Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1003,2,Mod(1,1003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1003, 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("1003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.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: | \(8.00899532273\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 16 x^{16} + 112 x^{15} + 52 x^{14} - 984 x^{13} + 431 x^{12} + 4304 x^{11} + \cdots + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.149899\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.149899 | −0.105995 | −0.0529973 | − | 0.998595i | \(-0.516877\pi\) | ||||
−0.0529973 | + | 0.998595i | \(0.516877\pi\) | |||||||
\(3\) | −2.07180 | −1.19615 | −0.598077 | − | 0.801439i | \(-0.704068\pi\) | ||||
−0.598077 | + | 0.801439i | \(0.704068\pi\) | |||||||
\(4\) | −1.97753 | −0.988765 | ||||||||
\(5\) | 4.08629 | 1.82744 | 0.913722 | − | 0.406341i | \(-0.133195\pi\) | ||||
0.913722 | + | 0.406341i | \(0.133195\pi\) | |||||||
\(6\) | 0.310561 | 0.126786 | ||||||||
\(7\) | 5.08021 | 1.92014 | 0.960070 | − | 0.279760i | \(-0.0902548\pi\) | ||||
0.960070 | + | 0.279760i | \(0.0902548\pi\) | |||||||
\(8\) | 0.596228 | 0.210799 | ||||||||
\(9\) | 1.29235 | 0.430782 | ||||||||
\(10\) | −0.612531 | −0.193699 | ||||||||
\(11\) | 6.60568 | 1.99169 | 0.995843 | − | 0.0910828i | \(-0.0290328\pi\) | ||||
0.995843 | + | 0.0910828i | \(0.0290328\pi\) | |||||||
\(12\) | 4.09704 | 1.18271 | ||||||||
\(13\) | −2.12783 | −0.590155 | −0.295078 | − | 0.955473i | \(-0.595346\pi\) | ||||
−0.295078 | + | 0.955473i | \(0.595346\pi\) | |||||||
\(14\) | −0.761519 | −0.203525 | ||||||||
\(15\) | −8.46596 | −2.18590 | ||||||||
\(16\) | 3.86569 | 0.966422 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −0.193722 | −0.0456606 | ||||||||
\(19\) | −4.59660 | −1.05453 | −0.527267 | − | 0.849700i | \(-0.676783\pi\) | ||||
−0.527267 | + | 0.849700i | \(0.676783\pi\) | |||||||
\(20\) | −8.08076 | −1.80691 | ||||||||
\(21\) | −10.5252 | −2.29678 | ||||||||
\(22\) | −0.990185 | −0.211108 | ||||||||
\(23\) | −5.10850 | −1.06520 | −0.532598 | − | 0.846368i | \(-0.678784\pi\) | ||||
−0.532598 | + | 0.846368i | \(0.678784\pi\) | |||||||
\(24\) | −1.23526 | −0.252147 | ||||||||
\(25\) | 11.6977 | 2.33955 | ||||||||
\(26\) | 0.318961 | 0.0625533 | ||||||||
\(27\) | 3.53791 | 0.680872 | ||||||||
\(28\) | −10.0463 | −1.89857 | ||||||||
\(29\) | −4.00448 | −0.743613 | −0.371807 | − | 0.928310i | \(-0.621262\pi\) | ||||
−0.371807 | + | 0.928310i | \(0.621262\pi\) | |||||||
\(30\) | 1.26904 | 0.231694 | ||||||||
\(31\) | −1.51654 | −0.272379 | −0.136189 | − | 0.990683i | \(-0.543486\pi\) | ||||
−0.136189 | + | 0.990683i | \(0.543486\pi\) | |||||||
\(32\) | −1.77192 | −0.313234 | ||||||||
\(33\) | −13.6856 | −2.38236 | ||||||||
\(34\) | −0.149899 | −0.0257075 | ||||||||
\(35\) | 20.7592 | 3.50895 | ||||||||
\(36\) | −2.55565 | −0.425942 | ||||||||
\(37\) | 2.41581 | 0.397156 | 0.198578 | − | 0.980085i | \(-0.436368\pi\) | ||||
0.198578 | + | 0.980085i | \(0.436368\pi\) | |||||||
\(38\) | 0.689027 | 0.111775 | ||||||||
\(39\) | 4.40844 | 0.705916 | ||||||||
\(40\) | 2.43636 | 0.385222 | ||||||||
\(41\) | 1.14518 | 0.178848 | 0.0894238 | − | 0.995994i | \(-0.471497\pi\) | ||||
0.0894238 | + | 0.995994i | \(0.471497\pi\) | |||||||
\(42\) | 1.57771 | 0.243447 | ||||||||
\(43\) | 7.94203 | 1.21115 | 0.605574 | − | 0.795789i | \(-0.292944\pi\) | ||||
0.605574 | + | 0.795789i | \(0.292944\pi\) | |||||||
\(44\) | −13.0629 | −1.96931 | ||||||||
\(45\) | 5.28090 | 0.787230 | ||||||||
\(46\) | 0.765760 | 0.112905 | ||||||||
\(47\) | −0.669492 | −0.0976554 | −0.0488277 | − | 0.998807i | \(-0.515549\pi\) | ||||
−0.0488277 | + | 0.998807i | \(0.515549\pi\) | |||||||
\(48\) | −8.00892 | −1.15599 | ||||||||
\(49\) | 18.8086 | 2.68694 | ||||||||
\(50\) | −1.75348 | −0.247980 | ||||||||
\(51\) | −2.07180 | −0.290110 | ||||||||
\(52\) | 4.20786 | 0.583525 | ||||||||
\(53\) | 0.270789 | 0.0371958 | 0.0185979 | − | 0.999827i | \(-0.494080\pi\) | ||||
0.0185979 | + | 0.999827i | \(0.494080\pi\) | |||||||
\(54\) | −0.530330 | −0.0721688 | ||||||||
\(55\) | 26.9927 | 3.63969 | ||||||||
\(56\) | 3.02897 | 0.404763 | ||||||||
\(57\) | 9.52324 | 1.26138 | ||||||||
\(58\) | 0.600268 | 0.0788190 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 16.7417 | 2.16134 | ||||||||
\(61\) | 3.88583 | 0.497529 | 0.248765 | − | 0.968564i | \(-0.419975\pi\) | ||||
0.248765 | + | 0.968564i | \(0.419975\pi\) | |||||||
\(62\) | 0.227328 | 0.0288707 | ||||||||
\(63\) | 6.56539 | 0.827162 | ||||||||
\(64\) | −7.46576 | −0.933220 | ||||||||
\(65\) | −8.69495 | −1.07848 | ||||||||
\(66\) | 2.05146 | 0.252518 | ||||||||
\(67\) | −13.6595 | −1.66878 | −0.834388 | − | 0.551177i | \(-0.814179\pi\) | ||||
−0.834388 | + | 0.551177i | \(0.814179\pi\) | |||||||
\(68\) | −1.97753 | −0.239811 | ||||||||
\(69\) | 10.5838 | 1.27414 | ||||||||
\(70\) | −3.11179 | −0.371930 | ||||||||
\(71\) | −7.63076 | −0.905604 | −0.452802 | − | 0.891611i | \(-0.649576\pi\) | ||||
−0.452802 | + | 0.891611i | \(0.649576\pi\) | |||||||
\(72\) | 0.770533 | 0.0908082 | ||||||||
\(73\) | −10.2193 | −1.19607 | −0.598037 | − | 0.801468i | \(-0.704053\pi\) | ||||
−0.598037 | + | 0.801468i | \(0.704053\pi\) | |||||||
\(74\) | −0.362127 | −0.0420964 | ||||||||
\(75\) | −24.2354 | −2.79846 | ||||||||
\(76\) | 9.08992 | 1.04269 | ||||||||
\(77\) | 33.5582 | 3.82432 | ||||||||
\(78\) | −0.660822 | −0.0748233 | ||||||||
\(79\) | −4.89550 | −0.550787 | −0.275394 | − | 0.961332i | \(-0.588808\pi\) | ||||
−0.275394 | + | 0.961332i | \(0.588808\pi\) | |||||||
\(80\) | 15.7963 | 1.76608 | ||||||||
\(81\) | −11.2069 | −1.24521 | ||||||||
\(82\) | −0.171662 | −0.0189569 | ||||||||
\(83\) | −3.63584 | −0.399086 | −0.199543 | − | 0.979889i | \(-0.563946\pi\) | ||||
−0.199543 | + | 0.979889i | \(0.563946\pi\) | |||||||
\(84\) | 20.8139 | 2.27098 | ||||||||
\(85\) | 4.08629 | 0.443220 | ||||||||
\(86\) | −1.19050 | −0.128375 | ||||||||
\(87\) | 8.29647 | 0.889475 | ||||||||
\(88\) | 3.93849 | 0.419845 | ||||||||
\(89\) | 7.06524 | 0.748914 | 0.374457 | − | 0.927244i | \(-0.377829\pi\) | ||||
0.374457 | + | 0.927244i | \(0.377829\pi\) | |||||||
\(90\) | −0.791602 | −0.0834422 | ||||||||
\(91\) | −10.8099 | −1.13318 | ||||||||
\(92\) | 10.1022 | 1.05323 | ||||||||
\(93\) | 3.14197 | 0.325807 | ||||||||
\(94\) | 0.100356 | 0.0103510 | ||||||||
\(95\) | −18.7830 | −1.92710 | ||||||||
\(96\) | 3.67106 | 0.374676 | ||||||||
\(97\) | 13.5650 | 1.37732 | 0.688660 | − | 0.725084i | \(-0.258199\pi\) | ||||
0.688660 | + | 0.725084i | \(0.258199\pi\) | |||||||
\(98\) | −2.81939 | −0.284801 | ||||||||
\(99\) | 8.53682 | 0.857983 | ||||||||
\(100\) | −23.1326 | −2.31326 | ||||||||
\(101\) | −1.87295 | −0.186365 | −0.0931825 | − | 0.995649i | \(-0.529704\pi\) | ||||
−0.0931825 | + | 0.995649i | \(0.529704\pi\) | |||||||
\(102\) | 0.310561 | 0.0307501 | ||||||||
\(103\) | 11.9970 | 1.18210 | 0.591048 | − | 0.806637i | \(-0.298715\pi\) | ||||
0.591048 | + | 0.806637i | \(0.298715\pi\) | |||||||
\(104\) | −1.26868 | −0.124404 | ||||||||
\(105\) | −43.0089 | −4.19724 | ||||||||
\(106\) | −0.0405911 | −0.00394255 | ||||||||
\(107\) | −1.16800 | −0.112915 | −0.0564573 | − | 0.998405i | \(-0.517980\pi\) | ||||
−0.0564573 | + | 0.998405i | \(0.517980\pi\) | |||||||
\(108\) | −6.99633 | −0.673222 | ||||||||
\(109\) | 8.94465 | 0.856742 | 0.428371 | − | 0.903603i | \(-0.359088\pi\) | ||||
0.428371 | + | 0.903603i | \(0.359088\pi\) | |||||||
\(110\) | −4.04618 | −0.385788 | ||||||||
\(111\) | −5.00506 | −0.475060 | ||||||||
\(112\) | 19.6385 | 1.85566 | ||||||||
\(113\) | 12.2756 | 1.15479 | 0.577397 | − | 0.816464i | \(-0.304069\pi\) | ||||
0.577397 | + | 0.816464i | \(0.304069\pi\) | |||||||
\(114\) | −1.42752 | −0.133700 | ||||||||
\(115\) | −20.8748 | −1.94659 | ||||||||
\(116\) | 7.91898 | 0.735259 | ||||||||
\(117\) | −2.74990 | −0.254228 | ||||||||
\(118\) | 0.149899 | 0.0137993 | ||||||||
\(119\) | 5.08021 | 0.465702 | ||||||||
\(120\) | −5.04765 | −0.460785 | ||||||||
\(121\) | 32.6350 | 2.96682 | ||||||||
\(122\) | −0.582482 | −0.0527354 | ||||||||
\(123\) | −2.37259 | −0.213929 | ||||||||
\(124\) | 2.99900 | 0.269319 | ||||||||
\(125\) | 27.3689 | 2.44795 | ||||||||
\(126\) | −0.984147 | −0.0876748 | ||||||||
\(127\) | −16.9940 | −1.50797 | −0.753985 | − | 0.656892i | \(-0.771871\pi\) | ||||
−0.753985 | + | 0.656892i | \(0.771871\pi\) | |||||||
\(128\) | 4.66295 | 0.412150 | ||||||||
\(129\) | −16.4543 | −1.44872 | ||||||||
\(130\) | 1.30336 | 0.114313 | ||||||||
\(131\) | −7.91793 | −0.691793 | −0.345896 | − | 0.938273i | \(-0.612425\pi\) | ||||
−0.345896 | + | 0.938273i | \(0.612425\pi\) | |||||||
\(132\) | 27.0637 | 2.35560 | ||||||||
\(133\) | −23.3517 | −2.02485 | ||||||||
\(134\) | 2.04755 | 0.176881 | ||||||||
\(135\) | 14.4569 | 1.24425 | ||||||||
\(136\) | 0.596228 | 0.0511261 | ||||||||
\(137\) | −1.42323 | −0.121595 | −0.0607975 | − | 0.998150i | \(-0.519364\pi\) | ||||
−0.0607975 | + | 0.998150i | \(0.519364\pi\) | |||||||
\(138\) | −1.58650 | −0.135052 | ||||||||
\(139\) | 5.22072 | 0.442815 | 0.221408 | − | 0.975181i | \(-0.428935\pi\) | ||||
0.221408 | + | 0.975181i | \(0.428935\pi\) | |||||||
\(140\) | −41.0520 | −3.46952 | ||||||||
\(141\) | 1.38705 | 0.116811 | ||||||||
\(142\) | 1.14384 | 0.0959892 | ||||||||
\(143\) | −14.0558 | −1.17540 | ||||||||
\(144\) | 4.99581 | 0.416317 | ||||||||
\(145\) | −16.3635 | −1.35891 | ||||||||
\(146\) | 1.53186 | 0.126778 | ||||||||
\(147\) | −38.9675 | −3.21399 | ||||||||
\(148\) | −4.77733 | −0.392694 | ||||||||
\(149\) | 4.45485 | 0.364956 | 0.182478 | − | 0.983210i | \(-0.441588\pi\) | ||||
0.182478 | + | 0.983210i | \(0.441588\pi\) | |||||||
\(150\) | 3.63286 | 0.296622 | ||||||||
\(151\) | 11.5879 | 0.943006 | 0.471503 | − | 0.881864i | \(-0.343712\pi\) | ||||
0.471503 | + | 0.881864i | \(0.343712\pi\) | |||||||
\(152\) | −2.74063 | −0.222294 | ||||||||
\(153\) | 1.29235 | 0.104480 | ||||||||
\(154\) | −5.03035 | −0.405357 | ||||||||
\(155\) | −6.19702 | −0.497757 | ||||||||
\(156\) | −8.71783 | −0.697985 | ||||||||
\(157\) | 6.25393 | 0.499118 | 0.249559 | − | 0.968360i | \(-0.419714\pi\) | ||||
0.249559 | + | 0.968360i | \(0.419714\pi\) | |||||||
\(158\) | 0.733831 | 0.0583805 | ||||||||
\(159\) | −0.561020 | −0.0444918 | ||||||||
\(160\) | −7.24057 | −0.572417 | ||||||||
\(161\) | −25.9523 | −2.04533 | ||||||||
\(162\) | 1.67990 | 0.131986 | ||||||||
\(163\) | −12.9166 | −1.01171 | −0.505855 | − | 0.862619i | \(-0.668823\pi\) | ||||
−0.505855 | + | 0.862619i | \(0.668823\pi\) | |||||||
\(164\) | −2.26463 | −0.176838 | ||||||||
\(165\) | −55.9234 | −4.35363 | ||||||||
\(166\) | 0.545009 | 0.0423009 | ||||||||
\(167\) | −6.72846 | −0.520664 | −0.260332 | − | 0.965519i | \(-0.583832\pi\) | ||||
−0.260332 | + | 0.965519i | \(0.583832\pi\) | |||||||
\(168\) | −6.27541 | −0.484158 | ||||||||
\(169\) | −8.47232 | −0.651717 | ||||||||
\(170\) | −0.612531 | −0.0469790 | ||||||||
\(171\) | −5.94040 | −0.454274 | ||||||||
\(172\) | −15.7056 | −1.19754 | ||||||||
\(173\) | 7.16826 | 0.544993 | 0.272496 | − | 0.962157i | \(-0.412151\pi\) | ||||
0.272496 | + | 0.962157i | \(0.412151\pi\) | |||||||
\(174\) | −1.24363 | −0.0942796 | ||||||||
\(175\) | 59.4270 | 4.49226 | ||||||||
\(176\) | 25.5355 | 1.92481 | ||||||||
\(177\) | 2.07180 | 0.155726 | ||||||||
\(178\) | −1.05907 | −0.0793809 | ||||||||
\(179\) | −8.26829 | −0.618001 | −0.309000 | − | 0.951062i | \(-0.599994\pi\) | ||||
−0.309000 | + | 0.951062i | \(0.599994\pi\) | |||||||
\(180\) | −10.4431 | −0.778385 | ||||||||
\(181\) | 14.9781 | 1.11331 | 0.556657 | − | 0.830743i | \(-0.312084\pi\) | ||||
0.556657 | + | 0.830743i | \(0.312084\pi\) | |||||||
\(182\) | 1.62039 | 0.120111 | ||||||||
\(183\) | −8.05065 | −0.595121 | ||||||||
\(184\) | −3.04583 | −0.224542 | ||||||||
\(185\) | 9.87168 | 0.725780 | ||||||||
\(186\) | −0.470978 | −0.0345338 | ||||||||
\(187\) | 6.60568 | 0.483055 | ||||||||
\(188\) | 1.32394 | 0.0965582 | ||||||||
\(189\) | 17.9734 | 1.30737 | ||||||||
\(190\) | 2.81556 | 0.204262 | ||||||||
\(191\) | −20.5741 | −1.48869 | −0.744344 | − | 0.667796i | \(-0.767238\pi\) | ||||
−0.744344 | + | 0.667796i | \(0.767238\pi\) | |||||||
\(192\) | 15.4676 | 1.11627 | ||||||||
\(193\) | −13.2340 | −0.952602 | −0.476301 | − | 0.879282i | \(-0.658023\pi\) | ||||
−0.476301 | + | 0.879282i | \(0.658023\pi\) | |||||||
\(194\) | −2.03339 | −0.145989 | ||||||||
\(195\) | 18.0142 | 1.29002 | ||||||||
\(196\) | −37.1945 | −2.65675 | ||||||||
\(197\) | −3.22632 | −0.229865 | −0.114933 | − | 0.993373i | \(-0.536665\pi\) | ||||
−0.114933 | + | 0.993373i | \(0.536665\pi\) | |||||||
\(198\) | −1.27966 | −0.0909416 | ||||||||
\(199\) | −10.2046 | −0.723386 | −0.361693 | − | 0.932297i | \(-0.617801\pi\) | ||||
−0.361693 | + | 0.932297i | \(0.617801\pi\) | |||||||
\(200\) | 6.97453 | 0.493173 | ||||||||
\(201\) | 28.2998 | 1.99611 | ||||||||
\(202\) | 0.280753 | 0.0197537 | ||||||||
\(203\) | −20.3436 | −1.42784 | ||||||||
\(204\) | 4.09704 | 0.286850 | ||||||||
\(205\) | 4.67955 | 0.326834 | ||||||||
\(206\) | −1.79833 | −0.125296 | ||||||||
\(207\) | −6.60195 | −0.458867 | ||||||||
\(208\) | −8.22554 | −0.570339 | ||||||||
\(209\) | −30.3637 | −2.10030 | ||||||||
\(210\) | 6.44699 | 0.444885 | ||||||||
\(211\) | −7.29336 | −0.502096 | −0.251048 | − | 0.967975i | \(-0.580775\pi\) | ||||
−0.251048 | + | 0.967975i | \(0.580775\pi\) | |||||||
\(212\) | −0.535494 | −0.0367779 | ||||||||
\(213\) | 15.8094 | 1.08324 | ||||||||
\(214\) | 0.175082 | 0.0119683 | ||||||||
\(215\) | 32.4534 | 2.21330 | ||||||||
\(216\) | 2.10940 | 0.143527 | ||||||||
\(217\) | −7.70435 | −0.523005 | ||||||||
\(218\) | −1.34079 | −0.0908101 | ||||||||
\(219\) | 21.1723 | 1.43069 | ||||||||
\(220\) | −53.3789 | −3.59880 | ||||||||
\(221\) | −2.12783 | −0.143134 | ||||||||
\(222\) | 0.750254 | 0.0503538 | ||||||||
\(223\) | 22.7424 | 1.52294 | 0.761472 | − | 0.648198i | \(-0.224477\pi\) | ||||
0.761472 | + | 0.648198i | \(0.224477\pi\) | |||||||
\(224\) | −9.00173 | −0.601453 | ||||||||
\(225\) | 15.1175 | 1.00784 | ||||||||
\(226\) | −1.84010 | −0.122402 | ||||||||
\(227\) | 13.4338 | 0.891631 | 0.445815 | − | 0.895125i | \(-0.352914\pi\) | ||||
0.445815 | + | 0.895125i | \(0.352914\pi\) | |||||||
\(228\) | −18.8325 | −1.24721 | ||||||||
\(229\) | −10.2134 | −0.674924 | −0.337462 | − | 0.941339i | \(-0.609568\pi\) | ||||
−0.337462 | + | 0.941339i | \(0.609568\pi\) | |||||||
\(230\) | 3.12911 | 0.206328 | ||||||||
\(231\) | −69.5259 | −4.57447 | ||||||||
\(232\) | −2.38758 | −0.156753 | ||||||||
\(233\) | 2.32044 | 0.152017 | 0.0760085 | − | 0.997107i | \(-0.475782\pi\) | ||||
0.0760085 | + | 0.997107i | \(0.475782\pi\) | |||||||
\(234\) | 0.412207 | 0.0269468 | ||||||||
\(235\) | −2.73574 | −0.178460 | ||||||||
\(236\) | 1.97753 | 0.128726 | ||||||||
\(237\) | 10.1425 | 0.658826 | ||||||||
\(238\) | −0.761519 | −0.0493620 | ||||||||
\(239\) | 18.6717 | 1.20777 | 0.603885 | − | 0.797071i | \(-0.293619\pi\) | ||||
0.603885 | + | 0.797071i | \(0.293619\pi\) | |||||||
\(240\) | −32.7268 | −2.11250 | ||||||||
\(241\) | −29.2196 | −1.88220 | −0.941099 | − | 0.338131i | \(-0.890205\pi\) | ||||
−0.941099 | + | 0.338131i | \(0.890205\pi\) | |||||||
\(242\) | −4.89195 | −0.314467 | ||||||||
\(243\) | 12.6046 | 0.808589 | ||||||||
\(244\) | −7.68434 | −0.491940 | ||||||||
\(245\) | 76.8572 | 4.91023 | ||||||||
\(246\) | 0.355649 | 0.0226753 | ||||||||
\(247\) | 9.78082 | 0.622338 | ||||||||
\(248\) | −0.904204 | −0.0574170 | ||||||||
\(249\) | 7.53273 | 0.477367 | ||||||||
\(250\) | −4.10258 | −0.259470 | ||||||||
\(251\) | 9.15802 | 0.578049 | 0.289024 | − | 0.957322i | \(-0.406669\pi\) | ||||
0.289024 | + | 0.957322i | \(0.406669\pi\) | |||||||
\(252\) | −12.9833 | −0.817869 | ||||||||
\(253\) | −33.7451 | −2.12154 | ||||||||
\(254\) | 2.54738 | 0.159837 | ||||||||
\(255\) | −8.46596 | −0.530159 | ||||||||
\(256\) | 14.2326 | 0.889535 | ||||||||
\(257\) | −3.48071 | −0.217121 | −0.108560 | − | 0.994090i | \(-0.534624\pi\) | ||||
−0.108560 | + | 0.994090i | \(0.534624\pi\) | |||||||
\(258\) | 2.46648 | 0.153556 | ||||||||
\(259\) | 12.2728 | 0.762595 | ||||||||
\(260\) | 17.1945 | 1.06636 | ||||||||
\(261\) | −5.17517 | −0.320335 | ||||||||
\(262\) | 1.18689 | 0.0733264 | ||||||||
\(263\) | 5.44026 | 0.335461 | 0.167730 | − | 0.985833i | \(-0.446356\pi\) | ||||
0.167730 | + | 0.985833i | \(0.446356\pi\) | |||||||
\(264\) | −8.15976 | −0.502198 | ||||||||
\(265\) | 1.10652 | 0.0679731 | ||||||||
\(266\) | 3.50040 | 0.214624 | ||||||||
\(267\) | −14.6378 | −0.895816 | ||||||||
\(268\) | 27.0121 | 1.65003 | ||||||||
\(269\) | −4.85862 | −0.296235 | −0.148118 | − | 0.988970i | \(-0.547321\pi\) | ||||
−0.148118 | + | 0.988970i | \(0.547321\pi\) | |||||||
\(270\) | −2.16708 | −0.131884 | ||||||||
\(271\) | −22.1008 | −1.34253 | −0.671263 | − | 0.741219i | \(-0.734248\pi\) | ||||
−0.671263 | + | 0.741219i | \(0.734248\pi\) | |||||||
\(272\) | 3.86569 | 0.234392 | ||||||||
\(273\) | 22.3958 | 1.35546 | ||||||||
\(274\) | 0.213341 | 0.0128884 | ||||||||
\(275\) | 77.2715 | 4.65965 | ||||||||
\(276\) | −20.9297 | −1.25982 | ||||||||
\(277\) | 1.14089 | 0.0685491 | 0.0342746 | − | 0.999412i | \(-0.489088\pi\) | ||||
0.0342746 | + | 0.999412i | \(0.489088\pi\) | |||||||
\(278\) | −0.782581 | −0.0469361 | ||||||||
\(279\) | −1.95990 | −0.117336 | ||||||||
\(280\) | 12.3772 | 0.739681 | ||||||||
\(281\) | −0.00789805 | −0.000471158 0 | −0.000235579 | − | 1.00000i | \(-0.500075\pi\) | ||||
−0.000235579 | 1.00000i | \(0.500075\pi\) | ||||||||
\(282\) | −0.207918 | −0.0123813 | ||||||||
\(283\) | −11.4040 | −0.677897 | −0.338949 | − | 0.940805i | \(-0.610071\pi\) | ||||
−0.338949 | + | 0.940805i | \(0.610071\pi\) | |||||||
\(284\) | 15.0901 | 0.895430 | ||||||||
\(285\) | 38.9147 | 2.30511 | ||||||||
\(286\) | 2.10695 | 0.124587 | ||||||||
\(287\) | 5.81778 | 0.343412 | ||||||||
\(288\) | −2.28993 | −0.134936 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 2.45287 | 0.144037 | ||||||||
\(291\) | −28.1040 | −1.64749 | ||||||||
\(292\) | 20.2089 | 1.18264 | ||||||||
\(293\) | 23.4881 | 1.37219 | 0.686096 | − | 0.727511i | \(-0.259323\pi\) | ||||
0.686096 | + | 0.727511i | \(0.259323\pi\) | |||||||
\(294\) | 5.84120 | 0.340666 | ||||||||
\(295\) | −4.08629 | −0.237913 | ||||||||
\(296\) | 1.44037 | 0.0837199 | ||||||||
\(297\) | 23.3703 | 1.35608 | ||||||||
\(298\) | −0.667778 | −0.0386833 | ||||||||
\(299\) | 10.8700 | 0.628631 | ||||||||
\(300\) | 47.9262 | 2.76702 | ||||||||
\(301\) | 40.3472 | 2.32557 | ||||||||
\(302\) | −1.73701 | −0.0999537 | ||||||||
\(303\) | 3.88036 | 0.222921 | ||||||||
\(304\) | −17.7690 | −1.01912 | ||||||||
\(305\) | 15.8786 | 0.909207 | ||||||||
\(306\) | −0.193722 | −0.0110743 | ||||||||
\(307\) | −22.1729 | −1.26547 | −0.632736 | − | 0.774368i | \(-0.718068\pi\) | ||||
−0.632736 | + | 0.774368i | \(0.718068\pi\) | |||||||
\(308\) | −66.3625 | −3.78135 | ||||||||
\(309\) | −24.8553 | −1.41397 | ||||||||
\(310\) | 0.928928 | 0.0527596 | ||||||||
\(311\) | 9.65728 | 0.547614 | 0.273807 | − | 0.961785i | \(-0.411717\pi\) | ||||
0.273807 | + | 0.961785i | \(0.411717\pi\) | |||||||
\(312\) | 2.62844 | 0.148806 | ||||||||
\(313\) | −6.97936 | −0.394497 | −0.197248 | − | 0.980354i | \(-0.563201\pi\) | ||||
−0.197248 | + | 0.980354i | \(0.563201\pi\) | |||||||
\(314\) | −0.937458 | −0.0529038 | ||||||||
\(315\) | 26.8281 | 1.51159 | ||||||||
\(316\) | 9.68100 | 0.544599 | ||||||||
\(317\) | −1.77872 | −0.0999027 | −0.0499513 | − | 0.998752i | \(-0.515907\pi\) | ||||
−0.0499513 | + | 0.998752i | \(0.515907\pi\) | |||||||
\(318\) | 0.0840965 | 0.00471590 | ||||||||
\(319\) | −26.4523 | −1.48104 | ||||||||
\(320\) | −30.5073 | −1.70541 | ||||||||
\(321\) | 2.41985 | 0.135063 | ||||||||
\(322\) | 3.89022 | 0.216794 | ||||||||
\(323\) | −4.59660 | −0.255762 | ||||||||
\(324\) | 22.1619 | 1.23122 | ||||||||
\(325\) | −24.8909 | −1.38070 | ||||||||
\(326\) | 1.93619 | 0.107236 | ||||||||
\(327\) | −18.5315 | −1.02479 | ||||||||
\(328\) | 0.682791 | 0.0377008 | ||||||||
\(329\) | −3.40116 | −0.187512 | ||||||||
\(330\) | 8.38287 | 0.461462 | ||||||||
\(331\) | 11.6046 | 0.637847 | 0.318924 | − | 0.947780i | \(-0.396679\pi\) | ||||
0.318924 | + | 0.947780i | \(0.396679\pi\) | |||||||
\(332\) | 7.18999 | 0.394602 | ||||||||
\(333\) | 3.12206 | 0.171088 | ||||||||
\(334\) | 1.00859 | 0.0551876 | ||||||||
\(335\) | −55.8168 | −3.04960 | ||||||||
\(336\) | −40.6870 | −2.21966 | ||||||||
\(337\) | −6.46296 | −0.352060 | −0.176030 | − | 0.984385i | \(-0.556326\pi\) | ||||
−0.176030 | + | 0.984385i | \(0.556326\pi\) | |||||||
\(338\) | 1.26999 | 0.0690785 | ||||||||
\(339\) | −25.4326 | −1.38131 | ||||||||
\(340\) | −8.08076 | −0.438241 | ||||||||
\(341\) | −10.0178 | −0.542493 | ||||||||
\(342\) | 0.890461 | 0.0481506 | ||||||||
\(343\) | 59.9900 | 3.23916 | ||||||||
\(344\) | 4.73526 | 0.255308 | ||||||||
\(345\) | 43.2484 | 2.32841 | ||||||||
\(346\) | −1.07452 | −0.0577663 | ||||||||
\(347\) | −16.2606 | −0.872917 | −0.436459 | − | 0.899724i | \(-0.643767\pi\) | ||||
−0.436459 | + | 0.899724i | \(0.643767\pi\) | |||||||
\(348\) | −16.4065 | −0.879482 | ||||||||
\(349\) | −24.8546 | −1.33044 | −0.665218 | − | 0.746649i | \(-0.731662\pi\) | ||||
−0.665218 | + | 0.746649i | \(0.731662\pi\) | |||||||
\(350\) | −8.90806 | −0.476156 | ||||||||
\(351\) | −7.52810 | −0.401820 | ||||||||
\(352\) | −11.7047 | −0.623864 | ||||||||
\(353\) | 30.2666 | 1.61093 | 0.805466 | − | 0.592643i | \(-0.201915\pi\) | ||||
0.805466 | + | 0.592643i | \(0.201915\pi\) | |||||||
\(354\) | −0.310561 | −0.0165061 | ||||||||
\(355\) | −31.1815 | −1.65494 | ||||||||
\(356\) | −13.9717 | −0.740500 | ||||||||
\(357\) | −10.5252 | −0.557051 | ||||||||
\(358\) | 1.23941 | 0.0655048 | ||||||||
\(359\) | −25.5406 | −1.34798 | −0.673991 | − | 0.738740i | \(-0.735421\pi\) | ||||
−0.673991 | + | 0.738740i | \(0.735421\pi\) | |||||||
\(360\) | 3.14862 | 0.165947 | ||||||||
\(361\) | 2.12877 | 0.112041 | ||||||||
\(362\) | −2.24520 | −0.118005 | ||||||||
\(363\) | −67.6131 | −3.54877 | ||||||||
\(364\) | 21.3768 | 1.12045 | ||||||||
\(365\) | −41.7589 | −2.18576 | ||||||||
\(366\) | 1.20679 | 0.0630797 | ||||||||
\(367\) | 25.7623 | 1.34478 | 0.672391 | − | 0.740197i | \(-0.265268\pi\) | ||||
0.672391 | + | 0.740197i | \(0.265268\pi\) | |||||||
\(368\) | −19.7479 | −1.02943 | ||||||||
\(369\) | 1.47997 | 0.0770443 | ||||||||
\(370\) | −1.47976 | −0.0769289 | ||||||||
\(371\) | 1.37567 | 0.0714211 | ||||||||
\(372\) | −6.21333 | −0.322146 | ||||||||
\(373\) | 6.63829 | 0.343718 | 0.171859 | − | 0.985122i | \(-0.445023\pi\) | ||||
0.171859 | + | 0.985122i | \(0.445023\pi\) | |||||||
\(374\) | −0.990185 | −0.0512013 | ||||||||
\(375\) | −56.7029 | −2.92812 | ||||||||
\(376\) | −0.399170 | −0.0205856 | ||||||||
\(377\) | 8.52087 | 0.438847 | ||||||||
\(378\) | −2.69419 | −0.138574 | ||||||||
\(379\) | 0.599995 | 0.0308197 | 0.0154098 | − | 0.999881i | \(-0.495095\pi\) | ||||
0.0154098 | + | 0.999881i | \(0.495095\pi\) | |||||||
\(380\) | 37.1440 | 1.90545 | ||||||||
\(381\) | 35.2080 | 1.80376 | ||||||||
\(382\) | 3.08404 | 0.157793 | ||||||||
\(383\) | −25.6842 | −1.31240 | −0.656200 | − | 0.754587i | \(-0.727837\pi\) | ||||
−0.656200 | + | 0.754587i | \(0.727837\pi\) | |||||||
\(384\) | −9.66069 | −0.492995 | ||||||||
\(385\) | 137.129 | 6.98872 | ||||||||
\(386\) | 1.98376 | 0.100971 | ||||||||
\(387\) | 10.2638 | 0.521741 | ||||||||
\(388\) | −26.8253 | −1.36185 | ||||||||
\(389\) | 8.96237 | 0.454410 | 0.227205 | − | 0.973847i | \(-0.427041\pi\) | ||||
0.227205 | + | 0.973847i | \(0.427041\pi\) | |||||||
\(390\) | −2.70031 | −0.136735 | ||||||||
\(391\) | −5.10850 | −0.258348 | ||||||||
\(392\) | 11.2142 | 0.566403 | ||||||||
\(393\) | 16.4044 | 0.827490 | ||||||||
\(394\) | 0.483622 | 0.0243645 | ||||||||
\(395\) | −20.0044 | −1.00653 | ||||||||
\(396\) | −16.8818 | −0.848344 | ||||||||
\(397\) | 0.681719 | 0.0342145 | 0.0171072 | − | 0.999854i | \(-0.494554\pi\) | ||||
0.0171072 | + | 0.999854i | \(0.494554\pi\) | |||||||
\(398\) | 1.52966 | 0.0766751 | ||||||||
\(399\) | 48.3801 | 2.42203 | ||||||||
\(400\) | 45.2198 | 2.26099 | ||||||||
\(401\) | 12.0985 | 0.604173 | 0.302086 | − | 0.953281i | \(-0.402317\pi\) | ||||
0.302086 | + | 0.953281i | \(0.402317\pi\) | |||||||
\(402\) | −4.24211 | −0.211577 | ||||||||
\(403\) | 3.22695 | 0.160746 | ||||||||
\(404\) | 3.70381 | 0.184271 | ||||||||
\(405\) | −45.7945 | −2.27555 | ||||||||
\(406\) | 3.04949 | 0.151344 | ||||||||
\(407\) | 15.9580 | 0.791011 | ||||||||
\(408\) | −1.23526 | −0.0611547 | ||||||||
\(409\) | −30.5143 | −1.50884 | −0.754419 | − | 0.656394i | \(-0.772081\pi\) | ||||
−0.754419 | + | 0.656394i | \(0.772081\pi\) | |||||||
\(410\) | −0.701460 | −0.0346426 | ||||||||
\(411\) | 2.94865 | 0.145446 | ||||||||
\(412\) | −23.7243 | −1.16881 | ||||||||
\(413\) | −5.08021 | −0.249981 | ||||||||
\(414\) | 0.989627 | 0.0486375 | ||||||||
\(415\) | −14.8571 | −0.729306 | ||||||||
\(416\) | 3.77035 | 0.184857 | ||||||||
\(417\) | −10.8163 | −0.529675 | ||||||||
\(418\) | 4.55149 | 0.222621 | ||||||||
\(419\) | 12.6964 | 0.620259 | 0.310130 | − | 0.950694i | \(-0.399628\pi\) | ||||
0.310130 | + | 0.950694i | \(0.399628\pi\) | |||||||
\(420\) | 85.0514 | 4.15008 | ||||||||
\(421\) | −5.56869 | −0.271401 | −0.135701 | − | 0.990750i | \(-0.543329\pi\) | ||||
−0.135701 | + | 0.990750i | \(0.543329\pi\) | |||||||
\(422\) | 1.09327 | 0.0532195 | ||||||||
\(423\) | −0.865215 | −0.0420682 | ||||||||
\(424\) | 0.161452 | 0.00784081 | ||||||||
\(425\) | 11.6977 | 0.567424 | ||||||||
\(426\) | −2.36981 | −0.114818 | ||||||||
\(427\) | 19.7408 | 0.955326 | ||||||||
\(428\) | 2.30975 | 0.111646 | ||||||||
\(429\) | 29.1208 | 1.40596 | ||||||||
\(430\) | −4.86474 | −0.234598 | ||||||||
\(431\) | 9.48862 | 0.457051 | 0.228525 | − | 0.973538i | \(-0.426610\pi\) | ||||
0.228525 | + | 0.973538i | \(0.426610\pi\) | |||||||
\(432\) | 13.6765 | 0.658009 | ||||||||
\(433\) | −0.147709 | −0.00709845 | −0.00354923 | − | 0.999994i | \(-0.501130\pi\) | ||||
−0.00354923 | + | 0.999994i | \(0.501130\pi\) | |||||||
\(434\) | 1.15488 | 0.0554358 | ||||||||
\(435\) | 33.9018 | 1.62547 | ||||||||
\(436\) | −17.6883 | −0.847117 | ||||||||
\(437\) | 23.4818 | 1.12328 | ||||||||
\(438\) | −3.17370 | −0.151645 | ||||||||
\(439\) | −31.8245 | −1.51890 | −0.759450 | − | 0.650566i | \(-0.774532\pi\) | ||||
−0.759450 | + | 0.650566i | \(0.774532\pi\) | |||||||
\(440\) | 16.0938 | 0.767242 | ||||||||
\(441\) | 24.3072 | 1.15748 | ||||||||
\(442\) | 0.318961 | 0.0151714 | ||||||||
\(443\) | 18.9816 | 0.901845 | 0.450923 | − | 0.892563i | \(-0.351095\pi\) | ||||
0.450923 | + | 0.892563i | \(0.351095\pi\) | |||||||
\(444\) | 9.89766 | 0.469722 | ||||||||
\(445\) | 28.8706 | 1.36860 | ||||||||
\(446\) | −3.40906 | −0.161424 | ||||||||
\(447\) | −9.22955 | −0.436543 | ||||||||
\(448\) | −37.9277 | −1.79191 | ||||||||
\(449\) | −34.9239 | −1.64816 | −0.824080 | − | 0.566474i | \(-0.808307\pi\) | ||||
−0.824080 | + | 0.566474i | \(0.808307\pi\) | |||||||
\(450\) | −2.26611 | −0.106825 | ||||||||
\(451\) | 7.56471 | 0.356208 | ||||||||
\(452\) | −24.2754 | −1.14182 | ||||||||
\(453\) | −24.0077 | −1.12798 | ||||||||
\(454\) | −2.01371 | −0.0945081 | ||||||||
\(455\) | −44.1722 | −2.07082 | ||||||||
\(456\) | 5.67802 | 0.265898 | ||||||||
\(457\) | 20.4519 | 0.956701 | 0.478351 | − | 0.878169i | \(-0.341235\pi\) | ||||
0.478351 | + | 0.878169i | \(0.341235\pi\) | |||||||
\(458\) | 1.53099 | 0.0715383 | ||||||||
\(459\) | 3.53791 | 0.165136 | ||||||||
\(460\) | 41.2806 | 1.92472 | ||||||||
\(461\) | 24.1918 | 1.12673 | 0.563363 | − | 0.826210i | \(-0.309507\pi\) | ||||
0.563363 | + | 0.826210i | \(0.309507\pi\) | |||||||
\(462\) | 10.4219 | 0.484869 | ||||||||
\(463\) | −2.97547 | −0.138282 | −0.0691410 | − | 0.997607i | \(-0.522026\pi\) | ||||
−0.0691410 | + | 0.997607i | \(0.522026\pi\) | |||||||
\(464\) | −15.4801 | −0.718644 | ||||||||
\(465\) | 12.8390 | 0.595393 | ||||||||
\(466\) | −0.347832 | −0.0161130 | ||||||||
\(467\) | 19.2108 | 0.888968 | 0.444484 | − | 0.895787i | \(-0.353387\pi\) | ||||
0.444484 | + | 0.895787i | \(0.353387\pi\) | |||||||
\(468\) | 5.43801 | 0.251372 | ||||||||
\(469\) | −69.3933 | −3.20429 | ||||||||
\(470\) | 0.410084 | 0.0189158 | ||||||||
\(471\) | −12.9569 | −0.597021 | ||||||||
\(472\) | −0.596228 | −0.0274436 | ||||||||
\(473\) | 52.4625 | 2.41223 | ||||||||
\(474\) | −1.52035 | −0.0698320 | ||||||||
\(475\) | −53.7699 | −2.46713 | ||||||||
\(476\) | −10.0463 | −0.460470 | ||||||||
\(477\) | 0.349953 | 0.0160233 | ||||||||
\(478\) | −2.79887 | −0.128017 | ||||||||
\(479\) | −22.9938 | −1.05061 | −0.525306 | − | 0.850914i | \(-0.676049\pi\) | ||||
−0.525306 | + | 0.850914i | \(0.676049\pi\) | |||||||
\(480\) | 15.0010 | 0.684699 | ||||||||
\(481\) | −5.14044 | −0.234384 | ||||||||
\(482\) | 4.37999 | 0.199503 | ||||||||
\(483\) | 53.7679 | 2.44652 | ||||||||
\(484\) | −64.5366 | −2.93348 | ||||||||
\(485\) | 55.4306 | 2.51697 | ||||||||
\(486\) | −1.88943 | −0.0857061 | ||||||||
\(487\) | −42.3789 | −1.92037 | −0.960186 | − | 0.279361i | \(-0.909877\pi\) | ||||
−0.960186 | + | 0.279361i | \(0.909877\pi\) | |||||||
\(488\) | 2.31684 | 0.104878 | ||||||||
\(489\) | 26.7607 | 1.21016 | ||||||||
\(490\) | −11.5208 | −0.520458 | ||||||||
\(491\) | 0.120943 | 0.00545810 | 0.00272905 | − | 0.999996i | \(-0.499131\pi\) | ||||
0.00272905 | + | 0.999996i | \(0.499131\pi\) | |||||||
\(492\) | 4.69186 | 0.211526 | ||||||||
\(493\) | −4.00448 | −0.180353 | ||||||||
\(494\) | −1.46614 | −0.0659646 | ||||||||
\(495\) | 34.8839 | 1.56792 | ||||||||
\(496\) | −5.86247 | −0.263233 | ||||||||
\(497\) | −38.7659 | −1.73889 | ||||||||
\(498\) | −1.12915 | −0.0505984 | ||||||||
\(499\) | 3.46624 | 0.155170 | 0.0775850 | − | 0.996986i | \(-0.475279\pi\) | ||||
0.0775850 | + | 0.996986i | \(0.475279\pi\) | |||||||
\(500\) | −54.1229 | −2.42045 | ||||||||
\(501\) | 13.9400 | 0.622794 | ||||||||
\(502\) | −1.37278 | −0.0612701 | ||||||||
\(503\) | −19.4597 | −0.867665 | −0.433832 | − | 0.900994i | \(-0.642839\pi\) | ||||
−0.433832 | + | 0.900994i | \(0.642839\pi\) | |||||||
\(504\) | 3.91447 | 0.174365 | ||||||||
\(505\) | −7.65339 | −0.340571 | ||||||||
\(506\) | 5.05836 | 0.224872 | ||||||||
\(507\) | 17.5529 | 0.779553 | ||||||||
\(508\) | 33.6061 | 1.49103 | ||||||||
\(509\) | −19.7458 | −0.875216 | −0.437608 | − | 0.899166i | \(-0.644174\pi\) | ||||
−0.437608 | + | 0.899166i | \(0.644174\pi\) | |||||||
\(510\) | 1.26904 | 0.0561940 | ||||||||
\(511\) | −51.9160 | −2.29663 | ||||||||
\(512\) | −11.4593 | −0.506436 | ||||||||
\(513\) | −16.2624 | −0.718002 | ||||||||
\(514\) | 0.521756 | 0.0230137 | ||||||||
\(515\) | 49.0230 | 2.16021 | ||||||||
\(516\) | 32.5388 | 1.43244 | ||||||||
\(517\) | −4.42245 | −0.194499 | ||||||||
\(518\) | −1.83968 | −0.0808311 | ||||||||
\(519\) | −14.8512 | −0.651895 | ||||||||
\(520\) | −5.18417 | −0.227341 | ||||||||
\(521\) | −30.3592 | −1.33006 | −0.665030 | − | 0.746817i | \(-0.731581\pi\) | ||||
−0.665030 | + | 0.746817i | \(0.731581\pi\) | |||||||
\(522\) | 0.775754 | 0.0339538 | ||||||||
\(523\) | −8.76375 | −0.383212 | −0.191606 | − | 0.981472i | \(-0.561370\pi\) | ||||
−0.191606 | + | 0.981472i | \(0.561370\pi\) | |||||||
\(524\) | 15.6579 | 0.684021 | ||||||||
\(525\) | −123.121 | −5.37343 | ||||||||
\(526\) | −0.815490 | −0.0355570 | ||||||||
\(527\) | −1.51654 | −0.0660615 | ||||||||
\(528\) | −52.9043 | −2.30237 | ||||||||
\(529\) | 3.09678 | 0.134643 | ||||||||
\(530\) | −0.165867 | −0.00720479 | ||||||||
\(531\) | −1.29235 | −0.0560831 | ||||||||
\(532\) | 46.1788 | 2.00210 | ||||||||
\(533\) | −2.43676 | −0.105548 | ||||||||
\(534\) | 2.19419 | 0.0949517 | ||||||||
\(535\) | −4.77277 | −0.206345 | ||||||||
\(536\) | −8.14420 | −0.351776 | ||||||||
\(537\) | 17.1302 | 0.739223 | ||||||||
\(538\) | 0.728303 | 0.0313994 | ||||||||
\(539\) | 124.243 | 5.35154 | ||||||||
\(540\) | −28.5890 | −1.23028 | ||||||||
\(541\) | 32.7384 | 1.40753 | 0.703767 | − | 0.710431i | \(-0.251500\pi\) | ||||
0.703767 | + | 0.710431i | \(0.251500\pi\) | |||||||
\(542\) | 3.31289 | 0.142301 | ||||||||
\(543\) | −31.0316 | −1.33169 | ||||||||
\(544\) | −1.77192 | −0.0759704 | ||||||||
\(545\) | 36.5504 | 1.56565 | ||||||||
\(546\) | −3.35712 | −0.143671 | ||||||||
\(547\) | 2.79045 | 0.119311 | 0.0596556 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596556 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(548\) | 2.81448 | 0.120229 | ||||||||
\(549\) | 5.02183 | 0.214327 | ||||||||
\(550\) | −11.5829 | −0.493898 | ||||||||
\(551\) | 18.4070 | 0.784165 | ||||||||
\(552\) | 6.31035 | 0.268586 | ||||||||
\(553\) | −24.8702 | −1.05759 | ||||||||
\(554\) | −0.171018 | −0.00726584 | ||||||||
\(555\) | −20.4521 | −0.868144 | ||||||||
\(556\) | −10.3241 | −0.437840 | ||||||||
\(557\) | −11.7867 | −0.499420 | −0.249710 | − | 0.968321i | \(-0.580335\pi\) | ||||
−0.249710 | + | 0.968321i | \(0.580335\pi\) | |||||||
\(558\) | 0.293787 | 0.0124370 | ||||||||
\(559\) | −16.8993 | −0.714765 | ||||||||
\(560\) | 80.2486 | 3.39112 | ||||||||
\(561\) | −13.6856 | −0.577808 | ||||||||
\(562\) | 0.00118391 | 4.99403e−5 0 | ||||||||
\(563\) | 25.5045 | 1.07489 | 0.537444 | − | 0.843299i | \(-0.319390\pi\) | ||||
0.537444 | + | 0.843299i | \(0.319390\pi\) | |||||||
\(564\) | −2.74294 | −0.115498 | ||||||||
\(565\) | 50.1617 | 2.11032 | ||||||||
\(566\) | 1.70945 | 0.0718535 | ||||||||
\(567\) | −56.9333 | −2.39098 | ||||||||
\(568\) | −4.54967 | −0.190900 | ||||||||
\(569\) | 19.3869 | 0.812743 | 0.406371 | − | 0.913708i | \(-0.366794\pi\) | ||||
0.406371 | + | 0.913708i | \(0.366794\pi\) | |||||||
\(570\) | −5.83328 | −0.244329 | ||||||||
\(571\) | −29.1693 | −1.22070 | −0.610349 | − | 0.792133i | \(-0.708971\pi\) | ||||
−0.610349 | + | 0.792133i | \(0.708971\pi\) | |||||||
\(572\) | 27.7958 | 1.16220 | ||||||||
\(573\) | 42.6253 | 1.78070 | ||||||||
\(574\) | −0.872079 | −0.0363999 | ||||||||
\(575\) | −59.7579 | −2.49208 | ||||||||
\(576\) | −9.64835 | −0.402015 | ||||||||
\(577\) | 13.1135 | 0.545922 | 0.272961 | − | 0.962025i | \(-0.411997\pi\) | ||||
0.272961 | + | 0.962025i | \(0.411997\pi\) | |||||||
\(578\) | −0.149899 | −0.00623498 | ||||||||
\(579\) | 27.4181 | 1.13946 | ||||||||
\(580\) | 32.3592 | 1.34364 | ||||||||
\(581\) | −18.4709 | −0.766300 | ||||||||
\(582\) | 4.21276 | 0.174625 | ||||||||
\(583\) | 1.78875 | 0.0740823 | ||||||||
\(584\) | −6.09301 | −0.252131 | ||||||||
\(585\) | −11.2369 | −0.464588 | ||||||||
\(586\) | −3.52085 | −0.145445 | ||||||||
\(587\) | −15.4022 | −0.635718 | −0.317859 | − | 0.948138i | \(-0.602964\pi\) | ||||
−0.317859 | + | 0.948138i | \(0.602964\pi\) | |||||||
\(588\) | 77.0595 | 3.17788 | ||||||||
\(589\) | 6.97094 | 0.287232 | ||||||||
\(590\) | 0.612531 | 0.0252175 | ||||||||
\(591\) | 6.68427 | 0.274954 | ||||||||
\(592\) | 9.33875 | 0.383820 | ||||||||
\(593\) | 22.4096 | 0.920250 | 0.460125 | − | 0.887854i | \(-0.347805\pi\) | ||||
0.460125 | + | 0.887854i | \(0.347805\pi\) | |||||||
\(594\) | −3.50319 | −0.143738 | ||||||||
\(595\) | 20.7592 | 0.851045 | ||||||||
\(596\) | −8.80960 | −0.360855 | ||||||||
\(597\) | 21.1419 | 0.865281 | ||||||||
\(598\) | −1.62941 | −0.0666315 | ||||||||
\(599\) | −26.7752 | −1.09400 | −0.547002 | − | 0.837131i | \(-0.684231\pi\) | ||||
−0.547002 | + | 0.837131i | \(0.684231\pi\) | |||||||
\(600\) | −14.4498 | −0.589911 | ||||||||
\(601\) | −33.5188 | −1.36726 | −0.683630 | − | 0.729829i | \(-0.739600\pi\) | ||||
−0.683630 | + | 0.729829i | \(0.739600\pi\) | |||||||
\(602\) | −6.04801 | −0.246498 | ||||||||
\(603\) | −17.6528 | −0.718879 | ||||||||
\(604\) | −22.9153 | −0.932412 | ||||||||
\(605\) | 133.356 | 5.42169 | ||||||||
\(606\) | −0.581663 | −0.0236284 | ||||||||
\(607\) | 20.8148 | 0.844846 | 0.422423 | − | 0.906399i | \(-0.361180\pi\) | ||||
0.422423 | + | 0.906399i | \(0.361180\pi\) | |||||||
\(608\) | 8.14481 | 0.330316 | ||||||||
\(609\) | 42.1478 | 1.70792 | ||||||||
\(610\) | −2.38019 | −0.0963710 | ||||||||
\(611\) | 1.42457 | 0.0576318 | ||||||||
\(612\) | −2.55565 | −0.103306 | ||||||||
\(613\) | −35.4269 | −1.43088 | −0.715440 | − | 0.698674i | \(-0.753774\pi\) | ||||
−0.715440 | + | 0.698674i | \(0.753774\pi\) | |||||||
\(614\) | 3.32369 | 0.134133 | ||||||||
\(615\) | −9.69508 | −0.390943 | ||||||||
\(616\) | 20.0084 | 0.806160 | ||||||||
\(617\) | 19.8081 | 0.797446 | 0.398723 | − | 0.917071i | \(-0.369453\pi\) | ||||
0.398723 | + | 0.917071i | \(0.369453\pi\) | |||||||
\(618\) | 3.72578 | 0.149873 | ||||||||
\(619\) | −32.6096 | −1.31069 | −0.655345 | − | 0.755329i | \(-0.727477\pi\) | ||||
−0.655345 | + | 0.755329i | \(0.727477\pi\) | |||||||
\(620\) | 12.2548 | 0.492164 | ||||||||
\(621\) | −18.0734 | −0.725262 | ||||||||
\(622\) | −1.44762 | −0.0580442 | ||||||||
\(623\) | 35.8929 | 1.43802 | ||||||||
\(624\) | 17.0417 | 0.682212 | ||||||||
\(625\) | 53.3485 | 2.13394 | ||||||||
\(626\) | 1.04620 | 0.0418146 | ||||||||
\(627\) | 62.9074 | 2.51228 | ||||||||
\(628\) | −12.3673 | −0.493510 | ||||||||
\(629\) | 2.41581 | 0.0963245 | ||||||||
\(630\) | −4.02151 | −0.160221 | ||||||||
\(631\) | 1.31670 | 0.0524169 | 0.0262085 | − | 0.999656i | \(-0.491657\pi\) | ||||
0.0262085 | + | 0.999656i | \(0.491657\pi\) | |||||||
\(632\) | −2.91884 | −0.116105 | ||||||||
\(633\) | 15.1104 | 0.600583 | ||||||||
\(634\) | 0.266628 | 0.0105892 | ||||||||
\(635\) | −69.4422 | −2.75573 | ||||||||
\(636\) | 1.10943 | 0.0439920 | ||||||||
\(637\) | −40.0215 | −1.58571 | ||||||||
\(638\) | 3.96518 | 0.156983 | ||||||||
\(639\) | −9.86158 | −0.390118 | ||||||||
\(640\) | 19.0542 | 0.753182 | ||||||||
\(641\) | 12.7181 | 0.502334 | 0.251167 | − | 0.967944i | \(-0.419186\pi\) | ||||
0.251167 | + | 0.967944i | \(0.419186\pi\) | |||||||
\(642\) | −0.362734 | −0.0143160 | ||||||||
\(643\) | −37.8467 | −1.49253 | −0.746265 | − | 0.665649i | \(-0.768155\pi\) | ||||
−0.746265 | + | 0.665649i | \(0.768155\pi\) | |||||||
\(644\) | 51.3214 | 2.02235 | ||||||||
\(645\) | −67.2369 | −2.64745 | ||||||||
\(646\) | 0.689027 | 0.0271094 | ||||||||
\(647\) | 0.0711931 | 0.00279889 | 0.00139944 | − | 0.999999i | \(-0.499555\pi\) | ||||
0.00139944 | + | 0.999999i | \(0.499555\pi\) | |||||||
\(648\) | −6.68186 | −0.262488 | ||||||||
\(649\) | −6.60568 | −0.259296 | ||||||||
\(650\) | 3.73112 | 0.146347 | ||||||||
\(651\) | 15.9619 | 0.625594 | ||||||||
\(652\) | 25.5431 | 1.00034 | ||||||||
\(653\) | 3.76552 | 0.147356 | 0.0736780 | − | 0.997282i | \(-0.476526\pi\) | ||||
0.0736780 | + | 0.997282i | \(0.476526\pi\) | |||||||
\(654\) | 2.77786 | 0.108623 | ||||||||
\(655\) | −32.3549 | −1.26421 | ||||||||
\(656\) | 4.42692 | 0.172842 | ||||||||
\(657\) | −13.2068 | −0.515247 | ||||||||
\(658\) | 0.509831 | 0.0198753 | ||||||||
\(659\) | 45.6920 | 1.77991 | 0.889954 | − | 0.456050i | \(-0.150736\pi\) | ||||
0.889954 | + | 0.456050i | \(0.150736\pi\) | |||||||
\(660\) | 110.590 | 4.30472 | ||||||||
\(661\) | −38.0042 | −1.47819 | −0.739097 | − | 0.673599i | \(-0.764747\pi\) | ||||
−0.739097 | + | 0.673599i | \(0.764747\pi\) | |||||||
\(662\) | −1.73952 | −0.0676084 | ||||||||
\(663\) | 4.40844 | 0.171210 | ||||||||
\(664\) | −2.16779 | −0.0841266 | ||||||||
\(665\) | −95.4219 | −3.70030 | ||||||||
\(666\) | −0.467994 | −0.0181344 | ||||||||
\(667\) | 20.4569 | 0.792094 | ||||||||
\(668\) | 13.3057 | 0.514815 | ||||||||
\(669\) | −47.1176 | −1.82167 | ||||||||
\(670\) | 8.36688 | 0.323241 | ||||||||
\(671\) | 25.6685 | 0.990922 | ||||||||
\(672\) | 18.6498 | 0.719430 | ||||||||
\(673\) | −39.6861 | −1.52979 | −0.764893 | − | 0.644157i | \(-0.777208\pi\) | ||||
−0.764893 | + | 0.644157i | \(0.777208\pi\) | |||||||
\(674\) | 0.968793 | 0.0373165 | ||||||||
\(675\) | 41.3856 | 1.59293 | ||||||||
\(676\) | 16.7543 | 0.644395 | ||||||||
\(677\) | 1.47460 | 0.0566733 | 0.0283367 | − | 0.999598i | \(-0.490979\pi\) | ||||
0.0283367 | + | 0.999598i | \(0.490979\pi\) | |||||||
\(678\) | 3.81233 | 0.146411 | ||||||||
\(679\) | 68.9132 | 2.64465 | ||||||||
\(680\) | 2.43636 | 0.0934301 | ||||||||
\(681\) | −27.8321 | −1.06653 | ||||||||
\(682\) | 1.50166 | 0.0575014 | ||||||||
\(683\) | 31.9921 | 1.22414 | 0.612072 | − | 0.790802i | \(-0.290336\pi\) | ||||
0.612072 | + | 0.790802i | \(0.290336\pi\) | |||||||
\(684\) | 11.7473 | 0.449170 | ||||||||
\(685\) | −5.81573 | −0.222208 | ||||||||
\(686\) | −8.99245 | −0.343333 | ||||||||
\(687\) | 21.1602 | 0.807312 | ||||||||
\(688\) | 30.7014 | 1.17048 | ||||||||
\(689\) | −0.576195 | −0.0219513 | ||||||||
\(690\) | −6.48289 | −0.246800 | ||||||||
\(691\) | −19.8948 | −0.756834 | −0.378417 | − | 0.925635i | \(-0.623531\pi\) | ||||
−0.378417 | + | 0.925635i | \(0.623531\pi\) | |||||||
\(692\) | −14.1755 | −0.538870 | ||||||||
\(693\) | 43.3689 | 1.64745 | ||||||||
\(694\) | 2.43746 | 0.0925246 | ||||||||
\(695\) | 21.3333 | 0.809220 | ||||||||
\(696\) | 4.94659 | 0.187500 | ||||||||
\(697\) | 1.14518 | 0.0433769 | ||||||||
\(698\) | 3.72568 | 0.141019 | ||||||||
\(699\) | −4.80748 | −0.181836 | ||||||||
\(700\) | −117.519 | −4.44179 | ||||||||
\(701\) | −49.0588 | −1.85293 | −0.926464 | − | 0.376385i | \(-0.877167\pi\) | ||||
−0.926464 | + | 0.376385i | \(0.877167\pi\) | |||||||
\(702\) | 1.12845 | 0.0425908 | ||||||||
\(703\) | −11.1045 | −0.418814 | ||||||||
\(704\) | −49.3164 | −1.85868 | ||||||||
\(705\) | 5.66789 | 0.213465 | ||||||||
\(706\) | −4.53694 | −0.170750 | ||||||||
\(707\) | −9.51496 | −0.357847 | ||||||||
\(708\) | −4.09704 | −0.153976 | ||||||||
\(709\) | 9.83165 | 0.369235 | 0.184618 | − | 0.982810i | \(-0.440895\pi\) | ||||
0.184618 | + | 0.982810i | \(0.440895\pi\) | |||||||
\(710\) | 4.67407 | 0.175415 | ||||||||
\(711\) | −6.32668 | −0.237269 | ||||||||
\(712\) | 4.21250 | 0.157870 | ||||||||
\(713\) | 7.74725 | 0.290137 | ||||||||
\(714\) | 1.57771 | 0.0590445 | ||||||||
\(715\) | −57.4360 | −2.14798 | ||||||||
\(716\) | 16.3508 | 0.611057 | ||||||||
\(717\) | −38.6839 | −1.44468 | ||||||||
\(718\) | 3.82851 | 0.142879 | ||||||||
\(719\) | 35.3055 | 1.31667 | 0.658337 | − | 0.752724i | \(-0.271260\pi\) | ||||
0.658337 | + | 0.752724i | \(0.271260\pi\) | |||||||
\(720\) | 20.4143 | 0.760796 | ||||||||
\(721\) | 60.9471 | 2.26979 | ||||||||
\(722\) | −0.319101 | −0.0118757 | ||||||||
\(723\) | 60.5371 | 2.25140 | ||||||||
\(724\) | −29.6197 | −1.10081 | ||||||||
\(725\) | −46.8434 | −1.73972 | ||||||||
\(726\) | 10.1351 | 0.376150 | ||||||||
\(727\) | 4.55419 | 0.168906 | 0.0844528 | − | 0.996427i | \(-0.473086\pi\) | ||||
0.0844528 | + | 0.996427i | \(0.473086\pi\) | |||||||
\(728\) | −6.44514 | −0.238873 | ||||||||
\(729\) | 7.50635 | 0.278013 | ||||||||
\(730\) | 6.25962 | 0.231679 | ||||||||
\(731\) | 7.94203 | 0.293746 | ||||||||
\(732\) | 15.9204 | 0.588435 | ||||||||
\(733\) | 48.2068 | 1.78056 | 0.890280 | − | 0.455414i | \(-0.150509\pi\) | ||||
0.890280 | + | 0.455414i | \(0.150509\pi\) | |||||||
\(734\) | −3.86175 | −0.142540 | ||||||||
\(735\) | −159.233 | −5.87338 | ||||||||
\(736\) | 9.05185 | 0.333656 | ||||||||
\(737\) | −90.2304 | −3.32368 | ||||||||
\(738\) | −0.221847 | −0.00816629 | ||||||||
\(739\) | 15.2916 | 0.562511 | 0.281256 | − | 0.959633i | \(-0.409249\pi\) | ||||
0.281256 | + | 0.959633i | \(0.409249\pi\) | |||||||
\(740\) | −19.5215 | −0.717626 | ||||||||
\(741\) | −20.2639 | −0.744412 | ||||||||
\(742\) | −0.206211 | −0.00757025 | ||||||||
\(743\) | −16.2719 | −0.596958 | −0.298479 | − | 0.954416i | \(-0.596479\pi\) | ||||
−0.298479 | + | 0.954416i | \(0.596479\pi\) | |||||||
\(744\) | 1.87333 | 0.0686795 | ||||||||
\(745\) | 18.2038 | 0.666936 | ||||||||
\(746\) | −0.995074 | −0.0364323 | ||||||||
\(747\) | −4.69877 | −0.171919 | ||||||||
\(748\) | −13.0629 | −0.477628 | ||||||||
\(749\) | −5.93367 | −0.216812 | ||||||||
\(750\) | 8.49971 | 0.310365 | ||||||||
\(751\) | 4.80309 | 0.175267 | 0.0876337 | − | 0.996153i | \(-0.472070\pi\) | ||||
0.0876337 | + | 0.996153i | \(0.472070\pi\) | |||||||
\(752\) | −2.58804 | −0.0943763 | ||||||||
\(753\) | −18.9736 | −0.691435 | ||||||||
\(754\) | −1.27727 | −0.0465155 | ||||||||
\(755\) | 47.3513 | 1.72329 | ||||||||
\(756\) | −35.5429 | −1.29268 | ||||||||
\(757\) | −18.8397 | −0.684740 | −0.342370 | − | 0.939565i | \(-0.611230\pi\) | ||||
−0.342370 | + | 0.939565i | \(0.611230\pi\) | |||||||
\(758\) | −0.0899387 | −0.00326672 | ||||||||
\(759\) | 69.9130 | 2.53768 | ||||||||
\(760\) | −11.1990 | −0.406230 | ||||||||
\(761\) | −20.3223 | −0.736682 | −0.368341 | − | 0.929691i | \(-0.620074\pi\) | ||||
−0.368341 | + | 0.929691i | \(0.620074\pi\) | |||||||
\(762\) | −5.27765 | −0.191189 | ||||||||
\(763\) | 45.4407 | 1.64506 | ||||||||
\(764\) | 40.6859 | 1.47196 | ||||||||
\(765\) | 5.28090 | 0.190931 | ||||||||
\(766\) | 3.85003 | 0.139107 | ||||||||
\(767\) | 2.12783 | 0.0768317 | ||||||||
\(768\) | −29.4870 | −1.06402 | ||||||||
\(769\) | −0.252234 | −0.00909580 | −0.00454790 | − | 0.999990i | \(-0.501448\pi\) | ||||
−0.00454790 | + | 0.999990i | \(0.501448\pi\) | |||||||
\(770\) | −20.5555 | −0.740767 | ||||||||
\(771\) | 7.21134 | 0.259710 | ||||||||
\(772\) | 26.1706 | 0.941899 | ||||||||
\(773\) | 51.2621 | 1.84377 | 0.921884 | − | 0.387466i | \(-0.126649\pi\) | ||||
0.921884 | + | 0.387466i | \(0.126649\pi\) | |||||||
\(774\) | −1.53854 | −0.0553017 | ||||||||
\(775\) | −17.7401 | −0.637243 | ||||||||
\(776\) | 8.08785 | 0.290337 | ||||||||
\(777\) | −25.4268 | −0.912181 | ||||||||
\(778\) | −1.34345 | −0.0481651 | ||||||||
\(779\) | −5.26395 | −0.188601 | ||||||||
\(780\) | −35.6236 | −1.27553 | ||||||||
\(781\) | −50.4063 | −1.80368 | ||||||||
\(782\) | 0.765760 | 0.0273835 | ||||||||
\(783\) | −14.1675 | −0.506305 | ||||||||
\(784\) | 72.7080 | 2.59672 | ||||||||
\(785\) | 25.5553 | 0.912109 | ||||||||
\(786\) | −2.45900 | −0.0877095 | ||||||||
\(787\) | −0.278652 | −0.00993287 | −0.00496644 | − | 0.999988i | \(-0.501581\pi\) | ||||
−0.00496644 | + | 0.999988i | \(0.501581\pi\) | |||||||
\(788\) | 6.38014 | 0.227283 | ||||||||
\(789\) | −11.2711 | −0.401262 | ||||||||
\(790\) | 2.99865 | 0.106687 | ||||||||
\(791\) | 62.3628 | 2.21737 | ||||||||
\(792\) | 5.08989 | 0.180862 | ||||||||
\(793\) | −8.26840 | −0.293619 | ||||||||
\(794\) | −0.102189 | −0.00362655 | ||||||||
\(795\) | −2.29249 | −0.0813063 | ||||||||
\(796\) | 20.1799 | 0.715259 | ||||||||
\(797\) | −46.6815 | −1.65354 | −0.826772 | − | 0.562537i | \(-0.809825\pi\) | ||||
−0.826772 | + | 0.562537i | \(0.809825\pi\) | |||||||
\(798\) | −7.25213 | −0.256723 | ||||||||
\(799\) | −0.669492 | −0.0236849 | ||||||||
\(800\) | −20.7275 | −0.732826 | ||||||||
\(801\) | 9.13074 | 0.322619 | ||||||||
\(802\) | −1.81356 | −0.0640391 | ||||||||
\(803\) | −67.5052 | −2.38221 | ||||||||
\(804\) | −55.9637 | −1.97369 | ||||||||
\(805\) | −106.048 | −3.73772 | ||||||||
\(806\) | −0.483717 | −0.0170382 | ||||||||
\(807\) | 10.0661 | 0.354343 | ||||||||
\(808\) | −1.11670 | −0.0392855 | ||||||||
\(809\) | −37.5786 | −1.32119 | −0.660597 | − | 0.750741i | \(-0.729697\pi\) | ||||
−0.660597 | + | 0.750741i | \(0.729697\pi\) | |||||||
\(810\) | 6.86456 | 0.241196 | ||||||||
\(811\) | 20.0715 | 0.704807 | 0.352403 | − | 0.935848i | \(-0.385365\pi\) | ||||
0.352403 | + | 0.935848i | \(0.385365\pi\) | |||||||
\(812\) | 40.2301 | 1.41180 | ||||||||
\(813\) | 45.7883 | 1.60587 | ||||||||
\(814\) | −2.39210 | −0.0838429 | ||||||||
\(815\) | −52.7811 | −1.84884 | ||||||||
\(816\) | −8.00892 | −0.280368 | ||||||||
\(817\) | −36.5064 | −1.27720 | ||||||||
\(818\) | 4.57407 | 0.159929 | ||||||||
\(819\) | −13.9701 | −0.488154 | ||||||||
\(820\) | −9.25395 | −0.323162 | ||||||||
\(821\) | −21.5071 | −0.750602 | −0.375301 | − | 0.926903i | \(-0.622461\pi\) | ||||
−0.375301 | + | 0.926903i | \(0.622461\pi\) | |||||||
\(822\) | −0.442000 | −0.0154165 | ||||||||
\(823\) | 28.8193 | 1.00458 | 0.502289 | − | 0.864700i | \(-0.332491\pi\) | ||||
0.502289 | + | 0.864700i | \(0.332491\pi\) | |||||||
\(824\) | 7.15292 | 0.249184 | ||||||||
\(825\) | −160.091 | −5.57365 | ||||||||
\(826\) | 0.761519 | 0.0264966 | ||||||||
\(827\) | −23.9255 | −0.831973 | −0.415986 | − | 0.909371i | \(-0.636564\pi\) | ||||
−0.415986 | + | 0.909371i | \(0.636564\pi\) | |||||||
\(828\) | 13.0556 | 0.453712 | ||||||||
\(829\) | 22.5719 | 0.783955 | 0.391978 | − | 0.919975i | \(-0.371791\pi\) | ||||
0.391978 | + | 0.919975i | \(0.371791\pi\) | |||||||
\(830\) | 2.22707 | 0.0773026 | ||||||||
\(831\) | −2.36368 | −0.0819953 | ||||||||
\(832\) | 15.8859 | 0.550745 | ||||||||
\(833\) | 18.8086 | 0.651678 | ||||||||
\(834\) | 1.62135 | 0.0561427 | ||||||||
\(835\) | −27.4944 | −0.951484 | ||||||||
\(836\) | 60.0451 | 2.07670 | ||||||||
\(837\) | −5.36539 | −0.185455 | ||||||||
\(838\) | −1.90318 | −0.0657442 | ||||||||
\(839\) | −37.9076 | −1.30872 | −0.654358 | − | 0.756185i | \(-0.727061\pi\) | ||||
−0.654358 | + | 0.756185i | \(0.727061\pi\) | |||||||
\(840\) | −25.6431 | −0.884772 | ||||||||
\(841\) | −12.9641 | −0.447039 | ||||||||
\(842\) | 0.834742 | 0.0287671 | ||||||||
\(843\) | 0.0163632 | 0.000563577 0 | ||||||||
\(844\) | 14.4228 | 0.496455 | ||||||||
\(845\) | −34.6203 | −1.19098 | ||||||||
\(846\) | 0.129695 | 0.00445900 | ||||||||
\(847\) | 165.793 | 5.69670 | ||||||||
\(848\) | 1.04679 | 0.0359468 | ||||||||
\(849\) | 23.6268 | 0.810869 | ||||||||
\(850\) | −1.75348 | −0.0601439 | ||||||||
\(851\) | −12.3412 | −0.423049 | ||||||||
\(852\) | −31.2635 | −1.07107 | ||||||||
\(853\) | 18.1315 | 0.620810 | 0.310405 | − | 0.950604i | \(-0.399535\pi\) | ||||
0.310405 | + | 0.950604i | \(0.399535\pi\) | |||||||
\(854\) | −2.95913 | −0.101259 | ||||||||
\(855\) | −24.2742 | −0.830160 | ||||||||
\(856\) | −0.696393 | −0.0238022 | ||||||||
\(857\) | 28.3037 | 0.966837 | 0.483418 | − | 0.875389i | \(-0.339395\pi\) | ||||
0.483418 | + | 0.875389i | \(0.339395\pi\) | |||||||
\(858\) | −4.36518 | −0.149025 | ||||||||
\(859\) | −41.9748 | −1.43216 | −0.716081 | − | 0.698017i | \(-0.754066\pi\) | ||||
−0.716081 | + | 0.698017i | \(0.754066\pi\) | |||||||
\(860\) | −64.1776 | −2.18844 | ||||||||
\(861\) | −12.0533 | −0.410774 | ||||||||
\(862\) | −1.42234 | −0.0484449 | ||||||||
\(863\) | 2.72900 | 0.0928963 | 0.0464482 | − | 0.998921i | \(-0.485210\pi\) | ||||
0.0464482 | + | 0.998921i | \(0.485210\pi\) | |||||||
\(864\) | −6.26890 | −0.213272 | ||||||||
\(865\) | 29.2916 | 0.995943 | ||||||||
\(866\) | 0.0221415 | 0.000752398 0 | ||||||||
\(867\) | −2.07180 | −0.0703619 | ||||||||
\(868\) | 15.2356 | 0.517129 | ||||||||
\(869\) | −32.3381 | −1.09700 | ||||||||
\(870\) | −5.08184 | −0.172291 | ||||||||
\(871\) | 29.0652 | 0.984837 | ||||||||
\(872\) | 5.33305 | 0.180600 | ||||||||
\(873\) | 17.5307 | 0.593325 | ||||||||
\(874\) | −3.51989 | −0.119062 | ||||||||
\(875\) | 139.040 | 4.70041 | ||||||||
\(876\) | −41.8688 | −1.41461 | ||||||||
\(877\) | 36.7073 | 1.23952 | 0.619759 | − | 0.784792i | \(-0.287230\pi\) | ||||
0.619759 | + | 0.784792i | \(0.287230\pi\) | |||||||
\(878\) | 4.77046 | 0.160995 | ||||||||
\(879\) | −48.6627 | −1.64135 | ||||||||
\(880\) | 104.345 | 3.51748 | ||||||||
\(881\) | −30.4784 | −1.02684 | −0.513422 | − | 0.858136i | \(-0.671622\pi\) | ||||
−0.513422 | + | 0.858136i | \(0.671622\pi\) | |||||||
\(882\) | −3.64362 | −0.122687 | ||||||||
\(883\) | 21.5609 | 0.725584 | 0.362792 | − | 0.931870i | \(-0.381824\pi\) | ||||
0.362792 | + | 0.931870i | \(0.381824\pi\) | |||||||
\(884\) | 4.20786 | 0.141526 | ||||||||
\(885\) | 8.46596 | 0.284580 | ||||||||
\(886\) | −2.84533 | −0.0955908 | ||||||||
\(887\) | 47.7601 | 1.60363 | 0.801813 | − | 0.597574i | \(-0.203869\pi\) | ||||
0.801813 | + | 0.597574i | \(0.203869\pi\) | |||||||
\(888\) | −2.98416 | −0.100142 | ||||||||
\(889\) | −86.3329 | −2.89551 | ||||||||
\(890\) | −4.32768 | −0.145064 | ||||||||
\(891\) | −74.0290 | −2.48007 | ||||||||
\(892\) | −44.9738 | −1.50583 | ||||||||
\(893\) | 3.07739 | 0.102981 | ||||||||
\(894\) | 1.38350 | 0.0462712 | ||||||||
\(895\) | −33.7866 | −1.12936 | ||||||||
\(896\) | 23.6888 | 0.791387 | ||||||||
\(897\) | −22.5205 | −0.751939 | ||||||||
\(898\) | 5.23506 | 0.174696 | ||||||||
\(899\) | 6.07296 | 0.202544 | ||||||||
\(900\) | −29.8954 | −0.996513 | ||||||||
\(901\) | 0.270789 | 0.00902130 | ||||||||
\(902\) | −1.13394 | −0.0377562 | ||||||||
\(903\) | −83.5912 | −2.78174 | ||||||||
\(904\) | 7.31907 | 0.243429 | ||||||||
\(905\) | 61.2048 | 2.03452 | ||||||||
\(906\) | 3.59873 | 0.119560 | ||||||||
\(907\) | −31.2119 | −1.03637 | −0.518187 | − | 0.855267i | \(-0.673393\pi\) | ||||
−0.518187 | + | 0.855267i | \(0.673393\pi\) | |||||||
\(908\) | −26.5657 | −0.881613 | ||||||||
\(909\) | −2.42049 | −0.0802827 | ||||||||
\(910\) | 6.62137 | 0.219496 | ||||||||
\(911\) | −16.6869 | −0.552861 | −0.276430 | − | 0.961034i | \(-0.589152\pi\) | ||||
−0.276430 | + | 0.961034i | \(0.589152\pi\) | |||||||
\(912\) | 36.8138 | 1.21903 | ||||||||
\(913\) | −24.0172 | −0.794853 | ||||||||
\(914\) | −3.06573 | −0.101405 | ||||||||
\(915\) | −32.8973 | −1.08755 | ||||||||
\(916\) | 20.1974 | 0.667341 | ||||||||
\(917\) | −40.2248 | −1.32834 | ||||||||
\(918\) | −0.530330 | −0.0175035 | ||||||||
\(919\) | −24.9073 | −0.821617 | −0.410808 | − | 0.911722i | \(-0.634753\pi\) | ||||
−0.410808 | + | 0.911722i | \(0.634753\pi\) | |||||||
\(920\) | −12.4461 | −0.410337 | ||||||||
\(921\) | 45.9377 | 1.51370 | ||||||||
\(922\) | −3.62633 | −0.119427 | ||||||||
\(923\) | 16.2370 | 0.534447 | ||||||||
\(924\) | 137.490 | 4.52308 | ||||||||
\(925\) | 28.2595 | 0.929166 | ||||||||
\(926\) | 0.446021 | 0.0146572 | ||||||||
\(927\) | 15.5042 | 0.509225 | ||||||||
\(928\) | 7.09561 | 0.232925 | ||||||||
\(929\) | 22.3531 | 0.733380 | 0.366690 | − | 0.930343i | \(-0.380491\pi\) | ||||
0.366690 | + | 0.930343i | \(0.380491\pi\) | |||||||
\(930\) | −1.92455 | −0.0631085 | ||||||||
\(931\) | −86.4555 | −2.83347 | ||||||||
\(932\) | −4.58874 | −0.150309 | ||||||||
\(933\) | −20.0079 | −0.655030 | ||||||||
\(934\) | −2.87968 | −0.0942259 | ||||||||
\(935\) | 26.9927 | 0.882756 | ||||||||
\(936\) | −1.63957 | −0.0535909 | ||||||||
\(937\) | 36.0925 | 1.17909 | 0.589545 | − | 0.807736i | \(-0.299307\pi\) | ||||
0.589545 | + | 0.807736i | \(0.299307\pi\) | |||||||
\(938\) | 10.4020 | 0.339637 | ||||||||
\(939\) | 14.4598 | 0.471879 | ||||||||
\(940\) | 5.41000 | 0.176455 | ||||||||
\(941\) | 24.3593 | 0.794091 | 0.397046 | − | 0.917799i | \(-0.370035\pi\) | ||||
0.397046 | + | 0.917799i | \(0.370035\pi\) | |||||||
\(942\) | 1.94222 | 0.0632811 | ||||||||
\(943\) | −5.85017 | −0.190508 | ||||||||
\(944\) | −3.86569 | −0.125817 | ||||||||
\(945\) | 73.4443 | 2.38914 | ||||||||
\(946\) | −7.86408 | −0.255683 | ||||||||
\(947\) | −22.2055 | −0.721581 | −0.360791 | − | 0.932647i | \(-0.617493\pi\) | ||||
−0.360791 | + | 0.932647i | \(0.617493\pi\) | |||||||
\(948\) | −20.0571 | −0.651424 | ||||||||
\(949\) | 21.7449 | 0.705870 | ||||||||
\(950\) | 8.06006 | 0.261503 | ||||||||
\(951\) | 3.68514 | 0.119499 | ||||||||
\(952\) | 3.02897 | 0.0981694 | ||||||||
\(953\) | −24.8691 | −0.805591 | −0.402795 | − | 0.915290i | \(-0.631961\pi\) | ||||
−0.402795 | + | 0.915290i | \(0.631961\pi\) | |||||||
\(954\) | −0.0524577 | −0.00169838 | ||||||||
\(955\) | −84.0716 | −2.72049 | ||||||||
\(956\) | −36.9238 | −1.19420 | ||||||||
\(957\) | 54.8038 | 1.77156 | ||||||||
\(958\) | 3.44674 | 0.111359 | ||||||||
\(959\) | −7.23032 | −0.233479 | ||||||||
\(960\) | 63.2049 | 2.03993 | ||||||||
\(961\) | −28.7001 | −0.925810 | ||||||||
\(962\) | 0.770547 | 0.0248434 | ||||||||
\(963\) | −1.50946 | −0.0486415 | ||||||||
\(964\) | 57.7826 | 1.86105 | ||||||||
\(965\) | −54.0778 | −1.74083 | ||||||||
\(966\) | −8.05976 | −0.259318 | ||||||||
\(967\) | −10.2864 | −0.330788 | −0.165394 | − | 0.986228i | \(-0.552890\pi\) | ||||
−0.165394 | + | 0.986228i | \(0.552890\pi\) | |||||||
\(968\) | 19.4579 | 0.625400 | ||||||||
\(969\) | 9.52324 | 0.305930 | ||||||||
\(970\) | −8.30900 | −0.266786 | ||||||||
\(971\) | 12.6425 | 0.405718 | 0.202859 | − | 0.979208i | \(-0.434977\pi\) | ||||
0.202859 | + | 0.979208i | \(0.434977\pi\) | |||||||
\(972\) | −24.9261 | −0.799504 | ||||||||
\(973\) | 26.5224 | 0.850268 | ||||||||
\(974\) | 6.35256 | 0.203549 | ||||||||
\(975\) | 51.5689 | 1.65153 | ||||||||
\(976\) | 15.0214 | 0.480823 | ||||||||
\(977\) | −56.1063 | −1.79500 | −0.897500 | − | 0.441014i | \(-0.854619\pi\) | ||||
−0.897500 | + | 0.441014i | \(0.854619\pi\) | |||||||
\(978\) | −4.01140 | −0.128270 | ||||||||
\(979\) | 46.6707 | 1.49160 | ||||||||
\(980\) | −151.987 | −4.85506 | ||||||||
\(981\) | 11.5596 | 0.369069 | ||||||||
\(982\) | −0.0181293 | −0.000578529 0 | ||||||||
\(983\) | 24.8351 | 0.792117 | 0.396058 | − | 0.918225i | \(-0.370378\pi\) | ||||
0.396058 | + | 0.918225i | \(0.370378\pi\) | |||||||
\(984\) | −1.41460 | −0.0450959 | ||||||||
\(985\) | −13.1837 | −0.420066 | ||||||||
\(986\) | 0.600268 | 0.0191164 | ||||||||
\(987\) | 7.04652 | 0.224293 | ||||||||
\(988\) | −19.3419 | −0.615347 | ||||||||
\(989\) | −40.5719 | −1.29011 | ||||||||
\(990\) | −5.22907 | −0.166191 | ||||||||
\(991\) | −43.9779 | −1.39700 | −0.698502 | − | 0.715608i | \(-0.746150\pi\) | ||||
−0.698502 | + | 0.715608i | \(0.746150\pi\) | |||||||
\(992\) | 2.68719 | 0.0853183 | ||||||||
\(993\) | −24.0424 | −0.762963 | ||||||||
\(994\) | 5.81097 | 0.184313 | ||||||||
\(995\) | −41.6990 | −1.32195 | ||||||||
\(996\) | −14.8962 | −0.472004 | ||||||||
\(997\) | 15.9262 | 0.504389 | 0.252194 | − | 0.967677i | \(-0.418848\pi\) | ||||
0.252194 | + | 0.967677i | \(0.418848\pi\) | |||||||
\(998\) | −0.519586 | −0.0164472 | ||||||||
\(999\) | 8.54691 | 0.270412 |
(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 | 1003.2.a.i.1.8 | ✓ | 18 | |
3.2 | odd | 2 | 9027.2.a.q.1.11 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1003.2.a.i.1.8 | ✓ | 18 | 1.1 | even | 1 | trivial | |
9027.2.a.q.1.11 | 18 | 3.2 | odd | 2 |