Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(75\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.17778 | −1.53992 | −0.769962 | − | 0.638089i | \(-0.779725\pi\) | ||||
−0.769962 | + | 0.638089i | \(0.779725\pi\) | |||||||
\(3\) | −1.25453 | −0.724301 | −0.362150 | − | 0.932120i | \(-0.617957\pi\) | ||||
−0.362150 | + | 0.932120i | \(0.617957\pi\) | |||||||
\(4\) | 2.74274 | 1.37137 | ||||||||
\(5\) | 2.27371 | 1.01683 | 0.508416 | − | 0.861111i | \(-0.330231\pi\) | ||||
0.508416 | + | 0.861111i | \(0.330231\pi\) | |||||||
\(6\) | 2.73208 | 1.11537 | ||||||||
\(7\) | −1.62232 | −0.613181 | −0.306591 | − | 0.951841i | \(-0.599188\pi\) | ||||
−0.306591 | + | 0.951841i | \(0.599188\pi\) | |||||||
\(8\) | −1.61752 | −0.571880 | ||||||||
\(9\) | −1.42616 | −0.475388 | ||||||||
\(10\) | −4.95164 | −1.56585 | ||||||||
\(11\) | 0.712705 | 0.214889 | 0.107444 | − | 0.994211i | \(-0.465733\pi\) | ||||
0.107444 | + | 0.994211i | \(0.465733\pi\) | |||||||
\(12\) | −3.44083 | −0.993283 | ||||||||
\(13\) | −6.45412 | −1.79005 | −0.895025 | − | 0.446016i | \(-0.852842\pi\) | ||||
−0.895025 | + | 0.446016i | \(0.852842\pi\) | |||||||
\(14\) | 3.53307 | 0.944253 | ||||||||
\(15\) | −2.85242 | −0.736493 | ||||||||
\(16\) | −1.96287 | −0.490717 | ||||||||
\(17\) | −3.12354 | −0.757569 | −0.378785 | − | 0.925485i | \(-0.623658\pi\) | ||||
−0.378785 | + | 0.925485i | \(0.623658\pi\) | |||||||
\(18\) | 3.10588 | 0.732062 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 6.23618 | 1.39445 | ||||||||
\(21\) | 2.03525 | 0.444128 | ||||||||
\(22\) | −1.55212 | −0.330912 | ||||||||
\(23\) | 7.14256 | 1.48933 | 0.744664 | − | 0.667440i | \(-0.232610\pi\) | ||||
0.744664 | + | 0.667440i | \(0.232610\pi\) | |||||||
\(24\) | 2.02922 | 0.414213 | ||||||||
\(25\) | 0.169744 | 0.0339488 | ||||||||
\(26\) | 14.0557 | 2.75654 | ||||||||
\(27\) | 5.55274 | 1.06863 | ||||||||
\(28\) | −4.44961 | −0.840897 | ||||||||
\(29\) | 8.26282 | 1.53437 | 0.767184 | − | 0.641427i | \(-0.221657\pi\) | ||||
0.767184 | + | 0.641427i | \(0.221657\pi\) | |||||||
\(30\) | 6.21196 | 1.13414 | ||||||||
\(31\) | 2.05885 | 0.369781 | 0.184891 | − | 0.982759i | \(-0.440807\pi\) | ||||
0.184891 | + | 0.982759i | \(0.440807\pi\) | |||||||
\(32\) | 7.50974 | 1.32755 | ||||||||
\(33\) | −0.894107 | −0.155644 | ||||||||
\(34\) | 6.80238 | 1.16660 | ||||||||
\(35\) | −3.68869 | −0.623503 | ||||||||
\(36\) | −3.91159 | −0.651932 | ||||||||
\(37\) | 7.42228 | 1.22021 | 0.610107 | − | 0.792319i | \(-0.291126\pi\) | ||||
0.610107 | + | 0.792319i | \(0.291126\pi\) | |||||||
\(38\) | 2.17778 | 0.353283 | ||||||||
\(39\) | 8.09686 | 1.29653 | ||||||||
\(40\) | −3.67777 | −0.581506 | ||||||||
\(41\) | −2.54806 | −0.397940 | −0.198970 | − | 0.980006i | \(-0.563760\pi\) | ||||
−0.198970 | + | 0.980006i | \(0.563760\pi\) | |||||||
\(42\) | −4.43233 | −0.683923 | ||||||||
\(43\) | −8.68556 | −1.32454 | −0.662268 | − | 0.749267i | \(-0.730406\pi\) | ||||
−0.662268 | + | 0.749267i | \(0.730406\pi\) | |||||||
\(44\) | 1.95476 | 0.294692 | ||||||||
\(45\) | −3.24268 | −0.483390 | ||||||||
\(46\) | −15.5549 | −2.29345 | ||||||||
\(47\) | 10.6920 | 1.55959 | 0.779794 | − | 0.626036i | \(-0.215324\pi\) | ||||
0.779794 | + | 0.626036i | \(0.215324\pi\) | |||||||
\(48\) | 2.46247 | 0.355427 | ||||||||
\(49\) | −4.36806 | −0.624009 | ||||||||
\(50\) | −0.369666 | −0.0522787 | ||||||||
\(51\) | 3.91856 | 0.548708 | ||||||||
\(52\) | −17.7019 | −2.45482 | ||||||||
\(53\) | 6.48311 | 0.890523 | 0.445262 | − | 0.895401i | \(-0.353111\pi\) | ||||
0.445262 | + | 0.895401i | \(0.353111\pi\) | |||||||
\(54\) | −12.0927 | −1.64560 | ||||||||
\(55\) | 1.62048 | 0.218506 | ||||||||
\(56\) | 2.62414 | 0.350666 | ||||||||
\(57\) | 1.25453 | 0.166166 | ||||||||
\(58\) | −17.9946 | −2.36281 | ||||||||
\(59\) | 7.84811 | 1.02174 | 0.510868 | − | 0.859659i | \(-0.329324\pi\) | ||||
0.510868 | + | 0.859659i | \(0.329324\pi\) | |||||||
\(60\) | −7.82345 | −1.01000 | ||||||||
\(61\) | −6.34020 | −0.811780 | −0.405890 | − | 0.913922i | \(-0.633038\pi\) | ||||
−0.405890 | + | 0.913922i | \(0.633038\pi\) | |||||||
\(62\) | −4.48374 | −0.569435 | ||||||||
\(63\) | 2.31370 | 0.291499 | ||||||||
\(64\) | −12.4288 | −1.55361 | ||||||||
\(65\) | −14.6748 | −1.82018 | ||||||||
\(66\) | 1.94717 | 0.239680 | ||||||||
\(67\) | 4.48368 | 0.547768 | 0.273884 | − | 0.961763i | \(-0.411692\pi\) | ||||
0.273884 | + | 0.961763i | \(0.411692\pi\) | |||||||
\(68\) | −8.56704 | −1.03891 | ||||||||
\(69\) | −8.96053 | −1.07872 | ||||||||
\(70\) | 8.03317 | 0.960147 | ||||||||
\(71\) | −12.7709 | −1.51563 | −0.757815 | − | 0.652469i | \(-0.773733\pi\) | ||||
−0.757815 | + | 0.652469i | \(0.773733\pi\) | |||||||
\(72\) | 2.30685 | 0.271865 | ||||||||
\(73\) | 16.5987 | 1.94273 | 0.971367 | − | 0.237582i | \(-0.0763549\pi\) | ||||
0.971367 | + | 0.237582i | \(0.0763549\pi\) | |||||||
\(74\) | −16.1641 | −1.87904 | ||||||||
\(75\) | −0.212949 | −0.0245892 | ||||||||
\(76\) | −2.74274 | −0.314614 | ||||||||
\(77\) | −1.15624 | −0.131766 | ||||||||
\(78\) | −17.6332 | −1.99657 | ||||||||
\(79\) | −7.83514 | −0.881522 | −0.440761 | − | 0.897625i | \(-0.645291\pi\) | ||||
−0.440761 | + | 0.897625i | \(0.645291\pi\) | |||||||
\(80\) | −4.46299 | −0.498977 | ||||||||
\(81\) | −2.68756 | −0.298618 | ||||||||
\(82\) | 5.54912 | 0.612798 | ||||||||
\(83\) | −0.482513 | −0.0529627 | −0.0264813 | − | 0.999649i | \(-0.508430\pi\) | ||||
−0.0264813 | + | 0.999649i | \(0.508430\pi\) | |||||||
\(84\) | 5.58215 | 0.609063 | ||||||||
\(85\) | −7.10201 | −0.770321 | ||||||||
\(86\) | 18.9153 | 2.03969 | ||||||||
\(87\) | −10.3659 | −1.11134 | ||||||||
\(88\) | −1.15281 | −0.122890 | ||||||||
\(89\) | −7.50702 | −0.795743 | −0.397871 | − | 0.917441i | \(-0.630251\pi\) | ||||
−0.397871 | + | 0.917441i | \(0.630251\pi\) | |||||||
\(90\) | 7.06185 | 0.744385 | ||||||||
\(91\) | 10.4707 | 1.09762 | ||||||||
\(92\) | 19.5902 | 2.04242 | ||||||||
\(93\) | −2.58289 | −0.267833 | ||||||||
\(94\) | −23.2849 | −2.40165 | ||||||||
\(95\) | −2.27371 | −0.233277 | ||||||||
\(96\) | −9.42116 | −0.961543 | ||||||||
\(97\) | −9.95412 | −1.01069 | −0.505344 | − | 0.862918i | \(-0.668634\pi\) | ||||
−0.505344 | + | 0.862918i | \(0.668634\pi\) | |||||||
\(98\) | 9.51269 | 0.960927 | ||||||||
\(99\) | −1.01643 | −0.102156 | ||||||||
\(100\) | 0.465564 | 0.0465564 | ||||||||
\(101\) | −10.5230 | −1.04708 | −0.523539 | − | 0.852002i | \(-0.675388\pi\) | ||||
−0.523539 | + | 0.852002i | \(0.675388\pi\) | |||||||
\(102\) | −8.53377 | −0.844969 | ||||||||
\(103\) | 10.0283 | 0.988114 | 0.494057 | − | 0.869430i | \(-0.335513\pi\) | ||||
0.494057 | + | 0.869430i | \(0.335513\pi\) | |||||||
\(104\) | 10.4397 | 1.02369 | ||||||||
\(105\) | 4.62756 | 0.451604 | ||||||||
\(106\) | −14.1188 | −1.37134 | ||||||||
\(107\) | −4.85447 | −0.469299 | −0.234650 | − | 0.972080i | \(-0.575394\pi\) | ||||
−0.234650 | + | 0.972080i | \(0.575394\pi\) | |||||||
\(108\) | 15.2297 | 1.46548 | ||||||||
\(109\) | 11.7741 | 1.12775 | 0.563875 | − | 0.825860i | \(-0.309310\pi\) | ||||
0.563875 | + | 0.825860i | \(0.309310\pi\) | |||||||
\(110\) | −3.52906 | −0.336483 | ||||||||
\(111\) | −9.31144 | −0.883803 | ||||||||
\(112\) | 3.18441 | 0.300898 | ||||||||
\(113\) | 12.9644 | 1.21959 | 0.609793 | − | 0.792561i | \(-0.291253\pi\) | ||||
0.609793 | + | 0.792561i | \(0.291253\pi\) | |||||||
\(114\) | −2.73208 | −0.255883 | ||||||||
\(115\) | 16.2401 | 1.51440 | ||||||||
\(116\) | 22.6628 | 2.10418 | ||||||||
\(117\) | 9.20463 | 0.850968 | ||||||||
\(118\) | −17.0915 | −1.57340 | ||||||||
\(119\) | 5.06739 | 0.464527 | ||||||||
\(120\) | 4.61385 | 0.421185 | ||||||||
\(121\) | −10.4921 | −0.953823 | ||||||||
\(122\) | 13.8076 | 1.25008 | ||||||||
\(123\) | 3.19661 | 0.288228 | ||||||||
\(124\) | 5.64690 | 0.507106 | ||||||||
\(125\) | −10.9826 | −0.982312 | ||||||||
\(126\) | −5.03874 | −0.448887 | ||||||||
\(127\) | −1.66599 | −0.147833 | −0.0739164 | − | 0.997264i | \(-0.523550\pi\) | ||||
−0.0739164 | + | 0.997264i | \(0.523550\pi\) | |||||||
\(128\) | 12.0478 | 1.06489 | ||||||||
\(129\) | 10.8963 | 0.959363 | ||||||||
\(130\) | 31.9585 | 2.80294 | ||||||||
\(131\) | −5.43444 | −0.474809 | −0.237405 | − | 0.971411i | \(-0.576297\pi\) | ||||
−0.237405 | + | 0.971411i | \(0.576297\pi\) | |||||||
\(132\) | −2.45230 | −0.213445 | ||||||||
\(133\) | 1.62232 | 0.140673 | ||||||||
\(134\) | −9.76447 | −0.843522 | ||||||||
\(135\) | 12.6253 | 1.08661 | ||||||||
\(136\) | 5.05238 | 0.433238 | ||||||||
\(137\) | 16.0015 | 1.36710 | 0.683549 | − | 0.729905i | \(-0.260436\pi\) | ||||
0.683549 | + | 0.729905i | \(0.260436\pi\) | |||||||
\(138\) | 19.5141 | 1.66115 | ||||||||
\(139\) | −15.9860 | −1.35591 | −0.677956 | − | 0.735102i | \(-0.737134\pi\) | ||||
−0.677956 | + | 0.735102i | \(0.737134\pi\) | |||||||
\(140\) | −10.1171 | −0.855052 | ||||||||
\(141\) | −13.4134 | −1.12961 | ||||||||
\(142\) | 27.8123 | 2.33396 | ||||||||
\(143\) | −4.59988 | −0.384661 | ||||||||
\(144\) | 2.79937 | 0.233281 | ||||||||
\(145\) | 18.7872 | 1.56020 | ||||||||
\(146\) | −36.1484 | −2.99167 | ||||||||
\(147\) | 5.47985 | 0.451970 | ||||||||
\(148\) | 20.3574 | 1.67336 | ||||||||
\(149\) | −1.84763 | −0.151364 | −0.0756818 | − | 0.997132i | \(-0.524113\pi\) | ||||
−0.0756818 | + | 0.997132i | \(0.524113\pi\) | |||||||
\(150\) | 0.463756 | 0.0378655 | ||||||||
\(151\) | −4.04319 | −0.329030 | −0.164515 | − | 0.986375i | \(-0.552606\pi\) | ||||
−0.164515 | + | 0.986375i | \(0.552606\pi\) | |||||||
\(152\) | 1.61752 | 0.131198 | ||||||||
\(153\) | 4.45468 | 0.360139 | ||||||||
\(154\) | 2.51804 | 0.202909 | ||||||||
\(155\) | 4.68123 | 0.376006 | ||||||||
\(156\) | 22.2075 | 1.77803 | ||||||||
\(157\) | −12.1727 | −0.971490 | −0.485745 | − | 0.874100i | \(-0.661452\pi\) | ||||
−0.485745 | + | 0.874100i | \(0.661452\pi\) | |||||||
\(158\) | 17.0632 | 1.35748 | ||||||||
\(159\) | −8.13323 | −0.645007 | ||||||||
\(160\) | 17.0749 | 1.34989 | ||||||||
\(161\) | −11.5876 | −0.913227 | ||||||||
\(162\) | 5.85292 | 0.459849 | ||||||||
\(163\) | −21.1981 | −1.66037 | −0.830183 | − | 0.557491i | \(-0.811764\pi\) | ||||
−0.830183 | + | 0.557491i | \(0.811764\pi\) | |||||||
\(164\) | −6.98866 | −0.545722 | ||||||||
\(165\) | −2.03294 | −0.158264 | ||||||||
\(166\) | 1.05081 | 0.0815585 | ||||||||
\(167\) | 12.8006 | 0.990543 | 0.495272 | − | 0.868738i | \(-0.335069\pi\) | ||||
0.495272 | + | 0.868738i | \(0.335069\pi\) | |||||||
\(168\) | −3.29205 | −0.253988 | ||||||||
\(169\) | 28.6556 | 2.20428 | ||||||||
\(170\) | 15.4666 | 1.18624 | ||||||||
\(171\) | 1.42616 | 0.109062 | ||||||||
\(172\) | −23.8222 | −1.81643 | ||||||||
\(173\) | −15.1651 | −1.15298 | −0.576490 | − | 0.817104i | \(-0.695578\pi\) | ||||
−0.576490 | + | 0.817104i | \(0.695578\pi\) | |||||||
\(174\) | 22.5747 | 1.71139 | ||||||||
\(175\) | −0.275380 | −0.0208168 | ||||||||
\(176\) | −1.39895 | −0.105450 | ||||||||
\(177\) | −9.84566 | −0.740045 | ||||||||
\(178\) | 16.3487 | 1.22538 | ||||||||
\(179\) | −0.483723 | −0.0361551 | −0.0180776 | − | 0.999837i | \(-0.505755\pi\) | ||||
−0.0180776 | + | 0.999837i | \(0.505755\pi\) | |||||||
\(180\) | −8.89382 | −0.662906 | ||||||||
\(181\) | 18.6568 | 1.38675 | 0.693374 | − | 0.720578i | \(-0.256123\pi\) | ||||
0.693374 | + | 0.720578i | \(0.256123\pi\) | |||||||
\(182\) | −22.8028 | −1.69026 | ||||||||
\(183\) | 7.95395 | 0.587973 | ||||||||
\(184\) | −11.5532 | −0.851716 | ||||||||
\(185\) | 16.8761 | 1.24075 | ||||||||
\(186\) | 5.62497 | 0.412443 | ||||||||
\(187\) | −2.22616 | −0.162793 | ||||||||
\(188\) | 29.3254 | 2.13877 | ||||||||
\(189\) | −9.00835 | −0.655261 | ||||||||
\(190\) | 4.95164 | 0.359230 | ||||||||
\(191\) | −25.9827 | −1.88004 | −0.940021 | − | 0.341116i | \(-0.889195\pi\) | ||||
−0.940021 | + | 0.341116i | \(0.889195\pi\) | |||||||
\(192\) | 15.5923 | 1.12528 | ||||||||
\(193\) | −22.3774 | −1.61076 | −0.805379 | − | 0.592760i | \(-0.798038\pi\) | ||||
−0.805379 | + | 0.592760i | \(0.798038\pi\) | |||||||
\(194\) | 21.6779 | 1.55638 | ||||||||
\(195\) | 18.4099 | 1.31836 | ||||||||
\(196\) | −11.9804 | −0.855746 | ||||||||
\(197\) | 8.25198 | 0.587929 | 0.293964 | − | 0.955816i | \(-0.405025\pi\) | ||||
0.293964 | + | 0.955816i | \(0.405025\pi\) | |||||||
\(198\) | 2.21357 | 0.157312 | ||||||||
\(199\) | −14.3758 | −1.01907 | −0.509536 | − | 0.860449i | \(-0.670183\pi\) | ||||
−0.509536 | + | 0.860449i | \(0.670183\pi\) | |||||||
\(200\) | −0.274565 | −0.0194147 | ||||||||
\(201\) | −5.62489 | −0.396749 | ||||||||
\(202\) | 22.9168 | 1.61242 | ||||||||
\(203\) | −13.4050 | −0.940845 | ||||||||
\(204\) | 10.7476 | 0.752481 | ||||||||
\(205\) | −5.79354 | −0.404638 | ||||||||
\(206\) | −21.8394 | −1.52162 | ||||||||
\(207\) | −10.1865 | −0.708009 | ||||||||
\(208\) | 12.6686 | 0.878408 | ||||||||
\(209\) | −0.712705 | −0.0492989 | ||||||||
\(210\) | −10.0778 | −0.695436 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 17.7815 | 1.22124 | ||||||||
\(213\) | 16.0215 | 1.09777 | ||||||||
\(214\) | 10.5720 | 0.722685 | ||||||||
\(215\) | −19.7484 | −1.34683 | ||||||||
\(216\) | −8.98166 | −0.611125 | ||||||||
\(217\) | −3.34013 | −0.226743 | ||||||||
\(218\) | −25.6413 | −1.73665 | ||||||||
\(219\) | −20.8235 | −1.40712 | ||||||||
\(220\) | 4.44456 | 0.299652 | ||||||||
\(221\) | 20.1597 | 1.35609 | ||||||||
\(222\) | 20.2783 | 1.36099 | ||||||||
\(223\) | 27.2686 | 1.82604 | 0.913020 | − | 0.407914i | \(-0.133744\pi\) | ||||
0.913020 | + | 0.407914i | \(0.133744\pi\) | |||||||
\(224\) | −12.1832 | −0.814027 | ||||||||
\(225\) | −0.242083 | −0.0161389 | ||||||||
\(226\) | −28.2336 | −1.87807 | ||||||||
\(227\) | −13.0188 | −0.864086 | −0.432043 | − | 0.901853i | \(-0.642207\pi\) | ||||
−0.432043 | + | 0.901853i | \(0.642207\pi\) | |||||||
\(228\) | 3.44083 | 0.227875 | ||||||||
\(229\) | 10.6244 | 0.702078 | 0.351039 | − | 0.936361i | \(-0.385828\pi\) | ||||
0.351039 | + | 0.936361i | \(0.385828\pi\) | |||||||
\(230\) | −35.3674 | −2.33206 | ||||||||
\(231\) | 1.45053 | 0.0954380 | ||||||||
\(232\) | −13.3653 | −0.877474 | ||||||||
\(233\) | −0.717334 | −0.0469941 | −0.0234970 | − | 0.999724i | \(-0.507480\pi\) | ||||
−0.0234970 | + | 0.999724i | \(0.507480\pi\) | |||||||
\(234\) | −20.0457 | −1.31043 | ||||||||
\(235\) | 24.3105 | 1.58584 | ||||||||
\(236\) | 21.5253 | 1.40118 | ||||||||
\(237\) | 9.82938 | 0.638487 | ||||||||
\(238\) | −11.0357 | −0.715337 | ||||||||
\(239\) | −22.1898 | −1.43534 | −0.717671 | − | 0.696382i | \(-0.754792\pi\) | ||||
−0.717671 | + | 0.696382i | \(0.754792\pi\) | |||||||
\(240\) | 5.59893 | 0.361410 | ||||||||
\(241\) | −21.2455 | −1.36855 | −0.684273 | − | 0.729226i | \(-0.739880\pi\) | ||||
−0.684273 | + | 0.729226i | \(0.739880\pi\) | |||||||
\(242\) | 22.8494 | 1.46882 | ||||||||
\(243\) | −13.2866 | −0.852336 | ||||||||
\(244\) | −17.3895 | −1.11325 | ||||||||
\(245\) | −9.93169 | −0.634513 | ||||||||
\(246\) | −6.96151 | −0.443850 | ||||||||
\(247\) | 6.45412 | 0.410666 | ||||||||
\(248\) | −3.33024 | −0.211470 | ||||||||
\(249\) | 0.605325 | 0.0383609 | ||||||||
\(250\) | 23.9177 | 1.51269 | ||||||||
\(251\) | 14.2507 | 0.899493 | 0.449747 | − | 0.893156i | \(-0.351514\pi\) | ||||
0.449747 | + | 0.893156i | \(0.351514\pi\) | |||||||
\(252\) | 6.34588 | 0.399753 | ||||||||
\(253\) | 5.09054 | 0.320040 | ||||||||
\(254\) | 3.62816 | 0.227651 | ||||||||
\(255\) | 8.90965 | 0.557944 | ||||||||
\(256\) | −1.37989 | −0.0862431 | ||||||||
\(257\) | −17.1217 | −1.06802 | −0.534012 | − | 0.845477i | \(-0.679316\pi\) | ||||
−0.534012 | + | 0.845477i | \(0.679316\pi\) | |||||||
\(258\) | −23.7297 | −1.47735 | ||||||||
\(259\) | −12.0413 | −0.748213 | ||||||||
\(260\) | −40.2490 | −2.49614 | ||||||||
\(261\) | −11.7841 | −0.729420 | ||||||||
\(262\) | 11.8350 | 0.731170 | ||||||||
\(263\) | 0.262179 | 0.0161667 | 0.00808333 | − | 0.999967i | \(-0.497427\pi\) | ||||
0.00808333 | + | 0.999967i | \(0.497427\pi\) | |||||||
\(264\) | 1.44624 | 0.0890097 | ||||||||
\(265\) | 14.7407 | 0.905513 | ||||||||
\(266\) | −3.53307 | −0.216626 | ||||||||
\(267\) | 9.41776 | 0.576357 | ||||||||
\(268\) | 12.2975 | 0.751192 | ||||||||
\(269\) | 18.7365 | 1.14239 | 0.571193 | − | 0.820816i | \(-0.306481\pi\) | ||||
0.571193 | + | 0.820816i | \(0.306481\pi\) | |||||||
\(270\) | −27.4952 | −1.67330 | ||||||||
\(271\) | 31.1309 | 1.89107 | 0.945533 | − | 0.325526i | \(-0.105542\pi\) | ||||
0.945533 | + | 0.325526i | \(0.105542\pi\) | |||||||
\(272\) | 6.13109 | 0.371752 | ||||||||
\(273\) | −13.1357 | −0.795011 | ||||||||
\(274\) | −34.8477 | −2.10523 | ||||||||
\(275\) | 0.120978 | 0.00729522 | ||||||||
\(276\) | −24.5764 | −1.47932 | ||||||||
\(277\) | −7.70318 | −0.462839 | −0.231420 | − | 0.972854i | \(-0.574337\pi\) | ||||
−0.231420 | + | 0.972854i | \(0.574337\pi\) | |||||||
\(278\) | 34.8140 | 2.08800 | ||||||||
\(279\) | −2.93627 | −0.175790 | ||||||||
\(280\) | 5.96653 | 0.356568 | ||||||||
\(281\) | 8.57365 | 0.511461 | 0.255731 | − | 0.966748i | \(-0.417684\pi\) | ||||
0.255731 | + | 0.966748i | \(0.417684\pi\) | |||||||
\(282\) | 29.2115 | 1.73952 | ||||||||
\(283\) | −28.0967 | −1.67018 | −0.835088 | − | 0.550116i | \(-0.814584\pi\) | ||||
−0.835088 | + | 0.550116i | \(0.814584\pi\) | |||||||
\(284\) | −35.0273 | −2.07849 | ||||||||
\(285\) | 2.85242 | 0.168963 | ||||||||
\(286\) | 10.0175 | 0.592350 | ||||||||
\(287\) | 4.13378 | 0.244009 | ||||||||
\(288\) | −10.7101 | −0.631100 | ||||||||
\(289\) | −7.24352 | −0.426089 | ||||||||
\(290\) | −40.9145 | −2.40258 | ||||||||
\(291\) | 12.4877 | 0.732042 | ||||||||
\(292\) | 45.5260 | 2.66421 | ||||||||
\(293\) | 23.7454 | 1.38722 | 0.693612 | − | 0.720349i | \(-0.256018\pi\) | ||||
0.693612 | + | 0.720349i | \(0.256018\pi\) | |||||||
\(294\) | −11.9339 | −0.696000 | ||||||||
\(295\) | 17.8443 | 1.03894 | ||||||||
\(296\) | −12.0057 | −0.697816 | ||||||||
\(297\) | 3.95747 | 0.229635 | ||||||||
\(298\) | 4.02373 | 0.233089 | ||||||||
\(299\) | −46.0989 | −2.66597 | ||||||||
\(300\) | −0.584062 | −0.0337208 | ||||||||
\(301\) | 14.0908 | 0.812180 | ||||||||
\(302\) | 8.80518 | 0.506681 | ||||||||
\(303\) | 13.2014 | 0.758399 | ||||||||
\(304\) | 1.96287 | 0.112578 | ||||||||
\(305\) | −14.4158 | −0.825444 | ||||||||
\(306\) | −9.70132 | −0.554588 | ||||||||
\(307\) | −23.4846 | −1.34034 | −0.670169 | − | 0.742209i | \(-0.733778\pi\) | ||||
−0.670169 | + | 0.742209i | \(0.733778\pi\) | |||||||
\(308\) | −3.17126 | −0.180699 | ||||||||
\(309\) | −12.5807 | −0.715692 | ||||||||
\(310\) | −10.1947 | −0.579020 | ||||||||
\(311\) | −26.2750 | −1.48992 | −0.744959 | − | 0.667110i | \(-0.767531\pi\) | ||||
−0.744959 | + | 0.667110i | \(0.767531\pi\) | |||||||
\(312\) | −13.0968 | −0.741462 | ||||||||
\(313\) | 24.8220 | 1.40302 | 0.701510 | − | 0.712660i | \(-0.252510\pi\) | ||||
0.701510 | + | 0.712660i | \(0.252510\pi\) | |||||||
\(314\) | 26.5096 | 1.49602 | ||||||||
\(315\) | 5.26068 | 0.296406 | ||||||||
\(316\) | −21.4897 | −1.20889 | ||||||||
\(317\) | −12.7207 | −0.714466 | −0.357233 | − | 0.934015i | \(-0.616280\pi\) | ||||
−0.357233 | + | 0.934015i | \(0.616280\pi\) | |||||||
\(318\) | 17.7124 | 0.993262 | ||||||||
\(319\) | 5.88896 | 0.329718 | ||||||||
\(320\) | −28.2595 | −1.57976 | ||||||||
\(321\) | 6.09006 | 0.339914 | ||||||||
\(322\) | 25.2352 | 1.40630 | ||||||||
\(323\) | 3.12354 | 0.173798 | ||||||||
\(324\) | −7.37127 | −0.409515 | ||||||||
\(325\) | −1.09555 | −0.0607701 | ||||||||
\(326\) | 46.1649 | 2.55684 | ||||||||
\(327\) | −14.7709 | −0.816831 | ||||||||
\(328\) | 4.12154 | 0.227574 | ||||||||
\(329\) | −17.3459 | −0.956311 | ||||||||
\(330\) | 4.42730 | 0.243715 | ||||||||
\(331\) | 10.8931 | 0.598741 | 0.299370 | − | 0.954137i | \(-0.403223\pi\) | ||||
0.299370 | + | 0.954137i | \(0.403223\pi\) | |||||||
\(332\) | −1.32341 | −0.0726313 | ||||||||
\(333\) | −10.5854 | −0.580076 | ||||||||
\(334\) | −27.8770 | −1.52536 | ||||||||
\(335\) | 10.1946 | 0.556989 | ||||||||
\(336\) | −3.99492 | −0.217941 | ||||||||
\(337\) | −20.2631 | −1.10380 | −0.551900 | − | 0.833910i | \(-0.686097\pi\) | ||||
−0.551900 | + | 0.833910i | \(0.686097\pi\) | |||||||
\(338\) | −62.4057 | −3.39442 | ||||||||
\(339\) | −16.2641 | −0.883347 | ||||||||
\(340\) | −19.4789 | −1.05639 | ||||||||
\(341\) | 1.46736 | 0.0794618 | ||||||||
\(342\) | −3.10588 | −0.167947 | ||||||||
\(343\) | 18.4427 | 0.995812 | ||||||||
\(344\) | 14.0491 | 0.757475 | ||||||||
\(345\) | −20.3736 | −1.09688 | ||||||||
\(346\) | 33.0263 | 1.77550 | ||||||||
\(347\) | 13.4010 | 0.719404 | 0.359702 | − | 0.933067i | \(-0.382878\pi\) | ||||
0.359702 | + | 0.933067i | \(0.382878\pi\) | |||||||
\(348\) | −28.4310 | −1.52406 | ||||||||
\(349\) | −17.4114 | −0.932011 | −0.466006 | − | 0.884782i | \(-0.654307\pi\) | ||||
−0.466006 | + | 0.884782i | \(0.654307\pi\) | |||||||
\(350\) | 0.599718 | 0.0320563 | ||||||||
\(351\) | −35.8380 | −1.91289 | ||||||||
\(352\) | 5.35223 | 0.285275 | ||||||||
\(353\) | −0.910640 | −0.0484685 | −0.0242342 | − | 0.999706i | \(-0.507715\pi\) | ||||
−0.0242342 | + | 0.999706i | \(0.507715\pi\) | |||||||
\(354\) | 21.4417 | 1.13961 | ||||||||
\(355\) | −29.0373 | −1.54114 | ||||||||
\(356\) | −20.5898 | −1.09126 | ||||||||
\(357\) | −6.35718 | −0.336457 | ||||||||
\(358\) | 1.05344 | 0.0556762 | ||||||||
\(359\) | 2.56165 | 0.135199 | 0.0675993 | − | 0.997713i | \(-0.478466\pi\) | ||||
0.0675993 | + | 0.997713i | \(0.478466\pi\) | |||||||
\(360\) | 5.24510 | 0.276441 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −40.6304 | −2.13549 | ||||||||
\(363\) | 13.1626 | 0.690855 | ||||||||
\(364\) | 28.7183 | 1.50525 | ||||||||
\(365\) | 37.7407 | 1.97544 | ||||||||
\(366\) | −17.3220 | −0.905434 | ||||||||
\(367\) | −16.8641 | −0.880300 | −0.440150 | − | 0.897924i | \(-0.645075\pi\) | ||||
−0.440150 | + | 0.897924i | \(0.645075\pi\) | |||||||
\(368\) | −14.0199 | −0.730838 | ||||||||
\(369\) | 3.63395 | 0.189176 | ||||||||
\(370\) | −36.7524 | −1.91067 | ||||||||
\(371\) | −10.5177 | −0.546052 | ||||||||
\(372\) | −7.08418 | −0.367298 | ||||||||
\(373\) | 25.4816 | 1.31939 | 0.659694 | − | 0.751534i | \(-0.270686\pi\) | ||||
0.659694 | + | 0.751534i | \(0.270686\pi\) | |||||||
\(374\) | 4.84810 | 0.250689 | ||||||||
\(375\) | 13.7779 | 0.711490 | ||||||||
\(376\) | −17.2945 | −0.891897 | ||||||||
\(377\) | −53.3292 | −2.74659 | ||||||||
\(378\) | 19.6182 | 1.00905 | ||||||||
\(379\) | −22.5136 | −1.15645 | −0.578224 | − | 0.815878i | \(-0.696254\pi\) | ||||
−0.578224 | + | 0.815878i | \(0.696254\pi\) | |||||||
\(380\) | −6.23618 | −0.319909 | ||||||||
\(381\) | 2.09003 | 0.107075 | ||||||||
\(382\) | 56.5847 | 2.89512 | ||||||||
\(383\) | 0.555086 | 0.0283636 | 0.0141818 | − | 0.999899i | \(-0.495486\pi\) | ||||
0.0141818 | + | 0.999899i | \(0.495486\pi\) | |||||||
\(384\) | −15.1143 | −0.771300 | ||||||||
\(385\) | −2.62895 | −0.133984 | ||||||||
\(386\) | 48.7330 | 2.48045 | ||||||||
\(387\) | 12.3870 | 0.629669 | ||||||||
\(388\) | −27.3015 | −1.38603 | ||||||||
\(389\) | −33.6053 | −1.70385 | −0.851927 | − | 0.523660i | \(-0.824566\pi\) | ||||
−0.851927 | + | 0.523660i | \(0.824566\pi\) | |||||||
\(390\) | −40.0927 | −2.03017 | ||||||||
\(391\) | −22.3101 | −1.12827 | ||||||||
\(392\) | 7.06543 | 0.356858 | ||||||||
\(393\) | 6.81764 | 0.343905 | ||||||||
\(394\) | −17.9710 | −0.905366 | ||||||||
\(395\) | −17.8148 | −0.896360 | ||||||||
\(396\) | −2.78781 | −0.140093 | ||||||||
\(397\) | −3.11457 | −0.156316 | −0.0781579 | − | 0.996941i | \(-0.524904\pi\) | ||||
−0.0781579 | + | 0.996941i | \(0.524904\pi\) | |||||||
\(398\) | 31.3073 | 1.56929 | ||||||||
\(399\) | −2.03525 | −0.101890 | ||||||||
\(400\) | −0.333185 | −0.0166593 | ||||||||
\(401\) | −17.4089 | −0.869360 | −0.434680 | − | 0.900585i | \(-0.643139\pi\) | ||||
−0.434680 | + | 0.900585i | \(0.643139\pi\) | |||||||
\(402\) | 12.2498 | 0.610964 | ||||||||
\(403\) | −13.2881 | −0.661927 | ||||||||
\(404\) | −28.8618 | −1.43593 | ||||||||
\(405\) | −6.11073 | −0.303644 | ||||||||
\(406\) | 29.1931 | 1.44883 | ||||||||
\(407\) | 5.28990 | 0.262210 | ||||||||
\(408\) | −6.33835 | −0.313795 | ||||||||
\(409\) | 21.9092 | 1.08334 | 0.541670 | − | 0.840591i | \(-0.317792\pi\) | ||||
0.541670 | + | 0.840591i | \(0.317792\pi\) | |||||||
\(410\) | 12.6171 | 0.623113 | ||||||||
\(411\) | −20.0743 | −0.990190 | ||||||||
\(412\) | 27.5049 | 1.35507 | ||||||||
\(413\) | −12.7322 | −0.626510 | ||||||||
\(414\) | 22.1839 | 1.09028 | ||||||||
\(415\) | −1.09709 | −0.0538542 | ||||||||
\(416\) | −48.4687 | −2.37637 | ||||||||
\(417\) | 20.0548 | 0.982088 | ||||||||
\(418\) | 1.55212 | 0.0759165 | ||||||||
\(419\) | −29.1254 | −1.42287 | −0.711434 | − | 0.702753i | \(-0.751954\pi\) | ||||
−0.711434 | + | 0.702753i | \(0.751954\pi\) | |||||||
\(420\) | 12.6922 | 0.619315 | ||||||||
\(421\) | 4.18309 | 0.203871 | 0.101936 | − | 0.994791i | \(-0.467496\pi\) | ||||
0.101936 | + | 0.994791i | \(0.467496\pi\) | |||||||
\(422\) | 2.17778 | 0.106013 | ||||||||
\(423\) | −15.2486 | −0.741410 | ||||||||
\(424\) | −10.4866 | −0.509272 | ||||||||
\(425\) | −0.530202 | −0.0257186 | ||||||||
\(426\) | −34.8913 | −1.69049 | ||||||||
\(427\) | 10.2859 | 0.497768 | ||||||||
\(428\) | −13.3145 | −0.643582 | ||||||||
\(429\) | 5.77067 | 0.278611 | ||||||||
\(430\) | 43.0078 | 2.07402 | ||||||||
\(431\) | 16.3175 | 0.785987 | 0.392994 | − | 0.919541i | \(-0.371439\pi\) | ||||
0.392994 | + | 0.919541i | \(0.371439\pi\) | |||||||
\(432\) | −10.8993 | −0.524392 | ||||||||
\(433\) | −14.8070 | −0.711577 | −0.355789 | − | 0.934566i | \(-0.615788\pi\) | ||||
−0.355789 | + | 0.934566i | \(0.615788\pi\) | |||||||
\(434\) | 7.27408 | 0.349167 | ||||||||
\(435\) | −23.5691 | −1.13005 | ||||||||
\(436\) | 32.2931 | 1.54656 | ||||||||
\(437\) | −7.14256 | −0.341675 | ||||||||
\(438\) | 45.3492 | 2.16687 | ||||||||
\(439\) | −8.60942 | −0.410905 | −0.205453 | − | 0.978667i | \(-0.565867\pi\) | ||||
−0.205453 | + | 0.978667i | \(0.565867\pi\) | |||||||
\(440\) | −2.62116 | −0.124959 | ||||||||
\(441\) | 6.22957 | 0.296646 | ||||||||
\(442\) | −43.9034 | −2.08827 | ||||||||
\(443\) | −10.1847 | −0.483890 | −0.241945 | − | 0.970290i | \(-0.577785\pi\) | ||||
−0.241945 | + | 0.970290i | \(0.577785\pi\) | |||||||
\(444\) | −25.5388 | −1.21202 | ||||||||
\(445\) | −17.0688 | −0.809137 | ||||||||
\(446\) | −59.3851 | −2.81197 | ||||||||
\(447\) | 2.31790 | 0.109633 | ||||||||
\(448\) | 20.1636 | 0.952642 | ||||||||
\(449\) | −3.23149 | −0.152503 | −0.0762516 | − | 0.997089i | \(-0.524295\pi\) | ||||
−0.0762516 | + | 0.997089i | \(0.524295\pi\) | |||||||
\(450\) | 0.527205 | 0.0248527 | ||||||||
\(451\) | −1.81602 | −0.0855128 | ||||||||
\(452\) | 35.5579 | 1.67250 | ||||||||
\(453\) | 5.07228 | 0.238317 | ||||||||
\(454\) | 28.3520 | 1.33063 | ||||||||
\(455\) | 23.8072 | 1.11610 | ||||||||
\(456\) | −2.02922 | −0.0950270 | ||||||||
\(457\) | −41.1592 | −1.92535 | −0.962674 | − | 0.270664i | \(-0.912757\pi\) | ||||
−0.962674 | + | 0.270664i | \(0.912757\pi\) | |||||||
\(458\) | −23.1376 | −1.08115 | ||||||||
\(459\) | −17.3442 | −0.809557 | ||||||||
\(460\) | 44.5423 | 2.07680 | ||||||||
\(461\) | 27.3481 | 1.27373 | 0.636864 | − | 0.770976i | \(-0.280231\pi\) | ||||
0.636864 | + | 0.770976i | \(0.280231\pi\) | |||||||
\(462\) | −3.15894 | −0.146967 | ||||||||
\(463\) | −11.6025 | −0.539215 | −0.269607 | − | 0.962970i | \(-0.586894\pi\) | ||||
−0.269607 | + | 0.962970i | \(0.586894\pi\) | |||||||
\(464\) | −16.2188 | −0.752940 | ||||||||
\(465\) | −5.87273 | −0.272341 | ||||||||
\(466\) | 1.56220 | 0.0723674 | ||||||||
\(467\) | −9.98224 | −0.461923 | −0.230962 | − | 0.972963i | \(-0.574187\pi\) | ||||
−0.230962 | + | 0.972963i | \(0.574187\pi\) | |||||||
\(468\) | 25.2459 | 1.16699 | ||||||||
\(469\) | −7.27398 | −0.335881 | ||||||||
\(470\) | −52.9429 | −2.44208 | ||||||||
\(471\) | 15.2710 | 0.703651 | ||||||||
\(472\) | −12.6945 | −0.584310 | ||||||||
\(473\) | −6.19025 | −0.284628 | ||||||||
\(474\) | −21.4063 | −0.983222 | ||||||||
\(475\) | −0.169744 | −0.00778840 | ||||||||
\(476\) | 13.8985 | 0.637038 | ||||||||
\(477\) | −9.24598 | −0.423344 | ||||||||
\(478\) | 48.3247 | 2.21032 | ||||||||
\(479\) | 1.33788 | 0.0611292 | 0.0305646 | − | 0.999533i | \(-0.490269\pi\) | ||||
0.0305646 | + | 0.999533i | \(0.490269\pi\) | |||||||
\(480\) | −21.4210 | −0.977729 | ||||||||
\(481\) | −47.9042 | −2.18425 | ||||||||
\(482\) | 46.2682 | 2.10746 | ||||||||
\(483\) | 14.5369 | 0.661452 | ||||||||
\(484\) | −28.7769 | −1.30804 | ||||||||
\(485\) | −22.6328 | −1.02770 | ||||||||
\(486\) | 28.9353 | 1.31253 | ||||||||
\(487\) | −13.0425 | −0.591010 | −0.295505 | − | 0.955341i | \(-0.595488\pi\) | ||||
−0.295505 | + | 0.955341i | \(0.595488\pi\) | |||||||
\(488\) | 10.2554 | 0.464240 | ||||||||
\(489\) | 26.5936 | 1.20260 | ||||||||
\(490\) | 21.6291 | 0.977102 | ||||||||
\(491\) | 5.72160 | 0.258212 | 0.129106 | − | 0.991631i | \(-0.458789\pi\) | ||||
0.129106 | + | 0.991631i | \(0.458789\pi\) | |||||||
\(492\) | 8.76745 | 0.395267 | ||||||||
\(493\) | −25.8092 | −1.16239 | ||||||||
\(494\) | −14.0557 | −0.632394 | ||||||||
\(495\) | −2.31108 | −0.103875 | ||||||||
\(496\) | −4.04126 | −0.181458 | ||||||||
\(497\) | 20.7186 | 0.929356 | ||||||||
\(498\) | −1.31827 | −0.0590729 | ||||||||
\(499\) | −25.0032 | −1.11930 | −0.559649 | − | 0.828730i | \(-0.689064\pi\) | ||||
−0.559649 | + | 0.828730i | \(0.689064\pi\) | |||||||
\(500\) | −30.1223 | −1.34711 | ||||||||
\(501\) | −16.0587 | −0.717451 | ||||||||
\(502\) | −31.0348 | −1.38515 | ||||||||
\(503\) | 27.5813 | 1.22979 | 0.614894 | − | 0.788610i | \(-0.289199\pi\) | ||||
0.614894 | + | 0.788610i | \(0.289199\pi\) | |||||||
\(504\) | −3.74246 | −0.166702 | ||||||||
\(505\) | −23.9262 | −1.06470 | ||||||||
\(506\) | −11.0861 | −0.492837 | ||||||||
\(507\) | −35.9492 | −1.59656 | ||||||||
\(508\) | −4.56937 | −0.202733 | ||||||||
\(509\) | 27.1055 | 1.20143 | 0.600715 | − | 0.799463i | \(-0.294883\pi\) | ||||
0.600715 | + | 0.799463i | \(0.294883\pi\) | |||||||
\(510\) | −19.4033 | −0.859192 | ||||||||
\(511\) | −26.9285 | −1.19125 | ||||||||
\(512\) | −21.0906 | −0.932081 | ||||||||
\(513\) | −5.55274 | −0.245159 | ||||||||
\(514\) | 37.2874 | 1.64468 | ||||||||
\(515\) | 22.8013 | 1.00475 | ||||||||
\(516\) | 29.8856 | 1.31564 | ||||||||
\(517\) | 7.62025 | 0.335138 | ||||||||
\(518\) | 26.2234 | 1.15219 | ||||||||
\(519\) | 19.0250 | 0.835105 | ||||||||
\(520\) | 23.7367 | 1.04092 | ||||||||
\(521\) | 35.4205 | 1.55180 | 0.775900 | − | 0.630856i | \(-0.217296\pi\) | ||||
0.775900 | + | 0.630856i | \(0.217296\pi\) | |||||||
\(522\) | 25.6633 | 1.12325 | ||||||||
\(523\) | 18.9029 | 0.826567 | 0.413283 | − | 0.910603i | \(-0.364382\pi\) | ||||
0.413283 | + | 0.910603i | \(0.364382\pi\) | |||||||
\(524\) | −14.9052 | −0.651138 | ||||||||
\(525\) | 0.345472 | 0.0150776 | ||||||||
\(526\) | −0.570969 | −0.0248954 | ||||||||
\(527\) | −6.43091 | −0.280135 | ||||||||
\(528\) | 1.75501 | 0.0763772 | ||||||||
\(529\) | 28.0162 | 1.21810 | ||||||||
\(530\) | −32.1020 | −1.39442 | ||||||||
\(531\) | −11.1927 | −0.485722 | ||||||||
\(532\) | 4.44961 | 0.192915 | ||||||||
\(533\) | 16.4455 | 0.712332 | ||||||||
\(534\) | −20.5098 | −0.887547 | ||||||||
\(535\) | −11.0376 | −0.477199 | ||||||||
\(536\) | −7.25243 | −0.313257 | ||||||||
\(537\) | 0.606843 | 0.0261872 | ||||||||
\(538\) | −40.8041 | −1.75919 | ||||||||
\(539\) | −3.11314 | −0.134092 | ||||||||
\(540\) | 34.6279 | 1.49015 | ||||||||
\(541\) | 4.66919 | 0.200744 | 0.100372 | − | 0.994950i | \(-0.467997\pi\) | ||||
0.100372 | + | 0.994950i | \(0.467997\pi\) | |||||||
\(542\) | −67.7963 | −2.91210 | ||||||||
\(543\) | −23.4054 | −1.00442 | ||||||||
\(544\) | −23.4569 | −1.00571 | ||||||||
\(545\) | 26.7708 | 1.14673 | ||||||||
\(546\) | 28.6068 | 1.22426 | ||||||||
\(547\) | −26.6989 | −1.14156 | −0.570782 | − | 0.821102i | \(-0.693360\pi\) | ||||
−0.570782 | + | 0.821102i | \(0.693360\pi\) | |||||||
\(548\) | 43.8878 | 1.87480 | ||||||||
\(549\) | 9.04217 | 0.385911 | ||||||||
\(550\) | −0.263463 | −0.0112341 | ||||||||
\(551\) | −8.26282 | −0.352008 | ||||||||
\(552\) | 14.4938 | 0.616899 | ||||||||
\(553\) | 12.7111 | 0.540533 | ||||||||
\(554\) | 16.7759 | 0.712738 | ||||||||
\(555\) | −21.1715 | −0.898680 | ||||||||
\(556\) | −43.8453 | −1.85946 | ||||||||
\(557\) | 2.55208 | 0.108135 | 0.0540675 | − | 0.998537i | \(-0.482781\pi\) | ||||
0.0540675 | + | 0.998537i | \(0.482781\pi\) | |||||||
\(558\) | 6.39455 | 0.270703 | ||||||||
\(559\) | 56.0576 | 2.37099 | ||||||||
\(560\) | 7.24041 | 0.305963 | ||||||||
\(561\) | 2.79278 | 0.117911 | ||||||||
\(562\) | −18.6715 | −0.787612 | ||||||||
\(563\) | −32.5993 | −1.37390 | −0.686949 | − | 0.726706i | \(-0.741050\pi\) | ||||
−0.686949 | + | 0.726706i | \(0.741050\pi\) | |||||||
\(564\) | −36.7894 | −1.54911 | ||||||||
\(565\) | 29.4772 | 1.24011 | ||||||||
\(566\) | 61.1886 | 2.57195 | ||||||||
\(567\) | 4.36010 | 0.183107 | ||||||||
\(568\) | 20.6572 | 0.866758 | ||||||||
\(569\) | −30.6223 | −1.28375 | −0.641876 | − | 0.766808i | \(-0.721844\pi\) | ||||
−0.641876 | + | 0.766808i | \(0.721844\pi\) | |||||||
\(570\) | −6.21196 | −0.260190 | ||||||||
\(571\) | −3.76798 | −0.157685 | −0.0788425 | − | 0.996887i | \(-0.525122\pi\) | ||||
−0.0788425 | + | 0.996887i | \(0.525122\pi\) | |||||||
\(572\) | −12.6163 | −0.527513 | ||||||||
\(573\) | 32.5960 | 1.36172 | ||||||||
\(574\) | −9.00247 | −0.375756 | ||||||||
\(575\) | 1.21241 | 0.0505609 | ||||||||
\(576\) | 17.7256 | 0.738566 | ||||||||
\(577\) | −10.3599 | −0.431287 | −0.215644 | − | 0.976472i | \(-0.569185\pi\) | ||||
−0.215644 | + | 0.976472i | \(0.569185\pi\) | |||||||
\(578\) | 15.7748 | 0.656145 | ||||||||
\(579\) | 28.0730 | 1.16667 | ||||||||
\(580\) | 51.5285 | 2.13960 | ||||||||
\(581\) | 0.782793 | 0.0324757 | ||||||||
\(582\) | −27.1955 | −1.12729 | ||||||||
\(583\) | 4.62054 | 0.191363 | ||||||||
\(584\) | −26.8488 | −1.11101 | ||||||||
\(585\) | 20.9286 | 0.865293 | ||||||||
\(586\) | −51.7124 | −2.13622 | ||||||||
\(587\) | −23.2242 | −0.958564 | −0.479282 | − | 0.877661i | \(-0.659103\pi\) | ||||
−0.479282 | + | 0.877661i | \(0.659103\pi\) | |||||||
\(588\) | 15.0298 | 0.619818 | ||||||||
\(589\) | −2.05885 | −0.0848336 | ||||||||
\(590\) | −38.8610 | −1.59988 | ||||||||
\(591\) | −10.3523 | −0.425837 | ||||||||
\(592\) | −14.5689 | −0.598780 | ||||||||
\(593\) | 14.6206 | 0.600394 | 0.300197 | − | 0.953877i | \(-0.402948\pi\) | ||||
0.300197 | + | 0.953877i | \(0.402948\pi\) | |||||||
\(594\) | −8.61850 | −0.353621 | ||||||||
\(595\) | 11.5218 | 0.472346 | ||||||||
\(596\) | −5.06756 | −0.207575 | ||||||||
\(597\) | 18.0348 | 0.738115 | ||||||||
\(598\) | 100.393 | 4.10539 | ||||||||
\(599\) | −14.0129 | −0.572553 | −0.286276 | − | 0.958147i | \(-0.592418\pi\) | ||||
−0.286276 | + | 0.958147i | \(0.592418\pi\) | |||||||
\(600\) | 0.344448 | 0.0140621 | ||||||||
\(601\) | −2.64546 | −0.107911 | −0.0539553 | − | 0.998543i | \(-0.517183\pi\) | ||||
−0.0539553 | + | 0.998543i | \(0.517183\pi\) | |||||||
\(602\) | −30.6867 | −1.25070 | ||||||||
\(603\) | −6.39446 | −0.260403 | ||||||||
\(604\) | −11.0894 | −0.451221 | ||||||||
\(605\) | −23.8559 | −0.969878 | ||||||||
\(606\) | −28.7497 | −1.16788 | ||||||||
\(607\) | 9.50925 | 0.385968 | 0.192984 | − | 0.981202i | \(-0.438183\pi\) | ||||
0.192984 | + | 0.981202i | \(0.438183\pi\) | |||||||
\(608\) | −7.50974 | −0.304560 | ||||||||
\(609\) | 16.8169 | 0.681455 | ||||||||
\(610\) | 31.3944 | 1.27112 | ||||||||
\(611\) | −69.0074 | −2.79174 | ||||||||
\(612\) | 12.2180 | 0.493884 | ||||||||
\(613\) | −17.9974 | −0.726907 | −0.363454 | − | 0.931612i | \(-0.618402\pi\) | ||||
−0.363454 | + | 0.931612i | \(0.618402\pi\) | |||||||
\(614\) | 51.1444 | 2.06402 | ||||||||
\(615\) | 7.26815 | 0.293080 | ||||||||
\(616\) | 1.87024 | 0.0753541 | ||||||||
\(617\) | 11.8842 | 0.478440 | 0.239220 | − | 0.970965i | \(-0.423108\pi\) | ||||
0.239220 | + | 0.970965i | \(0.423108\pi\) | |||||||
\(618\) | 27.3981 | 1.10211 | ||||||||
\(619\) | 43.0835 | 1.73167 | 0.865836 | − | 0.500329i | \(-0.166787\pi\) | ||||
0.865836 | + | 0.500329i | \(0.166787\pi\) | |||||||
\(620\) | 12.8394 | 0.515642 | ||||||||
\(621\) | 39.6608 | 1.59153 | ||||||||
\(622\) | 57.2212 | 2.29436 | ||||||||
\(623\) | 12.1788 | 0.487935 | ||||||||
\(624\) | −15.8931 | −0.636232 | ||||||||
\(625\) | −25.8199 | −1.03280 | ||||||||
\(626\) | −54.0568 | −2.16055 | ||||||||
\(627\) | 0.894107 | 0.0357072 | ||||||||
\(628\) | −33.3866 | −1.33227 | ||||||||
\(629\) | −23.1838 | −0.924397 | ||||||||
\(630\) | −11.4566 | −0.456443 | ||||||||
\(631\) | 42.9134 | 1.70835 | 0.854177 | − | 0.519982i | \(-0.174061\pi\) | ||||
0.854177 | + | 0.519982i | \(0.174061\pi\) | |||||||
\(632\) | 12.6735 | 0.504124 | ||||||||
\(633\) | 1.25453 | 0.0498629 | ||||||||
\(634\) | 27.7029 | 1.10022 | ||||||||
\(635\) | −3.78797 | −0.150321 | ||||||||
\(636\) | −22.3073 | −0.884542 | ||||||||
\(637\) | 28.1920 | 1.11701 | ||||||||
\(638\) | −12.8249 | −0.507741 | ||||||||
\(639\) | 18.2134 | 0.720513 | ||||||||
\(640\) | 27.3933 | 1.08281 | ||||||||
\(641\) | −21.2655 | −0.839938 | −0.419969 | − | 0.907538i | \(-0.637959\pi\) | ||||
−0.419969 | + | 0.907538i | \(0.637959\pi\) | |||||||
\(642\) | −13.2628 | −0.523442 | ||||||||
\(643\) | −38.0529 | −1.50066 | −0.750330 | − | 0.661063i | \(-0.770105\pi\) | ||||
−0.750330 | + | 0.661063i | \(0.770105\pi\) | |||||||
\(644\) | −31.7816 | −1.25237 | ||||||||
\(645\) | 24.7749 | 0.975511 | ||||||||
\(646\) | −6.80238 | −0.267636 | ||||||||
\(647\) | 19.0452 | 0.748744 | 0.374372 | − | 0.927279i | \(-0.377858\pi\) | ||||
0.374372 | + | 0.927279i | \(0.377858\pi\) | |||||||
\(648\) | 4.34718 | 0.170773 | ||||||||
\(649\) | 5.59339 | 0.219560 | ||||||||
\(650\) | 2.38587 | 0.0935814 | ||||||||
\(651\) | 4.19028 | 0.164230 | ||||||||
\(652\) | −58.1409 | −2.27697 | ||||||||
\(653\) | −1.97433 | −0.0772615 | −0.0386308 | − | 0.999254i | \(-0.512300\pi\) | ||||
−0.0386308 | + | 0.999254i | \(0.512300\pi\) | |||||||
\(654\) | 32.1677 | 1.25786 | ||||||||
\(655\) | −12.3563 | −0.482801 | ||||||||
\(656\) | 5.00150 | 0.195276 | ||||||||
\(657\) | −23.6725 | −0.923553 | ||||||||
\(658\) | 37.7756 | 1.47265 | ||||||||
\(659\) | −20.2403 | −0.788449 | −0.394224 | − | 0.919014i | \(-0.628987\pi\) | ||||
−0.394224 | + | 0.919014i | \(0.628987\pi\) | |||||||
\(660\) | −5.57581 | −0.217038 | ||||||||
\(661\) | −19.7257 | −0.767240 | −0.383620 | − | 0.923491i | \(-0.625323\pi\) | ||||
−0.383620 | + | 0.923491i | \(0.625323\pi\) | |||||||
\(662\) | −23.7229 | −0.922015 | ||||||||
\(663\) | −25.2908 | −0.982215 | ||||||||
\(664\) | 0.780474 | 0.0302883 | ||||||||
\(665\) | 3.68869 | 0.143041 | ||||||||
\(666\) | 23.0527 | 0.893273 | ||||||||
\(667\) | 59.0177 | 2.28518 | ||||||||
\(668\) | 35.1088 | 1.35840 | ||||||||
\(669\) | −34.2092 | −1.32260 | ||||||||
\(670\) | −22.2015 | −0.857721 | ||||||||
\(671\) | −4.51870 | −0.174442 | ||||||||
\(672\) | 15.2842 | 0.589600 | ||||||||
\(673\) | 22.4766 | 0.866408 | 0.433204 | − | 0.901296i | \(-0.357383\pi\) | ||||
0.433204 | + | 0.901296i | \(0.357383\pi\) | |||||||
\(674\) | 44.1285 | 1.69977 | ||||||||
\(675\) | 0.942545 | 0.0362786 | ||||||||
\(676\) | 78.5948 | 3.02288 | ||||||||
\(677\) | 18.0876 | 0.695165 | 0.347582 | − | 0.937649i | \(-0.387003\pi\) | ||||
0.347582 | + | 0.937649i | \(0.387003\pi\) | |||||||
\(678\) | 35.4198 | 1.36029 | ||||||||
\(679\) | 16.1488 | 0.619735 | ||||||||
\(680\) | 11.4876 | 0.440531 | ||||||||
\(681\) | 16.3324 | 0.625858 | ||||||||
\(682\) | −3.19558 | −0.122365 | ||||||||
\(683\) | −5.27378 | −0.201796 | −0.100898 | − | 0.994897i | \(-0.532171\pi\) | ||||
−0.100898 | + | 0.994897i | \(0.532171\pi\) | |||||||
\(684\) | 3.91159 | 0.149564 | ||||||||
\(685\) | 36.3827 | 1.39011 | ||||||||
\(686\) | −40.1642 | −1.53348 | ||||||||
\(687\) | −13.3286 | −0.508516 | ||||||||
\(688\) | 17.0486 | 0.649972 | ||||||||
\(689\) | −41.8427 | −1.59408 | ||||||||
\(690\) | 44.3693 | 1.68911 | ||||||||
\(691\) | 42.0872 | 1.60107 | 0.800536 | − | 0.599284i | \(-0.204548\pi\) | ||||
0.800536 | + | 0.599284i | \(0.204548\pi\) | |||||||
\(692\) | −41.5938 | −1.58116 | ||||||||
\(693\) | 1.64899 | 0.0626399 | ||||||||
\(694\) | −29.1845 | −1.10783 | ||||||||
\(695\) | −36.3474 | −1.37874 | ||||||||
\(696\) | 16.7671 | 0.635555 | ||||||||
\(697\) | 7.95896 | 0.301467 | ||||||||
\(698\) | 37.9183 | 1.43523 | ||||||||
\(699\) | 0.899914 | 0.0340379 | ||||||||
\(700\) | −0.755296 | −0.0285475 | ||||||||
\(701\) | −29.2419 | −1.10445 | −0.552225 | − | 0.833695i | \(-0.686221\pi\) | ||||
−0.552225 | + | 0.833695i | \(0.686221\pi\) | |||||||
\(702\) | 78.0474 | 2.94571 | ||||||||
\(703\) | −7.42228 | −0.279936 | ||||||||
\(704\) | −8.85810 | −0.333852 | ||||||||
\(705\) | −30.4981 | −1.14863 | ||||||||
\(706\) | 1.98318 | 0.0746378 | ||||||||
\(707\) | 17.0717 | 0.642048 | ||||||||
\(708\) | −27.0040 | −1.01487 | ||||||||
\(709\) | 31.2570 | 1.17388 | 0.586941 | − | 0.809630i | \(-0.300332\pi\) | ||||
0.586941 | + | 0.809630i | \(0.300332\pi\) | |||||||
\(710\) | 63.2370 | 2.37324 | ||||||||
\(711\) | 11.1742 | 0.419065 | ||||||||
\(712\) | 12.1428 | 0.455069 | ||||||||
\(713\) | 14.7055 | 0.550725 | ||||||||
\(714\) | 13.8445 | 0.518119 | ||||||||
\(715\) | −10.4588 | −0.391136 | ||||||||
\(716\) | −1.32672 | −0.0495820 | ||||||||
\(717\) | 27.8377 | 1.03962 | ||||||||
\(718\) | −5.57871 | −0.208196 | ||||||||
\(719\) | −16.1608 | −0.602698 | −0.301349 | − | 0.953514i | \(-0.597437\pi\) | ||||
−0.301349 | + | 0.953514i | \(0.597437\pi\) | |||||||
\(720\) | 6.36495 | 0.237208 | ||||||||
\(721\) | −16.2691 | −0.605893 | ||||||||
\(722\) | −2.17778 | −0.0810487 | ||||||||
\(723\) | 26.6531 | 0.991239 | ||||||||
\(724\) | 51.1707 | 1.90174 | ||||||||
\(725\) | 1.40257 | 0.0520900 | ||||||||
\(726\) | −28.6652 | −1.06386 | ||||||||
\(727\) | 8.97529 | 0.332875 | 0.166438 | − | 0.986052i | \(-0.446774\pi\) | ||||
0.166438 | + | 0.986052i | \(0.446774\pi\) | |||||||
\(728\) | −16.9365 | −0.627709 | ||||||||
\(729\) | 24.7311 | 0.915966 | ||||||||
\(730\) | −82.1910 | −3.04202 | ||||||||
\(731\) | 27.1297 | 1.00343 | ||||||||
\(732\) | 21.8156 | 0.806328 | ||||||||
\(733\) | −12.3542 | −0.456312 | −0.228156 | − | 0.973625i | \(-0.573270\pi\) | ||||
−0.228156 | + | 0.973625i | \(0.573270\pi\) | |||||||
\(734\) | 36.7264 | 1.35560 | ||||||||
\(735\) | 12.4596 | 0.459578 | ||||||||
\(736\) | 53.6388 | 1.97715 | ||||||||
\(737\) | 3.19554 | 0.117709 | ||||||||
\(738\) | −7.91396 | −0.291317 | ||||||||
\(739\) | −39.8909 | −1.46741 | −0.733704 | − | 0.679469i | \(-0.762210\pi\) | ||||
−0.733704 | + | 0.679469i | \(0.762210\pi\) | |||||||
\(740\) | 46.2867 | 1.70153 | ||||||||
\(741\) | −8.09686 | −0.297445 | ||||||||
\(742\) | 22.9053 | 0.840879 | ||||||||
\(743\) | −29.9849 | −1.10004 | −0.550020 | − | 0.835152i | \(-0.685380\pi\) | ||||
−0.550020 | + | 0.835152i | \(0.685380\pi\) | |||||||
\(744\) | 4.17787 | 0.153168 | ||||||||
\(745\) | −4.20096 | −0.153911 | ||||||||
\(746\) | −55.4934 | −2.03176 | ||||||||
\(747\) | 0.688143 | 0.0251778 | ||||||||
\(748\) | −6.10578 | −0.223249 | ||||||||
\(749\) | 7.87552 | 0.287765 | ||||||||
\(750\) | −30.0054 | −1.09564 | ||||||||
\(751\) | 21.1038 | 0.770087 | 0.385044 | − | 0.922898i | \(-0.374186\pi\) | ||||
0.385044 | + | 0.922898i | \(0.374186\pi\) | |||||||
\(752\) | −20.9870 | −0.765317 | ||||||||
\(753\) | −17.8778 | −0.651504 | ||||||||
\(754\) | 116.139 | 4.22955 | ||||||||
\(755\) | −9.19302 | −0.334568 | ||||||||
\(756\) | −24.7075 | −0.898604 | ||||||||
\(757\) | 49.6105 | 1.80313 | 0.901563 | − | 0.432649i | \(-0.142421\pi\) | ||||
0.901563 | + | 0.432649i | \(0.142421\pi\) | |||||||
\(758\) | 49.0298 | 1.78084 | ||||||||
\(759\) | −6.38622 | −0.231805 | ||||||||
\(760\) | 3.67777 | 0.133407 | ||||||||
\(761\) | −15.0888 | −0.546967 | −0.273483 | − | 0.961877i | \(-0.588176\pi\) | ||||
−0.273483 | + | 0.961877i | \(0.588176\pi\) | |||||||
\(762\) | −4.55163 | −0.164888 | ||||||||
\(763\) | −19.1014 | −0.691515 | ||||||||
\(764\) | −71.2637 | −2.57823 | ||||||||
\(765\) | 10.1286 | 0.366201 | ||||||||
\(766\) | −1.20886 | −0.0436778 | ||||||||
\(767\) | −50.6526 | −1.82896 | ||||||||
\(768\) | 1.73111 | 0.0624660 | ||||||||
\(769\) | 26.3814 | 0.951337 | 0.475668 | − | 0.879625i | \(-0.342206\pi\) | ||||
0.475668 | + | 0.879625i | \(0.342206\pi\) | |||||||
\(770\) | 5.72528 | 0.206325 | ||||||||
\(771\) | 21.4797 | 0.773571 | ||||||||
\(772\) | −61.3752 | −2.20894 | ||||||||
\(773\) | 43.4230 | 1.56182 | 0.780908 | − | 0.624646i | \(-0.214757\pi\) | ||||
0.780908 | + | 0.624646i | \(0.214757\pi\) | |||||||
\(774\) | −26.9763 | −0.969642 | ||||||||
\(775\) | 0.349479 | 0.0125536 | ||||||||
\(776\) | 16.1010 | 0.577992 | ||||||||
\(777\) | 15.1062 | 0.541931 | ||||||||
\(778\) | 73.1849 | 2.62381 | ||||||||
\(779\) | 2.54806 | 0.0912937 | ||||||||
\(780\) | 50.4935 | 1.80796 | ||||||||
\(781\) | −9.10191 | −0.325692 | ||||||||
\(782\) | 48.5865 | 1.73745 | ||||||||
\(783\) | 45.8813 | 1.63966 | ||||||||
\(784\) | 8.57393 | 0.306212 | ||||||||
\(785\) | −27.6772 | −0.987843 | ||||||||
\(786\) | −14.8473 | −0.529587 | ||||||||
\(787\) | 12.2713 | 0.437424 | 0.218712 | − | 0.975790i | \(-0.429815\pi\) | ||||
0.218712 | + | 0.975790i | \(0.429815\pi\) | |||||||
\(788\) | 22.6330 | 0.806267 | ||||||||
\(789\) | −0.328910 | −0.0117095 | ||||||||
\(790\) | 38.7968 | 1.38033 | ||||||||
\(791\) | −21.0324 | −0.747827 | ||||||||
\(792\) | 1.64410 | 0.0584207 | ||||||||
\(793\) | 40.9204 | 1.45313 | ||||||||
\(794\) | 6.78286 | 0.240715 | ||||||||
\(795\) | −18.4926 | −0.655864 | ||||||||
\(796\) | −39.4290 | −1.39752 | ||||||||
\(797\) | −17.6721 | −0.625979 | −0.312989 | − | 0.949757i | \(-0.601330\pi\) | ||||
−0.312989 | + | 0.949757i | \(0.601330\pi\) | |||||||
\(798\) | 4.43233 | 0.156903 | ||||||||
\(799\) | −33.3969 | −1.18150 | ||||||||
\(800\) | 1.27473 | 0.0450687 | ||||||||
\(801\) | 10.7063 | 0.378287 | ||||||||
\(802\) | 37.9129 | 1.33875 | ||||||||
\(803\) | 11.8300 | 0.417472 | ||||||||
\(804\) | −15.4276 | −0.544089 | ||||||||
\(805\) | −26.3467 | −0.928600 | ||||||||
\(806\) | 28.9386 | 1.01932 | ||||||||
\(807\) | −23.5055 | −0.827431 | ||||||||
\(808\) | 17.0212 | 0.598802 | ||||||||
\(809\) | −44.5671 | −1.56690 | −0.783448 | − | 0.621457i | \(-0.786541\pi\) | ||||
−0.783448 | + | 0.621457i | \(0.786541\pi\) | |||||||
\(810\) | 13.3078 | 0.467590 | ||||||||
\(811\) | 7.96283 | 0.279613 | 0.139806 | − | 0.990179i | \(-0.455352\pi\) | ||||
0.139806 | + | 0.990179i | \(0.455352\pi\) | |||||||
\(812\) | −36.7663 | −1.29025 | ||||||||
\(813\) | −39.0545 | −1.36970 | ||||||||
\(814\) | −11.5202 | −0.403784 | ||||||||
\(815\) | −48.1983 | −1.68831 | ||||||||
\(816\) | −7.69161 | −0.269260 | ||||||||
\(817\) | 8.68556 | 0.303869 | ||||||||
\(818\) | −47.7135 | −1.66826 | ||||||||
\(819\) | −14.9329 | −0.521798 | ||||||||
\(820\) | −15.8902 | −0.554908 | ||||||||
\(821\) | 6.66857 | 0.232735 | 0.116367 | − | 0.993206i | \(-0.462875\pi\) | ||||
0.116367 | + | 0.993206i | \(0.462875\pi\) | |||||||
\(822\) | 43.7174 | 1.52482 | ||||||||
\(823\) | −49.6409 | −1.73037 | −0.865187 | − | 0.501449i | \(-0.832800\pi\) | ||||
−0.865187 | + | 0.501449i | \(0.832800\pi\) | |||||||
\(824\) | −16.2209 | −0.565082 | ||||||||
\(825\) | −0.151770 | −0.00528394 | ||||||||
\(826\) | 27.7279 | 0.964778 | ||||||||
\(827\) | −37.6406 | −1.30889 | −0.654446 | − | 0.756109i | \(-0.727098\pi\) | ||||
−0.654446 | + | 0.756109i | \(0.727098\pi\) | |||||||
\(828\) | −27.9388 | −0.970941 | ||||||||
\(829\) | −19.3013 | −0.670363 | −0.335182 | − | 0.942154i | \(-0.608798\pi\) | ||||
−0.335182 | + | 0.942154i | \(0.608798\pi\) | |||||||
\(830\) | 2.38923 | 0.0829314 | ||||||||
\(831\) | 9.66384 | 0.335235 | ||||||||
\(832\) | 80.2172 | 2.78103 | ||||||||
\(833\) | 13.6438 | 0.472730 | ||||||||
\(834\) | −43.6750 | −1.51234 | ||||||||
\(835\) | 29.1049 | 1.00722 | ||||||||
\(836\) | −1.95476 | −0.0676069 | ||||||||
\(837\) | 11.4323 | 0.395157 | ||||||||
\(838\) | 63.4287 | 2.19111 | ||||||||
\(839\) | −46.6157 | −1.60935 | −0.804676 | − | 0.593714i | \(-0.797661\pi\) | ||||
−0.804676 | + | 0.593714i | \(0.797661\pi\) | |||||||
\(840\) | −7.48517 | −0.258263 | ||||||||
\(841\) | 39.2742 | 1.35428 | ||||||||
\(842\) | −9.10986 | −0.313946 | ||||||||
\(843\) | −10.7559 | −0.370452 | ||||||||
\(844\) | −2.74274 | −0.0944089 | ||||||||
\(845\) | 65.1545 | 2.24138 | ||||||||
\(846\) | 33.2080 | 1.14172 | ||||||||
\(847\) | 17.0215 | 0.584866 | ||||||||
\(848\) | −12.7255 | −0.436995 | ||||||||
\(849\) | 35.2481 | 1.20971 | ||||||||
\(850\) | 1.15467 | 0.0396047 | ||||||||
\(851\) | 53.0141 | 1.81730 | ||||||||
\(852\) | 43.9427 | 1.50545 | ||||||||
\(853\) | 30.6139 | 1.04820 | 0.524100 | − | 0.851657i | \(-0.324402\pi\) | ||||
0.524100 | + | 0.851657i | \(0.324402\pi\) | |||||||
\(854\) | −22.4004 | −0.766526 | ||||||||
\(855\) | 3.24268 | 0.110897 | ||||||||
\(856\) | 7.85220 | 0.268383 | ||||||||
\(857\) | −21.4588 | −0.733020 | −0.366510 | − | 0.930414i | \(-0.619447\pi\) | ||||
−0.366510 | + | 0.930414i | \(0.619447\pi\) | |||||||
\(858\) | −12.5673 | −0.429039 | ||||||||
\(859\) | −8.95932 | −0.305688 | −0.152844 | − | 0.988250i | \(-0.548843\pi\) | ||||
−0.152844 | + | 0.988250i | \(0.548843\pi\) | |||||||
\(860\) | −54.1647 | −1.84700 | ||||||||
\(861\) | −5.18593 | −0.176736 | ||||||||
\(862\) | −35.5360 | −1.21036 | ||||||||
\(863\) | 16.1485 | 0.549702 | 0.274851 | − | 0.961487i | \(-0.411371\pi\) | ||||
0.274851 | + | 0.961487i | \(0.411371\pi\) | |||||||
\(864\) | 41.6996 | 1.41865 | ||||||||
\(865\) | −34.4810 | −1.17239 | ||||||||
\(866\) | 32.2463 | 1.09578 | ||||||||
\(867\) | 9.08718 | 0.308617 | ||||||||
\(868\) | −9.16110 | −0.310948 | ||||||||
\(869\) | −5.58414 | −0.189429 | ||||||||
\(870\) | 51.3283 | 1.74019 | ||||||||
\(871\) | −28.9382 | −0.980532 | ||||||||
\(872\) | −19.0448 | −0.644937 | ||||||||
\(873\) | 14.1962 | 0.480469 | ||||||||
\(874\) | 15.5549 | 0.526154 | ||||||||
\(875\) | 17.8173 | 0.602336 | ||||||||
\(876\) | −57.1135 | −1.92969 | ||||||||
\(877\) | 40.2224 | 1.35821 | 0.679107 | − | 0.734040i | \(-0.262367\pi\) | ||||
0.679107 | + | 0.734040i | \(0.262367\pi\) | |||||||
\(878\) | 18.7494 | 0.632763 | ||||||||
\(879\) | −29.7893 | −1.00477 | ||||||||
\(880\) | −3.18079 | −0.107225 | ||||||||
\(881\) | 14.7861 | 0.498158 | 0.249079 | − | 0.968483i | \(-0.419872\pi\) | ||||
0.249079 | + | 0.968483i | \(0.419872\pi\) | |||||||
\(882\) | −13.5667 | −0.456813 | ||||||||
\(883\) | −4.64374 | −0.156274 | −0.0781371 | − | 0.996943i | \(-0.524897\pi\) | ||||
−0.0781371 | + | 0.996943i | \(0.524897\pi\) | |||||||
\(884\) | 55.2927 | 1.85969 | ||||||||
\(885\) | −22.3861 | −0.752502 | ||||||||
\(886\) | 22.1801 | 0.745155 | ||||||||
\(887\) | 45.2760 | 1.52022 | 0.760110 | − | 0.649794i | \(-0.225145\pi\) | ||||
0.760110 | + | 0.649794i | \(0.225145\pi\) | |||||||
\(888\) | 15.0614 | 0.505429 | ||||||||
\(889\) | 2.70278 | 0.0906482 | ||||||||
\(890\) | 37.1721 | 1.24601 | ||||||||
\(891\) | −1.91544 | −0.0641696 | ||||||||
\(892\) | 74.7906 | 2.50418 | ||||||||
\(893\) | −10.6920 | −0.357794 | ||||||||
\(894\) | −5.04788 | −0.168826 | ||||||||
\(895\) | −1.09984 | −0.0367637 | ||||||||
\(896\) | −19.5455 | −0.652970 | ||||||||
\(897\) | 57.8323 | 1.93096 | ||||||||
\(898\) | 7.03747 | 0.234844 | ||||||||
\(899\) | 17.0120 | 0.567380 | ||||||||
\(900\) | −0.663971 | −0.0221324 | ||||||||
\(901\) | −20.2502 | −0.674633 | ||||||||
\(902\) | 3.95489 | 0.131683 | ||||||||
\(903\) | −17.6773 | −0.588263 | ||||||||
\(904\) | −20.9701 | −0.697456 | ||||||||
\(905\) | 42.4201 | 1.41009 | ||||||||
\(906\) | −11.0463 | −0.366990 | ||||||||
\(907\) | −16.4443 | −0.546023 | −0.273012 | − | 0.962011i | \(-0.588020\pi\) | ||||
−0.273012 | + | 0.962011i | \(0.588020\pi\) | |||||||
\(908\) | −35.7071 | −1.18498 | ||||||||
\(909\) | 15.0075 | 0.497768 | ||||||||
\(910\) | −51.8470 | −1.71871 | ||||||||
\(911\) | −35.3486 | −1.17115 | −0.585576 | − | 0.810618i | \(-0.699132\pi\) | ||||
−0.585576 | + | 0.810618i | \(0.699132\pi\) | |||||||
\(912\) | −2.46247 | −0.0815405 | ||||||||
\(913\) | −0.343889 | −0.0113811 | ||||||||
\(914\) | 89.6359 | 2.96489 | ||||||||
\(915\) | 18.0850 | 0.597870 | ||||||||
\(916\) | 29.1399 | 0.962808 | ||||||||
\(917\) | 8.81642 | 0.291144 | ||||||||
\(918\) | 37.7719 | 1.24666 | ||||||||
\(919\) | −12.4219 | −0.409761 | −0.204880 | − | 0.978787i | \(-0.565681\pi\) | ||||
−0.204880 | + | 0.978787i | \(0.565681\pi\) | |||||||
\(920\) | −26.2687 | −0.866053 | ||||||||
\(921\) | 29.4621 | 0.970808 | ||||||||
\(922\) | −59.5582 | −1.96145 | ||||||||
\(923\) | 82.4250 | 2.71305 | ||||||||
\(924\) | 3.97843 | 0.130881 | ||||||||
\(925\) | 1.25989 | 0.0414249 | ||||||||
\(926\) | 25.2678 | 0.830350 | ||||||||
\(927\) | −14.3019 | −0.469738 | ||||||||
\(928\) | 62.0516 | 2.03694 | ||||||||
\(929\) | 53.7588 | 1.76377 | 0.881885 | − | 0.471465i | \(-0.156275\pi\) | ||||
0.881885 | + | 0.471465i | \(0.156275\pi\) | |||||||
\(930\) | 12.7895 | 0.419385 | ||||||||
\(931\) | 4.36806 | 0.143157 | ||||||||
\(932\) | −1.96746 | −0.0644462 | ||||||||
\(933\) | 32.9627 | 1.07915 | ||||||||
\(934\) | 21.7392 | 0.711327 | ||||||||
\(935\) | −5.06164 | −0.165533 | ||||||||
\(936\) | −14.8887 | −0.486651 | ||||||||
\(937\) | −1.50118 | −0.0490414 | −0.0245207 | − | 0.999699i | \(-0.507806\pi\) | ||||
−0.0245207 | + | 0.999699i | \(0.507806\pi\) | |||||||
\(938\) | 15.8411 | 0.517232 | ||||||||
\(939\) | −31.1398 | −1.01621 | ||||||||
\(940\) | 66.6773 | 2.17477 | ||||||||
\(941\) | 58.6855 | 1.91309 | 0.956547 | − | 0.291578i | \(-0.0941804\pi\) | ||||
0.956547 | + | 0.291578i | \(0.0941804\pi\) | |||||||
\(942\) | −33.2570 | −1.08357 | ||||||||
\(943\) | −18.1997 | −0.592663 | ||||||||
\(944\) | −15.4048 | −0.501384 | ||||||||
\(945\) | −20.4823 | −0.666291 | ||||||||
\(946\) | 13.4810 | 0.438305 | ||||||||
\(947\) | −41.5938 | −1.35162 | −0.675809 | − | 0.737077i | \(-0.736206\pi\) | ||||
−0.675809 | + | 0.737077i | \(0.736206\pi\) | |||||||
\(948\) | 26.9594 | 0.875601 | ||||||||
\(949\) | −107.130 | −3.47759 | ||||||||
\(950\) | 0.369666 | 0.0119936 | ||||||||
\(951\) | 15.9585 | 0.517488 | ||||||||
\(952\) | −8.19661 | −0.265654 | ||||||||
\(953\) | 4.64545 | 0.150481 | 0.0752404 | − | 0.997165i | \(-0.476028\pi\) | ||||
0.0752404 | + | 0.997165i | \(0.476028\pi\) | |||||||
\(954\) | 20.1357 | 0.651918 | ||||||||
\(955\) | −59.0770 | −1.91169 | ||||||||
\(956\) | −60.8609 | −1.96838 | ||||||||
\(957\) | −7.38785 | −0.238815 | ||||||||
\(958\) | −2.91360 | −0.0941343 | ||||||||
\(959\) | −25.9596 | −0.838279 | ||||||||
\(960\) | 35.4523 | 1.14422 | ||||||||
\(961\) | −26.7611 | −0.863262 | ||||||||
\(962\) | 104.325 | 3.36357 | ||||||||
\(963\) | 6.92327 | 0.223099 | ||||||||
\(964\) | −58.2709 | −1.87678 | ||||||||
\(965\) | −50.8796 | −1.63787 | ||||||||
\(966\) | −31.6582 | −1.01859 | ||||||||
\(967\) | 32.0649 | 1.03114 | 0.515568 | − | 0.856849i | \(-0.327581\pi\) | ||||
0.515568 | + | 0.856849i | \(0.327581\pi\) | |||||||
\(968\) | 16.9711 | 0.545472 | ||||||||
\(969\) | −3.91856 | −0.125882 | ||||||||
\(970\) | 49.2892 | 1.58258 | ||||||||
\(971\) | −29.7655 | −0.955222 | −0.477611 | − | 0.878571i | \(-0.658497\pi\) | ||||
−0.477611 | + | 0.878571i | \(0.658497\pi\) | |||||||
\(972\) | −36.4416 | −1.16887 | ||||||||
\(973\) | 25.9344 | 0.831420 | ||||||||
\(974\) | 28.4036 | 0.910111 | ||||||||
\(975\) | 1.37439 | 0.0440159 | ||||||||
\(976\) | 12.4450 | 0.398354 | ||||||||
\(977\) | −15.3194 | −0.490110 | −0.245055 | − | 0.969509i | \(-0.578806\pi\) | ||||
−0.245055 | + | 0.969509i | \(0.578806\pi\) | |||||||
\(978\) | −57.9151 | −1.85192 | ||||||||
\(979\) | −5.35030 | −0.170996 | ||||||||
\(980\) | −27.2400 | −0.870151 | ||||||||
\(981\) | −16.7917 | −0.536119 | ||||||||
\(982\) | −12.4604 | −0.397627 | ||||||||
\(983\) | −15.6221 | −0.498266 | −0.249133 | − | 0.968469i | \(-0.580146\pi\) | ||||
−0.249133 | + | 0.968469i | \(0.580146\pi\) | |||||||
\(984\) | −5.17057 | −0.164832 | ||||||||
\(985\) | 18.7626 | 0.597825 | ||||||||
\(986\) | 56.2069 | 1.78999 | ||||||||
\(987\) | 21.7609 | 0.692657 | ||||||||
\(988\) | 17.7019 | 0.563174 | ||||||||
\(989\) | −62.0372 | −1.97267 | ||||||||
\(990\) | 5.03302 | 0.159960 | ||||||||
\(991\) | 29.5564 | 0.938891 | 0.469445 | − | 0.882962i | \(-0.344454\pi\) | ||||
0.469445 | + | 0.882962i | \(0.344454\pi\) | |||||||
\(992\) | 15.4615 | 0.490902 | ||||||||
\(993\) | −13.6657 | −0.433668 | ||||||||
\(994\) | −45.1206 | −1.43114 | ||||||||
\(995\) | −32.6863 | −1.03623 | ||||||||
\(996\) | 1.66025 | 0.0526069 | ||||||||
\(997\) | −20.7357 | −0.656707 | −0.328354 | − | 0.944555i | \(-0.606494\pi\) | ||||
−0.328354 | + | 0.944555i | \(0.606494\pi\) | |||||||
\(998\) | 54.4516 | 1.72364 | ||||||||
\(999\) | 41.2140 | 1.30395 |
(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 | 4009.2.a.d.1.13 | ✓ | 75 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.d.1.13 | ✓ | 75 | 1.1 | even | 1 | trivial |