Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-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 | ||||||||
\(3\) | −1.70684 | −0.985443 | −0.492722 | − | 0.870187i | \(-0.663998\pi\) | ||||
−0.492722 | + | 0.870187i | \(0.663998\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.82175 | −1.26193 | −0.630963 | − | 0.775813i | \(-0.717340\pi\) | ||||
−0.630963 | + | 0.775813i | \(0.717340\pi\) | |||||||
\(6\) | −1.70684 | −0.696813 | ||||||||
\(7\) | 3.08724 | 1.16687 | 0.583434 | − | 0.812160i | \(-0.301709\pi\) | ||||
0.583434 | + | 0.812160i | \(0.301709\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.0867059 | −0.0289020 | ||||||||
\(10\) | −2.82175 | −0.892317 | ||||||||
\(11\) | −4.90438 | −1.47873 | −0.739363 | − | 0.673308i | \(-0.764873\pi\) | ||||
−0.739363 | + | 0.673308i | \(0.764873\pi\) | |||||||
\(12\) | −1.70684 | −0.492722 | ||||||||
\(13\) | 4.27139 | 1.18467 | 0.592335 | − | 0.805692i | \(-0.298206\pi\) | ||||
0.592335 | + | 0.805692i | \(0.298206\pi\) | |||||||
\(14\) | 3.08724 | 0.825101 | ||||||||
\(15\) | 4.81627 | 1.24356 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.86202 | −0.451606 | −0.225803 | − | 0.974173i | \(-0.572501\pi\) | ||||
−0.225803 | + | 0.974173i | \(0.572501\pi\) | |||||||
\(18\) | −0.0867059 | −0.0204368 | ||||||||
\(19\) | 2.06959 | 0.474797 | 0.237399 | − | 0.971412i | \(-0.423705\pi\) | ||||
0.237399 | + | 0.971412i | \(0.423705\pi\) | |||||||
\(20\) | −2.82175 | −0.630963 | ||||||||
\(21\) | −5.26942 | −1.14988 | ||||||||
\(22\) | −4.90438 | −1.04562 | ||||||||
\(23\) | 2.71479 | 0.566073 | 0.283037 | − | 0.959109i | \(-0.408658\pi\) | ||||
0.283037 | + | 0.959109i | \(0.408658\pi\) | |||||||
\(24\) | −1.70684 | −0.348407 | ||||||||
\(25\) | 2.96229 | 0.592458 | ||||||||
\(26\) | 4.27139 | 0.837688 | ||||||||
\(27\) | 5.26851 | 1.01392 | ||||||||
\(28\) | 3.08724 | 0.583434 | ||||||||
\(29\) | −6.82587 | −1.26753 | −0.633766 | − | 0.773525i | \(-0.718492\pi\) | ||||
−0.633766 | + | 0.773525i | \(0.718492\pi\) | |||||||
\(30\) | 4.81627 | 0.879327 | ||||||||
\(31\) | −3.46894 | −0.623040 | −0.311520 | − | 0.950240i | \(-0.600838\pi\) | ||||
−0.311520 | + | 0.950240i | \(0.600838\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 8.37097 | 1.45720 | ||||||||
\(34\) | −1.86202 | −0.319334 | ||||||||
\(35\) | −8.71144 | −1.47250 | ||||||||
\(36\) | −0.0867059 | −0.0144510 | ||||||||
\(37\) | 7.04587 | 1.15833 | 0.579167 | − | 0.815209i | \(-0.303378\pi\) | ||||
0.579167 | + | 0.815209i | \(0.303378\pi\) | |||||||
\(38\) | 2.06959 | 0.335732 | ||||||||
\(39\) | −7.29056 | −1.16742 | ||||||||
\(40\) | −2.82175 | −0.446158 | ||||||||
\(41\) | 2.46434 | 0.384865 | 0.192433 | − | 0.981310i | \(-0.438362\pi\) | ||||
0.192433 | + | 0.981310i | \(0.438362\pi\) | |||||||
\(42\) | −5.26942 | −0.813090 | ||||||||
\(43\) | 4.50056 | 0.686329 | 0.343165 | − | 0.939275i | \(-0.388501\pi\) | ||||
0.343165 | + | 0.939275i | \(0.388501\pi\) | |||||||
\(44\) | −4.90438 | −0.739363 | ||||||||
\(45\) | 0.244663 | 0.0364721 | ||||||||
\(46\) | 2.71479 | 0.400274 | ||||||||
\(47\) | −12.4312 | −1.81328 | −0.906638 | − | 0.421910i | \(-0.861360\pi\) | ||||
−0.906638 | + | 0.421910i | \(0.861360\pi\) | |||||||
\(48\) | −1.70684 | −0.246361 | ||||||||
\(49\) | 2.53108 | 0.361582 | ||||||||
\(50\) | 2.96229 | 0.418931 | ||||||||
\(51\) | 3.17816 | 0.445032 | ||||||||
\(52\) | 4.27139 | 0.592335 | ||||||||
\(53\) | −4.92975 | −0.677153 | −0.338576 | − | 0.940939i | \(-0.609945\pi\) | ||||
−0.338576 | + | 0.940939i | \(0.609945\pi\) | |||||||
\(54\) | 5.26851 | 0.716953 | ||||||||
\(55\) | 13.8389 | 1.86604 | ||||||||
\(56\) | 3.08724 | 0.412550 | ||||||||
\(57\) | −3.53246 | −0.467886 | ||||||||
\(58\) | −6.82587 | −0.896280 | ||||||||
\(59\) | 3.42311 | 0.445652 | 0.222826 | − | 0.974858i | \(-0.428472\pi\) | ||||
0.222826 | + | 0.974858i | \(0.428472\pi\) | |||||||
\(60\) | 4.81627 | 0.621778 | ||||||||
\(61\) | 3.82089 | 0.489215 | 0.244607 | − | 0.969622i | \(-0.421341\pi\) | ||||
0.244607 | + | 0.969622i | \(0.421341\pi\) | |||||||
\(62\) | −3.46894 | −0.440556 | ||||||||
\(63\) | −0.267682 | −0.0337248 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.0528 | −1.49497 | ||||||||
\(66\) | 8.37097 | 1.03040 | ||||||||
\(67\) | 4.78132 | 0.584131 | 0.292065 | − | 0.956398i | \(-0.405657\pi\) | ||||
0.292065 | + | 0.956398i | \(0.405657\pi\) | |||||||
\(68\) | −1.86202 | −0.225803 | ||||||||
\(69\) | −4.63371 | −0.557833 | ||||||||
\(70\) | −8.71144 | −1.04122 | ||||||||
\(71\) | 12.8785 | 1.52839 | 0.764197 | − | 0.644983i | \(-0.223136\pi\) | ||||
0.764197 | + | 0.644983i | \(0.223136\pi\) | |||||||
\(72\) | −0.0867059 | −0.0102184 | ||||||||
\(73\) | 2.86681 | 0.335534 | 0.167767 | − | 0.985827i | \(-0.446344\pi\) | ||||
0.167767 | + | 0.985827i | \(0.446344\pi\) | |||||||
\(74\) | 7.04587 | 0.819066 | ||||||||
\(75\) | −5.05615 | −0.583833 | ||||||||
\(76\) | 2.06959 | 0.237399 | ||||||||
\(77\) | −15.1410 | −1.72548 | ||||||||
\(78\) | −7.29056 | −0.825494 | ||||||||
\(79\) | −10.2935 | −1.15811 | −0.579053 | − | 0.815290i | \(-0.696578\pi\) | ||||
−0.579053 | + | 0.815290i | \(0.696578\pi\) | |||||||
\(80\) | −2.82175 | −0.315482 | ||||||||
\(81\) | −8.73236 | −0.970263 | ||||||||
\(82\) | 2.46434 | 0.272141 | ||||||||
\(83\) | 0.795079 | 0.0872713 | 0.0436356 | − | 0.999048i | \(-0.486106\pi\) | ||||
0.0436356 | + | 0.999048i | \(0.486106\pi\) | |||||||
\(84\) | −5.26942 | −0.574941 | ||||||||
\(85\) | 5.25416 | 0.569893 | ||||||||
\(86\) | 4.50056 | 0.485308 | ||||||||
\(87\) | 11.6506 | 1.24908 | ||||||||
\(88\) | −4.90438 | −0.522808 | ||||||||
\(89\) | 15.8941 | 1.68477 | 0.842384 | − | 0.538878i | \(-0.181152\pi\) | ||||
0.842384 | + | 0.538878i | \(0.181152\pi\) | |||||||
\(90\) | 0.244663 | 0.0257897 | ||||||||
\(91\) | 13.1868 | 1.38235 | ||||||||
\(92\) | 2.71479 | 0.283037 | ||||||||
\(93\) | 5.92092 | 0.613971 | ||||||||
\(94\) | −12.4312 | −1.28218 | ||||||||
\(95\) | −5.83988 | −0.599159 | ||||||||
\(96\) | −1.70684 | −0.174203 | ||||||||
\(97\) | 11.0382 | 1.12076 | 0.560381 | − | 0.828235i | \(-0.310655\pi\) | ||||
0.560381 | + | 0.828235i | \(0.310655\pi\) | |||||||
\(98\) | 2.53108 | 0.255677 | ||||||||
\(99\) | 0.425238 | 0.0427380 | ||||||||
\(100\) | 2.96229 | 0.296229 | ||||||||
\(101\) | −15.3300 | −1.52540 | −0.762698 | − | 0.646755i | \(-0.776126\pi\) | ||||
−0.762698 | + | 0.646755i | \(0.776126\pi\) | |||||||
\(102\) | 3.17816 | 0.314685 | ||||||||
\(103\) | −10.6269 | −1.04710 | −0.523548 | − | 0.851996i | \(-0.675392\pi\) | ||||
−0.523548 | + | 0.851996i | \(0.675392\pi\) | |||||||
\(104\) | 4.27139 | 0.418844 | ||||||||
\(105\) | 14.8690 | 1.45107 | ||||||||
\(106\) | −4.92975 | −0.478819 | ||||||||
\(107\) | −5.25181 | −0.507711 | −0.253856 | − | 0.967242i | \(-0.581699\pi\) | ||||
−0.253856 | + | 0.967242i | \(0.581699\pi\) | |||||||
\(108\) | 5.26851 | 0.506962 | ||||||||
\(109\) | −6.98503 | −0.669044 | −0.334522 | − | 0.942388i | \(-0.608575\pi\) | ||||
−0.334522 | + | 0.942388i | \(0.608575\pi\) | |||||||
\(110\) | 13.8389 | 1.31949 | ||||||||
\(111\) | −12.0262 | −1.14147 | ||||||||
\(112\) | 3.08724 | 0.291717 | ||||||||
\(113\) | −1.61175 | −0.151621 | −0.0758103 | − | 0.997122i | \(-0.524154\pi\) | ||||
−0.0758103 | + | 0.997122i | \(0.524154\pi\) | |||||||
\(114\) | −3.53246 | −0.330845 | ||||||||
\(115\) | −7.66047 | −0.714342 | ||||||||
\(116\) | −6.82587 | −0.633766 | ||||||||
\(117\) | −0.370354 | −0.0342393 | ||||||||
\(118\) | 3.42311 | 0.315123 | ||||||||
\(119\) | −5.74851 | −0.526965 | ||||||||
\(120\) | 4.81627 | 0.439664 | ||||||||
\(121\) | 13.0529 | 1.18663 | ||||||||
\(122\) | 3.82089 | 0.345927 | ||||||||
\(123\) | −4.20623 | −0.379263 | ||||||||
\(124\) | −3.46894 | −0.311520 | ||||||||
\(125\) | 5.74992 | 0.514288 | ||||||||
\(126\) | −0.267682 | −0.0238470 | ||||||||
\(127\) | −4.27704 | −0.379526 | −0.189763 | − | 0.981830i | \(-0.560772\pi\) | ||||
−0.189763 | + | 0.981830i | \(0.560772\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.68173 | −0.676338 | ||||||||
\(130\) | −12.0528 | −1.05710 | ||||||||
\(131\) | −11.3467 | −0.991369 | −0.495684 | − | 0.868503i | \(-0.665083\pi\) | ||||
−0.495684 | + | 0.868503i | \(0.665083\pi\) | |||||||
\(132\) | 8.37097 | 0.728600 | ||||||||
\(133\) | 6.38934 | 0.554026 | ||||||||
\(134\) | 4.78132 | 0.413043 | ||||||||
\(135\) | −14.8664 | −1.27950 | ||||||||
\(136\) | −1.86202 | −0.159667 | ||||||||
\(137\) | −12.3410 | −1.05436 | −0.527179 | − | 0.849754i | \(-0.676750\pi\) | ||||
−0.527179 | + | 0.849754i | \(0.676750\pi\) | |||||||
\(138\) | −4.63371 | −0.394447 | ||||||||
\(139\) | 14.9438 | 1.26752 | 0.633760 | − | 0.773530i | \(-0.281511\pi\) | ||||
0.633760 | + | 0.773530i | \(0.281511\pi\) | |||||||
\(140\) | −8.71144 | −0.736251 | ||||||||
\(141\) | 21.2180 | 1.78688 | ||||||||
\(142\) | 12.8785 | 1.08074 | ||||||||
\(143\) | −20.9485 | −1.75180 | ||||||||
\(144\) | −0.0867059 | −0.00722549 | ||||||||
\(145\) | 19.2609 | 1.59953 | ||||||||
\(146\) | 2.86681 | 0.237259 | ||||||||
\(147\) | −4.32014 | −0.356319 | ||||||||
\(148\) | 7.04587 | 0.579167 | ||||||||
\(149\) | 5.25295 | 0.430339 | 0.215169 | − | 0.976577i | \(-0.430970\pi\) | ||||
0.215169 | + | 0.976577i | \(0.430970\pi\) | |||||||
\(150\) | −5.05615 | −0.412833 | ||||||||
\(151\) | −19.4477 | −1.58263 | −0.791316 | − | 0.611407i | \(-0.790604\pi\) | ||||
−0.791316 | + | 0.611407i | \(0.790604\pi\) | |||||||
\(152\) | 2.06959 | 0.167866 | ||||||||
\(153\) | 0.161448 | 0.0130523 | ||||||||
\(154\) | −15.1410 | −1.22010 | ||||||||
\(155\) | 9.78849 | 0.786231 | ||||||||
\(156\) | −7.29056 | −0.583712 | ||||||||
\(157\) | −1.41664 | −0.113060 | −0.0565300 | − | 0.998401i | \(-0.518004\pi\) | ||||
−0.0565300 | + | 0.998401i | \(0.518004\pi\) | |||||||
\(158\) | −10.2935 | −0.818905 | ||||||||
\(159\) | 8.41428 | 0.667296 | ||||||||
\(160\) | −2.82175 | −0.223079 | ||||||||
\(161\) | 8.38122 | 0.660533 | ||||||||
\(162\) | −8.73236 | −0.686079 | ||||||||
\(163\) | 18.9578 | 1.48489 | 0.742445 | − | 0.669907i | \(-0.233666\pi\) | ||||
0.742445 | + | 0.669907i | \(0.233666\pi\) | |||||||
\(164\) | 2.46434 | 0.192433 | ||||||||
\(165\) | −23.6208 | −1.83888 | ||||||||
\(166\) | 0.795079 | 0.0617101 | ||||||||
\(167\) | −24.0862 | −1.86385 | −0.931924 | − | 0.362655i | \(-0.881870\pi\) | ||||
−0.931924 | + | 0.362655i | \(0.881870\pi\) | |||||||
\(168\) | −5.26942 | −0.406545 | ||||||||
\(169\) | 5.24474 | 0.403442 | ||||||||
\(170\) | 5.25416 | 0.402975 | ||||||||
\(171\) | −0.179446 | −0.0137226 | ||||||||
\(172\) | 4.50056 | 0.343165 | ||||||||
\(173\) | −17.6195 | −1.33959 | −0.669794 | − | 0.742547i | \(-0.733618\pi\) | ||||
−0.669794 | + | 0.742547i | \(0.733618\pi\) | |||||||
\(174\) | 11.6506 | 0.883233 | ||||||||
\(175\) | 9.14531 | 0.691320 | ||||||||
\(176\) | −4.90438 | −0.369681 | ||||||||
\(177\) | −5.84270 | −0.439164 | ||||||||
\(178\) | 15.8941 | 1.19131 | ||||||||
\(179\) | 14.9754 | 1.11931 | 0.559657 | − | 0.828725i | \(-0.310933\pi\) | ||||
0.559657 | + | 0.828725i | \(0.310933\pi\) | |||||||
\(180\) | 0.244663 | 0.0182361 | ||||||||
\(181\) | −15.6659 | −1.16444 | −0.582219 | − | 0.813032i | \(-0.697815\pi\) | ||||
−0.582219 | + | 0.813032i | \(0.697815\pi\) | |||||||
\(182\) | 13.1868 | 0.977472 | ||||||||
\(183\) | −6.52164 | −0.482093 | ||||||||
\(184\) | 2.71479 | 0.200137 | ||||||||
\(185\) | −19.8817 | −1.46173 | ||||||||
\(186\) | 5.92092 | 0.434143 | ||||||||
\(187\) | 9.13204 | 0.667801 | ||||||||
\(188\) | −12.4312 | −0.906638 | ||||||||
\(189\) | 16.2652 | 1.18312 | ||||||||
\(190\) | −5.83988 | −0.423670 | ||||||||
\(191\) | −12.9141 | −0.934430 | −0.467215 | − | 0.884144i | \(-0.654743\pi\) | ||||
−0.467215 | + | 0.884144i | \(0.654743\pi\) | |||||||
\(192\) | −1.70684 | −0.123180 | ||||||||
\(193\) | −5.68924 | −0.409521 | −0.204760 | − | 0.978812i | \(-0.565642\pi\) | ||||
−0.204760 | + | 0.978812i | \(0.565642\pi\) | |||||||
\(194\) | 11.0382 | 0.792499 | ||||||||
\(195\) | 20.5722 | 1.47320 | ||||||||
\(196\) | 2.53108 | 0.180791 | ||||||||
\(197\) | 17.1411 | 1.22125 | 0.610626 | − | 0.791919i | \(-0.290918\pi\) | ||||
0.610626 | + | 0.791919i | \(0.290918\pi\) | |||||||
\(198\) | 0.425238 | 0.0302204 | ||||||||
\(199\) | 6.80696 | 0.482532 | 0.241266 | − | 0.970459i | \(-0.422437\pi\) | ||||
0.241266 | + | 0.970459i | \(0.422437\pi\) | |||||||
\(200\) | 2.96229 | 0.209465 | ||||||||
\(201\) | −8.16093 | −0.575628 | ||||||||
\(202\) | −15.3300 | −1.07862 | ||||||||
\(203\) | −21.0731 | −1.47904 | ||||||||
\(204\) | 3.17816 | 0.222516 | ||||||||
\(205\) | −6.95376 | −0.485672 | ||||||||
\(206\) | −10.6269 | −0.740408 | ||||||||
\(207\) | −0.235388 | −0.0163606 | ||||||||
\(208\) | 4.27139 | 0.296167 | ||||||||
\(209\) | −10.1501 | −0.702095 | ||||||||
\(210\) | 14.8690 | 1.02606 | ||||||||
\(211\) | −16.0737 | −1.10656 | −0.553279 | − | 0.832996i | \(-0.686624\pi\) | ||||
−0.553279 | + | 0.832996i | \(0.686624\pi\) | |||||||
\(212\) | −4.92975 | −0.338576 | ||||||||
\(213\) | −21.9815 | −1.50614 | ||||||||
\(214\) | −5.25181 | −0.359006 | ||||||||
\(215\) | −12.6995 | −0.866097 | ||||||||
\(216\) | 5.26851 | 0.358476 | ||||||||
\(217\) | −10.7095 | −0.727006 | ||||||||
\(218\) | −6.98503 | −0.473086 | ||||||||
\(219\) | −4.89317 | −0.330650 | ||||||||
\(220\) | 13.8389 | 0.933021 | ||||||||
\(221\) | −7.95340 | −0.535004 | ||||||||
\(222\) | −12.0262 | −0.807143 | ||||||||
\(223\) | −27.7619 | −1.85907 | −0.929536 | − | 0.368732i | \(-0.879792\pi\) | ||||
−0.929536 | + | 0.368732i | \(0.879792\pi\) | |||||||
\(224\) | 3.08724 | 0.206275 | ||||||||
\(225\) | −0.256848 | −0.0171232 | ||||||||
\(226\) | −1.61175 | −0.107212 | ||||||||
\(227\) | 15.6189 | 1.03666 | 0.518332 | − | 0.855179i | \(-0.326553\pi\) | ||||
0.518332 | + | 0.855179i | \(0.326553\pi\) | |||||||
\(228\) | −3.53246 | −0.233943 | ||||||||
\(229\) | −23.9025 | −1.57952 | −0.789761 | − | 0.613415i | \(-0.789795\pi\) | ||||
−0.789761 | + | 0.613415i | \(0.789795\pi\) | |||||||
\(230\) | −7.66047 | −0.505116 | ||||||||
\(231\) | 25.8432 | 1.70036 | ||||||||
\(232\) | −6.82587 | −0.448140 | ||||||||
\(233\) | −25.1744 | −1.64923 | −0.824615 | − | 0.565694i | \(-0.808608\pi\) | ||||
−0.824615 | + | 0.565694i | \(0.808608\pi\) | |||||||
\(234\) | −0.370354 | −0.0242108 | ||||||||
\(235\) | 35.0778 | 2.28822 | ||||||||
\(236\) | 3.42311 | 0.222826 | ||||||||
\(237\) | 17.5693 | 1.14125 | ||||||||
\(238\) | −5.74851 | −0.372620 | ||||||||
\(239\) | 8.48723 | 0.548993 | 0.274497 | − | 0.961588i | \(-0.411489\pi\) | ||||
0.274497 | + | 0.961588i | \(0.411489\pi\) | |||||||
\(240\) | 4.81627 | 0.310889 | ||||||||
\(241\) | −15.9876 | −1.02985 | −0.514924 | − | 0.857236i | \(-0.672180\pi\) | ||||
−0.514924 | + | 0.857236i | \(0.672180\pi\) | |||||||
\(242\) | 13.0529 | 0.839073 | ||||||||
\(243\) | −0.900789 | −0.0577856 | ||||||||
\(244\) | 3.82089 | 0.244607 | ||||||||
\(245\) | −7.14207 | −0.456290 | ||||||||
\(246\) | −4.20623 | −0.268179 | ||||||||
\(247\) | 8.84003 | 0.562478 | ||||||||
\(248\) | −3.46894 | −0.220278 | ||||||||
\(249\) | −1.35707 | −0.0860009 | ||||||||
\(250\) | 5.74992 | 0.363657 | ||||||||
\(251\) | −5.52678 | −0.348847 | −0.174424 | − | 0.984671i | \(-0.555806\pi\) | ||||
−0.174424 | + | 0.984671i | \(0.555806\pi\) | |||||||
\(252\) | −0.267682 | −0.0168624 | ||||||||
\(253\) | −13.3144 | −0.837066 | ||||||||
\(254\) | −4.27704 | −0.268365 | ||||||||
\(255\) | −8.96799 | −0.561597 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.0469 | 1.06335 | 0.531677 | − | 0.846947i | \(-0.321562\pi\) | ||||
0.531677 | + | 0.846947i | \(0.321562\pi\) | |||||||
\(258\) | −7.68173 | −0.478243 | ||||||||
\(259\) | 21.7523 | 1.35162 | ||||||||
\(260\) | −12.0528 | −0.747483 | ||||||||
\(261\) | 0.591843 | 0.0366342 | ||||||||
\(262\) | −11.3467 | −0.701003 | ||||||||
\(263\) | −13.9641 | −0.861061 | −0.430531 | − | 0.902576i | \(-0.641674\pi\) | ||||
−0.430531 | + | 0.902576i | \(0.641674\pi\) | |||||||
\(264\) | 8.37097 | 0.515198 | ||||||||
\(265\) | 13.9105 | 0.854517 | ||||||||
\(266\) | 6.38934 | 0.391756 | ||||||||
\(267\) | −27.1286 | −1.66024 | ||||||||
\(268\) | 4.78132 | 0.292065 | ||||||||
\(269\) | 4.58325 | 0.279446 | 0.139723 | − | 0.990191i | \(-0.455379\pi\) | ||||
0.139723 | + | 0.990191i | \(0.455379\pi\) | |||||||
\(270\) | −14.8664 | −0.904741 | ||||||||
\(271\) | 19.4977 | 1.18440 | 0.592202 | − | 0.805790i | \(-0.298259\pi\) | ||||
0.592202 | + | 0.805790i | \(0.298259\pi\) | |||||||
\(272\) | −1.86202 | −0.112901 | ||||||||
\(273\) | −22.5077 | −1.36223 | ||||||||
\(274\) | −12.3410 | −0.745544 | ||||||||
\(275\) | −14.5282 | −0.876082 | ||||||||
\(276\) | −4.63371 | −0.278916 | ||||||||
\(277\) | 16.4752 | 0.989897 | 0.494948 | − | 0.868922i | \(-0.335187\pi\) | ||||
0.494948 | + | 0.868922i | \(0.335187\pi\) | |||||||
\(278\) | 14.9438 | 0.896272 | ||||||||
\(279\) | 0.300778 | 0.0180071 | ||||||||
\(280\) | −8.71144 | −0.520608 | ||||||||
\(281\) | −12.5757 | −0.750205 | −0.375103 | − | 0.926983i | \(-0.622393\pi\) | ||||
−0.375103 | + | 0.926983i | \(0.622393\pi\) | |||||||
\(282\) | 21.2180 | 1.26352 | ||||||||
\(283\) | −25.0183 | −1.48718 | −0.743591 | − | 0.668634i | \(-0.766879\pi\) | ||||
−0.743591 | + | 0.668634i | \(0.766879\pi\) | |||||||
\(284\) | 12.8785 | 0.764197 | ||||||||
\(285\) | 9.96773 | 0.590437 | ||||||||
\(286\) | −20.9485 | −1.23871 | ||||||||
\(287\) | 7.60802 | 0.449087 | ||||||||
\(288\) | −0.0867059 | −0.00510919 | ||||||||
\(289\) | −13.5329 | −0.796052 | ||||||||
\(290\) | 19.2609 | 1.13104 | ||||||||
\(291\) | −18.8405 | −1.10445 | ||||||||
\(292\) | 2.86681 | 0.167767 | ||||||||
\(293\) | 3.09061 | 0.180555 | 0.0902776 | − | 0.995917i | \(-0.471225\pi\) | ||||
0.0902776 | + | 0.995917i | \(0.471225\pi\) | |||||||
\(294\) | −4.32014 | −0.251955 | ||||||||
\(295\) | −9.65918 | −0.562379 | ||||||||
\(296\) | 7.04587 | 0.409533 | ||||||||
\(297\) | −25.8387 | −1.49932 | ||||||||
\(298\) | 5.25295 | 0.304295 | ||||||||
\(299\) | 11.5959 | 0.670610 | ||||||||
\(300\) | −5.05615 | −0.291917 | ||||||||
\(301\) | 13.8943 | 0.800856 | ||||||||
\(302\) | −19.4477 | −1.11909 | ||||||||
\(303\) | 26.1659 | 1.50319 | ||||||||
\(304\) | 2.06959 | 0.118699 | ||||||||
\(305\) | −10.7816 | −0.617353 | ||||||||
\(306\) | 0.161448 | 0.00922937 | ||||||||
\(307\) | 29.1634 | 1.66445 | 0.832223 | − | 0.554442i | \(-0.187068\pi\) | ||||
0.832223 | + | 0.554442i | \(0.187068\pi\) | |||||||
\(308\) | −15.1410 | −0.862739 | ||||||||
\(309\) | 18.1383 | 1.03185 | ||||||||
\(310\) | 9.78849 | 0.555949 | ||||||||
\(311\) | −5.57897 | −0.316354 | −0.158177 | − | 0.987411i | \(-0.550562\pi\) | ||||
−0.158177 | + | 0.987411i | \(0.550562\pi\) | |||||||
\(312\) | −7.29056 | −0.412747 | ||||||||
\(313\) | 2.04723 | 0.115716 | 0.0578581 | − | 0.998325i | \(-0.481573\pi\) | ||||
0.0578581 | + | 0.998325i | \(0.481573\pi\) | |||||||
\(314\) | −1.41664 | −0.0799456 | ||||||||
\(315\) | 0.755333 | 0.0425582 | ||||||||
\(316\) | −10.2935 | −0.579053 | ||||||||
\(317\) | 20.9604 | 1.17725 | 0.588627 | − | 0.808405i | \(-0.299669\pi\) | ||||
0.588627 | + | 0.808405i | \(0.299669\pi\) | |||||||
\(318\) | 8.41428 | 0.471849 | ||||||||
\(319\) | 33.4766 | 1.87433 | ||||||||
\(320\) | −2.82175 | −0.157741 | ||||||||
\(321\) | 8.96398 | 0.500321 | ||||||||
\(322\) | 8.38122 | 0.467067 | ||||||||
\(323\) | −3.85362 | −0.214421 | ||||||||
\(324\) | −8.73236 | −0.485131 | ||||||||
\(325\) | 12.6531 | 0.701867 | ||||||||
\(326\) | 18.9578 | 1.04998 | ||||||||
\(327\) | 11.9223 | 0.659305 | ||||||||
\(328\) | 2.46434 | 0.136070 | ||||||||
\(329\) | −38.3781 | −2.11585 | ||||||||
\(330\) | −23.6208 | −1.30028 | ||||||||
\(331\) | −1.44693 | −0.0795303 | −0.0397652 | − | 0.999209i | \(-0.512661\pi\) | ||||
−0.0397652 | + | 0.999209i | \(0.512661\pi\) | |||||||
\(332\) | 0.795079 | 0.0436356 | ||||||||
\(333\) | −0.610918 | −0.0334781 | ||||||||
\(334\) | −24.0862 | −1.31794 | ||||||||
\(335\) | −13.4917 | −0.737130 | ||||||||
\(336\) | −5.26942 | −0.287471 | ||||||||
\(337\) | −18.7472 | −1.02123 | −0.510613 | − | 0.859811i | \(-0.670581\pi\) | ||||
−0.510613 | + | 0.859811i | \(0.670581\pi\) | |||||||
\(338\) | 5.24474 | 0.285276 | ||||||||
\(339\) | 2.75100 | 0.149414 | ||||||||
\(340\) | 5.25416 | 0.284947 | ||||||||
\(341\) | 17.0130 | 0.921305 | ||||||||
\(342\) | −0.179446 | −0.00970332 | ||||||||
\(343\) | −13.7967 | −0.744950 | ||||||||
\(344\) | 4.50056 | 0.242654 | ||||||||
\(345\) | 13.0752 | 0.703944 | ||||||||
\(346\) | −17.6195 | −0.947231 | ||||||||
\(347\) | −31.6900 | −1.70121 | −0.850605 | − | 0.525805i | \(-0.823764\pi\) | ||||
−0.850605 | + | 0.525805i | \(0.823764\pi\) | |||||||
\(348\) | 11.6506 | 0.624540 | ||||||||
\(349\) | −21.1615 | −1.13275 | −0.566373 | − | 0.824149i | \(-0.691654\pi\) | ||||
−0.566373 | + | 0.824149i | \(0.691654\pi\) | |||||||
\(350\) | 9.14531 | 0.488837 | ||||||||
\(351\) | 22.5038 | 1.20117 | ||||||||
\(352\) | −4.90438 | −0.261404 | ||||||||
\(353\) | 1.21473 | 0.0646537 | 0.0323269 | − | 0.999477i | \(-0.489708\pi\) | ||||
0.0323269 | + | 0.999477i | \(0.489708\pi\) | |||||||
\(354\) | −5.84270 | −0.310536 | ||||||||
\(355\) | −36.3399 | −1.92872 | ||||||||
\(356\) | 15.8941 | 0.842384 | ||||||||
\(357\) | 9.81177 | 0.519294 | ||||||||
\(358\) | 14.9754 | 0.791474 | ||||||||
\(359\) | −21.2652 | −1.12233 | −0.561166 | − | 0.827703i | \(-0.689647\pi\) | ||||
−0.561166 | + | 0.827703i | \(0.689647\pi\) | |||||||
\(360\) | 0.244663 | 0.0128948 | ||||||||
\(361\) | −14.7168 | −0.774568 | ||||||||
\(362\) | −15.6659 | −0.823382 | ||||||||
\(363\) | −22.2792 | −1.16935 | ||||||||
\(364\) | 13.1868 | 0.691177 | ||||||||
\(365\) | −8.08942 | −0.423420 | ||||||||
\(366\) | −6.52164 | −0.340891 | ||||||||
\(367\) | −26.6271 | −1.38992 | −0.694961 | − | 0.719048i | \(-0.744578\pi\) | ||||
−0.694961 | + | 0.719048i | \(0.744578\pi\) | |||||||
\(368\) | 2.71479 | 0.141518 | ||||||||
\(369\) | −0.213673 | −0.0111234 | ||||||||
\(370\) | −19.8817 | −1.03360 | ||||||||
\(371\) | −15.2193 | −0.790148 | ||||||||
\(372\) | 5.92092 | 0.306985 | ||||||||
\(373\) | −25.0452 | −1.29679 | −0.648396 | − | 0.761303i | \(-0.724560\pi\) | ||||
−0.648396 | + | 0.761303i | \(0.724560\pi\) | |||||||
\(374\) | 9.13204 | 0.472207 | ||||||||
\(375\) | −9.81417 | −0.506802 | ||||||||
\(376\) | −12.4312 | −0.641090 | ||||||||
\(377\) | −29.1559 | −1.50161 | ||||||||
\(378\) | 16.2652 | 0.836590 | ||||||||
\(379\) | 34.2529 | 1.75945 | 0.879727 | − | 0.475479i | \(-0.157725\pi\) | ||||
0.879727 | + | 0.475479i | \(0.157725\pi\) | |||||||
\(380\) | −5.83988 | −0.299580 | ||||||||
\(381\) | 7.30021 | 0.374001 | ||||||||
\(382\) | −12.9141 | −0.660742 | ||||||||
\(383\) | 12.5747 | 0.642539 | 0.321269 | − | 0.946988i | \(-0.395890\pi\) | ||||
0.321269 | + | 0.946988i | \(0.395890\pi\) | |||||||
\(384\) | −1.70684 | −0.0871017 | ||||||||
\(385\) | 42.7242 | 2.17743 | ||||||||
\(386\) | −5.68924 | −0.289575 | ||||||||
\(387\) | −0.390225 | −0.0198363 | ||||||||
\(388\) | 11.0382 | 0.560381 | ||||||||
\(389\) | 11.7727 | 0.596900 | 0.298450 | − | 0.954425i | \(-0.403530\pi\) | ||||
0.298450 | + | 0.954425i | \(0.403530\pi\) | |||||||
\(390\) | 20.5722 | 1.04171 | ||||||||
\(391\) | −5.05499 | −0.255642 | ||||||||
\(392\) | 2.53108 | 0.127839 | ||||||||
\(393\) | 19.3670 | 0.976937 | ||||||||
\(394\) | 17.1411 | 0.863555 | ||||||||
\(395\) | 29.0456 | 1.46144 | ||||||||
\(396\) | 0.425238 | 0.0213690 | ||||||||
\(397\) | −9.59148 | −0.481382 | −0.240691 | − | 0.970602i | \(-0.577374\pi\) | ||||
−0.240691 | + | 0.970602i | \(0.577374\pi\) | |||||||
\(398\) | 6.80696 | 0.341202 | ||||||||
\(399\) | −10.9056 | −0.545961 | ||||||||
\(400\) | 2.96229 | 0.148114 | ||||||||
\(401\) | 12.9004 | 0.644216 | 0.322108 | − | 0.946703i | \(-0.395609\pi\) | ||||
0.322108 | + | 0.946703i | \(0.395609\pi\) | |||||||
\(402\) | −8.16093 | −0.407030 | ||||||||
\(403\) | −14.8172 | −0.738097 | ||||||||
\(404\) | −15.3300 | −0.762698 | ||||||||
\(405\) | 24.6406 | 1.22440 | ||||||||
\(406\) | −21.0731 | −1.04584 | ||||||||
\(407\) | −34.5556 | −1.71286 | ||||||||
\(408\) | 3.17816 | 0.157343 | ||||||||
\(409\) | −33.3682 | −1.64995 | −0.824975 | − | 0.565169i | \(-0.808811\pi\) | ||||
−0.824975 | + | 0.565169i | \(0.808811\pi\) | |||||||
\(410\) | −6.95376 | −0.343422 | ||||||||
\(411\) | 21.0640 | 1.03901 | ||||||||
\(412\) | −10.6269 | −0.523548 | ||||||||
\(413\) | 10.5680 | 0.520017 | ||||||||
\(414\) | −0.235388 | −0.0115687 | ||||||||
\(415\) | −2.24352 | −0.110130 | ||||||||
\(416\) | 4.27139 | 0.209422 | ||||||||
\(417\) | −25.5067 | −1.24907 | ||||||||
\(418\) | −10.1501 | −0.496456 | ||||||||
\(419\) | −37.9374 | −1.85336 | −0.926682 | − | 0.375847i | \(-0.877352\pi\) | ||||
−0.926682 | + | 0.375847i | \(0.877352\pi\) | |||||||
\(420\) | 14.8690 | 0.725533 | ||||||||
\(421\) | −20.4084 | −0.994643 | −0.497321 | − | 0.867566i | \(-0.665683\pi\) | ||||
−0.497321 | + | 0.867566i | \(0.665683\pi\) | |||||||
\(422\) | −16.0737 | −0.782455 | ||||||||
\(423\) | 1.07786 | 0.0524072 | ||||||||
\(424\) | −4.92975 | −0.239410 | ||||||||
\(425\) | −5.51584 | −0.267557 | ||||||||
\(426\) | −21.9815 | −1.06501 | ||||||||
\(427\) | 11.7960 | 0.570849 | ||||||||
\(428\) | −5.25181 | −0.253856 | ||||||||
\(429\) | 35.7557 | 1.72630 | ||||||||
\(430\) | −12.6995 | −0.612423 | ||||||||
\(431\) | 0.480525 | 0.0231461 | 0.0115730 | − | 0.999933i | \(-0.496316\pi\) | ||||
0.0115730 | + | 0.999933i | \(0.496316\pi\) | |||||||
\(432\) | 5.26851 | 0.253481 | ||||||||
\(433\) | 31.0825 | 1.49373 | 0.746865 | − | 0.664976i | \(-0.231558\pi\) | ||||
0.746865 | + | 0.664976i | \(0.231558\pi\) | |||||||
\(434\) | −10.7095 | −0.514071 | ||||||||
\(435\) | −32.8752 | −1.57625 | ||||||||
\(436\) | −6.98503 | −0.334522 | ||||||||
\(437\) | 5.61851 | 0.268770 | ||||||||
\(438\) | −4.89317 | −0.233805 | ||||||||
\(439\) | −26.0470 | −1.24315 | −0.621577 | − | 0.783353i | \(-0.713508\pi\) | ||||
−0.621577 | + | 0.783353i | \(0.713508\pi\) | |||||||
\(440\) | 13.8389 | 0.659745 | ||||||||
\(441\) | −0.219459 | −0.0104504 | ||||||||
\(442\) | −7.95340 | −0.378305 | ||||||||
\(443\) | 0.328188 | 0.0155927 | 0.00779634 | − | 0.999970i | \(-0.497518\pi\) | ||||
0.00779634 | + | 0.999970i | \(0.497518\pi\) | |||||||
\(444\) | −12.0262 | −0.570736 | ||||||||
\(445\) | −44.8491 | −2.12605 | ||||||||
\(446\) | −27.7619 | −1.31456 | ||||||||
\(447\) | −8.96593 | −0.424074 | ||||||||
\(448\) | 3.08724 | 0.145859 | ||||||||
\(449\) | 4.53151 | 0.213855 | 0.106928 | − | 0.994267i | \(-0.465899\pi\) | ||||
0.106928 | + | 0.994267i | \(0.465899\pi\) | |||||||
\(450\) | −0.256848 | −0.0121079 | ||||||||
\(451\) | −12.0860 | −0.569110 | ||||||||
\(452\) | −1.61175 | −0.0758103 | ||||||||
\(453\) | 33.1941 | 1.55959 | ||||||||
\(454\) | 15.6189 | 0.733032 | ||||||||
\(455\) | −37.2099 | −1.74443 | ||||||||
\(456\) | −3.53246 | −0.165423 | ||||||||
\(457\) | −10.6555 | −0.498444 | −0.249222 | − | 0.968446i | \(-0.580175\pi\) | ||||
−0.249222 | + | 0.968446i | \(0.580175\pi\) | |||||||
\(458\) | −23.9025 | −1.11689 | ||||||||
\(459\) | −9.81005 | −0.457894 | ||||||||
\(460\) | −7.66047 | −0.357171 | ||||||||
\(461\) | 29.2492 | 1.36227 | 0.681136 | − | 0.732157i | \(-0.261486\pi\) | ||||
0.681136 | + | 0.732157i | \(0.261486\pi\) | |||||||
\(462\) | 25.8432 | 1.20234 | ||||||||
\(463\) | −17.0576 | −0.792732 | −0.396366 | − | 0.918093i | \(-0.629729\pi\) | ||||
−0.396366 | + | 0.918093i | \(0.629729\pi\) | |||||||
\(464\) | −6.82587 | −0.316883 | ||||||||
\(465\) | −16.7074 | −0.774786 | ||||||||
\(466\) | −25.1744 | −1.16618 | ||||||||
\(467\) | −25.3357 | −1.17240 | −0.586199 | − | 0.810167i | \(-0.699376\pi\) | ||||
−0.586199 | + | 0.810167i | \(0.699376\pi\) | |||||||
\(468\) | −0.370354 | −0.0171196 | ||||||||
\(469\) | 14.7611 | 0.681604 | ||||||||
\(470\) | 35.0778 | 1.61802 | ||||||||
\(471\) | 2.41797 | 0.111414 | ||||||||
\(472\) | 3.42311 | 0.157562 | ||||||||
\(473\) | −22.0724 | −1.01489 | ||||||||
\(474\) | 17.5693 | 0.806984 | ||||||||
\(475\) | 6.13073 | 0.281297 | ||||||||
\(476\) | −5.74851 | −0.263482 | ||||||||
\(477\) | 0.427438 | 0.0195710 | ||||||||
\(478\) | 8.48723 | 0.388197 | ||||||||
\(479\) | 19.1424 | 0.874638 | 0.437319 | − | 0.899306i | \(-0.355928\pi\) | ||||
0.437319 | + | 0.899306i | \(0.355928\pi\) | |||||||
\(480\) | 4.81627 | 0.219832 | ||||||||
\(481\) | 30.0956 | 1.37224 | ||||||||
\(482\) | −15.9876 | −0.728213 | ||||||||
\(483\) | −14.3054 | −0.650918 | ||||||||
\(484\) | 13.0529 | 0.593314 | ||||||||
\(485\) | −31.1472 | −1.41432 | ||||||||
\(486\) | −0.900789 | −0.0408606 | ||||||||
\(487\) | −1.20359 | −0.0545398 | −0.0272699 | − | 0.999628i | \(-0.508681\pi\) | ||||
−0.0272699 | + | 0.999628i | \(0.508681\pi\) | |||||||
\(488\) | 3.82089 | 0.172964 | ||||||||
\(489\) | −32.3579 | −1.46328 | ||||||||
\(490\) | −7.14207 | −0.322646 | ||||||||
\(491\) | 32.5980 | 1.47113 | 0.735565 | − | 0.677455i | \(-0.236917\pi\) | ||||
0.735565 | + | 0.677455i | \(0.236917\pi\) | |||||||
\(492\) | −4.20623 | −0.189631 | ||||||||
\(493\) | 12.7099 | 0.572425 | ||||||||
\(494\) | 8.84003 | 0.397732 | ||||||||
\(495\) | −1.19992 | −0.0539323 | ||||||||
\(496\) | −3.46894 | −0.155760 | ||||||||
\(497\) | 39.7590 | 1.78343 | ||||||||
\(498\) | −1.35707 | −0.0608118 | ||||||||
\(499\) | 10.0147 | 0.448320 | 0.224160 | − | 0.974552i | \(-0.428036\pi\) | ||||
0.224160 | + | 0.974552i | \(0.428036\pi\) | |||||||
\(500\) | 5.74992 | 0.257144 | ||||||||
\(501\) | 41.1112 | 1.83672 | ||||||||
\(502\) | −5.52678 | −0.246672 | ||||||||
\(503\) | 9.21479 | 0.410867 | 0.205434 | − | 0.978671i | \(-0.434140\pi\) | ||||
0.205434 | + | 0.978671i | \(0.434140\pi\) | |||||||
\(504\) | −0.267682 | −0.0119235 | ||||||||
\(505\) | 43.2576 | 1.92494 | ||||||||
\(506\) | −13.3144 | −0.591895 | ||||||||
\(507\) | −8.95192 | −0.397569 | ||||||||
\(508\) | −4.27704 | −0.189763 | ||||||||
\(509\) | 27.8474 | 1.23431 | 0.617157 | − | 0.786840i | \(-0.288284\pi\) | ||||
0.617157 | + | 0.786840i | \(0.288284\pi\) | |||||||
\(510\) | −8.96799 | −0.397109 | ||||||||
\(511\) | 8.85053 | 0.391524 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 10.9037 | 0.481409 | ||||||||
\(514\) | 17.0469 | 0.751905 | ||||||||
\(515\) | 29.9864 | 1.32136 | ||||||||
\(516\) | −7.68173 | −0.338169 | ||||||||
\(517\) | 60.9672 | 2.68134 | ||||||||
\(518\) | 21.7523 | 0.955742 | ||||||||
\(519\) | 30.0737 | 1.32009 | ||||||||
\(520\) | −12.0528 | −0.528550 | ||||||||
\(521\) | 19.2339 | 0.842652 | 0.421326 | − | 0.906909i | \(-0.361565\pi\) | ||||
0.421326 | + | 0.906909i | \(0.361565\pi\) | |||||||
\(522\) | 0.591843 | 0.0259043 | ||||||||
\(523\) | 12.9035 | 0.564232 | 0.282116 | − | 0.959380i | \(-0.408964\pi\) | ||||
0.282116 | + | 0.959380i | \(0.408964\pi\) | |||||||
\(524\) | −11.3467 | −0.495684 | ||||||||
\(525\) | −15.6096 | −0.681257 | ||||||||
\(526\) | −13.9641 | −0.608862 | ||||||||
\(527\) | 6.45923 | 0.281369 | ||||||||
\(528\) | 8.37097 | 0.364300 | ||||||||
\(529\) | −15.6299 | −0.679561 | ||||||||
\(530\) | 13.9105 | 0.604235 | ||||||||
\(531\) | −0.296804 | −0.0128802 | ||||||||
\(532\) | 6.38934 | 0.277013 | ||||||||
\(533\) | 10.5261 | 0.455938 | ||||||||
\(534\) | −27.1286 | −1.17397 | ||||||||
\(535\) | 14.8193 | 0.640694 | ||||||||
\(536\) | 4.78132 | 0.206521 | ||||||||
\(537\) | −25.5606 | −1.10302 | ||||||||
\(538\) | 4.58325 | 0.197598 | ||||||||
\(539\) | −12.4133 | −0.534681 | ||||||||
\(540\) | −14.8664 | −0.639749 | ||||||||
\(541\) | 12.6438 | 0.543598 | 0.271799 | − | 0.962354i | \(-0.412381\pi\) | ||||
0.271799 | + | 0.962354i | \(0.412381\pi\) | |||||||
\(542\) | 19.4977 | 0.837500 | ||||||||
\(543\) | 26.7392 | 1.14749 | ||||||||
\(544\) | −1.86202 | −0.0798334 | ||||||||
\(545\) | 19.7100 | 0.844284 | ||||||||
\(546\) | −22.5077 | −0.963243 | ||||||||
\(547\) | −12.6650 | −0.541517 | −0.270759 | − | 0.962647i | \(-0.587275\pi\) | ||||
−0.270759 | + | 0.962647i | \(0.587275\pi\) | |||||||
\(548\) | −12.3410 | −0.527179 | ||||||||
\(549\) | −0.331294 | −0.0141393 | ||||||||
\(550\) | −14.5282 | −0.619484 | ||||||||
\(551\) | −14.1268 | −0.601821 | ||||||||
\(552\) | −4.63371 | −0.197224 | ||||||||
\(553\) | −31.7785 | −1.35136 | ||||||||
\(554\) | 16.4752 | 0.699963 | ||||||||
\(555\) | 33.9348 | 1.44045 | ||||||||
\(556\) | 14.9438 | 0.633760 | ||||||||
\(557\) | −37.9663 | −1.60868 | −0.804341 | − | 0.594167i | \(-0.797482\pi\) | ||||
−0.804341 | + | 0.594167i | \(0.797482\pi\) | |||||||
\(558\) | 0.300778 | 0.0127329 | ||||||||
\(559\) | 19.2236 | 0.813073 | ||||||||
\(560\) | −8.71144 | −0.368126 | ||||||||
\(561\) | −15.5869 | −0.658080 | ||||||||
\(562\) | −12.5757 | −0.530475 | ||||||||
\(563\) | −36.9059 | −1.55540 | −0.777698 | − | 0.628638i | \(-0.783613\pi\) | ||||
−0.777698 | + | 0.628638i | \(0.783613\pi\) | |||||||
\(564\) | 21.2180 | 0.893440 | ||||||||
\(565\) | 4.54796 | 0.191334 | ||||||||
\(566\) | −25.0183 | −1.05160 | ||||||||
\(567\) | −26.9589 | −1.13217 | ||||||||
\(568\) | 12.8785 | 0.540369 | ||||||||
\(569\) | 34.9042 | 1.46326 | 0.731630 | − | 0.681702i | \(-0.238760\pi\) | ||||
0.731630 | + | 0.681702i | \(0.238760\pi\) | |||||||
\(570\) | 9.96773 | 0.417502 | ||||||||
\(571\) | 41.5873 | 1.74037 | 0.870187 | − | 0.492722i | \(-0.163998\pi\) | ||||
0.870187 | + | 0.492722i | \(0.163998\pi\) | |||||||
\(572\) | −20.9485 | −0.875900 | ||||||||
\(573\) | 22.0422 | 0.920828 | ||||||||
\(574\) | 7.60802 | 0.317553 | ||||||||
\(575\) | 8.04200 | 0.335374 | ||||||||
\(576\) | −0.0867059 | −0.00361274 | ||||||||
\(577\) | 13.8486 | 0.576524 | 0.288262 | − | 0.957552i | \(-0.406923\pi\) | ||||
0.288262 | + | 0.957552i | \(0.406923\pi\) | |||||||
\(578\) | −13.5329 | −0.562894 | ||||||||
\(579\) | 9.71061 | 0.403559 | ||||||||
\(580\) | 19.2609 | 0.799766 | ||||||||
\(581\) | 2.45460 | 0.101834 | ||||||||
\(582\) | −18.8405 | −0.780962 | ||||||||
\(583\) | 24.1773 | 1.00132 | ||||||||
\(584\) | 2.86681 | 0.118629 | ||||||||
\(585\) | 1.04505 | 0.0432074 | ||||||||
\(586\) | 3.09061 | 0.127672 | ||||||||
\(587\) | −4.36473 | −0.180152 | −0.0900759 | − | 0.995935i | \(-0.528711\pi\) | ||||
−0.0900759 | + | 0.995935i | \(0.528711\pi\) | |||||||
\(588\) | −4.32014 | −0.178159 | ||||||||
\(589\) | −7.17930 | −0.295818 | ||||||||
\(590\) | −9.65918 | −0.397662 | ||||||||
\(591\) | −29.2570 | −1.20347 | ||||||||
\(592\) | 7.04587 | 0.289583 | ||||||||
\(593\) | −39.7743 | −1.63333 | −0.816667 | − | 0.577109i | \(-0.804181\pi\) | ||||
−0.816667 | + | 0.577109i | \(0.804181\pi\) | |||||||
\(594\) | −25.8387 | −1.06018 | ||||||||
\(595\) | 16.2209 | 0.664991 | ||||||||
\(596\) | 5.25295 | 0.215169 | ||||||||
\(597\) | −11.6184 | −0.475508 | ||||||||
\(598\) | 11.5959 | 0.474193 | ||||||||
\(599\) | 22.1781 | 0.906171 | 0.453085 | − | 0.891467i | \(-0.350323\pi\) | ||||
0.453085 | + | 0.891467i | \(0.350323\pi\) | |||||||
\(600\) | −5.05615 | −0.206416 | ||||||||
\(601\) | −4.96324 | −0.202455 | −0.101227 | − | 0.994863i | \(-0.532277\pi\) | ||||
−0.101227 | + | 0.994863i | \(0.532277\pi\) | |||||||
\(602\) | 13.8943 | 0.566291 | ||||||||
\(603\) | −0.414568 | −0.0168825 | ||||||||
\(604\) | −19.4477 | −0.791316 | ||||||||
\(605\) | −36.8321 | −1.49744 | ||||||||
\(606\) | 26.1659 | 1.06292 | ||||||||
\(607\) | −42.1484 | −1.71075 | −0.855376 | − | 0.518007i | \(-0.826674\pi\) | ||||
−0.855376 | + | 0.518007i | \(0.826674\pi\) | |||||||
\(608\) | 2.06959 | 0.0839331 | ||||||||
\(609\) | 35.9684 | 1.45751 | ||||||||
\(610\) | −10.7816 | −0.436535 | ||||||||
\(611\) | −53.0984 | −2.14813 | ||||||||
\(612\) | 0.161448 | 0.00652615 | ||||||||
\(613\) | 31.5622 | 1.27478 | 0.637392 | − | 0.770540i | \(-0.280013\pi\) | ||||
0.637392 | + | 0.770540i | \(0.280013\pi\) | |||||||
\(614\) | 29.1634 | 1.17694 | ||||||||
\(615\) | 11.8689 | 0.478602 | ||||||||
\(616\) | −15.1410 | −0.610049 | ||||||||
\(617\) | −45.7995 | −1.84382 | −0.921910 | − | 0.387405i | \(-0.873372\pi\) | ||||
−0.921910 | + | 0.387405i | \(0.873372\pi\) | |||||||
\(618\) | 18.1383 | 0.729630 | ||||||||
\(619\) | −39.2693 | −1.57837 | −0.789184 | − | 0.614157i | \(-0.789496\pi\) | ||||
−0.789184 | + | 0.614157i | \(0.789496\pi\) | |||||||
\(620\) | 9.78849 | 0.393115 | ||||||||
\(621\) | 14.3029 | 0.573955 | ||||||||
\(622\) | −5.57897 | −0.223696 | ||||||||
\(623\) | 49.0688 | 1.96590 | ||||||||
\(624\) | −7.29056 | −0.291856 | ||||||||
\(625\) | −31.0363 | −1.24145 | ||||||||
\(626\) | 2.04723 | 0.0818238 | ||||||||
\(627\) | 17.3245 | 0.691874 | ||||||||
\(628\) | −1.41664 | −0.0565300 | ||||||||
\(629\) | −13.1195 | −0.523110 | ||||||||
\(630\) | 0.755333 | 0.0300932 | ||||||||
\(631\) | −31.5596 | −1.25637 | −0.628185 | − | 0.778064i | \(-0.716202\pi\) | ||||
−0.628185 | + | 0.778064i | \(0.716202\pi\) | |||||||
\(632\) | −10.2935 | −0.409452 | ||||||||
\(633\) | 27.4352 | 1.09045 | ||||||||
\(634\) | 20.9604 | 0.832445 | ||||||||
\(635\) | 12.0687 | 0.478934 | ||||||||
\(636\) | 8.41428 | 0.333648 | ||||||||
\(637\) | 10.8112 | 0.428356 | ||||||||
\(638\) | 33.4766 | 1.32535 | ||||||||
\(639\) | −1.11664 | −0.0441736 | ||||||||
\(640\) | −2.82175 | −0.111540 | ||||||||
\(641\) | 8.93197 | 0.352791 | 0.176396 | − | 0.984319i | \(-0.443556\pi\) | ||||
0.176396 | + | 0.984319i | \(0.443556\pi\) | |||||||
\(642\) | 8.96398 | 0.353780 | ||||||||
\(643\) | 7.75384 | 0.305782 | 0.152891 | − | 0.988243i | \(-0.451142\pi\) | ||||
0.152891 | + | 0.988243i | \(0.451142\pi\) | |||||||
\(644\) | 8.38122 | 0.330266 | ||||||||
\(645\) | 21.6759 | 0.853489 | ||||||||
\(646\) | −3.85362 | −0.151619 | ||||||||
\(647\) | −38.3324 | −1.50700 | −0.753500 | − | 0.657447i | \(-0.771636\pi\) | ||||
−0.753500 | + | 0.657447i | \(0.771636\pi\) | |||||||
\(648\) | −8.73236 | −0.343040 | ||||||||
\(649\) | −16.7882 | −0.658996 | ||||||||
\(650\) | 12.6531 | 0.496295 | ||||||||
\(651\) | 18.2793 | 0.716423 | ||||||||
\(652\) | 18.9578 | 0.742445 | ||||||||
\(653\) | 2.42412 | 0.0948631 | 0.0474315 | − | 0.998874i | \(-0.484896\pi\) | ||||
0.0474315 | + | 0.998874i | \(0.484896\pi\) | |||||||
\(654\) | 11.9223 | 0.466199 | ||||||||
\(655\) | 32.0177 | 1.25103 | ||||||||
\(656\) | 2.46434 | 0.0962163 | ||||||||
\(657\) | −0.248569 | −0.00969760 | ||||||||
\(658\) | −38.3781 | −1.49614 | ||||||||
\(659\) | −38.5775 | −1.50277 | −0.751383 | − | 0.659867i | \(-0.770613\pi\) | ||||
−0.751383 | + | 0.659867i | \(0.770613\pi\) | |||||||
\(660\) | −23.6208 | −0.919439 | ||||||||
\(661\) | −9.75974 | −0.379610 | −0.189805 | − | 0.981822i | \(-0.560786\pi\) | ||||
−0.189805 | + | 0.981822i | \(0.560786\pi\) | |||||||
\(662\) | −1.44693 | −0.0562364 | ||||||||
\(663\) | 13.5752 | 0.527216 | ||||||||
\(664\) | 0.795079 | 0.0308550 | ||||||||
\(665\) | −18.0291 | −0.699140 | ||||||||
\(666\) | −0.610918 | −0.0236726 | ||||||||
\(667\) | −18.5308 | −0.717516 | ||||||||
\(668\) | −24.0862 | −0.931924 | ||||||||
\(669\) | 47.3850 | 1.83201 | ||||||||
\(670\) | −13.4917 | −0.521230 | ||||||||
\(671\) | −18.7391 | −0.723414 | ||||||||
\(672\) | −5.26942 | −0.203272 | ||||||||
\(673\) | −13.3783 | −0.515694 | −0.257847 | − | 0.966186i | \(-0.583013\pi\) | ||||
−0.257847 | + | 0.966186i | \(0.583013\pi\) | |||||||
\(674\) | −18.7472 | −0.722115 | ||||||||
\(675\) | 15.6068 | 0.600707 | ||||||||
\(676\) | 5.24474 | 0.201721 | ||||||||
\(677\) | −36.4979 | −1.40273 | −0.701365 | − | 0.712803i | \(-0.747426\pi\) | ||||
−0.701365 | + | 0.712803i | \(0.747426\pi\) | |||||||
\(678\) | 2.75100 | 0.105651 | ||||||||
\(679\) | 34.0777 | 1.30778 | ||||||||
\(680\) | 5.25416 | 0.201488 | ||||||||
\(681\) | −26.6590 | −1.02157 | ||||||||
\(682\) | 17.0130 | 0.651461 | ||||||||
\(683\) | −13.8067 | −0.528300 | −0.264150 | − | 0.964482i | \(-0.585091\pi\) | ||||
−0.264150 | + | 0.964482i | \(0.585091\pi\) | |||||||
\(684\) | −0.179446 | −0.00686129 | ||||||||
\(685\) | 34.8231 | 1.33052 | ||||||||
\(686\) | −13.7967 | −0.526759 | ||||||||
\(687\) | 40.7977 | 1.55653 | ||||||||
\(688\) | 4.50056 | 0.171582 | ||||||||
\(689\) | −21.0569 | −0.802202 | ||||||||
\(690\) | 13.0752 | 0.497763 | ||||||||
\(691\) | 40.2612 | 1.53161 | 0.765804 | − | 0.643075i | \(-0.222341\pi\) | ||||
0.765804 | + | 0.643075i | \(0.222341\pi\) | |||||||
\(692\) | −17.6195 | −0.669794 | ||||||||
\(693\) | 1.31281 | 0.0498697 | ||||||||
\(694\) | −31.6900 | −1.20294 | ||||||||
\(695\) | −42.1678 | −1.59952 | ||||||||
\(696\) | 11.6506 | 0.441617 | ||||||||
\(697\) | −4.58865 | −0.173807 | ||||||||
\(698\) | −21.1615 | −0.800973 | ||||||||
\(699\) | 42.9686 | 1.62522 | ||||||||
\(700\) | 9.14531 | 0.345660 | ||||||||
\(701\) | 4.17150 | 0.157556 | 0.0787778 | − | 0.996892i | \(-0.474898\pi\) | ||||
0.0787778 | + | 0.996892i | \(0.474898\pi\) | |||||||
\(702\) | 22.5038 | 0.849352 | ||||||||
\(703\) | 14.5821 | 0.549974 | ||||||||
\(704\) | −4.90438 | −0.184841 | ||||||||
\(705\) | −59.8720 | −2.25491 | ||||||||
\(706\) | 1.21473 | 0.0457171 | ||||||||
\(707\) | −47.3276 | −1.77994 | ||||||||
\(708\) | −5.84270 | −0.219582 | ||||||||
\(709\) | −26.6999 | −1.00274 | −0.501368 | − | 0.865234i | \(-0.667170\pi\) | ||||
−0.501368 | + | 0.865234i | \(0.667170\pi\) | |||||||
\(710\) | −36.3399 | −1.36381 | ||||||||
\(711\) | 0.892505 | 0.0334715 | ||||||||
\(712\) | 15.8941 | 0.595655 | ||||||||
\(713\) | −9.41745 | −0.352686 | ||||||||
\(714\) | 9.81177 | 0.367196 | ||||||||
\(715\) | 59.1114 | 2.21064 | ||||||||
\(716\) | 14.9754 | 0.559657 | ||||||||
\(717\) | −14.4863 | −0.541002 | ||||||||
\(718\) | −21.2652 | −0.793609 | ||||||||
\(719\) | 38.2674 | 1.42713 | 0.713567 | − | 0.700587i | \(-0.247079\pi\) | ||||
0.713567 | + | 0.700587i | \(0.247079\pi\) | |||||||
\(720\) | 0.244663 | 0.00911803 | ||||||||
\(721\) | −32.8077 | −1.22182 | ||||||||
\(722\) | −14.7168 | −0.547702 | ||||||||
\(723\) | 27.2882 | 1.01486 | ||||||||
\(724\) | −15.6659 | −0.582219 | ||||||||
\(725\) | −20.2202 | −0.750959 | ||||||||
\(726\) | −22.2792 | −0.826858 | ||||||||
\(727\) | 5.20464 | 0.193029 | 0.0965147 | − | 0.995332i | \(-0.469231\pi\) | ||||
0.0965147 | + | 0.995332i | \(0.469231\pi\) | |||||||
\(728\) | 13.1868 | 0.488736 | ||||||||
\(729\) | 27.7346 | 1.02721 | ||||||||
\(730\) | −8.08942 | −0.299403 | ||||||||
\(731\) | −8.38013 | −0.309950 | ||||||||
\(732\) | −6.52164 | −0.241047 | ||||||||
\(733\) | −46.1205 | −1.70350 | −0.851749 | − | 0.523949i | \(-0.824458\pi\) | ||||
−0.851749 | + | 0.523949i | \(0.824458\pi\) | |||||||
\(734\) | −26.6271 | −0.982823 | ||||||||
\(735\) | 12.1904 | 0.449648 | ||||||||
\(736\) | 2.71479 | 0.100069 | ||||||||
\(737\) | −23.4494 | −0.863769 | ||||||||
\(738\) | −0.213673 | −0.00786540 | ||||||||
\(739\) | 25.0390 | 0.921074 | 0.460537 | − | 0.887641i | \(-0.347657\pi\) | ||||
0.460537 | + | 0.887641i | \(0.347657\pi\) | |||||||
\(740\) | −19.8817 | −0.730866 | ||||||||
\(741\) | −15.0885 | −0.554290 | ||||||||
\(742\) | −15.2193 | −0.558719 | ||||||||
\(743\) | 12.9154 | 0.473819 | 0.236909 | − | 0.971532i | \(-0.423866\pi\) | ||||
0.236909 | + | 0.971532i | \(0.423866\pi\) | |||||||
\(744\) | 5.92092 | 0.217071 | ||||||||
\(745\) | −14.8225 | −0.543055 | ||||||||
\(746\) | −25.0452 | −0.916970 | ||||||||
\(747\) | −0.0689380 | −0.00252231 | ||||||||
\(748\) | 9.13204 | 0.333900 | ||||||||
\(749\) | −16.2136 | −0.592432 | ||||||||
\(750\) | −9.81417 | −0.358363 | ||||||||
\(751\) | 22.1175 | 0.807078 | 0.403539 | − | 0.914962i | \(-0.367780\pi\) | ||||
0.403539 | + | 0.914962i | \(0.367780\pi\) | |||||||
\(752\) | −12.4312 | −0.453319 | ||||||||
\(753\) | 9.43331 | 0.343769 | ||||||||
\(754\) | −29.1559 | −1.06180 | ||||||||
\(755\) | 54.8766 | 1.99716 | ||||||||
\(756\) | 16.2652 | 0.591558 | ||||||||
\(757\) | −11.0278 | −0.400812 | −0.200406 | − | 0.979713i | \(-0.564226\pi\) | ||||
−0.200406 | + | 0.979713i | \(0.564226\pi\) | |||||||
\(758\) | 34.2529 | 1.24412 | ||||||||
\(759\) | 22.7254 | 0.824881 | ||||||||
\(760\) | −5.83988 | −0.211835 | ||||||||
\(761\) | −12.4649 | −0.451854 | −0.225927 | − | 0.974144i | \(-0.572541\pi\) | ||||
−0.225927 | + | 0.974144i | \(0.572541\pi\) | |||||||
\(762\) | 7.30021 | 0.264459 | ||||||||
\(763\) | −21.5645 | −0.780687 | ||||||||
\(764\) | −12.9141 | −0.467215 | ||||||||
\(765\) | −0.455566 | −0.0164710 | ||||||||
\(766\) | 12.5747 | 0.454344 | ||||||||
\(767\) | 14.6214 | 0.527950 | ||||||||
\(768\) | −1.70684 | −0.0615902 | ||||||||
\(769\) | 49.1734 | 1.77324 | 0.886619 | − | 0.462500i | \(-0.153047\pi\) | ||||
0.886619 | + | 0.462500i | \(0.153047\pi\) | |||||||
\(770\) | 42.7242 | 1.53967 | ||||||||
\(771\) | −29.0962 | −1.04787 | ||||||||
\(772\) | −5.68924 | −0.204760 | ||||||||
\(773\) | −39.6495 | −1.42610 | −0.713048 | − | 0.701116i | \(-0.752686\pi\) | ||||
−0.713048 | + | 0.701116i | \(0.752686\pi\) | |||||||
\(774\) | −0.390225 | −0.0140264 | ||||||||
\(775\) | −10.2760 | −0.369125 | ||||||||
\(776\) | 11.0382 | 0.396249 | ||||||||
\(777\) | −37.1277 | −1.33195 | ||||||||
\(778\) | 11.7727 | 0.422072 | ||||||||
\(779\) | 5.10018 | 0.182733 | ||||||||
\(780\) | 20.5722 | 0.736602 | ||||||||
\(781\) | −63.1609 | −2.26007 | ||||||||
\(782\) | −5.05499 | −0.180766 | ||||||||
\(783\) | −35.9621 | −1.28518 | ||||||||
\(784\) | 2.53108 | 0.0903956 | ||||||||
\(785\) | 3.99740 | 0.142673 | ||||||||
\(786\) | 19.3670 | 0.690799 | ||||||||
\(787\) | 22.2282 | 0.792348 | 0.396174 | − | 0.918175i | \(-0.370338\pi\) | ||||
0.396174 | + | 0.918175i | \(0.370338\pi\) | |||||||
\(788\) | 17.1411 | 0.610626 | ||||||||
\(789\) | 23.8344 | 0.848527 | ||||||||
\(790\) | 29.0456 | 1.03340 | ||||||||
\(791\) | −4.97587 | −0.176921 | ||||||||
\(792\) | 0.425238 | 0.0151102 | ||||||||
\(793\) | 16.3205 | 0.579558 | ||||||||
\(794\) | −9.59148 | −0.340389 | ||||||||
\(795\) | −23.7430 | −0.842078 | ||||||||
\(796\) | 6.80696 | 0.241266 | ||||||||
\(797\) | −20.8894 | −0.739940 | −0.369970 | − | 0.929044i | \(-0.620632\pi\) | ||||
−0.369970 | + | 0.929044i | \(0.620632\pi\) | |||||||
\(798\) | −10.9056 | −0.386053 | ||||||||
\(799\) | 23.1471 | 0.818886 | ||||||||
\(800\) | 2.96229 | 0.104733 | ||||||||
\(801\) | −1.37811 | −0.0486931 | ||||||||
\(802\) | 12.9004 | 0.455530 | ||||||||
\(803\) | −14.0599 | −0.496163 | ||||||||
\(804\) | −8.16093 | −0.287814 | ||||||||
\(805\) | −23.6497 | −0.833544 | ||||||||
\(806\) | −14.8172 | −0.521913 | ||||||||
\(807\) | −7.82287 | −0.275378 | ||||||||
\(808\) | −15.3300 | −0.539309 | ||||||||
\(809\) | 6.45324 | 0.226884 | 0.113442 | − | 0.993545i | \(-0.463812\pi\) | ||||
0.113442 | + | 0.993545i | \(0.463812\pi\) | |||||||
\(810\) | 24.6406 | 0.865782 | ||||||||
\(811\) | 25.5681 | 0.897819 | 0.448909 | − | 0.893577i | \(-0.351813\pi\) | ||||
0.448909 | + | 0.893577i | \(0.351813\pi\) | |||||||
\(812\) | −21.0731 | −0.739522 | ||||||||
\(813\) | −33.2795 | −1.16716 | ||||||||
\(814\) | −34.5556 | −1.21117 | ||||||||
\(815\) | −53.4943 | −1.87382 | ||||||||
\(816\) | 3.17816 | 0.111258 | ||||||||
\(817\) | 9.31433 | 0.325867 | ||||||||
\(818\) | −33.3682 | −1.16669 | ||||||||
\(819\) | −1.14337 | −0.0399527 | ||||||||
\(820\) | −6.95376 | −0.242836 | ||||||||
\(821\) | 22.3784 | 0.781011 | 0.390506 | − | 0.920601i | \(-0.372300\pi\) | ||||
0.390506 | + | 0.920601i | \(0.372300\pi\) | |||||||
\(822\) | 21.0640 | 0.734691 | ||||||||
\(823\) | −1.18403 | −0.0412726 | −0.0206363 | − | 0.999787i | \(-0.506569\pi\) | ||||
−0.0206363 | + | 0.999787i | \(0.506569\pi\) | |||||||
\(824\) | −10.6269 | −0.370204 | ||||||||
\(825\) | 24.7972 | 0.863329 | ||||||||
\(826\) | 10.5680 | 0.367707 | ||||||||
\(827\) | 9.64076 | 0.335242 | 0.167621 | − | 0.985851i | \(-0.446391\pi\) | ||||
0.167621 | + | 0.985851i | \(0.446391\pi\) | |||||||
\(828\) | −0.235388 | −0.00818031 | ||||||||
\(829\) | 9.86036 | 0.342465 | 0.171232 | − | 0.985231i | \(-0.445225\pi\) | ||||
0.171232 | + | 0.985231i | \(0.445225\pi\) | |||||||
\(830\) | −2.24352 | −0.0778736 | ||||||||
\(831\) | −28.1204 | −0.975487 | ||||||||
\(832\) | 4.27139 | 0.148084 | ||||||||
\(833\) | −4.71291 | −0.163293 | ||||||||
\(834\) | −25.5067 | −0.883225 | ||||||||
\(835\) | 67.9653 | 2.35204 | ||||||||
\(836\) | −10.1501 | −0.351047 | ||||||||
\(837\) | −18.2761 | −0.631716 | ||||||||
\(838\) | −37.9374 | −1.31053 | ||||||||
\(839\) | 50.3599 | 1.73862 | 0.869308 | − | 0.494271i | \(-0.164565\pi\) | ||||
0.869308 | + | 0.494271i | \(0.164565\pi\) | |||||||
\(840\) | 14.8690 | 0.513030 | ||||||||
\(841\) | 17.5925 | 0.606637 | ||||||||
\(842\) | −20.4084 | −0.703318 | ||||||||
\(843\) | 21.4647 | 0.739285 | ||||||||
\(844\) | −16.0737 | −0.553279 | ||||||||
\(845\) | −14.7994 | −0.509114 | ||||||||
\(846\) | 1.07786 | 0.0370575 | ||||||||
\(847\) | 40.2975 | 1.38464 | ||||||||
\(848\) | −4.92975 | −0.169288 | ||||||||
\(849\) | 42.7022 | 1.46553 | ||||||||
\(850\) | −5.51584 | −0.189192 | ||||||||
\(851\) | 19.1281 | 0.655702 | ||||||||
\(852\) | −21.9815 | −0.753072 | ||||||||
\(853\) | −27.8290 | −0.952846 | −0.476423 | − | 0.879216i | \(-0.658067\pi\) | ||||
−0.476423 | + | 0.879216i | \(0.658067\pi\) | |||||||
\(854\) | 11.7960 | 0.403652 | ||||||||
\(855\) | 0.506352 | 0.0173169 | ||||||||
\(856\) | −5.25181 | −0.179503 | ||||||||
\(857\) | 13.3452 | 0.455865 | 0.227932 | − | 0.973677i | \(-0.426803\pi\) | ||||
0.227932 | + | 0.973677i | \(0.426803\pi\) | |||||||
\(858\) | 35.7557 | 1.22068 | ||||||||
\(859\) | −36.0157 | −1.22884 | −0.614420 | − | 0.788979i | \(-0.710610\pi\) | ||||
−0.614420 | + | 0.788979i | \(0.710610\pi\) | |||||||
\(860\) | −12.6995 | −0.433048 | ||||||||
\(861\) | −12.9857 | −0.442550 | ||||||||
\(862\) | 0.480525 | 0.0163668 | ||||||||
\(863\) | 41.5617 | 1.41478 | 0.707389 | − | 0.706824i | \(-0.249873\pi\) | ||||
0.707389 | + | 0.706824i | \(0.249873\pi\) | |||||||
\(864\) | 5.26851 | 0.179238 | ||||||||
\(865\) | 49.7179 | 1.69046 | ||||||||
\(866\) | 31.0825 | 1.05623 | ||||||||
\(867\) | 23.0984 | 0.784464 | ||||||||
\(868\) | −10.7095 | −0.363503 | ||||||||
\(869\) | 50.4831 | 1.71252 | ||||||||
\(870\) | −32.8752 | −1.11458 | ||||||||
\(871\) | 20.4229 | 0.692002 | ||||||||
\(872\) | −6.98503 | −0.236543 | ||||||||
\(873\) | −0.957079 | −0.0323922 | ||||||||
\(874\) | 5.61851 | 0.190049 | ||||||||
\(875\) | 17.7514 | 0.600107 | ||||||||
\(876\) | −4.89317 | −0.165325 | ||||||||
\(877\) | 6.46760 | 0.218395 | 0.109198 | − | 0.994020i | \(-0.465172\pi\) | ||||
0.109198 | + | 0.994020i | \(0.465172\pi\) | |||||||
\(878\) | −26.0470 | −0.879043 | ||||||||
\(879\) | −5.27517 | −0.177927 | ||||||||
\(880\) | 13.8389 | 0.466510 | ||||||||
\(881\) | −19.1361 | −0.644711 | −0.322355 | − | 0.946619i | \(-0.604475\pi\) | ||||
−0.322355 | + | 0.946619i | \(0.604475\pi\) | |||||||
\(882\) | −0.219459 | −0.00738958 | ||||||||
\(883\) | 15.0470 | 0.506372 | 0.253186 | − | 0.967418i | \(-0.418522\pi\) | ||||
0.253186 | + | 0.967418i | \(0.418522\pi\) | |||||||
\(884\) | −7.95340 | −0.267502 | ||||||||
\(885\) | 16.4867 | 0.554193 | ||||||||
\(886\) | 0.328188 | 0.0110257 | ||||||||
\(887\) | −48.1976 | −1.61832 | −0.809159 | − | 0.587590i | \(-0.800077\pi\) | ||||
−0.809159 | + | 0.587590i | \(0.800077\pi\) | |||||||
\(888\) | −12.0262 | −0.403571 | ||||||||
\(889\) | −13.2043 | −0.442857 | ||||||||
\(890\) | −44.8491 | −1.50335 | ||||||||
\(891\) | 42.8268 | 1.43475 | ||||||||
\(892\) | −27.7619 | −0.929536 | ||||||||
\(893\) | −25.7275 | −0.860938 | ||||||||
\(894\) | −8.96593 | −0.299866 | ||||||||
\(895\) | −42.2568 | −1.41249 | ||||||||
\(896\) | 3.08724 | 0.103138 | ||||||||
\(897\) | −19.7924 | −0.660847 | ||||||||
\(898\) | 4.53151 | 0.151218 | ||||||||
\(899\) | 23.6785 | 0.789723 | ||||||||
\(900\) | −0.256848 | −0.00856159 | ||||||||
\(901\) | 9.17928 | 0.305806 | ||||||||
\(902\) | −12.0860 | −0.402421 | ||||||||
\(903\) | −23.7154 | −0.789198 | ||||||||
\(904\) | −1.61175 | −0.0536060 | ||||||||
\(905\) | 44.2053 | 1.46943 | ||||||||
\(906\) | 33.1941 | 1.10280 | ||||||||
\(907\) | −5.11398 | −0.169807 | −0.0849035 | − | 0.996389i | \(-0.527058\pi\) | ||||
−0.0849035 | + | 0.996389i | \(0.527058\pi\) | |||||||
\(908\) | 15.6189 | 0.518332 | ||||||||
\(909\) | 1.32920 | 0.0440869 | ||||||||
\(910\) | −37.2099 | −1.23350 | ||||||||
\(911\) | 23.3633 | 0.774060 | 0.387030 | − | 0.922067i | \(-0.373501\pi\) | ||||
0.387030 | + | 0.922067i | \(0.373501\pi\) | |||||||
\(912\) | −3.53246 | −0.116971 | ||||||||
\(913\) | −3.89937 | −0.129050 | ||||||||
\(914\) | −10.6555 | −0.352453 | ||||||||
\(915\) | 18.4025 | 0.608366 | ||||||||
\(916\) | −23.9025 | −0.789761 | ||||||||
\(917\) | −35.0301 | −1.15680 | ||||||||
\(918\) | −9.81005 | −0.323780 | ||||||||
\(919\) | 19.1538 | 0.631827 | 0.315914 | − | 0.948788i | \(-0.397689\pi\) | ||||
0.315914 | + | 0.948788i | \(0.397689\pi\) | |||||||
\(920\) | −7.66047 | −0.252558 | ||||||||
\(921\) | −49.7773 | −1.64022 | ||||||||
\(922\) | 29.2492 | 0.963272 | ||||||||
\(923\) | 55.0089 | 1.81064 | ||||||||
\(924\) | 25.8432 | 0.850180 | ||||||||
\(925\) | 20.8719 | 0.686264 | ||||||||
\(926\) | −17.0576 | −0.560546 | ||||||||
\(927\) | 0.921411 | 0.0302631 | ||||||||
\(928\) | −6.82587 | −0.224070 | ||||||||
\(929\) | 14.4439 | 0.473890 | 0.236945 | − | 0.971523i | \(-0.423854\pi\) | ||||
0.236945 | + | 0.971523i | \(0.423854\pi\) | |||||||
\(930\) | −16.7074 | −0.547856 | ||||||||
\(931\) | 5.23830 | 0.171678 | ||||||||
\(932\) | −25.1744 | −0.824615 | ||||||||
\(933\) | 9.52239 | 0.311749 | ||||||||
\(934\) | −25.3357 | −0.829010 | ||||||||
\(935\) | −25.7684 | −0.842715 | ||||||||
\(936\) | −0.370354 | −0.0121054 | ||||||||
\(937\) | 7.51504 | 0.245506 | 0.122753 | − | 0.992437i | \(-0.460828\pi\) | ||||
0.122753 | + | 0.992437i | \(0.460828\pi\) | |||||||
\(938\) | 14.7611 | 0.481967 | ||||||||
\(939\) | −3.49429 | −0.114032 | ||||||||
\(940\) | 35.0778 | 1.14411 | ||||||||
\(941\) | 8.05139 | 0.262468 | 0.131234 | − | 0.991351i | \(-0.458106\pi\) | ||||
0.131234 | + | 0.991351i | \(0.458106\pi\) | |||||||
\(942\) | 2.41797 | 0.0787818 | ||||||||
\(943\) | 6.69017 | 0.217862 | ||||||||
\(944\) | 3.42311 | 0.111413 | ||||||||
\(945\) | −45.8963 | −1.49301 | ||||||||
\(946\) | −22.0724 | −0.717637 | ||||||||
\(947\) | −0.885851 | −0.0287863 | −0.0143932 | − | 0.999896i | \(-0.504582\pi\) | ||||
−0.0143932 | + | 0.999896i | \(0.504582\pi\) | |||||||
\(948\) | 17.5693 | 0.570624 | ||||||||
\(949\) | 12.2452 | 0.397497 | ||||||||
\(950\) | 6.13073 | 0.198907 | ||||||||
\(951\) | −35.7760 | −1.16012 | ||||||||
\(952\) | −5.74851 | −0.186310 | ||||||||
\(953\) | 10.9699 | 0.355349 | 0.177674 | − | 0.984089i | \(-0.443143\pi\) | ||||
0.177674 | + | 0.984089i | \(0.443143\pi\) | |||||||
\(954\) | 0.427438 | 0.0138388 | ||||||||
\(955\) | 36.4403 | 1.17918 | ||||||||
\(956\) | 8.48723 | 0.274497 | ||||||||
\(957\) | −57.1392 | −1.84705 | ||||||||
\(958\) | 19.1424 | 0.618463 | ||||||||
\(959\) | −38.0995 | −1.23030 | ||||||||
\(960\) | 4.81627 | 0.155445 | ||||||||
\(961\) | −18.9665 | −0.611821 | ||||||||
\(962\) | 30.0956 | 0.970322 | ||||||||
\(963\) | 0.455362 | 0.0146739 | ||||||||
\(964\) | −15.9876 | −0.514924 | ||||||||
\(965\) | 16.0536 | 0.516785 | ||||||||
\(966\) | −14.3054 | −0.460268 | ||||||||
\(967\) | −27.1806 | −0.874069 | −0.437034 | − | 0.899445i | \(-0.643971\pi\) | ||||
−0.437034 | + | 0.899445i | \(0.643971\pi\) | |||||||
\(968\) | 13.0529 | 0.419536 | ||||||||
\(969\) | 6.57751 | 0.211300 | ||||||||
\(970\) | −31.1472 | −1.00007 | ||||||||
\(971\) | 29.9932 | 0.962528 | 0.481264 | − | 0.876576i | \(-0.340178\pi\) | ||||
0.481264 | + | 0.876576i | \(0.340178\pi\) | |||||||
\(972\) | −0.900789 | −0.0288928 | ||||||||
\(973\) | 46.1353 | 1.47903 | ||||||||
\(974\) | −1.20359 | −0.0385654 | ||||||||
\(975\) | −21.5967 | −0.691650 | ||||||||
\(976\) | 3.82089 | 0.122304 | ||||||||
\(977\) | 57.8715 | 1.85147 | 0.925737 | − | 0.378168i | \(-0.123446\pi\) | ||||
0.925737 | + | 0.378168i | \(0.123446\pi\) | |||||||
\(978\) | −32.3579 | −1.03469 | ||||||||
\(979\) | −77.9505 | −2.49131 | ||||||||
\(980\) | −7.14207 | −0.228145 | ||||||||
\(981\) | 0.605643 | 0.0193367 | ||||||||
\(982\) | 32.5980 | 1.04025 | ||||||||
\(983\) | 27.7521 | 0.885155 | 0.442578 | − | 0.896730i | \(-0.354064\pi\) | ||||
0.442578 | + | 0.896730i | \(0.354064\pi\) | |||||||
\(984\) | −4.20623 | −0.134090 | ||||||||
\(985\) | −48.3679 | −1.54113 | ||||||||
\(986\) | 12.7099 | 0.404765 | ||||||||
\(987\) | 65.5052 | 2.08505 | ||||||||
\(988\) | 8.84003 | 0.281239 | ||||||||
\(989\) | 12.2181 | 0.388513 | ||||||||
\(990\) | −1.19992 | −0.0381359 | ||||||||
\(991\) | 18.4073 | 0.584727 | 0.292364 | − | 0.956307i | \(-0.405558\pi\) | ||||
0.292364 | + | 0.956307i | \(0.405558\pi\) | |||||||
\(992\) | −3.46894 | −0.110139 | ||||||||
\(993\) | 2.46967 | 0.0783726 | ||||||||
\(994\) | 39.7590 | 1.26108 | ||||||||
\(995\) | −19.2076 | −0.608920 | ||||||||
\(996\) | −1.35707 | −0.0430004 | ||||||||
\(997\) | 6.67212 | 0.211308 | 0.105654 | − | 0.994403i | \(-0.466306\pi\) | ||||
0.105654 | + | 0.994403i | \(0.466306\pi\) | |||||||
\(998\) | 10.0147 | 0.317010 | ||||||||
\(999\) | 37.1212 | 1.17446 |
(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 | 8026.2.a.a.1.20 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.a.1.20 | ✓ | 71 | 1.1 | even | 1 | trivial |