Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.23056 | −1.86517 | −0.932583 | − | 0.360956i | \(-0.882450\pi\) | ||||
−0.932583 | + | 0.360956i | \(0.882450\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.65226 | −1.63334 | −0.816670 | − | 0.577104i | \(-0.804183\pi\) | ||||
−0.816670 | + | 0.577104i | \(0.804183\pi\) | |||||||
\(6\) | −3.23056 | −1.31887 | ||||||||
\(7\) | 2.39039 | 0.903483 | 0.451742 | − | 0.892149i | \(-0.350803\pi\) | ||||
0.451742 | + | 0.892149i | \(0.350803\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.43653 | 2.47884 | ||||||||
\(10\) | −3.65226 | −1.15495 | ||||||||
\(11\) | 0.229147 | 0.0690904 | 0.0345452 | − | 0.999403i | \(-0.489002\pi\) | ||||
0.0345452 | + | 0.999403i | \(0.489002\pi\) | |||||||
\(12\) | −3.23056 | −0.932583 | ||||||||
\(13\) | −1.51971 | −0.421493 | −0.210746 | − | 0.977541i | \(-0.567589\pi\) | ||||
−0.210746 | + | 0.977541i | \(0.567589\pi\) | |||||||
\(14\) | 2.39039 | 0.638859 | ||||||||
\(15\) | 11.7989 | 3.04645 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.23485 | 0.299496 | 0.149748 | − | 0.988724i | \(-0.452154\pi\) | ||||
0.149748 | + | 0.988724i | \(0.452154\pi\) | |||||||
\(18\) | 7.43653 | 1.75281 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −3.65226 | −0.816670 | ||||||||
\(21\) | −7.72231 | −1.68515 | ||||||||
\(22\) | 0.229147 | 0.0488543 | ||||||||
\(23\) | −8.59225 | −1.79161 | −0.895804 | − | 0.444450i | \(-0.853399\pi\) | ||||
−0.895804 | + | 0.444450i | \(0.853399\pi\) | |||||||
\(24\) | −3.23056 | −0.659436 | ||||||||
\(25\) | 8.33901 | 1.66780 | ||||||||
\(26\) | −1.51971 | −0.298041 | ||||||||
\(27\) | −14.3325 | −2.75829 | ||||||||
\(28\) | 2.39039 | 0.451742 | ||||||||
\(29\) | −2.80955 | −0.521721 | −0.260860 | − | 0.965377i | \(-0.584006\pi\) | ||||
−0.260860 | + | 0.965377i | \(0.584006\pi\) | |||||||
\(30\) | 11.7989 | 2.15417 | ||||||||
\(31\) | 4.09925 | 0.736246 | 0.368123 | − | 0.929777i | \(-0.380000\pi\) | ||||
0.368123 | + | 0.929777i | \(0.380000\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.740273 | −0.128865 | ||||||||
\(34\) | 1.23485 | 0.211775 | ||||||||
\(35\) | −8.73034 | −1.47570 | ||||||||
\(36\) | 7.43653 | 1.23942 | ||||||||
\(37\) | −7.69336 | −1.26478 | −0.632391 | − | 0.774650i | \(-0.717926\pi\) | ||||
−0.632391 | + | 0.774650i | \(0.717926\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 4.90953 | 0.786154 | ||||||||
\(40\) | −3.65226 | −0.577473 | ||||||||
\(41\) | 6.97582 | 1.08944 | 0.544720 | − | 0.838618i | \(-0.316636\pi\) | ||||
0.544720 | + | 0.838618i | \(0.316636\pi\) | |||||||
\(42\) | −7.72231 | −1.19158 | ||||||||
\(43\) | −10.4732 | −1.59715 | −0.798573 | − | 0.601898i | \(-0.794411\pi\) | ||||
−0.798573 | + | 0.601898i | \(0.794411\pi\) | |||||||
\(44\) | 0.229147 | 0.0345452 | ||||||||
\(45\) | −27.1601 | −4.04880 | ||||||||
\(46\) | −8.59225 | −1.26686 | ||||||||
\(47\) | 11.1963 | 1.63315 | 0.816574 | − | 0.577241i | \(-0.195871\pi\) | ||||
0.816574 | + | 0.577241i | \(0.195871\pi\) | |||||||
\(48\) | −3.23056 | −0.466291 | ||||||||
\(49\) | −1.28603 | −0.183718 | ||||||||
\(50\) | 8.33901 | 1.17931 | ||||||||
\(51\) | −3.98926 | −0.558609 | ||||||||
\(52\) | −1.51971 | −0.210746 | ||||||||
\(53\) | 2.41819 | 0.332164 | 0.166082 | − | 0.986112i | \(-0.446888\pi\) | ||||
0.166082 | + | 0.986112i | \(0.446888\pi\) | |||||||
\(54\) | −14.3325 | −1.95040 | ||||||||
\(55\) | −0.836904 | −0.112848 | ||||||||
\(56\) | 2.39039 | 0.319430 | ||||||||
\(57\) | −3.23056 | −0.427898 | ||||||||
\(58\) | −2.80955 | −0.368912 | ||||||||
\(59\) | 5.91884 | 0.770567 | 0.385284 | − | 0.922798i | \(-0.374104\pi\) | ||||
0.385284 | + | 0.922798i | \(0.374104\pi\) | |||||||
\(60\) | 11.7989 | 1.52323 | ||||||||
\(61\) | 5.03288 | 0.644394 | 0.322197 | − | 0.946673i | \(-0.395579\pi\) | ||||
0.322197 | + | 0.946673i | \(0.395579\pi\) | |||||||
\(62\) | 4.09925 | 0.520605 | ||||||||
\(63\) | 17.7762 | 2.23959 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.55039 | 0.688442 | ||||||||
\(66\) | −0.740273 | −0.0911214 | ||||||||
\(67\) | −1.27570 | −0.155851 | −0.0779257 | − | 0.996959i | \(-0.524830\pi\) | ||||
−0.0779257 | + | 0.996959i | \(0.524830\pi\) | |||||||
\(68\) | 1.23485 | 0.149748 | ||||||||
\(69\) | 27.7578 | 3.34164 | ||||||||
\(70\) | −8.73034 | −1.04347 | ||||||||
\(71\) | 10.5869 | 1.25643 | 0.628214 | − | 0.778041i | \(-0.283786\pi\) | ||||
0.628214 | + | 0.778041i | \(0.283786\pi\) | |||||||
\(72\) | 7.43653 | 0.876403 | ||||||||
\(73\) | −5.30920 | −0.621395 | −0.310697 | − | 0.950509i | \(-0.600563\pi\) | ||||
−0.310697 | + | 0.950509i | \(0.600563\pi\) | |||||||
\(74\) | −7.69336 | −0.894335 | ||||||||
\(75\) | −26.9397 | −3.11073 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0.547751 | 0.0624220 | ||||||||
\(78\) | 4.90953 | 0.555895 | ||||||||
\(79\) | 4.63819 | 0.521838 | 0.260919 | − | 0.965361i | \(-0.415974\pi\) | ||||
0.260919 | + | 0.965361i | \(0.415974\pi\) | |||||||
\(80\) | −3.65226 | −0.408335 | ||||||||
\(81\) | 23.9924 | 2.66582 | ||||||||
\(82\) | 6.97582 | 0.770350 | ||||||||
\(83\) | 0.441306 | 0.0484396 | 0.0242198 | − | 0.999707i | \(-0.492290\pi\) | ||||
0.0242198 | + | 0.999707i | \(0.492290\pi\) | |||||||
\(84\) | −7.72231 | −0.842573 | ||||||||
\(85\) | −4.51000 | −0.489178 | ||||||||
\(86\) | −10.4732 | −1.12935 | ||||||||
\(87\) | 9.07644 | 0.973096 | ||||||||
\(88\) | 0.229147 | 0.0244271 | ||||||||
\(89\) | 3.69080 | 0.391224 | 0.195612 | − | 0.980681i | \(-0.437331\pi\) | ||||
0.195612 | + | 0.980681i | \(0.437331\pi\) | |||||||
\(90\) | −27.1601 | −2.86293 | ||||||||
\(91\) | −3.63271 | −0.380812 | ||||||||
\(92\) | −8.59225 | −0.895804 | ||||||||
\(93\) | −13.2429 | −1.37322 | ||||||||
\(94\) | 11.1963 | 1.15481 | ||||||||
\(95\) | −3.65226 | −0.374714 | ||||||||
\(96\) | −3.23056 | −0.329718 | ||||||||
\(97\) | 7.94507 | 0.806699 | 0.403350 | − | 0.915046i | \(-0.367846\pi\) | ||||
0.403350 | + | 0.915046i | \(0.367846\pi\) | |||||||
\(98\) | −1.28603 | −0.129908 | ||||||||
\(99\) | 1.70406 | 0.171264 | ||||||||
\(100\) | 8.33901 | 0.833901 | ||||||||
\(101\) | 15.3822 | 1.53059 | 0.765295 | − | 0.643679i | \(-0.222593\pi\) | ||||
0.765295 | + | 0.643679i | \(0.222593\pi\) | |||||||
\(102\) | −3.98926 | −0.394996 | ||||||||
\(103\) | 11.3311 | 1.11649 | 0.558243 | − | 0.829677i | \(-0.311476\pi\) | ||||
0.558243 | + | 0.829677i | \(0.311476\pi\) | |||||||
\(104\) | −1.51971 | −0.149020 | ||||||||
\(105\) | 28.2039 | 2.75242 | ||||||||
\(106\) | 2.41819 | 0.234875 | ||||||||
\(107\) | −7.66030 | −0.740549 | −0.370275 | − | 0.928922i | \(-0.620736\pi\) | ||||
−0.370275 | + | 0.928922i | \(0.620736\pi\) | |||||||
\(108\) | −14.3325 | −1.37914 | ||||||||
\(109\) | −3.71384 | −0.355721 | −0.177860 | − | 0.984056i | \(-0.556918\pi\) | ||||
−0.177860 | + | 0.984056i | \(0.556918\pi\) | |||||||
\(110\) | −0.836904 | −0.0797957 | ||||||||
\(111\) | 24.8539 | 2.35903 | ||||||||
\(112\) | 2.39039 | 0.225871 | ||||||||
\(113\) | −11.5383 | −1.08543 | −0.542716 | − | 0.839916i | \(-0.682604\pi\) | ||||
−0.542716 | + | 0.839916i | \(0.682604\pi\) | |||||||
\(114\) | −3.23056 | −0.302570 | ||||||||
\(115\) | 31.3811 | 2.92631 | ||||||||
\(116\) | −2.80955 | −0.260860 | ||||||||
\(117\) | −11.3014 | −1.04481 | ||||||||
\(118\) | 5.91884 | 0.544873 | ||||||||
\(119\) | 2.95178 | 0.270589 | ||||||||
\(120\) | 11.7989 | 1.07708 | ||||||||
\(121\) | −10.9475 | −0.995227 | ||||||||
\(122\) | 5.03288 | 0.455656 | ||||||||
\(123\) | −22.5358 | −2.03199 | ||||||||
\(124\) | 4.09925 | 0.368123 | ||||||||
\(125\) | −12.1949 | −1.09075 | ||||||||
\(126\) | 17.7762 | 1.58363 | ||||||||
\(127\) | 3.97747 | 0.352943 | 0.176471 | − | 0.984306i | \(-0.443532\pi\) | ||||
0.176471 | + | 0.984306i | \(0.443532\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 33.8343 | 2.97894 | ||||||||
\(130\) | 5.55039 | 0.486802 | ||||||||
\(131\) | 12.8956 | 1.12669 | 0.563346 | − | 0.826221i | \(-0.309514\pi\) | ||||
0.563346 | + | 0.826221i | \(0.309514\pi\) | |||||||
\(132\) | −0.740273 | −0.0644325 | ||||||||
\(133\) | 2.39039 | 0.207273 | ||||||||
\(134\) | −1.27570 | −0.110204 | ||||||||
\(135\) | 52.3460 | 4.50522 | ||||||||
\(136\) | 1.23485 | 0.105888 | ||||||||
\(137\) | 8.89558 | 0.760001 | 0.380000 | − | 0.924986i | \(-0.375924\pi\) | ||||
0.380000 | + | 0.924986i | \(0.375924\pi\) | |||||||
\(138\) | 27.7578 | 2.36290 | ||||||||
\(139\) | −18.2310 | −1.54634 | −0.773168 | − | 0.634202i | \(-0.781329\pi\) | ||||
−0.773168 | + | 0.634202i | \(0.781329\pi\) | |||||||
\(140\) | −8.73034 | −0.737848 | ||||||||
\(141\) | −36.1703 | −3.04609 | ||||||||
\(142\) | 10.5869 | 0.888429 | ||||||||
\(143\) | −0.348238 | −0.0291211 | ||||||||
\(144\) | 7.43653 | 0.619711 | ||||||||
\(145\) | 10.2612 | 0.852148 | ||||||||
\(146\) | −5.30920 | −0.439392 | ||||||||
\(147\) | 4.15458 | 0.342664 | ||||||||
\(148\) | −7.69336 | −0.632391 | ||||||||
\(149\) | 5.63027 | 0.461249 | 0.230625 | − | 0.973043i | \(-0.425923\pi\) | ||||
0.230625 | + | 0.973043i | \(0.425923\pi\) | |||||||
\(150\) | −26.9397 | −2.19962 | ||||||||
\(151\) | −22.9354 | −1.86646 | −0.933228 | − | 0.359284i | \(-0.883021\pi\) | ||||
−0.933228 | + | 0.359284i | \(0.883021\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 9.18301 | 0.742402 | ||||||||
\(154\) | 0.547751 | 0.0441390 | ||||||||
\(155\) | −14.9715 | −1.20254 | ||||||||
\(156\) | 4.90953 | 0.393077 | ||||||||
\(157\) | −14.9345 | −1.19191 | −0.595953 | − | 0.803020i | \(-0.703225\pi\) | ||||
−0.595953 | + | 0.803020i | \(0.703225\pi\) | |||||||
\(158\) | 4.63819 | 0.368995 | ||||||||
\(159\) | −7.81211 | −0.619541 | ||||||||
\(160\) | −3.65226 | −0.288737 | ||||||||
\(161\) | −20.5388 | −1.61869 | ||||||||
\(162\) | 23.9924 | 1.88502 | ||||||||
\(163\) | 9.70135 | 0.759868 | 0.379934 | − | 0.925014i | \(-0.375947\pi\) | ||||
0.379934 | + | 0.925014i | \(0.375947\pi\) | |||||||
\(164\) | 6.97582 | 0.544720 | ||||||||
\(165\) | 2.70367 | 0.210481 | ||||||||
\(166\) | 0.441306 | 0.0342520 | ||||||||
\(167\) | −15.6073 | −1.20773 | −0.603863 | − | 0.797088i | \(-0.706373\pi\) | ||||
−0.603863 | + | 0.797088i | \(0.706373\pi\) | |||||||
\(168\) | −7.72231 | −0.595789 | ||||||||
\(169\) | −10.6905 | −0.822344 | ||||||||
\(170\) | −4.51000 | −0.345901 | ||||||||
\(171\) | 7.43653 | 0.568686 | ||||||||
\(172\) | −10.4732 | −0.798573 | ||||||||
\(173\) | −6.52314 | −0.495945 | −0.247972 | − | 0.968767i | \(-0.579764\pi\) | ||||
−0.247972 | + | 0.968767i | \(0.579764\pi\) | |||||||
\(174\) | 9.07644 | 0.688083 | ||||||||
\(175\) | 19.9335 | 1.50683 | ||||||||
\(176\) | 0.229147 | 0.0172726 | ||||||||
\(177\) | −19.1212 | −1.43724 | ||||||||
\(178\) | 3.69080 | 0.276637 | ||||||||
\(179\) | −6.02767 | −0.450529 | −0.225265 | − | 0.974298i | \(-0.572325\pi\) | ||||
−0.225265 | + | 0.974298i | \(0.572325\pi\) | |||||||
\(180\) | −27.1601 | −2.02440 | ||||||||
\(181\) | 2.88974 | 0.214793 | 0.107396 | − | 0.994216i | \(-0.465749\pi\) | ||||
0.107396 | + | 0.994216i | \(0.465749\pi\) | |||||||
\(182\) | −3.63271 | −0.269275 | ||||||||
\(183\) | −16.2590 | −1.20190 | ||||||||
\(184\) | −8.59225 | −0.633429 | ||||||||
\(185\) | 28.0982 | 2.06582 | ||||||||
\(186\) | −13.2429 | −0.971014 | ||||||||
\(187\) | 0.282963 | 0.0206923 | ||||||||
\(188\) | 11.1963 | 0.816574 | ||||||||
\(189\) | −34.2603 | −2.49207 | ||||||||
\(190\) | −3.65226 | −0.264963 | ||||||||
\(191\) | 6.86116 | 0.496456 | 0.248228 | − | 0.968702i | \(-0.420152\pi\) | ||||
0.248228 | + | 0.968702i | \(0.420152\pi\) | |||||||
\(192\) | −3.23056 | −0.233146 | ||||||||
\(193\) | −1.24997 | −0.0899747 | −0.0449874 | − | 0.998988i | \(-0.514325\pi\) | ||||
−0.0449874 | + | 0.998988i | \(0.514325\pi\) | |||||||
\(194\) | 7.94507 | 0.570423 | ||||||||
\(195\) | −17.9309 | −1.28406 | ||||||||
\(196\) | −1.28603 | −0.0918590 | ||||||||
\(197\) | −0.390431 | −0.0278171 | −0.0139085 | − | 0.999903i | \(-0.504427\pi\) | ||||
−0.0139085 | + | 0.999903i | \(0.504427\pi\) | |||||||
\(198\) | 1.70406 | 0.121102 | ||||||||
\(199\) | −3.56651 | −0.252823 | −0.126411 | − | 0.991978i | \(-0.540346\pi\) | ||||
−0.126411 | + | 0.991978i | \(0.540346\pi\) | |||||||
\(200\) | 8.33901 | 0.589657 | ||||||||
\(201\) | 4.12122 | 0.290689 | ||||||||
\(202\) | 15.3822 | 1.08229 | ||||||||
\(203\) | −6.71593 | −0.471366 | ||||||||
\(204\) | −3.98926 | −0.279304 | ||||||||
\(205\) | −25.4775 | −1.77943 | ||||||||
\(206\) | 11.3311 | 0.789475 | ||||||||
\(207\) | −63.8965 | −4.44111 | ||||||||
\(208\) | −1.51971 | −0.105373 | ||||||||
\(209\) | 0.229147 | 0.0158504 | ||||||||
\(210\) | 28.2039 | 1.94625 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 2.41819 | 0.166082 | ||||||||
\(213\) | −34.2015 | −2.34345 | ||||||||
\(214\) | −7.66030 | −0.523647 | ||||||||
\(215\) | 38.2508 | 2.60868 | ||||||||
\(216\) | −14.3325 | −0.975202 | ||||||||
\(217\) | 9.79881 | 0.665186 | ||||||||
\(218\) | −3.71384 | −0.251533 | ||||||||
\(219\) | 17.1517 | 1.15900 | ||||||||
\(220\) | −0.836904 | −0.0564241 | ||||||||
\(221\) | −1.87662 | −0.126235 | ||||||||
\(222\) | 24.8539 | 1.66808 | ||||||||
\(223\) | −9.58727 | −0.642011 | −0.321006 | − | 0.947077i | \(-0.604021\pi\) | ||||
−0.321006 | + | 0.947077i | \(0.604021\pi\) | |||||||
\(224\) | 2.39039 | 0.159715 | ||||||||
\(225\) | 62.0133 | 4.13422 | ||||||||
\(226\) | −11.5383 | −0.767516 | ||||||||
\(227\) | −18.3617 | −1.21871 | −0.609354 | − | 0.792898i | \(-0.708571\pi\) | ||||
−0.609354 | + | 0.792898i | \(0.708571\pi\) | |||||||
\(228\) | −3.23056 | −0.213949 | ||||||||
\(229\) | 5.24337 | 0.346492 | 0.173246 | − | 0.984879i | \(-0.444574\pi\) | ||||
0.173246 | + | 0.984879i | \(0.444574\pi\) | |||||||
\(230\) | 31.3811 | 2.06921 | ||||||||
\(231\) | −1.76954 | −0.116427 | ||||||||
\(232\) | −2.80955 | −0.184456 | ||||||||
\(233\) | 2.53591 | 0.166133 | 0.0830666 | − | 0.996544i | \(-0.473529\pi\) | ||||
0.0830666 | + | 0.996544i | \(0.473529\pi\) | |||||||
\(234\) | −11.3014 | −0.738796 | ||||||||
\(235\) | −40.8918 | −2.66749 | ||||||||
\(236\) | 5.91884 | 0.385284 | ||||||||
\(237\) | −14.9840 | −0.973314 | ||||||||
\(238\) | 2.95178 | 0.191335 | ||||||||
\(239\) | −20.2316 | −1.30868 | −0.654338 | − | 0.756202i | \(-0.727052\pi\) | ||||
−0.654338 | + | 0.756202i | \(0.727052\pi\) | |||||||
\(240\) | 11.7989 | 0.761613 | ||||||||
\(241\) | 1.33108 | 0.0857424 | 0.0428712 | − | 0.999081i | \(-0.486349\pi\) | ||||
0.0428712 | + | 0.999081i | \(0.486349\pi\) | |||||||
\(242\) | −10.9475 | −0.703731 | ||||||||
\(243\) | −34.5114 | −2.21391 | ||||||||
\(244\) | 5.03288 | 0.322197 | ||||||||
\(245\) | 4.69690 | 0.300074 | ||||||||
\(246\) | −22.5358 | −1.43683 | ||||||||
\(247\) | −1.51971 | −0.0966971 | ||||||||
\(248\) | 4.09925 | 0.260302 | ||||||||
\(249\) | −1.42567 | −0.0903479 | ||||||||
\(250\) | −12.1949 | −0.771276 | ||||||||
\(251\) | 30.4215 | 1.92019 | 0.960093 | − | 0.279681i | \(-0.0902286\pi\) | ||||
0.960093 | + | 0.279681i | \(0.0902286\pi\) | |||||||
\(252\) | 17.7762 | 1.11980 | ||||||||
\(253\) | −1.96889 | −0.123783 | ||||||||
\(254\) | 3.97747 | 0.249568 | ||||||||
\(255\) | 14.5698 | 0.912399 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.4111 | 1.02369 | 0.511847 | − | 0.859077i | \(-0.328962\pi\) | ||||
0.511847 | + | 0.859077i | \(0.328962\pi\) | |||||||
\(258\) | 33.8343 | 2.10643 | ||||||||
\(259\) | −18.3902 | −1.14271 | ||||||||
\(260\) | 5.55039 | 0.344221 | ||||||||
\(261\) | −20.8933 | −1.29326 | ||||||||
\(262\) | 12.8956 | 0.796691 | ||||||||
\(263\) | −5.15303 | −0.317749 | −0.158875 | − | 0.987299i | \(-0.550787\pi\) | ||||
−0.158875 | + | 0.987299i | \(0.550787\pi\) | |||||||
\(264\) | −0.740273 | −0.0455607 | ||||||||
\(265\) | −8.83186 | −0.542537 | ||||||||
\(266\) | 2.39039 | 0.146564 | ||||||||
\(267\) | −11.9234 | −0.729698 | ||||||||
\(268\) | −1.27570 | −0.0779257 | ||||||||
\(269\) | 4.03782 | 0.246190 | 0.123095 | − | 0.992395i | \(-0.460718\pi\) | ||||
0.123095 | + | 0.992395i | \(0.460718\pi\) | |||||||
\(270\) | 52.3460 | 3.18567 | ||||||||
\(271\) | −13.4426 | −0.816579 | −0.408289 | − | 0.912853i | \(-0.633875\pi\) | ||||
−0.408289 | + | 0.912853i | \(0.633875\pi\) | |||||||
\(272\) | 1.23485 | 0.0748739 | ||||||||
\(273\) | 11.7357 | 0.710277 | ||||||||
\(274\) | 8.89558 | 0.537402 | ||||||||
\(275\) | 1.91086 | 0.115229 | ||||||||
\(276\) | 27.7578 | 1.67082 | ||||||||
\(277\) | 11.7483 | 0.705889 | 0.352944 | − | 0.935644i | \(-0.385180\pi\) | ||||
0.352944 | + | 0.935644i | \(0.385180\pi\) | |||||||
\(278\) | −18.2310 | −1.09342 | ||||||||
\(279\) | 30.4842 | 1.82504 | ||||||||
\(280\) | −8.73034 | −0.521737 | ||||||||
\(281\) | 14.9416 | 0.891340 | 0.445670 | − | 0.895197i | \(-0.352965\pi\) | ||||
0.445670 | + | 0.895197i | \(0.352965\pi\) | |||||||
\(282\) | −36.1703 | −2.15391 | ||||||||
\(283\) | 1.92528 | 0.114446 | 0.0572229 | − | 0.998361i | \(-0.481775\pi\) | ||||
0.0572229 | + | 0.998361i | \(0.481775\pi\) | |||||||
\(284\) | 10.5869 | 0.628214 | ||||||||
\(285\) | 11.7989 | 0.698904 | ||||||||
\(286\) | −0.348238 | −0.0205917 | ||||||||
\(287\) | 16.6749 | 0.984291 | ||||||||
\(288\) | 7.43653 | 0.438202 | ||||||||
\(289\) | −15.4751 | −0.910302 | ||||||||
\(290\) | 10.2612 | 0.602560 | ||||||||
\(291\) | −25.6670 | −1.50463 | ||||||||
\(292\) | −5.30920 | −0.310697 | ||||||||
\(293\) | −31.4958 | −1.84000 | −0.920002 | − | 0.391914i | \(-0.871813\pi\) | ||||
−0.920002 | + | 0.391914i | \(0.871813\pi\) | |||||||
\(294\) | 4.15458 | 0.242300 | ||||||||
\(295\) | −21.6171 | −1.25860 | ||||||||
\(296\) | −7.69336 | −0.447168 | ||||||||
\(297\) | −3.28424 | −0.190571 | ||||||||
\(298\) | 5.63027 | 0.326153 | ||||||||
\(299\) | 13.0578 | 0.755150 | ||||||||
\(300\) | −26.9397 | −1.55536 | ||||||||
\(301\) | −25.0350 | −1.44300 | ||||||||
\(302\) | −22.9354 | −1.31978 | ||||||||
\(303\) | −49.6933 | −2.85481 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −18.3814 | −1.05252 | ||||||||
\(306\) | 9.18301 | 0.524958 | ||||||||
\(307\) | 12.8647 | 0.734228 | 0.367114 | − | 0.930176i | \(-0.380346\pi\) | ||||
0.367114 | + | 0.930176i | \(0.380346\pi\) | |||||||
\(308\) | 0.547751 | 0.0312110 | ||||||||
\(309\) | −36.6058 | −2.08243 | ||||||||
\(310\) | −14.9715 | −0.850325 | ||||||||
\(311\) | −25.7290 | −1.45896 | −0.729478 | − | 0.684004i | \(-0.760237\pi\) | ||||
−0.729478 | + | 0.684004i | \(0.760237\pi\) | |||||||
\(312\) | 4.90953 | 0.277947 | ||||||||
\(313\) | −24.5398 | −1.38707 | −0.693537 | − | 0.720421i | \(-0.743948\pi\) | ||||
−0.693537 | + | 0.720421i | \(0.743948\pi\) | |||||||
\(314\) | −14.9345 | −0.842804 | ||||||||
\(315\) | −64.9234 | −3.65802 | ||||||||
\(316\) | 4.63819 | 0.260919 | ||||||||
\(317\) | 19.5030 | 1.09540 | 0.547698 | − | 0.836676i | \(-0.315504\pi\) | ||||
0.547698 | + | 0.836676i | \(0.315504\pi\) | |||||||
\(318\) | −7.81211 | −0.438082 | ||||||||
\(319\) | −0.643801 | −0.0360459 | ||||||||
\(320\) | −3.65226 | −0.204168 | ||||||||
\(321\) | 24.7471 | 1.38125 | ||||||||
\(322\) | −20.5388 | −1.14458 | ||||||||
\(323\) | 1.23485 | 0.0687090 | ||||||||
\(324\) | 23.9924 | 1.33291 | ||||||||
\(325\) | −12.6729 | −0.702967 | ||||||||
\(326\) | 9.70135 | 0.537308 | ||||||||
\(327\) | 11.9978 | 0.663478 | ||||||||
\(328\) | 6.97582 | 0.385175 | ||||||||
\(329\) | 26.7635 | 1.47552 | ||||||||
\(330\) | 2.70367 | 0.148832 | ||||||||
\(331\) | 8.66544 | 0.476296 | 0.238148 | − | 0.971229i | \(-0.423460\pi\) | ||||
0.238148 | + | 0.971229i | \(0.423460\pi\) | |||||||
\(332\) | 0.441306 | 0.0242198 | ||||||||
\(333\) | −57.2119 | −3.13519 | ||||||||
\(334\) | −15.6073 | −0.853991 | ||||||||
\(335\) | 4.65919 | 0.254558 | ||||||||
\(336\) | −7.72231 | −0.421287 | ||||||||
\(337\) | −14.4531 | −0.787309 | −0.393654 | − | 0.919259i | \(-0.628789\pi\) | ||||
−0.393654 | + | 0.919259i | \(0.628789\pi\) | |||||||
\(338\) | −10.6905 | −0.581485 | ||||||||
\(339\) | 37.2752 | 2.02451 | ||||||||
\(340\) | −4.51000 | −0.244589 | ||||||||
\(341\) | 0.939330 | 0.0508676 | ||||||||
\(342\) | 7.43653 | 0.402121 | ||||||||
\(343\) | −19.8069 | −1.06947 | ||||||||
\(344\) | −10.4732 | −0.564677 | ||||||||
\(345\) | −101.379 | −5.45804 | ||||||||
\(346\) | −6.52314 | −0.350686 | ||||||||
\(347\) | −0.431535 | −0.0231660 | −0.0115830 | − | 0.999933i | \(-0.503687\pi\) | ||||
−0.0115830 | + | 0.999933i | \(0.503687\pi\) | |||||||
\(348\) | 9.07644 | 0.486548 | ||||||||
\(349\) | −5.76879 | −0.308796 | −0.154398 | − | 0.988009i | \(-0.549344\pi\) | ||||
−0.154398 | + | 0.988009i | \(0.549344\pi\) | |||||||
\(350\) | 19.9335 | 1.06549 | ||||||||
\(351\) | 21.7813 | 1.16260 | ||||||||
\(352\) | 0.229147 | 0.0122136 | ||||||||
\(353\) | −16.3363 | −0.869494 | −0.434747 | − | 0.900553i | \(-0.643162\pi\) | ||||
−0.434747 | + | 0.900553i | \(0.643162\pi\) | |||||||
\(354\) | −19.1212 | −1.01628 | ||||||||
\(355\) | −38.6659 | −2.05218 | ||||||||
\(356\) | 3.69080 | 0.195612 | ||||||||
\(357\) | −9.53591 | −0.504694 | ||||||||
\(358\) | −6.02767 | −0.318572 | ||||||||
\(359\) | 10.6597 | 0.562600 | 0.281300 | − | 0.959620i | \(-0.409234\pi\) | ||||
0.281300 | + | 0.959620i | \(0.409234\pi\) | |||||||
\(360\) | −27.1601 | −1.43147 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 2.88974 | 0.151881 | ||||||||
\(363\) | 35.3665 | 1.85626 | ||||||||
\(364\) | −3.63271 | −0.190406 | ||||||||
\(365\) | 19.3906 | 1.01495 | ||||||||
\(366\) | −16.2590 | −0.849873 | ||||||||
\(367\) | −23.8708 | −1.24605 | −0.623023 | − | 0.782204i | \(-0.714096\pi\) | ||||
−0.623023 | + | 0.782204i | \(0.714096\pi\) | |||||||
\(368\) | −8.59225 | −0.447902 | ||||||||
\(369\) | 51.8759 | 2.70055 | ||||||||
\(370\) | 28.0982 | 1.46075 | ||||||||
\(371\) | 5.78042 | 0.300105 | ||||||||
\(372\) | −13.2429 | −0.686611 | ||||||||
\(373\) | −27.5695 | −1.42749 | −0.713747 | − | 0.700404i | \(-0.753003\pi\) | ||||
−0.713747 | + | 0.700404i | \(0.753003\pi\) | |||||||
\(374\) | 0.282963 | 0.0146316 | ||||||||
\(375\) | 39.3965 | 2.03443 | ||||||||
\(376\) | 11.1963 | 0.577405 | ||||||||
\(377\) | 4.26972 | 0.219902 | ||||||||
\(378\) | −34.2603 | −1.76216 | ||||||||
\(379\) | 4.83139 | 0.248172 | 0.124086 | − | 0.992271i | \(-0.460400\pi\) | ||||
0.124086 | + | 0.992271i | \(0.460400\pi\) | |||||||
\(380\) | −3.65226 | −0.187357 | ||||||||
\(381\) | −12.8494 | −0.658297 | ||||||||
\(382\) | 6.86116 | 0.351047 | ||||||||
\(383\) | 28.5696 | 1.45984 | 0.729919 | − | 0.683534i | \(-0.239558\pi\) | ||||
0.729919 | + | 0.683534i | \(0.239558\pi\) | |||||||
\(384\) | −3.23056 | −0.164859 | ||||||||
\(385\) | −2.00053 | −0.101956 | ||||||||
\(386\) | −1.24997 | −0.0636217 | ||||||||
\(387\) | −77.8842 | −3.95908 | ||||||||
\(388\) | 7.94507 | 0.403350 | ||||||||
\(389\) | 17.6906 | 0.896947 | 0.448474 | − | 0.893796i | \(-0.351968\pi\) | ||||
0.448474 | + | 0.893796i | \(0.351968\pi\) | |||||||
\(390\) | −17.9309 | −0.907966 | ||||||||
\(391\) | −10.6102 | −0.536578 | ||||||||
\(392\) | −1.28603 | −0.0649541 | ||||||||
\(393\) | −41.6600 | −2.10147 | ||||||||
\(394\) | −0.390431 | −0.0196696 | ||||||||
\(395\) | −16.9399 | −0.852339 | ||||||||
\(396\) | 1.70406 | 0.0856321 | ||||||||
\(397\) | −26.1741 | −1.31364 | −0.656821 | − | 0.754047i | \(-0.728099\pi\) | ||||
−0.656821 | + | 0.754047i | \(0.728099\pi\) | |||||||
\(398\) | −3.56651 | −0.178773 | ||||||||
\(399\) | −7.72231 | −0.386599 | ||||||||
\(400\) | 8.33901 | 0.416951 | ||||||||
\(401\) | −39.1083 | −1.95298 | −0.976489 | − | 0.215569i | \(-0.930839\pi\) | ||||
−0.976489 | + | 0.215569i | \(0.930839\pi\) | |||||||
\(402\) | 4.12122 | 0.205548 | ||||||||
\(403\) | −6.22968 | −0.310323 | ||||||||
\(404\) | 15.3822 | 0.765295 | ||||||||
\(405\) | −87.6264 | −4.35419 | ||||||||
\(406\) | −6.71593 | −0.333306 | ||||||||
\(407\) | −1.76291 | −0.0873842 | ||||||||
\(408\) | −3.98926 | −0.197498 | ||||||||
\(409\) | −30.0877 | −1.48774 | −0.743870 | − | 0.668324i | \(-0.767012\pi\) | ||||
−0.743870 | + | 0.668324i | \(0.767012\pi\) | |||||||
\(410\) | −25.4775 | −1.25824 | ||||||||
\(411\) | −28.7377 | −1.41753 | ||||||||
\(412\) | 11.3311 | 0.558243 | ||||||||
\(413\) | 14.1483 | 0.696195 | ||||||||
\(414\) | −63.8965 | −3.14034 | ||||||||
\(415\) | −1.61176 | −0.0791184 | ||||||||
\(416\) | −1.51971 | −0.0745101 | ||||||||
\(417\) | 58.8964 | 2.88417 | ||||||||
\(418\) | 0.229147 | 0.0112079 | ||||||||
\(419\) | −1.17310 | −0.0573098 | −0.0286549 | − | 0.999589i | \(-0.509122\pi\) | ||||
−0.0286549 | + | 0.999589i | \(0.509122\pi\) | |||||||
\(420\) | 28.2039 | 1.37621 | ||||||||
\(421\) | 16.7829 | 0.817950 | 0.408975 | − | 0.912546i | \(-0.365886\pi\) | ||||
0.408975 | + | 0.912546i | \(0.365886\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 83.2616 | 4.04832 | ||||||||
\(424\) | 2.41819 | 0.117438 | ||||||||
\(425\) | 10.2974 | 0.499499 | ||||||||
\(426\) | −34.2015 | −1.65707 | ||||||||
\(427\) | 12.0306 | 0.582200 | ||||||||
\(428\) | −7.66030 | −0.370275 | ||||||||
\(429\) | 1.12500 | 0.0543157 | ||||||||
\(430\) | 38.2508 | 1.84462 | ||||||||
\(431\) | −7.56515 | −0.364401 | −0.182200 | − | 0.983261i | \(-0.558322\pi\) | ||||
−0.182200 | + | 0.983261i | \(0.558322\pi\) | |||||||
\(432\) | −14.3325 | −0.689572 | ||||||||
\(433\) | 7.92605 | 0.380902 | 0.190451 | − | 0.981697i | \(-0.439005\pi\) | ||||
0.190451 | + | 0.981697i | \(0.439005\pi\) | |||||||
\(434\) | 9.79881 | 0.470358 | ||||||||
\(435\) | −33.1495 | −1.58940 | ||||||||
\(436\) | −3.71384 | −0.177860 | ||||||||
\(437\) | −8.59225 | −0.411023 | ||||||||
\(438\) | 17.1517 | 0.819539 | ||||||||
\(439\) | 8.97895 | 0.428542 | 0.214271 | − | 0.976774i | \(-0.431262\pi\) | ||||
0.214271 | + | 0.976774i | \(0.431262\pi\) | |||||||
\(440\) | −0.836904 | −0.0398979 | ||||||||
\(441\) | −9.56357 | −0.455408 | ||||||||
\(442\) | −1.87662 | −0.0892618 | ||||||||
\(443\) | 31.4899 | 1.49613 | 0.748065 | − | 0.663625i | \(-0.230983\pi\) | ||||
0.748065 | + | 0.663625i | \(0.230983\pi\) | |||||||
\(444\) | 24.8539 | 1.17951 | ||||||||
\(445\) | −13.4798 | −0.639002 | ||||||||
\(446\) | −9.58727 | −0.453970 | ||||||||
\(447\) | −18.1889 | −0.860306 | ||||||||
\(448\) | 2.39039 | 0.112935 | ||||||||
\(449\) | 15.3450 | 0.724176 | 0.362088 | − | 0.932144i | \(-0.382064\pi\) | ||||
0.362088 | + | 0.932144i | \(0.382064\pi\) | |||||||
\(450\) | 62.0133 | 2.92333 | ||||||||
\(451\) | 1.59849 | 0.0752698 | ||||||||
\(452\) | −11.5383 | −0.542716 | ||||||||
\(453\) | 74.0942 | 3.48125 | ||||||||
\(454\) | −18.3617 | −0.861756 | ||||||||
\(455\) | 13.2676 | 0.621995 | ||||||||
\(456\) | −3.23056 | −0.151285 | ||||||||
\(457\) | −19.5714 | −0.915510 | −0.457755 | − | 0.889078i | \(-0.651346\pi\) | ||||
−0.457755 | + | 0.889078i | \(0.651346\pi\) | |||||||
\(458\) | 5.24337 | 0.245007 | ||||||||
\(459\) | −17.6985 | −0.826095 | ||||||||
\(460\) | 31.3811 | 1.46315 | ||||||||
\(461\) | −6.56806 | −0.305905 | −0.152953 | − | 0.988234i | \(-0.548878\pi\) | ||||
−0.152953 | + | 0.988234i | \(0.548878\pi\) | |||||||
\(462\) | −1.76954 | −0.0823266 | ||||||||
\(463\) | −30.7081 | −1.42713 | −0.713563 | − | 0.700591i | \(-0.752920\pi\) | ||||
−0.713563 | + | 0.700591i | \(0.752920\pi\) | |||||||
\(464\) | −2.80955 | −0.130430 | ||||||||
\(465\) | 48.3664 | 2.24294 | ||||||||
\(466\) | 2.53591 | 0.117474 | ||||||||
\(467\) | 13.3222 | 0.616480 | 0.308240 | − | 0.951309i | \(-0.400260\pi\) | ||||
0.308240 | + | 0.951309i | \(0.400260\pi\) | |||||||
\(468\) | −11.3014 | −0.522407 | ||||||||
\(469\) | −3.04942 | −0.140809 | ||||||||
\(470\) | −40.8918 | −1.88620 | ||||||||
\(471\) | 48.2469 | 2.22310 | ||||||||
\(472\) | 5.91884 | 0.272437 | ||||||||
\(473\) | −2.39990 | −0.110347 | ||||||||
\(474\) | −14.9840 | −0.688237 | ||||||||
\(475\) | 8.33901 | 0.382620 | ||||||||
\(476\) | 2.95178 | 0.135295 | ||||||||
\(477\) | 17.9829 | 0.823383 | ||||||||
\(478\) | −20.2316 | −0.925373 | ||||||||
\(479\) | 32.9788 | 1.50684 | 0.753420 | − | 0.657540i | \(-0.228403\pi\) | ||||
0.753420 | + | 0.657540i | \(0.228403\pi\) | |||||||
\(480\) | 11.7989 | 0.538542 | ||||||||
\(481\) | 11.6917 | 0.533096 | ||||||||
\(482\) | 1.33108 | 0.0606290 | ||||||||
\(483\) | 66.3520 | 3.01912 | ||||||||
\(484\) | −10.9475 | −0.497613 | ||||||||
\(485\) | −29.0175 | −1.31762 | ||||||||
\(486\) | −34.5114 | −1.56547 | ||||||||
\(487\) | 30.1843 | 1.36778 | 0.683891 | − | 0.729584i | \(-0.260286\pi\) | ||||
0.683891 | + | 0.729584i | \(0.260286\pi\) | |||||||
\(488\) | 5.03288 | 0.227828 | ||||||||
\(489\) | −31.3408 | −1.41728 | ||||||||
\(490\) | 4.69690 | 0.212184 | ||||||||
\(491\) | −5.62352 | −0.253786 | −0.126893 | − | 0.991916i | \(-0.540500\pi\) | ||||
−0.126893 | + | 0.991916i | \(0.540500\pi\) | |||||||
\(492\) | −22.5358 | −1.01599 | ||||||||
\(493\) | −3.46938 | −0.156253 | ||||||||
\(494\) | −1.51971 | −0.0683752 | ||||||||
\(495\) | −6.22366 | −0.279733 | ||||||||
\(496\) | 4.09925 | 0.184062 | ||||||||
\(497\) | 25.3067 | 1.13516 | ||||||||
\(498\) | −1.42567 | −0.0638856 | ||||||||
\(499\) | −7.32951 | −0.328114 | −0.164057 | − | 0.986451i | \(-0.552458\pi\) | ||||
−0.164057 | + | 0.986451i | \(0.552458\pi\) | |||||||
\(500\) | −12.1949 | −0.545374 | ||||||||
\(501\) | 50.4202 | 2.25261 | ||||||||
\(502\) | 30.4215 | 1.35778 | ||||||||
\(503\) | −43.4235 | −1.93616 | −0.968078 | − | 0.250649i | \(-0.919356\pi\) | ||||
−0.968078 | + | 0.250649i | \(0.919356\pi\) | |||||||
\(504\) | 17.7762 | 0.791816 | ||||||||
\(505\) | −56.1800 | −2.49998 | ||||||||
\(506\) | −1.96889 | −0.0875277 | ||||||||
\(507\) | 34.5362 | 1.53381 | ||||||||
\(508\) | 3.97747 | 0.176471 | ||||||||
\(509\) | −3.39862 | −0.150641 | −0.0753206 | − | 0.997159i | \(-0.523998\pi\) | ||||
−0.0753206 | + | 0.997159i | \(0.523998\pi\) | |||||||
\(510\) | 14.5698 | 0.645163 | ||||||||
\(511\) | −12.6911 | −0.561420 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −14.3325 | −0.632795 | ||||||||
\(514\) | 16.4111 | 0.723860 | ||||||||
\(515\) | −41.3841 | −1.82360 | ||||||||
\(516\) | 33.8343 | 1.48947 | ||||||||
\(517\) | 2.56560 | 0.112835 | ||||||||
\(518\) | −18.3902 | −0.808017 | ||||||||
\(519\) | 21.0734 | 0.925020 | ||||||||
\(520\) | 5.55039 | 0.243401 | ||||||||
\(521\) | −13.3063 | −0.582960 | −0.291480 | − | 0.956577i | \(-0.594148\pi\) | ||||
−0.291480 | + | 0.956577i | \(0.594148\pi\) | |||||||
\(522\) | −20.8933 | −0.914476 | ||||||||
\(523\) | 7.85981 | 0.343686 | 0.171843 | − | 0.985124i | \(-0.445028\pi\) | ||||
0.171843 | + | 0.985124i | \(0.445028\pi\) | |||||||
\(524\) | 12.8956 | 0.563346 | ||||||||
\(525\) | −64.3964 | −2.81049 | ||||||||
\(526\) | −5.15303 | −0.224683 | ||||||||
\(527\) | 5.06196 | 0.220503 | ||||||||
\(528\) | −0.740273 | −0.0322163 | ||||||||
\(529\) | 50.8267 | 2.20986 | ||||||||
\(530\) | −8.83186 | −0.383632 | ||||||||
\(531\) | 44.0156 | 1.91012 | ||||||||
\(532\) | 2.39039 | 0.103637 | ||||||||
\(533\) | −10.6013 | −0.459191 | ||||||||
\(534\) | −11.9234 | −0.515974 | ||||||||
\(535\) | 27.9774 | 1.20957 | ||||||||
\(536\) | −1.27570 | −0.0551018 | ||||||||
\(537\) | 19.4728 | 0.840311 | ||||||||
\(538\) | 4.03782 | 0.174083 | ||||||||
\(539\) | −0.294689 | −0.0126931 | ||||||||
\(540\) | 52.3460 | 2.25261 | ||||||||
\(541\) | −27.9735 | −1.20268 | −0.601338 | − | 0.798995i | \(-0.705366\pi\) | ||||
−0.601338 | + | 0.798995i | \(0.705366\pi\) | |||||||
\(542\) | −13.4426 | −0.577409 | ||||||||
\(543\) | −9.33549 | −0.400624 | ||||||||
\(544\) | 1.23485 | 0.0529438 | ||||||||
\(545\) | 13.5639 | 0.581013 | ||||||||
\(546\) | 11.7357 | 0.502242 | ||||||||
\(547\) | 37.5390 | 1.60505 | 0.802525 | − | 0.596618i | \(-0.203489\pi\) | ||||
0.802525 | + | 0.596618i | \(0.203489\pi\) | |||||||
\(548\) | 8.89558 | 0.380000 | ||||||||
\(549\) | 37.4272 | 1.59735 | ||||||||
\(550\) | 1.91086 | 0.0814793 | ||||||||
\(551\) | −2.80955 | −0.119691 | ||||||||
\(552\) | 27.7578 | 1.18145 | ||||||||
\(553\) | 11.0871 | 0.471472 | ||||||||
\(554\) | 11.7483 | 0.499139 | ||||||||
\(555\) | −90.7729 | −3.85309 | ||||||||
\(556\) | −18.2310 | −0.773168 | ||||||||
\(557\) | 17.5000 | 0.741498 | 0.370749 | − | 0.928733i | \(-0.379101\pi\) | ||||
0.370749 | + | 0.928733i | \(0.379101\pi\) | |||||||
\(558\) | 30.4842 | 1.29050 | ||||||||
\(559\) | 15.9163 | 0.673186 | ||||||||
\(560\) | −8.73034 | −0.368924 | ||||||||
\(561\) | −0.914128 | −0.0385945 | ||||||||
\(562\) | 14.9416 | 0.630273 | ||||||||
\(563\) | −41.3629 | −1.74324 | −0.871619 | − | 0.490183i | \(-0.836930\pi\) | ||||
−0.871619 | + | 0.490183i | \(0.836930\pi\) | |||||||
\(564\) | −36.1703 | −1.52304 | ||||||||
\(565\) | 42.1409 | 1.77288 | ||||||||
\(566\) | 1.92528 | 0.0809253 | ||||||||
\(567\) | 57.3512 | 2.40852 | ||||||||
\(568\) | 10.5869 | 0.444214 | ||||||||
\(569\) | 1.60985 | 0.0674882 | 0.0337441 | − | 0.999431i | \(-0.489257\pi\) | ||||
0.0337441 | + | 0.999431i | \(0.489257\pi\) | |||||||
\(570\) | 11.7989 | 0.494200 | ||||||||
\(571\) | −24.5836 | −1.02879 | −0.514396 | − | 0.857553i | \(-0.671984\pi\) | ||||
−0.514396 | + | 0.857553i | \(0.671984\pi\) | |||||||
\(572\) | −0.348238 | −0.0145606 | ||||||||
\(573\) | −22.1654 | −0.925972 | ||||||||
\(574\) | 16.6749 | 0.695999 | ||||||||
\(575\) | −71.6508 | −2.98805 | ||||||||
\(576\) | 7.43653 | 0.309855 | ||||||||
\(577\) | −9.27040 | −0.385932 | −0.192966 | − | 0.981205i | \(-0.561811\pi\) | ||||
−0.192966 | + | 0.981205i | \(0.561811\pi\) | |||||||
\(578\) | −15.4751 | −0.643681 | ||||||||
\(579\) | 4.03810 | 0.167818 | ||||||||
\(580\) | 10.2612 | 0.426074 | ||||||||
\(581\) | 1.05489 | 0.0437644 | ||||||||
\(582\) | −25.6670 | −1.06393 | ||||||||
\(583\) | 0.554121 | 0.0229493 | ||||||||
\(584\) | −5.30920 | −0.219696 | ||||||||
\(585\) | 41.2757 | 1.70654 | ||||||||
\(586\) | −31.4958 | −1.30108 | ||||||||
\(587\) | −18.0076 | −0.743252 | −0.371626 | − | 0.928383i | \(-0.621200\pi\) | ||||
−0.371626 | + | 0.928383i | \(0.621200\pi\) | |||||||
\(588\) | 4.15458 | 0.171332 | ||||||||
\(589\) | 4.09925 | 0.168907 | ||||||||
\(590\) | −21.6171 | −0.889964 | ||||||||
\(591\) | 1.26131 | 0.0518834 | ||||||||
\(592\) | −7.69336 | −0.316195 | ||||||||
\(593\) | −23.9198 | −0.982270 | −0.491135 | − | 0.871084i | \(-0.663418\pi\) | ||||
−0.491135 | + | 0.871084i | \(0.663418\pi\) | |||||||
\(594\) | −3.28424 | −0.134754 | ||||||||
\(595\) | −10.7807 | −0.441964 | ||||||||
\(596\) | 5.63027 | 0.230625 | ||||||||
\(597\) | 11.5218 | 0.471557 | ||||||||
\(598\) | 13.0578 | 0.533972 | ||||||||
\(599\) | −11.3110 | −0.462156 | −0.231078 | − | 0.972935i | \(-0.574225\pi\) | ||||
−0.231078 | + | 0.972935i | \(0.574225\pi\) | |||||||
\(600\) | −26.9397 | −1.09981 | ||||||||
\(601\) | 13.2639 | 0.541047 | 0.270524 | − | 0.962713i | \(-0.412803\pi\) | ||||
0.270524 | + | 0.962713i | \(0.412803\pi\) | |||||||
\(602\) | −25.0350 | −1.02035 | ||||||||
\(603\) | −9.48677 | −0.386331 | ||||||||
\(604\) | −22.9354 | −0.933228 | ||||||||
\(605\) | 39.9831 | 1.62554 | ||||||||
\(606\) | −49.6933 | −2.01865 | ||||||||
\(607\) | 0.994203 | 0.0403535 | 0.0201767 | − | 0.999796i | \(-0.493577\pi\) | ||||
0.0201767 | + | 0.999796i | \(0.493577\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 21.6962 | 0.879176 | ||||||||
\(610\) | −18.3814 | −0.744241 | ||||||||
\(611\) | −17.0152 | −0.688360 | ||||||||
\(612\) | 9.18301 | 0.371201 | ||||||||
\(613\) | −10.7488 | −0.434139 | −0.217069 | − | 0.976156i | \(-0.569650\pi\) | ||||
−0.217069 | + | 0.976156i | \(0.569650\pi\) | |||||||
\(614\) | 12.8647 | 0.519178 | ||||||||
\(615\) | 82.3067 | 3.31892 | ||||||||
\(616\) | 0.547751 | 0.0220695 | ||||||||
\(617\) | −37.3375 | −1.50315 | −0.751575 | − | 0.659647i | \(-0.770706\pi\) | ||||
−0.751575 | + | 0.659647i | \(0.770706\pi\) | |||||||
\(618\) | −36.6058 | −1.47250 | ||||||||
\(619\) | −29.9203 | −1.20260 | −0.601300 | − | 0.799023i | \(-0.705350\pi\) | ||||
−0.601300 | + | 0.799023i | \(0.705350\pi\) | |||||||
\(620\) | −14.9715 | −0.601271 | ||||||||
\(621\) | 123.148 | 4.94177 | ||||||||
\(622\) | −25.7290 | −1.03164 | ||||||||
\(623\) | 8.82246 | 0.353464 | ||||||||
\(624\) | 4.90953 | 0.196539 | ||||||||
\(625\) | 2.84404 | 0.113762 | ||||||||
\(626\) | −24.5398 | −0.980809 | ||||||||
\(627\) | −0.740273 | −0.0295637 | ||||||||
\(628\) | −14.9345 | −0.595953 | ||||||||
\(629\) | −9.50016 | −0.378796 | ||||||||
\(630\) | −64.9234 | −2.58661 | ||||||||
\(631\) | 8.60650 | 0.342619 | 0.171310 | − | 0.985217i | \(-0.445200\pi\) | ||||
0.171310 | + | 0.985217i | \(0.445200\pi\) | |||||||
\(632\) | 4.63819 | 0.184497 | ||||||||
\(633\) | 3.23056 | 0.128403 | ||||||||
\(634\) | 19.5030 | 0.774562 | ||||||||
\(635\) | −14.5267 | −0.576476 | ||||||||
\(636\) | −7.81211 | −0.309770 | ||||||||
\(637\) | 1.95439 | 0.0774358 | ||||||||
\(638\) | −0.643801 | −0.0254883 | ||||||||
\(639\) | 78.7294 | 3.11449 | ||||||||
\(640\) | −3.65226 | −0.144368 | ||||||||
\(641\) | −18.2571 | −0.721111 | −0.360556 | − | 0.932738i | \(-0.617413\pi\) | ||||
−0.360556 | + | 0.932738i | \(0.617413\pi\) | |||||||
\(642\) | 24.7471 | 0.976689 | ||||||||
\(643\) | −39.5014 | −1.55778 | −0.778892 | − | 0.627158i | \(-0.784218\pi\) | ||||
−0.778892 | + | 0.627158i | \(0.784218\pi\) | |||||||
\(644\) | −20.5388 | −0.809344 | ||||||||
\(645\) | −123.572 | −4.86563 | ||||||||
\(646\) | 1.23485 | 0.0485846 | ||||||||
\(647\) | −12.9526 | −0.509219 | −0.254609 | − | 0.967044i | \(-0.581947\pi\) | ||||
−0.254609 | + | 0.967044i | \(0.581947\pi\) | |||||||
\(648\) | 23.9924 | 0.942510 | ||||||||
\(649\) | 1.35628 | 0.0532388 | ||||||||
\(650\) | −12.6729 | −0.497073 | ||||||||
\(651\) | −31.6557 | −1.24068 | ||||||||
\(652\) | 9.70135 | 0.379934 | ||||||||
\(653\) | −30.0711 | −1.17677 | −0.588387 | − | 0.808579i | \(-0.700237\pi\) | ||||
−0.588387 | + | 0.808579i | \(0.700237\pi\) | |||||||
\(654\) | 11.9978 | 0.469150 | ||||||||
\(655\) | −47.0980 | −1.84027 | ||||||||
\(656\) | 6.97582 | 0.272360 | ||||||||
\(657\) | −39.4820 | −1.54034 | ||||||||
\(658\) | 26.7635 | 1.04335 | ||||||||
\(659\) | 0.699015 | 0.0272298 | 0.0136149 | − | 0.999907i | \(-0.495666\pi\) | ||||
0.0136149 | + | 0.999907i | \(0.495666\pi\) | |||||||
\(660\) | 2.70367 | 0.105240 | ||||||||
\(661\) | −18.0802 | −0.703239 | −0.351619 | − | 0.936143i | \(-0.614369\pi\) | ||||
−0.351619 | + | 0.936143i | \(0.614369\pi\) | |||||||
\(662\) | 8.66544 | 0.336792 | ||||||||
\(663\) | 6.06254 | 0.235450 | ||||||||
\(664\) | 0.441306 | 0.0171260 | ||||||||
\(665\) | −8.73034 | −0.338548 | ||||||||
\(666\) | −57.2119 | −2.21692 | ||||||||
\(667\) | 24.1404 | 0.934719 | ||||||||
\(668\) | −15.6073 | −0.603863 | ||||||||
\(669\) | 30.9723 | 1.19746 | ||||||||
\(670\) | 4.65919 | 0.180000 | ||||||||
\(671\) | 1.15327 | 0.0445215 | ||||||||
\(672\) | −7.72231 | −0.297895 | ||||||||
\(673\) | −21.9960 | −0.847885 | −0.423943 | − | 0.905689i | \(-0.639354\pi\) | ||||
−0.423943 | + | 0.905689i | \(0.639354\pi\) | |||||||
\(674\) | −14.4531 | −0.556711 | ||||||||
\(675\) | −119.519 | −4.60028 | ||||||||
\(676\) | −10.6905 | −0.411172 | ||||||||
\(677\) | 39.9127 | 1.53397 | 0.766985 | − | 0.641665i | \(-0.221756\pi\) | ||||
0.766985 | + | 0.641665i | \(0.221756\pi\) | |||||||
\(678\) | 37.2752 | 1.43154 | ||||||||
\(679\) | 18.9918 | 0.728839 | ||||||||
\(680\) | −4.51000 | −0.172951 | ||||||||
\(681\) | 59.3185 | 2.27309 | ||||||||
\(682\) | 0.939330 | 0.0359688 | ||||||||
\(683\) | 4.85952 | 0.185945 | 0.0929723 | − | 0.995669i | \(-0.470363\pi\) | ||||
0.0929723 | + | 0.995669i | \(0.470363\pi\) | |||||||
\(684\) | 7.43653 | 0.284343 | ||||||||
\(685\) | −32.4890 | −1.24134 | ||||||||
\(686\) | −19.8069 | −0.756229 | ||||||||
\(687\) | −16.9390 | −0.646265 | ||||||||
\(688\) | −10.4732 | −0.399287 | ||||||||
\(689\) | −3.67496 | −0.140005 | ||||||||
\(690\) | −101.379 | −3.85942 | ||||||||
\(691\) | −17.1704 | −0.653194 | −0.326597 | − | 0.945164i | \(-0.605902\pi\) | ||||
−0.326597 | + | 0.945164i | \(0.605902\pi\) | |||||||
\(692\) | −6.52314 | −0.247972 | ||||||||
\(693\) | 4.07337 | 0.154734 | ||||||||
\(694\) | −0.431535 | −0.0163808 | ||||||||
\(695\) | 66.5845 | 2.52569 | ||||||||
\(696\) | 9.07644 | 0.344041 | ||||||||
\(697\) | 8.61410 | 0.326282 | ||||||||
\(698\) | −5.76879 | −0.218352 | ||||||||
\(699\) | −8.19242 | −0.309866 | ||||||||
\(700\) | 19.9335 | 0.753416 | ||||||||
\(701\) | −40.5003 | −1.52968 | −0.764838 | − | 0.644223i | \(-0.777181\pi\) | ||||
−0.764838 | + | 0.644223i | \(0.777181\pi\) | |||||||
\(702\) | 21.7813 | 0.822081 | ||||||||
\(703\) | −7.69336 | −0.290161 | ||||||||
\(704\) | 0.229147 | 0.00863630 | ||||||||
\(705\) | 132.103 | 4.97530 | ||||||||
\(706\) | −16.3363 | −0.614825 | ||||||||
\(707\) | 36.7696 | 1.38286 | ||||||||
\(708\) | −19.1212 | −0.718618 | ||||||||
\(709\) | −6.78729 | −0.254902 | −0.127451 | − | 0.991845i | \(-0.540680\pi\) | ||||
−0.127451 | + | 0.991845i | \(0.540680\pi\) | |||||||
\(710\) | −38.6659 | −1.45111 | ||||||||
\(711\) | 34.4921 | 1.29355 | ||||||||
\(712\) | 3.69080 | 0.138319 | ||||||||
\(713\) | −35.2217 | −1.31906 | ||||||||
\(714\) | −9.53591 | −0.356872 | ||||||||
\(715\) | 1.27186 | 0.0475647 | ||||||||
\(716\) | −6.02767 | −0.225265 | ||||||||
\(717\) | 65.3595 | 2.44090 | ||||||||
\(718\) | 10.6597 | 0.397818 | ||||||||
\(719\) | −25.9395 | −0.967379 | −0.483690 | − | 0.875240i | \(-0.660704\pi\) | ||||
−0.483690 | + | 0.875240i | \(0.660704\pi\) | |||||||
\(720\) | −27.1601 | −1.01220 | ||||||||
\(721\) | 27.0858 | 1.00873 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −4.30013 | −0.159924 | ||||||||
\(724\) | 2.88974 | 0.107396 | ||||||||
\(725\) | −23.4289 | −0.870127 | ||||||||
\(726\) | 35.3665 | 1.31258 | ||||||||
\(727\) | 48.0383 | 1.78164 | 0.890821 | − | 0.454354i | \(-0.150130\pi\) | ||||
0.890821 | + | 0.454354i | \(0.150130\pi\) | |||||||
\(728\) | −3.63271 | −0.134637 | ||||||||
\(729\) | 39.5141 | 1.46349 | ||||||||
\(730\) | 19.3906 | 0.717677 | ||||||||
\(731\) | −12.9328 | −0.478338 | ||||||||
\(732\) | −16.2590 | −0.600951 | ||||||||
\(733\) | 38.1311 | 1.40840 | 0.704202 | − | 0.710000i | \(-0.251305\pi\) | ||||
0.704202 | + | 0.710000i | \(0.251305\pi\) | |||||||
\(734\) | −23.8708 | −0.881087 | ||||||||
\(735\) | −15.1736 | −0.559688 | ||||||||
\(736\) | −8.59225 | −0.316714 | ||||||||
\(737\) | −0.292322 | −0.0107678 | ||||||||
\(738\) | 51.8759 | 1.90958 | ||||||||
\(739\) | 30.5081 | 1.12226 | 0.561130 | − | 0.827728i | \(-0.310367\pi\) | ||||
0.561130 | + | 0.827728i | \(0.310367\pi\) | |||||||
\(740\) | 28.0982 | 1.03291 | ||||||||
\(741\) | 4.90953 | 0.180356 | ||||||||
\(742\) | 5.78042 | 0.212206 | ||||||||
\(743\) | 49.0897 | 1.80093 | 0.900464 | − | 0.434931i | \(-0.143227\pi\) | ||||
0.900464 | + | 0.434931i | \(0.143227\pi\) | |||||||
\(744\) | −13.2429 | −0.485507 | ||||||||
\(745\) | −20.5632 | −0.753377 | ||||||||
\(746\) | −27.5695 | −1.00939 | ||||||||
\(747\) | 3.28178 | 0.120074 | ||||||||
\(748\) | 0.282963 | 0.0103461 | ||||||||
\(749\) | −18.3111 | −0.669074 | ||||||||
\(750\) | 39.3965 | 1.43856 | ||||||||
\(751\) | −20.4439 | −0.746009 | −0.373004 | − | 0.927830i | \(-0.621672\pi\) | ||||
−0.373004 | + | 0.927830i | \(0.621672\pi\) | |||||||
\(752\) | 11.1963 | 0.408287 | ||||||||
\(753\) | −98.2784 | −3.58147 | ||||||||
\(754\) | 4.26972 | 0.155494 | ||||||||
\(755\) | 83.7661 | 3.04856 | ||||||||
\(756\) | −34.2603 | −1.24603 | ||||||||
\(757\) | −10.5719 | −0.384242 | −0.192121 | − | 0.981371i | \(-0.561537\pi\) | ||||
−0.192121 | + | 0.981371i | \(0.561537\pi\) | |||||||
\(758\) | 4.83139 | 0.175484 | ||||||||
\(759\) | 6.36061 | 0.230876 | ||||||||
\(760\) | −3.65226 | −0.132481 | ||||||||
\(761\) | −32.1882 | −1.16682 | −0.583410 | − | 0.812178i | \(-0.698282\pi\) | ||||
−0.583410 | + | 0.812178i | \(0.698282\pi\) | |||||||
\(762\) | −12.8494 | −0.465486 | ||||||||
\(763\) | −8.87752 | −0.321388 | ||||||||
\(764\) | 6.86116 | 0.248228 | ||||||||
\(765\) | −33.5388 | −1.21260 | ||||||||
\(766\) | 28.5696 | 1.03226 | ||||||||
\(767\) | −8.99495 | −0.324789 | ||||||||
\(768\) | −3.23056 | −0.116573 | ||||||||
\(769\) | −51.8063 | −1.86818 | −0.934092 | − | 0.357032i | \(-0.883789\pi\) | ||||
−0.934092 | + | 0.357032i | \(0.883789\pi\) | |||||||
\(770\) | −2.00053 | −0.0720941 | ||||||||
\(771\) | −53.0169 | −1.90936 | ||||||||
\(772\) | −1.24997 | −0.0449874 | ||||||||
\(773\) | 16.1272 | 0.580056 | 0.290028 | − | 0.957018i | \(-0.406335\pi\) | ||||
0.290028 | + | 0.957018i | \(0.406335\pi\) | |||||||
\(774\) | −77.8842 | −2.79949 | ||||||||
\(775\) | 34.1837 | 1.22791 | ||||||||
\(776\) | 7.94507 | 0.285211 | ||||||||
\(777\) | 59.4105 | 2.13134 | ||||||||
\(778\) | 17.6906 | 0.634238 | ||||||||
\(779\) | 6.97582 | 0.249935 | ||||||||
\(780\) | −17.9309 | −0.642029 | ||||||||
\(781\) | 2.42594 | 0.0868071 | ||||||||
\(782\) | −10.6102 | −0.379418 | ||||||||
\(783\) | 40.2679 | 1.43906 | ||||||||
\(784\) | −1.28603 | −0.0459295 | ||||||||
\(785\) | 54.5448 | 1.94679 | ||||||||
\(786\) | −41.6600 | −1.48596 | ||||||||
\(787\) | 6.45141 | 0.229968 | 0.114984 | − | 0.993367i | \(-0.463318\pi\) | ||||
0.114984 | + | 0.993367i | \(0.463318\pi\) | |||||||
\(788\) | −0.390431 | −0.0139085 | ||||||||
\(789\) | 16.6472 | 0.592655 | ||||||||
\(790\) | −16.9399 | −0.602695 | ||||||||
\(791\) | −27.5811 | −0.980669 | ||||||||
\(792\) | 1.70406 | 0.0605511 | ||||||||
\(793\) | −7.64854 | −0.271608 | ||||||||
\(794\) | −26.1741 | −0.928885 | ||||||||
\(795\) | 28.5319 | 1.01192 | ||||||||
\(796\) | −3.56651 | −0.126411 | ||||||||
\(797\) | 12.7652 | 0.452166 | 0.226083 | − | 0.974108i | \(-0.427408\pi\) | ||||
0.226083 | + | 0.974108i | \(0.427408\pi\) | |||||||
\(798\) | −7.72231 | −0.273367 | ||||||||
\(799\) | 13.8258 | 0.489120 | ||||||||
\(800\) | 8.33901 | 0.294829 | ||||||||
\(801\) | 27.4467 | 0.969783 | ||||||||
\(802\) | −39.1083 | −1.38096 | ||||||||
\(803\) | −1.21659 | −0.0429324 | ||||||||
\(804\) | 4.12122 | 0.145344 | ||||||||
\(805\) | 75.0132 | 2.64387 | ||||||||
\(806\) | −6.22968 | −0.219431 | ||||||||
\(807\) | −13.0444 | −0.459186 | ||||||||
\(808\) | 15.3822 | 0.541146 | ||||||||
\(809\) | −24.6877 | −0.867973 | −0.433986 | − | 0.900919i | \(-0.642893\pi\) | ||||
−0.433986 | + | 0.900919i | \(0.642893\pi\) | |||||||
\(810\) | −87.6264 | −3.07888 | ||||||||
\(811\) | −17.4948 | −0.614326 | −0.307163 | − | 0.951657i | \(-0.599380\pi\) | ||||
−0.307163 | + | 0.951657i | \(0.599380\pi\) | |||||||
\(812\) | −6.71593 | −0.235683 | ||||||||
\(813\) | 43.4271 | 1.52306 | ||||||||
\(814\) | −1.76291 | −0.0617900 | ||||||||
\(815\) | −35.4319 | −1.24112 | ||||||||
\(816\) | −3.98926 | −0.139652 | ||||||||
\(817\) | −10.4732 | −0.366411 | ||||||||
\(818\) | −30.0877 | −1.05199 | ||||||||
\(819\) | −27.0148 | −0.943973 | ||||||||
\(820\) | −25.4775 | −0.889713 | ||||||||
\(821\) | −51.4035 | −1.79400 | −0.896998 | − | 0.442035i | \(-0.854257\pi\) | ||||
−0.896998 | + | 0.442035i | \(0.854257\pi\) | |||||||
\(822\) | −28.7377 | −1.00234 | ||||||||
\(823\) | 23.3674 | 0.814537 | 0.407268 | − | 0.913308i | \(-0.366481\pi\) | ||||
0.407268 | + | 0.913308i | \(0.366481\pi\) | |||||||
\(824\) | 11.3311 | 0.394738 | ||||||||
\(825\) | −6.17315 | −0.214921 | ||||||||
\(826\) | 14.1483 | 0.492284 | ||||||||
\(827\) | 0.778285 | 0.0270636 | 0.0135318 | − | 0.999908i | \(-0.495693\pi\) | ||||
0.0135318 | + | 0.999908i | \(0.495693\pi\) | |||||||
\(828\) | −63.8965 | −2.22056 | ||||||||
\(829\) | −40.8249 | −1.41791 | −0.708954 | − | 0.705255i | \(-0.750832\pi\) | ||||
−0.708954 | + | 0.705255i | \(0.750832\pi\) | |||||||
\(830\) | −1.61176 | −0.0559451 | ||||||||
\(831\) | −37.9537 | −1.31660 | ||||||||
\(832\) | −1.51971 | −0.0526866 | ||||||||
\(833\) | −1.58805 | −0.0550227 | ||||||||
\(834\) | 58.8964 | 2.03942 | ||||||||
\(835\) | 57.0018 | 1.97263 | ||||||||
\(836\) | 0.229147 | 0.00792521 | ||||||||
\(837\) | −58.7524 | −2.03078 | ||||||||
\(838\) | −1.17310 | −0.0405242 | ||||||||
\(839\) | 19.6042 | 0.676813 | 0.338407 | − | 0.941000i | \(-0.390112\pi\) | ||||
0.338407 | + | 0.941000i | \(0.390112\pi\) | |||||||
\(840\) | 28.2039 | 0.973127 | ||||||||
\(841\) | −21.1064 | −0.727807 | ||||||||
\(842\) | 16.7829 | 0.578378 | ||||||||
\(843\) | −48.2697 | −1.66250 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 39.0444 | 1.34317 | ||||||||
\(846\) | 83.2616 | 2.86259 | ||||||||
\(847\) | −26.1688 | −0.899171 | ||||||||
\(848\) | 2.41819 | 0.0830410 | ||||||||
\(849\) | −6.21972 | −0.213460 | ||||||||
\(850\) | 10.2974 | 0.353199 | ||||||||
\(851\) | 66.1033 | 2.26599 | ||||||||
\(852\) | −34.2015 | −1.17172 | ||||||||
\(853\) | 36.3411 | 1.24429 | 0.622147 | − | 0.782900i | \(-0.286261\pi\) | ||||
0.622147 | + | 0.782900i | \(0.286261\pi\) | |||||||
\(854\) | 12.0306 | 0.411677 | ||||||||
\(855\) | −27.1601 | −0.928857 | ||||||||
\(856\) | −7.66030 | −0.261824 | ||||||||
\(857\) | −30.1884 | −1.03122 | −0.515609 | − | 0.856824i | \(-0.672434\pi\) | ||||
−0.515609 | + | 0.856824i | \(0.672434\pi\) | |||||||
\(858\) | 1.12500 | 0.0384070 | ||||||||
\(859\) | 47.8902 | 1.63399 | 0.816996 | − | 0.576643i | \(-0.195638\pi\) | ||||
0.816996 | + | 0.576643i | \(0.195638\pi\) | |||||||
\(860\) | 38.2508 | 1.30434 | ||||||||
\(861\) | −53.8694 | −1.83587 | ||||||||
\(862\) | −7.56515 | −0.257670 | ||||||||
\(863\) | −35.5990 | −1.21180 | −0.605901 | − | 0.795540i | \(-0.707187\pi\) | ||||
−0.605901 | + | 0.795540i | \(0.707187\pi\) | |||||||
\(864\) | −14.3325 | −0.487601 | ||||||||
\(865\) | 23.8242 | 0.810047 | ||||||||
\(866\) | 7.92605 | 0.269338 | ||||||||
\(867\) | 49.9934 | 1.69786 | ||||||||
\(868\) | 9.79881 | 0.332593 | ||||||||
\(869\) | 1.06283 | 0.0360540 | ||||||||
\(870\) | −33.1495 | −1.12387 | ||||||||
\(871\) | 1.93870 | 0.0656903 | ||||||||
\(872\) | −3.71384 | −0.125766 | ||||||||
\(873\) | 59.0837 | 1.99968 | ||||||||
\(874\) | −8.59225 | −0.290637 | ||||||||
\(875\) | −29.1507 | −0.985473 | ||||||||
\(876\) | 17.1517 | 0.579502 | ||||||||
\(877\) | −26.1504 | −0.883035 | −0.441518 | − | 0.897253i | \(-0.645560\pi\) | ||||
−0.441518 | + | 0.897253i | \(0.645560\pi\) | |||||||
\(878\) | 8.97895 | 0.303025 | ||||||||
\(879\) | 101.749 | 3.43191 | ||||||||
\(880\) | −0.836904 | −0.0282120 | ||||||||
\(881\) | 19.1848 | 0.646353 | 0.323176 | − | 0.946339i | \(-0.395249\pi\) | ||||
0.323176 | + | 0.946339i | \(0.395249\pi\) | |||||||
\(882\) | −9.56357 | −0.322022 | ||||||||
\(883\) | −17.2507 | −0.580532 | −0.290266 | − | 0.956946i | \(-0.593744\pi\) | ||||
−0.290266 | + | 0.956946i | \(0.593744\pi\) | |||||||
\(884\) | −1.87662 | −0.0631176 | ||||||||
\(885\) | 69.8355 | 2.34750 | ||||||||
\(886\) | 31.4899 | 1.05792 | ||||||||
\(887\) | 18.2485 | 0.612726 | 0.306363 | − | 0.951915i | \(-0.400888\pi\) | ||||
0.306363 | + | 0.951915i | \(0.400888\pi\) | |||||||
\(888\) | 24.8539 | 0.834042 | ||||||||
\(889\) | 9.50770 | 0.318878 | ||||||||
\(890\) | −13.4798 | −0.451843 | ||||||||
\(891\) | 5.49778 | 0.184183 | ||||||||
\(892\) | −9.58727 | −0.321006 | ||||||||
\(893\) | 11.1963 | 0.374670 | ||||||||
\(894\) | −18.1889 | −0.608328 | ||||||||
\(895\) | 22.0146 | 0.735867 | ||||||||
\(896\) | 2.39039 | 0.0798574 | ||||||||
\(897\) | −42.1839 | −1.40848 | ||||||||
\(898\) | 15.3450 | 0.512070 | ||||||||
\(899\) | −11.5171 | −0.384115 | ||||||||
\(900\) | 62.0133 | 2.06711 | ||||||||
\(901\) | 2.98611 | 0.0994816 | ||||||||
\(902\) | 1.59849 | 0.0532238 | ||||||||
\(903\) | 80.8772 | 2.69143 | ||||||||
\(904\) | −11.5383 | −0.383758 | ||||||||
\(905\) | −10.5541 | −0.350830 | ||||||||
\(906\) | 74.0942 | 2.46162 | ||||||||
\(907\) | −36.7014 | −1.21865 | −0.609325 | − | 0.792920i | \(-0.708560\pi\) | ||||
−0.609325 | + | 0.792920i | \(0.708560\pi\) | |||||||
\(908\) | −18.3617 | −0.609354 | ||||||||
\(909\) | 114.391 | 3.79409 | ||||||||
\(910\) | 13.2676 | 0.439817 | ||||||||
\(911\) | 56.9332 | 1.88628 | 0.943141 | − | 0.332392i | \(-0.107856\pi\) | ||||
0.943141 | + | 0.332392i | \(0.107856\pi\) | |||||||
\(912\) | −3.23056 | −0.106975 | ||||||||
\(913\) | 0.101124 | 0.00334671 | ||||||||
\(914\) | −19.5714 | −0.647363 | ||||||||
\(915\) | 59.3822 | 1.96312 | ||||||||
\(916\) | 5.24337 | 0.173246 | ||||||||
\(917\) | 30.8255 | 1.01795 | ||||||||
\(918\) | −17.6985 | −0.584137 | ||||||||
\(919\) | −10.3542 | −0.341555 | −0.170777 | − | 0.985310i | \(-0.554628\pi\) | ||||
−0.170777 | + | 0.985310i | \(0.554628\pi\) | |||||||
\(920\) | 31.3811 | 1.03461 | ||||||||
\(921\) | −41.5603 | −1.36946 | ||||||||
\(922\) | −6.56806 | −0.216308 | ||||||||
\(923\) | −16.0890 | −0.529576 | ||||||||
\(924\) | −1.76954 | −0.0582137 | ||||||||
\(925\) | −64.1550 | −2.10940 | ||||||||
\(926\) | −30.7081 | −1.00913 | ||||||||
\(927\) | 84.2640 | 2.76759 | ||||||||
\(928\) | −2.80955 | −0.0922281 | ||||||||
\(929\) | 47.3203 | 1.55253 | 0.776265 | − | 0.630407i | \(-0.217112\pi\) | ||||
0.776265 | + | 0.630407i | \(0.217112\pi\) | |||||||
\(930\) | 48.3664 | 1.58600 | ||||||||
\(931\) | −1.28603 | −0.0421478 | ||||||||
\(932\) | 2.53591 | 0.0830666 | ||||||||
\(933\) | 83.1191 | 2.72120 | ||||||||
\(934\) | 13.3222 | 0.435917 | ||||||||
\(935\) | −1.03345 | −0.0337975 | ||||||||
\(936\) | −11.3014 | −0.369398 | ||||||||
\(937\) | 49.3905 | 1.61352 | 0.806759 | − | 0.590880i | \(-0.201219\pi\) | ||||
0.806759 | + | 0.590880i | \(0.201219\pi\) | |||||||
\(938\) | −3.04942 | −0.0995671 | ||||||||
\(939\) | 79.2774 | 2.58712 | ||||||||
\(940\) | −40.8918 | −1.33374 | ||||||||
\(941\) | −45.4484 | −1.48157 | −0.740787 | − | 0.671740i | \(-0.765547\pi\) | ||||
−0.740787 | + | 0.671740i | \(0.765547\pi\) | |||||||
\(942\) | 48.2469 | 1.57197 | ||||||||
\(943\) | −59.9379 | −1.95185 | ||||||||
\(944\) | 5.91884 | 0.192642 | ||||||||
\(945\) | 125.127 | 4.07039 | ||||||||
\(946\) | −2.39990 | −0.0780275 | ||||||||
\(947\) | −20.7896 | −0.675572 | −0.337786 | − | 0.941223i | \(-0.609678\pi\) | ||||
−0.337786 | + | 0.941223i | \(0.609678\pi\) | |||||||
\(948\) | −14.9840 | −0.486657 | ||||||||
\(949\) | 8.06846 | 0.261913 | ||||||||
\(950\) | 8.33901 | 0.270553 | ||||||||
\(951\) | −63.0055 | −2.04309 | ||||||||
\(952\) | 2.95178 | 0.0956677 | ||||||||
\(953\) | −20.4516 | −0.662492 | −0.331246 | − | 0.943545i | \(-0.607469\pi\) | ||||
−0.331246 | + | 0.943545i | \(0.607469\pi\) | |||||||
\(954\) | 17.9829 | 0.582219 | ||||||||
\(955\) | −25.0587 | −0.810882 | ||||||||
\(956\) | −20.2316 | −0.654338 | ||||||||
\(957\) | 2.07984 | 0.0672316 | ||||||||
\(958\) | 32.9788 | 1.06550 | ||||||||
\(959\) | 21.2639 | 0.686648 | ||||||||
\(960\) | 11.7989 | 0.380806 | ||||||||
\(961\) | −14.1962 | −0.457941 | ||||||||
\(962\) | 11.6917 | 0.376956 | ||||||||
\(963\) | −56.9661 | −1.83571 | ||||||||
\(964\) | 1.33108 | 0.0428712 | ||||||||
\(965\) | 4.56521 | 0.146959 | ||||||||
\(966\) | 66.3520 | 2.13484 | ||||||||
\(967\) | −14.1009 | −0.453453 | −0.226727 | − | 0.973958i | \(-0.572802\pi\) | ||||
−0.226727 | + | 0.973958i | \(0.572802\pi\) | |||||||
\(968\) | −10.9475 | −0.351866 | ||||||||
\(969\) | −3.98926 | −0.128154 | ||||||||
\(970\) | −29.0175 | −0.931695 | ||||||||
\(971\) | −47.7636 | −1.53281 | −0.766404 | − | 0.642359i | \(-0.777956\pi\) | ||||
−0.766404 | + | 0.642359i | \(0.777956\pi\) | |||||||
\(972\) | −34.5114 | −1.10695 | ||||||||
\(973\) | −43.5793 | −1.39709 | ||||||||
\(974\) | 30.1843 | 0.967168 | ||||||||
\(975\) | 40.9406 | 1.31115 | ||||||||
\(976\) | 5.03288 | 0.161099 | ||||||||
\(977\) | −29.6642 | −0.949041 | −0.474520 | − | 0.880245i | \(-0.657378\pi\) | ||||
−0.474520 | + | 0.880245i | \(0.657378\pi\) | |||||||
\(978\) | −31.3408 | −1.00217 | ||||||||
\(979\) | 0.845736 | 0.0270298 | ||||||||
\(980\) | 4.69690 | 0.150037 | ||||||||
\(981\) | −27.6180 | −0.881776 | ||||||||
\(982\) | −5.62352 | −0.179454 | ||||||||
\(983\) | 37.5964 | 1.19914 | 0.599569 | − | 0.800323i | \(-0.295339\pi\) | ||||
0.599569 | + | 0.800323i | \(0.295339\pi\) | |||||||
\(984\) | −22.5358 | −0.718415 | ||||||||
\(985\) | 1.42596 | 0.0454348 | ||||||||
\(986\) | −3.46938 | −0.110488 | ||||||||
\(987\) | −86.4612 | −2.75209 | ||||||||
\(988\) | −1.51971 | −0.0483486 | ||||||||
\(989\) | 89.9882 | 2.86146 | ||||||||
\(990\) | −6.22366 | −0.197801 | ||||||||
\(991\) | 55.2980 | 1.75660 | 0.878300 | − | 0.478110i | \(-0.158678\pi\) | ||||
0.878300 | + | 0.478110i | \(0.158678\pi\) | |||||||
\(992\) | 4.09925 | 0.130151 | ||||||||
\(993\) | −27.9942 | −0.888370 | ||||||||
\(994\) | 25.3067 | 0.802681 | ||||||||
\(995\) | 13.0258 | 0.412946 | ||||||||
\(996\) | −1.42567 | −0.0451739 | ||||||||
\(997\) | −41.9755 | −1.32938 | −0.664689 | − | 0.747120i | \(-0.731436\pi\) | ||||
−0.664689 | + | 0.747120i | \(0.731436\pi\) | |||||||
\(998\) | −7.32951 | −0.232012 | ||||||||
\(999\) | 110.265 | 3.48863 |
(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 | 8018.2.a.d.1.1 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.1 | ✓ | 30 | 1.1 | even | 1 | trivial |