Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(0\) |
Dimension: | \(119\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.22427 | −1.57280 | −0.786398 | − | 0.617720i | \(-0.788056\pi\) | ||||
−0.786398 | + | 0.617720i | \(0.788056\pi\) | |||||||
\(3\) | 3.08840 | 1.78309 | 0.891545 | − | 0.452933i | \(-0.149622\pi\) | ||||
0.891545 | + | 0.452933i | \(0.149622\pi\) | |||||||
\(4\) | 2.94737 | 1.47369 | ||||||||
\(5\) | −2.11023 | −0.943723 | −0.471862 | − | 0.881673i | \(-0.656418\pi\) | ||||
−0.471862 | + | 0.881673i | \(0.656418\pi\) | |||||||
\(6\) | −6.86944 | −2.80444 | ||||||||
\(7\) | 3.85755 | 1.45802 | 0.729008 | − | 0.684505i | \(-0.239982\pi\) | ||||
0.729008 | + | 0.684505i | \(0.239982\pi\) | |||||||
\(8\) | −2.10721 | −0.745012 | ||||||||
\(9\) | 6.53822 | 2.17941 | ||||||||
\(10\) | 4.69372 | 1.48428 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 9.10267 | 2.62771 | ||||||||
\(13\) | −0.535662 | −0.148566 | −0.0742829 | − | 0.997237i | \(-0.523667\pi\) | ||||
−0.0742829 | + | 0.997237i | \(0.523667\pi\) | |||||||
\(14\) | −8.58022 | −2.29316 | ||||||||
\(15\) | −6.51724 | −1.68274 | ||||||||
\(16\) | −1.20774 | −0.301935 | ||||||||
\(17\) | −3.98479 | −0.966455 | −0.483227 | − | 0.875495i | \(-0.660536\pi\) | ||||
−0.483227 | + | 0.875495i | \(0.660536\pi\) | |||||||
\(18\) | −14.5428 | −3.42776 | ||||||||
\(19\) | −1.04439 | −0.239600 | −0.119800 | − | 0.992798i | \(-0.538225\pi\) | ||||
−0.119800 | + | 0.992798i | \(0.538225\pi\) | |||||||
\(20\) | −6.21963 | −1.39075 | ||||||||
\(21\) | 11.9137 | 2.59977 | ||||||||
\(22\) | −2.22427 | −0.474216 | ||||||||
\(23\) | 6.16604 | 1.28571 | 0.642854 | − | 0.765989i | \(-0.277750\pi\) | ||||
0.642854 | + | 0.765989i | \(0.277750\pi\) | |||||||
\(24\) | −6.50791 | −1.32842 | ||||||||
\(25\) | −0.546930 | −0.109386 | ||||||||
\(26\) | 1.19146 | 0.233664 | ||||||||
\(27\) | 10.9275 | 2.10299 | ||||||||
\(28\) | 11.3696 | 2.14866 | ||||||||
\(29\) | 0.156851 | 0.0291266 | 0.0145633 | − | 0.999894i | \(-0.495364\pi\) | ||||
0.0145633 | + | 0.999894i | \(0.495364\pi\) | |||||||
\(30\) | 14.4961 | 2.64661 | ||||||||
\(31\) | −2.30672 | −0.414299 | −0.207149 | − | 0.978309i | \(-0.566419\pi\) | ||||
−0.207149 | + | 0.978309i | \(0.566419\pi\) | |||||||
\(32\) | 6.90076 | 1.21989 | ||||||||
\(33\) | 3.08840 | 0.537622 | ||||||||
\(34\) | 8.86325 | 1.52004 | ||||||||
\(35\) | −8.14031 | −1.37596 | ||||||||
\(36\) | 19.2706 | 3.21176 | ||||||||
\(37\) | 3.47103 | 0.570634 | 0.285317 | − | 0.958433i | \(-0.407901\pi\) | ||||
0.285317 | + | 0.958433i | \(0.407901\pi\) | |||||||
\(38\) | 2.32301 | 0.376842 | ||||||||
\(39\) | −1.65434 | −0.264906 | ||||||||
\(40\) | 4.44670 | 0.703085 | ||||||||
\(41\) | 4.04037 | 0.631000 | 0.315500 | − | 0.948925i | \(-0.397828\pi\) | ||||
0.315500 | + | 0.948925i | \(0.397828\pi\) | |||||||
\(42\) | −26.4992 | −4.08891 | ||||||||
\(43\) | 8.50197 | 1.29654 | 0.648269 | − | 0.761411i | \(-0.275493\pi\) | ||||
0.648269 | + | 0.761411i | \(0.275493\pi\) | |||||||
\(44\) | 2.94737 | 0.444333 | ||||||||
\(45\) | −13.7972 | −2.05676 | ||||||||
\(46\) | −13.7149 | −2.02216 | ||||||||
\(47\) | −6.52719 | −0.952088 | −0.476044 | − | 0.879421i | \(-0.657930\pi\) | ||||
−0.476044 | + | 0.879421i | \(0.657930\pi\) | |||||||
\(48\) | −3.72999 | −0.538377 | ||||||||
\(49\) | 7.88068 | 1.12581 | ||||||||
\(50\) | 1.21652 | 0.172042 | ||||||||
\(51\) | −12.3066 | −1.72328 | ||||||||
\(52\) | −1.57879 | −0.218939 | ||||||||
\(53\) | −12.8417 | −1.76395 | −0.881973 | − | 0.471300i | \(-0.843785\pi\) | ||||
−0.881973 | + | 0.471300i | \(0.843785\pi\) | |||||||
\(54\) | −24.3056 | −3.30757 | ||||||||
\(55\) | −2.11023 | −0.284543 | ||||||||
\(56\) | −8.12867 | −1.08624 | ||||||||
\(57\) | −3.22550 | −0.427228 | ||||||||
\(58\) | −0.348879 | −0.0458101 | ||||||||
\(59\) | −0.140032 | −0.0182306 | −0.00911528 | − | 0.999958i | \(-0.502902\pi\) | ||||
−0.00911528 | + | 0.999958i | \(0.502902\pi\) | |||||||
\(60\) | −19.2087 | −2.47984 | ||||||||
\(61\) | 3.16264 | 0.404934 | 0.202467 | − | 0.979289i | \(-0.435104\pi\) | ||||
0.202467 | + | 0.979289i | \(0.435104\pi\) | |||||||
\(62\) | 5.13076 | 0.651607 | ||||||||
\(63\) | 25.2215 | 3.17761 | ||||||||
\(64\) | −12.9337 | −1.61671 | ||||||||
\(65\) | 1.13037 | 0.140205 | ||||||||
\(66\) | −6.86944 | −0.845569 | ||||||||
\(67\) | 9.51054 | 1.16190 | 0.580949 | − | 0.813940i | \(-0.302682\pi\) | ||||
0.580949 | + | 0.813940i | \(0.302682\pi\) | |||||||
\(68\) | −11.7447 | −1.42425 | ||||||||
\(69\) | 19.0432 | 2.29253 | ||||||||
\(70\) | 18.1062 | 2.16411 | ||||||||
\(71\) | 5.43590 | 0.645123 | 0.322561 | − | 0.946549i | \(-0.395456\pi\) | ||||
0.322561 | + | 0.946549i | \(0.395456\pi\) | |||||||
\(72\) | −13.7774 | −1.62368 | ||||||||
\(73\) | 2.85653 | 0.334332 | 0.167166 | − | 0.985929i | \(-0.446538\pi\) | ||||
0.167166 | + | 0.985929i | \(0.446538\pi\) | |||||||
\(74\) | −7.72051 | −0.897491 | ||||||||
\(75\) | −1.68914 | −0.195045 | ||||||||
\(76\) | −3.07821 | −0.353095 | ||||||||
\(77\) | 3.85755 | 0.439608 | ||||||||
\(78\) | 3.67969 | 0.416643 | ||||||||
\(79\) | 10.8974 | 1.22606 | 0.613028 | − | 0.790061i | \(-0.289951\pi\) | ||||
0.613028 | + | 0.790061i | \(0.289951\pi\) | |||||||
\(80\) | 2.54861 | 0.284943 | ||||||||
\(81\) | 14.1337 | 1.57041 | ||||||||
\(82\) | −8.98688 | −0.992435 | ||||||||
\(83\) | 4.34014 | 0.476392 | 0.238196 | − | 0.971217i | \(-0.423444\pi\) | ||||
0.238196 | + | 0.971217i | \(0.423444\pi\) | |||||||
\(84\) | 35.1140 | 3.83125 | ||||||||
\(85\) | 8.40883 | 0.912066 | ||||||||
\(86\) | −18.9107 | −2.03919 | ||||||||
\(87\) | 0.484420 | 0.0519353 | ||||||||
\(88\) | −2.10721 | −0.224629 | ||||||||
\(89\) | −0.346987 | −0.0367806 | −0.0183903 | − | 0.999831i | \(-0.505854\pi\) | ||||
−0.0183903 | + | 0.999831i | \(0.505854\pi\) | |||||||
\(90\) | 30.6886 | 3.23486 | ||||||||
\(91\) | −2.06634 | −0.216611 | ||||||||
\(92\) | 18.1736 | 1.89473 | ||||||||
\(93\) | −7.12407 | −0.738732 | ||||||||
\(94\) | 14.5182 | 1.49744 | ||||||||
\(95\) | 2.20391 | 0.226116 | ||||||||
\(96\) | 21.3123 | 2.17518 | ||||||||
\(97\) | 10.3716 | 1.05307 | 0.526537 | − | 0.850152i | \(-0.323490\pi\) | ||||
0.526537 | + | 0.850152i | \(0.323490\pi\) | |||||||
\(98\) | −17.5287 | −1.77067 | ||||||||
\(99\) | 6.53822 | 0.657116 | ||||||||
\(100\) | −1.61201 | −0.161201 | ||||||||
\(101\) | 9.06625 | 0.902126 | 0.451063 | − | 0.892492i | \(-0.351045\pi\) | ||||
0.451063 | + | 0.892492i | \(0.351045\pi\) | |||||||
\(102\) | 27.3733 | 2.71036 | ||||||||
\(103\) | 12.2871 | 1.21068 | 0.605341 | − | 0.795966i | \(-0.293037\pi\) | ||||
0.605341 | + | 0.795966i | \(0.293037\pi\) | |||||||
\(104\) | 1.12875 | 0.110683 | ||||||||
\(105\) | −25.1406 | −2.45347 | ||||||||
\(106\) | 28.5634 | 2.77433 | ||||||||
\(107\) | −5.76006 | −0.556846 | −0.278423 | − | 0.960459i | \(-0.589812\pi\) | ||||
−0.278423 | + | 0.960459i | \(0.589812\pi\) | |||||||
\(108\) | 32.2073 | 3.09915 | ||||||||
\(109\) | −5.23952 | −0.501855 | −0.250927 | − | 0.968006i | \(-0.580736\pi\) | ||||
−0.250927 | + | 0.968006i | \(0.580736\pi\) | |||||||
\(110\) | 4.69372 | 0.447529 | ||||||||
\(111\) | 10.7199 | 1.01749 | ||||||||
\(112\) | −4.65892 | −0.440226 | ||||||||
\(113\) | 1.67660 | 0.157721 | 0.0788607 | − | 0.996886i | \(-0.474872\pi\) | ||||
0.0788607 | + | 0.996886i | \(0.474872\pi\) | |||||||
\(114\) | 7.17439 | 0.671943 | ||||||||
\(115\) | −13.0118 | −1.21335 | ||||||||
\(116\) | 0.462299 | 0.0429234 | ||||||||
\(117\) | −3.50228 | −0.323785 | ||||||||
\(118\) | 0.311468 | 0.0286729 | ||||||||
\(119\) | −15.3715 | −1.40911 | ||||||||
\(120\) | 13.7332 | 1.25366 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −7.03456 | −0.636879 | ||||||||
\(123\) | 12.4783 | 1.12513 | ||||||||
\(124\) | −6.79876 | −0.610546 | ||||||||
\(125\) | 11.7053 | 1.04695 | ||||||||
\(126\) | −56.0994 | −4.99774 | ||||||||
\(127\) | 12.8375 | 1.13914 | 0.569571 | − | 0.821942i | \(-0.307110\pi\) | ||||
0.569571 | + | 0.821942i | \(0.307110\pi\) | |||||||
\(128\) | 14.9664 | 1.32286 | ||||||||
\(129\) | 26.2575 | 2.31184 | ||||||||
\(130\) | −2.51424 | −0.220514 | ||||||||
\(131\) | 3.92349 | 0.342797 | 0.171399 | − | 0.985202i | \(-0.445171\pi\) | ||||
0.171399 | + | 0.985202i | \(0.445171\pi\) | |||||||
\(132\) | 9.10267 | 0.792286 | ||||||||
\(133\) | −4.02880 | −0.349341 | ||||||||
\(134\) | −21.1540 | −1.82743 | ||||||||
\(135\) | −23.0594 | −1.98464 | ||||||||
\(136\) | 8.39680 | 0.720020 | ||||||||
\(137\) | −14.5401 | −1.24224 | −0.621122 | − | 0.783714i | \(-0.713323\pi\) | ||||
−0.621122 | + | 0.783714i | \(0.713323\pi\) | |||||||
\(138\) | −42.3572 | −3.60569 | ||||||||
\(139\) | 8.17531 | 0.693420 | 0.346710 | − | 0.937972i | \(-0.387299\pi\) | ||||
0.346710 | + | 0.937972i | \(0.387299\pi\) | |||||||
\(140\) | −23.9925 | −2.02774 | ||||||||
\(141\) | −20.1586 | −1.69766 | ||||||||
\(142\) | −12.0909 | −1.01465 | ||||||||
\(143\) | −0.535662 | −0.0447943 | ||||||||
\(144\) | −7.89648 | −0.658040 | ||||||||
\(145\) | −0.330992 | −0.0274874 | ||||||||
\(146\) | −6.35369 | −0.525835 | ||||||||
\(147\) | 24.3387 | 2.00742 | ||||||||
\(148\) | 10.2304 | 0.840935 | ||||||||
\(149\) | 18.8259 | 1.54227 | 0.771137 | − | 0.636669i | \(-0.219688\pi\) | ||||
0.771137 | + | 0.636669i | \(0.219688\pi\) | |||||||
\(150\) | 3.75710 | 0.306766 | ||||||||
\(151\) | 3.93068 | 0.319874 | 0.159937 | − | 0.987127i | \(-0.448871\pi\) | ||||
0.159937 | + | 0.987127i | \(0.448871\pi\) | |||||||
\(152\) | 2.20076 | 0.178505 | ||||||||
\(153\) | −26.0535 | −2.10630 | ||||||||
\(154\) | −8.58022 | −0.691414 | ||||||||
\(155\) | 4.86770 | 0.390983 | ||||||||
\(156\) | −4.87595 | −0.390388 | ||||||||
\(157\) | 17.0071 | 1.35732 | 0.678658 | − | 0.734454i | \(-0.262562\pi\) | ||||
0.678658 | + | 0.734454i | \(0.262562\pi\) | |||||||
\(158\) | −24.2388 | −1.92834 | ||||||||
\(159\) | −39.6604 | −3.14527 | ||||||||
\(160\) | −14.5622 | −1.15124 | ||||||||
\(161\) | 23.7858 | 1.87458 | ||||||||
\(162\) | −31.4372 | −2.46994 | ||||||||
\(163\) | −1.17678 | −0.0921723 | −0.0460862 | − | 0.998937i | \(-0.514675\pi\) | ||||
−0.0460862 | + | 0.998937i | \(0.514675\pi\) | |||||||
\(164\) | 11.9085 | 0.929897 | ||||||||
\(165\) | −6.51724 | −0.507366 | ||||||||
\(166\) | −9.65364 | −0.749268 | ||||||||
\(167\) | −8.96042 | −0.693378 | −0.346689 | − | 0.937980i | \(-0.612694\pi\) | ||||
−0.346689 | + | 0.937980i | \(0.612694\pi\) | |||||||
\(168\) | −25.1046 | −1.93686 | ||||||||
\(169\) | −12.7131 | −0.977928 | ||||||||
\(170\) | −18.7035 | −1.43449 | ||||||||
\(171\) | −6.82847 | −0.522186 | ||||||||
\(172\) | 25.0585 | 1.91069 | ||||||||
\(173\) | −10.0532 | −0.764332 | −0.382166 | − | 0.924094i | \(-0.624822\pi\) | ||||
−0.382166 | + | 0.924094i | \(0.624822\pi\) | |||||||
\(174\) | −1.07748 | −0.0816835 | ||||||||
\(175\) | −2.10981 | −0.159487 | ||||||||
\(176\) | −1.20774 | −0.0910369 | ||||||||
\(177\) | −0.432474 | −0.0325067 | ||||||||
\(178\) | 0.771793 | 0.0578483 | ||||||||
\(179\) | −8.23468 | −0.615489 | −0.307745 | − | 0.951469i | \(-0.599574\pi\) | ||||
−0.307745 | + | 0.951469i | \(0.599574\pi\) | |||||||
\(180\) | −40.6654 | −3.03102 | ||||||||
\(181\) | −4.95249 | −0.368116 | −0.184058 | − | 0.982915i | \(-0.558923\pi\) | ||||
−0.184058 | + | 0.982915i | \(0.558923\pi\) | |||||||
\(182\) | 4.59610 | 0.340685 | ||||||||
\(183\) | 9.76750 | 0.722034 | ||||||||
\(184\) | −12.9931 | −0.957868 | ||||||||
\(185\) | −7.32467 | −0.538521 | ||||||||
\(186\) | 15.8459 | 1.16187 | ||||||||
\(187\) | −3.98479 | −0.291397 | ||||||||
\(188\) | −19.2381 | −1.40308 | ||||||||
\(189\) | 42.1532 | 3.06619 | ||||||||
\(190\) | −4.90209 | −0.355635 | ||||||||
\(191\) | 7.39271 | 0.534918 | 0.267459 | − | 0.963569i | \(-0.413816\pi\) | ||||
0.267459 | + | 0.963569i | \(0.413816\pi\) | |||||||
\(192\) | −39.9444 | −2.88274 | ||||||||
\(193\) | 7.02152 | 0.505420 | 0.252710 | − | 0.967542i | \(-0.418678\pi\) | ||||
0.252710 | + | 0.967542i | \(0.418678\pi\) | |||||||
\(194\) | −23.0692 | −1.65627 | ||||||||
\(195\) | 3.49103 | 0.249998 | ||||||||
\(196\) | 23.2273 | 1.65909 | ||||||||
\(197\) | −23.4547 | −1.67108 | −0.835539 | − | 0.549431i | \(-0.814844\pi\) | ||||
−0.835539 | + | 0.549431i | \(0.814844\pi\) | |||||||
\(198\) | −14.5428 | −1.03351 | ||||||||
\(199\) | 2.83149 | 0.200719 | 0.100359 | − | 0.994951i | \(-0.468001\pi\) | ||||
0.100359 | + | 0.994951i | \(0.468001\pi\) | |||||||
\(200\) | 1.15250 | 0.0814939 | ||||||||
\(201\) | 29.3724 | 2.07177 | ||||||||
\(202\) | −20.1658 | −1.41886 | ||||||||
\(203\) | 0.605061 | 0.0424670 | ||||||||
\(204\) | −36.2723 | −2.53957 | ||||||||
\(205\) | −8.52612 | −0.595490 | ||||||||
\(206\) | −27.3298 | −1.90416 | ||||||||
\(207\) | 40.3150 | 2.80208 | ||||||||
\(208\) | 0.646940 | 0.0448572 | ||||||||
\(209\) | −1.04439 | −0.0722422 | ||||||||
\(210\) | 55.9194 | 3.85880 | ||||||||
\(211\) | −19.3646 | −1.33311 | −0.666556 | − | 0.745455i | \(-0.732232\pi\) | ||||
−0.666556 | + | 0.745455i | \(0.732232\pi\) | |||||||
\(212\) | −37.8493 | −2.59950 | ||||||||
\(213\) | 16.7883 | 1.15031 | ||||||||
\(214\) | 12.8119 | 0.875805 | ||||||||
\(215\) | −17.9411 | −1.22357 | ||||||||
\(216\) | −23.0265 | −1.56675 | ||||||||
\(217\) | −8.89828 | −0.604054 | ||||||||
\(218\) | 11.6541 | 0.789315 | ||||||||
\(219\) | 8.82211 | 0.596143 | ||||||||
\(220\) | −6.21963 | −0.419328 | ||||||||
\(221\) | 2.13450 | 0.143582 | ||||||||
\(222\) | −23.8440 | −1.60031 | ||||||||
\(223\) | −2.46289 | −0.164927 | −0.0824637 | − | 0.996594i | \(-0.526279\pi\) | ||||
−0.0824637 | + | 0.996594i | \(0.526279\pi\) | |||||||
\(224\) | 26.6200 | 1.77863 | ||||||||
\(225\) | −3.57595 | −0.238397 | ||||||||
\(226\) | −3.72921 | −0.248064 | ||||||||
\(227\) | 12.3511 | 0.819771 | 0.409886 | − | 0.912137i | \(-0.365569\pi\) | ||||
0.409886 | + | 0.912137i | \(0.365569\pi\) | |||||||
\(228\) | −9.50676 | −0.629601 | ||||||||
\(229\) | −1.85335 | −0.122473 | −0.0612365 | − | 0.998123i | \(-0.519504\pi\) | ||||
−0.0612365 | + | 0.998123i | \(0.519504\pi\) | |||||||
\(230\) | 28.9417 | 1.90836 | ||||||||
\(231\) | 11.9137 | 0.783861 | ||||||||
\(232\) | −0.330519 | −0.0216996 | ||||||||
\(233\) | −0.198599 | −0.0130106 | −0.00650532 | − | 0.999979i | \(-0.502071\pi\) | ||||
−0.00650532 | + | 0.999979i | \(0.502071\pi\) | |||||||
\(234\) | 7.79000 | 0.509248 | ||||||||
\(235\) | 13.7739 | 0.898508 | ||||||||
\(236\) | −0.412725 | −0.0268661 | ||||||||
\(237\) | 33.6556 | 2.18617 | ||||||||
\(238\) | 34.1904 | 2.21624 | ||||||||
\(239\) | 9.27402 | 0.599887 | 0.299943 | − | 0.953957i | \(-0.403032\pi\) | ||||
0.299943 | + | 0.953957i | \(0.403032\pi\) | |||||||
\(240\) | 7.87113 | 0.508079 | ||||||||
\(241\) | 6.90113 | 0.444541 | 0.222271 | − | 0.974985i | \(-0.428653\pi\) | ||||
0.222271 | + | 0.974985i | \(0.428653\pi\) | |||||||
\(242\) | −2.22427 | −0.142981 | ||||||||
\(243\) | 10.8682 | 0.697194 | ||||||||
\(244\) | 9.32147 | 0.596746 | ||||||||
\(245\) | −16.6300 | −1.06245 | ||||||||
\(246\) | −27.7551 | −1.76960 | ||||||||
\(247\) | 0.559441 | 0.0355964 | ||||||||
\(248\) | 4.86074 | 0.308657 | ||||||||
\(249\) | 13.4041 | 0.849450 | ||||||||
\(250\) | −26.0357 | −1.64664 | ||||||||
\(251\) | −13.0171 | −0.821630 | −0.410815 | − | 0.911719i | \(-0.634756\pi\) | ||||
−0.410815 | + | 0.911719i | \(0.634756\pi\) | |||||||
\(252\) | 74.3372 | 4.68280 | ||||||||
\(253\) | 6.16604 | 0.387656 | ||||||||
\(254\) | −28.5540 | −1.79164 | ||||||||
\(255\) | 25.9698 | 1.62630 | ||||||||
\(256\) | −7.42204 | −0.463877 | ||||||||
\(257\) | −1.15523 | −0.0720612 | −0.0360306 | − | 0.999351i | \(-0.511471\pi\) | ||||
−0.0360306 | + | 0.999351i | \(0.511471\pi\) | |||||||
\(258\) | −58.4037 | −3.63606 | ||||||||
\(259\) | 13.3897 | 0.831994 | ||||||||
\(260\) | 3.33162 | 0.206618 | ||||||||
\(261\) | 1.02553 | 0.0634786 | ||||||||
\(262\) | −8.72691 | −0.539150 | ||||||||
\(263\) | 12.9324 | 0.797448 | 0.398724 | − | 0.917071i | \(-0.369453\pi\) | ||||
0.398724 | + | 0.917071i | \(0.369453\pi\) | |||||||
\(264\) | −6.50791 | −0.400534 | ||||||||
\(265\) | 27.0990 | 1.66468 | ||||||||
\(266\) | 8.96112 | 0.549442 | ||||||||
\(267\) | −1.07164 | −0.0655830 | ||||||||
\(268\) | 28.0311 | 1.71227 | ||||||||
\(269\) | −21.6300 | −1.31880 | −0.659402 | − | 0.751790i | \(-0.729191\pi\) | ||||
−0.659402 | + | 0.751790i | \(0.729191\pi\) | |||||||
\(270\) | 51.2904 | 3.12144 | ||||||||
\(271\) | 27.9706 | 1.69909 | 0.849546 | − | 0.527515i | \(-0.176876\pi\) | ||||
0.849546 | + | 0.527515i | \(0.176876\pi\) | |||||||
\(272\) | 4.81260 | 0.291807 | ||||||||
\(273\) | −6.38169 | −0.386237 | ||||||||
\(274\) | 32.3411 | 1.95380 | ||||||||
\(275\) | −0.546930 | −0.0329811 | ||||||||
\(276\) | 56.1274 | 3.37847 | ||||||||
\(277\) | 9.81001 | 0.589427 | 0.294713 | − | 0.955586i | \(-0.404776\pi\) | ||||
0.294713 | + | 0.955586i | \(0.404776\pi\) | |||||||
\(278\) | −18.1841 | −1.09061 | ||||||||
\(279\) | −15.0818 | −0.902926 | ||||||||
\(280\) | 17.1534 | 1.02511 | ||||||||
\(281\) | 14.1688 | 0.845243 | 0.422621 | − | 0.906306i | \(-0.361110\pi\) | ||||
0.422621 | + | 0.906306i | \(0.361110\pi\) | |||||||
\(282\) | 44.8381 | 2.67007 | ||||||||
\(283\) | 30.0213 | 1.78458 | 0.892292 | − | 0.451459i | \(-0.149096\pi\) | ||||
0.892292 | + | 0.451459i | \(0.149096\pi\) | |||||||
\(284\) | 16.0216 | 0.950709 | ||||||||
\(285\) | 6.80655 | 0.403185 | ||||||||
\(286\) | 1.19146 | 0.0704522 | ||||||||
\(287\) | 15.5859 | 0.920009 | ||||||||
\(288\) | 45.1187 | 2.65865 | ||||||||
\(289\) | −1.12141 | −0.0659655 | ||||||||
\(290\) | 0.736216 | 0.0432321 | ||||||||
\(291\) | 32.0316 | 1.87773 | ||||||||
\(292\) | 8.41926 | 0.492700 | ||||||||
\(293\) | −30.8962 | −1.80498 | −0.902488 | − | 0.430716i | \(-0.858261\pi\) | ||||
−0.902488 | + | 0.430716i | \(0.858261\pi\) | |||||||
\(294\) | −54.1358 | −3.15727 | ||||||||
\(295\) | 0.295499 | 0.0172046 | ||||||||
\(296\) | −7.31419 | −0.425129 | ||||||||
\(297\) | 10.9275 | 0.634075 | ||||||||
\(298\) | −41.8738 | −2.42568 | ||||||||
\(299\) | −3.30291 | −0.191012 | ||||||||
\(300\) | −4.97853 | −0.287435 | ||||||||
\(301\) | 32.7968 | 1.89037 | ||||||||
\(302\) | −8.74289 | −0.503097 | ||||||||
\(303\) | 28.0002 | 1.60857 | ||||||||
\(304\) | 1.26136 | 0.0723437 | ||||||||
\(305\) | −6.67389 | −0.382146 | ||||||||
\(306\) | 57.9499 | 3.31278 | ||||||||
\(307\) | −17.7558 | −1.01338 | −0.506688 | − | 0.862130i | \(-0.669130\pi\) | ||||
−0.506688 | + | 0.862130i | \(0.669130\pi\) | |||||||
\(308\) | 11.3696 | 0.647845 | ||||||||
\(309\) | 37.9474 | 2.15875 | ||||||||
\(310\) | −10.8271 | −0.614937 | ||||||||
\(311\) | −5.69279 | −0.322809 | −0.161404 | − | 0.986888i | \(-0.551602\pi\) | ||||
−0.161404 | + | 0.986888i | \(0.551602\pi\) | |||||||
\(312\) | 3.48604 | 0.197358 | ||||||||
\(313\) | 9.14950 | 0.517160 | 0.258580 | − | 0.965990i | \(-0.416745\pi\) | ||||
0.258580 | + | 0.965990i | \(0.416745\pi\) | |||||||
\(314\) | −37.8284 | −2.13478 | ||||||||
\(315\) | −53.2232 | −2.99879 | ||||||||
\(316\) | 32.1188 | 1.80682 | ||||||||
\(317\) | −5.59589 | −0.314296 | −0.157148 | − | 0.987575i | \(-0.550230\pi\) | ||||
−0.157148 | + | 0.987575i | \(0.550230\pi\) | |||||||
\(318\) | 88.2154 | 4.94687 | ||||||||
\(319\) | 0.156851 | 0.00878199 | ||||||||
\(320\) | 27.2930 | 1.52573 | ||||||||
\(321\) | −17.7894 | −0.992906 | ||||||||
\(322\) | −52.9060 | −2.94834 | ||||||||
\(323\) | 4.16169 | 0.231563 | ||||||||
\(324\) | 41.6573 | 2.31429 | ||||||||
\(325\) | 0.292970 | 0.0162510 | ||||||||
\(326\) | 2.61747 | 0.144968 | ||||||||
\(327\) | −16.1817 | −0.894852 | ||||||||
\(328\) | −8.51392 | −0.470103 | ||||||||
\(329\) | −25.1789 | −1.38816 | ||||||||
\(330\) | 14.4961 | 0.797983 | ||||||||
\(331\) | 7.13143 | 0.391979 | 0.195989 | − | 0.980606i | \(-0.437208\pi\) | ||||
0.195989 | + | 0.980606i | \(0.437208\pi\) | |||||||
\(332\) | 12.7920 | 0.702053 | ||||||||
\(333\) | 22.6944 | 1.24364 | ||||||||
\(334\) | 19.9304 | 1.09054 | ||||||||
\(335\) | −20.0694 | −1.09651 | ||||||||
\(336\) | −14.3886 | −0.784963 | ||||||||
\(337\) | −29.1161 | −1.58606 | −0.793028 | − | 0.609186i | \(-0.791496\pi\) | ||||
−0.793028 | + | 0.609186i | \(0.791496\pi\) | |||||||
\(338\) | 28.2773 | 1.53808 | ||||||||
\(339\) | 5.17802 | 0.281231 | ||||||||
\(340\) | 24.7840 | 1.34410 | ||||||||
\(341\) | −2.30672 | −0.124916 | ||||||||
\(342\) | 15.1884 | 0.821293 | ||||||||
\(343\) | 3.39726 | 0.183435 | ||||||||
\(344\) | −17.9154 | −0.965936 | ||||||||
\(345\) | −40.1855 | −2.16352 | ||||||||
\(346\) | 22.3611 | 1.20214 | ||||||||
\(347\) | −10.9029 | −0.585296 | −0.292648 | − | 0.956220i | \(-0.594536\pi\) | ||||
−0.292648 | + | 0.956220i | \(0.594536\pi\) | |||||||
\(348\) | 1.42777 | 0.0765363 | ||||||||
\(349\) | −4.53780 | −0.242903 | −0.121451 | − | 0.992597i | \(-0.538755\pi\) | ||||
−0.121451 | + | 0.992597i | \(0.538755\pi\) | |||||||
\(350\) | 4.69279 | 0.250840 | ||||||||
\(351\) | −5.85342 | −0.312432 | ||||||||
\(352\) | 6.90076 | 0.367812 | ||||||||
\(353\) | −19.0740 | −1.01521 | −0.507603 | − | 0.861591i | \(-0.669468\pi\) | ||||
−0.507603 | + | 0.861591i | \(0.669468\pi\) | |||||||
\(354\) | 0.961938 | 0.0511264 | ||||||||
\(355\) | −11.4710 | −0.608818 | ||||||||
\(356\) | −1.02270 | −0.0542030 | ||||||||
\(357\) | −47.4735 | −2.51256 | ||||||||
\(358\) | 18.3162 | 0.968039 | ||||||||
\(359\) | −1.05316 | −0.0555839 | −0.0277919 | − | 0.999614i | \(-0.508848\pi\) | ||||
−0.0277919 | + | 0.999614i | \(0.508848\pi\) | |||||||
\(360\) | 29.0735 | 1.53231 | ||||||||
\(361\) | −17.9092 | −0.942592 | ||||||||
\(362\) | 11.0157 | 0.578971 | ||||||||
\(363\) | 3.08840 | 0.162099 | ||||||||
\(364\) | −6.09027 | −0.319217 | ||||||||
\(365\) | −6.02793 | −0.315516 | ||||||||
\(366\) | −21.7255 | −1.13561 | ||||||||
\(367\) | −27.5353 | −1.43733 | −0.718666 | − | 0.695355i | \(-0.755247\pi\) | ||||
−0.718666 | + | 0.695355i | \(0.755247\pi\) | |||||||
\(368\) | −7.44698 | −0.388200 | ||||||||
\(369\) | 26.4169 | 1.37521 | ||||||||
\(370\) | 16.2920 | 0.846983 | ||||||||
\(371\) | −49.5376 | −2.57186 | ||||||||
\(372\) | −20.9973 | −1.08866 | ||||||||
\(373\) | 15.6898 | 0.812385 | 0.406193 | − | 0.913788i | \(-0.366856\pi\) | ||||
0.406193 | + | 0.913788i | \(0.366856\pi\) | |||||||
\(374\) | 8.86325 | 0.458308 | ||||||||
\(375\) | 36.1507 | 1.86681 | ||||||||
\(376\) | 13.7542 | 0.709317 | ||||||||
\(377\) | −0.0840192 | −0.00432721 | ||||||||
\(378\) | −93.7601 | −4.82250 | ||||||||
\(379\) | 14.6468 | 0.752355 | 0.376177 | − | 0.926548i | \(-0.377238\pi\) | ||||
0.376177 | + | 0.926548i | \(0.377238\pi\) | |||||||
\(380\) | 6.49574 | 0.333224 | ||||||||
\(381\) | 39.6473 | 2.03119 | ||||||||
\(382\) | −16.4434 | −0.841317 | ||||||||
\(383\) | 10.6062 | 0.541951 | 0.270976 | − | 0.962586i | \(-0.412654\pi\) | ||||
0.270976 | + | 0.962586i | \(0.412654\pi\) | |||||||
\(384\) | 46.2224 | 2.35878 | ||||||||
\(385\) | −8.14031 | −0.414869 | ||||||||
\(386\) | −15.6178 | −0.794923 | ||||||||
\(387\) | 55.5878 | 2.82569 | ||||||||
\(388\) | 30.5689 | 1.55190 | ||||||||
\(389\) | −12.3692 | −0.627145 | −0.313572 | − | 0.949564i | \(-0.601526\pi\) | ||||
−0.313572 | + | 0.949564i | \(0.601526\pi\) | |||||||
\(390\) | −7.76500 | −0.393196 | ||||||||
\(391\) | −24.5704 | −1.24258 | ||||||||
\(392\) | −16.6063 | −0.838742 | ||||||||
\(393\) | 12.1173 | 0.611238 | ||||||||
\(394\) | 52.1695 | 2.62826 | ||||||||
\(395\) | −22.9961 | −1.15706 | ||||||||
\(396\) | 19.2706 | 0.968383 | ||||||||
\(397\) | −12.5684 | −0.630789 | −0.315395 | − | 0.948961i | \(-0.602137\pi\) | ||||
−0.315395 | + | 0.948961i | \(0.602137\pi\) | |||||||
\(398\) | −6.29799 | −0.315690 | ||||||||
\(399\) | −12.4425 | −0.622906 | ||||||||
\(400\) | 0.660550 | 0.0330275 | ||||||||
\(401\) | −27.3621 | −1.36640 | −0.683199 | − | 0.730233i | \(-0.739412\pi\) | ||||
−0.683199 | + | 0.730233i | \(0.739412\pi\) | |||||||
\(402\) | −65.3320 | −3.25847 | ||||||||
\(403\) | 1.23562 | 0.0615506 | ||||||||
\(404\) | 26.7216 | 1.32945 | ||||||||
\(405\) | −29.8254 | −1.48203 | ||||||||
\(406\) | −1.34582 | −0.0667919 | ||||||||
\(407\) | 3.47103 | 0.172053 | ||||||||
\(408\) | 25.9327 | 1.28386 | ||||||||
\(409\) | 8.81213 | 0.435732 | 0.217866 | − | 0.975979i | \(-0.430090\pi\) | ||||
0.217866 | + | 0.975979i | \(0.430090\pi\) | |||||||
\(410\) | 18.9644 | 0.936584 | ||||||||
\(411\) | −44.9057 | −2.21503 | ||||||||
\(412\) | 36.2146 | 1.78417 | ||||||||
\(413\) | −0.540179 | −0.0265805 | ||||||||
\(414\) | −89.6713 | −4.40710 | ||||||||
\(415\) | −9.15869 | −0.449583 | ||||||||
\(416\) | −3.69647 | −0.181235 | ||||||||
\(417\) | 25.2486 | 1.23643 | ||||||||
\(418\) | 2.32301 | 0.113622 | ||||||||
\(419\) | 8.05450 | 0.393488 | 0.196744 | − | 0.980455i | \(-0.436963\pi\) | ||||
0.196744 | + | 0.980455i | \(0.436963\pi\) | |||||||
\(420\) | −74.0986 | −3.61564 | ||||||||
\(421\) | −19.9741 | −0.973479 | −0.486740 | − | 0.873547i | \(-0.661814\pi\) | ||||
−0.486740 | + | 0.873547i | \(0.661814\pi\) | |||||||
\(422\) | 43.0720 | 2.09671 | ||||||||
\(423\) | −42.6762 | −2.07499 | ||||||||
\(424\) | 27.0602 | 1.31416 | ||||||||
\(425\) | 2.17941 | 0.105717 | ||||||||
\(426\) | −37.3416 | −1.80921 | ||||||||
\(427\) | 12.2000 | 0.590401 | ||||||||
\(428\) | −16.9770 | −0.820616 | ||||||||
\(429\) | −1.65434 | −0.0798722 | ||||||||
\(430\) | 39.9058 | 1.92443 | ||||||||
\(431\) | −10.3440 | −0.498253 | −0.249126 | − | 0.968471i | \(-0.580143\pi\) | ||||
−0.249126 | + | 0.968471i | \(0.580143\pi\) | |||||||
\(432\) | −13.1975 | −0.634967 | ||||||||
\(433\) | 15.4161 | 0.740851 | 0.370426 | − | 0.928862i | \(-0.379212\pi\) | ||||
0.370426 | + | 0.928862i | \(0.379212\pi\) | |||||||
\(434\) | 19.7922 | 0.950054 | ||||||||
\(435\) | −1.02224 | −0.0490125 | ||||||||
\(436\) | −15.4428 | −0.739576 | ||||||||
\(437\) | −6.43977 | −0.308056 | ||||||||
\(438\) | −19.6227 | −0.937611 | ||||||||
\(439\) | 7.06583 | 0.337234 | 0.168617 | − | 0.985682i | \(-0.446070\pi\) | ||||
0.168617 | + | 0.985682i | \(0.446070\pi\) | |||||||
\(440\) | 4.44670 | 0.211988 | ||||||||
\(441\) | 51.5256 | 2.45360 | ||||||||
\(442\) | −4.74770 | −0.225825 | ||||||||
\(443\) | −19.7417 | −0.937956 | −0.468978 | − | 0.883210i | \(-0.655378\pi\) | ||||
−0.468978 | + | 0.883210i | \(0.655378\pi\) | |||||||
\(444\) | 31.5956 | 1.49946 | ||||||||
\(445\) | 0.732223 | 0.0347107 | ||||||||
\(446\) | 5.47813 | 0.259397 | ||||||||
\(447\) | 58.1418 | 2.75001 | ||||||||
\(448\) | −49.8923 | −2.35719 | ||||||||
\(449\) | 6.28157 | 0.296446 | 0.148223 | − | 0.988954i | \(-0.452645\pi\) | ||||
0.148223 | + | 0.988954i | \(0.452645\pi\) | |||||||
\(450\) | 7.95388 | 0.374950 | ||||||||
\(451\) | 4.04037 | 0.190254 | ||||||||
\(452\) | 4.94157 | 0.232432 | ||||||||
\(453\) | 12.1395 | 0.570364 | ||||||||
\(454\) | −27.4722 | −1.28933 | ||||||||
\(455\) | 4.36045 | 0.204421 | ||||||||
\(456\) | 6.79682 | 0.318290 | ||||||||
\(457\) | 24.0253 | 1.12385 | 0.561927 | − | 0.827187i | \(-0.310060\pi\) | ||||
0.561927 | + | 0.827187i | \(0.310060\pi\) | |||||||
\(458\) | 4.12235 | 0.192625 | ||||||||
\(459\) | −43.5437 | −2.03244 | ||||||||
\(460\) | −38.3505 | −1.78810 | ||||||||
\(461\) | 33.3526 | 1.55339 | 0.776693 | − | 0.629880i | \(-0.216896\pi\) | ||||
0.776693 | + | 0.629880i | \(0.216896\pi\) | |||||||
\(462\) | −26.4992 | −1.23285 | ||||||||
\(463\) | −13.9887 | −0.650111 | −0.325055 | − | 0.945695i | \(-0.605383\pi\) | ||||
−0.325055 | + | 0.945695i | \(0.605383\pi\) | |||||||
\(464\) | −0.189436 | −0.00879433 | ||||||||
\(465\) | 15.0334 | 0.697159 | ||||||||
\(466\) | 0.441737 | 0.0204631 | ||||||||
\(467\) | −36.3572 | −1.68241 | −0.841205 | − | 0.540717i | \(-0.818153\pi\) | ||||
−0.841205 | + | 0.540717i | \(0.818153\pi\) | |||||||
\(468\) | −10.3225 | −0.477158 | ||||||||
\(469\) | 36.6874 | 1.69406 | ||||||||
\(470\) | −30.6368 | −1.41317 | ||||||||
\(471\) | 52.5249 | 2.42022 | ||||||||
\(472\) | 0.295076 | 0.0135820 | ||||||||
\(473\) | 8.50197 | 0.390921 | ||||||||
\(474\) | −74.8591 | −3.43839 | ||||||||
\(475\) | 0.571210 | 0.0262089 | ||||||||
\(476\) | −45.3056 | −2.07658 | ||||||||
\(477\) | −83.9621 | −3.84436 | ||||||||
\(478\) | −20.6279 | −0.943499 | ||||||||
\(479\) | 41.0972 | 1.87778 | 0.938890 | − | 0.344217i | \(-0.111856\pi\) | ||||
0.938890 | + | 0.344217i | \(0.111856\pi\) | |||||||
\(480\) | −44.9739 | −2.05277 | ||||||||
\(481\) | −1.85930 | −0.0847767 | ||||||||
\(482\) | −15.3500 | −0.699172 | ||||||||
\(483\) | 73.4601 | 3.34255 | ||||||||
\(484\) | 2.94737 | 0.133971 | ||||||||
\(485\) | −21.8864 | −0.993811 | ||||||||
\(486\) | −24.1738 | −1.09654 | ||||||||
\(487\) | −9.62834 | −0.436302 | −0.218151 | − | 0.975915i | \(-0.570002\pi\) | ||||
−0.218151 | + | 0.975915i | \(0.570002\pi\) | |||||||
\(488\) | −6.66435 | −0.301681 | ||||||||
\(489\) | −3.63436 | −0.164351 | ||||||||
\(490\) | 36.9897 | 1.67102 | ||||||||
\(491\) | −38.0027 | −1.71504 | −0.857519 | − | 0.514452i | \(-0.827995\pi\) | ||||
−0.857519 | + | 0.514452i | \(0.827995\pi\) | |||||||
\(492\) | 36.7782 | 1.65809 | ||||||||
\(493\) | −0.625020 | −0.0281495 | ||||||||
\(494\) | −1.24435 | −0.0559858 | ||||||||
\(495\) | −13.7972 | −0.620136 | ||||||||
\(496\) | 2.78592 | 0.125091 | ||||||||
\(497\) | 20.9693 | 0.940600 | ||||||||
\(498\) | −29.8143 | −1.33601 | ||||||||
\(499\) | 0.226266 | 0.0101290 | 0.00506452 | − | 0.999987i | \(-0.498388\pi\) | ||||
0.00506452 | + | 0.999987i | \(0.498388\pi\) | |||||||
\(500\) | 34.4999 | 1.54288 | ||||||||
\(501\) | −27.6734 | −1.23636 | ||||||||
\(502\) | 28.9535 | 1.29226 | ||||||||
\(503\) | 30.0905 | 1.34167 | 0.670835 | − | 0.741607i | \(-0.265936\pi\) | ||||
0.670835 | + | 0.741607i | \(0.265936\pi\) | |||||||
\(504\) | −53.1471 | −2.36736 | ||||||||
\(505\) | −19.1319 | −0.851357 | ||||||||
\(506\) | −13.7149 | −0.609703 | ||||||||
\(507\) | −39.2631 | −1.74373 | ||||||||
\(508\) | 37.8368 | 1.67874 | ||||||||
\(509\) | 20.9211 | 0.927309 | 0.463655 | − | 0.886016i | \(-0.346538\pi\) | ||||
0.463655 | + | 0.886016i | \(0.346538\pi\) | |||||||
\(510\) | −57.7639 | −2.55783 | ||||||||
\(511\) | 11.0192 | 0.487461 | ||||||||
\(512\) | −13.4243 | −0.593274 | ||||||||
\(513\) | −11.4126 | −0.503877 | ||||||||
\(514\) | 2.56954 | 0.113337 | ||||||||
\(515\) | −25.9286 | −1.14255 | ||||||||
\(516\) | 77.3906 | 3.40693 | ||||||||
\(517\) | −6.52719 | −0.287065 | ||||||||
\(518\) | −29.7822 | −1.30856 | ||||||||
\(519\) | −31.0484 | −1.36287 | ||||||||
\(520\) | −2.38193 | −0.104454 | ||||||||
\(521\) | 5.93620 | 0.260070 | 0.130035 | − | 0.991509i | \(-0.458491\pi\) | ||||
0.130035 | + | 0.991509i | \(0.458491\pi\) | |||||||
\(522\) | −2.28105 | −0.0998389 | ||||||||
\(523\) | −5.09836 | −0.222936 | −0.111468 | − | 0.993768i | \(-0.535555\pi\) | ||||
−0.111468 | + | 0.993768i | \(0.535555\pi\) | |||||||
\(524\) | 11.5640 | 0.505176 | ||||||||
\(525\) | −6.51594 | −0.284379 | ||||||||
\(526\) | −28.7652 | −1.25422 | ||||||||
\(527\) | 9.19180 | 0.400401 | ||||||||
\(528\) | −3.72999 | −0.162327 | ||||||||
\(529\) | 15.0200 | 0.653045 | ||||||||
\(530\) | −60.2754 | −2.61820 | ||||||||
\(531\) | −0.915558 | −0.0397318 | ||||||||
\(532\) | −11.8744 | −0.514819 | ||||||||
\(533\) | −2.16427 | −0.0937451 | ||||||||
\(534\) | 2.38361 | 0.103149 | ||||||||
\(535\) | 12.1550 | 0.525509 | ||||||||
\(536\) | −20.0407 | −0.865627 | ||||||||
\(537\) | −25.4320 | −1.09747 | ||||||||
\(538\) | 48.1110 | 2.07421 | ||||||||
\(539\) | 7.88068 | 0.339445 | ||||||||
\(540\) | −67.9648 | −2.92474 | ||||||||
\(541\) | 37.7160 | 1.62154 | 0.810768 | − | 0.585367i | \(-0.199050\pi\) | ||||
0.810768 | + | 0.585367i | \(0.199050\pi\) | |||||||
\(542\) | −62.2141 | −2.67232 | ||||||||
\(543\) | −15.2953 | −0.656384 | ||||||||
\(544\) | −27.4981 | −1.17897 | ||||||||
\(545\) | 11.0566 | 0.473612 | ||||||||
\(546\) | 14.1946 | 0.607472 | ||||||||
\(547\) | −1.00000 | −0.0427569 | ||||||||
\(548\) | −42.8551 | −1.83068 | ||||||||
\(549\) | 20.6780 | 0.882517 | ||||||||
\(550\) | 1.21652 | 0.0518726 | ||||||||
\(551\) | −0.163814 | −0.00697873 | ||||||||
\(552\) | −40.1281 | −1.70796 | ||||||||
\(553\) | 42.0373 | 1.78761 | ||||||||
\(554\) | −21.8201 | −0.927048 | ||||||||
\(555\) | −22.6215 | −0.960231 | ||||||||
\(556\) | 24.0957 | 1.02188 | ||||||||
\(557\) | −1.18570 | −0.0502398 | −0.0251199 | − | 0.999684i | \(-0.507997\pi\) | ||||
−0.0251199 | + | 0.999684i | \(0.507997\pi\) | |||||||
\(558\) | 33.5461 | 1.42012 | ||||||||
\(559\) | −4.55418 | −0.192621 | ||||||||
\(560\) | 9.83139 | 0.415452 | ||||||||
\(561\) | −12.3066 | −0.519587 | ||||||||
\(562\) | −31.5153 | −1.32939 | ||||||||
\(563\) | 37.7381 | 1.59047 | 0.795235 | − | 0.606301i | \(-0.207347\pi\) | ||||
0.795235 | + | 0.606301i | \(0.207347\pi\) | |||||||
\(564\) | −59.4148 | −2.50182 | ||||||||
\(565\) | −3.53802 | −0.148845 | ||||||||
\(566\) | −66.7755 | −2.80678 | ||||||||
\(567\) | 54.5215 | 2.28969 | ||||||||
\(568\) | −11.4546 | −0.480624 | ||||||||
\(569\) | 43.6469 | 1.82977 | 0.914886 | − | 0.403712i | \(-0.132280\pi\) | ||||
0.914886 | + | 0.403712i | \(0.132280\pi\) | |||||||
\(570\) | −15.1396 | −0.634128 | ||||||||
\(571\) | −33.6250 | −1.40716 | −0.703581 | − | 0.710615i | \(-0.748417\pi\) | ||||
−0.703581 | + | 0.710615i | \(0.748417\pi\) | |||||||
\(572\) | −1.57879 | −0.0660127 | ||||||||
\(573\) | 22.8317 | 0.953807 | ||||||||
\(574\) | −34.6673 | −1.44699 | ||||||||
\(575\) | −3.37239 | −0.140639 | ||||||||
\(576\) | −84.5632 | −3.52347 | ||||||||
\(577\) | 16.9423 | 0.705319 | 0.352659 | − | 0.935752i | \(-0.385277\pi\) | ||||
0.352659 | + | 0.935752i | \(0.385277\pi\) | |||||||
\(578\) | 2.49433 | 0.103750 | ||||||||
\(579\) | 21.6853 | 0.901209 | ||||||||
\(580\) | −0.975557 | −0.0405078 | ||||||||
\(581\) | 16.7423 | 0.694588 | ||||||||
\(582\) | −71.2469 | −2.95328 | ||||||||
\(583\) | −12.8417 | −0.531850 | ||||||||
\(584\) | −6.01931 | −0.249081 | ||||||||
\(585\) | 7.39061 | 0.305564 | ||||||||
\(586\) | 68.7215 | 2.83886 | ||||||||
\(587\) | 38.1451 | 1.57442 | 0.787208 | − | 0.616688i | \(-0.211526\pi\) | ||||
0.787208 | + | 0.616688i | \(0.211526\pi\) | |||||||
\(588\) | 71.7352 | 2.95831 | ||||||||
\(589\) | 2.40912 | 0.0992660 | ||||||||
\(590\) | −0.657269 | −0.0270593 | ||||||||
\(591\) | −72.4375 | −2.97968 | ||||||||
\(592\) | −4.19210 | −0.172294 | ||||||||
\(593\) | 25.1129 | 1.03126 | 0.515631 | − | 0.856811i | \(-0.327558\pi\) | ||||
0.515631 | + | 0.856811i | \(0.327558\pi\) | |||||||
\(594\) | −24.3056 | −0.997271 | ||||||||
\(595\) | 32.4375 | 1.32981 | ||||||||
\(596\) | 55.4868 | 2.27283 | ||||||||
\(597\) | 8.74477 | 0.357900 | ||||||||
\(598\) | 7.34656 | 0.300423 | ||||||||
\(599\) | 24.9337 | 1.01876 | 0.509381 | − | 0.860541i | \(-0.329874\pi\) | ||||
0.509381 | + | 0.860541i | \(0.329874\pi\) | |||||||
\(600\) | 3.55938 | 0.145311 | ||||||||
\(601\) | −8.46712 | −0.345381 | −0.172691 | − | 0.984976i | \(-0.555246\pi\) | ||||
−0.172691 | + | 0.984976i | \(0.555246\pi\) | |||||||
\(602\) | −72.9488 | −2.97317 | ||||||||
\(603\) | 62.1820 | 2.53225 | ||||||||
\(604\) | 11.5852 | 0.471394 | ||||||||
\(605\) | −2.11023 | −0.0857930 | ||||||||
\(606\) | −62.2800 | −2.52995 | ||||||||
\(607\) | −5.03143 | −0.204219 | −0.102110 | − | 0.994773i | \(-0.532559\pi\) | ||||
−0.102110 | + | 0.994773i | \(0.532559\pi\) | |||||||
\(608\) | −7.20711 | −0.292287 | ||||||||
\(609\) | 1.86867 | 0.0757224 | ||||||||
\(610\) | 14.8445 | 0.601038 | ||||||||
\(611\) | 3.49636 | 0.141448 | ||||||||
\(612\) | −76.7893 | −3.10402 | ||||||||
\(613\) | 28.4623 | 1.14958 | 0.574791 | − | 0.818300i | \(-0.305083\pi\) | ||||
0.574791 | + | 0.818300i | \(0.305083\pi\) | |||||||
\(614\) | 39.4936 | 1.59383 | ||||||||
\(615\) | −26.3321 | −1.06181 | ||||||||
\(616\) | −8.12867 | −0.327513 | ||||||||
\(617\) | 35.5711 | 1.43204 | 0.716020 | − | 0.698080i | \(-0.245962\pi\) | ||||
0.716020 | + | 0.698080i | \(0.245962\pi\) | |||||||
\(618\) | −84.4053 | −3.39528 | ||||||||
\(619\) | −10.9889 | −0.441681 | −0.220841 | − | 0.975310i | \(-0.570880\pi\) | ||||
−0.220841 | + | 0.975310i | \(0.570880\pi\) | |||||||
\(620\) | 14.3469 | 0.576187 | ||||||||
\(621\) | 67.3791 | 2.70383 | ||||||||
\(622\) | 12.6623 | 0.507712 | ||||||||
\(623\) | −1.33852 | −0.0536267 | ||||||||
\(624\) | 1.99801 | 0.0799845 | ||||||||
\(625\) | −21.9662 | −0.878649 | ||||||||
\(626\) | −20.3509 | −0.813388 | ||||||||
\(627\) | −3.22550 | −0.128814 | ||||||||
\(628\) | 50.1264 | 2.00026 | ||||||||
\(629\) | −13.8313 | −0.551492 | ||||||||
\(630\) | 118.383 | 4.71648 | ||||||||
\(631\) | −37.6573 | −1.49911 | −0.749557 | − | 0.661940i | \(-0.769733\pi\) | ||||
−0.749557 | + | 0.661940i | \(0.769733\pi\) | |||||||
\(632\) | −22.9632 | −0.913426 | ||||||||
\(633\) | −59.8055 | −2.37706 | ||||||||
\(634\) | 12.4468 | 0.494324 | ||||||||
\(635\) | −27.0900 | −1.07503 | ||||||||
\(636\) | −116.894 | −4.63515 | ||||||||
\(637\) | −4.22138 | −0.167257 | ||||||||
\(638\) | −0.348879 | −0.0138123 | ||||||||
\(639\) | 35.5412 | 1.40599 | ||||||||
\(640\) | −31.5826 | −1.24841 | ||||||||
\(641\) | −10.3003 | −0.406839 | −0.203419 | − | 0.979092i | \(-0.565205\pi\) | ||||
−0.203419 | + | 0.979092i | \(0.565205\pi\) | |||||||
\(642\) | 39.5684 | 1.56164 | ||||||||
\(643\) | −47.8274 | −1.88613 | −0.943063 | − | 0.332613i | \(-0.892070\pi\) | ||||
−0.943063 | + | 0.332613i | \(0.892070\pi\) | |||||||
\(644\) | 70.1056 | 2.76255 | ||||||||
\(645\) | −55.4093 | −2.18174 | ||||||||
\(646\) | −9.25672 | −0.364201 | ||||||||
\(647\) | −3.68463 | −0.144858 | −0.0724289 | − | 0.997374i | \(-0.523075\pi\) | ||||
−0.0724289 | + | 0.997374i | \(0.523075\pi\) | |||||||
\(648\) | −29.7827 | −1.16998 | ||||||||
\(649\) | −0.140032 | −0.00549672 | ||||||||
\(650\) | −0.651643 | −0.0255596 | ||||||||
\(651\) | −27.4814 | −1.07708 | ||||||||
\(652\) | −3.46840 | −0.135833 | ||||||||
\(653\) | −11.5337 | −0.451350 | −0.225675 | − | 0.974203i | \(-0.572459\pi\) | ||||
−0.225675 | + | 0.974203i | \(0.572459\pi\) | |||||||
\(654\) | 35.9925 | 1.40742 | ||||||||
\(655\) | −8.27947 | −0.323506 | ||||||||
\(656\) | −4.87972 | −0.190521 | ||||||||
\(657\) | 18.6766 | 0.728645 | ||||||||
\(658\) | 56.0047 | 2.18329 | ||||||||
\(659\) | −16.3376 | −0.636424 | −0.318212 | − | 0.948020i | \(-0.603082\pi\) | ||||
−0.318212 | + | 0.948020i | \(0.603082\pi\) | |||||||
\(660\) | −19.2087 | −0.747699 | ||||||||
\(661\) | −11.2252 | −0.436608 | −0.218304 | − | 0.975881i | \(-0.570052\pi\) | ||||
−0.218304 | + | 0.975881i | \(0.570052\pi\) | |||||||
\(662\) | −15.8622 | −0.616502 | ||||||||
\(663\) | 6.59220 | 0.256020 | ||||||||
\(664\) | −9.14559 | −0.354918 | ||||||||
\(665\) | 8.50168 | 0.329681 | ||||||||
\(666\) | −50.4784 | −1.95600 | ||||||||
\(667\) | 0.967151 | 0.0374482 | ||||||||
\(668\) | −26.4097 | −1.02182 | ||||||||
\(669\) | −7.60639 | −0.294080 | ||||||||
\(670\) | 44.6398 | 1.72459 | ||||||||
\(671\) | 3.16264 | 0.122092 | ||||||||
\(672\) | 82.2133 | 3.17145 | ||||||||
\(673\) | −26.4883 | −1.02105 | −0.510525 | − | 0.859863i | \(-0.670549\pi\) | ||||
−0.510525 | + | 0.859863i | \(0.670549\pi\) | |||||||
\(674\) | 64.7620 | 2.49454 | ||||||||
\(675\) | −5.97656 | −0.230038 | ||||||||
\(676\) | −37.4701 | −1.44116 | ||||||||
\(677\) | −30.4686 | −1.17101 | −0.585503 | − | 0.810671i | \(-0.699103\pi\) | ||||
−0.585503 | + | 0.810671i | \(0.699103\pi\) | |||||||
\(678\) | −11.5173 | −0.442320 | ||||||||
\(679\) | 40.0089 | 1.53540 | ||||||||
\(680\) | −17.7192 | −0.679500 | ||||||||
\(681\) | 38.1451 | 1.46173 | ||||||||
\(682\) | 5.13076 | 0.196467 | ||||||||
\(683\) | 44.2609 | 1.69360 | 0.846798 | − | 0.531914i | \(-0.178527\pi\) | ||||
0.846798 | + | 0.531914i | \(0.178527\pi\) | |||||||
\(684\) | −20.1261 | −0.769539 | ||||||||
\(685\) | 30.6830 | 1.17234 | ||||||||
\(686\) | −7.55642 | −0.288506 | ||||||||
\(687\) | −5.72390 | −0.218380 | ||||||||
\(688\) | −10.2682 | −0.391470 | ||||||||
\(689\) | 6.87882 | 0.262062 | ||||||||
\(690\) | 89.3835 | 3.40277 | ||||||||
\(691\) | 44.0606 | 1.67615 | 0.838073 | − | 0.545558i | \(-0.183682\pi\) | ||||
0.838073 | + | 0.545558i | \(0.183682\pi\) | |||||||
\(692\) | −29.6306 | −1.12639 | ||||||||
\(693\) | 25.2215 | 0.958086 | ||||||||
\(694\) | 24.2509 | 0.920551 | ||||||||
\(695\) | −17.2518 | −0.654397 | ||||||||
\(696\) | −1.02077 | −0.0386924 | ||||||||
\(697\) | −16.1001 | −0.609833 | ||||||||
\(698\) | 10.0933 | 0.382036 | ||||||||
\(699\) | −0.613353 | −0.0231991 | ||||||||
\(700\) | −6.21840 | −0.235033 | ||||||||
\(701\) | 37.2516 | 1.40698 | 0.703488 | − | 0.710708i | \(-0.251625\pi\) | ||||
0.703488 | + | 0.710708i | \(0.251625\pi\) | |||||||
\(702\) | 13.0196 | 0.491392 | ||||||||
\(703\) | −3.62512 | −0.136724 | ||||||||
\(704\) | −12.9337 | −0.487456 | ||||||||
\(705\) | 42.5392 | 1.60212 | ||||||||
\(706\) | 42.4257 | 1.59671 | ||||||||
\(707\) | 34.9735 | 1.31531 | ||||||||
\(708\) | −1.27466 | −0.0479047 | ||||||||
\(709\) | 8.08734 | 0.303726 | 0.151863 | − | 0.988402i | \(-0.451473\pi\) | ||||
0.151863 | + | 0.988402i | \(0.451473\pi\) | |||||||
\(710\) | 25.5146 | 0.957546 | ||||||||
\(711\) | 71.2498 | 2.67208 | ||||||||
\(712\) | 0.731175 | 0.0274020 | ||||||||
\(713\) | −14.2233 | −0.532667 | ||||||||
\(714\) | 105.594 | 3.95175 | ||||||||
\(715\) | 1.13037 | 0.0422734 | ||||||||
\(716\) | −24.2707 | −0.907038 | ||||||||
\(717\) | 28.6419 | 1.06965 | ||||||||
\(718\) | 2.34252 | 0.0874221 | ||||||||
\(719\) | −31.9518 | −1.19160 | −0.595800 | − | 0.803133i | \(-0.703165\pi\) | ||||
−0.595800 | + | 0.803133i | \(0.703165\pi\) | |||||||
\(720\) | 16.6634 | 0.621008 | ||||||||
\(721\) | 47.3980 | 1.76519 | ||||||||
\(722\) | 39.8350 | 1.48250 | ||||||||
\(723\) | 21.3135 | 0.792657 | ||||||||
\(724\) | −14.5968 | −0.542487 | ||||||||
\(725\) | −0.0857867 | −0.00318604 | ||||||||
\(726\) | −6.86944 | −0.254949 | ||||||||
\(727\) | −34.4763 | −1.27865 | −0.639327 | − | 0.768935i | \(-0.720787\pi\) | ||||
−0.639327 | + | 0.768935i | \(0.720787\pi\) | |||||||
\(728\) | 4.35422 | 0.161378 | ||||||||
\(729\) | −8.83579 | −0.327252 | ||||||||
\(730\) | 13.4077 | 0.496243 | ||||||||
\(731\) | −33.8786 | −1.25305 | ||||||||
\(732\) | 28.7885 | 1.06405 | ||||||||
\(733\) | −15.8583 | −0.585741 | −0.292870 | − | 0.956152i | \(-0.594610\pi\) | ||||
−0.292870 | + | 0.956152i | \(0.594610\pi\) | |||||||
\(734\) | 61.2460 | 2.26063 | ||||||||
\(735\) | −51.3603 | −1.89445 | ||||||||
\(736\) | 42.5504 | 1.56843 | ||||||||
\(737\) | 9.51054 | 0.350325 | ||||||||
\(738\) | −58.7582 | −2.16292 | ||||||||
\(739\) | 34.3327 | 1.26295 | 0.631475 | − | 0.775397i | \(-0.282450\pi\) | ||||
0.631475 | + | 0.775397i | \(0.282450\pi\) | |||||||
\(740\) | −21.5885 | −0.793610 | ||||||||
\(741\) | 1.72778 | 0.0634715 | ||||||||
\(742\) | 110.185 | 4.04501 | ||||||||
\(743\) | 7.58532 | 0.278278 | 0.139139 | − | 0.990273i | \(-0.455566\pi\) | ||||
0.139139 | + | 0.990273i | \(0.455566\pi\) | |||||||
\(744\) | 15.0119 | 0.550364 | ||||||||
\(745\) | −39.7269 | −1.45548 | ||||||||
\(746\) | −34.8982 | −1.27772 | ||||||||
\(747\) | 28.3768 | 1.03825 | ||||||||
\(748\) | −11.7447 | −0.429428 | ||||||||
\(749\) | −22.2197 | −0.811890 | ||||||||
\(750\) | −80.4088 | −2.93611 | ||||||||
\(751\) | 0.351350 | 0.0128210 | 0.00641048 | − | 0.999979i | \(-0.497959\pi\) | ||||
0.00641048 | + | 0.999979i | \(0.497959\pi\) | |||||||
\(752\) | 7.88315 | 0.287469 | ||||||||
\(753\) | −40.2020 | −1.46504 | ||||||||
\(754\) | 0.186881 | 0.00680582 | ||||||||
\(755\) | −8.29464 | −0.301873 | ||||||||
\(756\) | 124.241 | 4.51861 | ||||||||
\(757\) | −9.63210 | −0.350085 | −0.175042 | − | 0.984561i | \(-0.556006\pi\) | ||||
−0.175042 | + | 0.984561i | \(0.556006\pi\) | |||||||
\(758\) | −32.5784 | −1.18330 | ||||||||
\(759\) | 19.0432 | 0.691225 | ||||||||
\(760\) | −4.64410 | −0.168459 | ||||||||
\(761\) | −24.3509 | −0.882721 | −0.441360 | − | 0.897330i | \(-0.645504\pi\) | ||||
−0.441360 | + | 0.897330i | \(0.645504\pi\) | |||||||
\(762\) | −88.1862 | −3.19465 | ||||||||
\(763\) | −20.2117 | −0.731712 | ||||||||
\(764\) | 21.7891 | 0.788301 | ||||||||
\(765\) | 54.9788 | 1.98776 | ||||||||
\(766\) | −23.5910 | −0.852378 | ||||||||
\(767\) | 0.0750095 | 0.00270844 | ||||||||
\(768\) | −22.9222 | −0.827135 | ||||||||
\(769\) | −12.6126 | −0.454821 | −0.227410 | − | 0.973799i | \(-0.573026\pi\) | ||||
−0.227410 | + | 0.973799i | \(0.573026\pi\) | |||||||
\(770\) | 18.1062 | 0.652504 | ||||||||
\(771\) | −3.56781 | −0.128492 | ||||||||
\(772\) | 20.6950 | 0.744831 | ||||||||
\(773\) | 11.8237 | 0.425267 | 0.212634 | − | 0.977132i | \(-0.431796\pi\) | ||||
0.212634 | + | 0.977132i | \(0.431796\pi\) | |||||||
\(774\) | −123.642 | −4.44423 | ||||||||
\(775\) | 1.26161 | 0.0453185 | ||||||||
\(776\) | −21.8551 | −0.784553 | ||||||||
\(777\) | 41.3527 | 1.48352 | ||||||||
\(778\) | 27.5125 | 0.986371 | ||||||||
\(779\) | −4.21974 | −0.151188 | ||||||||
\(780\) | 10.2894 | 0.368419 | ||||||||
\(781\) | 5.43590 | 0.194512 | ||||||||
\(782\) | 54.6512 | 1.95432 | ||||||||
\(783\) | 1.71399 | 0.0612529 | ||||||||
\(784\) | −9.51782 | −0.339922 | ||||||||
\(785\) | −35.8890 | −1.28093 | ||||||||
\(786\) | −26.9522 | −0.961353 | ||||||||
\(787\) | −53.3172 | −1.90055 | −0.950276 | − | 0.311408i | \(-0.899200\pi\) | ||||
−0.950276 | + | 0.311408i | \(0.899200\pi\) | |||||||
\(788\) | −69.1297 | −2.46264 | ||||||||
\(789\) | 39.9406 | 1.42192 | ||||||||
\(790\) | 51.1494 | 1.81982 | ||||||||
\(791\) | 6.46757 | 0.229960 | ||||||||
\(792\) | −13.7774 | −0.489559 | ||||||||
\(793\) | −1.69410 | −0.0601594 | ||||||||
\(794\) | 27.9555 | 0.992103 | ||||||||
\(795\) | 83.6925 | 2.96827 | ||||||||
\(796\) | 8.34545 | 0.295797 | ||||||||
\(797\) | 43.4209 | 1.53805 | 0.769024 | − | 0.639220i | \(-0.220743\pi\) | ||||
0.769024 | + | 0.639220i | \(0.220743\pi\) | |||||||
\(798\) | 27.6755 | 0.979704 | ||||||||
\(799\) | 26.0095 | 0.920150 | ||||||||
\(800\) | −3.77424 | −0.133439 | ||||||||
\(801\) | −2.26868 | −0.0801599 | ||||||||
\(802\) | 60.8606 | 2.14906 | ||||||||
\(803\) | 2.85653 | 0.100805 | ||||||||
\(804\) | 86.5713 | 3.05313 | ||||||||
\(805\) | −50.1935 | −1.76909 | ||||||||
\(806\) | −2.74835 | −0.0968066 | ||||||||
\(807\) | −66.8022 | −2.35155 | ||||||||
\(808\) | −19.1045 | −0.672094 | ||||||||
\(809\) | −16.8206 | −0.591382 | −0.295691 | − | 0.955284i | \(-0.595550\pi\) | ||||
−0.295691 | + | 0.955284i | \(0.595550\pi\) | |||||||
\(810\) | 66.3396 | 2.33094 | ||||||||
\(811\) | −21.1110 | −0.741309 | −0.370655 | − | 0.928771i | \(-0.620867\pi\) | ||||
−0.370655 | + | 0.928771i | \(0.620867\pi\) | |||||||
\(812\) | 1.78334 | 0.0625830 | ||||||||
\(813\) | 86.3844 | 3.02963 | ||||||||
\(814\) | −7.72051 | −0.270604 | ||||||||
\(815\) | 2.48327 | 0.0869852 | ||||||||
\(816\) | 14.8632 | 0.520317 | ||||||||
\(817\) | −8.87939 | −0.310651 | ||||||||
\(818\) | −19.6005 | −0.685317 | ||||||||
\(819\) | −13.5102 | −0.472085 | ||||||||
\(820\) | −25.1296 | −0.877565 | ||||||||
\(821\) | 20.4382 | 0.713300 | 0.356650 | − | 0.934238i | \(-0.383919\pi\) | ||||
0.356650 | + | 0.934238i | \(0.383919\pi\) | |||||||
\(822\) | 99.8823 | 3.48379 | ||||||||
\(823\) | 16.8610 | 0.587739 | 0.293869 | − | 0.955846i | \(-0.405057\pi\) | ||||
0.293869 | + | 0.955846i | \(0.405057\pi\) | |||||||
\(824\) | −25.8915 | −0.901972 | ||||||||
\(825\) | −1.68914 | −0.0588083 | ||||||||
\(826\) | 1.20150 | 0.0418056 | ||||||||
\(827\) | −32.1965 | −1.11958 | −0.559791 | − | 0.828634i | \(-0.689119\pi\) | ||||
−0.559791 | + | 0.828634i | \(0.689119\pi\) | |||||||
\(828\) | 118.823 | 4.12939 | ||||||||
\(829\) | −19.4300 | −0.674831 | −0.337416 | − | 0.941356i | \(-0.609553\pi\) | ||||
−0.337416 | + | 0.941356i | \(0.609553\pi\) | |||||||
\(830\) | 20.3714 | 0.707102 | ||||||||
\(831\) | 30.2973 | 1.05100 | ||||||||
\(832\) | 6.92807 | 0.240188 | ||||||||
\(833\) | −31.4029 | −1.08805 | ||||||||
\(834\) | −56.1597 | −1.94465 | ||||||||
\(835\) | 18.9085 | 0.654357 | ||||||||
\(836\) | −3.07821 | −0.106462 | ||||||||
\(837\) | −25.2066 | −0.871266 | ||||||||
\(838\) | −17.9154 | −0.618877 | ||||||||
\(839\) | 20.6987 | 0.714598 | 0.357299 | − | 0.933990i | \(-0.383698\pi\) | ||||
0.357299 | + | 0.933990i | \(0.383698\pi\) | |||||||
\(840\) | 52.9765 | 1.82786 | ||||||||
\(841\) | −28.9754 | −0.999152 | ||||||||
\(842\) | 44.4278 | 1.53108 | ||||||||
\(843\) | 43.7591 | 1.50714 | ||||||||
\(844\) | −57.0746 | −1.96459 | ||||||||
\(845\) | 26.8275 | 0.922894 | ||||||||
\(846\) | 94.9234 | 3.26353 | ||||||||
\(847\) | 3.85755 | 0.132547 | ||||||||
\(848\) | 15.5095 | 0.532597 | ||||||||
\(849\) | 92.7179 | 3.18207 | ||||||||
\(850\) | −4.84758 | −0.166271 | ||||||||
\(851\) | 21.4025 | 0.733669 | ||||||||
\(852\) | 49.4812 | 1.69520 | ||||||||
\(853\) | −38.2560 | −1.30986 | −0.654931 | − | 0.755689i | \(-0.727302\pi\) | ||||
−0.654931 | + | 0.755689i | \(0.727302\pi\) | |||||||
\(854\) | −27.1362 | −0.928580 | ||||||||
\(855\) | 14.4096 | 0.492800 | ||||||||
\(856\) | 12.1377 | 0.414857 | ||||||||
\(857\) | −45.2811 | −1.54677 | −0.773386 | − | 0.633935i | \(-0.781438\pi\) | ||||
−0.773386 | + | 0.633935i | \(0.781438\pi\) | |||||||
\(858\) | 3.67969 | 0.125623 | ||||||||
\(859\) | 12.6853 | 0.432817 | 0.216409 | − | 0.976303i | \(-0.430566\pi\) | ||||
0.216409 | + | 0.976303i | \(0.430566\pi\) | |||||||
\(860\) | −52.8791 | −1.80316 | ||||||||
\(861\) | 48.1356 | 1.64046 | ||||||||
\(862\) | 23.0078 | 0.783650 | ||||||||
\(863\) | −45.4025 | −1.54552 | −0.772759 | − | 0.634700i | \(-0.781124\pi\) | ||||
−0.772759 | + | 0.634700i | \(0.781124\pi\) | |||||||
\(864\) | 75.4078 | 2.56543 | ||||||||
\(865\) | 21.2146 | 0.721318 | ||||||||
\(866\) | −34.2896 | −1.16521 | ||||||||
\(867\) | −3.46338 | −0.117622 | ||||||||
\(868\) | −26.2265 | −0.890187 | ||||||||
\(869\) | 10.8974 | 0.369670 | ||||||||
\(870\) | 2.27373 | 0.0770867 | ||||||||
\(871\) | −5.09443 | −0.172618 | ||||||||
\(872\) | 11.0408 | 0.373888 | ||||||||
\(873\) | 67.8117 | 2.29508 | ||||||||
\(874\) | 14.3238 | 0.484509 | ||||||||
\(875\) | 45.1538 | 1.52648 | ||||||||
\(876\) | 26.0020 | 0.878528 | ||||||||
\(877\) | −13.1321 | −0.443440 | −0.221720 | − | 0.975110i | \(-0.571167\pi\) | ||||
−0.221720 | + | 0.975110i | \(0.571167\pi\) | |||||||
\(878\) | −15.7163 | −0.530400 | ||||||||
\(879\) | −95.4199 | −3.21843 | ||||||||
\(880\) | 2.54861 | 0.0859136 | ||||||||
\(881\) | 19.4261 | 0.654480 | 0.327240 | − | 0.944941i | \(-0.393881\pi\) | ||||
0.327240 | + | 0.944941i | \(0.393881\pi\) | |||||||
\(882\) | −114.607 | −3.85902 | ||||||||
\(883\) | 40.3950 | 1.35940 | 0.679699 | − | 0.733491i | \(-0.262110\pi\) | ||||
0.679699 | + | 0.733491i | \(0.262110\pi\) | |||||||
\(884\) | 6.29117 | 0.211595 | ||||||||
\(885\) | 0.912619 | 0.0306774 | ||||||||
\(886\) | 43.9108 | 1.47521 | ||||||||
\(887\) | 53.8087 | 1.80672 | 0.903360 | − | 0.428884i | \(-0.141093\pi\) | ||||
0.903360 | + | 0.428884i | \(0.141093\pi\) | |||||||
\(888\) | −22.5892 | −0.758043 | ||||||||
\(889\) | 49.5212 | 1.66089 | ||||||||
\(890\) | −1.62866 | −0.0545928 | ||||||||
\(891\) | 14.1337 | 0.473497 | ||||||||
\(892\) | −7.25906 | −0.243051 | ||||||||
\(893\) | 6.81695 | 0.228120 | ||||||||
\(894\) | −129.323 | −4.32521 | ||||||||
\(895\) | 17.3771 | 0.580852 | ||||||||
\(896\) | 57.7338 | 1.92875 | ||||||||
\(897\) | −10.2007 | −0.340592 | ||||||||
\(898\) | −13.9719 | −0.466249 | ||||||||
\(899\) | −0.361812 | −0.0120671 | ||||||||
\(900\) | −10.5397 | −0.351322 | ||||||||
\(901\) | 51.1716 | 1.70477 | ||||||||
\(902\) | −8.98688 | −0.299230 | ||||||||
\(903\) | 101.290 | 3.37070 | ||||||||
\(904\) | −3.53295 | −0.117504 | ||||||||
\(905\) | 10.4509 | 0.347400 | ||||||||
\(906\) | −27.0016 | −0.897067 | ||||||||
\(907\) | −25.4470 | −0.844954 | −0.422477 | − | 0.906374i | \(-0.638839\pi\) | ||||
−0.422477 | + | 0.906374i | \(0.638839\pi\) | |||||||
\(908\) | 36.4033 | 1.20809 | ||||||||
\(909\) | 59.2772 | 1.96610 | ||||||||
\(910\) | −9.69882 | −0.321513 | ||||||||
\(911\) | −42.8365 | −1.41924 | −0.709619 | − | 0.704586i | \(-0.751133\pi\) | ||||
−0.709619 | + | 0.704586i | \(0.751133\pi\) | |||||||
\(912\) | 3.89557 | 0.128995 | ||||||||
\(913\) | 4.34014 | 0.143638 | ||||||||
\(914\) | −53.4386 | −1.76759 | ||||||||
\(915\) | −20.6117 | −0.681401 | ||||||||
\(916\) | −5.46252 | −0.180487 | ||||||||
\(917\) | 15.1351 | 0.499804 | ||||||||
\(918\) | 96.8528 | 3.19662 | ||||||||
\(919\) | 26.9072 | 0.887585 | 0.443793 | − | 0.896129i | \(-0.353633\pi\) | ||||
0.443793 | + | 0.896129i | \(0.353633\pi\) | |||||||
\(920\) | 27.4185 | 0.903962 | ||||||||
\(921\) | −54.8369 | −1.80694 | ||||||||
\(922\) | −74.1852 | −2.44316 | ||||||||
\(923\) | −2.91180 | −0.0958432 | ||||||||
\(924\) | 35.1140 | 1.15517 | ||||||||
\(925\) | −1.89841 | −0.0624194 | ||||||||
\(926\) | 31.1147 | 1.02249 | ||||||||
\(927\) | 80.3357 | 2.63857 | ||||||||
\(928\) | 1.08239 | 0.0355313 | ||||||||
\(929\) | 36.9048 | 1.21081 | 0.605404 | − | 0.795919i | \(-0.293012\pi\) | ||||
0.605404 | + | 0.795919i | \(0.293012\pi\) | |||||||
\(930\) | −33.4384 | −1.09649 | ||||||||
\(931\) | −8.23052 | −0.269745 | ||||||||
\(932\) | −0.585345 | −0.0191736 | ||||||||
\(933\) | −17.5816 | −0.575597 | ||||||||
\(934\) | 80.8681 | 2.64609 | ||||||||
\(935\) | 8.40883 | 0.274998 | ||||||||
\(936\) | 7.38003 | 0.241224 | ||||||||
\(937\) | −34.5561 | −1.12890 | −0.564450 | − | 0.825467i | \(-0.690912\pi\) | ||||
−0.564450 | + | 0.825467i | \(0.690912\pi\) | |||||||
\(938\) | −81.6025 | −2.66442 | ||||||||
\(939\) | 28.2573 | 0.922143 | ||||||||
\(940\) | 40.5967 | 1.32412 | ||||||||
\(941\) | 37.1850 | 1.21220 | 0.606098 | − | 0.795390i | \(-0.292734\pi\) | ||||
0.606098 | + | 0.795390i | \(0.292734\pi\) | |||||||
\(942\) | −116.829 | −3.80651 | ||||||||
\(943\) | 24.9131 | 0.811282 | ||||||||
\(944\) | 0.169122 | 0.00550445 | ||||||||
\(945\) | −88.9529 | −2.89364 | ||||||||
\(946\) | −18.9107 | −0.614839 | ||||||||
\(947\) | 41.0397 | 1.33361 | 0.666806 | − | 0.745232i | \(-0.267661\pi\) | ||||
0.666806 | + | 0.745232i | \(0.267661\pi\) | |||||||
\(948\) | 99.1956 | 3.22172 | ||||||||
\(949\) | −1.53013 | −0.0496702 | ||||||||
\(950\) | −1.27052 | −0.0412213 | ||||||||
\(951\) | −17.2823 | −0.560419 | ||||||||
\(952\) | 32.3911 | 1.04980 | ||||||||
\(953\) | 16.6201 | 0.538376 | 0.269188 | − | 0.963088i | \(-0.413245\pi\) | ||||
0.269188 | + | 0.963088i | \(0.413245\pi\) | |||||||
\(954\) | 186.754 | 6.04639 | ||||||||
\(955\) | −15.6003 | −0.504815 | ||||||||
\(956\) | 27.3340 | 0.884045 | ||||||||
\(957\) | 0.484420 | 0.0156591 | ||||||||
\(958\) | −91.4113 | −2.95336 | ||||||||
\(959\) | −56.0891 | −1.81121 | ||||||||
\(960\) | 84.2918 | 2.72051 | ||||||||
\(961\) | −25.6791 | −0.828357 | ||||||||
\(962\) | 4.13558 | 0.133336 | ||||||||
\(963\) | −37.6606 | −1.21359 | ||||||||
\(964\) | 20.3402 | 0.655114 | ||||||||
\(965\) | −14.8170 | −0.476977 | ||||||||
\(966\) | −163.395 | −5.25715 | ||||||||
\(967\) | −7.22636 | −0.232384 | −0.116192 | − | 0.993227i | \(-0.537069\pi\) | ||||
−0.116192 | + | 0.993227i | \(0.537069\pi\) | |||||||
\(968\) | −2.10721 | −0.0677283 | ||||||||
\(969\) | 12.8530 | 0.412897 | ||||||||
\(970\) | 48.6813 | 1.56306 | ||||||||
\(971\) | −35.3856 | −1.13558 | −0.567789 | − | 0.823174i | \(-0.692201\pi\) | ||||
−0.567789 | + | 0.823174i | \(0.692201\pi\) | |||||||
\(972\) | 32.0326 | 1.02745 | ||||||||
\(973\) | 31.5366 | 1.01102 | ||||||||
\(974\) | 21.4160 | 0.686213 | ||||||||
\(975\) | 0.904808 | 0.0289770 | ||||||||
\(976\) | −3.81965 | −0.122264 | ||||||||
\(977\) | 33.6246 | 1.07575 | 0.537873 | − | 0.843026i | \(-0.319228\pi\) | ||||
0.537873 | + | 0.843026i | \(0.319228\pi\) | |||||||
\(978\) | 8.08380 | 0.258491 | ||||||||
\(979\) | −0.346987 | −0.0110898 | ||||||||
\(980\) | −49.0149 | −1.56572 | ||||||||
\(981\) | −34.2571 | −1.09375 | ||||||||
\(982\) | 84.5283 | 2.69740 | ||||||||
\(983\) | −12.1506 | −0.387543 | −0.193772 | − | 0.981047i | \(-0.562072\pi\) | ||||
−0.193772 | + | 0.981047i | \(0.562072\pi\) | |||||||
\(984\) | −26.2944 | −0.838235 | ||||||||
\(985\) | 49.4948 | 1.57704 | ||||||||
\(986\) | 1.39021 | 0.0442734 | ||||||||
\(987\) | −77.7627 | −2.47521 | ||||||||
\(988\) | 1.64888 | 0.0524579 | ||||||||
\(989\) | 52.4235 | 1.66697 | ||||||||
\(990\) | 30.6886 | 0.975347 | ||||||||
\(991\) | 18.2194 | 0.578760 | 0.289380 | − | 0.957214i | \(-0.406551\pi\) | ||||
0.289380 | + | 0.957214i | \(0.406551\pi\) | |||||||
\(992\) | −15.9181 | −0.505401 | ||||||||
\(993\) | 22.0247 | 0.698933 | ||||||||
\(994\) | −46.6413 | −1.47937 | ||||||||
\(995\) | −5.97509 | −0.189423 | ||||||||
\(996\) | 39.5069 | 1.25182 | ||||||||
\(997\) | 19.1067 | 0.605114 | 0.302557 | − | 0.953131i | \(-0.402160\pi\) | ||||
0.302557 | + | 0.953131i | \(0.402160\pi\) | |||||||
\(998\) | −0.503276 | −0.0159309 | ||||||||
\(999\) | 37.9295 | 1.20004 |
(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 | 6017.2.a.e.1.16 | ✓ | 119 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.e.1.16 | ✓ | 119 | 1.1 | even | 1 | trivial |