Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.10999 | −0.640856 | −0.320428 | − | 0.947273i | \(-0.603827\pi\) | ||||
−0.320428 | + | 0.947273i | \(0.603827\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.90024 | 1.74424 | 0.872120 | − | 0.489293i | \(-0.162745\pi\) | ||||
0.872120 | + | 0.489293i | \(0.162745\pi\) | |||||||
\(6\) | −1.10999 | −0.453154 | ||||||||
\(7\) | −4.77719 | −1.80561 | −0.902803 | − | 0.430054i | \(-0.858494\pi\) | ||||
−0.902803 | + | 0.430054i | \(0.858494\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.76791 | −0.589304 | ||||||||
\(10\) | 3.90024 | 1.23336 | ||||||||
\(11\) | 5.69601 | 1.71741 | 0.858705 | − | 0.512470i | \(-0.171269\pi\) | ||||
0.858705 | + | 0.512470i | \(0.171269\pi\) | |||||||
\(12\) | −1.10999 | −0.320428 | ||||||||
\(13\) | −4.09260 | −1.13508 | −0.567541 | − | 0.823345i | \(-0.692105\pi\) | ||||
−0.567541 | + | 0.823345i | \(0.692105\pi\) | |||||||
\(14\) | −4.77719 | −1.27676 | ||||||||
\(15\) | −4.32924 | −1.11781 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.265098 | −0.0642958 | −0.0321479 | − | 0.999483i | \(-0.510235\pi\) | ||||
−0.0321479 | + | 0.999483i | \(0.510235\pi\) | |||||||
\(18\) | −1.76791 | −0.416701 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.90024 | 0.872120 | ||||||||
\(21\) | 5.30265 | 1.15713 | ||||||||
\(22\) | 5.69601 | 1.21439 | ||||||||
\(23\) | −3.37328 | −0.703378 | −0.351689 | − | 0.936117i | \(-0.614392\pi\) | ||||
−0.351689 | + | 0.936117i | \(0.614392\pi\) | |||||||
\(24\) | −1.10999 | −0.226577 | ||||||||
\(25\) | 10.2119 | 2.04237 | ||||||||
\(26\) | −4.09260 | −0.802624 | ||||||||
\(27\) | 5.29236 | 1.01851 | ||||||||
\(28\) | −4.77719 | −0.902803 | ||||||||
\(29\) | −8.30007 | −1.54128 | −0.770642 | − | 0.637268i | \(-0.780065\pi\) | ||||
−0.770642 | + | 0.637268i | \(0.780065\pi\) | |||||||
\(30\) | −4.32924 | −0.790408 | ||||||||
\(31\) | −6.89712 | −1.23876 | −0.619380 | − | 0.785092i | \(-0.712616\pi\) | ||||
−0.619380 | + | 0.785092i | \(0.712616\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.32254 | −1.10061 | ||||||||
\(34\) | −0.265098 | −0.0454640 | ||||||||
\(35\) | −18.6322 | −3.14941 | ||||||||
\(36\) | −1.76791 | −0.294652 | ||||||||
\(37\) | 10.1552 | 1.66950 | 0.834752 | − | 0.550625i | \(-0.185611\pi\) | ||||
0.834752 | + | 0.550625i | \(0.185611\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 4.54276 | 0.727424 | ||||||||
\(40\) | 3.90024 | 0.616682 | ||||||||
\(41\) | 10.0818 | 1.57452 | 0.787260 | − | 0.616622i | \(-0.211499\pi\) | ||||
0.787260 | + | 0.616622i | \(0.211499\pi\) | |||||||
\(42\) | 5.30265 | 0.818217 | ||||||||
\(43\) | −2.35239 | −0.358735 | −0.179368 | − | 0.983782i | \(-0.557405\pi\) | ||||
−0.179368 | + | 0.983782i | \(0.557405\pi\) | |||||||
\(44\) | 5.69601 | 0.858705 | ||||||||
\(45\) | −6.89527 | −1.02789 | ||||||||
\(46\) | −3.37328 | −0.497363 | ||||||||
\(47\) | 0.906948 | 0.132292 | 0.0661460 | − | 0.997810i | \(-0.478930\pi\) | ||||
0.0661460 | + | 0.997810i | \(0.478930\pi\) | |||||||
\(48\) | −1.10999 | −0.160214 | ||||||||
\(49\) | 15.8215 | 2.26021 | ||||||||
\(50\) | 10.2119 | 1.44417 | ||||||||
\(51\) | 0.294258 | 0.0412043 | ||||||||
\(52\) | −4.09260 | −0.567541 | ||||||||
\(53\) | 11.1377 | 1.52989 | 0.764943 | − | 0.644098i | \(-0.222767\pi\) | ||||
0.764943 | + | 0.644098i | \(0.222767\pi\) | |||||||
\(54\) | 5.29236 | 0.720199 | ||||||||
\(55\) | 22.2158 | 2.99557 | ||||||||
\(56\) | −4.77719 | −0.638378 | ||||||||
\(57\) | 1.10999 | 0.147022 | ||||||||
\(58\) | −8.30007 | −1.08985 | ||||||||
\(59\) | 14.5586 | 1.89537 | 0.947685 | − | 0.319207i | \(-0.103416\pi\) | ||||
0.947685 | + | 0.319207i | \(0.103416\pi\) | |||||||
\(60\) | −4.32924 | −0.558903 | ||||||||
\(61\) | 3.09695 | 0.396524 | 0.198262 | − | 0.980149i | \(-0.436470\pi\) | ||||
0.198262 | + | 0.980149i | \(0.436470\pi\) | |||||||
\(62\) | −6.89712 | −0.875935 | ||||||||
\(63\) | 8.44564 | 1.06405 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −15.9621 | −1.97985 | ||||||||
\(66\) | −6.32254 | −0.778251 | ||||||||
\(67\) | 14.6212 | 1.78626 | 0.893130 | − | 0.449799i | \(-0.148504\pi\) | ||||
0.893130 | + | 0.449799i | \(0.148504\pi\) | |||||||
\(68\) | −0.265098 | −0.0321479 | ||||||||
\(69\) | 3.74432 | 0.450764 | ||||||||
\(70\) | −18.6322 | −2.22697 | ||||||||
\(71\) | −12.7624 | −1.51462 | −0.757311 | − | 0.653055i | \(-0.773487\pi\) | ||||
−0.757311 | + | 0.653055i | \(0.773487\pi\) | |||||||
\(72\) | −1.76791 | −0.208350 | ||||||||
\(73\) | −4.58606 | −0.536758 | −0.268379 | − | 0.963313i | \(-0.586488\pi\) | ||||
−0.268379 | + | 0.963313i | \(0.586488\pi\) | |||||||
\(74\) | 10.1552 | 1.18052 | ||||||||
\(75\) | −11.3351 | −1.30886 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −27.2109 | −3.10097 | ||||||||
\(78\) | 4.54276 | 0.514367 | ||||||||
\(79\) | −5.66673 | −0.637557 | −0.318778 | − | 0.947829i | \(-0.603273\pi\) | ||||
−0.318778 | + | 0.947829i | \(0.603273\pi\) | |||||||
\(80\) | 3.90024 | 0.436060 | ||||||||
\(81\) | −0.570756 | −0.0634174 | ||||||||
\(82\) | 10.0818 | 1.11335 | ||||||||
\(83\) | 9.13201 | 1.00237 | 0.501184 | − | 0.865341i | \(-0.332898\pi\) | ||||
0.501184 | + | 0.865341i | \(0.332898\pi\) | |||||||
\(84\) | 5.30265 | 0.578567 | ||||||||
\(85\) | −1.03395 | −0.112147 | ||||||||
\(86\) | −2.35239 | −0.253664 | ||||||||
\(87\) | 9.21304 | 0.987742 | ||||||||
\(88\) | 5.69601 | 0.607196 | ||||||||
\(89\) | −6.19037 | −0.656178 | −0.328089 | − | 0.944647i | \(-0.606405\pi\) | ||||
−0.328089 | + | 0.944647i | \(0.606405\pi\) | |||||||
\(90\) | −6.89527 | −0.726826 | ||||||||
\(91\) | 19.5511 | 2.04951 | ||||||||
\(92\) | −3.37328 | −0.351689 | ||||||||
\(93\) | 7.65577 | 0.793866 | ||||||||
\(94\) | 0.906948 | 0.0935446 | ||||||||
\(95\) | −3.90024 | −0.400156 | ||||||||
\(96\) | −1.10999 | −0.113288 | ||||||||
\(97\) | 8.89825 | 0.903481 | 0.451740 | − | 0.892149i | \(-0.350803\pi\) | ||||
0.451740 | + | 0.892149i | \(0.350803\pi\) | |||||||
\(98\) | 15.8215 | 1.59821 | ||||||||
\(99\) | −10.0700 | −1.01208 | ||||||||
\(100\) | 10.2119 | 1.02119 | ||||||||
\(101\) | 8.26913 | 0.822809 | 0.411405 | − | 0.911453i | \(-0.365038\pi\) | ||||
0.411405 | + | 0.911453i | \(0.365038\pi\) | |||||||
\(102\) | 0.294258 | 0.0291359 | ||||||||
\(103\) | 17.0859 | 1.68352 | 0.841760 | − | 0.539852i | \(-0.181520\pi\) | ||||
0.841760 | + | 0.539852i | \(0.181520\pi\) | |||||||
\(104\) | −4.09260 | −0.401312 | ||||||||
\(105\) | 20.6816 | 2.01832 | ||||||||
\(106\) | 11.1377 | 1.08179 | ||||||||
\(107\) | −6.12056 | −0.591697 | −0.295848 | − | 0.955235i | \(-0.595602\pi\) | ||||
−0.295848 | + | 0.955235i | \(0.595602\pi\) | |||||||
\(108\) | 5.29236 | 0.509257 | ||||||||
\(109\) | −2.99120 | −0.286505 | −0.143252 | − | 0.989686i | \(-0.545756\pi\) | ||||
−0.143252 | + | 0.989686i | \(0.545756\pi\) | |||||||
\(110\) | 22.2158 | 2.11819 | ||||||||
\(111\) | −11.2722 | −1.06991 | ||||||||
\(112\) | −4.77719 | −0.451402 | ||||||||
\(113\) | 8.75944 | 0.824019 | 0.412010 | − | 0.911180i | \(-0.364827\pi\) | ||||
0.412010 | + | 0.911180i | \(0.364827\pi\) | |||||||
\(114\) | 1.10999 | 0.103961 | ||||||||
\(115\) | −13.1566 | −1.22686 | ||||||||
\(116\) | −8.30007 | −0.770642 | ||||||||
\(117\) | 7.23535 | 0.668908 | ||||||||
\(118\) | 14.5586 | 1.34023 | ||||||||
\(119\) | 1.26642 | 0.116093 | ||||||||
\(120\) | −4.32924 | −0.395204 | ||||||||
\(121\) | 21.4445 | 1.94950 | ||||||||
\(122\) | 3.09695 | 0.280385 | ||||||||
\(123\) | −11.1908 | −1.00904 | ||||||||
\(124\) | −6.89712 | −0.619380 | ||||||||
\(125\) | 20.3275 | 1.81814 | ||||||||
\(126\) | 8.44564 | 0.752397 | ||||||||
\(127\) | −8.60658 | −0.763711 | −0.381855 | − | 0.924222i | \(-0.624715\pi\) | ||||
−0.381855 | + | 0.924222i | \(0.624715\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.61114 | 0.229898 | ||||||||
\(130\) | −15.9621 | −1.39997 | ||||||||
\(131\) | −8.06289 | −0.704458 | −0.352229 | − | 0.935914i | \(-0.614576\pi\) | ||||
−0.352229 | + | 0.935914i | \(0.614576\pi\) | |||||||
\(132\) | −6.32254 | −0.550306 | ||||||||
\(133\) | 4.77719 | 0.414234 | ||||||||
\(134\) | 14.6212 | 1.26308 | ||||||||
\(135\) | 20.6414 | 1.77653 | ||||||||
\(136\) | −0.265098 | −0.0227320 | ||||||||
\(137\) | 6.95245 | 0.593988 | 0.296994 | − | 0.954879i | \(-0.404016\pi\) | ||||
0.296994 | + | 0.954879i | \(0.404016\pi\) | |||||||
\(138\) | 3.74432 | 0.318738 | ||||||||
\(139\) | 17.1520 | 1.45481 | 0.727406 | − | 0.686208i | \(-0.240726\pi\) | ||||
0.727406 | + | 0.686208i | \(0.240726\pi\) | |||||||
\(140\) | −18.6322 | −1.57470 | ||||||||
\(141\) | −1.00671 | −0.0847801 | ||||||||
\(142\) | −12.7624 | −1.07100 | ||||||||
\(143\) | −23.3115 | −1.94940 | ||||||||
\(144\) | −1.76791 | −0.147326 | ||||||||
\(145\) | −32.3723 | −2.68837 | ||||||||
\(146\) | −4.58606 | −0.379545 | ||||||||
\(147\) | −17.5618 | −1.44847 | ||||||||
\(148\) | 10.1552 | 0.834752 | ||||||||
\(149\) | −16.3458 | −1.33910 | −0.669552 | − | 0.742765i | \(-0.733514\pi\) | ||||
−0.669552 | + | 0.742765i | \(0.733514\pi\) | |||||||
\(150\) | −11.3351 | −0.925507 | ||||||||
\(151\) | −10.9227 | −0.888880 | −0.444440 | − | 0.895809i | \(-0.646597\pi\) | ||||
−0.444440 | + | 0.895809i | \(0.646597\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0.468670 | 0.0378897 | ||||||||
\(154\) | −27.2109 | −2.19271 | ||||||||
\(155\) | −26.9004 | −2.16069 | ||||||||
\(156\) | 4.54276 | 0.363712 | ||||||||
\(157\) | −2.38660 | −0.190472 | −0.0952359 | − | 0.995455i | \(-0.530361\pi\) | ||||
−0.0952359 | + | 0.995455i | \(0.530361\pi\) | |||||||
\(158\) | −5.66673 | −0.450821 | ||||||||
\(159\) | −12.3628 | −0.980437 | ||||||||
\(160\) | 3.90024 | 0.308341 | ||||||||
\(161\) | 16.1148 | 1.27002 | ||||||||
\(162\) | −0.570756 | −0.0448428 | ||||||||
\(163\) | 3.26419 | 0.255671 | 0.127836 | − | 0.991795i | \(-0.459197\pi\) | ||||
0.127836 | + | 0.991795i | \(0.459197\pi\) | |||||||
\(164\) | 10.0818 | 0.787260 | ||||||||
\(165\) | −24.6594 | −1.91973 | ||||||||
\(166\) | 9.13201 | 0.708782 | ||||||||
\(167\) | 2.79406 | 0.216211 | 0.108105 | − | 0.994139i | \(-0.465522\pi\) | ||||
0.108105 | + | 0.994139i | \(0.465522\pi\) | |||||||
\(168\) | 5.30265 | 0.409108 | ||||||||
\(169\) | 3.74935 | 0.288412 | ||||||||
\(170\) | −1.03395 | −0.0793001 | ||||||||
\(171\) | 1.76791 | 0.135196 | ||||||||
\(172\) | −2.35239 | −0.179368 | ||||||||
\(173\) | 16.5663 | 1.25951 | 0.629756 | − | 0.776793i | \(-0.283155\pi\) | ||||
0.629756 | + | 0.776793i | \(0.283155\pi\) | |||||||
\(174\) | 9.21304 | 0.698439 | ||||||||
\(175\) | −48.7839 | −3.68772 | ||||||||
\(176\) | 5.69601 | 0.429353 | ||||||||
\(177\) | −16.1600 | −1.21466 | ||||||||
\(178\) | −6.19037 | −0.463988 | ||||||||
\(179\) | 11.5835 | 0.865793 | 0.432897 | − | 0.901444i | \(-0.357492\pi\) | ||||
0.432897 | + | 0.901444i | \(0.357492\pi\) | |||||||
\(180\) | −6.89527 | −0.513943 | ||||||||
\(181\) | −1.55513 | −0.115592 | −0.0577960 | − | 0.998328i | \(-0.518407\pi\) | ||||
−0.0577960 | + | 0.998328i | \(0.518407\pi\) | |||||||
\(182\) | 19.5511 | 1.44922 | ||||||||
\(183\) | −3.43760 | −0.254115 | ||||||||
\(184\) | −3.37328 | −0.248682 | ||||||||
\(185\) | 39.6077 | 2.91202 | ||||||||
\(186\) | 7.65577 | 0.561348 | ||||||||
\(187\) | −1.51000 | −0.110422 | ||||||||
\(188\) | 0.906948 | 0.0661460 | ||||||||
\(189\) | −25.2826 | −1.83904 | ||||||||
\(190\) | −3.90024 | −0.282953 | ||||||||
\(191\) | 2.81445 | 0.203647 | 0.101823 | − | 0.994802i | \(-0.467532\pi\) | ||||
0.101823 | + | 0.994802i | \(0.467532\pi\) | |||||||
\(192\) | −1.10999 | −0.0801070 | ||||||||
\(193\) | 12.1750 | 0.876378 | 0.438189 | − | 0.898883i | \(-0.355620\pi\) | ||||
0.438189 | + | 0.898883i | \(0.355620\pi\) | |||||||
\(194\) | 8.89825 | 0.638857 | ||||||||
\(195\) | 17.7179 | 1.26880 | ||||||||
\(196\) | 15.8215 | 1.13011 | ||||||||
\(197\) | 19.1442 | 1.36397 | 0.681983 | − | 0.731368i | \(-0.261118\pi\) | ||||
0.681983 | + | 0.731368i | \(0.261118\pi\) | |||||||
\(198\) | −10.0700 | −0.715646 | ||||||||
\(199\) | 8.27226 | 0.586405 | 0.293203 | − | 0.956050i | \(-0.405279\pi\) | ||||
0.293203 | + | 0.956050i | \(0.405279\pi\) | |||||||
\(200\) | 10.2119 | 0.722087 | ||||||||
\(201\) | −16.2294 | −1.14474 | ||||||||
\(202\) | 8.26913 | 0.581814 | ||||||||
\(203\) | 39.6510 | 2.78295 | ||||||||
\(204\) | 0.294258 | 0.0206022 | ||||||||
\(205\) | 39.3216 | 2.74634 | ||||||||
\(206\) | 17.0859 | 1.19043 | ||||||||
\(207\) | 5.96366 | 0.414503 | ||||||||
\(208\) | −4.09260 | −0.283771 | ||||||||
\(209\) | −5.69601 | −0.394001 | ||||||||
\(210\) | 20.6816 | 1.42717 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 11.1377 | 0.764943 | ||||||||
\(213\) | 14.1662 | 0.970654 | ||||||||
\(214\) | −6.12056 | −0.418393 | ||||||||
\(215\) | −9.17486 | −0.625720 | ||||||||
\(216\) | 5.29236 | 0.360099 | ||||||||
\(217\) | 32.9488 | 2.23671 | ||||||||
\(218\) | −2.99120 | −0.202589 | ||||||||
\(219\) | 5.09051 | 0.343984 | ||||||||
\(220\) | 22.2158 | 1.49779 | ||||||||
\(221\) | 1.08494 | 0.0729810 | ||||||||
\(222\) | −11.2722 | −0.756542 | ||||||||
\(223\) | −19.2777 | −1.29093 | −0.645465 | − | 0.763790i | \(-0.723336\pi\) | ||||
−0.645465 | + | 0.763790i | \(0.723336\pi\) | |||||||
\(224\) | −4.77719 | −0.319189 | ||||||||
\(225\) | −18.0536 | −1.20358 | ||||||||
\(226\) | 8.75944 | 0.582670 | ||||||||
\(227\) | 8.67176 | 0.575565 | 0.287782 | − | 0.957696i | \(-0.407082\pi\) | ||||
0.287782 | + | 0.957696i | \(0.407082\pi\) | |||||||
\(228\) | 1.10999 | 0.0735112 | ||||||||
\(229\) | 9.69642 | 0.640758 | 0.320379 | − | 0.947290i | \(-0.396190\pi\) | ||||
0.320379 | + | 0.947290i | \(0.396190\pi\) | |||||||
\(230\) | −13.1566 | −0.867520 | ||||||||
\(231\) | 30.2039 | 1.98727 | ||||||||
\(232\) | −8.30007 | −0.544927 | ||||||||
\(233\) | −7.18392 | −0.470634 | −0.235317 | − | 0.971919i | \(-0.575613\pi\) | ||||
−0.235317 | + | 0.971919i | \(0.575613\pi\) | |||||||
\(234\) | 7.23535 | 0.472990 | ||||||||
\(235\) | 3.53731 | 0.230749 | ||||||||
\(236\) | 14.5586 | 0.947685 | ||||||||
\(237\) | 6.29004 | 0.408582 | ||||||||
\(238\) | 1.26642 | 0.0820901 | ||||||||
\(239\) | 0.963091 | 0.0622972 | 0.0311486 | − | 0.999515i | \(-0.490083\pi\) | ||||
0.0311486 | + | 0.999515i | \(0.490083\pi\) | |||||||
\(240\) | −4.32924 | −0.279451 | ||||||||
\(241\) | −11.6759 | −0.752111 | −0.376055 | − | 0.926597i | \(-0.622720\pi\) | ||||
−0.376055 | + | 0.926597i | \(0.622720\pi\) | |||||||
\(242\) | 21.4445 | 1.37850 | ||||||||
\(243\) | −15.2435 | −0.977873 | ||||||||
\(244\) | 3.09695 | 0.198262 | ||||||||
\(245\) | 61.7076 | 3.94235 | ||||||||
\(246\) | −11.1908 | −0.713499 | ||||||||
\(247\) | 4.09260 | 0.260406 | ||||||||
\(248\) | −6.89712 | −0.437968 | ||||||||
\(249\) | −10.1365 | −0.642374 | ||||||||
\(250\) | 20.3275 | 1.28562 | ||||||||
\(251\) | −18.5865 | −1.17317 | −0.586586 | − | 0.809887i | \(-0.699529\pi\) | ||||
−0.586586 | + | 0.809887i | \(0.699529\pi\) | |||||||
\(252\) | 8.44564 | 0.532025 | ||||||||
\(253\) | −19.2142 | −1.20799 | ||||||||
\(254\) | −8.60658 | −0.540025 | ||||||||
\(255\) | 1.14768 | 0.0718702 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.1609 | 1.07047 | 0.535235 | − | 0.844703i | \(-0.320223\pi\) | ||||
0.535235 | + | 0.844703i | \(0.320223\pi\) | |||||||
\(258\) | 2.61114 | 0.162562 | ||||||||
\(259\) | −48.5133 | −3.01447 | ||||||||
\(260\) | −15.9621 | −0.989927 | ||||||||
\(261\) | 14.6738 | 0.908285 | ||||||||
\(262\) | −8.06289 | −0.498127 | ||||||||
\(263\) | −8.25844 | −0.509237 | −0.254619 | − | 0.967042i | \(-0.581950\pi\) | ||||
−0.254619 | + | 0.967042i | \(0.581950\pi\) | |||||||
\(264\) | −6.32254 | −0.389125 | ||||||||
\(265\) | 43.4398 | 2.66849 | ||||||||
\(266\) | 4.77719 | 0.292908 | ||||||||
\(267\) | 6.87128 | 0.420516 | ||||||||
\(268\) | 14.6212 | 0.893130 | ||||||||
\(269\) | 17.4591 | 1.06450 | 0.532249 | − | 0.846588i | \(-0.321347\pi\) | ||||
0.532249 | + | 0.846588i | \(0.321347\pi\) | |||||||
\(270\) | 20.6414 | 1.25620 | ||||||||
\(271\) | −8.67176 | −0.526772 | −0.263386 | − | 0.964691i | \(-0.584839\pi\) | ||||
−0.263386 | + | 0.964691i | \(0.584839\pi\) | |||||||
\(272\) | −0.265098 | −0.0160739 | ||||||||
\(273\) | −21.7016 | −1.31344 | ||||||||
\(274\) | 6.95245 | 0.420013 | ||||||||
\(275\) | 58.1668 | 3.50759 | ||||||||
\(276\) | 3.74432 | 0.225382 | ||||||||
\(277\) | 13.0111 | 0.781763 | 0.390881 | − | 0.920441i | \(-0.372170\pi\) | ||||
0.390881 | + | 0.920441i | \(0.372170\pi\) | |||||||
\(278\) | 17.1520 | 1.02871 | ||||||||
\(279\) | 12.1935 | 0.730005 | ||||||||
\(280\) | −18.6322 | −1.11348 | ||||||||
\(281\) | −15.3504 | −0.915730 | −0.457865 | − | 0.889022i | \(-0.651386\pi\) | ||||
−0.457865 | + | 0.889022i | \(0.651386\pi\) | |||||||
\(282\) | −1.00671 | −0.0599486 | ||||||||
\(283\) | −26.4750 | −1.57377 | −0.786887 | − | 0.617097i | \(-0.788308\pi\) | ||||
−0.786887 | + | 0.617097i | \(0.788308\pi\) | |||||||
\(284\) | −12.7624 | −0.757311 | ||||||||
\(285\) | 4.32924 | 0.256442 | ||||||||
\(286\) | −23.3115 | −1.37844 | ||||||||
\(287\) | −48.1628 | −2.84296 | ||||||||
\(288\) | −1.76791 | −0.104175 | ||||||||
\(289\) | −16.9297 | −0.995866 | ||||||||
\(290\) | −32.3723 | −1.90096 | ||||||||
\(291\) | −9.87702 | −0.579001 | ||||||||
\(292\) | −4.58606 | −0.268379 | ||||||||
\(293\) | −27.8945 | −1.62961 | −0.814806 | − | 0.579734i | \(-0.803157\pi\) | ||||
−0.814806 | + | 0.579734i | \(0.803157\pi\) | |||||||
\(294\) | −17.5618 | −1.02422 | ||||||||
\(295\) | 56.7821 | 3.30598 | ||||||||
\(296\) | 10.1552 | 0.590259 | ||||||||
\(297\) | 30.1453 | 1.74921 | ||||||||
\(298\) | −16.3458 | −0.946889 | ||||||||
\(299\) | 13.8055 | 0.798392 | ||||||||
\(300\) | −11.3351 | −0.654432 | ||||||||
\(301\) | 11.2378 | 0.647735 | ||||||||
\(302\) | −10.9227 | −0.628533 | ||||||||
\(303\) | −9.17869 | −0.527302 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 12.0788 | 0.691632 | ||||||||
\(306\) | 0.468670 | 0.0267921 | ||||||||
\(307\) | 5.14591 | 0.293693 | 0.146846 | − | 0.989159i | \(-0.453088\pi\) | ||||
0.146846 | + | 0.989159i | \(0.453088\pi\) | |||||||
\(308\) | −27.2109 | −1.55048 | ||||||||
\(309\) | −18.9652 | −1.07889 | ||||||||
\(310\) | −26.9004 | −1.52784 | ||||||||
\(311\) | −0.505072 | −0.0286400 | −0.0143200 | − | 0.999897i | \(-0.504558\pi\) | ||||
−0.0143200 | + | 0.999897i | \(0.504558\pi\) | |||||||
\(312\) | 4.54276 | 0.257183 | ||||||||
\(313\) | −13.1933 | −0.745727 | −0.372863 | − | 0.927886i | \(-0.621624\pi\) | ||||
−0.372863 | + | 0.927886i | \(0.621624\pi\) | |||||||
\(314\) | −2.38660 | −0.134684 | ||||||||
\(315\) | 32.9400 | 1.85596 | ||||||||
\(316\) | −5.66673 | −0.318778 | ||||||||
\(317\) | 30.1676 | 1.69438 | 0.847190 | − | 0.531290i | \(-0.178292\pi\) | ||||
0.847190 | + | 0.531290i | \(0.178292\pi\) | |||||||
\(318\) | −12.3628 | −0.693273 | ||||||||
\(319\) | −47.2773 | −2.64702 | ||||||||
\(320\) | 3.90024 | 0.218030 | ||||||||
\(321\) | 6.79379 | 0.379192 | ||||||||
\(322\) | 16.1148 | 0.898042 | ||||||||
\(323\) | 0.265098 | 0.0147505 | ||||||||
\(324\) | −0.570756 | −0.0317087 | ||||||||
\(325\) | −41.7930 | −2.31826 | ||||||||
\(326\) | 3.26419 | 0.180787 | ||||||||
\(327\) | 3.32021 | 0.183608 | ||||||||
\(328\) | 10.0818 | 0.556677 | ||||||||
\(329\) | −4.33266 | −0.238867 | ||||||||
\(330\) | −24.6594 | −1.35746 | ||||||||
\(331\) | 12.9868 | 0.713818 | 0.356909 | − | 0.934139i | \(-0.383831\pi\) | ||||
0.356909 | + | 0.934139i | \(0.383831\pi\) | |||||||
\(332\) | 9.13201 | 0.501184 | ||||||||
\(333\) | −17.9535 | −0.983845 | ||||||||
\(334\) | 2.79406 | 0.152884 | ||||||||
\(335\) | 57.0260 | 3.11566 | ||||||||
\(336\) | 5.30265 | 0.289283 | ||||||||
\(337\) | 14.6345 | 0.797190 | 0.398595 | − | 0.917127i | \(-0.369498\pi\) | ||||
0.398595 | + | 0.917127i | \(0.369498\pi\) | |||||||
\(338\) | 3.74935 | 0.203938 | ||||||||
\(339\) | −9.72294 | −0.528078 | ||||||||
\(340\) | −1.03395 | −0.0560736 | ||||||||
\(341\) | −39.2860 | −2.12746 | ||||||||
\(342\) | 1.76791 | 0.0955977 | ||||||||
\(343\) | −42.1419 | −2.27545 | ||||||||
\(344\) | −2.35239 | −0.126832 | ||||||||
\(345\) | 14.6038 | 0.786240 | ||||||||
\(346\) | 16.5663 | 0.890609 | ||||||||
\(347\) | 13.9248 | 0.747522 | 0.373761 | − | 0.927525i | \(-0.378068\pi\) | ||||
0.373761 | + | 0.927525i | \(0.378068\pi\) | |||||||
\(348\) | 9.21304 | 0.493871 | ||||||||
\(349\) | 12.9954 | 0.695628 | 0.347814 | − | 0.937564i | \(-0.386924\pi\) | ||||
0.347814 | + | 0.937564i | \(0.386924\pi\) | |||||||
\(350\) | −48.7839 | −2.60761 | ||||||||
\(351\) | −21.6595 | −1.15610 | ||||||||
\(352\) | 5.69601 | 0.303598 | ||||||||
\(353\) | −0.158909 | −0.00845787 | −0.00422893 | − | 0.999991i | \(-0.501346\pi\) | ||||
−0.00422893 | + | 0.999991i | \(0.501346\pi\) | |||||||
\(354\) | −16.1600 | −0.858894 | ||||||||
\(355\) | −49.7765 | −2.64186 | ||||||||
\(356\) | −6.19037 | −0.328089 | ||||||||
\(357\) | −1.40572 | −0.0743988 | ||||||||
\(358\) | 11.5835 | 0.612208 | ||||||||
\(359\) | −20.9540 | −1.10591 | −0.552955 | − | 0.833211i | \(-0.686500\pi\) | ||||
−0.552955 | + | 0.833211i | \(0.686500\pi\) | |||||||
\(360\) | −6.89527 | −0.363413 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −1.55513 | −0.0817359 | ||||||||
\(363\) | −23.8033 | −1.24935 | ||||||||
\(364\) | 19.5511 | 1.02476 | ||||||||
\(365\) | −17.8867 | −0.936234 | ||||||||
\(366\) | −3.43760 | −0.179686 | ||||||||
\(367\) | −17.7347 | −0.925745 | −0.462873 | − | 0.886425i | \(-0.653181\pi\) | ||||
−0.462873 | + | 0.886425i | \(0.653181\pi\) | |||||||
\(368\) | −3.37328 | −0.175844 | ||||||||
\(369\) | −17.8238 | −0.927870 | ||||||||
\(370\) | 39.6077 | 2.05911 | ||||||||
\(371\) | −53.2071 | −2.76237 | ||||||||
\(372\) | 7.65577 | 0.396933 | ||||||||
\(373\) | −3.71068 | −0.192131 | −0.0960657 | − | 0.995375i | \(-0.530626\pi\) | ||||
−0.0960657 | + | 0.995375i | \(0.530626\pi\) | |||||||
\(374\) | −1.51000 | −0.0780803 | ||||||||
\(375\) | −22.5634 | −1.16517 | ||||||||
\(376\) | 0.906948 | 0.0467723 | ||||||||
\(377\) | 33.9689 | 1.74949 | ||||||||
\(378\) | −25.2826 | −1.30040 | ||||||||
\(379\) | 30.0212 | 1.54209 | 0.771043 | − | 0.636783i | \(-0.219735\pi\) | ||||
0.771043 | + | 0.636783i | \(0.219735\pi\) | |||||||
\(380\) | −3.90024 | −0.200078 | ||||||||
\(381\) | 9.55326 | 0.489428 | ||||||||
\(382\) | 2.81445 | 0.144000 | ||||||||
\(383\) | −14.3270 | −0.732077 | −0.366039 | − | 0.930600i | \(-0.619286\pi\) | ||||
−0.366039 | + | 0.930600i | \(0.619286\pi\) | |||||||
\(384\) | −1.10999 | −0.0566442 | ||||||||
\(385\) | −106.129 | −5.40883 | ||||||||
\(386\) | 12.1750 | 0.619693 | ||||||||
\(387\) | 4.15881 | 0.211404 | ||||||||
\(388\) | 8.89825 | 0.451740 | ||||||||
\(389\) | 2.66506 | 0.135124 | 0.0675619 | − | 0.997715i | \(-0.478478\pi\) | ||||
0.0675619 | + | 0.997715i | \(0.478478\pi\) | |||||||
\(390\) | 17.7179 | 0.897178 | ||||||||
\(391\) | 0.894251 | 0.0452242 | ||||||||
\(392\) | 15.8215 | 0.799106 | ||||||||
\(393\) | 8.94976 | 0.451456 | ||||||||
\(394\) | 19.1442 | 0.964469 | ||||||||
\(395\) | −22.1016 | −1.11205 | ||||||||
\(396\) | −10.0700 | −0.506038 | ||||||||
\(397\) | −8.22764 | −0.412933 | −0.206467 | − | 0.978454i | \(-0.566197\pi\) | ||||
−0.206467 | + | 0.978454i | \(0.566197\pi\) | |||||||
\(398\) | 8.27226 | 0.414651 | ||||||||
\(399\) | −5.30265 | −0.265465 | ||||||||
\(400\) | 10.2119 | 0.510593 | ||||||||
\(401\) | 16.2754 | 0.812757 | 0.406378 | − | 0.913705i | \(-0.366792\pi\) | ||||
0.406378 | + | 0.913705i | \(0.366792\pi\) | |||||||
\(402\) | −16.2294 | −0.809450 | ||||||||
\(403\) | 28.2271 | 1.40609 | ||||||||
\(404\) | 8.26913 | 0.411405 | ||||||||
\(405\) | −2.22608 | −0.110615 | ||||||||
\(406\) | 39.6510 | 1.96785 | ||||||||
\(407\) | 57.8441 | 2.86722 | ||||||||
\(408\) | 0.294258 | 0.0145679 | ||||||||
\(409\) | −2.15867 | −0.106740 | −0.0533698 | − | 0.998575i | \(-0.516996\pi\) | ||||
−0.0533698 | + | 0.998575i | \(0.516996\pi\) | |||||||
\(410\) | 39.3216 | 1.94195 | ||||||||
\(411\) | −7.71718 | −0.380661 | ||||||||
\(412\) | 17.0859 | 0.841760 | ||||||||
\(413\) | −69.5492 | −3.42229 | ||||||||
\(414\) | 5.96366 | 0.293098 | ||||||||
\(415\) | 35.6170 | 1.74837 | ||||||||
\(416\) | −4.09260 | −0.200656 | ||||||||
\(417\) | −19.0386 | −0.932324 | ||||||||
\(418\) | −5.69601 | −0.278601 | ||||||||
\(419\) | −12.5558 | −0.613393 | −0.306697 | − | 0.951807i | \(-0.599224\pi\) | ||||
−0.306697 | + | 0.951807i | \(0.599224\pi\) | |||||||
\(420\) | 20.6816 | 1.00916 | ||||||||
\(421\) | −16.4123 | −0.799889 | −0.399944 | − | 0.916539i | \(-0.630971\pi\) | ||||
−0.399944 | + | 0.916539i | \(0.630971\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −1.60340 | −0.0779602 | ||||||||
\(424\) | 11.1377 | 0.540897 | ||||||||
\(425\) | −2.70714 | −0.131316 | ||||||||
\(426\) | 14.1662 | 0.686356 | ||||||||
\(427\) | −14.7947 | −0.715966 | ||||||||
\(428\) | −6.12056 | −0.295848 | ||||||||
\(429\) | 25.8756 | 1.24929 | ||||||||
\(430\) | −9.17486 | −0.442451 | ||||||||
\(431\) | 6.50015 | 0.313101 | 0.156551 | − | 0.987670i | \(-0.449963\pi\) | ||||
0.156551 | + | 0.987670i | \(0.449963\pi\) | |||||||
\(432\) | 5.29236 | 0.254629 | ||||||||
\(433\) | 11.9525 | 0.574399 | 0.287200 | − | 0.957871i | \(-0.407276\pi\) | ||||
0.287200 | + | 0.957871i | \(0.407276\pi\) | |||||||
\(434\) | 32.9488 | 1.58159 | ||||||||
\(435\) | 35.9330 | 1.72286 | ||||||||
\(436\) | −2.99120 | −0.143252 | ||||||||
\(437\) | 3.37328 | 0.161366 | ||||||||
\(438\) | 5.09051 | 0.243234 | ||||||||
\(439\) | −12.3919 | −0.591434 | −0.295717 | − | 0.955276i | \(-0.595559\pi\) | ||||
−0.295717 | + | 0.955276i | \(0.595559\pi\) | |||||||
\(440\) | 22.2158 | 1.05910 | ||||||||
\(441\) | −27.9710 | −1.33195 | ||||||||
\(442\) | 1.08494 | 0.0516054 | ||||||||
\(443\) | −13.0536 | −0.620194 | −0.310097 | − | 0.950705i | \(-0.600362\pi\) | ||||
−0.310097 | + | 0.950705i | \(0.600362\pi\) | |||||||
\(444\) | −11.2722 | −0.534956 | ||||||||
\(445\) | −24.1439 | −1.14453 | ||||||||
\(446\) | −19.2777 | −0.912826 | ||||||||
\(447\) | 18.1438 | 0.858173 | ||||||||
\(448\) | −4.77719 | −0.225701 | ||||||||
\(449\) | 29.4917 | 1.39180 | 0.695900 | − | 0.718139i | \(-0.255006\pi\) | ||||
0.695900 | + | 0.718139i | \(0.255006\pi\) | |||||||
\(450\) | −18.0536 | −0.851057 | ||||||||
\(451\) | 57.4262 | 2.70410 | ||||||||
\(452\) | 8.75944 | 0.412010 | ||||||||
\(453\) | 12.1242 | 0.569644 | ||||||||
\(454\) | 8.67176 | 0.406986 | ||||||||
\(455\) | 76.2539 | 3.57484 | ||||||||
\(456\) | 1.10999 | 0.0519803 | ||||||||
\(457\) | −0.324966 | −0.0152013 | −0.00760063 | − | 0.999971i | \(-0.502419\pi\) | ||||
−0.00760063 | + | 0.999971i | \(0.502419\pi\) | |||||||
\(458\) | 9.69642 | 0.453084 | ||||||||
\(459\) | −1.40300 | −0.0654862 | ||||||||
\(460\) | −13.1566 | −0.613429 | ||||||||
\(461\) | 38.2872 | 1.78321 | 0.891607 | − | 0.452811i | \(-0.149579\pi\) | ||||
0.891607 | + | 0.452811i | \(0.149579\pi\) | |||||||
\(462\) | 30.2039 | 1.40521 | ||||||||
\(463\) | 34.0027 | 1.58024 | 0.790119 | − | 0.612953i | \(-0.210019\pi\) | ||||
0.790119 | + | 0.612953i | \(0.210019\pi\) | |||||||
\(464\) | −8.30007 | −0.385321 | ||||||||
\(465\) | 29.8593 | 1.38469 | ||||||||
\(466\) | −7.18392 | −0.332788 | ||||||||
\(467\) | −21.4709 | −0.993556 | −0.496778 | − | 0.867878i | \(-0.665484\pi\) | ||||
−0.496778 | + | 0.867878i | \(0.665484\pi\) | |||||||
\(468\) | 7.23535 | 0.334454 | ||||||||
\(469\) | −69.8480 | −3.22528 | ||||||||
\(470\) | 3.53731 | 0.163164 | ||||||||
\(471\) | 2.64912 | 0.122065 | ||||||||
\(472\) | 14.5586 | 0.670115 | ||||||||
\(473\) | −13.3992 | −0.616096 | ||||||||
\(474\) | 6.29004 | 0.288911 | ||||||||
\(475\) | −10.2119 | −0.468552 | ||||||||
\(476\) | 1.26642 | 0.0580464 | ||||||||
\(477\) | −19.6905 | −0.901568 | ||||||||
\(478\) | 0.963091 | 0.0440508 | ||||||||
\(479\) | 5.37891 | 0.245769 | 0.122884 | − | 0.992421i | \(-0.460786\pi\) | ||||
0.122884 | + | 0.992421i | \(0.460786\pi\) | |||||||
\(480\) | −4.32924 | −0.197602 | ||||||||
\(481\) | −41.5612 | −1.89503 | ||||||||
\(482\) | −11.6759 | −0.531823 | ||||||||
\(483\) | −17.8873 | −0.813902 | ||||||||
\(484\) | 21.4445 | 0.974749 | ||||||||
\(485\) | 34.7053 | 1.57589 | ||||||||
\(486\) | −15.2435 | −0.691461 | ||||||||
\(487\) | −14.1416 | −0.640815 | −0.320407 | − | 0.947280i | \(-0.603820\pi\) | ||||
−0.320407 | + | 0.947280i | \(0.603820\pi\) | |||||||
\(488\) | 3.09695 | 0.140192 | ||||||||
\(489\) | −3.62324 | −0.163848 | ||||||||
\(490\) | 61.7076 | 2.78767 | ||||||||
\(491\) | 19.7165 | 0.889791 | 0.444895 | − | 0.895582i | \(-0.353241\pi\) | ||||
0.444895 | + | 0.895582i | \(0.353241\pi\) | |||||||
\(492\) | −11.1908 | −0.504520 | ||||||||
\(493\) | 2.20034 | 0.0990981 | ||||||||
\(494\) | 4.09260 | 0.184135 | ||||||||
\(495\) | −39.2755 | −1.76530 | ||||||||
\(496\) | −6.89712 | −0.309690 | ||||||||
\(497\) | 60.9685 | 2.73481 | ||||||||
\(498\) | −10.1365 | −0.454227 | ||||||||
\(499\) | −38.5801 | −1.72708 | −0.863541 | − | 0.504278i | \(-0.831759\pi\) | ||||
−0.863541 | + | 0.504278i | \(0.831759\pi\) | |||||||
\(500\) | 20.3275 | 0.909071 | ||||||||
\(501\) | −3.10139 | −0.138560 | ||||||||
\(502\) | −18.5865 | −0.829558 | ||||||||
\(503\) | 33.1204 | 1.47677 | 0.738383 | − | 0.674381i | \(-0.235590\pi\) | ||||
0.738383 | + | 0.674381i | \(0.235590\pi\) | |||||||
\(504\) | 8.44564 | 0.376199 | ||||||||
\(505\) | 32.2516 | 1.43518 | ||||||||
\(506\) | −19.2142 | −0.854177 | ||||||||
\(507\) | −4.16176 | −0.184830 | ||||||||
\(508\) | −8.60658 | −0.381855 | ||||||||
\(509\) | −35.2099 | −1.56065 | −0.780326 | − | 0.625373i | \(-0.784947\pi\) | ||||
−0.780326 | + | 0.625373i | \(0.784947\pi\) | |||||||
\(510\) | 1.14768 | 0.0508199 | ||||||||
\(511\) | 21.9085 | 0.969173 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.29236 | −0.233663 | ||||||||
\(514\) | 17.1609 | 0.756937 | ||||||||
\(515\) | 66.6389 | 2.93646 | ||||||||
\(516\) | 2.61114 | 0.114949 | ||||||||
\(517\) | 5.16598 | 0.227200 | ||||||||
\(518\) | −48.5133 | −2.13155 | ||||||||
\(519\) | −18.3885 | −0.807165 | ||||||||
\(520\) | −15.9621 | −0.699984 | ||||||||
\(521\) | 1.90798 | 0.0835903 | 0.0417952 | − | 0.999126i | \(-0.486692\pi\) | ||||
0.0417952 | + | 0.999126i | \(0.486692\pi\) | |||||||
\(522\) | 14.6738 | 0.642254 | ||||||||
\(523\) | −15.5924 | −0.681808 | −0.340904 | − | 0.940098i | \(-0.610733\pi\) | ||||
−0.340904 | + | 0.940098i | \(0.610733\pi\) | |||||||
\(524\) | −8.06289 | −0.352229 | ||||||||
\(525\) | 54.1499 | 2.36329 | ||||||||
\(526\) | −8.25844 | −0.360085 | ||||||||
\(527\) | 1.82841 | 0.0796470 | ||||||||
\(528\) | −6.32254 | −0.275153 | ||||||||
\(529\) | −11.6210 | −0.505260 | ||||||||
\(530\) | 43.4398 | 1.88691 | ||||||||
\(531\) | −25.7383 | −1.11695 | ||||||||
\(532\) | 4.77719 | 0.207117 | ||||||||
\(533\) | −41.2609 | −1.78721 | ||||||||
\(534\) | 6.87128 | 0.297349 | ||||||||
\(535\) | −23.8716 | −1.03206 | ||||||||
\(536\) | 14.6212 | 0.631538 | ||||||||
\(537\) | −12.8577 | −0.554849 | ||||||||
\(538\) | 17.4591 | 0.752713 | ||||||||
\(539\) | 90.1193 | 3.88171 | ||||||||
\(540\) | 20.6414 | 0.888267 | ||||||||
\(541\) | −15.8687 | −0.682249 | −0.341125 | − | 0.940018i | \(-0.610808\pi\) | ||||
−0.341125 | + | 0.940018i | \(0.610808\pi\) | |||||||
\(542\) | −8.67176 | −0.372484 | ||||||||
\(543\) | 1.72619 | 0.0740778 | ||||||||
\(544\) | −0.265098 | −0.0113660 | ||||||||
\(545\) | −11.6664 | −0.499733 | ||||||||
\(546\) | −21.7016 | −0.928744 | ||||||||
\(547\) | 43.4619 | 1.85830 | 0.929149 | − | 0.369706i | \(-0.120542\pi\) | ||||
0.929149 | + | 0.369706i | \(0.120542\pi\) | |||||||
\(548\) | 6.95245 | 0.296994 | ||||||||
\(549\) | −5.47513 | −0.233673 | ||||||||
\(550\) | 58.1668 | 2.48024 | ||||||||
\(551\) | 8.30007 | 0.353595 | ||||||||
\(552\) | 3.74432 | 0.159369 | ||||||||
\(553\) | 27.0710 | 1.15118 | ||||||||
\(554\) | 13.0111 | 0.552790 | ||||||||
\(555\) | −43.9643 | −1.86618 | ||||||||
\(556\) | 17.1520 | 0.727406 | ||||||||
\(557\) | −3.97633 | −0.168483 | −0.0842413 | − | 0.996445i | \(-0.526847\pi\) | ||||
−0.0842413 | + | 0.996445i | \(0.526847\pi\) | |||||||
\(558\) | 12.1935 | 0.516192 | ||||||||
\(559\) | 9.62737 | 0.407194 | ||||||||
\(560\) | −18.6322 | −0.787352 | ||||||||
\(561\) | 1.67609 | 0.0707647 | ||||||||
\(562\) | −15.3504 | −0.647519 | ||||||||
\(563\) | −15.0266 | −0.633298 | −0.316649 | − | 0.948543i | \(-0.602558\pi\) | ||||
−0.316649 | + | 0.948543i | \(0.602558\pi\) | |||||||
\(564\) | −1.00671 | −0.0423901 | ||||||||
\(565\) | 34.1639 | 1.43729 | ||||||||
\(566\) | −26.4750 | −1.11283 | ||||||||
\(567\) | 2.72661 | 0.114507 | ||||||||
\(568\) | −12.7624 | −0.535499 | ||||||||
\(569\) | 42.1744 | 1.76804 | 0.884022 | − | 0.467446i | \(-0.154826\pi\) | ||||
0.884022 | + | 0.467446i | \(0.154826\pi\) | |||||||
\(570\) | 4.32924 | 0.181332 | ||||||||
\(571\) | −23.6897 | −0.991384 | −0.495692 | − | 0.868498i | \(-0.665086\pi\) | ||||
−0.495692 | + | 0.868498i | \(0.665086\pi\) | |||||||
\(572\) | −23.3115 | −0.974701 | ||||||||
\(573\) | −3.12403 | −0.130508 | ||||||||
\(574\) | −48.1628 | −2.01028 | ||||||||
\(575\) | −34.4474 | −1.43656 | ||||||||
\(576\) | −1.76791 | −0.0736630 | ||||||||
\(577\) | −20.6733 | −0.860639 | −0.430320 | − | 0.902677i | \(-0.641599\pi\) | ||||
−0.430320 | + | 0.902677i | \(0.641599\pi\) | |||||||
\(578\) | −16.9297 | −0.704184 | ||||||||
\(579\) | −13.5142 | −0.561632 | ||||||||
\(580\) | −32.3723 | −1.34418 | ||||||||
\(581\) | −43.6253 | −1.80988 | ||||||||
\(582\) | −9.87702 | −0.409416 | ||||||||
\(583\) | 63.4406 | 2.62744 | ||||||||
\(584\) | −4.58606 | −0.189773 | ||||||||
\(585\) | 28.2196 | 1.16674 | ||||||||
\(586\) | −27.8945 | −1.15231 | ||||||||
\(587\) | 41.0597 | 1.69472 | 0.847358 | − | 0.531022i | \(-0.178192\pi\) | ||||
0.847358 | + | 0.531022i | \(0.178192\pi\) | |||||||
\(588\) | −17.5618 | −0.724236 | ||||||||
\(589\) | 6.89712 | 0.284191 | ||||||||
\(590\) | 56.7821 | 2.33768 | ||||||||
\(591\) | −21.2499 | −0.874106 | ||||||||
\(592\) | 10.1552 | 0.417376 | ||||||||
\(593\) | −12.9632 | −0.532334 | −0.266167 | − | 0.963927i | \(-0.585757\pi\) | ||||
−0.266167 | + | 0.963927i | \(0.585757\pi\) | |||||||
\(594\) | 30.1453 | 1.23688 | ||||||||
\(595\) | 4.93935 | 0.202494 | ||||||||
\(596\) | −16.3458 | −0.669552 | ||||||||
\(597\) | −9.18217 | −0.375801 | ||||||||
\(598\) | 13.8055 | 0.564548 | ||||||||
\(599\) | 15.9737 | 0.652669 | 0.326334 | − | 0.945254i | \(-0.394186\pi\) | ||||
0.326334 | + | 0.945254i | \(0.394186\pi\) | |||||||
\(600\) | −11.3351 | −0.462754 | ||||||||
\(601\) | 24.8221 | 1.01251 | 0.506257 | − | 0.862383i | \(-0.331029\pi\) | ||||
0.506257 | + | 0.862383i | \(0.331029\pi\) | |||||||
\(602\) | 11.2378 | 0.458018 | ||||||||
\(603\) | −25.8489 | −1.05265 | ||||||||
\(604\) | −10.9227 | −0.444440 | ||||||||
\(605\) | 83.6386 | 3.40039 | ||||||||
\(606\) | −9.17869 | −0.372859 | ||||||||
\(607\) | −7.47649 | −0.303462 | −0.151731 | − | 0.988422i | \(-0.548485\pi\) | ||||
−0.151731 | + | 0.988422i | \(0.548485\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −44.0124 | −1.78347 | ||||||||
\(610\) | 12.0788 | 0.489058 | ||||||||
\(611\) | −3.71178 | −0.150162 | ||||||||
\(612\) | 0.468670 | 0.0189449 | ||||||||
\(613\) | −17.7196 | −0.715689 | −0.357844 | − | 0.933781i | \(-0.616488\pi\) | ||||
−0.357844 | + | 0.933781i | \(0.616488\pi\) | |||||||
\(614\) | 5.14591 | 0.207672 | ||||||||
\(615\) | −43.6468 | −1.76001 | ||||||||
\(616\) | −27.2109 | −1.09636 | ||||||||
\(617\) | 43.5877 | 1.75477 | 0.877387 | − | 0.479784i | \(-0.159285\pi\) | ||||
0.877387 | + | 0.479784i | \(0.159285\pi\) | |||||||
\(618\) | −18.9652 | −0.762893 | ||||||||
\(619\) | −16.3139 | −0.655712 | −0.327856 | − | 0.944728i | \(-0.606326\pi\) | ||||
−0.327856 | + | 0.944728i | \(0.606326\pi\) | |||||||
\(620\) | −26.9004 | −1.08035 | ||||||||
\(621\) | −17.8526 | −0.716400 | ||||||||
\(622\) | −0.505072 | −0.0202516 | ||||||||
\(623\) | 29.5726 | 1.18480 | ||||||||
\(624\) | 4.54276 | 0.181856 | ||||||||
\(625\) | 28.2226 | 1.12891 | ||||||||
\(626\) | −13.1933 | −0.527308 | ||||||||
\(627\) | 6.32254 | 0.252498 | ||||||||
\(628\) | −2.38660 | −0.0952359 | ||||||||
\(629\) | −2.69213 | −0.107342 | ||||||||
\(630\) | 32.9400 | 1.31236 | ||||||||
\(631\) | −7.93271 | −0.315796 | −0.157898 | − | 0.987455i | \(-0.550472\pi\) | ||||
−0.157898 | + | 0.987455i | \(0.550472\pi\) | |||||||
\(632\) | −5.66673 | −0.225410 | ||||||||
\(633\) | 1.10999 | 0.0441183 | ||||||||
\(634\) | 30.1676 | 1.19811 | ||||||||
\(635\) | −33.5677 | −1.33209 | ||||||||
\(636\) | −12.3628 | −0.490218 | ||||||||
\(637\) | −64.7510 | −2.56553 | ||||||||
\(638\) | −47.2773 | −1.87172 | ||||||||
\(639\) | 22.5628 | 0.892572 | ||||||||
\(640\) | 3.90024 | 0.154170 | ||||||||
\(641\) | 44.2457 | 1.74760 | 0.873799 | − | 0.486287i | \(-0.161649\pi\) | ||||
0.873799 | + | 0.486287i | \(0.161649\pi\) | |||||||
\(642\) | 6.79379 | 0.268129 | ||||||||
\(643\) | 20.3317 | 0.801805 | 0.400903 | − | 0.916121i | \(-0.368697\pi\) | ||||
0.400903 | + | 0.916121i | \(0.368697\pi\) | |||||||
\(644\) | 16.1148 | 0.635012 | ||||||||
\(645\) | 10.1840 | 0.400997 | ||||||||
\(646\) | 0.265098 | 0.0104302 | ||||||||
\(647\) | 38.4286 | 1.51078 | 0.755391 | − | 0.655274i | \(-0.227447\pi\) | ||||
0.755391 | + | 0.655274i | \(0.227447\pi\) | |||||||
\(648\) | −0.570756 | −0.0224214 | ||||||||
\(649\) | 82.9260 | 3.25513 | ||||||||
\(650\) | −41.7930 | −1.63926 | ||||||||
\(651\) | −36.5730 | −1.43341 | ||||||||
\(652\) | 3.26419 | 0.127836 | ||||||||
\(653\) | −15.8840 | −0.621587 | −0.310794 | − | 0.950477i | \(-0.600595\pi\) | ||||
−0.310794 | + | 0.950477i | \(0.600595\pi\) | |||||||
\(654\) | 3.32021 | 0.129831 | ||||||||
\(655\) | −31.4472 | −1.22874 | ||||||||
\(656\) | 10.0818 | 0.393630 | ||||||||
\(657\) | 8.10775 | 0.316313 | ||||||||
\(658\) | −4.33266 | −0.168905 | ||||||||
\(659\) | −17.8974 | −0.697185 | −0.348592 | − | 0.937274i | \(-0.613340\pi\) | ||||
−0.348592 | + | 0.937274i | \(0.613340\pi\) | |||||||
\(660\) | −24.6594 | −0.959866 | ||||||||
\(661\) | −46.5929 | −1.81225 | −0.906127 | − | 0.423005i | \(-0.860975\pi\) | ||||
−0.906127 | + | 0.423005i | \(0.860975\pi\) | |||||||
\(662\) | 12.9868 | 0.504745 | ||||||||
\(663\) | −1.20428 | −0.0467703 | ||||||||
\(664\) | 9.13201 | 0.354391 | ||||||||
\(665\) | 18.6322 | 0.722524 | ||||||||
\(666\) | −17.9535 | −0.695684 | ||||||||
\(667\) | 27.9985 | 1.08411 | ||||||||
\(668\) | 2.79406 | 0.108105 | ||||||||
\(669\) | 21.3982 | 0.827300 | ||||||||
\(670\) | 57.0260 | 2.20311 | ||||||||
\(671\) | 17.6402 | 0.680994 | ||||||||
\(672\) | 5.30265 | 0.204554 | ||||||||
\(673\) | 11.6224 | 0.448012 | 0.224006 | − | 0.974588i | \(-0.428086\pi\) | ||||
0.224006 | + | 0.974588i | \(0.428086\pi\) | |||||||
\(674\) | 14.6345 | 0.563699 | ||||||||
\(675\) | 54.0448 | 2.08018 | ||||||||
\(676\) | 3.74935 | 0.144206 | ||||||||
\(677\) | 24.5098 | 0.941988 | 0.470994 | − | 0.882137i | \(-0.343895\pi\) | ||||
0.470994 | + | 0.882137i | \(0.343895\pi\) | |||||||
\(678\) | −9.72294 | −0.373407 | ||||||||
\(679\) | −42.5086 | −1.63133 | ||||||||
\(680\) | −1.03395 | −0.0396500 | ||||||||
\(681\) | −9.62561 | −0.368854 | ||||||||
\(682\) | −39.2860 | −1.50434 | ||||||||
\(683\) | 43.1677 | 1.65176 | 0.825882 | − | 0.563843i | \(-0.190678\pi\) | ||||
0.825882 | + | 0.563843i | \(0.190678\pi\) | |||||||
\(684\) | 1.76791 | 0.0675978 | ||||||||
\(685\) | 27.1162 | 1.03606 | ||||||||
\(686\) | −42.1419 | −1.60899 | ||||||||
\(687\) | −10.7630 | −0.410633 | ||||||||
\(688\) | −2.35239 | −0.0896839 | ||||||||
\(689\) | −45.5823 | −1.73655 | ||||||||
\(690\) | 14.6038 | 0.555955 | ||||||||
\(691\) | −35.8995 | −1.36568 | −0.682841 | − | 0.730567i | \(-0.739256\pi\) | ||||
−0.682841 | + | 0.730567i | \(0.739256\pi\) | |||||||
\(692\) | 16.5663 | 0.629756 | ||||||||
\(693\) | 48.1064 | 1.82741 | ||||||||
\(694\) | 13.9248 | 0.528578 | ||||||||
\(695\) | 66.8968 | 2.53754 | ||||||||
\(696\) | 9.21304 | 0.349219 | ||||||||
\(697\) | −2.67268 | −0.101235 | ||||||||
\(698\) | 12.9954 | 0.491883 | ||||||||
\(699\) | 7.97411 | 0.301609 | ||||||||
\(700\) | −48.7839 | −1.84386 | ||||||||
\(701\) | 49.3097 | 1.86240 | 0.931201 | − | 0.364506i | \(-0.118762\pi\) | ||||
0.931201 | + | 0.364506i | \(0.118762\pi\) | |||||||
\(702\) | −21.6595 | −0.817485 | ||||||||
\(703\) | −10.1552 | −0.383011 | ||||||||
\(704\) | 5.69601 | 0.214676 | ||||||||
\(705\) | −3.92640 | −0.147877 | ||||||||
\(706\) | −0.158909 | −0.00598061 | ||||||||
\(707\) | −39.5032 | −1.48567 | ||||||||
\(708\) | −16.1600 | −0.607330 | ||||||||
\(709\) | −20.2346 | −0.759925 | −0.379962 | − | 0.925002i | \(-0.624063\pi\) | ||||
−0.379962 | + | 0.925002i | \(0.624063\pi\) | |||||||
\(710\) | −49.7765 | −1.86808 | ||||||||
\(711\) | 10.0183 | 0.375714 | ||||||||
\(712\) | −6.19037 | −0.231994 | ||||||||
\(713\) | 23.2659 | 0.871316 | ||||||||
\(714\) | −1.40572 | −0.0526079 | ||||||||
\(715\) | −90.9202 | −3.40022 | ||||||||
\(716\) | 11.5835 | 0.432897 | ||||||||
\(717\) | −1.06903 | −0.0399235 | ||||||||
\(718\) | −20.9540 | −0.781997 | ||||||||
\(719\) | −0.478346 | −0.0178393 | −0.00891966 | − | 0.999960i | \(-0.502839\pi\) | ||||
−0.00891966 | + | 0.999960i | \(0.502839\pi\) | |||||||
\(720\) | −6.89527 | −0.256972 | ||||||||
\(721\) | −81.6223 | −3.03977 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 12.9602 | 0.481995 | ||||||||
\(724\) | −1.55513 | −0.0577960 | ||||||||
\(725\) | −84.7591 | −3.14787 | ||||||||
\(726\) | −23.8033 | −0.883422 | ||||||||
\(727\) | 1.60528 | 0.0595366 | 0.0297683 | − | 0.999557i | \(-0.490523\pi\) | ||||
0.0297683 | + | 0.999557i | \(0.490523\pi\) | |||||||
\(728\) | 19.5511 | 0.724612 | ||||||||
\(729\) | 18.6325 | 0.690093 | ||||||||
\(730\) | −17.8867 | −0.662018 | ||||||||
\(731\) | 0.623613 | 0.0230652 | ||||||||
\(732\) | −3.43760 | −0.127057 | ||||||||
\(733\) | 0.287647 | 0.0106245 | 0.00531224 | − | 0.999986i | \(-0.498309\pi\) | ||||
0.00531224 | + | 0.999986i | \(0.498309\pi\) | |||||||
\(734\) | −17.7347 | −0.654601 | ||||||||
\(735\) | −68.4951 | −2.52648 | ||||||||
\(736\) | −3.37328 | −0.124341 | ||||||||
\(737\) | 83.2822 | 3.06774 | ||||||||
\(738\) | −17.8238 | −0.656103 | ||||||||
\(739\) | −25.5231 | −0.938882 | −0.469441 | − | 0.882964i | \(-0.655544\pi\) | ||||
−0.469441 | + | 0.882964i | \(0.655544\pi\) | |||||||
\(740\) | 39.6077 | 1.45601 | ||||||||
\(741\) | −4.54276 | −0.166883 | ||||||||
\(742\) | −53.2071 | −1.95329 | ||||||||
\(743\) | −50.6257 | −1.85728 | −0.928638 | − | 0.370987i | \(-0.879020\pi\) | ||||
−0.928638 | + | 0.370987i | \(0.879020\pi\) | |||||||
\(744\) | 7.65577 | 0.280674 | ||||||||
\(745\) | −63.7527 | −2.33572 | ||||||||
\(746\) | −3.71068 | −0.135857 | ||||||||
\(747\) | −16.1446 | −0.590700 | ||||||||
\(748\) | −1.51000 | −0.0552111 | ||||||||
\(749\) | 29.2390 | 1.06837 | ||||||||
\(750\) | −22.5634 | −0.823898 | ||||||||
\(751\) | 43.1146 | 1.57327 | 0.786637 | − | 0.617416i | \(-0.211820\pi\) | ||||
0.786637 | + | 0.617416i | \(0.211820\pi\) | |||||||
\(752\) | 0.906948 | 0.0330730 | ||||||||
\(753\) | 20.6310 | 0.751835 | ||||||||
\(754\) | 33.9689 | 1.23707 | ||||||||
\(755\) | −42.6013 | −1.55042 | ||||||||
\(756\) | −25.2826 | −0.919518 | ||||||||
\(757\) | −20.1770 | −0.733345 | −0.366672 | − | 0.930350i | \(-0.619503\pi\) | ||||
−0.366672 | + | 0.930350i | \(0.619503\pi\) | |||||||
\(758\) | 30.0212 | 1.09042 | ||||||||
\(759\) | 21.3277 | 0.774146 | ||||||||
\(760\) | −3.90024 | −0.141476 | ||||||||
\(761\) | 52.9210 | 1.91838 | 0.959192 | − | 0.282757i | \(-0.0912488\pi\) | ||||
0.959192 | + | 0.282757i | \(0.0912488\pi\) | |||||||
\(762\) | 9.55326 | 0.346078 | ||||||||
\(763\) | 14.2895 | 0.517315 | ||||||||
\(764\) | 2.81445 | 0.101823 | ||||||||
\(765\) | 1.82793 | 0.0660888 | ||||||||
\(766\) | −14.3270 | −0.517657 | ||||||||
\(767\) | −59.5826 | −2.15140 | ||||||||
\(768\) | −1.10999 | −0.0400535 | ||||||||
\(769\) | 0.842653 | 0.0303869 | 0.0151934 | − | 0.999885i | \(-0.495164\pi\) | ||||
0.0151934 | + | 0.999885i | \(0.495164\pi\) | |||||||
\(770\) | −106.129 | −3.82462 | ||||||||
\(771\) | −19.0486 | −0.686017 | ||||||||
\(772\) | 12.1750 | 0.438189 | ||||||||
\(773\) | −4.54848 | −0.163598 | −0.0817988 | − | 0.996649i | \(-0.526066\pi\) | ||||
−0.0817988 | + | 0.996649i | \(0.526066\pi\) | |||||||
\(774\) | 4.15881 | 0.149485 | ||||||||
\(775\) | −70.4324 | −2.53000 | ||||||||
\(776\) | 8.89825 | 0.319429 | ||||||||
\(777\) | 53.8495 | 1.93184 | ||||||||
\(778\) | 2.66506 | 0.0955470 | ||||||||
\(779\) | −10.0818 | −0.361220 | ||||||||
\(780\) | 17.7179 | 0.634401 | ||||||||
\(781\) | −72.6948 | −2.60123 | ||||||||
\(782\) | 0.894251 | 0.0319784 | ||||||||
\(783\) | −43.9270 | −1.56982 | ||||||||
\(784\) | 15.8215 | 0.565054 | ||||||||
\(785\) | −9.30832 | −0.332228 | ||||||||
\(786\) | 8.94976 | 0.319228 | ||||||||
\(787\) | 40.8477 | 1.45606 | 0.728032 | − | 0.685544i | \(-0.240435\pi\) | ||||
0.728032 | + | 0.685544i | \(0.240435\pi\) | |||||||
\(788\) | 19.1442 | 0.681983 | ||||||||
\(789\) | 9.16683 | 0.326348 | ||||||||
\(790\) | −22.1016 | −0.786339 | ||||||||
\(791\) | −41.8455 | −1.48785 | ||||||||
\(792\) | −10.0700 | −0.357823 | ||||||||
\(793\) | −12.6746 | −0.450087 | ||||||||
\(794\) | −8.22764 | −0.291988 | ||||||||
\(795\) | −48.2180 | −1.71012 | ||||||||
\(796\) | 8.27226 | 0.293203 | ||||||||
\(797\) | 39.1845 | 1.38798 | 0.693992 | − | 0.719982i | \(-0.255850\pi\) | ||||
0.693992 | + | 0.719982i | \(0.255850\pi\) | |||||||
\(798\) | −5.30265 | −0.187712 | ||||||||
\(799\) | −0.240431 | −0.00850582 | ||||||||
\(800\) | 10.2119 | 0.361043 | ||||||||
\(801\) | 10.9440 | 0.386688 | ||||||||
\(802\) | 16.2754 | 0.574706 | ||||||||
\(803\) | −26.1222 | −0.921834 | ||||||||
\(804\) | −16.2294 | −0.572368 | ||||||||
\(805\) | 62.8515 | 2.21522 | ||||||||
\(806\) | 28.2271 | 0.994258 | ||||||||
\(807\) | −19.3795 | −0.682189 | ||||||||
\(808\) | 8.26913 | 0.290907 | ||||||||
\(809\) | 10.3248 | 0.363000 | 0.181500 | − | 0.983391i | \(-0.441905\pi\) | ||||
0.181500 | + | 0.983391i | \(0.441905\pi\) | |||||||
\(810\) | −2.22608 | −0.0782166 | ||||||||
\(811\) | −39.6352 | −1.39178 | −0.695890 | − | 0.718149i | \(-0.744990\pi\) | ||||
−0.695890 | + | 0.718149i | \(0.744990\pi\) | |||||||
\(812\) | 39.6510 | 1.39148 | ||||||||
\(813\) | 9.62561 | 0.337585 | ||||||||
\(814\) | 57.8441 | 2.02743 | ||||||||
\(815\) | 12.7311 | 0.445952 | ||||||||
\(816\) | 0.294258 | 0.0103011 | ||||||||
\(817\) | 2.35239 | 0.0822996 | ||||||||
\(818\) | −2.15867 | −0.0754763 | ||||||||
\(819\) | −34.5646 | −1.20778 | ||||||||
\(820\) | 39.3216 | 1.37317 | ||||||||
\(821\) | 11.2275 | 0.391844 | 0.195922 | − | 0.980620i | \(-0.437230\pi\) | ||||
0.195922 | + | 0.980620i | \(0.437230\pi\) | |||||||
\(822\) | −7.71718 | −0.269168 | ||||||||
\(823\) | 35.1955 | 1.22684 | 0.613420 | − | 0.789757i | \(-0.289793\pi\) | ||||
0.613420 | + | 0.789757i | \(0.289793\pi\) | |||||||
\(824\) | 17.0859 | 0.595214 | ||||||||
\(825\) | −64.5648 | −2.24786 | ||||||||
\(826\) | −69.5492 | −2.41993 | ||||||||
\(827\) | −42.5451 | −1.47944 | −0.739719 | − | 0.672916i | \(-0.765041\pi\) | ||||
−0.739719 | + | 0.672916i | \(0.765041\pi\) | |||||||
\(828\) | 5.96366 | 0.207252 | ||||||||
\(829\) | 4.57321 | 0.158834 | 0.0794171 | − | 0.996841i | \(-0.474694\pi\) | ||||
0.0794171 | + | 0.996841i | \(0.474694\pi\) | |||||||
\(830\) | 35.6170 | 1.23628 | ||||||||
\(831\) | −14.4423 | −0.500997 | ||||||||
\(832\) | −4.09260 | −0.141885 | ||||||||
\(833\) | −4.19425 | −0.145322 | ||||||||
\(834\) | −19.0386 | −0.659253 | ||||||||
\(835\) | 10.8975 | 0.377123 | ||||||||
\(836\) | −5.69601 | −0.197000 | ||||||||
\(837\) | −36.5020 | −1.26169 | ||||||||
\(838\) | −12.5558 | −0.433734 | ||||||||
\(839\) | −42.4314 | −1.46489 | −0.732447 | − | 0.680824i | \(-0.761622\pi\) | ||||
−0.732447 | + | 0.680824i | \(0.761622\pi\) | |||||||
\(840\) | 20.6816 | 0.713583 | ||||||||
\(841\) | 39.8912 | 1.37556 | ||||||||
\(842\) | −16.4123 | −0.565607 | ||||||||
\(843\) | 17.0389 | 0.586851 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 14.6234 | 0.503059 | ||||||||
\(846\) | −1.60340 | −0.0551262 | ||||||||
\(847\) | −102.444 | −3.52003 | ||||||||
\(848\) | 11.1377 | 0.382472 | ||||||||
\(849\) | 29.3871 | 1.00856 | ||||||||
\(850\) | −2.70714 | −0.0928543 | ||||||||
\(851\) | −34.2563 | −1.17429 | ||||||||
\(852\) | 14.1662 | 0.485327 | ||||||||
\(853\) | −27.7354 | −0.949641 | −0.474820 | − | 0.880083i | \(-0.657487\pi\) | ||||
−0.474820 | + | 0.880083i | \(0.657487\pi\) | |||||||
\(854\) | −14.7947 | −0.506264 | ||||||||
\(855\) | 6.89527 | 0.235813 | ||||||||
\(856\) | −6.12056 | −0.209196 | ||||||||
\(857\) | −29.3738 | −1.00339 | −0.501695 | − | 0.865045i | \(-0.667290\pi\) | ||||
−0.501695 | + | 0.865045i | \(0.667290\pi\) | |||||||
\(858\) | 25.8756 | 0.883378 | ||||||||
\(859\) | 36.3973 | 1.24186 | 0.620930 | − | 0.783866i | \(-0.286755\pi\) | ||||
0.620930 | + | 0.783866i | \(0.286755\pi\) | |||||||
\(860\) | −9.17486 | −0.312860 | ||||||||
\(861\) | 53.4605 | 1.82193 | ||||||||
\(862\) | 6.50015 | 0.221396 | ||||||||
\(863\) | 41.5384 | 1.41398 | 0.706992 | − | 0.707221i | \(-0.250052\pi\) | ||||
0.706992 | + | 0.707221i | \(0.250052\pi\) | |||||||
\(864\) | 5.29236 | 0.180050 | ||||||||
\(865\) | 64.6124 | 2.19689 | ||||||||
\(866\) | 11.9525 | 0.406161 | ||||||||
\(867\) | 18.7919 | 0.638207 | ||||||||
\(868\) | 32.9488 | 1.11836 | ||||||||
\(869\) | −32.2777 | −1.09495 | ||||||||
\(870\) | 35.9330 | 1.21824 | ||||||||
\(871\) | −59.8386 | −2.02755 | ||||||||
\(872\) | −2.99120 | −0.101295 | ||||||||
\(873\) | −15.7313 | −0.532425 | ||||||||
\(874\) | 3.37328 | 0.114103 | ||||||||
\(875\) | −97.1080 | −3.28285 | ||||||||
\(876\) | 5.09051 | 0.171992 | ||||||||
\(877\) | −19.7182 | −0.665837 | −0.332918 | − | 0.942956i | \(-0.608033\pi\) | ||||
−0.332918 | + | 0.942956i | \(0.608033\pi\) | |||||||
\(878\) | −12.3919 | −0.418207 | ||||||||
\(879\) | 30.9627 | 1.04435 | ||||||||
\(880\) | 22.2158 | 0.748894 | ||||||||
\(881\) | 30.6119 | 1.03134 | 0.515670 | − | 0.856787i | \(-0.327543\pi\) | ||||
0.515670 | + | 0.856787i | \(0.327543\pi\) | |||||||
\(882\) | −27.9710 | −0.941833 | ||||||||
\(883\) | −44.0343 | −1.48187 | −0.740937 | − | 0.671575i | \(-0.765618\pi\) | ||||
−0.740937 | + | 0.671575i | \(0.765618\pi\) | |||||||
\(884\) | 1.08494 | 0.0364905 | ||||||||
\(885\) | −63.0278 | −2.11866 | ||||||||
\(886\) | −13.0536 | −0.438544 | ||||||||
\(887\) | 14.0781 | 0.472696 | 0.236348 | − | 0.971668i | \(-0.424049\pi\) | ||||
0.236348 | + | 0.971668i | \(0.424049\pi\) | |||||||
\(888\) | −11.2722 | −0.378271 | ||||||||
\(889\) | 41.1152 | 1.37896 | ||||||||
\(890\) | −24.1439 | −0.809306 | ||||||||
\(891\) | −3.25103 | −0.108914 | ||||||||
\(892\) | −19.2777 | −0.645465 | ||||||||
\(893\) | −0.906948 | −0.0303499 | ||||||||
\(894\) | 18.1438 | 0.606820 | ||||||||
\(895\) | 45.1785 | 1.51015 | ||||||||
\(896\) | −4.77719 | −0.159595 | ||||||||
\(897\) | −15.3240 | −0.511654 | ||||||||
\(898\) | 29.4917 | 0.984151 | ||||||||
\(899\) | 57.2466 | 1.90928 | ||||||||
\(900\) | −18.0536 | −0.601788 | ||||||||
\(901\) | −2.95260 | −0.0983653 | ||||||||
\(902\) | 57.4262 | 1.91208 | ||||||||
\(903\) | −12.4739 | −0.415105 | ||||||||
\(904\) | 8.75944 | 0.291335 | ||||||||
\(905\) | −6.06538 | −0.201620 | ||||||||
\(906\) | 12.1242 | 0.402799 | ||||||||
\(907\) | −22.2892 | −0.740101 | −0.370050 | − | 0.929012i | \(-0.620660\pi\) | ||||
−0.370050 | + | 0.929012i | \(0.620660\pi\) | |||||||
\(908\) | 8.67176 | 0.287782 | ||||||||
\(909\) | −14.6191 | −0.484885 | ||||||||
\(910\) | 76.2539 | 2.52779 | ||||||||
\(911\) | −35.2058 | −1.16642 | −0.583210 | − | 0.812321i | \(-0.698204\pi\) | ||||
−0.583210 | + | 0.812321i | \(0.698204\pi\) | |||||||
\(912\) | 1.10999 | 0.0367556 | ||||||||
\(913\) | 52.0160 | 1.72148 | ||||||||
\(914\) | −0.324966 | −0.0107489 | ||||||||
\(915\) | −13.4075 | −0.443237 | ||||||||
\(916\) | 9.69642 | 0.320379 | ||||||||
\(917\) | 38.5179 | 1.27197 | ||||||||
\(918\) | −1.40300 | −0.0463057 | ||||||||
\(919\) | −33.0931 | −1.09164 | −0.545820 | − | 0.837902i | \(-0.683782\pi\) | ||||
−0.545820 | + | 0.837902i | \(0.683782\pi\) | |||||||
\(920\) | −13.1566 | −0.433760 | ||||||||
\(921\) | −5.71194 | −0.188215 | ||||||||
\(922\) | 38.2872 | 1.26092 | ||||||||
\(923\) | 52.2315 | 1.71922 | ||||||||
\(924\) | 30.2039 | 0.993636 | ||||||||
\(925\) | 103.703 | 3.40975 | ||||||||
\(926\) | 34.0027 | 1.11740 | ||||||||
\(927\) | −30.2063 | −0.992105 | ||||||||
\(928\) | −8.30007 | −0.272463 | ||||||||
\(929\) | −15.3128 | −0.502396 | −0.251198 | − | 0.967936i | \(-0.580825\pi\) | ||||
−0.251198 | + | 0.967936i | \(0.580825\pi\) | |||||||
\(930\) | 29.8593 | 0.979125 | ||||||||
\(931\) | −15.8215 | −0.518529 | ||||||||
\(932\) | −7.18392 | −0.235317 | ||||||||
\(933\) | 0.560628 | 0.0183541 | ||||||||
\(934\) | −21.4709 | −0.702550 | ||||||||
\(935\) | −5.88936 | −0.192603 | ||||||||
\(936\) | 7.23535 | 0.236495 | ||||||||
\(937\) | 22.5877 | 0.737909 | 0.368955 | − | 0.929447i | \(-0.379716\pi\) | ||||
0.368955 | + | 0.929447i | \(0.379716\pi\) | |||||||
\(938\) | −69.8480 | −2.28062 | ||||||||
\(939\) | 14.6444 | 0.477903 | ||||||||
\(940\) | 3.53731 | 0.115374 | ||||||||
\(941\) | 4.08923 | 0.133305 | 0.0666525 | − | 0.997776i | \(-0.478768\pi\) | ||||
0.0666525 | + | 0.997776i | \(0.478768\pi\) | |||||||
\(942\) | 2.64912 | 0.0863130 | ||||||||
\(943\) | −34.0089 | −1.10748 | ||||||||
\(944\) | 14.5586 | 0.473843 | ||||||||
\(945\) | −98.6080 | −3.20772 | ||||||||
\(946\) | −13.3992 | −0.435646 | ||||||||
\(947\) | −17.9025 | −0.581752 | −0.290876 | − | 0.956761i | \(-0.593947\pi\) | ||||
−0.290876 | + | 0.956761i | \(0.593947\pi\) | |||||||
\(948\) | 6.29004 | 0.204291 | ||||||||
\(949\) | 18.7689 | 0.609264 | ||||||||
\(950\) | −10.2119 | −0.331316 | ||||||||
\(951\) | −33.4859 | −1.08585 | ||||||||
\(952\) | 1.26642 | 0.0410450 | ||||||||
\(953\) | −7.02237 | −0.227477 | −0.113738 | − | 0.993511i | \(-0.536283\pi\) | ||||
−0.113738 | + | 0.993511i | \(0.536283\pi\) | |||||||
\(954\) | −19.6905 | −0.637505 | ||||||||
\(955\) | 10.9770 | 0.355209 | ||||||||
\(956\) | 0.963091 | 0.0311486 | ||||||||
\(957\) | 52.4775 | 1.69636 | ||||||||
\(958\) | 5.37891 | 0.173785 | ||||||||
\(959\) | −33.2131 | −1.07251 | ||||||||
\(960\) | −4.32924 | −0.139726 | ||||||||
\(961\) | 16.5703 | 0.534525 | ||||||||
\(962\) | −41.5612 | −1.33999 | ||||||||
\(963\) | 10.8206 | 0.348689 | ||||||||
\(964\) | −11.6759 | −0.376055 | ||||||||
\(965\) | 47.4855 | 1.52861 | ||||||||
\(966\) | −17.8873 | −0.575515 | ||||||||
\(967\) | −22.6933 | −0.729768 | −0.364884 | − | 0.931053i | \(-0.618891\pi\) | ||||
−0.364884 | + | 0.931053i | \(0.618891\pi\) | |||||||
\(968\) | 21.4445 | 0.689252 | ||||||||
\(969\) | −0.294258 | −0.00945292 | ||||||||
\(970\) | 34.7053 | 1.11432 | ||||||||
\(971\) | −39.1564 | −1.25659 | −0.628294 | − | 0.777976i | \(-0.716247\pi\) | ||||
−0.628294 | + | 0.777976i | \(0.716247\pi\) | |||||||
\(972\) | −15.2435 | −0.488937 | ||||||||
\(973\) | −81.9381 | −2.62682 | ||||||||
\(974\) | −14.1416 | −0.453124 | ||||||||
\(975\) | 46.3900 | 1.48567 | ||||||||
\(976\) | 3.09695 | 0.0991310 | ||||||||
\(977\) | 54.7113 | 1.75037 | 0.875184 | − | 0.483790i | \(-0.160740\pi\) | ||||
0.875184 | + | 0.483790i | \(0.160740\pi\) | |||||||
\(978\) | −3.62324 | −0.115858 | ||||||||
\(979\) | −35.2604 | −1.12693 | ||||||||
\(980\) | 61.7076 | 1.97118 | ||||||||
\(981\) | 5.28817 | 0.168838 | ||||||||
\(982\) | 19.7165 | 0.629177 | ||||||||
\(983\) | −35.1469 | −1.12101 | −0.560506 | − | 0.828150i | \(-0.689393\pi\) | ||||
−0.560506 | + | 0.828150i | \(0.689393\pi\) | |||||||
\(984\) | −11.1908 | −0.356750 | ||||||||
\(985\) | 74.6668 | 2.37908 | ||||||||
\(986\) | 2.20034 | 0.0700730 | ||||||||
\(987\) | 4.80923 | 0.153080 | ||||||||
\(988\) | 4.09260 | 0.130203 | ||||||||
\(989\) | 7.93526 | 0.252326 | ||||||||
\(990\) | −39.2755 | −1.24826 | ||||||||
\(991\) | −26.9873 | −0.857279 | −0.428640 | − | 0.903476i | \(-0.641007\pi\) | ||||
−0.428640 | + | 0.903476i | \(0.641007\pi\) | |||||||
\(992\) | −6.89712 | −0.218984 | ||||||||
\(993\) | −14.4153 | −0.457454 | ||||||||
\(994\) | 60.9685 | 1.93380 | ||||||||
\(995\) | 32.2638 | 1.02283 | ||||||||
\(996\) | −10.1365 | −0.321187 | ||||||||
\(997\) | −6.27963 | −0.198878 | −0.0994389 | − | 0.995044i | \(-0.531705\pi\) | ||||
−0.0994389 | + | 0.995044i | \(0.531705\pi\) | |||||||
\(998\) | −38.5801 | −1.22123 | ||||||||
\(999\) | 53.7450 | 1.70042 |
(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 | 8018.2.a.j.1.16 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.16 | ✓ | 47 | 1.1 | even | 1 | trivial |