Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2556185065\) |
Analytic rank: | \(1\) |
Dimension: | \(142\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65232 | −1.87547 | −0.937737 | − | 0.347346i | \(-0.887083\pi\) | ||||
−0.937737 | + | 0.347346i | \(0.887083\pi\) | |||||||
\(3\) | 2.65488 | 1.53280 | 0.766398 | − | 0.642366i | \(-0.222047\pi\) | ||||
0.766398 | + | 0.642366i | \(0.222047\pi\) | |||||||
\(4\) | 5.03481 | 2.51740 | ||||||||
\(5\) | −0.675897 | −0.302270 | −0.151135 | − | 0.988513i | \(-0.548293\pi\) | ||||
−0.151135 | + | 0.988513i | \(0.548293\pi\) | |||||||
\(6\) | −7.04159 | −2.87472 | ||||||||
\(7\) | −2.02772 | −0.766406 | −0.383203 | − | 0.923664i | \(-0.625179\pi\) | ||||
−0.383203 | + | 0.923664i | \(0.625179\pi\) | |||||||
\(8\) | −8.04928 | −2.84585 | ||||||||
\(9\) | 4.04839 | 1.34946 | ||||||||
\(10\) | 1.79269 | 0.566900 | ||||||||
\(11\) | 4.17036 | 1.25741 | 0.628705 | − | 0.777644i | \(-0.283585\pi\) | ||||
0.628705 | + | 0.777644i | \(0.283585\pi\) | |||||||
\(12\) | 13.3668 | 3.85866 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 5.37816 | 1.43737 | ||||||||
\(15\) | −1.79442 | −0.463318 | ||||||||
\(16\) | 11.2797 | 2.81991 | ||||||||
\(17\) | −7.58358 | −1.83929 | −0.919644 | − | 0.392753i | \(-0.871523\pi\) | ||||
−0.919644 | + | 0.392753i | \(0.871523\pi\) | |||||||
\(18\) | −10.7376 | −2.53088 | ||||||||
\(19\) | 6.75596 | 1.54992 | 0.774962 | − | 0.632008i | \(-0.217769\pi\) | ||||
0.774962 | + | 0.632008i | \(0.217769\pi\) | |||||||
\(20\) | −3.40301 | −0.760936 | ||||||||
\(21\) | −5.38335 | −1.17474 | ||||||||
\(22\) | −11.0611 | −2.35824 | ||||||||
\(23\) | −6.60775 | −1.37781 | −0.688906 | − | 0.724851i | \(-0.741909\pi\) | ||||
−0.688906 | + | 0.724851i | \(0.741909\pi\) | |||||||
\(24\) | −21.3699 | −4.36211 | ||||||||
\(25\) | −4.54316 | −0.908633 | ||||||||
\(26\) | −2.65232 | −0.520163 | ||||||||
\(27\) | 2.78334 | 0.535655 | ||||||||
\(28\) | −10.2092 | −1.92935 | ||||||||
\(29\) | 1.94163 | 0.360552 | 0.180276 | − | 0.983616i | \(-0.442301\pi\) | ||||
0.180276 | + | 0.983616i | \(0.442301\pi\) | |||||||
\(30\) | 4.75939 | 0.868941 | ||||||||
\(31\) | 4.58793 | 0.824016 | 0.412008 | − | 0.911180i | \(-0.364828\pi\) | ||||
0.412008 | + | 0.911180i | \(0.364828\pi\) | |||||||
\(32\) | −13.8187 | −2.44283 | ||||||||
\(33\) | 11.0718 | 1.92735 | ||||||||
\(34\) | 20.1141 | 3.44954 | ||||||||
\(35\) | 1.37053 | 0.231662 | ||||||||
\(36\) | 20.3828 | 3.39714 | ||||||||
\(37\) | −5.32619 | −0.875621 | −0.437810 | − | 0.899067i | \(-0.644246\pi\) | ||||
−0.437810 | + | 0.899067i | \(0.644246\pi\) | |||||||
\(38\) | −17.9190 | −2.90684 | ||||||||
\(39\) | 2.65488 | 0.425121 | ||||||||
\(40\) | 5.44048 | 0.860215 | ||||||||
\(41\) | −3.19215 | −0.498529 | −0.249265 | − | 0.968435i | \(-0.580189\pi\) | ||||
−0.249265 | + | 0.968435i | \(0.580189\pi\) | |||||||
\(42\) | 14.2784 | 2.20320 | ||||||||
\(43\) | −1.32584 | −0.202188 | −0.101094 | − | 0.994877i | \(-0.532234\pi\) | ||||
−0.101094 | + | 0.994877i | \(0.532234\pi\) | |||||||
\(44\) | 20.9970 | 3.16541 | ||||||||
\(45\) | −2.73629 | −0.407902 | ||||||||
\(46\) | 17.5259 | 2.58405 | ||||||||
\(47\) | 5.32709 | 0.777036 | 0.388518 | − | 0.921441i | \(-0.372987\pi\) | ||||
0.388518 | + | 0.921441i | \(0.372987\pi\) | |||||||
\(48\) | 29.9461 | 4.32235 | ||||||||
\(49\) | −2.88835 | −0.412622 | ||||||||
\(50\) | 12.0499 | 1.70412 | ||||||||
\(51\) | −20.1335 | −2.81925 | ||||||||
\(52\) | 5.03481 | 0.698202 | ||||||||
\(53\) | 0.0678960 | 0.00932623 | 0.00466311 | − | 0.999989i | \(-0.498516\pi\) | ||||
0.00466311 | + | 0.999989i | \(0.498516\pi\) | |||||||
\(54\) | −7.38232 | −1.00461 | ||||||||
\(55\) | −2.81873 | −0.380078 | ||||||||
\(56\) | 16.3217 | 2.18108 | ||||||||
\(57\) | 17.9363 | 2.37572 | ||||||||
\(58\) | −5.14983 | −0.676206 | ||||||||
\(59\) | 6.08981 | 0.792826 | 0.396413 | − | 0.918072i | \(-0.370255\pi\) | ||||
0.396413 | + | 0.918072i | \(0.370255\pi\) | |||||||
\(60\) | −9.03458 | −1.16636 | ||||||||
\(61\) | 3.16482 | 0.405214 | 0.202607 | − | 0.979260i | \(-0.435059\pi\) | ||||
0.202607 | + | 0.979260i | \(0.435059\pi\) | |||||||
\(62\) | −12.1687 | −1.54542 | ||||||||
\(63\) | −8.20899 | −1.03424 | ||||||||
\(64\) | 14.0923 | 1.76154 | ||||||||
\(65\) | −0.675897 | −0.0838346 | ||||||||
\(66\) | −29.3660 | −3.61470 | ||||||||
\(67\) | 5.30065 | 0.647577 | 0.323789 | − | 0.946129i | \(-0.395043\pi\) | ||||
0.323789 | + | 0.946129i | \(0.395043\pi\) | |||||||
\(68\) | −38.1819 | −4.63023 | ||||||||
\(69\) | −17.5428 | −2.11190 | ||||||||
\(70\) | −3.63508 | −0.434475 | ||||||||
\(71\) | −10.6088 | −1.25904 | −0.629519 | − | 0.776985i | \(-0.716748\pi\) | ||||
−0.629519 | + | 0.776985i | \(0.716748\pi\) | |||||||
\(72\) | −32.5866 | −3.84037 | ||||||||
\(73\) | 3.17585 | 0.371705 | 0.185852 | − | 0.982578i | \(-0.440495\pi\) | ||||
0.185852 | + | 0.982578i | \(0.440495\pi\) | |||||||
\(74\) | 14.1268 | 1.64220 | ||||||||
\(75\) | −12.0616 | −1.39275 | ||||||||
\(76\) | 34.0149 | 3.90178 | ||||||||
\(77\) | −8.45632 | −0.963687 | ||||||||
\(78\) | −7.04159 | −0.797303 | ||||||||
\(79\) | 2.37979 | 0.267747 | 0.133873 | − | 0.990998i | \(-0.457258\pi\) | ||||
0.133873 | + | 0.990998i | \(0.457258\pi\) | |||||||
\(80\) | −7.62388 | −0.852376 | ||||||||
\(81\) | −4.75572 | −0.528413 | ||||||||
\(82\) | 8.46660 | 0.934979 | ||||||||
\(83\) | −17.5188 | −1.92294 | −0.961471 | − | 0.274905i | \(-0.911354\pi\) | ||||
−0.961471 | + | 0.274905i | \(0.911354\pi\) | |||||||
\(84\) | −27.1041 | −2.95730 | ||||||||
\(85\) | 5.12572 | 0.555962 | ||||||||
\(86\) | 3.51655 | 0.379199 | ||||||||
\(87\) | 5.15480 | 0.552653 | ||||||||
\(88\) | −33.5684 | −3.57840 | ||||||||
\(89\) | −15.0412 | −1.59436 | −0.797182 | − | 0.603739i | \(-0.793677\pi\) | ||||
−0.797182 | + | 0.603739i | \(0.793677\pi\) | |||||||
\(90\) | 7.25752 | 0.765010 | ||||||||
\(91\) | −2.02772 | −0.212563 | ||||||||
\(92\) | −33.2687 | −3.46851 | ||||||||
\(93\) | 12.1804 | 1.26305 | ||||||||
\(94\) | −14.1291 | −1.45731 | ||||||||
\(95\) | −4.56633 | −0.468496 | ||||||||
\(96\) | −36.6870 | −3.74435 | ||||||||
\(97\) | −6.42427 | −0.652286 | −0.326143 | − | 0.945320i | \(-0.605749\pi\) | ||||
−0.326143 | + | 0.945320i | \(0.605749\pi\) | |||||||
\(98\) | 7.66084 | 0.773862 | ||||||||
\(99\) | 16.8832 | 1.69683 | ||||||||
\(100\) | −22.8739 | −2.28739 | ||||||||
\(101\) | 1.06135 | 0.105608 | 0.0528040 | − | 0.998605i | \(-0.483184\pi\) | ||||
0.0528040 | + | 0.998605i | \(0.483184\pi\) | |||||||
\(102\) | 53.4005 | 5.28744 | ||||||||
\(103\) | −7.78643 | −0.767220 | −0.383610 | − | 0.923495i | \(-0.625319\pi\) | ||||
−0.383610 | + | 0.923495i | \(0.625319\pi\) | |||||||
\(104\) | −8.04928 | −0.789297 | ||||||||
\(105\) | 3.63859 | 0.355090 | ||||||||
\(106\) | −0.180082 | −0.0174911 | ||||||||
\(107\) | 16.3875 | 1.58424 | 0.792118 | − | 0.610368i | \(-0.208979\pi\) | ||||
0.792118 | + | 0.610368i | \(0.208979\pi\) | |||||||
\(108\) | 14.0136 | 1.34846 | ||||||||
\(109\) | 15.2001 | 1.45590 | 0.727952 | − | 0.685628i | \(-0.240472\pi\) | ||||
0.727952 | + | 0.685628i | \(0.240472\pi\) | |||||||
\(110\) | 7.47618 | 0.712826 | ||||||||
\(111\) | −14.1404 | −1.34215 | ||||||||
\(112\) | −22.8720 | −2.16120 | ||||||||
\(113\) | −17.4658 | −1.64304 | −0.821522 | − | 0.570176i | \(-0.806875\pi\) | ||||
−0.821522 | + | 0.570176i | \(0.806875\pi\) | |||||||
\(114\) | −47.5727 | −4.45559 | ||||||||
\(115\) | 4.46616 | 0.416471 | ||||||||
\(116\) | 9.77574 | 0.907655 | ||||||||
\(117\) | 4.04839 | 0.374274 | ||||||||
\(118\) | −16.1521 | −1.48693 | ||||||||
\(119\) | 15.3774 | 1.40964 | ||||||||
\(120\) | 14.4438 | 1.31853 | ||||||||
\(121\) | 6.39191 | 0.581082 | ||||||||
\(122\) | −8.39412 | −0.759968 | ||||||||
\(123\) | −8.47476 | −0.764144 | ||||||||
\(124\) | 23.0993 | 2.07438 | ||||||||
\(125\) | 6.45019 | 0.576923 | ||||||||
\(126\) | 21.7729 | 1.93968 | ||||||||
\(127\) | −18.8641 | −1.67392 | −0.836959 | − | 0.547265i | \(-0.815669\pi\) | ||||
−0.836959 | + | 0.547265i | \(0.815669\pi\) | |||||||
\(128\) | −9.73998 | −0.860901 | ||||||||
\(129\) | −3.51994 | −0.309913 | ||||||||
\(130\) | 1.79269 | 0.157230 | ||||||||
\(131\) | −7.52297 | −0.657285 | −0.328643 | − | 0.944454i | \(-0.606591\pi\) | ||||
−0.328643 | + | 0.944454i | \(0.606591\pi\) | |||||||
\(132\) | 55.7444 | 4.85193 | ||||||||
\(133\) | −13.6992 | −1.18787 | ||||||||
\(134\) | −14.0590 | −1.21451 | ||||||||
\(135\) | −1.88125 | −0.161912 | ||||||||
\(136\) | 61.0423 | 5.23434 | ||||||||
\(137\) | −4.44277 | −0.379572 | −0.189786 | − | 0.981826i | \(-0.560779\pi\) | ||||
−0.189786 | + | 0.981826i | \(0.560779\pi\) | |||||||
\(138\) | 46.5291 | 3.96082 | ||||||||
\(139\) | 10.7970 | 0.915793 | 0.457897 | − | 0.889006i | \(-0.348603\pi\) | ||||
0.457897 | + | 0.889006i | \(0.348603\pi\) | |||||||
\(140\) | 6.90034 | 0.583186 | ||||||||
\(141\) | 14.1428 | 1.19104 | ||||||||
\(142\) | 28.1380 | 2.36129 | ||||||||
\(143\) | 4.17036 | 0.348743 | ||||||||
\(144\) | 45.6644 | 3.80537 | ||||||||
\(145\) | −1.31234 | −0.108984 | ||||||||
\(146\) | −8.42336 | −0.697122 | ||||||||
\(147\) | −7.66823 | −0.632465 | ||||||||
\(148\) | −26.8164 | −2.20429 | ||||||||
\(149\) | 11.2924 | 0.925111 | 0.462556 | − | 0.886590i | \(-0.346933\pi\) | ||||
0.462556 | + | 0.886590i | \(0.346933\pi\) | |||||||
\(150\) | 31.9911 | 2.61206 | ||||||||
\(151\) | −17.7733 | −1.44637 | −0.723186 | − | 0.690654i | \(-0.757323\pi\) | ||||
−0.723186 | + | 0.690654i | \(0.757323\pi\) | |||||||
\(152\) | −54.3806 | −4.41085 | ||||||||
\(153\) | −30.7013 | −2.48205 | ||||||||
\(154\) | 22.4289 | 1.80737 | ||||||||
\(155\) | −3.10096 | −0.249075 | ||||||||
\(156\) | 13.3668 | 1.07020 | ||||||||
\(157\) | −7.20266 | −0.574835 | −0.287417 | − | 0.957805i | \(-0.592797\pi\) | ||||
−0.287417 | + | 0.957805i | \(0.592797\pi\) | |||||||
\(158\) | −6.31196 | −0.502152 | ||||||||
\(159\) | 0.180256 | 0.0142952 | ||||||||
\(160\) | 9.34002 | 0.738393 | ||||||||
\(161\) | 13.3987 | 1.05596 | ||||||||
\(162\) | 12.6137 | 0.991026 | ||||||||
\(163\) | 3.00219 | 0.235149 | 0.117575 | − | 0.993064i | \(-0.462488\pi\) | ||||
0.117575 | + | 0.993064i | \(0.462488\pi\) | |||||||
\(164\) | −16.0718 | −1.25500 | ||||||||
\(165\) | −7.48340 | −0.582582 | ||||||||
\(166\) | 46.4656 | 3.60643 | ||||||||
\(167\) | 18.2577 | 1.41283 | 0.706413 | − | 0.707800i | \(-0.250312\pi\) | ||||
0.706413 | + | 0.707800i | \(0.250312\pi\) | |||||||
\(168\) | 43.3321 | 3.34314 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −13.5950 | −1.04269 | ||||||||
\(171\) | 27.3507 | 2.09156 | ||||||||
\(172\) | −6.67533 | −0.508989 | ||||||||
\(173\) | 19.5427 | 1.48581 | 0.742903 | − | 0.669399i | \(-0.233448\pi\) | ||||
0.742903 | + | 0.669399i | \(0.233448\pi\) | |||||||
\(174\) | −13.6722 | −1.03649 | ||||||||
\(175\) | 9.21226 | 0.696382 | ||||||||
\(176\) | 47.0402 | 3.54579 | ||||||||
\(177\) | 16.1677 | 1.21524 | ||||||||
\(178\) | 39.8941 | 2.99019 | ||||||||
\(179\) | −16.0057 | −1.19632 | −0.598161 | − | 0.801376i | \(-0.704102\pi\) | ||||
−0.598161 | + | 0.801376i | \(0.704102\pi\) | |||||||
\(180\) | −13.7767 | −1.02685 | ||||||||
\(181\) | −5.70087 | −0.423742 | −0.211871 | − | 0.977298i | \(-0.567956\pi\) | ||||
−0.211871 | + | 0.977298i | \(0.567956\pi\) | |||||||
\(182\) | 5.37816 | 0.398656 | ||||||||
\(183\) | 8.40222 | 0.621110 | ||||||||
\(184\) | 53.1876 | 3.92104 | ||||||||
\(185\) | 3.59996 | 0.264674 | ||||||||
\(186\) | −32.3063 | −2.36881 | ||||||||
\(187\) | −31.6263 | −2.31274 | ||||||||
\(188\) | 26.8209 | 1.95611 | ||||||||
\(189\) | −5.64384 | −0.410529 | ||||||||
\(190\) | 12.1114 | 0.878651 | ||||||||
\(191\) | −12.7839 | −0.925013 | −0.462506 | − | 0.886616i | \(-0.653050\pi\) | ||||
−0.462506 | + | 0.886616i | \(0.653050\pi\) | |||||||
\(192\) | 37.4135 | 2.70008 | ||||||||
\(193\) | −4.09396 | −0.294690 | −0.147345 | − | 0.989085i | \(-0.547073\pi\) | ||||
−0.147345 | + | 0.989085i | \(0.547073\pi\) | |||||||
\(194\) | 17.0392 | 1.22334 | ||||||||
\(195\) | −1.79442 | −0.128501 | ||||||||
\(196\) | −14.5423 | −1.03874 | ||||||||
\(197\) | −5.62001 | −0.400409 | −0.200205 | − | 0.979754i | \(-0.564161\pi\) | ||||
−0.200205 | + | 0.979754i | \(0.564161\pi\) | |||||||
\(198\) | −44.7798 | −3.18236 | ||||||||
\(199\) | 2.91254 | 0.206464 | 0.103232 | − | 0.994657i | \(-0.467082\pi\) | ||||
0.103232 | + | 0.994657i | \(0.467082\pi\) | |||||||
\(200\) | 36.5692 | 2.58583 | ||||||||
\(201\) | 14.0726 | 0.992603 | ||||||||
\(202\) | −2.81503 | −0.198065 | ||||||||
\(203\) | −3.93708 | −0.276329 | ||||||||
\(204\) | −101.368 | −7.09720 | ||||||||
\(205\) | 2.15756 | 0.150691 | ||||||||
\(206\) | 20.6521 | 1.43890 | ||||||||
\(207\) | −26.7507 | −1.85930 | ||||||||
\(208\) | 11.2797 | 0.782103 | ||||||||
\(209\) | 28.1748 | 1.94889 | ||||||||
\(210\) | −9.65070 | −0.665962 | ||||||||
\(211\) | 9.23335 | 0.635650 | 0.317825 | − | 0.948149i | \(-0.397048\pi\) | ||||
0.317825 | + | 0.948149i | \(0.397048\pi\) | |||||||
\(212\) | 0.341843 | 0.0234779 | ||||||||
\(213\) | −28.1652 | −1.92985 | ||||||||
\(214\) | −43.4648 | −2.97119 | ||||||||
\(215\) | 0.896129 | 0.0611155 | ||||||||
\(216\) | −22.4039 | −1.52439 | ||||||||
\(217\) | −9.30303 | −0.631531 | ||||||||
\(218\) | −40.3155 | −2.73051 | ||||||||
\(219\) | 8.43149 | 0.569747 | ||||||||
\(220\) | −14.1918 | −0.956809 | ||||||||
\(221\) | −7.58358 | −0.510127 | ||||||||
\(222\) | 37.5049 | 2.51716 | ||||||||
\(223\) | 23.3764 | 1.56540 | 0.782700 | − | 0.622399i | \(-0.213842\pi\) | ||||
0.782700 | + | 0.622399i | \(0.213842\pi\) | |||||||
\(224\) | 28.0205 | 1.87220 | ||||||||
\(225\) | −18.3925 | −1.22617 | ||||||||
\(226\) | 46.3249 | 3.08149 | ||||||||
\(227\) | −8.21570 | −0.545295 | −0.272647 | − | 0.962114i | \(-0.587899\pi\) | ||||
−0.272647 | + | 0.962114i | \(0.587899\pi\) | |||||||
\(228\) | 90.3056 | 5.98063 | ||||||||
\(229\) | 8.37014 | 0.553114 | 0.276557 | − | 0.960997i | \(-0.410806\pi\) | ||||
0.276557 | + | 0.960997i | \(0.410806\pi\) | |||||||
\(230\) | −11.8457 | −0.781081 | ||||||||
\(231\) | −22.4505 | −1.47714 | ||||||||
\(232\) | −15.6287 | −1.02608 | ||||||||
\(233\) | −3.23985 | −0.212250 | −0.106125 | − | 0.994353i | \(-0.533844\pi\) | ||||
−0.106125 | + | 0.994353i | \(0.533844\pi\) | |||||||
\(234\) | −10.7376 | −0.701940 | ||||||||
\(235\) | −3.60056 | −0.234875 | ||||||||
\(236\) | 30.6610 | 1.99586 | ||||||||
\(237\) | 6.31805 | 0.410401 | ||||||||
\(238\) | −40.7857 | −2.64375 | ||||||||
\(239\) | −19.1651 | −1.23969 | −0.619844 | − | 0.784725i | \(-0.712804\pi\) | ||||
−0.619844 | + | 0.784725i | \(0.712804\pi\) | |||||||
\(240\) | −20.2405 | −1.30652 | ||||||||
\(241\) | −12.3213 | −0.793683 | −0.396842 | − | 0.917887i | \(-0.629894\pi\) | ||||
−0.396842 | + | 0.917887i | \(0.629894\pi\) | |||||||
\(242\) | −16.9534 | −1.08980 | ||||||||
\(243\) | −20.9759 | −1.34560 | ||||||||
\(244\) | 15.9343 | 1.02009 | ||||||||
\(245\) | 1.95223 | 0.124723 | ||||||||
\(246\) | 22.4778 | 1.43313 | ||||||||
\(247\) | 6.75596 | 0.429871 | ||||||||
\(248\) | −36.9295 | −2.34503 | ||||||||
\(249\) | −46.5104 | −2.94748 | ||||||||
\(250\) | −17.1080 | −1.08200 | ||||||||
\(251\) | −4.25886 | −0.268817 | −0.134409 | − | 0.990926i | \(-0.542913\pi\) | ||||
−0.134409 | + | 0.990926i | \(0.542913\pi\) | |||||||
\(252\) | −41.3307 | −2.60359 | ||||||||
\(253\) | −27.5567 | −1.73247 | ||||||||
\(254\) | 50.0336 | 3.13939 | ||||||||
\(255\) | 13.6082 | 0.852176 | ||||||||
\(256\) | −2.35112 | −0.146945 | ||||||||
\(257\) | −5.69565 | −0.355285 | −0.177643 | − | 0.984095i | \(-0.556847\pi\) | ||||
−0.177643 | + | 0.984095i | \(0.556847\pi\) | |||||||
\(258\) | 9.33601 | 0.581235 | ||||||||
\(259\) | 10.8000 | 0.671081 | ||||||||
\(260\) | −3.40301 | −0.211046 | ||||||||
\(261\) | 7.86048 | 0.486551 | ||||||||
\(262\) | 19.9533 | 1.23272 | ||||||||
\(263\) | −17.3913 | −1.07239 | −0.536196 | − | 0.844093i | \(-0.680139\pi\) | ||||
−0.536196 | + | 0.844093i | \(0.680139\pi\) | |||||||
\(264\) | −89.1200 | −5.48496 | ||||||||
\(265\) | −0.0458907 | −0.00281904 | ||||||||
\(266\) | 36.3346 | 2.22782 | ||||||||
\(267\) | −39.9326 | −2.44383 | ||||||||
\(268\) | 26.6877 | 1.63021 | ||||||||
\(269\) | −10.9477 | −0.667491 | −0.333745 | − | 0.942663i | \(-0.608313\pi\) | ||||
−0.333745 | + | 0.942663i | \(0.608313\pi\) | |||||||
\(270\) | 4.98968 | 0.303662 | ||||||||
\(271\) | −24.4905 | −1.48769 | −0.743845 | − | 0.668353i | \(-0.767000\pi\) | ||||
−0.743845 | + | 0.668353i | \(0.767000\pi\) | |||||||
\(272\) | −85.5402 | −5.18663 | ||||||||
\(273\) | −5.38335 | −0.325815 | ||||||||
\(274\) | 11.7837 | 0.711877 | ||||||||
\(275\) | −18.9466 | −1.14252 | ||||||||
\(276\) | −88.3245 | −5.31651 | ||||||||
\(277\) | −4.53142 | −0.272266 | −0.136133 | − | 0.990691i | \(-0.543468\pi\) | ||||
−0.136133 | + | 0.990691i | \(0.543468\pi\) | |||||||
\(278\) | −28.6372 | −1.71755 | ||||||||
\(279\) | 18.5737 | 1.11198 | ||||||||
\(280\) | −11.0318 | −0.659274 | ||||||||
\(281\) | −10.4551 | −0.623696 | −0.311848 | − | 0.950132i | \(-0.600948\pi\) | ||||
−0.311848 | + | 0.950132i | \(0.600948\pi\) | |||||||
\(282\) | −37.5112 | −2.23376 | ||||||||
\(283\) | −1.09779 | −0.0652568 | −0.0326284 | − | 0.999468i | \(-0.510388\pi\) | ||||
−0.0326284 | + | 0.999468i | \(0.510388\pi\) | |||||||
\(284\) | −53.4134 | −3.16950 | ||||||||
\(285\) | −12.1231 | −0.718108 | ||||||||
\(286\) | −11.0611 | −0.654059 | ||||||||
\(287\) | 6.47278 | 0.382076 | ||||||||
\(288\) | −55.9435 | −3.29650 | ||||||||
\(289\) | 40.5107 | 2.38298 | ||||||||
\(290\) | 3.48075 | 0.204397 | ||||||||
\(291\) | −17.0557 | −0.999821 | ||||||||
\(292\) | 15.9898 | 0.935730 | ||||||||
\(293\) | −12.0396 | −0.703358 | −0.351679 | − | 0.936121i | \(-0.614389\pi\) | ||||
−0.351679 | + | 0.936121i | \(0.614389\pi\) | |||||||
\(294\) | 20.3386 | 1.18617 | ||||||||
\(295\) | −4.11608 | −0.239648 | ||||||||
\(296\) | 42.8720 | 2.49189 | ||||||||
\(297\) | 11.6075 | 0.673538 | ||||||||
\(298\) | −29.9511 | −1.73502 | ||||||||
\(299\) | −6.60775 | −0.382136 | ||||||||
\(300\) | −60.7276 | −3.50611 | ||||||||
\(301\) | 2.68843 | 0.154958 | ||||||||
\(302\) | 47.1405 | 2.71263 | ||||||||
\(303\) | 2.81775 | 0.161876 | ||||||||
\(304\) | 76.2049 | 4.37065 | ||||||||
\(305\) | −2.13909 | −0.122484 | ||||||||
\(306\) | 81.4296 | 4.65502 | ||||||||
\(307\) | −25.9279 | −1.47978 | −0.739892 | − | 0.672726i | \(-0.765123\pi\) | ||||
−0.739892 | + | 0.672726i | \(0.765123\pi\) | |||||||
\(308\) | −42.5759 | −2.42599 | ||||||||
\(309\) | −20.6720 | −1.17599 | ||||||||
\(310\) | 8.22475 | 0.467134 | ||||||||
\(311\) | 25.2114 | 1.42961 | 0.714805 | − | 0.699324i | \(-0.246515\pi\) | ||||
0.714805 | + | 0.699324i | \(0.246515\pi\) | |||||||
\(312\) | −21.3699 | −1.20983 | ||||||||
\(313\) | −19.7808 | −1.11808 | −0.559040 | − | 0.829141i | \(-0.688830\pi\) | ||||
−0.559040 | + | 0.829141i | \(0.688830\pi\) | |||||||
\(314\) | 19.1038 | 1.07809 | ||||||||
\(315\) | 5.54843 | 0.312619 | ||||||||
\(316\) | 11.9818 | 0.674027 | ||||||||
\(317\) | 23.6474 | 1.32817 | 0.664085 | − | 0.747657i | \(-0.268821\pi\) | ||||
0.664085 | + | 0.747657i | \(0.268821\pi\) | |||||||
\(318\) | −0.478096 | −0.0268103 | ||||||||
\(319\) | 8.09730 | 0.453362 | ||||||||
\(320\) | −9.52496 | −0.532462 | ||||||||
\(321\) | 43.5067 | 2.42831 | ||||||||
\(322\) | −35.5376 | −1.98043 | ||||||||
\(323\) | −51.2344 | −2.85076 | ||||||||
\(324\) | −23.9441 | −1.33023 | ||||||||
\(325\) | −4.54316 | −0.252009 | ||||||||
\(326\) | −7.96276 | −0.441017 | ||||||||
\(327\) | 40.3544 | 2.23160 | ||||||||
\(328\) | 25.6945 | 1.41874 | ||||||||
\(329\) | −10.8018 | −0.595525 | ||||||||
\(330\) | 19.8484 | 1.09262 | ||||||||
\(331\) | −15.4593 | −0.849717 | −0.424859 | − | 0.905260i | \(-0.639676\pi\) | ||||
−0.424859 | + | 0.905260i | \(0.639676\pi\) | |||||||
\(332\) | −88.2040 | −4.84082 | ||||||||
\(333\) | −21.5625 | −1.18162 | ||||||||
\(334\) | −48.4254 | −2.64972 | ||||||||
\(335\) | −3.58269 | −0.195743 | ||||||||
\(336\) | −60.7223 | −3.31268 | ||||||||
\(337\) | 32.2627 | 1.75746 | 0.878729 | − | 0.477320i | \(-0.158392\pi\) | ||||
0.878729 | + | 0.477320i | \(0.158392\pi\) | |||||||
\(338\) | −2.65232 | −0.144267 | ||||||||
\(339\) | −46.3696 | −2.51845 | ||||||||
\(340\) | 25.8070 | 1.39958 | ||||||||
\(341\) | 19.1333 | 1.03613 | ||||||||
\(342\) | −72.5429 | −3.92267 | ||||||||
\(343\) | 20.0508 | 1.08264 | ||||||||
\(344\) | 10.6720 | 0.575398 | ||||||||
\(345\) | 11.8571 | 0.638365 | ||||||||
\(346\) | −51.8336 | −2.78659 | ||||||||
\(347\) | −12.5919 | −0.675970 | −0.337985 | − | 0.941152i | \(-0.609745\pi\) | ||||
−0.337985 | + | 0.941152i | \(0.609745\pi\) | |||||||
\(348\) | 25.9534 | 1.39125 | ||||||||
\(349\) | 13.2680 | 0.710220 | 0.355110 | − | 0.934824i | \(-0.384443\pi\) | ||||
0.355110 | + | 0.934824i | \(0.384443\pi\) | |||||||
\(350\) | −24.4339 | −1.30605 | ||||||||
\(351\) | 2.78334 | 0.148564 | ||||||||
\(352\) | −57.6290 | −3.07164 | ||||||||
\(353\) | −14.4219 | −0.767598 | −0.383799 | − | 0.923417i | \(-0.625384\pi\) | ||||
−0.383799 | + | 0.923417i | \(0.625384\pi\) | |||||||
\(354\) | −42.8820 | −2.27915 | ||||||||
\(355\) | 7.17048 | 0.380569 | ||||||||
\(356\) | −75.7295 | −4.01366 | ||||||||
\(357\) | 40.8251 | 2.16069 | ||||||||
\(358\) | 42.4523 | 2.24367 | ||||||||
\(359\) | −17.6046 | −0.929137 | −0.464568 | − | 0.885537i | \(-0.653791\pi\) | ||||
−0.464568 | + | 0.885537i | \(0.653791\pi\) | |||||||
\(360\) | 22.0252 | 1.16083 | ||||||||
\(361\) | 26.6430 | 1.40226 | ||||||||
\(362\) | 15.1205 | 0.794717 | ||||||||
\(363\) | 16.9697 | 0.890680 | ||||||||
\(364\) | −10.2092 | −0.535106 | ||||||||
\(365\) | −2.14654 | −0.112355 | ||||||||
\(366\) | −22.2854 | −1.16488 | ||||||||
\(367\) | 18.9707 | 0.990263 | 0.495132 | − | 0.868818i | \(-0.335120\pi\) | ||||
0.495132 | + | 0.868818i | \(0.335120\pi\) | |||||||
\(368\) | −74.5331 | −3.88531 | ||||||||
\(369\) | −12.9230 | −0.672747 | ||||||||
\(370\) | −9.54824 | −0.496389 | ||||||||
\(371\) | −0.137674 | −0.00714768 | ||||||||
\(372\) | 61.3259 | 3.17960 | ||||||||
\(373\) | 27.8996 | 1.44459 | 0.722294 | − | 0.691586i | \(-0.243088\pi\) | ||||
0.722294 | + | 0.691586i | \(0.243088\pi\) | |||||||
\(374\) | 83.8830 | 4.33749 | ||||||||
\(375\) | 17.1245 | 0.884305 | ||||||||
\(376\) | −42.8792 | −2.21133 | ||||||||
\(377\) | 1.94163 | 0.0999991 | ||||||||
\(378\) | 14.9693 | 0.769936 | ||||||||
\(379\) | −13.0842 | −0.672092 | −0.336046 | − | 0.941846i | \(-0.609090\pi\) | ||||
−0.336046 | + | 0.941846i | \(0.609090\pi\) | |||||||
\(380\) | −22.9906 | −1.17939 | ||||||||
\(381\) | −50.0819 | −2.56577 | ||||||||
\(382\) | 33.9071 | 1.73484 | ||||||||
\(383\) | −11.8640 | −0.606221 | −0.303110 | − | 0.952955i | \(-0.598025\pi\) | ||||
−0.303110 | + | 0.952955i | \(0.598025\pi\) | |||||||
\(384\) | −25.8585 | −1.31958 | ||||||||
\(385\) | 5.71560 | 0.291294 | ||||||||
\(386\) | 10.8585 | 0.552683 | ||||||||
\(387\) | −5.36750 | −0.272846 | ||||||||
\(388\) | −32.3449 | −1.64207 | ||||||||
\(389\) | 24.6338 | 1.24898 | 0.624490 | − | 0.781032i | \(-0.285307\pi\) | ||||
0.624490 | + | 0.781032i | \(0.285307\pi\) | |||||||
\(390\) | 4.75939 | 0.241001 | ||||||||
\(391\) | 50.1104 | 2.53419 | ||||||||
\(392\) | 23.2492 | 1.17426 | ||||||||
\(393\) | −19.9726 | −1.00748 | ||||||||
\(394\) | 14.9061 | 0.750957 | ||||||||
\(395\) | −1.60849 | −0.0809319 | ||||||||
\(396\) | 85.0038 | 4.27160 | ||||||||
\(397\) | 23.7086 | 1.18990 | 0.594951 | − | 0.803762i | \(-0.297172\pi\) | ||||
0.594951 | + | 0.803762i | \(0.297172\pi\) | |||||||
\(398\) | −7.72498 | −0.387218 | ||||||||
\(399\) | −36.3697 | −1.82076 | ||||||||
\(400\) | −51.2453 | −2.56227 | ||||||||
\(401\) | 20.8539 | 1.04139 | 0.520697 | − | 0.853742i | \(-0.325672\pi\) | ||||
0.520697 | + | 0.853742i | \(0.325672\pi\) | |||||||
\(402\) | −37.3250 | −1.86160 | ||||||||
\(403\) | 4.58793 | 0.228541 | ||||||||
\(404\) | 5.34368 | 0.265858 | ||||||||
\(405\) | 3.21438 | 0.159724 | ||||||||
\(406\) | 10.4424 | 0.518248 | ||||||||
\(407\) | −22.2121 | −1.10102 | ||||||||
\(408\) | 162.060 | 8.02317 | ||||||||
\(409\) | −13.6370 | −0.674307 | −0.337153 | − | 0.941450i | \(-0.609464\pi\) | ||||
−0.337153 | + | 0.941450i | \(0.609464\pi\) | |||||||
\(410\) | −5.72254 | −0.282616 | ||||||||
\(411\) | −11.7950 | −0.581806 | ||||||||
\(412\) | −39.2032 | −1.93140 | ||||||||
\(413\) | −12.3484 | −0.607627 | ||||||||
\(414\) | 70.9515 | 3.48708 | ||||||||
\(415\) | 11.8409 | 0.581248 | ||||||||
\(416\) | −13.8187 | −0.677518 | ||||||||
\(417\) | 28.6648 | 1.40372 | ||||||||
\(418\) | −74.7286 | −3.65509 | ||||||||
\(419\) | 8.05087 | 0.393311 | 0.196655 | − | 0.980473i | \(-0.436992\pi\) | ||||
0.196655 | + | 0.980473i | \(0.436992\pi\) | |||||||
\(420\) | 18.3196 | 0.893904 | ||||||||
\(421\) | 18.0995 | 0.882115 | 0.441058 | − | 0.897479i | \(-0.354603\pi\) | ||||
0.441058 | + | 0.897479i | \(0.354603\pi\) | |||||||
\(422\) | −24.4898 | −1.19214 | ||||||||
\(423\) | 21.5661 | 1.04858 | ||||||||
\(424\) | −0.546514 | −0.0265410 | ||||||||
\(425\) | 34.4534 | 1.67124 | ||||||||
\(426\) | 74.7031 | 3.61938 | ||||||||
\(427\) | −6.41737 | −0.310558 | ||||||||
\(428\) | 82.5077 | 3.98816 | ||||||||
\(429\) | 11.0718 | 0.534552 | ||||||||
\(430\) | −2.37682 | −0.114621 | ||||||||
\(431\) | −1.89215 | −0.0911415 | −0.0455707 | − | 0.998961i | \(-0.514511\pi\) | ||||
−0.0455707 | + | 0.998961i | \(0.514511\pi\) | |||||||
\(432\) | 31.3951 | 1.51050 | ||||||||
\(433\) | −23.6368 | −1.13591 | −0.567955 | − | 0.823060i | \(-0.692265\pi\) | ||||
−0.567955 | + | 0.823060i | \(0.692265\pi\) | |||||||
\(434\) | 24.6746 | 1.18442 | ||||||||
\(435\) | −3.48411 | −0.167050 | ||||||||
\(436\) | 76.5295 | 3.66510 | ||||||||
\(437\) | −44.6417 | −2.13550 | ||||||||
\(438\) | −22.3630 | −1.06855 | ||||||||
\(439\) | −1.78920 | −0.0853940 | −0.0426970 | − | 0.999088i | \(-0.513595\pi\) | ||||
−0.0426970 | + | 0.999088i | \(0.513595\pi\) | |||||||
\(440\) | 22.6888 | 1.08164 | ||||||||
\(441\) | −11.6932 | −0.556818 | ||||||||
\(442\) | 20.1141 | 0.956730 | ||||||||
\(443\) | −10.4222 | −0.495172 | −0.247586 | − | 0.968866i | \(-0.579637\pi\) | ||||
−0.247586 | + | 0.968866i | \(0.579637\pi\) | |||||||
\(444\) | −71.1942 | −3.37873 | ||||||||
\(445\) | 10.1663 | 0.481929 | ||||||||
\(446\) | −62.0018 | −2.93587 | ||||||||
\(447\) | 29.9800 | 1.41801 | ||||||||
\(448\) | −28.5753 | −1.35006 | ||||||||
\(449\) | −13.2999 | −0.627662 | −0.313831 | − | 0.949479i | \(-0.601613\pi\) | ||||
−0.313831 | + | 0.949479i | \(0.601613\pi\) | |||||||
\(450\) | 48.7828 | 2.29964 | ||||||||
\(451\) | −13.3124 | −0.626856 | ||||||||
\(452\) | −87.9369 | −4.13621 | ||||||||
\(453\) | −47.1860 | −2.21699 | ||||||||
\(454\) | 21.7907 | 1.02269 | ||||||||
\(455\) | 1.37053 | 0.0642514 | ||||||||
\(456\) | −144.374 | −6.76093 | ||||||||
\(457\) | −5.73775 | −0.268401 | −0.134200 | − | 0.990954i | \(-0.542847\pi\) | ||||
−0.134200 | + | 0.990954i | \(0.542847\pi\) | |||||||
\(458\) | −22.2003 | −1.03735 | ||||||||
\(459\) | −21.1077 | −0.985223 | ||||||||
\(460\) | 22.4862 | 1.04843 | ||||||||
\(461\) | −23.8884 | −1.11259 | −0.556297 | − | 0.830983i | \(-0.687778\pi\) | ||||
−0.556297 | + | 0.830983i | \(0.687778\pi\) | |||||||
\(462\) | 59.5460 | 2.77033 | ||||||||
\(463\) | −23.1888 | −1.07768 | −0.538838 | − | 0.842409i | \(-0.681137\pi\) | ||||
−0.538838 | + | 0.842409i | \(0.681137\pi\) | |||||||
\(464\) | 21.9009 | 1.01673 | ||||||||
\(465\) | −8.23269 | −0.381782 | ||||||||
\(466\) | 8.59313 | 0.398069 | ||||||||
\(467\) | −39.2218 | −1.81497 | −0.907484 | − | 0.420086i | \(-0.862000\pi\) | ||||
−0.907484 | + | 0.420086i | \(0.862000\pi\) | |||||||
\(468\) | 20.3828 | 0.942197 | ||||||||
\(469\) | −10.7482 | −0.496307 | ||||||||
\(470\) | 9.54984 | 0.440501 | ||||||||
\(471\) | −19.1222 | −0.881104 | ||||||||
\(472\) | −49.0186 | −2.25626 | ||||||||
\(473\) | −5.52922 | −0.254234 | ||||||||
\(474\) | −16.7575 | −0.769697 | ||||||||
\(475\) | −30.6934 | −1.40831 | ||||||||
\(476\) | 77.4221 | 3.54864 | ||||||||
\(477\) | 0.274869 | 0.0125854 | ||||||||
\(478\) | 50.8320 | 2.32500 | ||||||||
\(479\) | 10.4636 | 0.478095 | 0.239048 | − | 0.971008i | \(-0.423165\pi\) | ||||
0.239048 | + | 0.971008i | \(0.423165\pi\) | |||||||
\(480\) | 24.7966 | 1.13181 | ||||||||
\(481\) | −5.32619 | −0.242854 | ||||||||
\(482\) | 32.6800 | 1.48853 | ||||||||
\(483\) | 35.5718 | 1.61857 | ||||||||
\(484\) | 32.1820 | 1.46282 | ||||||||
\(485\) | 4.34214 | 0.197166 | ||||||||
\(486\) | 55.6348 | 2.52365 | ||||||||
\(487\) | −29.8670 | −1.35340 | −0.676702 | − | 0.736257i | \(-0.736592\pi\) | ||||
−0.676702 | + | 0.736257i | \(0.736592\pi\) | |||||||
\(488\) | −25.4745 | −1.15318 | ||||||||
\(489\) | 7.97045 | 0.360436 | ||||||||
\(490\) | −5.17794 | −0.233915 | ||||||||
\(491\) | 3.61598 | 0.163187 | 0.0815934 | − | 0.996666i | \(-0.473999\pi\) | ||||
0.0815934 | + | 0.996666i | \(0.473999\pi\) | |||||||
\(492\) | −42.6688 | −1.92366 | ||||||||
\(493\) | −14.7245 | −0.663159 | ||||||||
\(494\) | −17.9190 | −0.806213 | ||||||||
\(495\) | −11.4113 | −0.512901 | ||||||||
\(496\) | 51.7502 | 2.32365 | ||||||||
\(497\) | 21.5117 | 0.964934 | ||||||||
\(498\) | 123.361 | 5.52792 | ||||||||
\(499\) | 31.9605 | 1.43075 | 0.715375 | − | 0.698741i | \(-0.246256\pi\) | ||||
0.715375 | + | 0.698741i | \(0.246256\pi\) | |||||||
\(500\) | 32.4755 | 1.45235 | ||||||||
\(501\) | 48.4721 | 2.16557 | ||||||||
\(502\) | 11.2959 | 0.504159 | ||||||||
\(503\) | 26.4512 | 1.17940 | 0.589700 | − | 0.807623i | \(-0.299246\pi\) | ||||
0.589700 | + | 0.807623i | \(0.299246\pi\) | |||||||
\(504\) | 66.0765 | 2.94328 | ||||||||
\(505\) | −0.717361 | −0.0319222 | ||||||||
\(506\) | 73.0892 | 3.24921 | ||||||||
\(507\) | 2.65488 | 0.117907 | ||||||||
\(508\) | −94.9771 | −4.21393 | ||||||||
\(509\) | 30.0576 | 1.33228 | 0.666141 | − | 0.745826i | \(-0.267945\pi\) | ||||
0.666141 | + | 0.745826i | \(0.267945\pi\) | |||||||
\(510\) | −36.0932 | −1.59823 | ||||||||
\(511\) | −6.43972 | −0.284877 | ||||||||
\(512\) | 25.7159 | 1.13649 | ||||||||
\(513\) | 18.8042 | 0.830224 | ||||||||
\(514\) | 15.1067 | 0.666328 | ||||||||
\(515\) | 5.26282 | 0.231908 | ||||||||
\(516\) | −17.7222 | −0.780177 | ||||||||
\(517\) | 22.2159 | 0.977053 | ||||||||
\(518\) | −28.6451 | −1.25860 | ||||||||
\(519\) | 51.8836 | 2.27744 | ||||||||
\(520\) | 5.44048 | 0.238581 | ||||||||
\(521\) | −33.9334 | −1.48665 | −0.743324 | − | 0.668931i | \(-0.766752\pi\) | ||||
−0.743324 | + | 0.668931i | \(0.766752\pi\) | |||||||
\(522\) | −20.8485 | −0.912514 | ||||||||
\(523\) | −2.14534 | −0.0938091 | −0.0469045 | − | 0.998899i | \(-0.514936\pi\) | ||||
−0.0469045 | + | 0.998899i | \(0.514936\pi\) | |||||||
\(524\) | −37.8767 | −1.65465 | ||||||||
\(525\) | 24.4574 | 1.06741 | ||||||||
\(526\) | 46.1273 | 2.01124 | ||||||||
\(527\) | −34.7929 | −1.51560 | ||||||||
\(528\) | 124.886 | 5.43497 | ||||||||
\(529\) | 20.6624 | 0.898363 | ||||||||
\(530\) | 0.121717 | 0.00528704 | ||||||||
\(531\) | 24.6539 | 1.06989 | ||||||||
\(532\) | −68.9728 | −2.99035 | ||||||||
\(533\) | −3.19215 | −0.138267 | ||||||||
\(534\) | 105.914 | 4.58335 | ||||||||
\(535\) | −11.0762 | −0.478867 | ||||||||
\(536\) | −42.6664 | −1.84291 | ||||||||
\(537\) | −42.4932 | −1.83372 | ||||||||
\(538\) | 29.0367 | 1.25186 | ||||||||
\(539\) | −12.0455 | −0.518835 | ||||||||
\(540\) | −9.47174 | −0.407599 | ||||||||
\(541\) | −15.9938 | −0.687628 | −0.343814 | − | 0.939038i | \(-0.611719\pi\) | ||||
−0.343814 | + | 0.939038i | \(0.611719\pi\) | |||||||
\(542\) | 64.9565 | 2.79012 | ||||||||
\(543\) | −15.1351 | −0.649510 | ||||||||
\(544\) | 104.795 | 4.49306 | ||||||||
\(545\) | −10.2737 | −0.440077 | ||||||||
\(546\) | 14.2784 | 0.611058 | ||||||||
\(547\) | 23.5127 | 1.00533 | 0.502665 | − | 0.864482i | \(-0.332353\pi\) | ||||
0.502665 | + | 0.864482i | \(0.332353\pi\) | |||||||
\(548\) | −22.3685 | −0.955535 | ||||||||
\(549\) | 12.8124 | 0.546821 | ||||||||
\(550\) | 50.2525 | 2.14278 | ||||||||
\(551\) | 13.1176 | 0.558828 | ||||||||
\(552\) | 141.207 | 6.01016 | ||||||||
\(553\) | −4.82554 | −0.205203 | ||||||||
\(554\) | 12.0188 | 0.510629 | ||||||||
\(555\) | 9.55745 | 0.405691 | ||||||||
\(556\) | 54.3610 | 2.30542 | ||||||||
\(557\) | 42.8701 | 1.81647 | 0.908233 | − | 0.418465i | \(-0.137432\pi\) | ||||
0.908233 | + | 0.418465i | \(0.137432\pi\) | |||||||
\(558\) | −49.2634 | −2.08549 | ||||||||
\(559\) | −1.32584 | −0.0560770 | ||||||||
\(560\) | 15.4591 | 0.653266 | ||||||||
\(561\) | −83.9639 | −3.54496 | ||||||||
\(562\) | 27.7302 | 1.16973 | ||||||||
\(563\) | 1.75569 | 0.0739937 | 0.0369968 | − | 0.999315i | \(-0.488221\pi\) | ||||
0.0369968 | + | 0.999315i | \(0.488221\pi\) | |||||||
\(564\) | 71.2061 | 2.99832 | ||||||||
\(565\) | 11.8051 | 0.496643 | ||||||||
\(566\) | 2.91169 | 0.122387 | ||||||||
\(567\) | 9.64327 | 0.404979 | ||||||||
\(568\) | 85.3935 | 3.58303 | ||||||||
\(569\) | −31.6560 | −1.32709 | −0.663545 | − | 0.748137i | \(-0.730949\pi\) | ||||
−0.663545 | + | 0.748137i | \(0.730949\pi\) | |||||||
\(570\) | 32.1542 | 1.34679 | ||||||||
\(571\) | −33.1136 | −1.38576 | −0.692880 | − | 0.721053i | \(-0.743659\pi\) | ||||
−0.692880 | + | 0.721053i | \(0.743659\pi\) | |||||||
\(572\) | 20.9970 | 0.877927 | ||||||||
\(573\) | −33.9398 | −1.41786 | ||||||||
\(574\) | −17.1679 | −0.716573 | ||||||||
\(575\) | 30.0201 | 1.25192 | ||||||||
\(576\) | 57.0512 | 2.37713 | ||||||||
\(577\) | 5.32609 | 0.221728 | 0.110864 | − | 0.993836i | \(-0.464638\pi\) | ||||
0.110864 | + | 0.993836i | \(0.464638\pi\) | |||||||
\(578\) | −107.447 | −4.46922 | ||||||||
\(579\) | −10.8690 | −0.451699 | ||||||||
\(580\) | −6.60739 | −0.274357 | ||||||||
\(581\) | 35.5233 | 1.47375 | ||||||||
\(582\) | 45.2371 | 1.87514 | ||||||||
\(583\) | 0.283151 | 0.0117269 | ||||||||
\(584\) | −25.5633 | −1.05782 | ||||||||
\(585\) | −2.73629 | −0.113132 | ||||||||
\(586\) | 31.9328 | 1.31913 | ||||||||
\(587\) | 6.78547 | 0.280066 | 0.140033 | − | 0.990147i | \(-0.455279\pi\) | ||||
0.140033 | + | 0.990147i | \(0.455279\pi\) | |||||||
\(588\) | −38.6081 | −1.59217 | ||||||||
\(589\) | 30.9958 | 1.27716 | ||||||||
\(590\) | 10.9172 | 0.449453 | ||||||||
\(591\) | −14.9204 | −0.613745 | ||||||||
\(592\) | −60.0776 | −2.46918 | ||||||||
\(593\) | 12.3768 | 0.508256 | 0.254128 | − | 0.967171i | \(-0.418212\pi\) | ||||
0.254128 | + | 0.967171i | \(0.418212\pi\) | |||||||
\(594\) | −30.7869 | −1.26320 | ||||||||
\(595\) | −10.3935 | −0.426093 | ||||||||
\(596\) | 56.8552 | 2.32888 | ||||||||
\(597\) | 7.73244 | 0.316468 | ||||||||
\(598\) | 17.5259 | 0.716686 | ||||||||
\(599\) | −31.6676 | −1.29390 | −0.646952 | − | 0.762531i | \(-0.723956\pi\) | ||||
−0.646952 | + | 0.762531i | \(0.723956\pi\) | |||||||
\(600\) | 97.0868 | 3.96355 | ||||||||
\(601\) | 16.0706 | 0.655532 | 0.327766 | − | 0.944759i | \(-0.393704\pi\) | ||||
0.327766 | + | 0.944759i | \(0.393704\pi\) | |||||||
\(602\) | −7.13057 | −0.290620 | ||||||||
\(603\) | 21.4591 | 0.873881 | ||||||||
\(604\) | −89.4851 | −3.64110 | ||||||||
\(605\) | −4.32027 | −0.175644 | ||||||||
\(606\) | −7.47358 | −0.303593 | ||||||||
\(607\) | −11.1798 | −0.453775 | −0.226887 | − | 0.973921i | \(-0.572855\pi\) | ||||
−0.226887 | + | 0.973921i | \(0.572855\pi\) | |||||||
\(608\) | −93.3586 | −3.78619 | ||||||||
\(609\) | −10.4525 | −0.423556 | ||||||||
\(610\) | 5.67355 | 0.229716 | ||||||||
\(611\) | 5.32709 | 0.215511 | ||||||||
\(612\) | −154.575 | −6.24832 | ||||||||
\(613\) | 11.5790 | 0.467672 | 0.233836 | − | 0.972276i | \(-0.424872\pi\) | ||||
0.233836 | + | 0.972276i | \(0.424872\pi\) | |||||||
\(614\) | 68.7691 | 2.77530 | ||||||||
\(615\) | 5.72806 | 0.230978 | ||||||||
\(616\) | 68.0673 | 2.74251 | ||||||||
\(617\) | −6.61498 | −0.266309 | −0.133155 | − | 0.991095i | \(-0.542511\pi\) | ||||
−0.133155 | + | 0.991095i | \(0.542511\pi\) | |||||||
\(618\) | 54.8289 | 2.20554 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | −15.6127 | −0.627023 | ||||||||
\(621\) | −18.3916 | −0.738031 | ||||||||
\(622\) | −66.8688 | −2.68120 | ||||||||
\(623\) | 30.4993 | 1.22193 | ||||||||
\(624\) | 29.9461 | 1.19880 | ||||||||
\(625\) | 18.3562 | 0.734246 | ||||||||
\(626\) | 52.4651 | 2.09693 | ||||||||
\(627\) | 74.8007 | 2.98725 | ||||||||
\(628\) | −36.2640 | −1.44709 | ||||||||
\(629\) | 40.3916 | 1.61052 | ||||||||
\(630\) | −14.7162 | −0.586308 | ||||||||
\(631\) | 29.1933 | 1.16217 | 0.581083 | − | 0.813844i | \(-0.302629\pi\) | ||||
0.581083 | + | 0.813844i | \(0.302629\pi\) | |||||||
\(632\) | −19.1556 | −0.761967 | ||||||||
\(633\) | 24.5134 | 0.974321 | ||||||||
\(634\) | −62.7205 | −2.49095 | ||||||||
\(635\) | 12.7502 | 0.505975 | ||||||||
\(636\) | 0.907552 | 0.0359868 | ||||||||
\(637\) | −2.88835 | −0.114441 | ||||||||
\(638\) | −21.4766 | −0.850269 | ||||||||
\(639\) | −42.9487 | −1.69902 | ||||||||
\(640\) | 6.58322 | 0.260225 | ||||||||
\(641\) | −44.3376 | −1.75123 | −0.875615 | − | 0.483009i | \(-0.839544\pi\) | ||||
−0.875615 | + | 0.483009i | \(0.839544\pi\) | |||||||
\(642\) | −115.394 | −4.55423 | ||||||||
\(643\) | 14.9821 | 0.590837 | 0.295419 | − | 0.955368i | \(-0.404541\pi\) | ||||
0.295419 | + | 0.955368i | \(0.404541\pi\) | |||||||
\(644\) | 67.4597 | 2.65828 | ||||||||
\(645\) | 2.37912 | 0.0936776 | ||||||||
\(646\) | 135.890 | 5.34652 | ||||||||
\(647\) | −42.6475 | −1.67665 | −0.838324 | − | 0.545173i | \(-0.816464\pi\) | ||||
−0.838324 | + | 0.545173i | \(0.816464\pi\) | |||||||
\(648\) | 38.2801 | 1.50379 | ||||||||
\(649\) | 25.3967 | 0.996909 | ||||||||
\(650\) | 12.0499 | 0.472637 | ||||||||
\(651\) | −24.6984 | −0.968008 | ||||||||
\(652\) | 15.1154 | 0.591966 | ||||||||
\(653\) | −43.4618 | −1.70079 | −0.850395 | − | 0.526144i | \(-0.823637\pi\) | ||||
−0.850395 | + | 0.526144i | \(0.823637\pi\) | |||||||
\(654\) | −107.033 | −4.18532 | ||||||||
\(655\) | 5.08475 | 0.198678 | ||||||||
\(656\) | −36.0063 | −1.40581 | ||||||||
\(657\) | 12.8571 | 0.501601 | ||||||||
\(658\) | 28.6499 | 1.11689 | ||||||||
\(659\) | −7.02027 | −0.273471 | −0.136735 | − | 0.990608i | \(-0.543661\pi\) | ||||
−0.136735 | + | 0.990608i | \(0.543661\pi\) | |||||||
\(660\) | −37.6774 | −1.46659 | ||||||||
\(661\) | −40.1422 | −1.56135 | −0.780676 | − | 0.624936i | \(-0.785125\pi\) | ||||
−0.780676 | + | 0.624936i | \(0.785125\pi\) | |||||||
\(662\) | 41.0029 | 1.59362 | ||||||||
\(663\) | −20.1335 | −0.781920 | ||||||||
\(664\) | 141.014 | 5.47241 | ||||||||
\(665\) | 9.25924 | 0.359058 | ||||||||
\(666\) | 57.1907 | 2.21609 | ||||||||
\(667\) | −12.8298 | −0.496773 | ||||||||
\(668\) | 91.9241 | 3.55665 | ||||||||
\(669\) | 62.0616 | 2.39944 | ||||||||
\(670\) | 9.50244 | 0.367111 | ||||||||
\(671\) | 13.1984 | 0.509520 | ||||||||
\(672\) | 74.3910 | 2.86969 | ||||||||
\(673\) | 26.0043 | 1.00239 | 0.501196 | − | 0.865334i | \(-0.332893\pi\) | ||||
0.501196 | + | 0.865334i | \(0.332893\pi\) | |||||||
\(674\) | −85.5709 | −3.29607 | ||||||||
\(675\) | −12.6452 | −0.486713 | ||||||||
\(676\) | 5.03481 | 0.193646 | ||||||||
\(677\) | −5.85024 | −0.224843 | −0.112421 | − | 0.993661i | \(-0.535861\pi\) | ||||
−0.112421 | + | 0.993661i | \(0.535861\pi\) | |||||||
\(678\) | 122.987 | 4.72329 | ||||||||
\(679\) | 13.0266 | 0.499916 | ||||||||
\(680\) | −41.2583 | −1.58218 | ||||||||
\(681\) | −21.8117 | −0.835826 | ||||||||
\(682\) | −50.7477 | −1.94323 | ||||||||
\(683\) | 19.6830 | 0.753149 | 0.376574 | − | 0.926386i | \(-0.377102\pi\) | ||||
0.376574 | + | 0.926386i | \(0.377102\pi\) | |||||||
\(684\) | 137.706 | 5.26531 | ||||||||
\(685\) | 3.00285 | 0.114733 | ||||||||
\(686\) | −53.1812 | −2.03047 | ||||||||
\(687\) | 22.2217 | 0.847811 | ||||||||
\(688\) | −14.9550 | −0.570154 | ||||||||
\(689\) | 0.0678960 | 0.00258663 | ||||||||
\(690\) | −31.4488 | −1.19724 | ||||||||
\(691\) | −45.7830 | −1.74167 | −0.870833 | − | 0.491579i | \(-0.836420\pi\) | ||||
−0.870833 | + | 0.491579i | \(0.836420\pi\) | |||||||
\(692\) | 98.3939 | 3.74037 | ||||||||
\(693\) | −34.2345 | −1.30046 | ||||||||
\(694\) | 33.3978 | 1.26776 | ||||||||
\(695\) | −7.29768 | −0.276817 | ||||||||
\(696\) | −41.4924 | −1.57277 | ||||||||
\(697\) | 24.2079 | 0.916939 | ||||||||
\(698\) | −35.1910 | −1.33200 | ||||||||
\(699\) | −8.60143 | −0.325336 | ||||||||
\(700\) | 46.3819 | 1.75307 | ||||||||
\(701\) | −5.54535 | −0.209445 | −0.104722 | − | 0.994501i | \(-0.533395\pi\) | ||||
−0.104722 | + | 0.994501i | \(0.533395\pi\) | |||||||
\(702\) | −7.38232 | −0.278628 | ||||||||
\(703\) | −35.9836 | −1.35715 | ||||||||
\(704\) | 58.7701 | 2.21498 | ||||||||
\(705\) | −9.55906 | −0.360015 | ||||||||
\(706\) | 38.2514 | 1.43961 | ||||||||
\(707\) | −2.15212 | −0.0809386 | ||||||||
\(708\) | 81.4014 | 3.05925 | ||||||||
\(709\) | −24.2147 | −0.909402 | −0.454701 | − | 0.890644i | \(-0.650254\pi\) | ||||
−0.454701 | + | 0.890644i | \(0.650254\pi\) | |||||||
\(710\) | −19.0184 | −0.713748 | ||||||||
\(711\) | 9.63430 | 0.361314 | ||||||||
\(712\) | 121.071 | 4.53732 | ||||||||
\(713\) | −30.3159 | −1.13534 | ||||||||
\(714\) | −108.281 | −4.05232 | ||||||||
\(715\) | −2.81873 | −0.105415 | ||||||||
\(716\) | −80.5856 | −3.01163 | ||||||||
\(717\) | −50.8810 | −1.90019 | ||||||||
\(718\) | 46.6931 | 1.74257 | ||||||||
\(719\) | −24.2294 | −0.903603 | −0.451802 | − | 0.892118i | \(-0.649219\pi\) | ||||
−0.451802 | + | 0.892118i | \(0.649219\pi\) | |||||||
\(720\) | −30.8644 | −1.15025 | ||||||||
\(721\) | 15.7887 | 0.588002 | ||||||||
\(722\) | −70.6657 | −2.62991 | ||||||||
\(723\) | −32.7115 | −1.21655 | ||||||||
\(724\) | −28.7028 | −1.06673 | ||||||||
\(725\) | −8.82115 | −0.327609 | ||||||||
\(726\) | −45.0092 | −1.67045 | ||||||||
\(727\) | −15.9663 | −0.592158 | −0.296079 | − | 0.955163i | \(-0.595679\pi\) | ||||
−0.296079 | + | 0.955163i | \(0.595679\pi\) | |||||||
\(728\) | 16.3217 | 0.604922 | ||||||||
\(729\) | −41.4213 | −1.53412 | ||||||||
\(730\) | 5.69332 | 0.210719 | ||||||||
\(731\) | 10.0546 | 0.371883 | ||||||||
\(732\) | 42.3035 | 1.56358 | ||||||||
\(733\) | −2.61233 | −0.0964885 | −0.0482442 | − | 0.998836i | \(-0.515363\pi\) | ||||
−0.0482442 | + | 0.998836i | \(0.515363\pi\) | |||||||
\(734\) | −50.3164 | −1.85721 | ||||||||
\(735\) | 5.18293 | 0.191175 | ||||||||
\(736\) | 91.3106 | 3.36575 | ||||||||
\(737\) | 22.1056 | 0.814271 | ||||||||
\(738\) | 34.2761 | 1.26172 | ||||||||
\(739\) | 27.8598 | 1.02484 | 0.512419 | − | 0.858735i | \(-0.328749\pi\) | ||||
0.512419 | + | 0.858735i | \(0.328749\pi\) | |||||||
\(740\) | 18.1251 | 0.666291 | ||||||||
\(741\) | 17.9363 | 0.658905 | ||||||||
\(742\) | 0.365156 | 0.0134053 | ||||||||
\(743\) | 15.9448 | 0.584957 | 0.292478 | − | 0.956272i | \(-0.405520\pi\) | ||||
0.292478 | + | 0.956272i | \(0.405520\pi\) | |||||||
\(744\) | −98.0434 | −3.59444 | ||||||||
\(745\) | −7.63251 | −0.279634 | ||||||||
\(746\) | −73.9987 | −2.70929 | ||||||||
\(747\) | −70.9231 | −2.59494 | ||||||||
\(748\) | −159.232 | −5.82210 | ||||||||
\(749\) | −33.2292 | −1.21417 | ||||||||
\(750\) | −45.4196 | −1.65849 | ||||||||
\(751\) | −10.7258 | −0.391391 | −0.195695 | − | 0.980665i | \(-0.562696\pi\) | ||||
−0.195695 | + | 0.980665i | \(0.562696\pi\) | |||||||
\(752\) | 60.0877 | 2.19117 | ||||||||
\(753\) | −11.3068 | −0.412042 | ||||||||
\(754\) | −5.14983 | −0.187546 | ||||||||
\(755\) | 12.0129 | 0.437195 | ||||||||
\(756\) | −28.4156 | −1.03347 | ||||||||
\(757\) | 16.2845 | 0.591871 | 0.295936 | − | 0.955208i | \(-0.404369\pi\) | ||||
0.295936 | + | 0.955208i | \(0.404369\pi\) | |||||||
\(758\) | 34.7036 | 1.26049 | ||||||||
\(759\) | −73.1597 | −2.65553 | ||||||||
\(760\) | 36.7557 | 1.33327 | ||||||||
\(761\) | −38.0708 | −1.38007 | −0.690033 | − | 0.723778i | \(-0.742404\pi\) | ||||
−0.690033 | + | 0.723778i | \(0.742404\pi\) | |||||||
\(762\) | 132.833 | 4.81204 | ||||||||
\(763\) | −30.8215 | −1.11581 | ||||||||
\(764\) | −64.3646 | −2.32863 | ||||||||
\(765\) | 20.7509 | 0.750250 | ||||||||
\(766\) | 31.4671 | 1.13695 | ||||||||
\(767\) | 6.08981 | 0.219890 | ||||||||
\(768\) | −6.24194 | −0.225237 | ||||||||
\(769\) | 32.4063 | 1.16860 | 0.584301 | − | 0.811537i | \(-0.301369\pi\) | ||||
0.584301 | + | 0.811537i | \(0.301369\pi\) | |||||||
\(770\) | −15.1596 | −0.546314 | ||||||||
\(771\) | −15.1213 | −0.544580 | ||||||||
\(772\) | −20.6123 | −0.741853 | ||||||||
\(773\) | 36.3400 | 1.30706 | 0.653529 | − | 0.756902i | \(-0.273288\pi\) | ||||
0.653529 | + | 0.756902i | \(0.273288\pi\) | |||||||
\(774\) | 14.2363 | 0.511715 | ||||||||
\(775\) | −20.8437 | −0.748728 | ||||||||
\(776\) | 51.7107 | 1.85631 | ||||||||
\(777\) | 28.6728 | 1.02863 | ||||||||
\(778\) | −65.3366 | −2.34243 | ||||||||
\(779\) | −21.5660 | −0.772682 | ||||||||
\(780\) | −9.03458 | −0.323490 | ||||||||
\(781\) | −44.2427 | −1.58313 | ||||||||
\(782\) | −132.909 | −4.75281 | ||||||||
\(783\) | 5.40423 | 0.193131 | ||||||||
\(784\) | −32.5796 | −1.16356 | ||||||||
\(785\) | 4.86825 | 0.173755 | ||||||||
\(786\) | 52.9737 | 1.88951 | ||||||||
\(787\) | 41.9470 | 1.49525 | 0.747625 | − | 0.664121i | \(-0.231194\pi\) | ||||
0.747625 | + | 0.664121i | \(0.231194\pi\) | |||||||
\(788\) | −28.2957 | −1.00799 | ||||||||
\(789\) | −46.1718 | −1.64376 | ||||||||
\(790\) | 4.26623 | 0.151786 | ||||||||
\(791\) | 35.4158 | 1.25924 | ||||||||
\(792\) | −135.898 | −4.82892 | ||||||||
\(793\) | 3.16482 | 0.112386 | ||||||||
\(794\) | −62.8829 | −2.23163 | ||||||||
\(795\) | −0.121834 | −0.00432101 | ||||||||
\(796\) | 14.6641 | 0.519754 | ||||||||
\(797\) | −12.4774 | −0.441971 | −0.220985 | − | 0.975277i | \(-0.570927\pi\) | ||||
−0.220985 | + | 0.975277i | \(0.570927\pi\) | |||||||
\(798\) | 96.4641 | 3.41479 | ||||||||
\(799\) | −40.3984 | −1.42919 | ||||||||
\(800\) | 62.7807 | 2.21963 | ||||||||
\(801\) | −60.8926 | −2.15153 | ||||||||
\(802\) | −55.3112 | −1.95311 | ||||||||
\(803\) | 13.2444 | 0.467385 | ||||||||
\(804\) | 70.8527 | 2.49878 | ||||||||
\(805\) | −9.05611 | −0.319186 | ||||||||
\(806\) | −12.1687 | −0.428623 | ||||||||
\(807\) | −29.0647 | −1.02313 | ||||||||
\(808\) | −8.54308 | −0.300545 | ||||||||
\(809\) | 3.14230 | 0.110477 | 0.0552387 | − | 0.998473i | \(-0.482408\pi\) | ||||
0.0552387 | + | 0.998473i | \(0.482408\pi\) | |||||||
\(810\) | −8.52555 | −0.299557 | ||||||||
\(811\) | 40.3363 | 1.41640 | 0.708200 | − | 0.706012i | \(-0.249508\pi\) | ||||
0.708200 | + | 0.706012i | \(0.249508\pi\) | |||||||
\(812\) | −19.8225 | −0.695632 | ||||||||
\(813\) | −65.0192 | −2.28032 | ||||||||
\(814\) | 58.9137 | 2.06493 | ||||||||
\(815\) | −2.02917 | −0.0710787 | ||||||||
\(816\) | −227.099 | −7.95005 | ||||||||
\(817\) | −8.95730 | −0.313376 | ||||||||
\(818\) | 36.1697 | 1.26465 | ||||||||
\(819\) | −8.20899 | −0.286845 | ||||||||
\(820\) | 10.8629 | 0.379349 | ||||||||
\(821\) | 14.6295 | 0.510571 | 0.255286 | − | 0.966866i | \(-0.417830\pi\) | ||||
0.255286 | + | 0.966866i | \(0.417830\pi\) | |||||||
\(822\) | 31.2842 | 1.09116 | ||||||||
\(823\) | −24.9658 | −0.870253 | −0.435127 | − | 0.900369i | \(-0.643296\pi\) | ||||
−0.435127 | + | 0.900369i | \(0.643296\pi\) | |||||||
\(824\) | 62.6752 | 2.18339 | ||||||||
\(825\) | −50.3010 | −1.75126 | ||||||||
\(826\) | 32.7520 | 1.13959 | ||||||||
\(827\) | −5.77869 | −0.200945 | −0.100472 | − | 0.994940i | \(-0.532035\pi\) | ||||
−0.100472 | + | 0.994940i | \(0.532035\pi\) | |||||||
\(828\) | −134.685 | −4.68062 | ||||||||
\(829\) | −24.7007 | −0.857892 | −0.428946 | − | 0.903330i | \(-0.641115\pi\) | ||||
−0.428946 | + | 0.903330i | \(0.641115\pi\) | |||||||
\(830\) | −31.4059 | −1.09012 | ||||||||
\(831\) | −12.0304 | −0.417329 | ||||||||
\(832\) | 14.0923 | 0.488564 | ||||||||
\(833\) | 21.9041 | 0.758931 | ||||||||
\(834\) | −76.0284 | −2.63265 | ||||||||
\(835\) | −12.3403 | −0.427055 | ||||||||
\(836\) | 141.855 | 4.90614 | ||||||||
\(837\) | 12.7698 | 0.441388 | ||||||||
\(838\) | −21.3535 | −0.737644 | ||||||||
\(839\) | −22.4046 | −0.773492 | −0.386746 | − | 0.922186i | \(-0.626401\pi\) | ||||
−0.386746 | + | 0.922186i | \(0.626401\pi\) | |||||||
\(840\) | −29.2880 | −1.01053 | ||||||||
\(841\) | −25.2301 | −0.870002 | ||||||||
\(842\) | −48.0057 | −1.65438 | ||||||||
\(843\) | −27.7569 | −0.955999 | ||||||||
\(844\) | 46.4881 | 1.60019 | ||||||||
\(845\) | −0.675897 | −0.0232515 | ||||||||
\(846\) | −57.2003 | −1.96659 | ||||||||
\(847\) | −12.9610 | −0.445345 | ||||||||
\(848\) | 0.765843 | 0.0262992 | ||||||||
\(849\) | −2.91450 | −0.100025 | ||||||||
\(850\) | −91.3816 | −3.13436 | ||||||||
\(851\) | 35.1942 | 1.20644 | ||||||||
\(852\) | −141.806 | −4.85820 | ||||||||
\(853\) | −27.3428 | −0.936201 | −0.468101 | − | 0.883675i | \(-0.655061\pi\) | ||||
−0.468101 | + | 0.883675i | \(0.655061\pi\) | |||||||
\(854\) | 17.0209 | 0.582444 | ||||||||
\(855\) | −18.4863 | −0.632217 | ||||||||
\(856\) | −131.907 | −4.50850 | ||||||||
\(857\) | −28.0922 | −0.959612 | −0.479806 | − | 0.877375i | \(-0.659293\pi\) | ||||
−0.479806 | + | 0.877375i | \(0.659293\pi\) | |||||||
\(858\) | −29.3660 | −1.00254 | ||||||||
\(859\) | −44.6057 | −1.52193 | −0.760963 | − | 0.648795i | \(-0.775273\pi\) | ||||
−0.760963 | + | 0.648795i | \(0.775273\pi\) | |||||||
\(860\) | 4.51184 | 0.153852 | ||||||||
\(861\) | 17.1844 | 0.585644 | ||||||||
\(862\) | 5.01858 | 0.170933 | ||||||||
\(863\) | −37.2624 | −1.26843 | −0.634213 | − | 0.773158i | \(-0.718676\pi\) | ||||
−0.634213 | + | 0.773158i | \(0.718676\pi\) | |||||||
\(864\) | −38.4622 | −1.30851 | ||||||||
\(865\) | −13.2089 | −0.449115 | ||||||||
\(866\) | 62.6923 | 2.13037 | ||||||||
\(867\) | 107.551 | 3.65262 | ||||||||
\(868\) | −46.8389 | −1.58982 | ||||||||
\(869\) | 9.92457 | 0.336668 | ||||||||
\(870\) | 9.24098 | 0.313299 | ||||||||
\(871\) | 5.30065 | 0.179606 | ||||||||
\(872\) | −122.350 | −4.14329 | ||||||||
\(873\) | −26.0079 | −0.880235 | ||||||||
\(874\) | 118.404 | 4.00508 | ||||||||
\(875\) | −13.0792 | −0.442157 | ||||||||
\(876\) | 42.4509 | 1.43428 | ||||||||
\(877\) | 44.1809 | 1.49188 | 0.745942 | − | 0.666011i | \(-0.231999\pi\) | ||||
0.745942 | + | 0.666011i | \(0.231999\pi\) | |||||||
\(878\) | 4.74554 | 0.160154 | ||||||||
\(879\) | −31.9636 | −1.07810 | ||||||||
\(880\) | −31.7943 | −1.07179 | ||||||||
\(881\) | 0.720633 | 0.0242788 | 0.0121394 | − | 0.999926i | \(-0.496136\pi\) | ||||
0.0121394 | + | 0.999926i | \(0.496136\pi\) | |||||||
\(882\) | 31.0141 | 1.04430 | ||||||||
\(883\) | −15.3712 | −0.517283 | −0.258642 | − | 0.965973i | \(-0.583275\pi\) | ||||
−0.258642 | + | 0.965973i | \(0.583275\pi\) | |||||||
\(884\) | −38.1819 | −1.28419 | ||||||||
\(885\) | −10.9277 | −0.367331 | ||||||||
\(886\) | 27.6430 | 0.928683 | ||||||||
\(887\) | −9.82372 | −0.329848 | −0.164924 | − | 0.986306i | \(-0.552738\pi\) | ||||
−0.164924 | + | 0.986306i | \(0.552738\pi\) | |||||||
\(888\) | 113.820 | 3.81955 | ||||||||
\(889\) | 38.2511 | 1.28290 | ||||||||
\(890\) | −26.9643 | −0.903845 | ||||||||
\(891\) | −19.8331 | −0.664433 | ||||||||
\(892\) | 117.696 | 3.94074 | ||||||||
\(893\) | 35.9896 | 1.20435 | ||||||||
\(894\) | −79.5167 | −2.65943 | ||||||||
\(895\) | 10.8182 | 0.361613 | ||||||||
\(896\) | 19.7499 | 0.659799 | ||||||||
\(897\) | −17.5428 | −0.585736 | ||||||||
\(898\) | 35.2757 | 1.17716 | ||||||||
\(899\) | 8.90806 | 0.297101 | ||||||||
\(900\) | −92.6026 | −3.08675 | ||||||||
\(901\) | −0.514895 | −0.0171536 | ||||||||
\(902\) | 35.3088 | 1.17565 | ||||||||
\(903\) | 7.13745 | 0.237519 | ||||||||
\(904\) | 140.587 | 4.67586 | ||||||||
\(905\) | 3.85320 | 0.128085 | ||||||||
\(906\) | 125.152 | 4.15791 | ||||||||
\(907\) | 36.6227 | 1.21604 | 0.608019 | − | 0.793923i | \(-0.291964\pi\) | ||||
0.608019 | + | 0.793923i | \(0.291964\pi\) | |||||||
\(908\) | −41.3644 | −1.37273 | ||||||||
\(909\) | 4.29675 | 0.142514 | ||||||||
\(910\) | −3.63508 | −0.120502 | ||||||||
\(911\) | 20.0404 | 0.663968 | 0.331984 | − | 0.943285i | \(-0.392282\pi\) | ||||
0.331984 | + | 0.943285i | \(0.392282\pi\) | |||||||
\(912\) | 202.315 | 6.69931 | ||||||||
\(913\) | −73.0599 | −2.41793 | ||||||||
\(914\) | 15.2184 | 0.503379 | ||||||||
\(915\) | −5.67903 | −0.187743 | ||||||||
\(916\) | 42.1420 | 1.39241 | ||||||||
\(917\) | 15.2545 | 0.503747 | ||||||||
\(918\) | 55.9844 | 1.84776 | ||||||||
\(919\) | −10.1625 | −0.335229 | −0.167615 | − | 0.985853i | \(-0.553606\pi\) | ||||
−0.167615 | + | 0.985853i | \(0.553606\pi\) | |||||||
\(920\) | −35.9493 | −1.18521 | ||||||||
\(921\) | −68.8355 | −2.26821 | ||||||||
\(922\) | 63.3597 | 2.08664 | ||||||||
\(923\) | −10.6088 | −0.349194 | ||||||||
\(924\) | −113.034 | −3.71855 | ||||||||
\(925\) | 24.1978 | 0.795618 | ||||||||
\(926\) | 61.5042 | 2.02115 | ||||||||
\(927\) | −31.5225 | −1.03533 | ||||||||
\(928\) | −26.8308 | −0.880766 | ||||||||
\(929\) | 16.2125 | 0.531915 | 0.265958 | − | 0.963985i | \(-0.414312\pi\) | ||||
0.265958 | + | 0.963985i | \(0.414312\pi\) | |||||||
\(930\) | 21.8357 | 0.716022 | ||||||||
\(931\) | −19.5136 | −0.639532 | ||||||||
\(932\) | −16.3120 | −0.534319 | ||||||||
\(933\) | 66.9334 | 2.19130 | ||||||||
\(934\) | 104.029 | 3.40393 | ||||||||
\(935\) | 21.3761 | 0.699073 | ||||||||
\(936\) | −32.5866 | −1.06513 | ||||||||
\(937\) | 25.4576 | 0.831664 | 0.415832 | − | 0.909441i | \(-0.363490\pi\) | ||||
0.415832 | + | 0.909441i | \(0.363490\pi\) | |||||||
\(938\) | 28.5077 | 0.930811 | ||||||||
\(939\) | −52.5158 | −1.71379 | ||||||||
\(940\) | −18.1281 | −0.591274 | ||||||||
\(941\) | 17.0178 | 0.554763 | 0.277382 | − | 0.960760i | \(-0.410533\pi\) | ||||
0.277382 | + | 0.960760i | \(0.410533\pi\) | |||||||
\(942\) | 50.7182 | 1.65249 | ||||||||
\(943\) | 21.0929 | 0.686879 | ||||||||
\(944\) | 68.6910 | 2.23570 | ||||||||
\(945\) | 3.81465 | 0.124091 | ||||||||
\(946\) | 14.6653 | 0.476809 | ||||||||
\(947\) | 34.6990 | 1.12757 | 0.563783 | − | 0.825923i | \(-0.309346\pi\) | ||||
0.563783 | + | 0.825923i | \(0.309346\pi\) | |||||||
\(948\) | 31.8101 | 1.03315 | ||||||||
\(949\) | 3.17585 | 0.103092 | ||||||||
\(950\) | 81.4088 | 2.64125 | ||||||||
\(951\) | 62.7810 | 2.03581 | ||||||||
\(952\) | −123.777 | −4.01163 | ||||||||
\(953\) | 44.0452 | 1.42676 | 0.713382 | − | 0.700776i | \(-0.247163\pi\) | ||||
0.713382 | + | 0.700776i | \(0.247163\pi\) | |||||||
\(954\) | −0.729041 | −0.0236036 | ||||||||
\(955\) | 8.64061 | 0.279604 | ||||||||
\(956\) | −96.4926 | −3.12079 | ||||||||
\(957\) | 21.4974 | 0.694911 | ||||||||
\(958\) | −27.7529 | −0.896655 | ||||||||
\(959\) | 9.00870 | 0.290906 | ||||||||
\(960\) | −25.2876 | −0.816155 | ||||||||
\(961\) | −9.95093 | −0.320998 | ||||||||
\(962\) | 14.1268 | 0.455466 | ||||||||
\(963\) | 66.3428 | 2.13787 | ||||||||
\(964\) | −62.0352 | −1.99802 | ||||||||
\(965\) | 2.76710 | 0.0890760 | ||||||||
\(966\) | −94.3479 | −3.03560 | ||||||||
\(967\) | −11.1452 | −0.358405 | −0.179202 | − | 0.983812i | \(-0.557352\pi\) | ||||
−0.179202 | + | 0.983812i | \(0.557352\pi\) | |||||||
\(968\) | −51.4502 | −1.65367 | ||||||||
\(969\) | −136.021 | −4.36963 | ||||||||
\(970\) | −11.5168 | −0.369781 | ||||||||
\(971\) | 37.4073 | 1.20046 | 0.600229 | − | 0.799828i | \(-0.295076\pi\) | ||||
0.600229 | + | 0.799828i | \(0.295076\pi\) | |||||||
\(972\) | −105.610 | −3.38743 | ||||||||
\(973\) | −21.8934 | −0.701869 | ||||||||
\(974\) | 79.2170 | 2.53828 | ||||||||
\(975\) | −12.0616 | −0.386279 | ||||||||
\(976\) | 35.6981 | 1.14267 | ||||||||
\(977\) | −49.0615 | −1.56962 | −0.784808 | − | 0.619739i | \(-0.787239\pi\) | ||||
−0.784808 | + | 0.619739i | \(0.787239\pi\) | |||||||
\(978\) | −21.1402 | −0.675989 | ||||||||
\(979\) | −62.7272 | −2.00477 | ||||||||
\(980\) | 9.82909 | 0.313979 | ||||||||
\(981\) | 61.5359 | 1.96469 | ||||||||
\(982\) | −9.59073 | −0.306053 | ||||||||
\(983\) | 52.2865 | 1.66768 | 0.833841 | − | 0.552005i | \(-0.186137\pi\) | ||||
0.833841 | + | 0.552005i | \(0.186137\pi\) | |||||||
\(984\) | 68.2157 | 2.17464 | ||||||||
\(985\) | 3.79854 | 0.121032 | ||||||||
\(986\) | 39.0542 | 1.24374 | ||||||||
\(987\) | −28.6776 | −0.912818 | ||||||||
\(988\) | 34.0149 | 1.08216 | ||||||||
\(989\) | 8.76080 | 0.278577 | ||||||||
\(990\) | 30.2665 | 0.961932 | ||||||||
\(991\) | −21.6858 | −0.688872 | −0.344436 | − | 0.938810i | \(-0.611930\pi\) | ||||
−0.344436 | + | 0.938810i | \(0.611930\pi\) | |||||||
\(992\) | −63.3992 | −2.01293 | ||||||||
\(993\) | −41.0425 | −1.30244 | ||||||||
\(994\) | −57.0561 | −1.80971 | ||||||||
\(995\) | −1.96857 | −0.0624080 | ||||||||
\(996\) | −234.171 | −7.41999 | ||||||||
\(997\) | 23.1905 | 0.734450 | 0.367225 | − | 0.930132i | \(-0.380308\pi\) | ||||
0.367225 | + | 0.930132i | \(0.380308\pi\) | |||||||
\(998\) | −84.7696 | −2.68333 | ||||||||
\(999\) | −14.8246 | −0.469030 |
(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 | 8047.2.a.b.1.7 | ✓ | 142 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.b.1.7 | ✓ | 142 | 1.1 | even | 1 | trivial |