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: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.08104 | −1.47152 | −0.735759 | − | 0.677243i | \(-0.763175\pi\) | ||||
−0.735759 | + | 0.677243i | \(0.763175\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.33074 | 1.16537 | ||||||||
\(5\) | 1.74075 | 0.778487 | 0.389244 | − | 0.921135i | \(-0.372736\pi\) | ||||
0.389244 | + | 0.921135i | \(0.372736\pi\) | |||||||
\(6\) | 2.08104 | 0.849582 | ||||||||
\(7\) | −0.124046 | −0.0468849 | −0.0234424 | − | 0.999725i | \(-0.507463\pi\) | ||||
−0.0234424 | + | 0.999725i | \(0.507463\pi\) | |||||||
\(8\) | −0.688276 | −0.243342 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.62257 | −1.14556 | ||||||||
\(11\) | −0.521753 | −0.157314 | −0.0786572 | − | 0.996902i | \(-0.525063\pi\) | ||||
−0.0786572 | + | 0.996902i | \(0.525063\pi\) | |||||||
\(12\) | −2.33074 | −0.672826 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0.258144 | 0.0689920 | ||||||||
\(15\) | −1.74075 | −0.449460 | ||||||||
\(16\) | −3.22914 | −0.807285 | ||||||||
\(17\) | 3.38824 | 0.821769 | 0.410885 | − | 0.911687i | \(-0.365220\pi\) | ||||
0.410885 | + | 0.911687i | \(0.365220\pi\) | |||||||
\(18\) | −2.08104 | −0.490506 | ||||||||
\(19\) | −2.62024 | −0.601125 | −0.300563 | − | 0.953762i | \(-0.597174\pi\) | ||||
−0.300563 | + | 0.953762i | \(0.597174\pi\) | |||||||
\(20\) | 4.05723 | 0.907224 | ||||||||
\(21\) | 0.124046 | 0.0270690 | ||||||||
\(22\) | 1.08579 | 0.231491 | ||||||||
\(23\) | 1.07192 | 0.223510 | 0.111755 | − | 0.993736i | \(-0.464353\pi\) | ||||
0.111755 | + | 0.993736i | \(0.464353\pi\) | |||||||
\(24\) | 0.688276 | 0.140494 | ||||||||
\(25\) | −1.96979 | −0.393958 | ||||||||
\(26\) | 2.08104 | 0.408126 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.289118 | −0.0546381 | ||||||||
\(29\) | 1.51771 | 0.281831 | 0.140916 | − | 0.990022i | \(-0.454995\pi\) | ||||
0.140916 | + | 0.990022i | \(0.454995\pi\) | |||||||
\(30\) | 3.62257 | 0.661389 | ||||||||
\(31\) | 4.90595 | 0.881135 | 0.440567 | − | 0.897720i | \(-0.354777\pi\) | ||||
0.440567 | + | 0.897720i | \(0.354777\pi\) | |||||||
\(32\) | 8.09653 | 1.43128 | ||||||||
\(33\) | 0.521753 | 0.0908255 | ||||||||
\(34\) | −7.05107 | −1.20925 | ||||||||
\(35\) | −0.215933 | −0.0364993 | ||||||||
\(36\) | 2.33074 | 0.388456 | ||||||||
\(37\) | 5.89933 | 0.969843 | 0.484922 | − | 0.874558i | \(-0.338848\pi\) | ||||
0.484922 | + | 0.874558i | \(0.338848\pi\) | |||||||
\(38\) | 5.45284 | 0.884567 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.19812 | −0.189439 | ||||||||
\(41\) | −10.0270 | −1.56595 | −0.782977 | − | 0.622050i | \(-0.786300\pi\) | ||||
−0.782977 | + | 0.622050i | \(0.786300\pi\) | |||||||
\(42\) | −0.258144 | −0.0398325 | ||||||||
\(43\) | 0.753761 | 0.114948 | 0.0574738 | − | 0.998347i | \(-0.481695\pi\) | ||||
0.0574738 | + | 0.998347i | \(0.481695\pi\) | |||||||
\(44\) | −1.21607 | −0.183329 | ||||||||
\(45\) | 1.74075 | 0.259496 | ||||||||
\(46\) | −2.23070 | −0.328899 | ||||||||
\(47\) | −3.90948 | −0.570256 | −0.285128 | − | 0.958489i | \(-0.592036\pi\) | ||||
−0.285128 | + | 0.958489i | \(0.592036\pi\) | |||||||
\(48\) | 3.22914 | 0.466086 | ||||||||
\(49\) | −6.98461 | −0.997802 | ||||||||
\(50\) | 4.09921 | 0.579716 | ||||||||
\(51\) | −3.38824 | −0.474449 | ||||||||
\(52\) | −2.33074 | −0.323215 | ||||||||
\(53\) | −13.3889 | −1.83910 | −0.919552 | − | 0.392967i | \(-0.871449\pi\) | ||||
−0.919552 | + | 0.392967i | \(0.871449\pi\) | |||||||
\(54\) | 2.08104 | 0.283194 | ||||||||
\(55\) | −0.908242 | −0.122467 | ||||||||
\(56\) | 0.0853777 | 0.0114091 | ||||||||
\(57\) | 2.62024 | 0.347060 | ||||||||
\(58\) | −3.15841 | −0.414720 | ||||||||
\(59\) | −3.35885 | −0.437285 | −0.218643 | − | 0.975805i | \(-0.570163\pi\) | ||||
−0.218643 | + | 0.975805i | \(0.570163\pi\) | |||||||
\(60\) | −4.05723 | −0.523786 | ||||||||
\(61\) | 2.34011 | 0.299620 | 0.149810 | − | 0.988715i | \(-0.452134\pi\) | ||||
0.149810 | + | 0.988715i | \(0.452134\pi\) | |||||||
\(62\) | −10.2095 | −1.29661 | ||||||||
\(63\) | −0.124046 | −0.0156283 | ||||||||
\(64\) | −10.3909 | −1.29887 | ||||||||
\(65\) | −1.74075 | −0.215913 | ||||||||
\(66\) | −1.08579 | −0.133651 | ||||||||
\(67\) | 6.79145 | 0.829707 | 0.414854 | − | 0.909888i | \(-0.363833\pi\) | ||||
0.414854 | + | 0.909888i | \(0.363833\pi\) | |||||||
\(68\) | 7.89710 | 0.957664 | ||||||||
\(69\) | −1.07192 | −0.129044 | ||||||||
\(70\) | 0.449365 | 0.0537094 | ||||||||
\(71\) | −8.69610 | −1.03204 | −0.516019 | − | 0.856577i | \(-0.672587\pi\) | ||||
−0.516019 | + | 0.856577i | \(0.672587\pi\) | |||||||
\(72\) | −0.688276 | −0.0811141 | ||||||||
\(73\) | −10.5845 | −1.23882 | −0.619409 | − | 0.785068i | \(-0.712628\pi\) | ||||
−0.619409 | + | 0.785068i | \(0.712628\pi\) | |||||||
\(74\) | −12.2767 | −1.42714 | ||||||||
\(75\) | 1.96979 | 0.227452 | ||||||||
\(76\) | −6.10710 | −0.700532 | ||||||||
\(77\) | 0.0647212 | 0.00737567 | ||||||||
\(78\) | −2.08104 | −0.235632 | ||||||||
\(79\) | 11.4711 | 1.29060 | 0.645301 | − | 0.763929i | \(-0.276732\pi\) | ||||
0.645301 | + | 0.763929i | \(0.276732\pi\) | |||||||
\(80\) | −5.62113 | −0.628461 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.8666 | 2.30433 | ||||||||
\(83\) | −15.8964 | −1.74485 | −0.872426 | − | 0.488746i | \(-0.837455\pi\) | ||||
−0.872426 | + | 0.488746i | \(0.837455\pi\) | |||||||
\(84\) | 0.289118 | 0.0315453 | ||||||||
\(85\) | 5.89808 | 0.639737 | ||||||||
\(86\) | −1.56861 | −0.169147 | ||||||||
\(87\) | −1.51771 | −0.162715 | ||||||||
\(88\) | 0.359110 | 0.0382813 | ||||||||
\(89\) | 6.43563 | 0.682176 | 0.341088 | − | 0.940031i | \(-0.389205\pi\) | ||||
0.341088 | + | 0.940031i | \(0.389205\pi\) | |||||||
\(90\) | −3.62257 | −0.381853 | ||||||||
\(91\) | 0.124046 | 0.0130035 | ||||||||
\(92\) | 2.49836 | 0.260472 | ||||||||
\(93\) | −4.90595 | −0.508723 | ||||||||
\(94\) | 8.13579 | 0.839142 | ||||||||
\(95\) | −4.56119 | −0.467968 | ||||||||
\(96\) | −8.09653 | −0.826349 | ||||||||
\(97\) | 11.4486 | 1.16243 | 0.581214 | − | 0.813751i | \(-0.302578\pi\) | ||||
0.581214 | + | 0.813751i | \(0.302578\pi\) | |||||||
\(98\) | 14.5353 | 1.46828 | ||||||||
\(99\) | −0.521753 | −0.0524381 | ||||||||
\(100\) | −4.59106 | −0.459106 | ||||||||
\(101\) | 13.0315 | 1.29668 | 0.648341 | − | 0.761350i | \(-0.275463\pi\) | ||||
0.648341 | + | 0.761350i | \(0.275463\pi\) | |||||||
\(102\) | 7.05107 | 0.698160 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 0.688276 | 0.0674910 | ||||||||
\(105\) | 0.215933 | 0.0210729 | ||||||||
\(106\) | 27.8628 | 2.70628 | ||||||||
\(107\) | −6.66516 | −0.644345 | −0.322173 | − | 0.946681i | \(-0.604413\pi\) | ||||
−0.322173 | + | 0.946681i | \(0.604413\pi\) | |||||||
\(108\) | −2.33074 | −0.224275 | ||||||||
\(109\) | 1.80728 | 0.173106 | 0.0865531 | − | 0.996247i | \(-0.472415\pi\) | ||||
0.0865531 | + | 0.996247i | \(0.472415\pi\) | |||||||
\(110\) | 1.89009 | 0.180213 | ||||||||
\(111\) | −5.89933 | −0.559939 | ||||||||
\(112\) | 0.400561 | 0.0378495 | ||||||||
\(113\) | −1.77919 | −0.167372 | −0.0836861 | − | 0.996492i | \(-0.526669\pi\) | ||||
−0.0836861 | + | 0.996492i | \(0.526669\pi\) | |||||||
\(114\) | −5.45284 | −0.510705 | ||||||||
\(115\) | 1.86594 | 0.174000 | ||||||||
\(116\) | 3.53738 | 0.328437 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 6.98991 | 0.643473 | ||||||||
\(119\) | −0.420297 | −0.0385285 | ||||||||
\(120\) | 1.19812 | 0.109373 | ||||||||
\(121\) | −10.7278 | −0.975252 | ||||||||
\(122\) | −4.86987 | −0.440897 | ||||||||
\(123\) | 10.0270 | 0.904104 | ||||||||
\(124\) | 11.4345 | 1.02685 | ||||||||
\(125\) | −12.1327 | −1.08518 | ||||||||
\(126\) | 0.258144 | 0.0229973 | ||||||||
\(127\) | −2.12556 | −0.188613 | −0.0943066 | − | 0.995543i | \(-0.530063\pi\) | ||||
−0.0943066 | + | 0.995543i | \(0.530063\pi\) | |||||||
\(128\) | 5.43092 | 0.480030 | ||||||||
\(129\) | −0.753761 | −0.0663650 | ||||||||
\(130\) | 3.62257 | 0.317721 | ||||||||
\(131\) | −11.1284 | −0.972289 | −0.486144 | − | 0.873878i | \(-0.661597\pi\) | ||||
−0.486144 | + | 0.873878i | \(0.661597\pi\) | |||||||
\(132\) | 1.21607 | 0.105845 | ||||||||
\(133\) | 0.325030 | 0.0281837 | ||||||||
\(134\) | −14.1333 | −1.22093 | ||||||||
\(135\) | −1.74075 | −0.149820 | ||||||||
\(136\) | −2.33204 | −0.199971 | ||||||||
\(137\) | 2.19152 | 0.187235 | 0.0936173 | − | 0.995608i | \(-0.470157\pi\) | ||||
0.0936173 | + | 0.995608i | \(0.470157\pi\) | |||||||
\(138\) | 2.23070 | 0.189890 | ||||||||
\(139\) | 13.0881 | 1.11012 | 0.555061 | − | 0.831810i | \(-0.312695\pi\) | ||||
0.555061 | + | 0.831810i | \(0.312695\pi\) | |||||||
\(140\) | −0.503282 | −0.0425351 | ||||||||
\(141\) | 3.90948 | 0.329237 | ||||||||
\(142\) | 18.0970 | 1.51866 | ||||||||
\(143\) | 0.521753 | 0.0436312 | ||||||||
\(144\) | −3.22914 | −0.269095 | ||||||||
\(145\) | 2.64195 | 0.219402 | ||||||||
\(146\) | 22.0267 | 1.82294 | ||||||||
\(147\) | 6.98461 | 0.576081 | ||||||||
\(148\) | 13.7498 | 1.13022 | ||||||||
\(149\) | 18.2394 | 1.49423 | 0.747116 | − | 0.664694i | \(-0.231438\pi\) | ||||
0.747116 | + | 0.664694i | \(0.231438\pi\) | |||||||
\(150\) | −4.09921 | −0.334699 | ||||||||
\(151\) | −16.9669 | −1.38075 | −0.690375 | − | 0.723451i | \(-0.742555\pi\) | ||||
−0.690375 | + | 0.723451i | \(0.742555\pi\) | |||||||
\(152\) | 1.80345 | 0.146279 | ||||||||
\(153\) | 3.38824 | 0.273923 | ||||||||
\(154\) | −0.134688 | −0.0108534 | ||||||||
\(155\) | 8.54003 | 0.685952 | ||||||||
\(156\) | 2.33074 | 0.186608 | ||||||||
\(157\) | −14.6396 | −1.16836 | −0.584182 | − | 0.811623i | \(-0.698585\pi\) | ||||
−0.584182 | + | 0.811623i | \(0.698585\pi\) | |||||||
\(158\) | −23.8719 | −1.89914 | ||||||||
\(159\) | 13.3889 | 1.06181 | ||||||||
\(160\) | 14.0940 | 1.11423 | ||||||||
\(161\) | −0.132967 | −0.0104792 | ||||||||
\(162\) | −2.08104 | −0.163502 | ||||||||
\(163\) | 0.586063 | 0.0459040 | 0.0229520 | − | 0.999737i | \(-0.492694\pi\) | ||||
0.0229520 | + | 0.999737i | \(0.492694\pi\) | |||||||
\(164\) | −23.3703 | −1.82491 | ||||||||
\(165\) | 0.908242 | 0.0707065 | ||||||||
\(166\) | 33.0810 | 2.56758 | ||||||||
\(167\) | −5.12247 | −0.396389 | −0.198194 | − | 0.980163i | \(-0.563508\pi\) | ||||
−0.198194 | + | 0.980163i | \(0.563508\pi\) | |||||||
\(168\) | −0.0853777 | −0.00658703 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −12.2742 | −0.941385 | ||||||||
\(171\) | −2.62024 | −0.200375 | ||||||||
\(172\) | 1.75682 | 0.133956 | ||||||||
\(173\) | 5.66494 | 0.430697 | 0.215349 | − | 0.976537i | \(-0.430911\pi\) | ||||
0.215349 | + | 0.976537i | \(0.430911\pi\) | |||||||
\(174\) | 3.15841 | 0.239439 | ||||||||
\(175\) | 0.244344 | 0.0184707 | ||||||||
\(176\) | 1.68481 | 0.126998 | ||||||||
\(177\) | 3.35885 | 0.252467 | ||||||||
\(178\) | −13.3928 | −1.00383 | ||||||||
\(179\) | −17.1537 | −1.28213 | −0.641064 | − | 0.767487i | \(-0.721507\pi\) | ||||
−0.641064 | + | 0.767487i | \(0.721507\pi\) | |||||||
\(180\) | 4.05723 | 0.302408 | ||||||||
\(181\) | 5.79668 | 0.430864 | 0.215432 | − | 0.976519i | \(-0.430884\pi\) | ||||
0.215432 | + | 0.976519i | \(0.430884\pi\) | |||||||
\(182\) | −0.258144 | −0.0191349 | ||||||||
\(183\) | −2.34011 | −0.172986 | ||||||||
\(184\) | −0.737775 | −0.0543895 | ||||||||
\(185\) | 10.2693 | 0.755010 | ||||||||
\(186\) | 10.2095 | 0.748596 | ||||||||
\(187\) | −1.76782 | −0.129276 | ||||||||
\(188\) | −9.11196 | −0.664558 | ||||||||
\(189\) | 0.124046 | 0.00902300 | ||||||||
\(190\) | 9.49203 | 0.688624 | ||||||||
\(191\) | 10.0894 | 0.730044 | 0.365022 | − | 0.930999i | \(-0.381062\pi\) | ||||
0.365022 | + | 0.930999i | \(0.381062\pi\) | |||||||
\(192\) | 10.3909 | 0.749901 | ||||||||
\(193\) | 21.3866 | 1.53944 | 0.769722 | − | 0.638379i | \(-0.220395\pi\) | ||||
0.769722 | + | 0.638379i | \(0.220395\pi\) | |||||||
\(194\) | −23.8250 | −1.71054 | ||||||||
\(195\) | 1.74075 | 0.124658 | ||||||||
\(196\) | −16.2793 | −1.16281 | ||||||||
\(197\) | 14.6160 | 1.04135 | 0.520673 | − | 0.853756i | \(-0.325681\pi\) | ||||
0.520673 | + | 0.853756i | \(0.325681\pi\) | |||||||
\(198\) | 1.08579 | 0.0771637 | ||||||||
\(199\) | 19.4870 | 1.38140 | 0.690699 | − | 0.723143i | \(-0.257303\pi\) | ||||
0.690699 | + | 0.723143i | \(0.257303\pi\) | |||||||
\(200\) | 1.35576 | 0.0958666 | ||||||||
\(201\) | −6.79145 | −0.479032 | ||||||||
\(202\) | −27.1191 | −1.90809 | ||||||||
\(203\) | −0.188265 | −0.0132136 | ||||||||
\(204\) | −7.89710 | −0.552907 | ||||||||
\(205\) | −17.4545 | −1.21908 | ||||||||
\(206\) | 2.08104 | 0.144993 | ||||||||
\(207\) | 1.07192 | 0.0745034 | ||||||||
\(208\) | 3.22914 | 0.223901 | ||||||||
\(209\) | 1.36712 | 0.0945657 | ||||||||
\(210\) | −0.449365 | −0.0310091 | ||||||||
\(211\) | −22.4629 | −1.54641 | −0.773206 | − | 0.634155i | \(-0.781348\pi\) | ||||
−0.773206 | + | 0.634155i | \(0.781348\pi\) | |||||||
\(212\) | −31.2060 | −2.14323 | ||||||||
\(213\) | 8.69610 | 0.595847 | ||||||||
\(214\) | 13.8705 | 0.948166 | ||||||||
\(215\) | 1.31211 | 0.0894852 | ||||||||
\(216\) | 0.688276 | 0.0468312 | ||||||||
\(217\) | −0.608562 | −0.0413119 | ||||||||
\(218\) | −3.76103 | −0.254729 | ||||||||
\(219\) | 10.5845 | 0.715232 | ||||||||
\(220\) | −2.11687 | −0.142719 | ||||||||
\(221\) | −3.38824 | −0.227918 | ||||||||
\(222\) | 12.2767 | 0.823961 | ||||||||
\(223\) | 1.58222 | 0.105953 | 0.0529765 | − | 0.998596i | \(-0.483129\pi\) | ||||
0.0529765 | + | 0.998596i | \(0.483129\pi\) | |||||||
\(224\) | −1.00434 | −0.0671053 | ||||||||
\(225\) | −1.96979 | −0.131319 | ||||||||
\(226\) | 3.70257 | 0.246291 | ||||||||
\(227\) | −26.3243 | −1.74721 | −0.873603 | − | 0.486639i | \(-0.838223\pi\) | ||||
−0.873603 | + | 0.486639i | \(0.838223\pi\) | |||||||
\(228\) | 6.10710 | 0.404453 | ||||||||
\(229\) | 12.3705 | 0.817468 | 0.408734 | − | 0.912654i | \(-0.365970\pi\) | ||||
0.408734 | + | 0.912654i | \(0.365970\pi\) | |||||||
\(230\) | −3.88310 | −0.256044 | ||||||||
\(231\) | −0.0647212 | −0.00425834 | ||||||||
\(232\) | −1.04460 | −0.0685815 | ||||||||
\(233\) | −8.60177 | −0.563521 | −0.281760 | − | 0.959485i | \(-0.590918\pi\) | ||||
−0.281760 | + | 0.959485i | \(0.590918\pi\) | |||||||
\(234\) | 2.08104 | 0.136042 | ||||||||
\(235\) | −6.80542 | −0.443937 | ||||||||
\(236\) | −7.82860 | −0.509598 | ||||||||
\(237\) | −11.4711 | −0.745129 | ||||||||
\(238\) | 0.874655 | 0.0566955 | ||||||||
\(239\) | 2.22240 | 0.143755 | 0.0718774 | − | 0.997413i | \(-0.477101\pi\) | ||||
0.0718774 | + | 0.997413i | \(0.477101\pi\) | |||||||
\(240\) | 5.62113 | 0.362842 | ||||||||
\(241\) | 26.3501 | 1.69736 | 0.848679 | − | 0.528908i | \(-0.177398\pi\) | ||||
0.848679 | + | 0.528908i | \(0.177398\pi\) | |||||||
\(242\) | 22.3249 | 1.43510 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.45418 | 0.349168 | ||||||||
\(245\) | −12.1585 | −0.776776 | ||||||||
\(246\) | −20.8666 | −1.33041 | ||||||||
\(247\) | 2.62024 | 0.166722 | ||||||||
\(248\) | −3.37665 | −0.214417 | ||||||||
\(249\) | 15.8964 | 1.00739 | ||||||||
\(250\) | 25.2486 | 1.59686 | ||||||||
\(251\) | 16.9216 | 1.06808 | 0.534041 | − | 0.845458i | \(-0.320673\pi\) | ||||
0.534041 | + | 0.845458i | \(0.320673\pi\) | |||||||
\(252\) | −0.289118 | −0.0182127 | ||||||||
\(253\) | −0.559276 | −0.0351614 | ||||||||
\(254\) | 4.42338 | 0.277548 | ||||||||
\(255\) | −5.89808 | −0.369352 | ||||||||
\(256\) | 9.47991 | 0.592494 | ||||||||
\(257\) | −14.9316 | −0.931411 | −0.465705 | − | 0.884940i | \(-0.654199\pi\) | ||||
−0.465705 | + | 0.884940i | \(0.654199\pi\) | |||||||
\(258\) | 1.56861 | 0.0976573 | ||||||||
\(259\) | −0.731786 | −0.0454710 | ||||||||
\(260\) | −4.05723 | −0.251619 | ||||||||
\(261\) | 1.51771 | 0.0939438 | ||||||||
\(262\) | 23.1586 | 1.43074 | ||||||||
\(263\) | −7.43575 | −0.458508 | −0.229254 | − | 0.973367i | \(-0.573629\pi\) | ||||
−0.229254 | + | 0.973367i | \(0.573629\pi\) | |||||||
\(264\) | −0.359110 | −0.0221017 | ||||||||
\(265\) | −23.3067 | −1.43172 | ||||||||
\(266\) | −0.676401 | −0.0414728 | ||||||||
\(267\) | −6.43563 | −0.393854 | ||||||||
\(268\) | 15.8291 | 0.966914 | ||||||||
\(269\) | −3.21442 | −0.195987 | −0.0979934 | − | 0.995187i | \(-0.531242\pi\) | ||||
−0.0979934 | + | 0.995187i | \(0.531242\pi\) | |||||||
\(270\) | 3.62257 | 0.220463 | ||||||||
\(271\) | −23.8045 | −1.44602 | −0.723011 | − | 0.690836i | \(-0.757243\pi\) | ||||
−0.723011 | + | 0.690836i | \(0.757243\pi\) | |||||||
\(272\) | −10.9411 | −0.663402 | ||||||||
\(273\) | −0.124046 | −0.00750759 | ||||||||
\(274\) | −4.56065 | −0.275519 | ||||||||
\(275\) | 1.02774 | 0.0619752 | ||||||||
\(276\) | −2.49836 | −0.150383 | ||||||||
\(277\) | 11.1743 | 0.671397 | 0.335699 | − | 0.941969i | \(-0.391028\pi\) | ||||
0.335699 | + | 0.941969i | \(0.391028\pi\) | |||||||
\(278\) | −27.2370 | −1.63357 | ||||||||
\(279\) | 4.90595 | 0.293712 | ||||||||
\(280\) | 0.148621 | 0.00888182 | ||||||||
\(281\) | −3.08517 | −0.184046 | −0.0920230 | − | 0.995757i | \(-0.529333\pi\) | ||||
−0.0920230 | + | 0.995757i | \(0.529333\pi\) | |||||||
\(282\) | −8.13579 | −0.484479 | ||||||||
\(283\) | −24.0540 | −1.42986 | −0.714931 | − | 0.699195i | \(-0.753542\pi\) | ||||
−0.714931 | + | 0.699195i | \(0.753542\pi\) | |||||||
\(284\) | −20.2683 | −1.20270 | ||||||||
\(285\) | 4.56119 | 0.270182 | ||||||||
\(286\) | −1.08579 | −0.0642041 | ||||||||
\(287\) | 1.24381 | 0.0734196 | ||||||||
\(288\) | 8.09653 | 0.477093 | ||||||||
\(289\) | −5.51982 | −0.324695 | ||||||||
\(290\) | −5.49801 | −0.322854 | ||||||||
\(291\) | −11.4486 | −0.671128 | ||||||||
\(292\) | −24.6696 | −1.44368 | ||||||||
\(293\) | 20.9087 | 1.22150 | 0.610750 | − | 0.791824i | \(-0.290868\pi\) | ||||
0.610750 | + | 0.791824i | \(0.290868\pi\) | |||||||
\(294\) | −14.5353 | −0.847714 | ||||||||
\(295\) | −5.84692 | −0.340421 | ||||||||
\(296\) | −4.06036 | −0.236004 | ||||||||
\(297\) | 0.521753 | 0.0302752 | ||||||||
\(298\) | −37.9570 | −2.19879 | ||||||||
\(299\) | −1.07192 | −0.0619906 | ||||||||
\(300\) | 4.59106 | 0.265065 | ||||||||
\(301\) | −0.0935009 | −0.00538930 | ||||||||
\(302\) | 35.3089 | 2.03180 | ||||||||
\(303\) | −13.0315 | −0.748639 | ||||||||
\(304\) | 8.46114 | 0.485280 | ||||||||
\(305\) | 4.07355 | 0.233251 | ||||||||
\(306\) | −7.05107 | −0.403083 | ||||||||
\(307\) | −29.4633 | −1.68156 | −0.840780 | − | 0.541377i | \(-0.817903\pi\) | ||||
−0.840780 | + | 0.541377i | \(0.817903\pi\) | |||||||
\(308\) | 0.150848 | 0.00859537 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −17.7722 | −1.00939 | ||||||||
\(311\) | −8.55254 | −0.484970 | −0.242485 | − | 0.970155i | \(-0.577963\pi\) | ||||
−0.242485 | + | 0.970155i | \(0.577963\pi\) | |||||||
\(312\) | −0.688276 | −0.0389660 | ||||||||
\(313\) | 17.0478 | 0.963598 | 0.481799 | − | 0.876282i | \(-0.339984\pi\) | ||||
0.481799 | + | 0.876282i | \(0.339984\pi\) | |||||||
\(314\) | 30.4655 | 1.71927 | ||||||||
\(315\) | −0.215933 | −0.0121664 | ||||||||
\(316\) | 26.7362 | 1.50403 | ||||||||
\(317\) | −20.9238 | −1.17520 | −0.587598 | − | 0.809153i | \(-0.699926\pi\) | ||||
−0.587598 | + | 0.809153i | \(0.699926\pi\) | |||||||
\(318\) | −27.8628 | −1.56247 | ||||||||
\(319\) | −0.791869 | −0.0443361 | ||||||||
\(320\) | −18.0880 | −1.01115 | ||||||||
\(321\) | 6.66516 | 0.372013 | ||||||||
\(322\) | 0.276709 | 0.0154204 | ||||||||
\(323\) | −8.87802 | −0.493986 | ||||||||
\(324\) | 2.33074 | 0.129485 | ||||||||
\(325\) | 1.96979 | 0.109264 | ||||||||
\(326\) | −1.21962 | −0.0675486 | ||||||||
\(327\) | −1.80728 | −0.0999429 | ||||||||
\(328\) | 6.90134 | 0.381063 | ||||||||
\(329\) | 0.484954 | 0.0267364 | ||||||||
\(330\) | −1.89009 | −0.104046 | ||||||||
\(331\) | −14.1579 | −0.778186 | −0.389093 | − | 0.921198i | \(-0.627212\pi\) | ||||
−0.389093 | + | 0.921198i | \(0.627212\pi\) | |||||||
\(332\) | −37.0502 | −2.03340 | ||||||||
\(333\) | 5.89933 | 0.323281 | ||||||||
\(334\) | 10.6601 | 0.583293 | ||||||||
\(335\) | 11.8222 | 0.645916 | ||||||||
\(336\) | −0.400561 | −0.0218524 | ||||||||
\(337\) | −9.46821 | −0.515766 | −0.257883 | − | 0.966176i | \(-0.583025\pi\) | ||||
−0.257883 | + | 0.966176i | \(0.583025\pi\) | |||||||
\(338\) | −2.08104 | −0.113194 | ||||||||
\(339\) | 1.77919 | 0.0966324 | ||||||||
\(340\) | 13.7469 | 0.745529 | ||||||||
\(341\) | −2.55969 | −0.138615 | ||||||||
\(342\) | 5.45284 | 0.294856 | ||||||||
\(343\) | 1.73473 | 0.0936667 | ||||||||
\(344\) | −0.518796 | −0.0279716 | ||||||||
\(345\) | −1.86594 | −0.100459 | ||||||||
\(346\) | −11.7890 | −0.633779 | ||||||||
\(347\) | −24.3508 | −1.30722 | −0.653610 | − | 0.756832i | \(-0.726746\pi\) | ||||
−0.653610 | + | 0.756832i | \(0.726746\pi\) | |||||||
\(348\) | −3.53738 | −0.189623 | ||||||||
\(349\) | 21.2313 | 1.13649 | 0.568243 | − | 0.822861i | \(-0.307623\pi\) | ||||
0.568243 | + | 0.822861i | \(0.307623\pi\) | |||||||
\(350\) | −0.508490 | −0.0271799 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −4.22439 | −0.225161 | ||||||||
\(353\) | −17.0348 | −0.906671 | −0.453336 | − | 0.891340i | \(-0.649766\pi\) | ||||
−0.453336 | + | 0.891340i | \(0.649766\pi\) | |||||||
\(354\) | −6.98991 | −0.371510 | ||||||||
\(355\) | −15.1377 | −0.803428 | ||||||||
\(356\) | 14.9998 | 0.794986 | ||||||||
\(357\) | 0.420297 | 0.0222445 | ||||||||
\(358\) | 35.6976 | 1.88668 | ||||||||
\(359\) | −28.3209 | −1.49472 | −0.747359 | − | 0.664420i | \(-0.768678\pi\) | ||||
−0.747359 | + | 0.664420i | \(0.768678\pi\) | |||||||
\(360\) | −1.19812 | −0.0631463 | ||||||||
\(361\) | −12.1343 | −0.638648 | ||||||||
\(362\) | −12.0631 | −0.634024 | ||||||||
\(363\) | 10.7278 | 0.563062 | ||||||||
\(364\) | 0.289118 | 0.0151539 | ||||||||
\(365\) | −18.4249 | −0.964404 | ||||||||
\(366\) | 4.86987 | 0.254552 | ||||||||
\(367\) | 13.2963 | 0.694061 | 0.347031 | − | 0.937854i | \(-0.387190\pi\) | ||||
0.347031 | + | 0.937854i | \(0.387190\pi\) | |||||||
\(368\) | −3.46137 | −0.180436 | ||||||||
\(369\) | −10.0270 | −0.521985 | ||||||||
\(370\) | −21.3707 | −1.11101 | ||||||||
\(371\) | 1.66083 | 0.0862262 | ||||||||
\(372\) | −11.4345 | −0.592850 | ||||||||
\(373\) | −21.7336 | −1.12532 | −0.562661 | − | 0.826688i | \(-0.690222\pi\) | ||||
−0.562661 | + | 0.826688i | \(0.690222\pi\) | |||||||
\(374\) | 3.67892 | 0.190232 | ||||||||
\(375\) | 12.1327 | 0.626528 | ||||||||
\(376\) | 2.69080 | 0.138767 | ||||||||
\(377\) | −1.51771 | −0.0781660 | ||||||||
\(378\) | −0.258144 | −0.0132775 | ||||||||
\(379\) | −25.0970 | −1.28914 | −0.644572 | − | 0.764544i | \(-0.722964\pi\) | ||||
−0.644572 | + | 0.764544i | \(0.722964\pi\) | |||||||
\(380\) | −10.6309 | −0.545355 | ||||||||
\(381\) | 2.12556 | 0.108896 | ||||||||
\(382\) | −20.9965 | −1.07427 | ||||||||
\(383\) | −37.4375 | −1.91296 | −0.956482 | − | 0.291790i | \(-0.905749\pi\) | ||||
−0.956482 | + | 0.291790i | \(0.905749\pi\) | |||||||
\(384\) | −5.43092 | −0.277145 | ||||||||
\(385\) | 0.112663 | 0.00574186 | ||||||||
\(386\) | −44.5065 | −2.26532 | ||||||||
\(387\) | 0.753761 | 0.0383158 | ||||||||
\(388\) | 26.6836 | 1.35466 | ||||||||
\(389\) | −0.692861 | −0.0351294 | −0.0175647 | − | 0.999846i | \(-0.505591\pi\) | ||||
−0.0175647 | + | 0.999846i | \(0.505591\pi\) | |||||||
\(390\) | −3.62257 | −0.183436 | ||||||||
\(391\) | 3.63191 | 0.183674 | ||||||||
\(392\) | 4.80734 | 0.242807 | ||||||||
\(393\) | 11.1284 | 0.561351 | ||||||||
\(394\) | −30.4165 | −1.53236 | ||||||||
\(395\) | 19.9684 | 1.00472 | ||||||||
\(396\) | −1.21607 | −0.0611097 | ||||||||
\(397\) | −17.3398 | −0.870258 | −0.435129 | − | 0.900368i | \(-0.643297\pi\) | ||||
−0.435129 | + | 0.900368i | \(0.643297\pi\) | |||||||
\(398\) | −40.5533 | −2.03275 | ||||||||
\(399\) | −0.325030 | −0.0162719 | ||||||||
\(400\) | 6.36073 | 0.318036 | ||||||||
\(401\) | 5.79042 | 0.289160 | 0.144580 | − | 0.989493i | \(-0.453817\pi\) | ||||
0.144580 | + | 0.989493i | \(0.453817\pi\) | |||||||
\(402\) | 14.1333 | 0.704904 | ||||||||
\(403\) | −4.90595 | −0.244383 | ||||||||
\(404\) | 30.3730 | 1.51111 | ||||||||
\(405\) | 1.74075 | 0.0864986 | ||||||||
\(406\) | 0.391788 | 0.0194441 | ||||||||
\(407\) | −3.07799 | −0.152570 | ||||||||
\(408\) | 2.33204 | 0.115453 | ||||||||
\(409\) | 20.0783 | 0.992810 | 0.496405 | − | 0.868091i | \(-0.334653\pi\) | ||||
0.496405 | + | 0.868091i | \(0.334653\pi\) | |||||||
\(410\) | 36.3236 | 1.79389 | ||||||||
\(411\) | −2.19152 | −0.108100 | ||||||||
\(412\) | −2.33074 | −0.114827 | ||||||||
\(413\) | 0.416651 | 0.0205021 | ||||||||
\(414\) | −2.23070 | −0.109633 | ||||||||
\(415\) | −27.6716 | −1.35835 | ||||||||
\(416\) | −8.09653 | −0.396965 | ||||||||
\(417\) | −13.0881 | −0.640929 | ||||||||
\(418\) | −2.84504 | −0.139155 | ||||||||
\(419\) | −4.01294 | −0.196045 | −0.0980224 | − | 0.995184i | \(-0.531252\pi\) | ||||
−0.0980224 | + | 0.995184i | \(0.531252\pi\) | |||||||
\(420\) | 0.503282 | 0.0245576 | ||||||||
\(421\) | 24.6861 | 1.20313 | 0.601564 | − | 0.798824i | \(-0.294544\pi\) | ||||
0.601564 | + | 0.798824i | \(0.294544\pi\) | |||||||
\(422\) | 46.7463 | 2.27558 | ||||||||
\(423\) | −3.90948 | −0.190085 | ||||||||
\(424\) | 9.21525 | 0.447532 | ||||||||
\(425\) | −6.67412 | −0.323742 | ||||||||
\(426\) | −18.0970 | −0.876800 | ||||||||
\(427\) | −0.290281 | −0.0140477 | ||||||||
\(428\) | −15.5347 | −0.750900 | ||||||||
\(429\) | −0.521753 | −0.0251905 | ||||||||
\(430\) | −2.73056 | −0.131679 | ||||||||
\(431\) | −4.02554 | −0.193903 | −0.0969516 | − | 0.995289i | \(-0.530909\pi\) | ||||
−0.0969516 | + | 0.995289i | \(0.530909\pi\) | |||||||
\(432\) | 3.22914 | 0.155362 | ||||||||
\(433\) | 6.38826 | 0.307000 | 0.153500 | − | 0.988149i | \(-0.450945\pi\) | ||||
0.153500 | + | 0.988149i | \(0.450945\pi\) | |||||||
\(434\) | 1.26644 | 0.0607912 | ||||||||
\(435\) | −2.64195 | −0.126672 | ||||||||
\(436\) | 4.21230 | 0.201732 | ||||||||
\(437\) | −2.80869 | −0.134358 | ||||||||
\(438\) | −22.0267 | −1.05248 | ||||||||
\(439\) | −31.2808 | −1.49295 | −0.746476 | − | 0.665413i | \(-0.768256\pi\) | ||||
−0.746476 | + | 0.665413i | \(0.768256\pi\) | |||||||
\(440\) | 0.625121 | 0.0298015 | ||||||||
\(441\) | −6.98461 | −0.332601 | ||||||||
\(442\) | 7.05107 | 0.335385 | ||||||||
\(443\) | 3.76786 | 0.179016 | 0.0895081 | − | 0.995986i | \(-0.471470\pi\) | ||||
0.0895081 | + | 0.995986i | \(0.471470\pi\) | |||||||
\(444\) | −13.7498 | −0.652535 | ||||||||
\(445\) | 11.2028 | 0.531065 | ||||||||
\(446\) | −3.29266 | −0.155912 | ||||||||
\(447\) | −18.2394 | −0.862695 | ||||||||
\(448\) | 1.28895 | 0.0608972 | ||||||||
\(449\) | −26.5743 | −1.25412 | −0.627060 | − | 0.778971i | \(-0.715742\pi\) | ||||
−0.627060 | + | 0.778971i | \(0.715742\pi\) | |||||||
\(450\) | 4.09921 | 0.193239 | ||||||||
\(451\) | 5.23162 | 0.246347 | ||||||||
\(452\) | −4.14683 | −0.195050 | ||||||||
\(453\) | 16.9669 | 0.797177 | ||||||||
\(454\) | 54.7820 | 2.57105 | ||||||||
\(455\) | 0.215933 | 0.0101231 | ||||||||
\(456\) | −1.80345 | −0.0844544 | ||||||||
\(457\) | −27.1593 | −1.27046 | −0.635229 | − | 0.772323i | \(-0.719094\pi\) | ||||
−0.635229 | + | 0.772323i | \(0.719094\pi\) | |||||||
\(458\) | −25.7436 | −1.20292 | ||||||||
\(459\) | −3.38824 | −0.158150 | ||||||||
\(460\) | 4.34901 | 0.202774 | ||||||||
\(461\) | 37.8715 | 1.76385 | 0.881926 | − | 0.471388i | \(-0.156247\pi\) | ||||
0.881926 | + | 0.471388i | \(0.156247\pi\) | |||||||
\(462\) | 0.134688 | 0.00626623 | ||||||||
\(463\) | 18.4681 | 0.858285 | 0.429143 | − | 0.903237i | \(-0.358816\pi\) | ||||
0.429143 | + | 0.903237i | \(0.358816\pi\) | |||||||
\(464\) | −4.90089 | −0.227518 | ||||||||
\(465\) | −8.54003 | −0.396035 | ||||||||
\(466\) | 17.9006 | 0.829231 | ||||||||
\(467\) | −21.0049 | −0.971989 | −0.485995 | − | 0.873962i | \(-0.661543\pi\) | ||||
−0.485995 | + | 0.873962i | \(0.661543\pi\) | |||||||
\(468\) | −2.33074 | −0.107738 | ||||||||
\(469\) | −0.842450 | −0.0389007 | ||||||||
\(470\) | 14.1624 | 0.653262 | ||||||||
\(471\) | 14.6396 | 0.674555 | ||||||||
\(472\) | 2.31182 | 0.106410 | ||||||||
\(473\) | −0.393277 | −0.0180829 | ||||||||
\(474\) | 23.8719 | 1.09647 | ||||||||
\(475\) | 5.16133 | 0.236818 | ||||||||
\(476\) | −0.979601 | −0.0448999 | ||||||||
\(477\) | −13.3889 | −0.613035 | ||||||||
\(478\) | −4.62490 | −0.211538 | ||||||||
\(479\) | 16.9260 | 0.773368 | 0.386684 | − | 0.922212i | \(-0.373620\pi\) | ||||
0.386684 | + | 0.922212i | \(0.373620\pi\) | |||||||
\(480\) | −14.0940 | −0.643302 | ||||||||
\(481\) | −5.89933 | −0.268986 | ||||||||
\(482\) | −54.8356 | −2.49769 | ||||||||
\(483\) | 0.132967 | 0.00605020 | ||||||||
\(484\) | −25.0036 | −1.13653 | ||||||||
\(485\) | 19.9291 | 0.904936 | ||||||||
\(486\) | 2.08104 | 0.0943980 | ||||||||
\(487\) | −7.12339 | −0.322791 | −0.161396 | − | 0.986890i | \(-0.551600\pi\) | ||||
−0.161396 | + | 0.986890i | \(0.551600\pi\) | |||||||
\(488\) | −1.61064 | −0.0729103 | ||||||||
\(489\) | −0.586063 | −0.0265027 | ||||||||
\(490\) | 25.3023 | 1.14304 | ||||||||
\(491\) | 14.7857 | 0.667267 | 0.333634 | − | 0.942703i | \(-0.391725\pi\) | ||||
0.333634 | + | 0.942703i | \(0.391725\pi\) | |||||||
\(492\) | 23.3703 | 1.05361 | ||||||||
\(493\) | 5.14236 | 0.231600 | ||||||||
\(494\) | −5.45284 | −0.245335 | ||||||||
\(495\) | −0.908242 | −0.0408224 | ||||||||
\(496\) | −15.8420 | −0.711327 | ||||||||
\(497\) | 1.07871 | 0.0483869 | ||||||||
\(498\) | −33.0810 | −1.48239 | ||||||||
\(499\) | 34.1869 | 1.53042 | 0.765208 | − | 0.643783i | \(-0.222636\pi\) | ||||
0.765208 | + | 0.643783i | \(0.222636\pi\) | |||||||
\(500\) | −28.2780 | −1.26463 | ||||||||
\(501\) | 5.12247 | 0.228855 | ||||||||
\(502\) | −35.2146 | −1.57170 | ||||||||
\(503\) | −32.8667 | −1.46545 | −0.732727 | − | 0.680522i | \(-0.761753\pi\) | ||||
−0.732727 | + | 0.680522i | \(0.761753\pi\) | |||||||
\(504\) | 0.0853777 | 0.00380302 | ||||||||
\(505\) | 22.6846 | 1.00945 | ||||||||
\(506\) | 1.16388 | 0.0517406 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −4.95412 | −0.219804 | ||||||||
\(509\) | −22.3042 | −0.988614 | −0.494307 | − | 0.869287i | \(-0.664578\pi\) | ||||
−0.494307 | + | 0.869287i | \(0.664578\pi\) | |||||||
\(510\) | 12.2742 | 0.543509 | ||||||||
\(511\) | 1.31296 | 0.0580818 | ||||||||
\(512\) | −30.5899 | −1.35190 | ||||||||
\(513\) | 2.62024 | 0.115687 | ||||||||
\(514\) | 31.0734 | 1.37059 | ||||||||
\(515\) | −1.74075 | −0.0767066 | ||||||||
\(516\) | −1.75682 | −0.0773396 | ||||||||
\(517\) | 2.03978 | 0.0897095 | ||||||||
\(518\) | 1.52288 | 0.0669114 | ||||||||
\(519\) | −5.66494 | −0.248663 | ||||||||
\(520\) | 1.19812 | 0.0525409 | ||||||||
\(521\) | 3.02739 | 0.132632 | 0.0663162 | − | 0.997799i | \(-0.478875\pi\) | ||||
0.0663162 | + | 0.997799i | \(0.478875\pi\) | |||||||
\(522\) | −3.15841 | −0.138240 | ||||||||
\(523\) | −25.5829 | −1.11866 | −0.559332 | − | 0.828944i | \(-0.688942\pi\) | ||||
−0.559332 | + | 0.828944i | \(0.688942\pi\) | |||||||
\(524\) | −25.9373 | −1.13307 | ||||||||
\(525\) | −0.244344 | −0.0106640 | ||||||||
\(526\) | 15.4741 | 0.674703 | ||||||||
\(527\) | 16.6225 | 0.724089 | ||||||||
\(528\) | −1.68481 | −0.0733221 | ||||||||
\(529\) | −21.8510 | −0.950043 | ||||||||
\(530\) | 48.5022 | 2.10680 | ||||||||
\(531\) | −3.35885 | −0.145762 | ||||||||
\(532\) | 0.757560 | 0.0328444 | ||||||||
\(533\) | 10.0270 | 0.434318 | ||||||||
\(534\) | 13.3928 | 0.579564 | ||||||||
\(535\) | −11.6024 | −0.501615 | ||||||||
\(536\) | −4.67439 | −0.201903 | ||||||||
\(537\) | 17.1537 | 0.740237 | ||||||||
\(538\) | 6.68935 | 0.288398 | ||||||||
\(539\) | 3.64424 | 0.156969 | ||||||||
\(540\) | −4.05723 | −0.174595 | ||||||||
\(541\) | 0.0872630 | 0.00375173 | 0.00187586 | − | 0.999998i | \(-0.499403\pi\) | ||||
0.00187586 | + | 0.999998i | \(0.499403\pi\) | |||||||
\(542\) | 49.5382 | 2.12785 | ||||||||
\(543\) | −5.79668 | −0.248759 | ||||||||
\(544\) | 27.4330 | 1.17618 | ||||||||
\(545\) | 3.14602 | 0.134761 | ||||||||
\(546\) | 0.258144 | 0.0110476 | ||||||||
\(547\) | −26.4282 | −1.12999 | −0.564994 | − | 0.825095i | \(-0.691121\pi\) | ||||
−0.564994 | + | 0.825095i | \(0.691121\pi\) | |||||||
\(548\) | 5.10786 | 0.218197 | ||||||||
\(549\) | 2.34011 | 0.0998735 | ||||||||
\(550\) | −2.13878 | −0.0911977 | ||||||||
\(551\) | −3.97677 | −0.169416 | ||||||||
\(552\) | 0.737775 | 0.0314018 | ||||||||
\(553\) | −1.42294 | −0.0605097 | ||||||||
\(554\) | −23.2541 | −0.987973 | ||||||||
\(555\) | −10.2693 | −0.435905 | ||||||||
\(556\) | 30.5050 | 1.29370 | ||||||||
\(557\) | −9.63573 | −0.408279 | −0.204140 | − | 0.978942i | \(-0.565440\pi\) | ||||
−0.204140 | + | 0.978942i | \(0.565440\pi\) | |||||||
\(558\) | −10.2095 | −0.432202 | ||||||||
\(559\) | −0.753761 | −0.0318807 | ||||||||
\(560\) | 0.697277 | 0.0294653 | ||||||||
\(561\) | 1.76782 | 0.0746376 | ||||||||
\(562\) | 6.42038 | 0.270827 | ||||||||
\(563\) | 18.7778 | 0.791392 | 0.395696 | − | 0.918382i | \(-0.370503\pi\) | ||||
0.395696 | + | 0.918382i | \(0.370503\pi\) | |||||||
\(564\) | 9.11196 | 0.383683 | ||||||||
\(565\) | −3.09713 | −0.130297 | ||||||||
\(566\) | 50.0574 | 2.10407 | ||||||||
\(567\) | −0.124046 | −0.00520943 | ||||||||
\(568\) | 5.98532 | 0.251138 | ||||||||
\(569\) | −14.5123 | −0.608389 | −0.304194 | − | 0.952610i | \(-0.598387\pi\) | ||||
−0.304194 | + | 0.952610i | \(0.598387\pi\) | |||||||
\(570\) | −9.49203 | −0.397578 | ||||||||
\(571\) | 11.9296 | 0.499240 | 0.249620 | − | 0.968344i | \(-0.419694\pi\) | ||||
0.249620 | + | 0.968344i | \(0.419694\pi\) | |||||||
\(572\) | 1.21607 | 0.0508464 | ||||||||
\(573\) | −10.0894 | −0.421491 | ||||||||
\(574\) | −2.58841 | −0.108038 | ||||||||
\(575\) | −2.11145 | −0.0880536 | ||||||||
\(576\) | −10.3909 | −0.432956 | ||||||||
\(577\) | −28.9260 | −1.20420 | −0.602102 | − | 0.798419i | \(-0.705670\pi\) | ||||
−0.602102 | + | 0.798419i | \(0.705670\pi\) | |||||||
\(578\) | 11.4870 | 0.477795 | ||||||||
\(579\) | −21.3866 | −0.888799 | ||||||||
\(580\) | 6.15769 | 0.255684 | ||||||||
\(581\) | 1.97188 | 0.0818072 | ||||||||
\(582\) | 23.8250 | 0.987578 | ||||||||
\(583\) | 6.98569 | 0.289318 | ||||||||
\(584\) | 7.28504 | 0.301457 | ||||||||
\(585\) | −1.74075 | −0.0719712 | ||||||||
\(586\) | −43.5119 | −1.79746 | ||||||||
\(587\) | 4.30846 | 0.177829 | 0.0889146 | − | 0.996039i | \(-0.471660\pi\) | ||||
0.0889146 | + | 0.996039i | \(0.471660\pi\) | |||||||
\(588\) | 16.2793 | 0.671347 | ||||||||
\(589\) | −12.8548 | −0.529672 | ||||||||
\(590\) | 12.1677 | 0.500936 | ||||||||
\(591\) | −14.6160 | −0.601222 | ||||||||
\(592\) | −19.0498 | −0.782940 | ||||||||
\(593\) | −26.2928 | −1.07971 | −0.539857 | − | 0.841757i | \(-0.681522\pi\) | ||||
−0.539857 | + | 0.841757i | \(0.681522\pi\) | |||||||
\(594\) | −1.08579 | −0.0445505 | ||||||||
\(595\) | −0.731632 | −0.0299940 | ||||||||
\(596\) | 42.5113 | 1.74133 | ||||||||
\(597\) | −19.4870 | −0.797550 | ||||||||
\(598\) | 2.23070 | 0.0912203 | ||||||||
\(599\) | −14.5575 | −0.594803 | −0.297402 | − | 0.954752i | \(-0.596120\pi\) | ||||
−0.297402 | + | 0.954752i | \(0.596120\pi\) | |||||||
\(600\) | −1.35576 | −0.0553486 | ||||||||
\(601\) | 2.12829 | 0.0868146 | 0.0434073 | − | 0.999057i | \(-0.486179\pi\) | ||||
0.0434073 | + | 0.999057i | \(0.486179\pi\) | |||||||
\(602\) | 0.194579 | 0.00793046 | ||||||||
\(603\) | 6.79145 | 0.276569 | ||||||||
\(604\) | −39.5455 | −1.60908 | ||||||||
\(605\) | −18.6744 | −0.759221 | ||||||||
\(606\) | 27.1191 | 1.10164 | ||||||||
\(607\) | 36.7833 | 1.49299 | 0.746494 | − | 0.665392i | \(-0.231736\pi\) | ||||
0.746494 | + | 0.665392i | \(0.231736\pi\) | |||||||
\(608\) | −21.2149 | −0.860378 | ||||||||
\(609\) | 0.188265 | 0.00762889 | ||||||||
\(610\) | −8.47723 | −0.343233 | ||||||||
\(611\) | 3.90948 | 0.158161 | ||||||||
\(612\) | 7.89710 | 0.319221 | ||||||||
\(613\) | 9.47479 | 0.382683 | 0.191341 | − | 0.981524i | \(-0.438716\pi\) | ||||
0.191341 | + | 0.981524i | \(0.438716\pi\) | |||||||
\(614\) | 61.3144 | 2.47445 | ||||||||
\(615\) | 17.4545 | 0.703833 | ||||||||
\(616\) | −0.0445461 | −0.00179481 | ||||||||
\(617\) | −29.7893 | −1.19927 | −0.599636 | − | 0.800273i | \(-0.704688\pi\) | ||||
−0.599636 | + | 0.800273i | \(0.704688\pi\) | |||||||
\(618\) | −2.08104 | −0.0837118 | ||||||||
\(619\) | 9.38507 | 0.377218 | 0.188609 | − | 0.982052i | \(-0.439602\pi\) | ||||
0.188609 | + | 0.982052i | \(0.439602\pi\) | |||||||
\(620\) | 19.9046 | 0.799387 | ||||||||
\(621\) | −1.07192 | −0.0430146 | ||||||||
\(622\) | 17.7982 | 0.713642 | ||||||||
\(623\) | −0.798313 | −0.0319837 | ||||||||
\(624\) | −3.22914 | −0.129269 | ||||||||
\(625\) | −11.2710 | −0.450840 | ||||||||
\(626\) | −35.4772 | −1.41795 | ||||||||
\(627\) | −1.36712 | −0.0545975 | ||||||||
\(628\) | −34.1210 | −1.36157 | ||||||||
\(629\) | 19.9883 | 0.796987 | ||||||||
\(630\) | 0.449365 | 0.0179031 | ||||||||
\(631\) | 18.8535 | 0.750547 | 0.375273 | − | 0.926914i | \(-0.377549\pi\) | ||||
0.375273 | + | 0.926914i | \(0.377549\pi\) | |||||||
\(632\) | −7.89529 | −0.314058 | ||||||||
\(633\) | 22.4629 | 0.892822 | ||||||||
\(634\) | 43.5432 | 1.72932 | ||||||||
\(635\) | −3.70007 | −0.146833 | ||||||||
\(636\) | 31.2060 | 1.23740 | ||||||||
\(637\) | 6.98461 | 0.276740 | ||||||||
\(638\) | 1.64791 | 0.0652415 | ||||||||
\(639\) | −8.69610 | −0.344013 | ||||||||
\(640\) | 9.45387 | 0.373697 | ||||||||
\(641\) | −14.3596 | −0.567169 | −0.283584 | − | 0.958947i | \(-0.591524\pi\) | ||||
−0.283584 | + | 0.958947i | \(0.591524\pi\) | |||||||
\(642\) | −13.8705 | −0.547424 | ||||||||
\(643\) | −16.1661 | −0.637527 | −0.318763 | − | 0.947834i | \(-0.603268\pi\) | ||||
−0.318763 | + | 0.947834i | \(0.603268\pi\) | |||||||
\(644\) | −0.309910 | −0.0122122 | ||||||||
\(645\) | −1.31211 | −0.0516643 | ||||||||
\(646\) | 18.4755 | 0.726910 | ||||||||
\(647\) | −44.2051 | −1.73788 | −0.868940 | − | 0.494917i | \(-0.835198\pi\) | ||||
−0.868940 | + | 0.494917i | \(0.835198\pi\) | |||||||
\(648\) | −0.688276 | −0.0270380 | ||||||||
\(649\) | 1.75249 | 0.0687913 | ||||||||
\(650\) | −4.09921 | −0.160784 | ||||||||
\(651\) | 0.608562 | 0.0238514 | ||||||||
\(652\) | 1.36596 | 0.0534950 | ||||||||
\(653\) | 48.2627 | 1.88867 | 0.944333 | − | 0.328992i | \(-0.106709\pi\) | ||||
0.944333 | + | 0.328992i | \(0.106709\pi\) | |||||||
\(654\) | 3.76103 | 0.147068 | ||||||||
\(655\) | −19.3717 | −0.756914 | ||||||||
\(656\) | 32.3786 | 1.26417 | ||||||||
\(657\) | −10.5845 | −0.412939 | ||||||||
\(658\) | −1.00921 | −0.0393431 | ||||||||
\(659\) | −1.98083 | −0.0771623 | −0.0385811 | − | 0.999255i | \(-0.512284\pi\) | ||||
−0.0385811 | + | 0.999255i | \(0.512284\pi\) | |||||||
\(660\) | 2.11687 | 0.0823991 | ||||||||
\(661\) | −0.846173 | −0.0329123 | −0.0164562 | − | 0.999865i | \(-0.505238\pi\) | ||||
−0.0164562 | + | 0.999865i | \(0.505238\pi\) | |||||||
\(662\) | 29.4631 | 1.14512 | ||||||||
\(663\) | 3.38824 | 0.131588 | ||||||||
\(664\) | 10.9411 | 0.424596 | ||||||||
\(665\) | 0.565796 | 0.0219406 | ||||||||
\(666\) | −12.2767 | −0.475714 | ||||||||
\(667\) | 1.62686 | 0.0629922 | ||||||||
\(668\) | −11.9391 | −0.461939 | ||||||||
\(669\) | −1.58222 | −0.0611720 | ||||||||
\(670\) | −24.6025 | −0.950478 | ||||||||
\(671\) | −1.22096 | −0.0471346 | ||||||||
\(672\) | 1.00434 | 0.0387433 | ||||||||
\(673\) | 20.4834 | 0.789577 | 0.394789 | − | 0.918772i | \(-0.370818\pi\) | ||||
0.394789 | + | 0.918772i | \(0.370818\pi\) | |||||||
\(674\) | 19.7037 | 0.758960 | ||||||||
\(675\) | 1.96979 | 0.0758172 | ||||||||
\(676\) | 2.33074 | 0.0896437 | ||||||||
\(677\) | 7.47659 | 0.287349 | 0.143674 | − | 0.989625i | \(-0.454108\pi\) | ||||
0.143674 | + | 0.989625i | \(0.454108\pi\) | |||||||
\(678\) | −3.70257 | −0.142196 | ||||||||
\(679\) | −1.42015 | −0.0545003 | ||||||||
\(680\) | −4.05951 | −0.155675 | ||||||||
\(681\) | 26.3243 | 1.00875 | ||||||||
\(682\) | 5.32683 | 0.203975 | ||||||||
\(683\) | −43.3259 | −1.65782 | −0.828909 | − | 0.559384i | \(-0.811038\pi\) | ||||
−0.828909 | + | 0.559384i | \(0.811038\pi\) | |||||||
\(684\) | −6.10710 | −0.233511 | ||||||||
\(685\) | 3.81490 | 0.145760 | ||||||||
\(686\) | −3.61005 | −0.137832 | ||||||||
\(687\) | −12.3705 | −0.471965 | ||||||||
\(688\) | −2.43400 | −0.0927955 | ||||||||
\(689\) | 13.3889 | 0.510076 | ||||||||
\(690\) | 3.88310 | 0.147827 | ||||||||
\(691\) | 40.1250 | 1.52643 | 0.763214 | − | 0.646146i | \(-0.223620\pi\) | ||||
0.763214 | + | 0.646146i | \(0.223620\pi\) | |||||||
\(692\) | 13.2035 | 0.501921 | ||||||||
\(693\) | 0.0647212 | 0.00245856 | ||||||||
\(694\) | 50.6750 | 1.92360 | ||||||||
\(695\) | 22.7832 | 0.864216 | ||||||||
\(696\) | 1.04460 | 0.0395955 | ||||||||
\(697\) | −33.9739 | −1.28685 | ||||||||
\(698\) | −44.1832 | −1.67236 | ||||||||
\(699\) | 8.60177 | 0.325349 | ||||||||
\(700\) | 0.569501 | 0.0215251 | ||||||||
\(701\) | 1.66315 | 0.0628163 | 0.0314082 | − | 0.999507i | \(-0.490001\pi\) | ||||
0.0314082 | + | 0.999507i | \(0.490001\pi\) | |||||||
\(702\) | −2.08104 | −0.0785439 | ||||||||
\(703\) | −15.4577 | −0.582997 | ||||||||
\(704\) | 5.42150 | 0.204331 | ||||||||
\(705\) | 6.80542 | 0.256307 | ||||||||
\(706\) | 35.4502 | 1.33418 | ||||||||
\(707\) | −1.61650 | −0.0607947 | ||||||||
\(708\) | 7.82860 | 0.294217 | ||||||||
\(709\) | −18.3290 | −0.688360 | −0.344180 | − | 0.938904i | \(-0.611843\pi\) | ||||
−0.344180 | + | 0.938904i | \(0.611843\pi\) | |||||||
\(710\) | 31.5023 | 1.18226 | ||||||||
\(711\) | 11.4711 | 0.430201 | ||||||||
\(712\) | −4.42949 | −0.166002 | ||||||||
\(713\) | 5.25877 | 0.196943 | ||||||||
\(714\) | −0.874655 | −0.0327332 | ||||||||
\(715\) | 0.908242 | 0.0339663 | ||||||||
\(716\) | −39.9808 | −1.49415 | ||||||||
\(717\) | −2.22240 | −0.0829969 | ||||||||
\(718\) | 58.9369 | 2.19951 | ||||||||
\(719\) | −3.48289 | −0.129890 | −0.0649449 | − | 0.997889i | \(-0.520687\pi\) | ||||
−0.0649449 | + | 0.997889i | \(0.520687\pi\) | |||||||
\(720\) | −5.62113 | −0.209487 | ||||||||
\(721\) | 0.124046 | 0.00461970 | ||||||||
\(722\) | 25.2520 | 0.939783 | ||||||||
\(723\) | −26.3501 | −0.979970 | ||||||||
\(724\) | 13.5105 | 0.502115 | ||||||||
\(725\) | −2.98956 | −0.111030 | ||||||||
\(726\) | −22.3249 | −0.828557 | ||||||||
\(727\) | 22.9774 | 0.852185 | 0.426092 | − | 0.904680i | \(-0.359890\pi\) | ||||
0.426092 | + | 0.904680i | \(0.359890\pi\) | |||||||
\(728\) | −0.0853777 | −0.00316431 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 38.3430 | 1.41914 | ||||||||
\(731\) | 2.55393 | 0.0944603 | ||||||||
\(732\) | −5.45418 | −0.201592 | ||||||||
\(733\) | −4.39702 | −0.162407 | −0.0812037 | − | 0.996698i | \(-0.525876\pi\) | ||||
−0.0812037 | + | 0.996698i | \(0.525876\pi\) | |||||||
\(734\) | −27.6702 | −1.02132 | ||||||||
\(735\) | 12.1585 | 0.448472 | ||||||||
\(736\) | 8.67881 | 0.319905 | ||||||||
\(737\) | −3.54346 | −0.130525 | ||||||||
\(738\) | 20.8666 | 0.768110 | ||||||||
\(739\) | 15.1383 | 0.556873 | 0.278436 | − | 0.960455i | \(-0.410184\pi\) | ||||
0.278436 | + | 0.960455i | \(0.410184\pi\) | |||||||
\(740\) | 23.9349 | 0.879865 | ||||||||
\(741\) | −2.62024 | −0.0962571 | ||||||||
\(742\) | −3.45626 | −0.126883 | ||||||||
\(743\) | 4.92880 | 0.180820 | 0.0904101 | − | 0.995905i | \(-0.471182\pi\) | ||||
0.0904101 | + | 0.995905i | \(0.471182\pi\) | |||||||
\(744\) | 3.37665 | 0.123794 | ||||||||
\(745\) | 31.7503 | 1.16324 | ||||||||
\(746\) | 45.2285 | 1.65593 | ||||||||
\(747\) | −15.8964 | −0.581617 | ||||||||
\(748\) | −4.12033 | −0.150654 | ||||||||
\(749\) | 0.826785 | 0.0302101 | ||||||||
\(750\) | −25.2486 | −0.921948 | ||||||||
\(751\) | −33.0389 | −1.20561 | −0.602804 | − | 0.797890i | \(-0.705950\pi\) | ||||
−0.602804 | + | 0.797890i | \(0.705950\pi\) | |||||||
\(752\) | 12.6243 | 0.460359 | ||||||||
\(753\) | −16.9216 | −0.616658 | ||||||||
\(754\) | 3.15841 | 0.115023 | ||||||||
\(755\) | −29.5352 | −1.07490 | ||||||||
\(756\) | 0.289118 | 0.0105151 | ||||||||
\(757\) | −42.9269 | −1.56020 | −0.780102 | − | 0.625652i | \(-0.784833\pi\) | ||||
−0.780102 | + | 0.625652i | \(0.784833\pi\) | |||||||
\(758\) | 52.2278 | 1.89700 | ||||||||
\(759\) | 0.559276 | 0.0203004 | ||||||||
\(760\) | 3.13936 | 0.113877 | ||||||||
\(761\) | −28.4025 | −1.02959 | −0.514795 | − | 0.857313i | \(-0.672132\pi\) | ||||
−0.514795 | + | 0.857313i | \(0.672132\pi\) | |||||||
\(762\) | −4.42338 | −0.160242 | ||||||||
\(763\) | −0.224185 | −0.00811606 | ||||||||
\(764\) | 23.5157 | 0.850770 | ||||||||
\(765\) | 5.89808 | 0.213246 | ||||||||
\(766\) | 77.9089 | 2.81496 | ||||||||
\(767\) | 3.35885 | 0.121281 | ||||||||
\(768\) | −9.47991 | −0.342077 | ||||||||
\(769\) | 12.8874 | 0.464732 | 0.232366 | − | 0.972628i | \(-0.425353\pi\) | ||||
0.232366 | + | 0.972628i | \(0.425353\pi\) | |||||||
\(770\) | −0.234457 | −0.00844926 | ||||||||
\(771\) | 14.9316 | 0.537750 | ||||||||
\(772\) | 49.8466 | 1.79402 | ||||||||
\(773\) | 30.0515 | 1.08088 | 0.540439 | − | 0.841383i | \(-0.318258\pi\) | ||||
0.540439 | + | 0.841383i | \(0.318258\pi\) | |||||||
\(774\) | −1.56861 | −0.0563825 | ||||||||
\(775\) | −9.66368 | −0.347130 | ||||||||
\(776\) | −7.87979 | −0.282868 | ||||||||
\(777\) | 0.731786 | 0.0262527 | ||||||||
\(778\) | 1.44187 | 0.0516936 | ||||||||
\(779\) | 26.2732 | 0.941335 | ||||||||
\(780\) | 4.05723 | 0.145272 | ||||||||
\(781\) | 4.53722 | 0.162354 | ||||||||
\(782\) | −7.55817 | −0.270279 | ||||||||
\(783\) | −1.51771 | −0.0542385 | ||||||||
\(784\) | 22.5543 | 0.805511 | ||||||||
\(785\) | −25.4838 | −0.909557 | ||||||||
\(786\) | −23.1586 | −0.826039 | ||||||||
\(787\) | 46.1545 | 1.64523 | 0.822615 | − | 0.568599i | \(-0.192514\pi\) | ||||
0.822615 | + | 0.568599i | \(0.192514\pi\) | |||||||
\(788\) | 34.0660 | 1.21355 | ||||||||
\(789\) | 7.43575 | 0.264720 | ||||||||
\(790\) | −41.5550 | −1.47846 | ||||||||
\(791\) | 0.220701 | 0.00784723 | ||||||||
\(792\) | 0.359110 | 0.0127604 | ||||||||
\(793\) | −2.34011 | −0.0830998 | ||||||||
\(794\) | 36.0848 | 1.28060 | ||||||||
\(795\) | 23.3067 | 0.826604 | ||||||||
\(796\) | 45.4191 | 1.60984 | ||||||||
\(797\) | −37.0747 | −1.31325 | −0.656627 | − | 0.754215i | \(-0.728018\pi\) | ||||
−0.656627 | + | 0.754215i | \(0.728018\pi\) | |||||||
\(798\) | 0.676401 | 0.0239444 | ||||||||
\(799\) | −13.2463 | −0.468619 | ||||||||
\(800\) | −15.9485 | −0.563863 | ||||||||
\(801\) | 6.43563 | 0.227392 | ||||||||
\(802\) | −12.0501 | −0.425504 | ||||||||
\(803\) | 5.52248 | 0.194884 | ||||||||
\(804\) | −15.8291 | −0.558248 | ||||||||
\(805\) | −0.231462 | −0.00815796 | ||||||||
\(806\) | 10.2095 | 0.359614 | ||||||||
\(807\) | 3.21442 | 0.113153 | ||||||||
\(808\) | −8.96926 | −0.315537 | ||||||||
\(809\) | 28.3290 | 0.995993 | 0.497996 | − | 0.867179i | \(-0.334069\pi\) | ||||
0.497996 | + | 0.867179i | \(0.334069\pi\) | |||||||
\(810\) | −3.62257 | −0.127284 | ||||||||
\(811\) | 52.7307 | 1.85163 | 0.925813 | − | 0.377983i | \(-0.123382\pi\) | ||||
0.925813 | + | 0.377983i | \(0.123382\pi\) | |||||||
\(812\) | −0.438797 | −0.0153987 | ||||||||
\(813\) | 23.8045 | 0.834862 | ||||||||
\(814\) | 6.40543 | 0.224510 | ||||||||
\(815\) | 1.02019 | 0.0357357 | ||||||||
\(816\) | 10.9411 | 0.383015 | ||||||||
\(817\) | −1.97504 | −0.0690979 | ||||||||
\(818\) | −41.7839 | −1.46094 | ||||||||
\(819\) | 0.124046 | 0.00433451 | ||||||||
\(820\) | −40.6818 | −1.42067 | ||||||||
\(821\) | −0.760391 | −0.0265378 | −0.0132689 | − | 0.999912i | \(-0.504224\pi\) | ||||
−0.0132689 | + | 0.999912i | \(0.504224\pi\) | |||||||
\(822\) | 4.56065 | 0.159071 | ||||||||
\(823\) | −17.7904 | −0.620133 | −0.310067 | − | 0.950715i | \(-0.600351\pi\) | ||||
−0.310067 | + | 0.950715i | \(0.600351\pi\) | |||||||
\(824\) | 0.688276 | 0.0239772 | ||||||||
\(825\) | −1.02774 | −0.0357814 | ||||||||
\(826\) | −0.867068 | −0.0301692 | ||||||||
\(827\) | 19.2396 | 0.669025 | 0.334512 | − | 0.942391i | \(-0.391428\pi\) | ||||
0.334512 | + | 0.942391i | \(0.391428\pi\) | |||||||
\(828\) | 2.49836 | 0.0868239 | ||||||||
\(829\) | −0.830396 | −0.0288408 | −0.0144204 | − | 0.999896i | \(-0.504590\pi\) | ||||
−0.0144204 | + | 0.999896i | \(0.504590\pi\) | |||||||
\(830\) | 57.5858 | 1.99883 | ||||||||
\(831\) | −11.1743 | −0.387631 | ||||||||
\(832\) | 10.3909 | 0.360241 | ||||||||
\(833\) | −23.6656 | −0.819963 | ||||||||
\(834\) | 27.2370 | 0.943140 | ||||||||
\(835\) | −8.91694 | −0.308583 | ||||||||
\(836\) | 3.18640 | 0.110204 | ||||||||
\(837\) | −4.90595 | −0.169574 | ||||||||
\(838\) | 8.35109 | 0.288484 | ||||||||
\(839\) | 31.4278 | 1.08501 | 0.542504 | − | 0.840053i | \(-0.317476\pi\) | ||||
0.542504 | + | 0.840053i | \(0.317476\pi\) | |||||||
\(840\) | −0.148621 | −0.00512792 | ||||||||
\(841\) | −26.6966 | −0.920571 | ||||||||
\(842\) | −51.3729 | −1.77043 | ||||||||
\(843\) | 3.08517 | 0.106259 | ||||||||
\(844\) | −52.3552 | −1.80214 | ||||||||
\(845\) | 1.74075 | 0.0598836 | ||||||||
\(846\) | 8.13579 | 0.279714 | ||||||||
\(847\) | 1.33073 | 0.0457246 | ||||||||
\(848\) | 43.2346 | 1.48468 | ||||||||
\(849\) | 24.0540 | 0.825532 | ||||||||
\(850\) | 13.8891 | 0.476393 | ||||||||
\(851\) | 6.32359 | 0.216770 | ||||||||
\(852\) | 20.2683 | 0.694381 | ||||||||
\(853\) | −51.9791 | −1.77973 | −0.889864 | − | 0.456225i | \(-0.849201\pi\) | ||||
−0.889864 | + | 0.456225i | \(0.849201\pi\) | |||||||
\(854\) | 0.604086 | 0.0206714 | ||||||||
\(855\) | −4.56119 | −0.155989 | ||||||||
\(856\) | 4.58747 | 0.156796 | ||||||||
\(857\) | 40.0693 | 1.36874 | 0.684371 | − | 0.729134i | \(-0.260077\pi\) | ||||
0.684371 | + | 0.729134i | \(0.260077\pi\) | |||||||
\(858\) | 1.08579 | 0.0370683 | ||||||||
\(859\) | −45.7856 | −1.56218 | −0.781092 | − | 0.624416i | \(-0.785337\pi\) | ||||
−0.781092 | + | 0.624416i | \(0.785337\pi\) | |||||||
\(860\) | 3.05818 | 0.104283 | ||||||||
\(861\) | −1.24381 | −0.0423888 | ||||||||
\(862\) | 8.37731 | 0.285332 | ||||||||
\(863\) | 44.4216 | 1.51213 | 0.756064 | − | 0.654498i | \(-0.227120\pi\) | ||||
0.756064 | + | 0.654498i | \(0.227120\pi\) | |||||||
\(864\) | −8.09653 | −0.275450 | ||||||||
\(865\) | 9.86124 | 0.335292 | ||||||||
\(866\) | −13.2942 | −0.451757 | ||||||||
\(867\) | 5.51982 | 0.187463 | ||||||||
\(868\) | −1.41840 | −0.0481436 | ||||||||
\(869\) | −5.98509 | −0.203030 | ||||||||
\(870\) | 5.49801 | 0.186400 | ||||||||
\(871\) | −6.79145 | −0.230119 | ||||||||
\(872\) | −1.24391 | −0.0421240 | ||||||||
\(873\) | 11.4486 | 0.387476 | ||||||||
\(874\) | 5.84499 | 0.197710 | ||||||||
\(875\) | 1.50500 | 0.0508784 | ||||||||
\(876\) | 24.6696 | 0.833509 | ||||||||
\(877\) | 42.7401 | 1.44323 | 0.721615 | − | 0.692295i | \(-0.243400\pi\) | ||||
0.721615 | + | 0.692295i | \(0.243400\pi\) | |||||||
\(878\) | 65.0967 | 2.19691 | ||||||||
\(879\) | −20.9087 | −0.705233 | ||||||||
\(880\) | 2.93284 | 0.0988660 | ||||||||
\(881\) | −37.5588 | −1.26539 | −0.632694 | − | 0.774402i | \(-0.718051\pi\) | ||||
−0.632694 | + | 0.774402i | \(0.718051\pi\) | |||||||
\(882\) | 14.5353 | 0.489428 | ||||||||
\(883\) | −56.5648 | −1.90356 | −0.951778 | − | 0.306786i | \(-0.900746\pi\) | ||||
−0.951778 | + | 0.306786i | \(0.900746\pi\) | |||||||
\(884\) | −7.89710 | −0.265608 | ||||||||
\(885\) | 5.84692 | 0.196542 | ||||||||
\(886\) | −7.84107 | −0.263426 | ||||||||
\(887\) | −22.9713 | −0.771301 | −0.385651 | − | 0.922645i | \(-0.626023\pi\) | ||||
−0.385651 | + | 0.922645i | \(0.626023\pi\) | |||||||
\(888\) | 4.06036 | 0.136257 | ||||||||
\(889\) | 0.263667 | 0.00884310 | ||||||||
\(890\) | −23.3136 | −0.781473 | ||||||||
\(891\) | −0.521753 | −0.0174794 | ||||||||
\(892\) | 3.68773 | 0.123474 | ||||||||
\(893\) | 10.2438 | 0.342795 | ||||||||
\(894\) | 37.9570 | 1.26947 | ||||||||
\(895\) | −29.8603 | −0.998120 | ||||||||
\(896\) | −0.673682 | −0.0225061 | ||||||||
\(897\) | 1.07192 | 0.0357903 | ||||||||
\(898\) | 55.3023 | 1.84546 | ||||||||
\(899\) | 7.44580 | 0.248331 | ||||||||
\(900\) | −4.59106 | −0.153035 | ||||||||
\(901\) | −45.3648 | −1.51132 | ||||||||
\(902\) | −10.8872 | −0.362505 | ||||||||
\(903\) | 0.0935009 | 0.00311151 | ||||||||
\(904\) | 1.22457 | 0.0407288 | ||||||||
\(905\) | 10.0906 | 0.335422 | ||||||||
\(906\) | −35.3089 | −1.17306 | ||||||||
\(907\) | 51.8600 | 1.72198 | 0.860991 | − | 0.508620i | \(-0.169844\pi\) | ||||
0.860991 | + | 0.508620i | \(0.169844\pi\) | |||||||
\(908\) | −61.3550 | −2.03614 | ||||||||
\(909\) | 13.0315 | 0.432227 | ||||||||
\(910\) | −0.449365 | −0.0148963 | ||||||||
\(911\) | −8.44497 | −0.279794 | −0.139897 | − | 0.990166i | \(-0.544677\pi\) | ||||
−0.139897 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(912\) | −8.46114 | −0.280176 | ||||||||
\(913\) | 8.29397 | 0.274490 | ||||||||
\(914\) | 56.5197 | 1.86950 | ||||||||
\(915\) | −4.07355 | −0.134667 | ||||||||
\(916\) | 28.8325 | 0.952651 | ||||||||
\(917\) | 1.38042 | 0.0455856 | ||||||||
\(918\) | 7.05107 | 0.232720 | ||||||||
\(919\) | −7.14499 | −0.235691 | −0.117846 | − | 0.993032i | \(-0.537599\pi\) | ||||
−0.117846 | + | 0.993032i | \(0.537599\pi\) | |||||||
\(920\) | −1.28428 | −0.0423415 | ||||||||
\(921\) | 29.4633 | 0.970849 | ||||||||
\(922\) | −78.8122 | −2.59554 | ||||||||
\(923\) | 8.69610 | 0.286236 | ||||||||
\(924\) | −0.150848 | −0.00496254 | ||||||||
\(925\) | −11.6204 | −0.382077 | ||||||||
\(926\) | −38.4329 | −1.26298 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 12.2882 | 0.403379 | ||||||||
\(929\) | 49.7567 | 1.63246 | 0.816232 | − | 0.577724i | \(-0.196059\pi\) | ||||
0.816232 | + | 0.577724i | \(0.196059\pi\) | |||||||
\(930\) | 17.7722 | 0.582772 | ||||||||
\(931\) | 18.3014 | 0.599804 | ||||||||
\(932\) | −20.0485 | −0.656709 | ||||||||
\(933\) | 8.55254 | 0.279998 | ||||||||
\(934\) | 43.7120 | 1.43030 | ||||||||
\(935\) | −3.07734 | −0.100640 | ||||||||
\(936\) | 0.688276 | 0.0224970 | ||||||||
\(937\) | −56.9541 | −1.86061 | −0.930305 | − | 0.366786i | \(-0.880458\pi\) | ||||
−0.930305 | + | 0.366786i | \(0.880458\pi\) | |||||||
\(938\) | 1.75317 | 0.0572431 | ||||||||
\(939\) | −17.0478 | −0.556334 | ||||||||
\(940\) | −15.8616 | −0.517350 | ||||||||
\(941\) | 47.9269 | 1.56237 | 0.781186 | − | 0.624299i | \(-0.214615\pi\) | ||||
0.781186 | + | 0.624299i | \(0.214615\pi\) | |||||||
\(942\) | −30.4655 | −0.992621 | ||||||||
\(943\) | −10.7481 | −0.350007 | ||||||||
\(944\) | 10.8462 | 0.353014 | ||||||||
\(945\) | 0.215933 | 0.00702429 | ||||||||
\(946\) | 0.818426 | 0.0266093 | ||||||||
\(947\) | −28.2081 | −0.916641 | −0.458321 | − | 0.888787i | \(-0.651549\pi\) | ||||
−0.458321 | + | 0.888787i | \(0.651549\pi\) | |||||||
\(948\) | −26.7362 | −0.868350 | ||||||||
\(949\) | 10.5845 | 0.343586 | ||||||||
\(950\) | −10.7409 | −0.348482 | ||||||||
\(951\) | 20.9238 | 0.678499 | ||||||||
\(952\) | 0.289280 | 0.00937562 | ||||||||
\(953\) | 46.5837 | 1.50899 | 0.754497 | − | 0.656304i | \(-0.227881\pi\) | ||||
0.754497 | + | 0.656304i | \(0.227881\pi\) | |||||||
\(954\) | 27.8628 | 0.902093 | ||||||||
\(955\) | 17.5631 | 0.568330 | ||||||||
\(956\) | 5.17982 | 0.167527 | ||||||||
\(957\) | 0.791869 | 0.0255975 | ||||||||
\(958\) | −35.2237 | −1.13803 | ||||||||
\(959\) | −0.271849 | −0.00877847 | ||||||||
\(960\) | 18.0880 | 0.583789 | ||||||||
\(961\) | −6.93165 | −0.223602 | ||||||||
\(962\) | 12.2767 | 0.395818 | ||||||||
\(963\) | −6.66516 | −0.214782 | ||||||||
\(964\) | 61.4151 | 1.97805 | ||||||||
\(965\) | 37.2288 | 1.19844 | ||||||||
\(966\) | −0.276709 | −0.00890298 | ||||||||
\(967\) | 27.8886 | 0.896838 | 0.448419 | − | 0.893823i | \(-0.351987\pi\) | ||||
0.448419 | + | 0.893823i | \(0.351987\pi\) | |||||||
\(968\) | 7.38367 | 0.237320 | ||||||||
\(969\) | 8.87802 | 0.285203 | ||||||||
\(970\) | −41.4734 | −1.33163 | ||||||||
\(971\) | −49.7229 | −1.59569 | −0.797843 | − | 0.602866i | \(-0.794025\pi\) | ||||
−0.797843 | + | 0.602866i | \(0.794025\pi\) | |||||||
\(972\) | −2.33074 | −0.0747584 | ||||||||
\(973\) | −1.62353 | −0.0520479 | ||||||||
\(974\) | 14.8241 | 0.474994 | ||||||||
\(975\) | −1.96979 | −0.0630837 | ||||||||
\(976\) | −7.55655 | −0.241879 | ||||||||
\(977\) | 33.0058 | 1.05595 | 0.527974 | − | 0.849260i | \(-0.322952\pi\) | ||||
0.527974 | + | 0.849260i | \(0.322952\pi\) | |||||||
\(978\) | 1.21962 | 0.0389992 | ||||||||
\(979\) | −3.35781 | −0.107316 | ||||||||
\(980\) | −28.3382 | −0.905230 | ||||||||
\(981\) | 1.80728 | 0.0577020 | ||||||||
\(982\) | −30.7696 | −0.981897 | ||||||||
\(983\) | 34.7938 | 1.10975 | 0.554876 | − | 0.831933i | \(-0.312766\pi\) | ||||
0.554876 | + | 0.831933i | \(0.312766\pi\) | |||||||
\(984\) | −6.90134 | −0.220007 | ||||||||
\(985\) | 25.4428 | 0.810675 | ||||||||
\(986\) | −10.7015 | −0.340804 | ||||||||
\(987\) | −0.484954 | −0.0154363 | ||||||||
\(988\) | 6.10710 | 0.194293 | ||||||||
\(989\) | 0.807970 | 0.0256919 | ||||||||
\(990\) | 1.89009 | 0.0600710 | ||||||||
\(991\) | 44.6099 | 1.41708 | 0.708540 | − | 0.705671i | \(-0.249354\pi\) | ||||
0.708540 | + | 0.705671i | \(0.249354\pi\) | |||||||
\(992\) | 39.7212 | 1.26115 | ||||||||
\(993\) | 14.1579 | 0.449286 | ||||||||
\(994\) | −2.24485 | −0.0712023 | ||||||||
\(995\) | 33.9220 | 1.07540 | ||||||||
\(996\) | 37.0502 | 1.17398 | ||||||||
\(997\) | 32.1140 | 1.01706 | 0.508531 | − | 0.861044i | \(-0.330189\pi\) | ||||
0.508531 | + | 0.861044i | \(0.330189\pi\) | |||||||
\(998\) | −71.1444 | −2.25204 | ||||||||
\(999\) | −5.89933 | −0.186646 |
(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.i.1.6 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.i.1.6 | ✓ | 25 | 1.1 | even | 1 | trivial |