Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70166 | −1.20325 | −0.601626 | − | 0.798778i | \(-0.705480\pi\) | ||||
−0.601626 | + | 0.798778i | \(0.705480\pi\) | |||||||
\(3\) | 2.90991 | 1.68004 | 0.840019 | − | 0.542557i | \(-0.182544\pi\) | ||||
0.840019 | + | 0.542557i | \(0.182544\pi\) | |||||||
\(4\) | 0.895633 | 0.447817 | ||||||||
\(5\) | −0.762355 | −0.340935 | −0.170468 | − | 0.985363i | \(-0.554528\pi\) | ||||
−0.170468 | + | 0.985363i | \(0.554528\pi\) | |||||||
\(6\) | −4.95167 | −2.02151 | ||||||||
\(7\) | 4.85107 | 1.83353 | 0.916765 | − | 0.399426i | \(-0.130791\pi\) | ||||
0.916765 | + | 0.399426i | \(0.130791\pi\) | |||||||
\(8\) | 1.87925 | 0.664416 | ||||||||
\(9\) | 5.46758 | 1.82253 | ||||||||
\(10\) | 1.29727 | 0.410231 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.60621 | 0.752349 | ||||||||
\(13\) | −1.16100 | −0.322004 | −0.161002 | − | 0.986954i | \(-0.551473\pi\) | ||||
−0.161002 | + | 0.986954i | \(0.551473\pi\) | |||||||
\(14\) | −8.25485 | −2.20620 | ||||||||
\(15\) | −2.21838 | −0.572784 | ||||||||
\(16\) | −4.98911 | −1.24728 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −9.30394 | −2.19296 | ||||||||
\(19\) | 3.00298 | 0.688931 | 0.344465 | − | 0.938799i | \(-0.388060\pi\) | ||||
0.344465 | + | 0.938799i | \(0.388060\pi\) | |||||||
\(20\) | −0.682790 | −0.152677 | ||||||||
\(21\) | 14.1162 | 3.08040 | ||||||||
\(22\) | −1.70166 | −0.362794 | ||||||||
\(23\) | −6.18094 | −1.28882 | −0.644408 | − | 0.764682i | \(-0.722896\pi\) | ||||
−0.644408 | + | 0.764682i | \(0.722896\pi\) | |||||||
\(24\) | 5.46846 | 1.11624 | ||||||||
\(25\) | −4.41882 | −0.883763 | ||||||||
\(26\) | 1.97562 | 0.387452 | ||||||||
\(27\) | 7.18044 | 1.38188 | ||||||||
\(28\) | 4.34478 | 0.821086 | ||||||||
\(29\) | −0.453833 | −0.0842747 | −0.0421373 | − | 0.999112i | \(-0.513417\pi\) | ||||
−0.0421373 | + | 0.999112i | \(0.513417\pi\) | |||||||
\(30\) | 3.77493 | 0.689204 | ||||||||
\(31\) | −6.53377 | −1.17350 | −0.586749 | − | 0.809769i | \(-0.699593\pi\) | ||||
−0.586749 | + | 0.809769i | \(0.699593\pi\) | |||||||
\(32\) | 4.73124 | 0.836373 | ||||||||
\(33\) | 2.90991 | 0.506550 | ||||||||
\(34\) | −1.70166 | −0.291832 | ||||||||
\(35\) | −3.69823 | −0.625115 | ||||||||
\(36\) | 4.89695 | 0.816158 | ||||||||
\(37\) | 1.16400 | 0.191361 | 0.0956804 | − | 0.995412i | \(-0.469497\pi\) | ||||
0.0956804 | + | 0.995412i | \(0.469497\pi\) | |||||||
\(38\) | −5.11004 | −0.828958 | ||||||||
\(39\) | −3.37841 | −0.540979 | ||||||||
\(40\) | −1.43266 | −0.226523 | ||||||||
\(41\) | 4.26888 | 0.666686 | 0.333343 | − | 0.942806i | \(-0.391823\pi\) | ||||
0.333343 | + | 0.942806i | \(0.391823\pi\) | |||||||
\(42\) | −24.0209 | −3.70650 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 0.895633 | 0.135022 | ||||||||
\(45\) | −4.16824 | −0.621364 | ||||||||
\(46\) | 10.5178 | 1.55077 | ||||||||
\(47\) | −1.17938 | −0.172031 | −0.0860153 | − | 0.996294i | \(-0.527413\pi\) | ||||
−0.0860153 | + | 0.996294i | \(0.527413\pi\) | |||||||
\(48\) | −14.5179 | −2.09547 | ||||||||
\(49\) | 16.5328 | 2.36184 | ||||||||
\(50\) | 7.51930 | 1.06339 | ||||||||
\(51\) | 2.90991 | 0.407469 | ||||||||
\(52\) | −1.03983 | −0.144199 | ||||||||
\(53\) | 11.6707 | 1.60309 | 0.801547 | − | 0.597932i | \(-0.204011\pi\) | ||||
0.801547 | + | 0.597932i | \(0.204011\pi\) | |||||||
\(54\) | −12.2186 | −1.66275 | ||||||||
\(55\) | −0.762355 | −0.102796 | ||||||||
\(56\) | 9.11638 | 1.21823 | ||||||||
\(57\) | 8.73840 | 1.15743 | ||||||||
\(58\) | 0.772268 | 0.101404 | ||||||||
\(59\) | −4.03069 | −0.524752 | −0.262376 | − | 0.964966i | \(-0.584506\pi\) | ||||
−0.262376 | + | 0.964966i | \(0.584506\pi\) | |||||||
\(60\) | −1.98686 | −0.256502 | ||||||||
\(61\) | −5.54122 | −0.709481 | −0.354740 | − | 0.934965i | \(-0.615431\pi\) | ||||
−0.354740 | + | 0.934965i | \(0.615431\pi\) | |||||||
\(62\) | 11.1182 | 1.41202 | ||||||||
\(63\) | 26.5236 | 3.34166 | ||||||||
\(64\) | 1.92727 | 0.240909 | ||||||||
\(65\) | 0.885095 | 0.109782 | ||||||||
\(66\) | −4.95167 | −0.609508 | ||||||||
\(67\) | 2.59019 | 0.316442 | 0.158221 | − | 0.987404i | \(-0.449424\pi\) | ||||
0.158221 | + | 0.987404i | \(0.449424\pi\) | |||||||
\(68\) | 0.895633 | 0.108611 | ||||||||
\(69\) | −17.9860 | −2.16526 | ||||||||
\(70\) | 6.29312 | 0.752172 | ||||||||
\(71\) | 14.4353 | 1.71316 | 0.856579 | − | 0.516016i | \(-0.172586\pi\) | ||||
0.856579 | + | 0.516016i | \(0.172586\pi\) | |||||||
\(72\) | 10.2750 | 1.21092 | ||||||||
\(73\) | 0.103162 | 0.0120742 | 0.00603710 | − | 0.999982i | \(-0.498078\pi\) | ||||
0.00603710 | + | 0.999982i | \(0.498078\pi\) | |||||||
\(74\) | −1.98073 | −0.230255 | ||||||||
\(75\) | −12.8584 | −1.48476 | ||||||||
\(76\) | 2.68957 | 0.308515 | ||||||||
\(77\) | 4.85107 | 0.552830 | ||||||||
\(78\) | 5.74889 | 0.650934 | ||||||||
\(79\) | −0.329877 | −0.0371141 | −0.0185571 | − | 0.999828i | \(-0.505907\pi\) | ||||
−0.0185571 | + | 0.999828i | \(0.505907\pi\) | |||||||
\(80\) | 3.80347 | 0.425241 | ||||||||
\(81\) | 4.49170 | 0.499077 | ||||||||
\(82\) | −7.26416 | −0.802192 | ||||||||
\(83\) | 11.1939 | 1.22869 | 0.614344 | − | 0.789039i | \(-0.289421\pi\) | ||||
0.614344 | + | 0.789039i | \(0.289421\pi\) | |||||||
\(84\) | 12.6429 | 1.37945 | ||||||||
\(85\) | −0.762355 | −0.0826890 | ||||||||
\(86\) | −1.70166 | −0.183494 | ||||||||
\(87\) | −1.32061 | −0.141585 | ||||||||
\(88\) | 1.87925 | 0.200329 | ||||||||
\(89\) | −7.70401 | −0.816624 | −0.408312 | − | 0.912843i | \(-0.633882\pi\) | ||||
−0.408312 | + | 0.912843i | \(0.633882\pi\) | |||||||
\(90\) | 7.09290 | 0.747658 | ||||||||
\(91\) | −5.63209 | −0.590404 | ||||||||
\(92\) | −5.53586 | −0.577153 | ||||||||
\(93\) | −19.0127 | −1.97152 | ||||||||
\(94\) | 2.00690 | 0.206996 | ||||||||
\(95\) | −2.28933 | −0.234881 | ||||||||
\(96\) | 13.7675 | 1.40514 | ||||||||
\(97\) | 5.71368 | 0.580136 | 0.290068 | − | 0.957006i | \(-0.406322\pi\) | ||||
0.290068 | + | 0.957006i | \(0.406322\pi\) | |||||||
\(98\) | −28.1332 | −2.84188 | ||||||||
\(99\) | 5.46758 | 0.549513 | ||||||||
\(100\) | −3.95764 | −0.395764 | ||||||||
\(101\) | 13.6973 | 1.36294 | 0.681468 | − | 0.731848i | \(-0.261342\pi\) | ||||
0.681468 | + | 0.731848i | \(0.261342\pi\) | |||||||
\(102\) | −4.95167 | −0.490288 | ||||||||
\(103\) | 10.7993 | 1.06408 | 0.532042 | − | 0.846718i | \(-0.321425\pi\) | ||||
0.532042 | + | 0.846718i | \(0.321425\pi\) | |||||||
\(104\) | −2.18181 | −0.213945 | ||||||||
\(105\) | −10.7615 | −1.05022 | ||||||||
\(106\) | −19.8595 | −1.92893 | ||||||||
\(107\) | 12.2453 | 1.18379 | 0.591897 | − | 0.806014i | \(-0.298379\pi\) | ||||
0.591897 | + | 0.806014i | \(0.298379\pi\) | |||||||
\(108\) | 6.43104 | 0.618827 | ||||||||
\(109\) | 13.4994 | 1.29301 | 0.646504 | − | 0.762911i | \(-0.276230\pi\) | ||||
0.646504 | + | 0.762911i | \(0.276230\pi\) | |||||||
\(110\) | 1.29727 | 0.123689 | ||||||||
\(111\) | 3.38714 | 0.321494 | ||||||||
\(112\) | −24.2025 | −2.28692 | ||||||||
\(113\) | 11.6167 | 1.09281 | 0.546403 | − | 0.837522i | \(-0.315997\pi\) | ||||
0.546403 | + | 0.837522i | \(0.315997\pi\) | |||||||
\(114\) | −14.8698 | −1.39268 | ||||||||
\(115\) | 4.71207 | 0.439403 | ||||||||
\(116\) | −0.406468 | −0.0377396 | ||||||||
\(117\) | −6.34787 | −0.586861 | ||||||||
\(118\) | 6.85885 | 0.631409 | ||||||||
\(119\) | 4.85107 | 0.444697 | ||||||||
\(120\) | −4.16890 | −0.380567 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 9.42925 | 0.853684 | ||||||||
\(123\) | 12.4220 | 1.12006 | ||||||||
\(124\) | −5.85186 | −0.525512 | ||||||||
\(125\) | 7.18048 | 0.642241 | ||||||||
\(126\) | −45.1340 | −4.02086 | ||||||||
\(127\) | −13.9686 | −1.23952 | −0.619758 | − | 0.784793i | \(-0.712769\pi\) | ||||
−0.619758 | + | 0.784793i | \(0.712769\pi\) | |||||||
\(128\) | −12.7420 | −1.12625 | ||||||||
\(129\) | 2.90991 | 0.256203 | ||||||||
\(130\) | −1.50613 | −0.132096 | ||||||||
\(131\) | −0.502347 | −0.0438903 | −0.0219451 | − | 0.999759i | \(-0.506986\pi\) | ||||
−0.0219451 | + | 0.999759i | \(0.506986\pi\) | |||||||
\(132\) | 2.60621 | 0.226842 | ||||||||
\(133\) | 14.5677 | 1.26318 | ||||||||
\(134\) | −4.40762 | −0.380760 | ||||||||
\(135\) | −5.47404 | −0.471130 | ||||||||
\(136\) | 1.87925 | 0.161145 | ||||||||
\(137\) | −6.56384 | −0.560787 | −0.280394 | − | 0.959885i | \(-0.590465\pi\) | ||||
−0.280394 | + | 0.959885i | \(0.590465\pi\) | |||||||
\(138\) | 30.6060 | 2.60535 | ||||||||
\(139\) | 17.4228 | 1.47778 | 0.738892 | − | 0.673823i | \(-0.235349\pi\) | ||||
0.738892 | + | 0.673823i | \(0.235349\pi\) | |||||||
\(140\) | −3.31226 | −0.279937 | ||||||||
\(141\) | −3.43190 | −0.289018 | ||||||||
\(142\) | −24.5640 | −2.06136 | ||||||||
\(143\) | −1.16100 | −0.0970878 | ||||||||
\(144\) | −27.2783 | −2.27320 | ||||||||
\(145\) | 0.345982 | 0.0287322 | ||||||||
\(146\) | −0.175546 | −0.0145283 | ||||||||
\(147\) | 48.1091 | 3.96797 | ||||||||
\(148\) | 1.04252 | 0.0856946 | ||||||||
\(149\) | 24.1066 | 1.97489 | 0.987446 | − | 0.157954i | \(-0.0504899\pi\) | ||||
0.987446 | + | 0.157954i | \(0.0504899\pi\) | |||||||
\(150\) | 21.8805 | 1.78654 | ||||||||
\(151\) | 16.6535 | 1.35524 | 0.677622 | − | 0.735411i | \(-0.263011\pi\) | ||||
0.677622 | + | 0.735411i | \(0.263011\pi\) | |||||||
\(152\) | 5.64336 | 0.457737 | ||||||||
\(153\) | 5.46758 | 0.442028 | ||||||||
\(154\) | −8.25485 | −0.665195 | ||||||||
\(155\) | 4.98105 | 0.400087 | ||||||||
\(156\) | −3.02582 | −0.242259 | ||||||||
\(157\) | 9.30870 | 0.742915 | 0.371458 | − | 0.928450i | \(-0.378858\pi\) | ||||
0.371458 | + | 0.928450i | \(0.378858\pi\) | |||||||
\(158\) | 0.561338 | 0.0446576 | ||||||||
\(159\) | 33.9607 | 2.69326 | ||||||||
\(160\) | −3.60688 | −0.285149 | ||||||||
\(161\) | −29.9842 | −2.36308 | ||||||||
\(162\) | −7.64332 | −0.600516 | ||||||||
\(163\) | −7.60346 | −0.595549 | −0.297775 | − | 0.954636i | \(-0.596244\pi\) | ||||
−0.297775 | + | 0.954636i | \(0.596244\pi\) | |||||||
\(164\) | 3.82335 | 0.298553 | ||||||||
\(165\) | −2.21838 | −0.172701 | ||||||||
\(166\) | −19.0481 | −1.47842 | ||||||||
\(167\) | 13.1221 | 1.01542 | 0.507710 | − | 0.861528i | \(-0.330492\pi\) | ||||
0.507710 | + | 0.861528i | \(0.330492\pi\) | |||||||
\(168\) | 26.5278 | 2.04667 | ||||||||
\(169\) | −11.6521 | −0.896314 | ||||||||
\(170\) | 1.29727 | 0.0994957 | ||||||||
\(171\) | 16.4190 | 1.25559 | ||||||||
\(172\) | 0.895633 | 0.0682914 | ||||||||
\(173\) | 12.7566 | 0.969865 | 0.484933 | − | 0.874551i | \(-0.338844\pi\) | ||||
0.484933 | + | 0.874551i | \(0.338844\pi\) | |||||||
\(174\) | 2.24723 | 0.170362 | ||||||||
\(175\) | −21.4360 | −1.62041 | ||||||||
\(176\) | −4.98911 | −0.376068 | ||||||||
\(177\) | −11.7290 | −0.881602 | ||||||||
\(178\) | 13.1096 | 0.982605 | ||||||||
\(179\) | 17.6730 | 1.32094 | 0.660470 | − | 0.750853i | \(-0.270357\pi\) | ||||
0.660470 | + | 0.750853i | \(0.270357\pi\) | |||||||
\(180\) | −3.73321 | −0.278257 | ||||||||
\(181\) | −2.86258 | −0.212774 | −0.106387 | − | 0.994325i | \(-0.533928\pi\) | ||||
−0.106387 | + | 0.994325i | \(0.533928\pi\) | |||||||
\(182\) | 9.58389 | 0.710405 | ||||||||
\(183\) | −16.1245 | −1.19195 | ||||||||
\(184\) | −11.6155 | −0.856310 | ||||||||
\(185\) | −0.887383 | −0.0652417 | ||||||||
\(186\) | 32.3530 | 2.37224 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −1.05629 | −0.0770382 | ||||||||
\(189\) | 34.8328 | 2.53371 | ||||||||
\(190\) | 3.89566 | 0.282621 | ||||||||
\(191\) | −26.5347 | −1.91998 | −0.959992 | − | 0.280026i | \(-0.909657\pi\) | ||||
−0.959992 | + | 0.280026i | \(0.909657\pi\) | |||||||
\(192\) | 5.60819 | 0.404736 | ||||||||
\(193\) | −24.5924 | −1.77020 | −0.885101 | − | 0.465400i | \(-0.845911\pi\) | ||||
−0.885101 | + | 0.465400i | \(0.845911\pi\) | |||||||
\(194\) | −9.72272 | −0.698050 | ||||||||
\(195\) | 2.57555 | 0.184439 | ||||||||
\(196\) | 14.8074 | 1.05767 | ||||||||
\(197\) | −13.9348 | −0.992813 | −0.496407 | − | 0.868090i | \(-0.665348\pi\) | ||||
−0.496407 | + | 0.868090i | \(0.665348\pi\) | |||||||
\(198\) | −9.30394 | −0.661202 | ||||||||
\(199\) | −15.5954 | −1.10553 | −0.552765 | − | 0.833337i | \(-0.686427\pi\) | ||||
−0.552765 | + | 0.833337i | \(0.686427\pi\) | |||||||
\(200\) | −8.30407 | −0.587186 | ||||||||
\(201\) | 7.53723 | 0.531635 | ||||||||
\(202\) | −23.3082 | −1.63996 | ||||||||
\(203\) | −2.20157 | −0.154520 | ||||||||
\(204\) | 2.60621 | 0.182471 | ||||||||
\(205\) | −3.25440 | −0.227297 | ||||||||
\(206\) | −18.3766 | −1.28036 | ||||||||
\(207\) | −33.7948 | −2.34890 | ||||||||
\(208\) | 5.79236 | 0.401628 | ||||||||
\(209\) | 3.00298 | 0.207720 | ||||||||
\(210\) | 18.3124 | 1.26368 | ||||||||
\(211\) | 18.7580 | 1.29135 | 0.645676 | − | 0.763611i | \(-0.276575\pi\) | ||||
0.645676 | + | 0.763611i | \(0.276575\pi\) | |||||||
\(212\) | 10.4527 | 0.717892 | ||||||||
\(213\) | 42.0055 | 2.87817 | ||||||||
\(214\) | −20.8372 | −1.42440 | ||||||||
\(215\) | −0.762355 | −0.0519922 | ||||||||
\(216\) | 13.4939 | 0.918141 | ||||||||
\(217\) | −31.6957 | −2.15165 | ||||||||
\(218\) | −22.9713 | −1.55582 | ||||||||
\(219\) | 0.300192 | 0.0202851 | ||||||||
\(220\) | −0.682790 | −0.0460337 | ||||||||
\(221\) | −1.16100 | −0.0780974 | ||||||||
\(222\) | −5.76375 | −0.386838 | ||||||||
\(223\) | 0.892655 | 0.0597766 | 0.0298883 | − | 0.999553i | \(-0.490485\pi\) | ||||
0.0298883 | + | 0.999553i | \(0.490485\pi\) | |||||||
\(224\) | 22.9516 | 1.53352 | ||||||||
\(225\) | −24.1602 | −1.61068 | ||||||||
\(226\) | −19.7676 | −1.31492 | ||||||||
\(227\) | −5.77038 | −0.382994 | −0.191497 | − | 0.981493i | \(-0.561334\pi\) | ||||
−0.191497 | + | 0.981493i | \(0.561334\pi\) | |||||||
\(228\) | 7.82640 | 0.518316 | ||||||||
\(229\) | 5.49590 | 0.363179 | 0.181590 | − | 0.983374i | \(-0.441876\pi\) | ||||
0.181590 | + | 0.983374i | \(0.441876\pi\) | |||||||
\(230\) | −8.01832 | −0.528712 | ||||||||
\(231\) | 14.1162 | 0.928776 | ||||||||
\(232\) | −0.852867 | −0.0559934 | ||||||||
\(233\) | 7.60808 | 0.498422 | 0.249211 | − | 0.968449i | \(-0.419829\pi\) | ||||
0.249211 | + | 0.968449i | \(0.419829\pi\) | |||||||
\(234\) | 10.8019 | 0.706142 | ||||||||
\(235\) | 0.899107 | 0.0586513 | ||||||||
\(236\) | −3.61002 | −0.234992 | ||||||||
\(237\) | −0.959914 | −0.0623531 | ||||||||
\(238\) | −8.25485 | −0.535082 | ||||||||
\(239\) | 13.7662 | 0.890461 | 0.445230 | − | 0.895416i | \(-0.353122\pi\) | ||||
0.445230 | + | 0.895416i | \(0.353122\pi\) | |||||||
\(240\) | 11.0678 | 0.714421 | ||||||||
\(241\) | −29.4154 | −1.89481 | −0.947406 | − | 0.320036i | \(-0.896305\pi\) | ||||
−0.947406 | + | 0.320036i | \(0.896305\pi\) | |||||||
\(242\) | −1.70166 | −0.109387 | ||||||||
\(243\) | −8.47088 | −0.543407 | ||||||||
\(244\) | −4.96290 | −0.317717 | ||||||||
\(245\) | −12.6039 | −0.805233 | ||||||||
\(246\) | −21.1381 | −1.34771 | ||||||||
\(247\) | −3.48646 | −0.221838 | ||||||||
\(248\) | −12.2786 | −0.779691 | ||||||||
\(249\) | 32.5732 | 2.06424 | ||||||||
\(250\) | −12.2187 | −0.772779 | ||||||||
\(251\) | −1.42081 | −0.0896810 | −0.0448405 | − | 0.998994i | \(-0.514278\pi\) | ||||
−0.0448405 | + | 0.998994i | \(0.514278\pi\) | |||||||
\(252\) | 23.7554 | 1.49645 | ||||||||
\(253\) | −6.18094 | −0.388593 | ||||||||
\(254\) | 23.7698 | 1.49145 | ||||||||
\(255\) | −2.21838 | −0.138921 | ||||||||
\(256\) | 17.8280 | 1.11425 | ||||||||
\(257\) | 5.39743 | 0.336682 | 0.168341 | − | 0.985729i | \(-0.446159\pi\) | ||||
0.168341 | + | 0.985729i | \(0.446159\pi\) | |||||||
\(258\) | −4.95167 | −0.308277 | ||||||||
\(259\) | 5.64666 | 0.350866 | ||||||||
\(260\) | 0.792720 | 0.0491624 | ||||||||
\(261\) | −2.48137 | −0.153593 | ||||||||
\(262\) | 0.854823 | 0.0528111 | ||||||||
\(263\) | −16.1186 | −0.993913 | −0.496956 | − | 0.867776i | \(-0.665549\pi\) | ||||
−0.496956 | + | 0.867776i | \(0.665549\pi\) | |||||||
\(264\) | 5.46846 | 0.336560 | ||||||||
\(265\) | −8.89721 | −0.546551 | ||||||||
\(266\) | −24.7891 | −1.51992 | ||||||||
\(267\) | −22.4180 | −1.37196 | ||||||||
\(268\) | 2.31986 | 0.141708 | ||||||||
\(269\) | 27.5344 | 1.67880 | 0.839400 | − | 0.543514i | \(-0.182907\pi\) | ||||
0.839400 | + | 0.543514i | \(0.182907\pi\) | |||||||
\(270\) | 9.31494 | 0.566889 | ||||||||
\(271\) | 13.0403 | 0.792144 | 0.396072 | − | 0.918219i | \(-0.370373\pi\) | ||||
0.396072 | + | 0.918219i | \(0.370373\pi\) | |||||||
\(272\) | −4.98911 | −0.302509 | ||||||||
\(273\) | −16.3889 | −0.991901 | ||||||||
\(274\) | 11.1694 | 0.674768 | ||||||||
\(275\) | −4.41882 | −0.266465 | ||||||||
\(276\) | −16.1089 | −0.969639 | ||||||||
\(277\) | −6.60009 | −0.396561 | −0.198281 | − | 0.980145i | \(-0.563536\pi\) | ||||
−0.198281 | + | 0.980145i | \(0.563536\pi\) | |||||||
\(278\) | −29.6477 | −1.77815 | ||||||||
\(279\) | −35.7239 | −2.13873 | ||||||||
\(280\) | −6.94991 | −0.415337 | ||||||||
\(281\) | −27.0009 | −1.61074 | −0.805369 | − | 0.592774i | \(-0.798033\pi\) | ||||
−0.805369 | + | 0.592774i | \(0.798033\pi\) | |||||||
\(282\) | 5.83991 | 0.347761 | ||||||||
\(283\) | −14.9926 | −0.891218 | −0.445609 | − | 0.895228i | \(-0.647013\pi\) | ||||
−0.445609 | + | 0.895228i | \(0.647013\pi\) | |||||||
\(284\) | 12.9288 | 0.767180 | ||||||||
\(285\) | −6.66176 | −0.394609 | ||||||||
\(286\) | 1.97562 | 0.116821 | ||||||||
\(287\) | 20.7086 | 1.22239 | ||||||||
\(288\) | 25.8684 | 1.52431 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.588742 | −0.0345721 | ||||||||
\(291\) | 16.6263 | 0.974651 | ||||||||
\(292\) | 0.0923954 | 0.00540703 | ||||||||
\(293\) | −32.5125 | −1.89940 | −0.949700 | − | 0.313162i | \(-0.898612\pi\) | ||||
−0.949700 | + | 0.313162i | \(0.898612\pi\) | |||||||
\(294\) | −81.8652 | −4.77447 | ||||||||
\(295\) | 3.07282 | 0.178906 | ||||||||
\(296\) | 2.18745 | 0.127143 | ||||||||
\(297\) | 7.18044 | 0.416651 | ||||||||
\(298\) | −41.0212 | −2.37629 | ||||||||
\(299\) | 7.17608 | 0.415004 | ||||||||
\(300\) | −11.5164 | −0.664898 | ||||||||
\(301\) | 4.85107 | 0.279611 | ||||||||
\(302\) | −28.3385 | −1.63070 | ||||||||
\(303\) | 39.8580 | 2.28978 | ||||||||
\(304\) | −14.9822 | −0.859287 | ||||||||
\(305\) | 4.22438 | 0.241887 | ||||||||
\(306\) | −9.30394 | −0.531871 | ||||||||
\(307\) | −1.88110 | −0.107360 | −0.0536800 | − | 0.998558i | \(-0.517095\pi\) | ||||
−0.0536800 | + | 0.998558i | \(0.517095\pi\) | |||||||
\(308\) | 4.34478 | 0.247567 | ||||||||
\(309\) | 31.4249 | 1.78770 | ||||||||
\(310\) | −8.47603 | −0.481406 | ||||||||
\(311\) | 22.3152 | 1.26538 | 0.632689 | − | 0.774406i | \(-0.281951\pi\) | ||||
0.632689 | + | 0.774406i | \(0.281951\pi\) | |||||||
\(312\) | −6.34889 | −0.359435 | ||||||||
\(313\) | −0.459320 | −0.0259623 | −0.0129811 | − | 0.999916i | \(-0.504132\pi\) | ||||
−0.0129811 | + | 0.999916i | \(0.504132\pi\) | |||||||
\(314\) | −15.8402 | −0.893914 | ||||||||
\(315\) | −20.2204 | −1.13929 | ||||||||
\(316\) | −0.295449 | −0.0166203 | ||||||||
\(317\) | −9.73978 | −0.547041 | −0.273520 | − | 0.961866i | \(-0.588188\pi\) | ||||
−0.273520 | + | 0.961866i | \(0.588188\pi\) | |||||||
\(318\) | −57.7894 | −3.24067 | ||||||||
\(319\) | −0.453833 | −0.0254098 | ||||||||
\(320\) | −1.46926 | −0.0821344 | ||||||||
\(321\) | 35.6326 | 1.98882 | ||||||||
\(322\) | 51.0227 | 2.84339 | ||||||||
\(323\) | 3.00298 | 0.167090 | ||||||||
\(324\) | 4.02291 | 0.223495 | ||||||||
\(325\) | 5.13025 | 0.284575 | ||||||||
\(326\) | 12.9385 | 0.716596 | ||||||||
\(327\) | 39.2820 | 2.17230 | ||||||||
\(328\) | 8.02230 | 0.442957 | ||||||||
\(329\) | −5.72126 | −0.315423 | ||||||||
\(330\) | 3.77493 | 0.207803 | ||||||||
\(331\) | 4.13443 | 0.227249 | 0.113624 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113624 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(332\) | 10.0256 | 0.550227 | ||||||||
\(333\) | 6.36428 | 0.348760 | ||||||||
\(334\) | −22.3293 | −1.22181 | ||||||||
\(335\) | −1.97465 | −0.107886 | ||||||||
\(336\) | −70.4271 | −3.84211 | ||||||||
\(337\) | −34.2926 | −1.86804 | −0.934019 | − | 0.357223i | \(-0.883724\pi\) | ||||
−0.934019 | + | 0.357223i | \(0.883724\pi\) | |||||||
\(338\) | 19.8278 | 1.07849 | ||||||||
\(339\) | 33.8035 | 1.83596 | ||||||||
\(340\) | −0.682790 | −0.0370295 | ||||||||
\(341\) | −6.53377 | −0.353823 | ||||||||
\(342\) | −27.9395 | −1.51080 | ||||||||
\(343\) | 46.2445 | 2.49697 | ||||||||
\(344\) | 1.87925 | 0.101322 | ||||||||
\(345\) | 13.7117 | 0.738213 | ||||||||
\(346\) | −21.7073 | −1.16699 | ||||||||
\(347\) | −25.6726 | −1.37818 | −0.689088 | − | 0.724678i | \(-0.741989\pi\) | ||||
−0.689088 | + | 0.724678i | \(0.741989\pi\) | |||||||
\(348\) | −1.18279 | −0.0634040 | ||||||||
\(349\) | −17.0157 | −0.910829 | −0.455414 | − | 0.890280i | \(-0.650509\pi\) | ||||
−0.455414 | + | 0.890280i | \(0.650509\pi\) | |||||||
\(350\) | 36.4766 | 1.94976 | ||||||||
\(351\) | −8.33650 | −0.444969 | ||||||||
\(352\) | 4.73124 | 0.252176 | ||||||||
\(353\) | 19.4200 | 1.03362 | 0.516811 | − | 0.856100i | \(-0.327119\pi\) | ||||
0.516811 | + | 0.856100i | \(0.327119\pi\) | |||||||
\(354\) | 19.9587 | 1.06079 | ||||||||
\(355\) | −11.0048 | −0.584076 | ||||||||
\(356\) | −6.89997 | −0.365698 | ||||||||
\(357\) | 14.1162 | 0.747107 | ||||||||
\(358\) | −30.0733 | −1.58942 | ||||||||
\(359\) | 16.2396 | 0.857094 | 0.428547 | − | 0.903520i | \(-0.359026\pi\) | ||||
0.428547 | + | 0.903520i | \(0.359026\pi\) | |||||||
\(360\) | −7.83317 | −0.412844 | ||||||||
\(361\) | −9.98212 | −0.525375 | ||||||||
\(362\) | 4.87112 | 0.256021 | ||||||||
\(363\) | 2.90991 | 0.152731 | ||||||||
\(364\) | −5.04429 | −0.264393 | ||||||||
\(365\) | −0.0786461 | −0.00411652 | ||||||||
\(366\) | 27.4383 | 1.43422 | ||||||||
\(367\) | −4.61048 | −0.240665 | −0.120333 | − | 0.992734i | \(-0.538396\pi\) | ||||
−0.120333 | + | 0.992734i | \(0.538396\pi\) | |||||||
\(368\) | 30.8374 | 1.60751 | ||||||||
\(369\) | 23.3404 | 1.21505 | ||||||||
\(370\) | 1.51002 | 0.0785022 | ||||||||
\(371\) | 56.6153 | 2.93932 | ||||||||
\(372\) | −17.0284 | −0.882881 | ||||||||
\(373\) | 6.26221 | 0.324245 | 0.162122 | − | 0.986771i | \(-0.448166\pi\) | ||||
0.162122 | + | 0.986771i | \(0.448166\pi\) | |||||||
\(374\) | −1.70166 | −0.0879905 | ||||||||
\(375\) | 20.8945 | 1.07899 | ||||||||
\(376\) | −2.21636 | −0.114300 | ||||||||
\(377\) | 0.526901 | 0.0271368 | ||||||||
\(378\) | −59.2734 | −3.04870 | ||||||||
\(379\) | −0.362889 | −0.0186404 | −0.00932018 | − | 0.999957i | \(-0.502967\pi\) | ||||
−0.00932018 | + | 0.999957i | \(0.502967\pi\) | |||||||
\(380\) | −2.05040 | −0.105184 | ||||||||
\(381\) | −40.6475 | −2.08243 | ||||||||
\(382\) | 45.1530 | 2.31023 | ||||||||
\(383\) | 27.6383 | 1.41225 | 0.706126 | − | 0.708086i | \(-0.250441\pi\) | ||||
0.706126 | + | 0.708086i | \(0.250441\pi\) | |||||||
\(384\) | −37.0782 | −1.89214 | ||||||||
\(385\) | −3.69823 | −0.188479 | ||||||||
\(386\) | 41.8478 | 2.13000 | ||||||||
\(387\) | 5.46758 | 0.277933 | ||||||||
\(388\) | 5.11736 | 0.259795 | ||||||||
\(389\) | 15.2017 | 0.770759 | 0.385380 | − | 0.922758i | \(-0.374071\pi\) | ||||
0.385380 | + | 0.922758i | \(0.374071\pi\) | |||||||
\(390\) | −4.38269 | −0.221926 | ||||||||
\(391\) | −6.18094 | −0.312584 | ||||||||
\(392\) | 31.0694 | 1.56924 | ||||||||
\(393\) | −1.46179 | −0.0737374 | ||||||||
\(394\) | 23.7122 | 1.19461 | ||||||||
\(395\) | 0.251484 | 0.0126535 | ||||||||
\(396\) | 4.89695 | 0.246081 | ||||||||
\(397\) | 24.1442 | 1.21176 | 0.605881 | − | 0.795555i | \(-0.292821\pi\) | ||||
0.605881 | + | 0.795555i | \(0.292821\pi\) | |||||||
\(398\) | 26.5380 | 1.33023 | ||||||||
\(399\) | 42.3906 | 2.12218 | ||||||||
\(400\) | 22.0459 | 1.10230 | ||||||||
\(401\) | −22.3239 | −1.11480 | −0.557401 | − | 0.830244i | \(-0.688201\pi\) | ||||
−0.557401 | + | 0.830244i | \(0.688201\pi\) | |||||||
\(402\) | −12.8258 | −0.639691 | ||||||||
\(403\) | 7.58571 | 0.377871 | ||||||||
\(404\) | 12.2678 | 0.610345 | ||||||||
\(405\) | −3.42427 | −0.170153 | ||||||||
\(406\) | 3.74632 | 0.185927 | ||||||||
\(407\) | 1.16400 | 0.0576975 | ||||||||
\(408\) | 5.46846 | 0.270729 | ||||||||
\(409\) | −31.0517 | −1.53541 | −0.767703 | − | 0.640806i | \(-0.778600\pi\) | ||||
−0.767703 | + | 0.640806i | \(0.778600\pi\) | |||||||
\(410\) | 5.53786 | 0.273496 | ||||||||
\(411\) | −19.1002 | −0.942143 | ||||||||
\(412\) | 9.67218 | 0.476514 | ||||||||
\(413\) | −19.5532 | −0.962148 | ||||||||
\(414\) | 57.5071 | 2.82632 | ||||||||
\(415\) | −8.53370 | −0.418903 | ||||||||
\(416\) | −5.49298 | −0.269315 | ||||||||
\(417\) | 50.6989 | 2.48273 | ||||||||
\(418\) | −5.11004 | −0.249940 | ||||||||
\(419\) | 11.1652 | 0.545455 | 0.272727 | − | 0.962091i | \(-0.412074\pi\) | ||||
0.272727 | + | 0.962091i | \(0.412074\pi\) | |||||||
\(420\) | −9.63838 | −0.470305 | ||||||||
\(421\) | 12.1029 | 0.589860 | 0.294930 | − | 0.955519i | \(-0.404704\pi\) | ||||
0.294930 | + | 0.955519i | \(0.404704\pi\) | |||||||
\(422\) | −31.9196 | −1.55382 | ||||||||
\(423\) | −6.44837 | −0.313530 | ||||||||
\(424\) | 21.9322 | 1.06512 | ||||||||
\(425\) | −4.41882 | −0.214344 | ||||||||
\(426\) | −71.4789 | −3.46316 | ||||||||
\(427\) | −26.8808 | −1.30085 | ||||||||
\(428\) | 10.9673 | 0.530123 | ||||||||
\(429\) | −3.37841 | −0.163111 | ||||||||
\(430\) | 1.29727 | 0.0625597 | ||||||||
\(431\) | −17.9494 | −0.864592 | −0.432296 | − | 0.901732i | \(-0.642296\pi\) | ||||
−0.432296 | + | 0.901732i | \(0.642296\pi\) | |||||||
\(432\) | −35.8240 | −1.72358 | ||||||||
\(433\) | 15.5663 | 0.748069 | 0.374035 | − | 0.927415i | \(-0.377974\pi\) | ||||
0.374035 | + | 0.927415i | \(0.377974\pi\) | |||||||
\(434\) | 53.9352 | 2.58897 | ||||||||
\(435\) | 1.00678 | 0.0482712 | ||||||||
\(436\) | 12.0905 | 0.579030 | ||||||||
\(437\) | −18.5612 | −0.887905 | ||||||||
\(438\) | −0.510824 | −0.0244081 | ||||||||
\(439\) | −27.8099 | −1.32729 | −0.663646 | − | 0.748047i | \(-0.730992\pi\) | ||||
−0.663646 | + | 0.748047i | \(0.730992\pi\) | |||||||
\(440\) | −1.43266 | −0.0682992 | ||||||||
\(441\) | 90.3947 | 4.30451 | ||||||||
\(442\) | 1.97562 | 0.0939709 | ||||||||
\(443\) | −0.274111 | −0.0130234 | −0.00651170 | − | 0.999979i | \(-0.502073\pi\) | ||||
−0.00651170 | + | 0.999979i | \(0.502073\pi\) | |||||||
\(444\) | 3.03364 | 0.143970 | ||||||||
\(445\) | 5.87319 | 0.278416 | ||||||||
\(446\) | −1.51899 | −0.0719264 | ||||||||
\(447\) | 70.1482 | 3.31789 | ||||||||
\(448\) | 9.34932 | 0.441714 | ||||||||
\(449\) | 25.3890 | 1.19818 | 0.599092 | − | 0.800680i | \(-0.295529\pi\) | ||||
0.599092 | + | 0.800680i | \(0.295529\pi\) | |||||||
\(450\) | 41.1124 | 1.93806 | ||||||||
\(451\) | 4.26888 | 0.201014 | ||||||||
\(452\) | 10.4043 | 0.489377 | ||||||||
\(453\) | 48.4602 | 2.27686 | ||||||||
\(454\) | 9.81921 | 0.460838 | ||||||||
\(455\) | 4.29365 | 0.201290 | ||||||||
\(456\) | 16.4217 | 0.769015 | ||||||||
\(457\) | −36.6655 | −1.71514 | −0.857571 | − | 0.514366i | \(-0.828027\pi\) | ||||
−0.857571 | + | 0.514366i | \(0.828027\pi\) | |||||||
\(458\) | −9.35213 | −0.436996 | ||||||||
\(459\) | 7.18044 | 0.335154 | ||||||||
\(460\) | 4.22029 | 0.196772 | ||||||||
\(461\) | −11.4090 | −0.531371 | −0.265685 | − | 0.964060i | \(-0.585598\pi\) | ||||
−0.265685 | + | 0.964060i | \(0.585598\pi\) | |||||||
\(462\) | −24.0209 | −1.11755 | ||||||||
\(463\) | 19.2671 | 0.895418 | 0.447709 | − | 0.894179i | \(-0.352240\pi\) | ||||
0.447709 | + | 0.894179i | \(0.352240\pi\) | |||||||
\(464\) | 2.26422 | 0.105114 | ||||||||
\(465\) | 14.4944 | 0.672162 | ||||||||
\(466\) | −12.9463 | −0.599728 | ||||||||
\(467\) | −18.7069 | −0.865654 | −0.432827 | − | 0.901477i | \(-0.642484\pi\) | ||||
−0.432827 | + | 0.901477i | \(0.642484\pi\) | |||||||
\(468\) | −5.68536 | −0.262806 | ||||||||
\(469\) | 12.5652 | 0.580207 | ||||||||
\(470\) | −1.52997 | −0.0705723 | ||||||||
\(471\) | 27.0875 | 1.24813 | ||||||||
\(472\) | −7.57469 | −0.348653 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 1.63344 | 0.0750265 | ||||||||
\(475\) | −13.2696 | −0.608851 | ||||||||
\(476\) | 4.34478 | 0.199143 | ||||||||
\(477\) | 63.8105 | 2.92168 | ||||||||
\(478\) | −23.4253 | −1.07145 | ||||||||
\(479\) | −40.4258 | −1.84710 | −0.923550 | − | 0.383478i | \(-0.874726\pi\) | ||||
−0.923550 | + | 0.383478i | \(0.874726\pi\) | |||||||
\(480\) | −10.4957 | −0.479061 | ||||||||
\(481\) | −1.35141 | −0.0616189 | ||||||||
\(482\) | 50.0549 | 2.27994 | ||||||||
\(483\) | −87.2512 | −3.97007 | ||||||||
\(484\) | 0.895633 | 0.0407106 | ||||||||
\(485\) | −4.35585 | −0.197789 | ||||||||
\(486\) | 14.4145 | 0.653856 | ||||||||
\(487\) | 18.8515 | 0.854242 | 0.427121 | − | 0.904194i | \(-0.359528\pi\) | ||||
0.427121 | + | 0.904194i | \(0.359528\pi\) | |||||||
\(488\) | −10.4134 | −0.471390 | ||||||||
\(489\) | −22.1254 | −1.00055 | ||||||||
\(490\) | 21.4475 | 0.968899 | ||||||||
\(491\) | −10.0230 | −0.452331 | −0.226166 | − | 0.974089i | \(-0.572619\pi\) | ||||
−0.226166 | + | 0.974089i | \(0.572619\pi\) | |||||||
\(492\) | 11.1256 | 0.501581 | ||||||||
\(493\) | −0.453833 | −0.0204396 | ||||||||
\(494\) | 5.93276 | 0.266928 | ||||||||
\(495\) | −4.16824 | −0.187348 | ||||||||
\(496\) | 32.5977 | 1.46368 | ||||||||
\(497\) | 70.0267 | 3.14113 | ||||||||
\(498\) | −55.4283 | −2.48380 | ||||||||
\(499\) | −13.9057 | −0.622504 | −0.311252 | − | 0.950327i | \(-0.600748\pi\) | ||||
−0.311252 | + | 0.950327i | \(0.600748\pi\) | |||||||
\(500\) | 6.43107 | 0.287606 | ||||||||
\(501\) | 38.1842 | 1.70594 | ||||||||
\(502\) | 2.41774 | 0.107909 | ||||||||
\(503\) | 10.9632 | 0.488824 | 0.244412 | − | 0.969671i | \(-0.421405\pi\) | ||||
0.244412 | + | 0.969671i | \(0.421405\pi\) | |||||||
\(504\) | 49.8445 | 2.22025 | ||||||||
\(505\) | −10.4422 | −0.464673 | ||||||||
\(506\) | 10.5178 | 0.467575 | ||||||||
\(507\) | −33.9065 | −1.50584 | ||||||||
\(508\) | −12.5108 | −0.555076 | ||||||||
\(509\) | −34.2212 | −1.51683 | −0.758414 | − | 0.651773i | \(-0.774025\pi\) | ||||
−0.758414 | + | 0.651773i | \(0.774025\pi\) | |||||||
\(510\) | 3.77493 | 0.167157 | ||||||||
\(511\) | 0.500446 | 0.0221384 | ||||||||
\(512\) | −4.85308 | −0.214478 | ||||||||
\(513\) | 21.5627 | 0.952017 | ||||||||
\(514\) | −9.18457 | −0.405114 | ||||||||
\(515\) | −8.23287 | −0.362784 | ||||||||
\(516\) | 2.60621 | 0.114732 | ||||||||
\(517\) | −1.17938 | −0.0518692 | ||||||||
\(518\) | −9.60866 | −0.422180 | ||||||||
\(519\) | 37.1205 | 1.62941 | ||||||||
\(520\) | 1.66332 | 0.0729412 | ||||||||
\(521\) | −6.92194 | −0.303256 | −0.151628 | − | 0.988438i | \(-0.548452\pi\) | ||||
−0.151628 | + | 0.988438i | \(0.548452\pi\) | |||||||
\(522\) | 4.22244 | 0.184811 | ||||||||
\(523\) | −4.78597 | −0.209276 | −0.104638 | − | 0.994510i | \(-0.533368\pi\) | ||||
−0.104638 | + | 0.994510i | \(0.533368\pi\) | |||||||
\(524\) | −0.449919 | −0.0196548 | ||||||||
\(525\) | −62.3768 | −2.72234 | ||||||||
\(526\) | 27.4282 | 1.19593 | ||||||||
\(527\) | −6.53377 | −0.284615 | ||||||||
\(528\) | −14.5179 | −0.631809 | ||||||||
\(529\) | 15.2040 | 0.661045 | ||||||||
\(530\) | 15.1400 | 0.657639 | ||||||||
\(531\) | −22.0381 | −0.956374 | ||||||||
\(532\) | 13.0473 | 0.565671 | ||||||||
\(533\) | −4.95617 | −0.214676 | ||||||||
\(534\) | 38.1477 | 1.65081 | ||||||||
\(535\) | −9.33523 | −0.403597 | ||||||||
\(536\) | 4.86763 | 0.210249 | ||||||||
\(537\) | 51.4267 | 2.21923 | ||||||||
\(538\) | −46.8540 | −2.02002 | ||||||||
\(539\) | 16.5328 | 0.712120 | ||||||||
\(540\) | −4.90273 | −0.210980 | ||||||||
\(541\) | −2.35057 | −0.101059 | −0.0505295 | − | 0.998723i | \(-0.516091\pi\) | ||||
−0.0505295 | + | 0.998723i | \(0.516091\pi\) | |||||||
\(542\) | −22.1902 | −0.953149 | ||||||||
\(543\) | −8.32985 | −0.357468 | ||||||||
\(544\) | 4.73124 | 0.202850 | ||||||||
\(545\) | −10.2913 | −0.440832 | ||||||||
\(546\) | 27.8883 | 1.19351 | ||||||||
\(547\) | −28.9499 | −1.23781 | −0.618904 | − | 0.785466i | \(-0.712423\pi\) | ||||
−0.618904 | + | 0.785466i | \(0.712423\pi\) | |||||||
\(548\) | −5.87880 | −0.251130 | ||||||||
\(549\) | −30.2971 | −1.29305 | ||||||||
\(550\) | 7.51930 | 0.320624 | ||||||||
\(551\) | −1.36285 | −0.0580594 | ||||||||
\(552\) | −33.8002 | −1.43863 | ||||||||
\(553\) | −1.60026 | −0.0680499 | ||||||||
\(554\) | 11.2311 | 0.477163 | ||||||||
\(555\) | −2.58220 | −0.109608 | ||||||||
\(556\) | 15.6045 | 0.661777 | ||||||||
\(557\) | 24.8573 | 1.05324 | 0.526620 | − | 0.850101i | \(-0.323459\pi\) | ||||
0.526620 | + | 0.850101i | \(0.323459\pi\) | |||||||
\(558\) | 60.7898 | 2.57344 | ||||||||
\(559\) | −1.16100 | −0.0491051 | ||||||||
\(560\) | 18.4509 | 0.779692 | ||||||||
\(561\) | 2.90991 | 0.122857 | ||||||||
\(562\) | 45.9462 | 1.93812 | ||||||||
\(563\) | 41.9189 | 1.76667 | 0.883336 | − | 0.468740i | \(-0.155292\pi\) | ||||
0.883336 | + | 0.468740i | \(0.155292\pi\) | |||||||
\(564\) | −3.07372 | −0.129427 | ||||||||
\(565\) | −8.85604 | −0.372576 | ||||||||
\(566\) | 25.5123 | 1.07236 | ||||||||
\(567\) | 21.7895 | 0.915074 | ||||||||
\(568\) | 27.1276 | 1.13825 | ||||||||
\(569\) | −6.29638 | −0.263958 | −0.131979 | − | 0.991253i | \(-0.542133\pi\) | ||||
−0.131979 | + | 0.991253i | \(0.542133\pi\) | |||||||
\(570\) | 11.3360 | 0.474814 | ||||||||
\(571\) | 16.1733 | 0.676831 | 0.338415 | − | 0.940997i | \(-0.390109\pi\) | ||||
0.338415 | + | 0.940997i | \(0.390109\pi\) | |||||||
\(572\) | −1.03983 | −0.0434775 | ||||||||
\(573\) | −77.2137 | −3.22565 | ||||||||
\(574\) | −35.2389 | −1.47084 | ||||||||
\(575\) | 27.3124 | 1.13901 | ||||||||
\(576\) | 10.5375 | 0.439063 | ||||||||
\(577\) | 17.0022 | 0.707812 | 0.353906 | − | 0.935281i | \(-0.384853\pi\) | ||||
0.353906 | + | 0.935281i | \(0.384853\pi\) | |||||||
\(578\) | −1.70166 | −0.0707796 | ||||||||
\(579\) | −71.5617 | −2.97400 | ||||||||
\(580\) | 0.309873 | 0.0128668 | ||||||||
\(581\) | 54.3022 | 2.25284 | ||||||||
\(582\) | −28.2922 | −1.17275 | ||||||||
\(583\) | 11.6707 | 0.483351 | ||||||||
\(584\) | 0.193868 | 0.00802229 | ||||||||
\(585\) | 4.83933 | 0.200082 | ||||||||
\(586\) | 55.3251 | 2.28546 | ||||||||
\(587\) | −29.1572 | −1.20344 | −0.601722 | − | 0.798705i | \(-0.705519\pi\) | ||||
−0.601722 | + | 0.798705i | \(0.705519\pi\) | |||||||
\(588\) | 43.0881 | 1.77692 | ||||||||
\(589\) | −19.6208 | −0.808459 | ||||||||
\(590\) | −5.22888 | −0.215270 | ||||||||
\(591\) | −40.5490 | −1.66796 | ||||||||
\(592\) | −5.80734 | −0.238680 | ||||||||
\(593\) | −17.6820 | −0.726112 | −0.363056 | − | 0.931767i | \(-0.618267\pi\) | ||||
−0.363056 | + | 0.931767i | \(0.618267\pi\) | |||||||
\(594\) | −12.2186 | −0.501337 | ||||||||
\(595\) | −3.69823 | −0.151613 | ||||||||
\(596\) | 21.5907 | 0.884390 | ||||||||
\(597\) | −45.3813 | −1.85733 | ||||||||
\(598\) | −12.2112 | −0.499354 | ||||||||
\(599\) | −34.0242 | −1.39019 | −0.695096 | − | 0.718917i | \(-0.744638\pi\) | ||||
−0.695096 | + | 0.718917i | \(0.744638\pi\) | |||||||
\(600\) | −24.1641 | −0.986495 | ||||||||
\(601\) | 29.1288 | 1.18819 | 0.594094 | − | 0.804396i | \(-0.297511\pi\) | ||||
0.594094 | + | 0.804396i | \(0.297511\pi\) | |||||||
\(602\) | −8.25485 | −0.336442 | ||||||||
\(603\) | 14.1621 | 0.576725 | ||||||||
\(604\) | 14.9154 | 0.606900 | ||||||||
\(605\) | −0.762355 | −0.0309941 | ||||||||
\(606\) | −67.8247 | −2.75519 | ||||||||
\(607\) | −29.2933 | −1.18898 | −0.594489 | − | 0.804104i | \(-0.702646\pi\) | ||||
−0.594489 | + | 0.804104i | \(0.702646\pi\) | |||||||
\(608\) | 14.2078 | 0.576203 | ||||||||
\(609\) | −6.40638 | −0.259600 | ||||||||
\(610\) | −7.18843 | −0.291051 | ||||||||
\(611\) | 1.36926 | 0.0553945 | ||||||||
\(612\) | 4.89695 | 0.197947 | ||||||||
\(613\) | 13.9395 | 0.563012 | 0.281506 | − | 0.959560i | \(-0.409166\pi\) | ||||
0.281506 | + | 0.959560i | \(0.409166\pi\) | |||||||
\(614\) | 3.20099 | 0.129181 | ||||||||
\(615\) | −9.47001 | −0.381867 | ||||||||
\(616\) | 9.11638 | 0.367309 | ||||||||
\(617\) | 0.573538 | 0.0230898 | 0.0115449 | − | 0.999933i | \(-0.496325\pi\) | ||||
0.0115449 | + | 0.999933i | \(0.496325\pi\) | |||||||
\(618\) | −53.4744 | −2.15105 | ||||||||
\(619\) | −47.6883 | −1.91676 | −0.958378 | − | 0.285503i | \(-0.907839\pi\) | ||||
−0.958378 | + | 0.285503i | \(0.907839\pi\) | |||||||
\(620\) | 4.46119 | 0.179166 | ||||||||
\(621\) | −44.3819 | −1.78098 | ||||||||
\(622\) | −37.9728 | −1.52257 | ||||||||
\(623\) | −37.3727 | −1.49730 | ||||||||
\(624\) | 16.8553 | 0.674750 | ||||||||
\(625\) | 16.6200 | 0.664800 | ||||||||
\(626\) | 0.781604 | 0.0312392 | ||||||||
\(627\) | 8.73840 | 0.348978 | ||||||||
\(628\) | 8.33718 | 0.332690 | ||||||||
\(629\) | 1.16400 | 0.0464118 | ||||||||
\(630\) | 34.4081 | 1.37085 | ||||||||
\(631\) | −16.1955 | −0.644731 | −0.322366 | − | 0.946615i | \(-0.604478\pi\) | ||||
−0.322366 | + | 0.946615i | \(0.604478\pi\) | |||||||
\(632\) | −0.619923 | −0.0246592 | ||||||||
\(633\) | 54.5841 | 2.16952 | ||||||||
\(634\) | 16.5738 | 0.658228 | ||||||||
\(635\) | 10.6491 | 0.422595 | ||||||||
\(636\) | 30.4163 | 1.20609 | ||||||||
\(637\) | −19.1947 | −0.760520 | ||||||||
\(638\) | 0.772268 | 0.0305744 | ||||||||
\(639\) | 78.9263 | 3.12228 | ||||||||
\(640\) | 9.71395 | 0.383978 | ||||||||
\(641\) | −30.1235 | −1.18981 | −0.594904 | − | 0.803797i | \(-0.702810\pi\) | ||||
−0.594904 | + | 0.803797i | \(0.702810\pi\) | |||||||
\(642\) | −60.6345 | −2.39305 | ||||||||
\(643\) | −26.6063 | −1.04925 | −0.524626 | − | 0.851333i | \(-0.675795\pi\) | ||||
−0.524626 | + | 0.851333i | \(0.675795\pi\) | |||||||
\(644\) | −26.8548 | −1.05823 | ||||||||
\(645\) | −2.21838 | −0.0873488 | ||||||||
\(646\) | −5.11004 | −0.201052 | ||||||||
\(647\) | −7.53738 | −0.296325 | −0.148163 | − | 0.988963i | \(-0.547336\pi\) | ||||
−0.148163 | + | 0.988963i | \(0.547336\pi\) | |||||||
\(648\) | 8.44103 | 0.331595 | ||||||||
\(649\) | −4.03069 | −0.158219 | ||||||||
\(650\) | −8.72992 | −0.342416 | ||||||||
\(651\) | −92.2317 | −3.61485 | ||||||||
\(652\) | −6.80992 | −0.266697 | ||||||||
\(653\) | 47.4065 | 1.85516 | 0.927579 | − | 0.373627i | \(-0.121886\pi\) | ||||
0.927579 | + | 0.373627i | \(0.121886\pi\) | |||||||
\(654\) | −66.8445 | −2.61383 | ||||||||
\(655\) | 0.382967 | 0.0149638 | ||||||||
\(656\) | −21.2979 | −0.831543 | ||||||||
\(657\) | 0.564047 | 0.0220056 | ||||||||
\(658\) | 9.73562 | 0.379534 | ||||||||
\(659\) | −30.9022 | −1.20378 | −0.601889 | − | 0.798580i | \(-0.705585\pi\) | ||||
−0.601889 | + | 0.798580i | \(0.705585\pi\) | |||||||
\(660\) | −1.98686 | −0.0773384 | ||||||||
\(661\) | −4.57688 | −0.178020 | −0.0890100 | − | 0.996031i | \(-0.528370\pi\) | ||||
−0.0890100 | + | 0.996031i | \(0.528370\pi\) | |||||||
\(662\) | −7.03538 | −0.273438 | ||||||||
\(663\) | −3.37841 | −0.131207 | ||||||||
\(664\) | 21.0361 | 0.816359 | ||||||||
\(665\) | −11.1057 | −0.430661 | ||||||||
\(666\) | −10.8298 | −0.419647 | ||||||||
\(667\) | 2.80512 | 0.108615 | ||||||||
\(668\) | 11.7526 | 0.454722 | ||||||||
\(669\) | 2.59755 | 0.100427 | ||||||||
\(670\) | 3.36017 | 0.129815 | ||||||||
\(671\) | −5.54122 | −0.213916 | ||||||||
\(672\) | 66.7870 | 2.57636 | ||||||||
\(673\) | −16.9192 | −0.652186 | −0.326093 | − | 0.945338i | \(-0.605732\pi\) | ||||
−0.326093 | + | 0.945338i | \(0.605732\pi\) | |||||||
\(674\) | 58.3543 | 2.24772 | ||||||||
\(675\) | −31.7290 | −1.22125 | ||||||||
\(676\) | −10.4360 | −0.401384 | ||||||||
\(677\) | −0.491343 | −0.0188838 | −0.00944191 | − | 0.999955i | \(-0.503005\pi\) | ||||
−0.00944191 | + | 0.999955i | \(0.503005\pi\) | |||||||
\(678\) | −57.5220 | −2.20912 | ||||||||
\(679\) | 27.7174 | 1.06370 | ||||||||
\(680\) | −1.43266 | −0.0549399 | ||||||||
\(681\) | −16.7913 | −0.643444 | ||||||||
\(682\) | 11.1182 | 0.425739 | ||||||||
\(683\) | −34.0326 | −1.30222 | −0.651111 | − | 0.758982i | \(-0.725697\pi\) | ||||
−0.651111 | + | 0.758982i | \(0.725697\pi\) | |||||||
\(684\) | 14.7054 | 0.562276 | ||||||||
\(685\) | 5.00398 | 0.191192 | ||||||||
\(686\) | −78.6922 | −3.00448 | ||||||||
\(687\) | 15.9926 | 0.610155 | ||||||||
\(688\) | −4.98911 | −0.190208 | ||||||||
\(689\) | −13.5497 | −0.516202 | ||||||||
\(690\) | −23.3326 | −0.888257 | ||||||||
\(691\) | 20.4091 | 0.776397 | 0.388199 | − | 0.921576i | \(-0.373097\pi\) | ||||
0.388199 | + | 0.921576i | \(0.373097\pi\) | |||||||
\(692\) | 11.4252 | 0.434322 | ||||||||
\(693\) | 26.5236 | 1.00755 | ||||||||
\(694\) | 43.6859 | 1.65829 | ||||||||
\(695\) | −13.2824 | −0.503829 | ||||||||
\(696\) | −2.48177 | −0.0940711 | ||||||||
\(697\) | 4.26888 | 0.161695 | ||||||||
\(698\) | 28.9549 | 1.09596 | ||||||||
\(699\) | 22.1388 | 0.837368 | ||||||||
\(700\) | −19.1988 | −0.725645 | ||||||||
\(701\) | 39.9271 | 1.50803 | 0.754013 | − | 0.656859i | \(-0.228115\pi\) | ||||
0.754013 | + | 0.656859i | \(0.228115\pi\) | |||||||
\(702\) | 14.1859 | 0.535411 | ||||||||
\(703\) | 3.49548 | 0.131834 | ||||||||
\(704\) | 1.92727 | 0.0726368 | ||||||||
\(705\) | 2.61632 | 0.0985364 | ||||||||
\(706\) | −33.0461 | −1.24371 | ||||||||
\(707\) | 66.4467 | 2.49899 | ||||||||
\(708\) | −10.5048 | −0.394796 | ||||||||
\(709\) | −36.9640 | −1.38821 | −0.694106 | − | 0.719873i | \(-0.744200\pi\) | ||||
−0.694106 | + | 0.719873i | \(0.744200\pi\) | |||||||
\(710\) | 18.7264 | 0.702791 | ||||||||
\(711\) | −1.80363 | −0.0676415 | ||||||||
\(712\) | −14.4778 | −0.542578 | ||||||||
\(713\) | 40.3848 | 1.51242 | ||||||||
\(714\) | −24.0209 | −0.898958 | ||||||||
\(715\) | 0.885095 | 0.0331007 | ||||||||
\(716\) | 15.8285 | 0.591539 | ||||||||
\(717\) | 40.0584 | 1.49601 | ||||||||
\(718\) | −27.6342 | −1.03130 | ||||||||
\(719\) | −43.0630 | −1.60598 | −0.802989 | − | 0.595994i | \(-0.796758\pi\) | ||||
−0.802989 | + | 0.595994i | \(0.796758\pi\) | |||||||
\(720\) | 20.7958 | 0.775013 | ||||||||
\(721\) | 52.3880 | 1.95103 | ||||||||
\(722\) | 16.9861 | 0.632158 | ||||||||
\(723\) | −85.5961 | −3.18335 | ||||||||
\(724\) | −2.56382 | −0.0952836 | ||||||||
\(725\) | 2.00540 | 0.0744788 | ||||||||
\(726\) | −4.95167 | −0.183774 | ||||||||
\(727\) | 43.0776 | 1.59766 | 0.798829 | − | 0.601558i | \(-0.205453\pi\) | ||||
0.798829 | + | 0.601558i | \(0.205453\pi\) | |||||||
\(728\) | −10.5841 | −0.392274 | ||||||||
\(729\) | −38.1246 | −1.41202 | ||||||||
\(730\) | 0.133829 | 0.00495322 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −14.4416 | −0.533777 | ||||||||
\(733\) | −35.5631 | −1.31355 | −0.656777 | − | 0.754085i | \(-0.728081\pi\) | ||||
−0.656777 | + | 0.754085i | \(0.728081\pi\) | |||||||
\(734\) | 7.84545 | 0.289581 | ||||||||
\(735\) | −36.6762 | −1.35282 | ||||||||
\(736\) | −29.2435 | −1.07793 | ||||||||
\(737\) | 2.59019 | 0.0954110 | ||||||||
\(738\) | −39.7174 | −1.46202 | ||||||||
\(739\) | 3.01489 | 0.110904 | 0.0554522 | − | 0.998461i | \(-0.482340\pi\) | ||||
0.0554522 | + | 0.998461i | \(0.482340\pi\) | |||||||
\(740\) | −0.794770 | −0.0292163 | ||||||||
\(741\) | −10.1453 | −0.372697 | ||||||||
\(742\) | −96.3398 | −3.53675 | ||||||||
\(743\) | 38.3071 | 1.40535 | 0.702675 | − | 0.711511i | \(-0.251989\pi\) | ||||
0.702675 | + | 0.711511i | \(0.251989\pi\) | |||||||
\(744\) | −35.7296 | −1.30991 | ||||||||
\(745\) | −18.3778 | −0.673311 | ||||||||
\(746\) | −10.6561 | −0.390148 | ||||||||
\(747\) | 61.2034 | 2.23932 | ||||||||
\(748\) | 0.895633 | 0.0327476 | ||||||||
\(749\) | 59.4026 | 2.17052 | ||||||||
\(750\) | −35.5553 | −1.29830 | ||||||||
\(751\) | −22.5715 | −0.823644 | −0.411822 | − | 0.911264i | \(-0.635107\pi\) | ||||
−0.411822 | + | 0.911264i | \(0.635107\pi\) | |||||||
\(752\) | 5.88407 | 0.214570 | ||||||||
\(753\) | −4.13444 | −0.150667 | ||||||||
\(754\) | −0.896604 | −0.0326524 | ||||||||
\(755\) | −12.6959 | −0.462050 | ||||||||
\(756\) | 31.1974 | 1.13464 | ||||||||
\(757\) | 36.0553 | 1.31045 | 0.655226 | − | 0.755433i | \(-0.272573\pi\) | ||||
0.655226 | + | 0.755433i | \(0.272573\pi\) | |||||||
\(758\) | 0.617512 | 0.0224291 | ||||||||
\(759\) | −17.9860 | −0.652850 | ||||||||
\(760\) | −4.30224 | −0.156059 | ||||||||
\(761\) | 4.40959 | 0.159848 | 0.0799238 | − | 0.996801i | \(-0.474532\pi\) | ||||
0.0799238 | + | 0.996801i | \(0.474532\pi\) | |||||||
\(762\) | 69.1680 | 2.50569 | ||||||||
\(763\) | 65.4865 | 2.37077 | ||||||||
\(764\) | −23.7654 | −0.859801 | ||||||||
\(765\) | −4.16824 | −0.150703 | ||||||||
\(766\) | −47.0309 | −1.69930 | ||||||||
\(767\) | 4.67964 | 0.168972 | ||||||||
\(768\) | 51.8779 | 1.87198 | ||||||||
\(769\) | 14.6180 | 0.527140 | 0.263570 | − | 0.964640i | \(-0.415100\pi\) | ||||
0.263570 | + | 0.964640i | \(0.415100\pi\) | |||||||
\(770\) | 6.29312 | 0.226788 | ||||||||
\(771\) | 15.7060 | 0.565639 | ||||||||
\(772\) | −22.0258 | −0.792726 | ||||||||
\(773\) | −53.4906 | −1.92392 | −0.961962 | − | 0.273183i | \(-0.911924\pi\) | ||||
−0.961962 | + | 0.273183i | \(0.911924\pi\) | |||||||
\(774\) | −9.30394 | −0.334423 | ||||||||
\(775\) | 28.8715 | 1.03710 | ||||||||
\(776\) | 10.7374 | 0.385452 | ||||||||
\(777\) | 16.4313 | 0.589468 | ||||||||
\(778\) | −25.8681 | −0.927418 | ||||||||
\(779\) | 12.8193 | 0.459301 | ||||||||
\(780\) | 2.30675 | 0.0825947 | ||||||||
\(781\) | 14.4353 | 0.516536 | ||||||||
\(782\) | 10.5178 | 0.376117 | ||||||||
\(783\) | −3.25872 | −0.116457 | ||||||||
\(784\) | −82.4842 | −2.94586 | ||||||||
\(785\) | −7.09653 | −0.253286 | ||||||||
\(786\) | 2.48746 | 0.0887247 | ||||||||
\(787\) | 14.9521 | 0.532984 | 0.266492 | − | 0.963837i | \(-0.414135\pi\) | ||||
0.266492 | + | 0.963837i | \(0.414135\pi\) | |||||||
\(788\) | −12.4805 | −0.444598 | ||||||||
\(789\) | −46.9036 | −1.66981 | ||||||||
\(790\) | −0.427939 | −0.0152254 | ||||||||
\(791\) | 56.3533 | 2.00369 | ||||||||
\(792\) | 10.2750 | 0.365105 | ||||||||
\(793\) | 6.43336 | 0.228455 | ||||||||
\(794\) | −41.0851 | −1.45806 | ||||||||
\(795\) | −25.8901 | −0.918227 | ||||||||
\(796\) | −13.9678 | −0.495075 | ||||||||
\(797\) | 31.0101 | 1.09843 | 0.549217 | − | 0.835680i | \(-0.314926\pi\) | ||||
0.549217 | + | 0.835680i | \(0.314926\pi\) | |||||||
\(798\) | −72.1342 | −2.55352 | ||||||||
\(799\) | −1.17938 | −0.0417235 | ||||||||
\(800\) | −20.9065 | −0.739156 | ||||||||
\(801\) | −42.1223 | −1.48832 | ||||||||
\(802\) | 37.9876 | 1.34139 | ||||||||
\(803\) | 0.103162 | 0.00364051 | ||||||||
\(804\) | 6.75059 | 0.238075 | ||||||||
\(805\) | 22.8586 | 0.805659 | ||||||||
\(806\) | −12.9083 | −0.454674 | ||||||||
\(807\) | 80.1225 | 2.82045 | ||||||||
\(808\) | 25.7408 | 0.905557 | ||||||||
\(809\) | 27.8537 | 0.979282 | 0.489641 | − | 0.871924i | \(-0.337128\pi\) | ||||
0.489641 | + | 0.871924i | \(0.337128\pi\) | |||||||
\(810\) | 5.82692 | 0.204737 | ||||||||
\(811\) | −35.2939 | −1.23934 | −0.619668 | − | 0.784864i | \(-0.712733\pi\) | ||||
−0.619668 | + | 0.784864i | \(0.712733\pi\) | |||||||
\(812\) | −1.97180 | −0.0691967 | ||||||||
\(813\) | 37.9462 | 1.33083 | ||||||||
\(814\) | −1.98073 | −0.0694246 | ||||||||
\(815\) | 5.79654 | 0.203044 | ||||||||
\(816\) | −14.5179 | −0.508227 | ||||||||
\(817\) | 3.00298 | 0.105061 | ||||||||
\(818\) | 52.8393 | 1.84748 | ||||||||
\(819\) | −30.7939 | −1.07603 | ||||||||
\(820\) | −2.91475 | −0.101787 | ||||||||
\(821\) | 8.12327 | 0.283504 | 0.141752 | − | 0.989902i | \(-0.454726\pi\) | ||||
0.141752 | + | 0.989902i | \(0.454726\pi\) | |||||||
\(822\) | 32.5020 | 1.13364 | ||||||||
\(823\) | −18.3269 | −0.638837 | −0.319418 | − | 0.947614i | \(-0.603488\pi\) | ||||
−0.319418 | + | 0.947614i | \(0.603488\pi\) | |||||||
\(824\) | 20.2945 | 0.706994 | ||||||||
\(825\) | −12.8584 | −0.447671 | ||||||||
\(826\) | 33.2728 | 1.15771 | ||||||||
\(827\) | −14.7052 | −0.511350 | −0.255675 | − | 0.966763i | \(-0.582298\pi\) | ||||
−0.255675 | + | 0.966763i | \(0.582298\pi\) | |||||||
\(828\) | −30.2677 | −1.05188 | ||||||||
\(829\) | −40.6716 | −1.41258 | −0.706292 | − | 0.707921i | \(-0.749633\pi\) | ||||
−0.706292 | + | 0.707921i | \(0.749633\pi\) | |||||||
\(830\) | 14.5214 | 0.504046 | ||||||||
\(831\) | −19.2057 | −0.666238 | ||||||||
\(832\) | −2.23756 | −0.0775736 | ||||||||
\(833\) | 16.5328 | 0.572829 | ||||||||
\(834\) | −86.2720 | −2.98736 | ||||||||
\(835\) | −10.0037 | −0.346193 | ||||||||
\(836\) | 2.68957 | 0.0930207 | ||||||||
\(837\) | −46.9153 | −1.62163 | ||||||||
\(838\) | −18.9993 | −0.656320 | ||||||||
\(839\) | 19.3637 | 0.668509 | 0.334254 | − | 0.942483i | \(-0.391516\pi\) | ||||
0.334254 | + | 0.942483i | \(0.391516\pi\) | |||||||
\(840\) | −20.2236 | −0.697781 | ||||||||
\(841\) | −28.7940 | −0.992898 | ||||||||
\(842\) | −20.5950 | −0.709751 | ||||||||
\(843\) | −78.5702 | −2.70610 | ||||||||
\(844\) | 16.8003 | 0.578289 | ||||||||
\(845\) | 8.88301 | 0.305585 | ||||||||
\(846\) | 10.9729 | 0.377256 | ||||||||
\(847\) | 4.85107 | 0.166685 | ||||||||
\(848\) | −58.2264 | −1.99950 | ||||||||
\(849\) | −43.6271 | −1.49728 | ||||||||
\(850\) | 7.51930 | 0.257910 | ||||||||
\(851\) | −7.19463 | −0.246629 | ||||||||
\(852\) | 37.6215 | 1.28889 | ||||||||
\(853\) | −31.4458 | −1.07668 | −0.538342 | − | 0.842726i | \(-0.680949\pi\) | ||||
−0.538342 | + | 0.842726i | \(0.680949\pi\) | |||||||
\(854\) | 45.7419 | 1.56526 | ||||||||
\(855\) | −12.5171 | −0.428077 | ||||||||
\(856\) | 23.0119 | 0.786532 | ||||||||
\(857\) | −8.41670 | −0.287509 | −0.143754 | − | 0.989613i | \(-0.545918\pi\) | ||||
−0.143754 | + | 0.989613i | \(0.545918\pi\) | |||||||
\(858\) | 5.74889 | 0.196264 | ||||||||
\(859\) | 7.20630 | 0.245876 | 0.122938 | − | 0.992414i | \(-0.460768\pi\) | ||||
0.122938 | + | 0.992414i | \(0.460768\pi\) | |||||||
\(860\) | −0.682790 | −0.0232830 | ||||||||
\(861\) | 60.2602 | 2.05366 | ||||||||
\(862\) | 30.5437 | 1.04032 | ||||||||
\(863\) | −12.1313 | −0.412956 | −0.206478 | − | 0.978451i | \(-0.566200\pi\) | ||||
−0.206478 | + | 0.978451i | \(0.566200\pi\) | |||||||
\(864\) | 33.9724 | 1.15576 | ||||||||
\(865\) | −9.72504 | −0.330661 | ||||||||
\(866\) | −26.4885 | −0.900116 | ||||||||
\(867\) | 2.90991 | 0.0988258 | ||||||||
\(868\) | −28.3878 | −0.963543 | ||||||||
\(869\) | −0.329877 | −0.0111903 | ||||||||
\(870\) | −1.71319 | −0.0580824 | ||||||||
\(871\) | −3.00722 | −0.101896 | ||||||||
\(872\) | 25.3688 | 0.859095 | ||||||||
\(873\) | 31.2400 | 1.05731 | ||||||||
\(874\) | 31.5848 | 1.06837 | ||||||||
\(875\) | 34.8330 | 1.17757 | ||||||||
\(876\) | 0.268862 | 0.00908401 | ||||||||
\(877\) | −40.7127 | −1.37477 | −0.687385 | − | 0.726293i | \(-0.741242\pi\) | ||||
−0.687385 | + | 0.726293i | \(0.741242\pi\) | |||||||
\(878\) | 47.3228 | 1.59707 | ||||||||
\(879\) | −94.6084 | −3.19106 | ||||||||
\(880\) | 3.80347 | 0.128215 | ||||||||
\(881\) | −13.3840 | −0.450918 | −0.225459 | − | 0.974253i | \(-0.572388\pi\) | ||||
−0.225459 | + | 0.974253i | \(0.572388\pi\) | |||||||
\(882\) | −153.821 | −5.17941 | ||||||||
\(883\) | 4.13366 | 0.139109 | 0.0695544 | − | 0.997578i | \(-0.477842\pi\) | ||||
0.0695544 | + | 0.997578i | \(0.477842\pi\) | |||||||
\(884\) | −1.03983 | −0.0349733 | ||||||||
\(885\) | 8.94162 | 0.300569 | ||||||||
\(886\) | 0.466442 | 0.0156704 | ||||||||
\(887\) | 33.9265 | 1.13914 | 0.569571 | − | 0.821942i | \(-0.307109\pi\) | ||||
0.569571 | + | 0.821942i | \(0.307109\pi\) | |||||||
\(888\) | 6.36530 | 0.213605 | ||||||||
\(889\) | −67.7628 | −2.27269 | ||||||||
\(890\) | −9.99415 | −0.335005 | ||||||||
\(891\) | 4.49170 | 0.150478 | ||||||||
\(892\) | 0.799492 | 0.0267690 | ||||||||
\(893\) | −3.54166 | −0.118517 | ||||||||
\(894\) | −119.368 | −3.99227 | ||||||||
\(895\) | −13.4731 | −0.450355 | ||||||||
\(896\) | −61.8125 | −2.06501 | ||||||||
\(897\) | 20.8818 | 0.697222 | ||||||||
\(898\) | −43.2034 | −1.44172 | ||||||||
\(899\) | 2.96524 | 0.0988962 | ||||||||
\(900\) | −21.6387 | −0.721290 | ||||||||
\(901\) | 11.6707 | 0.388807 | ||||||||
\(902\) | −7.26416 | −0.241870 | ||||||||
\(903\) | 14.1162 | 0.469757 | ||||||||
\(904\) | 21.8307 | 0.726078 | ||||||||
\(905\) | 2.18230 | 0.0725421 | ||||||||
\(906\) | −82.4626 | −2.73964 | ||||||||
\(907\) | 12.7248 | 0.422519 | 0.211260 | − | 0.977430i | \(-0.432243\pi\) | ||||
0.211260 | + | 0.977430i | \(0.432243\pi\) | |||||||
\(908\) | −5.16815 | −0.171511 | ||||||||
\(909\) | 74.8913 | 2.48399 | ||||||||
\(910\) | −7.30632 | −0.242202 | ||||||||
\(911\) | 2.28872 | 0.0758287 | 0.0379144 | − | 0.999281i | \(-0.487929\pi\) | ||||
0.0379144 | + | 0.999281i | \(0.487929\pi\) | |||||||
\(912\) | −43.5968 | −1.44364 | ||||||||
\(913\) | 11.1939 | 0.370463 | ||||||||
\(914\) | 62.3921 | 2.06375 | ||||||||
\(915\) | 12.2926 | 0.406379 | ||||||||
\(916\) | 4.92231 | 0.162638 | ||||||||
\(917\) | −2.43692 | −0.0804742 | ||||||||
\(918\) | −12.2186 | −0.403275 | ||||||||
\(919\) | −52.0715 | −1.71768 | −0.858840 | − | 0.512244i | \(-0.828814\pi\) | ||||
−0.858840 | + | 0.512244i | \(0.828814\pi\) | |||||||
\(920\) | 8.85517 | 0.291946 | ||||||||
\(921\) | −5.47383 | −0.180369 | ||||||||
\(922\) | 19.4142 | 0.639373 | ||||||||
\(923\) | −16.7594 | −0.551643 | ||||||||
\(924\) | 12.6429 | 0.415921 | ||||||||
\(925\) | −5.14351 | −0.169118 | ||||||||
\(926\) | −32.7860 | −1.07741 | ||||||||
\(927\) | 59.0459 | 1.93932 | ||||||||
\(928\) | −2.14719 | −0.0704851 | ||||||||
\(929\) | 8.63984 | 0.283464 | 0.141732 | − | 0.989905i | \(-0.454733\pi\) | ||||
0.141732 | + | 0.989905i | \(0.454733\pi\) | |||||||
\(930\) | −24.6645 | −0.808780 | ||||||||
\(931\) | 49.6478 | 1.62714 | ||||||||
\(932\) | 6.81405 | 0.223202 | ||||||||
\(933\) | 64.9352 | 2.12588 | ||||||||
\(934\) | 31.8328 | 1.04160 | ||||||||
\(935\) | −0.762355 | −0.0249317 | ||||||||
\(936\) | −11.9292 | −0.389920 | ||||||||
\(937\) | 29.5769 | 0.966236 | 0.483118 | − | 0.875555i | \(-0.339504\pi\) | ||||
0.483118 | + | 0.875555i | \(0.339504\pi\) | |||||||
\(938\) | −21.3816 | −0.698135 | ||||||||
\(939\) | −1.33658 | −0.0436176 | ||||||||
\(940\) | 0.805271 | 0.0262650 | ||||||||
\(941\) | −44.8128 | −1.46085 | −0.730427 | − | 0.682991i | \(-0.760679\pi\) | ||||
−0.730427 | + | 0.682991i | \(0.760679\pi\) | |||||||
\(942\) | −46.0936 | −1.50181 | ||||||||
\(943\) | −26.3857 | −0.859236 | ||||||||
\(944\) | 20.1096 | 0.654510 | ||||||||
\(945\) | −26.5549 | −0.863832 | ||||||||
\(946\) | −1.70166 | −0.0553256 | ||||||||
\(947\) | −18.6867 | −0.607237 | −0.303618 | − | 0.952794i | \(-0.598195\pi\) | ||||
−0.303618 | + | 0.952794i | \(0.598195\pi\) | |||||||
\(948\) | −0.859731 | −0.0279228 | ||||||||
\(949\) | −0.119771 | −0.00388794 | ||||||||
\(950\) | 22.5803 | 0.732602 | ||||||||
\(951\) | −28.3419 | −0.919049 | ||||||||
\(952\) | 9.11638 | 0.295464 | ||||||||
\(953\) | 25.1447 | 0.814518 | 0.407259 | − | 0.913313i | \(-0.366485\pi\) | ||||
0.407259 | + | 0.913313i | \(0.366485\pi\) | |||||||
\(954\) | −108.583 | −3.51552 | ||||||||
\(955\) | 20.2289 | 0.654591 | ||||||||
\(956\) | 12.3295 | 0.398763 | ||||||||
\(957\) | −1.32061 | −0.0426894 | ||||||||
\(958\) | 68.7907 | 2.22253 | ||||||||
\(959\) | −31.8416 | −1.02822 | ||||||||
\(960\) | −4.27543 | −0.137989 | ||||||||
\(961\) | 11.6901 | 0.377100 | ||||||||
\(962\) | 2.29963 | 0.0741431 | ||||||||
\(963\) | 66.9520 | 2.15750 | ||||||||
\(964\) | −26.3454 | −0.848528 | ||||||||
\(965\) | 18.7481 | 0.603524 | ||||||||
\(966\) | 148.472 | 4.77700 | ||||||||
\(967\) | 7.68107 | 0.247007 | 0.123503 | − | 0.992344i | \(-0.460587\pi\) | ||||
0.123503 | + | 0.992344i | \(0.460587\pi\) | |||||||
\(968\) | 1.87925 | 0.0604015 | ||||||||
\(969\) | 8.73840 | 0.280718 | ||||||||
\(970\) | 7.41216 | 0.237990 | ||||||||
\(971\) | 34.2057 | 1.09771 | 0.548857 | − | 0.835916i | \(-0.315063\pi\) | ||||
0.548857 | + | 0.835916i | \(0.315063\pi\) | |||||||
\(972\) | −7.58680 | −0.243347 | ||||||||
\(973\) | 84.5193 | 2.70956 | ||||||||
\(974\) | −32.0787 | −1.02787 | ||||||||
\(975\) | 14.9286 | 0.478097 | ||||||||
\(976\) | 27.6457 | 0.884919 | ||||||||
\(977\) | 39.3289 | 1.25824 | 0.629122 | − | 0.777306i | \(-0.283414\pi\) | ||||
0.629122 | + | 0.777306i | \(0.283414\pi\) | |||||||
\(978\) | 37.6498 | 1.20391 | ||||||||
\(979\) | −7.70401 | −0.246221 | ||||||||
\(980\) | −11.2885 | −0.360597 | ||||||||
\(981\) | 73.8091 | 2.35654 | ||||||||
\(982\) | 17.0557 | 0.544269 | ||||||||
\(983\) | −48.2168 | −1.53788 | −0.768938 | − | 0.639323i | \(-0.779215\pi\) | ||||
−0.768938 | + | 0.639323i | \(0.779215\pi\) | |||||||
\(984\) | 23.3442 | 0.744185 | ||||||||
\(985\) | 10.6233 | 0.338485 | ||||||||
\(986\) | 0.772268 | 0.0245940 | ||||||||
\(987\) | −16.6484 | −0.529923 | ||||||||
\(988\) | −3.12259 | −0.0993429 | ||||||||
\(989\) | −6.18094 | −0.196543 | ||||||||
\(990\) | 7.09290 | 0.225427 | ||||||||
\(991\) | −7.02450 | −0.223140 | −0.111570 | − | 0.993757i | \(-0.535588\pi\) | ||||
−0.111570 | + | 0.993757i | \(0.535588\pi\) | |||||||
\(992\) | −30.9128 | −0.981483 | ||||||||
\(993\) | 12.0308 | 0.381787 | ||||||||
\(994\) | −119.161 | −3.77957 | ||||||||
\(995\) | 11.8892 | 0.376914 | ||||||||
\(996\) | 29.1736 | 0.924401 | ||||||||
\(997\) | 5.96495 | 0.188912 | 0.0944559 | − | 0.995529i | \(-0.469889\pi\) | ||||
0.0944559 | + | 0.995529i | \(0.469889\pi\) | |||||||
\(998\) | 23.6627 | 0.749030 | ||||||||
\(999\) | 8.35805 | 0.264437 |
(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 | 8041.2.a.j.1.18 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.18 | ✓ | 82 | 1.1 | even | 1 | trivial |