Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 637) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.565505 | 0.399873 | 0.199936 | − | 0.979809i | \(-0.435926\pi\) | ||||
0.199936 | + | 0.979809i | \(0.435926\pi\) | |||||||
\(3\) | −3.09111 | −1.78466 | −0.892328 | − | 0.451388i | \(-0.850929\pi\) | ||||
−0.892328 | + | 0.451388i | \(0.850929\pi\) | |||||||
\(4\) | −1.68020 | −0.840102 | ||||||||
\(5\) | −1.80514 | −0.807283 | −0.403642 | − | 0.914917i | \(-0.632256\pi\) | ||||
−0.403642 | + | 0.914917i | \(0.632256\pi\) | |||||||
\(6\) | −1.74804 | −0.713635 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.08118 | −0.735806 | ||||||||
\(9\) | 6.55499 | 2.18500 | ||||||||
\(10\) | −1.02082 | −0.322811 | ||||||||
\(11\) | −3.58433 | −1.08072 | −0.540358 | − | 0.841436i | \(-0.681711\pi\) | ||||
−0.540358 | + | 0.841436i | \(0.681711\pi\) | |||||||
\(12\) | 5.19370 | 1.49929 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.57989 | 1.44072 | ||||||||
\(16\) | 2.18349 | 0.545873 | ||||||||
\(17\) | −6.14919 | −1.49140 | −0.745699 | − | 0.666283i | \(-0.767884\pi\) | ||||
−0.745699 | + | 0.666283i | \(0.767884\pi\) | |||||||
\(18\) | 3.70688 | 0.873720 | ||||||||
\(19\) | 2.51075 | 0.576006 | 0.288003 | − | 0.957629i | \(-0.407009\pi\) | ||||
0.288003 | + | 0.957629i | \(0.407009\pi\) | |||||||
\(20\) | 3.03300 | 0.678200 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.02696 | −0.432148 | ||||||||
\(23\) | 4.13185 | 0.861550 | 0.430775 | − | 0.902459i | \(-0.358240\pi\) | ||||
0.430775 | + | 0.902459i | \(0.358240\pi\) | |||||||
\(24\) | 6.43315 | 1.31316 | ||||||||
\(25\) | −1.74147 | −0.348294 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10.9889 | −2.11481 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.11133 | 0.949151 | 0.474576 | − | 0.880215i | \(-0.342602\pi\) | ||||
0.474576 | + | 0.880215i | \(0.342602\pi\) | |||||||
\(30\) | 3.15546 | 0.576106 | ||||||||
\(31\) | −4.55318 | −0.817775 | −0.408888 | − | 0.912585i | \(-0.634083\pi\) | ||||
−0.408888 | + | 0.912585i | \(0.634083\pi\) | |||||||
\(32\) | 5.39713 | 0.954086 | ||||||||
\(33\) | 11.0796 | 1.92870 | ||||||||
\(34\) | −3.47740 | −0.596369 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.0137 | −1.83562 | ||||||||
\(37\) | −11.7215 | −1.92700 | −0.963500 | − | 0.267708i | \(-0.913734\pi\) | ||||
−0.963500 | + | 0.267708i | \(0.913734\pi\) | |||||||
\(38\) | 1.41984 | 0.230329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.75681 | 0.594004 | ||||||||
\(41\) | 1.86640 | 0.291483 | 0.145742 | − | 0.989323i | \(-0.453443\pi\) | ||||
0.145742 | + | 0.989323i | \(0.453443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.42314 | −0.217026 | −0.108513 | − | 0.994095i | \(-0.534609\pi\) | ||||
−0.108513 | + | 0.994095i | \(0.534609\pi\) | |||||||
\(44\) | 6.02240 | 0.907911 | ||||||||
\(45\) | −11.8327 | −1.76391 | ||||||||
\(46\) | 2.33658 | 0.344510 | ||||||||
\(47\) | −8.86595 | −1.29323 | −0.646616 | − | 0.762816i | \(-0.723816\pi\) | ||||
−0.646616 | + | 0.762816i | \(0.723816\pi\) | |||||||
\(48\) | −6.74942 | −0.974195 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.984810 | −0.139273 | ||||||||
\(51\) | 19.0078 | 2.66163 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.02920 | 0.278732 | 0.139366 | − | 0.990241i | \(-0.455494\pi\) | ||||
0.139366 | + | 0.990241i | \(0.455494\pi\) | |||||||
\(54\) | −6.21427 | −0.845655 | ||||||||
\(55\) | 6.47021 | 0.872443 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.76102 | −1.02797 | ||||||||
\(58\) | 2.89049 | 0.379540 | ||||||||
\(59\) | −9.10752 | −1.18570 | −0.592849 | − | 0.805314i | \(-0.701997\pi\) | ||||
−0.592849 | + | 0.805314i | \(0.701997\pi\) | |||||||
\(60\) | −9.37536 | −1.21035 | ||||||||
\(61\) | −5.47841 | −0.701438 | −0.350719 | − | 0.936481i | \(-0.614063\pi\) | ||||
−0.350719 | + | 0.936481i | \(0.614063\pi\) | |||||||
\(62\) | −2.57485 | −0.327006 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.31488 | −0.164360 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.26555 | 0.771236 | ||||||||
\(67\) | 7.02055 | 0.857697 | 0.428849 | − | 0.903376i | \(-0.358919\pi\) | ||||
0.428849 | + | 0.903376i | \(0.358919\pi\) | |||||||
\(68\) | 10.3319 | 1.25293 | ||||||||
\(69\) | −12.7720 | −1.53757 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.49410 | −0.533351 | −0.266676 | − | 0.963786i | \(-0.585925\pi\) | ||||
−0.266676 | + | 0.963786i | \(0.585925\pi\) | |||||||
\(72\) | −13.6421 | −1.60773 | ||||||||
\(73\) | −9.35564 | −1.09499 | −0.547497 | − | 0.836807i | \(-0.684419\pi\) | ||||
−0.547497 | + | 0.836807i | \(0.684419\pi\) | |||||||
\(74\) | −6.62856 | −0.770555 | ||||||||
\(75\) | 5.38308 | 0.621584 | ||||||||
\(76\) | −4.21858 | −0.483904 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.20970 | 0.586137 | 0.293069 | − | 0.956091i | \(-0.405324\pi\) | ||||
0.293069 | + | 0.956091i | \(0.405324\pi\) | |||||||
\(80\) | −3.94151 | −0.440674 | ||||||||
\(81\) | 14.3029 | 1.58921 | ||||||||
\(82\) | 1.05546 | 0.116556 | ||||||||
\(83\) | −9.42491 | −1.03452 | −0.517259 | − | 0.855829i | \(-0.673048\pi\) | ||||
−0.517259 | + | 0.855829i | \(0.673048\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.1001 | 1.20398 | ||||||||
\(86\) | −0.804791 | −0.0867829 | ||||||||
\(87\) | −15.7997 | −1.69391 | ||||||||
\(88\) | 7.45961 | 0.795197 | ||||||||
\(89\) | −0.355648 | −0.0376986 | −0.0188493 | − | 0.999822i | \(-0.506000\pi\) | ||||
−0.0188493 | + | 0.999822i | \(0.506000\pi\) | |||||||
\(90\) | −6.69144 | −0.705340 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.94235 | −0.723790 | ||||||||
\(93\) | 14.0744 | 1.45945 | ||||||||
\(94\) | −5.01374 | −0.517128 | ||||||||
\(95\) | −4.53226 | −0.465000 | ||||||||
\(96\) | −16.6831 | −1.70272 | ||||||||
\(97\) | −10.6035 | −1.07663 | −0.538313 | − | 0.842745i | \(-0.680938\pi\) | ||||
−0.538313 | + | 0.842745i | \(0.680938\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −23.4952 | −2.36136 | ||||||||
\(100\) | 2.92602 | 0.292602 | ||||||||
\(101\) | 3.42508 | 0.340808 | 0.170404 | − | 0.985374i | \(-0.445493\pi\) | ||||
0.170404 | + | 0.985374i | \(0.445493\pi\) | |||||||
\(102\) | 10.7490 | 1.06431 | ||||||||
\(103\) | −12.9558 | −1.27658 | −0.638288 | − | 0.769798i | \(-0.720357\pi\) | ||||
−0.638288 | + | 0.769798i | \(0.720357\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.14752 | 0.111457 | ||||||||
\(107\) | −18.1696 | −1.75653 | −0.878263 | − | 0.478179i | \(-0.841297\pi\) | ||||
−0.878263 | + | 0.478179i | \(0.841297\pi\) | |||||||
\(108\) | 18.4635 | 1.77666 | ||||||||
\(109\) | −13.9294 | −1.33420 | −0.667098 | − | 0.744970i | \(-0.732464\pi\) | ||||
−0.667098 | + | 0.744970i | \(0.732464\pi\) | |||||||
\(110\) | 3.65894 | 0.348866 | ||||||||
\(111\) | 36.2324 | 3.43903 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.1281 | −0.952770 | −0.476385 | − | 0.879237i | \(-0.658053\pi\) | ||||
−0.476385 | + | 0.879237i | \(0.658053\pi\) | |||||||
\(114\) | −4.38890 | −0.411058 | ||||||||
\(115\) | −7.45857 | −0.695515 | ||||||||
\(116\) | −8.58808 | −0.797383 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.15035 | −0.474128 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −11.6127 | −1.06009 | ||||||||
\(121\) | 1.84739 | 0.167945 | ||||||||
\(122\) | −3.09807 | −0.280486 | ||||||||
\(123\) | −5.76927 | −0.520197 | ||||||||
\(124\) | 7.65027 | 0.687014 | ||||||||
\(125\) | 12.1693 | 1.08845 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.10219 | 0.541482 | 0.270741 | − | 0.962652i | \(-0.412731\pi\) | ||||
0.270741 | + | 0.962652i | \(0.412731\pi\) | |||||||
\(128\) | −11.5378 | −1.01981 | ||||||||
\(129\) | 4.39908 | 0.387317 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.97266 | −0.521833 | −0.260917 | − | 0.965361i | \(-0.584025\pi\) | ||||
−0.260917 | + | 0.965361i | \(0.584025\pi\) | |||||||
\(132\) | −18.6159 | −1.62031 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.97016 | 0.342970 | ||||||||
\(135\) | 19.8365 | 1.70725 | ||||||||
\(136\) | 12.7975 | 1.09738 | ||||||||
\(137\) | −3.60737 | −0.308198 | −0.154099 | − | 0.988055i | \(-0.549247\pi\) | ||||
−0.154099 | + | 0.988055i | \(0.549247\pi\) | |||||||
\(138\) | −7.22265 | −0.614833 | ||||||||
\(139\) | −12.9167 | −1.09558 | −0.547789 | − | 0.836617i | \(-0.684530\pi\) | ||||
−0.547789 | + | 0.836617i | \(0.684530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.4057 | 2.30797 | ||||||||
\(142\) | −2.54144 | −0.213273 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 14.3128 | 1.19273 | ||||||||
\(145\) | −9.22668 | −0.766234 | ||||||||
\(146\) | −5.29067 | −0.437859 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 19.6945 | 1.61888 | ||||||||
\(149\) | −2.19416 | −0.179753 | −0.0898763 | − | 0.995953i | \(-0.528647\pi\) | ||||
−0.0898763 | + | 0.995953i | \(0.528647\pi\) | |||||||
\(150\) | 3.04416 | 0.248555 | ||||||||
\(151\) | −1.94893 | −0.158602 | −0.0793009 | − | 0.996851i | \(-0.525269\pi\) | ||||
−0.0793009 | + | 0.996851i | \(0.525269\pi\) | |||||||
\(152\) | −5.22532 | −0.423829 | ||||||||
\(153\) | −40.3078 | −3.25870 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.21913 | 0.660176 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.3508 | −1.46455 | −0.732275 | − | 0.681009i | \(-0.761541\pi\) | ||||
−0.732275 | + | 0.681009i | \(0.761541\pi\) | |||||||
\(158\) | 2.94611 | 0.234380 | ||||||||
\(159\) | −6.27248 | −0.497440 | ||||||||
\(160\) | −9.74257 | −0.770218 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.08836 | 0.635482 | ||||||||
\(163\) | −22.0599 | −1.72786 | −0.863931 | − | 0.503611i | \(-0.832004\pi\) | ||||
−0.863931 | + | 0.503611i | \(0.832004\pi\) | |||||||
\(164\) | −3.13594 | −0.244876 | ||||||||
\(165\) | −20.0002 | −1.55701 | ||||||||
\(166\) | −5.32984 | −0.413676 | ||||||||
\(167\) | 2.83878 | 0.219672 | 0.109836 | − | 0.993950i | \(-0.464967\pi\) | ||||
0.109836 | + | 0.993950i | \(0.464967\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 6.27719 | 0.481439 | ||||||||
\(171\) | 16.4580 | 1.25857 | ||||||||
\(172\) | 2.39116 | 0.182324 | ||||||||
\(173\) | 3.52822 | 0.268246 | 0.134123 | − | 0.990965i | \(-0.457178\pi\) | ||||
0.134123 | + | 0.990965i | \(0.457178\pi\) | |||||||
\(174\) | −8.93483 | −0.677347 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.82635 | −0.589933 | ||||||||
\(177\) | 28.1524 | 2.11606 | ||||||||
\(178\) | −0.201121 | −0.0150746 | ||||||||
\(179\) | −6.69470 | −0.500385 | −0.250193 | − | 0.968196i | \(-0.580494\pi\) | ||||
−0.250193 | + | 0.968196i | \(0.580494\pi\) | |||||||
\(180\) | 19.8813 | 1.48186 | ||||||||
\(181\) | −12.5317 | −0.931476 | −0.465738 | − | 0.884923i | \(-0.654211\pi\) | ||||
−0.465738 | + | 0.884923i | \(0.654211\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.9344 | 1.25183 | ||||||||
\(184\) | −8.59910 | −0.633934 | ||||||||
\(185\) | 21.1589 | 1.55563 | ||||||||
\(186\) | 7.95915 | 0.583593 | ||||||||
\(187\) | 22.0407 | 1.61178 | ||||||||
\(188\) | 14.8966 | 1.08645 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.56302 | −0.185941 | ||||||||
\(191\) | 3.03641 | 0.219707 | 0.109854 | − | 0.993948i | \(-0.464962\pi\) | ||||
0.109854 | + | 0.993948i | \(0.464962\pi\) | |||||||
\(192\) | 4.06444 | 0.293326 | ||||||||
\(193\) | 26.9449 | 1.93954 | 0.969769 | − | 0.244023i | \(-0.0784673\pi\) | ||||
0.969769 | + | 0.244023i | \(0.0784673\pi\) | |||||||
\(194\) | −5.99635 | −0.430513 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.29898 | −0.662525 | −0.331262 | − | 0.943539i | \(-0.607475\pi\) | ||||
−0.331262 | + | 0.943539i | \(0.607475\pi\) | |||||||
\(198\) | −13.2867 | −0.944242 | ||||||||
\(199\) | 17.3848 | 1.23238 | 0.616190 | − | 0.787598i | \(-0.288676\pi\) | ||||
0.616190 | + | 0.787598i | \(0.288676\pi\) | |||||||
\(200\) | 3.62430 | 0.256277 | ||||||||
\(201\) | −21.7013 | −1.53069 | ||||||||
\(202\) | 1.93690 | 0.136280 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −31.9370 | −2.23604 | ||||||||
\(205\) | −3.36912 | −0.235310 | ||||||||
\(206\) | −7.32659 | −0.510468 | ||||||||
\(207\) | 27.0842 | 1.88248 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.99936 | −0.622499 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.8236 | 1.50240 | 0.751199 | − | 0.660075i | \(-0.229476\pi\) | ||||
0.751199 | + | 0.660075i | \(0.229476\pi\) | |||||||
\(212\) | −3.40947 | −0.234163 | ||||||||
\(213\) | 13.8918 | 0.951849 | ||||||||
\(214\) | −10.2750 | −0.702386 | ||||||||
\(215\) | 2.56896 | 0.175202 | ||||||||
\(216\) | 22.8698 | 1.55609 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.87716 | −0.533508 | ||||||||
\(219\) | 28.9194 | 1.95419 | ||||||||
\(220\) | −10.8713 | −0.732941 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 20.4896 | 1.37517 | ||||||||
\(223\) | 1.91187 | 0.128029 | 0.0640143 | − | 0.997949i | \(-0.479610\pi\) | ||||
0.0640143 | + | 0.997949i | \(0.479610\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.4153 | −0.761020 | ||||||||
\(226\) | −5.72749 | −0.380987 | ||||||||
\(227\) | 10.3347 | 0.685939 | 0.342969 | − | 0.939347i | \(-0.388567\pi\) | ||||
0.342969 | + | 0.939347i | \(0.388567\pi\) | |||||||
\(228\) | 13.0401 | 0.863602 | ||||||||
\(229\) | −6.10394 | −0.403360 | −0.201680 | − | 0.979451i | \(-0.564640\pi\) | ||||
−0.201680 | + | 0.979451i | \(0.564640\pi\) | |||||||
\(230\) | −4.21786 | −0.278118 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.6376 | −0.698391 | ||||||||
\(233\) | 7.12776 | 0.466955 | 0.233478 | − | 0.972362i | \(-0.424989\pi\) | ||||
0.233478 | + | 0.972362i | \(0.424989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0043 | 1.04400 | ||||||||
\(236\) | 15.3025 | 0.996107 | ||||||||
\(237\) | −16.1038 | −1.04605 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.32349 | −0.473717 | −0.236859 | − | 0.971544i | \(-0.576118\pi\) | ||||
−0.236859 | + | 0.971544i | \(0.576118\pi\) | |||||||
\(240\) | 12.1837 | 0.786451 | ||||||||
\(241\) | 0.263098 | 0.0169477 | 0.00847383 | − | 0.999964i | \(-0.497303\pi\) | ||||
0.00847383 | + | 0.999964i | \(0.497303\pi\) | |||||||
\(242\) | 1.04471 | 0.0671566 | ||||||||
\(243\) | −11.2453 | −0.721384 | ||||||||
\(244\) | 9.20484 | 0.589280 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.26255 | −0.208013 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.47596 | 0.601724 | ||||||||
\(249\) | 29.1335 | 1.84626 | ||||||||
\(250\) | 6.88180 | 0.435243 | ||||||||
\(251\) | −13.2819 | −0.838347 | −0.419173 | − | 0.907906i | \(-0.637680\pi\) | ||||
−0.419173 | + | 0.907906i | \(0.637680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.8099 | −0.931090 | ||||||||
\(254\) | 3.45082 | 0.216524 | ||||||||
\(255\) | −34.3118 | −2.14869 | ||||||||
\(256\) | −3.89494 | −0.243434 | ||||||||
\(257\) | −17.4144 | −1.08628 | −0.543139 | − | 0.839643i | \(-0.682764\pi\) | ||||
−0.543139 | + | 0.839643i | \(0.682764\pi\) | |||||||
\(258\) | 2.48770 | 0.154878 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 33.5047 | 2.07389 | ||||||||
\(262\) | −3.37757 | −0.208667 | ||||||||
\(263\) | −12.7276 | −0.784820 | −0.392410 | − | 0.919790i | \(-0.628359\pi\) | ||||
−0.392410 | + | 0.919790i | \(0.628359\pi\) | |||||||
\(264\) | −23.0585 | −1.41915 | ||||||||
\(265\) | −3.66299 | −0.225015 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.09935 | 0.0672790 | ||||||||
\(268\) | −11.7960 | −0.720553 | ||||||||
\(269\) | −2.16163 | −0.131797 | −0.0658985 | − | 0.997826i | \(-0.520991\pi\) | ||||
−0.0658985 | + | 0.997826i | \(0.520991\pi\) | |||||||
\(270\) | 11.2176 | 0.682683 | ||||||||
\(271\) | 5.82966 | 0.354127 | 0.177063 | − | 0.984199i | \(-0.443340\pi\) | ||||
0.177063 | + | 0.984199i | \(0.443340\pi\) | |||||||
\(272\) | −13.4267 | −0.814113 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.03999 | −0.123240 | ||||||||
\(275\) | 6.24199 | 0.376406 | ||||||||
\(276\) | 21.4596 | 1.29172 | ||||||||
\(277\) | −11.6473 | −0.699820 | −0.349910 | − | 0.936783i | \(-0.613788\pi\) | ||||
−0.349910 | + | 0.936783i | \(0.613788\pi\) | |||||||
\(278\) | −7.30445 | −0.438092 | ||||||||
\(279\) | −29.8460 | −1.78684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.7940 | 1.47908 | 0.739542 | − | 0.673110i | \(-0.235042\pi\) | ||||
0.739542 | + | 0.673110i | \(0.235042\pi\) | |||||||
\(282\) | 15.4981 | 0.922896 | ||||||||
\(283\) | 15.1432 | 0.900172 | 0.450086 | − | 0.892985i | \(-0.351393\pi\) | ||||
0.450086 | + | 0.892985i | \(0.351393\pi\) | |||||||
\(284\) | 7.55100 | 0.448069 | ||||||||
\(285\) | 14.0097 | 0.829865 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 35.3781 | 2.08467 | ||||||||
\(289\) | 20.8125 | 1.22427 | ||||||||
\(290\) | −5.21773 | −0.306396 | ||||||||
\(291\) | 32.7767 | 1.92141 | ||||||||
\(292\) | 15.7194 | 0.919907 | ||||||||
\(293\) | −24.9203 | −1.45586 | −0.727929 | − | 0.685652i | \(-0.759517\pi\) | ||||
−0.727929 | + | 0.685652i | \(0.759517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.4404 | 0.957194 | ||||||||
\(296\) | 24.3945 | 1.41790 | ||||||||
\(297\) | 39.3877 | 2.28551 | ||||||||
\(298\) | −1.24081 | −0.0718782 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −9.04467 | −0.522194 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.10213 | −0.0634205 | ||||||||
\(303\) | −10.5873 | −0.608225 | ||||||||
\(304\) | 5.48221 | 0.314426 | ||||||||
\(305\) | 9.88930 | 0.566259 | ||||||||
\(306\) | −22.7943 | −1.30306 | ||||||||
\(307\) | −3.90158 | −0.222675 | −0.111337 | − | 0.993783i | \(-0.535513\pi\) | ||||
−0.111337 | + | 0.993783i | \(0.535513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40.0479 | 2.27825 | ||||||||
\(310\) | 4.64796 | 0.263986 | ||||||||
\(311\) | 19.7180 | 1.11810 | 0.559052 | − | 0.829132i | \(-0.311165\pi\) | ||||
0.559052 | + | 0.829132i | \(0.311165\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.89235 | 0.163485 | 0.0817427 | − | 0.996653i | \(-0.473951\pi\) | ||||
0.0817427 | + | 0.996653i | \(0.473951\pi\) | |||||||
\(314\) | −10.3775 | −0.585633 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.75336 | −0.492415 | ||||||||
\(317\) | 15.9537 | 0.896046 | 0.448023 | − | 0.894022i | \(-0.352128\pi\) | ||||
0.448023 | + | 0.894022i | \(0.352128\pi\) | |||||||
\(318\) | −3.54712 | −0.198913 | ||||||||
\(319\) | −18.3207 | −1.02576 | ||||||||
\(320\) | 2.37354 | 0.132685 | ||||||||
\(321\) | 56.1644 | 3.13479 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.4391 | −0.859054 | ||||||||
\(324\) | −24.0318 | −1.33510 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.4750 | −0.690924 | ||||||||
\(327\) | 43.0574 | 2.38108 | ||||||||
\(328\) | −3.88431 | −0.214475 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −11.3102 | −0.622606 | ||||||||
\(331\) | −3.82678 | −0.210339 | −0.105169 | − | 0.994454i | \(-0.533538\pi\) | ||||
−0.105169 | + | 0.994454i | \(0.533538\pi\) | |||||||
\(332\) | 15.8358 | 0.869101 | ||||||||
\(333\) | −76.8342 | −4.21049 | ||||||||
\(334\) | 1.60535 | 0.0878407 | ||||||||
\(335\) | −12.6731 | −0.692405 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.78172 | −0.532844 | −0.266422 | − | 0.963856i | \(-0.585842\pi\) | ||||
−0.266422 | + | 0.963856i | \(0.585842\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.3071 | 1.70037 | ||||||||
\(340\) | −18.6505 | −1.01147 | ||||||||
\(341\) | 16.3201 | 0.883782 | ||||||||
\(342\) | 9.30706 | 0.503268 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.96180 | 0.159689 | ||||||||
\(345\) | 23.0553 | 1.24126 | ||||||||
\(346\) | 1.99523 | 0.107264 | ||||||||
\(347\) | 5.33403 | 0.286346 | 0.143173 | − | 0.989698i | \(-0.454269\pi\) | ||||
0.143173 | + | 0.989698i | \(0.454269\pi\) | |||||||
\(348\) | 26.5467 | 1.42305 | ||||||||
\(349\) | −14.7030 | −0.787032 | −0.393516 | − | 0.919318i | \(-0.628741\pi\) | ||||
−0.393516 | + | 0.919318i | \(0.628741\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19.3451 | −1.03110 | ||||||||
\(353\) | 35.5173 | 1.89039 | 0.945196 | − | 0.326502i | \(-0.105870\pi\) | ||||
0.945196 | + | 0.326502i | \(0.105870\pi\) | |||||||
\(354\) | 15.9203 | 0.846156 | ||||||||
\(355\) | 8.11248 | 0.430566 | ||||||||
\(356\) | 0.597560 | 0.0316706 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.78589 | −0.200090 | ||||||||
\(359\) | −15.9147 | −0.839945 | −0.419972 | − | 0.907537i | \(-0.637960\pi\) | ||||
−0.419972 | + | 0.907537i | \(0.637960\pi\) | |||||||
\(360\) | 24.6259 | 1.29790 | ||||||||
\(361\) | −12.6961 | −0.668217 | ||||||||
\(362\) | −7.08676 | −0.372472 | ||||||||
\(363\) | −5.71051 | −0.299724 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.8882 | 0.883971 | ||||||||
\(366\) | 9.57649 | 0.500571 | ||||||||
\(367\) | −18.2446 | −0.952361 | −0.476181 | − | 0.879348i | \(-0.657979\pi\) | ||||
−0.476181 | + | 0.879348i | \(0.657979\pi\) | |||||||
\(368\) | 9.02186 | 0.470297 | ||||||||
\(369\) | 12.2343 | 0.636890 | ||||||||
\(370\) | 11.9655 | 0.622056 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −23.6479 | −1.22608 | ||||||||
\(373\) | −13.5744 | −0.702856 | −0.351428 | − | 0.936215i | \(-0.614304\pi\) | ||||
−0.351428 | + | 0.936215i | \(0.614304\pi\) | |||||||
\(374\) | 12.4641 | 0.644505 | ||||||||
\(375\) | −37.6167 | −1.94252 | ||||||||
\(376\) | 18.4516 | 0.951568 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.23572 | −0.371674 | −0.185837 | − | 0.982581i | \(-0.559500\pi\) | ||||
−0.185837 | + | 0.982581i | \(0.559500\pi\) | |||||||
\(380\) | 7.61512 | 0.390648 | ||||||||
\(381\) | −18.8626 | −0.966359 | ||||||||
\(382\) | 1.71711 | 0.0878549 | ||||||||
\(383\) | 20.3464 | 1.03965 | 0.519827 | − | 0.854272i | \(-0.325996\pi\) | ||||
0.519827 | + | 0.854272i | \(0.325996\pi\) | |||||||
\(384\) | 35.6647 | 1.82001 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.2375 | 0.775569 | ||||||||
\(387\) | −9.32864 | −0.474202 | ||||||||
\(388\) | 17.8161 | 0.904475 | ||||||||
\(389\) | 2.48306 | 0.125896 | 0.0629481 | − | 0.998017i | \(-0.479950\pi\) | ||||
0.0629481 | + | 0.998017i | \(0.479950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.4075 | −1.28491 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.4622 | 0.931293 | ||||||||
\(394\) | −5.25862 | −0.264926 | ||||||||
\(395\) | −9.40424 | −0.473179 | ||||||||
\(396\) | 39.4767 | 1.98378 | ||||||||
\(397\) | −10.7391 | −0.538980 | −0.269490 | − | 0.963003i | \(-0.586855\pi\) | ||||
−0.269490 | + | 0.963003i | \(0.586855\pi\) | |||||||
\(398\) | 9.83122 | 0.492795 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.80248 | −0.190124 | ||||||||
\(401\) | −14.7540 | −0.736778 | −0.368389 | − | 0.929672i | \(-0.620091\pi\) | ||||
−0.368389 | + | 0.929672i | \(0.620091\pi\) | |||||||
\(402\) | −12.2722 | −0.612083 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.75483 | −0.286313 | ||||||||
\(405\) | −25.8187 | −1.28294 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42.0136 | 2.08254 | ||||||||
\(408\) | −39.5586 | −1.95844 | ||||||||
\(409\) | −6.34448 | −0.313714 | −0.156857 | − | 0.987621i | \(-0.550136\pi\) | ||||
−0.156857 | + | 0.987621i | \(0.550136\pi\) | |||||||
\(410\) | −1.90526 | −0.0940939 | ||||||||
\(411\) | 11.1508 | 0.550028 | ||||||||
\(412\) | 21.7684 | 1.07245 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 15.3163 | 0.752754 | ||||||||
\(415\) | 17.0133 | 0.835150 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 39.9269 | 1.95523 | ||||||||
\(418\) | −5.08919 | −0.248920 | ||||||||
\(419\) | 18.0851 | 0.883513 | 0.441756 | − | 0.897135i | \(-0.354356\pi\) | ||||
0.441756 | + | 0.897135i | \(0.354356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.7043 | −0.960327 | −0.480164 | − | 0.877179i | \(-0.659423\pi\) | ||||
−0.480164 | + | 0.877179i | \(0.659423\pi\) | |||||||
\(422\) | 12.3414 | 0.600768 | ||||||||
\(423\) | −58.1162 | −2.82571 | ||||||||
\(424\) | −4.22312 | −0.205093 | ||||||||
\(425\) | 10.7086 | 0.519444 | ||||||||
\(426\) | 7.85587 | 0.380618 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 30.5287 | 1.47566 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.45276 | 0.0700584 | ||||||||
\(431\) | −10.5039 | −0.505953 | −0.252977 | − | 0.967472i | \(-0.581410\pi\) | ||||
−0.252977 | + | 0.967472i | \(0.581410\pi\) | |||||||
\(432\) | −23.9941 | −1.15442 | ||||||||
\(433\) | −9.11805 | −0.438186 | −0.219093 | − | 0.975704i | \(-0.570310\pi\) | ||||
−0.219093 | + | 0.975704i | \(0.570310\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 28.5207 | 1.36746 | ||||||||
\(436\) | 23.4043 | 1.12086 | ||||||||
\(437\) | 10.3741 | 0.496258 | ||||||||
\(438\) | 16.3541 | 0.781427 | ||||||||
\(439\) | 29.2801 | 1.39746 | 0.698731 | − | 0.715384i | \(-0.253748\pi\) | ||||
0.698731 | + | 0.715384i | \(0.253748\pi\) | |||||||
\(440\) | −13.4656 | −0.641949 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.7353 | −1.27023 | −0.635117 | − | 0.772416i | \(-0.719048\pi\) | ||||
−0.635117 | + | 0.772416i | \(0.719048\pi\) | |||||||
\(444\) | −60.8779 | −2.88914 | ||||||||
\(445\) | 0.641994 | 0.0304334 | ||||||||
\(446\) | 1.08118 | 0.0511951 | ||||||||
\(447\) | 6.78240 | 0.320797 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.2155 | −1.00122 | −0.500611 | − | 0.865673i | \(-0.666891\pi\) | ||||
−0.500611 | + | 0.865673i | \(0.666891\pi\) | |||||||
\(450\) | −6.45542 | −0.304311 | ||||||||
\(451\) | −6.68980 | −0.315010 | ||||||||
\(452\) | 17.0172 | 0.800424 | ||||||||
\(453\) | 6.02437 | 0.283050 | ||||||||
\(454\) | 5.84433 | 0.274288 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.1521 | 0.756389 | ||||||||
\(457\) | −14.6446 | −0.685046 | −0.342523 | − | 0.939509i | \(-0.611282\pi\) | ||||
−0.342523 | + | 0.939509i | \(0.611282\pi\) | |||||||
\(458\) | −3.45181 | −0.161293 | ||||||||
\(459\) | 67.5726 | 3.15402 | ||||||||
\(460\) | 12.5319 | 0.584304 | ||||||||
\(461\) | 24.8946 | 1.15946 | 0.579729 | − | 0.814810i | \(-0.303159\pi\) | ||||
0.579729 | + | 0.814810i | \(0.303159\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.1069 | −0.469706 | −0.234853 | − | 0.972031i | \(-0.575461\pi\) | ||||
−0.234853 | + | 0.972031i | \(0.575461\pi\) | |||||||
\(464\) | 11.1606 | 0.518116 | ||||||||
\(465\) | −25.4063 | −1.17819 | ||||||||
\(466\) | 4.03079 | 0.186723 | ||||||||
\(467\) | 11.4825 | 0.531346 | 0.265673 | − | 0.964063i | \(-0.414406\pi\) | ||||
0.265673 | + | 0.964063i | \(0.414406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.05051 | 0.417469 | ||||||||
\(471\) | 56.7243 | 2.61372 | ||||||||
\(472\) | 18.9543 | 0.872444 | ||||||||
\(473\) | 5.10099 | 0.234544 | ||||||||
\(474\) | −9.10678 | −0.418288 | ||||||||
\(475\) | −4.37240 | −0.200619 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.3014 | 0.609028 | ||||||||
\(478\) | −4.14147 | −0.189427 | ||||||||
\(479\) | −1.08116 | −0.0493997 | −0.0246998 | − | 0.999695i | \(-0.507863\pi\) | ||||
−0.0246998 | + | 0.999695i | \(0.507863\pi\) | |||||||
\(480\) | 30.1154 | 1.37457 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.148784 | 0.00677691 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.10400 | −0.141091 | ||||||||
\(485\) | 19.1409 | 0.869142 | ||||||||
\(486\) | −6.35926 | −0.288462 | ||||||||
\(487\) | −25.2677 | −1.14499 | −0.572493 | − | 0.819909i | \(-0.694024\pi\) | ||||
−0.572493 | + | 0.819909i | \(0.694024\pi\) | |||||||
\(488\) | 11.4015 | 0.516123 | ||||||||
\(489\) | 68.1895 | 3.08364 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.7180 | 1.88271 | 0.941355 | − | 0.337419i | \(-0.109554\pi\) | ||||
0.941355 | + | 0.337419i | \(0.109554\pi\) | |||||||
\(492\) | 9.69354 | 0.437019 | ||||||||
\(493\) | −31.4306 | −1.41556 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 42.4122 | 1.90628 | ||||||||
\(496\) | −9.94183 | −0.446401 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 16.4751 | 0.738269 | ||||||||
\(499\) | −10.4684 | −0.468628 | −0.234314 | − | 0.972161i | \(-0.575284\pi\) | ||||
−0.234314 | + | 0.972161i | \(0.575284\pi\) | |||||||
\(500\) | −20.4469 | −0.914413 | ||||||||
\(501\) | −8.77501 | −0.392038 | ||||||||
\(502\) | −7.51099 | −0.335232 | ||||||||
\(503\) | 2.57470 | 0.114800 | 0.0574001 | − | 0.998351i | \(-0.481719\pi\) | ||||
0.0574001 | + | 0.998351i | \(0.481719\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.18275 | −0.275129 | ||||||||
\(506\) | −8.37508 | −0.372318 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.2529 | −0.454900 | ||||||||
\(509\) | 7.52681 | 0.333620 | 0.166810 | − | 0.985989i | \(-0.446653\pi\) | ||||
0.166810 | + | 0.985989i | \(0.446653\pi\) | |||||||
\(510\) | −19.4035 | −0.859202 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.8730 | 0.922467 | ||||||||
\(513\) | −27.5903 | −1.21814 | ||||||||
\(514\) | −9.84792 | −0.434373 | ||||||||
\(515\) | 23.3871 | 1.03056 | ||||||||
\(516\) | −7.39135 | −0.325386 | ||||||||
\(517\) | 31.7785 | 1.39761 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.9061 | −0.478726 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.0156677 | 0.000686413 0 | 0.000343207 | − | 1.00000i | \(-0.499891\pi\) | ||||
0.000343207 | 1.00000i | \(0.499891\pi\) | ||||||||
\(522\) | 18.9471 | 0.829292 | ||||||||
\(523\) | 24.0715 | 1.05257 | 0.526286 | − | 0.850308i | \(-0.323584\pi\) | ||||
0.526286 | + | 0.850308i | \(0.323584\pi\) | |||||||
\(524\) | 10.0353 | 0.438393 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.19755 | −0.313828 | ||||||||
\(527\) | 27.9984 | 1.21963 | ||||||||
\(528\) | 24.1921 | 1.05283 | ||||||||
\(529\) | −5.92781 | −0.257731 | ||||||||
\(530\) | −2.07144 | −0.0899775 | ||||||||
\(531\) | −59.6997 | −2.59075 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.621687 | 0.0269030 | ||||||||
\(535\) | 32.7987 | 1.41801 | ||||||||
\(536\) | −14.6110 | −0.631099 | ||||||||
\(537\) | 20.6941 | 0.893015 | ||||||||
\(538\) | −1.22241 | −0.0527020 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −33.3293 | −1.43426 | ||||||||
\(541\) | −37.7763 | −1.62413 | −0.812065 | − | 0.583567i | \(-0.801656\pi\) | ||||
−0.812065 | + | 0.583567i | \(0.801656\pi\) | |||||||
\(542\) | 3.29671 | 0.141606 | ||||||||
\(543\) | 38.7370 | 1.66236 | ||||||||
\(544\) | −33.1879 | −1.42292 | ||||||||
\(545\) | 25.1445 | 1.07707 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.4925 | 1.21825 | 0.609126 | − | 0.793074i | \(-0.291521\pi\) | ||||
0.609126 | + | 0.793074i | \(0.291521\pi\) | |||||||
\(548\) | 6.06111 | 0.258918 | ||||||||
\(549\) | −35.9109 | −1.53264 | ||||||||
\(550\) | 3.52988 | 0.150515 | ||||||||
\(551\) | 12.8333 | 0.546717 | ||||||||
\(552\) | 26.5808 | 1.13135 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.58663 | −0.279839 | ||||||||
\(555\) | −65.4046 | −2.77627 | ||||||||
\(556\) | 21.7026 | 0.920397 | ||||||||
\(557\) | 19.8646 | 0.841692 | 0.420846 | − | 0.907132i | \(-0.361733\pi\) | ||||
0.420846 | + | 0.907132i | \(0.361733\pi\) | |||||||
\(558\) | −16.8781 | −0.714507 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −68.1303 | −2.87646 | ||||||||
\(562\) | 14.0211 | 0.591445 | ||||||||
\(563\) | −15.5397 | −0.654919 | −0.327459 | − | 0.944865i | \(-0.606192\pi\) | ||||
−0.327459 | + | 0.944865i | \(0.606192\pi\) | |||||||
\(564\) | −46.0471 | −1.93893 | ||||||||
\(565\) | 18.2826 | 0.769155 | ||||||||
\(566\) | 8.56358 | 0.359954 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.35301 | 0.392443 | ||||||||
\(569\) | −31.1088 | −1.30415 | −0.652075 | − | 0.758154i | \(-0.726101\pi\) | ||||
−0.652075 | + | 0.758154i | \(0.726101\pi\) | |||||||
\(570\) | 7.92258 | 0.331840 | ||||||||
\(571\) | −0.602653 | −0.0252202 | −0.0126101 | − | 0.999920i | \(-0.504014\pi\) | ||||
−0.0126101 | + | 0.999920i | \(0.504014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.38590 | −0.392102 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.19549 | −0.300073 | ||||||||
\(576\) | −8.61902 | −0.359126 | ||||||||
\(577\) | −5.21634 | −0.217159 | −0.108580 | − | 0.994088i | \(-0.534630\pi\) | ||||
−0.108580 | + | 0.994088i | \(0.534630\pi\) | |||||||
\(578\) | 11.7696 | 0.489550 | ||||||||
\(579\) | −83.2899 | −3.46141 | ||||||||
\(580\) | 15.5027 | 0.643714 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 18.5354 | 0.768318 | ||||||||
\(583\) | −7.27331 | −0.301230 | ||||||||
\(584\) | 19.4707 | 0.805704 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0926 | −0.582158 | ||||||||
\(587\) | 17.1895 | 0.709487 | 0.354743 | − | 0.934964i | \(-0.384568\pi\) | ||||
0.354743 | + | 0.934964i | \(0.384568\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.4319 | −0.471044 | ||||||||
\(590\) | 9.29711 | 0.382756 | ||||||||
\(591\) | 28.7442 | 1.18238 | ||||||||
\(592\) | −25.5938 | −1.05190 | ||||||||
\(593\) | −10.6452 | −0.437147 | −0.218574 | − | 0.975820i | \(-0.570140\pi\) | ||||
−0.218574 | + | 0.975820i | \(0.570140\pi\) | |||||||
\(594\) | 22.2740 | 0.913912 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.68664 | 0.151011 | ||||||||
\(597\) | −53.7385 | −2.19937 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.1472 | 1.02749 | 0.513744 | − | 0.857944i | \(-0.328258\pi\) | ||||
0.513744 | + | 0.857944i | \(0.328258\pi\) | |||||||
\(600\) | −11.2031 | −0.457366 | ||||||||
\(601\) | −3.24667 | −0.132434 | −0.0662172 | − | 0.997805i | \(-0.521093\pi\) | ||||
−0.0662172 | + | 0.997805i | \(0.521093\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 46.0196 | 1.87406 | ||||||||
\(604\) | 3.27460 | 0.133242 | ||||||||
\(605\) | −3.33481 | −0.135579 | ||||||||
\(606\) | −5.98718 | −0.243213 | ||||||||
\(607\) | 17.1124 | 0.694572 | 0.347286 | − | 0.937759i | \(-0.387103\pi\) | ||||
0.347286 | + | 0.937759i | \(0.387103\pi\) | |||||||
\(608\) | 13.5509 | 0.549560 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.59245 | 0.226432 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 67.7254 | 2.73764 | ||||||||
\(613\) | 28.0427 | 1.13264 | 0.566318 | − | 0.824187i | \(-0.308368\pi\) | ||||
0.566318 | + | 0.824187i | \(0.308368\pi\) | |||||||
\(614\) | −2.20636 | −0.0890415 | ||||||||
\(615\) | 10.4143 | 0.419947 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.0926 | 1.69459 | 0.847293 | − | 0.531126i | \(-0.178231\pi\) | ||||
0.847293 | + | 0.531126i | \(0.178231\pi\) | |||||||
\(618\) | 22.6473 | 0.911009 | ||||||||
\(619\) | −27.1308 | −1.09048 | −0.545239 | − | 0.838280i | \(-0.683561\pi\) | ||||
−0.545239 | + | 0.838280i | \(0.683561\pi\) | |||||||
\(620\) | −13.8098 | −0.554615 | ||||||||
\(621\) | −45.4044 | −1.82201 | ||||||||
\(622\) | 11.1506 | 0.447099 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.2599 | −0.530398 | ||||||||
\(626\) | 1.63564 | 0.0653733 | ||||||||
\(627\) | 27.8180 | 1.11095 | ||||||||
\(628\) | 30.8330 | 1.23037 | ||||||||
\(629\) | 72.0776 | 2.87392 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0095 | 0.637329 | 0.318665 | − | 0.947868i | \(-0.396766\pi\) | ||||
0.318665 | + | 0.947868i | \(0.396766\pi\) | |||||||
\(632\) | −10.8423 | −0.431284 | ||||||||
\(633\) | −67.4593 | −2.68126 | ||||||||
\(634\) | 9.02188 | 0.358304 | ||||||||
\(635\) | −11.0153 | −0.437129 | ||||||||
\(636\) | 10.5390 | 0.417900 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.3604 | −0.410174 | ||||||||
\(639\) | −29.4588 | −1.16537 | ||||||||
\(640\) | 20.8274 | 0.823275 | ||||||||
\(641\) | −14.6814 | −0.579880 | −0.289940 | − | 0.957045i | \(-0.593635\pi\) | ||||
−0.289940 | + | 0.957045i | \(0.593635\pi\) | |||||||
\(642\) | 31.7613 | 1.25352 | ||||||||
\(643\) | −37.1435 | −1.46480 | −0.732399 | − | 0.680875i | \(-0.761600\pi\) | ||||
−0.732399 | + | 0.680875i | \(0.761600\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.94095 | −0.312675 | ||||||||
\(646\) | −8.73089 | −0.343512 | ||||||||
\(647\) | 14.2284 | 0.559377 | 0.279689 | − | 0.960091i | \(-0.409769\pi\) | ||||
0.279689 | + | 0.960091i | \(0.409769\pi\) | |||||||
\(648\) | −29.7668 | −1.16935 | ||||||||
\(649\) | 32.6443 | 1.28140 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 37.0650 | 1.45158 | ||||||||
\(653\) | −21.8455 | −0.854880 | −0.427440 | − | 0.904044i | \(-0.640585\pi\) | ||||
−0.427440 | + | 0.904044i | \(0.640585\pi\) | |||||||
\(654\) | 24.3492 | 0.952129 | ||||||||
\(655\) | 10.7815 | 0.421267 | ||||||||
\(656\) | 4.07528 | 0.159113 | ||||||||
\(657\) | −61.3261 | −2.39256 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.1051 | 1.28959 | 0.644796 | − | 0.764355i | \(-0.276943\pi\) | ||||
0.644796 | + | 0.764355i | \(0.276943\pi\) | |||||||
\(660\) | 33.6043 | 1.30805 | ||||||||
\(661\) | −23.3428 | −0.907930 | −0.453965 | − | 0.891020i | \(-0.649991\pi\) | ||||
−0.453965 | + | 0.891020i | \(0.649991\pi\) | |||||||
\(662\) | −2.16406 | −0.0841087 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.6149 | 0.761206 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −43.4501 | −1.68366 | ||||||||
\(667\) | 21.1193 | 0.817741 | ||||||||
\(668\) | −4.76974 | −0.184547 | ||||||||
\(669\) | −5.90982 | −0.228487 | ||||||||
\(670\) | −7.16670 | −0.276874 | ||||||||
\(671\) | 19.6364 | 0.758055 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.4847 | −1.86895 | −0.934474 | − | 0.356030i | \(-0.884130\pi\) | ||||
−0.934474 | + | 0.356030i | \(0.884130\pi\) | |||||||
\(674\) | −5.53162 | −0.213070 | ||||||||
\(675\) | 19.1368 | 0.736575 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.8976 | −1.68712 | −0.843560 | − | 0.537034i | \(-0.819545\pi\) | ||||
−0.843560 | + | 0.537034i | \(0.819545\pi\) | |||||||
\(678\) | 17.7043 | 0.679930 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −23.1013 | −0.885896 | ||||||||
\(681\) | −31.9458 | −1.22416 | ||||||||
\(682\) | 9.22909 | 0.353400 | ||||||||
\(683\) | −44.9278 | −1.71912 | −0.859558 | − | 0.511039i | \(-0.829261\pi\) | ||||
−0.859558 | + | 0.511039i | \(0.829261\pi\) | |||||||
\(684\) | −27.6527 | −1.05733 | ||||||||
\(685\) | 6.51180 | 0.248803 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.8680 | 0.719859 | ||||||||
\(688\) | −3.10741 | −0.118469 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 13.0379 | 0.496344 | ||||||||
\(691\) | 45.4493 | 1.72897 | 0.864486 | − | 0.502656i | \(-0.167644\pi\) | ||||
0.864486 | + | 0.502656i | \(0.167644\pi\) | |||||||
\(692\) | −5.92813 | −0.225354 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.01643 | 0.114502 | ||||||||
\(695\) | 23.3164 | 0.884441 | ||||||||
\(696\) | 32.8820 | 1.24639 | ||||||||
\(697\) | −11.4769 | −0.434717 | ||||||||
\(698\) | −8.31461 | −0.314713 | ||||||||
\(699\) | −22.0327 | −0.833354 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.7914 | −1.08744 | −0.543718 | − | 0.839268i | \(-0.682984\pi\) | ||||
−0.543718 | + | 0.839268i | \(0.682984\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.4298 | −1.10996 | ||||||||
\(704\) | 4.71296 | 0.177626 | ||||||||
\(705\) | −49.4711 | −1.86319 | ||||||||
\(706\) | 20.0852 | 0.755916 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −47.3017 | −1.77771 | ||||||||
\(709\) | 17.3626 | 0.652068 | 0.326034 | − | 0.945358i | \(-0.394288\pi\) | ||||
0.326034 | + | 0.945358i | \(0.394288\pi\) | |||||||
\(710\) | 4.58765 | 0.172171 | ||||||||
\(711\) | 34.1495 | 1.28071 | ||||||||
\(712\) | 0.740165 | 0.0277389 | ||||||||
\(713\) | −18.8131 | −0.704554 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.2485 | 0.420374 | ||||||||
\(717\) | 22.6377 | 0.845422 | ||||||||
\(718\) | −8.99984 | −0.335871 | ||||||||
\(719\) | 9.98708 | 0.372455 | 0.186228 | − | 0.982507i | \(-0.440374\pi\) | ||||
0.186228 | + | 0.982507i | \(0.440374\pi\) | |||||||
\(720\) | −25.8365 | −0.962871 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.17972 | −0.267202 | ||||||||
\(723\) | −0.813267 | −0.0302457 | ||||||||
\(724\) | 21.0558 | 0.782534 | ||||||||
\(725\) | −8.90123 | −0.330583 | ||||||||
\(726\) | −3.22932 | −0.119851 | ||||||||
\(727\) | −8.00409 | −0.296855 | −0.148428 | − | 0.988923i | \(-0.547421\pi\) | ||||
−0.148428 | + | 0.988923i | \(0.547421\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.14827 | −0.301788 | ||||||||
\(730\) | 9.55039 | 0.353476 | ||||||||
\(731\) | 8.75114 | 0.323672 | ||||||||
\(732\) | −28.4532 | −1.05166 | ||||||||
\(733\) | −44.8461 | −1.65643 | −0.828214 | − | 0.560412i | \(-0.810643\pi\) | ||||
−0.828214 | + | 0.560412i | \(0.810643\pi\) | |||||||
\(734\) | −10.3174 | −0.380823 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.3001 | 0.821993 | ||||||||
\(737\) | −25.1640 | −0.926926 | ||||||||
\(738\) | 6.91854 | 0.254675 | ||||||||
\(739\) | 25.0756 | 0.922421 | 0.461210 | − | 0.887291i | \(-0.347415\pi\) | ||||
0.461210 | + | 0.887291i | \(0.347415\pi\) | |||||||
\(740\) | −35.5513 | −1.30689 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.4191 | 0.675733 | 0.337866 | − | 0.941194i | \(-0.390295\pi\) | ||||
0.337866 | + | 0.941194i | \(0.390295\pi\) | |||||||
\(744\) | −29.2913 | −1.07387 | ||||||||
\(745\) | 3.96077 | 0.145111 | ||||||||
\(746\) | −7.67639 | −0.281053 | ||||||||
\(747\) | −61.7802 | −2.26042 | ||||||||
\(748\) | −37.0329 | −1.35406 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −21.2724 | −0.776760 | ||||||||
\(751\) | 11.6918 | 0.426638 | 0.213319 | − | 0.976983i | \(-0.431573\pi\) | ||||
0.213319 | + | 0.976983i | \(0.431573\pi\) | |||||||
\(752\) | −19.3587 | −0.705940 | ||||||||
\(753\) | 41.0559 | 1.49616 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.51810 | 0.128037 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5490 | 0.565137 | 0.282569 | − | 0.959247i | \(-0.408814\pi\) | ||||
0.282569 | + | 0.959247i | \(0.408814\pi\) | |||||||
\(758\) | −4.09184 | −0.148622 | ||||||||
\(759\) | 45.7791 | 1.66168 | ||||||||
\(760\) | 9.43243 | 0.342150 | ||||||||
\(761\) | 31.9505 | 1.15821 | 0.579103 | − | 0.815254i | \(-0.303403\pi\) | ||||
0.579103 | + | 0.815254i | \(0.303403\pi\) | |||||||
\(762\) | −10.6669 | −0.386420 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.10179 | −0.184576 | ||||||||
\(765\) | 72.7613 | 2.63069 | ||||||||
\(766\) | 11.5060 | 0.415729 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 12.0397 | 0.434446 | ||||||||
\(769\) | −14.5302 | −0.523972 | −0.261986 | − | 0.965072i | \(-0.584377\pi\) | ||||
−0.261986 | + | 0.965072i | \(0.584377\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 53.8298 | 1.93863 | ||||||||
\(772\) | −45.2730 | −1.62941 | ||||||||
\(773\) | 42.1103 | 1.51460 | 0.757301 | − | 0.653066i | \(-0.226518\pi\) | ||||
0.757301 | + | 0.653066i | \(0.226518\pi\) | |||||||
\(774\) | −5.27540 | −0.189620 | ||||||||
\(775\) | 7.92922 | 0.284826 | ||||||||
\(776\) | 22.0678 | 0.792188 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.40418 | 0.0503424 | ||||||||
\(779\) | 4.68608 | 0.167896 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.1083 | 0.576401 | ||||||||
\(782\) | −14.3681 | −0.513802 | ||||||||
\(783\) | −56.1678 | −2.00727 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.1257 | 1.18231 | ||||||||
\(786\) | 10.4405 | 0.372399 | ||||||||
\(787\) | 6.09474 | 0.217254 | 0.108627 | − | 0.994083i | \(-0.465355\pi\) | ||||
0.108627 | + | 0.994083i | \(0.465355\pi\) | |||||||
\(788\) | 15.6242 | 0.556588 | ||||||||
\(789\) | 39.3426 | 1.40063 | ||||||||
\(790\) | −5.31815 | −0.189211 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 48.8976 | 1.73750 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −6.07302 | −0.215523 | ||||||||
\(795\) | 11.3227 | 0.401575 | ||||||||
\(796\) | −29.2101 | −1.03532 | ||||||||
\(797\) | 36.8038 | 1.30366 | 0.651830 | − | 0.758366i | \(-0.274002\pi\) | ||||
0.651830 | + | 0.758366i | \(0.274002\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.5184 | 1.92872 | ||||||||
\(800\) | −9.39893 | −0.332302 | ||||||||
\(801\) | −2.33127 | −0.0823712 | ||||||||
\(802\) | −8.34345 | −0.294617 | ||||||||
\(803\) | 33.5337 | 1.18338 | ||||||||
\(804\) | 36.4627 | 1.28594 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.68185 | 0.235212 | ||||||||
\(808\) | −7.12819 | −0.250769 | ||||||||
\(809\) | −8.73333 | −0.307048 | −0.153524 | − | 0.988145i | \(-0.549062\pi\) | ||||
−0.153524 | + | 0.988145i | \(0.549062\pi\) | |||||||
\(810\) | −14.6006 | −0.513014 | ||||||||
\(811\) | −37.1024 | −1.30284 | −0.651421 | − | 0.758716i | \(-0.725827\pi\) | ||||
−0.651421 | + | 0.758716i | \(0.725827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.0202 | −0.631995 | ||||||||
\(814\) | 23.7589 | 0.832750 | ||||||||
\(815\) | 39.8211 | 1.39487 | ||||||||
\(816\) | 41.5035 | 1.45291 | ||||||||
\(817\) | −3.57314 | −0.125009 | ||||||||
\(818\) | −3.58784 | −0.125446 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.66081 | 0.197684 | ||||||||
\(821\) | −42.1578 | −1.47132 | −0.735658 | − | 0.677353i | \(-0.763127\pi\) | ||||
−0.735658 | + | 0.677353i | \(0.763127\pi\) | |||||||
\(822\) | 6.30583 | 0.219941 | ||||||||
\(823\) | −18.5452 | −0.646445 | −0.323223 | − | 0.946323i | \(-0.604766\pi\) | ||||
−0.323223 | + | 0.946323i | \(0.604766\pi\) | |||||||
\(824\) | 26.9633 | 0.939312 | ||||||||
\(825\) | −19.2947 | −0.671756 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.5050 | −0.434841 | −0.217420 | − | 0.976078i | \(-0.569764\pi\) | ||||
−0.217420 | + | 0.976078i | \(0.569764\pi\) | |||||||
\(828\) | −45.5070 | −1.58148 | ||||||||
\(829\) | −45.7666 | −1.58954 | −0.794770 | − | 0.606911i | \(-0.792409\pi\) | ||||
−0.794770 | + | 0.606911i | \(0.792409\pi\) | |||||||
\(830\) | 9.62111 | 0.333954 | ||||||||
\(831\) | 36.0032 | 1.24894 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 22.5789 | 0.781843 | ||||||||
\(835\) | −5.12440 | −0.177337 | ||||||||
\(836\) | 15.1208 | 0.522962 | ||||||||
\(837\) | 50.0343 | 1.72944 | ||||||||
\(838\) | 10.2272 | 0.353293 | ||||||||
\(839\) | −12.8196 | −0.442580 | −0.221290 | − | 0.975208i | \(-0.571027\pi\) | ||||
−0.221290 | + | 0.975208i | \(0.571027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.87426 | −0.0991124 | ||||||||
\(842\) | −11.1429 | −0.384009 | ||||||||
\(843\) | −76.6410 | −2.63966 | ||||||||
\(844\) | −36.6681 | −1.26217 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −32.8650 | −1.12992 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.43074 | 0.152152 | ||||||||
\(849\) | −46.8095 | −1.60650 | ||||||||
\(850\) | 6.05578 | 0.207712 | ||||||||
\(851\) | −48.4314 | −1.66021 | ||||||||
\(852\) | −23.3410 | −0.799650 | ||||||||
\(853\) | 4.51954 | 0.154746 | 0.0773730 | − | 0.997002i | \(-0.475347\pi\) | ||||
0.0773730 | + | 0.997002i | \(0.475347\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −29.7089 | −1.01602 | ||||||||
\(856\) | 37.8142 | 1.29246 | ||||||||
\(857\) | 47.2746 | 1.61487 | 0.807435 | − | 0.589957i | \(-0.200855\pi\) | ||||
0.807435 | + | 0.589957i | \(0.200855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.0543 | 1.63959 | 0.819795 | − | 0.572657i | \(-0.194087\pi\) | ||||
0.819795 | + | 0.572657i | \(0.194087\pi\) | |||||||
\(860\) | −4.31638 | −0.147187 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.93999 | −0.202317 | ||||||||
\(863\) | 27.5799 | 0.938831 | 0.469415 | − | 0.882977i | \(-0.344465\pi\) | ||||
0.469415 | + | 0.882977i | \(0.344465\pi\) | |||||||
\(864\) | −59.3083 | −2.01771 | ||||||||
\(865\) | −6.36893 | −0.216550 | ||||||||
\(866\) | −5.15631 | −0.175218 | ||||||||
\(867\) | −64.3339 | −2.18489 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.6733 | −0.633447 | ||||||||
\(870\) | 16.1286 | 0.546811 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 28.9895 | 0.981710 | ||||||||
\(873\) | −69.5060 | −2.35242 | ||||||||
\(874\) | 5.86659 | 0.198440 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −48.5904 | −1.64172 | ||||||||
\(877\) | −49.4487 | −1.66976 | −0.834882 | − | 0.550430i | \(-0.814464\pi\) | ||||
−0.834882 | + | 0.550430i | \(0.814464\pi\) | |||||||
\(878\) | 16.5581 | 0.558807 | ||||||||
\(879\) | 77.0315 | 2.59821 | ||||||||
\(880\) | 14.1277 | 0.476243 | ||||||||
\(881\) | −1.23791 | −0.0417061 | −0.0208530 | − | 0.999783i | \(-0.506638\pi\) | ||||
−0.0208530 | + | 0.999783i | \(0.506638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.4537 | 1.39503 | 0.697514 | − | 0.716571i | \(-0.254289\pi\) | ||||
0.697514 | + | 0.716571i | \(0.254289\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −50.8190 | −1.70826 | ||||||||
\(886\) | −15.1190 | −0.507932 | ||||||||
\(887\) | −1.17172 | −0.0393426 | −0.0196713 | − | 0.999807i | \(-0.506262\pi\) | ||||
−0.0196713 | + | 0.999807i | \(0.506262\pi\) | |||||||
\(888\) | −75.4061 | −2.53046 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.363051 | 0.0121695 | ||||||||
\(891\) | −51.2662 | −1.71748 | ||||||||
\(892\) | −3.21234 | −0.107557 | ||||||||
\(893\) | −22.2602 | −0.744910 | ||||||||
\(894\) | 3.83548 | 0.128278 | ||||||||
\(895\) | 12.0849 | 0.403952 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.9975 | −0.400361 | ||||||||
\(899\) | −23.2728 | −0.776192 | ||||||||
\(900\) | 19.1800 | 0.639335 | ||||||||
\(901\) | −12.4779 | −0.415700 | ||||||||
\(902\) | −3.78312 | −0.125964 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.0783 | 0.701054 | ||||||||
\(905\) | 22.6215 | 0.751965 | ||||||||
\(906\) | 3.40681 | 0.113184 | ||||||||
\(907\) | −42.9537 | −1.42625 | −0.713127 | − | 0.701035i | \(-0.752722\pi\) | ||||
−0.713127 | + | 0.701035i | \(0.752722\pi\) | |||||||
\(908\) | −17.3644 | −0.576258 | ||||||||
\(909\) | 22.4513 | 0.744664 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5412 | 0.813085 | 0.406543 | − | 0.913632i | \(-0.366734\pi\) | ||||
0.406543 | + | 0.913632i | \(0.366734\pi\) | |||||||
\(912\) | −16.9461 | −0.561142 | ||||||||
\(913\) | 33.7820 | 1.11802 | ||||||||
\(914\) | −8.28161 | −0.273931 | ||||||||
\(915\) | −30.5689 | −1.01058 | ||||||||
\(916\) | 10.2559 | 0.338863 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 38.2127 | 1.26121 | ||||||||
\(919\) | 36.6615 | 1.20935 | 0.604675 | − | 0.796472i | \(-0.293303\pi\) | ||||
0.604675 | + | 0.796472i | \(0.293303\pi\) | |||||||
\(920\) | 15.5226 | 0.511765 | ||||||||
\(921\) | 12.0602 | 0.397398 | ||||||||
\(922\) | 14.0780 | 0.463635 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.4126 | 0.671162 | ||||||||
\(926\) | −5.71549 | −0.187823 | ||||||||
\(927\) | −84.9253 | −2.78931 | ||||||||
\(928\) | 27.5865 | 0.905572 | ||||||||
\(929\) | −25.9653 | −0.851894 | −0.425947 | − | 0.904748i | \(-0.640059\pi\) | ||||
−0.425947 | + | 0.904748i | \(0.640059\pi\) | |||||||
\(930\) | −14.3674 | −0.471125 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.9761 | −0.392290 | ||||||||
\(933\) | −60.9506 | −1.99543 | ||||||||
\(934\) | 6.49340 | 0.212471 | ||||||||
\(935\) | −39.7865 | −1.30116 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.8632 | 0.387554 | 0.193777 | − | 0.981046i | \(-0.437926\pi\) | ||||
0.193777 | + | 0.981046i | \(0.437926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.94059 | −0.291765 | ||||||||
\(940\) | −26.8905 | −0.877070 | ||||||||
\(941\) | 9.51954 | 0.310328 | 0.155164 | − | 0.987889i | \(-0.450409\pi\) | ||||
0.155164 | + | 0.987889i | \(0.450409\pi\) | |||||||
\(942\) | 32.0779 | 1.04515 | ||||||||
\(943\) | 7.71170 | 0.251128 | ||||||||
\(944\) | −19.8862 | −0.647241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.88464 | 0.0937876 | ||||||||
\(947\) | −42.5868 | −1.38388 | −0.691942 | − | 0.721953i | \(-0.743245\pi\) | ||||
−0.691942 | + | 0.721953i | \(0.743245\pi\) | |||||||
\(948\) | 27.0576 | 0.878791 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.47261 | −0.0802222 | ||||||||
\(951\) | −49.3146 | −1.59913 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.4390 | 1.01841 | 0.509204 | − | 0.860646i | \(-0.329940\pi\) | ||||
0.509204 | + | 0.860646i | \(0.329940\pi\) | |||||||
\(954\) | 7.52199 | 0.243534 | ||||||||
\(955\) | −5.48115 | −0.177366 | ||||||||
\(956\) | 12.3050 | 0.397971 | ||||||||
\(957\) | 56.6313 | 1.83063 | ||||||||
\(958\) | −0.611404 | −0.0197536 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −7.33689 | −0.236797 | ||||||||
\(961\) | −10.2686 | −0.331244 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −119.102 | −3.83800 | ||||||||
\(964\) | −0.442059 | −0.0142378 | ||||||||
\(965\) | −48.6394 | −1.56576 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.05894 | 0.194842 | 0.0974212 | − | 0.995243i | \(-0.468941\pi\) | ||||
0.0974212 | + | 0.995243i | \(0.468941\pi\) | |||||||
\(968\) | −3.84475 | −0.123575 | ||||||||
\(969\) | 47.7240 | 1.53312 | ||||||||
\(970\) | 10.8243 | 0.347546 | ||||||||
\(971\) | −43.4692 | −1.39499 | −0.697497 | − | 0.716588i | \(-0.745703\pi\) | ||||
−0.697497 | + | 0.716588i | \(0.745703\pi\) | |||||||
\(972\) | 18.8943 | 0.606036 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −14.2890 | −0.457849 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.9621 | −0.382896 | ||||||||
\(977\) | −28.8178 | −0.921964 | −0.460982 | − | 0.887409i | \(-0.652503\pi\) | ||||
−0.460982 | + | 0.887409i | \(0.652503\pi\) | |||||||
\(978\) | 38.5615 | 1.23306 | ||||||||
\(979\) | 1.27476 | 0.0407414 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −91.3071 | −2.91521 | ||||||||
\(982\) | 23.5918 | 0.752844 | ||||||||
\(983\) | −31.1850 | −0.994647 | −0.497323 | − | 0.867565i | \(-0.665684\pi\) | ||||
−0.497323 | + | 0.867565i | \(0.665684\pi\) | |||||||
\(984\) | 12.0069 | 0.382765 | ||||||||
\(985\) | 16.7860 | 0.534845 | ||||||||
\(986\) | −17.7742 | −0.566044 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.88019 | −0.186979 | ||||||||
\(990\) | 23.9843 | 0.762271 | ||||||||
\(991\) | −62.1395 | −1.97393 | −0.986963 | − | 0.160946i | \(-0.948546\pi\) | ||||
−0.986963 | + | 0.160946i | \(0.948546\pi\) | |||||||
\(992\) | −24.5741 | −0.780228 | ||||||||
\(993\) | 11.8290 | 0.375382 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.3821 | −0.994879 | ||||||||
\(996\) | −48.9502 | −1.55105 | ||||||||
\(997\) | 17.3144 | 0.548351 | 0.274176 | − | 0.961680i | \(-0.411595\pi\) | ||||
0.274176 | + | 0.961680i | \(0.411595\pi\) | |||||||
\(998\) | −5.91991 | −0.187392 | ||||||||
\(999\) | 128.806 | 4.07524 |
(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 | 8281.2.a.cx.1.19 | 32 | ||
7.6 | odd | 2 | inner | 8281.2.a.cx.1.20 | 32 | ||
13.2 | odd | 12 | 637.2.q.j.589.10 | yes | 32 | ||
13.7 | odd | 12 | 637.2.q.j.491.10 | yes | 32 | ||
13.12 | even | 2 | inner | 8281.2.a.cx.1.13 | 32 | ||
91.2 | odd | 12 | 637.2.k.j.459.8 | 32 | |||
91.20 | even | 12 | 637.2.q.j.491.9 | ✓ | 32 | ||
91.33 | even | 12 | 637.2.u.j.361.8 | 32 | |||
91.41 | even | 12 | 637.2.q.j.589.9 | yes | 32 | ||
91.46 | odd | 12 | 637.2.k.j.569.10 | 32 | |||
91.54 | even | 12 | 637.2.k.j.459.7 | 32 | |||
91.59 | even | 12 | 637.2.k.j.569.9 | 32 | |||
91.67 | odd | 12 | 637.2.u.j.30.7 | 32 | |||
91.72 | odd | 12 | 637.2.u.j.361.7 | 32 | |||
91.80 | even | 12 | 637.2.u.j.30.8 | 32 | |||
91.90 | odd | 2 | inner | 8281.2.a.cx.1.14 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.k.j.459.7 | 32 | 91.54 | even | 12 | |||
637.2.k.j.459.8 | 32 | 91.2 | odd | 12 | |||
637.2.k.j.569.9 | 32 | 91.59 | even | 12 | |||
637.2.k.j.569.10 | 32 | 91.46 | odd | 12 | |||
637.2.q.j.491.9 | ✓ | 32 | 91.20 | even | 12 | ||
637.2.q.j.491.10 | yes | 32 | 13.7 | odd | 12 | ||
637.2.q.j.589.9 | yes | 32 | 91.41 | even | 12 | ||
637.2.q.j.589.10 | yes | 32 | 13.2 | odd | 12 | ||
637.2.u.j.30.7 | 32 | 91.67 | odd | 12 | |||
637.2.u.j.30.8 | 32 | 91.80 | even | 12 | |||
637.2.u.j.361.7 | 32 | 91.72 | odd | 12 | |||
637.2.u.j.361.8 | 32 | 91.33 | even | 12 | |||
8281.2.a.cx.1.13 | 32 | 13.12 | even | 2 | inner | ||
8281.2.a.cx.1.14 | 32 | 91.90 | odd | 2 | inner | ||
8281.2.a.cx.1.19 | 32 | 1.1 | even | 1 | trivial | ||
8281.2.a.cx.1.20 | 32 | 7.6 | odd | 2 | inner |