0.558001\pi\) | ||||
−0.181209 | + | 0.983445i | \(0.558001\pi\) | |||||||
\(500\) | 5.21954 | 0.233425 | ||||||||
\(501\) | −10.8810 | −0.486128 | ||||||||
\(502\) | 8.29260 | 0.370117 | ||||||||
\(503\) | 28.9531 | 1.29095 | 0.645476 | − | 0.763780i | \(-0.276659\pi\) | ||||
0.645476 | + | 0.763780i | \(0.276659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.4306 | −1.26515 | ||||||||
\(506\) | −50.5208 | −2.24592 | ||||||||
\(507\) | 2.83016 | 0.125692 | ||||||||
\(508\) | 3.93618 | 0.174640 | ||||||||
\(509\) | −16.0637 | −0.712009 | −0.356005 | − | 0.934484i | \(-0.615861\pi\) | ||||
−0.356005 | + | 0.934484i | \(0.615861\pi\) | |||||||
\(510\) | −14.6016 | −0.646569 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 25.0514 | 1.10713 | ||||||||
\(513\) | −8.31403 | −0.367073 | ||||||||
\(514\) | 9.39319 | 0.414316 | ||||||||
\(515\) | 26.4338 | 1.16481 | ||||||||
\(516\) | 1.74240 | 0.0767047 | ||||||||
\(517\) | 4.66743 | 0.205273 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.5148 | −0.637128 | ||||||||
\(520\) | 17.1145 | 0.750520 | ||||||||
\(521\) | 39.7632 | 1.74206 | 0.871028 | − | 0.491234i | \(-0.163454\pi\) | ||||
0.871028 | + | 0.491234i | \(0.163454\pi\) | |||||||
\(522\) | 9.76911 | 0.427582 | ||||||||
\(523\) | −22.5014 | −0.983918 | −0.491959 | − | 0.870618i | \(-0.663719\pi\) | ||||
−0.491959 | + | 0.870618i | \(0.663719\pi\) | |||||||
\(524\) | 2.29761 | 0.100372 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.3232 | 1.01694 | ||||||||
\(527\) | −6.88203 | −0.299786 | ||||||||
\(528\) | −14.3174 | −0.623085 | ||||||||
\(529\) | 46.2928 | 2.01273 | ||||||||
\(530\) | −12.1936 | −0.529655 | ||||||||
\(531\) | 9.28053 | 0.402741 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.18902 | 0.138132 | ||||||||
\(534\) | 13.1471 | 0.568930 | ||||||||
\(535\) | −25.9990 | −1.12403 | ||||||||
\(536\) | 18.4158 | 0.795440 | ||||||||
\(537\) | −14.3925 | −0.621082 | ||||||||
\(538\) | 14.7334 | 0.635204 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.757219 | 0.0325855 | ||||||||
\(541\) | −15.6936 | −0.674720 | −0.337360 | − | 0.941376i | \(-0.609534\pi\) | ||||
−0.337360 | + | 0.941376i | \(0.609534\pi\) | |||||||
\(542\) | 28.8787 | 1.24045 | ||||||||
\(543\) | −10.9137 | −0.468351 | ||||||||
\(544\) | 15.7634 | 0.675850 | ||||||||
\(545\) | 11.6936 | 0.500900 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.27073 | 0.396388 | 0.198194 | − | 0.980163i | \(-0.436492\pi\) | ||||
0.198194 | + | 0.980163i | \(0.436492\pi\) | |||||||
\(548\) | −8.71219 | −0.372166 | ||||||||
\(549\) | −11.2178 | −0.478764 | ||||||||
\(550\) | −11.4892 | −0.489899 | ||||||||
\(551\) | −64.8127 | −2.76111 | ||||||||
\(552\) | 25.3445 | 1.07873 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −36.4276 | −1.54766 | ||||||||
\(555\) | −6.32190 | −0.268350 | ||||||||
\(556\) | 1.18331 | 0.0501837 | ||||||||
\(557\) | −5.25651 | −0.222725 | −0.111363 | − | 0.993780i | \(-0.535522\pi\) | ||||
−0.111363 | + | 0.993780i | \(0.535522\pi\) | |||||||
\(558\) | −1.30466 | −0.0552307 | ||||||||
\(559\) | 12.9345 | 0.547071 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.0144 | −1.35165 | ||||||||
\(562\) | −18.7189 | −0.789608 | ||||||||
\(563\) | 32.3319 | 1.36263 | 0.681313 | − | 0.731992i | \(-0.261409\pi\) | ||||
0.681313 | + | 0.731992i | \(0.261409\pi\) | |||||||
\(564\) | −0.414011 | −0.0174330 | ||||||||
\(565\) | −2.38096 | −0.100168 | ||||||||
\(566\) | −13.2804 | −0.558219 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 30.2642 | 1.26986 | ||||||||
\(569\) | 26.4828 | 1.11022 | 0.555109 | − | 0.831777i | \(-0.312676\pi\) | ||||
0.555109 | + | 0.831777i | \(0.312676\pi\) | |||||||
\(570\) | 18.3648 | 0.769215 | ||||||||
\(571\) | −20.4141 | −0.854304 | −0.427152 | − | 0.904180i | \(-0.640483\pi\) | ||||
−0.427152 | + | 0.904180i | \(0.640483\pi\) | |||||||
\(572\) | 6.63485 | 0.277417 | ||||||||
\(573\) | −2.59146 | −0.108260 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.7582 | 0.657161 | ||||||||
\(576\) | 8.90089 | 0.370870 | ||||||||
\(577\) | 19.1030 | 0.795267 | 0.397633 | − | 0.917544i | \(-0.369832\pi\) | ||||
0.397633 | + | 0.917544i | \(0.369832\pi\) | |||||||
\(578\) | −33.4556 | −1.39157 | ||||||||
\(579\) | 15.2810 | 0.635058 | ||||||||
\(580\) | 5.90296 | 0.245107 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.1601 | 0.586953 | ||||||||
\(583\) | −26.7348 | −1.10724 | ||||||||
\(584\) | 11.4416 | 0.473457 | ||||||||
\(585\) | 5.62114 | 0.232406 | ||||||||
\(586\) | 40.9117 | 1.69005 | ||||||||
\(587\) | −40.4928 | −1.67132 | −0.835658 | − | 0.549251i | \(-0.814913\pi\) | ||||
−0.835658 | + | 0.549251i | \(0.814913\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.65571 | 0.356652 | ||||||||
\(590\) | −20.4997 | −0.843957 | ||||||||
\(591\) | −14.9063 | −0.613161 | ||||||||
\(592\) | −10.6029 | −0.435777 | ||||||||
\(593\) | 25.7064 | 1.05563 | 0.527817 | − | 0.849358i | \(-0.323011\pi\) | ||||
0.527817 | + | 0.849358i | \(0.323011\pi\) | |||||||
\(594\) | −6.06913 | −0.249019 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.09496 | −0.167736 | ||||||||
\(597\) | −3.57408 | −0.146277 | ||||||||
\(598\) | 33.2666 | 1.36037 | ||||||||
\(599\) | −33.6227 | −1.37378 | −0.686892 | − | 0.726759i | \(-0.741026\pi\) | ||||
−0.686892 | + | 0.726759i | \(0.741026\pi\) | |||||||
\(600\) | 5.76370 | 0.235302 | ||||||||
\(601\) | −28.5731 | −1.16552 | −0.582760 | − | 0.812644i | \(-0.698027\pi\) | ||||
−0.582760 | + | 0.812644i | \(0.698027\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.04854 | 0.246315 | ||||||||
\(604\) | 2.44402 | 0.0994456 | ||||||||
\(605\) | 21.9543 | 0.892567 | ||||||||
\(606\) | −20.2128 | −0.821087 | ||||||||
\(607\) | −4.85008 | −0.196859 | −0.0984293 | − | 0.995144i | \(-0.531382\pi\) | ||||
−0.0984293 | + | 0.995144i | \(0.531382\pi\) | |||||||
\(608\) | −19.8260 | −0.804052 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.7788 | 1.00327 | ||||||||
\(611\) | −3.07337 | −0.124335 | ||||||||
\(612\) | 2.83975 | 0.114790 | ||||||||
\(613\) | 38.6074 | 1.55934 | 0.779668 | − | 0.626193i | \(-0.215388\pi\) | ||||
0.779668 | + | 0.626193i | \(0.215388\pi\) | |||||||
\(614\) | 18.1965 | 0.734351 | ||||||||
\(615\) | −1.76265 | −0.0710771 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.33494 | 0.134260 | 0.0671298 | − | 0.997744i | \(-0.478616\pi\) | ||||
0.0671298 | + | 0.997744i | \(0.478616\pi\) | |||||||
\(618\) | 18.7931 | 0.755969 | ||||||||
\(619\) | −12.7195 | −0.511239 | −0.255620 | − | 0.966777i | \(-0.582279\pi\) | ||||
−0.255620 | + | 0.966777i | \(0.582279\pi\) | |||||||
\(620\) | −0.788338 | −0.0316604 | ||||||||
\(621\) | 8.32423 | 0.334040 | ||||||||
\(622\) | −3.86482 | −0.154965 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.42761 | 0.377406 | ||||||||
\(625\) | −11.9511 | −0.478045 | ||||||||
\(626\) | 10.4888 | 0.419217 | ||||||||
\(627\) | 40.2653 | 1.60804 | ||||||||
\(628\) | −4.68766 | −0.187058 | ||||||||
\(629\) | −23.7086 | −0.945325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.7041 | 0.465934 | 0.232967 | − | 0.972485i | \(-0.425157\pi\) | ||||
0.232967 | + | 0.972485i | \(0.425157\pi\) | |||||||
\(632\) | −41.9973 | −1.67056 | ||||||||
\(633\) | −1.16912 | −0.0464684 | ||||||||
\(634\) | −30.6332 | −1.21660 | ||||||||
\(635\) | −16.1506 | −0.640917 | ||||||||
\(636\) | 2.37143 | 0.0940335 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −47.3124 | −1.87312 | ||||||||
\(639\) | 9.94007 | 0.393223 | ||||||||
\(640\) | −11.2545 | −0.444871 | ||||||||
\(641\) | −26.0873 | −1.03039 | −0.515193 | − | 0.857074i | \(-0.672280\pi\) | ||||
−0.515193 | + | 0.857074i | \(0.672280\pi\) | |||||||
\(642\) | −18.4840 | −0.729504 | ||||||||
\(643\) | 29.1704 | 1.15037 | 0.575183 | − | 0.818025i | \(-0.304931\pi\) | ||||
0.575183 | + | 0.818025i | \(0.304931\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.14924 | −0.281501 | ||||||||
\(646\) | 68.8722 | 2.70974 | ||||||||
\(647\) | 23.9403 | 0.941190 | 0.470595 | − | 0.882349i | \(-0.344039\pi\) | ||||
0.470595 | + | 0.882349i | \(0.344039\pi\) | |||||||
\(648\) | 3.04466 | 0.119606 | ||||||||
\(649\) | −44.9461 | −1.76429 | ||||||||
\(650\) | 7.56529 | 0.296735 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.15976 | 0.0454198 | ||||||||
\(653\) | −2.94297 | −0.115167 | −0.0575837 | − | 0.998341i | \(-0.518340\pi\) | ||||
−0.0575837 | + | 0.998341i | \(0.518340\pi\) | |||||||
\(654\) | 8.31359 | 0.325087 | ||||||||
\(655\) | −9.42736 | −0.368357 | ||||||||
\(656\) | −2.95627 | −0.115423 | ||||||||
\(657\) | 3.75792 | 0.146611 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.3049 | 0.479330 | 0.239665 | − | 0.970856i | \(-0.422962\pi\) | ||||
0.239665 | + | 0.970856i | \(0.422962\pi\) | |||||||
\(660\) | −3.66725 | −0.142748 | ||||||||
\(661\) | 14.4635 | 0.562565 | 0.281283 | − | 0.959625i | \(-0.409240\pi\) | ||||
0.281283 | + | 0.959625i | \(0.409240\pi\) | |||||||
\(662\) | 21.5998 | 0.839499 | ||||||||
\(663\) | 21.0806 | 0.818703 | ||||||||
\(664\) | −24.6956 | −0.958375 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.49456 | −0.174161 | ||||||||
\(667\) | 64.8922 | 2.51264 | ||||||||
\(668\) | −4.67437 | −0.180857 | ||||||||
\(669\) | −1.28838 | −0.0498117 | ||||||||
\(670\) | −13.3605 | −0.516163 | ||||||||
\(671\) | 54.3284 | 2.09733 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.1510 | 0.584028 | 0.292014 | − | 0.956414i | \(-0.405675\pi\) | ||||
0.292014 | + | 0.956414i | \(0.405675\pi\) | |||||||
\(674\) | 15.3736 | 0.592169 | ||||||||
\(675\) | 1.89305 | 0.0728635 | ||||||||
\(676\) | 1.21581 | 0.0467618 | ||||||||
\(677\) | −1.19895 | −0.0460794 | −0.0230397 | − | 0.999735i | \(-0.507334\pi\) | ||||
−0.0230397 | + | 0.999735i | \(0.507334\pi\) | |||||||
\(678\) | −1.69274 | −0.0650095 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −35.4758 | −1.36044 | ||||||||
\(681\) | 24.1040 | 0.923667 | ||||||||
\(682\) | 6.31855 | 0.241950 | ||||||||
\(683\) | 47.9227 | 1.83371 | 0.916855 | − | 0.399219i | \(-0.130719\pi\) | ||||
0.916855 | + | 0.399219i | \(0.130719\pi\) | |||||||
\(684\) | −3.57162 | −0.136564 | ||||||||
\(685\) | 35.7471 | 1.36583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.361413 | 0.0137888 | ||||||||
\(688\) | −11.9905 | −0.457133 | ||||||||
\(689\) | 17.6041 | 0.670663 | ||||||||
\(690\) | −18.3873 | −0.699993 | ||||||||
\(691\) | −20.1592 | −0.766891 | −0.383446 | − | 0.923563i | \(-0.625263\pi\) | ||||
−0.383446 | + | 0.923563i | \(0.625263\pi\) | |||||||
\(692\) | −6.23540 | −0.237034 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.7229 | 1.35602 | ||||||||
\(695\) | −4.85527 | −0.184171 | ||||||||
\(696\) | 23.7349 | 0.899670 | ||||||||
\(697\) | −6.61037 | −0.250386 | ||||||||
\(698\) | −31.9974 | −1.21112 | ||||||||
\(699\) | −0.141975 | −0.00536998 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.4825 | −0.886921 | −0.443461 | − | 0.896294i | \(-0.646249\pi\) | ||||
−0.443461 | + | 0.896294i | \(0.646249\pi\) | |||||||
\(702\) | 3.99635 | 0.150833 | ||||||||
\(703\) | 29.8189 | 1.12464 | ||||||||
\(704\) | −43.1075 | −1.62468 | ||||||||
\(705\) | 1.69873 | 0.0639780 | ||||||||
\(706\) | −17.3774 | −0.654007 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.98682 | 0.149834 | ||||||||
\(709\) | −37.8630 | −1.42197 | −0.710987 | − | 0.703205i | \(-0.751752\pi\) | ||||
−0.710987 | + | 0.703205i | \(0.751752\pi\) | |||||||
\(710\) | −21.9565 | −0.824013 | ||||||||
\(711\) | −13.7937 | −0.517306 | ||||||||
\(712\) | 31.9420 | 1.19708 | ||||||||
\(713\) | −8.66633 | −0.324556 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.2235 | −1.01810 | ||||||||
\(716\) | −6.18287 | −0.231065 | ||||||||
\(717\) | −11.9975 | −0.448056 | ||||||||
\(718\) | −39.4985 | −1.47407 | ||||||||
\(719\) | −11.3752 | −0.424222 | −0.212111 | − | 0.977246i | \(-0.568034\pi\) | ||||
−0.212111 | + | 0.977246i | \(0.568034\pi\) | |||||||
\(720\) | −5.21089 | −0.194198 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −62.8123 | −2.33763 | ||||||||
\(723\) | −1.49883 | −0.0557419 | ||||||||
\(724\) | −4.68841 | −0.174243 | ||||||||
\(725\) | 14.7574 | 0.548077 | ||||||||
\(726\) | 15.6084 | 0.579282 | ||||||||
\(727\) | −16.0406 | −0.594913 | −0.297456 | − | 0.954735i | \(-0.596138\pi\) | ||||
−0.297456 | + | 0.954735i | \(0.596138\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.30083 | −0.307228 | ||||||||
\(731\) | −26.8113 | −0.991654 | ||||||||
\(732\) | −4.81905 | −0.178117 | ||||||||
\(733\) | −51.7349 | −1.91087 | −0.955436 | − | 0.295197i | \(-0.904615\pi\) | ||||
−0.955436 | + | 0.295197i | \(0.904615\pi\) | |||||||
\(734\) | 11.3602 | 0.419312 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.8504 | 0.731694 | ||||||||
\(737\) | −29.2934 | −1.07904 | ||||||||
\(738\) | −1.25316 | −0.0461295 | ||||||||
\(739\) | −6.31420 | −0.232272 | −0.116136 | − | 0.993233i | \(-0.537051\pi\) | ||||
−0.116136 | + | 0.993233i | \(0.537051\pi\) | |||||||
\(740\) | −2.71582 | −0.0998357 | ||||||||
\(741\) | −26.5136 | −0.974002 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.6582 | 0.794562 | 0.397281 | − | 0.917697i | \(-0.369954\pi\) | ||||
0.397281 | + | 0.917697i | \(0.369954\pi\) | |||||||
\(744\) | −3.16979 | −0.116210 | ||||||||
\(745\) | 16.8021 | 0.615580 | ||||||||
\(746\) | −10.3834 | −0.380163 | ||||||||
\(747\) | −8.11111 | −0.296770 | ||||||||
\(748\) | −13.7531 | −0.502862 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −15.2260 | −0.555974 | ||||||||
\(751\) | −44.2185 | −1.61355 | −0.806777 | − | 0.590856i | \(-0.798790\pi\) | ||||
−0.806777 | + | 0.590856i | \(0.798790\pi\) | |||||||
\(752\) | 2.84906 | 0.103895 | ||||||||
\(753\) | 6.61735 | 0.241150 | ||||||||
\(754\) | 31.1539 | 1.13456 | ||||||||
\(755\) | −10.0281 | −0.364959 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.39895 | 0.268919 | 0.134460 | − | 0.990919i | \(-0.457070\pi\) | ||||
0.134460 | + | 0.990919i | \(0.457070\pi\) | |||||||
\(758\) | 26.2064 | 0.951861 | ||||||||
\(759\) | −40.3147 | −1.46333 | ||||||||
\(760\) | 44.6189 | 1.61850 | ||||||||
\(761\) | −19.8652 | −0.720112 | −0.360056 | − | 0.932931i | \(-0.617242\pi\) | ||||
−0.360056 | + | 0.932931i | \(0.617242\pi\) | |||||||
\(762\) | −11.4823 | −0.415959 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.11327 | −0.0402765 | ||||||||
\(765\) | −11.6518 | −0.421272 | ||||||||
\(766\) | −5.91712 | −0.213794 | ||||||||
\(767\) | 29.5958 | 1.06864 | ||||||||
\(768\) | 9.80042 | 0.353642 | ||||||||
\(769\) | 39.2767 | 1.41635 | 0.708177 | − | 0.706034i | \(-0.249518\pi\) | ||||
0.708177 | + | 0.706034i | \(0.249518\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.49560 | 0.269947 | ||||||||
\(772\) | 6.56458 | 0.236264 | ||||||||
\(773\) | −47.1966 | −1.69754 | −0.848771 | − | 0.528760i | \(-0.822657\pi\) | ||||
−0.848771 | + | 0.528760i | \(0.822657\pi\) | |||||||
\(774\) | −5.08276 | −0.182696 | ||||||||
\(775\) | −1.97085 | −0.0707949 | ||||||||
\(776\) | 34.4031 | 1.23500 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.8769 | −1.21455 | ||||||||
\(779\) | 8.31403 | 0.297881 | ||||||||
\(780\) | 2.41479 | 0.0864632 | ||||||||
\(781\) | −48.1403 | −1.72260 | ||||||||
\(782\) | −68.9567 | −2.46589 | ||||||||
\(783\) | 7.79558 | 0.278591 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.2340 | 0.686491 | ||||||||
\(786\) | −6.70238 | −0.239066 | ||||||||
\(787\) | 13.5666 | 0.483598 | 0.241799 | − | 0.970326i | \(-0.422262\pi\) | ||||
0.241799 | + | 0.970326i | \(0.422262\pi\) | |||||||
\(788\) | −6.40358 | −0.228118 | ||||||||
\(789\) | 18.6115 | 0.662588 | ||||||||
\(790\) | 30.4688 | 1.08403 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.7455 | −0.523958 | ||||||||
\(793\) | −35.7738 | −1.27036 | ||||||||
\(794\) | −36.2225 | −1.28549 | ||||||||
\(795\) | −9.73025 | −0.345097 | ||||||||
\(796\) | −1.53539 | −0.0544204 | ||||||||
\(797\) | −11.8546 | −0.419911 | −0.209955 | − | 0.977711i | \(-0.567332\pi\) | ||||
−0.209955 | + | 0.977711i | \(0.567332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.37065 | 0.225377 | ||||||||
\(800\) | 4.51425 | 0.159603 | ||||||||
\(801\) | 10.4911 | 0.370686 | ||||||||
\(802\) | −44.6887 | −1.57801 | ||||||||
\(803\) | −18.1998 | −0.642258 | ||||||||
\(804\) | 2.59839 | 0.0916382 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.16059 | −0.146550 | ||||||||
\(807\) | 11.7570 | 0.413867 | ||||||||
\(808\) | −49.1087 | −1.72764 | ||||||||
\(809\) | 15.5888 | 0.548072 | 0.274036 | − | 0.961719i | \(-0.411641\pi\) | ||||
0.274036 | + | 0.961719i | \(0.411641\pi\) | |||||||
\(810\) | −2.20889 | −0.0776124 | ||||||||
\(811\) | −18.1848 | −0.638556 | −0.319278 | − | 0.947661i | \(-0.603440\pi\) | ||||
−0.319278 | + | 0.947661i | \(0.603440\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.0447 | 0.808213 | ||||||||
\(814\) | 21.7674 | 0.762947 | ||||||||
\(815\) | −4.75863 | −0.166687 | ||||||||
\(816\) | −19.5421 | −0.684109 | ||||||||
\(817\) | 33.7213 | 1.17976 | ||||||||
\(818\) | −2.13086 | −0.0745038 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.757219 | −0.0264432 | ||||||||
\(821\) | 2.30128 | 0.0803152 | 0.0401576 | − | 0.999193i | \(-0.487214\pi\) | ||||
0.0401576 | + | 0.999193i | \(0.487214\pi\) | |||||||
\(822\) | 25.4144 | 0.886429 | ||||||||
\(823\) | −12.7773 | −0.445389 | −0.222694 | − | 0.974888i | \(-0.571485\pi\) | ||||
−0.222694 | + | 0.974888i | \(0.571485\pi\) | |||||||
\(824\) | 45.6595 | 1.59062 | ||||||||
\(825\) | −9.16814 | −0.319194 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2044 | −0.389615 | −0.194808 | − | 0.980841i | \(-0.562408\pi\) | ||||
−0.194808 | + | 0.980841i | \(0.562408\pi\) | |||||||
\(828\) | 3.57601 | 0.124275 | ||||||||
\(829\) | 39.4628 | 1.37060 | 0.685300 | − | 0.728261i | \(-0.259671\pi\) | ||||
0.685300 | + | 0.728261i | \(0.259671\pi\) | |||||||
\(830\) | 17.9165 | 0.621892 | ||||||||
\(831\) | −29.0686 | −1.00838 | ||||||||
\(832\) | 28.3851 | 0.984077 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.45185 | −0.119528 | ||||||||
\(835\) | 19.1795 | 0.663733 | ||||||||
\(836\) | 17.2976 | 0.598249 | ||||||||
\(837\) | −1.04110 | −0.0359856 | ||||||||
\(838\) | −15.8515 | −0.547582 | ||||||||
\(839\) | −36.6572 | −1.26555 | −0.632773 | − | 0.774338i | \(-0.718083\pi\) | ||||
−0.632773 | + | 0.774338i | \(0.718083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.7711 | 1.09555 | ||||||||
\(842\) | −40.7794 | −1.40535 | ||||||||
\(843\) | −14.9373 | −0.514469 | ||||||||
\(844\) | −0.502243 | −0.0172879 | ||||||||
\(845\) | −4.98859 | −0.171613 | ||||||||
\(846\) | 1.20771 | 0.0415221 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −16.3193 | −0.560407 | ||||||||
\(849\) | −10.5976 | −0.363707 | ||||||||
\(850\) | −15.6817 | −0.537879 | ||||||||
\(851\) | −29.8555 | −1.02343 | ||||||||
\(852\) | 4.27015 | 0.146293 | ||||||||
\(853\) | 31.0819 | 1.06422 | 0.532112 | − | 0.846674i | \(-0.321399\pi\) | ||||
0.532112 | + | 0.846674i | \(0.321399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.6548 | 0.501182 | ||||||||
\(856\) | −44.9085 | −1.53494 | ||||||||
\(857\) | 53.1841 | 1.81674 | 0.908368 | − | 0.418173i | \(-0.137329\pi\) | ||||
0.908368 | + | 0.418173i | \(0.137329\pi\) | |||||||
\(858\) | −19.3546 | −0.660754 | ||||||||
\(859\) | −12.7611 | −0.435404 | −0.217702 | − | 0.976015i | \(-0.569856\pi\) | ||||
−0.217702 | + | 0.976015i | \(0.569856\pi\) | |||||||
\(860\) | −3.07124 | −0.104728 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.1585 | 1.02720 | ||||||||
\(863\) | −9.99019 | −0.340070 | −0.170035 | − | 0.985438i | \(-0.554388\pi\) | ||||
−0.170035 | + | 0.985438i | \(0.554388\pi\) | |||||||
\(864\) | 2.38465 | 0.0811273 | ||||||||
\(865\) | 25.5845 | 0.869900 | ||||||||
\(866\) | −3.18292 | −0.108160 | ||||||||
\(867\) | −26.6970 | −0.906678 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66.8039 | 2.26617 | ||||||||
\(870\) | −17.2196 | −0.583798 | ||||||||
\(871\) | 19.2889 | 0.653580 | ||||||||
\(872\) | 20.1986 | 0.684011 | ||||||||
\(873\) | 11.2995 | 0.382430 | ||||||||
\(874\) | 86.7286 | 2.93364 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.61437 | 0.0545444 | ||||||||
\(877\) | 33.4455 | 1.12938 | 0.564688 | − | 0.825305i | \(-0.308997\pi\) | ||||
0.564688 | + | 0.825305i | \(0.308997\pi\) | |||||||
\(878\) | −15.8892 | −0.536234 | ||||||||
\(879\) | 32.6469 | 1.10115 | ||||||||
\(880\) | 25.2366 | 0.850727 | ||||||||
\(881\) | 42.8300 | 1.44298 | 0.721489 | − | 0.692425i | \(-0.243458\pi\) | ||||
0.721489 | + | 0.692425i | \(0.243458\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.3926 | −1.19106 | −0.595529 | − | 0.803334i | \(-0.703057\pi\) | ||||
−0.595529 | + | 0.803334i | \(0.703057\pi\) | |||||||
\(884\) | 9.05602 | 0.304587 | ||||||||
\(885\) | −16.3584 | −0.549881 | ||||||||
\(886\) | −13.0607 | −0.438783 | ||||||||
\(887\) | −3.59794 | −0.120807 | −0.0604035 | − | 0.998174i | \(-0.519239\pi\) | ||||
−0.0604035 | + | 0.998174i | \(0.519239\pi\) | |||||||
\(888\) | −10.9199 | −0.366449 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −23.1738 | −0.776786 | ||||||||
\(891\) | −4.84306 | −0.162249 | ||||||||
\(892\) | −0.553475 | −0.0185317 | ||||||||
\(893\) | −8.01252 | −0.268129 | ||||||||
\(894\) | 11.9454 | 0.399515 | ||||||||
\(895\) | 25.3690 | 0.847992 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.5461 | 0.886350 | ||||||||
\(898\) | −45.3224 | −1.51243 | ||||||||
\(899\) | −8.11595 | −0.270682 | ||||||||
\(900\) | 0.813234 | 0.0271078 | ||||||||
\(901\) | −36.4908 | −1.21568 | ||||||||
\(902\) | 6.06913 | 0.202080 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.11268 | −0.136786 | ||||||||
\(905\) | 19.2371 | 0.639462 | ||||||||
\(906\) | −7.12946 | −0.236860 | ||||||||
\(907\) | −17.9810 | −0.597050 | −0.298525 | − | 0.954402i | \(-0.596495\pi\) | ||||
−0.298525 | + | 0.954402i | \(0.596495\pi\) | |||||||
\(908\) | 10.3548 | 0.343637 | ||||||||
\(909\) | −16.1294 | −0.534979 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.4282 | 1.50510 | 0.752552 | − | 0.658533i | \(-0.228823\pi\) | ||||
0.752552 | + | 0.658533i | \(0.228823\pi\) | |||||||
\(912\) | 24.5785 | 0.813877 | ||||||||
\(913\) | 39.2826 | 1.30006 | ||||||||
\(914\) | 4.32056 | 0.142911 | ||||||||
\(915\) | 19.7731 | 0.653678 | ||||||||
\(916\) | 0.155259 | 0.00512991 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.28385 | −0.273408 | ||||||||
\(919\) | 17.0040 | 0.560910 | 0.280455 | − | 0.959867i | \(-0.409515\pi\) | ||||
0.280455 | + | 0.959867i | \(0.409515\pi\) | |||||||
\(920\) | −44.6736 | −1.47284 | ||||||||
\(921\) | 14.5205 | 0.478467 | ||||||||
\(922\) | −49.2066 | −1.62053 | ||||||||
\(923\) | 31.6991 | 1.04339 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.78957 | −0.223240 | ||||||||
\(926\) | −21.4435 | −0.704676 | ||||||||
\(927\) | 14.9966 | 0.492552 | ||||||||
\(928\) | 18.5897 | 0.610237 | ||||||||
\(929\) | −6.37929 | −0.209298 | −0.104649 | − | 0.994509i | \(-0.533372\pi\) | ||||
−0.104649 | + | 0.994509i | \(0.533372\pi\) | |||||||
\(930\) | 2.29967 | 0.0754090 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.0609909 | −0.00199782 | ||||||||
\(933\) | −3.08406 | −0.100967 | ||||||||
\(934\) | −51.4083 | −1.68213 | ||||||||
\(935\) | 56.4304 | 1.84547 | ||||||||
\(936\) | 9.70950 | 0.317365 | ||||||||
\(937\) | 25.1791 | 0.822565 | 0.411282 | − | 0.911508i | \(-0.365081\pi\) | ||||
0.411282 | + | 0.911508i | \(0.365081\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.36990 | 0.273141 | ||||||||
\(940\) | 0.729758 | 0.0238021 | ||||||||
\(941\) | −23.3195 | −0.760195 | −0.380097 | − | 0.924946i | \(-0.624110\pi\) | ||||
−0.380097 | + | 0.924946i | \(0.624110\pi\) | |||||||
\(942\) | 13.6744 | 0.445537 | ||||||||
\(943\) | −8.32423 | −0.271074 | ||||||||
\(944\) | −27.4358 | −0.892958 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.6161 | 0.800338 | ||||||||
\(947\) | 31.0089 | 1.00765 | 0.503827 | − | 0.863805i | \(-0.331925\pi\) | ||||
0.503827 | + | 0.863805i | \(0.331925\pi\) | |||||||
\(948\) | −5.92565 | −0.192456 | ||||||||
\(949\) | 11.9841 | 0.389020 | ||||||||
\(950\) | 19.7233 | 0.639909 | ||||||||
\(951\) | −24.4448 | −0.792676 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.2352 | 1.04420 | 0.522101 | − | 0.852884i | \(-0.325149\pi\) | ||||
0.522101 | + | 0.852884i | \(0.325149\pi\) | |||||||
\(954\) | −6.91773 | −0.223970 | ||||||||
\(955\) | 4.56785 | 0.147812 | ||||||||
\(956\) | −5.15401 | −0.166693 | ||||||||
\(957\) | −37.7545 | −1.22043 | ||||||||
\(958\) | 1.75035 | 0.0565513 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −15.6892 | −0.506367 | ||||||||
\(961\) | −29.9161 | −0.965036 | ||||||||
\(962\) | −14.3332 | −0.462122 | ||||||||
\(963\) | −14.7499 | −0.475309 | ||||||||
\(964\) | −0.643880 | −0.0207380 | ||||||||
\(965\) | −26.9352 | −0.867075 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.3185 | 1.29656 | 0.648279 | − | 0.761403i | \(-0.275489\pi\) | ||||
0.648279 | + | 0.761403i | \(0.275489\pi\) | |||||||
\(968\) | 37.9220 | 1.21886 | ||||||||
\(969\) | 54.9588 | 1.76553 | ||||||||
\(970\) | −24.9593 | −0.801395 | ||||||||
\(971\) | −32.0847 | −1.02965 | −0.514824 | − | 0.857296i | \(-0.672143\pi\) | ||||
−0.514824 | + | 0.857296i | \(0.672143\pi\) | |||||||
\(972\) | 0.429590 | 0.0137791 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −38.5128 | −1.23403 | ||||||||
\(975\) | 6.03697 | 0.193338 | ||||||||
\(976\) | 33.1628 | 1.06152 | ||||||||
\(977\) | −57.6281 | −1.84369 | −0.921844 | − | 0.387562i | \(-0.873317\pi\) | ||||
−0.921844 | + | 0.387562i | \(0.873317\pi\) | |||||||
\(978\) | −3.38315 | −0.108181 | ||||||||
\(979\) | −50.8092 | −1.62387 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.63410 | 0.211811 | ||||||||
\(982\) | −29.7991 | −0.950929 | ||||||||
\(983\) | 3.19824 | 0.102008 | 0.0510040 | − | 0.998698i | \(-0.483758\pi\) | ||||
0.0510040 | + | 0.998698i | \(0.483758\pi\) | |||||||
\(984\) | −3.04466 | −0.0970604 | ||||||||
\(985\) | 26.2746 | 0.837178 | ||||||||
\(986\) | −64.5775 | −2.05657 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.3900 | −0.362363 | ||||||||
\(989\) | −33.7627 | −1.07359 | ||||||||
\(990\) | 10.6978 | 0.339998 | ||||||||
\(991\) | 59.2649 | 1.88261 | 0.941306 | − | 0.337553i | \(-0.109599\pi\) | ||||
0.941306 | + | 0.337553i | \(0.109599\pi\) | |||||||
\(992\) | −2.48265 | −0.0788241 | ||||||||
\(993\) | 17.2362 | 0.546976 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.29987 | 0.199719 | ||||||||
\(996\) | −3.48445 | −0.110409 | ||||||||
\(997\) | 37.9055 | 1.20048 | 0.600239 | − | 0.799820i | \(-0.295072\pi\) | ||||
0.600239 | + | 0.799820i | \(0.295072\pi\) | |||||||
\(998\) | 10.1453 | 0.321145 | ||||||||
\(999\) | −3.58658 | −0.113474 |
(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 | 6027.2.a.bn.1.7 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.7 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.7 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.7 | yes | 24 | 7.6 | odd | 2 |