Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.74061 | −1.23080 | −0.615398 | − | 0.788217i | \(-0.711005\pi\) | ||||
−0.615398 | + | 0.788217i | \(0.711005\pi\) | |||||||
\(3\) | −3.34117 | −1.92903 | −0.964513 | − | 0.264036i | \(-0.914946\pi\) | ||||
−0.964513 | + | 0.264036i | \(0.914946\pi\) | |||||||
\(4\) | 1.02972 | 0.514859 | ||||||||
\(5\) | −2.66559 | −1.19209 | −0.596044 | − | 0.802952i | \(-0.703262\pi\) | ||||
−0.596044 | + | 0.802952i | \(0.703262\pi\) | |||||||
\(6\) | 5.81567 | 2.37424 | ||||||||
\(7\) | 0.0455688 | 0.0172234 | 0.00861169 | − | 0.999963i | \(-0.497259\pi\) | ||||
0.00861169 | + | 0.999963i | \(0.497259\pi\) | |||||||
\(8\) | 1.68888 | 0.597110 | ||||||||
\(9\) | 8.16342 | 2.72114 | ||||||||
\(10\) | 4.63975 | 1.46722 | ||||||||
\(11\) | −5.77378 | −1.74086 | −0.870430 | − | 0.492292i | \(-0.836159\pi\) | ||||
−0.870430 | + | 0.492292i | \(0.836159\pi\) | |||||||
\(12\) | −3.44046 | −0.993176 | ||||||||
\(13\) | 5.44313 | 1.50965 | 0.754826 | − | 0.655925i | \(-0.227721\pi\) | ||||
0.754826 | + | 0.655925i | \(0.227721\pi\) | |||||||
\(14\) | −0.0793174 | −0.0211985 | ||||||||
\(15\) | 8.90619 | 2.29957 | ||||||||
\(16\) | −4.99912 | −1.24978 | ||||||||
\(17\) | −2.61660 | −0.634620 | −0.317310 | − | 0.948322i | \(-0.602780\pi\) | ||||
−0.317310 | + | 0.948322i | \(0.602780\pi\) | |||||||
\(18\) | −14.2093 | −3.34917 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −2.74481 | −0.613757 | ||||||||
\(21\) | −0.152253 | −0.0332244 | ||||||||
\(22\) | 10.0499 | 2.14264 | ||||||||
\(23\) | −5.93212 | −1.23693 | −0.618466 | − | 0.785812i | \(-0.712246\pi\) | ||||
−0.618466 | + | 0.785812i | \(0.712246\pi\) | |||||||
\(24\) | −5.64284 | −1.15184 | ||||||||
\(25\) | 2.10537 | 0.421075 | ||||||||
\(26\) | −9.47436 | −1.85807 | ||||||||
\(27\) | −17.2519 | −3.32012 | ||||||||
\(28\) | 0.0469230 | 0.00886761 | ||||||||
\(29\) | −1.01835 | −0.189102 | −0.0945510 | − | 0.995520i | \(-0.530142\pi\) | ||||
−0.0945510 | + | 0.995520i | \(0.530142\pi\) | |||||||
\(30\) | −15.5022 | −2.83030 | ||||||||
\(31\) | 5.87824 | 1.05576 | 0.527881 | − | 0.849318i | \(-0.322987\pi\) | ||||
0.527881 | + | 0.849318i | \(0.322987\pi\) | |||||||
\(32\) | 5.32374 | 0.941114 | ||||||||
\(33\) | 19.2912 | 3.35816 | ||||||||
\(34\) | 4.55448 | 0.781087 | ||||||||
\(35\) | −0.121468 | −0.0205318 | ||||||||
\(36\) | 8.40602 | 1.40100 | ||||||||
\(37\) | −5.35484 | −0.880330 | −0.440165 | − | 0.897917i | \(-0.645080\pi\) | ||||
−0.440165 | + | 0.897917i | \(0.645080\pi\) | |||||||
\(38\) | −1.74061 | −0.282364 | ||||||||
\(39\) | −18.1864 | −2.91216 | ||||||||
\(40\) | −4.50187 | −0.711808 | ||||||||
\(41\) | −6.75452 | −1.05488 | −0.527439 | − | 0.849593i | \(-0.676848\pi\) | ||||
−0.527439 | + | 0.849593i | \(0.676848\pi\) | |||||||
\(42\) | 0.265013 | 0.0408924 | ||||||||
\(43\) | 8.74809 | 1.33407 | 0.667036 | − | 0.745026i | \(-0.267563\pi\) | ||||
0.667036 | + | 0.745026i | \(0.267563\pi\) | |||||||
\(44\) | −5.94537 | −0.896298 | ||||||||
\(45\) | −21.7603 | −3.24384 | ||||||||
\(46\) | 10.3255 | 1.52241 | ||||||||
\(47\) | −9.44683 | −1.37796 | −0.688981 | − | 0.724779i | \(-0.741942\pi\) | ||||
−0.688981 | + | 0.724779i | \(0.741942\pi\) | |||||||
\(48\) | 16.7029 | 2.41086 | ||||||||
\(49\) | −6.99792 | −0.999703 | ||||||||
\(50\) | −3.66463 | −0.518257 | ||||||||
\(51\) | 8.74252 | 1.22420 | ||||||||
\(52\) | 5.60489 | 0.777258 | ||||||||
\(53\) | 0.930586 | 0.127826 | 0.0639129 | − | 0.997955i | \(-0.479642\pi\) | ||||
0.0639129 | + | 0.997955i | \(0.479642\pi\) | |||||||
\(54\) | 30.0287 | 4.08639 | ||||||||
\(55\) | 15.3905 | 2.07526 | ||||||||
\(56\) | 0.0769603 | 0.0102843 | ||||||||
\(57\) | −3.34117 | −0.442549 | ||||||||
\(58\) | 1.77254 | 0.232746 | ||||||||
\(59\) | 6.84591 | 0.891261 | 0.445631 | − | 0.895217i | \(-0.352979\pi\) | ||||
0.445631 | + | 0.895217i | \(0.352979\pi\) | |||||||
\(60\) | 9.17087 | 1.18395 | ||||||||
\(61\) | 3.42660 | 0.438731 | 0.219366 | − | 0.975643i | \(-0.429601\pi\) | ||||
0.219366 | + | 0.975643i | \(0.429601\pi\) | |||||||
\(62\) | −10.2317 | −1.29943 | ||||||||
\(63\) | 0.371997 | 0.0468672 | ||||||||
\(64\) | 0.731682 | 0.0914603 | ||||||||
\(65\) | −14.5092 | −1.79964 | ||||||||
\(66\) | −33.5784 | −4.13322 | ||||||||
\(67\) | 12.3645 | 1.51057 | 0.755285 | − | 0.655397i | \(-0.227499\pi\) | ||||
0.755285 | + | 0.655397i | \(0.227499\pi\) | |||||||
\(68\) | −2.69436 | −0.326740 | ||||||||
\(69\) | 19.8202 | 2.38607 | ||||||||
\(70\) | 0.211428 | 0.0252705 | ||||||||
\(71\) | 1.90288 | 0.225831 | 0.112915 | − | 0.993605i | \(-0.463981\pi\) | ||||
0.112915 | + | 0.993605i | \(0.463981\pi\) | |||||||
\(72\) | 13.7870 | 1.62482 | ||||||||
\(73\) | 0.651226 | 0.0762203 | 0.0381101 | − | 0.999274i | \(-0.487866\pi\) | ||||
0.0381101 | + | 0.999274i | \(0.487866\pi\) | |||||||
\(74\) | 9.32067 | 1.08351 | ||||||||
\(75\) | −7.03441 | −0.812264 | ||||||||
\(76\) | 1.02972 | 0.118117 | ||||||||
\(77\) | −0.263104 | −0.0299835 | ||||||||
\(78\) | 31.6554 | 3.58427 | ||||||||
\(79\) | −8.80260 | −0.990370 | −0.495185 | − | 0.868788i | \(-0.664900\pi\) | ||||
−0.495185 | + | 0.868788i | \(0.664900\pi\) | |||||||
\(80\) | 13.3256 | 1.48985 | ||||||||
\(81\) | 33.1512 | 3.68346 | ||||||||
\(82\) | 11.7570 | 1.29834 | ||||||||
\(83\) | −2.19419 | −0.240843 | −0.120422 | − | 0.992723i | \(-0.538425\pi\) | ||||
−0.120422 | + | 0.992723i | \(0.538425\pi\) | |||||||
\(84\) | −0.156778 | −0.0171059 | ||||||||
\(85\) | 6.97480 | 0.756523 | ||||||||
\(86\) | −15.2270 | −1.64197 | ||||||||
\(87\) | 3.40247 | 0.364783 | ||||||||
\(88\) | −9.75123 | −1.03948 | ||||||||
\(89\) | −5.58740 | −0.592264 | −0.296132 | − | 0.955147i | \(-0.595697\pi\) | ||||
−0.296132 | + | 0.955147i | \(0.595697\pi\) | |||||||
\(90\) | 37.8762 | 3.99250 | ||||||||
\(91\) | 0.248037 | 0.0260013 | ||||||||
\(92\) | −6.10841 | −0.636846 | ||||||||
\(93\) | −19.6402 | −2.03659 | ||||||||
\(94\) | 16.4432 | 1.69599 | ||||||||
\(95\) | −2.66559 | −0.273484 | ||||||||
\(96\) | −17.7875 | −1.81543 | ||||||||
\(97\) | 15.4317 | 1.56685 | 0.783427 | − | 0.621484i | \(-0.213470\pi\) | ||||
0.783427 | + | 0.621484i | \(0.213470\pi\) | |||||||
\(98\) | 12.1806 | 1.23043 | ||||||||
\(99\) | −47.1338 | −4.73713 | ||||||||
\(100\) | 2.16794 | 0.216794 | ||||||||
\(101\) | 16.2442 | 1.61636 | 0.808181 | − | 0.588934i | \(-0.200452\pi\) | ||||
0.808181 | + | 0.588934i | \(0.200452\pi\) | |||||||
\(102\) | −15.2173 | −1.50674 | ||||||||
\(103\) | −19.4403 | −1.91551 | −0.957753 | − | 0.287592i | \(-0.907145\pi\) | ||||
−0.957753 | + | 0.287592i | \(0.907145\pi\) | |||||||
\(104\) | 9.19280 | 0.901428 | ||||||||
\(105\) | 0.405845 | 0.0396064 | ||||||||
\(106\) | −1.61979 | −0.157327 | ||||||||
\(107\) | 19.9334 | 1.92704 | 0.963519 | − | 0.267641i | \(-0.0862442\pi\) | ||||
0.963519 | + | 0.267641i | \(0.0862442\pi\) | |||||||
\(108\) | −17.7646 | −1.70939 | ||||||||
\(109\) | 3.64550 | 0.349176 | 0.174588 | − | 0.984642i | \(-0.444141\pi\) | ||||
0.174588 | + | 0.984642i | \(0.444141\pi\) | |||||||
\(110\) | −26.7889 | −2.55422 | ||||||||
\(111\) | 17.8914 | 1.69818 | ||||||||
\(112\) | −0.227804 | −0.0215254 | ||||||||
\(113\) | 16.2367 | 1.52742 | 0.763710 | − | 0.645559i | \(-0.223376\pi\) | ||||
0.763710 | + | 0.645559i | \(0.223376\pi\) | |||||||
\(114\) | 5.81567 | 0.544687 | ||||||||
\(115\) | 15.8126 | 1.47453 | ||||||||
\(116\) | −1.04861 | −0.0973609 | ||||||||
\(117\) | 44.4345 | 4.10798 | ||||||||
\(118\) | −11.9160 | −1.09696 | ||||||||
\(119\) | −0.119236 | −0.0109303 | ||||||||
\(120\) | 15.0415 | 1.37310 | ||||||||
\(121\) | 22.3366 | 2.03060 | ||||||||
\(122\) | −5.96437 | −0.539989 | ||||||||
\(123\) | 22.5680 | 2.03489 | ||||||||
\(124\) | 6.05293 | 0.543569 | ||||||||
\(125\) | 7.71589 | 0.690130 | ||||||||
\(126\) | −0.647502 | −0.0576840 | ||||||||
\(127\) | −9.77740 | −0.867604 | −0.433802 | − | 0.901008i | \(-0.642828\pi\) | ||||
−0.433802 | + | 0.901008i | \(0.642828\pi\) | |||||||
\(128\) | −11.9211 | −1.05368 | ||||||||
\(129\) | −29.2289 | −2.57346 | ||||||||
\(130\) | 25.2548 | 2.21499 | ||||||||
\(131\) | −3.36722 | −0.294196 | −0.147098 | − | 0.989122i | \(-0.546993\pi\) | ||||
−0.147098 | + | 0.989122i | \(0.546993\pi\) | |||||||
\(132\) | 19.8645 | 1.72898 | ||||||||
\(133\) | 0.0455688 | 0.00395132 | ||||||||
\(134\) | −21.5218 | −1.85920 | ||||||||
\(135\) | 45.9864 | 3.95788 | ||||||||
\(136\) | −4.41913 | −0.378938 | ||||||||
\(137\) | 12.3070 | 1.05145 | 0.525727 | − | 0.850653i | \(-0.323793\pi\) | ||||
0.525727 | + | 0.850653i | \(0.323793\pi\) | |||||||
\(138\) | −34.4992 | −2.93677 | ||||||||
\(139\) | −5.54031 | −0.469923 | −0.234962 | − | 0.972005i | \(-0.575496\pi\) | ||||
−0.234962 | + | 0.972005i | \(0.575496\pi\) | |||||||
\(140\) | −0.125078 | −0.0105710 | ||||||||
\(141\) | 31.5635 | 2.65812 | ||||||||
\(142\) | −3.31217 | −0.277951 | ||||||||
\(143\) | −31.4274 | −2.62809 | ||||||||
\(144\) | −40.8099 | −3.40082 | ||||||||
\(145\) | 2.71449 | 0.225426 | ||||||||
\(146\) | −1.13353 | −0.0938116 | ||||||||
\(147\) | 23.3813 | 1.92845 | ||||||||
\(148\) | −5.51397 | −0.453246 | ||||||||
\(149\) | 4.46211 | 0.365551 | 0.182775 | − | 0.983155i | \(-0.441492\pi\) | ||||
0.182775 | + | 0.983155i | \(0.441492\pi\) | |||||||
\(150\) | 12.2442 | 0.999732 | ||||||||
\(151\) | −16.9640 | −1.38051 | −0.690257 | − | 0.723564i | \(-0.742503\pi\) | ||||
−0.690257 | + | 0.723564i | \(0.742503\pi\) | |||||||
\(152\) | 1.68888 | 0.136986 | ||||||||
\(153\) | −21.3604 | −1.72689 | ||||||||
\(154\) | 0.457962 | 0.0369036 | ||||||||
\(155\) | −15.6690 | −1.25856 | ||||||||
\(156\) | −18.7269 | −1.49935 | ||||||||
\(157\) | 6.02503 | 0.480849 | 0.240425 | − | 0.970668i | \(-0.422713\pi\) | ||||
0.240425 | + | 0.970668i | \(0.422713\pi\) | |||||||
\(158\) | 15.3219 | 1.21894 | ||||||||
\(159\) | −3.10925 | −0.246579 | ||||||||
\(160\) | −14.1909 | −1.12189 | ||||||||
\(161\) | −0.270319 | −0.0213042 | ||||||||
\(162\) | −57.7032 | −4.53359 | ||||||||
\(163\) | 0.00745152 | 0.000583648 0 | 0.000291824 | − | 1.00000i | \(-0.499907\pi\) | ||||
0.000291824 | 1.00000i | \(0.499907\pi\) | ||||||||
\(164\) | −6.95525 | −0.543114 | ||||||||
\(165\) | −51.4224 | −4.00323 | ||||||||
\(166\) | 3.81922 | 0.296429 | ||||||||
\(167\) | 19.1424 | 1.48128 | 0.740642 | − | 0.671900i | \(-0.234521\pi\) | ||||
0.740642 | + | 0.671900i | \(0.234521\pi\) | |||||||
\(168\) | −0.257137 | −0.0198386 | ||||||||
\(169\) | 16.6277 | 1.27905 | ||||||||
\(170\) | −12.1404 | −0.931125 | ||||||||
\(171\) | 8.16342 | 0.624272 | ||||||||
\(172\) | 9.00807 | 0.686859 | ||||||||
\(173\) | −0.0597609 | −0.00454354 | −0.00227177 | − | 0.999997i | \(-0.500723\pi\) | ||||
−0.00227177 | + | 0.999997i | \(0.500723\pi\) | |||||||
\(174\) | −5.92236 | −0.448973 | ||||||||
\(175\) | 0.0959394 | 0.00725234 | ||||||||
\(176\) | 28.8638 | 2.17569 | ||||||||
\(177\) | −22.8733 | −1.71927 | ||||||||
\(178\) | 9.72548 | 0.728956 | ||||||||
\(179\) | −13.8722 | −1.03685 | −0.518427 | − | 0.855122i | \(-0.673482\pi\) | ||||
−0.518427 | + | 0.855122i | \(0.673482\pi\) | |||||||
\(180\) | −22.4070 | −1.67012 | ||||||||
\(181\) | 3.34790 | 0.248848 | 0.124424 | − | 0.992229i | \(-0.460292\pi\) | ||||
0.124424 | + | 0.992229i | \(0.460292\pi\) | |||||||
\(182\) | −0.431735 | −0.0320023 | ||||||||
\(183\) | −11.4489 | −0.846324 | ||||||||
\(184\) | −10.0186 | −0.738584 | ||||||||
\(185\) | 14.2738 | 1.04943 | ||||||||
\(186\) | 34.1859 | 2.50663 | ||||||||
\(187\) | 15.1077 | 1.10478 | ||||||||
\(188\) | −9.72757 | −0.709456 | ||||||||
\(189\) | −0.786147 | −0.0571838 | ||||||||
\(190\) | 4.63975 | 0.336603 | ||||||||
\(191\) | 21.5384 | 1.55846 | 0.779231 | − | 0.626736i | \(-0.215610\pi\) | ||||
0.779231 | + | 0.626736i | \(0.215610\pi\) | |||||||
\(192\) | −2.44467 | −0.176429 | ||||||||
\(193\) | 1.73663 | 0.125005 | 0.0625026 | − | 0.998045i | \(-0.480092\pi\) | ||||
0.0625026 | + | 0.998045i | \(0.480092\pi\) | |||||||
\(194\) | −26.8606 | −1.92848 | ||||||||
\(195\) | 48.4776 | 3.47155 | ||||||||
\(196\) | −7.20589 | −0.514706 | ||||||||
\(197\) | −22.6717 | −1.61529 | −0.807644 | − | 0.589670i | \(-0.799258\pi\) | ||||
−0.807644 | + | 0.589670i | \(0.799258\pi\) | |||||||
\(198\) | 82.0415 | 5.83044 | ||||||||
\(199\) | −14.8533 | −1.05292 | −0.526460 | − | 0.850200i | \(-0.676481\pi\) | ||||
−0.526460 | + | 0.850200i | \(0.676481\pi\) | |||||||
\(200\) | 3.55573 | 0.251428 | ||||||||
\(201\) | −41.3120 | −2.91393 | ||||||||
\(202\) | −28.2749 | −1.98941 | ||||||||
\(203\) | −0.0464048 | −0.00325698 | ||||||||
\(204\) | 9.00233 | 0.630289 | ||||||||
\(205\) | 18.0048 | 1.25751 | ||||||||
\(206\) | 33.8379 | 2.35760 | ||||||||
\(207\) | −48.4264 | −3.36587 | ||||||||
\(208\) | −27.2108 | −1.88673 | ||||||||
\(209\) | −5.77378 | −0.399381 | ||||||||
\(210\) | −0.706416 | −0.0487474 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | 0.958241 | 0.0658123 | ||||||||
\(213\) | −6.35785 | −0.435633 | ||||||||
\(214\) | −34.6963 | −2.37179 | ||||||||
\(215\) | −23.3188 | −1.59033 | ||||||||
\(216\) | −29.1364 | −1.98248 | ||||||||
\(217\) | 0.267864 | 0.0181838 | ||||||||
\(218\) | −6.34539 | −0.429764 | ||||||||
\(219\) | −2.17586 | −0.147031 | ||||||||
\(220\) | 15.8479 | 1.06847 | ||||||||
\(221\) | −14.2425 | −0.958055 | ||||||||
\(222\) | −31.1420 | −2.09011 | ||||||||
\(223\) | 7.03060 | 0.470804 | 0.235402 | − | 0.971898i | \(-0.424359\pi\) | ||||
0.235402 | + | 0.971898i | \(0.424359\pi\) | |||||||
\(224\) | 0.242597 | 0.0162092 | ||||||||
\(225\) | 17.1871 | 1.14580 | ||||||||
\(226\) | −28.2617 | −1.87994 | ||||||||
\(227\) | −20.5078 | −1.36115 | −0.680576 | − | 0.732677i | \(-0.738271\pi\) | ||||
−0.680576 | + | 0.732677i | \(0.738271\pi\) | |||||||
\(228\) | −3.44046 | −0.227850 | ||||||||
\(229\) | 18.4436 | 1.21879 | 0.609395 | − | 0.792867i | \(-0.291413\pi\) | ||||
0.609395 | + | 0.792867i | \(0.291413\pi\) | |||||||
\(230\) | −27.5235 | −1.81485 | ||||||||
\(231\) | 0.879076 | 0.0578390 | ||||||||
\(232\) | −1.71986 | −0.112915 | ||||||||
\(233\) | 23.4767 | 1.53801 | 0.769004 | − | 0.639244i | \(-0.220753\pi\) | ||||
0.769004 | + | 0.639244i | \(0.220753\pi\) | |||||||
\(234\) | −77.3431 | −5.05608 | ||||||||
\(235\) | 25.1814 | 1.64265 | ||||||||
\(236\) | 7.04935 | 0.458874 | ||||||||
\(237\) | 29.4110 | 1.91045 | ||||||||
\(238\) | 0.207542 | 0.0134530 | ||||||||
\(239\) | −9.84627 | −0.636902 | −0.318451 | − | 0.947939i | \(-0.603163\pi\) | ||||
−0.318451 | + | 0.947939i | \(0.603163\pi\) | |||||||
\(240\) | −44.5231 | −2.87395 | ||||||||
\(241\) | −1.95165 | −0.125717 | −0.0628584 | − | 0.998022i | \(-0.520022\pi\) | ||||
−0.0628584 | + | 0.998022i | \(0.520022\pi\) | |||||||
\(242\) | −38.8792 | −2.49925 | ||||||||
\(243\) | −59.0081 | −3.78537 | ||||||||
\(244\) | 3.52843 | 0.225885 | ||||||||
\(245\) | 18.6536 | 1.19173 | ||||||||
\(246\) | −39.2821 | −2.50453 | ||||||||
\(247\) | 5.44313 | 0.346338 | ||||||||
\(248\) | 9.92765 | 0.630406 | ||||||||
\(249\) | 7.33115 | 0.464593 | ||||||||
\(250\) | −13.4303 | −0.849409 | ||||||||
\(251\) | −0.0590057 | −0.00372441 | −0.00186220 | − | 0.999998i | \(-0.500593\pi\) | ||||
−0.00186220 | + | 0.999998i | \(0.500593\pi\) | |||||||
\(252\) | 0.383052 | 0.0241300 | ||||||||
\(253\) | 34.2508 | 2.15333 | ||||||||
\(254\) | 17.0186 | 1.06784 | ||||||||
\(255\) | −23.3040 | −1.45935 | ||||||||
\(256\) | 19.2865 | 1.20541 | ||||||||
\(257\) | 13.9070 | 0.867495 | 0.433747 | − | 0.901035i | \(-0.357191\pi\) | ||||
0.433747 | + | 0.901035i | \(0.357191\pi\) | |||||||
\(258\) | 50.8760 | 3.16740 | ||||||||
\(259\) | −0.244013 | −0.0151623 | ||||||||
\(260\) | −14.9403 | −0.926560 | ||||||||
\(261\) | −8.31318 | −0.514573 | ||||||||
\(262\) | 5.86102 | 0.362095 | ||||||||
\(263\) | 21.7293 | 1.33988 | 0.669942 | − | 0.742413i | \(-0.266319\pi\) | ||||
0.669942 | + | 0.742413i | \(0.266319\pi\) | |||||||
\(264\) | 32.5805 | 2.00519 | ||||||||
\(265\) | −2.48056 | −0.152380 | ||||||||
\(266\) | −0.0793174 | −0.00486326 | ||||||||
\(267\) | 18.6685 | 1.14249 | ||||||||
\(268\) | 12.7320 | 0.777730 | ||||||||
\(269\) | −24.6374 | −1.50217 | −0.751084 | − | 0.660207i | \(-0.770468\pi\) | ||||
−0.751084 | + | 0.660207i | \(0.770468\pi\) | |||||||
\(270\) | −80.0443 | −4.87134 | ||||||||
\(271\) | −19.3262 | −1.17399 | −0.586993 | − | 0.809592i | \(-0.699688\pi\) | ||||
−0.586993 | + | 0.809592i | \(0.699688\pi\) | |||||||
\(272\) | 13.0807 | 0.793134 | ||||||||
\(273\) | −0.828733 | −0.0501572 | ||||||||
\(274\) | −21.4216 | −1.29413 | ||||||||
\(275\) | −12.1560 | −0.733033 | ||||||||
\(276\) | 20.4092 | 1.22849 | ||||||||
\(277\) | −5.80451 | −0.348759 | −0.174380 | − | 0.984679i | \(-0.555792\pi\) | ||||
−0.174380 | + | 0.984679i | \(0.555792\pi\) | |||||||
\(278\) | 9.64351 | 0.578380 | ||||||||
\(279\) | 47.9865 | 2.87288 | ||||||||
\(280\) | −0.205145 | −0.0122597 | ||||||||
\(281\) | 2.12615 | 0.126836 | 0.0634178 | − | 0.997987i | \(-0.479800\pi\) | ||||
0.0634178 | + | 0.997987i | \(0.479800\pi\) | |||||||
\(282\) | −54.9397 | −3.27161 | ||||||||
\(283\) | −2.58168 | −0.153465 | −0.0767326 | − | 0.997052i | \(-0.524449\pi\) | ||||
−0.0767326 | + | 0.997052i | \(0.524449\pi\) | |||||||
\(284\) | 1.95943 | 0.116271 | ||||||||
\(285\) | 8.90619 | 0.527557 | ||||||||
\(286\) | 54.7029 | 3.23465 | ||||||||
\(287\) | −0.307795 | −0.0181686 | ||||||||
\(288\) | 43.4599 | 2.56090 | ||||||||
\(289\) | −10.1534 | −0.597258 | ||||||||
\(290\) | −4.72487 | −0.277454 | ||||||||
\(291\) | −51.5600 | −3.02250 | ||||||||
\(292\) | 0.670580 | 0.0392427 | ||||||||
\(293\) | 21.6572 | 1.26523 | 0.632614 | − | 0.774468i | \(-0.281982\pi\) | ||||
0.632614 | + | 0.774468i | \(0.281982\pi\) | |||||||
\(294\) | −40.6976 | −2.37353 | ||||||||
\(295\) | −18.2484 | −1.06246 | ||||||||
\(296\) | −9.04368 | −0.525653 | ||||||||
\(297\) | 99.6085 | 5.77987 | ||||||||
\(298\) | −7.76679 | −0.449918 | ||||||||
\(299\) | −32.2893 | −1.86734 | ||||||||
\(300\) | −7.24346 | −0.418201 | ||||||||
\(301\) | 0.398640 | 0.0229772 | ||||||||
\(302\) | 29.5278 | 1.69913 | ||||||||
\(303\) | −54.2748 | −3.11800 | ||||||||
\(304\) | −4.99912 | −0.286719 | ||||||||
\(305\) | −9.13392 | −0.523007 | ||||||||
\(306\) | 37.1802 | 2.12545 | ||||||||
\(307\) | 27.9345 | 1.59430 | 0.797152 | − | 0.603779i | \(-0.206339\pi\) | ||||
0.797152 | + | 0.603779i | \(0.206339\pi\) | |||||||
\(308\) | −0.270923 | −0.0154373 | ||||||||
\(309\) | 64.9532 | 3.69506 | ||||||||
\(310\) | 27.2736 | 1.54903 | ||||||||
\(311\) | 11.4609 | 0.649886 | 0.324943 | − | 0.945734i | \(-0.394655\pi\) | ||||
0.324943 | + | 0.945734i | \(0.394655\pi\) | |||||||
\(312\) | −30.7147 | −1.73888 | ||||||||
\(313\) | −5.97637 | −0.337804 | −0.168902 | − | 0.985633i | \(-0.554022\pi\) | ||||
−0.168902 | + | 0.985633i | \(0.554022\pi\) | |||||||
\(314\) | −10.4872 | −0.591828 | ||||||||
\(315\) | −0.991592 | −0.0558699 | ||||||||
\(316\) | −9.06419 | −0.509901 | ||||||||
\(317\) | 12.0415 | 0.676320 | 0.338160 | − | 0.941089i | \(-0.390195\pi\) | ||||
0.338160 | + | 0.941089i | \(0.390195\pi\) | |||||||
\(318\) | 5.41198 | 0.303489 | ||||||||
\(319\) | 5.87970 | 0.329200 | ||||||||
\(320\) | −1.95036 | −0.109029 | ||||||||
\(321\) | −66.6010 | −3.71730 | ||||||||
\(322\) | 0.470520 | 0.0262211 | ||||||||
\(323\) | −2.61660 | −0.145592 | ||||||||
\(324\) | 34.1363 | 1.89646 | ||||||||
\(325\) | 11.4598 | 0.635677 | ||||||||
\(326\) | −0.0129702 | −0.000718351 0 | ||||||||
\(327\) | −12.1802 | −0.673569 | ||||||||
\(328\) | −11.4076 | −0.629878 | ||||||||
\(329\) | −0.430481 | −0.0237332 | ||||||||
\(330\) | 89.5063 | 4.92716 | ||||||||
\(331\) | −29.6154 | −1.62781 | −0.813904 | − | 0.581000i | \(-0.802662\pi\) | ||||
−0.813904 | + | 0.581000i | \(0.802662\pi\) | |||||||
\(332\) | −2.25939 | −0.124000 | ||||||||
\(333\) | −43.7138 | −2.39550 | ||||||||
\(334\) | −33.3194 | −1.82316 | ||||||||
\(335\) | −32.9588 | −1.80073 | ||||||||
\(336\) | 0.761131 | 0.0415231 | ||||||||
\(337\) | 17.7117 | 0.964817 | 0.482409 | − | 0.875946i | \(-0.339762\pi\) | ||||
0.482409 | + | 0.875946i | \(0.339762\pi\) | |||||||
\(338\) | −28.9422 | −1.57425 | ||||||||
\(339\) | −54.2496 | −2.94643 | ||||||||
\(340\) | 7.18207 | 0.389503 | ||||||||
\(341\) | −33.9397 | −1.83794 | ||||||||
\(342\) | −14.2093 | −0.768352 | ||||||||
\(343\) | −0.637869 | −0.0344417 | ||||||||
\(344\) | 14.7745 | 0.796587 | ||||||||
\(345\) | −52.8326 | −2.84441 | ||||||||
\(346\) | 0.104020 | 0.00559217 | ||||||||
\(347\) | 13.0704 | 0.701658 | 0.350829 | − | 0.936440i | \(-0.385900\pi\) | ||||
0.350829 | + | 0.936440i | \(0.385900\pi\) | |||||||
\(348\) | 3.50358 | 0.187812 | ||||||||
\(349\) | 0.495731 | 0.0265359 | 0.0132679 | − | 0.999912i | \(-0.495777\pi\) | ||||
0.0132679 | + | 0.999912i | \(0.495777\pi\) | |||||||
\(350\) | −0.166993 | −0.00892615 | ||||||||
\(351\) | −93.9041 | −5.01223 | ||||||||
\(352\) | −30.7381 | −1.63835 | ||||||||
\(353\) | 21.6028 | 1.14980 | 0.574901 | − | 0.818223i | \(-0.305040\pi\) | ||||
0.574901 | + | 0.818223i | \(0.305040\pi\) | |||||||
\(354\) | 39.8135 | 2.11607 | ||||||||
\(355\) | −5.07231 | −0.269210 | ||||||||
\(356\) | −5.75345 | −0.304932 | ||||||||
\(357\) | 0.398386 | 0.0210848 | ||||||||
\(358\) | 24.1460 | 1.27616 | ||||||||
\(359\) | −29.3675 | −1.54995 | −0.774977 | − | 0.631989i | \(-0.782239\pi\) | ||||
−0.774977 | + | 0.631989i | \(0.782239\pi\) | |||||||
\(360\) | −36.7506 | −1.93693 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −5.82739 | −0.306281 | ||||||||
\(363\) | −74.6302 | −3.91707 | ||||||||
\(364\) | 0.255408 | 0.0133870 | ||||||||
\(365\) | −1.73590 | −0.0908613 | ||||||||
\(366\) | 19.9280 | 1.04165 | ||||||||
\(367\) | 1.84372 | 0.0962414 | 0.0481207 | − | 0.998842i | \(-0.484677\pi\) | ||||
0.0481207 | + | 0.998842i | \(0.484677\pi\) | |||||||
\(368\) | 29.6553 | 1.54589 | ||||||||
\(369\) | −55.1400 | −2.87047 | ||||||||
\(370\) | −24.8451 | −1.29164 | ||||||||
\(371\) | 0.0424057 | 0.00220159 | ||||||||
\(372\) | −20.2239 | −1.04856 | ||||||||
\(373\) | −5.04481 | −0.261210 | −0.130605 | − | 0.991434i | \(-0.541692\pi\) | ||||
−0.130605 | + | 0.991434i | \(0.541692\pi\) | |||||||
\(374\) | −26.2966 | −1.35976 | ||||||||
\(375\) | −25.7801 | −1.33128 | ||||||||
\(376\) | −15.9546 | −0.822795 | ||||||||
\(377\) | −5.54299 | −0.285478 | ||||||||
\(378\) | 1.36837 | 0.0703815 | ||||||||
\(379\) | 13.9046 | 0.714233 | 0.357117 | − | 0.934060i | \(-0.383760\pi\) | ||||
0.357117 | + | 0.934060i | \(0.383760\pi\) | |||||||
\(380\) | −2.74481 | −0.140806 | ||||||||
\(381\) | 32.6680 | 1.67363 | ||||||||
\(382\) | −37.4899 | −1.91815 | ||||||||
\(383\) | −36.4675 | −1.86340 | −0.931701 | − | 0.363226i | \(-0.881675\pi\) | ||||
−0.931701 | + | 0.363226i | \(0.881675\pi\) | |||||||
\(384\) | 39.8303 | 2.03258 | ||||||||
\(385\) | 0.701328 | 0.0357430 | ||||||||
\(386\) | −3.02279 | −0.153856 | ||||||||
\(387\) | 71.4143 | 3.63020 | ||||||||
\(388\) | 15.8903 | 0.806708 | ||||||||
\(389\) | −27.3415 | −1.38627 | −0.693134 | − | 0.720808i | \(-0.743771\pi\) | ||||
−0.693134 | + | 0.720808i | \(0.743771\pi\) | |||||||
\(390\) | −84.3805 | −4.27277 | ||||||||
\(391\) | 15.5220 | 0.784981 | ||||||||
\(392\) | −11.8187 | −0.596933 | ||||||||
\(393\) | 11.2505 | 0.567511 | ||||||||
\(394\) | 39.4625 | 1.98809 | ||||||||
\(395\) | 23.4641 | 1.18061 | ||||||||
\(396\) | −48.5345 | −2.43895 | ||||||||
\(397\) | 6.47117 | 0.324779 | 0.162389 | − | 0.986727i | \(-0.448080\pi\) | ||||
0.162389 | + | 0.986727i | \(0.448080\pi\) | |||||||
\(398\) | 25.8537 | 1.29593 | ||||||||
\(399\) | −0.152253 | −0.00762219 | ||||||||
\(400\) | −10.5250 | −0.526251 | ||||||||
\(401\) | −22.4117 | −1.11919 | −0.559594 | − | 0.828767i | \(-0.689043\pi\) | ||||
−0.559594 | + | 0.828767i | \(0.689043\pi\) | |||||||
\(402\) | 71.9081 | 3.58645 | ||||||||
\(403\) | 31.9960 | 1.59383 | ||||||||
\(404\) | 16.7270 | 0.832198 | ||||||||
\(405\) | −88.3674 | −4.39101 | ||||||||
\(406\) | 0.0807725 | 0.00400867 | ||||||||
\(407\) | 30.9177 | 1.53253 | ||||||||
\(408\) | 14.7651 | 0.730980 | ||||||||
\(409\) | 36.2751 | 1.79369 | 0.896845 | − | 0.442345i | \(-0.145853\pi\) | ||||
0.896845 | + | 0.442345i | \(0.145853\pi\) | |||||||
\(410\) | −31.3393 | −1.54774 | ||||||||
\(411\) | −41.1196 | −2.02828 | ||||||||
\(412\) | −20.0180 | −0.986216 | ||||||||
\(413\) | 0.311960 | 0.0153505 | ||||||||
\(414\) | 84.2913 | 4.14269 | ||||||||
\(415\) | 5.84880 | 0.287106 | ||||||||
\(416\) | 28.9778 | 1.42075 | ||||||||
\(417\) | 18.5111 | 0.906494 | ||||||||
\(418\) | 10.0499 | 0.491556 | ||||||||
\(419\) | −15.5144 | −0.757928 | −0.378964 | − | 0.925411i | \(-0.623720\pi\) | ||||
−0.378964 | + | 0.925411i | \(0.623720\pi\) | |||||||
\(420\) | 0.417905 | 0.0203917 | ||||||||
\(421\) | 4.98991 | 0.243193 | 0.121597 | − | 0.992580i | \(-0.461199\pi\) | ||||
0.121597 | + | 0.992580i | \(0.461199\pi\) | |||||||
\(422\) | −1.74061 | −0.0847315 | ||||||||
\(423\) | −77.1185 | −3.74963 | ||||||||
\(424\) | 1.57165 | 0.0763260 | ||||||||
\(425\) | −5.50893 | −0.267222 | ||||||||
\(426\) | 11.0665 | 0.536175 | ||||||||
\(427\) | 0.156146 | 0.00755644 | ||||||||
\(428\) | 20.5258 | 0.992152 | ||||||||
\(429\) | 105.004 | 5.06966 | ||||||||
\(430\) | 40.5890 | 1.95737 | ||||||||
\(431\) | −0.927561 | −0.0446791 | −0.0223395 | − | 0.999750i | \(-0.507111\pi\) | ||||
−0.0223395 | + | 0.999750i | \(0.507111\pi\) | |||||||
\(432\) | 86.2441 | 4.14942 | ||||||||
\(433\) | 4.49916 | 0.216216 | 0.108108 | − | 0.994139i | \(-0.465521\pi\) | ||||
0.108108 | + | 0.994139i | \(0.465521\pi\) | |||||||
\(434\) | −0.466247 | −0.0223806 | ||||||||
\(435\) | −9.06958 | −0.434853 | ||||||||
\(436\) | 3.75384 | 0.179776 | ||||||||
\(437\) | −5.93212 | −0.283772 | ||||||||
\(438\) | 3.78732 | 0.180965 | ||||||||
\(439\) | −20.3729 | −0.972345 | −0.486172 | − | 0.873863i | \(-0.661607\pi\) | ||||
−0.486172 | + | 0.873863i | \(0.661607\pi\) | |||||||
\(440\) | 25.9928 | 1.23916 | ||||||||
\(441\) | −57.1270 | −2.72033 | ||||||||
\(442\) | 24.7906 | 1.17917 | ||||||||
\(443\) | 39.2967 | 1.86704 | 0.933522 | − | 0.358521i | \(-0.116719\pi\) | ||||
0.933522 | + | 0.358521i | \(0.116719\pi\) | |||||||
\(444\) | 18.4231 | 0.874322 | ||||||||
\(445\) | 14.8937 | 0.706031 | ||||||||
\(446\) | −12.2375 | −0.579464 | ||||||||
\(447\) | −14.9087 | −0.705156 | ||||||||
\(448\) | 0.0333419 | 0.00157526 | ||||||||
\(449\) | 15.8914 | 0.749964 | 0.374982 | − | 0.927032i | \(-0.377649\pi\) | ||||
0.374982 | + | 0.927032i | \(0.377649\pi\) | |||||||
\(450\) | −29.9159 | −1.41025 | ||||||||
\(451\) | 38.9991 | 1.83640 | ||||||||
\(452\) | 16.7192 | 0.786406 | ||||||||
\(453\) | 56.6798 | 2.66305 | ||||||||
\(454\) | 35.6961 | 1.67530 | ||||||||
\(455\) | −0.661165 | −0.0309959 | ||||||||
\(456\) | −5.64284 | −0.264250 | ||||||||
\(457\) | −14.8024 | −0.692426 | −0.346213 | − | 0.938156i | \(-0.612533\pi\) | ||||
−0.346213 | + | 0.938156i | \(0.612533\pi\) | |||||||
\(458\) | −32.1031 | −1.50008 | ||||||||
\(459\) | 45.1413 | 2.10702 | ||||||||
\(460\) | 16.2825 | 0.759176 | ||||||||
\(461\) | 31.9799 | 1.48945 | 0.744726 | − | 0.667371i | \(-0.232580\pi\) | ||||
0.744726 | + | 0.667371i | \(0.232580\pi\) | |||||||
\(462\) | −1.53013 | −0.0711880 | ||||||||
\(463\) | 9.86644 | 0.458532 | 0.229266 | − | 0.973364i | \(-0.426367\pi\) | ||||
0.229266 | + | 0.973364i | \(0.426367\pi\) | |||||||
\(464\) | 5.09083 | 0.236336 | ||||||||
\(465\) | 52.3527 | 2.42780 | ||||||||
\(466\) | −40.8637 | −1.89297 | ||||||||
\(467\) | 28.9588 | 1.34005 | 0.670026 | − | 0.742337i | \(-0.266283\pi\) | ||||
0.670026 | + | 0.742337i | \(0.266283\pi\) | |||||||
\(468\) | 45.7550 | 2.11503 | ||||||||
\(469\) | 0.563437 | 0.0260171 | ||||||||
\(470\) | −43.8310 | −2.02177 | ||||||||
\(471\) | −20.1306 | −0.927571 | ||||||||
\(472\) | 11.5619 | 0.532181 | ||||||||
\(473\) | −50.5096 | −2.32243 | ||||||||
\(474\) | −51.1930 | −2.35137 | ||||||||
\(475\) | 2.10537 | 0.0966012 | ||||||||
\(476\) | −0.122779 | −0.00562756 | ||||||||
\(477\) | 7.59676 | 0.347832 | ||||||||
\(478\) | 17.1385 | 0.783897 | ||||||||
\(479\) | −12.6325 | −0.577193 | −0.288597 | − | 0.957451i | \(-0.593189\pi\) | ||||
−0.288597 | + | 0.957451i | \(0.593189\pi\) | |||||||
\(480\) | 47.4143 | 2.16416 | ||||||||
\(481\) | −29.1471 | −1.32899 | ||||||||
\(482\) | 3.39706 | 0.154732 | ||||||||
\(483\) | 0.903183 | 0.0410963 | ||||||||
\(484\) | 23.0004 | 1.04547 | ||||||||
\(485\) | −41.1346 | −1.86783 | ||||||||
\(486\) | 102.710 | 4.65902 | ||||||||
\(487\) | −23.9161 | −1.08374 | −0.541870 | − | 0.840462i | \(-0.682283\pi\) | ||||
−0.541870 | + | 0.840462i | \(0.682283\pi\) | |||||||
\(488\) | 5.78712 | 0.261971 | ||||||||
\(489\) | −0.0248968 | −0.00112587 | ||||||||
\(490\) | −32.4686 | −1.46678 | ||||||||
\(491\) | 1.45598 | 0.0657076 | 0.0328538 | − | 0.999460i | \(-0.489540\pi\) | ||||
0.0328538 | + | 0.999460i | \(0.489540\pi\) | |||||||
\(492\) | 23.2387 | 1.04768 | ||||||||
\(493\) | 2.66461 | 0.120008 | ||||||||
\(494\) | −9.47436 | −0.426271 | ||||||||
\(495\) | 125.639 | 5.64707 | ||||||||
\(496\) | −29.3860 | −1.31947 | ||||||||
\(497\) | 0.0867121 | 0.00388957 | ||||||||
\(498\) | −12.7607 | −0.571819 | ||||||||
\(499\) | −15.2554 | −0.682925 | −0.341463 | − | 0.939895i | \(-0.610922\pi\) | ||||
−0.341463 | + | 0.939895i | \(0.610922\pi\) | |||||||
\(500\) | 7.94519 | 0.355320 | ||||||||
\(501\) | −63.9581 | −2.85744 | ||||||||
\(502\) | 0.102706 | 0.00458399 | ||||||||
\(503\) | 28.9694 | 1.29168 | 0.645842 | − | 0.763471i | \(-0.276507\pi\) | ||||
0.645842 | + | 0.763471i | \(0.276507\pi\) | |||||||
\(504\) | 0.628259 | 0.0279849 | ||||||||
\(505\) | −43.3005 | −1.92685 | ||||||||
\(506\) | −59.6172 | −2.65031 | ||||||||
\(507\) | −55.5558 | −2.46732 | ||||||||
\(508\) | −10.0680 | −0.446694 | ||||||||
\(509\) | 4.96622 | 0.220124 | 0.110062 | − | 0.993925i | \(-0.464895\pi\) | ||||
0.110062 | + | 0.993925i | \(0.464895\pi\) | |||||||
\(510\) | 40.5631 | 1.79616 | ||||||||
\(511\) | 0.0296756 | 0.00131277 | ||||||||
\(512\) | −9.72818 | −0.429929 | ||||||||
\(513\) | −17.2519 | −0.761688 | ||||||||
\(514\) | −24.2066 | −1.06771 | ||||||||
\(515\) | 51.8198 | 2.28345 | ||||||||
\(516\) | −30.0975 | −1.32497 | ||||||||
\(517\) | 54.5440 | 2.39884 | ||||||||
\(518\) | 0.424732 | 0.0186616 | ||||||||
\(519\) | 0.199671 | 0.00876460 | ||||||||
\(520\) | −24.5042 | −1.07458 | ||||||||
\(521\) | 14.7790 | 0.647481 | 0.323741 | − | 0.946146i | \(-0.395059\pi\) | ||||
0.323741 | + | 0.946146i | \(0.395059\pi\) | |||||||
\(522\) | 14.4700 | 0.633334 | ||||||||
\(523\) | −4.11833 | −0.180082 | −0.0900410 | − | 0.995938i | \(-0.528700\pi\) | ||||
−0.0900410 | + | 0.995938i | \(0.528700\pi\) | |||||||
\(524\) | −3.46729 | −0.151469 | ||||||||
\(525\) | −0.320550 | −0.0139899 | ||||||||
\(526\) | −37.8222 | −1.64912 | ||||||||
\(527\) | −15.3810 | −0.670008 | ||||||||
\(528\) | −96.4389 | −4.19696 | ||||||||
\(529\) | 12.1900 | 0.530001 | ||||||||
\(530\) | 4.31769 | 0.187548 | ||||||||
\(531\) | 55.8860 | 2.42525 | ||||||||
\(532\) | 0.0469230 | 0.00203437 | ||||||||
\(533\) | −36.7657 | −1.59250 | ||||||||
\(534\) | −32.4945 | −1.40617 | ||||||||
\(535\) | −53.1344 | −2.29720 | ||||||||
\(536\) | 20.8822 | 0.901975 | ||||||||
\(537\) | 46.3492 | 2.00012 | ||||||||
\(538\) | 42.8840 | 1.84886 | ||||||||
\(539\) | 40.4045 | 1.74034 | ||||||||
\(540\) | 47.3530 | 2.03775 | ||||||||
\(541\) | −12.5585 | −0.539933 | −0.269967 | − | 0.962870i | \(-0.587013\pi\) | ||||
−0.269967 | + | 0.962870i | \(0.587013\pi\) | |||||||
\(542\) | 33.6394 | 1.44494 | ||||||||
\(543\) | −11.1859 | −0.480033 | ||||||||
\(544\) | −13.9301 | −0.597249 | ||||||||
\(545\) | −9.71741 | −0.416248 | ||||||||
\(546\) | 1.44250 | 0.0617333 | ||||||||
\(547\) | −4.37116 | −0.186897 | −0.0934486 | − | 0.995624i | \(-0.529789\pi\) | ||||
−0.0934486 | + | 0.995624i | \(0.529789\pi\) | |||||||
\(548\) | 12.6727 | 0.541351 | ||||||||
\(549\) | 27.9728 | 1.19385 | ||||||||
\(550\) | 21.1588 | 0.902214 | ||||||||
\(551\) | −1.01835 | −0.0433830 | ||||||||
\(552\) | 33.4740 | 1.42475 | ||||||||
\(553\) | −0.401124 | −0.0170575 | ||||||||
\(554\) | 10.1034 | 0.429251 | ||||||||
\(555\) | −47.6912 | −2.02438 | ||||||||
\(556\) | −5.70496 | −0.241944 | ||||||||
\(557\) | −26.0003 | −1.10167 | −0.550835 | − | 0.834614i | \(-0.685690\pi\) | ||||
−0.550835 | + | 0.834614i | \(0.685690\pi\) | |||||||
\(558\) | −83.5257 | −3.53593 | ||||||||
\(559\) | 47.6170 | 2.01398 | ||||||||
\(560\) | 0.607232 | 0.0256602 | ||||||||
\(561\) | −50.4774 | −2.13116 | ||||||||
\(562\) | −3.70080 | −0.156109 | ||||||||
\(563\) | −16.9417 | −0.714007 | −0.357004 | − | 0.934103i | \(-0.616202\pi\) | ||||
−0.357004 | + | 0.934103i | \(0.616202\pi\) | |||||||
\(564\) | 32.5015 | 1.36856 | ||||||||
\(565\) | −43.2804 | −1.82082 | ||||||||
\(566\) | 4.49370 | 0.188884 | ||||||||
\(567\) | 1.51066 | 0.0634417 | ||||||||
\(568\) | 3.21374 | 0.134846 | ||||||||
\(569\) | −39.1407 | −1.64086 | −0.820431 | − | 0.571745i | \(-0.806267\pi\) | ||||
−0.820431 | + | 0.571745i | \(0.806267\pi\) | |||||||
\(570\) | −15.5022 | −0.649316 | ||||||||
\(571\) | −14.0289 | −0.587090 | −0.293545 | − | 0.955945i | \(-0.594835\pi\) | ||||
−0.293545 | + | 0.955945i | \(0.594835\pi\) | |||||||
\(572\) | −32.3614 | −1.35310 | ||||||||
\(573\) | −71.9634 | −3.00631 | ||||||||
\(574\) | 0.535751 | 0.0223618 | ||||||||
\(575\) | −12.4893 | −0.520841 | ||||||||
\(576\) | 5.97303 | 0.248876 | ||||||||
\(577\) | −37.9296 | −1.57903 | −0.789515 | − | 0.613731i | \(-0.789668\pi\) | ||||
−0.789515 | + | 0.613731i | \(0.789668\pi\) | |||||||
\(578\) | 17.6731 | 0.735103 | ||||||||
\(579\) | −5.80237 | −0.241138 | ||||||||
\(580\) | 2.79516 | 0.116063 | ||||||||
\(581\) | −0.0999864 | −0.00414814 | ||||||||
\(582\) | 89.7458 | 3.72008 | ||||||||
\(583\) | −5.37300 | −0.222527 | ||||||||
\(584\) | 1.09984 | 0.0455119 | ||||||||
\(585\) | −118.444 | −4.89707 | ||||||||
\(586\) | −37.6967 | −1.55724 | ||||||||
\(587\) | −1.21754 | −0.0502534 | −0.0251267 | − | 0.999684i | \(-0.507999\pi\) | ||||
−0.0251267 | + | 0.999684i | \(0.507999\pi\) | |||||||
\(588\) | 24.0761 | 0.992881 | ||||||||
\(589\) | 5.87824 | 0.242209 | ||||||||
\(590\) | 31.7633 | 1.30767 | ||||||||
\(591\) | 75.7499 | 3.11593 | ||||||||
\(592\) | 26.7695 | 1.10022 | ||||||||
\(593\) | 38.6941 | 1.58898 | 0.794488 | − | 0.607279i | \(-0.207739\pi\) | ||||
0.794488 | + | 0.607279i | \(0.207739\pi\) | |||||||
\(594\) | −173.379 | −7.11384 | ||||||||
\(595\) | 0.317833 | 0.0130299 | ||||||||
\(596\) | 4.59472 | 0.188207 | ||||||||
\(597\) | 49.6273 | 2.03111 | ||||||||
\(598\) | 56.2030 | 2.29831 | ||||||||
\(599\) | 16.5459 | 0.676048 | 0.338024 | − | 0.941137i | \(-0.390242\pi\) | ||||
0.338024 | + | 0.941137i | \(0.390242\pi\) | |||||||
\(600\) | −11.8803 | −0.485011 | ||||||||
\(601\) | −32.3580 | −1.31991 | −0.659954 | − | 0.751306i | \(-0.729424\pi\) | ||||
−0.659954 | + | 0.751306i | \(0.729424\pi\) | |||||||
\(602\) | −0.693876 | −0.0282803 | ||||||||
\(603\) | 100.937 | 4.11047 | ||||||||
\(604\) | −17.4682 | −0.710770 | ||||||||
\(605\) | −59.5401 | −2.42065 | ||||||||
\(606\) | 94.4711 | 3.83763 | ||||||||
\(607\) | 34.4933 | 1.40004 | 0.700019 | − | 0.714124i | \(-0.253175\pi\) | ||||
0.700019 | + | 0.714124i | \(0.253175\pi\) | |||||||
\(608\) | 5.32374 | 0.215906 | ||||||||
\(609\) | 0.155046 | 0.00628279 | ||||||||
\(610\) | 15.8986 | 0.643714 | ||||||||
\(611\) | −51.4203 | −2.08024 | ||||||||
\(612\) | −21.9952 | −0.889104 | ||||||||
\(613\) | −1.13192 | −0.0457177 | −0.0228589 | − | 0.999739i | \(-0.507277\pi\) | ||||
−0.0228589 | + | 0.999739i | \(0.507277\pi\) | |||||||
\(614\) | −48.6230 | −1.96226 | ||||||||
\(615\) | −60.1570 | −2.42577 | ||||||||
\(616\) | −0.444352 | −0.0179034 | ||||||||
\(617\) | 9.00443 | 0.362505 | 0.181252 | − | 0.983437i | \(-0.441985\pi\) | ||||
0.181252 | + | 0.983437i | \(0.441985\pi\) | |||||||
\(618\) | −113.058 | −4.54787 | ||||||||
\(619\) | 20.1918 | 0.811579 | 0.405789 | − | 0.913967i | \(-0.366997\pi\) | ||||
0.405789 | + | 0.913967i | \(0.366997\pi\) | |||||||
\(620\) | −16.1346 | −0.647982 | ||||||||
\(621\) | 102.340 | 4.10677 | ||||||||
\(622\) | −19.9489 | −0.799877 | ||||||||
\(623\) | −0.254611 | −0.0102008 | ||||||||
\(624\) | 90.9160 | 3.63955 | ||||||||
\(625\) | −31.0943 | −1.24377 | ||||||||
\(626\) | 10.4025 | 0.415768 | ||||||||
\(627\) | 19.2912 | 0.770416 | ||||||||
\(628\) | 6.20408 | 0.247570 | ||||||||
\(629\) | 14.0115 | 0.558674 | ||||||||
\(630\) | 1.72597 | 0.0687645 | ||||||||
\(631\) | −32.4333 | −1.29115 | −0.645575 | − | 0.763696i | \(-0.723382\pi\) | ||||
−0.645575 | + | 0.763696i | \(0.723382\pi\) | |||||||
\(632\) | −14.8665 | −0.591359 | ||||||||
\(633\) | −3.34117 | −0.132800 | ||||||||
\(634\) | −20.9596 | −0.832413 | ||||||||
\(635\) | 26.0626 | 1.03426 | ||||||||
\(636\) | −3.20165 | −0.126954 | ||||||||
\(637\) | −38.0906 | −1.50920 | ||||||||
\(638\) | −10.2343 | −0.405178 | ||||||||
\(639\) | 15.5340 | 0.614517 | ||||||||
\(640\) | 31.7767 | 1.25608 | ||||||||
\(641\) | 11.0757 | 0.437462 | 0.218731 | − | 0.975785i | \(-0.429808\pi\) | ||||
0.218731 | + | 0.975785i | \(0.429808\pi\) | |||||||
\(642\) | 115.926 | 4.57524 | ||||||||
\(643\) | 10.7261 | 0.422995 | 0.211498 | − | 0.977378i | \(-0.432166\pi\) | ||||
0.211498 | + | 0.977378i | \(0.432166\pi\) | |||||||
\(644\) | −0.278353 | −0.0109686 | ||||||||
\(645\) | 77.9122 | 3.06779 | ||||||||
\(646\) | 4.55448 | 0.179194 | ||||||||
\(647\) | −7.37626 | −0.289991 | −0.144995 | − | 0.989432i | \(-0.546317\pi\) | ||||
−0.144995 | + | 0.989432i | \(0.546317\pi\) | |||||||
\(648\) | 55.9884 | 2.19943 | ||||||||
\(649\) | −39.5268 | −1.55156 | ||||||||
\(650\) | −19.9471 | −0.782388 | ||||||||
\(651\) | −0.894980 | −0.0350770 | ||||||||
\(652\) | 0.00767296 | 0.000300496 0 | ||||||||
\(653\) | 21.5605 | 0.843726 | 0.421863 | − | 0.906660i | \(-0.361376\pi\) | ||||
0.421863 | + | 0.906660i | \(0.361376\pi\) | |||||||
\(654\) | 21.2010 | 0.829026 | ||||||||
\(655\) | 8.97564 | 0.350707 | ||||||||
\(656\) | 33.7666 | 1.31837 | ||||||||
\(657\) | 5.31623 | 0.207406 | ||||||||
\(658\) | 0.749299 | 0.0292107 | ||||||||
\(659\) | −13.1817 | −0.513488 | −0.256744 | − | 0.966480i | \(-0.582650\pi\) | ||||
−0.256744 | + | 0.966480i | \(0.582650\pi\) | |||||||
\(660\) | −52.9506 | −2.06110 | ||||||||
\(661\) | 40.8506 | 1.58890 | 0.794452 | − | 0.607326i | \(-0.207758\pi\) | ||||
0.794452 | + | 0.607326i | \(0.207758\pi\) | |||||||
\(662\) | 51.5487 | 2.00350 | ||||||||
\(663\) | 47.5867 | 1.84811 | ||||||||
\(664\) | −3.70572 | −0.143810 | ||||||||
\(665\) | −0.121468 | −0.00471032 | ||||||||
\(666\) | 76.0886 | 2.94837 | ||||||||
\(667\) | 6.04094 | 0.233906 | ||||||||
\(668\) | 19.7113 | 0.762652 | ||||||||
\(669\) | −23.4904 | −0.908193 | ||||||||
\(670\) | 57.3684 | 2.21633 | ||||||||
\(671\) | −19.7844 | −0.763770 | ||||||||
\(672\) | −0.810556 | −0.0312679 | ||||||||
\(673\) | −12.9417 | −0.498865 | −0.249432 | − | 0.968392i | \(-0.580244\pi\) | ||||
−0.249432 | + | 0.968392i | \(0.580244\pi\) | |||||||
\(674\) | −30.8291 | −1.18749 | ||||||||
\(675\) | −36.3216 | −1.39802 | ||||||||
\(676\) | 17.1218 | 0.658531 | ||||||||
\(677\) | −42.5408 | −1.63498 | −0.817488 | − | 0.575946i | \(-0.804634\pi\) | ||||
−0.817488 | + | 0.575946i | \(0.804634\pi\) | |||||||
\(678\) | 94.4273 | 3.62646 | ||||||||
\(679\) | 0.703205 | 0.0269865 | ||||||||
\(680\) | 11.7796 | 0.451727 | ||||||||
\(681\) | 68.5202 | 2.62570 | ||||||||
\(682\) | 59.0757 | 2.26212 | ||||||||
\(683\) | −22.0731 | −0.844603 | −0.422301 | − | 0.906455i | \(-0.638778\pi\) | ||||
−0.422301 | + | 0.906455i | \(0.638778\pi\) | |||||||
\(684\) | 8.40602 | 0.321412 | ||||||||
\(685\) | −32.8053 | −1.25343 | ||||||||
\(686\) | 1.11028 | 0.0423907 | ||||||||
\(687\) | −61.6233 | −2.35108 | ||||||||
\(688\) | −43.7327 | −1.66729 | ||||||||
\(689\) | 5.06530 | 0.192973 | ||||||||
\(690\) | 91.9608 | 3.50089 | ||||||||
\(691\) | −18.0550 | −0.686845 | −0.343422 | − | 0.939181i | \(-0.611586\pi\) | ||||
−0.343422 | + | 0.939181i | \(0.611586\pi\) | |||||||
\(692\) | −0.0615369 | −0.00233928 | ||||||||
\(693\) | −2.14783 | −0.0815893 | ||||||||
\(694\) | −22.7505 | −0.863598 | ||||||||
\(695\) | 14.7682 | 0.560190 | ||||||||
\(696\) | 5.74636 | 0.217815 | ||||||||
\(697\) | 17.6739 | 0.669447 | ||||||||
\(698\) | −0.862874 | −0.0326603 | ||||||||
\(699\) | −78.4395 | −2.96686 | ||||||||
\(700\) | 0.0987905 | 0.00373393 | ||||||||
\(701\) | 6.75406 | 0.255097 | 0.127549 | − | 0.991832i | \(-0.459289\pi\) | ||||
0.127549 | + | 0.991832i | \(0.459289\pi\) | |||||||
\(702\) | 163.450 | 6.16903 | ||||||||
\(703\) | −5.35484 | −0.201961 | ||||||||
\(704\) | −4.22457 | −0.159220 | ||||||||
\(705\) | −84.1353 | −3.16872 | ||||||||
\(706\) | −37.6021 | −1.41517 | ||||||||
\(707\) | 0.740230 | 0.0278392 | ||||||||
\(708\) | −23.5531 | −0.885179 | ||||||||
\(709\) | −20.9893 | −0.788268 | −0.394134 | − | 0.919053i | \(-0.628955\pi\) | ||||
−0.394134 | + | 0.919053i | \(0.628955\pi\) | |||||||
\(710\) | 8.82890 | 0.331343 | ||||||||
\(711\) | −71.8593 | −2.69493 | ||||||||
\(712\) | −9.43646 | −0.353646 | ||||||||
\(713\) | −34.8704 | −1.30591 | ||||||||
\(714\) | −0.693434 | −0.0259511 | ||||||||
\(715\) | 83.7727 | 3.13292 | ||||||||
\(716\) | −14.2844 | −0.533833 | ||||||||
\(717\) | 32.8981 | 1.22860 | ||||||||
\(718\) | 51.1172 | 1.90768 | ||||||||
\(719\) | 22.2685 | 0.830476 | 0.415238 | − | 0.909713i | \(-0.363698\pi\) | ||||
0.415238 | + | 0.909713i | \(0.363698\pi\) | |||||||
\(720\) | 108.782 | 4.05408 | ||||||||
\(721\) | −0.885870 | −0.0329915 | ||||||||
\(722\) | −1.74061 | −0.0647787 | ||||||||
\(723\) | 6.52079 | 0.242511 | ||||||||
\(724\) | 3.44739 | 0.128121 | ||||||||
\(725\) | −2.14400 | −0.0796261 | ||||||||
\(726\) | 129.902 | 4.82112 | ||||||||
\(727\) | −35.3705 | −1.31182 | −0.655910 | − | 0.754839i | \(-0.727715\pi\) | ||||
−0.655910 | + | 0.754839i | \(0.727715\pi\) | |||||||
\(728\) | 0.418905 | 0.0155256 | ||||||||
\(729\) | 97.7026 | 3.61861 | ||||||||
\(730\) | 3.02153 | 0.111832 | ||||||||
\(731\) | −22.8903 | −0.846628 | ||||||||
\(732\) | −11.7891 | −0.435737 | ||||||||
\(733\) | 44.8057 | 1.65494 | 0.827469 | − | 0.561511i | \(-0.189780\pi\) | ||||
0.827469 | + | 0.561511i | \(0.189780\pi\) | |||||||
\(734\) | −3.20919 | −0.118454 | ||||||||
\(735\) | −62.3249 | −2.29889 | ||||||||
\(736\) | −31.5811 | −1.16409 | ||||||||
\(737\) | −71.3902 | −2.62969 | ||||||||
\(738\) | 95.9771 | 3.53297 | ||||||||
\(739\) | 11.3703 | 0.418263 | 0.209132 | − | 0.977887i | \(-0.432936\pi\) | ||||
0.209132 | + | 0.977887i | \(0.432936\pi\) | |||||||
\(740\) | 14.6980 | 0.540309 | ||||||||
\(741\) | −18.1864 | −0.668095 | ||||||||
\(742\) | −0.0738117 | −0.00270971 | ||||||||
\(743\) | −48.6553 | −1.78499 | −0.892496 | − | 0.451056i | \(-0.851047\pi\) | ||||
−0.892496 | + | 0.451056i | \(0.851047\pi\) | |||||||
\(744\) | −33.1700 | −1.21607 | ||||||||
\(745\) | −11.8942 | −0.435769 | ||||||||
\(746\) | 8.78103 | 0.321496 | ||||||||
\(747\) | −17.9121 | −0.655368 | ||||||||
\(748\) | 15.5567 | 0.568808 | ||||||||
\(749\) | 0.908342 | 0.0331901 | ||||||||
\(750\) | 44.8731 | 1.63853 | ||||||||
\(751\) | 22.6187 | 0.825369 | 0.412685 | − | 0.910874i | \(-0.364591\pi\) | ||||
0.412685 | + | 0.910874i | \(0.364591\pi\) | |||||||
\(752\) | 47.2258 | 1.72215 | ||||||||
\(753\) | 0.197148 | 0.00718448 | ||||||||
\(754\) | 9.64817 | 0.351366 | ||||||||
\(755\) | 45.2192 | 1.64570 | ||||||||
\(756\) | −0.809509 | −0.0294416 | ||||||||
\(757\) | −40.2314 | −1.46223 | −0.731117 | − | 0.682252i | \(-0.761001\pi\) | ||||
−0.731117 | + | 0.682252i | \(0.761001\pi\) | |||||||
\(758\) | −24.2025 | −0.879075 | ||||||||
\(759\) | −114.438 | −4.15382 | ||||||||
\(760\) | −4.50187 | −0.163300 | ||||||||
\(761\) | 10.9158 | 0.395696 | 0.197848 | − | 0.980233i | \(-0.436605\pi\) | ||||
0.197848 | + | 0.980233i | \(0.436605\pi\) | |||||||
\(762\) | −56.8621 | −2.05990 | ||||||||
\(763\) | 0.166121 | 0.00601399 | ||||||||
\(764\) | 22.1785 | 0.802388 | ||||||||
\(765\) | 56.9382 | 2.05860 | ||||||||
\(766\) | 63.4756 | 2.29347 | ||||||||
\(767\) | 37.2632 | 1.34549 | ||||||||
\(768\) | −64.4396 | −2.32526 | ||||||||
\(769\) | −40.0451 | −1.44406 | −0.722031 | − | 0.691861i | \(-0.756791\pi\) | ||||
−0.722031 | + | 0.691861i | \(0.756791\pi\) | |||||||
\(770\) | −1.22074 | −0.0439924 | ||||||||
\(771\) | −46.4657 | −1.67342 | ||||||||
\(772\) | 1.78824 | 0.0643600 | ||||||||
\(773\) | 15.4759 | 0.556630 | 0.278315 | − | 0.960490i | \(-0.410224\pi\) | ||||
0.278315 | + | 0.960490i | \(0.410224\pi\) | |||||||
\(774\) | −124.304 | −4.46803 | ||||||||
\(775\) | 12.3759 | 0.444555 | ||||||||
\(776\) | 26.0623 | 0.935583 | ||||||||
\(777\) | 0.815291 | 0.0292484 | ||||||||
\(778\) | 47.5908 | 1.70621 | ||||||||
\(779\) | −6.75452 | −0.242006 | ||||||||
\(780\) | 49.9182 | 1.78736 | ||||||||
\(781\) | −10.9868 | −0.393140 | ||||||||
\(782\) | −27.0177 | −0.966152 | ||||||||
\(783\) | 17.5684 | 0.627842 | ||||||||
\(784\) | 34.9834 | 1.24941 | ||||||||
\(785\) | −16.0603 | −0.573215 | ||||||||
\(786\) | −19.5827 | −0.698490 | ||||||||
\(787\) | 25.3333 | 0.903036 | 0.451518 | − | 0.892262i | \(-0.350883\pi\) | ||||
0.451518 | + | 0.892262i | \(0.350883\pi\) | |||||||
\(788\) | −23.3454 | −0.831646 | ||||||||
\(789\) | −72.6012 | −2.58467 | ||||||||
\(790\) | −40.8418 | −1.45309 | ||||||||
\(791\) | 0.739887 | 0.0263074 | ||||||||
\(792\) | −79.6034 | −2.82858 | ||||||||
\(793\) | 18.6514 | 0.662332 | ||||||||
\(794\) | −11.2638 | −0.399736 | ||||||||
\(795\) | 8.28798 | 0.293944 | ||||||||
\(796\) | −15.2947 | −0.542105 | ||||||||
\(797\) | −15.9386 | −0.564573 | −0.282286 | − | 0.959330i | \(-0.591093\pi\) | ||||
−0.282286 | + | 0.959330i | \(0.591093\pi\) | |||||||
\(798\) | 0.265013 | 0.00938136 | ||||||||
\(799\) | 24.7186 | 0.874482 | ||||||||
\(800\) | 11.2085 | 0.396279 | ||||||||
\(801\) | −45.6123 | −1.61163 | ||||||||
\(802\) | 39.0100 | 1.37749 | ||||||||
\(803\) | −3.76004 | −0.132689 | ||||||||
\(804\) | −42.5397 | −1.50026 | ||||||||
\(805\) | 0.720561 | 0.0253964 | ||||||||
\(806\) | −55.6925 | −1.96169 | ||||||||
\(807\) | 82.3177 | 2.89772 | ||||||||
\(808\) | 27.4346 | 0.965145 | ||||||||
\(809\) | 21.5734 | 0.758481 | 0.379240 | − | 0.925298i | \(-0.376185\pi\) | ||||
0.379240 | + | 0.925298i | \(0.376185\pi\) | |||||||
\(810\) | 153.813 | 5.40444 | ||||||||
\(811\) | −28.2124 | −0.990673 | −0.495336 | − | 0.868701i | \(-0.664955\pi\) | ||||
−0.495336 | + | 0.868701i | \(0.664955\pi\) | |||||||
\(812\) | −0.0477838 | −0.00167688 | ||||||||
\(813\) | 64.5723 | 2.26465 | ||||||||
\(814\) | −53.8155 | −1.88623 | ||||||||
\(815\) | −0.0198627 | −0.000695760 0 | ||||||||
\(816\) | −43.7049 | −1.52998 | ||||||||
\(817\) | 8.74809 | 0.306057 | ||||||||
\(818\) | −63.1408 | −2.20767 | ||||||||
\(819\) | 2.02483 | 0.0707532 | ||||||||
\(820\) | 18.5398 | 0.647440 | ||||||||
\(821\) | 14.2937 | 0.498853 | 0.249426 | − | 0.968394i | \(-0.419758\pi\) | ||||
0.249426 | + | 0.968394i | \(0.419758\pi\) | |||||||
\(822\) | 71.5732 | 2.49640 | ||||||||
\(823\) | 8.02738 | 0.279817 | 0.139908 | − | 0.990164i | \(-0.455319\pi\) | ||||
0.139908 | + | 0.990164i | \(0.455319\pi\) | |||||||
\(824\) | −32.8323 | −1.14377 | ||||||||
\(825\) | 40.6152 | 1.41404 | ||||||||
\(826\) | −0.543000 | −0.0188934 | ||||||||
\(827\) | 35.4635 | 1.23319 | 0.616594 | − | 0.787281i | \(-0.288512\pi\) | ||||
0.616594 | + | 0.787281i | \(0.288512\pi\) | |||||||
\(828\) | −49.8655 | −1.73295 | ||||||||
\(829\) | 1.85139 | 0.0643013 | 0.0321507 | − | 0.999483i | \(-0.489764\pi\) | ||||
0.0321507 | + | 0.999483i | \(0.489764\pi\) | |||||||
\(830\) | −10.1805 | −0.353369 | ||||||||
\(831\) | 19.3939 | 0.672765 | ||||||||
\(832\) | 3.98264 | 0.138073 | ||||||||
\(833\) | 18.3108 | 0.634431 | ||||||||
\(834\) | −32.2206 | −1.11571 | ||||||||
\(835\) | −51.0258 | −1.76582 | ||||||||
\(836\) | −5.94537 | −0.205625 | ||||||||
\(837\) | −101.411 | −3.50526 | ||||||||
\(838\) | 27.0045 | 0.932855 | ||||||||
\(839\) | −15.8569 | −0.547440 | −0.273720 | − | 0.961809i | \(-0.588254\pi\) | ||||
−0.273720 | + | 0.961809i | \(0.588254\pi\) | |||||||
\(840\) | 0.685423 | 0.0236493 | ||||||||
\(841\) | −27.9630 | −0.964240 | ||||||||
\(842\) | −8.68548 | −0.299321 | ||||||||
\(843\) | −7.10383 | −0.244669 | ||||||||
\(844\) | 1.02972 | 0.0354444 | ||||||||
\(845\) | −44.3225 | −1.52474 | ||||||||
\(846\) | 134.233 | 4.61503 | ||||||||
\(847\) | 1.01785 | 0.0349737 | ||||||||
\(848\) | −4.65211 | −0.159754 | ||||||||
\(849\) | 8.62584 | 0.296038 | ||||||||
\(850\) | 9.58889 | 0.328896 | ||||||||
\(851\) | 31.7655 | 1.08891 | ||||||||
\(852\) | −6.54680 | −0.224290 | ||||||||
\(853\) | 37.3340 | 1.27829 | 0.639146 | − | 0.769085i | \(-0.279288\pi\) | ||||
0.639146 | + | 0.769085i | \(0.279288\pi\) | |||||||
\(854\) | −0.271789 | −0.00930044 | ||||||||
\(855\) | −21.7603 | −0.744188 | ||||||||
\(856\) | 33.6652 | 1.15065 | ||||||||
\(857\) | −29.6198 | −1.01179 | −0.505896 | − | 0.862594i | \(-0.668838\pi\) | ||||
−0.505896 | + | 0.862594i | \(0.668838\pi\) | |||||||
\(858\) | −182.772 | −6.23972 | ||||||||
\(859\) | 42.0851 | 1.43593 | 0.717963 | − | 0.696082i | \(-0.245075\pi\) | ||||
0.717963 | + | 0.696082i | \(0.245075\pi\) | |||||||
\(860\) | −24.0118 | −0.818796 | ||||||||
\(861\) | 1.02840 | 0.0350477 | ||||||||
\(862\) | 1.61452 | 0.0549908 | ||||||||
\(863\) | 5.08070 | 0.172949 | 0.0864745 | − | 0.996254i | \(-0.472440\pi\) | ||||
0.0864745 | + | 0.996254i | \(0.472440\pi\) | |||||||
\(864\) | −91.8445 | −3.12461 | ||||||||
\(865\) | 0.159298 | 0.00541630 | ||||||||
\(866\) | −7.83127 | −0.266117 | ||||||||
\(867\) | 33.9242 | 1.15213 | ||||||||
\(868\) | 0.275825 | 0.00936210 | ||||||||
\(869\) | 50.8243 | 1.72410 | ||||||||
\(870\) | 15.7866 | 0.535215 | ||||||||
\(871\) | 67.3018 | 2.28043 | ||||||||
\(872\) | 6.15682 | 0.208496 | ||||||||
\(873\) | 125.976 | 4.26363 | ||||||||
\(874\) | 10.3255 | 0.349265 | ||||||||
\(875\) | 0.351604 | 0.0118864 | ||||||||
\(876\) | −2.24052 | −0.0757002 | ||||||||
\(877\) | 31.7332 | 1.07155 | 0.535777 | − | 0.844359i | \(-0.320019\pi\) | ||||
0.535777 | + | 0.844359i | \(0.320019\pi\) | |||||||
\(878\) | 35.4612 | 1.19676 | ||||||||
\(879\) | −72.3604 | −2.44066 | ||||||||
\(880\) | −76.9391 | −2.59362 | ||||||||
\(881\) | −17.1482 | −0.577737 | −0.288868 | − | 0.957369i | \(-0.593279\pi\) | ||||
−0.288868 | + | 0.957369i | \(0.593279\pi\) | |||||||
\(882\) | 99.4357 | 3.34817 | ||||||||
\(883\) | −29.1692 | −0.981622 | −0.490811 | − | 0.871266i | \(-0.663300\pi\) | ||||
−0.490811 | + | 0.871266i | \(0.663300\pi\) | |||||||
\(884\) | −14.6658 | −0.493263 | ||||||||
\(885\) | 60.9710 | 2.04952 | ||||||||
\(886\) | −68.4002 | −2.29795 | ||||||||
\(887\) | 8.50695 | 0.285635 | 0.142818 | − | 0.989749i | \(-0.454384\pi\) | ||||
0.142818 | + | 0.989749i | \(0.454384\pi\) | |||||||
\(888\) | 30.2165 | 1.01400 | ||||||||
\(889\) | −0.445544 | −0.0149431 | ||||||||
\(890\) | −25.9242 | −0.868980 | ||||||||
\(891\) | −191.408 | −6.41239 | ||||||||
\(892\) | 7.23954 | 0.242398 | ||||||||
\(893\) | −9.44683 | −0.316126 | ||||||||
\(894\) | 25.9502 | 0.867904 | ||||||||
\(895\) | 36.9775 | 1.23602 | ||||||||
\(896\) | −0.543228 | −0.0181480 | ||||||||
\(897\) | 107.884 | 3.60214 | ||||||||
\(898\) | −27.6608 | −0.923052 | ||||||||
\(899\) | −5.98608 | −0.199647 | ||||||||
\(900\) | 17.6978 | 0.589927 | ||||||||
\(901\) | −2.43497 | −0.0811208 | ||||||||
\(902\) | −67.8822 | −2.26023 | ||||||||
\(903\) | −1.33192 | −0.0443237 | ||||||||
\(904\) | 27.4219 | 0.912038 | ||||||||
\(905\) | −8.92414 | −0.296648 | ||||||||
\(906\) | −98.6573 | −3.27767 | ||||||||
\(907\) | −33.1020 | −1.09913 | −0.549566 | − | 0.835450i | \(-0.685207\pi\) | ||||
−0.549566 | + | 0.835450i | \(0.685207\pi\) | |||||||
\(908\) | −21.1173 | −0.700802 | ||||||||
\(909\) | 132.609 | 4.39835 | ||||||||
\(910\) | 1.15083 | 0.0381496 | ||||||||
\(911\) | 13.7116 | 0.454285 | 0.227143 | − | 0.973861i | \(-0.427062\pi\) | ||||
0.227143 | + | 0.973861i | \(0.427062\pi\) | |||||||
\(912\) | 16.7029 | 0.553088 | ||||||||
\(913\) | 12.6688 | 0.419274 | ||||||||
\(914\) | 25.7651 | 0.852235 | ||||||||
\(915\) | 30.5180 | 1.00889 | ||||||||
\(916\) | 18.9917 | 0.627504 | ||||||||
\(917\) | −0.153440 | −0.00506705 | ||||||||
\(918\) | −78.5733 | −2.59331 | ||||||||
\(919\) | −22.0703 | −0.728031 | −0.364016 | − | 0.931393i | \(-0.618594\pi\) | ||||
−0.364016 | + | 0.931393i | \(0.618594\pi\) | |||||||
\(920\) | 26.7056 | 0.880458 | ||||||||
\(921\) | −93.3338 | −3.07545 | ||||||||
\(922\) | −55.6644 | −1.83321 | ||||||||
\(923\) | 10.3576 | 0.340926 | ||||||||
\(924\) | 0.905201 | 0.0297789 | ||||||||
\(925\) | −11.2739 | −0.370685 | ||||||||
\(926\) | −17.1736 | −0.564360 | ||||||||
\(927\) | −158.699 | −5.21236 | ||||||||
\(928\) | −5.42141 | −0.177966 | ||||||||
\(929\) | −20.5367 | −0.673788 | −0.336894 | − | 0.941543i | \(-0.609376\pi\) | ||||
−0.336894 | + | 0.941543i | \(0.609376\pi\) | |||||||
\(930\) | −91.1256 | −2.98813 | ||||||||
\(931\) | −6.99792 | −0.229348 | ||||||||
\(932\) | 24.1743 | 0.791857 | ||||||||
\(933\) | −38.2927 | −1.25365 | ||||||||
\(934\) | −50.4059 | −1.64933 | ||||||||
\(935\) | −40.2709 | −1.31700 | ||||||||
\(936\) | 75.0447 | 2.45291 | ||||||||
\(937\) | −39.4019 | −1.28720 | −0.643602 | − | 0.765360i | \(-0.722561\pi\) | ||||
−0.643602 | + | 0.765360i | \(0.722561\pi\) | |||||||
\(938\) | −0.980724 | −0.0320218 | ||||||||
\(939\) | 19.9681 | 0.651633 | ||||||||
\(940\) | 25.9297 | 0.845735 | ||||||||
\(941\) | −28.9711 | −0.944432 | −0.472216 | − | 0.881483i | \(-0.656546\pi\) | ||||
−0.472216 | + | 0.881483i | \(0.656546\pi\) | |||||||
\(942\) | 35.0396 | 1.14165 | ||||||||
\(943\) | 40.0686 | 1.30481 | ||||||||
\(944\) | −34.2235 | −1.11388 | ||||||||
\(945\) | 2.09555 | 0.0681681 | ||||||||
\(946\) | 87.9174 | 2.85844 | ||||||||
\(947\) | 8.24181 | 0.267823 | 0.133911 | − | 0.990993i | \(-0.457246\pi\) | ||||
0.133911 | + | 0.990993i | \(0.457246\pi\) | |||||||
\(948\) | 30.2850 | 0.983611 | ||||||||
\(949\) | 3.54471 | 0.115066 | ||||||||
\(950\) | −3.66463 | −0.118896 | ||||||||
\(951\) | −40.2328 | −1.30464 | ||||||||
\(952\) | −0.201375 | −0.00652659 | ||||||||
\(953\) | −28.2162 | −0.914012 | −0.457006 | − | 0.889463i | \(-0.651078\pi\) | ||||
−0.457006 | + | 0.889463i | \(0.651078\pi\) | |||||||
\(954\) | −13.2230 | −0.428110 | ||||||||
\(955\) | −57.4125 | −1.85783 | ||||||||
\(956\) | −10.1389 | −0.327915 | ||||||||
\(957\) | −19.6451 | −0.635036 | ||||||||
\(958\) | 21.9882 | 0.710407 | ||||||||
\(959\) | 0.560813 | 0.0181096 | ||||||||
\(960\) | 6.51650 | 0.210319 | ||||||||
\(961\) | 3.55368 | 0.114635 | ||||||||
\(962\) | 50.7336 | 1.63572 | ||||||||
\(963\) | 162.725 | 5.24374 | ||||||||
\(964\) | −2.00965 | −0.0647264 | ||||||||
\(965\) | −4.62914 | −0.149017 | ||||||||
\(966\) | −1.57209 | −0.0505811 | ||||||||
\(967\) | −24.0414 | −0.773120 | −0.386560 | − | 0.922264i | \(-0.626337\pi\) | ||||
−0.386560 | + | 0.922264i | \(0.626337\pi\) | |||||||
\(968\) | 37.7238 | 1.21249 | ||||||||
\(969\) | 8.74252 | 0.280850 | ||||||||
\(970\) | 71.5993 | 2.29892 | ||||||||
\(971\) | 47.5150 | 1.52483 | 0.762415 | − | 0.647089i | \(-0.224014\pi\) | ||||
0.762415 | + | 0.647089i | \(0.224014\pi\) | |||||||
\(972\) | −60.7617 | −1.94893 | ||||||||
\(973\) | −0.252465 | −0.00809367 | ||||||||
\(974\) | 41.6285 | 1.33386 | ||||||||
\(975\) | −38.2892 | −1.22624 | ||||||||
\(976\) | −17.1300 | −0.548317 | ||||||||
\(977\) | −50.4242 | −1.61321 | −0.806607 | − | 0.591088i | \(-0.798698\pi\) | ||||
−0.806607 | + | 0.591088i | \(0.798698\pi\) | |||||||
\(978\) | 0.0433356 | 0.00138572 | ||||||||
\(979\) | 32.2604 | 1.03105 | ||||||||
\(980\) | 19.2079 | 0.613575 | ||||||||
\(981\) | 29.7598 | 0.950156 | ||||||||
\(982\) | −2.53430 | −0.0808726 | ||||||||
\(983\) | −37.6059 | −1.19944 | −0.599722 | − | 0.800209i | \(-0.704722\pi\) | ||||
−0.599722 | + | 0.800209i | \(0.704722\pi\) | |||||||
\(984\) | 38.1147 | 1.21505 | ||||||||
\(985\) | 60.4334 | 1.92557 | ||||||||
\(986\) | −4.63804 | −0.147705 | ||||||||
\(987\) | 1.43831 | 0.0457819 | ||||||||
\(988\) | 5.60489 | 0.178315 | ||||||||
\(989\) | −51.8947 | −1.65016 | ||||||||
\(990\) | −218.689 | −6.95039 | ||||||||
\(991\) | −24.7989 | −0.787763 | −0.393882 | − | 0.919161i | \(-0.628868\pi\) | ||||
−0.393882 | + | 0.919161i | \(0.628868\pi\) | |||||||
\(992\) | 31.2942 | 0.993593 | ||||||||
\(993\) | 98.9499 | 3.14008 | ||||||||
\(994\) | −0.150932 | −0.00478727 | ||||||||
\(995\) | 39.5927 | 1.25517 | ||||||||
\(996\) | 7.54901 | 0.239200 | ||||||||
\(997\) | 31.1879 | 0.987732 | 0.493866 | − | 0.869538i | \(-0.335583\pi\) | ||||
0.493866 | + | 0.869538i | \(0.335583\pi\) | |||||||
\(998\) | 26.5537 | 0.840542 | ||||||||
\(999\) | 92.3809 | 2.92280 |
(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 | 4009.2.a.c.1.19 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.19 | ✓ | 71 | 1.1 | even | 1 | trivial |