Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54449 | −1.79922 | −0.899612 | − | 0.436690i | \(-0.856151\pi\) | ||||
−0.899612 | + | 0.436690i | \(0.856151\pi\) | |||||||
\(3\) | −2.75216 | −1.58896 | −0.794481 | − | 0.607288i | \(-0.792257\pi\) | ||||
−0.794481 | + | 0.607288i | \(0.792257\pi\) | |||||||
\(4\) | 4.47442 | 2.23721 | ||||||||
\(5\) | −0.0821866 | −0.0367550 | −0.0183775 | − | 0.999831i | \(-0.505850\pi\) | ||||
−0.0183775 | + | 0.999831i | \(0.505850\pi\) | |||||||
\(6\) | 7.00285 | 2.85890 | ||||||||
\(7\) | −2.51361 | −0.950056 | −0.475028 | − | 0.879971i | \(-0.657562\pi\) | ||||
−0.475028 | + | 0.879971i | \(0.657562\pi\) | |||||||
\(8\) | −6.29612 | −2.22601 | ||||||||
\(9\) | 4.57441 | 1.52480 | ||||||||
\(10\) | 0.209123 | 0.0661304 | ||||||||
\(11\) | −4.33563 | −1.30724 | −0.653621 | − | 0.756822i | \(-0.726751\pi\) | ||||
−0.653621 | + | 0.756822i | \(0.726751\pi\) | |||||||
\(12\) | −12.3143 | −3.55484 | ||||||||
\(13\) | −6.03114 | −1.67274 | −0.836369 | − | 0.548166i | \(-0.815326\pi\) | ||||
−0.836369 | + | 0.548166i | \(0.815326\pi\) | |||||||
\(14\) | 6.39585 | 1.70936 | ||||||||
\(15\) | 0.226191 | 0.0584023 | ||||||||
\(16\) | 7.07156 | 1.76789 | ||||||||
\(17\) | −4.63559 | −1.12429 | −0.562147 | − | 0.827037i | \(-0.690025\pi\) | ||||
−0.562147 | + | 0.827037i | \(0.690025\pi\) | |||||||
\(18\) | −11.6395 | −2.74346 | ||||||||
\(19\) | 1.23205 | 0.282652 | 0.141326 | − | 0.989963i | \(-0.454863\pi\) | ||||
0.141326 | + | 0.989963i | \(0.454863\pi\) | |||||||
\(20\) | −0.367737 | −0.0822285 | ||||||||
\(21\) | 6.91787 | 1.50960 | ||||||||
\(22\) | 11.0320 | 2.35202 | ||||||||
\(23\) | −8.79311 | −1.83349 | −0.916745 | − | 0.399473i | \(-0.869193\pi\) | ||||
−0.916745 | + | 0.399473i | \(0.869193\pi\) | |||||||
\(24\) | 17.3280 | 3.53705 | ||||||||
\(25\) | −4.99325 | −0.998649 | ||||||||
\(26\) | 15.3462 | 3.00963 | ||||||||
\(27\) | −4.33303 | −0.833893 | ||||||||
\(28\) | −11.2469 | −2.12547 | ||||||||
\(29\) | −3.61276 | −0.670873 | −0.335436 | − | 0.942063i | \(-0.608884\pi\) | ||||
−0.335436 | + | 0.942063i | \(0.608884\pi\) | |||||||
\(30\) | −0.575540 | −0.105079 | ||||||||
\(31\) | −6.33205 | −1.13727 | −0.568635 | − | 0.822590i | \(-0.692528\pi\) | ||||
−0.568635 | + | 0.822590i | \(0.692528\pi\) | |||||||
\(32\) | −5.40126 | −0.954817 | ||||||||
\(33\) | 11.9324 | 2.07716 | ||||||||
\(34\) | 11.7952 | 2.02286 | ||||||||
\(35\) | 0.206585 | 0.0349193 | ||||||||
\(36\) | 20.4678 | 3.41130 | ||||||||
\(37\) | 2.98659 | 0.490992 | 0.245496 | − | 0.969398i | \(-0.421049\pi\) | ||||
0.245496 | + | 0.969398i | \(0.421049\pi\) | |||||||
\(38\) | −3.13494 | −0.508555 | ||||||||
\(39\) | 16.5987 | 2.65792 | ||||||||
\(40\) | 0.517457 | 0.0818171 | ||||||||
\(41\) | 11.0158 | 1.72038 | 0.860189 | − | 0.509976i | \(-0.170346\pi\) | ||||
0.860189 | + | 0.509976i | \(0.170346\pi\) | |||||||
\(42\) | −17.6024 | −2.71612 | ||||||||
\(43\) | −0.747991 | −0.114068 | −0.0570338 | − | 0.998372i | \(-0.518164\pi\) | ||||
−0.0570338 | + | 0.998372i | \(0.518164\pi\) | |||||||
\(44\) | −19.3994 | −2.92457 | ||||||||
\(45\) | −0.375955 | −0.0560441 | ||||||||
\(46\) | 22.3740 | 3.29886 | ||||||||
\(47\) | 4.74881 | 0.692685 | 0.346343 | − | 0.938108i | \(-0.387424\pi\) | ||||
0.346343 | + | 0.938108i | \(0.387424\pi\) | |||||||
\(48\) | −19.4621 | −2.80911 | ||||||||
\(49\) | −0.681756 | −0.0973937 | ||||||||
\(50\) | 12.7052 | 1.79679 | ||||||||
\(51\) | 12.7579 | 1.78646 | ||||||||
\(52\) | −26.9858 | −3.74226 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 11.0254 | 1.50036 | ||||||||
\(55\) | 0.356331 | 0.0480476 | ||||||||
\(56\) | 15.8260 | 2.11484 | ||||||||
\(57\) | −3.39081 | −0.449124 | ||||||||
\(58\) | 9.19262 | 1.20705 | ||||||||
\(59\) | 15.0256 | 1.95617 | 0.978086 | − | 0.208203i | \(-0.0667616\pi\) | ||||
0.978086 | + | 0.208203i | \(0.0667616\pi\) | |||||||
\(60\) | 1.01207 | 0.130658 | ||||||||
\(61\) | −8.06472 | −1.03258 | −0.516291 | − | 0.856413i | \(-0.672688\pi\) | ||||
−0.516291 | + | 0.856413i | \(0.672688\pi\) | |||||||
\(62\) | 16.1118 | 2.04620 | ||||||||
\(63\) | −11.4983 | −1.44865 | ||||||||
\(64\) | −0.399679 | −0.0499599 | ||||||||
\(65\) | 0.495679 | 0.0614814 | ||||||||
\(66\) | −30.3618 | −3.73728 | ||||||||
\(67\) | 1.53748 | 0.187833 | 0.0939166 | − | 0.995580i | \(-0.470061\pi\) | ||||
0.0939166 | + | 0.995580i | \(0.470061\pi\) | |||||||
\(68\) | −20.7415 | −2.51528 | ||||||||
\(69\) | 24.2001 | 2.91335 | ||||||||
\(70\) | −0.525653 | −0.0628276 | ||||||||
\(71\) | 10.6166 | 1.25996 | 0.629978 | − | 0.776613i | \(-0.283064\pi\) | ||||
0.629978 | + | 0.776613i | \(0.283064\pi\) | |||||||
\(72\) | −28.8010 | −3.39423 | ||||||||
\(73\) | 0.140557 | 0.0164510 | 0.00822550 | − | 0.999966i | \(-0.497382\pi\) | ||||
0.00822550 | + | 0.999966i | \(0.497382\pi\) | |||||||
\(74\) | −7.59933 | −0.883404 | ||||||||
\(75\) | 13.7422 | 1.58682 | ||||||||
\(76\) | 5.51272 | 0.632352 | ||||||||
\(77\) | 10.8981 | 1.24195 | ||||||||
\(78\) | −42.2352 | −4.78219 | ||||||||
\(79\) | 9.74079 | 1.09592 | 0.547962 | − | 0.836503i | \(-0.315404\pi\) | ||||
0.547962 | + | 0.836503i | \(0.315404\pi\) | |||||||
\(80\) | −0.581188 | −0.0649788 | ||||||||
\(81\) | −1.79800 | −0.199778 | ||||||||
\(82\) | −28.0295 | −3.09535 | ||||||||
\(83\) | 7.93714 | 0.871214 | 0.435607 | − | 0.900137i | \(-0.356534\pi\) | ||||
0.435607 | + | 0.900137i | \(0.356534\pi\) | |||||||
\(84\) | 30.9534 | 3.37730 | ||||||||
\(85\) | 0.380983 | 0.0413234 | ||||||||
\(86\) | 1.90325 | 0.205233 | ||||||||
\(87\) | 9.94291 | 1.06599 | ||||||||
\(88\) | 27.2977 | 2.90994 | ||||||||
\(89\) | −1.05875 | −0.112228 | −0.0561138 | − | 0.998424i | \(-0.517871\pi\) | ||||
−0.0561138 | + | 0.998424i | \(0.517871\pi\) | |||||||
\(90\) | 0.956613 | 0.100836 | ||||||||
\(91\) | 15.1600 | 1.58920 | ||||||||
\(92\) | −39.3440 | −4.10190 | ||||||||
\(93\) | 17.4268 | 1.80708 | ||||||||
\(94\) | −12.0833 | −1.24630 | ||||||||
\(95\) | −0.101258 | −0.0103889 | ||||||||
\(96\) | 14.8652 | 1.51717 | ||||||||
\(97\) | 8.11423 | 0.823875 | 0.411938 | − | 0.911212i | \(-0.364852\pi\) | ||||
0.411938 | + | 0.911212i | \(0.364852\pi\) | |||||||
\(98\) | 1.73472 | 0.175233 | ||||||||
\(99\) | −19.8330 | −1.99329 | ||||||||
\(100\) | −22.3419 | −2.23419 | ||||||||
\(101\) | −2.76688 | −0.275315 | −0.137658 | − | 0.990480i | \(-0.543957\pi\) | ||||
−0.137658 | + | 0.990480i | \(0.543957\pi\) | |||||||
\(102\) | −32.4623 | −3.21425 | ||||||||
\(103\) | 12.4584 | 1.22756 | 0.613782 | − | 0.789475i | \(-0.289647\pi\) | ||||
0.613782 | + | 0.789475i | \(0.289647\pi\) | |||||||
\(104\) | 37.9728 | 3.72354 | ||||||||
\(105\) | −0.568556 | −0.0554854 | ||||||||
\(106\) | 2.54449 | 0.247142 | ||||||||
\(107\) | −9.01422 | −0.871437 | −0.435719 | − | 0.900083i | \(-0.643506\pi\) | ||||
−0.435719 | + | 0.900083i | \(0.643506\pi\) | |||||||
\(108\) | −19.3878 | −1.86559 | ||||||||
\(109\) | 0.0571811 | 0.00547696 | 0.00273848 | − | 0.999996i | \(-0.499128\pi\) | ||||
0.00273848 | + | 0.999996i | \(0.499128\pi\) | |||||||
\(110\) | −0.906679 | −0.0864485 | ||||||||
\(111\) | −8.21958 | −0.780168 | ||||||||
\(112\) | −17.7752 | −1.67959 | ||||||||
\(113\) | −3.77611 | −0.355226 | −0.177613 | − | 0.984100i | \(-0.556838\pi\) | ||||
−0.177613 | + | 0.984100i | \(0.556838\pi\) | |||||||
\(114\) | 8.62788 | 0.808075 | ||||||||
\(115\) | 0.722676 | 0.0673899 | ||||||||
\(116\) | −16.1650 | −1.50088 | ||||||||
\(117\) | −27.5889 | −2.55060 | ||||||||
\(118\) | −38.2325 | −3.51959 | ||||||||
\(119\) | 11.6521 | 1.06814 | ||||||||
\(120\) | −1.42413 | −0.130004 | ||||||||
\(121\) | 7.79771 | 0.708882 | ||||||||
\(122\) | 20.5206 | 1.85785 | ||||||||
\(123\) | −30.3173 | −2.73362 | ||||||||
\(124\) | −28.3322 | −2.54431 | ||||||||
\(125\) | 0.821311 | 0.0734603 | ||||||||
\(126\) | 29.2573 | 2.60644 | ||||||||
\(127\) | −18.1415 | −1.60979 | −0.804897 | − | 0.593414i | \(-0.797780\pi\) | ||||
−0.804897 | + | 0.593414i | \(0.797780\pi\) | |||||||
\(128\) | 11.8195 | 1.04471 | ||||||||
\(129\) | 2.05859 | 0.181249 | ||||||||
\(130\) | −1.26125 | −0.110619 | ||||||||
\(131\) | 10.4895 | 0.916469 | 0.458234 | − | 0.888831i | \(-0.348482\pi\) | ||||
0.458234 | + | 0.888831i | \(0.348482\pi\) | |||||||
\(132\) | 53.3904 | 4.64704 | ||||||||
\(133\) | −3.09690 | −0.268535 | ||||||||
\(134\) | −3.91210 | −0.337954 | ||||||||
\(135\) | 0.356117 | 0.0306497 | ||||||||
\(136\) | 29.1862 | 2.50270 | ||||||||
\(137\) | 10.0206 | 0.856116 | 0.428058 | − | 0.903751i | \(-0.359198\pi\) | ||||
0.428058 | + | 0.903751i | \(0.359198\pi\) | |||||||
\(138\) | −61.5768 | −5.24177 | ||||||||
\(139\) | −1.80560 | −0.153149 | −0.0765745 | − | 0.997064i | \(-0.524398\pi\) | ||||
−0.0765745 | + | 0.997064i | \(0.524398\pi\) | |||||||
\(140\) | 0.924348 | 0.0781217 | ||||||||
\(141\) | −13.0695 | −1.10065 | ||||||||
\(142\) | −27.0138 | −2.26694 | ||||||||
\(143\) | 26.1488 | 2.18667 | ||||||||
\(144\) | 32.3482 | 2.69569 | ||||||||
\(145\) | 0.296921 | 0.0246579 | ||||||||
\(146\) | −0.357647 | −0.0295990 | ||||||||
\(147\) | 1.87631 | 0.154755 | ||||||||
\(148\) | 13.3632 | 1.09845 | ||||||||
\(149\) | −11.5656 | −0.947494 | −0.473747 | − | 0.880661i | \(-0.657099\pi\) | ||||
−0.473747 | + | 0.880661i | \(0.657099\pi\) | |||||||
\(150\) | −34.9669 | −2.85504 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | −7.75715 | −0.629188 | ||||||||
\(153\) | −21.2051 | −1.71433 | ||||||||
\(154\) | −27.7301 | −2.23455 | ||||||||
\(155\) | 0.520410 | 0.0418003 | ||||||||
\(156\) | 74.2695 | 5.94632 | ||||||||
\(157\) | −21.3893 | −1.70705 | −0.853525 | − | 0.521052i | \(-0.825540\pi\) | ||||
−0.853525 | + | 0.521052i | \(0.825540\pi\) | |||||||
\(158\) | −24.7853 | −1.97181 | ||||||||
\(159\) | 2.75216 | 0.218261 | ||||||||
\(160\) | 0.443911 | 0.0350943 | ||||||||
\(161\) | 22.1025 | 1.74192 | ||||||||
\(162\) | 4.57500 | 0.359446 | ||||||||
\(163\) | −6.07776 | −0.476047 | −0.238023 | − | 0.971259i | \(-0.576499\pi\) | ||||
−0.238023 | + | 0.971259i | \(0.576499\pi\) | |||||||
\(164\) | 49.2892 | 3.84884 | ||||||||
\(165\) | −0.980681 | −0.0763459 | ||||||||
\(166\) | −20.1960 | −1.56751 | ||||||||
\(167\) | 5.43525 | 0.420592 | 0.210296 | − | 0.977638i | \(-0.432557\pi\) | ||||
0.210296 | + | 0.977638i | \(0.432557\pi\) | |||||||
\(168\) | −43.5557 | −3.36040 | ||||||||
\(169\) | 23.3747 | 1.79805 | ||||||||
\(170\) | −0.969406 | −0.0743501 | ||||||||
\(171\) | 5.63591 | 0.430989 | ||||||||
\(172\) | −3.34682 | −0.255193 | ||||||||
\(173\) | −12.0989 | −0.919864 | −0.459932 | − | 0.887954i | \(-0.652126\pi\) | ||||
−0.459932 | + | 0.887954i | \(0.652126\pi\) | |||||||
\(174\) | −25.2996 | −1.91796 | ||||||||
\(175\) | 12.5511 | 0.948772 | ||||||||
\(176\) | −30.6597 | −2.31106 | ||||||||
\(177\) | −41.3530 | −3.10828 | ||||||||
\(178\) | 2.69398 | 0.201922 | ||||||||
\(179\) | −12.9739 | −0.969713 | −0.484856 | − | 0.874594i | \(-0.661128\pi\) | ||||
−0.484856 | + | 0.874594i | \(0.661128\pi\) | |||||||
\(180\) | −1.68218 | −0.125382 | ||||||||
\(181\) | 1.53497 | 0.114093 | 0.0570466 | − | 0.998372i | \(-0.481832\pi\) | ||||
0.0570466 | + | 0.998372i | \(0.481832\pi\) | |||||||
\(182\) | −38.5743 | −2.85932 | ||||||||
\(183\) | 22.1955 | 1.64073 | ||||||||
\(184\) | 55.3625 | 4.08137 | ||||||||
\(185\) | −0.245457 | −0.0180464 | ||||||||
\(186\) | −44.3424 | −3.25134 | ||||||||
\(187\) | 20.0982 | 1.46973 | ||||||||
\(188\) | 21.2481 | 1.54968 | ||||||||
\(189\) | 10.8916 | 0.792245 | ||||||||
\(190\) | 0.257650 | 0.0186919 | ||||||||
\(191\) | −10.0634 | −0.728159 | −0.364079 | − | 0.931368i | \(-0.618616\pi\) | ||||
−0.364079 | + | 0.931368i | \(0.618616\pi\) | |||||||
\(192\) | 1.09998 | 0.0793844 | ||||||||
\(193\) | 1.53965 | 0.110827 | 0.0554133 | − | 0.998464i | \(-0.482352\pi\) | ||||
0.0554133 | + | 0.998464i | \(0.482352\pi\) | |||||||
\(194\) | −20.6466 | −1.48234 | ||||||||
\(195\) | −1.36419 | −0.0976917 | ||||||||
\(196\) | −3.05046 | −0.217890 | ||||||||
\(197\) | 21.5930 | 1.53843 | 0.769217 | − | 0.638987i | \(-0.220646\pi\) | ||||
0.769217 | + | 0.638987i | \(0.220646\pi\) | |||||||
\(198\) | 50.4647 | 3.58637 | ||||||||
\(199\) | 9.94310 | 0.704847 | 0.352424 | − | 0.935841i | \(-0.385358\pi\) | ||||
0.352424 | + | 0.935841i | \(0.385358\pi\) | |||||||
\(200\) | 31.4381 | 2.22301 | ||||||||
\(201\) | −4.23140 | −0.298460 | ||||||||
\(202\) | 7.04030 | 0.495354 | ||||||||
\(203\) | 9.08108 | 0.637367 | ||||||||
\(204\) | 57.0841 | 3.99669 | ||||||||
\(205\) | −0.905350 | −0.0632324 | ||||||||
\(206\) | −31.7003 | −2.20866 | ||||||||
\(207\) | −40.2233 | −2.79571 | ||||||||
\(208\) | −42.6496 | −2.95722 | ||||||||
\(209\) | −5.34173 | −0.369495 | ||||||||
\(210\) | 1.44668 | 0.0998307 | ||||||||
\(211\) | 12.5417 | 0.863404 | 0.431702 | − | 0.902016i | \(-0.357913\pi\) | ||||
0.431702 | + | 0.902016i | \(0.357913\pi\) | |||||||
\(212\) | −4.47442 | −0.307304 | ||||||||
\(213\) | −29.2186 | −2.00202 | ||||||||
\(214\) | 22.9366 | 1.56791 | ||||||||
\(215\) | 0.0614748 | 0.00419255 | ||||||||
\(216\) | 27.2813 | 1.85626 | ||||||||
\(217\) | 15.9163 | 1.08047 | ||||||||
\(218\) | −0.145497 | −0.00985428 | ||||||||
\(219\) | −0.386837 | −0.0261400 | ||||||||
\(220\) | 1.59437 | 0.107493 | ||||||||
\(221\) | 27.9579 | 1.88065 | ||||||||
\(222\) | 20.9146 | 1.40370 | ||||||||
\(223\) | −0.124446 | −0.00833353 | −0.00416677 | − | 0.999991i | \(-0.501326\pi\) | ||||
−0.00416677 | + | 0.999991i | \(0.501326\pi\) | |||||||
\(224\) | 13.5767 | 0.907130 | ||||||||
\(225\) | −22.8412 | −1.52274 | ||||||||
\(226\) | 9.60825 | 0.639131 | ||||||||
\(227\) | 12.9103 | 0.856888 | 0.428444 | − | 0.903568i | \(-0.359062\pi\) | ||||
0.428444 | + | 0.903568i | \(0.359062\pi\) | |||||||
\(228\) | −15.1719 | −1.00478 | ||||||||
\(229\) | −25.7767 | −1.70338 | −0.851688 | − | 0.524050i | \(-0.824421\pi\) | ||||
−0.851688 | + | 0.524050i | \(0.824421\pi\) | |||||||
\(230\) | −1.83884 | −0.121249 | ||||||||
\(231\) | −29.9934 | −1.97342 | ||||||||
\(232\) | 22.7464 | 1.49337 | ||||||||
\(233\) | −3.43074 | −0.224755 | −0.112378 | − | 0.993666i | \(-0.535847\pi\) | ||||
−0.112378 | + | 0.993666i | \(0.535847\pi\) | |||||||
\(234\) | 70.1997 | 4.58910 | ||||||||
\(235\) | −0.390288 | −0.0254596 | ||||||||
\(236\) | 67.2309 | 4.37636 | ||||||||
\(237\) | −26.8083 | −1.74138 | ||||||||
\(238\) | −29.6485 | −1.92183 | ||||||||
\(239\) | 27.0614 | 1.75046 | 0.875228 | − | 0.483711i | \(-0.160711\pi\) | ||||
0.875228 | + | 0.483711i | \(0.160711\pi\) | |||||||
\(240\) | 1.59952 | 0.103249 | ||||||||
\(241\) | −11.8479 | −0.763188 | −0.381594 | − | 0.924330i | \(-0.624625\pi\) | ||||
−0.381594 | + | 0.924330i | \(0.624625\pi\) | |||||||
\(242\) | −19.8412 | −1.27544 | ||||||||
\(243\) | 17.9475 | 1.15133 | ||||||||
\(244\) | −36.0849 | −2.31010 | ||||||||
\(245\) | 0.0560312 | 0.00357970 | ||||||||
\(246\) | 77.1419 | 4.91839 | ||||||||
\(247\) | −7.43069 | −0.472803 | ||||||||
\(248\) | 39.8673 | 2.53158 | ||||||||
\(249\) | −21.8443 | −1.38433 | ||||||||
\(250\) | −2.08981 | −0.132171 | ||||||||
\(251\) | −15.4632 | −0.976027 | −0.488014 | − | 0.872836i | \(-0.662278\pi\) | ||||
−0.488014 | + | 0.872836i | \(0.662278\pi\) | |||||||
\(252\) | −51.4481 | −3.24093 | ||||||||
\(253\) | 38.1237 | 2.39682 | ||||||||
\(254\) | 46.1607 | 2.89638 | ||||||||
\(255\) | −1.04853 | −0.0656614 | ||||||||
\(256\) | −29.2752 | −1.82970 | ||||||||
\(257\) | −19.7042 | −1.22912 | −0.614558 | − | 0.788872i | \(-0.710666\pi\) | ||||
−0.614558 | + | 0.788872i | \(0.710666\pi\) | |||||||
\(258\) | −5.23807 | −0.326108 | ||||||||
\(259\) | −7.50712 | −0.466470 | ||||||||
\(260\) | 2.21787 | 0.137547 | ||||||||
\(261\) | −16.5262 | −1.02295 | ||||||||
\(262\) | −26.6903 | −1.64893 | ||||||||
\(263\) | −1.81497 | −0.111916 | −0.0559578 | − | 0.998433i | \(-0.517821\pi\) | ||||
−0.0559578 | + | 0.998433i | \(0.517821\pi\) | |||||||
\(264\) | −75.1276 | −4.62379 | ||||||||
\(265\) | 0.0821866 | 0.00504868 | ||||||||
\(266\) | 7.88003 | 0.483155 | ||||||||
\(267\) | 2.91386 | 0.178325 | ||||||||
\(268\) | 6.87933 | 0.420222 | ||||||||
\(269\) | −10.4110 | −0.634767 | −0.317384 | − | 0.948297i | \(-0.602804\pi\) | ||||
−0.317384 | + | 0.948297i | \(0.602804\pi\) | |||||||
\(270\) | −0.906136 | −0.0551457 | ||||||||
\(271\) | −0.454510 | −0.0276095 | −0.0138048 | − | 0.999905i | \(-0.504394\pi\) | ||||
−0.0138048 | + | 0.999905i | \(0.504394\pi\) | |||||||
\(272\) | −32.7808 | −1.98763 | ||||||||
\(273\) | −41.7227 | −2.52517 | ||||||||
\(274\) | −25.4972 | −1.54034 | ||||||||
\(275\) | 21.6489 | 1.30548 | ||||||||
\(276\) | 108.281 | 6.51776 | ||||||||
\(277\) | 9.13852 | 0.549080 | 0.274540 | − | 0.961576i | \(-0.411474\pi\) | ||||
0.274540 | + | 0.961576i | \(0.411474\pi\) | |||||||
\(278\) | 4.59432 | 0.275549 | ||||||||
\(279\) | −28.9654 | −1.73411 | ||||||||
\(280\) | −1.30068 | −0.0777308 | ||||||||
\(281\) | 22.9703 | 1.37030 | 0.685148 | − | 0.728404i | \(-0.259738\pi\) | ||||
0.685148 | + | 0.728404i | \(0.259738\pi\) | |||||||
\(282\) | 33.2552 | 1.98032 | ||||||||
\(283\) | 7.83880 | 0.465968 | 0.232984 | − | 0.972481i | \(-0.425151\pi\) | ||||
0.232984 | + | 0.972481i | \(0.425151\pi\) | |||||||
\(284\) | 47.5030 | 2.81879 | ||||||||
\(285\) | 0.278679 | 0.0165075 | ||||||||
\(286\) | −66.5354 | −3.93432 | ||||||||
\(287\) | −27.6894 | −1.63446 | ||||||||
\(288\) | −24.7076 | −1.45591 | ||||||||
\(289\) | 4.48866 | 0.264039 | ||||||||
\(290\) | −0.755511 | −0.0443651 | ||||||||
\(291\) | −22.3317 | −1.30911 | ||||||||
\(292\) | 0.628912 | 0.0368043 | ||||||||
\(293\) | 5.44982 | 0.318382 | 0.159191 | − | 0.987248i | \(-0.449111\pi\) | ||||
0.159191 | + | 0.987248i | \(0.449111\pi\) | |||||||
\(294\) | −4.77423 | −0.278439 | ||||||||
\(295\) | −1.23491 | −0.0718990 | ||||||||
\(296\) | −18.8039 | −1.09295 | ||||||||
\(297\) | 18.7864 | 1.09010 | ||||||||
\(298\) | 29.4286 | 1.70475 | ||||||||
\(299\) | 53.0325 | 3.06695 | ||||||||
\(300\) | 61.4885 | 3.55004 | ||||||||
\(301\) | 1.88016 | 0.108371 | ||||||||
\(302\) | 2.54449 | 0.146419 | ||||||||
\(303\) | 7.61492 | 0.437465 | ||||||||
\(304\) | 8.71254 | 0.499698 | ||||||||
\(305\) | 0.662812 | 0.0379525 | ||||||||
\(306\) | 53.9560 | 3.08446 | ||||||||
\(307\) | −10.1468 | −0.579109 | −0.289554 | − | 0.957162i | \(-0.593507\pi\) | ||||
−0.289554 | + | 0.957162i | \(0.593507\pi\) | |||||||
\(308\) | 48.7626 | 2.77851 | ||||||||
\(309\) | −34.2876 | −1.95055 | ||||||||
\(310\) | −1.32418 | −0.0752081 | ||||||||
\(311\) | 16.3459 | 0.926894 | 0.463447 | − | 0.886125i | \(-0.346613\pi\) | ||||
0.463447 | + | 0.886125i | \(0.346613\pi\) | |||||||
\(312\) | −104.507 | −5.91657 | ||||||||
\(313\) | −25.5288 | −1.44297 | −0.721487 | − | 0.692428i | \(-0.756541\pi\) | ||||
−0.721487 | + | 0.692428i | \(0.756541\pi\) | |||||||
\(314\) | 54.4247 | 3.07137 | ||||||||
\(315\) | 0.945005 | 0.0532450 | ||||||||
\(316\) | 43.5843 | 2.45181 | ||||||||
\(317\) | 0.404252 | 0.0227050 | 0.0113525 | − | 0.999936i | \(-0.496386\pi\) | ||||
0.0113525 | + | 0.999936i | \(0.496386\pi\) | |||||||
\(318\) | −7.00285 | −0.392700 | ||||||||
\(319\) | 15.6636 | 0.876993 | ||||||||
\(320\) | 0.0328483 | 0.00183627 | ||||||||
\(321\) | 24.8086 | 1.38468 | ||||||||
\(322\) | −56.2394 | −3.13410 | ||||||||
\(323\) | −5.71129 | −0.317784 | ||||||||
\(324\) | −8.04502 | −0.446946 | ||||||||
\(325\) | 30.1150 | 1.67048 | ||||||||
\(326\) | 15.4648 | 0.856514 | ||||||||
\(327\) | −0.157372 | −0.00870269 | ||||||||
\(328\) | −69.3567 | −3.82958 | ||||||||
\(329\) | −11.9367 | −0.658089 | ||||||||
\(330\) | 2.49533 | 0.137363 | ||||||||
\(331\) | 23.6570 | 1.30031 | 0.650153 | − | 0.759803i | \(-0.274705\pi\) | ||||
0.650153 | + | 0.759803i | \(0.274705\pi\) | |||||||
\(332\) | 35.5141 | 1.94909 | ||||||||
\(333\) | 13.6619 | 0.748666 | ||||||||
\(334\) | −13.8299 | −0.756740 | ||||||||
\(335\) | −0.126360 | −0.00690380 | ||||||||
\(336\) | 48.9202 | 2.66881 | ||||||||
\(337\) | 1.17881 | 0.0642137 | 0.0321069 | − | 0.999484i | \(-0.489778\pi\) | ||||
0.0321069 | + | 0.999484i | \(0.489778\pi\) | |||||||
\(338\) | −59.4766 | −3.23510 | ||||||||
\(339\) | 10.3925 | 0.564441 | ||||||||
\(340\) | 1.70468 | 0.0924490 | ||||||||
\(341\) | 27.4534 | 1.48669 | ||||||||
\(342\) | −14.3405 | −0.775446 | ||||||||
\(343\) | 19.3090 | 1.04259 | ||||||||
\(344\) | 4.70944 | 0.253916 | ||||||||
\(345\) | −1.98892 | −0.107080 | ||||||||
\(346\) | 30.7856 | 1.65504 | ||||||||
\(347\) | 5.11097 | 0.274371 | 0.137186 | − | 0.990545i | \(-0.456194\pi\) | ||||
0.137186 | + | 0.990545i | \(0.456194\pi\) | |||||||
\(348\) | 44.4887 | 2.38485 | ||||||||
\(349\) | 22.5638 | 1.20781 | 0.603906 | − | 0.797055i | \(-0.293610\pi\) | ||||
0.603906 | + | 0.797055i | \(0.293610\pi\) | |||||||
\(350\) | −31.9361 | −1.70705 | ||||||||
\(351\) | 26.1332 | 1.39488 | ||||||||
\(352\) | 23.4179 | 1.24818 | ||||||||
\(353\) | 31.8014 | 1.69262 | 0.846309 | − | 0.532692i | \(-0.178819\pi\) | ||||
0.846309 | + | 0.532692i | \(0.178819\pi\) | |||||||
\(354\) | 105.222 | 5.59250 | ||||||||
\(355\) | −0.872541 | −0.0463097 | ||||||||
\(356\) | −4.73730 | −0.251076 | ||||||||
\(357\) | −32.0684 | −1.69724 | ||||||||
\(358\) | 33.0119 | 1.74473 | ||||||||
\(359\) | −32.3931 | −1.70964 | −0.854820 | − | 0.518925i | \(-0.826332\pi\) | ||||
−0.854820 | + | 0.518925i | \(0.826332\pi\) | |||||||
\(360\) | 2.36706 | 0.124755 | ||||||||
\(361\) | −17.4820 | −0.920108 | ||||||||
\(362\) | −3.90570 | −0.205279 | ||||||||
\(363\) | −21.4606 | −1.12639 | ||||||||
\(364\) | 67.8319 | 3.55536 | ||||||||
\(365\) | −0.0115519 | −0.000604656 0 | ||||||||
\(366\) | −56.4760 | −2.95205 | ||||||||
\(367\) | 2.80775 | 0.146563 | 0.0732817 | − | 0.997311i | \(-0.476653\pi\) | ||||
0.0732817 | + | 0.997311i | \(0.476653\pi\) | |||||||
\(368\) | −62.1810 | −3.24141 | ||||||||
\(369\) | 50.3907 | 2.62324 | ||||||||
\(370\) | 0.624563 | 0.0324695 | ||||||||
\(371\) | 2.51361 | 0.130500 | ||||||||
\(372\) | 77.9750 | 4.04281 | ||||||||
\(373\) | 27.7629 | 1.43751 | 0.718754 | − | 0.695264i | \(-0.244713\pi\) | ||||
0.718754 | + | 0.695264i | \(0.244713\pi\) | |||||||
\(374\) | −51.1396 | −2.64437 | ||||||||
\(375\) | −2.26038 | −0.116726 | ||||||||
\(376\) | −29.8991 | −1.54193 | ||||||||
\(377\) | 21.7891 | 1.12220 | ||||||||
\(378\) | −27.7135 | −1.42543 | ||||||||
\(379\) | 15.3066 | 0.786246 | 0.393123 | − | 0.919486i | \(-0.371395\pi\) | ||||
0.393123 | + | 0.919486i | \(0.371395\pi\) | |||||||
\(380\) | −0.453071 | −0.0232421 | ||||||||
\(381\) | 49.9283 | 2.55790 | ||||||||
\(382\) | 25.6061 | 1.31012 | ||||||||
\(383\) | 7.84978 | 0.401105 | 0.200552 | − | 0.979683i | \(-0.435726\pi\) | ||||
0.200552 | + | 0.979683i | \(0.435726\pi\) | |||||||
\(384\) | −32.5292 | −1.66000 | ||||||||
\(385\) | −0.895677 | −0.0456479 | ||||||||
\(386\) | −3.91762 | −0.199402 | ||||||||
\(387\) | −3.42162 | −0.173931 | ||||||||
\(388\) | 36.3064 | 1.84318 | ||||||||
\(389\) | −2.75006 | −0.139433 | −0.0697167 | − | 0.997567i | \(-0.522210\pi\) | ||||
−0.0697167 | + | 0.997567i | \(0.522210\pi\) | |||||||
\(390\) | 3.47117 | 0.175769 | ||||||||
\(391\) | 40.7612 | 2.06138 | ||||||||
\(392\) | 4.29242 | 0.216800 | ||||||||
\(393\) | −28.8687 | −1.45624 | ||||||||
\(394\) | −54.9430 | −2.76799 | ||||||||
\(395\) | −0.800562 | −0.0402807 | ||||||||
\(396\) | −88.7409 | −4.45940 | ||||||||
\(397\) | −20.2299 | −1.01531 | −0.507655 | − | 0.861561i | \(-0.669487\pi\) | ||||
−0.507655 | + | 0.861561i | \(0.669487\pi\) | |||||||
\(398\) | −25.3001 | −1.26818 | ||||||||
\(399\) | 8.52318 | 0.426693 | ||||||||
\(400\) | −35.3100 | −1.76550 | ||||||||
\(401\) | −16.4144 | −0.819696 | −0.409848 | − | 0.912154i | \(-0.634418\pi\) | ||||
−0.409848 | + | 0.912154i | \(0.634418\pi\) | |||||||
\(402\) | 10.7667 | 0.536996 | ||||||||
\(403\) | 38.1895 | 1.90236 | ||||||||
\(404\) | −12.3802 | −0.615937 | ||||||||
\(405\) | 0.147772 | 0.00734284 | ||||||||
\(406\) | −23.1067 | −1.14677 | ||||||||
\(407\) | −12.9487 | −0.641845 | ||||||||
\(408\) | −80.3252 | −3.97669 | ||||||||
\(409\) | −21.3334 | −1.05487 | −0.527434 | − | 0.849596i | \(-0.676846\pi\) | ||||
−0.527434 | + | 0.849596i | \(0.676846\pi\) | |||||||
\(410\) | 2.30365 | 0.113769 | ||||||||
\(411\) | −27.5783 | −1.36034 | ||||||||
\(412\) | 55.7441 | 2.74632 | ||||||||
\(413\) | −37.7686 | −1.85847 | ||||||||
\(414\) | 102.348 | 5.03011 | ||||||||
\(415\) | −0.652327 | −0.0320214 | ||||||||
\(416\) | 32.5758 | 1.59716 | ||||||||
\(417\) | 4.96931 | 0.243348 | ||||||||
\(418\) | 13.5920 | 0.664804 | ||||||||
\(419\) | 20.4484 | 0.998970 | 0.499485 | − | 0.866323i | \(-0.333523\pi\) | ||||
0.499485 | + | 0.866323i | \(0.333523\pi\) | |||||||
\(420\) | −2.54396 | −0.124132 | ||||||||
\(421\) | −16.7493 | −0.816311 | −0.408156 | − | 0.912912i | \(-0.633828\pi\) | ||||
−0.408156 | + | 0.912912i | \(0.633828\pi\) | |||||||
\(422\) | −31.9121 | −1.55346 | ||||||||
\(423\) | 21.7230 | 1.05621 | ||||||||
\(424\) | 6.29612 | 0.305767 | ||||||||
\(425\) | 23.1466 | 1.12278 | ||||||||
\(426\) | 74.3463 | 3.60209 | ||||||||
\(427\) | 20.2716 | 0.981011 | ||||||||
\(428\) | −40.3334 | −1.94959 | ||||||||
\(429\) | −71.9659 | −3.47454 | ||||||||
\(430\) | −0.156422 | −0.00754334 | ||||||||
\(431\) | 22.6048 | 1.08884 | 0.544418 | − | 0.838814i | \(-0.316751\pi\) | ||||
0.544418 | + | 0.838814i | \(0.316751\pi\) | |||||||
\(432\) | −30.6413 | −1.47423 | ||||||||
\(433\) | 17.3449 | 0.833541 | 0.416770 | − | 0.909012i | \(-0.363162\pi\) | ||||
0.416770 | + | 0.909012i | \(0.363162\pi\) | |||||||
\(434\) | −40.4989 | −1.94401 | ||||||||
\(435\) | −0.817174 | −0.0391805 | ||||||||
\(436\) | 0.255852 | 0.0122531 | ||||||||
\(437\) | −10.8336 | −0.518240 | ||||||||
\(438\) | 0.984302 | 0.0470318 | ||||||||
\(439\) | 14.7166 | 0.702383 | 0.351191 | − | 0.936304i | \(-0.385777\pi\) | ||||
0.351191 | + | 0.936304i | \(0.385777\pi\) | |||||||
\(440\) | −2.24350 | −0.106955 | ||||||||
\(441\) | −3.11863 | −0.148506 | ||||||||
\(442\) | −71.1385 | −3.38371 | ||||||||
\(443\) | 20.6598 | 0.981576 | 0.490788 | − | 0.871279i | \(-0.336709\pi\) | ||||
0.490788 | + | 0.871279i | \(0.336709\pi\) | |||||||
\(444\) | −36.7778 | −1.74540 | ||||||||
\(445\) | 0.0870152 | 0.00412492 | ||||||||
\(446\) | 0.316652 | 0.0149939 | ||||||||
\(447\) | 31.8305 | 1.50553 | ||||||||
\(448\) | 1.00464 | 0.0474647 | ||||||||
\(449\) | 2.46837 | 0.116489 | 0.0582447 | − | 0.998302i | \(-0.481450\pi\) | ||||
0.0582447 | + | 0.998302i | \(0.481450\pi\) | |||||||
\(450\) | 58.1190 | 2.73976 | ||||||||
\(451\) | −47.7604 | −2.24895 | ||||||||
\(452\) | −16.8959 | −0.794715 | ||||||||
\(453\) | 2.75216 | 0.129308 | ||||||||
\(454\) | −32.8502 | −1.54173 | ||||||||
\(455\) | −1.24595 | −0.0584108 | ||||||||
\(456\) | 21.3490 | 0.999756 | ||||||||
\(457\) | 3.60533 | 0.168650 | 0.0843251 | − | 0.996438i | \(-0.473127\pi\) | ||||
0.0843251 | + | 0.996438i | \(0.473127\pi\) | |||||||
\(458\) | 65.5886 | 3.06475 | ||||||||
\(459\) | 20.0862 | 0.937541 | ||||||||
\(460\) | 3.23355 | 0.150765 | ||||||||
\(461\) | 25.7420 | 1.19893 | 0.599463 | − | 0.800403i | \(-0.295381\pi\) | ||||
0.599463 | + | 0.800403i | \(0.295381\pi\) | |||||||
\(462\) | 76.3177 | 3.55062 | ||||||||
\(463\) | −19.7761 | −0.919072 | −0.459536 | − | 0.888159i | \(-0.651984\pi\) | ||||
−0.459536 | + | 0.888159i | \(0.651984\pi\) | |||||||
\(464\) | −25.5479 | −1.18603 | ||||||||
\(465\) | −1.43225 | −0.0664192 | ||||||||
\(466\) | 8.72948 | 0.404385 | ||||||||
\(467\) | −6.27833 | −0.290526 | −0.145263 | − | 0.989393i | \(-0.546403\pi\) | ||||
−0.145263 | + | 0.989393i | \(0.546403\pi\) | |||||||
\(468\) | −123.444 | −5.70622 | ||||||||
\(469\) | −3.86463 | −0.178452 | ||||||||
\(470\) | 0.993084 | 0.0458075 | ||||||||
\(471\) | 58.8668 | 2.71244 | ||||||||
\(472\) | −94.6032 | −4.35446 | ||||||||
\(473\) | 3.24301 | 0.149114 | ||||||||
\(474\) | 68.2133 | 3.13314 | ||||||||
\(475\) | −6.15194 | −0.282270 | ||||||||
\(476\) | 52.1362 | 2.38966 | ||||||||
\(477\) | −4.57441 | −0.209448 | ||||||||
\(478\) | −68.8574 | −3.14946 | ||||||||
\(479\) | −36.6003 | −1.67231 | −0.836155 | − | 0.548494i | \(-0.815202\pi\) | ||||
−0.836155 | + | 0.548494i | \(0.815202\pi\) | |||||||
\(480\) | −1.22172 | −0.0557635 | ||||||||
\(481\) | −18.0125 | −0.821301 | ||||||||
\(482\) | 30.1468 | 1.37315 | ||||||||
\(483\) | −60.8296 | −2.76784 | ||||||||
\(484\) | 34.8902 | 1.58592 | ||||||||
\(485\) | −0.666881 | −0.0302815 | ||||||||
\(486\) | −45.6672 | −2.07151 | ||||||||
\(487\) | −20.9091 | −0.947481 | −0.473741 | − | 0.880664i | \(-0.657097\pi\) | ||||
−0.473741 | + | 0.880664i | \(0.657097\pi\) | |||||||
\(488\) | 50.7765 | 2.29854 | ||||||||
\(489\) | 16.7270 | 0.756420 | ||||||||
\(490\) | −0.142571 | −0.00644069 | ||||||||
\(491\) | 30.6214 | 1.38192 | 0.690962 | − | 0.722891i | \(-0.257187\pi\) | ||||
0.690962 | + | 0.722891i | \(0.257187\pi\) | |||||||
\(492\) | −135.652 | −6.11567 | ||||||||
\(493\) | 16.7473 | 0.754259 | ||||||||
\(494\) | 18.9073 | 0.850679 | ||||||||
\(495\) | 1.63000 | 0.0732632 | ||||||||
\(496\) | −44.7775 | −2.01057 | ||||||||
\(497\) | −26.6860 | −1.19703 | ||||||||
\(498\) | 55.5826 | 2.49072 | ||||||||
\(499\) | −30.7377 | −1.37601 | −0.688003 | − | 0.725707i | \(-0.741513\pi\) | ||||
−0.688003 | + | 0.725707i | \(0.741513\pi\) | |||||||
\(500\) | 3.67489 | 0.164346 | ||||||||
\(501\) | −14.9587 | −0.668305 | ||||||||
\(502\) | 39.3459 | 1.75609 | ||||||||
\(503\) | 39.7702 | 1.77327 | 0.886634 | − | 0.462473i | \(-0.153038\pi\) | ||||
0.886634 | + | 0.462473i | \(0.153038\pi\) | |||||||
\(504\) | 72.3946 | 3.22471 | ||||||||
\(505\) | 0.227401 | 0.0101192 | ||||||||
\(506\) | −97.0052 | −4.31241 | ||||||||
\(507\) | −64.3310 | −2.85704 | ||||||||
\(508\) | −81.1724 | −3.60144 | ||||||||
\(509\) | −15.1723 | −0.672502 | −0.336251 | − | 0.941772i | \(-0.609159\pi\) | ||||
−0.336251 | + | 0.941772i | \(0.609159\pi\) | |||||||
\(510\) | 2.66797 | 0.118140 | ||||||||
\(511\) | −0.353307 | −0.0156294 | ||||||||
\(512\) | 50.8514 | 2.24734 | ||||||||
\(513\) | −5.33853 | −0.235702 | ||||||||
\(514\) | 50.1371 | 2.21145 | ||||||||
\(515\) | −1.02391 | −0.0451191 | ||||||||
\(516\) | 9.21101 | 0.405492 | ||||||||
\(517\) | −20.5891 | −0.905507 | ||||||||
\(518\) | 19.1018 | 0.839283 | ||||||||
\(519\) | 33.2982 | 1.46163 | ||||||||
\(520\) | −3.12086 | −0.136859 | ||||||||
\(521\) | 39.8510 | 1.74590 | 0.872952 | − | 0.487807i | \(-0.162203\pi\) | ||||
0.872952 | + | 0.487807i | \(0.162203\pi\) | |||||||
\(522\) | 42.0508 | 1.84051 | ||||||||
\(523\) | −33.0569 | −1.44548 | −0.722738 | − | 0.691122i | \(-0.757117\pi\) | ||||
−0.722738 | + | 0.691122i | \(0.757117\pi\) | |||||||
\(524\) | 46.9342 | 2.05033 | ||||||||
\(525\) | −34.5426 | −1.50756 | ||||||||
\(526\) | 4.61816 | 0.201361 | ||||||||
\(527\) | 29.3528 | 1.27863 | ||||||||
\(528\) | 84.3805 | 3.67219 | ||||||||
\(529\) | 54.3188 | 2.36169 | ||||||||
\(530\) | −0.209123 | −0.00908371 | ||||||||
\(531\) | 68.7334 | 2.98278 | ||||||||
\(532\) | −13.8568 | −0.600770 | ||||||||
\(533\) | −66.4378 | −2.87774 | ||||||||
\(534\) | −7.41428 | −0.320847 | ||||||||
\(535\) | 0.740848 | 0.0320296 | ||||||||
\(536\) | −9.68016 | −0.418119 | ||||||||
\(537\) | 35.7062 | 1.54084 | ||||||||
\(538\) | 26.4905 | 1.14209 | ||||||||
\(539\) | 2.95584 | 0.127317 | ||||||||
\(540\) | 1.59342 | 0.0685698 | ||||||||
\(541\) | −7.65697 | −0.329199 | −0.164600 | − | 0.986360i | \(-0.552633\pi\) | ||||
−0.164600 | + | 0.986360i | \(0.552633\pi\) | |||||||
\(542\) | 1.15650 | 0.0496757 | ||||||||
\(543\) | −4.22448 | −0.181290 | ||||||||
\(544\) | 25.0380 | 1.07350 | ||||||||
\(545\) | −0.00469952 | −0.000201305 0 | ||||||||
\(546\) | 106.163 | 4.54335 | ||||||||
\(547\) | 6.11122 | 0.261297 | 0.130648 | − | 0.991429i | \(-0.458294\pi\) | ||||
0.130648 | + | 0.991429i | \(0.458294\pi\) | |||||||
\(548\) | 44.8362 | 1.91531 | ||||||||
\(549\) | −36.8914 | −1.57448 | ||||||||
\(550\) | −55.0853 | −2.34884 | ||||||||
\(551\) | −4.45111 | −0.189624 | ||||||||
\(552\) | −152.367 | −6.48515 | ||||||||
\(553\) | −24.4846 | −1.04119 | ||||||||
\(554\) | −23.2528 | −0.987919 | ||||||||
\(555\) | 0.675539 | 0.0286750 | ||||||||
\(556\) | −8.07900 | −0.342626 | ||||||||
\(557\) | −19.9654 | −0.845960 | −0.422980 | − | 0.906139i | \(-0.639016\pi\) | ||||
−0.422980 | + | 0.906139i | \(0.639016\pi\) | |||||||
\(558\) | 73.7021 | 3.12006 | ||||||||
\(559\) | 4.51124 | 0.190805 | ||||||||
\(560\) | 1.46088 | 0.0617334 | ||||||||
\(561\) | −55.3135 | −2.33534 | ||||||||
\(562\) | −58.4478 | −2.46547 | ||||||||
\(563\) | 13.7152 | 0.578028 | 0.289014 | − | 0.957325i | \(-0.406673\pi\) | ||||
0.289014 | + | 0.957325i | \(0.406673\pi\) | |||||||
\(564\) | −58.4784 | −2.46238 | ||||||||
\(565\) | 0.310345 | 0.0130563 | ||||||||
\(566\) | −19.9457 | −0.838382 | ||||||||
\(567\) | 4.51949 | 0.189801 | ||||||||
\(568\) | −66.8433 | −2.80468 | ||||||||
\(569\) | 17.1926 | 0.720751 | 0.360376 | − | 0.932807i | \(-0.382649\pi\) | ||||
0.360376 | + | 0.932807i | \(0.382649\pi\) | |||||||
\(570\) | −0.709096 | −0.0297008 | ||||||||
\(571\) | −39.7594 | −1.66388 | −0.831939 | − | 0.554867i | \(-0.812769\pi\) | ||||
−0.831939 | + | 0.554867i | \(0.812769\pi\) | |||||||
\(572\) | 117.001 | 4.89205 | ||||||||
\(573\) | 27.6960 | 1.15702 | ||||||||
\(574\) | 70.4554 | 2.94075 | ||||||||
\(575\) | 43.9062 | 1.83101 | ||||||||
\(576\) | −1.82830 | −0.0761790 | ||||||||
\(577\) | 6.22280 | 0.259059 | 0.129529 | − | 0.991576i | \(-0.458653\pi\) | ||||
0.129529 | + | 0.991576i | \(0.458653\pi\) | |||||||
\(578\) | −11.4213 | −0.475065 | ||||||||
\(579\) | −4.23737 | −0.176099 | ||||||||
\(580\) | 1.32855 | 0.0551649 | ||||||||
\(581\) | −19.9509 | −0.827702 | ||||||||
\(582\) | 56.8227 | 2.35538 | ||||||||
\(583\) | 4.33563 | 0.179564 | ||||||||
\(584\) | −0.884966 | −0.0366202 | ||||||||
\(585\) | 2.26744 | 0.0937471 | ||||||||
\(586\) | −13.8670 | −0.572840 | ||||||||
\(587\) | −4.57601 | −0.188872 | −0.0944361 | − | 0.995531i | \(-0.530105\pi\) | ||||
−0.0944361 | + | 0.995531i | \(0.530105\pi\) | |||||||
\(588\) | 8.39537 | 0.346219 | ||||||||
\(589\) | −7.80142 | −0.321452 | ||||||||
\(590\) | 3.14220 | 0.129362 | ||||||||
\(591\) | −59.4274 | −2.44452 | ||||||||
\(592\) | 21.1198 | 0.868020 | ||||||||
\(593\) | −27.8178 | −1.14234 | −0.571171 | − | 0.820831i | \(-0.693511\pi\) | ||||
−0.571171 | + | 0.820831i | \(0.693511\pi\) | |||||||
\(594\) | −47.8019 | −1.96133 | ||||||||
\(595\) | −0.957643 | −0.0392595 | ||||||||
\(596\) | −51.7495 | −2.11974 | ||||||||
\(597\) | −27.3650 | −1.11998 | ||||||||
\(598\) | −134.941 | −5.51813 | ||||||||
\(599\) | −35.2287 | −1.43940 | −0.719702 | − | 0.694283i | \(-0.755722\pi\) | ||||
−0.719702 | + | 0.694283i | \(0.755722\pi\) | |||||||
\(600\) | −86.5227 | −3.53228 | ||||||||
\(601\) | −29.1471 | −1.18894 | −0.594468 | − | 0.804119i | \(-0.702637\pi\) | ||||
−0.594468 | + | 0.804119i | \(0.702637\pi\) | |||||||
\(602\) | −4.78404 | −0.194983 | ||||||||
\(603\) | 7.03307 | 0.286409 | ||||||||
\(604\) | −4.47442 | −0.182061 | ||||||||
\(605\) | −0.640867 | −0.0260549 | ||||||||
\(606\) | −19.3761 | −0.787099 | ||||||||
\(607\) | 20.3246 | 0.824948 | 0.412474 | − | 0.910969i | \(-0.364665\pi\) | ||||
0.412474 | + | 0.910969i | \(0.364665\pi\) | |||||||
\(608\) | −6.65464 | −0.269881 | ||||||||
\(609\) | −24.9926 | −1.01275 | ||||||||
\(610\) | −1.68652 | −0.0682851 | ||||||||
\(611\) | −28.6408 | −1.15868 | ||||||||
\(612\) | −94.8803 | −3.83531 | ||||||||
\(613\) | −18.1015 | −0.731112 | −0.365556 | − | 0.930789i | \(-0.619121\pi\) | ||||
−0.365556 | + | 0.930789i | \(0.619121\pi\) | |||||||
\(614\) | 25.8184 | 1.04195 | ||||||||
\(615\) | 2.49167 | 0.100474 | ||||||||
\(616\) | −68.6157 | −2.76461 | ||||||||
\(617\) | −43.0603 | −1.73354 | −0.866771 | − | 0.498707i | \(-0.833808\pi\) | ||||
−0.866771 | + | 0.498707i | \(0.833808\pi\) | |||||||
\(618\) | 87.2444 | 3.50948 | ||||||||
\(619\) | −37.2095 | −1.49557 | −0.747787 | − | 0.663938i | \(-0.768884\pi\) | ||||
−0.747787 | + | 0.663938i | \(0.768884\pi\) | |||||||
\(620\) | 2.32853 | 0.0935160 | ||||||||
\(621\) | 38.1008 | 1.52893 | ||||||||
\(622\) | −41.5920 | −1.66769 | ||||||||
\(623\) | 2.66129 | 0.106622 | ||||||||
\(624\) | 117.379 | 4.69891 | ||||||||
\(625\) | 24.8987 | 0.995949 | ||||||||
\(626\) | 64.9578 | 2.59624 | ||||||||
\(627\) | 14.7013 | 0.587114 | ||||||||
\(628\) | −95.7045 | −3.81903 | ||||||||
\(629\) | −13.8446 | −0.552019 | ||||||||
\(630\) | −2.40455 | −0.0957997 | ||||||||
\(631\) | −27.0966 | −1.07870 | −0.539349 | − | 0.842082i | \(-0.681330\pi\) | ||||
−0.539349 | + | 0.842082i | \(0.681330\pi\) | |||||||
\(632\) | −61.3292 | −2.43954 | ||||||||
\(633\) | −34.5168 | −1.37192 | ||||||||
\(634\) | −1.02861 | −0.0408514 | ||||||||
\(635\) | 1.49099 | 0.0591679 | ||||||||
\(636\) | 12.3143 | 0.488295 | ||||||||
\(637\) | 4.11177 | 0.162914 | ||||||||
\(638\) | −39.8558 | −1.57791 | ||||||||
\(639\) | 48.5646 | 1.92119 | ||||||||
\(640\) | −0.971405 | −0.0383981 | ||||||||
\(641\) | −25.8139 | −1.01959 | −0.509795 | − | 0.860296i | \(-0.670279\pi\) | ||||
−0.509795 | + | 0.860296i | \(0.670279\pi\) | |||||||
\(642\) | −63.1252 | −2.49135 | ||||||||
\(643\) | 36.8107 | 1.45167 | 0.725836 | − | 0.687868i | \(-0.241453\pi\) | ||||
0.725836 | + | 0.687868i | \(0.241453\pi\) | |||||||
\(644\) | 98.8956 | 3.89703 | ||||||||
\(645\) | −0.169189 | −0.00666180 | ||||||||
\(646\) | 14.5323 | 0.571765 | ||||||||
\(647\) | −21.3255 | −0.838393 | −0.419196 | − | 0.907896i | \(-0.637688\pi\) | ||||
−0.419196 | + | 0.907896i | \(0.637688\pi\) | |||||||
\(648\) | 11.3205 | 0.444709 | ||||||||
\(649\) | −65.1456 | −2.55719 | ||||||||
\(650\) | −76.6272 | −3.00557 | ||||||||
\(651\) | −43.8043 | −1.71683 | ||||||||
\(652\) | −27.1944 | −1.06502 | ||||||||
\(653\) | 27.6488 | 1.08198 | 0.540991 | − | 0.841028i | \(-0.318049\pi\) | ||||
0.540991 | + | 0.841028i | \(0.318049\pi\) | |||||||
\(654\) | 0.400431 | 0.0156581 | ||||||||
\(655\) | −0.862094 | −0.0336848 | ||||||||
\(656\) | 77.8989 | 3.04144 | ||||||||
\(657\) | 0.642967 | 0.0250845 | ||||||||
\(658\) | 30.3727 | 1.18405 | ||||||||
\(659\) | −1.84756 | −0.0719707 | −0.0359853 | − | 0.999352i | \(-0.511457\pi\) | ||||
−0.0359853 | + | 0.999352i | \(0.511457\pi\) | |||||||
\(660\) | −4.38797 | −0.170802 | ||||||||
\(661\) | 3.21923 | 0.125213 | 0.0626067 | − | 0.998038i | \(-0.480059\pi\) | ||||
0.0626067 | + | 0.998038i | \(0.480059\pi\) | |||||||
\(662\) | −60.1949 | −2.33954 | ||||||||
\(663\) | −76.9447 | −2.98829 | ||||||||
\(664\) | −49.9732 | −1.93934 | ||||||||
\(665\) | 0.254524 | 0.00987001 | ||||||||
\(666\) | −34.7625 | −1.34702 | ||||||||
\(667\) | 31.7674 | 1.23004 | ||||||||
\(668\) | 24.3196 | 0.940952 | ||||||||
\(669\) | 0.342496 | 0.0132417 | ||||||||
\(670\) | 0.321522 | 0.0124215 | ||||||||
\(671\) | 34.9657 | 1.34984 | ||||||||
\(672\) | −37.3653 | −1.44140 | ||||||||
\(673\) | 21.8528 | 0.842362 | 0.421181 | − | 0.906977i | \(-0.361616\pi\) | ||||
0.421181 | + | 0.906977i | \(0.361616\pi\) | |||||||
\(674\) | −2.99946 | −0.115535 | ||||||||
\(675\) | 21.6359 | 0.832766 | ||||||||
\(676\) | 104.588 | 4.02262 | ||||||||
\(677\) | −35.8799 | −1.37898 | −0.689488 | − | 0.724297i | \(-0.742165\pi\) | ||||
−0.689488 | + | 0.724297i | \(0.742165\pi\) | |||||||
\(678\) | −26.4435 | −1.01556 | ||||||||
\(679\) | −20.3960 | −0.782727 | ||||||||
\(680\) | −2.39871 | −0.0919865 | ||||||||
\(681\) | −35.5313 | −1.36156 | ||||||||
\(682\) | −69.8549 | −2.67488 | ||||||||
\(683\) | −24.3429 | −0.931457 | −0.465728 | − | 0.884928i | \(-0.654208\pi\) | ||||
−0.465728 | + | 0.884928i | \(0.654208\pi\) | |||||||
\(684\) | 25.2174 | 0.964212 | ||||||||
\(685\) | −0.823557 | −0.0314665 | ||||||||
\(686\) | −49.1314 | −1.87584 | ||||||||
\(687\) | 70.9418 | 2.70660 | ||||||||
\(688\) | −5.28946 | −0.201659 | ||||||||
\(689\) | 6.03114 | 0.229768 | ||||||||
\(690\) | 5.06079 | 0.192661 | ||||||||
\(691\) | −0.695643 | −0.0264635 | −0.0132318 | − | 0.999912i | \(-0.504212\pi\) | ||||
−0.0132318 | + | 0.999912i | \(0.504212\pi\) | |||||||
\(692\) | −54.1356 | −2.05793 | ||||||||
\(693\) | 49.8524 | 1.89373 | ||||||||
\(694\) | −13.0048 | −0.493655 | ||||||||
\(695\) | 0.148396 | 0.00562898 | ||||||||
\(696\) | −62.6018 | −2.37291 | ||||||||
\(697\) | −51.0646 | −1.93421 | ||||||||
\(698\) | −57.4133 | −2.17313 | ||||||||
\(699\) | 9.44197 | 0.357128 | ||||||||
\(700\) | 56.1587 | 2.12260 | ||||||||
\(701\) | −18.4070 | −0.695224 | −0.347612 | − | 0.937638i | \(-0.613007\pi\) | ||||
−0.347612 | + | 0.937638i | \(0.613007\pi\) | |||||||
\(702\) | −66.4955 | −2.50971 | ||||||||
\(703\) | 3.67963 | 0.138780 | ||||||||
\(704\) | 1.73286 | 0.0653097 | ||||||||
\(705\) | 1.07414 | 0.0404544 | ||||||||
\(706\) | −80.9183 | −3.04540 | ||||||||
\(707\) | 6.95487 | 0.261565 | ||||||||
\(708\) | −185.031 | −6.95388 | ||||||||
\(709\) | 33.5958 | 1.26172 | 0.630859 | − | 0.775897i | \(-0.282703\pi\) | ||||
0.630859 | + | 0.775897i | \(0.282703\pi\) | |||||||
\(710\) | 2.22017 | 0.0833215 | ||||||||
\(711\) | 44.5584 | 1.67107 | ||||||||
\(712\) | 6.66603 | 0.249820 | ||||||||
\(713\) | 55.6784 | 2.08517 | ||||||||
\(714\) | 81.5976 | 3.05371 | ||||||||
\(715\) | −2.14908 | −0.0803711 | ||||||||
\(716\) | −58.0505 | −2.16945 | ||||||||
\(717\) | −74.4774 | −2.78141 | ||||||||
\(718\) | 82.4237 | 3.07603 | ||||||||
\(719\) | −19.6546 | −0.732992 | −0.366496 | − | 0.930420i | \(-0.619443\pi\) | ||||
−0.366496 | + | 0.930420i | \(0.619443\pi\) | |||||||
\(720\) | −2.65859 | −0.0990798 | ||||||||
\(721\) | −31.3156 | −1.16625 | ||||||||
\(722\) | 44.4828 | 1.65548 | ||||||||
\(723\) | 32.6073 | 1.21268 | ||||||||
\(724\) | 6.86808 | 0.255250 | ||||||||
\(725\) | 18.0394 | 0.669967 | ||||||||
\(726\) | 54.6061 | 2.02662 | ||||||||
\(727\) | −2.90746 | −0.107832 | −0.0539158 | − | 0.998545i | \(-0.517170\pi\) | ||||
−0.0539158 | + | 0.998545i | \(0.517170\pi\) | |||||||
\(728\) | −95.4489 | −3.53757 | ||||||||
\(729\) | −44.0005 | −1.62965 | ||||||||
\(730\) | 0.0293937 | 0.00108791 | ||||||||
\(731\) | 3.46738 | 0.128246 | ||||||||
\(732\) | 99.3117 | 3.67066 | ||||||||
\(733\) | 15.5628 | 0.574823 | 0.287412 | − | 0.957807i | \(-0.407205\pi\) | ||||
0.287412 | + | 0.957807i | \(0.407205\pi\) | |||||||
\(734\) | −7.14429 | −0.263700 | ||||||||
\(735\) | −0.154207 | −0.00568802 | ||||||||
\(736\) | 47.4939 | 1.75065 | ||||||||
\(737\) | −6.66595 | −0.245543 | ||||||||
\(738\) | −128.219 | −4.71979 | ||||||||
\(739\) | 37.7847 | 1.38993 | 0.694966 | − | 0.719043i | \(-0.255419\pi\) | ||||
0.694966 | + | 0.719043i | \(0.255419\pi\) | |||||||
\(740\) | −1.09828 | −0.0403735 | ||||||||
\(741\) | 20.4505 | 0.751267 | ||||||||
\(742\) | −6.39585 | −0.234799 | ||||||||
\(743\) | 3.52976 | 0.129494 | 0.0647472 | − | 0.997902i | \(-0.479376\pi\) | ||||
0.0647472 | + | 0.997902i | \(0.479376\pi\) | |||||||
\(744\) | −109.721 | −4.02259 | ||||||||
\(745\) | 0.950540 | 0.0348251 | ||||||||
\(746\) | −70.6424 | −2.58640 | ||||||||
\(747\) | 36.3077 | 1.32843 | ||||||||
\(748\) | 89.9277 | 3.28808 | ||||||||
\(749\) | 22.6582 | 0.827914 | ||||||||
\(750\) | 5.75151 | 0.210016 | ||||||||
\(751\) | −37.5878 | −1.37160 | −0.685800 | − | 0.727790i | \(-0.740548\pi\) | ||||
−0.685800 | + | 0.727790i | \(0.740548\pi\) | |||||||
\(752\) | 33.5815 | 1.22459 | ||||||||
\(753\) | 42.5572 | 1.55087 | ||||||||
\(754\) | −55.4421 | −2.01908 | ||||||||
\(755\) | 0.0821866 | 0.00299108 | ||||||||
\(756\) | 48.7334 | 1.77242 | ||||||||
\(757\) | −40.2226 | −1.46191 | −0.730957 | − | 0.682423i | \(-0.760926\pi\) | ||||
−0.730957 | + | 0.682423i | \(0.760926\pi\) | |||||||
\(758\) | −38.9474 | −1.41463 | ||||||||
\(759\) | −104.923 | −3.80845 | ||||||||
\(760\) | 0.637534 | 0.0231258 | ||||||||
\(761\) | 35.9693 | 1.30389 | 0.651943 | − | 0.758268i | \(-0.273954\pi\) | ||||
0.651943 | + | 0.758268i | \(0.273954\pi\) | |||||||
\(762\) | −127.042 | −4.60224 | ||||||||
\(763\) | −0.143731 | −0.00520342 | ||||||||
\(764\) | −45.0276 | −1.62904 | ||||||||
\(765\) | 1.74277 | 0.0630101 | ||||||||
\(766\) | −19.9737 | −0.721678 | ||||||||
\(767\) | −90.6218 | −3.27216 | ||||||||
\(768\) | 80.5702 | 2.90733 | ||||||||
\(769\) | 42.6516 | 1.53806 | 0.769028 | − | 0.639215i | \(-0.220741\pi\) | ||||
0.769028 | + | 0.639215i | \(0.220741\pi\) | |||||||
\(770\) | 2.27904 | 0.0821309 | ||||||||
\(771\) | 54.2293 | 1.95302 | ||||||||
\(772\) | 6.88904 | 0.247942 | ||||||||
\(773\) | −11.2535 | −0.404761 | −0.202381 | − | 0.979307i | \(-0.564868\pi\) | ||||
−0.202381 | + | 0.979307i | \(0.564868\pi\) | |||||||
\(774\) | 8.70626 | 0.312940 | ||||||||
\(775\) | 31.6175 | 1.13573 | ||||||||
\(776\) | −51.0881 | −1.83396 | ||||||||
\(777\) | 20.6608 | 0.741203 | ||||||||
\(778\) | 6.99748 | 0.250872 | ||||||||
\(779\) | 13.5720 | 0.486269 | ||||||||
\(780\) | −6.10396 | −0.218557 | ||||||||
\(781\) | −46.0296 | −1.64707 | ||||||||
\(782\) | −103.716 | −3.70889 | ||||||||
\(783\) | 15.6542 | 0.559436 | ||||||||
\(784\) | −4.82108 | −0.172181 | ||||||||
\(785\) | 1.75791 | 0.0627426 | ||||||||
\(786\) | 73.4561 | 2.62009 | ||||||||
\(787\) | 11.1517 | 0.397515 | 0.198757 | − | 0.980049i | \(-0.436309\pi\) | ||||
0.198757 | + | 0.980049i | \(0.436309\pi\) | |||||||
\(788\) | 96.6158 | 3.44180 | ||||||||
\(789\) | 4.99509 | 0.177830 | ||||||||
\(790\) | 2.03702 | 0.0724740 | ||||||||
\(791\) | 9.49166 | 0.337485 | ||||||||
\(792\) | 124.871 | 4.43709 | ||||||||
\(793\) | 48.6395 | 1.72724 | ||||||||
\(794\) | 51.4747 | 1.82677 | ||||||||
\(795\) | −0.226191 | −0.00802217 | ||||||||
\(796\) | 44.4895 | 1.57689 | ||||||||
\(797\) | 23.0908 | 0.817920 | 0.408960 | − | 0.912552i | \(-0.365892\pi\) | ||||
0.408960 | + | 0.912552i | \(0.365892\pi\) | |||||||
\(798\) | −21.6871 | −0.767716 | ||||||||
\(799\) | −22.0135 | −0.778782 | ||||||||
\(800\) | 26.9698 | 0.953528 | ||||||||
\(801\) | −4.84317 | −0.171125 | ||||||||
\(802\) | 41.7662 | 1.47482 | ||||||||
\(803\) | −0.609405 | −0.0215054 | ||||||||
\(804\) | −18.9330 | −0.667717 | ||||||||
\(805\) | −1.81653 | −0.0640241 | ||||||||
\(806\) | −97.1727 | −3.42276 | ||||||||
\(807\) | 28.6527 | 1.00862 | ||||||||
\(808\) | 17.4206 | 0.612855 | ||||||||
\(809\) | 41.9200 | 1.47383 | 0.736914 | − | 0.675986i | \(-0.236282\pi\) | ||||
0.736914 | + | 0.675986i | \(0.236282\pi\) | |||||||
\(810\) | −0.376004 | −0.0132114 | ||||||||
\(811\) | 31.9734 | 1.12274 | 0.561369 | − | 0.827566i | \(-0.310275\pi\) | ||||
0.561369 | + | 0.827566i | \(0.310275\pi\) | |||||||
\(812\) | 40.6325 | 1.42592 | ||||||||
\(813\) | 1.25089 | 0.0438705 | ||||||||
\(814\) | 32.9479 | 1.15482 | ||||||||
\(815\) | 0.499510 | 0.0174971 | ||||||||
\(816\) | 90.2182 | 3.15827 | ||||||||
\(817\) | −0.921564 | −0.0322415 | ||||||||
\(818\) | 54.2826 | 1.89795 | ||||||||
\(819\) | 69.3479 | 2.42321 | ||||||||
\(820\) | −4.05091 | −0.141464 | ||||||||
\(821\) | 9.34786 | 0.326243 | 0.163121 | − | 0.986606i | \(-0.447844\pi\) | ||||
0.163121 | + | 0.986606i | \(0.447844\pi\) | |||||||
\(822\) | 70.1726 | 2.44755 | ||||||||
\(823\) | 25.9014 | 0.902865 | 0.451433 | − | 0.892305i | \(-0.350913\pi\) | ||||
0.451433 | + | 0.892305i | \(0.350913\pi\) | |||||||
\(824\) | −78.4397 | −2.73258 | ||||||||
\(825\) | −59.5813 | −2.07435 | ||||||||
\(826\) | 96.1018 | 3.34381 | ||||||||
\(827\) | −28.0019 | −0.973722 | −0.486861 | − | 0.873479i | \(-0.661858\pi\) | ||||
−0.486861 | + | 0.873479i | \(0.661858\pi\) | |||||||
\(828\) | −179.976 | −6.25459 | ||||||||
\(829\) | 38.4111 | 1.33407 | 0.667036 | − | 0.745025i | \(-0.267563\pi\) | ||||
0.667036 | + | 0.745025i | \(0.267563\pi\) | |||||||
\(830\) | 1.65984 | 0.0576138 | ||||||||
\(831\) | −25.1507 | −0.872468 | ||||||||
\(832\) | 2.41052 | 0.0835698 | ||||||||
\(833\) | 3.16034 | 0.109499 | ||||||||
\(834\) | −12.6443 | −0.437838 | ||||||||
\(835\) | −0.446705 | −0.0154588 | ||||||||
\(836\) | −23.9011 | −0.826637 | ||||||||
\(837\) | 27.4370 | 0.948361 | ||||||||
\(838\) | −52.0307 | −1.79737 | ||||||||
\(839\) | 29.9158 | 1.03281 | 0.516405 | − | 0.856345i | \(-0.327270\pi\) | ||||
0.516405 | + | 0.856345i | \(0.327270\pi\) | |||||||
\(840\) | 3.57970 | 0.123511 | ||||||||
\(841\) | −15.9480 | −0.549930 | ||||||||
\(842\) | 42.6184 | 1.46873 | ||||||||
\(843\) | −63.2182 | −2.17735 | ||||||||
\(844\) | 56.1167 | 1.93162 | ||||||||
\(845\) | −1.92109 | −0.0660874 | ||||||||
\(846\) | −55.2739 | −1.90036 | ||||||||
\(847\) | −19.6004 | −0.673478 | ||||||||
\(848\) | −7.07156 | −0.242838 | ||||||||
\(849\) | −21.5737 | −0.740407 | ||||||||
\(850\) | −58.8963 | −2.02013 | ||||||||
\(851\) | −26.2614 | −0.900228 | ||||||||
\(852\) | −130.736 | −4.47895 | ||||||||
\(853\) | −51.3535 | −1.75831 | −0.879155 | − | 0.476537i | \(-0.841892\pi\) | ||||
−0.879155 | + | 0.476537i | \(0.841892\pi\) | |||||||
\(854\) | −51.5808 | −1.76506 | ||||||||
\(855\) | −0.463197 | −0.0158410 | ||||||||
\(856\) | 56.7546 | 1.93983 | ||||||||
\(857\) | 12.4954 | 0.426833 | 0.213417 | − | 0.976961i | \(-0.431541\pi\) | ||||
0.213417 | + | 0.976961i | \(0.431541\pi\) | |||||||
\(858\) | 183.116 | 6.25149 | ||||||||
\(859\) | 0.742927 | 0.0253483 | 0.0126742 | − | 0.999920i | \(-0.495966\pi\) | ||||
0.0126742 | + | 0.999920i | \(0.495966\pi\) | |||||||
\(860\) | 0.275064 | 0.00937960 | ||||||||
\(861\) | 76.2059 | 2.59709 | ||||||||
\(862\) | −57.5176 | −1.95906 | ||||||||
\(863\) | 12.4872 | 0.425069 | 0.212534 | − | 0.977154i | \(-0.431828\pi\) | ||||
0.212534 | + | 0.977154i | \(0.431828\pi\) | |||||||
\(864\) | 23.4039 | 0.796216 | ||||||||
\(865\) | 0.994370 | 0.0338096 | ||||||||
\(866\) | −44.1338 | −1.49973 | ||||||||
\(867\) | −12.3535 | −0.419547 | ||||||||
\(868\) | 71.2162 | 2.41724 | ||||||||
\(869\) | −42.2325 | −1.43264 | ||||||||
\(870\) | 2.07929 | 0.0704945 | ||||||||
\(871\) | −9.27277 | −0.314196 | ||||||||
\(872\) | −0.360019 | −0.0121918 | ||||||||
\(873\) | 37.1178 | 1.25625 | ||||||||
\(874\) | 27.5659 | 0.932430 | ||||||||
\(875\) | −2.06446 | −0.0697914 | ||||||||
\(876\) | −1.73087 | −0.0584807 | ||||||||
\(877\) | 13.8040 | 0.466127 | 0.233064 | − | 0.972461i | \(-0.425125\pi\) | ||||
0.233064 | + | 0.972461i | \(0.425125\pi\) | |||||||
\(878\) | −37.4461 | −1.26374 | ||||||||
\(879\) | −14.9988 | −0.505897 | ||||||||
\(880\) | 2.51982 | 0.0849430 | ||||||||
\(881\) | −6.26251 | −0.210989 | −0.105495 | − | 0.994420i | \(-0.533643\pi\) | ||||
−0.105495 | + | 0.994420i | \(0.533643\pi\) | |||||||
\(882\) | 7.93532 | 0.267196 | ||||||||
\(883\) | 37.9742 | 1.27793 | 0.638966 | − | 0.769235i | \(-0.279362\pi\) | ||||
0.638966 | + | 0.769235i | \(0.279362\pi\) | |||||||
\(884\) | 125.095 | 4.20741 | ||||||||
\(885\) | 3.39866 | 0.114245 | ||||||||
\(886\) | −52.5686 | −1.76608 | ||||||||
\(887\) | −6.05758 | −0.203394 | −0.101697 | − | 0.994815i | \(-0.532427\pi\) | ||||
−0.101697 | + | 0.994815i | \(0.532427\pi\) | |||||||
\(888\) | 51.7514 | 1.73666 | ||||||||
\(889\) | 45.6006 | 1.52939 | ||||||||
\(890\) | −0.221409 | −0.00742165 | ||||||||
\(891\) | 7.79549 | 0.261159 | ||||||||
\(892\) | −0.556824 | −0.0186438 | ||||||||
\(893\) | 5.85078 | 0.195789 | ||||||||
\(894\) | −80.9924 | −2.70879 | ||||||||
\(895\) | 1.06628 | 0.0356418 | ||||||||
\(896\) | −29.7096 | −0.992530 | ||||||||
\(897\) | −145.954 | −4.87327 | ||||||||
\(898\) | −6.28073 | −0.209591 | ||||||||
\(899\) | 22.8762 | 0.762964 | ||||||||
\(900\) | −102.201 | −3.40669 | ||||||||
\(901\) | 4.63559 | 0.154434 | ||||||||
\(902\) | 121.526 | 4.04637 | ||||||||
\(903\) | −5.17451 | −0.172197 | ||||||||
\(904\) | 23.7748 | 0.790738 | ||||||||
\(905\) | −0.126154 | −0.00419349 | ||||||||
\(906\) | −7.00285 | −0.232654 | ||||||||
\(907\) | 16.4302 | 0.545557 | 0.272778 | − | 0.962077i | \(-0.412057\pi\) | ||||
0.272778 | + | 0.962077i | \(0.412057\pi\) | |||||||
\(908\) | 57.7662 | 1.91704 | ||||||||
\(909\) | −12.6569 | −0.419801 | ||||||||
\(910\) | 3.17029 | 0.105094 | ||||||||
\(911\) | 6.22670 | 0.206300 | 0.103150 | − | 0.994666i | \(-0.467108\pi\) | ||||
0.103150 | + | 0.994666i | \(0.467108\pi\) | |||||||
\(912\) | −23.9783 | −0.794002 | ||||||||
\(913\) | −34.4125 | −1.13889 | ||||||||
\(914\) | −9.17371 | −0.303439 | ||||||||
\(915\) | −1.82417 | −0.0603051 | ||||||||
\(916\) | −115.336 | −3.81080 | ||||||||
\(917\) | −26.3664 | −0.870697 | ||||||||
\(918\) | −51.1090 | −1.68685 | ||||||||
\(919\) | −25.8843 | −0.853843 | −0.426922 | − | 0.904289i | \(-0.640402\pi\) | ||||
−0.426922 | + | 0.904289i | \(0.640402\pi\) | |||||||
\(920\) | −4.55005 | −0.150011 | ||||||||
\(921\) | 27.9257 | 0.920182 | ||||||||
\(922\) | −65.5003 | −2.15714 | ||||||||
\(923\) | −64.0302 | −2.10758 | ||||||||
\(924\) | −134.203 | −4.41495 | ||||||||
\(925\) | −14.9128 | −0.490328 | ||||||||
\(926\) | 50.3200 | 1.65362 | ||||||||
\(927\) | 56.9899 | 1.87179 | ||||||||
\(928\) | 19.5135 | 0.640561 | ||||||||
\(929\) | −10.9990 | −0.360864 | −0.180432 | − | 0.983587i | \(-0.557750\pi\) | ||||
−0.180432 | + | 0.983587i | \(0.557750\pi\) | |||||||
\(930\) | 3.64435 | 0.119503 | ||||||||
\(931\) | −0.839959 | −0.0275286 | ||||||||
\(932\) | −15.3506 | −0.502825 | ||||||||
\(933\) | −44.9867 | −1.47280 | ||||||||
\(934\) | 15.9751 | 0.522722 | ||||||||
\(935\) | −1.65180 | −0.0540197 | ||||||||
\(936\) | 173.703 | 5.67767 | ||||||||
\(937\) | 8.73378 | 0.285320 | 0.142660 | − | 0.989772i | \(-0.454434\pi\) | ||||
0.142660 | + | 0.989772i | \(0.454434\pi\) | |||||||
\(938\) | 9.83350 | 0.321075 | ||||||||
\(939\) | 70.2595 | 2.29283 | ||||||||
\(940\) | −1.74631 | −0.0569584 | ||||||||
\(941\) | 17.3878 | 0.566825 | 0.283412 | − | 0.958998i | \(-0.408533\pi\) | ||||
0.283412 | + | 0.958998i | \(0.408533\pi\) | |||||||
\(942\) | −149.786 | −4.88029 | ||||||||
\(943\) | −96.8631 | −3.15430 | ||||||||
\(944\) | 106.255 | 3.45830 | ||||||||
\(945\) | −0.895141 | −0.0291189 | ||||||||
\(946\) | −8.25181 | −0.268289 | ||||||||
\(947\) | 42.6828 | 1.38700 | 0.693502 | − | 0.720455i | \(-0.256067\pi\) | ||||
0.693502 | + | 0.720455i | \(0.256067\pi\) | |||||||
\(948\) | −119.951 | −3.89584 | ||||||||
\(949\) | −0.847722 | −0.0275182 | ||||||||
\(950\) | 15.6535 | 0.507868 | ||||||||
\(951\) | −1.11257 | −0.0360774 | ||||||||
\(952\) | −73.3628 | −2.37770 | ||||||||
\(953\) | −15.6047 | −0.505484 | −0.252742 | − | 0.967534i | \(-0.581332\pi\) | ||||
−0.252742 | + | 0.967534i | \(0.581332\pi\) | |||||||
\(954\) | 11.6395 | 0.376844 | ||||||||
\(955\) | 0.827073 | 0.0267634 | ||||||||
\(956\) | 121.084 | 3.91613 | ||||||||
\(957\) | −43.1088 | −1.39351 | ||||||||
\(958\) | 93.1289 | 3.00886 | ||||||||
\(959\) | −25.1878 | −0.813358 | ||||||||
\(960\) | −0.0904038 | −0.00291777 | ||||||||
\(961\) | 9.09487 | 0.293383 | ||||||||
\(962\) | 45.8327 | 1.47770 | ||||||||
\(963\) | −41.2347 | −1.32877 | ||||||||
\(964\) | −53.0123 | −1.70741 | ||||||||
\(965\) | −0.126539 | −0.00407343 | ||||||||
\(966\) | 154.780 | 4.97997 | ||||||||
\(967\) | 44.5276 | 1.43191 | 0.715955 | − | 0.698146i | \(-0.245992\pi\) | ||||
0.715955 | + | 0.698146i | \(0.245992\pi\) | |||||||
\(968\) | −49.0953 | −1.57798 | ||||||||
\(969\) | 15.7184 | 0.504948 | ||||||||
\(970\) | 1.69687 | 0.0544832 | ||||||||
\(971\) | 9.85220 | 0.316172 | 0.158086 | − | 0.987425i | \(-0.449468\pi\) | ||||
0.158086 | + | 0.987425i | \(0.449468\pi\) | |||||||
\(972\) | 80.3046 | 2.57577 | ||||||||
\(973\) | 4.53858 | 0.145500 | ||||||||
\(974\) | 53.2029 | 1.70473 | ||||||||
\(975\) | −82.8814 | −2.65433 | ||||||||
\(976\) | −57.0302 | −1.82549 | ||||||||
\(977\) | 19.0304 | 0.608837 | 0.304418 | − | 0.952538i | \(-0.401538\pi\) | ||||
0.304418 | + | 0.952538i | \(0.401538\pi\) | |||||||
\(978\) | −42.5616 | −1.36097 | ||||||||
\(979\) | 4.59036 | 0.146709 | ||||||||
\(980\) | 0.250707 | 0.00800854 | ||||||||
\(981\) | 0.261570 | 0.00835129 | ||||||||
\(982\) | −77.9158 | −2.48639 | ||||||||
\(983\) | −19.9750 | −0.637104 | −0.318552 | − | 0.947905i | \(-0.603196\pi\) | ||||
−0.318552 | + | 0.947905i | \(0.603196\pi\) | |||||||
\(984\) | 190.881 | 6.08507 | ||||||||
\(985\) | −1.77465 | −0.0565451 | ||||||||
\(986\) | −42.6132 | −1.35708 | ||||||||
\(987\) | 32.8517 | 1.04568 | ||||||||
\(988\) | −33.2480 | −1.05776 | ||||||||
\(989\) | 6.57717 | 0.209142 | ||||||||
\(990\) | −4.14752 | −0.131817 | ||||||||
\(991\) | −19.6606 | −0.624539 | −0.312270 | − | 0.949994i | \(-0.601089\pi\) | ||||
−0.312270 | + | 0.949994i | \(0.601089\pi\) | |||||||
\(992\) | 34.2011 | 1.08589 | ||||||||
\(993\) | −65.1079 | −2.06614 | ||||||||
\(994\) | 67.9021 | 2.15372 | ||||||||
\(995\) | −0.817189 | −0.0259066 | ||||||||
\(996\) | −97.7405 | −3.09703 | ||||||||
\(997\) | 16.2073 | 0.513291 | 0.256646 | − | 0.966506i | \(-0.417383\pi\) | ||||
0.256646 | + | 0.966506i | \(0.417383\pi\) | |||||||
\(998\) | 78.2116 | 2.47574 | ||||||||
\(999\) | −12.9410 | −0.409435 |
(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 | 8003.2.a.b.1.9 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.b.1.9 | ✓ | 153 | 1.1 | even | 1 | trivial |