Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, 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("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.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: | \(48.0220317756\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6014.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.531212 | −0.306695 | −0.153348 | − | 0.988172i | \(-0.549005\pi\) | ||||
−0.153348 | + | 0.988172i | \(0.549005\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.86385 | 0.833539 | 0.416770 | − | 0.909012i | \(-0.363162\pi\) | ||||
0.416770 | + | 0.909012i | \(0.363162\pi\) | |||||||
\(6\) | 0.531212 | 0.216866 | ||||||||
\(7\) | −4.06404 | −1.53606 | −0.768031 | − | 0.640413i | \(-0.778763\pi\) | ||||
−0.768031 | + | 0.640413i | \(0.778763\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.71781 | −0.905938 | ||||||||
\(10\) | −1.86385 | −0.589401 | ||||||||
\(11\) | 2.15501 | 0.649761 | 0.324880 | − | 0.945755i | \(-0.394676\pi\) | ||||
0.324880 | + | 0.945755i | \(0.394676\pi\) | |||||||
\(12\) | −0.531212 | −0.153348 | ||||||||
\(13\) | 0.240812 | 0.0667892 | 0.0333946 | − | 0.999442i | \(-0.489368\pi\) | ||||
0.0333946 | + | 0.999442i | \(0.489368\pi\) | |||||||
\(14\) | 4.06404 | 1.08616 | ||||||||
\(15\) | −0.990100 | −0.255643 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.05056 | 1.22494 | 0.612470 | − | 0.790493i | \(-0.290176\pi\) | ||||
0.612470 | + | 0.790493i | \(0.290176\pi\) | |||||||
\(18\) | 2.71781 | 0.640595 | ||||||||
\(19\) | −2.35517 | −0.540312 | −0.270156 | − | 0.962817i | \(-0.587075\pi\) | ||||
−0.270156 | + | 0.962817i | \(0.587075\pi\) | |||||||
\(20\) | 1.86385 | 0.416770 | ||||||||
\(21\) | 2.15886 | 0.471103 | ||||||||
\(22\) | −2.15501 | −0.459450 | ||||||||
\(23\) | 6.69545 | 1.39610 | 0.698048 | − | 0.716051i | \(-0.254052\pi\) | ||||
0.698048 | + | 0.716051i | \(0.254052\pi\) | |||||||
\(24\) | 0.531212 | 0.108433 | ||||||||
\(25\) | −1.52606 | −0.305213 | ||||||||
\(26\) | −0.240812 | −0.0472271 | ||||||||
\(27\) | 3.03737 | 0.584542 | ||||||||
\(28\) | −4.06404 | −0.768031 | ||||||||
\(29\) | −7.35248 | −1.36532 | −0.682661 | − | 0.730736i | \(-0.739177\pi\) | ||||
−0.682661 | + | 0.730736i | \(0.739177\pi\) | |||||||
\(30\) | 0.990100 | 0.180767 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.14477 | −0.199279 | ||||||||
\(34\) | −5.05056 | −0.866164 | ||||||||
\(35\) | −7.57475 | −1.28037 | ||||||||
\(36\) | −2.71781 | −0.452969 | ||||||||
\(37\) | 1.51194 | 0.248561 | 0.124280 | − | 0.992247i | \(-0.460338\pi\) | ||||
0.124280 | + | 0.992247i | \(0.460338\pi\) | |||||||
\(38\) | 2.35517 | 0.382058 | ||||||||
\(39\) | −0.127922 | −0.0204840 | ||||||||
\(40\) | −1.86385 | −0.294701 | ||||||||
\(41\) | 0.437600 | 0.0683416 | 0.0341708 | − | 0.999416i | \(-0.489121\pi\) | ||||
0.0341708 | + | 0.999416i | \(0.489121\pi\) | |||||||
\(42\) | −2.15886 | −0.333120 | ||||||||
\(43\) | −2.73910 | −0.417709 | −0.208854 | − | 0.977947i | \(-0.566973\pi\) | ||||
−0.208854 | + | 0.977947i | \(0.566973\pi\) | |||||||
\(44\) | 2.15501 | 0.324880 | ||||||||
\(45\) | −5.06560 | −0.755135 | ||||||||
\(46\) | −6.69545 | −0.987190 | ||||||||
\(47\) | −11.2456 | −1.64034 | −0.820168 | − | 0.572123i | \(-0.806120\pi\) | ||||
−0.820168 | + | 0.572123i | \(0.806120\pi\) | |||||||
\(48\) | −0.531212 | −0.0766739 | ||||||||
\(49\) | 9.51638 | 1.35948 | ||||||||
\(50\) | 1.52606 | 0.215818 | ||||||||
\(51\) | −2.68292 | −0.375684 | ||||||||
\(52\) | 0.240812 | 0.0333946 | ||||||||
\(53\) | −10.9375 | −1.50238 | −0.751190 | − | 0.660086i | \(-0.770520\pi\) | ||||
−0.751190 | + | 0.660086i | \(0.770520\pi\) | |||||||
\(54\) | −3.03737 | −0.413334 | ||||||||
\(55\) | 4.01662 | 0.541601 | ||||||||
\(56\) | 4.06404 | 0.543080 | ||||||||
\(57\) | 1.25109 | 0.165711 | ||||||||
\(58\) | 7.35248 | 0.965428 | ||||||||
\(59\) | 9.67425 | 1.25948 | 0.629740 | − | 0.776806i | \(-0.283161\pi\) | ||||
0.629740 | + | 0.776806i | \(0.283161\pi\) | |||||||
\(60\) | −0.990100 | −0.127821 | ||||||||
\(61\) | 15.2735 | 1.95557 | 0.977785 | − | 0.209611i | \(-0.0672199\pi\) | ||||
0.977785 | + | 0.209611i | \(0.0672199\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 11.0453 | 1.39158 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.448838 | 0.0556714 | ||||||||
\(66\) | 1.14477 | 0.140911 | ||||||||
\(67\) | 3.34422 | 0.408562 | 0.204281 | − | 0.978912i | \(-0.434514\pi\) | ||||
0.204281 | + | 0.978912i | \(0.434514\pi\) | |||||||
\(68\) | 5.05056 | 0.612470 | ||||||||
\(69\) | −3.55670 | −0.428177 | ||||||||
\(70\) | 7.57475 | 0.905356 | ||||||||
\(71\) | 1.95372 | 0.231864 | 0.115932 | − | 0.993257i | \(-0.463014\pi\) | ||||
0.115932 | + | 0.993257i | \(0.463014\pi\) | |||||||
\(72\) | 2.71781 | 0.320297 | ||||||||
\(73\) | 1.25545 | 0.146939 | 0.0734696 | − | 0.997297i | \(-0.476593\pi\) | ||||
0.0734696 | + | 0.997297i | \(0.476593\pi\) | |||||||
\(74\) | −1.51194 | −0.175759 | ||||||||
\(75\) | 0.810663 | 0.0936073 | ||||||||
\(76\) | −2.35517 | −0.270156 | ||||||||
\(77\) | −8.75805 | −0.998072 | ||||||||
\(78\) | 0.127922 | 0.0144843 | ||||||||
\(79\) | 6.32603 | 0.711734 | 0.355867 | − | 0.934537i | \(-0.384186\pi\) | ||||
0.355867 | + | 0.934537i | \(0.384186\pi\) | |||||||
\(80\) | 1.86385 | 0.208385 | ||||||||
\(81\) | 6.53995 | 0.726661 | ||||||||
\(82\) | −0.437600 | −0.0483248 | ||||||||
\(83\) | 9.96182 | 1.09345 | 0.546726 | − | 0.837312i | \(-0.315874\pi\) | ||||
0.546726 | + | 0.837312i | \(0.315874\pi\) | |||||||
\(84\) | 2.15886 | 0.235551 | ||||||||
\(85\) | 9.41349 | 1.02104 | ||||||||
\(86\) | 2.73910 | 0.295365 | ||||||||
\(87\) | 3.90573 | 0.418738 | ||||||||
\(88\) | −2.15501 | −0.229725 | ||||||||
\(89\) | −14.0185 | −1.48596 | −0.742978 | − | 0.669316i | \(-0.766587\pi\) | ||||
−0.742978 | + | 0.669316i | \(0.766587\pi\) | |||||||
\(90\) | 5.06560 | 0.533961 | ||||||||
\(91\) | −0.978669 | −0.102592 | ||||||||
\(92\) | 6.69545 | 0.698048 | ||||||||
\(93\) | −0.531212 | −0.0550841 | ||||||||
\(94\) | 11.2456 | 1.15989 | ||||||||
\(95\) | −4.38968 | −0.450371 | ||||||||
\(96\) | 0.531212 | 0.0542166 | ||||||||
\(97\) | 1.00000 | 0.101535 | ||||||||
\(98\) | −9.51638 | −0.961300 | ||||||||
\(99\) | −5.85692 | −0.588643 | ||||||||
\(100\) | −1.52606 | −0.152606 | ||||||||
\(101\) | −5.00795 | −0.498310 | −0.249155 | − | 0.968464i | \(-0.580153\pi\) | ||||
−0.249155 | + | 0.968464i | \(0.580153\pi\) | |||||||
\(102\) | 2.68292 | 0.265649 | ||||||||
\(103\) | 11.1096 | 1.09466 | 0.547329 | − | 0.836918i | \(-0.315645\pi\) | ||||
0.547329 | + | 0.836918i | \(0.315645\pi\) | |||||||
\(104\) | −0.240812 | −0.0236136 | ||||||||
\(105\) | 4.02380 | 0.392683 | ||||||||
\(106\) | 10.9375 | 1.06234 | ||||||||
\(107\) | −5.19849 | −0.502557 | −0.251279 | − | 0.967915i | \(-0.580851\pi\) | ||||
−0.251279 | + | 0.967915i | \(0.580851\pi\) | |||||||
\(108\) | 3.03737 | 0.292271 | ||||||||
\(109\) | −17.4332 | −1.66979 | −0.834897 | − | 0.550407i | \(-0.814473\pi\) | ||||
−0.834897 | + | 0.550407i | \(0.814473\pi\) | |||||||
\(110\) | −4.01662 | −0.382970 | ||||||||
\(111\) | −0.803159 | −0.0762325 | ||||||||
\(112\) | −4.06404 | −0.384015 | ||||||||
\(113\) | −1.86512 | −0.175456 | −0.0877280 | − | 0.996144i | \(-0.527961\pi\) | ||||
−0.0877280 | + | 0.996144i | \(0.527961\pi\) | |||||||
\(114\) | −1.25109 | −0.117176 | ||||||||
\(115\) | 12.4793 | 1.16370 | ||||||||
\(116\) | −7.35248 | −0.682661 | ||||||||
\(117\) | −0.654482 | −0.0605069 | ||||||||
\(118\) | −9.67425 | −0.890587 | ||||||||
\(119\) | −20.5257 | −1.88158 | ||||||||
\(120\) | 0.990100 | 0.0903833 | ||||||||
\(121\) | −6.35592 | −0.577811 | ||||||||
\(122\) | −15.2735 | −1.38280 | ||||||||
\(123\) | −0.232458 | −0.0209601 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | −12.1636 | −1.08795 | ||||||||
\(126\) | −11.0453 | −0.983993 | ||||||||
\(127\) | −9.43734 | −0.837429 | −0.418714 | − | 0.908118i | \(-0.637519\pi\) | ||||
−0.418714 | + | 0.908118i | \(0.637519\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.45504 | 0.128109 | ||||||||
\(130\) | −0.448838 | −0.0393657 | ||||||||
\(131\) | −3.80936 | −0.332826 | −0.166413 | − | 0.986056i | \(-0.553218\pi\) | ||||
−0.166413 | + | 0.986056i | \(0.553218\pi\) | |||||||
\(132\) | −1.14477 | −0.0996393 | ||||||||
\(133\) | 9.57148 | 0.829953 | ||||||||
\(134\) | −3.34422 | −0.288897 | ||||||||
\(135\) | 5.66120 | 0.487239 | ||||||||
\(136\) | −5.05056 | −0.433082 | ||||||||
\(137\) | −9.27362 | −0.792299 | −0.396149 | − | 0.918186i | \(-0.629654\pi\) | ||||
−0.396149 | + | 0.918186i | \(0.629654\pi\) | |||||||
\(138\) | 3.55670 | 0.302767 | ||||||||
\(139\) | 0.598622 | 0.0507745 | 0.0253872 | − | 0.999678i | \(-0.491918\pi\) | ||||
0.0253872 | + | 0.999678i | \(0.491918\pi\) | |||||||
\(140\) | −7.57475 | −0.640183 | ||||||||
\(141\) | 5.97378 | 0.503083 | ||||||||
\(142\) | −1.95372 | −0.163953 | ||||||||
\(143\) | 0.518953 | 0.0433970 | ||||||||
\(144\) | −2.71781 | −0.226484 | ||||||||
\(145\) | −13.7039 | −1.13805 | ||||||||
\(146\) | −1.25545 | −0.103902 | ||||||||
\(147\) | −5.05522 | −0.416947 | ||||||||
\(148\) | 1.51194 | 0.124280 | ||||||||
\(149\) | 15.0404 | 1.23215 | 0.616077 | − | 0.787686i | \(-0.288721\pi\) | ||||
0.616077 | + | 0.787686i | \(0.288721\pi\) | |||||||
\(150\) | −0.810663 | −0.0661904 | ||||||||
\(151\) | −2.61615 | −0.212899 | −0.106449 | − | 0.994318i | \(-0.533948\pi\) | ||||
−0.106449 | + | 0.994318i | \(0.533948\pi\) | |||||||
\(152\) | 2.35517 | 0.191029 | ||||||||
\(153\) | −13.7265 | −1.10972 | ||||||||
\(154\) | 8.75805 | 0.705744 | ||||||||
\(155\) | 1.86385 | 0.149708 | ||||||||
\(156\) | −0.127922 | −0.0102420 | ||||||||
\(157\) | 14.3268 | 1.14340 | 0.571702 | − | 0.820461i | \(-0.306283\pi\) | ||||
0.571702 | + | 0.820461i | \(0.306283\pi\) | |||||||
\(158\) | −6.32603 | −0.503272 | ||||||||
\(159\) | 5.81013 | 0.460773 | ||||||||
\(160\) | −1.86385 | −0.147350 | ||||||||
\(161\) | −27.2105 | −2.14449 | ||||||||
\(162\) | −6.53995 | −0.513827 | ||||||||
\(163\) | −21.7235 | −1.70151 | −0.850756 | − | 0.525560i | \(-0.823856\pi\) | ||||
−0.850756 | + | 0.525560i | \(0.823856\pi\) | |||||||
\(164\) | 0.437600 | 0.0341708 | ||||||||
\(165\) | −2.13368 | −0.166107 | ||||||||
\(166\) | −9.96182 | −0.773187 | ||||||||
\(167\) | 7.18386 | 0.555904 | 0.277952 | − | 0.960595i | \(-0.410344\pi\) | ||||
0.277952 | + | 0.960595i | \(0.410344\pi\) | |||||||
\(168\) | −2.15886 | −0.166560 | ||||||||
\(169\) | −12.9420 | −0.995539 | ||||||||
\(170\) | −9.41349 | −0.721982 | ||||||||
\(171\) | 6.40090 | 0.489489 | ||||||||
\(172\) | −2.73910 | −0.208854 | ||||||||
\(173\) | 15.9336 | 1.21141 | 0.605703 | − | 0.795691i | \(-0.292892\pi\) | ||||
0.605703 | + | 0.795691i | \(0.292892\pi\) | |||||||
\(174\) | −3.90573 | −0.296092 | ||||||||
\(175\) | 6.20198 | 0.468825 | ||||||||
\(176\) | 2.15501 | 0.162440 | ||||||||
\(177\) | −5.13908 | −0.386277 | ||||||||
\(178\) | 14.0185 | 1.05073 | ||||||||
\(179\) | −13.9130 | −1.03990 | −0.519952 | − | 0.854195i | \(-0.674050\pi\) | ||||
−0.519952 | + | 0.854195i | \(0.674050\pi\) | |||||||
\(180\) | −5.06560 | −0.377567 | ||||||||
\(181\) | 7.67066 | 0.570156 | 0.285078 | − | 0.958504i | \(-0.407981\pi\) | ||||
0.285078 | + | 0.958504i | \(0.407981\pi\) | |||||||
\(182\) | 0.978669 | 0.0725438 | ||||||||
\(183\) | −8.11346 | −0.599764 | ||||||||
\(184\) | −6.69545 | −0.493595 | ||||||||
\(185\) | 2.81802 | 0.207185 | ||||||||
\(186\) | 0.531212 | 0.0389504 | ||||||||
\(187\) | 10.8840 | 0.795919 | ||||||||
\(188\) | −11.2456 | −0.820168 | ||||||||
\(189\) | −12.3440 | −0.897893 | ||||||||
\(190\) | 4.38968 | 0.318461 | ||||||||
\(191\) | −21.9540 | −1.58853 | −0.794267 | − | 0.607568i | \(-0.792145\pi\) | ||||
−0.794267 | + | 0.607568i | \(0.792145\pi\) | |||||||
\(192\) | −0.531212 | −0.0383369 | ||||||||
\(193\) | 4.32134 | 0.311057 | 0.155528 | − | 0.987831i | \(-0.450292\pi\) | ||||
0.155528 | + | 0.987831i | \(0.450292\pi\) | |||||||
\(194\) | −1.00000 | −0.0717958 | ||||||||
\(195\) | −0.238428 | −0.0170742 | ||||||||
\(196\) | 9.51638 | 0.679742 | ||||||||
\(197\) | −19.4316 | −1.38444 | −0.692222 | − | 0.721684i | \(-0.743368\pi\) | ||||
−0.692222 | + | 0.721684i | \(0.743368\pi\) | |||||||
\(198\) | 5.85692 | 0.416233 | ||||||||
\(199\) | 5.99771 | 0.425167 | 0.212583 | − | 0.977143i | \(-0.431812\pi\) | ||||
0.212583 | + | 0.977143i | \(0.431812\pi\) | |||||||
\(200\) | 1.52606 | 0.107909 | ||||||||
\(201\) | −1.77649 | −0.125304 | ||||||||
\(202\) | 5.00795 | 0.352358 | ||||||||
\(203\) | 29.8807 | 2.09722 | ||||||||
\(204\) | −2.68292 | −0.187842 | ||||||||
\(205\) | 0.815620 | 0.0569654 | ||||||||
\(206\) | −11.1096 | −0.774040 | ||||||||
\(207\) | −18.1970 | −1.26478 | ||||||||
\(208\) | 0.240812 | 0.0166973 | ||||||||
\(209\) | −5.07541 | −0.351074 | ||||||||
\(210\) | −4.02380 | −0.277669 | ||||||||
\(211\) | 10.5332 | 0.725135 | 0.362567 | − | 0.931958i | \(-0.381900\pi\) | ||||
0.362567 | + | 0.931958i | \(0.381900\pi\) | |||||||
\(212\) | −10.9375 | −0.751190 | ||||||||
\(213\) | −1.03784 | −0.0711117 | ||||||||
\(214\) | 5.19849 | 0.355362 | ||||||||
\(215\) | −5.10527 | −0.348176 | ||||||||
\(216\) | −3.03737 | −0.206667 | ||||||||
\(217\) | −4.06404 | −0.275885 | ||||||||
\(218\) | 17.4332 | 1.18072 | ||||||||
\(219\) | −0.666909 | −0.0450656 | ||||||||
\(220\) | 4.01662 | 0.270800 | ||||||||
\(221\) | 1.21624 | 0.0818129 | ||||||||
\(222\) | 0.803159 | 0.0539045 | ||||||||
\(223\) | 14.8409 | 0.993820 | 0.496910 | − | 0.867802i | \(-0.334468\pi\) | ||||
0.496910 | + | 0.867802i | \(0.334468\pi\) | |||||||
\(224\) | 4.06404 | 0.271540 | ||||||||
\(225\) | 4.14756 | 0.276504 | ||||||||
\(226\) | 1.86512 | 0.124066 | ||||||||
\(227\) | 11.4527 | 0.760143 | 0.380072 | − | 0.924957i | \(-0.375899\pi\) | ||||
0.380072 | + | 0.924957i | \(0.375899\pi\) | |||||||
\(228\) | 1.25109 | 0.0828557 | ||||||||
\(229\) | −14.1093 | −0.932370 | −0.466185 | − | 0.884687i | \(-0.654372\pi\) | ||||
−0.466185 | + | 0.884687i | \(0.654372\pi\) | |||||||
\(230\) | −12.4793 | −0.822861 | ||||||||
\(231\) | 4.65238 | 0.306104 | ||||||||
\(232\) | 7.35248 | 0.482714 | ||||||||
\(233\) | −17.7045 | −1.15986 | −0.579931 | − | 0.814666i | \(-0.696921\pi\) | ||||
−0.579931 | + | 0.814666i | \(0.696921\pi\) | |||||||
\(234\) | 0.654482 | 0.0427848 | ||||||||
\(235\) | −20.9601 | −1.36728 | ||||||||
\(236\) | 9.67425 | 0.629740 | ||||||||
\(237\) | −3.36046 | −0.218286 | ||||||||
\(238\) | 20.5257 | 1.33048 | ||||||||
\(239\) | 10.8794 | 0.703731 | 0.351865 | − | 0.936051i | \(-0.385548\pi\) | ||||
0.351865 | + | 0.936051i | \(0.385548\pi\) | |||||||
\(240\) | −0.990100 | −0.0639107 | ||||||||
\(241\) | −23.9685 | −1.54395 | −0.771973 | − | 0.635655i | \(-0.780730\pi\) | ||||
−0.771973 | + | 0.635655i | \(0.780730\pi\) | |||||||
\(242\) | 6.35592 | 0.408574 | ||||||||
\(243\) | −12.5862 | −0.807406 | ||||||||
\(244\) | 15.2735 | 0.977785 | ||||||||
\(245\) | 17.7371 | 1.13318 | ||||||||
\(246\) | 0.232458 | 0.0148210 | ||||||||
\(247\) | −0.567153 | −0.0360871 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | −5.29184 | −0.335357 | ||||||||
\(250\) | 12.1636 | 0.769294 | ||||||||
\(251\) | 20.6521 | 1.30355 | 0.651775 | − | 0.758412i | \(-0.274025\pi\) | ||||
0.651775 | + | 0.758412i | \(0.274025\pi\) | |||||||
\(252\) | 11.0453 | 0.695788 | ||||||||
\(253\) | 14.4288 | 0.907129 | ||||||||
\(254\) | 9.43734 | 0.592152 | ||||||||
\(255\) | −5.00056 | −0.313147 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.2771 | 0.890578 | 0.445289 | − | 0.895387i | \(-0.353101\pi\) | ||||
0.445289 | + | 0.895387i | \(0.353101\pi\) | |||||||
\(258\) | −1.45504 | −0.0905870 | ||||||||
\(259\) | −6.14456 | −0.381805 | ||||||||
\(260\) | 0.448838 | 0.0278357 | ||||||||
\(261\) | 19.9827 | 1.23690 | ||||||||
\(262\) | 3.80936 | 0.235343 | ||||||||
\(263\) | −15.8164 | −0.975282 | −0.487641 | − | 0.873044i | \(-0.662142\pi\) | ||||
−0.487641 | + | 0.873044i | \(0.662142\pi\) | |||||||
\(264\) | 1.14477 | 0.0704556 | ||||||||
\(265\) | −20.3858 | −1.25229 | ||||||||
\(266\) | −9.57148 | −0.586865 | ||||||||
\(267\) | 7.44678 | 0.455736 | ||||||||
\(268\) | 3.34422 | 0.204281 | ||||||||
\(269\) | −31.4323 | −1.91646 | −0.958231 | − | 0.285995i | \(-0.907676\pi\) | ||||
−0.958231 | + | 0.285995i | \(0.907676\pi\) | |||||||
\(270\) | −5.66120 | −0.344530 | ||||||||
\(271\) | −10.1062 | −0.613911 | −0.306955 | − | 0.951724i | \(-0.599310\pi\) | ||||
−0.306955 | + | 0.951724i | \(0.599310\pi\) | |||||||
\(272\) | 5.05056 | 0.306235 | ||||||||
\(273\) | 0.519881 | 0.0314646 | ||||||||
\(274\) | 9.27362 | 0.560240 | ||||||||
\(275\) | −3.28869 | −0.198315 | ||||||||
\(276\) | −3.55670 | −0.214088 | ||||||||
\(277\) | −3.04574 | −0.183001 | −0.0915005 | − | 0.995805i | \(-0.529166\pi\) | ||||
−0.0915005 | + | 0.995805i | \(0.529166\pi\) | |||||||
\(278\) | −0.598622 | −0.0359030 | ||||||||
\(279\) | −2.71781 | −0.162711 | ||||||||
\(280\) | 7.57475 | 0.452678 | ||||||||
\(281\) | −21.8794 | −1.30522 | −0.652608 | − | 0.757696i | \(-0.726325\pi\) | ||||
−0.652608 | + | 0.757696i | \(0.726325\pi\) | |||||||
\(282\) | −5.97378 | −0.355734 | ||||||||
\(283\) | 8.90262 | 0.529206 | 0.264603 | − | 0.964357i | \(-0.414759\pi\) | ||||
0.264603 | + | 0.964357i | \(0.414759\pi\) | |||||||
\(284\) | 1.95372 | 0.115932 | ||||||||
\(285\) | 2.33185 | 0.138127 | ||||||||
\(286\) | −0.518953 | −0.0306863 | ||||||||
\(287\) | −1.77842 | −0.104977 | ||||||||
\(288\) | 2.71781 | 0.160149 | ||||||||
\(289\) | 8.50817 | 0.500480 | ||||||||
\(290\) | 13.7039 | 0.804722 | ||||||||
\(291\) | −0.531212 | −0.0311402 | ||||||||
\(292\) | 1.25545 | 0.0734696 | ||||||||
\(293\) | −19.5925 | −1.14461 | −0.572304 | − | 0.820041i | \(-0.693950\pi\) | ||||
−0.572304 | + | 0.820041i | \(0.693950\pi\) | |||||||
\(294\) | 5.05522 | 0.294826 | ||||||||
\(295\) | 18.0314 | 1.04983 | ||||||||
\(296\) | −1.51194 | −0.0878795 | ||||||||
\(297\) | 6.54557 | 0.379813 | ||||||||
\(298\) | −15.0404 | −0.871264 | ||||||||
\(299\) | 1.61234 | 0.0932443 | ||||||||
\(300\) | 0.810663 | 0.0468037 | ||||||||
\(301\) | 11.1318 | 0.641626 | ||||||||
\(302\) | 2.61615 | 0.150542 | ||||||||
\(303\) | 2.66028 | 0.152829 | ||||||||
\(304\) | −2.35517 | −0.135078 | ||||||||
\(305\) | 28.4675 | 1.63004 | ||||||||
\(306\) | 13.7265 | 0.784691 | ||||||||
\(307\) | −32.2620 | −1.84129 | −0.920646 | − | 0.390399i | \(-0.872337\pi\) | ||||
−0.920646 | + | 0.390399i | \(0.872337\pi\) | |||||||
\(308\) | −8.75805 | −0.499036 | ||||||||
\(309\) | −5.90153 | −0.335727 | ||||||||
\(310\) | −1.86385 | −0.105860 | ||||||||
\(311\) | −18.8003 | −1.06607 | −0.533033 | − | 0.846094i | \(-0.678948\pi\) | ||||
−0.533033 | + | 0.846094i | \(0.678948\pi\) | |||||||
\(312\) | 0.127922 | 0.00724217 | ||||||||
\(313\) | −11.9552 | −0.675748 | −0.337874 | − | 0.941191i | \(-0.609708\pi\) | ||||
−0.337874 | + | 0.941191i | \(0.609708\pi\) | |||||||
\(314\) | −14.3268 | −0.808509 | ||||||||
\(315\) | 20.5868 | 1.15993 | ||||||||
\(316\) | 6.32603 | 0.355867 | ||||||||
\(317\) | −14.1818 | −0.796527 | −0.398263 | − | 0.917271i | \(-0.630387\pi\) | ||||
−0.398263 | + | 0.917271i | \(0.630387\pi\) | |||||||
\(318\) | −5.81013 | −0.325816 | ||||||||
\(319\) | −15.8447 | −0.887132 | ||||||||
\(320\) | 1.86385 | 0.104192 | ||||||||
\(321\) | 2.76150 | 0.154132 | ||||||||
\(322\) | 27.2105 | 1.51638 | ||||||||
\(323\) | −11.8949 | −0.661851 | ||||||||
\(324\) | 6.53995 | 0.363331 | ||||||||
\(325\) | −0.367494 | −0.0203849 | ||||||||
\(326\) | 21.7235 | 1.20315 | ||||||||
\(327\) | 9.26070 | 0.512118 | ||||||||
\(328\) | −0.437600 | −0.0241624 | ||||||||
\(329\) | 45.7024 | 2.51965 | ||||||||
\(330\) | 2.13368 | 0.117455 | ||||||||
\(331\) | −35.6196 | −1.95783 | −0.978916 | − | 0.204265i | \(-0.934520\pi\) | ||||
−0.978916 | + | 0.204265i | \(0.934520\pi\) | |||||||
\(332\) | 9.96182 | 0.546726 | ||||||||
\(333\) | −4.10916 | −0.225181 | ||||||||
\(334\) | −7.18386 | −0.393083 | ||||||||
\(335\) | 6.23312 | 0.340552 | ||||||||
\(336\) | 2.15886 | 0.117776 | ||||||||
\(337\) | −13.4426 | −0.732264 | −0.366132 | − | 0.930563i | \(-0.619318\pi\) | ||||
−0.366132 | + | 0.930563i | \(0.619318\pi\) | |||||||
\(338\) | 12.9420 | 0.703953 | ||||||||
\(339\) | 0.990775 | 0.0538115 | ||||||||
\(340\) | 9.41349 | 0.510518 | ||||||||
\(341\) | 2.15501 | 0.116700 | ||||||||
\(342\) | −6.40090 | −0.346121 | ||||||||
\(343\) | −10.2267 | −0.552188 | ||||||||
\(344\) | 2.73910 | 0.147682 | ||||||||
\(345\) | −6.62916 | −0.356902 | ||||||||
\(346\) | −15.9336 | −0.856594 | ||||||||
\(347\) | 4.58164 | 0.245955 | 0.122978 | − | 0.992409i | \(-0.460756\pi\) | ||||
0.122978 | + | 0.992409i | \(0.460756\pi\) | |||||||
\(348\) | 3.90573 | 0.209369 | ||||||||
\(349\) | 26.1860 | 1.40170 | 0.700851 | − | 0.713307i | \(-0.252804\pi\) | ||||
0.700851 | + | 0.713307i | \(0.252804\pi\) | |||||||
\(350\) | −6.20198 | −0.331510 | ||||||||
\(351\) | 0.731436 | 0.0390411 | ||||||||
\(352\) | −2.15501 | −0.114863 | ||||||||
\(353\) | −8.49199 | −0.451983 | −0.225991 | − | 0.974129i | \(-0.572562\pi\) | ||||
−0.225991 | + | 0.974129i | \(0.572562\pi\) | |||||||
\(354\) | 5.13908 | 0.273139 | ||||||||
\(355\) | 3.64145 | 0.193268 | ||||||||
\(356\) | −14.0185 | −0.742978 | ||||||||
\(357\) | 10.9035 | 0.577073 | ||||||||
\(358\) | 13.9130 | 0.735324 | ||||||||
\(359\) | 13.2984 | 0.701862 | 0.350931 | − | 0.936401i | \(-0.385865\pi\) | ||||
0.350931 | + | 0.936401i | \(0.385865\pi\) | |||||||
\(360\) | 5.06560 | 0.266980 | ||||||||
\(361\) | −13.4532 | −0.708063 | ||||||||
\(362\) | −7.67066 | −0.403161 | ||||||||
\(363\) | 3.37634 | 0.177212 | ||||||||
\(364\) | −0.978669 | −0.0512962 | ||||||||
\(365\) | 2.33997 | 0.122479 | ||||||||
\(366\) | 8.11346 | 0.424097 | ||||||||
\(367\) | −21.5352 | −1.12413 | −0.562065 | − | 0.827093i | \(-0.689993\pi\) | ||||
−0.562065 | + | 0.827093i | \(0.689993\pi\) | |||||||
\(368\) | 6.69545 | 0.349024 | ||||||||
\(369\) | −1.18931 | −0.0619132 | ||||||||
\(370\) | −2.81802 | −0.146502 | ||||||||
\(371\) | 44.4504 | 2.30775 | ||||||||
\(372\) | −0.531212 | −0.0275421 | ||||||||
\(373\) | 25.5012 | 1.32040 | 0.660200 | − | 0.751090i | \(-0.270472\pi\) | ||||
0.660200 | + | 0.751090i | \(0.270472\pi\) | |||||||
\(374\) | −10.8840 | −0.562799 | ||||||||
\(375\) | 6.46145 | 0.333668 | ||||||||
\(376\) | 11.2456 | 0.579946 | ||||||||
\(377\) | −1.77057 | −0.0911888 | ||||||||
\(378\) | 12.3440 | 0.634906 | ||||||||
\(379\) | −2.19932 | −0.112972 | −0.0564858 | − | 0.998403i | \(-0.517990\pi\) | ||||
−0.0564858 | + | 0.998403i | \(0.517990\pi\) | |||||||
\(380\) | −4.38968 | −0.225186 | ||||||||
\(381\) | 5.01323 | 0.256836 | ||||||||
\(382\) | 21.9540 | 1.12326 | ||||||||
\(383\) | 29.0342 | 1.48358 | 0.741789 | − | 0.670633i | \(-0.233978\pi\) | ||||
0.741789 | + | 0.670633i | \(0.233978\pi\) | |||||||
\(384\) | 0.531212 | 0.0271083 | ||||||||
\(385\) | −16.3237 | −0.831932 | ||||||||
\(386\) | −4.32134 | −0.219950 | ||||||||
\(387\) | 7.44436 | 0.378418 | ||||||||
\(388\) | 1.00000 | 0.0507673 | ||||||||
\(389\) | −17.1770 | −0.870907 | −0.435453 | − | 0.900211i | \(-0.643412\pi\) | ||||
−0.435453 | + | 0.900211i | \(0.643412\pi\) | |||||||
\(390\) | 0.238428 | 0.0120733 | ||||||||
\(391\) | 33.8158 | 1.71014 | ||||||||
\(392\) | −9.51638 | −0.480650 | ||||||||
\(393\) | 2.02358 | 0.102076 | ||||||||
\(394\) | 19.4316 | 0.978950 | ||||||||
\(395\) | 11.7908 | 0.593258 | ||||||||
\(396\) | −5.85692 | −0.294321 | ||||||||
\(397\) | 5.42066 | 0.272055 | 0.136027 | − | 0.990705i | \(-0.456566\pi\) | ||||
0.136027 | + | 0.990705i | \(0.456566\pi\) | |||||||
\(398\) | −5.99771 | −0.300638 | ||||||||
\(399\) | −5.08449 | −0.254543 | ||||||||
\(400\) | −1.52606 | −0.0763032 | ||||||||
\(401\) | 19.7790 | 0.987715 | 0.493858 | − | 0.869543i | \(-0.335586\pi\) | ||||
0.493858 | + | 0.869543i | \(0.335586\pi\) | |||||||
\(402\) | 1.77649 | 0.0886033 | ||||||||
\(403\) | 0.240812 | 0.0119957 | ||||||||
\(404\) | −5.00795 | −0.249155 | ||||||||
\(405\) | 12.1895 | 0.605701 | ||||||||
\(406\) | −29.8807 | −1.48296 | ||||||||
\(407\) | 3.25824 | 0.161505 | ||||||||
\(408\) | 2.68292 | 0.132824 | ||||||||
\(409\) | −30.9625 | −1.53100 | −0.765499 | − | 0.643437i | \(-0.777508\pi\) | ||||
−0.765499 | + | 0.643437i | \(0.777508\pi\) | |||||||
\(410\) | −0.815620 | −0.0402806 | ||||||||
\(411\) | 4.92626 | 0.242994 | ||||||||
\(412\) | 11.1096 | 0.547329 | ||||||||
\(413\) | −39.3165 | −1.93464 | ||||||||
\(414\) | 18.1970 | 0.894333 | ||||||||
\(415\) | 18.5673 | 0.911435 | ||||||||
\(416\) | −0.240812 | −0.0118068 | ||||||||
\(417\) | −0.317995 | −0.0155723 | ||||||||
\(418\) | 5.07541 | 0.248247 | ||||||||
\(419\) | −32.8771 | −1.60615 | −0.803075 | − | 0.595879i | \(-0.796804\pi\) | ||||
−0.803075 | + | 0.595879i | \(0.796804\pi\) | |||||||
\(420\) | 4.02380 | 0.196341 | ||||||||
\(421\) | −16.5914 | −0.808613 | −0.404306 | − | 0.914624i | \(-0.632487\pi\) | ||||
−0.404306 | + | 0.914624i | \(0.632487\pi\) | |||||||
\(422\) | −10.5332 | −0.512748 | ||||||||
\(423\) | 30.5634 | 1.48604 | ||||||||
\(424\) | 10.9375 | 0.531172 | ||||||||
\(425\) | −7.70748 | −0.373868 | ||||||||
\(426\) | 1.03784 | 0.0502836 | ||||||||
\(427\) | −62.0720 | −3.00387 | ||||||||
\(428\) | −5.19849 | −0.251279 | ||||||||
\(429\) | −0.275674 | −0.0133097 | ||||||||
\(430\) | 5.10527 | 0.246198 | ||||||||
\(431\) | 22.0837 | 1.06374 | 0.531868 | − | 0.846827i | \(-0.321490\pi\) | ||||
0.531868 | + | 0.846827i | \(0.321490\pi\) | |||||||
\(432\) | 3.03737 | 0.146136 | ||||||||
\(433\) | −12.5493 | −0.603082 | −0.301541 | − | 0.953453i | \(-0.597501\pi\) | ||||
−0.301541 | + | 0.953453i | \(0.597501\pi\) | |||||||
\(434\) | 4.06404 | 0.195080 | ||||||||
\(435\) | 7.27969 | 0.349034 | ||||||||
\(436\) | −17.4332 | −0.834897 | ||||||||
\(437\) | −15.7689 | −0.754328 | ||||||||
\(438\) | 0.666909 | 0.0318662 | ||||||||
\(439\) | −16.1761 | −0.772044 | −0.386022 | − | 0.922490i | \(-0.626151\pi\) | ||||
−0.386022 | + | 0.922490i | \(0.626151\pi\) | |||||||
\(440\) | −4.01662 | −0.191485 | ||||||||
\(441\) | −25.8638 | −1.23161 | ||||||||
\(442\) | −1.21624 | −0.0578504 | ||||||||
\(443\) | 4.03243 | 0.191586 | 0.0957932 | − | 0.995401i | \(-0.469461\pi\) | ||||
0.0957932 | + | 0.995401i | \(0.469461\pi\) | |||||||
\(444\) | −0.803159 | −0.0381162 | ||||||||
\(445\) | −26.1283 | −1.23860 | ||||||||
\(446\) | −14.8409 | −0.702737 | ||||||||
\(447\) | −7.98962 | −0.377896 | ||||||||
\(448\) | −4.06404 | −0.192008 | ||||||||
\(449\) | 25.5043 | 1.20362 | 0.601811 | − | 0.798639i | \(-0.294446\pi\) | ||||
0.601811 | + | 0.798639i | \(0.294446\pi\) | |||||||
\(450\) | −4.14756 | −0.195518 | ||||||||
\(451\) | 0.943033 | 0.0444057 | ||||||||
\(452\) | −1.86512 | −0.0877280 | ||||||||
\(453\) | 1.38973 | 0.0652951 | ||||||||
\(454\) | −11.4527 | −0.537502 | ||||||||
\(455\) | −1.82409 | −0.0855147 | ||||||||
\(456\) | −1.25109 | −0.0585878 | ||||||||
\(457\) | −21.2751 | −0.995208 | −0.497604 | − | 0.867404i | \(-0.665787\pi\) | ||||
−0.497604 | + | 0.867404i | \(0.665787\pi\) | |||||||
\(458\) | 14.1093 | 0.659285 | ||||||||
\(459\) | 15.3404 | 0.716030 | ||||||||
\(460\) | 12.4793 | 0.581851 | ||||||||
\(461\) | −21.4885 | −1.00082 | −0.500410 | − | 0.865789i | \(-0.666817\pi\) | ||||
−0.500410 | + | 0.865789i | \(0.666817\pi\) | |||||||
\(462\) | −4.65238 | −0.216448 | ||||||||
\(463\) | 10.9892 | 0.510711 | 0.255356 | − | 0.966847i | \(-0.417807\pi\) | ||||
0.255356 | + | 0.966847i | \(0.417807\pi\) | |||||||
\(464\) | −7.35248 | −0.341330 | ||||||||
\(465\) | −0.990100 | −0.0459148 | ||||||||
\(466\) | 17.7045 | 0.820146 | ||||||||
\(467\) | −1.30362 | −0.0603246 | −0.0301623 | − | 0.999545i | \(-0.509602\pi\) | ||||
−0.0301623 | + | 0.999545i | \(0.509602\pi\) | |||||||
\(468\) | −0.654482 | −0.0302535 | ||||||||
\(469\) | −13.5910 | −0.627575 | ||||||||
\(470\) | 20.9601 | 0.966815 | ||||||||
\(471\) | −7.61058 | −0.350677 | ||||||||
\(472\) | −9.67425 | −0.445294 | ||||||||
\(473\) | −5.90279 | −0.271411 | ||||||||
\(474\) | 3.36046 | 0.154351 | ||||||||
\(475\) | 3.59413 | 0.164910 | ||||||||
\(476\) | −20.5257 | −0.940792 | ||||||||
\(477\) | 29.7261 | 1.36106 | ||||||||
\(478\) | −10.8794 | −0.497613 | ||||||||
\(479\) | −9.66601 | −0.441651 | −0.220826 | − | 0.975313i | \(-0.570875\pi\) | ||||
−0.220826 | + | 0.975313i | \(0.570875\pi\) | |||||||
\(480\) | 0.990100 | 0.0451917 | ||||||||
\(481\) | 0.364093 | 0.0166012 | ||||||||
\(482\) | 23.9685 | 1.09174 | ||||||||
\(483\) | 14.4546 | 0.657705 | ||||||||
\(484\) | −6.35592 | −0.288905 | ||||||||
\(485\) | 1.86385 | 0.0846331 | ||||||||
\(486\) | 12.5862 | 0.570922 | ||||||||
\(487\) | 13.2452 | 0.600197 | 0.300098 | − | 0.953908i | \(-0.402981\pi\) | ||||
0.300098 | + | 0.953908i | \(0.402981\pi\) | |||||||
\(488\) | −15.2735 | −0.691398 | ||||||||
\(489\) | 11.5398 | 0.521846 | ||||||||
\(490\) | −17.7371 | −0.801281 | ||||||||
\(491\) | 20.0511 | 0.904894 | 0.452447 | − | 0.891791i | \(-0.350551\pi\) | ||||
0.452447 | + | 0.891791i | \(0.350551\pi\) | |||||||
\(492\) | −0.232458 | −0.0104800 | ||||||||
\(493\) | −37.1341 | −1.67244 | ||||||||
\(494\) | 0.567153 | 0.0255174 | ||||||||
\(495\) | −10.9164 | −0.490657 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −7.94000 | −0.356158 | ||||||||
\(498\) | 5.29184 | 0.237133 | ||||||||
\(499\) | −26.4689 | −1.18491 | −0.592455 | − | 0.805604i | \(-0.701841\pi\) | ||||
−0.592455 | + | 0.805604i | \(0.701841\pi\) | |||||||
\(500\) | −12.1636 | −0.543973 | ||||||||
\(501\) | −3.81615 | −0.170493 | ||||||||
\(502\) | −20.6521 | −0.921749 | ||||||||
\(503\) | −5.09601 | −0.227220 | −0.113610 | − | 0.993525i | \(-0.536241\pi\) | ||||
−0.113610 | + | 0.993525i | \(0.536241\pi\) | |||||||
\(504\) | −11.0453 | −0.491996 | ||||||||
\(505\) | −9.33407 | −0.415361 | ||||||||
\(506\) | −14.4288 | −0.641437 | ||||||||
\(507\) | 6.87495 | 0.305327 | ||||||||
\(508\) | −9.43734 | −0.418714 | ||||||||
\(509\) | −15.1369 | −0.670930 | −0.335465 | − | 0.942053i | \(-0.608893\pi\) | ||||
−0.335465 | + | 0.942053i | \(0.608893\pi\) | |||||||
\(510\) | 5.00056 | 0.221428 | ||||||||
\(511\) | −5.10219 | −0.225707 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.15352 | −0.315835 | ||||||||
\(514\) | −14.2771 | −0.629734 | ||||||||
\(515\) | 20.7066 | 0.912440 | ||||||||
\(516\) | 1.45504 | 0.0640547 | ||||||||
\(517\) | −24.2343 | −1.06583 | ||||||||
\(518\) | 6.14456 | 0.269977 | ||||||||
\(519\) | −8.46410 | −0.371533 | ||||||||
\(520\) | −0.448838 | −0.0196828 | ||||||||
\(521\) | 22.1551 | 0.970631 | 0.485316 | − | 0.874339i | \(-0.338705\pi\) | ||||
0.485316 | + | 0.874339i | \(0.338705\pi\) | |||||||
\(522\) | −19.9827 | −0.874618 | ||||||||
\(523\) | 14.9344 | 0.653035 | 0.326518 | − | 0.945191i | \(-0.394125\pi\) | ||||
0.326518 | + | 0.945191i | \(0.394125\pi\) | |||||||
\(524\) | −3.80936 | −0.166413 | ||||||||
\(525\) | −3.29456 | −0.143787 | ||||||||
\(526\) | 15.8164 | 0.689628 | ||||||||
\(527\) | 5.05056 | 0.220006 | ||||||||
\(528\) | −1.14477 | −0.0498197 | ||||||||
\(529\) | 21.8290 | 0.949087 | ||||||||
\(530\) | 20.3858 | 0.885504 | ||||||||
\(531\) | −26.2928 | −1.14101 | ||||||||
\(532\) | 9.57148 | 0.414976 | ||||||||
\(533\) | 0.105379 | 0.00456448 | ||||||||
\(534\) | −7.44678 | −0.322254 | ||||||||
\(535\) | −9.68921 | −0.418901 | ||||||||
\(536\) | −3.34422 | −0.144448 | ||||||||
\(537\) | 7.39074 | 0.318934 | ||||||||
\(538\) | 31.4323 | 1.35514 | ||||||||
\(539\) | 20.5079 | 0.883339 | ||||||||
\(540\) | 5.66120 | 0.243619 | ||||||||
\(541\) | 9.13240 | 0.392632 | 0.196316 | − | 0.980541i | \(-0.437102\pi\) | ||||
0.196316 | + | 0.980541i | \(0.437102\pi\) | |||||||
\(542\) | 10.1062 | 0.434100 | ||||||||
\(543\) | −4.07475 | −0.174864 | ||||||||
\(544\) | −5.05056 | −0.216541 | ||||||||
\(545\) | −32.4928 | −1.39184 | ||||||||
\(546\) | −0.519881 | −0.0222488 | ||||||||
\(547\) | 3.98086 | 0.170209 | 0.0851047 | − | 0.996372i | \(-0.472878\pi\) | ||||
0.0851047 | + | 0.996372i | \(0.472878\pi\) | |||||||
\(548\) | −9.27362 | −0.396149 | ||||||||
\(549\) | −41.5105 | −1.77162 | ||||||||
\(550\) | 3.28869 | 0.140230 | ||||||||
\(551\) | 17.3163 | 0.737700 | ||||||||
\(552\) | 3.55670 | 0.151383 | ||||||||
\(553\) | −25.7092 | −1.09327 | ||||||||
\(554\) | 3.04574 | 0.129401 | ||||||||
\(555\) | −1.49697 | −0.0635427 | ||||||||
\(556\) | 0.598622 | 0.0253872 | ||||||||
\(557\) | −27.2244 | −1.15354 | −0.576768 | − | 0.816908i | \(-0.695686\pi\) | ||||
−0.576768 | + | 0.816908i | \(0.695686\pi\) | |||||||
\(558\) | 2.71781 | 0.115054 | ||||||||
\(559\) | −0.659608 | −0.0278984 | ||||||||
\(560\) | −7.57475 | −0.320092 | ||||||||
\(561\) | −5.78172 | −0.244105 | ||||||||
\(562\) | 21.8794 | 0.922927 | ||||||||
\(563\) | 26.4386 | 1.11425 | 0.557127 | − | 0.830427i | \(-0.311904\pi\) | ||||
0.557127 | + | 0.830427i | \(0.311904\pi\) | |||||||
\(564\) | 5.97378 | 0.251542 | ||||||||
\(565\) | −3.47631 | −0.146249 | ||||||||
\(566\) | −8.90262 | −0.374205 | ||||||||
\(567\) | −26.5786 | −1.11620 | ||||||||
\(568\) | −1.95372 | −0.0819764 | ||||||||
\(569\) | 20.5608 | 0.861953 | 0.430976 | − | 0.902363i | \(-0.358169\pi\) | ||||
0.430976 | + | 0.902363i | \(0.358169\pi\) | |||||||
\(570\) | −2.33185 | −0.0976704 | ||||||||
\(571\) | −1.90737 | −0.0798208 | −0.0399104 | − | 0.999203i | \(-0.512707\pi\) | ||||
−0.0399104 | + | 0.999203i | \(0.512707\pi\) | |||||||
\(572\) | 0.518953 | 0.0216985 | ||||||||
\(573\) | 11.6622 | 0.487196 | ||||||||
\(574\) | 1.77842 | 0.0742299 | ||||||||
\(575\) | −10.2177 | −0.426107 | ||||||||
\(576\) | −2.71781 | −0.113242 | ||||||||
\(577\) | 26.6219 | 1.10828 | 0.554142 | − | 0.832422i | \(-0.313046\pi\) | ||||
0.554142 | + | 0.832422i | \(0.313046\pi\) | |||||||
\(578\) | −8.50817 | −0.353893 | ||||||||
\(579\) | −2.29555 | −0.0953997 | ||||||||
\(580\) | −13.7039 | −0.569024 | ||||||||
\(581\) | −40.4852 | −1.67961 | ||||||||
\(582\) | 0.531212 | 0.0220194 | ||||||||
\(583\) | −23.5704 | −0.976188 | ||||||||
\(584\) | −1.25545 | −0.0519508 | ||||||||
\(585\) | −1.21986 | −0.0504349 | ||||||||
\(586\) | 19.5925 | 0.809360 | ||||||||
\(587\) | −17.4559 | −0.720480 | −0.360240 | − | 0.932860i | \(-0.617305\pi\) | ||||
−0.360240 | + | 0.932860i | \(0.617305\pi\) | |||||||
\(588\) | −5.05522 | −0.208474 | ||||||||
\(589\) | −2.35517 | −0.0970430 | ||||||||
\(590\) | −18.0314 | −0.742339 | ||||||||
\(591\) | 10.3223 | 0.424603 | ||||||||
\(592\) | 1.51194 | 0.0621402 | ||||||||
\(593\) | 36.1070 | 1.48274 | 0.741368 | − | 0.671099i | \(-0.234177\pi\) | ||||
0.741368 | + | 0.671099i | \(0.234177\pi\) | |||||||
\(594\) | −6.54557 | −0.268568 | ||||||||
\(595\) | −38.2567 | −1.56837 | ||||||||
\(596\) | 15.0404 | 0.616077 | ||||||||
\(597\) | −3.18606 | −0.130397 | ||||||||
\(598\) | −1.61234 | −0.0659337 | ||||||||
\(599\) | 5.59080 | 0.228434 | 0.114217 | − | 0.993456i | \(-0.463564\pi\) | ||||
0.114217 | + | 0.993456i | \(0.463564\pi\) | |||||||
\(600\) | −0.810663 | −0.0330952 | ||||||||
\(601\) | 12.5228 | 0.510815 | 0.255408 | − | 0.966833i | \(-0.417790\pi\) | ||||
0.255408 | + | 0.966833i | \(0.417790\pi\) | |||||||
\(602\) | −11.1318 | −0.453698 | ||||||||
\(603\) | −9.08897 | −0.370131 | ||||||||
\(604\) | −2.61615 | −0.106449 | ||||||||
\(605\) | −11.8465 | −0.481628 | ||||||||
\(606\) | −2.66028 | −0.108067 | ||||||||
\(607\) | 8.42948 | 0.342142 | 0.171071 | − | 0.985259i | \(-0.445277\pi\) | ||||
0.171071 | + | 0.985259i | \(0.445277\pi\) | |||||||
\(608\) | 2.35517 | 0.0955146 | ||||||||
\(609\) | −15.8730 | −0.643207 | ||||||||
\(610\) | −28.4675 | −1.15261 | ||||||||
\(611\) | −2.70807 | −0.109557 | ||||||||
\(612\) | −13.7265 | −0.554860 | ||||||||
\(613\) | 10.4446 | 0.421855 | 0.210927 | − | 0.977502i | \(-0.432352\pi\) | ||||
0.210927 | + | 0.977502i | \(0.432352\pi\) | |||||||
\(614\) | 32.2620 | 1.30199 | ||||||||
\(615\) | −0.433267 | −0.0174710 | ||||||||
\(616\) | 8.75805 | 0.352872 | ||||||||
\(617\) | 1.61686 | 0.0650922 | 0.0325461 | − | 0.999470i | \(-0.489638\pi\) | ||||
0.0325461 | + | 0.999470i | \(0.489638\pi\) | |||||||
\(618\) | 5.90153 | 0.237395 | ||||||||
\(619\) | 5.28772 | 0.212531 | 0.106266 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106266 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(620\) | 1.86385 | 0.0748540 | ||||||||
\(621\) | 20.3366 | 0.816078 | ||||||||
\(622\) | 18.8003 | 0.753822 | ||||||||
\(623\) | 56.9716 | 2.28252 | ||||||||
\(624\) | −0.127922 | −0.00512099 | ||||||||
\(625\) | −15.0408 | −0.601633 | ||||||||
\(626\) | 11.9552 | 0.477826 | ||||||||
\(627\) | 2.69612 | 0.107673 | ||||||||
\(628\) | 14.3268 | 0.571702 | ||||||||
\(629\) | 7.63613 | 0.304472 | ||||||||
\(630\) | −20.5868 | −0.820196 | ||||||||
\(631\) | 7.79917 | 0.310480 | 0.155240 | − | 0.987877i | \(-0.450385\pi\) | ||||
0.155240 | + | 0.987877i | \(0.450385\pi\) | |||||||
\(632\) | −6.32603 | −0.251636 | ||||||||
\(633\) | −5.59536 | −0.222396 | ||||||||
\(634\) | 14.1818 | 0.563230 | ||||||||
\(635\) | −17.5898 | −0.698030 | ||||||||
\(636\) | 5.81013 | 0.230387 | ||||||||
\(637\) | 2.29166 | 0.0907989 | ||||||||
\(638\) | 15.8447 | 0.627297 | ||||||||
\(639\) | −5.30985 | −0.210055 | ||||||||
\(640\) | −1.86385 | −0.0736751 | ||||||||
\(641\) | −35.0667 | −1.38505 | −0.692525 | − | 0.721394i | \(-0.743502\pi\) | ||||
−0.692525 | + | 0.721394i | \(0.743502\pi\) | |||||||
\(642\) | −2.76150 | −0.108988 | ||||||||
\(643\) | −13.3830 | −0.527772 | −0.263886 | − | 0.964554i | \(-0.585004\pi\) | ||||
−0.263886 | + | 0.964554i | \(0.585004\pi\) | |||||||
\(644\) | −27.2105 | −1.07225 | ||||||||
\(645\) | 2.71198 | 0.106784 | ||||||||
\(646\) | 11.8949 | 0.467999 | ||||||||
\(647\) | 14.4181 | 0.566836 | 0.283418 | − | 0.958997i | \(-0.408532\pi\) | ||||
0.283418 | + | 0.958997i | \(0.408532\pi\) | |||||||
\(648\) | −6.53995 | −0.256914 | ||||||||
\(649\) | 20.8481 | 0.818361 | ||||||||
\(650\) | 0.367494 | 0.0144143 | ||||||||
\(651\) | 2.15886 | 0.0846126 | ||||||||
\(652\) | −21.7235 | −0.850756 | ||||||||
\(653\) | −17.6995 | −0.692633 | −0.346317 | − | 0.938118i | \(-0.612568\pi\) | ||||
−0.346317 | + | 0.938118i | \(0.612568\pi\) | |||||||
\(654\) | −9.26070 | −0.362122 | ||||||||
\(655\) | −7.10008 | −0.277423 | ||||||||
\(656\) | 0.437600 | 0.0170854 | ||||||||
\(657\) | −3.41207 | −0.133118 | ||||||||
\(658\) | −45.7024 | −1.78167 | ||||||||
\(659\) | −9.55989 | −0.372401 | −0.186200 | − | 0.982512i | \(-0.559617\pi\) | ||||
−0.186200 | + | 0.982512i | \(0.559617\pi\) | |||||||
\(660\) | −2.13368 | −0.0830533 | ||||||||
\(661\) | −36.9183 | −1.43596 | −0.717978 | − | 0.696066i | \(-0.754932\pi\) | ||||
−0.717978 | + | 0.696066i | \(0.754932\pi\) | |||||||
\(662\) | 35.6196 | 1.38440 | ||||||||
\(663\) | −0.646079 | −0.0250916 | ||||||||
\(664\) | −9.96182 | −0.386593 | ||||||||
\(665\) | 17.8398 | 0.691798 | ||||||||
\(666\) | 4.10916 | 0.159227 | ||||||||
\(667\) | −49.2281 | −1.90612 | ||||||||
\(668\) | 7.18386 | 0.277952 | ||||||||
\(669\) | −7.88366 | −0.304800 | ||||||||
\(670\) | −6.23312 | −0.240807 | ||||||||
\(671\) | 32.9146 | 1.27065 | ||||||||
\(672\) | −2.15886 | −0.0832800 | ||||||||
\(673\) | −13.9201 | −0.536581 | −0.268290 | − | 0.963338i | \(-0.586459\pi\) | ||||
−0.268290 | + | 0.963338i | \(0.586459\pi\) | |||||||
\(674\) | 13.4426 | 0.517789 | ||||||||
\(675\) | −4.63522 | −0.178410 | ||||||||
\(676\) | −12.9420 | −0.497770 | ||||||||
\(677\) | 13.3426 | 0.512798 | 0.256399 | − | 0.966571i | \(-0.417464\pi\) | ||||
0.256399 | + | 0.966571i | \(0.417464\pi\) | |||||||
\(678\) | −0.990775 | −0.0380505 | ||||||||
\(679\) | −4.06404 | −0.155963 | ||||||||
\(680\) | −9.41349 | −0.360991 | ||||||||
\(681\) | −6.08382 | −0.233132 | ||||||||
\(682\) | −2.15501 | −0.0825197 | ||||||||
\(683\) | 18.6396 | 0.713226 | 0.356613 | − | 0.934252i | \(-0.383931\pi\) | ||||
0.356613 | + | 0.934252i | \(0.383931\pi\) | |||||||
\(684\) | 6.40090 | 0.244745 | ||||||||
\(685\) | −17.2846 | −0.660412 | ||||||||
\(686\) | 10.2267 | 0.390456 | ||||||||
\(687\) | 7.49504 | 0.285954 | ||||||||
\(688\) | −2.73910 | −0.104427 | ||||||||
\(689\) | −2.63388 | −0.100343 | ||||||||
\(690\) | 6.62916 | 0.252368 | ||||||||
\(691\) | −25.2602 | −0.960945 | −0.480472 | − | 0.877010i | \(-0.659535\pi\) | ||||
−0.480472 | + | 0.877010i | \(0.659535\pi\) | |||||||
\(692\) | 15.9336 | 0.605703 | ||||||||
\(693\) | 23.8027 | 0.904191 | ||||||||
\(694\) | −4.58164 | −0.173917 | ||||||||
\(695\) | 1.11574 | 0.0423225 | ||||||||
\(696\) | −3.90573 | −0.148046 | ||||||||
\(697\) | 2.21012 | 0.0837144 | ||||||||
\(698\) | −26.1860 | −0.991153 | ||||||||
\(699\) | 9.40486 | 0.355724 | ||||||||
\(700\) | 6.20198 | 0.234413 | ||||||||
\(701\) | −29.4721 | −1.11315 | −0.556573 | − | 0.830799i | \(-0.687884\pi\) | ||||
−0.556573 | + | 0.830799i | \(0.687884\pi\) | |||||||
\(702\) | −0.731436 | −0.0276063 | ||||||||
\(703\) | −3.56086 | −0.134300 | ||||||||
\(704\) | 2.15501 | 0.0812201 | ||||||||
\(705\) | 11.1342 | 0.419340 | ||||||||
\(706\) | 8.49199 | 0.319600 | ||||||||
\(707\) | 20.3525 | 0.765434 | ||||||||
\(708\) | −5.13908 | −0.193138 | ||||||||
\(709\) | −40.4421 | −1.51884 | −0.759418 | − | 0.650603i | \(-0.774516\pi\) | ||||
−0.759418 | + | 0.650603i | \(0.774516\pi\) | |||||||
\(710\) | −3.64145 | −0.136661 | ||||||||
\(711\) | −17.1930 | −0.644787 | ||||||||
\(712\) | 14.0185 | 0.525364 | ||||||||
\(713\) | 6.69545 | 0.250746 | ||||||||
\(714\) | −10.9035 | −0.408052 | ||||||||
\(715\) | 0.967251 | 0.0361731 | ||||||||
\(716\) | −13.9130 | −0.519952 | ||||||||
\(717\) | −5.77927 | −0.215831 | ||||||||
\(718\) | −13.2984 | −0.496291 | ||||||||
\(719\) | 5.73213 | 0.213773 | 0.106886 | − | 0.994271i | \(-0.465912\pi\) | ||||
0.106886 | + | 0.994271i | \(0.465912\pi\) | |||||||
\(720\) | −5.06560 | −0.188784 | ||||||||
\(721\) | −45.1497 | −1.68146 | ||||||||
\(722\) | 13.4532 | 0.500676 | ||||||||
\(723\) | 12.7324 | 0.473521 | ||||||||
\(724\) | 7.67066 | 0.285078 | ||||||||
\(725\) | 11.2204 | 0.416713 | ||||||||
\(726\) | −3.37634 | −0.125308 | ||||||||
\(727\) | 31.8915 | 1.18279 | 0.591395 | − | 0.806382i | \(-0.298578\pi\) | ||||
0.591395 | + | 0.806382i | \(0.298578\pi\) | |||||||
\(728\) | 0.978669 | 0.0362719 | ||||||||
\(729\) | −12.9339 | −0.479034 | ||||||||
\(730\) | −2.33997 | −0.0866061 | ||||||||
\(731\) | −13.8340 | −0.511668 | ||||||||
\(732\) | −8.11346 | −0.299882 | ||||||||
\(733\) | −34.3205 | −1.26766 | −0.633828 | − | 0.773474i | \(-0.718517\pi\) | ||||
−0.633828 | + | 0.773474i | \(0.718517\pi\) | |||||||
\(734\) | 21.5352 | 0.794880 | ||||||||
\(735\) | −9.42217 | −0.347542 | ||||||||
\(736\) | −6.69545 | −0.246797 | ||||||||
\(737\) | 7.20684 | 0.265467 | ||||||||
\(738\) | 1.18931 | 0.0437793 | ||||||||
\(739\) | −33.8462 | −1.24505 | −0.622526 | − | 0.782599i | \(-0.713893\pi\) | ||||
−0.622526 | + | 0.782599i | \(0.713893\pi\) | |||||||
\(740\) | 2.81802 | 0.103593 | ||||||||
\(741\) | 0.301278 | 0.0110677 | ||||||||
\(742\) | −44.4504 | −1.63182 | ||||||||
\(743\) | −28.2921 | −1.03793 | −0.518967 | − | 0.854794i | \(-0.673683\pi\) | ||||
−0.518967 | + | 0.854794i | \(0.673683\pi\) | |||||||
\(744\) | 0.531212 | 0.0194752 | ||||||||
\(745\) | 28.0330 | 1.02705 | ||||||||
\(746\) | −25.5012 | −0.933664 | ||||||||
\(747\) | −27.0744 | −0.990599 | ||||||||
\(748\) | 10.8840 | 0.397959 | ||||||||
\(749\) | 21.1269 | 0.771959 | ||||||||
\(750\) | −6.46145 | −0.235939 | ||||||||
\(751\) | −28.4785 | −1.03920 | −0.519598 | − | 0.854411i | \(-0.673918\pi\) | ||||
−0.519598 | + | 0.854411i | \(0.673918\pi\) | |||||||
\(752\) | −11.2456 | −0.410084 | ||||||||
\(753\) | −10.9707 | −0.399793 | ||||||||
\(754\) | 1.77057 | 0.0644802 | ||||||||
\(755\) | −4.87610 | −0.177460 | ||||||||
\(756\) | −12.3440 | −0.448946 | ||||||||
\(757\) | −22.6135 | −0.821903 | −0.410951 | − | 0.911657i | \(-0.634803\pi\) | ||||
−0.410951 | + | 0.911657i | \(0.634803\pi\) | |||||||
\(758\) | 2.19932 | 0.0798830 | ||||||||
\(759\) | −7.66474 | −0.278212 | ||||||||
\(760\) | 4.38968 | 0.159230 | ||||||||
\(761\) | −34.7144 | −1.25840 | −0.629199 | − | 0.777245i | \(-0.716617\pi\) | ||||
−0.629199 | + | 0.777245i | \(0.716617\pi\) | |||||||
\(762\) | −5.01323 | −0.181610 | ||||||||
\(763\) | 70.8490 | 2.56490 | ||||||||
\(764\) | −21.9540 | −0.794267 | ||||||||
\(765\) | −25.5841 | −0.924995 | ||||||||
\(766\) | −29.0342 | −1.04905 | ||||||||
\(767\) | 2.32968 | 0.0841197 | ||||||||
\(768\) | −0.531212 | −0.0191685 | ||||||||
\(769\) | 0.645198 | 0.0232664 | 0.0116332 | − | 0.999932i | \(-0.496297\pi\) | ||||
0.0116332 | + | 0.999932i | \(0.496297\pi\) | |||||||
\(770\) | 16.3237 | 0.588265 | ||||||||
\(771\) | −7.58414 | −0.273136 | ||||||||
\(772\) | 4.32134 | 0.155528 | ||||||||
\(773\) | 7.58398 | 0.272777 | 0.136388 | − | 0.990655i | \(-0.456450\pi\) | ||||
0.136388 | + | 0.990655i | \(0.456450\pi\) | |||||||
\(774\) | −7.44436 | −0.267582 | ||||||||
\(775\) | −1.52606 | −0.0548178 | ||||||||
\(776\) | −1.00000 | −0.0358979 | ||||||||
\(777\) | 3.26407 | 0.117098 | ||||||||
\(778\) | 17.1770 | 0.615824 | ||||||||
\(779\) | −1.03062 | −0.0369258 | ||||||||
\(780\) | −0.238428 | −0.00853709 | ||||||||
\(781\) | 4.21030 | 0.150656 | ||||||||
\(782\) | −33.8158 | −1.20925 | ||||||||
\(783\) | −22.3322 | −0.798088 | ||||||||
\(784\) | 9.51638 | 0.339871 | ||||||||
\(785\) | 26.7030 | 0.953073 | ||||||||
\(786\) | −2.02358 | −0.0721787 | ||||||||
\(787\) | −3.19935 | −0.114044 | −0.0570222 | − | 0.998373i | \(-0.518161\pi\) | ||||
−0.0570222 | + | 0.998373i | \(0.518161\pi\) | |||||||
\(788\) | −19.4316 | −0.692222 | ||||||||
\(789\) | 8.40187 | 0.299114 | ||||||||
\(790\) | −11.7908 | −0.419497 | ||||||||
\(791\) | 7.57992 | 0.269511 | ||||||||
\(792\) | 5.85692 | 0.208117 | ||||||||
\(793\) | 3.67804 | 0.130611 | ||||||||
\(794\) | −5.42066 | −0.192372 | ||||||||
\(795\) | 10.8292 | 0.384072 | ||||||||
\(796\) | 5.99771 | 0.212583 | ||||||||
\(797\) | 3.47876 | 0.123224 | 0.0616120 | − | 0.998100i | \(-0.480376\pi\) | ||||
0.0616120 | + | 0.998100i | \(0.480376\pi\) | |||||||
\(798\) | 5.08449 | 0.179989 | ||||||||
\(799\) | −56.7964 | −2.00931 | ||||||||
\(800\) | 1.52606 | 0.0539545 | ||||||||
\(801\) | 38.0996 | 1.34618 | ||||||||
\(802\) | −19.7790 | −0.698420 | ||||||||
\(803\) | 2.70551 | 0.0954753 | ||||||||
\(804\) | −1.77649 | −0.0626520 | ||||||||
\(805\) | −50.7163 | −1.78752 | ||||||||
\(806\) | −0.240812 | −0.00848224 | ||||||||
\(807\) | 16.6972 | 0.587770 | ||||||||
\(808\) | 5.00795 | 0.176179 | ||||||||
\(809\) | −28.0693 | −0.986863 | −0.493432 | − | 0.869785i | \(-0.664258\pi\) | ||||
−0.493432 | + | 0.869785i | \(0.664258\pi\) | |||||||
\(810\) | −12.1895 | −0.428295 | ||||||||
\(811\) | 8.34633 | 0.293079 | 0.146540 | − | 0.989205i | \(-0.453186\pi\) | ||||
0.146540 | + | 0.989205i | \(0.453186\pi\) | |||||||
\(812\) | 29.8807 | 1.04861 | ||||||||
\(813\) | 5.36856 | 0.188284 | ||||||||
\(814\) | −3.25824 | −0.114201 | ||||||||
\(815\) | −40.4893 | −1.41828 | ||||||||
\(816\) | −2.68292 | −0.0939209 | ||||||||
\(817\) | 6.45103 | 0.225693 | ||||||||
\(818\) | 30.9625 | 1.08258 | ||||||||
\(819\) | 2.65984 | 0.0929423 | ||||||||
\(820\) | 0.815620 | 0.0284827 | ||||||||
\(821\) | 31.9483 | 1.11500 | 0.557501 | − | 0.830176i | \(-0.311760\pi\) | ||||
0.557501 | + | 0.830176i | \(0.311760\pi\) | |||||||
\(822\) | −4.92626 | −0.171823 | ||||||||
\(823\) | 11.6495 | 0.406076 | 0.203038 | − | 0.979171i | \(-0.434919\pi\) | ||||
0.203038 | + | 0.979171i | \(0.434919\pi\) | |||||||
\(824\) | −11.1096 | −0.387020 | ||||||||
\(825\) | 1.74699 | 0.0608224 | ||||||||
\(826\) | 39.3165 | 1.36800 | ||||||||
\(827\) | −4.86571 | −0.169197 | −0.0845986 | − | 0.996415i | \(-0.526961\pi\) | ||||
−0.0845986 | + | 0.996415i | \(0.526961\pi\) | |||||||
\(828\) | −18.1970 | −0.632389 | ||||||||
\(829\) | −30.2881 | −1.05195 | −0.525975 | − | 0.850500i | \(-0.676299\pi\) | ||||
−0.525975 | + | 0.850500i | \(0.676299\pi\) | |||||||
\(830\) | −18.5673 | −0.644482 | ||||||||
\(831\) | 1.61794 | 0.0561256 | ||||||||
\(832\) | 0.240812 | 0.00834866 | ||||||||
\(833\) | 48.0631 | 1.66529 | ||||||||
\(834\) | 0.317995 | 0.0110113 | ||||||||
\(835\) | 13.3896 | 0.463368 | ||||||||
\(836\) | −5.07541 | −0.175537 | ||||||||
\(837\) | 3.03737 | 0.104987 | ||||||||
\(838\) | 32.8771 | 1.13572 | ||||||||
\(839\) | 43.3356 | 1.49611 | 0.748055 | − | 0.663636i | \(-0.230988\pi\) | ||||
0.748055 | + | 0.663636i | \(0.230988\pi\) | |||||||
\(840\) | −4.02380 | −0.138834 | ||||||||
\(841\) | 25.0590 | 0.864102 | ||||||||
\(842\) | 16.5914 | 0.571776 | ||||||||
\(843\) | 11.6226 | 0.400304 | ||||||||
\(844\) | 10.5332 | 0.362567 | ||||||||
\(845\) | −24.1220 | −0.829821 | ||||||||
\(846\) | −30.5634 | −1.05079 | ||||||||
\(847\) | 25.8307 | 0.887553 | ||||||||
\(848\) | −10.9375 | −0.375595 | ||||||||
\(849\) | −4.72918 | −0.162305 | ||||||||
\(850\) | 7.70748 | 0.264364 | ||||||||
\(851\) | 10.1231 | 0.347015 | ||||||||
\(852\) | −1.03784 | −0.0355558 | ||||||||
\(853\) | 23.6902 | 0.811137 | 0.405569 | − | 0.914065i | \(-0.367074\pi\) | ||||
0.405569 | + | 0.914065i | \(0.367074\pi\) | |||||||
\(854\) | 62.0720 | 2.12406 | ||||||||
\(855\) | 11.9303 | 0.408009 | ||||||||
\(856\) | 5.19849 | 0.177681 | ||||||||
\(857\) | −44.5713 | −1.52253 | −0.761263 | − | 0.648443i | \(-0.775420\pi\) | ||||
−0.761263 | + | 0.648443i | \(0.775420\pi\) | |||||||
\(858\) | 0.275674 | 0.00941136 | ||||||||
\(859\) | 3.79116 | 0.129353 | 0.0646763 | − | 0.997906i | \(-0.479399\pi\) | ||||
0.0646763 | + | 0.997906i | \(0.479399\pi\) | |||||||
\(860\) | −5.10527 | −0.174088 | ||||||||
\(861\) | 0.944719 | 0.0321959 | ||||||||
\(862\) | −22.0837 | −0.752175 | ||||||||
\(863\) | −10.2311 | −0.348271 | −0.174136 | − | 0.984722i | \(-0.555713\pi\) | ||||
−0.174136 | + | 0.984722i | \(0.555713\pi\) | |||||||
\(864\) | −3.03737 | −0.103333 | ||||||||
\(865\) | 29.6978 | 1.00975 | ||||||||
\(866\) | 12.5493 | 0.426443 | ||||||||
\(867\) | −4.51964 | −0.153495 | ||||||||
\(868\) | −4.06404 | −0.137942 | ||||||||
\(869\) | 13.6327 | 0.462457 | ||||||||
\(870\) | −7.27969 | −0.246804 | ||||||||
\(871\) | 0.805329 | 0.0272875 | ||||||||
\(872\) | 17.4332 | 0.590361 | ||||||||
\(873\) | −2.71781 | −0.0919841 | ||||||||
\(874\) | 15.7689 | 0.533391 | ||||||||
\(875\) | 49.4333 | 1.67115 | ||||||||
\(876\) | −0.666909 | −0.0225328 | ||||||||
\(877\) | 8.30377 | 0.280398 | 0.140199 | − | 0.990123i | \(-0.455226\pi\) | ||||
0.140199 | + | 0.990123i | \(0.455226\pi\) | |||||||
\(878\) | 16.1761 | 0.545917 | ||||||||
\(879\) | 10.4078 | 0.351046 | ||||||||
\(880\) | 4.01662 | 0.135400 | ||||||||
\(881\) | 2.17468 | 0.0732669 | 0.0366334 | − | 0.999329i | \(-0.488337\pi\) | ||||
0.0366334 | + | 0.999329i | \(0.488337\pi\) | |||||||
\(882\) | 25.8638 | 0.870878 | ||||||||
\(883\) | 17.3317 | 0.583258 | 0.291629 | − | 0.956532i | \(-0.405803\pi\) | ||||
0.291629 | + | 0.956532i | \(0.405803\pi\) | |||||||
\(884\) | 1.21624 | 0.0409064 | ||||||||
\(885\) | −9.57847 | −0.321977 | ||||||||
\(886\) | −4.03243 | −0.135472 | ||||||||
\(887\) | 5.05505 | 0.169732 | 0.0848660 | − | 0.996392i | \(-0.472954\pi\) | ||||
0.0848660 | + | 0.996392i | \(0.472954\pi\) | |||||||
\(888\) | 0.803159 | 0.0269522 | ||||||||
\(889\) | 38.3537 | 1.28634 | ||||||||
\(890\) | 26.1283 | 0.875824 | ||||||||
\(891\) | 14.0937 | 0.472156 | ||||||||
\(892\) | 14.8409 | 0.496910 | ||||||||
\(893\) | 26.4852 | 0.886293 | ||||||||
\(894\) | 7.98962 | 0.267213 | ||||||||
\(895\) | −25.9317 | −0.866801 | ||||||||
\(896\) | 4.06404 | 0.135770 | ||||||||
\(897\) | −0.856497 | −0.0285976 | ||||||||
\(898\) | −25.5043 | −0.851089 | ||||||||
\(899\) | −7.35248 | −0.245219 | ||||||||
\(900\) | 4.14756 | 0.138252 | ||||||||
\(901\) | −55.2405 | −1.84033 | ||||||||
\(902\) | −0.943033 | −0.0313996 | ||||||||
\(903\) | −5.91334 | −0.196784 | ||||||||
\(904\) | 1.86512 | 0.0620330 | ||||||||
\(905\) | 14.2970 | 0.475247 | ||||||||
\(906\) | −1.38973 | −0.0461706 | ||||||||
\(907\) | −6.71882 | −0.223095 | −0.111547 | − | 0.993759i | \(-0.535581\pi\) | ||||
−0.111547 | + | 0.993759i | \(0.535581\pi\) | |||||||
\(908\) | 11.4527 | 0.380072 | ||||||||
\(909\) | 13.6107 | 0.451438 | ||||||||
\(910\) | 1.82409 | 0.0604680 | ||||||||
\(911\) | 7.13853 | 0.236510 | 0.118255 | − | 0.992983i | \(-0.462270\pi\) | ||||
0.118255 | + | 0.992983i | \(0.462270\pi\) | |||||||
\(912\) | 1.25109 | 0.0414278 | ||||||||
\(913\) | 21.4678 | 0.710482 | ||||||||
\(914\) | 21.2751 | 0.703718 | ||||||||
\(915\) | −15.1223 | −0.499927 | ||||||||
\(916\) | −14.1093 | −0.466185 | ||||||||
\(917\) | 15.4814 | 0.511240 | ||||||||
\(918\) | −15.3404 | −0.506310 | ||||||||
\(919\) | −24.4581 | −0.806798 | −0.403399 | − | 0.915024i | \(-0.632171\pi\) | ||||
−0.403399 | + | 0.915024i | \(0.632171\pi\) | |||||||
\(920\) | −12.4793 | −0.411431 | ||||||||
\(921\) | 17.1380 | 0.564716 | ||||||||
\(922\) | 21.4885 | 0.707687 | ||||||||
\(923\) | 0.470480 | 0.0154860 | ||||||||
\(924\) | 4.65238 | 0.153052 | ||||||||
\(925\) | −2.30731 | −0.0758639 | ||||||||
\(926\) | −10.9892 | −0.361127 | ||||||||
\(927\) | −30.1937 | −0.991692 | ||||||||
\(928\) | 7.35248 | 0.241357 | ||||||||
\(929\) | −31.3613 | −1.02893 | −0.514465 | − | 0.857511i | \(-0.672009\pi\) | ||||
−0.514465 | + | 0.857511i | \(0.672009\pi\) | |||||||
\(930\) | 0.990100 | 0.0324666 | ||||||||
\(931\) | −22.4127 | −0.734546 | ||||||||
\(932\) | −17.7045 | −0.579931 | ||||||||
\(933\) | 9.98693 | 0.326958 | ||||||||
\(934\) | 1.30362 | 0.0426559 | ||||||||
\(935\) | 20.2862 | 0.663429 | ||||||||
\(936\) | 0.654482 | 0.0213924 | ||||||||
\(937\) | 51.1150 | 1.66986 | 0.834928 | − | 0.550360i | \(-0.185509\pi\) | ||||
0.834928 | + | 0.550360i | \(0.185509\pi\) | |||||||
\(938\) | 13.5910 | 0.443763 | ||||||||
\(939\) | 6.35074 | 0.207249 | ||||||||
\(940\) | −20.9601 | −0.683642 | ||||||||
\(941\) | 41.6596 | 1.35807 | 0.679033 | − | 0.734108i | \(-0.262399\pi\) | ||||
0.679033 | + | 0.734108i | \(0.262399\pi\) | |||||||
\(942\) | 7.61058 | 0.247966 | ||||||||
\(943\) | 2.92993 | 0.0954115 | ||||||||
\(944\) | 9.67425 | 0.314870 | ||||||||
\(945\) | −23.0073 | −0.748429 | ||||||||
\(946\) | 5.90279 | 0.191916 | ||||||||
\(947\) | −50.2070 | −1.63151 | −0.815754 | − | 0.578399i | \(-0.803678\pi\) | ||||
−0.815754 | + | 0.578399i | \(0.803678\pi\) | |||||||
\(948\) | −3.36046 | −0.109143 | ||||||||
\(949\) | 0.302327 | 0.00981395 | ||||||||
\(950\) | −3.59413 | −0.116609 | ||||||||
\(951\) | 7.53352 | 0.244291 | ||||||||
\(952\) | 20.5257 | 0.665240 | ||||||||
\(953\) | 17.4563 | 0.565466 | 0.282733 | − | 0.959199i | \(-0.408759\pi\) | ||||
0.282733 | + | 0.959199i | \(0.408759\pi\) | |||||||
\(954\) | −29.7261 | −0.962417 | ||||||||
\(955\) | −40.9189 | −1.32411 | ||||||||
\(956\) | 10.8794 | 0.351865 | ||||||||
\(957\) | 8.41689 | 0.272079 | ||||||||
\(958\) | 9.66601 | 0.312294 | ||||||||
\(959\) | 37.6883 | 1.21702 | ||||||||
\(960\) | −0.990100 | −0.0319553 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −0.364093 | −0.0117388 | ||||||||
\(963\) | 14.1285 | 0.455286 | ||||||||
\(964\) | −23.9685 | −0.771973 | ||||||||
\(965\) | 8.05432 | 0.259278 | ||||||||
\(966\) | −14.4546 | −0.465068 | ||||||||
\(967\) | −15.2711 | −0.491085 | −0.245543 | − | 0.969386i | \(-0.578966\pi\) | ||||
−0.245543 | + | 0.969386i | \(0.578966\pi\) | |||||||
\(968\) | 6.35592 | 0.204287 | ||||||||
\(969\) | 6.31872 | 0.202987 | ||||||||
\(970\) | −1.86385 | −0.0598446 | ||||||||
\(971\) | 10.0477 | 0.322445 | 0.161223 | − | 0.986918i | \(-0.448456\pi\) | ||||
0.161223 | + | 0.986918i | \(0.448456\pi\) | |||||||
\(972\) | −12.5862 | −0.403703 | ||||||||
\(973\) | −2.43282 | −0.0779927 | ||||||||
\(974\) | −13.2452 | −0.424403 | ||||||||
\(975\) | 0.195218 | 0.00625196 | ||||||||
\(976\) | 15.2735 | 0.488892 | ||||||||
\(977\) | −14.2628 | −0.456307 | −0.228154 | − | 0.973625i | \(-0.573269\pi\) | ||||
−0.228154 | + | 0.973625i | \(0.573269\pi\) | |||||||
\(978\) | −11.5398 | −0.369001 | ||||||||
\(979\) | −30.2100 | −0.965515 | ||||||||
\(980\) | 17.7371 | 0.566591 | ||||||||
\(981\) | 47.3801 | 1.51273 | ||||||||
\(982\) | −20.0511 | −0.639857 | ||||||||
\(983\) | 44.8520 | 1.43056 | 0.715279 | − | 0.698839i | \(-0.246300\pi\) | ||||
0.715279 | + | 0.698839i | \(0.246300\pi\) | |||||||
\(984\) | 0.232458 | 0.00741050 | ||||||||
\(985\) | −36.2176 | −1.15399 | ||||||||
\(986\) | 37.1341 | 1.18259 | ||||||||
\(987\) | −24.2777 | −0.772767 | ||||||||
\(988\) | −0.567153 | −0.0180435 | ||||||||
\(989\) | −18.3395 | −0.583162 | ||||||||
\(990\) | 10.9164 | 0.346947 | ||||||||
\(991\) | −3.76510 | −0.119602 | −0.0598011 | − | 0.998210i | \(-0.519047\pi\) | ||||
−0.0598011 | + | 0.998210i | \(0.519047\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | 18.9216 | 0.600458 | ||||||||
\(994\) | 7.94000 | 0.251841 | ||||||||
\(995\) | 11.1788 | 0.354393 | ||||||||
\(996\) | −5.29184 | −0.167678 | ||||||||
\(997\) | −6.19708 | −0.196264 | −0.0981318 | − | 0.995173i | \(-0.531287\pi\) | ||||
−0.0981318 | + | 0.995173i | \(0.531287\pi\) | |||||||
\(998\) | 26.4689 | 0.837858 | ||||||||
\(999\) | 4.59231 | 0.145294 |
(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 | 6014.2.a.f.1.10 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6014.2.a.f.1.10 | ✓ | 22 | 1.1 | even | 1 | trivial |