Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 16 x^{17} + 77 x^{16} + 88 x^{15} - 594 x^{14} - 154 x^{13} + 2388 x^{12} - 278 x^{11} - 5460 x^{10} + 1491 x^{9} + 7285 x^{8} - 2223 x^{7} - 5579 x^{6} + 1430 x^{5} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(-2.08649\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.08649 | 1.47537 | 0.737684 | − | 0.675146i | \(-0.235919\pi\) | ||||
0.737684 | + | 0.675146i | \(0.235919\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.35342 | 1.17671 | ||||||||
\(5\) | 0.146235 | 0.0653981 | 0.0326990 | − | 0.999465i | \(-0.489590\pi\) | ||||
0.0326990 | + | 0.999465i | \(0.489590\pi\) | |||||||
\(6\) | 2.08649 | 0.851804 | ||||||||
\(7\) | −2.80287 | −1.05938 | −0.529692 | − | 0.848190i | \(-0.677692\pi\) | ||||
−0.529692 | + | 0.848190i | \(0.677692\pi\) | |||||||
\(8\) | 0.737414 | 0.260715 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.305116 | 0.0964863 | ||||||||
\(11\) | −2.41948 | −0.729500 | −0.364750 | − | 0.931106i | \(-0.618846\pi\) | ||||
−0.364750 | + | 0.931106i | \(0.618846\pi\) | |||||||
\(12\) | 2.35342 | 0.679375 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −5.84814 | −1.56298 | ||||||||
\(15\) | 0.146235 | 0.0377576 | ||||||||
\(16\) | −3.16824 | −0.792061 | ||||||||
\(17\) | −7.90000 | −1.91603 | −0.958016 | − | 0.286714i | \(-0.907437\pi\) | ||||
−0.958016 | + | 0.286714i | \(0.907437\pi\) | |||||||
\(18\) | 2.08649 | 0.491789 | ||||||||
\(19\) | −1.37004 | −0.314308 | −0.157154 | − | 0.987574i | \(-0.550232\pi\) | ||||
−0.157154 | + | 0.987574i | \(0.550232\pi\) | |||||||
\(20\) | 0.344152 | 0.0769547 | ||||||||
\(21\) | −2.80287 | −0.611635 | ||||||||
\(22\) | −5.04821 | −1.07628 | ||||||||
\(23\) | 2.00810 | 0.418718 | 0.209359 | − | 0.977839i | \(-0.432862\pi\) | ||||
0.209359 | + | 0.977839i | \(0.432862\pi\) | |||||||
\(24\) | 0.737414 | 0.150524 | ||||||||
\(25\) | −4.97862 | −0.995723 | ||||||||
\(26\) | 2.08649 | 0.409194 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.59633 | −1.24659 | ||||||||
\(29\) | 0.323878 | 0.0601427 | 0.0300713 | − | 0.999548i | \(-0.490427\pi\) | ||||
0.0300713 | + | 0.999548i | \(0.490427\pi\) | |||||||
\(30\) | 0.305116 | 0.0557064 | ||||||||
\(31\) | −2.15569 | −0.387174 | −0.193587 | − | 0.981083i | \(-0.562012\pi\) | ||||
−0.193587 | + | 0.981083i | \(0.562012\pi\) | |||||||
\(32\) | −8.08532 | −1.42930 | ||||||||
\(33\) | −2.41948 | −0.421177 | ||||||||
\(34\) | −16.4832 | −2.82685 | ||||||||
\(35\) | −0.409876 | −0.0692817 | ||||||||
\(36\) | 2.35342 | 0.392237 | ||||||||
\(37\) | 8.53857 | 1.40373 | 0.701866 | − | 0.712309i | \(-0.252350\pi\) | ||||
0.701866 | + | 0.712309i | \(0.252350\pi\) | |||||||
\(38\) | −2.85856 | −0.463720 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0.107835 | 0.0170503 | ||||||||
\(41\) | −1.40537 | −0.219483 | −0.109741 | − | 0.993960i | \(-0.535002\pi\) | ||||
−0.109741 | + | 0.993960i | \(0.535002\pi\) | |||||||
\(42\) | −5.84814 | −0.902387 | ||||||||
\(43\) | −3.63358 | −0.554116 | −0.277058 | − | 0.960853i | \(-0.589359\pi\) | ||||
−0.277058 | + | 0.960853i | \(0.589359\pi\) | |||||||
\(44\) | −5.69406 | −0.858411 | ||||||||
\(45\) | 0.146235 | 0.0217994 | ||||||||
\(46\) | 4.18988 | 0.617764 | ||||||||
\(47\) | 1.09047 | 0.159062 | 0.0795308 | − | 0.996832i | \(-0.474658\pi\) | ||||
0.0795308 | + | 0.996832i | \(0.474658\pi\) | |||||||
\(48\) | −3.16824 | −0.457297 | ||||||||
\(49\) | 0.856054 | 0.122293 | ||||||||
\(50\) | −10.3878 | −1.46906 | ||||||||
\(51\) | −7.90000 | −1.10622 | ||||||||
\(52\) | 2.35342 | 0.326361 | ||||||||
\(53\) | 5.59115 | 0.768003 | 0.384002 | − | 0.923332i | \(-0.374546\pi\) | ||||
0.384002 | + | 0.923332i | \(0.374546\pi\) | |||||||
\(54\) | 2.08649 | 0.283935 | ||||||||
\(55\) | −0.353811 | −0.0477079 | ||||||||
\(56\) | −2.06687 | −0.276197 | ||||||||
\(57\) | −1.37004 | −0.181466 | ||||||||
\(58\) | 0.675767 | 0.0887326 | ||||||||
\(59\) | −5.92594 | −0.771491 | −0.385746 | − | 0.922605i | \(-0.626056\pi\) | ||||
−0.385746 | + | 0.922605i | \(0.626056\pi\) | |||||||
\(60\) | 0.344152 | 0.0444298 | ||||||||
\(61\) | −5.22961 | −0.669583 | −0.334792 | − | 0.942292i | \(-0.608666\pi\) | ||||
−0.334792 | + | 0.942292i | \(0.608666\pi\) | |||||||
\(62\) | −4.49782 | −0.571224 | ||||||||
\(63\) | −2.80287 | −0.353128 | ||||||||
\(64\) | −10.5334 | −1.31668 | ||||||||
\(65\) | 0.146235 | 0.0181382 | ||||||||
\(66\) | −5.04821 | −0.621391 | ||||||||
\(67\) | −15.2322 | −1.86091 | −0.930456 | − | 0.366403i | \(-0.880589\pi\) | ||||
−0.930456 | + | 0.366403i | \(0.880589\pi\) | |||||||
\(68\) | −18.5921 | −2.25462 | ||||||||
\(69\) | 2.00810 | 0.241747 | ||||||||
\(70\) | −0.855200 | −0.102216 | ||||||||
\(71\) | −7.85364 | −0.932055 | −0.466028 | − | 0.884770i | \(-0.654315\pi\) | ||||
−0.466028 | + | 0.884770i | \(0.654315\pi\) | |||||||
\(72\) | 0.737414 | 0.0869051 | ||||||||
\(73\) | 5.89036 | 0.689415 | 0.344707 | − | 0.938710i | \(-0.387978\pi\) | ||||
0.344707 | + | 0.938710i | \(0.387978\pi\) | |||||||
\(74\) | 17.8156 | 2.07102 | ||||||||
\(75\) | −4.97862 | −0.574881 | ||||||||
\(76\) | −3.22428 | −0.369850 | ||||||||
\(77\) | 6.78147 | 0.772820 | ||||||||
\(78\) | 2.08649 | 0.236248 | ||||||||
\(79\) | 10.9860 | 1.23602 | 0.618010 | − | 0.786170i | \(-0.287939\pi\) | ||||
0.618010 | + | 0.786170i | \(0.287939\pi\) | |||||||
\(80\) | −0.463307 | −0.0517993 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.93229 | −0.323818 | ||||||||
\(83\) | 6.84744 | 0.751604 | 0.375802 | − | 0.926700i | \(-0.377367\pi\) | ||||
0.375802 | + | 0.926700i | \(0.377367\pi\) | |||||||
\(84\) | −6.59633 | −0.719719 | ||||||||
\(85\) | −1.15525 | −0.125305 | ||||||||
\(86\) | −7.58142 | −0.817526 | ||||||||
\(87\) | 0.323878 | 0.0347234 | ||||||||
\(88\) | −1.78416 | −0.190192 | ||||||||
\(89\) | 1.55874 | 0.165226 | 0.0826130 | − | 0.996582i | \(-0.473673\pi\) | ||||
0.0826130 | + | 0.996582i | \(0.473673\pi\) | |||||||
\(90\) | 0.305116 | 0.0321621 | ||||||||
\(91\) | −2.80287 | −0.293820 | ||||||||
\(92\) | 4.72592 | 0.492711 | ||||||||
\(93\) | −2.15569 | −0.223535 | ||||||||
\(94\) | 2.27525 | 0.234675 | ||||||||
\(95\) | −0.200347 | −0.0205551 | ||||||||
\(96\) | −8.08532 | −0.825205 | ||||||||
\(97\) | 3.05667 | 0.310358 | 0.155179 | − | 0.987886i | \(-0.450405\pi\) | ||||
0.155179 | + | 0.987886i | \(0.450405\pi\) | |||||||
\(98\) | 1.78614 | 0.180428 | ||||||||
\(99\) | −2.41948 | −0.243167 | ||||||||
\(100\) | −11.7168 | −1.17168 | ||||||||
\(101\) | 8.97677 | 0.893222 | 0.446611 | − | 0.894728i | \(-0.352631\pi\) | ||||
0.446611 | + | 0.894728i | \(0.352631\pi\) | |||||||
\(102\) | −16.4832 | −1.63208 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 0.737414 | 0.0723094 | ||||||||
\(105\) | −0.409876 | −0.0399998 | ||||||||
\(106\) | 11.6659 | 1.13309 | ||||||||
\(107\) | 10.9794 | 1.06142 | 0.530711 | − | 0.847553i | \(-0.321925\pi\) | ||||
0.530711 | + | 0.847553i | \(0.321925\pi\) | |||||||
\(108\) | 2.35342 | 0.226458 | ||||||||
\(109\) | −14.8721 | −1.42449 | −0.712245 | − | 0.701931i | \(-0.752322\pi\) | ||||
−0.712245 | + | 0.701931i | \(0.752322\pi\) | |||||||
\(110\) | −0.738222 | −0.0703867 | ||||||||
\(111\) | 8.53857 | 0.810445 | ||||||||
\(112\) | 8.88016 | 0.839096 | ||||||||
\(113\) | 3.10936 | 0.292504 | 0.146252 | − | 0.989247i | \(-0.453279\pi\) | ||||
0.146252 | + | 0.989247i | \(0.453279\pi\) | |||||||
\(114\) | −2.85856 | −0.267729 | ||||||||
\(115\) | 0.293654 | 0.0273834 | ||||||||
\(116\) | 0.762223 | 0.0707706 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −12.3644 | −1.13823 | ||||||||
\(119\) | 22.1426 | 2.02981 | ||||||||
\(120\) | 0.107835 | 0.00984398 | ||||||||
\(121\) | −5.14613 | −0.467830 | ||||||||
\(122\) | −10.9115 | −0.987882 | ||||||||
\(123\) | −1.40537 | −0.126718 | ||||||||
\(124\) | −5.07326 | −0.455592 | ||||||||
\(125\) | −1.45922 | −0.130516 | ||||||||
\(126\) | −5.84814 | −0.520994 | ||||||||
\(127\) | 0.420464 | 0.0373101 | 0.0186551 | − | 0.999826i | \(-0.494062\pi\) | ||||
0.0186551 | + | 0.999826i | \(0.494062\pi\) | |||||||
\(128\) | −5.80720 | −0.513289 | ||||||||
\(129\) | −3.63358 | −0.319919 | ||||||||
\(130\) | 0.305116 | 0.0267605 | ||||||||
\(131\) | −12.3974 | −1.08316 | −0.541582 | − | 0.840648i | \(-0.682174\pi\) | ||||
−0.541582 | + | 0.840648i | \(0.682174\pi\) | |||||||
\(132\) | −5.69406 | −0.495604 | ||||||||
\(133\) | 3.84003 | 0.332973 | ||||||||
\(134\) | −31.7818 | −2.74553 | ||||||||
\(135\) | 0.146235 | 0.0125859 | ||||||||
\(136\) | −5.82557 | −0.499539 | ||||||||
\(137\) | −5.62724 | −0.480768 | −0.240384 | − | 0.970678i | \(-0.577273\pi\) | ||||
−0.240384 | + | 0.970678i | \(0.577273\pi\) | |||||||
\(138\) | 4.18988 | 0.356666 | ||||||||
\(139\) | 16.6873 | 1.41540 | 0.707699 | − | 0.706514i | \(-0.249733\pi\) | ||||
0.707699 | + | 0.706514i | \(0.249733\pi\) | |||||||
\(140\) | −0.964612 | −0.0815246 | ||||||||
\(141\) | 1.09047 | 0.0918343 | ||||||||
\(142\) | −16.3865 | −1.37512 | ||||||||
\(143\) | −2.41948 | −0.202327 | ||||||||
\(144\) | −3.16824 | −0.264020 | ||||||||
\(145\) | 0.0473622 | 0.00393322 | ||||||||
\(146\) | 12.2902 | 1.01714 | ||||||||
\(147\) | 0.856054 | 0.0706061 | ||||||||
\(148\) | 20.0949 | 1.65179 | ||||||||
\(149\) | 18.9510 | 1.55253 | 0.776264 | − | 0.630409i | \(-0.217113\pi\) | ||||
0.776264 | + | 0.630409i | \(0.217113\pi\) | |||||||
\(150\) | −10.3878 | −0.848161 | ||||||||
\(151\) | −10.8437 | −0.882445 | −0.441222 | − | 0.897398i | \(-0.645455\pi\) | ||||
−0.441222 | + | 0.897398i | \(0.645455\pi\) | |||||||
\(152\) | −1.01028 | −0.0819449 | ||||||||
\(153\) | −7.90000 | −0.638677 | ||||||||
\(154\) | 14.1494 | 1.14019 | ||||||||
\(155\) | −0.315237 | −0.0253204 | ||||||||
\(156\) | 2.35342 | 0.188425 | ||||||||
\(157\) | 6.43435 | 0.513517 | 0.256759 | − | 0.966476i | \(-0.417345\pi\) | ||||
0.256759 | + | 0.966476i | \(0.417345\pi\) | |||||||
\(158\) | 22.9221 | 1.82358 | ||||||||
\(159\) | 5.59115 | 0.443407 | ||||||||
\(160\) | −1.18235 | −0.0934733 | ||||||||
\(161\) | −5.62844 | −0.443583 | ||||||||
\(162\) | 2.08649 | 0.163930 | ||||||||
\(163\) | −10.8170 | −0.847251 | −0.423626 | − | 0.905837i | \(-0.639243\pi\) | ||||
−0.423626 | + | 0.905837i | \(0.639243\pi\) | |||||||
\(164\) | −3.30744 | −0.258268 | ||||||||
\(165\) | −0.353811 | −0.0275442 | ||||||||
\(166\) | 14.2871 | 1.10889 | ||||||||
\(167\) | 3.13564 | 0.242643 | 0.121322 | − | 0.992613i | \(-0.461287\pi\) | ||||
0.121322 | + | 0.992613i | \(0.461287\pi\) | |||||||
\(168\) | −2.06687 | −0.159463 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.41042 | −0.184871 | ||||||||
\(171\) | −1.37004 | −0.104769 | ||||||||
\(172\) | −8.55136 | −0.652035 | ||||||||
\(173\) | 12.7567 | 0.969872 | 0.484936 | − | 0.874550i | \(-0.338843\pi\) | ||||
0.484936 | + | 0.874550i | \(0.338843\pi\) | |||||||
\(174\) | 0.675767 | 0.0512298 | ||||||||
\(175\) | 13.9544 | 1.05485 | ||||||||
\(176\) | 7.66550 | 0.577808 | ||||||||
\(177\) | −5.92594 | −0.445421 | ||||||||
\(178\) | 3.25229 | 0.243769 | ||||||||
\(179\) | −15.1240 | −1.13042 | −0.565209 | − | 0.824948i | \(-0.691205\pi\) | ||||
−0.565209 | + | 0.824948i | \(0.691205\pi\) | |||||||
\(180\) | 0.344152 | 0.0256516 | ||||||||
\(181\) | −21.6386 | −1.60838 | −0.804192 | − | 0.594369i | \(-0.797402\pi\) | ||||
−0.804192 | + | 0.594369i | \(0.797402\pi\) | |||||||
\(182\) | −5.84814 | −0.433493 | ||||||||
\(183\) | −5.22961 | −0.386584 | ||||||||
\(184\) | 1.48080 | 0.109166 | ||||||||
\(185\) | 1.24863 | 0.0918014 | ||||||||
\(186\) | −4.49782 | −0.329796 | ||||||||
\(187\) | 19.1139 | 1.39775 | ||||||||
\(188\) | 2.56634 | 0.187170 | ||||||||
\(189\) | −2.80287 | −0.203878 | ||||||||
\(190\) | −0.418021 | −0.0303264 | ||||||||
\(191\) | −18.6747 | −1.35126 | −0.675628 | − | 0.737243i | \(-0.736127\pi\) | ||||
−0.675628 | + | 0.737243i | \(0.736127\pi\) | |||||||
\(192\) | −10.5334 | −0.760185 | ||||||||
\(193\) | 6.17826 | 0.444721 | 0.222360 | − | 0.974965i | \(-0.428624\pi\) | ||||
0.222360 | + | 0.974965i | \(0.428624\pi\) | |||||||
\(194\) | 6.37770 | 0.457892 | ||||||||
\(195\) | 0.146235 | 0.0104721 | ||||||||
\(196\) | 2.01466 | 0.143904 | ||||||||
\(197\) | 7.93563 | 0.565390 | 0.282695 | − | 0.959210i | \(-0.408772\pi\) | ||||
0.282695 | + | 0.959210i | \(0.408772\pi\) | |||||||
\(198\) | −5.04821 | −0.358760 | ||||||||
\(199\) | 18.7223 | 1.32719 | 0.663593 | − | 0.748094i | \(-0.269031\pi\) | ||||
0.663593 | + | 0.748094i | \(0.269031\pi\) | |||||||
\(200\) | −3.67130 | −0.259600 | ||||||||
\(201\) | −15.2322 | −1.07440 | ||||||||
\(202\) | 18.7299 | 1.31783 | ||||||||
\(203\) | −0.907787 | −0.0637142 | ||||||||
\(204\) | −18.5921 | −1.30170 | ||||||||
\(205\) | −0.205514 | −0.0143537 | ||||||||
\(206\) | −2.08649 | −0.145372 | ||||||||
\(207\) | 2.00810 | 0.139573 | ||||||||
\(208\) | −3.16824 | −0.219678 | ||||||||
\(209\) | 3.31477 | 0.229288 | ||||||||
\(210\) | −0.855200 | −0.0590144 | ||||||||
\(211\) | 23.7261 | 1.63337 | 0.816685 | − | 0.577084i | \(-0.195809\pi\) | ||||
0.816685 | + | 0.577084i | \(0.195809\pi\) | |||||||
\(212\) | 13.1583 | 0.903719 | ||||||||
\(213\) | −7.85364 | −0.538122 | ||||||||
\(214\) | 22.9084 | 1.56599 | ||||||||
\(215\) | −0.531356 | −0.0362382 | ||||||||
\(216\) | 0.737414 | 0.0501747 | ||||||||
\(217\) | 6.04212 | 0.410166 | ||||||||
\(218\) | −31.0305 | −2.10165 | ||||||||
\(219\) | 5.89036 | 0.398034 | ||||||||
\(220\) | −0.832668 | −0.0561385 | ||||||||
\(221\) | −7.90000 | −0.531412 | ||||||||
\(222\) | 17.8156 | 1.19571 | ||||||||
\(223\) | −4.25945 | −0.285234 | −0.142617 | − | 0.989778i | \(-0.545552\pi\) | ||||
−0.142617 | + | 0.989778i | \(0.545552\pi\) | |||||||
\(224\) | 22.6621 | 1.51417 | ||||||||
\(225\) | −4.97862 | −0.331908 | ||||||||
\(226\) | 6.48764 | 0.431551 | ||||||||
\(227\) | −11.3346 | −0.752304 | −0.376152 | − | 0.926558i | \(-0.622753\pi\) | ||||
−0.376152 | + | 0.926558i | \(0.622753\pi\) | |||||||
\(228\) | −3.22428 | −0.213533 | ||||||||
\(229\) | −2.19287 | −0.144909 | −0.0724545 | − | 0.997372i | \(-0.523083\pi\) | ||||
−0.0724545 | + | 0.997372i | \(0.523083\pi\) | |||||||
\(230\) | 0.612705 | 0.0404006 | ||||||||
\(231\) | 6.78147 | 0.446188 | ||||||||
\(232\) | 0.238832 | 0.0156801 | ||||||||
\(233\) | −17.0845 | −1.11924 | −0.559621 | − | 0.828749i | \(-0.689053\pi\) | ||||
−0.559621 | + | 0.828749i | \(0.689053\pi\) | |||||||
\(234\) | 2.08649 | 0.136398 | ||||||||
\(235\) | 0.159465 | 0.0104023 | ||||||||
\(236\) | −13.9462 | −0.907823 | ||||||||
\(237\) | 10.9860 | 0.713617 | ||||||||
\(238\) | 46.2003 | 2.99472 | ||||||||
\(239\) | −15.7266 | −1.01727 | −0.508634 | − | 0.860983i | \(-0.669849\pi\) | ||||
−0.508634 | + | 0.860983i | \(0.669849\pi\) | |||||||
\(240\) | −0.463307 | −0.0299063 | ||||||||
\(241\) | −28.3568 | −1.82662 | −0.913310 | − | 0.407266i | \(-0.866482\pi\) | ||||
−0.913310 | + | 0.407266i | \(0.866482\pi\) | |||||||
\(242\) | −10.7373 | −0.690221 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −12.3075 | −0.787906 | ||||||||
\(245\) | 0.125185 | 0.00799776 | ||||||||
\(246\) | −2.93229 | −0.186956 | ||||||||
\(247\) | −1.37004 | −0.0871734 | ||||||||
\(248\) | −1.58964 | −0.100942 | ||||||||
\(249\) | 6.84744 | 0.433939 | ||||||||
\(250\) | −3.04464 | −0.192560 | ||||||||
\(251\) | −10.1004 | −0.637534 | −0.318767 | − | 0.947833i | \(-0.603269\pi\) | ||||
−0.318767 | + | 0.947833i | \(0.603269\pi\) | |||||||
\(252\) | −6.59633 | −0.415530 | ||||||||
\(253\) | −4.85856 | −0.305455 | ||||||||
\(254\) | 0.877291 | 0.0550461 | ||||||||
\(255\) | −1.15525 | −0.0723448 | ||||||||
\(256\) | 8.95021 | 0.559388 | ||||||||
\(257\) | −19.2020 | −1.19779 | −0.598895 | − | 0.800827i | \(-0.704394\pi\) | ||||
−0.598895 | + | 0.800827i | \(0.704394\pi\) | |||||||
\(258\) | −7.58142 | −0.471999 | ||||||||
\(259\) | −23.9325 | −1.48709 | ||||||||
\(260\) | 0.344152 | 0.0213434 | ||||||||
\(261\) | 0.323878 | 0.0200476 | ||||||||
\(262\) | −25.8670 | −1.59807 | ||||||||
\(263\) | 1.09765 | 0.0676842 | 0.0338421 | − | 0.999427i | \(-0.489226\pi\) | ||||
0.0338421 | + | 0.999427i | \(0.489226\pi\) | |||||||
\(264\) | −1.78416 | −0.109807 | ||||||||
\(265\) | 0.817619 | 0.0502259 | ||||||||
\(266\) | 8.01217 | 0.491258 | ||||||||
\(267\) | 1.55874 | 0.0953933 | ||||||||
\(268\) | −35.8479 | −2.18976 | ||||||||
\(269\) | −4.22283 | −0.257471 | −0.128735 | − | 0.991679i | \(-0.541092\pi\) | ||||
−0.128735 | + | 0.991679i | \(0.541092\pi\) | |||||||
\(270\) | 0.305116 | 0.0185688 | ||||||||
\(271\) | 11.1291 | 0.676046 | 0.338023 | − | 0.941138i | \(-0.390242\pi\) | ||||
0.338023 | + | 0.941138i | \(0.390242\pi\) | |||||||
\(272\) | 25.0291 | 1.51761 | ||||||||
\(273\) | −2.80287 | −0.169637 | ||||||||
\(274\) | −11.7412 | −0.709310 | ||||||||
\(275\) | 12.0456 | 0.726380 | ||||||||
\(276\) | 4.72592 | 0.284467 | ||||||||
\(277\) | −26.1321 | −1.57012 | −0.785062 | − | 0.619417i | \(-0.787369\pi\) | ||||
−0.785062 | + | 0.619417i | \(0.787369\pi\) | |||||||
\(278\) | 34.8178 | 2.08823 | ||||||||
\(279\) | −2.15569 | −0.129058 | ||||||||
\(280\) | −0.302248 | −0.0180628 | ||||||||
\(281\) | 12.9257 | 0.771081 | 0.385541 | − | 0.922691i | \(-0.374015\pi\) | ||||
0.385541 | + | 0.922691i | \(0.374015\pi\) | |||||||
\(282\) | 2.27525 | 0.135489 | ||||||||
\(283\) | −9.74679 | −0.579387 | −0.289693 | − | 0.957120i | \(-0.593553\pi\) | ||||
−0.289693 | + | 0.957120i | \(0.593553\pi\) | |||||||
\(284\) | −18.4829 | −1.09676 | ||||||||
\(285\) | −0.200347 | −0.0118675 | ||||||||
\(286\) | −5.04821 | −0.298507 | ||||||||
\(287\) | 3.93907 | 0.232516 | ||||||||
\(288\) | −8.08532 | −0.476432 | ||||||||
\(289\) | 45.4101 | 2.67118 | ||||||||
\(290\) | 0.0988206 | 0.00580294 | ||||||||
\(291\) | 3.05667 | 0.179185 | ||||||||
\(292\) | 13.8625 | 0.811243 | ||||||||
\(293\) | 9.92718 | 0.579952 | 0.289976 | − | 0.957034i | \(-0.406353\pi\) | ||||
0.289976 | + | 0.957034i | \(0.406353\pi\) | |||||||
\(294\) | 1.78614 | 0.104170 | ||||||||
\(295\) | −0.866577 | −0.0504540 | ||||||||
\(296\) | 6.29646 | 0.365974 | ||||||||
\(297\) | −2.41948 | −0.140392 | ||||||||
\(298\) | 39.5410 | 2.29055 | ||||||||
\(299\) | 2.00810 | 0.116132 | ||||||||
\(300\) | −11.7168 | −0.676469 | ||||||||
\(301\) | 10.1844 | 0.587022 | ||||||||
\(302\) | −22.6252 | −1.30193 | ||||||||
\(303\) | 8.97677 | 0.515702 | ||||||||
\(304\) | 4.34061 | 0.248951 | ||||||||
\(305\) | −0.764750 | −0.0437895 | ||||||||
\(306\) | −16.4832 | −0.942285 | ||||||||
\(307\) | 15.2886 | 0.872566 | 0.436283 | − | 0.899809i | \(-0.356295\pi\) | ||||
0.436283 | + | 0.899809i | \(0.356295\pi\) | |||||||
\(308\) | 15.9597 | 0.909387 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −0.657737 | −0.0373570 | ||||||||
\(311\) | 7.38549 | 0.418793 | 0.209396 | − | 0.977831i | \(-0.432850\pi\) | ||||
0.209396 | + | 0.977831i | \(0.432850\pi\) | |||||||
\(312\) | 0.737414 | 0.0417478 | ||||||||
\(313\) | 12.9545 | 0.732230 | 0.366115 | − | 0.930570i | \(-0.380688\pi\) | ||||
0.366115 | + | 0.930570i | \(0.380688\pi\) | |||||||
\(314\) | 13.4252 | 0.757627 | ||||||||
\(315\) | −0.409876 | −0.0230939 | ||||||||
\(316\) | 25.8547 | 1.45444 | ||||||||
\(317\) | 26.3027 | 1.47731 | 0.738654 | − | 0.674085i | \(-0.235462\pi\) | ||||
0.738654 | + | 0.674085i | \(0.235462\pi\) | |||||||
\(318\) | 11.6659 | 0.654188 | ||||||||
\(319\) | −0.783616 | −0.0438741 | ||||||||
\(320\) | −1.54035 | −0.0861083 | ||||||||
\(321\) | 10.9794 | 0.612812 | ||||||||
\(322\) | −11.7437 | −0.654449 | ||||||||
\(323\) | 10.8233 | 0.602224 | ||||||||
\(324\) | 2.35342 | 0.130746 | ||||||||
\(325\) | −4.97862 | −0.276164 | ||||||||
\(326\) | −22.5695 | −1.25001 | ||||||||
\(327\) | −14.8721 | −0.822430 | ||||||||
\(328\) | −1.03634 | −0.0572224 | ||||||||
\(329\) | −3.05645 | −0.168507 | ||||||||
\(330\) | −0.738222 | −0.0406378 | ||||||||
\(331\) | −6.14631 | −0.337832 | −0.168916 | − | 0.985630i | \(-0.554027\pi\) | ||||
−0.168916 | + | 0.985630i | \(0.554027\pi\) | |||||||
\(332\) | 16.1149 | 0.884421 | ||||||||
\(333\) | 8.53857 | 0.467911 | ||||||||
\(334\) | 6.54248 | 0.357988 | ||||||||
\(335\) | −2.22748 | −0.121700 | ||||||||
\(336\) | 8.88016 | 0.484453 | ||||||||
\(337\) | 1.99702 | 0.108785 | 0.0543923 | − | 0.998520i | \(-0.482678\pi\) | ||||
0.0543923 | + | 0.998520i | \(0.482678\pi\) | |||||||
\(338\) | 2.08649 | 0.113490 | ||||||||
\(339\) | 3.10936 | 0.168877 | ||||||||
\(340\) | −2.71880 | −0.147448 | ||||||||
\(341\) | 5.21565 | 0.282443 | ||||||||
\(342\) | −2.85856 | −0.154573 | ||||||||
\(343\) | 17.2207 | 0.929828 | ||||||||
\(344\) | −2.67946 | −0.144467 | ||||||||
\(345\) | 0.293654 | 0.0158098 | ||||||||
\(346\) | 26.6166 | 1.43092 | ||||||||
\(347\) | −2.07380 | −0.111327 | −0.0556636 | − | 0.998450i | \(-0.517727\pi\) | ||||
−0.0556636 | + | 0.998450i | \(0.517727\pi\) | |||||||
\(348\) | 0.762223 | 0.0408594 | ||||||||
\(349\) | −16.6784 | −0.892777 | −0.446388 | − | 0.894839i | \(-0.647290\pi\) | ||||
−0.446388 | + | 0.894839i | \(0.647290\pi\) | |||||||
\(350\) | 29.1156 | 1.55630 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 19.5623 | 1.04267 | ||||||||
\(353\) | −27.1474 | −1.44491 | −0.722454 | − | 0.691419i | \(-0.756986\pi\) | ||||
−0.722454 | + | 0.691419i | \(0.756986\pi\) | |||||||
\(354\) | −12.3644 | −0.657159 | ||||||||
\(355\) | −1.14847 | −0.0609546 | ||||||||
\(356\) | 3.66837 | 0.194423 | ||||||||
\(357\) | 22.1426 | 1.17191 | ||||||||
\(358\) | −31.5559 | −1.66778 | ||||||||
\(359\) | 17.0340 | 0.899021 | 0.449511 | − | 0.893275i | \(-0.351598\pi\) | ||||
0.449511 | + | 0.893275i | \(0.351598\pi\) | |||||||
\(360\) | 0.107835 | 0.00568342 | ||||||||
\(361\) | −17.1230 | −0.901210 | ||||||||
\(362\) | −45.1486 | −2.37296 | ||||||||
\(363\) | −5.14613 | −0.270102 | ||||||||
\(364\) | −6.59633 | −0.345742 | ||||||||
\(365\) | 0.861375 | 0.0450864 | ||||||||
\(366\) | −10.9115 | −0.570354 | ||||||||
\(367\) | 32.0657 | 1.67382 | 0.836908 | − | 0.547343i | \(-0.184361\pi\) | ||||
0.836908 | + | 0.547343i | \(0.184361\pi\) | |||||||
\(368\) | −6.36216 | −0.331651 | ||||||||
\(369\) | −1.40537 | −0.0731609 | ||||||||
\(370\) | 2.60526 | 0.135441 | ||||||||
\(371\) | −15.6712 | −0.813610 | ||||||||
\(372\) | −5.07326 | −0.263036 | ||||||||
\(373\) | −14.7862 | −0.765601 | −0.382800 | − | 0.923831i | \(-0.625040\pi\) | ||||
−0.382800 | + | 0.923831i | \(0.625040\pi\) | |||||||
\(374\) | 39.8808 | 2.06219 | ||||||||
\(375\) | −1.45922 | −0.0753537 | ||||||||
\(376\) | 0.804129 | 0.0414698 | ||||||||
\(377\) | 0.323878 | 0.0166806 | ||||||||
\(378\) | −5.84814 | −0.300796 | ||||||||
\(379\) | −30.5037 | −1.56687 | −0.783435 | − | 0.621473i | \(-0.786534\pi\) | ||||
−0.783435 | + | 0.621473i | \(0.786534\pi\) | |||||||
\(380\) | −0.471501 | −0.0241875 | ||||||||
\(381\) | 0.420464 | 0.0215410 | ||||||||
\(382\) | −38.9645 | −1.99360 | ||||||||
\(383\) | 30.7228 | 1.56986 | 0.784932 | − | 0.619582i | \(-0.212698\pi\) | ||||
0.784932 | + | 0.619582i | \(0.212698\pi\) | |||||||
\(384\) | −5.80720 | −0.296347 | ||||||||
\(385\) | 0.991685 | 0.0505410 | ||||||||
\(386\) | 12.8909 | 0.656127 | ||||||||
\(387\) | −3.63358 | −0.184705 | ||||||||
\(388\) | 7.19364 | 0.365202 | ||||||||
\(389\) | 18.9137 | 0.958962 | 0.479481 | − | 0.877552i | \(-0.340825\pi\) | ||||
0.479481 | + | 0.877552i | \(0.340825\pi\) | |||||||
\(390\) | 0.305116 | 0.0154502 | ||||||||
\(391\) | −15.8640 | −0.802278 | ||||||||
\(392\) | 0.631266 | 0.0318837 | ||||||||
\(393\) | −12.3974 | −0.625365 | ||||||||
\(394\) | 16.5576 | 0.834159 | ||||||||
\(395\) | 1.60653 | 0.0808334 | ||||||||
\(396\) | −5.69406 | −0.286137 | ||||||||
\(397\) | −23.7380 | −1.19138 | −0.595688 | − | 0.803216i | \(-0.703120\pi\) | ||||
−0.595688 | + | 0.803216i | \(0.703120\pi\) | |||||||
\(398\) | 39.0637 | 1.95809 | ||||||||
\(399\) | 3.84003 | 0.192242 | ||||||||
\(400\) | 15.7735 | 0.788673 | ||||||||
\(401\) | 37.0937 | 1.85237 | 0.926186 | − | 0.377067i | \(-0.123067\pi\) | ||||
0.926186 | + | 0.377067i | \(0.123067\pi\) | |||||||
\(402\) | −31.7818 | −1.58513 | ||||||||
\(403\) | −2.15569 | −0.107383 | ||||||||
\(404\) | 21.1261 | 1.05106 | ||||||||
\(405\) | 0.146235 | 0.00726645 | ||||||||
\(406\) | −1.89408 | −0.0940019 | ||||||||
\(407\) | −20.6589 | −1.02402 | ||||||||
\(408\) | −5.82557 | −0.288409 | ||||||||
\(409\) | −20.1546 | −0.996582 | −0.498291 | − | 0.867010i | \(-0.666039\pi\) | ||||
−0.498291 | + | 0.867010i | \(0.666039\pi\) | |||||||
\(410\) | −0.428803 | −0.0211771 | ||||||||
\(411\) | −5.62724 | −0.277571 | ||||||||
\(412\) | −2.35342 | −0.115945 | ||||||||
\(413\) | 16.6096 | 0.817305 | ||||||||
\(414\) | 4.18988 | 0.205921 | ||||||||
\(415\) | 1.00133 | 0.0491534 | ||||||||
\(416\) | −8.08532 | −0.396416 | ||||||||
\(417\) | 16.6873 | 0.817181 | ||||||||
\(418\) | 6.91623 | 0.338284 | ||||||||
\(419\) | 5.64622 | 0.275836 | 0.137918 | − | 0.990444i | \(-0.455959\pi\) | ||||
0.137918 | + | 0.990444i | \(0.455959\pi\) | |||||||
\(420\) | −0.964612 | −0.0470682 | ||||||||
\(421\) | 32.4072 | 1.57943 | 0.789714 | − | 0.613475i | \(-0.210229\pi\) | ||||
0.789714 | + | 0.613475i | \(0.210229\pi\) | |||||||
\(422\) | 49.5041 | 2.40982 | ||||||||
\(423\) | 1.09047 | 0.0530206 | ||||||||
\(424\) | 4.12299 | 0.200230 | ||||||||
\(425\) | 39.3311 | 1.90784 | ||||||||
\(426\) | −16.3865 | −0.793929 | ||||||||
\(427\) | 14.6579 | 0.709345 | ||||||||
\(428\) | 25.8392 | 1.24899 | ||||||||
\(429\) | −2.41948 | −0.116813 | ||||||||
\(430\) | −1.10867 | −0.0534646 | ||||||||
\(431\) | −33.5759 | −1.61729 | −0.808647 | − | 0.588294i | \(-0.799800\pi\) | ||||
−0.808647 | + | 0.588294i | \(0.799800\pi\) | |||||||
\(432\) | −3.16824 | −0.152432 | ||||||||
\(433\) | 13.3542 | 0.641762 | 0.320881 | − | 0.947119i | \(-0.396021\pi\) | ||||
0.320881 | + | 0.947119i | \(0.396021\pi\) | |||||||
\(434\) | 12.6068 | 0.605146 | ||||||||
\(435\) | 0.0473622 | 0.00227084 | ||||||||
\(436\) | −35.0004 | −1.67622 | ||||||||
\(437\) | −2.75118 | −0.131607 | ||||||||
\(438\) | 12.2902 | 0.587247 | ||||||||
\(439\) | −8.79526 | −0.419775 | −0.209887 | − | 0.977726i | \(-0.567310\pi\) | ||||
−0.209887 | + | 0.977726i | \(0.567310\pi\) | |||||||
\(440\) | −0.260905 | −0.0124382 | ||||||||
\(441\) | 0.856054 | 0.0407645 | ||||||||
\(442\) | −16.4832 | −0.784028 | ||||||||
\(443\) | −3.23353 | −0.153630 | −0.0768149 | − | 0.997045i | \(-0.524475\pi\) | ||||
−0.0768149 | + | 0.997045i | \(0.524475\pi\) | |||||||
\(444\) | 20.0949 | 0.953660 | ||||||||
\(445\) | 0.227942 | 0.0108055 | ||||||||
\(446\) | −8.88729 | −0.420825 | ||||||||
\(447\) | 18.9510 | 0.896352 | ||||||||
\(448\) | 29.5238 | 1.39487 | ||||||||
\(449\) | 2.81077 | 0.132648 | 0.0663242 | − | 0.997798i | \(-0.478873\pi\) | ||||
0.0663242 | + | 0.997798i | \(0.478873\pi\) | |||||||
\(450\) | −10.3878 | −0.489686 | ||||||||
\(451\) | 3.40027 | 0.160113 | ||||||||
\(452\) | 7.31764 | 0.344193 | ||||||||
\(453\) | −10.8437 | −0.509480 | ||||||||
\(454\) | −23.6495 | −1.10993 | ||||||||
\(455\) | −0.409876 | −0.0192153 | ||||||||
\(456\) | −1.01028 | −0.0473109 | ||||||||
\(457\) | −4.12736 | −0.193070 | −0.0965349 | − | 0.995330i | \(-0.530776\pi\) | ||||
−0.0965349 | + | 0.995330i | \(0.530776\pi\) | |||||||
\(458\) | −4.57539 | −0.213794 | ||||||||
\(459\) | −7.90000 | −0.368741 | ||||||||
\(460\) | 0.691093 | 0.0322224 | ||||||||
\(461\) | −3.09660 | −0.144223 | −0.0721116 | − | 0.997397i | \(-0.522974\pi\) | ||||
−0.0721116 | + | 0.997397i | \(0.522974\pi\) | |||||||
\(462\) | 14.1494 | 0.658292 | ||||||||
\(463\) | 1.63629 | 0.0760447 | 0.0380223 | − | 0.999277i | \(-0.487894\pi\) | ||||
0.0380223 | + | 0.999277i | \(0.487894\pi\) | |||||||
\(464\) | −1.02613 | −0.0476367 | ||||||||
\(465\) | −0.315237 | −0.0146188 | ||||||||
\(466\) | −35.6466 | −1.65129 | ||||||||
\(467\) | −26.3373 | −1.21875 | −0.609373 | − | 0.792884i | \(-0.708579\pi\) | ||||
−0.609373 | + | 0.792884i | \(0.708579\pi\) | |||||||
\(468\) | 2.35342 | 0.108787 | ||||||||
\(469\) | 42.6939 | 1.97142 | ||||||||
\(470\) | 0.332721 | 0.0153473 | ||||||||
\(471\) | 6.43435 | 0.296479 | ||||||||
\(472\) | −4.36987 | −0.201139 | ||||||||
\(473\) | 8.79138 | 0.404228 | ||||||||
\(474\) | 22.9221 | 1.05285 | ||||||||
\(475\) | 6.82089 | 0.312964 | ||||||||
\(476\) | 52.1110 | 2.38851 | ||||||||
\(477\) | 5.59115 | 0.256001 | ||||||||
\(478\) | −32.8133 | −1.50085 | ||||||||
\(479\) | 11.3171 | 0.517090 | 0.258545 | − | 0.965999i | \(-0.416757\pi\) | ||||
0.258545 | + | 0.965999i | \(0.416757\pi\) | |||||||
\(480\) | −1.18235 | −0.0539668 | ||||||||
\(481\) | 8.53857 | 0.389325 | ||||||||
\(482\) | −59.1660 | −2.69494 | ||||||||
\(483\) | −5.62844 | −0.256103 | ||||||||
\(484\) | −12.1110 | −0.550501 | ||||||||
\(485\) | 0.446991 | 0.0202968 | ||||||||
\(486\) | 2.08649 | 0.0946449 | ||||||||
\(487\) | −35.4588 | −1.60679 | −0.803396 | − | 0.595445i | \(-0.796976\pi\) | ||||
−0.803396 | + | 0.595445i | \(0.796976\pi\) | |||||||
\(488\) | −3.85639 | −0.174570 | ||||||||
\(489\) | −10.8170 | −0.489161 | ||||||||
\(490\) | 0.261196 | 0.0117996 | ||||||||
\(491\) | −11.7787 | −0.531564 | −0.265782 | − | 0.964033i | \(-0.585630\pi\) | ||||
−0.265782 | + | 0.964033i | \(0.585630\pi\) | |||||||
\(492\) | −3.30744 | −0.149111 | ||||||||
\(493\) | −2.55864 | −0.115235 | ||||||||
\(494\) | −2.85856 | −0.128613 | ||||||||
\(495\) | −0.353811 | −0.0159026 | ||||||||
\(496\) | 6.82976 | 0.306665 | ||||||||
\(497\) | 22.0127 | 0.987404 | ||||||||
\(498\) | 14.2871 | 0.640219 | ||||||||
\(499\) | −6.67864 | −0.298977 | −0.149489 | − | 0.988763i | \(-0.547763\pi\) | ||||
−0.149489 | + | 0.988763i | \(0.547763\pi\) | |||||||
\(500\) | −3.43416 | −0.153580 | ||||||||
\(501\) | 3.13564 | 0.140090 | ||||||||
\(502\) | −21.0744 | −0.940598 | ||||||||
\(503\) | −38.2115 | −1.70376 | −0.851882 | − | 0.523733i | \(-0.824539\pi\) | ||||
−0.851882 | + | 0.523733i | \(0.824539\pi\) | |||||||
\(504\) | −2.06687 | −0.0920658 | ||||||||
\(505\) | 1.31271 | 0.0584150 | ||||||||
\(506\) | −10.1373 | −0.450659 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0.989529 | 0.0439032 | ||||||||
\(509\) | 14.3663 | 0.636775 | 0.318388 | − | 0.947961i | \(-0.396859\pi\) | ||||
0.318388 | + | 0.947961i | \(0.396859\pi\) | |||||||
\(510\) | −2.41042 | −0.106735 | ||||||||
\(511\) | −16.5099 | −0.730355 | ||||||||
\(512\) | 30.2889 | 1.33859 | ||||||||
\(513\) | −1.37004 | −0.0604886 | ||||||||
\(514\) | −40.0648 | −1.76718 | ||||||||
\(515\) | −0.146235 | −0.00644387 | ||||||||
\(516\) | −8.55136 | −0.376453 | ||||||||
\(517\) | −2.63837 | −0.116035 | ||||||||
\(518\) | −49.9347 | −2.19401 | ||||||||
\(519\) | 12.7567 | 0.559956 | ||||||||
\(520\) | 0.107835 | 0.00472889 | ||||||||
\(521\) | −6.96588 | −0.305181 | −0.152590 | − | 0.988290i | \(-0.548761\pi\) | ||||
−0.152590 | + | 0.988290i | \(0.548761\pi\) | |||||||
\(522\) | 0.675767 | 0.0295775 | ||||||||
\(523\) | 17.9076 | 0.783045 | 0.391522 | − | 0.920169i | \(-0.371949\pi\) | ||||
0.391522 | + | 0.920169i | \(0.371949\pi\) | |||||||
\(524\) | −29.1763 | −1.27457 | ||||||||
\(525\) | 13.9544 | 0.609019 | ||||||||
\(526\) | 2.29024 | 0.0998591 | ||||||||
\(527\) | 17.0300 | 0.741838 | ||||||||
\(528\) | 7.66550 | 0.333598 | ||||||||
\(529\) | −18.9675 | −0.824675 | ||||||||
\(530\) | 1.70595 | 0.0741018 | ||||||||
\(531\) | −5.92594 | −0.257164 | ||||||||
\(532\) | 9.03722 | 0.391813 | ||||||||
\(533\) | −1.40537 | −0.0608735 | ||||||||
\(534\) | 3.25229 | 0.140740 | ||||||||
\(535\) | 1.60557 | 0.0694149 | ||||||||
\(536\) | −11.2325 | −0.485168 | ||||||||
\(537\) | −15.1240 | −0.652647 | ||||||||
\(538\) | −8.81089 | −0.379864 | ||||||||
\(539\) | −2.07120 | −0.0892130 | ||||||||
\(540\) | 0.344152 | 0.0148099 | ||||||||
\(541\) | −14.2551 | −0.612875 | −0.306438 | − | 0.951891i | \(-0.599137\pi\) | ||||
−0.306438 | + | 0.951891i | \(0.599137\pi\) | |||||||
\(542\) | 23.2207 | 0.997416 | ||||||||
\(543\) | −21.6386 | −0.928601 | ||||||||
\(544\) | 63.8741 | 2.73858 | ||||||||
\(545\) | −2.17482 | −0.0931590 | ||||||||
\(546\) | −5.84814 | −0.250277 | ||||||||
\(547\) | −29.1336 | −1.24566 | −0.622831 | − | 0.782357i | \(-0.714017\pi\) | ||||
−0.622831 | + | 0.782357i | \(0.714017\pi\) | |||||||
\(548\) | −13.2433 | −0.565725 | ||||||||
\(549\) | −5.22961 | −0.223194 | ||||||||
\(550\) | 25.1331 | 1.07168 | ||||||||
\(551\) | −0.443725 | −0.0189033 | ||||||||
\(552\) | 1.48080 | 0.0630272 | ||||||||
\(553\) | −30.7922 | −1.30942 | ||||||||
\(554\) | −54.5242 | −2.31651 | ||||||||
\(555\) | 1.24863 | 0.0530016 | ||||||||
\(556\) | 39.2723 | 1.66552 | ||||||||
\(557\) | −30.2608 | −1.28219 | −0.641095 | − | 0.767462i | \(-0.721519\pi\) | ||||
−0.641095 | + | 0.767462i | \(0.721519\pi\) | |||||||
\(558\) | −4.49782 | −0.190408 | ||||||||
\(559\) | −3.63358 | −0.153684 | ||||||||
\(560\) | 1.29859 | 0.0548753 | ||||||||
\(561\) | 19.1139 | 0.806989 | ||||||||
\(562\) | 26.9692 | 1.13763 | ||||||||
\(563\) | −4.15922 | −0.175290 | −0.0876451 | − | 0.996152i | \(-0.527934\pi\) | ||||
−0.0876451 | + | 0.996152i | \(0.527934\pi\) | |||||||
\(564\) | 2.56634 | 0.108063 | ||||||||
\(565\) | 0.454696 | 0.0191292 | ||||||||
\(566\) | −20.3365 | −0.854809 | ||||||||
\(567\) | −2.80287 | −0.117709 | ||||||||
\(568\) | −5.79138 | −0.243001 | ||||||||
\(569\) | 28.3380 | 1.18799 | 0.593995 | − | 0.804469i | \(-0.297550\pi\) | ||||
0.593995 | + | 0.804469i | \(0.297550\pi\) | |||||||
\(570\) | −0.418021 | −0.0175090 | ||||||||
\(571\) | −17.5850 | −0.735907 | −0.367954 | − | 0.929844i | \(-0.619941\pi\) | ||||
−0.367954 | + | 0.929844i | \(0.619941\pi\) | |||||||
\(572\) | −5.69406 | −0.238080 | ||||||||
\(573\) | −18.6747 | −0.780148 | ||||||||
\(574\) | 8.21882 | 0.343047 | ||||||||
\(575\) | −9.99757 | −0.416928 | ||||||||
\(576\) | −10.5334 | −0.438893 | ||||||||
\(577\) | 20.1078 | 0.837098 | 0.418549 | − | 0.908194i | \(-0.362539\pi\) | ||||
0.418549 | + | 0.908194i | \(0.362539\pi\) | |||||||
\(578\) | 94.7475 | 3.94098 | ||||||||
\(579\) | 6.17826 | 0.256760 | ||||||||
\(580\) | 0.111463 | 0.00462826 | ||||||||
\(581\) | −19.1924 | −0.796237 | ||||||||
\(582\) | 6.37770 | 0.264364 | ||||||||
\(583\) | −13.5277 | −0.560258 | ||||||||
\(584\) | 4.34364 | 0.179741 | ||||||||
\(585\) | 0.146235 | 0.00604606 | ||||||||
\(586\) | 20.7129 | 0.855643 | ||||||||
\(587\) | −36.8883 | −1.52254 | −0.761271 | − | 0.648434i | \(-0.775424\pi\) | ||||
−0.761271 | + | 0.648434i | \(0.775424\pi\) | |||||||
\(588\) | 2.01466 | 0.0830831 | ||||||||
\(589\) | 2.95338 | 0.121692 | ||||||||
\(590\) | −1.80810 | −0.0744383 | ||||||||
\(591\) | 7.93563 | 0.326428 | ||||||||
\(592\) | −27.0523 | −1.11184 | ||||||||
\(593\) | −8.10709 | −0.332918 | −0.166459 | − | 0.986048i | \(-0.553233\pi\) | ||||
−0.166459 | + | 0.986048i | \(0.553233\pi\) | |||||||
\(594\) | −5.04821 | −0.207130 | ||||||||
\(595\) | 3.23802 | 0.132746 | ||||||||
\(596\) | 44.5998 | 1.82688 | ||||||||
\(597\) | 18.7223 | 0.766251 | ||||||||
\(598\) | 4.18988 | 0.171337 | ||||||||
\(599\) | −25.2371 | −1.03116 | −0.515581 | − | 0.856841i | \(-0.672424\pi\) | ||||
−0.515581 | + | 0.856841i | \(0.672424\pi\) | |||||||
\(600\) | −3.67130 | −0.149880 | ||||||||
\(601\) | 14.9142 | 0.608363 | 0.304182 | − | 0.952614i | \(-0.401617\pi\) | ||||
0.304182 | + | 0.952614i | \(0.401617\pi\) | |||||||
\(602\) | 21.2497 | 0.866073 | ||||||||
\(603\) | −15.2322 | −0.620304 | ||||||||
\(604\) | −25.5197 | −1.03838 | ||||||||
\(605\) | −0.752542 | −0.0305952 | ||||||||
\(606\) | 18.7299 | 0.760850 | ||||||||
\(607\) | −2.66643 | −0.108227 | −0.0541135 | − | 0.998535i | \(-0.517233\pi\) | ||||
−0.0541135 | + | 0.998535i | \(0.517233\pi\) | |||||||
\(608\) | 11.0772 | 0.449240 | ||||||||
\(609\) | −0.907787 | −0.0367854 | ||||||||
\(610\) | −1.59564 | −0.0646056 | ||||||||
\(611\) | 1.09047 | 0.0441158 | ||||||||
\(612\) | −18.5921 | −0.751539 | ||||||||
\(613\) | 33.3423 | 1.34668 | 0.673341 | − | 0.739332i | \(-0.264859\pi\) | ||||
0.673341 | + | 0.739332i | \(0.264859\pi\) | |||||||
\(614\) | 31.8994 | 1.28736 | ||||||||
\(615\) | −0.205514 | −0.00828714 | ||||||||
\(616\) | 5.00075 | 0.201486 | ||||||||
\(617\) | 9.02258 | 0.363235 | 0.181618 | − | 0.983369i | \(-0.441867\pi\) | ||||
0.181618 | + | 0.983369i | \(0.441867\pi\) | |||||||
\(618\) | −2.08649 | −0.0839308 | ||||||||
\(619\) | −18.6711 | −0.750455 | −0.375228 | − | 0.926933i | \(-0.622435\pi\) | ||||
−0.375228 | + | 0.926933i | \(0.622435\pi\) | |||||||
\(620\) | −0.741886 | −0.0297949 | ||||||||
\(621\) | 2.00810 | 0.0805824 | ||||||||
\(622\) | 15.4097 | 0.617873 | ||||||||
\(623\) | −4.36894 | −0.175038 | ||||||||
\(624\) | −3.16824 | −0.126831 | ||||||||
\(625\) | 24.6797 | 0.987188 | ||||||||
\(626\) | 27.0293 | 1.08031 | ||||||||
\(627\) | 3.31477 | 0.132379 | ||||||||
\(628\) | 15.1428 | 0.604262 | ||||||||
\(629\) | −67.4547 | −2.68960 | ||||||||
\(630\) | −0.855200 | −0.0340720 | ||||||||
\(631\) | −9.70059 | −0.386174 | −0.193087 | − | 0.981182i | \(-0.561850\pi\) | ||||
−0.193087 | + | 0.981182i | \(0.561850\pi\) | |||||||
\(632\) | 8.10122 | 0.322249 | ||||||||
\(633\) | 23.7261 | 0.943027 | ||||||||
\(634\) | 54.8802 | 2.17957 | ||||||||
\(635\) | 0.0614863 | 0.00244001 | ||||||||
\(636\) | 13.1583 | 0.521762 | ||||||||
\(637\) | 0.856054 | 0.0339181 | ||||||||
\(638\) | −1.63500 | −0.0647304 | ||||||||
\(639\) | −7.85364 | −0.310685 | ||||||||
\(640\) | −0.849214 | −0.0335681 | ||||||||
\(641\) | −4.30276 | −0.169949 | −0.0849745 | − | 0.996383i | \(-0.527081\pi\) | ||||
−0.0849745 | + | 0.996383i | \(0.527081\pi\) | |||||||
\(642\) | 22.9084 | 0.904123 | ||||||||
\(643\) | −14.7586 | −0.582022 | −0.291011 | − | 0.956720i | \(-0.593992\pi\) | ||||
−0.291011 | + | 0.956720i | \(0.593992\pi\) | |||||||
\(644\) | −13.2461 | −0.521970 | ||||||||
\(645\) | −0.531356 | −0.0209221 | ||||||||
\(646\) | 22.5827 | 0.888503 | ||||||||
\(647\) | 5.11283 | 0.201006 | 0.100503 | − | 0.994937i | \(-0.467955\pi\) | ||||
0.100503 | + | 0.994937i | \(0.467955\pi\) | |||||||
\(648\) | 0.737414 | 0.0289684 | ||||||||
\(649\) | 14.3377 | 0.562803 | ||||||||
\(650\) | −10.3878 | −0.407443 | ||||||||
\(651\) | 6.04212 | 0.236809 | ||||||||
\(652\) | −25.4569 | −0.996970 | ||||||||
\(653\) | 24.6570 | 0.964903 | 0.482451 | − | 0.875923i | \(-0.339746\pi\) | ||||
0.482451 | + | 0.875923i | \(0.339746\pi\) | |||||||
\(654\) | −31.0305 | −1.21339 | ||||||||
\(655\) | −1.81293 | −0.0708369 | ||||||||
\(656\) | 4.45257 | 0.173844 | ||||||||
\(657\) | 5.89036 | 0.229805 | ||||||||
\(658\) | −6.37723 | −0.248610 | ||||||||
\(659\) | 7.51441 | 0.292720 | 0.146360 | − | 0.989231i | \(-0.453244\pi\) | ||||
0.146360 | + | 0.989231i | \(0.453244\pi\) | |||||||
\(660\) | −0.832668 | −0.0324116 | ||||||||
\(661\) | 30.7298 | 1.19525 | 0.597625 | − | 0.801776i | \(-0.296111\pi\) | ||||
0.597625 | + | 0.801776i | \(0.296111\pi\) | |||||||
\(662\) | −12.8242 | −0.498426 | ||||||||
\(663\) | −7.90000 | −0.306811 | ||||||||
\(664\) | 5.04939 | 0.195954 | ||||||||
\(665\) | 0.561545 | 0.0217758 | ||||||||
\(666\) | 17.8156 | 0.690341 | ||||||||
\(667\) | 0.650381 | 0.0251829 | ||||||||
\(668\) | 7.37950 | 0.285521 | ||||||||
\(669\) | −4.25945 | −0.164680 | ||||||||
\(670\) | −4.64760 | −0.179553 | ||||||||
\(671\) | 12.6529 | 0.488461 | ||||||||
\(672\) | 22.6621 | 0.874209 | ||||||||
\(673\) | 44.7534 | 1.72512 | 0.862559 | − | 0.505956i | \(-0.168860\pi\) | ||||
0.862559 | + | 0.505956i | \(0.168860\pi\) | |||||||
\(674\) | 4.16675 | 0.160497 | ||||||||
\(675\) | −4.97862 | −0.191627 | ||||||||
\(676\) | 2.35342 | 0.0905163 | ||||||||
\(677\) | −7.23229 | −0.277959 | −0.138980 | − | 0.990295i | \(-0.544382\pi\) | ||||
−0.138980 | + | 0.990295i | \(0.544382\pi\) | |||||||
\(678\) | 6.48764 | 0.249156 | ||||||||
\(679\) | −8.56744 | −0.328788 | ||||||||
\(680\) | −0.851900 | −0.0326689 | ||||||||
\(681\) | −11.3346 | −0.434343 | ||||||||
\(682\) | 10.8824 | 0.416708 | ||||||||
\(683\) | −27.9454 | −1.06930 | −0.534651 | − | 0.845073i | \(-0.679557\pi\) | ||||
−0.534651 | + | 0.845073i | \(0.679557\pi\) | |||||||
\(684\) | −3.22428 | −0.123283 | ||||||||
\(685\) | −0.822898 | −0.0314413 | ||||||||
\(686\) | 35.9307 | 1.37184 | ||||||||
\(687\) | −2.19287 | −0.0836632 | ||||||||
\(688\) | 11.5121 | 0.438894 | ||||||||
\(689\) | 5.59115 | 0.213006 | ||||||||
\(690\) | 0.612705 | 0.0233253 | ||||||||
\(691\) | −30.4955 | −1.16010 | −0.580051 | − | 0.814580i | \(-0.696967\pi\) | ||||
−0.580051 | + | 0.814580i | \(0.696967\pi\) | |||||||
\(692\) | 30.0219 | 1.14126 | ||||||||
\(693\) | 6.78147 | 0.257607 | ||||||||
\(694\) | −4.32695 | −0.164249 | ||||||||
\(695\) | 2.44026 | 0.0925644 | ||||||||
\(696\) | 0.238832 | 0.00905291 | ||||||||
\(697\) | 11.1025 | 0.420536 | ||||||||
\(698\) | −34.7993 | −1.31717 | ||||||||
\(699\) | −17.0845 | −0.646195 | ||||||||
\(700\) | 32.8406 | 1.24126 | ||||||||
\(701\) | 43.0145 | 1.62463 | 0.812317 | − | 0.583216i | \(-0.198206\pi\) | ||||
0.812317 | + | 0.583216i | \(0.198206\pi\) | |||||||
\(702\) | 2.08649 | 0.0787493 | ||||||||
\(703\) | −11.6982 | −0.441204 | ||||||||
\(704\) | 25.4854 | 0.960517 | ||||||||
\(705\) | 0.159465 | 0.00600579 | ||||||||
\(706\) | −56.6426 | −2.13177 | ||||||||
\(707\) | −25.1607 | −0.946265 | ||||||||
\(708\) | −13.9462 | −0.524132 | ||||||||
\(709\) | −18.9440 | −0.711456 | −0.355728 | − | 0.934590i | \(-0.615767\pi\) | ||||
−0.355728 | + | 0.934590i | \(0.615767\pi\) | |||||||
\(710\) | −2.39627 | −0.0899305 | ||||||||
\(711\) | 10.9860 | 0.412007 | ||||||||
\(712\) | 1.14944 | 0.0430769 | ||||||||
\(713\) | −4.32885 | −0.162117 | ||||||||
\(714\) | 46.2003 | 1.72900 | ||||||||
\(715\) | −0.353811 | −0.0132318 | ||||||||
\(716\) | −35.5931 | −1.33018 | ||||||||
\(717\) | −15.7266 | −0.587320 | ||||||||
\(718\) | 35.5412 | 1.32639 | ||||||||
\(719\) | −0.439285 | −0.0163826 | −0.00819128 | − | 0.999966i | \(-0.502607\pi\) | ||||
−0.00819128 | + | 0.999966i | \(0.502607\pi\) | |||||||
\(720\) | −0.463307 | −0.0172664 | ||||||||
\(721\) | 2.80287 | 0.104384 | ||||||||
\(722\) | −35.7269 | −1.32962 | ||||||||
\(723\) | −28.3568 | −1.05460 | ||||||||
\(724\) | −50.9248 | −1.89261 | ||||||||
\(725\) | −1.61247 | −0.0598855 | ||||||||
\(726\) | −10.7373 | −0.398500 | ||||||||
\(727\) | 32.6780 | 1.21196 | 0.605980 | − | 0.795480i | \(-0.292781\pi\) | ||||
0.605980 | + | 0.795480i | \(0.292781\pi\) | |||||||
\(728\) | −2.06687 | −0.0766034 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.79725 | 0.0665191 | ||||||||
\(731\) | 28.7053 | 1.06171 | ||||||||
\(732\) | −12.3075 | −0.454898 | ||||||||
\(733\) | −40.6150 | −1.50015 | −0.750075 | − | 0.661353i | \(-0.769983\pi\) | ||||
−0.750075 | + | 0.661353i | \(0.769983\pi\) | |||||||
\(734\) | 66.9047 | 2.46950 | ||||||||
\(735\) | 0.125185 | 0.00461751 | ||||||||
\(736\) | −16.2362 | −0.598473 | ||||||||
\(737\) | 36.8540 | 1.35754 | ||||||||
\(738\) | −2.93229 | −0.107939 | ||||||||
\(739\) | −27.7466 | −1.02067 | −0.510337 | − | 0.859974i | \(-0.670479\pi\) | ||||
−0.510337 | + | 0.859974i | \(0.670479\pi\) | |||||||
\(740\) | 2.93857 | 0.108024 | ||||||||
\(741\) | −1.37004 | −0.0503296 | ||||||||
\(742\) | −32.6978 | −1.20037 | ||||||||
\(743\) | −2.39602 | −0.0879016 | −0.0439508 | − | 0.999034i | \(-0.513994\pi\) | ||||
−0.0439508 | + | 0.999034i | \(0.513994\pi\) | |||||||
\(744\) | −1.58964 | −0.0582790 | ||||||||
\(745\) | 2.77129 | 0.101532 | ||||||||
\(746\) | −30.8512 | −1.12954 | ||||||||
\(747\) | 6.84744 | 0.250535 | ||||||||
\(748\) | 44.9831 | 1.64474 | ||||||||
\(749\) | −30.7739 | −1.12445 | ||||||||
\(750\) | −3.04464 | −0.111175 | ||||||||
\(751\) | 27.5007 | 1.00351 | 0.501757 | − | 0.865009i | \(-0.332687\pi\) | ||||
0.501757 | + | 0.865009i | \(0.332687\pi\) | |||||||
\(752\) | −3.45488 | −0.125987 | ||||||||
\(753\) | −10.1004 | −0.368081 | ||||||||
\(754\) | 0.675767 | 0.0246100 | ||||||||
\(755\) | −1.58572 | −0.0577102 | ||||||||
\(756\) | −6.59633 | −0.239906 | ||||||||
\(757\) | −35.7589 | −1.29968 | −0.649839 | − | 0.760072i | \(-0.725164\pi\) | ||||
−0.649839 | + | 0.760072i | \(0.725164\pi\) | |||||||
\(758\) | −63.6456 | −2.31171 | ||||||||
\(759\) | −4.85856 | −0.176355 | ||||||||
\(760\) | −0.147738 | −0.00535904 | ||||||||
\(761\) | 19.3590 | 0.701762 | 0.350881 | − | 0.936420i | \(-0.385882\pi\) | ||||
0.350881 | + | 0.936420i | \(0.385882\pi\) | |||||||
\(762\) | 0.877291 | 0.0317809 | ||||||||
\(763\) | 41.6845 | 1.50908 | ||||||||
\(764\) | −43.9495 | −1.59004 | ||||||||
\(765\) | −1.15525 | −0.0417683 | ||||||||
\(766\) | 64.1028 | 2.31613 | ||||||||
\(767\) | −5.92594 | −0.213973 | ||||||||
\(768\) | 8.95021 | 0.322963 | ||||||||
\(769\) | −44.5091 | −1.60504 | −0.802520 | − | 0.596625i | \(-0.796508\pi\) | ||||
−0.802520 | + | 0.596625i | \(0.796508\pi\) | |||||||
\(770\) | 2.06914 | 0.0745665 | ||||||||
\(771\) | −19.2020 | −0.691545 | ||||||||
\(772\) | 14.5401 | 0.523308 | ||||||||
\(773\) | 8.15875 | 0.293450 | 0.146725 | − | 0.989177i | \(-0.453127\pi\) | ||||
0.146725 | + | 0.989177i | \(0.453127\pi\) | |||||||
\(774\) | −7.58142 | −0.272509 | ||||||||
\(775\) | 10.7324 | 0.385518 | ||||||||
\(776\) | 2.25403 | 0.0809150 | ||||||||
\(777\) | −23.9325 | −0.858572 | ||||||||
\(778\) | 39.4631 | 1.41482 | ||||||||
\(779\) | 1.92541 | 0.0689851 | ||||||||
\(780\) | 0.344152 | 0.0123226 | ||||||||
\(781\) | 19.0017 | 0.679934 | ||||||||
\(782\) | −33.1001 | −1.18366 | ||||||||
\(783\) | 0.323878 | 0.0115745 | ||||||||
\(784\) | −2.71219 | −0.0968638 | ||||||||
\(785\) | 0.940924 | 0.0335830 | ||||||||
\(786\) | −25.8670 | −0.922644 | ||||||||
\(787\) | −9.93833 | −0.354263 | −0.177132 | − | 0.984187i | \(-0.556682\pi\) | ||||
−0.177132 | + | 0.984187i | \(0.556682\pi\) | |||||||
\(788\) | 18.6759 | 0.665301 | ||||||||
\(789\) | 1.09765 | 0.0390775 | ||||||||
\(790\) | 3.35200 | 0.119259 | ||||||||
\(791\) | −8.71512 | −0.309874 | ||||||||
\(792\) | −1.78416 | −0.0633972 | ||||||||
\(793\) | −5.22961 | −0.185709 | ||||||||
\(794\) | −49.5290 | −1.75772 | ||||||||
\(795\) | 0.817619 | 0.0289980 | ||||||||
\(796\) | 44.0614 | 1.56172 | ||||||||
\(797\) | 1.76945 | 0.0626772 | 0.0313386 | − | 0.999509i | \(-0.490023\pi\) | ||||
0.0313386 | + | 0.999509i | \(0.490023\pi\) | |||||||
\(798\) | 8.01217 | 0.283628 | ||||||||
\(799\) | −8.61473 | −0.304767 | ||||||||
\(800\) | 40.2537 | 1.42318 | ||||||||
\(801\) | 1.55874 | 0.0550754 | ||||||||
\(802\) | 77.3955 | 2.73293 | ||||||||
\(803\) | −14.2516 | −0.502928 | ||||||||
\(804\) | −35.8479 | −1.26426 | ||||||||
\(805\) | −0.823073 | −0.0290095 | ||||||||
\(806\) | −4.49782 | −0.158429 | ||||||||
\(807\) | −4.22283 | −0.148651 | ||||||||
\(808\) | 6.61959 | 0.232876 | ||||||||
\(809\) | 25.9916 | 0.913817 | 0.456908 | − | 0.889514i | \(-0.348957\pi\) | ||||
0.456908 | + | 0.889514i | \(0.348957\pi\) | |||||||
\(810\) | 0.305116 | 0.0107207 | ||||||||
\(811\) | −19.4633 | −0.683449 | −0.341724 | − | 0.939800i | \(-0.611011\pi\) | ||||
−0.341724 | + | 0.939800i | \(0.611011\pi\) | |||||||
\(812\) | −2.13641 | −0.0749732 | ||||||||
\(813\) | 11.1291 | 0.390315 | ||||||||
\(814\) | −43.1045 | −1.51081 | ||||||||
\(815\) | −1.58182 | −0.0554086 | ||||||||
\(816\) | 25.0291 | 0.876195 | ||||||||
\(817\) | 4.97815 | 0.174163 | ||||||||
\(818\) | −42.0523 | −1.47033 | ||||||||
\(819\) | −2.80287 | −0.0979400 | ||||||||
\(820\) | −0.483662 | −0.0168902 | ||||||||
\(821\) | 6.41589 | 0.223916 | 0.111958 | − | 0.993713i | \(-0.464288\pi\) | ||||
0.111958 | + | 0.993713i | \(0.464288\pi\) | |||||||
\(822\) | −11.7412 | −0.409520 | ||||||||
\(823\) | 28.1445 | 0.981057 | 0.490529 | − | 0.871425i | \(-0.336804\pi\) | ||||
0.490529 | + | 0.871425i | \(0.336804\pi\) | |||||||
\(824\) | −0.737414 | −0.0256890 | ||||||||
\(825\) | 12.0456 | 0.419376 | ||||||||
\(826\) | 34.6557 | 1.20583 | ||||||||
\(827\) | 34.5645 | 1.20192 | 0.600962 | − | 0.799277i | \(-0.294784\pi\) | ||||
0.600962 | + | 0.799277i | \(0.294784\pi\) | |||||||
\(828\) | 4.72592 | 0.164237 | ||||||||
\(829\) | 33.4554 | 1.16195 | 0.580977 | − | 0.813920i | \(-0.302671\pi\) | ||||
0.580977 | + | 0.813920i | \(0.302671\pi\) | |||||||
\(830\) | 2.08926 | 0.0725194 | ||||||||
\(831\) | −26.1321 | −0.906512 | ||||||||
\(832\) | −10.5334 | −0.365181 | ||||||||
\(833\) | −6.76283 | −0.234318 | ||||||||
\(834\) | 34.8178 | 1.20564 | ||||||||
\(835\) | 0.458540 | 0.0158684 | ||||||||
\(836\) | 7.80107 | 0.269806 | ||||||||
\(837\) | −2.15569 | −0.0745117 | ||||||||
\(838\) | 11.7808 | 0.406960 | ||||||||
\(839\) | 12.5178 | 0.432164 | 0.216082 | − | 0.976375i | \(-0.430672\pi\) | ||||
0.216082 | + | 0.976375i | \(0.430672\pi\) | |||||||
\(840\) | −0.302248 | −0.0104285 | ||||||||
\(841\) | −28.8951 | −0.996383 | ||||||||
\(842\) | 67.6171 | 2.33024 | ||||||||
\(843\) | 12.9257 | 0.445184 | ||||||||
\(844\) | 55.8375 | 1.92201 | ||||||||
\(845\) | 0.146235 | 0.00503062 | ||||||||
\(846\) | 2.27525 | 0.0782249 | ||||||||
\(847\) | 14.4239 | 0.495611 | ||||||||
\(848\) | −17.7141 | −0.608305 | ||||||||
\(849\) | −9.74679 | −0.334509 | ||||||||
\(850\) | 82.0638 | 2.81476 | ||||||||
\(851\) | 17.1463 | 0.587769 | ||||||||
\(852\) | −18.4829 | −0.633215 | ||||||||
\(853\) | −20.3982 | −0.698421 | −0.349210 | − | 0.937044i | \(-0.613550\pi\) | ||||
−0.349210 | + | 0.937044i | \(0.613550\pi\) | |||||||
\(854\) | 30.5835 | 1.04655 | ||||||||
\(855\) | −0.200347 | −0.00685172 | ||||||||
\(856\) | 8.09638 | 0.276729 | ||||||||
\(857\) | 9.18933 | 0.313901 | 0.156951 | − | 0.987606i | \(-0.449834\pi\) | ||||
0.156951 | + | 0.987606i | \(0.449834\pi\) | |||||||
\(858\) | −5.04821 | −0.172343 | ||||||||
\(859\) | −4.60595 | −0.157153 | −0.0785764 | − | 0.996908i | \(-0.525037\pi\) | ||||
−0.0785764 | + | 0.996908i | \(0.525037\pi\) | |||||||
\(860\) | −1.25051 | −0.0426419 | ||||||||
\(861\) | 3.93907 | 0.134243 | ||||||||
\(862\) | −70.0556 | −2.38610 | ||||||||
\(863\) | −9.37107 | −0.318995 | −0.159498 | − | 0.987198i | \(-0.550987\pi\) | ||||
−0.159498 | + | 0.987198i | \(0.550987\pi\) | |||||||
\(864\) | −8.08532 | −0.275068 | ||||||||
\(865\) | 1.86547 | 0.0634278 | ||||||||
\(866\) | 27.8634 | 0.946836 | ||||||||
\(867\) | 45.4101 | 1.54221 | ||||||||
\(868\) | 14.2197 | 0.482647 | ||||||||
\(869\) | −26.5803 | −0.901677 | ||||||||
\(870\) | 0.0988206 | 0.00335033 | ||||||||
\(871\) | −15.2322 | −0.516124 | ||||||||
\(872\) | −10.9669 | −0.371386 | ||||||||
\(873\) | 3.05667 | 0.103453 | ||||||||
\(874\) | −5.74029 | −0.194168 | ||||||||
\(875\) | 4.08999 | 0.138267 | ||||||||
\(876\) | 13.8625 | 0.468371 | ||||||||
\(877\) | −32.6386 | −1.10213 | −0.551063 | − | 0.834463i | \(-0.685778\pi\) | ||||
−0.551063 | + | 0.834463i | \(0.685778\pi\) | |||||||
\(878\) | −18.3512 | −0.619322 | ||||||||
\(879\) | 9.92718 | 0.334836 | ||||||||
\(880\) | 1.12096 | 0.0377876 | ||||||||
\(881\) | 22.9829 | 0.774312 | 0.387156 | − | 0.922014i | \(-0.373457\pi\) | ||||
0.387156 | + | 0.922014i | \(0.373457\pi\) | |||||||
\(882\) | 1.78614 | 0.0601426 | ||||||||
\(883\) | −20.0153 | −0.673569 | −0.336784 | − | 0.941582i | \(-0.609339\pi\) | ||||
−0.336784 | + | 0.941582i | \(0.609339\pi\) | |||||||
\(884\) | −18.5921 | −0.625319 | ||||||||
\(885\) | −0.866577 | −0.0291297 | ||||||||
\(886\) | −6.74672 | −0.226661 | ||||||||
\(887\) | 8.18702 | 0.274893 | 0.137447 | − | 0.990509i | \(-0.456110\pi\) | ||||
0.137447 | + | 0.990509i | \(0.456110\pi\) | |||||||
\(888\) | 6.29646 | 0.211295 | ||||||||
\(889\) | −1.17850 | −0.0395257 | ||||||||
\(890\) | 0.475597 | 0.0159420 | ||||||||
\(891\) | −2.41948 | −0.0810555 | ||||||||
\(892\) | −10.0243 | −0.335638 | ||||||||
\(893\) | −1.49399 | −0.0499944 | ||||||||
\(894\) | 39.5410 | 1.32245 | ||||||||
\(895\) | −2.21165 | −0.0739272 | ||||||||
\(896\) | 16.2768 | 0.543770 | ||||||||
\(897\) | 2.00810 | 0.0670486 | ||||||||
\(898\) | 5.86463 | 0.195705 | ||||||||
\(899\) | −0.698182 | −0.0232857 | ||||||||
\(900\) | −11.7168 | −0.390560 | ||||||||
\(901\) | −44.1701 | −1.47152 | ||||||||
\(902\) | 7.09462 | 0.236225 | ||||||||
\(903\) | 10.1844 | 0.338917 | ||||||||
\(904\) | 2.29289 | 0.0762602 | ||||||||
\(905\) | −3.16431 | −0.105185 | ||||||||
\(906\) | −22.6252 | −0.751670 | ||||||||
\(907\) | 46.0972 | 1.53063 | 0.765316 | − | 0.643655i | \(-0.222583\pi\) | ||||
0.765316 | + | 0.643655i | \(0.222583\pi\) | |||||||
\(908\) | −26.6751 | −0.885245 | ||||||||
\(909\) | 8.97677 | 0.297741 | ||||||||
\(910\) | −0.855200 | −0.0283496 | ||||||||
\(911\) | 48.7577 | 1.61542 | 0.807708 | − | 0.589583i | \(-0.200708\pi\) | ||||
0.807708 | + | 0.589583i | \(0.200708\pi\) | |||||||
\(912\) | 4.34061 | 0.143732 | ||||||||
\(913\) | −16.5672 | −0.548295 | ||||||||
\(914\) | −8.61168 | −0.284849 | ||||||||
\(915\) | −0.764750 | −0.0252819 | ||||||||
\(916\) | −5.16075 | −0.170516 | ||||||||
\(917\) | 34.7482 | 1.14749 | ||||||||
\(918\) | −16.4832 | −0.544028 | ||||||||
\(919\) | 21.7702 | 0.718134 | 0.359067 | − | 0.933312i | \(-0.383095\pi\) | ||||
0.359067 | + | 0.933312i | \(0.383095\pi\) | |||||||
\(920\) | 0.216545 | 0.00713926 | ||||||||
\(921\) | 15.2886 | 0.503776 | ||||||||
\(922\) | −6.46102 | −0.212782 | ||||||||
\(923\) | −7.85364 | −0.258506 | ||||||||
\(924\) | 15.9597 | 0.525035 | ||||||||
\(925\) | −42.5103 | −1.39773 | ||||||||
\(926\) | 3.41409 | 0.112194 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −2.61866 | −0.0859617 | ||||||||
\(929\) | 39.7530 | 1.30425 | 0.652127 | − | 0.758110i | \(-0.273877\pi\) | ||||
0.652127 | + | 0.758110i | \(0.273877\pi\) | |||||||
\(930\) | −0.657737 | −0.0215681 | ||||||||
\(931\) | −1.17283 | −0.0384378 | ||||||||
\(932\) | −40.2071 | −1.31703 | ||||||||
\(933\) | 7.38549 | 0.241790 | ||||||||
\(934\) | −54.9525 | −1.79810 | ||||||||
\(935\) | 2.79511 | 0.0914099 | ||||||||
\(936\) | 0.737414 | 0.0241031 | ||||||||
\(937\) | −51.5931 | −1.68547 | −0.842737 | − | 0.538326i | \(-0.819057\pi\) | ||||
−0.842737 | + | 0.538326i | \(0.819057\pi\) | |||||||
\(938\) | 89.0802 | 2.90857 | ||||||||
\(939\) | 12.9545 | 0.422753 | ||||||||
\(940\) | 0.375288 | 0.0122405 | ||||||||
\(941\) | −44.0246 | −1.43516 | −0.717580 | − | 0.696476i | \(-0.754750\pi\) | ||||
−0.717580 | + | 0.696476i | \(0.754750\pi\) | |||||||
\(942\) | 13.4252 | 0.437416 | ||||||||
\(943\) | −2.82214 | −0.0919014 | ||||||||
\(944\) | 18.7748 | 0.611068 | ||||||||
\(945\) | −0.409876 | −0.0133333 | ||||||||
\(946\) | 18.3431 | 0.596385 | ||||||||
\(947\) | −36.6363 | −1.19052 | −0.595260 | − | 0.803533i | \(-0.702951\pi\) | ||||
−0.595260 | + | 0.803533i | \(0.702951\pi\) | |||||||
\(948\) | 25.8547 | 0.839721 | ||||||||
\(949\) | 5.89036 | 0.191209 | ||||||||
\(950\) | 14.2317 | 0.461737 | ||||||||
\(951\) | 26.3027 | 0.852924 | ||||||||
\(952\) | 16.3283 | 0.529203 | ||||||||
\(953\) | −16.2708 | −0.527061 | −0.263531 | − | 0.964651i | \(-0.584887\pi\) | ||||
−0.263531 | + | 0.964651i | \(0.584887\pi\) | |||||||
\(954\) | 11.6659 | 0.377696 | ||||||||
\(955\) | −2.73089 | −0.0883695 | ||||||||
\(956\) | −37.0113 | −1.19703 | ||||||||
\(957\) | −0.783616 | −0.0253307 | ||||||||
\(958\) | 23.6129 | 0.762898 | ||||||||
\(959\) | 15.7724 | 0.509318 | ||||||||
\(960\) | −1.54035 | −0.0497146 | ||||||||
\(961\) | −26.3530 | −0.850096 | ||||||||
\(962\) | 17.8156 | 0.574398 | ||||||||
\(963\) | 10.9794 | 0.353807 | ||||||||
\(964\) | −66.7355 | −2.14940 | ||||||||
\(965\) | 0.903475 | 0.0290839 | ||||||||
\(966\) | −11.7437 | −0.377846 | ||||||||
\(967\) | 16.2190 | 0.521568 | 0.260784 | − | 0.965397i | \(-0.416019\pi\) | ||||
0.260784 | + | 0.965397i | \(0.416019\pi\) | |||||||
\(968\) | −3.79483 | −0.121970 | ||||||||
\(969\) | 10.8233 | 0.347694 | ||||||||
\(970\) | 0.932640 | 0.0299453 | ||||||||
\(971\) | −10.3109 | −0.330892 | −0.165446 | − | 0.986219i | \(-0.552906\pi\) | ||||
−0.165446 | + | 0.986219i | \(0.552906\pi\) | |||||||
\(972\) | 2.35342 | 0.0754861 | ||||||||
\(973\) | −46.7723 | −1.49945 | ||||||||
\(974\) | −73.9843 | −2.37061 | ||||||||
\(975\) | −4.97862 | −0.159443 | ||||||||
\(976\) | 16.5687 | 0.530351 | ||||||||
\(977\) | −11.0022 | −0.351993 | −0.175997 | − | 0.984391i | \(-0.556315\pi\) | ||||
−0.175997 | + | 0.984391i | \(0.556315\pi\) | |||||||
\(978\) | −22.5695 | −0.721692 | ||||||||
\(979\) | −3.77134 | −0.120532 | ||||||||
\(980\) | 0.294613 | 0.00941105 | ||||||||
\(981\) | −14.8721 | −0.474830 | ||||||||
\(982\) | −24.5760 | −0.784253 | ||||||||
\(983\) | −30.2120 | −0.963612 | −0.481806 | − | 0.876278i | \(-0.660019\pi\) | ||||
−0.481806 | + | 0.876278i | \(0.660019\pi\) | |||||||
\(984\) | −1.03634 | −0.0330374 | ||||||||
\(985\) | 1.16046 | 0.0369754 | ||||||||
\(986\) | −5.33857 | −0.170015 | ||||||||
\(987\) | −3.05645 | −0.0972877 | ||||||||
\(988\) | −3.22428 | −0.102578 | ||||||||
\(989\) | −7.29661 | −0.232019 | ||||||||
\(990\) | −0.738222 | −0.0234622 | ||||||||
\(991\) | −5.35669 | −0.170161 | −0.0850805 | − | 0.996374i | \(-0.527115\pi\) | ||||
−0.0850805 | + | 0.996374i | \(0.527115\pi\) | |||||||
\(992\) | 17.4295 | 0.553387 | ||||||||
\(993\) | −6.14631 | −0.195047 | ||||||||
\(994\) | 45.9292 | 1.45678 | ||||||||
\(995\) | 2.73784 | 0.0867955 | ||||||||
\(996\) | 16.1149 | 0.510621 | ||||||||
\(997\) | 21.8763 | 0.692828 | 0.346414 | − | 0.938082i | \(-0.387399\pi\) | ||||
0.346414 | + | 0.938082i | \(0.387399\pi\) | |||||||
\(998\) | −13.9349 | −0.441101 | ||||||||
\(999\) | 8.53857 | 0.270148 |
(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 | 4017.2.a.f.1.18 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.f.1.18 | ✓ | 19 | 1.1 | even | 1 | trivial |