Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 17x^{8} + 23x^{7} + 69x^{6} - 88x^{5} - 106x^{4} + 101x^{3} + 60x^{2} - 23x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.435319\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09108 | −1.47862 | −0.739309 | − | 0.673366i | \(-0.764848\pi\) | ||||
−0.739309 | + | 0.673366i | \(0.764848\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.37262 | 1.18631 | ||||||||
\(5\) | 4.27000 | 1.90960 | 0.954801 | − | 0.297247i | \(-0.0960684\pi\) | ||||
0.954801 | + | 0.297247i | \(0.0960684\pi\) | |||||||
\(6\) | 2.09108 | 0.853680 | ||||||||
\(7\) | 3.25035 | 1.22852 | 0.614259 | − | 0.789104i | \(-0.289455\pi\) | ||||
0.614259 | + | 0.789104i | \(0.289455\pi\) | |||||||
\(8\) | −0.779182 | −0.275482 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −8.92891 | −2.82357 | ||||||||
\(11\) | −3.52823 | −1.06380 | −0.531901 | − | 0.846806i | \(-0.678522\pi\) | ||||
−0.531901 | + | 0.846806i | \(0.678522\pi\) | |||||||
\(12\) | −2.37262 | −0.684917 | ||||||||
\(13\) | −5.02055 | −1.39245 | −0.696225 | − | 0.717824i | \(-0.745138\pi\) | ||||
−0.696225 | + | 0.717824i | \(0.745138\pi\) | |||||||
\(14\) | −6.79676 | −1.81651 | ||||||||
\(15\) | −4.27000 | −1.10251 | ||||||||
\(16\) | −3.11591 | −0.778978 | ||||||||
\(17\) | 0.0201193 | 0.00487966 | 0.00243983 | − | 0.999997i | \(-0.499223\pi\) | ||||
0.00243983 | + | 0.999997i | \(0.499223\pi\) | |||||||
\(18\) | −2.09108 | −0.492873 | ||||||||
\(19\) | −0.844205 | −0.193674 | −0.0968369 | − | 0.995300i | \(-0.530873\pi\) | ||||
−0.0968369 | + | 0.995300i | \(0.530873\pi\) | |||||||
\(20\) | 10.1311 | 2.26538 | ||||||||
\(21\) | −3.25035 | −0.709285 | ||||||||
\(22\) | 7.37782 | 1.57296 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0.779182 | 0.159050 | ||||||||
\(25\) | 13.2329 | 2.64658 | ||||||||
\(26\) | 10.4984 | 2.05890 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 7.71186 | 1.45740 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 8.92891 | 1.63019 | ||||||||
\(31\) | 9.32330 | 1.67451 | 0.837257 | − | 0.546809i | \(-0.184158\pi\) | ||||
0.837257 | + | 0.546809i | \(0.184158\pi\) | |||||||
\(32\) | 8.07399 | 1.42729 | ||||||||
\(33\) | 3.52823 | 0.614187 | ||||||||
\(34\) | −0.0420712 | −0.00721515 | ||||||||
\(35\) | 13.8790 | 2.34598 | ||||||||
\(36\) | 2.37262 | 0.395437 | ||||||||
\(37\) | −8.07528 | −1.32757 | −0.663784 | − | 0.747925i | \(-0.731050\pi\) | ||||
−0.663784 | + | 0.747925i | \(0.731050\pi\) | |||||||
\(38\) | 1.76530 | 0.286370 | ||||||||
\(39\) | 5.02055 | 0.803931 | ||||||||
\(40\) | −3.32711 | −0.526062 | ||||||||
\(41\) | 2.76429 | 0.431710 | 0.215855 | − | 0.976425i | \(-0.430746\pi\) | ||||
0.215855 | + | 0.976425i | \(0.430746\pi\) | |||||||
\(42\) | 6.79676 | 1.04876 | ||||||||
\(43\) | −0.721845 | −0.110080 | −0.0550402 | − | 0.998484i | \(-0.517529\pi\) | ||||
−0.0550402 | + | 0.998484i | \(0.517529\pi\) | |||||||
\(44\) | −8.37116 | −1.26200 | ||||||||
\(45\) | 4.27000 | 0.636534 | ||||||||
\(46\) | 2.09108 | 0.308313 | ||||||||
\(47\) | 5.90133 | 0.860798 | 0.430399 | − | 0.902639i | \(-0.358373\pi\) | ||||
0.430399 | + | 0.902639i | \(0.358373\pi\) | |||||||
\(48\) | 3.11591 | 0.449743 | ||||||||
\(49\) | 3.56480 | 0.509257 | ||||||||
\(50\) | −27.6710 | −3.91328 | ||||||||
\(51\) | −0.0201193 | −0.00281727 | ||||||||
\(52\) | −11.9119 | −1.65188 | ||||||||
\(53\) | 11.8408 | 1.62646 | 0.813232 | − | 0.581940i | \(-0.197706\pi\) | ||||
0.813232 | + | 0.581940i | \(0.197706\pi\) | |||||||
\(54\) | 2.09108 | 0.284560 | ||||||||
\(55\) | −15.0656 | −2.03144 | ||||||||
\(56\) | −2.53262 | −0.338435 | ||||||||
\(57\) | 0.844205 | 0.111818 | ||||||||
\(58\) | −2.09108 | −0.274572 | ||||||||
\(59\) | 2.90270 | 0.377899 | 0.188949 | − | 0.981987i | \(-0.439492\pi\) | ||||
0.188949 | + | 0.981987i | \(0.439492\pi\) | |||||||
\(60\) | −10.1311 | −1.30792 | ||||||||
\(61\) | −13.8176 | −1.76916 | −0.884581 | − | 0.466386i | \(-0.845556\pi\) | ||||
−0.884581 | + | 0.466386i | \(0.845556\pi\) | |||||||
\(62\) | −19.4958 | −2.47597 | ||||||||
\(63\) | 3.25035 | 0.409506 | ||||||||
\(64\) | −10.6515 | −1.33144 | ||||||||
\(65\) | −21.4377 | −2.65902 | ||||||||
\(66\) | −7.37782 | −0.908147 | ||||||||
\(67\) | 11.5596 | 1.41223 | 0.706117 | − | 0.708095i | \(-0.250445\pi\) | ||||
0.706117 | + | 0.708095i | \(0.250445\pi\) | |||||||
\(68\) | 0.0477356 | 0.00578879 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −29.0221 | −3.46881 | ||||||||
\(71\) | 11.2291 | 1.33265 | 0.666324 | − | 0.745662i | \(-0.267867\pi\) | ||||
0.666324 | + | 0.745662i | \(0.267867\pi\) | |||||||
\(72\) | −0.779182 | −0.0918275 | ||||||||
\(73\) | 1.28040 | 0.149860 | 0.0749300 | − | 0.997189i | \(-0.476127\pi\) | ||||
0.0749300 | + | 0.997189i | \(0.476127\pi\) | |||||||
\(74\) | 16.8861 | 1.96297 | ||||||||
\(75\) | −13.2329 | −1.52800 | ||||||||
\(76\) | −2.00298 | −0.229757 | ||||||||
\(77\) | −11.4680 | −1.30690 | ||||||||
\(78\) | −10.4984 | −1.18871 | ||||||||
\(79\) | 7.24288 | 0.814887 | 0.407444 | − | 0.913230i | \(-0.366420\pi\) | ||||
0.407444 | + | 0.913230i | \(0.366420\pi\) | |||||||
\(80\) | −13.3049 | −1.48754 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.78036 | −0.638334 | ||||||||
\(83\) | 6.40814 | 0.703385 | 0.351692 | − | 0.936116i | \(-0.385606\pi\) | ||||
0.351692 | + | 0.936116i | \(0.385606\pi\) | |||||||
\(84\) | −7.71186 | −0.841433 | ||||||||
\(85\) | 0.0859096 | 0.00931820 | ||||||||
\(86\) | 1.50944 | 0.162767 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 2.74914 | 0.293059 | ||||||||
\(89\) | 18.1777 | 1.92683 | 0.963414 | − | 0.268018i | \(-0.0863686\pi\) | ||||
0.963414 | + | 0.268018i | \(0.0863686\pi\) | |||||||
\(90\) | −8.92891 | −0.941190 | ||||||||
\(91\) | −16.3186 | −1.71065 | ||||||||
\(92\) | −2.37262 | −0.247363 | ||||||||
\(93\) | −9.32330 | −0.966781 | ||||||||
\(94\) | −12.3402 | −1.27279 | ||||||||
\(95\) | −3.60475 | −0.369840 | ||||||||
\(96\) | −8.07399 | −0.824048 | ||||||||
\(97\) | −5.01067 | −0.508757 | −0.254378 | − | 0.967105i | \(-0.581871\pi\) | ||||
−0.254378 | + | 0.967105i | \(0.581871\pi\) | |||||||
\(98\) | −7.45429 | −0.752997 | ||||||||
\(99\) | −3.52823 | −0.354601 | ||||||||
\(100\) | 31.3966 | 3.13966 | ||||||||
\(101\) | 2.10491 | 0.209447 | 0.104723 | − | 0.994501i | \(-0.466604\pi\) | ||||
0.104723 | + | 0.994501i | \(0.466604\pi\) | |||||||
\(102\) | 0.0420712 | 0.00416567 | ||||||||
\(103\) | 15.6569 | 1.54272 | 0.771360 | − | 0.636400i | \(-0.219577\pi\) | ||||
0.771360 | + | 0.636400i | \(0.219577\pi\) | |||||||
\(104\) | 3.91192 | 0.383595 | ||||||||
\(105\) | −13.8790 | −1.35445 | ||||||||
\(106\) | −24.7602 | −2.40492 | ||||||||
\(107\) | 5.88378 | 0.568806 | 0.284403 | − | 0.958705i | \(-0.408205\pi\) | ||||
0.284403 | + | 0.958705i | \(0.408205\pi\) | |||||||
\(108\) | −2.37262 | −0.228306 | ||||||||
\(109\) | 1.60764 | 0.153984 | 0.0769921 | − | 0.997032i | \(-0.475468\pi\) | ||||
0.0769921 | + | 0.997032i | \(0.475468\pi\) | |||||||
\(110\) | 31.5033 | 3.00372 | ||||||||
\(111\) | 8.07528 | 0.766472 | ||||||||
\(112\) | −10.1278 | −0.956988 | ||||||||
\(113\) | 1.85337 | 0.174351 | 0.0871753 | − | 0.996193i | \(-0.472216\pi\) | ||||
0.0871753 | + | 0.996193i | \(0.472216\pi\) | |||||||
\(114\) | −1.76530 | −0.165336 | ||||||||
\(115\) | −4.27000 | −0.398179 | ||||||||
\(116\) | 2.37262 | 0.220292 | ||||||||
\(117\) | −5.02055 | −0.464150 | ||||||||
\(118\) | −6.06977 | −0.558768 | ||||||||
\(119\) | 0.0653950 | 0.00599475 | ||||||||
\(120\) | 3.32711 | 0.303722 | ||||||||
\(121\) | 1.44844 | 0.131676 | ||||||||
\(122\) | 28.8937 | 2.61592 | ||||||||
\(123\) | −2.76429 | −0.249248 | ||||||||
\(124\) | 22.1207 | 1.98649 | ||||||||
\(125\) | 35.1544 | 3.14431 | ||||||||
\(126\) | −6.79676 | −0.605503 | ||||||||
\(127\) | 12.0665 | 1.07073 | 0.535364 | − | 0.844621i | \(-0.320174\pi\) | ||||
0.535364 | + | 0.844621i | \(0.320174\pi\) | |||||||
\(128\) | 6.12527 | 0.541402 | ||||||||
\(129\) | 0.721845 | 0.0635549 | ||||||||
\(130\) | 44.8280 | 3.93168 | ||||||||
\(131\) | 3.85596 | 0.336897 | 0.168448 | − | 0.985710i | \(-0.446124\pi\) | ||||
0.168448 | + | 0.985710i | \(0.446124\pi\) | |||||||
\(132\) | 8.37116 | 0.728616 | ||||||||
\(133\) | −2.74396 | −0.237932 | ||||||||
\(134\) | −24.1722 | −2.08816 | ||||||||
\(135\) | −4.27000 | −0.367503 | ||||||||
\(136\) | −0.0156766 | −0.00134426 | ||||||||
\(137\) | −15.6037 | −1.33311 | −0.666557 | − | 0.745454i | \(-0.732233\pi\) | ||||
−0.666557 | + | 0.745454i | \(0.732233\pi\) | |||||||
\(138\) | −2.09108 | −0.178005 | ||||||||
\(139\) | −6.24868 | −0.530006 | −0.265003 | − | 0.964248i | \(-0.585373\pi\) | ||||
−0.265003 | + | 0.964248i | \(0.585373\pi\) | |||||||
\(140\) | 32.9296 | 2.78306 | ||||||||
\(141\) | −5.90133 | −0.496982 | ||||||||
\(142\) | −23.4809 | −1.97048 | ||||||||
\(143\) | 17.7137 | 1.48129 | ||||||||
\(144\) | −3.11591 | −0.259659 | ||||||||
\(145\) | 4.27000 | 0.354604 | ||||||||
\(146\) | −2.67743 | −0.221586 | ||||||||
\(147\) | −3.56480 | −0.294020 | ||||||||
\(148\) | −19.1596 | −1.57491 | ||||||||
\(149\) | 14.5432 | 1.19142 | 0.595712 | − | 0.803198i | \(-0.296870\pi\) | ||||
0.595712 | + | 0.803198i | \(0.296870\pi\) | |||||||
\(150\) | 27.6710 | 2.25933 | ||||||||
\(151\) | −10.6692 | −0.868246 | −0.434123 | − | 0.900854i | \(-0.642942\pi\) | ||||
−0.434123 | + | 0.900854i | \(0.642942\pi\) | |||||||
\(152\) | 0.657789 | 0.0533538 | ||||||||
\(153\) | 0.0201193 | 0.00162655 | ||||||||
\(154\) | 23.9805 | 1.93241 | ||||||||
\(155\) | 39.8105 | 3.19765 | ||||||||
\(156\) | 11.9119 | 0.953712 | ||||||||
\(157\) | −15.7549 | −1.25738 | −0.628690 | − | 0.777656i | \(-0.716409\pi\) | ||||
−0.628690 | + | 0.777656i | \(0.716409\pi\) | |||||||
\(158\) | −15.1454 | −1.20491 | ||||||||
\(159\) | −11.8408 | −0.939039 | ||||||||
\(160\) | 34.4759 | 2.72556 | ||||||||
\(161\) | −3.25035 | −0.256164 | ||||||||
\(162\) | −2.09108 | −0.164291 | ||||||||
\(163\) | −12.9934 | −1.01772 | −0.508859 | − | 0.860850i | \(-0.669933\pi\) | ||||
−0.508859 | + | 0.860850i | \(0.669933\pi\) | |||||||
\(164\) | 6.55862 | 0.512142 | ||||||||
\(165\) | 15.0656 | 1.17285 | ||||||||
\(166\) | −13.3999 | −1.04004 | ||||||||
\(167\) | 6.37516 | 0.493325 | 0.246662 | − | 0.969101i | \(-0.420666\pi\) | ||||
0.246662 | + | 0.969101i | \(0.420666\pi\) | |||||||
\(168\) | 2.53262 | 0.195396 | ||||||||
\(169\) | 12.2059 | 0.938915 | ||||||||
\(170\) | −0.179644 | −0.0137781 | ||||||||
\(171\) | −0.844205 | −0.0645580 | ||||||||
\(172\) | −1.71267 | −0.130590 | ||||||||
\(173\) | −3.84645 | −0.292440 | −0.146220 | − | 0.989252i | \(-0.546711\pi\) | ||||
−0.146220 | + | 0.989252i | \(0.546711\pi\) | |||||||
\(174\) | 2.09108 | 0.158524 | ||||||||
\(175\) | 43.0116 | 3.25137 | ||||||||
\(176\) | 10.9937 | 0.828678 | ||||||||
\(177\) | −2.90270 | −0.218180 | ||||||||
\(178\) | −38.0110 | −2.84904 | ||||||||
\(179\) | 6.55212 | 0.489728 | 0.244864 | − | 0.969557i | \(-0.421257\pi\) | ||||
0.244864 | + | 0.969557i | \(0.421257\pi\) | |||||||
\(180\) | 10.1311 | 0.755127 | ||||||||
\(181\) | −18.2300 | −1.35502 | −0.677512 | − | 0.735511i | \(-0.736942\pi\) | ||||
−0.677512 | + | 0.735511i | \(0.736942\pi\) | |||||||
\(182\) | 34.1234 | 2.52940 | ||||||||
\(183\) | 13.8176 | 1.02143 | ||||||||
\(184\) | 0.779182 | 0.0574421 | ||||||||
\(185\) | −34.4814 | −2.53512 | ||||||||
\(186\) | 19.4958 | 1.42950 | ||||||||
\(187\) | −0.0709858 | −0.00519099 | ||||||||
\(188\) | 14.0016 | 1.02117 | ||||||||
\(189\) | −3.25035 | −0.236428 | ||||||||
\(190\) | 7.53783 | 0.546852 | ||||||||
\(191\) | 9.76931 | 0.706882 | 0.353441 | − | 0.935457i | \(-0.385011\pi\) | ||||
0.353441 | + | 0.935457i | \(0.385011\pi\) | |||||||
\(192\) | 10.6515 | 0.768709 | ||||||||
\(193\) | −1.59407 | −0.114743 | −0.0573717 | − | 0.998353i | \(-0.518272\pi\) | ||||
−0.0573717 | + | 0.998353i | \(0.518272\pi\) | |||||||
\(194\) | 10.4777 | 0.752257 | ||||||||
\(195\) | 21.4377 | 1.53519 | ||||||||
\(196\) | 8.45793 | 0.604138 | ||||||||
\(197\) | −17.4479 | −1.24311 | −0.621555 | − | 0.783370i | \(-0.713499\pi\) | ||||
−0.621555 | + | 0.783370i | \(0.713499\pi\) | |||||||
\(198\) | 7.37782 | 0.524319 | ||||||||
\(199\) | 15.9600 | 1.13137 | 0.565686 | − | 0.824620i | \(-0.308611\pi\) | ||||
0.565686 | + | 0.824620i | \(0.308611\pi\) | |||||||
\(200\) | −10.3108 | −0.729086 | ||||||||
\(201\) | −11.5596 | −0.815354 | ||||||||
\(202\) | −4.40155 | −0.309692 | ||||||||
\(203\) | 3.25035 | 0.228130 | ||||||||
\(204\) | −0.0477356 | −0.00334216 | ||||||||
\(205\) | 11.8035 | 0.824394 | ||||||||
\(206\) | −32.7398 | −2.28109 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 15.6436 | 1.08469 | ||||||||
\(209\) | 2.97855 | 0.206031 | ||||||||
\(210\) | 29.0221 | 2.00272 | ||||||||
\(211\) | −7.87384 | −0.542057 | −0.271029 | − | 0.962571i | \(-0.587364\pi\) | ||||
−0.271029 | + | 0.962571i | \(0.587364\pi\) | |||||||
\(212\) | 28.0938 | 1.92949 | ||||||||
\(213\) | −11.2291 | −0.769405 | ||||||||
\(214\) | −12.3035 | −0.841047 | ||||||||
\(215\) | −3.08228 | −0.210210 | ||||||||
\(216\) | 0.779182 | 0.0530166 | ||||||||
\(217\) | 30.3040 | 2.05717 | ||||||||
\(218\) | −3.36171 | −0.227684 | ||||||||
\(219\) | −1.28040 | −0.0865217 | ||||||||
\(220\) | −35.7449 | −2.40992 | ||||||||
\(221\) | −0.101010 | −0.00679468 | ||||||||
\(222\) | −16.8861 | −1.13332 | ||||||||
\(223\) | −19.3035 | −1.29266 | −0.646330 | − | 0.763058i | \(-0.723697\pi\) | ||||
−0.646330 | + | 0.763058i | \(0.723697\pi\) | |||||||
\(224\) | 26.2433 | 1.75346 | ||||||||
\(225\) | 13.2329 | 0.882192 | ||||||||
\(226\) | −3.87555 | −0.257798 | ||||||||
\(227\) | −18.1220 | −1.20280 | −0.601401 | − | 0.798947i | \(-0.705391\pi\) | ||||
−0.601401 | + | 0.798947i | \(0.705391\pi\) | |||||||
\(228\) | 2.00298 | 0.132651 | ||||||||
\(229\) | 5.94760 | 0.393029 | 0.196514 | − | 0.980501i | \(-0.437038\pi\) | ||||
0.196514 | + | 0.980501i | \(0.437038\pi\) | |||||||
\(230\) | 8.92891 | 0.588755 | ||||||||
\(231\) | 11.4680 | 0.754540 | ||||||||
\(232\) | −0.779182 | −0.0511558 | ||||||||
\(233\) | −7.09230 | −0.464632 | −0.232316 | − | 0.972640i | \(-0.574630\pi\) | ||||
−0.232316 | + | 0.972640i | \(0.574630\pi\) | |||||||
\(234\) | 10.4984 | 0.686300 | ||||||||
\(235\) | 25.1987 | 1.64378 | ||||||||
\(236\) | 6.88700 | 0.448306 | ||||||||
\(237\) | −7.24288 | −0.470475 | ||||||||
\(238\) | −0.136746 | −0.00886394 | ||||||||
\(239\) | 9.30675 | 0.602004 | 0.301002 | − | 0.953624i | \(-0.402679\pi\) | ||||
0.301002 | + | 0.953624i | \(0.402679\pi\) | |||||||
\(240\) | 13.3049 | 0.858830 | ||||||||
\(241\) | 6.58703 | 0.424308 | 0.212154 | − | 0.977236i | \(-0.431952\pi\) | ||||
0.212154 | + | 0.977236i | \(0.431952\pi\) | |||||||
\(242\) | −3.02880 | −0.194698 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −32.7839 | −2.09878 | ||||||||
\(245\) | 15.2217 | 0.972479 | ||||||||
\(246\) | 5.78036 | 0.368543 | ||||||||
\(247\) | 4.23837 | 0.269681 | ||||||||
\(248\) | −7.26455 | −0.461299 | ||||||||
\(249\) | −6.40814 | −0.406099 | ||||||||
\(250\) | −73.5107 | −4.64923 | ||||||||
\(251\) | −10.0983 | −0.637397 | −0.318698 | − | 0.947856i | \(-0.603246\pi\) | ||||
−0.318698 | + | 0.947856i | \(0.603246\pi\) | |||||||
\(252\) | 7.71186 | 0.485802 | ||||||||
\(253\) | 3.52823 | 0.221818 | ||||||||
\(254\) | −25.2320 | −1.58320 | ||||||||
\(255\) | −0.0859096 | −0.00537987 | ||||||||
\(256\) | 8.49465 | 0.530915 | ||||||||
\(257\) | −2.03420 | −0.126890 | −0.0634449 | − | 0.997985i | \(-0.520209\pi\) | ||||
−0.0634449 | + | 0.997985i | \(0.520209\pi\) | |||||||
\(258\) | −1.50944 | −0.0939735 | ||||||||
\(259\) | −26.2475 | −1.63094 | ||||||||
\(260\) | −50.8636 | −3.15443 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | −8.06312 | −0.498142 | ||||||||
\(263\) | −31.4605 | −1.93994 | −0.969968 | − | 0.243232i | \(-0.921792\pi\) | ||||
−0.969968 | + | 0.243232i | \(0.921792\pi\) | |||||||
\(264\) | −2.74914 | −0.169198 | ||||||||
\(265\) | 50.5603 | 3.10590 | ||||||||
\(266\) | 5.73785 | 0.351810 | ||||||||
\(267\) | −18.1777 | −1.11245 | ||||||||
\(268\) | 27.4267 | 1.67535 | ||||||||
\(269\) | 3.12220 | 0.190364 | 0.0951820 | − | 0.995460i | \(-0.469657\pi\) | ||||
0.0951820 | + | 0.995460i | \(0.469657\pi\) | |||||||
\(270\) | 8.92891 | 0.543396 | ||||||||
\(271\) | 29.0814 | 1.76657 | 0.883284 | − | 0.468838i | \(-0.155327\pi\) | ||||
0.883284 | + | 0.468838i | \(0.155327\pi\) | |||||||
\(272\) | −0.0626901 | −0.00380114 | ||||||||
\(273\) | 16.3186 | 0.987644 | ||||||||
\(274\) | 32.6286 | 1.97117 | ||||||||
\(275\) | −46.6887 | −2.81544 | ||||||||
\(276\) | 2.37262 | 0.142815 | ||||||||
\(277\) | 22.0686 | 1.32598 | 0.662988 | − | 0.748630i | \(-0.269288\pi\) | ||||
0.662988 | + | 0.748630i | \(0.269288\pi\) | |||||||
\(278\) | 13.0665 | 0.783676 | ||||||||
\(279\) | 9.32330 | 0.558171 | ||||||||
\(280\) | −10.8143 | −0.646276 | ||||||||
\(281\) | 12.6153 | 0.752568 | 0.376284 | − | 0.926504i | \(-0.377202\pi\) | ||||
0.376284 | + | 0.926504i | \(0.377202\pi\) | |||||||
\(282\) | 12.3402 | 0.734846 | ||||||||
\(283\) | −19.5697 | −1.16330 | −0.581649 | − | 0.813440i | \(-0.697592\pi\) | ||||
−0.581649 | + | 0.813440i | \(0.697592\pi\) | |||||||
\(284\) | 26.6424 | 1.58093 | ||||||||
\(285\) | 3.60475 | 0.213527 | ||||||||
\(286\) | −37.0407 | −2.19026 | ||||||||
\(287\) | 8.98493 | 0.530364 | ||||||||
\(288\) | 8.07399 | 0.475764 | ||||||||
\(289\) | −16.9996 | −0.999976 | ||||||||
\(290\) | −8.92891 | −0.524324 | ||||||||
\(291\) | 5.01067 | 0.293731 | ||||||||
\(292\) | 3.03791 | 0.177781 | ||||||||
\(293\) | 14.4860 | 0.846281 | 0.423141 | − | 0.906064i | \(-0.360928\pi\) | ||||
0.423141 | + | 0.906064i | \(0.360928\pi\) | |||||||
\(294\) | 7.45429 | 0.434743 | ||||||||
\(295\) | 12.3945 | 0.721636 | ||||||||
\(296\) | 6.29211 | 0.365722 | ||||||||
\(297\) | 3.52823 | 0.204729 | ||||||||
\(298\) | −30.4110 | −1.76166 | ||||||||
\(299\) | 5.02055 | 0.290346 | ||||||||
\(300\) | −31.3966 | −1.81269 | ||||||||
\(301\) | −2.34625 | −0.135236 | ||||||||
\(302\) | 22.3101 | 1.28380 | ||||||||
\(303\) | −2.10491 | −0.120924 | ||||||||
\(304\) | 2.63047 | 0.150868 | ||||||||
\(305\) | −59.0011 | −3.37840 | ||||||||
\(306\) | −0.0420712 | −0.00240505 | ||||||||
\(307\) | −27.0211 | −1.54218 | −0.771088 | − | 0.636729i | \(-0.780287\pi\) | ||||
−0.771088 | + | 0.636729i | \(0.780287\pi\) | |||||||
\(308\) | −27.2092 | −1.55039 | ||||||||
\(309\) | −15.6569 | −0.890689 | ||||||||
\(310\) | −83.2470 | −4.72811 | ||||||||
\(311\) | 24.1529 | 1.36959 | 0.684793 | − | 0.728737i | \(-0.259892\pi\) | ||||
0.684793 | + | 0.728737i | \(0.259892\pi\) | |||||||
\(312\) | −3.91192 | −0.221469 | ||||||||
\(313\) | 25.3428 | 1.43246 | 0.716229 | − | 0.697865i | \(-0.245866\pi\) | ||||
0.716229 | + | 0.697865i | \(0.245866\pi\) | |||||||
\(314\) | 32.9448 | 1.85918 | ||||||||
\(315\) | 13.8790 | 0.781993 | ||||||||
\(316\) | 17.1846 | 0.966710 | ||||||||
\(317\) | 6.57718 | 0.369411 | 0.184706 | − | 0.982794i | \(-0.440867\pi\) | ||||
0.184706 | + | 0.982794i | \(0.440867\pi\) | |||||||
\(318\) | 24.7602 | 1.38848 | ||||||||
\(319\) | −3.52823 | −0.197543 | ||||||||
\(320\) | −45.4821 | −2.54252 | ||||||||
\(321\) | −5.88378 | −0.328400 | ||||||||
\(322\) | 6.79676 | 0.378768 | ||||||||
\(323\) | −0.0169848 | −0.000945062 0 | ||||||||
\(324\) | 2.37262 | 0.131812 | ||||||||
\(325\) | −66.4363 | −3.68522 | ||||||||
\(326\) | 27.1702 | 1.50482 | ||||||||
\(327\) | −1.60764 | −0.0889028 | ||||||||
\(328\) | −2.15389 | −0.118929 | ||||||||
\(329\) | 19.1814 | 1.05751 | ||||||||
\(330\) | −31.5033 | −1.73420 | ||||||||
\(331\) | 28.9988 | 1.59392 | 0.796958 | − | 0.604034i | \(-0.206441\pi\) | ||||
0.796958 | + | 0.604034i | \(0.206441\pi\) | |||||||
\(332\) | 15.2041 | 0.834433 | ||||||||
\(333\) | −8.07528 | −0.442523 | ||||||||
\(334\) | −13.3310 | −0.729439 | ||||||||
\(335\) | 49.3597 | 2.69681 | ||||||||
\(336\) | 10.1278 | 0.552517 | ||||||||
\(337\) | 14.4842 | 0.789003 | 0.394501 | − | 0.918895i | \(-0.370917\pi\) | ||||
0.394501 | + | 0.918895i | \(0.370917\pi\) | |||||||
\(338\) | −25.5235 | −1.38830 | ||||||||
\(339\) | −1.85337 | −0.100661 | ||||||||
\(340\) | 0.203831 | 0.0110543 | ||||||||
\(341\) | −32.8948 | −1.78135 | ||||||||
\(342\) | 1.76530 | 0.0954566 | ||||||||
\(343\) | −11.1656 | −0.602886 | ||||||||
\(344\) | 0.562449 | 0.0303252 | ||||||||
\(345\) | 4.27000 | 0.229889 | ||||||||
\(346\) | 8.04324 | 0.432407 | ||||||||
\(347\) | −1.73755 | −0.0932764 | −0.0466382 | − | 0.998912i | \(-0.514851\pi\) | ||||
−0.0466382 | + | 0.998912i | \(0.514851\pi\) | |||||||
\(348\) | −2.37262 | −0.127186 | ||||||||
\(349\) | 9.73121 | 0.520900 | 0.260450 | − | 0.965487i | \(-0.416129\pi\) | ||||
0.260450 | + | 0.965487i | \(0.416129\pi\) | |||||||
\(350\) | −89.9407 | −4.80753 | ||||||||
\(351\) | 5.02055 | 0.267977 | ||||||||
\(352\) | −28.4869 | −1.51836 | ||||||||
\(353\) | 3.57545 | 0.190302 | 0.0951511 | − | 0.995463i | \(-0.469667\pi\) | ||||
0.0951511 | + | 0.995463i | \(0.469667\pi\) | |||||||
\(354\) | 6.06977 | 0.322605 | ||||||||
\(355\) | 47.9482 | 2.54483 | ||||||||
\(356\) | 43.1287 | 2.28582 | ||||||||
\(357\) | −0.0653950 | −0.00346107 | ||||||||
\(358\) | −13.7010 | −0.724121 | ||||||||
\(359\) | −17.1057 | −0.902803 | −0.451402 | − | 0.892321i | \(-0.649076\pi\) | ||||
−0.451402 | + | 0.892321i | \(0.649076\pi\) | |||||||
\(360\) | −3.32711 | −0.175354 | ||||||||
\(361\) | −18.2873 | −0.962490 | ||||||||
\(362\) | 38.1204 | 2.00356 | ||||||||
\(363\) | −1.44844 | −0.0760231 | ||||||||
\(364\) | −38.7178 | −2.02936 | ||||||||
\(365\) | 5.46732 | 0.286173 | ||||||||
\(366\) | −28.8937 | −1.51030 | ||||||||
\(367\) | −25.8324 | −1.34844 | −0.674219 | − | 0.738532i | \(-0.735520\pi\) | ||||
−0.674219 | + | 0.738532i | \(0.735520\pi\) | |||||||
\(368\) | 3.11591 | 0.162428 | ||||||||
\(369\) | 2.76429 | 0.143903 | ||||||||
\(370\) | 72.1035 | 3.74848 | ||||||||
\(371\) | 38.4869 | 1.99814 | ||||||||
\(372\) | −22.1207 | −1.14690 | ||||||||
\(373\) | 0.929245 | 0.0481145 | 0.0240572 | − | 0.999711i | \(-0.492342\pi\) | ||||
0.0240572 | + | 0.999711i | \(0.492342\pi\) | |||||||
\(374\) | 0.148437 | 0.00767549 | ||||||||
\(375\) | −35.1544 | −1.81537 | ||||||||
\(376\) | −4.59821 | −0.237135 | ||||||||
\(377\) | −5.02055 | −0.258571 | ||||||||
\(378\) | 6.79676 | 0.349587 | ||||||||
\(379\) | 34.0540 | 1.74924 | 0.874619 | − | 0.484810i | \(-0.161111\pi\) | ||||
0.874619 | + | 0.484810i | \(0.161111\pi\) | |||||||
\(380\) | −8.55272 | −0.438745 | ||||||||
\(381\) | −12.0665 | −0.618185 | ||||||||
\(382\) | −20.4284 | −1.04521 | ||||||||
\(383\) | 11.4951 | 0.587371 | 0.293685 | − | 0.955902i | \(-0.405118\pi\) | ||||
0.293685 | + | 0.955902i | \(0.405118\pi\) | |||||||
\(384\) | −6.12527 | −0.312579 | ||||||||
\(385\) | −48.9684 | −2.49566 | ||||||||
\(386\) | 3.33332 | 0.169662 | ||||||||
\(387\) | −0.721845 | −0.0366935 | ||||||||
\(388\) | −11.8884 | −0.603544 | ||||||||
\(389\) | −37.5870 | −1.90574 | −0.952869 | − | 0.303382i | \(-0.901884\pi\) | ||||
−0.952869 | + | 0.303382i | \(0.901884\pi\) | |||||||
\(390\) | −44.8280 | −2.26996 | ||||||||
\(391\) | −0.0201193 | −0.00101748 | ||||||||
\(392\) | −2.77763 | −0.140291 | ||||||||
\(393\) | −3.85596 | −0.194507 | ||||||||
\(394\) | 36.4850 | 1.83809 | ||||||||
\(395\) | 30.9271 | 1.55611 | ||||||||
\(396\) | −8.37116 | −0.420667 | ||||||||
\(397\) | −25.4305 | −1.27632 | −0.638161 | − | 0.769903i | \(-0.720305\pi\) | ||||
−0.638161 | + | 0.769903i | \(0.720305\pi\) | |||||||
\(398\) | −33.3736 | −1.67287 | ||||||||
\(399\) | 2.74396 | 0.137370 | ||||||||
\(400\) | −41.2325 | −2.06162 | ||||||||
\(401\) | −35.8401 | −1.78977 | −0.894886 | − | 0.446296i | \(-0.852743\pi\) | ||||
−0.894886 | + | 0.446296i | \(0.852743\pi\) | |||||||
\(402\) | 24.1722 | 1.20560 | ||||||||
\(403\) | −46.8081 | −2.33168 | ||||||||
\(404\) | 4.99417 | 0.248469 | ||||||||
\(405\) | 4.27000 | 0.212178 | ||||||||
\(406\) | −6.79676 | −0.337317 | ||||||||
\(407\) | 28.4915 | 1.41227 | ||||||||
\(408\) | 0.0156766 | 0.000776109 0 | ||||||||
\(409\) | 2.10354 | 0.104013 | 0.0520067 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520067 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(410\) | −24.6821 | −1.21896 | ||||||||
\(411\) | 15.6037 | 0.769674 | ||||||||
\(412\) | 37.1479 | 1.83014 | ||||||||
\(413\) | 9.43479 | 0.464256 | ||||||||
\(414\) | 2.09108 | 0.102771 | ||||||||
\(415\) | 27.3627 | 1.34318 | ||||||||
\(416\) | −40.5358 | −1.98743 | ||||||||
\(417\) | 6.24868 | 0.305999 | ||||||||
\(418\) | −6.22840 | −0.304641 | ||||||||
\(419\) | 1.76510 | 0.0862309 | 0.0431154 | − | 0.999070i | \(-0.486272\pi\) | ||||
0.0431154 | + | 0.999070i | \(0.486272\pi\) | |||||||
\(420\) | −32.9296 | −1.60680 | ||||||||
\(421\) | 35.8642 | 1.74791 | 0.873957 | − | 0.486004i | \(-0.161546\pi\) | ||||
0.873957 | + | 0.486004i | \(0.161546\pi\) | |||||||
\(422\) | 16.4648 | 0.801495 | ||||||||
\(423\) | 5.90133 | 0.286933 | ||||||||
\(424\) | −9.22617 | −0.448062 | ||||||||
\(425\) | 0.266237 | 0.0129144 | ||||||||
\(426\) | 23.4809 | 1.13766 | ||||||||
\(427\) | −44.9121 | −2.17345 | ||||||||
\(428\) | 13.9600 | 0.674781 | ||||||||
\(429\) | −17.7137 | −0.855224 | ||||||||
\(430\) | 6.44529 | 0.310820 | ||||||||
\(431\) | 23.2484 | 1.11984 | 0.559918 | − | 0.828548i | \(-0.310833\pi\) | ||||
0.559918 | + | 0.828548i | \(0.310833\pi\) | |||||||
\(432\) | 3.11591 | 0.149914 | ||||||||
\(433\) | 6.84029 | 0.328724 | 0.164362 | − | 0.986400i | \(-0.447444\pi\) | ||||
0.164362 | + | 0.986400i | \(0.447444\pi\) | |||||||
\(434\) | −63.3682 | −3.04177 | ||||||||
\(435\) | −4.27000 | −0.204731 | ||||||||
\(436\) | 3.81433 | 0.182673 | ||||||||
\(437\) | 0.844205 | 0.0403838 | ||||||||
\(438\) | 2.67743 | 0.127933 | ||||||||
\(439\) | −10.6962 | −0.510503 | −0.255251 | − | 0.966875i | \(-0.582158\pi\) | ||||
−0.255251 | + | 0.966875i | \(0.582158\pi\) | |||||||
\(440\) | 11.7388 | 0.559626 | ||||||||
\(441\) | 3.56480 | 0.169752 | ||||||||
\(442\) | 0.211220 | 0.0100467 | ||||||||
\(443\) | 0.758143 | 0.0360205 | 0.0180102 | − | 0.999838i | \(-0.494267\pi\) | ||||
0.0180102 | + | 0.999838i | \(0.494267\pi\) | |||||||
\(444\) | 19.1596 | 0.909273 | ||||||||
\(445\) | 77.6186 | 3.67947 | ||||||||
\(446\) | 40.3652 | 1.91135 | ||||||||
\(447\) | −14.5432 | −0.687868 | ||||||||
\(448\) | −34.6213 | −1.63570 | ||||||||
\(449\) | −17.2635 | −0.814714 | −0.407357 | − | 0.913269i | \(-0.633549\pi\) | ||||
−0.407357 | + | 0.913269i | \(0.633549\pi\) | |||||||
\(450\) | −27.6710 | −1.30443 | ||||||||
\(451\) | −9.75308 | −0.459254 | ||||||||
\(452\) | 4.39735 | 0.206834 | ||||||||
\(453\) | 10.6692 | 0.501282 | ||||||||
\(454\) | 37.8947 | 1.77849 | ||||||||
\(455\) | −69.6802 | −3.26666 | ||||||||
\(456\) | −0.657789 | −0.0308038 | ||||||||
\(457\) | 0.915744 | 0.0428367 | 0.0214183 | − | 0.999771i | \(-0.493182\pi\) | ||||
0.0214183 | + | 0.999771i | \(0.493182\pi\) | |||||||
\(458\) | −12.4369 | −0.581139 | ||||||||
\(459\) | −0.0201193 | −0.000939091 0 | ||||||||
\(460\) | −10.1311 | −0.472365 | ||||||||
\(461\) | 21.5469 | 1.00354 | 0.501769 | − | 0.865002i | \(-0.332683\pi\) | ||||
0.501769 | + | 0.865002i | \(0.332683\pi\) | |||||||
\(462\) | −23.9805 | −1.11568 | ||||||||
\(463\) | −27.0273 | −1.25607 | −0.628034 | − | 0.778186i | \(-0.716140\pi\) | ||||
−0.628034 | + | 0.778186i | \(0.716140\pi\) | |||||||
\(464\) | −3.11591 | −0.144652 | ||||||||
\(465\) | −39.8105 | −1.84617 | ||||||||
\(466\) | 14.8306 | 0.687013 | ||||||||
\(467\) | −28.9856 | −1.34130 | −0.670648 | − | 0.741776i | \(-0.733984\pi\) | ||||
−0.670648 | + | 0.741776i | \(0.733984\pi\) | |||||||
\(468\) | −11.9119 | −0.550626 | ||||||||
\(469\) | 37.5729 | 1.73496 | ||||||||
\(470\) | −52.6925 | −2.43052 | ||||||||
\(471\) | 15.7549 | 0.725949 | ||||||||
\(472\) | −2.26173 | −0.104105 | ||||||||
\(473\) | 2.54684 | 0.117104 | ||||||||
\(474\) | 15.1454 | 0.695653 | ||||||||
\(475\) | −11.1713 | −0.512573 | ||||||||
\(476\) | 0.155158 | 0.00711164 | ||||||||
\(477\) | 11.8408 | 0.542155 | ||||||||
\(478\) | −19.4612 | −0.890134 | ||||||||
\(479\) | 5.03847 | 0.230214 | 0.115107 | − | 0.993353i | \(-0.463279\pi\) | ||||
0.115107 | + | 0.993353i | \(0.463279\pi\) | |||||||
\(480\) | −34.4759 | −1.57360 | ||||||||
\(481\) | 40.5423 | 1.84857 | ||||||||
\(482\) | −13.7740 | −0.627390 | ||||||||
\(483\) | 3.25035 | 0.147896 | ||||||||
\(484\) | 3.43659 | 0.156209 | ||||||||
\(485\) | −21.3956 | −0.971523 | ||||||||
\(486\) | 2.09108 | 0.0948534 | ||||||||
\(487\) | −23.8712 | −1.08171 | −0.540854 | − | 0.841117i | \(-0.681899\pi\) | ||||
−0.540854 | + | 0.841117i | \(0.681899\pi\) | |||||||
\(488\) | 10.7664 | 0.487373 | ||||||||
\(489\) | 12.9934 | 0.587580 | ||||||||
\(490\) | −31.8298 | −1.43792 | ||||||||
\(491\) | 28.4182 | 1.28249 | 0.641247 | − | 0.767335i | \(-0.278417\pi\) | ||||
0.641247 | + | 0.767335i | \(0.278417\pi\) | |||||||
\(492\) | −6.55862 | −0.295686 | ||||||||
\(493\) | 0.0201193 | 0.000906130 0 | ||||||||
\(494\) | −8.86278 | −0.398755 | ||||||||
\(495\) | −15.0656 | −0.677146 | ||||||||
\(496\) | −29.0506 | −1.30441 | ||||||||
\(497\) | 36.4985 | 1.63718 | ||||||||
\(498\) | 13.3999 | 0.600466 | ||||||||
\(499\) | 29.2166 | 1.30792 | 0.653958 | − | 0.756531i | \(-0.273107\pi\) | ||||
0.653958 | + | 0.756531i | \(0.273107\pi\) | |||||||
\(500\) | 83.4081 | 3.73012 | ||||||||
\(501\) | −6.37516 | −0.284821 | ||||||||
\(502\) | 21.1163 | 0.942466 | ||||||||
\(503\) | 7.41728 | 0.330720 | 0.165360 | − | 0.986233i | \(-0.447121\pi\) | ||||
0.165360 | + | 0.986233i | \(0.447121\pi\) | |||||||
\(504\) | −2.53262 | −0.112812 | ||||||||
\(505\) | 8.98798 | 0.399960 | ||||||||
\(506\) | −7.37782 | −0.327984 | ||||||||
\(507\) | −12.2059 | −0.542083 | ||||||||
\(508\) | 28.6292 | 1.27022 | ||||||||
\(509\) | −34.3566 | −1.52283 | −0.761415 | − | 0.648264i | \(-0.775495\pi\) | ||||
−0.761415 | + | 0.648264i | \(0.775495\pi\) | |||||||
\(510\) | 0.179644 | 0.00795477 | ||||||||
\(511\) | 4.16177 | 0.184106 | ||||||||
\(512\) | −30.0135 | −1.32642 | ||||||||
\(513\) | 0.844205 | 0.0372726 | ||||||||
\(514\) | 4.25367 | 0.187621 | ||||||||
\(515\) | 66.8549 | 2.94598 | ||||||||
\(516\) | 1.71267 | 0.0753959 | ||||||||
\(517\) | −20.8213 | −0.915719 | ||||||||
\(518\) | 54.8857 | 2.41154 | ||||||||
\(519\) | 3.84645 | 0.168840 | ||||||||
\(520\) | 16.7039 | 0.732514 | ||||||||
\(521\) | −8.80762 | −0.385869 | −0.192935 | − | 0.981212i | \(-0.561800\pi\) | ||||
−0.192935 | + | 0.981212i | \(0.561800\pi\) | |||||||
\(522\) | −2.09108 | −0.0915241 | ||||||||
\(523\) | 8.70954 | 0.380842 | 0.190421 | − | 0.981703i | \(-0.439015\pi\) | ||||
0.190421 | + | 0.981703i | \(0.439015\pi\) | |||||||
\(524\) | 9.14873 | 0.399664 | ||||||||
\(525\) | −43.0116 | −1.87718 | ||||||||
\(526\) | 65.7864 | 2.86842 | ||||||||
\(527\) | 0.187579 | 0.00817106 | ||||||||
\(528\) | −10.9937 | −0.478438 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −105.726 | −4.59244 | ||||||||
\(531\) | 2.90270 | 0.125966 | ||||||||
\(532\) | −6.51039 | −0.282261 | ||||||||
\(533\) | −13.8783 | −0.601134 | ||||||||
\(534\) | 38.0110 | 1.64490 | ||||||||
\(535\) | 25.1237 | 1.08619 | ||||||||
\(536\) | −9.00706 | −0.389046 | ||||||||
\(537\) | −6.55212 | −0.282745 | ||||||||
\(538\) | −6.52878 | −0.281476 | ||||||||
\(539\) | −12.5775 | −0.541749 | ||||||||
\(540\) | −10.1311 | −0.435973 | ||||||||
\(541\) | −45.0504 | −1.93687 | −0.968434 | − | 0.249271i | \(-0.919809\pi\) | ||||
−0.968434 | + | 0.249271i | \(0.919809\pi\) | |||||||
\(542\) | −60.8116 | −2.61208 | ||||||||
\(543\) | 18.2300 | 0.782324 | ||||||||
\(544\) | 0.162443 | 0.00696470 | ||||||||
\(545\) | 6.86463 | 0.294048 | ||||||||
\(546\) | −34.1234 | −1.46035 | ||||||||
\(547\) | −22.2007 | −0.949234 | −0.474617 | − | 0.880192i | \(-0.657413\pi\) | ||||
−0.474617 | + | 0.880192i | \(0.657413\pi\) | |||||||
\(548\) | −37.0217 | −1.58149 | ||||||||
\(549\) | −13.8176 | −0.589721 | ||||||||
\(550\) | 97.6299 | 4.16295 | ||||||||
\(551\) | −0.844205 | −0.0359643 | ||||||||
\(552\) | −0.779182 | −0.0331642 | ||||||||
\(553\) | 23.5419 | 1.00110 | ||||||||
\(554\) | −46.1473 | −1.96061 | ||||||||
\(555\) | 34.4814 | 1.46366 | ||||||||
\(556\) | −14.8257 | −0.628752 | ||||||||
\(557\) | −36.5137 | −1.54714 | −0.773568 | − | 0.633713i | \(-0.781530\pi\) | ||||
−0.773568 | + | 0.633713i | \(0.781530\pi\) | |||||||
\(558\) | −19.4958 | −0.825322 | ||||||||
\(559\) | 3.62406 | 0.153281 | ||||||||
\(560\) | −43.2457 | −1.82747 | ||||||||
\(561\) | 0.0709858 | 0.00299702 | ||||||||
\(562\) | −26.3797 | −1.11276 | ||||||||
\(563\) | −27.9546 | −1.17814 | −0.589072 | − | 0.808080i | \(-0.700507\pi\) | ||||
−0.589072 | + | 0.808080i | \(0.700507\pi\) | |||||||
\(564\) | −14.0016 | −0.589575 | ||||||||
\(565\) | 7.91390 | 0.332940 | ||||||||
\(566\) | 40.9218 | 1.72007 | ||||||||
\(567\) | 3.25035 | 0.136502 | ||||||||
\(568\) | −8.74951 | −0.367121 | ||||||||
\(569\) | 15.4258 | 0.646684 | 0.323342 | − | 0.946282i | \(-0.395194\pi\) | ||||
0.323342 | + | 0.946282i | \(0.395194\pi\) | |||||||
\(570\) | −7.53783 | −0.315725 | ||||||||
\(571\) | −9.08243 | −0.380088 | −0.190044 | − | 0.981776i | \(-0.560863\pi\) | ||||
−0.190044 | + | 0.981776i | \(0.560863\pi\) | |||||||
\(572\) | 42.0278 | 1.75727 | ||||||||
\(573\) | −9.76931 | −0.408119 | ||||||||
\(574\) | −18.7882 | −0.784205 | ||||||||
\(575\) | −13.2329 | −0.551850 | ||||||||
\(576\) | −10.6515 | −0.443814 | ||||||||
\(577\) | 10.7508 | 0.447563 | 0.223781 | − | 0.974639i | \(-0.428160\pi\) | ||||
0.223781 | + | 0.974639i | \(0.428160\pi\) | |||||||
\(578\) | 35.5475 | 1.47858 | ||||||||
\(579\) | 1.59407 | 0.0662471 | ||||||||
\(580\) | 10.1311 | 0.420671 | ||||||||
\(581\) | 20.8287 | 0.864121 | ||||||||
\(582\) | −10.4777 | −0.434316 | ||||||||
\(583\) | −41.7772 | −1.73024 | ||||||||
\(584\) | −0.997668 | −0.0412838 | ||||||||
\(585\) | −21.4377 | −0.886341 | ||||||||
\(586\) | −30.2914 | −1.25133 | ||||||||
\(587\) | −3.81891 | −0.157623 | −0.0788117 | − | 0.996890i | \(-0.525113\pi\) | ||||
−0.0788117 | + | 0.996890i | \(0.525113\pi\) | |||||||
\(588\) | −8.45793 | −0.348799 | ||||||||
\(589\) | −7.87078 | −0.324310 | ||||||||
\(590\) | −25.9179 | −1.06702 | ||||||||
\(591\) | 17.4479 | 0.717710 | ||||||||
\(592\) | 25.1618 | 1.03415 | ||||||||
\(593\) | −27.3374 | −1.12261 | −0.561306 | − | 0.827608i | \(-0.689701\pi\) | ||||
−0.561306 | + | 0.827608i | \(0.689701\pi\) | |||||||
\(594\) | −7.37782 | −0.302716 | ||||||||
\(595\) | 0.279237 | 0.0114476 | ||||||||
\(596\) | 34.5054 | 1.41340 | ||||||||
\(597\) | −15.9600 | −0.653198 | ||||||||
\(598\) | −10.4984 | −0.429310 | ||||||||
\(599\) | −15.7743 | −0.644519 | −0.322259 | − | 0.946651i | \(-0.604442\pi\) | ||||
−0.322259 | + | 0.946651i | \(0.604442\pi\) | |||||||
\(600\) | 10.3108 | 0.420938 | ||||||||
\(601\) | −20.0160 | −0.816468 | −0.408234 | − | 0.912877i | \(-0.633855\pi\) | ||||
−0.408234 | + | 0.912877i | \(0.633855\pi\) | |||||||
\(602\) | 4.90621 | 0.199962 | ||||||||
\(603\) | 11.5596 | 0.470745 | ||||||||
\(604\) | −25.3139 | −1.03001 | ||||||||
\(605\) | 6.18482 | 0.251449 | ||||||||
\(606\) | 4.40155 | 0.178801 | ||||||||
\(607\) | −27.9764 | −1.13553 | −0.567763 | − | 0.823192i | \(-0.692191\pi\) | ||||
−0.567763 | + | 0.823192i | \(0.692191\pi\) | |||||||
\(608\) | −6.81610 | −0.276429 | ||||||||
\(609\) | −3.25035 | −0.131711 | ||||||||
\(610\) | 123.376 | 4.99536 | ||||||||
\(611\) | −29.6279 | −1.19862 | ||||||||
\(612\) | 0.0477356 | 0.00192960 | ||||||||
\(613\) | 17.7179 | 0.715620 | 0.357810 | − | 0.933794i | \(-0.383524\pi\) | ||||
0.357810 | + | 0.933794i | \(0.383524\pi\) | |||||||
\(614\) | 56.5033 | 2.28029 | ||||||||
\(615\) | −11.8035 | −0.475964 | ||||||||
\(616\) | 8.93567 | 0.360028 | ||||||||
\(617\) | 36.5526 | 1.47155 | 0.735777 | − | 0.677224i | \(-0.236817\pi\) | ||||
0.735777 | + | 0.677224i | \(0.236817\pi\) | |||||||
\(618\) | 32.7398 | 1.31699 | ||||||||
\(619\) | 1.85013 | 0.0743631 | 0.0371815 | − | 0.999309i | \(-0.488162\pi\) | ||||
0.0371815 | + | 0.999309i | \(0.488162\pi\) | |||||||
\(620\) | 94.4552 | 3.79341 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −50.5057 | −2.02510 | ||||||||
\(623\) | 59.0838 | 2.36714 | ||||||||
\(624\) | −15.6436 | −0.626244 | ||||||||
\(625\) | 83.9449 | 3.35779 | ||||||||
\(626\) | −52.9938 | −2.11806 | ||||||||
\(627\) | −2.97855 | −0.118952 | ||||||||
\(628\) | −37.3805 | −1.49164 | ||||||||
\(629\) | −0.162469 | −0.00647808 | ||||||||
\(630\) | −29.0221 | −1.15627 | ||||||||
\(631\) | −4.10725 | −0.163507 | −0.0817535 | − | 0.996653i | \(-0.526052\pi\) | ||||
−0.0817535 | + | 0.996653i | \(0.526052\pi\) | |||||||
\(632\) | −5.64352 | −0.224487 | ||||||||
\(633\) | 7.87384 | 0.312957 | ||||||||
\(634\) | −13.7534 | −0.546218 | ||||||||
\(635\) | 51.5239 | 2.04466 | ||||||||
\(636\) | −28.0938 | −1.11399 | ||||||||
\(637\) | −17.8973 | −0.709115 | ||||||||
\(638\) | 7.37782 | 0.292091 | ||||||||
\(639\) | 11.2291 | 0.444216 | ||||||||
\(640\) | 26.1549 | 1.03386 | ||||||||
\(641\) | −10.0818 | −0.398209 | −0.199104 | − | 0.979978i | \(-0.563803\pi\) | ||||
−0.199104 | + | 0.979978i | \(0.563803\pi\) | |||||||
\(642\) | 12.3035 | 0.485579 | ||||||||
\(643\) | 13.9525 | 0.550233 | 0.275117 | − | 0.961411i | \(-0.411284\pi\) | ||||
0.275117 | + | 0.961411i | \(0.411284\pi\) | |||||||
\(644\) | −7.71186 | −0.303890 | ||||||||
\(645\) | 3.08228 | 0.121365 | ||||||||
\(646\) | 0.0355167 | 0.00139739 | ||||||||
\(647\) | −5.56296 | −0.218703 | −0.109351 | − | 0.994003i | \(-0.534877\pi\) | ||||
−0.109351 | + | 0.994003i | \(0.534877\pi\) | |||||||
\(648\) | −0.779182 | −0.0306092 | ||||||||
\(649\) | −10.2414 | −0.402010 | ||||||||
\(650\) | 138.924 | 5.44904 | ||||||||
\(651\) | −30.3040 | −1.18771 | ||||||||
\(652\) | −30.8283 | −1.20733 | ||||||||
\(653\) | 16.9574 | 0.663593 | 0.331796 | − | 0.943351i | \(-0.392345\pi\) | ||||
0.331796 | + | 0.943351i | \(0.392345\pi\) | |||||||
\(654\) | 3.36171 | 0.131453 | ||||||||
\(655\) | 16.4649 | 0.643338 | ||||||||
\(656\) | −8.61329 | −0.336293 | ||||||||
\(657\) | 1.28040 | 0.0499533 | ||||||||
\(658\) | −40.1099 | −1.56365 | ||||||||
\(659\) | −21.7981 | −0.849134 | −0.424567 | − | 0.905396i | \(-0.639574\pi\) | ||||
−0.424567 | + | 0.905396i | \(0.639574\pi\) | |||||||
\(660\) | 35.7449 | 1.39137 | ||||||||
\(661\) | −47.7860 | −1.85866 | −0.929330 | − | 0.369249i | \(-0.879615\pi\) | ||||
−0.929330 | + | 0.369249i | \(0.879615\pi\) | |||||||
\(662\) | −60.6388 | −2.35679 | ||||||||
\(663\) | 0.101010 | 0.00392291 | ||||||||
\(664\) | −4.99311 | −0.193770 | ||||||||
\(665\) | −11.7167 | −0.454355 | ||||||||
\(666\) | 16.8861 | 0.654322 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 15.1258 | 0.585237 | ||||||||
\(669\) | 19.3035 | 0.746317 | ||||||||
\(670\) | −103.215 | −3.98755 | ||||||||
\(671\) | 48.7517 | 1.88204 | ||||||||
\(672\) | −26.2433 | −1.01236 | ||||||||
\(673\) | −26.7260 | −1.03021 | −0.515107 | − | 0.857126i | \(-0.672248\pi\) | ||||
−0.515107 | + | 0.857126i | \(0.672248\pi\) | |||||||
\(674\) | −30.2876 | −1.16663 | ||||||||
\(675\) | −13.2329 | −0.509334 | ||||||||
\(676\) | 28.9600 | 1.11384 | ||||||||
\(677\) | 11.9940 | 0.460965 | 0.230483 | − | 0.973076i | \(-0.425970\pi\) | ||||
0.230483 | + | 0.973076i | \(0.425970\pi\) | |||||||
\(678\) | 3.87555 | 0.148840 | ||||||||
\(679\) | −16.2865 | −0.625017 | ||||||||
\(680\) | −0.0669392 | −0.00256700 | ||||||||
\(681\) | 18.1220 | 0.694438 | ||||||||
\(682\) | 68.7857 | 2.63394 | ||||||||
\(683\) | −9.29936 | −0.355830 | −0.177915 | − | 0.984046i | \(-0.556935\pi\) | ||||
−0.177915 | + | 0.984046i | \(0.556935\pi\) | |||||||
\(684\) | −2.00298 | −0.0765858 | ||||||||
\(685\) | −66.6278 | −2.54572 | ||||||||
\(686\) | 23.3482 | 0.891438 | ||||||||
\(687\) | −5.94760 | −0.226915 | ||||||||
\(688\) | 2.24920 | 0.0857501 | ||||||||
\(689\) | −59.4475 | −2.26477 | ||||||||
\(690\) | −8.92891 | −0.339918 | ||||||||
\(691\) | 15.0512 | 0.572575 | 0.286288 | − | 0.958144i | \(-0.407579\pi\) | ||||
0.286288 | + | 0.958144i | \(0.407579\pi\) | |||||||
\(692\) | −9.12617 | −0.346925 | ||||||||
\(693\) | −11.4680 | −0.435634 | ||||||||
\(694\) | 3.63335 | 0.137920 | ||||||||
\(695\) | −26.6818 | −1.01210 | ||||||||
\(696\) | 0.779182 | 0.0295348 | ||||||||
\(697\) | 0.0556158 | 0.00210660 | ||||||||
\(698\) | −20.3487 | −0.770211 | ||||||||
\(699\) | 7.09230 | 0.268255 | ||||||||
\(700\) | 102.050 | 3.85713 | ||||||||
\(701\) | −29.8218 | −1.12635 | −0.563176 | − | 0.826337i | \(-0.690421\pi\) | ||||
−0.563176 | + | 0.826337i | \(0.690421\pi\) | |||||||
\(702\) | −10.4984 | −0.396236 | ||||||||
\(703\) | 6.81719 | 0.257115 | ||||||||
\(704\) | 37.5811 | 1.41639 | ||||||||
\(705\) | −25.1987 | −0.949037 | ||||||||
\(706\) | −7.47656 | −0.281384 | ||||||||
\(707\) | 6.84172 | 0.257309 | ||||||||
\(708\) | −6.88700 | −0.258829 | ||||||||
\(709\) | 34.5946 | 1.29923 | 0.649614 | − | 0.760264i | \(-0.274931\pi\) | ||||
0.649614 | + | 0.760264i | \(0.274931\pi\) | |||||||
\(710\) | −100.264 | −3.76283 | ||||||||
\(711\) | 7.24288 | 0.271629 | ||||||||
\(712\) | −14.1637 | −0.530807 | ||||||||
\(713\) | −9.32330 | −0.349160 | ||||||||
\(714\) | 0.136746 | 0.00511760 | ||||||||
\(715\) | 75.6373 | 2.82868 | ||||||||
\(716\) | 15.5457 | 0.580970 | ||||||||
\(717\) | −9.30675 | −0.347567 | ||||||||
\(718\) | 35.7694 | 1.33490 | ||||||||
\(719\) | 9.33825 | 0.348258 | 0.174129 | − | 0.984723i | \(-0.444289\pi\) | ||||
0.174129 | + | 0.984723i | \(0.444289\pi\) | |||||||
\(720\) | −13.3049 | −0.495846 | ||||||||
\(721\) | 50.8904 | 1.89526 | ||||||||
\(722\) | 38.2403 | 1.42316 | ||||||||
\(723\) | −6.58703 | −0.244974 | ||||||||
\(724\) | −43.2529 | −1.60748 | ||||||||
\(725\) | 13.2329 | 0.491457 | ||||||||
\(726\) | 3.02880 | 0.112409 | ||||||||
\(727\) | −5.85769 | −0.217250 | −0.108625 | − | 0.994083i | \(-0.534645\pi\) | ||||
−0.108625 | + | 0.994083i | \(0.534645\pi\) | |||||||
\(728\) | 12.7151 | 0.471254 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.4326 | −0.423140 | ||||||||
\(731\) | −0.0145231 | −0.000537155 0 | ||||||||
\(732\) | 32.7839 | 1.21173 | ||||||||
\(733\) | −9.06161 | −0.334698 | −0.167349 | − | 0.985898i | \(-0.553521\pi\) | ||||
−0.167349 | + | 0.985898i | \(0.553521\pi\) | |||||||
\(734\) | 54.0176 | 1.99382 | ||||||||
\(735\) | −15.2217 | −0.561461 | ||||||||
\(736\) | −8.07399 | −0.297611 | ||||||||
\(737\) | −40.7851 | −1.50234 | ||||||||
\(738\) | −5.78036 | −0.212778 | ||||||||
\(739\) | 25.4207 | 0.935115 | 0.467557 | − | 0.883963i | \(-0.345134\pi\) | ||||
0.467557 | + | 0.883963i | \(0.345134\pi\) | |||||||
\(740\) | −81.8114 | −3.00745 | ||||||||
\(741\) | −4.23837 | −0.155700 | ||||||||
\(742\) | −80.4793 | −2.95449 | ||||||||
\(743\) | 34.5910 | 1.26902 | 0.634510 | − | 0.772914i | \(-0.281202\pi\) | ||||
0.634510 | + | 0.772914i | \(0.281202\pi\) | |||||||
\(744\) | 7.26455 | 0.266331 | ||||||||
\(745\) | 62.0993 | 2.27514 | ||||||||
\(746\) | −1.94313 | −0.0711429 | ||||||||
\(747\) | 6.40814 | 0.234462 | ||||||||
\(748\) | −0.168422 | −0.00615813 | ||||||||
\(749\) | 19.1244 | 0.698789 | ||||||||
\(750\) | 73.5107 | 2.68423 | ||||||||
\(751\) | 13.9340 | 0.508458 | 0.254229 | − | 0.967144i | \(-0.418178\pi\) | ||||
0.254229 | + | 0.967144i | \(0.418178\pi\) | |||||||
\(752\) | −18.3880 | −0.670542 | ||||||||
\(753\) | 10.0983 | 0.368001 | ||||||||
\(754\) | 10.4984 | 0.382328 | ||||||||
\(755\) | −45.5574 | −1.65800 | ||||||||
\(756\) | −7.71186 | −0.280478 | ||||||||
\(757\) | −31.3210 | −1.13838 | −0.569191 | − | 0.822206i | \(-0.692743\pi\) | ||||
−0.569191 | + | 0.822206i | \(0.692743\pi\) | |||||||
\(758\) | −71.2098 | −2.58646 | ||||||||
\(759\) | −3.52823 | −0.128067 | ||||||||
\(760\) | 2.80876 | 0.101884 | ||||||||
\(761\) | 35.8476 | 1.29947 | 0.649737 | − | 0.760159i | \(-0.274879\pi\) | ||||
0.649737 | + | 0.760159i | \(0.274879\pi\) | |||||||
\(762\) | 25.2320 | 0.914060 | ||||||||
\(763\) | 5.22541 | 0.189172 | ||||||||
\(764\) | 23.1789 | 0.838582 | ||||||||
\(765\) | 0.0859096 | 0.00310607 | ||||||||
\(766\) | −24.0371 | −0.868497 | ||||||||
\(767\) | −14.5731 | −0.526205 | ||||||||
\(768\) | −8.49465 | −0.306524 | ||||||||
\(769\) | 35.7151 | 1.28792 | 0.643959 | − | 0.765060i | \(-0.277291\pi\) | ||||
0.643959 | + | 0.765060i | \(0.277291\pi\) | |||||||
\(770\) | 102.397 | 3.69013 | ||||||||
\(771\) | 2.03420 | 0.0732598 | ||||||||
\(772\) | −3.78211 | −0.136121 | ||||||||
\(773\) | −43.2256 | −1.55472 | −0.777358 | − | 0.629058i | \(-0.783441\pi\) | ||||
−0.777358 | + | 0.629058i | \(0.783441\pi\) | |||||||
\(774\) | 1.50944 | 0.0542556 | ||||||||
\(775\) | 123.374 | 4.43173 | ||||||||
\(776\) | 3.90423 | 0.140154 | ||||||||
\(777\) | 26.2475 | 0.941624 | ||||||||
\(778\) | 78.5975 | 2.81786 | ||||||||
\(779\) | −2.33363 | −0.0836110 | ||||||||
\(780\) | 50.8636 | 1.82121 | ||||||||
\(781\) | −39.6189 | −1.41767 | ||||||||
\(782\) | 0.0420712 | 0.00150446 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | −11.1076 | −0.396700 | ||||||||
\(785\) | −67.2735 | −2.40109 | ||||||||
\(786\) | 8.06312 | 0.287602 | ||||||||
\(787\) | 17.2847 | 0.616133 | 0.308066 | − | 0.951365i | \(-0.400318\pi\) | ||||
0.308066 | + | 0.951365i | \(0.400318\pi\) | |||||||
\(788\) | −41.3972 | −1.47472 | ||||||||
\(789\) | 31.4605 | 1.12002 | ||||||||
\(790\) | −64.6710 | −2.30089 | ||||||||
\(791\) | 6.02412 | 0.214193 | ||||||||
\(792\) | 2.74914 | 0.0976863 | ||||||||
\(793\) | 69.3719 | 2.46347 | ||||||||
\(794\) | 53.1773 | 1.88719 | ||||||||
\(795\) | −50.5603 | −1.79319 | ||||||||
\(796\) | 37.8670 | 1.34216 | ||||||||
\(797\) | −4.41343 | −0.156332 | −0.0781659 | − | 0.996940i | \(-0.524906\pi\) | ||||
−0.0781659 | + | 0.996940i | \(0.524906\pi\) | |||||||
\(798\) | −5.73785 | −0.203118 | ||||||||
\(799\) | 0.118731 | 0.00420040 | ||||||||
\(800\) | 106.842 | 3.77744 | ||||||||
\(801\) | 18.1777 | 0.642276 | ||||||||
\(802\) | 74.9446 | 2.64639 | ||||||||
\(803\) | −4.51757 | −0.159421 | ||||||||
\(804\) | −27.4267 | −0.967264 | ||||||||
\(805\) | −13.8790 | −0.489171 | ||||||||
\(806\) | 97.8795 | 3.44766 | ||||||||
\(807\) | −3.12220 | −0.109907 | ||||||||
\(808\) | −1.64011 | −0.0576989 | ||||||||
\(809\) | −7.24744 | −0.254807 | −0.127403 | − | 0.991851i | \(-0.540664\pi\) | ||||
−0.127403 | + | 0.991851i | \(0.540664\pi\) | |||||||
\(810\) | −8.92891 | −0.313730 | ||||||||
\(811\) | 42.3629 | 1.48756 | 0.743782 | − | 0.668422i | \(-0.233030\pi\) | ||||
0.743782 | + | 0.668422i | \(0.233030\pi\) | |||||||
\(812\) | 7.71186 | 0.270633 | ||||||||
\(813\) | −29.0814 | −1.01993 | ||||||||
\(814\) | −59.5780 | −2.08821 | ||||||||
\(815\) | −55.4816 | −1.94344 | ||||||||
\(816\) | 0.0626901 | 0.00219459 | ||||||||
\(817\) | 0.609385 | 0.0213197 | ||||||||
\(818\) | −4.39868 | −0.153796 | ||||||||
\(819\) | −16.3186 | −0.570216 | ||||||||
\(820\) | 28.0053 | 0.977988 | ||||||||
\(821\) | 18.6464 | 0.650763 | 0.325382 | − | 0.945583i | \(-0.394507\pi\) | ||||
0.325382 | + | 0.945583i | \(0.394507\pi\) | |||||||
\(822\) | −32.6286 | −1.13805 | ||||||||
\(823\) | −20.6409 | −0.719497 | −0.359749 | − | 0.933049i | \(-0.617138\pi\) | ||||
−0.359749 | + | 0.933049i | \(0.617138\pi\) | |||||||
\(824\) | −12.1996 | −0.424992 | ||||||||
\(825\) | 46.6887 | 1.62549 | ||||||||
\(826\) | −19.7289 | −0.686457 | ||||||||
\(827\) | −10.0136 | −0.348208 | −0.174104 | − | 0.984727i | \(-0.555703\pi\) | ||||
−0.174104 | + | 0.984727i | \(0.555703\pi\) | |||||||
\(828\) | −2.37262 | −0.0824543 | ||||||||
\(829\) | −8.49741 | −0.295127 | −0.147564 | − | 0.989053i | \(-0.547143\pi\) | ||||
−0.147564 | + | 0.989053i | \(0.547143\pi\) | |||||||
\(830\) | −57.2177 | −1.98606 | ||||||||
\(831\) | −22.0686 | −0.765553 | ||||||||
\(832\) | 53.4766 | 1.85397 | ||||||||
\(833\) | 0.0717215 | 0.00248500 | ||||||||
\(834\) | −13.0665 | −0.452456 | ||||||||
\(835\) | 27.2219 | 0.942054 | ||||||||
\(836\) | 7.06698 | 0.244417 | ||||||||
\(837\) | −9.32330 | −0.322260 | ||||||||
\(838\) | −3.69097 | −0.127503 | ||||||||
\(839\) | 23.9144 | 0.825616 | 0.412808 | − | 0.910818i | \(-0.364548\pi\) | ||||
0.412808 | + | 0.910818i | \(0.364548\pi\) | |||||||
\(840\) | 10.8143 | 0.373128 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −74.9949 | −2.58450 | ||||||||
\(843\) | −12.6153 | −0.434495 | ||||||||
\(844\) | −18.6816 | −0.643048 | ||||||||
\(845\) | 52.1191 | 1.79295 | ||||||||
\(846\) | −12.3402 | −0.424264 | ||||||||
\(847\) | 4.70793 | 0.161766 | ||||||||
\(848\) | −36.8950 | −1.26698 | ||||||||
\(849\) | 19.5697 | 0.671630 | ||||||||
\(850\) | −0.556723 | −0.0190955 | ||||||||
\(851\) | 8.07528 | 0.276817 | ||||||||
\(852\) | −26.6424 | −0.912753 | ||||||||
\(853\) | 48.7794 | 1.67018 | 0.835088 | − | 0.550116i | \(-0.185417\pi\) | ||||
0.835088 | + | 0.550116i | \(0.185417\pi\) | |||||||
\(854\) | 93.9149 | 3.21370 | ||||||||
\(855\) | −3.60475 | −0.123280 | ||||||||
\(856\) | −4.58453 | −0.156696 | ||||||||
\(857\) | −27.7788 | −0.948906 | −0.474453 | − | 0.880281i | \(-0.657354\pi\) | ||||
−0.474453 | + | 0.880281i | \(0.657354\pi\) | |||||||
\(858\) | 37.0407 | 1.26455 | ||||||||
\(859\) | 6.01242 | 0.205141 | 0.102571 | − | 0.994726i | \(-0.467293\pi\) | ||||
0.102571 | + | 0.994726i | \(0.467293\pi\) | |||||||
\(860\) | −7.31308 | −0.249374 | ||||||||
\(861\) | −8.98493 | −0.306206 | ||||||||
\(862\) | −48.6143 | −1.65581 | ||||||||
\(863\) | −28.4007 | −0.966771 | −0.483385 | − | 0.875408i | \(-0.660593\pi\) | ||||
−0.483385 | + | 0.875408i | \(0.660593\pi\) | |||||||
\(864\) | −8.07399 | −0.274683 | ||||||||
\(865\) | −16.4243 | −0.558444 | ||||||||
\(866\) | −14.3036 | −0.486056 | ||||||||
\(867\) | 16.9996 | 0.577337 | ||||||||
\(868\) | 71.9000 | 2.44044 | ||||||||
\(869\) | −25.5546 | −0.866879 | ||||||||
\(870\) | 8.92891 | 0.302719 | ||||||||
\(871\) | −58.0357 | −1.96647 | ||||||||
\(872\) | −1.25265 | −0.0424199 | ||||||||
\(873\) | −5.01067 | −0.169586 | ||||||||
\(874\) | −1.76530 | −0.0597122 | ||||||||
\(875\) | 114.264 | 3.86284 | ||||||||
\(876\) | −3.03791 | −0.102642 | ||||||||
\(877\) | 25.2774 | 0.853558 | 0.426779 | − | 0.904356i | \(-0.359648\pi\) | ||||
0.426779 | + | 0.904356i | \(0.359648\pi\) | |||||||
\(878\) | 22.3667 | 0.754839 | ||||||||
\(879\) | −14.4860 | −0.488601 | ||||||||
\(880\) | 46.9429 | 1.58245 | ||||||||
\(881\) | −21.9829 | −0.740624 | −0.370312 | − | 0.928907i | \(-0.620749\pi\) | ||||
−0.370312 | + | 0.928907i | \(0.620749\pi\) | |||||||
\(882\) | −7.45429 | −0.250999 | ||||||||
\(883\) | −21.2605 | −0.715472 | −0.357736 | − | 0.933823i | \(-0.616451\pi\) | ||||
−0.357736 | + | 0.933823i | \(0.616451\pi\) | |||||||
\(884\) | −0.239659 | −0.00806060 | ||||||||
\(885\) | −12.3945 | −0.416637 | ||||||||
\(886\) | −1.58534 | −0.0532605 | ||||||||
\(887\) | −23.2355 | −0.780173 | −0.390087 | − | 0.920778i | \(-0.627555\pi\) | ||||
−0.390087 | + | 0.920778i | \(0.627555\pi\) | |||||||
\(888\) | −6.29211 | −0.211149 | ||||||||
\(889\) | 39.2204 | 1.31541 | ||||||||
\(890\) | −162.307 | −5.44053 | ||||||||
\(891\) | −3.52823 | −0.118200 | ||||||||
\(892\) | −45.7999 | −1.53350 | ||||||||
\(893\) | −4.98193 | −0.166714 | ||||||||
\(894\) | 30.4110 | 1.01709 | ||||||||
\(895\) | 27.9775 | 0.935186 | ||||||||
\(896\) | 19.9093 | 0.665123 | ||||||||
\(897\) | −5.02055 | −0.167631 | ||||||||
\(898\) | 36.0993 | 1.20465 | ||||||||
\(899\) | 9.32330 | 0.310949 | ||||||||
\(900\) | 31.3966 | 1.04655 | ||||||||
\(901\) | 0.238230 | 0.00793659 | ||||||||
\(902\) | 20.3945 | 0.679062 | ||||||||
\(903\) | 2.34625 | 0.0780784 | ||||||||
\(904\) | −1.44411 | −0.0480305 | ||||||||
\(905\) | −77.8420 | −2.58756 | ||||||||
\(906\) | −22.3101 | −0.741204 | ||||||||
\(907\) | 40.7049 | 1.35158 | 0.675791 | − | 0.737093i | \(-0.263802\pi\) | ||||
0.675791 | + | 0.737093i | \(0.263802\pi\) | |||||||
\(908\) | −42.9968 | −1.42690 | ||||||||
\(909\) | 2.10491 | 0.0698156 | ||||||||
\(910\) | 145.707 | 4.83014 | ||||||||
\(911\) | −11.8285 | −0.391896 | −0.195948 | − | 0.980614i | \(-0.562778\pi\) | ||||
−0.195948 | + | 0.980614i | \(0.562778\pi\) | |||||||
\(912\) | −2.63047 | −0.0871035 | ||||||||
\(913\) | −22.6094 | −0.748262 | ||||||||
\(914\) | −1.91489 | −0.0633391 | ||||||||
\(915\) | 59.0011 | 1.95052 | ||||||||
\(916\) | 14.1114 | 0.466254 | ||||||||
\(917\) | 12.5332 | 0.413884 | ||||||||
\(918\) | 0.0420712 | 0.00138856 | ||||||||
\(919\) | 10.3685 | 0.342025 | 0.171012 | − | 0.985269i | \(-0.445296\pi\) | ||||
0.171012 | + | 0.985269i | \(0.445296\pi\) | |||||||
\(920\) | 3.32711 | 0.109691 | ||||||||
\(921\) | 27.0211 | 0.890375 | ||||||||
\(922\) | −45.0563 | −1.48385 | ||||||||
\(923\) | −56.3762 | −1.85564 | ||||||||
\(924\) | 27.2092 | 0.895119 | ||||||||
\(925\) | −106.859 | −3.51351 | ||||||||
\(926\) | 56.5164 | 1.85724 | ||||||||
\(927\) | 15.6569 | 0.514240 | ||||||||
\(928\) | 8.07399 | 0.265042 | ||||||||
\(929\) | −4.53697 | −0.148853 | −0.0744266 | − | 0.997226i | \(-0.523713\pi\) | ||||
−0.0744266 | + | 0.997226i | \(0.523713\pi\) | |||||||
\(930\) | 83.2470 | 2.72978 | ||||||||
\(931\) | −3.00942 | −0.0986299 | ||||||||
\(932\) | −16.8273 | −0.551198 | ||||||||
\(933\) | −24.1529 | −0.790731 | ||||||||
\(934\) | 60.6113 | 1.98326 | ||||||||
\(935\) | −0.303109 | −0.00991273 | ||||||||
\(936\) | 3.91192 | 0.127865 | ||||||||
\(937\) | −54.6753 | −1.78616 | −0.893082 | − | 0.449893i | \(-0.851462\pi\) | ||||
−0.893082 | + | 0.449893i | \(0.851462\pi\) | |||||||
\(938\) | −78.5681 | −2.56534 | ||||||||
\(939\) | −25.3428 | −0.827030 | ||||||||
\(940\) | 59.7869 | 1.95003 | ||||||||
\(941\) | −50.3720 | −1.64208 | −0.821040 | − | 0.570870i | \(-0.806606\pi\) | ||||
−0.821040 | + | 0.570870i | \(0.806606\pi\) | |||||||
\(942\) | −32.9448 | −1.07340 | ||||||||
\(943\) | −2.76429 | −0.0900178 | ||||||||
\(944\) | −9.04454 | −0.294375 | ||||||||
\(945\) | −13.8790 | −0.451484 | ||||||||
\(946\) | −5.32565 | −0.173152 | ||||||||
\(947\) | 40.8001 | 1.32582 | 0.662912 | − | 0.748697i | \(-0.269320\pi\) | ||||
0.662912 | + | 0.748697i | \(0.269320\pi\) | |||||||
\(948\) | −17.1846 | −0.558130 | ||||||||
\(949\) | −6.42833 | −0.208672 | ||||||||
\(950\) | 23.3600 | 0.757899 | ||||||||
\(951\) | −6.57718 | −0.213280 | ||||||||
\(952\) | −0.0509546 | −0.00165145 | ||||||||
\(953\) | 2.47746 | 0.0802527 | 0.0401263 | − | 0.999195i | \(-0.487224\pi\) | ||||
0.0401263 | + | 0.999195i | \(0.487224\pi\) | |||||||
\(954\) | −24.7602 | −0.801640 | ||||||||
\(955\) | 41.7149 | 1.34986 | ||||||||
\(956\) | 22.0814 | 0.714164 | ||||||||
\(957\) | 3.52823 | 0.114052 | ||||||||
\(958\) | −10.5359 | −0.340398 | ||||||||
\(959\) | −50.7175 | −1.63775 | ||||||||
\(960\) | 45.4821 | 1.46793 | ||||||||
\(961\) | 55.9239 | 1.80400 | ||||||||
\(962\) | −84.7773 | −2.73333 | ||||||||
\(963\) | 5.88378 | 0.189602 | ||||||||
\(964\) | 15.6285 | 0.503361 | ||||||||
\(965\) | −6.80666 | −0.219114 | ||||||||
\(966\) | −6.79676 | −0.218682 | ||||||||
\(967\) | −41.8313 | −1.34520 | −0.672602 | − | 0.740004i | \(-0.734823\pi\) | ||||
−0.672602 | + | 0.740004i | \(0.734823\pi\) | |||||||
\(968\) | −1.12859 | −0.0362744 | ||||||||
\(969\) | 0.0169848 | 0.000545632 0 | ||||||||
\(970\) | 44.7399 | 1.43651 | ||||||||
\(971\) | 56.6545 | 1.81813 | 0.909064 | − | 0.416657i | \(-0.136798\pi\) | ||||
0.909064 | + | 0.416657i | \(0.136798\pi\) | |||||||
\(972\) | −2.37262 | −0.0761019 | ||||||||
\(973\) | −20.3104 | −0.651122 | ||||||||
\(974\) | 49.9166 | 1.59943 | ||||||||
\(975\) | 66.4363 | 2.12767 | ||||||||
\(976\) | 43.0544 | 1.37814 | ||||||||
\(977\) | −30.0914 | −0.962708 | −0.481354 | − | 0.876526i | \(-0.659855\pi\) | ||||
−0.481354 | + | 0.876526i | \(0.659855\pi\) | |||||||
\(978\) | −27.1702 | −0.868806 | ||||||||
\(979\) | −64.1350 | −2.04976 | ||||||||
\(980\) | 36.1153 | 1.15366 | ||||||||
\(981\) | 1.60764 | 0.0513281 | ||||||||
\(982\) | −59.4247 | −1.89632 | ||||||||
\(983\) | 56.8366 | 1.81281 | 0.906403 | − | 0.422414i | \(-0.138817\pi\) | ||||
0.906403 | + | 0.422414i | \(0.138817\pi\) | |||||||
\(984\) | 2.15389 | 0.0686634 | ||||||||
\(985\) | −74.5025 | −2.37385 | ||||||||
\(986\) | −0.0420712 | −0.00133982 | ||||||||
\(987\) | −19.1814 | −0.610551 | ||||||||
\(988\) | 10.0560 | 0.319926 | ||||||||
\(989\) | 0.721845 | 0.0229533 | ||||||||
\(990\) | 31.5033 | 1.00124 | ||||||||
\(991\) | −44.2480 | −1.40558 | −0.702792 | − | 0.711396i | \(-0.748063\pi\) | ||||
−0.702792 | + | 0.711396i | \(0.748063\pi\) | |||||||
\(992\) | 75.2762 | 2.39002 | ||||||||
\(993\) | −28.9988 | −0.920248 | ||||||||
\(994\) | −76.3214 | −2.42077 | ||||||||
\(995\) | 68.1491 | 2.16047 | ||||||||
\(996\) | −15.2041 | −0.481760 | ||||||||
\(997\) | −59.7747 | −1.89308 | −0.946541 | − | 0.322583i | \(-0.895449\pi\) | ||||
−0.946541 | + | 0.322583i | \(0.895449\pi\) | |||||||
\(998\) | −61.0944 | −1.93391 | ||||||||
\(999\) | 8.07528 | 0.255491 |
(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 | 2001.2.a.k.1.3 | ✓ | 10 | |
3.2 | odd | 2 | 6003.2.a.k.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.k.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6003.2.a.k.1.8 | 10 | 3.2 | odd | 2 |