Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5239,2,Mod(1,5239)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5239, 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("5239.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5239 = 13^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5239.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: | \(41.8336256189\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | no (minimal twist has level 403) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 5239.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80367 | −1.27539 | −0.637694 | − | 0.770290i | \(-0.720111\pi\) | ||||
−0.637694 | + | 0.770290i | \(0.720111\pi\) | |||||||
\(3\) | −1.10798 | −0.639694 | −0.319847 | − | 0.947469i | \(-0.603632\pi\) | ||||
−0.319847 | + | 0.947469i | \(0.603632\pi\) | |||||||
\(4\) | 1.25322 | 0.626612 | ||||||||
\(5\) | 0.771735 | 0.345130 | 0.172565 | − | 0.984998i | \(-0.444794\pi\) | ||||
0.172565 | + | 0.984998i | \(0.444794\pi\) | |||||||
\(6\) | 1.99844 | 0.815858 | ||||||||
\(7\) | 4.39563 | 1.66139 | 0.830695 | − | 0.556727i | \(-0.187943\pi\) | ||||
0.830695 | + | 0.556727i | \(0.187943\pi\) | |||||||
\(8\) | 1.34694 | 0.476214 | ||||||||
\(9\) | −1.77237 | −0.590791 | ||||||||
\(10\) | −1.39195 | −0.440175 | ||||||||
\(11\) | −5.43090 | −1.63748 | −0.818740 | − | 0.574165i | \(-0.805327\pi\) | ||||
−0.818740 | + | 0.574165i | \(0.805327\pi\) | |||||||
\(12\) | −1.38855 | −0.400840 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −7.92826 | −2.11892 | ||||||||
\(15\) | −0.855069 | −0.220778 | ||||||||
\(16\) | −4.93588 | −1.23397 | ||||||||
\(17\) | −1.17127 | −0.284074 | −0.142037 | − | 0.989861i | \(-0.545365\pi\) | ||||
−0.142037 | + | 0.989861i | \(0.545365\pi\) | |||||||
\(18\) | 3.19678 | 0.753487 | ||||||||
\(19\) | 6.05291 | 1.38863 | 0.694316 | − | 0.719670i | \(-0.255707\pi\) | ||||
0.694316 | + | 0.719670i | \(0.255707\pi\) | |||||||
\(20\) | 0.967157 | 0.216263 | ||||||||
\(21\) | −4.87028 | −1.06278 | ||||||||
\(22\) | 9.79556 | 2.08842 | ||||||||
\(23\) | −1.15047 | −0.239891 | −0.119945 | − | 0.992781i | \(-0.538272\pi\) | ||||
−0.119945 | + | 0.992781i | \(0.538272\pi\) | |||||||
\(24\) | −1.49238 | −0.304631 | ||||||||
\(25\) | −4.40443 | −0.880885 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.28771 | 1.01762 | ||||||||
\(28\) | 5.50871 | 1.04105 | ||||||||
\(29\) | 4.82434 | 0.895858 | 0.447929 | − | 0.894069i | \(-0.352162\pi\) | ||||
0.447929 | + | 0.894069i | \(0.352162\pi\) | |||||||
\(30\) | 1.54226 | 0.281577 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 6.20882 | 1.09757 | ||||||||
\(33\) | 6.01735 | 1.04749 | ||||||||
\(34\) | 2.11258 | 0.362304 | ||||||||
\(35\) | 3.39226 | 0.573396 | ||||||||
\(36\) | −2.22118 | −0.370197 | ||||||||
\(37\) | 6.37694 | 1.04836 | 0.524181 | − | 0.851607i | \(-0.324371\pi\) | ||||
0.524181 | + | 0.851607i | \(0.324371\pi\) | |||||||
\(38\) | −10.9175 | −1.77104 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.03948 | 0.164356 | ||||||||
\(41\) | −11.7350 | −1.83270 | −0.916350 | − | 0.400377i | \(-0.868879\pi\) | ||||
−0.916350 | + | 0.400377i | \(0.868879\pi\) | |||||||
\(42\) | 8.78438 | 1.35546 | ||||||||
\(43\) | −5.64848 | −0.861385 | −0.430692 | − | 0.902499i | \(-0.641731\pi\) | ||||
−0.430692 | + | 0.902499i | \(0.641731\pi\) | |||||||
\(44\) | −6.80614 | −1.02606 | ||||||||
\(45\) | −1.36780 | −0.203900 | ||||||||
\(46\) | 2.07508 | 0.305953 | ||||||||
\(47\) | 4.06481 | 0.592914 | 0.296457 | − | 0.955046i | \(-0.404195\pi\) | ||||
0.296457 | + | 0.955046i | \(0.404195\pi\) | |||||||
\(48\) | 5.46887 | 0.789363 | ||||||||
\(49\) | 12.3215 | 1.76022 | ||||||||
\(50\) | 7.94413 | 1.12347 | ||||||||
\(51\) | 1.29774 | 0.181720 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.26335 | 0.173535 | 0.0867674 | − | 0.996229i | \(-0.472346\pi\) | ||||
0.0867674 | + | 0.996229i | \(0.472346\pi\) | |||||||
\(54\) | −9.53728 | −1.29786 | ||||||||
\(55\) | −4.19122 | −0.565143 | ||||||||
\(56\) | 5.92063 | 0.791177 | ||||||||
\(57\) | −6.70652 | −0.888301 | ||||||||
\(58\) | −8.70152 | −1.14257 | ||||||||
\(59\) | −8.62832 | −1.12331 | −0.561656 | − | 0.827371i | \(-0.689835\pi\) | ||||
−0.561656 | + | 0.827371i | \(0.689835\pi\) | |||||||
\(60\) | −1.07159 | −0.138342 | ||||||||
\(61\) | 0.975562 | 0.124908 | 0.0624540 | − | 0.998048i | \(-0.480107\pi\) | ||||
0.0624540 | + | 0.998048i | \(0.480107\pi\) | |||||||
\(62\) | −1.80367 | −0.229066 | ||||||||
\(63\) | −7.79069 | −0.981535 | ||||||||
\(64\) | −1.32691 | −0.165863 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −10.8533 | −1.33595 | ||||||||
\(67\) | −8.48686 | −1.03683 | −0.518417 | − | 0.855128i | \(-0.673479\pi\) | ||||
−0.518417 | + | 0.855128i | \(0.673479\pi\) | |||||||
\(68\) | −1.46786 | −0.178004 | ||||||||
\(69\) | 1.27471 | 0.153457 | ||||||||
\(70\) | −6.11851 | −0.731302 | ||||||||
\(71\) | 3.84007 | 0.455732 | 0.227866 | − | 0.973693i | \(-0.426825\pi\) | ||||
0.227866 | + | 0.973693i | \(0.426825\pi\) | |||||||
\(72\) | −2.38727 | −0.281343 | ||||||||
\(73\) | −4.37422 | −0.511964 | −0.255982 | − | 0.966682i | \(-0.582399\pi\) | ||||
−0.255982 | + | 0.966682i | \(0.582399\pi\) | |||||||
\(74\) | −11.5019 | −1.33707 | ||||||||
\(75\) | 4.88003 | 0.563497 | ||||||||
\(76\) | 7.58565 | 0.870134 | ||||||||
\(77\) | −23.8722 | −2.72049 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.38024 | 0.942851 | 0.471425 | − | 0.881906i | \(-0.343740\pi\) | ||||
0.471425 | + | 0.881906i | \(0.343740\pi\) | |||||||
\(80\) | −3.80919 | −0.425880 | ||||||||
\(81\) | −0.541573 | −0.0601748 | ||||||||
\(82\) | 21.1661 | 2.33740 | ||||||||
\(83\) | −12.8430 | −1.40971 | −0.704853 | − | 0.709353i | \(-0.748987\pi\) | ||||
−0.704853 | + | 0.709353i | \(0.748987\pi\) | |||||||
\(84\) | −6.10355 | −0.665952 | ||||||||
\(85\) | −0.903906 | −0.0980424 | ||||||||
\(86\) | 10.1880 | 1.09860 | ||||||||
\(87\) | −5.34529 | −0.573076 | ||||||||
\(88\) | −7.31508 | −0.779790 | ||||||||
\(89\) | 10.8208 | 1.14700 | 0.573499 | − | 0.819206i | \(-0.305586\pi\) | ||||
0.573499 | + | 0.819206i | \(0.305586\pi\) | |||||||
\(90\) | 2.46706 | 0.260051 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.44180 | −0.150318 | ||||||||
\(93\) | −1.10798 | −0.114893 | ||||||||
\(94\) | −7.33158 | −0.756195 | ||||||||
\(95\) | 4.67124 | 0.479259 | ||||||||
\(96\) | −6.87927 | −0.702112 | ||||||||
\(97\) | −0.0691975 | −0.00702595 | −0.00351297 | − | 0.999994i | \(-0.501118\pi\) | ||||
−0.00351297 | + | 0.999994i | \(0.501118\pi\) | |||||||
\(98\) | −22.2240 | −2.24496 | ||||||||
\(99\) | 9.62559 | 0.967408 | ||||||||
\(100\) | −5.51973 | −0.551973 | ||||||||
\(101\) | 1.54300 | 0.153534 | 0.0767670 | − | 0.997049i | \(-0.475540\pi\) | ||||
0.0767670 | + | 0.997049i | \(0.475540\pi\) | |||||||
\(102\) | −2.34070 | −0.231764 | ||||||||
\(103\) | 4.80271 | 0.473225 | 0.236612 | − | 0.971604i | \(-0.423963\pi\) | ||||
0.236612 | + | 0.971604i | \(0.423963\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.75856 | −0.366798 | ||||||||
\(106\) | −2.27867 | −0.221324 | ||||||||
\(107\) | −12.3706 | −1.19591 | −0.597957 | − | 0.801528i | \(-0.704021\pi\) | ||||
−0.597957 | + | 0.801528i | \(0.704021\pi\) | |||||||
\(108\) | 6.62669 | 0.637653 | ||||||||
\(109\) | −6.83808 | −0.654970 | −0.327485 | − | 0.944856i | \(-0.606201\pi\) | ||||
−0.327485 | + | 0.944856i | \(0.606201\pi\) | |||||||
\(110\) | 7.55957 | 0.720777 | ||||||||
\(111\) | −7.06554 | −0.670632 | ||||||||
\(112\) | −21.6963 | −2.05011 | ||||||||
\(113\) | −6.97786 | −0.656422 | −0.328211 | − | 0.944604i | \(-0.606446\pi\) | ||||
−0.328211 | + | 0.944604i | \(0.606446\pi\) | |||||||
\(114\) | 12.0964 | 1.13293 | ||||||||
\(115\) | −0.887861 | −0.0827935 | ||||||||
\(116\) | 6.04599 | 0.561356 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.5626 | 1.43266 | ||||||||
\(119\) | −5.14844 | −0.471957 | ||||||||
\(120\) | −1.15172 | −0.105137 | ||||||||
\(121\) | 18.4947 | 1.68134 | ||||||||
\(122\) | −1.75959 | −0.159306 | ||||||||
\(123\) | 13.0022 | 1.17237 | ||||||||
\(124\) | 1.25322 | 0.112543 | ||||||||
\(125\) | −7.25772 | −0.649150 | ||||||||
\(126\) | 14.0518 | 1.25184 | ||||||||
\(127\) | −14.7534 | −1.30915 | −0.654577 | − | 0.755995i | \(-0.727153\pi\) | ||||
−0.654577 | + | 0.755995i | \(0.727153\pi\) | |||||||
\(128\) | −10.0243 | −0.886035 | ||||||||
\(129\) | 6.25842 | 0.551023 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.3028 | −1.51175 | −0.755875 | − | 0.654716i | \(-0.772788\pi\) | ||||
−0.755875 | + | 0.654716i | \(0.772788\pi\) | |||||||
\(132\) | 7.54109 | 0.656368 | ||||||||
\(133\) | 26.6063 | 2.30706 | ||||||||
\(134\) | 15.3075 | 1.32237 | ||||||||
\(135\) | 4.08071 | 0.351211 | ||||||||
\(136\) | −1.57762 | −0.135280 | ||||||||
\(137\) | 1.54150 | 0.131699 | 0.0658495 | − | 0.997830i | \(-0.479024\pi\) | ||||
0.0658495 | + | 0.997830i | \(0.479024\pi\) | |||||||
\(138\) | −2.29915 | −0.195717 | ||||||||
\(139\) | 16.9217 | 1.43528 | 0.717638 | − | 0.696416i | \(-0.245223\pi\) | ||||
0.717638 | + | 0.696416i | \(0.245223\pi\) | |||||||
\(140\) | 4.25126 | 0.359297 | ||||||||
\(141\) | −4.50375 | −0.379284 | ||||||||
\(142\) | −6.92621 | −0.581235 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.74822 | 0.729018 | ||||||||
\(145\) | 3.72311 | 0.309188 | ||||||||
\(146\) | 7.88966 | 0.652953 | ||||||||
\(147\) | −13.6520 | −1.12600 | ||||||||
\(148\) | 7.99174 | 0.656917 | ||||||||
\(149\) | −9.23408 | −0.756486 | −0.378243 | − | 0.925706i | \(-0.623472\pi\) | ||||
−0.378243 | + | 0.925706i | \(0.623472\pi\) | |||||||
\(150\) | −8.80196 | −0.718677 | ||||||||
\(151\) | −21.7043 | −1.76627 | −0.883135 | − | 0.469119i | \(-0.844571\pi\) | ||||
−0.883135 | + | 0.469119i | \(0.844571\pi\) | |||||||
\(152\) | 8.15288 | 0.661286 | ||||||||
\(153\) | 2.07592 | 0.167828 | ||||||||
\(154\) | 43.0576 | 3.46968 | ||||||||
\(155\) | 0.771735 | 0.0619872 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.7044 | 1.81201 | 0.906003 | − | 0.423272i | \(-0.139119\pi\) | ||||
0.906003 | + | 0.423272i | \(0.139119\pi\) | |||||||
\(158\) | −15.1152 | −1.20250 | ||||||||
\(159\) | −1.39977 | −0.111009 | ||||||||
\(160\) | 4.79156 | 0.378806 | ||||||||
\(161\) | −5.05706 | −0.398552 | ||||||||
\(162\) | 0.976819 | 0.0767462 | ||||||||
\(163\) | −3.65029 | −0.285913 | −0.142956 | − | 0.989729i | \(-0.545661\pi\) | ||||
−0.142956 | + | 0.989729i | \(0.545661\pi\) | |||||||
\(164\) | −14.7066 | −1.14839 | ||||||||
\(165\) | 4.64380 | 0.361519 | ||||||||
\(166\) | 23.1646 | 1.79792 | ||||||||
\(167\) | 20.8732 | 1.61521 | 0.807607 | − | 0.589721i | \(-0.200762\pi\) | ||||
0.807607 | + | 0.589721i | \(0.200762\pi\) | |||||||
\(168\) | −6.55996 | −0.506112 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.63035 | 0.125042 | ||||||||
\(171\) | −10.7280 | −0.820392 | ||||||||
\(172\) | −7.07881 | −0.539754 | ||||||||
\(173\) | −8.11798 | −0.617198 | −0.308599 | − | 0.951192i | \(-0.599860\pi\) | ||||
−0.308599 | + | 0.951192i | \(0.599860\pi\) | |||||||
\(174\) | 9.64114 | 0.730893 | ||||||||
\(175\) | −19.3602 | −1.46349 | ||||||||
\(176\) | 26.8063 | 2.02060 | ||||||||
\(177\) | 9.56003 | 0.718576 | ||||||||
\(178\) | −19.5171 | −1.46287 | ||||||||
\(179\) | 23.1226 | 1.72826 | 0.864132 | − | 0.503266i | \(-0.167868\pi\) | ||||
0.864132 | + | 0.503266i | \(0.167868\pi\) | |||||||
\(180\) | −1.71416 | −0.127766 | ||||||||
\(181\) | 8.27560 | 0.615120 | 0.307560 | − | 0.951529i | \(-0.400487\pi\) | ||||
0.307560 | + | 0.951529i | \(0.400487\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.08091 | −0.0799029 | ||||||||
\(184\) | −1.54962 | −0.114239 | ||||||||
\(185\) | 4.92131 | 0.361822 | ||||||||
\(186\) | 1.99844 | 0.146532 | ||||||||
\(187\) | 6.36103 | 0.465165 | ||||||||
\(188\) | 5.09412 | 0.371527 | ||||||||
\(189\) | 23.2428 | 1.69066 | ||||||||
\(190\) | −8.42537 | −0.611241 | ||||||||
\(191\) | 11.9829 | 0.867049 | 0.433524 | − | 0.901142i | \(-0.357270\pi\) | ||||
0.433524 | + | 0.901142i | \(0.357270\pi\) | |||||||
\(192\) | 1.47019 | 0.106102 | ||||||||
\(193\) | −6.79106 | −0.488831 | −0.244416 | − | 0.969671i | \(-0.578596\pi\) | ||||
−0.244416 | + | 0.969671i | \(0.578596\pi\) | |||||||
\(194\) | 0.124810 | 0.00896080 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.4416 | 1.10297 | ||||||||
\(197\) | 2.55648 | 0.182141 | 0.0910707 | − | 0.995844i | \(-0.470971\pi\) | ||||
0.0910707 | + | 0.995844i | \(0.470971\pi\) | |||||||
\(198\) | −17.3614 | −1.23382 | ||||||||
\(199\) | −5.05390 | −0.358262 | −0.179131 | − | 0.983825i | \(-0.557329\pi\) | ||||
−0.179131 | + | 0.983825i | \(0.557329\pi\) | |||||||
\(200\) | −5.93248 | −0.419490 | ||||||||
\(201\) | 9.40329 | 0.663257 | ||||||||
\(202\) | −2.78306 | −0.195815 | ||||||||
\(203\) | 21.2060 | 1.48837 | ||||||||
\(204\) | 1.62636 | 0.113868 | ||||||||
\(205\) | −9.05631 | −0.632520 | ||||||||
\(206\) | −8.66250 | −0.603545 | ||||||||
\(207\) | 2.03907 | 0.141725 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.8728 | −2.27386 | ||||||||
\(210\) | 6.77921 | 0.467810 | ||||||||
\(211\) | 11.5141 | 0.792665 | 0.396332 | − | 0.918107i | \(-0.370283\pi\) | ||||
0.396332 | + | 0.918107i | \(0.370283\pi\) | |||||||
\(212\) | 1.58326 | 0.108739 | ||||||||
\(213\) | −4.25473 | −0.291529 | ||||||||
\(214\) | 22.3125 | 1.52525 | ||||||||
\(215\) | −4.35912 | −0.297290 | ||||||||
\(216\) | 7.12221 | 0.484605 | ||||||||
\(217\) | 4.39563 | 0.298395 | ||||||||
\(218\) | 12.3336 | 0.835340 | ||||||||
\(219\) | 4.84657 | 0.327501 | ||||||||
\(220\) | −5.25253 | −0.354126 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 12.7439 | 0.855315 | ||||||||
\(223\) | −5.79039 | −0.387753 | −0.193877 | − | 0.981026i | \(-0.562106\pi\) | ||||
−0.193877 | + | 0.981026i | \(0.562106\pi\) | |||||||
\(224\) | 27.2917 | 1.82350 | ||||||||
\(225\) | 7.80629 | 0.520419 | ||||||||
\(226\) | 12.5858 | 0.837192 | ||||||||
\(227\) | −11.2255 | −0.745064 | −0.372532 | − | 0.928019i | \(-0.621510\pi\) | ||||
−0.372532 | + | 0.928019i | \(0.621510\pi\) | |||||||
\(228\) | −8.40478 | −0.556620 | ||||||||
\(229\) | 26.0722 | 1.72290 | 0.861450 | − | 0.507842i | \(-0.169556\pi\) | ||||
0.861450 | + | 0.507842i | \(0.169556\pi\) | |||||||
\(230\) | 1.60141 | 0.105594 | ||||||||
\(231\) | 26.4500 | 1.74028 | ||||||||
\(232\) | 6.49809 | 0.426620 | ||||||||
\(233\) | −3.14064 | −0.205750 | −0.102875 | − | 0.994694i | \(-0.532804\pi\) | ||||
−0.102875 | + | 0.994694i | \(0.532804\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.13696 | 0.204633 | ||||||||
\(236\) | −10.8132 | −0.703880 | ||||||||
\(237\) | −9.28517 | −0.603136 | ||||||||
\(238\) | 9.28609 | 0.601928 | ||||||||
\(239\) | 10.9723 | 0.709737 | 0.354868 | − | 0.934916i | \(-0.384526\pi\) | ||||
0.354868 | + | 0.934916i | \(0.384526\pi\) | |||||||
\(240\) | 4.22052 | 0.272433 | ||||||||
\(241\) | −6.64065 | −0.427762 | −0.213881 | − | 0.976860i | \(-0.568610\pi\) | ||||
−0.213881 | + | 0.976860i | \(0.568610\pi\) | |||||||
\(242\) | −33.3584 | −2.14436 | ||||||||
\(243\) | −15.2631 | −0.979127 | ||||||||
\(244\) | 1.22260 | 0.0782688 | ||||||||
\(245\) | 9.50895 | 0.607505 | ||||||||
\(246\) | −23.4517 | −1.49522 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.34694 | 0.0855305 | ||||||||
\(249\) | 14.2299 | 0.901781 | ||||||||
\(250\) | 13.0905 | 0.827918 | ||||||||
\(251\) | −12.1934 | −0.769642 | −0.384821 | − | 0.922991i | \(-0.625737\pi\) | ||||
−0.384821 | + | 0.922991i | \(0.625737\pi\) | |||||||
\(252\) | −9.76348 | −0.615042 | ||||||||
\(253\) | 6.24812 | 0.392816 | ||||||||
\(254\) | 26.6103 | 1.66968 | ||||||||
\(255\) | 1.00151 | 0.0627171 | ||||||||
\(256\) | 20.7344 | 1.29590 | ||||||||
\(257\) | 18.8733 | 1.17728 | 0.588641 | − | 0.808394i | \(-0.299663\pi\) | ||||
0.588641 | + | 0.808394i | \(0.299663\pi\) | |||||||
\(258\) | −11.2881 | −0.702767 | ||||||||
\(259\) | 28.0306 | 1.74174 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.55054 | −0.529265 | ||||||||
\(262\) | 31.2085 | 1.92807 | ||||||||
\(263\) | −7.28401 | −0.449151 | −0.224576 | − | 0.974457i | \(-0.572100\pi\) | ||||
−0.224576 | + | 0.974457i | \(0.572100\pi\) | |||||||
\(264\) | 8.10499 | 0.498828 | ||||||||
\(265\) | 0.974973 | 0.0598921 | ||||||||
\(266\) | −47.9890 | −2.94240 | ||||||||
\(267\) | −11.9892 | −0.733728 | ||||||||
\(268\) | −10.6359 | −0.649693 | ||||||||
\(269\) | −18.0480 | −1.10041 | −0.550203 | − | 0.835031i | \(-0.685450\pi\) | ||||
−0.550203 | + | 0.835031i | \(0.685450\pi\) | |||||||
\(270\) | −7.36025 | −0.447931 | ||||||||
\(271\) | −0.880778 | −0.0535034 | −0.0267517 | − | 0.999642i | \(-0.508516\pi\) | ||||
−0.0267517 | + | 0.999642i | \(0.508516\pi\) | |||||||
\(272\) | 5.78122 | 0.350538 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.78035 | −0.167967 | ||||||||
\(275\) | 23.9200 | 1.44243 | ||||||||
\(276\) | 1.59749 | 0.0961578 | ||||||||
\(277\) | 21.3545 | 1.28307 | 0.641534 | − | 0.767094i | \(-0.278298\pi\) | ||||
0.641534 | + | 0.767094i | \(0.278298\pi\) | |||||||
\(278\) | −30.5211 | −1.83053 | ||||||||
\(279\) | −1.77237 | −0.106109 | ||||||||
\(280\) | 4.56915 | 0.273059 | ||||||||
\(281\) | −16.9935 | −1.01374 | −0.506872 | − | 0.862021i | \(-0.669198\pi\) | ||||
−0.506872 | + | 0.862021i | \(0.669198\pi\) | |||||||
\(282\) | 8.12327 | 0.483734 | ||||||||
\(283\) | −20.0191 | −1.19001 | −0.595006 | − | 0.803721i | \(-0.702850\pi\) | ||||
−0.595006 | + | 0.803721i | \(0.702850\pi\) | |||||||
\(284\) | 4.81246 | 0.285567 | ||||||||
\(285\) | −5.17566 | −0.306579 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −51.5827 | −3.04483 | ||||||||
\(288\) | −11.0043 | −0.648437 | ||||||||
\(289\) | −15.6281 | −0.919302 | ||||||||
\(290\) | −6.71527 | −0.394334 | ||||||||
\(291\) | 0.0766697 | 0.00449446 | ||||||||
\(292\) | −5.48188 | −0.320803 | ||||||||
\(293\) | −26.7083 | −1.56032 | −0.780158 | − | 0.625583i | \(-0.784861\pi\) | ||||
−0.780158 | + | 0.625583i | \(0.784861\pi\) | |||||||
\(294\) | 24.6238 | 1.43609 | ||||||||
\(295\) | −6.65877 | −0.387689 | ||||||||
\(296\) | 8.58933 | 0.499245 | ||||||||
\(297\) | −28.7170 | −1.66633 | ||||||||
\(298\) | 16.6552 | 0.964812 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 6.11577 | 0.353094 | ||||||||
\(301\) | −24.8286 | −1.43110 | ||||||||
\(302\) | 39.1474 | 2.25268 | ||||||||
\(303\) | −1.70962 | −0.0982148 | ||||||||
\(304\) | −29.8764 | −1.71353 | ||||||||
\(305\) | 0.752875 | 0.0431095 | ||||||||
\(306\) | −3.74427 | −0.214046 | ||||||||
\(307\) | 26.9507 | 1.53816 | 0.769080 | − | 0.639152i | \(-0.220715\pi\) | ||||
0.769080 | + | 0.639152i | \(0.220715\pi\) | |||||||
\(308\) | −29.9173 | −1.70469 | ||||||||
\(309\) | −5.32132 | −0.302719 | ||||||||
\(310\) | −1.39195 | −0.0790577 | ||||||||
\(311\) | −17.1492 | −0.972443 | −0.486222 | − | 0.873836i | \(-0.661625\pi\) | ||||
−0.486222 | + | 0.873836i | \(0.661625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.2964 | −1.03417 | −0.517087 | − | 0.855933i | \(-0.672984\pi\) | ||||
−0.517087 | + | 0.855933i | \(0.672984\pi\) | |||||||
\(314\) | −40.9512 | −2.31101 | ||||||||
\(315\) | −6.01235 | −0.338757 | ||||||||
\(316\) | 10.5023 | 0.590802 | ||||||||
\(317\) | −20.2800 | −1.13904 | −0.569519 | − | 0.821978i | \(-0.692870\pi\) | ||||
−0.569519 | + | 0.821978i | \(0.692870\pi\) | |||||||
\(318\) | 2.52473 | 0.141580 | ||||||||
\(319\) | −26.2006 | −1.46695 | ||||||||
\(320\) | −1.02402 | −0.0572444 | ||||||||
\(321\) | 13.7065 | 0.765020 | ||||||||
\(322\) | 9.12126 | 0.508308 | ||||||||
\(323\) | −7.08956 | −0.394474 | ||||||||
\(324\) | −0.678713 | −0.0377063 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.58391 | 0.364649 | ||||||||
\(327\) | 7.57648 | 0.418980 | ||||||||
\(328\) | −15.8063 | −0.872758 | ||||||||
\(329\) | 17.8674 | 0.985062 | ||||||||
\(330\) | −8.37588 | −0.461077 | ||||||||
\(331\) | −29.8669 | −1.64163 | −0.820817 | − | 0.571191i | \(-0.806482\pi\) | ||||
−0.820817 | + | 0.571191i | \(0.806482\pi\) | |||||||
\(332\) | −16.0952 | −0.883339 | ||||||||
\(333\) | −11.3023 | −0.619363 | ||||||||
\(334\) | −37.6483 | −2.06002 | ||||||||
\(335\) | −6.54960 | −0.357843 | ||||||||
\(336\) | 24.0391 | 1.31144 | ||||||||
\(337\) | −25.6842 | −1.39911 | −0.699555 | − | 0.714579i | \(-0.746618\pi\) | ||||
−0.699555 | + | 0.714579i | \(0.746618\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.73136 | 0.419910 | ||||||||
\(340\) | −1.13280 | −0.0614345 | ||||||||
\(341\) | −5.43090 | −0.294100 | ||||||||
\(342\) | 19.3498 | 1.04632 | ||||||||
\(343\) | 23.3915 | 1.26302 | ||||||||
\(344\) | −7.60814 | −0.410203 | ||||||||
\(345\) | 0.983735 | 0.0529625 | ||||||||
\(346\) | 14.6421 | 0.787167 | ||||||||
\(347\) | 4.35012 | 0.233527 | 0.116763 | − | 0.993160i | \(-0.462748\pi\) | ||||
0.116763 | + | 0.993160i | \(0.462748\pi\) | |||||||
\(348\) | −6.69885 | −0.359096 | ||||||||
\(349\) | −4.98391 | −0.266782 | −0.133391 | − | 0.991063i | \(-0.542587\pi\) | ||||
−0.133391 | + | 0.991063i | \(0.542587\pi\) | |||||||
\(350\) | 34.9194 | 1.86652 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −33.7195 | −1.79726 | ||||||||
\(353\) | −9.63154 | −0.512635 | −0.256318 | − | 0.966593i | \(-0.582509\pi\) | ||||
−0.256318 | + | 0.966593i | \(0.582509\pi\) | |||||||
\(354\) | −17.2431 | −0.916462 | ||||||||
\(355\) | 2.96351 | 0.157287 | ||||||||
\(356\) | 13.5608 | 0.718723 | ||||||||
\(357\) | 5.70439 | 0.301908 | ||||||||
\(358\) | −41.7055 | −2.20420 | ||||||||
\(359\) | 36.8886 | 1.94691 | 0.973453 | − | 0.228887i | \(-0.0735088\pi\) | ||||
0.973453 | + | 0.228887i | \(0.0735088\pi\) | |||||||
\(360\) | −1.84234 | −0.0970999 | ||||||||
\(361\) | 17.6377 | 0.928301 | ||||||||
\(362\) | −14.9264 | −0.784516 | ||||||||
\(363\) | −20.4918 | −1.07554 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.37574 | −0.176694 | ||||||||
\(366\) | 1.94960 | 0.101907 | ||||||||
\(367\) | −3.13314 | −0.163549 | −0.0817743 | − | 0.996651i | \(-0.526059\pi\) | ||||
−0.0817743 | + | 0.996651i | \(0.526059\pi\) | |||||||
\(368\) | 5.67860 | 0.296018 | ||||||||
\(369\) | 20.7988 | 1.08274 | ||||||||
\(370\) | −8.87641 | −0.461463 | ||||||||
\(371\) | 5.55323 | 0.288309 | ||||||||
\(372\) | −1.38855 | −0.0719930 | ||||||||
\(373\) | −17.5456 | −0.908478 | −0.454239 | − | 0.890880i | \(-0.650089\pi\) | ||||
−0.454239 | + | 0.890880i | \(0.650089\pi\) | |||||||
\(374\) | −11.4732 | −0.593265 | ||||||||
\(375\) | 8.04143 | 0.415258 | ||||||||
\(376\) | 5.47505 | 0.282354 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −41.9223 | −2.15625 | ||||||||
\(379\) | −28.4806 | −1.46295 | −0.731476 | − | 0.681867i | \(-0.761168\pi\) | ||||
−0.731476 | + | 0.681867i | \(0.761168\pi\) | |||||||
\(380\) | 5.85411 | 0.300310 | ||||||||
\(381\) | 16.3465 | 0.837459 | ||||||||
\(382\) | −21.6131 | −1.10582 | ||||||||
\(383\) | 10.6706 | 0.545240 | 0.272620 | − | 0.962122i | \(-0.412110\pi\) | ||||
0.272620 | + | 0.962122i | \(0.412110\pi\) | |||||||
\(384\) | 11.1068 | 0.566792 | ||||||||
\(385\) | −18.4230 | −0.938924 | ||||||||
\(386\) | 12.2488 | 0.623449 | ||||||||
\(387\) | 10.0112 | 0.508898 | ||||||||
\(388\) | −0.0867201 | −0.00440254 | ||||||||
\(389\) | 14.5072 | 0.735545 | 0.367773 | − | 0.929916i | \(-0.380120\pi\) | ||||
0.367773 | + | 0.929916i | \(0.380120\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.34751 | 0.0681466 | ||||||||
\(392\) | 16.5963 | 0.838241 | ||||||||
\(393\) | 19.1712 | 0.967058 | ||||||||
\(394\) | −4.61104 | −0.232301 | ||||||||
\(395\) | 6.46732 | 0.325406 | ||||||||
\(396\) | 12.0630 | 0.606190 | ||||||||
\(397\) | 30.7256 | 1.54207 | 0.771037 | − | 0.636790i | \(-0.219738\pi\) | ||||
0.771037 | + | 0.636790i | \(0.219738\pi\) | |||||||
\(398\) | 9.11557 | 0.456922 | ||||||||
\(399\) | −29.4794 | −1.47581 | ||||||||
\(400\) | 21.7397 | 1.08699 | ||||||||
\(401\) | −31.0341 | −1.54977 | −0.774885 | − | 0.632102i | \(-0.782192\pi\) | ||||
−0.774885 | + | 0.632102i | \(0.782192\pi\) | |||||||
\(402\) | −16.9604 | −0.845910 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.93372 | 0.0962063 | ||||||||
\(405\) | −0.417951 | −0.0207681 | ||||||||
\(406\) | −38.2487 | −1.89825 | ||||||||
\(407\) | −34.6326 | −1.71667 | ||||||||
\(408\) | 1.74798 | 0.0865377 | ||||||||
\(409\) | −1.81236 | −0.0896156 | −0.0448078 | − | 0.998996i | \(-0.514268\pi\) | ||||
−0.0448078 | + | 0.998996i | \(0.514268\pi\) | |||||||
\(410\) | 16.3346 | 0.806708 | ||||||||
\(411\) | −1.70795 | −0.0842471 | ||||||||
\(412\) | 6.01887 | 0.296528 | ||||||||
\(413\) | −37.9269 | −1.86626 | ||||||||
\(414\) | −3.67781 | −0.180755 | ||||||||
\(415\) | −9.91142 | −0.486532 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.7489 | −0.918139 | ||||||||
\(418\) | 59.2916 | 2.90005 | ||||||||
\(419\) | −18.5901 | −0.908187 | −0.454094 | − | 0.890954i | \(-0.650037\pi\) | ||||
−0.454094 | + | 0.890954i | \(0.650037\pi\) | |||||||
\(420\) | −4.71032 | −0.229840 | ||||||||
\(421\) | −5.36839 | −0.261639 | −0.130820 | − | 0.991406i | \(-0.541761\pi\) | ||||
−0.130820 | + | 0.991406i | \(0.541761\pi\) | |||||||
\(422\) | −20.7677 | −1.01095 | ||||||||
\(423\) | −7.20437 | −0.350288 | ||||||||
\(424\) | 1.70166 | 0.0826397 | ||||||||
\(425\) | 5.15875 | 0.250236 | ||||||||
\(426\) | 7.67413 | 0.371813 | ||||||||
\(427\) | 4.28821 | 0.207521 | ||||||||
\(428\) | −15.5032 | −0.749375 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.86242 | 0.379160 | ||||||||
\(431\) | −22.4260 | −1.08022 | −0.540111 | − | 0.841594i | \(-0.681618\pi\) | ||||
−0.540111 | + | 0.841594i | \(0.681618\pi\) | |||||||
\(432\) | −26.0995 | −1.25571 | ||||||||
\(433\) | −13.2953 | −0.638930 | −0.319465 | − | 0.947598i | \(-0.603503\pi\) | ||||
−0.319465 | + | 0.947598i | \(0.603503\pi\) | |||||||
\(434\) | −7.92826 | −0.380569 | ||||||||
\(435\) | −4.12515 | −0.197786 | ||||||||
\(436\) | −8.56965 | −0.410412 | ||||||||
\(437\) | −6.96372 | −0.333120 | ||||||||
\(438\) | −8.74161 | −0.417690 | ||||||||
\(439\) | −31.6140 | −1.50885 | −0.754426 | − | 0.656385i | \(-0.772085\pi\) | ||||
−0.754426 | + | 0.656385i | \(0.772085\pi\) | |||||||
\(440\) | −5.64530 | −0.269129 | ||||||||
\(441\) | −21.8384 | −1.03992 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.6865 | 1.26791 | 0.633957 | − | 0.773368i | \(-0.281430\pi\) | ||||
0.633957 | + | 0.773368i | \(0.281430\pi\) | |||||||
\(444\) | −8.85471 | −0.420226 | ||||||||
\(445\) | 8.35075 | 0.395863 | ||||||||
\(446\) | 10.4440 | 0.494535 | ||||||||
\(447\) | 10.2312 | 0.483920 | ||||||||
\(448\) | −5.83258 | −0.275564 | ||||||||
\(449\) | 19.8020 | 0.934512 | 0.467256 | − | 0.884122i | \(-0.345243\pi\) | ||||
0.467256 | + | 0.884122i | \(0.345243\pi\) | |||||||
\(450\) | −14.0800 | −0.663736 | ||||||||
\(451\) | 63.7317 | 3.00101 | ||||||||
\(452\) | −8.74483 | −0.411322 | ||||||||
\(453\) | 24.0480 | 1.12987 | ||||||||
\(454\) | 20.2471 | 0.950246 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.03326 | −0.423021 | ||||||||
\(457\) | −22.2437 | −1.04052 | −0.520258 | − | 0.854009i | \(-0.674164\pi\) | ||||
−0.520258 | + | 0.854009i | \(0.674164\pi\) | |||||||
\(458\) | −47.0257 | −2.19737 | ||||||||
\(459\) | −6.19331 | −0.289079 | ||||||||
\(460\) | −1.11269 | −0.0518794 | ||||||||
\(461\) | −5.25642 | −0.244816 | −0.122408 | − | 0.992480i | \(-0.539062\pi\) | ||||
−0.122408 | + | 0.992480i | \(0.539062\pi\) | |||||||
\(462\) | −47.7071 | −2.21954 | ||||||||
\(463\) | −1.95426 | −0.0908223 | −0.0454112 | − | 0.998968i | \(-0.514460\pi\) | ||||
−0.0454112 | + | 0.998968i | \(0.514460\pi\) | |||||||
\(464\) | −23.8124 | −1.10546 | ||||||||
\(465\) | −0.855069 | −0.0396529 | ||||||||
\(466\) | 5.66468 | 0.262411 | ||||||||
\(467\) | −32.8358 | −1.51946 | −0.759730 | − | 0.650239i | \(-0.774669\pi\) | ||||
−0.759730 | + | 0.650239i | \(0.774669\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −37.3051 | −1.72259 | ||||||||
\(470\) | −5.65804 | −0.260986 | ||||||||
\(471\) | −25.1561 | −1.15913 | ||||||||
\(472\) | −11.6218 | −0.534936 | ||||||||
\(473\) | 30.6763 | 1.41050 | ||||||||
\(474\) | 16.7474 | 0.769232 | ||||||||
\(475\) | −26.6596 | −1.22323 | ||||||||
\(476\) | −6.45216 | −0.295734 | ||||||||
\(477\) | −2.23913 | −0.102523 | ||||||||
\(478\) | −19.7903 | −0.905189 | ||||||||
\(479\) | 14.0568 | 0.642270 | 0.321135 | − | 0.947033i | \(-0.395936\pi\) | ||||
0.321135 | + | 0.947033i | \(0.395936\pi\) | |||||||
\(480\) | −5.30897 | −0.242320 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 11.9775 | 0.545562 | ||||||||
\(483\) | 5.60314 | 0.254951 | ||||||||
\(484\) | 23.1780 | 1.05355 | ||||||||
\(485\) | −0.0534021 | −0.00242487 | ||||||||
\(486\) | 27.5295 | 1.24877 | ||||||||
\(487\) | 7.66454 | 0.347313 | 0.173657 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(488\) | 1.31402 | 0.0594829 | ||||||||
\(489\) | 4.04446 | 0.182897 | ||||||||
\(490\) | −17.1510 | −0.774804 | ||||||||
\(491\) | −33.8981 | −1.52980 | −0.764901 | − | 0.644148i | \(-0.777212\pi\) | ||||
−0.764901 | + | 0.644148i | \(0.777212\pi\) | |||||||
\(492\) | 16.2947 | 0.734620 | ||||||||
\(493\) | −5.65059 | −0.254490 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.42840 | 0.333882 | ||||||||
\(496\) | −4.93588 | −0.221627 | ||||||||
\(497\) | 16.8795 | 0.757149 | ||||||||
\(498\) | −25.6660 | −1.15012 | ||||||||
\(499\) | −31.4186 | −1.40649 | −0.703245 | − | 0.710947i | \(-0.748266\pi\) | ||||
−0.703245 | + | 0.710947i | \(0.748266\pi\) | |||||||
\(500\) | −9.09555 | −0.406765 | ||||||||
\(501\) | −23.1271 | −1.03324 | ||||||||
\(502\) | 21.9929 | 0.981591 | ||||||||
\(503\) | −16.8502 | −0.751311 | −0.375656 | − | 0.926759i | \(-0.622582\pi\) | ||||
−0.375656 | + | 0.926759i | \(0.622582\pi\) | |||||||
\(504\) | −10.4936 | −0.467421 | ||||||||
\(505\) | 1.19078 | 0.0529892 | ||||||||
\(506\) | −11.2695 | −0.500992 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.4893 | −0.820332 | ||||||||
\(509\) | 23.7192 | 1.05134 | 0.525668 | − | 0.850690i | \(-0.323815\pi\) | ||||
0.525668 | + | 0.850690i | \(0.323815\pi\) | |||||||
\(510\) | −1.80640 | −0.0799886 | ||||||||
\(511\) | −19.2275 | −0.850573 | ||||||||
\(512\) | −17.3493 | −0.766740 | ||||||||
\(513\) | 32.0060 | 1.41310 | ||||||||
\(514\) | −34.0412 | −1.50149 | ||||||||
\(515\) | 3.70641 | 0.163324 | ||||||||
\(516\) | 7.84320 | 0.345278 | ||||||||
\(517\) | −22.0756 | −0.970884 | ||||||||
\(518\) | −50.5580 | −2.22139 | ||||||||
\(519\) | 8.99458 | 0.394818 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.07286 | 0.353678 | 0.176839 | − | 0.984240i | \(-0.443413\pi\) | ||||
0.176839 | + | 0.984240i | \(0.443413\pi\) | |||||||
\(522\) | 15.4223 | 0.675018 | ||||||||
\(523\) | 32.9375 | 1.44026 | 0.720128 | − | 0.693841i | \(-0.244083\pi\) | ||||
0.720128 | + | 0.693841i | \(0.244083\pi\) | |||||||
\(524\) | −21.6843 | −0.947281 | ||||||||
\(525\) | 21.4508 | 0.936189 | ||||||||
\(526\) | 13.1379 | 0.572841 | ||||||||
\(527\) | −1.17127 | −0.0510211 | ||||||||
\(528\) | −29.7009 | −1.29257 | ||||||||
\(529\) | −21.6764 | −0.942452 | ||||||||
\(530\) | −1.75853 | −0.0763856 | ||||||||
\(531\) | 15.2926 | 0.663642 | ||||||||
\(532\) | 33.3437 | 1.44563 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 21.6246 | 0.935787 | ||||||||
\(535\) | −9.54685 | −0.412746 | ||||||||
\(536\) | −11.4313 | −0.493755 | ||||||||
\(537\) | −25.6194 | −1.10556 | ||||||||
\(538\) | 32.5526 | 1.40344 | ||||||||
\(539\) | −66.9171 | −2.88232 | ||||||||
\(540\) | 5.11404 | 0.220073 | ||||||||
\(541\) | 22.2562 | 0.956871 | 0.478435 | − | 0.878123i | \(-0.341204\pi\) | ||||
0.478435 | + | 0.878123i | \(0.341204\pi\) | |||||||
\(542\) | 1.58863 | 0.0682376 | ||||||||
\(543\) | −9.16922 | −0.393489 | ||||||||
\(544\) | −7.27217 | −0.311792 | ||||||||
\(545\) | −5.27718 | −0.226050 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.321415 | −0.0137427 | −0.00687136 | − | 0.999976i | \(-0.502187\pi\) | ||||
−0.00687136 | + | 0.999976i | \(0.502187\pi\) | |||||||
\(548\) | 1.93184 | 0.0825242 | ||||||||
\(549\) | −1.72906 | −0.0737945 | ||||||||
\(550\) | −43.1438 | −1.83966 | ||||||||
\(551\) | 29.2013 | 1.24402 | ||||||||
\(552\) | 1.71695 | 0.0730782 | ||||||||
\(553\) | 36.8364 | 1.56644 | ||||||||
\(554\) | −38.5165 | −1.63641 | ||||||||
\(555\) | −5.45272 | −0.231455 | ||||||||
\(556\) | 21.2066 | 0.899362 | ||||||||
\(557\) | −32.8068 | −1.39007 | −0.695034 | − | 0.718977i | \(-0.744611\pi\) | ||||
−0.695034 | + | 0.718977i | \(0.744611\pi\) | |||||||
\(558\) | 3.19678 | 0.135330 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −16.7438 | −0.707553 | ||||||||
\(561\) | −7.04791 | −0.297563 | ||||||||
\(562\) | 30.6506 | 1.29292 | ||||||||
\(563\) | 13.1109 | 0.552557 | 0.276278 | − | 0.961078i | \(-0.410899\pi\) | ||||
0.276278 | + | 0.961078i | \(0.410899\pi\) | |||||||
\(564\) | −5.64420 | −0.237664 | ||||||||
\(565\) | −5.38506 | −0.226551 | ||||||||
\(566\) | 36.1079 | 1.51773 | ||||||||
\(567\) | −2.38055 | −0.0999738 | ||||||||
\(568\) | 5.17232 | 0.217026 | ||||||||
\(569\) | −7.92078 | −0.332056 | −0.166028 | − | 0.986121i | \(-0.553094\pi\) | ||||
−0.166028 | + | 0.986121i | \(0.553094\pi\) | |||||||
\(570\) | 9.33517 | 0.391007 | ||||||||
\(571\) | 25.1527 | 1.05261 | 0.526304 | − | 0.850297i | \(-0.323578\pi\) | ||||
0.526304 | + | 0.850297i | \(0.323578\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.2768 | −0.554646 | ||||||||
\(574\) | 93.0382 | 3.88334 | ||||||||
\(575\) | 5.06718 | 0.211316 | ||||||||
\(576\) | 2.35177 | 0.0979905 | ||||||||
\(577\) | −8.99328 | −0.374395 | −0.187198 | − | 0.982322i | \(-0.559940\pi\) | ||||
−0.187198 | + | 0.982322i | \(0.559940\pi\) | |||||||
\(578\) | 28.1880 | 1.17247 | ||||||||
\(579\) | 7.52438 | 0.312702 | ||||||||
\(580\) | 4.66590 | 0.193741 | ||||||||
\(581\) | −56.4532 | −2.34207 | ||||||||
\(582\) | −0.138287 | −0.00573217 | ||||||||
\(583\) | −6.86115 | −0.284160 | ||||||||
\(584\) | −5.89180 | −0.243804 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 48.1730 | 1.99001 | ||||||||
\(587\) | −5.36014 | −0.221237 | −0.110618 | − | 0.993863i | \(-0.535283\pi\) | ||||
−0.110618 | + | 0.993863i | \(0.535283\pi\) | |||||||
\(588\) | −17.1091 | −0.705567 | ||||||||
\(589\) | 6.05291 | 0.249406 | ||||||||
\(590\) | 12.0102 | 0.494453 | ||||||||
\(591\) | −2.83253 | −0.116515 | ||||||||
\(592\) | −31.4758 | −1.29365 | ||||||||
\(593\) | −15.8227 | −0.649759 | −0.324879 | − | 0.945755i | \(-0.605324\pi\) | ||||
−0.324879 | + | 0.945755i | \(0.605324\pi\) | |||||||
\(594\) | 51.7961 | 2.12522 | ||||||||
\(595\) | −3.97323 | −0.162887 | ||||||||
\(596\) | −11.5724 | −0.474023 | ||||||||
\(597\) | 5.59964 | 0.229178 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.5066 | 0.919593 | 0.459797 | − | 0.888024i | \(-0.347922\pi\) | ||||
0.459797 | + | 0.888024i | \(0.347922\pi\) | |||||||
\(600\) | 6.57309 | 0.268345 | ||||||||
\(601\) | −9.23527 | −0.376714 | −0.188357 | − | 0.982101i | \(-0.560316\pi\) | ||||
−0.188357 | + | 0.982101i | \(0.560316\pi\) | |||||||
\(602\) | 44.7826 | 1.82520 | ||||||||
\(603\) | 15.0419 | 0.612553 | ||||||||
\(604\) | −27.2003 | −1.10677 | ||||||||
\(605\) | 14.2730 | 0.580280 | ||||||||
\(606\) | 3.08358 | 0.125262 | ||||||||
\(607\) | 8.22103 | 0.333681 | 0.166841 | − | 0.985984i | \(-0.446643\pi\) | ||||
0.166841 | + | 0.985984i | \(0.446643\pi\) | |||||||
\(608\) | 37.5814 | 1.52413 | ||||||||
\(609\) | −23.4959 | −0.952102 | ||||||||
\(610\) | −1.35794 | −0.0549813 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.60159 | 0.105163 | ||||||||
\(613\) | 6.63476 | 0.267975 | 0.133988 | − | 0.990983i | \(-0.457222\pi\) | ||||
0.133988 | + | 0.990983i | \(0.457222\pi\) | |||||||
\(614\) | −48.6102 | −1.96175 | ||||||||
\(615\) | 10.0342 | 0.404620 | ||||||||
\(616\) | −32.1544 | −1.29554 | ||||||||
\(617\) | −24.2825 | −0.977576 | −0.488788 | − | 0.872403i | \(-0.662561\pi\) | ||||
−0.488788 | + | 0.872403i | \(0.662561\pi\) | |||||||
\(618\) | 9.59790 | 0.386084 | ||||||||
\(619\) | −6.89786 | −0.277248 | −0.138624 | − | 0.990345i | \(-0.544268\pi\) | ||||
−0.138624 | + | 0.990345i | \(0.544268\pi\) | |||||||
\(620\) | 0.967157 | 0.0388419 | ||||||||
\(621\) | −6.08338 | −0.244118 | ||||||||
\(622\) | 30.9315 | 1.24024 | ||||||||
\(623\) | 47.5640 | 1.90561 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.4211 | 0.656844 | ||||||||
\(626\) | 33.0007 | 1.31897 | ||||||||
\(627\) | 36.4225 | 1.45457 | ||||||||
\(628\) | 28.4537 | 1.13542 | ||||||||
\(629\) | −7.46909 | −0.297812 | ||||||||
\(630\) | 10.8443 | 0.432047 | ||||||||
\(631\) | −8.02010 | −0.319275 | −0.159638 | − | 0.987176i | \(-0.551033\pi\) | ||||
−0.159638 | + | 0.987176i | \(0.551033\pi\) | |||||||
\(632\) | 11.2877 | 0.448999 | ||||||||
\(633\) | −12.7574 | −0.507063 | ||||||||
\(634\) | 36.5784 | 1.45271 | ||||||||
\(635\) | −11.3857 | −0.451829 | ||||||||
\(636\) | −1.75423 | −0.0695597 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 47.2571 | 1.87093 | ||||||||
\(639\) | −6.80603 | −0.269242 | ||||||||
\(640\) | −7.73613 | −0.305797 | ||||||||
\(641\) | −31.1453 | −1.23016 | −0.615082 | − | 0.788463i | \(-0.710877\pi\) | ||||
−0.615082 | + | 0.788463i | \(0.710877\pi\) | |||||||
\(642\) | −24.7219 | −0.975697 | ||||||||
\(643\) | −26.6445 | −1.05076 | −0.525378 | − | 0.850869i | \(-0.676076\pi\) | ||||
−0.525378 | + | 0.850869i | \(0.676076\pi\) | |||||||
\(644\) | −6.33763 | −0.249738 | ||||||||
\(645\) | 4.82984 | 0.190175 | ||||||||
\(646\) | 12.7872 | 0.503107 | ||||||||
\(647\) | −1.24485 | −0.0489402 | −0.0244701 | − | 0.999701i | \(-0.507790\pi\) | ||||
−0.0244701 | + | 0.999701i | \(0.507790\pi\) | |||||||
\(648\) | −0.729465 | −0.0286561 | ||||||||
\(649\) | 46.8596 | 1.83940 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.87028 | −0.190881 | ||||||||
\(652\) | −4.57463 | −0.179156 | ||||||||
\(653\) | 18.3460 | 0.717936 | 0.358968 | − | 0.933350i | \(-0.383129\pi\) | ||||
0.358968 | + | 0.933350i | \(0.383129\pi\) | |||||||
\(654\) | −13.6655 | −0.534362 | ||||||||
\(655\) | −13.3531 | −0.521751 | ||||||||
\(656\) | 57.9226 | 2.26150 | ||||||||
\(657\) | 7.75276 | 0.302464 | ||||||||
\(658\) | −32.2269 | −1.25634 | ||||||||
\(659\) | 16.3726 | 0.637785 | 0.318893 | − | 0.947791i | \(-0.396689\pi\) | ||||
0.318893 | + | 0.947791i | \(0.396689\pi\) | |||||||
\(660\) | 5.81972 | 0.226532 | ||||||||
\(661\) | −20.7767 | −0.808121 | −0.404060 | − | 0.914732i | \(-0.632401\pi\) | ||||
−0.404060 | + | 0.914732i | \(0.632401\pi\) | |||||||
\(662\) | 53.8701 | 2.09372 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.2988 | −0.671322 | ||||||||
\(665\) | 20.5330 | 0.796237 | ||||||||
\(666\) | 20.3857 | 0.789928 | ||||||||
\(667\) | −5.55029 | −0.214908 | ||||||||
\(668\) | 26.1588 | 1.01211 | ||||||||
\(669\) | 6.41565 | 0.248044 | ||||||||
\(670\) | 11.8133 | 0.456388 | ||||||||
\(671\) | −5.29818 | −0.204534 | ||||||||
\(672\) | −30.2387 | −1.16648 | ||||||||
\(673\) | 13.3140 | 0.513216 | 0.256608 | − | 0.966516i | \(-0.417395\pi\) | ||||
0.256608 | + | 0.966516i | \(0.417395\pi\) | |||||||
\(674\) | 46.3259 | 1.78441 | ||||||||
\(675\) | −23.2893 | −0.896406 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.58632 | 0.368432 | 0.184216 | − | 0.982886i | \(-0.441025\pi\) | ||||
0.184216 | + | 0.982886i | \(0.441025\pi\) | |||||||
\(678\) | −13.9448 | −0.535547 | ||||||||
\(679\) | −0.304167 | −0.0116728 | ||||||||
\(680\) | −1.21750 | −0.0466891 | ||||||||
\(681\) | 12.4377 | 0.476614 | ||||||||
\(682\) | 9.79556 | 0.375091 | ||||||||
\(683\) | 23.3627 | 0.893947 | 0.446974 | − | 0.894547i | \(-0.352502\pi\) | ||||
0.446974 | + | 0.894547i | \(0.352502\pi\) | |||||||
\(684\) | −13.4446 | −0.514068 | ||||||||
\(685\) | 1.18963 | 0.0454533 | ||||||||
\(686\) | −42.1905 | −1.61084 | ||||||||
\(687\) | −28.8876 | −1.10213 | ||||||||
\(688\) | 27.8802 | 1.06292 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.77433 | −0.0675477 | ||||||||
\(691\) | 5.49572 | 0.209067 | 0.104534 | − | 0.994521i | \(-0.466665\pi\) | ||||
0.104534 | + | 0.994521i | \(0.466665\pi\) | |||||||
\(692\) | −10.1736 | −0.386744 | ||||||||
\(693\) | 42.3105 | 1.60724 | ||||||||
\(694\) | −7.84618 | −0.297837 | ||||||||
\(695\) | 13.0590 | 0.495357 | ||||||||
\(696\) | −7.19977 | −0.272907 | ||||||||
\(697\) | 13.7448 | 0.520622 | ||||||||
\(698\) | 8.98932 | 0.340251 | ||||||||
\(699\) | 3.47977 | 0.131617 | ||||||||
\(700\) | −24.2627 | −0.917043 | ||||||||
\(701\) | 43.4482 | 1.64101 | 0.820507 | − | 0.571636i | \(-0.193691\pi\) | ||||
0.820507 | + | 0.571636i | \(0.193691\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.5990 | 1.45579 | ||||||||
\(704\) | 7.20630 | 0.271598 | ||||||||
\(705\) | −3.47570 | −0.130902 | ||||||||
\(706\) | 17.3721 | 0.653808 | ||||||||
\(707\) | 6.78244 | 0.255080 | ||||||||
\(708\) | 11.9809 | 0.450268 | ||||||||
\(709\) | −2.98948 | −0.112272 | −0.0561361 | − | 0.998423i | \(-0.517878\pi\) | ||||
−0.0561361 | + | 0.998423i | \(0.517878\pi\) | |||||||
\(710\) | −5.34520 | −0.200602 | ||||||||
\(711\) | −14.8529 | −0.557028 | ||||||||
\(712\) | 14.5749 | 0.546216 | ||||||||
\(713\) | −1.15047 | −0.0430856 | ||||||||
\(714\) | −10.2888 | −0.385050 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 28.9778 | 1.08295 | ||||||||
\(717\) | −12.1571 | −0.454015 | ||||||||
\(718\) | −66.5348 | −2.48306 | ||||||||
\(719\) | −8.67861 | −0.323658 | −0.161829 | − | 0.986819i | \(-0.551739\pi\) | ||||
−0.161829 | + | 0.986819i | \(0.551739\pi\) | |||||||
\(720\) | 6.75130 | 0.251606 | ||||||||
\(721\) | 21.1109 | 0.786211 | ||||||||
\(722\) | −31.8126 | −1.18394 | ||||||||
\(723\) | 7.35773 | 0.273637 | ||||||||
\(724\) | 10.3712 | 0.385442 | ||||||||
\(725\) | −21.2485 | −0.789148 | ||||||||
\(726\) | 36.9605 | 1.37173 | ||||||||
\(727\) | −3.15935 | −0.117174 | −0.0585869 | − | 0.998282i | \(-0.518659\pi\) | ||||
−0.0585869 | + | 0.998282i | \(0.518659\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.5359 | 0.686517 | ||||||||
\(730\) | 6.08872 | 0.225354 | ||||||||
\(731\) | 6.61586 | 0.244697 | ||||||||
\(732\) | −1.35462 | −0.0500681 | ||||||||
\(733\) | −28.0004 | −1.03422 | −0.517109 | − | 0.855920i | \(-0.672992\pi\) | ||||
−0.517109 | + | 0.855920i | \(0.672992\pi\) | |||||||
\(734\) | 5.65115 | 0.208588 | ||||||||
\(735\) | −10.5358 | −0.388617 | ||||||||
\(736\) | −7.14309 | −0.263298 | ||||||||
\(737\) | 46.0913 | 1.69779 | ||||||||
\(738\) | −37.5142 | −1.38092 | ||||||||
\(739\) | 48.9381 | 1.80022 | 0.900109 | − | 0.435664i | \(-0.143487\pi\) | ||||
0.900109 | + | 0.435664i | \(0.143487\pi\) | |||||||
\(740\) | 6.16750 | 0.226722 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.0162 | −0.367706 | ||||||||
\(743\) | −15.1832 | −0.557019 | −0.278509 | − | 0.960434i | \(-0.589840\pi\) | ||||
−0.278509 | + | 0.960434i | \(0.589840\pi\) | |||||||
\(744\) | −1.49238 | −0.0547134 | ||||||||
\(745\) | −7.12626 | −0.261086 | ||||||||
\(746\) | 31.6465 | 1.15866 | ||||||||
\(747\) | 22.7627 | 0.832842 | ||||||||
\(748\) | 7.97180 | 0.291478 | ||||||||
\(749\) | −54.3767 | −1.98688 | ||||||||
\(750\) | −14.5041 | −0.529614 | ||||||||
\(751\) | 15.9198 | 0.580923 | 0.290462 | − | 0.956887i | \(-0.406191\pi\) | ||||
0.290462 | + | 0.956887i | \(0.406191\pi\) | |||||||
\(752\) | −20.0634 | −0.731638 | ||||||||
\(753\) | 13.5101 | 0.492335 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.7499 | −0.609593 | ||||||||
\(756\) | 29.1284 | 1.05939 | ||||||||
\(757\) | −22.5455 | −0.819431 | −0.409715 | − | 0.912213i | \(-0.634372\pi\) | ||||
−0.409715 | + | 0.912213i | \(0.634372\pi\) | |||||||
\(758\) | 51.3697 | 1.86583 | ||||||||
\(759\) | −6.92281 | −0.251282 | ||||||||
\(760\) | 6.29186 | 0.228230 | ||||||||
\(761\) | −19.7074 | −0.714392 | −0.357196 | − | 0.934029i | \(-0.616267\pi\) | ||||
−0.357196 | + | 0.934029i | \(0.616267\pi\) | |||||||
\(762\) | −29.4838 | −1.06808 | ||||||||
\(763\) | −30.0577 | −1.08816 | ||||||||
\(764\) | 15.0172 | 0.543303 | ||||||||
\(765\) | 1.60206 | 0.0579225 | ||||||||
\(766\) | −19.2462 | −0.695392 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −22.9734 | −0.828980 | ||||||||
\(769\) | −4.89356 | −0.176466 | −0.0882332 | − | 0.996100i | \(-0.528122\pi\) | ||||
−0.0882332 | + | 0.996100i | \(0.528122\pi\) | |||||||
\(770\) | 33.2290 | 1.19749 | ||||||||
\(771\) | −20.9113 | −0.753101 | ||||||||
\(772\) | −8.51072 | −0.306308 | ||||||||
\(773\) | −39.8265 | −1.43246 | −0.716231 | − | 0.697864i | \(-0.754134\pi\) | ||||
−0.716231 | + | 0.697864i | \(0.754134\pi\) | |||||||
\(774\) | −18.0569 | −0.649042 | ||||||||
\(775\) | −4.40443 | −0.158212 | ||||||||
\(776\) | −0.0932047 | −0.00334585 | ||||||||
\(777\) | −31.0575 | −1.11418 | ||||||||
\(778\) | −26.1662 | −0.938105 | ||||||||
\(779\) | −71.0310 | −2.54495 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.8550 | −0.746252 | ||||||||
\(782\) | −2.43047 | −0.0869133 | ||||||||
\(783\) | 25.5097 | 0.911644 | ||||||||
\(784\) | −60.8176 | −2.17206 | ||||||||
\(785\) | 17.5217 | 0.625378 | ||||||||
\(786\) | −34.5785 | −1.23337 | ||||||||
\(787\) | 26.2552 | 0.935896 | 0.467948 | − | 0.883756i | \(-0.344993\pi\) | ||||
0.467948 | + | 0.883756i | \(0.344993\pi\) | |||||||
\(788\) | 3.20384 | 0.114132 | ||||||||
\(789\) | 8.07056 | 0.287319 | ||||||||
\(790\) | −11.6649 | −0.415019 | ||||||||
\(791\) | −30.6721 | −1.09057 | ||||||||
\(792\) | 12.9651 | 0.460693 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −55.4188 | −1.96674 | ||||||||
\(795\) | −1.08025 | −0.0383126 | ||||||||
\(796\) | −6.33367 | −0.224491 | ||||||||
\(797\) | −16.3967 | −0.580800 | −0.290400 | − | 0.956905i | \(-0.593788\pi\) | ||||
−0.290400 | + | 0.956905i | \(0.593788\pi\) | |||||||
\(798\) | 53.1710 | 1.88223 | ||||||||
\(799\) | −4.76098 | −0.168431 | ||||||||
\(800\) | −27.3463 | −0.966837 | ||||||||
\(801\) | −19.1784 | −0.677636 | ||||||||
\(802\) | 55.9753 | 1.97656 | ||||||||
\(803\) | 23.7560 | 0.838331 | ||||||||
\(804\) | 11.7844 | 0.415605 | ||||||||
\(805\) | −3.90271 | −0.137552 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.9969 | 0.703924 | ||||||||
\(808\) | 2.07832 | 0.0731150 | ||||||||
\(809\) | −14.1592 | −0.497809 | −0.248905 | − | 0.968528i | \(-0.580071\pi\) | ||||
−0.248905 | + | 0.968528i | \(0.580071\pi\) | |||||||
\(810\) | 0.753845 | 0.0264874 | ||||||||
\(811\) | −20.7922 | −0.730114 | −0.365057 | − | 0.930985i | \(-0.618951\pi\) | ||||
−0.365057 | + | 0.930985i | \(0.618951\pi\) | |||||||
\(812\) | 26.5759 | 0.932631 | ||||||||
\(813\) | 0.975887 | 0.0342259 | ||||||||
\(814\) | 62.4657 | 2.18942 | ||||||||
\(815\) | −2.81705 | −0.0986771 | ||||||||
\(816\) | −6.40550 | −0.224237 | ||||||||
\(817\) | −34.1897 | −1.19615 | ||||||||
\(818\) | 3.26891 | 0.114295 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.3496 | −0.396345 | ||||||||
\(821\) | −26.8337 | −0.936502 | −0.468251 | − | 0.883596i | \(-0.655116\pi\) | ||||
−0.468251 | + | 0.883596i | \(0.655116\pi\) | |||||||
\(822\) | 3.08058 | 0.107448 | ||||||||
\(823\) | 1.19210 | 0.0415542 | 0.0207771 | − | 0.999784i | \(-0.493386\pi\) | ||||
0.0207771 | + | 0.999784i | \(0.493386\pi\) | |||||||
\(824\) | 6.46894 | 0.225356 | ||||||||
\(825\) | −26.5030 | −0.922715 | ||||||||
\(826\) | 68.4075 | 2.38020 | ||||||||
\(827\) | −8.94631 | −0.311094 | −0.155547 | − | 0.987829i | \(-0.549714\pi\) | ||||
−0.155547 | + | 0.987829i | \(0.549714\pi\) | |||||||
\(828\) | 2.55541 | 0.0888068 | ||||||||
\(829\) | −47.7351 | −1.65791 | −0.828955 | − | 0.559315i | \(-0.811064\pi\) | ||||
−0.828955 | + | 0.559315i | \(0.811064\pi\) | |||||||
\(830\) | 17.8769 | 0.620517 | ||||||||
\(831\) | −23.6605 | −0.820772 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.4318 | −0.500032 | ||||||||
\(834\) | 33.8169 | 1.17098 | ||||||||
\(835\) | 16.1085 | 0.557459 | ||||||||
\(836\) | −41.1970 | −1.42483 | ||||||||
\(837\) | 5.28771 | 0.182770 | ||||||||
\(838\) | 33.5304 | 1.15829 | ||||||||
\(839\) | −49.2176 | −1.69918 | −0.849591 | − | 0.527442i | \(-0.823151\pi\) | ||||
−0.849591 | + | 0.527442i | \(0.823151\pi\) | |||||||
\(840\) | −5.06255 | −0.174674 | ||||||||
\(841\) | −5.72570 | −0.197438 | ||||||||
\(842\) | 9.68281 | 0.333692 | ||||||||
\(843\) | 18.8285 | 0.648487 | ||||||||
\(844\) | 14.4298 | 0.496693 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.9943 | 0.446753 | ||||||||
\(847\) | 81.2959 | 2.79336 | ||||||||
\(848\) | −6.23575 | −0.214137 | ||||||||
\(849\) | 22.1808 | 0.761244 | ||||||||
\(850\) | −9.30468 | −0.319148 | ||||||||
\(851\) | −7.33651 | −0.251492 | ||||||||
\(852\) | −5.33213 | −0.182676 | ||||||||
\(853\) | −46.8047 | −1.60256 | −0.801281 | − | 0.598288i | \(-0.795848\pi\) | ||||
−0.801281 | + | 0.598288i | \(0.795848\pi\) | |||||||
\(854\) | −7.73451 | −0.264669 | ||||||||
\(855\) | −8.27918 | −0.283142 | ||||||||
\(856\) | −16.6625 | −0.569511 | ||||||||
\(857\) | −26.2083 | −0.895257 | −0.447629 | − | 0.894220i | \(-0.647731\pi\) | ||||
−0.447629 | + | 0.894220i | \(0.647731\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.6143 | 1.35162 | 0.675812 | − | 0.737074i | \(-0.263793\pi\) | ||||
0.675812 | + | 0.737074i | \(0.263793\pi\) | |||||||
\(860\) | −5.46296 | −0.186285 | ||||||||
\(861\) | 57.1528 | 1.94776 | ||||||||
\(862\) | 40.4491 | 1.37770 | ||||||||
\(863\) | 57.2856 | 1.95003 | 0.975013 | − | 0.222149i | \(-0.0713072\pi\) | ||||
0.975013 | + | 0.222149i | \(0.0713072\pi\) | |||||||
\(864\) | 32.8304 | 1.11691 | ||||||||
\(865\) | −6.26492 | −0.213014 | ||||||||
\(866\) | 23.9803 | 0.814883 | ||||||||
\(867\) | 17.3157 | 0.588072 | ||||||||
\(868\) | 5.50871 | 0.186978 | ||||||||
\(869\) | −45.5123 | −1.54390 | ||||||||
\(870\) | 7.44040 | 0.252253 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −9.21046 | −0.311906 | ||||||||
\(873\) | 0.122644 | 0.00415087 | ||||||||
\(874\) | 12.5603 | 0.424857 | ||||||||
\(875\) | −31.9022 | −1.07849 | ||||||||
\(876\) | 6.07384 | 0.205216 | ||||||||
\(877\) | −48.8415 | −1.64926 | −0.824630 | − | 0.565672i | \(-0.808617\pi\) | ||||
−0.824630 | + | 0.565672i | \(0.808617\pi\) | |||||||
\(878\) | 57.0211 | 1.92437 | ||||||||
\(879\) | 29.5923 | 0.998125 | ||||||||
\(880\) | 20.6873 | 0.697370 | ||||||||
\(881\) | −31.1046 | −1.04794 | −0.523971 | − | 0.851736i | \(-0.675550\pi\) | ||||
−0.523971 | + | 0.851736i | \(0.675550\pi\) | |||||||
\(882\) | 39.3892 | 1.32630 | ||||||||
\(883\) | 32.2081 | 1.08389 | 0.541945 | − | 0.840414i | \(-0.317688\pi\) | ||||
0.541945 | + | 0.840414i | \(0.317688\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.37780 | 0.248002 | ||||||||
\(886\) | −48.1336 | −1.61708 | ||||||||
\(887\) | −19.7522 | −0.663213 | −0.331607 | − | 0.943418i | \(-0.607591\pi\) | ||||
−0.331607 | + | 0.943418i | \(0.607591\pi\) | |||||||
\(888\) | −9.51684 | −0.319364 | ||||||||
\(889\) | −64.8505 | −2.17502 | ||||||||
\(890\) | −15.0620 | −0.504879 | ||||||||
\(891\) | 2.94123 | 0.0985350 | ||||||||
\(892\) | −7.25666 | −0.242971 | ||||||||
\(893\) | 24.6040 | 0.823340 | ||||||||
\(894\) | −18.4537 | −0.617185 | ||||||||
\(895\) | 17.8445 | 0.596476 | ||||||||
\(896\) | −44.0633 | −1.47205 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35.7162 | −1.19186 | ||||||||
\(899\) | 4.82434 | 0.160901 | ||||||||
\(900\) | 9.78303 | 0.326101 | ||||||||
\(901\) | −1.47972 | −0.0492966 | ||||||||
\(902\) | −114.951 | −3.82745 | ||||||||
\(903\) | 27.5097 | 0.915464 | ||||||||
\(904\) | −9.39874 | −0.312597 | ||||||||
\(905\) | 6.38656 | 0.212297 | ||||||||
\(906\) | −43.3746 | −1.44103 | ||||||||
\(907\) | 44.9806 | 1.49356 | 0.746778 | − | 0.665073i | \(-0.231600\pi\) | ||||
0.746778 | + | 0.665073i | \(0.231600\pi\) | |||||||
\(908\) | −14.0681 | −0.466866 | ||||||||
\(909\) | −2.73477 | −0.0907065 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.7942 | −0.821469 | −0.410735 | − | 0.911755i | \(-0.634728\pi\) | ||||
−0.410735 | + | 0.911755i | \(0.634728\pi\) | |||||||
\(912\) | 33.1026 | 1.09614 | ||||||||
\(913\) | 69.7493 | 2.30836 | ||||||||
\(914\) | 40.1203 | 1.32706 | ||||||||
\(915\) | −0.834173 | −0.0275769 | ||||||||
\(916\) | 32.6743 | 1.07959 | ||||||||
\(917\) | −76.0565 | −2.51161 | ||||||||
\(918\) | 11.1707 | 0.368688 | ||||||||
\(919\) | −51.7865 | −1.70828 | −0.854140 | − | 0.520044i | \(-0.825916\pi\) | ||||
−0.854140 | + | 0.520044i | \(0.825916\pi\) | |||||||
\(920\) | −1.19589 | −0.0394274 | ||||||||
\(921\) | −29.8610 | −0.983952 | ||||||||
\(922\) | 9.48084 | 0.312235 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 33.1478 | 1.09048 | ||||||||
\(925\) | −28.0868 | −0.923487 | ||||||||
\(926\) | 3.52485 | 0.115834 | ||||||||
\(927\) | −8.51219 | −0.279577 | ||||||||
\(928\) | 29.9535 | 0.983271 | ||||||||
\(929\) | −28.3489 | −0.930096 | −0.465048 | − | 0.885285i | \(-0.653963\pi\) | ||||
−0.465048 | + | 0.885285i | \(0.653963\pi\) | |||||||
\(930\) | 1.54226 | 0.0505728 | ||||||||
\(931\) | 74.5811 | 2.44430 | ||||||||
\(932\) | −3.93593 | −0.128926 | ||||||||
\(933\) | 19.0010 | 0.622066 | ||||||||
\(934\) | 59.2249 | 1.93790 | ||||||||
\(935\) | 4.90903 | 0.160542 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.21095 | 0.0722287 | 0.0361143 | − | 0.999348i | \(-0.488502\pi\) | ||||
0.0361143 | + | 0.999348i | \(0.488502\pi\) | |||||||
\(938\) | 67.2860 | 2.19697 | ||||||||
\(939\) | 20.2721 | 0.661555 | ||||||||
\(940\) | 3.93131 | 0.128225 | ||||||||
\(941\) | −22.2919 | −0.726694 | −0.363347 | − | 0.931654i | \(-0.618366\pi\) | ||||
−0.363347 | + | 0.931654i | \(0.618366\pi\) | |||||||
\(942\) | 45.3732 | 1.47834 | ||||||||
\(943\) | 13.5008 | 0.439648 | ||||||||
\(944\) | 42.5883 | 1.38613 | ||||||||
\(945\) | 17.9373 | 0.583499 | ||||||||
\(946\) | −55.3300 | −1.79893 | ||||||||
\(947\) | 14.2509 | 0.463092 | 0.231546 | − | 0.972824i | \(-0.425622\pi\) | ||||
0.231546 | + | 0.972824i | \(0.425622\pi\) | |||||||
\(948\) | −11.6364 | −0.377933 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 48.0851 | 1.56009 | ||||||||
\(951\) | 22.4699 | 0.728636 | ||||||||
\(952\) | −6.93463 | −0.224753 | ||||||||
\(953\) | 39.6157 | 1.28328 | 0.641639 | − | 0.767007i | \(-0.278255\pi\) | ||||
0.641639 | + | 0.767007i | \(0.278255\pi\) | |||||||
\(954\) | 4.03865 | 0.130756 | ||||||||
\(955\) | 9.24758 | 0.299245 | ||||||||
\(956\) | 13.7507 | 0.444730 | ||||||||
\(957\) | 29.0298 | 0.938399 | ||||||||
\(958\) | −25.3538 | −0.819143 | ||||||||
\(959\) | 6.77585 | 0.218803 | ||||||||
\(960\) | 1.13460 | 0.0366189 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.9254 | 0.706536 | ||||||||
\(964\) | −8.32222 | −0.268041 | ||||||||
\(965\) | −5.24089 | −0.168710 | ||||||||
\(966\) | −10.1062 | −0.325162 | ||||||||
\(967\) | 35.4974 | 1.14152 | 0.570760 | − | 0.821117i | \(-0.306649\pi\) | ||||
0.570760 | + | 0.821117i | \(0.306649\pi\) | |||||||
\(968\) | 24.9112 | 0.800677 | ||||||||
\(969\) | 7.85512 | 0.252343 | ||||||||
\(970\) | 0.0963198 | 0.00309264 | ||||||||
\(971\) | −5.93044 | −0.190317 | −0.0951584 | − | 0.995462i | \(-0.530336\pi\) | ||||
−0.0951584 | + | 0.995462i | \(0.530336\pi\) | |||||||
\(972\) | −19.1281 | −0.613533 | ||||||||
\(973\) | 74.3813 | 2.38456 | ||||||||
\(974\) | −13.8243 | −0.442959 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.81525 | −0.154133 | ||||||||
\(977\) | −10.4010 | −0.332758 | −0.166379 | − | 0.986062i | \(-0.553208\pi\) | ||||
−0.166379 | + | 0.986062i | \(0.553208\pi\) | |||||||
\(978\) | −7.29487 | −0.233264 | ||||||||
\(979\) | −58.7665 | −1.87818 | ||||||||
\(980\) | 11.9169 | 0.380670 | ||||||||
\(981\) | 12.1196 | 0.386950 | ||||||||
\(982\) | 61.1410 | 1.95109 | ||||||||
\(983\) | −21.6354 | −0.690062 | −0.345031 | − | 0.938591i | \(-0.612132\pi\) | ||||
−0.345031 | + | 0.938591i | \(0.612132\pi\) | |||||||
\(984\) | 17.5131 | 0.558298 | ||||||||
\(985\) | 1.97292 | 0.0628625 | ||||||||
\(986\) | 10.1918 | 0.324573 | ||||||||
\(987\) | −19.7968 | −0.630139 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.49843 | 0.206638 | ||||||||
\(990\) | −13.3984 | −0.425828 | ||||||||
\(991\) | 26.4991 | 0.841772 | 0.420886 | − | 0.907114i | \(-0.361719\pi\) | ||||
0.420886 | + | 0.907114i | \(0.361719\pi\) | |||||||
\(992\) | 6.20882 | 0.197130 | ||||||||
\(993\) | 33.0920 | 1.05014 | ||||||||
\(994\) | −30.4450 | −0.965658 | ||||||||
\(995\) | −3.90027 | −0.123647 | ||||||||
\(996\) | 17.8332 | 0.565067 | ||||||||
\(997\) | 15.2917 | 0.484293 | 0.242147 | − | 0.970240i | \(-0.422149\pi\) | ||||
0.242147 | + | 0.970240i | \(0.422149\pi\) | |||||||
\(998\) | 56.6688 | 1.79382 | ||||||||
\(999\) | 33.7194 | 1.06683 |
(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 | 5239.2.a.q.1.10 | 34 | ||
13.2 | odd | 12 | 403.2.r.a.342.8 | yes | 68 | ||
13.7 | odd | 12 | 403.2.r.a.218.8 | ✓ | 68 | ||
13.12 | even | 2 | 5239.2.a.r.1.25 | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.r.a.218.8 | ✓ | 68 | 13.7 | odd | 12 | ||
403.2.r.a.342.8 | yes | 68 | 13.2 | odd | 12 | ||
5239.2.a.q.1.10 | 34 | 1.1 | even | 1 | trivial | ||
5239.2.a.r.1.25 | 34 | 13.12 | even | 2 |