Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2005,2,Mod(1,2005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2005, 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("2005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2005 = 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2005.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: | \(16.0100056053\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 2005.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0686864 | 0.0485686 | 0.0242843 | − | 0.999705i | \(-0.492269\pi\) | ||||
0.0242843 | + | 0.999705i | \(0.492269\pi\) | |||||||
\(3\) | −2.29330 | −1.32404 | −0.662018 | − | 0.749488i | \(-0.730300\pi\) | ||||
−0.662018 | + | 0.749488i | \(0.730300\pi\) | |||||||
\(4\) | −1.99528 | −0.997641 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.157518 | −0.0643067 | ||||||||
\(7\) | −2.03277 | −0.768314 | −0.384157 | − | 0.923268i | \(-0.625508\pi\) | ||||
−0.384157 | + | 0.923268i | \(0.625508\pi\) | |||||||
\(8\) | −0.274422 | −0.0970227 | ||||||||
\(9\) | 2.25922 | 0.753073 | ||||||||
\(10\) | 0.0686864 | 0.0217206 | ||||||||
\(11\) | 1.26389 | 0.381076 | 0.190538 | − | 0.981680i | \(-0.438977\pi\) | ||||
0.190538 | + | 0.981680i | \(0.438977\pi\) | |||||||
\(12\) | 4.57578 | 1.32091 | ||||||||
\(13\) | −4.81535 | −1.33554 | −0.667769 | − | 0.744368i | \(-0.732751\pi\) | ||||
−0.667769 | + | 0.744368i | \(0.732751\pi\) | |||||||
\(14\) | −0.139624 | −0.0373160 | ||||||||
\(15\) | −2.29330 | −0.592127 | ||||||||
\(16\) | 3.97172 | 0.992929 | ||||||||
\(17\) | −2.38909 | −0.579438 | −0.289719 | − | 0.957112i | \(-0.593562\pi\) | ||||
−0.289719 | + | 0.957112i | \(0.593562\pi\) | |||||||
\(18\) | 0.155178 | 0.0365757 | ||||||||
\(19\) | −7.50921 | −1.72273 | −0.861365 | − | 0.507986i | \(-0.830390\pi\) | ||||
−0.861365 | + | 0.507986i | \(0.830390\pi\) | |||||||
\(20\) | −1.99528 | −0.446159 | ||||||||
\(21\) | 4.66175 | 1.01728 | ||||||||
\(22\) | 0.0868118 | 0.0185083 | ||||||||
\(23\) | 4.71068 | 0.982244 | 0.491122 | − | 0.871091i | \(-0.336587\pi\) | ||||
0.491122 | + | 0.871091i | \(0.336587\pi\) | |||||||
\(24\) | 0.629331 | 0.128462 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.330749 | −0.0648653 | ||||||||
\(27\) | 1.69883 | 0.326940 | ||||||||
\(28\) | 4.05595 | 0.766502 | ||||||||
\(29\) | −7.82808 | −1.45364 | −0.726819 | − | 0.686829i | \(-0.759002\pi\) | ||||
−0.726819 | + | 0.686829i | \(0.759002\pi\) | |||||||
\(30\) | −0.157518 | −0.0287588 | ||||||||
\(31\) | −10.0129 | −1.79838 | −0.899189 | − | 0.437561i | \(-0.855843\pi\) | ||||
−0.899189 | + | 0.437561i | \(0.855843\pi\) | |||||||
\(32\) | 0.821646 | 0.145248 | ||||||||
\(33\) | −2.89847 | −0.504559 | ||||||||
\(34\) | −0.164098 | −0.0281425 | ||||||||
\(35\) | −2.03277 | −0.343601 | ||||||||
\(36\) | −4.50778 | −0.751297 | ||||||||
\(37\) | −1.21553 | −0.199831 | −0.0999157 | − | 0.994996i | \(-0.531857\pi\) | ||||
−0.0999157 | + | 0.994996i | \(0.531857\pi\) | |||||||
\(38\) | −0.515781 | −0.0836707 | ||||||||
\(39\) | 11.0430 | 1.76830 | ||||||||
\(40\) | −0.274422 | −0.0433899 | ||||||||
\(41\) | −5.30331 | −0.828238 | −0.414119 | − | 0.910223i | \(-0.635910\pi\) | ||||
−0.414119 | + | 0.910223i | \(0.635910\pi\) | |||||||
\(42\) | 0.320199 | 0.0494077 | ||||||||
\(43\) | 11.1157 | 1.69513 | 0.847564 | − | 0.530693i | \(-0.178068\pi\) | ||||
0.847564 | + | 0.530693i | \(0.178068\pi\) | |||||||
\(44\) | −2.52181 | −0.380177 | ||||||||
\(45\) | 2.25922 | 0.336785 | ||||||||
\(46\) | 0.323560 | 0.0477063 | ||||||||
\(47\) | −1.14647 | −0.167230 | −0.0836152 | − | 0.996498i | \(-0.526647\pi\) | ||||
−0.0836152 | + | 0.996498i | \(0.526647\pi\) | |||||||
\(48\) | −9.10833 | −1.31467 | ||||||||
\(49\) | −2.86785 | −0.409693 | ||||||||
\(50\) | 0.0686864 | 0.00971373 | ||||||||
\(51\) | 5.47889 | 0.767198 | ||||||||
\(52\) | 9.60799 | 1.33239 | ||||||||
\(53\) | −4.81033 | −0.660749 | −0.330375 | − | 0.943850i | \(-0.607175\pi\) | ||||
−0.330375 | + | 0.943850i | \(0.607175\pi\) | |||||||
\(54\) | 0.116687 | 0.0158790 | ||||||||
\(55\) | 1.26389 | 0.170422 | ||||||||
\(56\) | 0.557836 | 0.0745439 | ||||||||
\(57\) | 17.2209 | 2.28096 | ||||||||
\(58\) | −0.537683 | −0.0706012 | ||||||||
\(59\) | −12.1261 | −1.57868 | −0.789341 | − | 0.613955i | \(-0.789578\pi\) | ||||
−0.789341 | + | 0.613955i | \(0.789578\pi\) | |||||||
\(60\) | 4.57578 | 0.590730 | ||||||||
\(61\) | 11.7159 | 1.50007 | 0.750035 | − | 0.661398i | \(-0.230036\pi\) | ||||
0.750035 | + | 0.661398i | \(0.230036\pi\) | |||||||
\(62\) | −0.687753 | −0.0873448 | ||||||||
\(63\) | −4.59247 | −0.578597 | ||||||||
\(64\) | −7.88699 | −0.985874 | ||||||||
\(65\) | −4.81535 | −0.597271 | ||||||||
\(66\) | −0.199085 | −0.0245057 | ||||||||
\(67\) | 6.36635 | 0.777774 | 0.388887 | − | 0.921286i | \(-0.372860\pi\) | ||||
0.388887 | + | 0.921286i | \(0.372860\pi\) | |||||||
\(68\) | 4.76690 | 0.578071 | ||||||||
\(69\) | −10.8030 | −1.30053 | ||||||||
\(70\) | −0.139624 | −0.0166882 | ||||||||
\(71\) | 7.57731 | 0.899261 | 0.449630 | − | 0.893215i | \(-0.351556\pi\) | ||||
0.449630 | + | 0.893215i | \(0.351556\pi\) | |||||||
\(72\) | −0.619979 | −0.0730652 | ||||||||
\(73\) | 8.79484 | 1.02936 | 0.514679 | − | 0.857383i | \(-0.327911\pi\) | ||||
0.514679 | + | 0.857383i | \(0.327911\pi\) | |||||||
\(74\) | −0.0834902 | −0.00970554 | ||||||||
\(75\) | −2.29330 | −0.264807 | ||||||||
\(76\) | 14.9830 | 1.71867 | ||||||||
\(77\) | −2.56919 | −0.292786 | ||||||||
\(78\) | 0.758507 | 0.0858840 | ||||||||
\(79\) | 7.66525 | 0.862408 | 0.431204 | − | 0.902255i | \(-0.358089\pi\) | ||||
0.431204 | + | 0.902255i | \(0.358089\pi\) | |||||||
\(80\) | 3.97172 | 0.444051 | ||||||||
\(81\) | −10.6736 | −1.18595 | ||||||||
\(82\) | −0.364265 | −0.0402264 | ||||||||
\(83\) | −0.963961 | −0.105808 | −0.0529042 | − | 0.998600i | \(-0.516848\pi\) | ||||
−0.0529042 | + | 0.998600i | \(0.516848\pi\) | |||||||
\(84\) | −9.30150 | −1.01488 | ||||||||
\(85\) | −2.38909 | −0.259133 | ||||||||
\(86\) | 0.763498 | 0.0823301 | ||||||||
\(87\) | 17.9521 | 1.92467 | ||||||||
\(88\) | −0.346838 | −0.0369730 | ||||||||
\(89\) | −4.66081 | −0.494045 | −0.247022 | − | 0.969010i | \(-0.579452\pi\) | ||||
−0.247022 | + | 0.969010i | \(0.579452\pi\) | |||||||
\(90\) | 0.155178 | 0.0163572 | ||||||||
\(91\) | 9.78850 | 1.02611 | ||||||||
\(92\) | −9.39913 | −0.979927 | ||||||||
\(93\) | 22.9627 | 2.38112 | ||||||||
\(94\) | −0.0787472 | −0.00812215 | ||||||||
\(95\) | −7.50921 | −0.770428 | ||||||||
\(96\) | −1.88428 | −0.192314 | ||||||||
\(97\) | −3.28704 | −0.333748 | −0.166874 | − | 0.985978i | \(-0.553367\pi\) | ||||
−0.166874 | + | 0.985978i | \(0.553367\pi\) | |||||||
\(98\) | −0.196982 | −0.0198982 | ||||||||
\(99\) | 2.85540 | 0.286978 | ||||||||
\(100\) | −1.99528 | −0.199528 | ||||||||
\(101\) | 0.173128 | 0.0172269 | 0.00861346 | − | 0.999963i | \(-0.497258\pi\) | ||||
0.00861346 | + | 0.999963i | \(0.497258\pi\) | |||||||
\(102\) | 0.376325 | 0.0372617 | ||||||||
\(103\) | 0.382084 | 0.0376479 | 0.0188239 | − | 0.999823i | \(-0.494008\pi\) | ||||
0.0188239 | + | 0.999823i | \(0.494008\pi\) | |||||||
\(104\) | 1.32144 | 0.129578 | ||||||||
\(105\) | 4.66175 | 0.454940 | ||||||||
\(106\) | −0.330404 | −0.0320917 | ||||||||
\(107\) | 14.9058 | 1.44100 | 0.720501 | − | 0.693454i | \(-0.243912\pi\) | ||||
0.720501 | + | 0.693454i | \(0.243912\pi\) | |||||||
\(108\) | −3.38965 | −0.326169 | ||||||||
\(109\) | 11.7215 | 1.12272 | 0.561358 | − | 0.827573i | \(-0.310279\pi\) | ||||
0.561358 | + | 0.827573i | \(0.310279\pi\) | |||||||
\(110\) | 0.0868118 | 0.00827718 | ||||||||
\(111\) | 2.78757 | 0.264584 | ||||||||
\(112\) | −8.07358 | −0.762881 | ||||||||
\(113\) | 18.6465 | 1.75412 | 0.877060 | − | 0.480381i | \(-0.159502\pi\) | ||||
0.877060 | + | 0.480381i | \(0.159502\pi\) | |||||||
\(114\) | 1.18284 | 0.110783 | ||||||||
\(115\) | 4.71068 | 0.439273 | ||||||||
\(116\) | 15.6192 | 1.45021 | ||||||||
\(117\) | −10.8789 | −1.00576 | ||||||||
\(118\) | −0.832898 | −0.0766744 | ||||||||
\(119\) | 4.85646 | 0.445191 | ||||||||
\(120\) | 0.629331 | 0.0574498 | ||||||||
\(121\) | −9.40259 | −0.854781 | ||||||||
\(122\) | 0.804725 | 0.0728564 | ||||||||
\(123\) | 12.1621 | 1.09662 | ||||||||
\(124\) | 19.9786 | 1.79414 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.315440 | −0.0281017 | ||||||||
\(127\) | 8.19546 | 0.727229 | 0.363615 | − | 0.931549i | \(-0.381542\pi\) | ||||
0.363615 | + | 0.931549i | \(0.381542\pi\) | |||||||
\(128\) | −2.18502 | −0.193130 | ||||||||
\(129\) | −25.4916 | −2.24441 | ||||||||
\(130\) | −0.330749 | −0.0290086 | ||||||||
\(131\) | 9.86588 | 0.861986 | 0.430993 | − | 0.902355i | \(-0.358163\pi\) | ||||
0.430993 | + | 0.902355i | \(0.358163\pi\) | |||||||
\(132\) | 5.78326 | 0.503368 | ||||||||
\(133\) | 15.2645 | 1.32360 | ||||||||
\(134\) | 0.437282 | 0.0377754 | ||||||||
\(135\) | 1.69883 | 0.146212 | ||||||||
\(136\) | 0.655617 | 0.0562187 | ||||||||
\(137\) | 7.67423 | 0.655653 | 0.327827 | − | 0.944738i | \(-0.393684\pi\) | ||||
0.327827 | + | 0.944738i | \(0.393684\pi\) | |||||||
\(138\) | −0.742019 | −0.0631648 | ||||||||
\(139\) | 0.743374 | 0.0630522 | 0.0315261 | − | 0.999503i | \(-0.489963\pi\) | ||||
0.0315261 | + | 0.999503i | \(0.489963\pi\) | |||||||
\(140\) | 4.05595 | 0.342790 | ||||||||
\(141\) | 2.62921 | 0.221419 | ||||||||
\(142\) | 0.520458 | 0.0436759 | ||||||||
\(143\) | −6.08606 | −0.508942 | ||||||||
\(144\) | 8.97298 | 0.747748 | ||||||||
\(145\) | −7.82808 | −0.650087 | ||||||||
\(146\) | 0.604086 | 0.0499945 | ||||||||
\(147\) | 6.57684 | 0.542449 | ||||||||
\(148\) | 2.42532 | 0.199360 | ||||||||
\(149\) | 13.1477 | 1.07710 | 0.538552 | − | 0.842592i | \(-0.318971\pi\) | ||||
0.538552 | + | 0.842592i | \(0.318971\pi\) | |||||||
\(150\) | −0.157518 | −0.0128613 | ||||||||
\(151\) | 3.78434 | 0.307965 | 0.153983 | − | 0.988074i | \(-0.450790\pi\) | ||||
0.153983 | + | 0.988074i | \(0.450790\pi\) | |||||||
\(152\) | 2.06069 | 0.167144 | ||||||||
\(153\) | −5.39747 | −0.436359 | ||||||||
\(154\) | −0.176468 | −0.0142202 | ||||||||
\(155\) | −10.0129 | −0.804259 | ||||||||
\(156\) | −22.0340 | −1.76413 | ||||||||
\(157\) | −17.9124 | −1.42957 | −0.714784 | − | 0.699345i | \(-0.753475\pi\) | ||||
−0.714784 | + | 0.699345i | \(0.753475\pi\) | |||||||
\(158\) | 0.526498 | 0.0418860 | ||||||||
\(159\) | 11.0315 | 0.874856 | ||||||||
\(160\) | 0.821646 | 0.0649568 | ||||||||
\(161\) | −9.57572 | −0.754672 | ||||||||
\(162\) | −0.733130 | −0.0576002 | ||||||||
\(163\) | 19.8035 | 1.55113 | 0.775565 | − | 0.631268i | \(-0.217465\pi\) | ||||
0.775565 | + | 0.631268i | \(0.217465\pi\) | |||||||
\(164\) | 10.5816 | 0.826284 | ||||||||
\(165\) | −2.89847 | −0.225645 | ||||||||
\(166\) | −0.0662110 | −0.00513897 | ||||||||
\(167\) | −9.99112 | −0.773136 | −0.386568 | − | 0.922261i | \(-0.626340\pi\) | ||||
−0.386568 | + | 0.922261i | \(0.626340\pi\) | |||||||
\(168\) | −1.27928 | −0.0986989 | ||||||||
\(169\) | 10.1876 | 0.783663 | ||||||||
\(170\) | −0.164098 | −0.0125857 | ||||||||
\(171\) | −16.9649 | −1.29734 | ||||||||
\(172\) | −22.1790 | −1.69113 | ||||||||
\(173\) | −14.5582 | −1.10684 | −0.553421 | − | 0.832902i | \(-0.686678\pi\) | ||||
−0.553421 | + | 0.832902i | \(0.686678\pi\) | |||||||
\(174\) | 1.23307 | 0.0934786 | ||||||||
\(175\) | −2.03277 | −0.153663 | ||||||||
\(176\) | 5.01980 | 0.378381 | ||||||||
\(177\) | 27.8087 | 2.09023 | ||||||||
\(178\) | −0.320134 | −0.0239951 | ||||||||
\(179\) | −4.72802 | −0.353389 | −0.176694 | − | 0.984266i | \(-0.556540\pi\) | ||||
−0.176694 | + | 0.984266i | \(0.556540\pi\) | |||||||
\(180\) | −4.50778 | −0.335990 | ||||||||
\(181\) | −4.53675 | −0.337214 | −0.168607 | − | 0.985683i | \(-0.553927\pi\) | ||||
−0.168607 | + | 0.985683i | \(0.553927\pi\) | |||||||
\(182\) | 0.672337 | 0.0498369 | ||||||||
\(183\) | −26.8681 | −1.98615 | ||||||||
\(184\) | −1.29271 | −0.0953000 | ||||||||
\(185\) | −1.21553 | −0.0893673 | ||||||||
\(186\) | 1.57722 | 0.115648 | ||||||||
\(187\) | −3.01953 | −0.220810 | ||||||||
\(188\) | 2.28754 | 0.166836 | ||||||||
\(189\) | −3.45333 | −0.251193 | ||||||||
\(190\) | −0.515781 | −0.0374187 | ||||||||
\(191\) | 20.8682 | 1.50997 | 0.754984 | − | 0.655743i | \(-0.227644\pi\) | ||||
0.754984 | + | 0.655743i | \(0.227644\pi\) | |||||||
\(192\) | 18.0872 | 1.30533 | ||||||||
\(193\) | −16.6824 | −1.20082 | −0.600411 | − | 0.799691i | \(-0.704996\pi\) | ||||
−0.600411 | + | 0.799691i | \(0.704996\pi\) | |||||||
\(194\) | −0.225775 | −0.0162097 | ||||||||
\(195\) | 11.0430 | 0.790809 | ||||||||
\(196\) | 5.72217 | 0.408727 | ||||||||
\(197\) | −18.9546 | −1.35046 | −0.675229 | − | 0.737608i | \(-0.735955\pi\) | ||||
−0.675229 | + | 0.737608i | \(0.735955\pi\) | |||||||
\(198\) | 0.196127 | 0.0139381 | ||||||||
\(199\) | −10.4269 | −0.739142 | −0.369571 | − | 0.929202i | \(-0.620495\pi\) | ||||
−0.369571 | + | 0.929202i | \(0.620495\pi\) | |||||||
\(200\) | −0.274422 | −0.0194045 | ||||||||
\(201\) | −14.5999 | −1.02980 | ||||||||
\(202\) | 0.0118916 | 0.000836688 0 | ||||||||
\(203\) | 15.9127 | 1.11685 | ||||||||
\(204\) | −10.9319 | −0.765388 | ||||||||
\(205\) | −5.30331 | −0.370399 | ||||||||
\(206\) | 0.0262440 | 0.00182851 | ||||||||
\(207\) | 10.6425 | 0.739702 | ||||||||
\(208\) | −19.1252 | −1.32609 | ||||||||
\(209\) | −9.49078 | −0.656491 | ||||||||
\(210\) | 0.320199 | 0.0220958 | ||||||||
\(211\) | −2.66555 | −0.183504 | −0.0917519 | − | 0.995782i | \(-0.529247\pi\) | ||||
−0.0917519 | + | 0.995782i | \(0.529247\pi\) | |||||||
\(212\) | 9.59796 | 0.659190 | ||||||||
\(213\) | −17.3770 | −1.19065 | ||||||||
\(214\) | 1.02383 | 0.0699875 | ||||||||
\(215\) | 11.1157 | 0.758085 | ||||||||
\(216\) | −0.466196 | −0.0317206 | ||||||||
\(217\) | 20.3540 | 1.38172 | ||||||||
\(218\) | 0.805108 | 0.0545288 | ||||||||
\(219\) | −20.1692 | −1.36291 | ||||||||
\(220\) | −2.52181 | −0.170020 | ||||||||
\(221\) | 11.5043 | 0.773862 | ||||||||
\(222\) | 0.191468 | 0.0128505 | ||||||||
\(223\) | −2.25357 | −0.150910 | −0.0754550 | − | 0.997149i | \(-0.524041\pi\) | ||||
−0.0754550 | + | 0.997149i | \(0.524041\pi\) | |||||||
\(224\) | −1.67022 | −0.111596 | ||||||||
\(225\) | 2.25922 | 0.150615 | ||||||||
\(226\) | 1.28076 | 0.0851952 | ||||||||
\(227\) | 23.5087 | 1.56033 | 0.780163 | − | 0.625576i | \(-0.215136\pi\) | ||||
0.780163 | + | 0.625576i | \(0.215136\pi\) | |||||||
\(228\) | −34.3605 | −2.27558 | ||||||||
\(229\) | 22.5757 | 1.49185 | 0.745923 | − | 0.666032i | \(-0.232009\pi\) | ||||
0.745923 | + | 0.666032i | \(0.232009\pi\) | |||||||
\(230\) | 0.323560 | 0.0213349 | ||||||||
\(231\) | 5.89192 | 0.387660 | ||||||||
\(232\) | 2.14820 | 0.141036 | ||||||||
\(233\) | −21.1051 | −1.38264 | −0.691319 | − | 0.722550i | \(-0.742970\pi\) | ||||
−0.691319 | + | 0.722550i | \(0.742970\pi\) | |||||||
\(234\) | −0.747235 | −0.0488483 | ||||||||
\(235\) | −1.14647 | −0.0747877 | ||||||||
\(236\) | 24.1950 | 1.57496 | ||||||||
\(237\) | −17.5787 | −1.14186 | ||||||||
\(238\) | 0.333573 | 0.0216223 | ||||||||
\(239\) | −18.4318 | −1.19225 | −0.596126 | − | 0.802891i | \(-0.703294\pi\) | ||||
−0.596126 | + | 0.802891i | \(0.703294\pi\) | |||||||
\(240\) | −9.10833 | −0.587940 | ||||||||
\(241\) | 26.9333 | 1.73493 | 0.867463 | − | 0.497502i | \(-0.165749\pi\) | ||||
0.867463 | + | 0.497502i | \(0.165749\pi\) | |||||||
\(242\) | −0.645830 | −0.0415156 | ||||||||
\(243\) | 19.3812 | 1.24331 | ||||||||
\(244\) | −23.3766 | −1.49653 | ||||||||
\(245\) | −2.86785 | −0.183220 | ||||||||
\(246\) | 0.835369 | 0.0532612 | ||||||||
\(247\) | 36.1595 | 2.30077 | ||||||||
\(248\) | 2.74777 | 0.174483 | ||||||||
\(249\) | 2.21065 | 0.140094 | ||||||||
\(250\) | 0.0686864 | 0.00434411 | ||||||||
\(251\) | 5.92164 | 0.373771 | 0.186885 | − | 0.982382i | \(-0.440161\pi\) | ||||
0.186885 | + | 0.982382i | \(0.440161\pi\) | |||||||
\(252\) | 9.16327 | 0.577232 | ||||||||
\(253\) | 5.95376 | 0.374310 | ||||||||
\(254\) | 0.562917 | 0.0353205 | ||||||||
\(255\) | 5.47889 | 0.343101 | ||||||||
\(256\) | 15.6239 | 0.976494 | ||||||||
\(257\) | −2.79072 | −0.174080 | −0.0870401 | − | 0.996205i | \(-0.527741\pi\) | ||||
−0.0870401 | + | 0.996205i | \(0.527741\pi\) | |||||||
\(258\) | −1.75093 | −0.109008 | ||||||||
\(259\) | 2.47089 | 0.153533 | ||||||||
\(260\) | 9.60799 | 0.595862 | ||||||||
\(261\) | −17.6854 | −1.09470 | ||||||||
\(262\) | 0.677652 | 0.0418655 | ||||||||
\(263\) | −2.32513 | −0.143374 | −0.0716869 | − | 0.997427i | \(-0.522838\pi\) | ||||
−0.0716869 | + | 0.997427i | \(0.522838\pi\) | |||||||
\(264\) | 0.795403 | 0.0489536 | ||||||||
\(265\) | −4.81033 | −0.295496 | ||||||||
\(266\) | 1.04846 | 0.0642854 | ||||||||
\(267\) | 10.6886 | 0.654133 | ||||||||
\(268\) | −12.7027 | −0.775939 | ||||||||
\(269\) | −7.98611 | −0.486922 | −0.243461 | − | 0.969911i | \(-0.578283\pi\) | ||||
−0.243461 | + | 0.969911i | \(0.578283\pi\) | |||||||
\(270\) | 0.116687 | 0.00710132 | ||||||||
\(271\) | 6.28776 | 0.381954 | 0.190977 | − | 0.981595i | \(-0.438834\pi\) | ||||
0.190977 | + | 0.981595i | \(0.438834\pi\) | |||||||
\(272\) | −9.48877 | −0.575341 | ||||||||
\(273\) | −22.4479 | −1.35861 | ||||||||
\(274\) | 0.527115 | 0.0318442 | ||||||||
\(275\) | 1.26389 | 0.0762152 | ||||||||
\(276\) | 21.5550 | 1.29746 | ||||||||
\(277\) | 26.1777 | 1.57287 | 0.786434 | − | 0.617674i | \(-0.211925\pi\) | ||||
0.786434 | + | 0.617674i | \(0.211925\pi\) | |||||||
\(278\) | 0.0510597 | 0.00306236 | ||||||||
\(279\) | −22.6214 | −1.35431 | ||||||||
\(280\) | 0.557836 | 0.0333371 | ||||||||
\(281\) | −28.1138 | −1.67713 | −0.838566 | − | 0.544801i | \(-0.816605\pi\) | ||||
−0.838566 | + | 0.544801i | \(0.816605\pi\) | |||||||
\(282\) | 0.180591 | 0.0107540 | ||||||||
\(283\) | 11.7982 | 0.701331 | 0.350665 | − | 0.936501i | \(-0.385955\pi\) | ||||
0.350665 | + | 0.936501i | \(0.385955\pi\) | |||||||
\(284\) | −15.1189 | −0.897140 | ||||||||
\(285\) | 17.2209 | 1.02008 | ||||||||
\(286\) | −0.418030 | −0.0247186 | ||||||||
\(287\) | 10.7804 | 0.636347 | ||||||||
\(288\) | 1.85628 | 0.109382 | ||||||||
\(289\) | −11.2923 | −0.664251 | ||||||||
\(290\) | −0.537683 | −0.0315738 | ||||||||
\(291\) | 7.53817 | 0.441895 | ||||||||
\(292\) | −17.5482 | −1.02693 | ||||||||
\(293\) | −10.0677 | −0.588163 | −0.294082 | − | 0.955780i | \(-0.595014\pi\) | ||||
−0.294082 | + | 0.955780i | \(0.595014\pi\) | |||||||
\(294\) | 0.451740 | 0.0263460 | ||||||||
\(295\) | −12.1261 | −0.706008 | ||||||||
\(296\) | 0.333567 | 0.0193882 | ||||||||
\(297\) | 2.14713 | 0.124589 | ||||||||
\(298\) | 0.903071 | 0.0523135 | ||||||||
\(299\) | −22.6836 | −1.31182 | ||||||||
\(300\) | 4.57578 | 0.264183 | ||||||||
\(301\) | −22.5956 | −1.30239 | ||||||||
\(302\) | 0.259933 | 0.0149574 | ||||||||
\(303\) | −0.397035 | −0.0228091 | ||||||||
\(304\) | −29.8244 | −1.71055 | ||||||||
\(305\) | 11.7159 | 0.670852 | ||||||||
\(306\) | −0.370733 | −0.0211934 | ||||||||
\(307\) | −12.8876 | −0.735534 | −0.367767 | − | 0.929918i | \(-0.619878\pi\) | ||||
−0.367767 | + | 0.929918i | \(0.619878\pi\) | |||||||
\(308\) | 5.12626 | 0.292096 | ||||||||
\(309\) | −0.876233 | −0.0498472 | ||||||||
\(310\) | −0.687753 | −0.0390618 | ||||||||
\(311\) | −12.9711 | −0.735525 | −0.367763 | − | 0.929920i | \(-0.619876\pi\) | ||||
−0.367763 | + | 0.929920i | \(0.619876\pi\) | |||||||
\(312\) | −3.03045 | −0.171565 | ||||||||
\(313\) | −8.49231 | −0.480014 | −0.240007 | − | 0.970771i | \(-0.577150\pi\) | ||||
−0.240007 | + | 0.970771i | \(0.577150\pi\) | |||||||
\(314\) | −1.23034 | −0.0694322 | ||||||||
\(315\) | −4.59247 | −0.258756 | ||||||||
\(316\) | −15.2943 | −0.860373 | ||||||||
\(317\) | 11.2023 | 0.629183 | 0.314592 | − | 0.949227i | \(-0.398132\pi\) | ||||
0.314592 | + | 0.949227i | \(0.398132\pi\) | |||||||
\(318\) | 0.757715 | 0.0424906 | ||||||||
\(319\) | −9.89381 | −0.553947 | ||||||||
\(320\) | −7.88699 | −0.440896 | ||||||||
\(321\) | −34.1835 | −1.90794 | ||||||||
\(322\) | −0.657722 | −0.0366534 | ||||||||
\(323\) | 17.9401 | 0.998216 | ||||||||
\(324\) | 21.2968 | 1.18316 | ||||||||
\(325\) | −4.81535 | −0.267108 | ||||||||
\(326\) | 1.36023 | 0.0753363 | ||||||||
\(327\) | −26.8809 | −1.48652 | ||||||||
\(328\) | 1.45534 | 0.0803579 | ||||||||
\(329\) | 2.33051 | 0.128485 | ||||||||
\(330\) | −0.199085 | −0.0109593 | ||||||||
\(331\) | −13.3112 | −0.731647 | −0.365824 | − | 0.930684i | \(-0.619213\pi\) | ||||
−0.365824 | + | 0.930684i | \(0.619213\pi\) | |||||||
\(332\) | 1.92337 | 0.105559 | ||||||||
\(333\) | −2.74614 | −0.150488 | ||||||||
\(334\) | −0.686254 | −0.0375502 | ||||||||
\(335\) | 6.36635 | 0.347831 | ||||||||
\(336\) | 18.5151 | 1.01008 | ||||||||
\(337\) | −30.9921 | −1.68825 | −0.844123 | − | 0.536149i | \(-0.819879\pi\) | ||||
−0.844123 | + | 0.536149i | \(0.819879\pi\) | |||||||
\(338\) | 0.699751 | 0.0380614 | ||||||||
\(339\) | −42.7621 | −2.32252 | ||||||||
\(340\) | 4.76690 | 0.258521 | ||||||||
\(341\) | −12.6552 | −0.685319 | ||||||||
\(342\) | −1.16526 | −0.0630101 | ||||||||
\(343\) | 20.0591 | 1.08309 | ||||||||
\(344\) | −3.05039 | −0.164466 | ||||||||
\(345\) | −10.8030 | −0.581614 | ||||||||
\(346\) | −0.999953 | −0.0537578 | ||||||||
\(347\) | 15.5828 | 0.836528 | 0.418264 | − | 0.908326i | \(-0.362639\pi\) | ||||
0.418264 | + | 0.908326i | \(0.362639\pi\) | |||||||
\(348\) | −35.8196 | −1.92013 | ||||||||
\(349\) | 2.73748 | 0.146534 | 0.0732671 | − | 0.997312i | \(-0.476657\pi\) | ||||
0.0732671 | + | 0.997312i | \(0.476657\pi\) | |||||||
\(350\) | −0.139624 | −0.00746320 | ||||||||
\(351\) | −8.18047 | −0.436641 | ||||||||
\(352\) | 1.03847 | 0.0553505 | ||||||||
\(353\) | −27.5367 | −1.46563 | −0.732815 | − | 0.680428i | \(-0.761794\pi\) | ||||
−0.732815 | + | 0.680428i | \(0.761794\pi\) | |||||||
\(354\) | 1.91008 | 0.101520 | ||||||||
\(355\) | 7.57731 | 0.402162 | ||||||||
\(356\) | 9.29963 | 0.492879 | ||||||||
\(357\) | −11.1373 | −0.589449 | ||||||||
\(358\) | −0.324751 | −0.0171636 | ||||||||
\(359\) | 17.8466 | 0.941906 | 0.470953 | − | 0.882158i | \(-0.343910\pi\) | ||||
0.470953 | + | 0.882158i | \(0.343910\pi\) | |||||||
\(360\) | −0.619979 | −0.0326757 | ||||||||
\(361\) | 37.3882 | 1.96780 | ||||||||
\(362\) | −0.311613 | −0.0163780 | ||||||||
\(363\) | 21.5630 | 1.13176 | ||||||||
\(364\) | −19.5308 | −1.02369 | ||||||||
\(365\) | 8.79484 | 0.460343 | ||||||||
\(366\) | −1.84548 | −0.0964645 | ||||||||
\(367\) | 7.65545 | 0.399611 | 0.199806 | − | 0.979836i | \(-0.435969\pi\) | ||||
0.199806 | + | 0.979836i | \(0.435969\pi\) | |||||||
\(368\) | 18.7095 | 0.975299 | ||||||||
\(369\) | −11.9813 | −0.623724 | ||||||||
\(370\) | −0.0834902 | −0.00434045 | ||||||||
\(371\) | 9.77828 | 0.507663 | ||||||||
\(372\) | −45.8170 | −2.37550 | ||||||||
\(373\) | −0.560977 | −0.0290463 | −0.0145232 | − | 0.999895i | \(-0.504623\pi\) | ||||
−0.0145232 | + | 0.999895i | \(0.504623\pi\) | |||||||
\(374\) | −0.207401 | −0.0107244 | ||||||||
\(375\) | −2.29330 | −0.118425 | ||||||||
\(376\) | 0.314617 | 0.0162251 | ||||||||
\(377\) | 37.6950 | 1.94139 | ||||||||
\(378\) | −0.237197 | −0.0122001 | ||||||||
\(379\) | −11.3575 | −0.583397 | −0.291699 | − | 0.956510i | \(-0.594220\pi\) | ||||
−0.291699 | + | 0.956510i | \(0.594220\pi\) | |||||||
\(380\) | 14.9830 | 0.768611 | ||||||||
\(381\) | −18.7946 | −0.962879 | ||||||||
\(382\) | 1.43336 | 0.0733371 | ||||||||
\(383\) | −11.6322 | −0.594378 | −0.297189 | − | 0.954819i | \(-0.596049\pi\) | ||||
−0.297189 | + | 0.954819i | \(0.596049\pi\) | |||||||
\(384\) | 5.01091 | 0.255712 | ||||||||
\(385\) | −2.56919 | −0.130938 | ||||||||
\(386\) | −1.14585 | −0.0583223 | ||||||||
\(387\) | 25.1128 | 1.27656 | ||||||||
\(388\) | 6.55857 | 0.332961 | ||||||||
\(389\) | 2.60796 | 0.132229 | 0.0661144 | − | 0.997812i | \(-0.478940\pi\) | ||||
0.0661144 | + | 0.997812i | \(0.478940\pi\) | |||||||
\(390\) | 0.758507 | 0.0384085 | ||||||||
\(391\) | −11.2542 | −0.569150 | ||||||||
\(392\) | 0.787001 | 0.0397495 | ||||||||
\(393\) | −22.6254 | −1.14130 | ||||||||
\(394\) | −1.30192 | −0.0655899 | ||||||||
\(395\) | 7.66525 | 0.385680 | ||||||||
\(396\) | −5.69732 | −0.286301 | ||||||||
\(397\) | 8.66596 | 0.434932 | 0.217466 | − | 0.976068i | \(-0.430221\pi\) | ||||
0.217466 | + | 0.976068i | \(0.430221\pi\) | |||||||
\(398\) | −0.716185 | −0.0358991 | ||||||||
\(399\) | −35.0060 | −1.75249 | ||||||||
\(400\) | 3.97172 | 0.198586 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | −1.00282 | −0.0500160 | ||||||||
\(403\) | 48.2159 | 2.40180 | ||||||||
\(404\) | −0.345440 | −0.0171863 | ||||||||
\(405\) | −10.6736 | −0.530375 | ||||||||
\(406\) | 1.09299 | 0.0542439 | ||||||||
\(407\) | −1.53629 | −0.0761510 | ||||||||
\(408\) | −1.50353 | −0.0744356 | ||||||||
\(409\) | 17.1486 | 0.847945 | 0.423973 | − | 0.905675i | \(-0.360635\pi\) | ||||
0.423973 | + | 0.905675i | \(0.360635\pi\) | |||||||
\(410\) | −0.364265 | −0.0179898 | ||||||||
\(411\) | −17.5993 | −0.868109 | ||||||||
\(412\) | −0.762366 | −0.0375591 | ||||||||
\(413\) | 24.6495 | 1.21292 | ||||||||
\(414\) | 0.730992 | 0.0359263 | ||||||||
\(415\) | −0.963961 | −0.0473190 | ||||||||
\(416\) | −3.95652 | −0.193984 | ||||||||
\(417\) | −1.70478 | −0.0834834 | ||||||||
\(418\) | −0.651888 | −0.0318849 | ||||||||
\(419\) | −2.89009 | −0.141190 | −0.0705951 | − | 0.997505i | \(-0.522490\pi\) | ||||
−0.0705951 | + | 0.997505i | \(0.522490\pi\) | |||||||
\(420\) | −9.30150 | −0.453867 | ||||||||
\(421\) | −26.2090 | −1.27735 | −0.638675 | − | 0.769477i | \(-0.720517\pi\) | ||||
−0.638675 | + | 0.769477i | \(0.720517\pi\) | |||||||
\(422\) | −0.183087 | −0.00891253 | ||||||||
\(423\) | −2.59013 | −0.125937 | ||||||||
\(424\) | 1.32006 | 0.0641077 | ||||||||
\(425\) | −2.38909 | −0.115888 | ||||||||
\(426\) | −1.19357 | −0.0578285 | ||||||||
\(427\) | −23.8158 | −1.15253 | ||||||||
\(428\) | −29.7414 | −1.43760 | ||||||||
\(429\) | 13.9571 | 0.673857 | ||||||||
\(430\) | 0.763498 | 0.0368191 | ||||||||
\(431\) | −22.3806 | −1.07803 | −0.539017 | − | 0.842295i | \(-0.681204\pi\) | ||||
−0.539017 | + | 0.842295i | \(0.681204\pi\) | |||||||
\(432\) | 6.74728 | 0.324628 | ||||||||
\(433\) | 21.2078 | 1.01918 | 0.509591 | − | 0.860417i | \(-0.329797\pi\) | ||||
0.509591 | + | 0.860417i | \(0.329797\pi\) | |||||||
\(434\) | 1.39804 | 0.0671082 | ||||||||
\(435\) | 17.9521 | 0.860739 | ||||||||
\(436\) | −23.3877 | −1.12007 | ||||||||
\(437\) | −35.3735 | −1.69214 | ||||||||
\(438\) | −1.38535 | −0.0661946 | ||||||||
\(439\) | −26.6625 | −1.27253 | −0.636265 | − | 0.771471i | \(-0.719521\pi\) | ||||
−0.636265 | + | 0.771471i | \(0.719521\pi\) | |||||||
\(440\) | −0.346838 | −0.0165348 | ||||||||
\(441\) | −6.47911 | −0.308529 | ||||||||
\(442\) | 0.790188 | 0.0375854 | ||||||||
\(443\) | −24.0130 | −1.14089 | −0.570446 | − | 0.821335i | \(-0.693230\pi\) | ||||
−0.570446 | + | 0.821335i | \(0.693230\pi\) | |||||||
\(444\) | −5.56198 | −0.263960 | ||||||||
\(445\) | −4.66081 | −0.220944 | ||||||||
\(446\) | −0.154789 | −0.00732949 | ||||||||
\(447\) | −30.1517 | −1.42613 | ||||||||
\(448\) | 16.0324 | 0.757461 | ||||||||
\(449\) | 21.4170 | 1.01073 | 0.505366 | − | 0.862905i | \(-0.331357\pi\) | ||||
0.505366 | + | 0.862905i | \(0.331357\pi\) | |||||||
\(450\) | 0.155178 | 0.00731515 | ||||||||
\(451\) | −6.70278 | −0.315622 | ||||||||
\(452\) | −37.2051 | −1.74998 | ||||||||
\(453\) | −8.67862 | −0.407757 | ||||||||
\(454\) | 1.61473 | 0.0757829 | ||||||||
\(455\) | 9.78850 | 0.458892 | ||||||||
\(456\) | −4.72578 | −0.221305 | ||||||||
\(457\) | 10.3582 | 0.484536 | 0.242268 | − | 0.970209i | \(-0.422109\pi\) | ||||
0.242268 | + | 0.970209i | \(0.422109\pi\) | |||||||
\(458\) | 1.55065 | 0.0724569 | ||||||||
\(459\) | −4.05865 | −0.189442 | ||||||||
\(460\) | −9.39913 | −0.438237 | ||||||||
\(461\) | 19.2891 | 0.898384 | 0.449192 | − | 0.893435i | \(-0.351712\pi\) | ||||
0.449192 | + | 0.893435i | \(0.351712\pi\) | |||||||
\(462\) | 0.404695 | 0.0188281 | ||||||||
\(463\) | −18.4897 | −0.859290 | −0.429645 | − | 0.902998i | \(-0.641361\pi\) | ||||
−0.429645 | + | 0.902998i | \(0.641361\pi\) | |||||||
\(464\) | −31.0909 | −1.44336 | ||||||||
\(465\) | 22.9627 | 1.06487 | ||||||||
\(466\) | −1.44963 | −0.0671528 | ||||||||
\(467\) | 34.2749 | 1.58605 | 0.793026 | − | 0.609188i | \(-0.208504\pi\) | ||||
0.793026 | + | 0.609188i | \(0.208504\pi\) | |||||||
\(468\) | 21.7065 | 1.00339 | ||||||||
\(469\) | −12.9413 | −0.597575 | ||||||||
\(470\) | −0.0787472 | −0.00363234 | ||||||||
\(471\) | 41.0786 | 1.89280 | ||||||||
\(472\) | 3.32766 | 0.153168 | ||||||||
\(473\) | 14.0490 | 0.645973 | ||||||||
\(474\) | −1.20742 | −0.0554586 | ||||||||
\(475\) | −7.50921 | −0.344546 | ||||||||
\(476\) | −9.69000 | −0.444141 | ||||||||
\(477\) | −10.8676 | −0.497592 | ||||||||
\(478\) | −1.26601 | −0.0579061 | ||||||||
\(479\) | 28.6185 | 1.30761 | 0.653807 | − | 0.756661i | \(-0.273171\pi\) | ||||
0.653807 | + | 0.756661i | \(0.273171\pi\) | |||||||
\(480\) | −1.88428 | −0.0860052 | ||||||||
\(481\) | 5.85319 | 0.266883 | ||||||||
\(482\) | 1.84995 | 0.0842630 | ||||||||
\(483\) | 21.9600 | 0.999214 | ||||||||
\(484\) | 18.7608 | 0.852765 | ||||||||
\(485\) | −3.28704 | −0.149257 | ||||||||
\(486\) | 1.33123 | 0.0603857 | ||||||||
\(487\) | 38.3521 | 1.73790 | 0.868949 | − | 0.494902i | \(-0.164796\pi\) | ||||
0.868949 | + | 0.494902i | \(0.164796\pi\) | |||||||
\(488\) | −3.21510 | −0.145541 | ||||||||
\(489\) | −45.4153 | −2.05375 | ||||||||
\(490\) | −0.196982 | −0.00889876 | ||||||||
\(491\) | 14.7490 | 0.665614 | 0.332807 | − | 0.942995i | \(-0.392004\pi\) | ||||
0.332807 | + | 0.942995i | \(0.392004\pi\) | |||||||
\(492\) | −24.2668 | −1.09403 | ||||||||
\(493\) | 18.7020 | 0.842294 | ||||||||
\(494\) | 2.48367 | 0.111745 | ||||||||
\(495\) | 2.85540 | 0.128341 | ||||||||
\(496\) | −39.7686 | −1.78566 | ||||||||
\(497\) | −15.4029 | −0.690915 | ||||||||
\(498\) | 0.151842 | 0.00680419 | ||||||||
\(499\) | 19.7799 | 0.885468 | 0.442734 | − | 0.896653i | \(-0.354009\pi\) | ||||
0.442734 | + | 0.896653i | \(0.354009\pi\) | |||||||
\(500\) | −1.99528 | −0.0892317 | ||||||||
\(501\) | 22.9126 | 1.02366 | ||||||||
\(502\) | 0.406736 | 0.0181535 | ||||||||
\(503\) | 6.51523 | 0.290500 | 0.145250 | − | 0.989395i | \(-0.453601\pi\) | ||||
0.145250 | + | 0.989395i | \(0.453601\pi\) | |||||||
\(504\) | 1.26027 | 0.0561370 | ||||||||
\(505\) | 0.173128 | 0.00770411 | ||||||||
\(506\) | 0.408943 | 0.0181797 | ||||||||
\(507\) | −23.3632 | −1.03760 | ||||||||
\(508\) | −16.3523 | −0.725514 | ||||||||
\(509\) | −21.9119 | −0.971229 | −0.485614 | − | 0.874173i | \(-0.661404\pi\) | ||||
−0.485614 | + | 0.874173i | \(0.661404\pi\) | |||||||
\(510\) | 0.376325 | 0.0166640 | ||||||||
\(511\) | −17.8779 | −0.790871 | ||||||||
\(512\) | 5.44319 | 0.240557 | ||||||||
\(513\) | −12.7569 | −0.563230 | ||||||||
\(514\) | −0.191684 | −0.00845484 | ||||||||
\(515\) | 0.382084 | 0.0168366 | ||||||||
\(516\) | 50.8630 | 2.23912 | ||||||||
\(517\) | −1.44901 | −0.0637275 | ||||||||
\(518\) | 0.169716 | 0.00745691 | ||||||||
\(519\) | 33.3864 | 1.46550 | ||||||||
\(520\) | 1.32144 | 0.0579488 | ||||||||
\(521\) | 41.9668 | 1.83860 | 0.919300 | − | 0.393558i | \(-0.128756\pi\) | ||||
0.919300 | + | 0.393558i | \(0.128756\pi\) | |||||||
\(522\) | −1.21474 | −0.0531679 | ||||||||
\(523\) | −30.6394 | −1.33977 | −0.669883 | − | 0.742467i | \(-0.733656\pi\) | ||||
−0.669883 | + | 0.742467i | \(0.733656\pi\) | |||||||
\(524\) | −19.6852 | −0.859953 | ||||||||
\(525\) | 4.66175 | 0.203455 | ||||||||
\(526\) | −0.159705 | −0.00696347 | ||||||||
\(527\) | 23.9218 | 1.04205 | ||||||||
\(528\) | −11.5119 | −0.500991 | ||||||||
\(529\) | −0.809511 | −0.0351961 | ||||||||
\(530\) | −0.330404 | −0.0143518 | ||||||||
\(531\) | −27.3955 | −1.18886 | ||||||||
\(532\) | −30.4569 | −1.32048 | ||||||||
\(533\) | 25.5373 | 1.10614 | ||||||||
\(534\) | 0.734164 | 0.0317704 | ||||||||
\(535\) | 14.9058 | 0.644436 | ||||||||
\(536\) | −1.74706 | −0.0754617 | ||||||||
\(537\) | 10.8428 | 0.467900 | ||||||||
\(538\) | −0.548537 | −0.0236491 | ||||||||
\(539\) | −3.62464 | −0.156124 | ||||||||
\(540\) | −3.38965 | −0.145867 | ||||||||
\(541\) | −17.7533 | −0.763275 | −0.381637 | − | 0.924312i | \(-0.624640\pi\) | ||||
−0.381637 | + | 0.924312i | \(0.624640\pi\) | |||||||
\(542\) | 0.431884 | 0.0185510 | ||||||||
\(543\) | 10.4041 | 0.446484 | ||||||||
\(544\) | −1.96298 | −0.0841622 | ||||||||
\(545\) | 11.7215 | 0.502094 | ||||||||
\(546\) | −1.54187 | −0.0659859 | ||||||||
\(547\) | 6.85761 | 0.293210 | 0.146605 | − | 0.989195i | \(-0.453165\pi\) | ||||
0.146605 | + | 0.989195i | \(0.453165\pi\) | |||||||
\(548\) | −15.3122 | −0.654107 | ||||||||
\(549\) | 26.4688 | 1.12966 | ||||||||
\(550\) | 0.0868118 | 0.00370167 | ||||||||
\(551\) | 58.7827 | 2.50423 | ||||||||
\(552\) | 2.96458 | 0.126181 | ||||||||
\(553\) | −15.5817 | −0.662600 | ||||||||
\(554\) | 1.79806 | 0.0763921 | ||||||||
\(555\) | 2.78757 | 0.118326 | ||||||||
\(556\) | −1.48324 | −0.0629035 | ||||||||
\(557\) | −27.3532 | −1.15899 | −0.579496 | − | 0.814975i | \(-0.696751\pi\) | ||||
−0.579496 | + | 0.814975i | \(0.696751\pi\) | |||||||
\(558\) | −1.55379 | −0.0657770 | ||||||||
\(559\) | −53.5260 | −2.26391 | ||||||||
\(560\) | −8.07358 | −0.341171 | ||||||||
\(561\) | 6.92469 | 0.292361 | ||||||||
\(562\) | −1.93104 | −0.0814560 | ||||||||
\(563\) | 37.8474 | 1.59508 | 0.797539 | − | 0.603268i | \(-0.206135\pi\) | ||||
0.797539 | + | 0.603268i | \(0.206135\pi\) | |||||||
\(564\) | −5.24601 | −0.220897 | ||||||||
\(565\) | 18.6465 | 0.784466 | ||||||||
\(566\) | 0.810377 | 0.0340627 | ||||||||
\(567\) | 21.6969 | 0.911185 | ||||||||
\(568\) | −2.07938 | −0.0872487 | ||||||||
\(569\) | −5.48139 | −0.229792 | −0.114896 | − | 0.993378i | \(-0.536653\pi\) | ||||
−0.114896 | + | 0.993378i | \(0.536653\pi\) | |||||||
\(570\) | 1.18284 | 0.0495437 | ||||||||
\(571\) | −39.4038 | −1.64900 | −0.824499 | − | 0.565864i | \(-0.808543\pi\) | ||||
−0.824499 | + | 0.565864i | \(0.808543\pi\) | |||||||
\(572\) | 12.1434 | 0.507741 | ||||||||
\(573\) | −47.8570 | −1.99925 | ||||||||
\(574\) | 0.740467 | 0.0309065 | ||||||||
\(575\) | 4.71068 | 0.196449 | ||||||||
\(576\) | −17.8185 | −0.742435 | ||||||||
\(577\) | −10.1073 | −0.420773 | −0.210386 | − | 0.977618i | \(-0.567472\pi\) | ||||
−0.210386 | + | 0.977618i | \(0.567472\pi\) | |||||||
\(578\) | −0.775626 | −0.0322618 | ||||||||
\(579\) | 38.2576 | 1.58993 | ||||||||
\(580\) | 15.6192 | 0.648553 | ||||||||
\(581\) | 1.95951 | 0.0812942 | ||||||||
\(582\) | 0.517770 | 0.0214622 | ||||||||
\(583\) | −6.07970 | −0.251796 | ||||||||
\(584\) | −2.41350 | −0.0998711 | ||||||||
\(585\) | −10.8789 | −0.449789 | ||||||||
\(586\) | −0.691516 | −0.0285663 | ||||||||
\(587\) | 10.8190 | 0.446550 | 0.223275 | − | 0.974756i | \(-0.428325\pi\) | ||||
0.223275 | + | 0.974756i | \(0.428325\pi\) | |||||||
\(588\) | −13.1227 | −0.541169 | ||||||||
\(589\) | 75.1893 | 3.09812 | ||||||||
\(590\) | −0.832898 | −0.0342899 | ||||||||
\(591\) | 43.4685 | 1.78806 | ||||||||
\(592\) | −4.82773 | −0.198418 | ||||||||
\(593\) | 23.6934 | 0.972971 | 0.486485 | − | 0.873689i | \(-0.338279\pi\) | ||||
0.486485 | + | 0.873689i | \(0.338279\pi\) | |||||||
\(594\) | 0.147479 | 0.00605112 | ||||||||
\(595\) | 4.85646 | 0.199095 | ||||||||
\(596\) | −26.2334 | −1.07456 | ||||||||
\(597\) | 23.9120 | 0.978651 | ||||||||
\(598\) | −1.55805 | −0.0637136 | ||||||||
\(599\) | −3.11993 | −0.127477 | −0.0637384 | − | 0.997967i | \(-0.520302\pi\) | ||||
−0.0637384 | + | 0.997967i | \(0.520302\pi\) | |||||||
\(600\) | 0.629331 | 0.0256923 | ||||||||
\(601\) | 25.4983 | 1.04010 | 0.520048 | − | 0.854137i | \(-0.325914\pi\) | ||||
0.520048 | + | 0.854137i | \(0.325914\pi\) | |||||||
\(602\) | −1.55201 | −0.0632554 | ||||||||
\(603\) | 14.3830 | 0.585720 | ||||||||
\(604\) | −7.55082 | −0.307239 | ||||||||
\(605\) | −9.40259 | −0.382270 | ||||||||
\(606\) | −0.0272709 | −0.00110781 | ||||||||
\(607\) | 15.2032 | 0.617081 | 0.308540 | − | 0.951211i | \(-0.400160\pi\) | ||||
0.308540 | + | 0.951211i | \(0.400160\pi\) | |||||||
\(608\) | −6.16991 | −0.250223 | ||||||||
\(609\) | −36.4925 | −1.47875 | ||||||||
\(610\) | 0.804725 | 0.0325824 | ||||||||
\(611\) | 5.52067 | 0.223343 | ||||||||
\(612\) | 10.7695 | 0.435330 | ||||||||
\(613\) | −0.324285 | −0.0130977 | −0.00654887 | − | 0.999979i | \(-0.502085\pi\) | ||||
−0.00654887 | + | 0.999979i | \(0.502085\pi\) | |||||||
\(614\) | −0.885203 | −0.0357239 | ||||||||
\(615\) | 12.1621 | 0.490422 | ||||||||
\(616\) | 0.705041 | 0.0284069 | ||||||||
\(617\) | 26.3365 | 1.06027 | 0.530133 | − | 0.847914i | \(-0.322142\pi\) | ||||
0.530133 | + | 0.847914i | \(0.322142\pi\) | |||||||
\(618\) | −0.0601853 | −0.00242101 | ||||||||
\(619\) | 17.6193 | 0.708181 | 0.354090 | − | 0.935211i | \(-0.384791\pi\) | ||||
0.354090 | + | 0.935211i | \(0.384791\pi\) | |||||||
\(620\) | 19.9786 | 0.802362 | ||||||||
\(621\) | 8.00265 | 0.321135 | ||||||||
\(622\) | −0.890941 | −0.0357235 | ||||||||
\(623\) | 9.47435 | 0.379582 | ||||||||
\(624\) | 43.8598 | 1.75580 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −0.583307 | −0.0233136 | ||||||||
\(627\) | 21.7652 | 0.869218 | ||||||||
\(628\) | 35.7404 | 1.42620 | ||||||||
\(629\) | 2.90400 | 0.115790 | ||||||||
\(630\) | −0.315440 | −0.0125674 | ||||||||
\(631\) | −41.5355 | −1.65350 | −0.826752 | − | 0.562567i | \(-0.809814\pi\) | ||||
−0.826752 | + | 0.562567i | \(0.809814\pi\) | |||||||
\(632\) | −2.10351 | −0.0836731 | ||||||||
\(633\) | 6.11289 | 0.242966 | ||||||||
\(634\) | 0.769445 | 0.0305586 | ||||||||
\(635\) | 8.19546 | 0.325227 | ||||||||
\(636\) | −22.0110 | −0.872792 | ||||||||
\(637\) | 13.8097 | 0.547161 | ||||||||
\(638\) | −0.679570 | −0.0269044 | ||||||||
\(639\) | 17.1188 | 0.677209 | ||||||||
\(640\) | −2.18502 | −0.0863706 | ||||||||
\(641\) | −28.5960 | −1.12947 | −0.564737 | − | 0.825271i | \(-0.691022\pi\) | ||||
−0.564737 | + | 0.825271i | \(0.691022\pi\) | |||||||
\(642\) | −2.34795 | −0.0926660 | ||||||||
\(643\) | 31.2100 | 1.23080 | 0.615402 | − | 0.788214i | \(-0.288994\pi\) | ||||
0.615402 | + | 0.788214i | \(0.288994\pi\) | |||||||
\(644\) | 19.1063 | 0.752892 | ||||||||
\(645\) | −25.4916 | −1.00373 | ||||||||
\(646\) | 1.23224 | 0.0484820 | ||||||||
\(647\) | 41.9392 | 1.64880 | 0.824400 | − | 0.566007i | \(-0.191513\pi\) | ||||
0.824400 | + | 0.566007i | \(0.191513\pi\) | |||||||
\(648\) | 2.92906 | 0.115064 | ||||||||
\(649\) | −15.3260 | −0.601598 | ||||||||
\(650\) | −0.330749 | −0.0129731 | ||||||||
\(651\) | −46.6778 | −1.82945 | ||||||||
\(652\) | −39.5136 | −1.54747 | ||||||||
\(653\) | −3.98499 | −0.155945 | −0.0779724 | − | 0.996956i | \(-0.524845\pi\) | ||||
−0.0779724 | + | 0.996956i | \(0.524845\pi\) | |||||||
\(654\) | −1.84635 | −0.0721981 | ||||||||
\(655\) | 9.86588 | 0.385492 | ||||||||
\(656\) | −21.0632 | −0.822381 | ||||||||
\(657\) | 19.8695 | 0.775182 | ||||||||
\(658\) | 0.160075 | 0.00624036 | ||||||||
\(659\) | 29.7898 | 1.16044 | 0.580222 | − | 0.814458i | \(-0.302966\pi\) | ||||
0.580222 | + | 0.814458i | \(0.302966\pi\) | |||||||
\(660\) | 5.78326 | 0.225113 | ||||||||
\(661\) | −21.8127 | −0.848416 | −0.424208 | − | 0.905565i | \(-0.639447\pi\) | ||||
−0.424208 | + | 0.905565i | \(0.639447\pi\) | |||||||
\(662\) | −0.914296 | −0.0355351 | ||||||||
\(663\) | −26.3828 | −1.02462 | ||||||||
\(664\) | 0.264532 | 0.0102658 | ||||||||
\(665\) | 15.2645 | 0.591931 | ||||||||
\(666\) | −0.188623 | −0.00730898 | ||||||||
\(667\) | −36.8756 | −1.42783 | ||||||||
\(668\) | 19.9351 | 0.771312 | ||||||||
\(669\) | 5.16810 | 0.199810 | ||||||||
\(670\) | 0.437282 | 0.0168937 | ||||||||
\(671\) | 14.8076 | 0.571641 | ||||||||
\(672\) | 3.83031 | 0.147757 | ||||||||
\(673\) | −8.02898 | −0.309495 | −0.154747 | − | 0.987954i | \(-0.549456\pi\) | ||||
−0.154747 | + | 0.987954i | \(0.549456\pi\) | |||||||
\(674\) | −2.12874 | −0.0819959 | ||||||||
\(675\) | 1.69883 | 0.0653881 | ||||||||
\(676\) | −20.3272 | −0.781814 | ||||||||
\(677\) | 27.4427 | 1.05471 | 0.527355 | − | 0.849645i | \(-0.323184\pi\) | ||||
0.527355 | + | 0.849645i | \(0.323184\pi\) | |||||||
\(678\) | −2.93718 | −0.112802 | ||||||||
\(679\) | 6.68179 | 0.256424 | ||||||||
\(680\) | 0.655617 | 0.0251418 | ||||||||
\(681\) | −53.9124 | −2.06593 | ||||||||
\(682\) | −0.869242 | −0.0332850 | ||||||||
\(683\) | −33.7349 | −1.29083 | −0.645414 | − | 0.763833i | \(-0.723315\pi\) | ||||
−0.645414 | + | 0.763833i | \(0.723315\pi\) | |||||||
\(684\) | 33.8499 | 1.29428 | ||||||||
\(685\) | 7.67423 | 0.293217 | ||||||||
\(686\) | 1.37779 | 0.0526041 | ||||||||
\(687\) | −51.7729 | −1.97526 | ||||||||
\(688\) | 44.1484 | 1.68314 | ||||||||
\(689\) | 23.1634 | 0.882456 | ||||||||
\(690\) | −0.742019 | −0.0282482 | ||||||||
\(691\) | −16.0490 | −0.610531 | −0.305266 | − | 0.952267i | \(-0.598745\pi\) | ||||
−0.305266 | + | 0.952267i | \(0.598745\pi\) | |||||||
\(692\) | 29.0478 | 1.10423 | ||||||||
\(693\) | −5.80436 | −0.220489 | ||||||||
\(694\) | 1.07033 | 0.0406290 | ||||||||
\(695\) | 0.743374 | 0.0281978 | ||||||||
\(696\) | −4.92645 | −0.186737 | ||||||||
\(697\) | 12.6701 | 0.479913 | ||||||||
\(698\) | 0.188028 | 0.00711696 | ||||||||
\(699\) | 48.4002 | 1.83066 | ||||||||
\(700\) | 4.05595 | 0.153300 | ||||||||
\(701\) | 1.59219 | 0.0601363 | 0.0300681 | − | 0.999548i | \(-0.490428\pi\) | ||||
0.0300681 | + | 0.999548i | \(0.490428\pi\) | |||||||
\(702\) | −0.561887 | −0.0212071 | ||||||||
\(703\) | 9.12765 | 0.344256 | ||||||||
\(704\) | −9.96826 | −0.375693 | ||||||||
\(705\) | 2.62921 | 0.0990216 | ||||||||
\(706\) | −1.89140 | −0.0711837 | ||||||||
\(707\) | −0.351930 | −0.0132357 | ||||||||
\(708\) | −55.4863 | −2.08530 | ||||||||
\(709\) | −38.6350 | −1.45097 | −0.725484 | − | 0.688239i | \(-0.758384\pi\) | ||||
−0.725484 | + | 0.688239i | \(0.758384\pi\) | |||||||
\(710\) | 0.520458 | 0.0195324 | ||||||||
\(711\) | 17.3175 | 0.649456 | ||||||||
\(712\) | 1.27903 | 0.0479336 | ||||||||
\(713\) | −47.1678 | −1.76645 | ||||||||
\(714\) | −0.764982 | −0.0286287 | ||||||||
\(715\) | −6.08606 | −0.227606 | ||||||||
\(716\) | 9.43373 | 0.352555 | ||||||||
\(717\) | 42.2696 | 1.57859 | ||||||||
\(718\) | 1.22582 | 0.0457471 | ||||||||
\(719\) | 31.5917 | 1.17817 | 0.589086 | − | 0.808070i | \(-0.299488\pi\) | ||||
0.589086 | + | 0.808070i | \(0.299488\pi\) | |||||||
\(720\) | 8.97298 | 0.334403 | ||||||||
\(721\) | −0.776689 | −0.0289254 | ||||||||
\(722\) | 2.56806 | 0.0955734 | ||||||||
\(723\) | −61.7661 | −2.29711 | ||||||||
\(724\) | 9.05210 | 0.336419 | ||||||||
\(725\) | −7.82808 | −0.290728 | ||||||||
\(726\) | 1.48108 | 0.0549681 | ||||||||
\(727\) | −18.6686 | −0.692380 | −0.346190 | − | 0.938164i | \(-0.612525\pi\) | ||||
−0.346190 | + | 0.938164i | \(0.612525\pi\) | |||||||
\(728\) | −2.68618 | −0.0995563 | ||||||||
\(729\) | −12.4262 | −0.460229 | ||||||||
\(730\) | 0.604086 | 0.0223582 | ||||||||
\(731\) | −26.5564 | −0.982222 | ||||||||
\(732\) | 53.6095 | 1.98146 | ||||||||
\(733\) | 50.2011 | 1.85422 | 0.927110 | − | 0.374790i | \(-0.122285\pi\) | ||||
0.927110 | + | 0.374790i | \(0.122285\pi\) | |||||||
\(734\) | 0.525826 | 0.0194086 | ||||||||
\(735\) | 6.57684 | 0.242590 | ||||||||
\(736\) | 3.87051 | 0.142669 | ||||||||
\(737\) | 8.04634 | 0.296391 | ||||||||
\(738\) | −0.822955 | −0.0302934 | ||||||||
\(739\) | 14.4025 | 0.529804 | 0.264902 | − | 0.964275i | \(-0.414660\pi\) | ||||
0.264902 | + | 0.964275i | \(0.414660\pi\) | |||||||
\(740\) | 2.42532 | 0.0891565 | ||||||||
\(741\) | −82.9245 | −3.04631 | ||||||||
\(742\) | 0.671635 | 0.0246565 | ||||||||
\(743\) | 28.7991 | 1.05654 | 0.528269 | − | 0.849077i | \(-0.322841\pi\) | ||||
0.528269 | + | 0.849077i | \(0.322841\pi\) | |||||||
\(744\) | −6.30145 | −0.231023 | ||||||||
\(745\) | 13.1477 | 0.481696 | ||||||||
\(746\) | −0.0385315 | −0.00141074 | ||||||||
\(747\) | −2.17780 | −0.0796815 | ||||||||
\(748\) | 6.02482 | 0.220289 | ||||||||
\(749\) | −30.3001 | −1.10714 | ||||||||
\(750\) | −0.157518 | −0.00575176 | ||||||||
\(751\) | −10.6209 | −0.387561 | −0.193780 | − | 0.981045i | \(-0.562075\pi\) | ||||
−0.193780 | + | 0.981045i | \(0.562075\pi\) | |||||||
\(752\) | −4.55347 | −0.166048 | ||||||||
\(753\) | −13.5801 | −0.494886 | ||||||||
\(754\) | 2.58913 | 0.0942907 | ||||||||
\(755\) | 3.78434 | 0.137726 | ||||||||
\(756\) | 6.89037 | 0.250600 | ||||||||
\(757\) | −14.6026 | −0.530740 | −0.265370 | − | 0.964147i | \(-0.585494\pi\) | ||||
−0.265370 | + | 0.964147i | \(0.585494\pi\) | |||||||
\(758\) | −0.780108 | −0.0283348 | ||||||||
\(759\) | −13.6538 | −0.495600 | ||||||||
\(760\) | 2.06069 | 0.0747491 | ||||||||
\(761\) | 3.50797 | 0.127164 | 0.0635819 | − | 0.997977i | \(-0.479748\pi\) | ||||
0.0635819 | + | 0.997977i | \(0.479748\pi\) | |||||||
\(762\) | −1.29094 | −0.0467657 | ||||||||
\(763\) | −23.8271 | −0.862599 | ||||||||
\(764\) | −41.6379 | −1.50641 | ||||||||
\(765\) | −5.39747 | −0.195146 | ||||||||
\(766\) | −0.798975 | −0.0288681 | ||||||||
\(767\) | 58.3914 | 2.10839 | ||||||||
\(768\) | −35.8303 | −1.29291 | ||||||||
\(769\) | −42.2575 | −1.52384 | −0.761922 | − | 0.647669i | \(-0.775744\pi\) | ||||
−0.761922 | + | 0.647669i | \(0.775744\pi\) | |||||||
\(770\) | −0.176468 | −0.00635948 | ||||||||
\(771\) | 6.39995 | 0.230489 | ||||||||
\(772\) | 33.2860 | 1.19799 | ||||||||
\(773\) | −35.0490 | −1.26062 | −0.630312 | − | 0.776342i | \(-0.717073\pi\) | ||||
−0.630312 | + | 0.776342i | \(0.717073\pi\) | |||||||
\(774\) | 1.72491 | 0.0620006 | ||||||||
\(775\) | −10.0129 | −0.359676 | ||||||||
\(776\) | 0.902035 | 0.0323812 | ||||||||
\(777\) | −5.66648 | −0.203284 | ||||||||
\(778\) | 0.179132 | 0.00642218 | ||||||||
\(779\) | 39.8237 | 1.42683 | ||||||||
\(780\) | −22.0340 | −0.788943 | ||||||||
\(781\) | 9.57685 | 0.342687 | ||||||||
\(782\) | −0.773012 | −0.0276428 | ||||||||
\(783\) | −13.2986 | −0.475253 | ||||||||
\(784\) | −11.3903 | −0.406796 | ||||||||
\(785\) | −17.9124 | −0.639323 | ||||||||
\(786\) | −1.55406 | −0.0554315 | ||||||||
\(787\) | −3.51929 | −0.125449 | −0.0627246 | − | 0.998031i | \(-0.519979\pi\) | ||||
−0.0627246 | + | 0.998031i | \(0.519979\pi\) | |||||||
\(788\) | 37.8197 | 1.34727 | ||||||||
\(789\) | 5.33222 | 0.189832 | ||||||||
\(790\) | 0.526498 | 0.0187320 | ||||||||
\(791\) | −37.9041 | −1.34772 | ||||||||
\(792\) | −0.783583 | −0.0278434 | ||||||||
\(793\) | −56.4163 | −2.00340 | ||||||||
\(794\) | 0.595234 | 0.0211241 | ||||||||
\(795\) | 11.0315 | 0.391248 | ||||||||
\(796\) | 20.8046 | 0.737398 | ||||||||
\(797\) | −38.8055 | −1.37456 | −0.687281 | − | 0.726392i | \(-0.741196\pi\) | ||||
−0.687281 | + | 0.726392i | \(0.741196\pi\) | |||||||
\(798\) | −2.40444 | −0.0851162 | ||||||||
\(799\) | 2.73902 | 0.0968996 | ||||||||
\(800\) | 0.821646 | 0.0290496 | ||||||||
\(801\) | −10.5298 | −0.372052 | ||||||||
\(802\) | −0.0686864 | −0.00242540 | ||||||||
\(803\) | 11.1157 | 0.392264 | ||||||||
\(804\) | 29.1310 | 1.02737 | ||||||||
\(805\) | −9.57572 | −0.337500 | ||||||||
\(806\) | 3.31177 | 0.116652 | ||||||||
\(807\) | 18.3145 | 0.644702 | ||||||||
\(808\) | −0.0475102 | −0.00167140 | ||||||||
\(809\) | −4.66124 | −0.163881 | −0.0819403 | − | 0.996637i | \(-0.526112\pi\) | ||||
−0.0819403 | + | 0.996637i | \(0.526112\pi\) | |||||||
\(810\) | −0.733130 | −0.0257596 | ||||||||
\(811\) | 12.2621 | 0.430579 | 0.215289 | − | 0.976550i | \(-0.430930\pi\) | ||||
0.215289 | + | 0.976550i | \(0.430930\pi\) | |||||||
\(812\) | −31.7503 | −1.11422 | ||||||||
\(813\) | −14.4197 | −0.505721 | ||||||||
\(814\) | −0.105522 | −0.00369855 | ||||||||
\(815\) | 19.8035 | 0.693686 | ||||||||
\(816\) | 21.7606 | 0.761773 | ||||||||
\(817\) | −83.4701 | −2.92025 | ||||||||
\(818\) | 1.17788 | 0.0411835 | ||||||||
\(819\) | 22.1144 | 0.772738 | ||||||||
\(820\) | 10.5816 | 0.369525 | ||||||||
\(821\) | 23.8589 | 0.832683 | 0.416341 | − | 0.909208i | \(-0.363312\pi\) | ||||
0.416341 | + | 0.909208i | \(0.363312\pi\) | |||||||
\(822\) | −1.20883 | −0.0421629 | ||||||||
\(823\) | −18.5900 | −0.648008 | −0.324004 | − | 0.946056i | \(-0.605029\pi\) | ||||
−0.324004 | + | 0.946056i | \(0.605029\pi\) | |||||||
\(824\) | −0.104852 | −0.00365270 | ||||||||
\(825\) | −2.89847 | −0.100912 | ||||||||
\(826\) | 1.69309 | 0.0589101 | ||||||||
\(827\) | 7.47569 | 0.259955 | 0.129978 | − | 0.991517i | \(-0.458509\pi\) | ||||
0.129978 | + | 0.991517i | \(0.458509\pi\) | |||||||
\(828\) | −21.2347 | −0.737957 | ||||||||
\(829\) | 43.4384 | 1.50868 | 0.754338 | − | 0.656486i | \(-0.227958\pi\) | ||||
0.754338 | + | 0.656486i | \(0.227958\pi\) | |||||||
\(830\) | −0.0662110 | −0.00229822 | ||||||||
\(831\) | −60.0334 | −2.08254 | ||||||||
\(832\) | 37.9787 | 1.31667 | ||||||||
\(833\) | 6.85154 | 0.237392 | ||||||||
\(834\) | −0.117095 | −0.00405468 | ||||||||
\(835\) | −9.99112 | −0.345757 | ||||||||
\(836\) | 18.9368 | 0.654943 | ||||||||
\(837\) | −17.0103 | −0.587962 | ||||||||
\(838\) | −0.198510 | −0.00685742 | ||||||||
\(839\) | 1.10795 | 0.0382506 | 0.0191253 | − | 0.999817i | \(-0.493912\pi\) | ||||
0.0191253 | + | 0.999817i | \(0.493912\pi\) | |||||||
\(840\) | −1.27928 | −0.0441395 | ||||||||
\(841\) | 32.2789 | 1.11307 | ||||||||
\(842\) | −1.80020 | −0.0620392 | ||||||||
\(843\) | 64.4734 | 2.22058 | ||||||||
\(844\) | 5.31852 | 0.183071 | ||||||||
\(845\) | 10.1876 | 0.350465 | ||||||||
\(846\) | −0.177907 | −0.00611657 | ||||||||
\(847\) | 19.1133 | 0.656741 | ||||||||
\(848\) | −19.1052 | −0.656077 | ||||||||
\(849\) | −27.0568 | −0.928587 | ||||||||
\(850\) | −0.164098 | −0.00562851 | ||||||||
\(851\) | −5.72596 | −0.196283 | ||||||||
\(852\) | 34.6721 | 1.18785 | ||||||||
\(853\) | 35.2400 | 1.20659 | 0.603297 | − | 0.797516i | \(-0.293853\pi\) | ||||
0.603297 | + | 0.797516i | \(0.293853\pi\) | |||||||
\(854\) | −1.63582 | −0.0559766 | ||||||||
\(855\) | −16.9649 | −0.580189 | ||||||||
\(856\) | −4.09048 | −0.139810 | ||||||||
\(857\) | 19.6165 | 0.670088 | 0.335044 | − | 0.942202i | \(-0.391249\pi\) | ||||
0.335044 | + | 0.942202i | \(0.391249\pi\) | |||||||
\(858\) | 0.958667 | 0.0327283 | ||||||||
\(859\) | 18.2577 | 0.622946 | 0.311473 | − | 0.950255i | \(-0.399178\pi\) | ||||
0.311473 | + | 0.950255i | \(0.399178\pi\) | |||||||
\(860\) | −22.1790 | −0.756296 | ||||||||
\(861\) | −24.7227 | −0.842547 | ||||||||
\(862\) | −1.53724 | −0.0523586 | ||||||||
\(863\) | −22.6540 | −0.771150 | −0.385575 | − | 0.922676i | \(-0.625997\pi\) | ||||
−0.385575 | + | 0.922676i | \(0.625997\pi\) | |||||||
\(864\) | 1.39584 | 0.0474874 | ||||||||
\(865\) | −14.5582 | −0.494995 | ||||||||
\(866\) | 1.45669 | 0.0495003 | ||||||||
\(867\) | 25.8966 | 0.879493 | ||||||||
\(868\) | −40.6120 | −1.37846 | ||||||||
\(869\) | 9.68800 | 0.328643 | ||||||||
\(870\) | 1.23307 | 0.0418049 | ||||||||
\(871\) | −30.6562 | −1.03875 | ||||||||
\(872\) | −3.21663 | −0.108929 | ||||||||
\(873\) | −7.42615 | −0.251337 | ||||||||
\(874\) | −2.42968 | −0.0821850 | ||||||||
\(875\) | −2.03277 | −0.0687201 | ||||||||
\(876\) | 40.2432 | 1.35969 | ||||||||
\(877\) | −38.3278 | −1.29424 | −0.647118 | − | 0.762390i | \(-0.724026\pi\) | ||||
−0.647118 | + | 0.762390i | \(0.724026\pi\) | |||||||
\(878\) | −1.83135 | −0.0618050 | ||||||||
\(879\) | 23.0883 | 0.778749 | ||||||||
\(880\) | 5.01980 | 0.169217 | ||||||||
\(881\) | 0.681458 | 0.0229589 | 0.0114795 | − | 0.999934i | \(-0.496346\pi\) | ||||
0.0114795 | + | 0.999934i | \(0.496346\pi\) | |||||||
\(882\) | −0.445027 | −0.0149848 | ||||||||
\(883\) | 51.2132 | 1.72346 | 0.861730 | − | 0.507367i | \(-0.169381\pi\) | ||||
0.861730 | + | 0.507367i | \(0.169381\pi\) | |||||||
\(884\) | −22.9543 | −0.772037 | ||||||||
\(885\) | 27.8087 | 0.934781 | ||||||||
\(886\) | −1.64937 | −0.0554116 | ||||||||
\(887\) | −54.8540 | −1.84182 | −0.920908 | − | 0.389780i | \(-0.872551\pi\) | ||||
−0.920908 | + | 0.389780i | \(0.872551\pi\) | |||||||
\(888\) | −0.764969 | −0.0256707 | ||||||||
\(889\) | −16.6595 | −0.558741 | ||||||||
\(890\) | −0.320134 | −0.0107309 | ||||||||
\(891\) | −13.4902 | −0.451939 | ||||||||
\(892\) | 4.49650 | 0.150554 | ||||||||
\(893\) | 8.60911 | 0.288093 | ||||||||
\(894\) | −2.07101 | −0.0692650 | ||||||||
\(895\) | −4.72802 | −0.158040 | ||||||||
\(896\) | 4.44164 | 0.148385 | ||||||||
\(897\) | 52.0202 | 1.73690 | ||||||||
\(898\) | 1.47106 | 0.0490899 | ||||||||
\(899\) | 78.3822 | 2.61419 | ||||||||
\(900\) | −4.50778 | −0.150259 | ||||||||
\(901\) | 11.4923 | 0.382863 | ||||||||
\(902\) | −0.460390 | −0.0153293 | ||||||||
\(903\) | 51.8186 | 1.72441 | ||||||||
\(904\) | −5.11702 | −0.170189 | ||||||||
\(905\) | −4.53675 | −0.150807 | ||||||||
\(906\) | −0.596103 | −0.0198042 | ||||||||
\(907\) | −54.0409 | −1.79440 | −0.897200 | − | 0.441625i | \(-0.854402\pi\) | ||||
−0.897200 | + | 0.441625i | \(0.854402\pi\) | |||||||
\(908\) | −46.9064 | −1.55665 | ||||||||
\(909\) | 0.391135 | 0.0129731 | ||||||||
\(910\) | 0.672337 | 0.0222877 | ||||||||
\(911\) | 27.6933 | 0.917518 | 0.458759 | − | 0.888561i | \(-0.348294\pi\) | ||||
0.458759 | + | 0.888561i | \(0.348294\pi\) | |||||||
\(912\) | 68.3963 | 2.26483 | ||||||||
\(913\) | −1.21834 | −0.0403211 | ||||||||
\(914\) | 0.711467 | 0.0235332 | ||||||||
\(915\) | −26.8681 | −0.888233 | ||||||||
\(916\) | −45.0450 | −1.48833 | ||||||||
\(917\) | −20.0551 | −0.662276 | ||||||||
\(918\) | −0.278774 | −0.00920093 | ||||||||
\(919\) | −6.18778 | −0.204116 | −0.102058 | − | 0.994778i | \(-0.532543\pi\) | ||||
−0.102058 | + | 0.994778i | \(0.532543\pi\) | |||||||
\(920\) | −1.29271 | −0.0426195 | ||||||||
\(921\) | 29.5551 | 0.973874 | ||||||||
\(922\) | 1.32490 | 0.0436333 | ||||||||
\(923\) | −36.4874 | −1.20100 | ||||||||
\(924\) | −11.7560 | −0.386745 | ||||||||
\(925\) | −1.21553 | −0.0399663 | ||||||||
\(926\) | −1.26999 | −0.0417345 | ||||||||
\(927\) | 0.863212 | 0.0283516 | ||||||||
\(928\) | −6.43192 | −0.211138 | ||||||||
\(929\) | 7.32688 | 0.240387 | 0.120194 | − | 0.992750i | \(-0.461648\pi\) | ||||
0.120194 | + | 0.992750i | \(0.461648\pi\) | |||||||
\(930\) | 1.57722 | 0.0517192 | ||||||||
\(931\) | 21.5353 | 0.705791 | ||||||||
\(932\) | 42.1105 | 1.37938 | ||||||||
\(933\) | 29.7467 | 0.973862 | ||||||||
\(934\) | 2.35422 | 0.0770324 | ||||||||
\(935\) | −3.01953 | −0.0987493 | ||||||||
\(936\) | 2.98542 | 0.0975814 | ||||||||
\(937\) | −35.2493 | −1.15155 | −0.575773 | − | 0.817610i | \(-0.695299\pi\) | ||||
−0.575773 | + | 0.817610i | \(0.695299\pi\) | |||||||
\(938\) | −0.888893 | −0.0290234 | ||||||||
\(939\) | 19.4754 | 0.635556 | ||||||||
\(940\) | 2.28754 | 0.0746113 | ||||||||
\(941\) | −41.0123 | −1.33696 | −0.668481 | − | 0.743729i | \(-0.733055\pi\) | ||||
−0.668481 | + | 0.743729i | \(0.733055\pi\) | |||||||
\(942\) | 2.82154 | 0.0919308 | ||||||||
\(943\) | −24.9822 | −0.813532 | ||||||||
\(944\) | −48.1614 | −1.56752 | ||||||||
\(945\) | −3.45333 | −0.112337 | ||||||||
\(946\) | 0.964974 | 0.0313740 | ||||||||
\(947\) | 45.2788 | 1.47136 | 0.735681 | − | 0.677328i | \(-0.236862\pi\) | ||||
0.735681 | + | 0.677328i | \(0.236862\pi\) | |||||||
\(948\) | 35.0745 | 1.13917 | ||||||||
\(949\) | −42.3503 | −1.37475 | ||||||||
\(950\) | −0.515781 | −0.0167341 | ||||||||
\(951\) | −25.6902 | −0.833061 | ||||||||
\(952\) | −1.33272 | −0.0431936 | ||||||||
\(953\) | −9.34121 | −0.302591 | −0.151296 | − | 0.988489i | \(-0.548345\pi\) | ||||
−0.151296 | + | 0.988489i | \(0.548345\pi\) | |||||||
\(954\) | −0.746455 | −0.0241674 | ||||||||
\(955\) | 20.8682 | 0.675278 | ||||||||
\(956\) | 36.7766 | 1.18944 | ||||||||
\(957\) | 22.6895 | 0.733446 | ||||||||
\(958\) | 1.96571 | 0.0635091 | ||||||||
\(959\) | −15.5999 | −0.503748 | ||||||||
\(960\) | 18.0872 | 0.583763 | ||||||||
\(961\) | 69.2590 | 2.23416 | ||||||||
\(962\) | 0.402035 | 0.0129621 | ||||||||
\(963\) | 33.6756 | 1.08518 | ||||||||
\(964\) | −53.7395 | −1.73083 | ||||||||
\(965\) | −16.6824 | −0.537024 | ||||||||
\(966\) | 1.50835 | 0.0485305 | ||||||||
\(967\) | −5.58522 | −0.179609 | −0.0898043 | − | 0.995959i | \(-0.528624\pi\) | ||||
−0.0898043 | + | 0.995959i | \(0.528624\pi\) | |||||||
\(968\) | 2.58027 | 0.0829332 | ||||||||
\(969\) | −41.1421 | −1.32167 | ||||||||
\(970\) | −0.225775 | −0.00724920 | ||||||||
\(971\) | 6.65089 | 0.213437 | 0.106719 | − | 0.994289i | \(-0.465966\pi\) | ||||
0.106719 | + | 0.994289i | \(0.465966\pi\) | |||||||
\(972\) | −38.6710 | −1.24037 | ||||||||
\(973\) | −1.51111 | −0.0484439 | ||||||||
\(974\) | 2.63427 | 0.0844073 | ||||||||
\(975\) | 11.0430 | 0.353660 | ||||||||
\(976\) | 46.5323 | 1.48946 | ||||||||
\(977\) | 51.0852 | 1.63436 | 0.817180 | − | 0.576383i | \(-0.195536\pi\) | ||||
0.817180 | + | 0.576383i | \(0.195536\pi\) | |||||||
\(978\) | −3.11942 | −0.0997480 | ||||||||
\(979\) | −5.89073 | −0.188269 | ||||||||
\(980\) | 5.72217 | 0.182788 | ||||||||
\(981\) | 26.4814 | 0.845487 | ||||||||
\(982\) | 1.01306 | 0.0323280 | ||||||||
\(983\) | 13.6611 | 0.435722 | 0.217861 | − | 0.975980i | \(-0.430092\pi\) | ||||
0.217861 | + | 0.975980i | \(0.430092\pi\) | |||||||
\(984\) | −3.33754 | −0.106397 | ||||||||
\(985\) | −18.9546 | −0.603943 | ||||||||
\(986\) | 1.28457 | 0.0409091 | ||||||||
\(987\) | −5.34457 | −0.170119 | ||||||||
\(988\) | −72.1484 | −2.29535 | ||||||||
\(989\) | 52.3625 | 1.66503 | ||||||||
\(990\) | 0.196127 | 0.00623332 | ||||||||
\(991\) | −30.3668 | −0.964632 | −0.482316 | − | 0.875997i | \(-0.660204\pi\) | ||||
−0.482316 | + | 0.875997i | \(0.660204\pi\) | |||||||
\(992\) | −8.22710 | −0.261211 | ||||||||
\(993\) | 30.5265 | 0.968728 | ||||||||
\(994\) | −1.05797 | −0.0335568 | ||||||||
\(995\) | −10.4269 | −0.330554 | ||||||||
\(996\) | −4.41087 | −0.139764 | ||||||||
\(997\) | −41.6293 | −1.31841 | −0.659207 | − | 0.751962i | \(-0.729108\pi\) | ||||
−0.659207 | + | 0.751962i | \(0.729108\pi\) | |||||||
\(998\) | 1.35861 | 0.0430060 | ||||||||
\(999\) | −2.06498 | −0.0653329 |
(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 | 2005.2.a.g.1.16 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2005.2.a.g.1.16 | ✓ | 37 | 1.1 | even | 1 | trivial |