Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, 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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75717 | −1.94962 | −0.974808 | − | 0.223046i | \(-0.928400\pi\) | ||||
−0.974808 | + | 0.223046i | \(0.928400\pi\) | |||||||
\(3\) | −0.782411 | −0.451725 | −0.225863 | − | 0.974159i | \(-0.572520\pi\) | ||||
−0.225863 | + | 0.974159i | \(0.572520\pi\) | |||||||
\(4\) | 5.60200 | 2.80100 | ||||||||
\(5\) | −3.11881 | −1.39477 | −0.697386 | − | 0.716695i | \(-0.745654\pi\) | ||||
−0.697386 | + | 0.716695i | \(0.745654\pi\) | |||||||
\(6\) | 2.15724 | 0.880690 | ||||||||
\(7\) | 0.297168 | 0.112319 | 0.0561595 | − | 0.998422i | \(-0.482114\pi\) | ||||
0.0561595 | + | 0.998422i | \(0.482114\pi\) | |||||||
\(8\) | −9.93135 | −3.51126 | ||||||||
\(9\) | −2.38783 | −0.795944 | ||||||||
\(10\) | 8.59909 | 2.71927 | ||||||||
\(11\) | −5.63230 | −1.69820 | −0.849102 | − | 0.528229i | \(-0.822856\pi\) | ||||
−0.849102 | + | 0.528229i | \(0.822856\pi\) | |||||||
\(12\) | −4.38307 | −1.26528 | ||||||||
\(13\) | 6.65009 | 1.84440 | 0.922201 | − | 0.386710i | \(-0.126389\pi\) | ||||
0.922201 | + | 0.386710i | \(0.126389\pi\) | |||||||
\(14\) | −0.819343 | −0.218979 | ||||||||
\(15\) | 2.44019 | 0.630054 | ||||||||
\(16\) | 16.1784 | 4.04461 | ||||||||
\(17\) | −7.57293 | −1.83671 | −0.918353 | − | 0.395762i | \(-0.870481\pi\) | ||||
−0.918353 | + | 0.395762i | \(0.870481\pi\) | |||||||
\(18\) | 6.58367 | 1.55179 | ||||||||
\(19\) | −2.96394 | −0.679974 | −0.339987 | − | 0.940430i | \(-0.610423\pi\) | ||||
−0.339987 | + | 0.940430i | \(0.610423\pi\) | |||||||
\(20\) | −17.4716 | −3.90676 | ||||||||
\(21\) | −0.232507 | −0.0507373 | ||||||||
\(22\) | 15.5292 | 3.31084 | ||||||||
\(23\) | 6.58625 | 1.37333 | 0.686664 | − | 0.726975i | \(-0.259074\pi\) | ||||
0.686664 | + | 0.726975i | \(0.259074\pi\) | |||||||
\(24\) | 7.77040 | 1.58613 | ||||||||
\(25\) | 4.72695 | 0.945391 | ||||||||
\(26\) | −18.3354 | −3.59588 | ||||||||
\(27\) | 4.21550 | 0.811273 | ||||||||
\(28\) | 1.66474 | 0.314606 | ||||||||
\(29\) | 3.55881 | 0.660854 | 0.330427 | − | 0.943832i | \(-0.392807\pi\) | ||||
0.330427 | + | 0.943832i | \(0.392807\pi\) | |||||||
\(30\) | −6.72802 | −1.22836 | ||||||||
\(31\) | −2.84059 | −0.510186 | −0.255093 | − | 0.966917i | \(-0.582106\pi\) | ||||
−0.255093 | + | 0.966917i | \(0.582106\pi\) | |||||||
\(32\) | −24.7441 | −4.37417 | ||||||||
\(33\) | 4.40678 | 0.767121 | ||||||||
\(34\) | 20.8799 | 3.58087 | ||||||||
\(35\) | −0.926809 | −0.156659 | ||||||||
\(36\) | −13.3767 | −2.22944 | ||||||||
\(37\) | −9.75146 | −1.60313 | −0.801565 | − | 0.597908i | \(-0.795999\pi\) | ||||
−0.801565 | + | 0.597908i | \(0.795999\pi\) | |||||||
\(38\) | 8.17209 | 1.32569 | ||||||||
\(39\) | −5.20310 | −0.833163 | ||||||||
\(40\) | 30.9740 | 4.89741 | ||||||||
\(41\) | −8.15833 | −1.27412 | −0.637058 | − | 0.770816i | \(-0.719849\pi\) | ||||
−0.637058 | + | 0.770816i | \(0.719849\pi\) | |||||||
\(42\) | 0.641063 | 0.0989182 | ||||||||
\(43\) | 2.40358 | 0.366542 | 0.183271 | − | 0.983062i | \(-0.441331\pi\) | ||||
0.183271 | + | 0.983062i | \(0.441331\pi\) | |||||||
\(44\) | −31.5522 | −4.75667 | ||||||||
\(45\) | 7.44719 | 1.11016 | ||||||||
\(46\) | −18.1594 | −2.67746 | ||||||||
\(47\) | 9.95062 | 1.45145 | 0.725724 | − | 0.687986i | \(-0.241505\pi\) | ||||
0.725724 | + | 0.687986i | \(0.241505\pi\) | |||||||
\(48\) | −12.6582 | −1.82705 | ||||||||
\(49\) | −6.91169 | −0.987384 | ||||||||
\(50\) | −13.0330 | −1.84315 | ||||||||
\(51\) | 5.92515 | 0.829686 | ||||||||
\(52\) | 37.2538 | 5.16618 | ||||||||
\(53\) | 7.58554 | 1.04195 | 0.520977 | − | 0.853571i | \(-0.325568\pi\) | ||||
0.520977 | + | 0.853571i | \(0.325568\pi\) | |||||||
\(54\) | −11.6229 | −1.58167 | ||||||||
\(55\) | 17.5661 | 2.36861 | ||||||||
\(56\) | −2.95128 | −0.394381 | ||||||||
\(57\) | 2.31902 | 0.307161 | ||||||||
\(58\) | −9.81225 | −1.28841 | ||||||||
\(59\) | −5.25491 | −0.684131 | −0.342066 | − | 0.939676i | \(-0.611126\pi\) | ||||
−0.342066 | + | 0.939676i | \(0.611126\pi\) | |||||||
\(60\) | 13.6699 | 1.76478 | ||||||||
\(61\) | 4.99706 | 0.639808 | 0.319904 | − | 0.947450i | \(-0.396349\pi\) | ||||
0.319904 | + | 0.947450i | \(0.396349\pi\) | |||||||
\(62\) | 7.83201 | 0.994666 | ||||||||
\(63\) | −0.709587 | −0.0893996 | ||||||||
\(64\) | 35.8668 | 4.48335 | ||||||||
\(65\) | −20.7403 | −2.57252 | ||||||||
\(66\) | −12.1502 | −1.49559 | ||||||||
\(67\) | −13.8137 | −1.68761 | −0.843804 | − | 0.536652i | \(-0.819689\pi\) | ||||
−0.843804 | + | 0.536652i | \(0.819689\pi\) | |||||||
\(68\) | −42.4236 | −5.14462 | ||||||||
\(69\) | −5.15315 | −0.620367 | ||||||||
\(70\) | 2.55537 | 0.305426 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | 23.7144 | 2.79477 | ||||||||
\(73\) | 1.20986 | 0.141604 | 0.0708020 | − | 0.997490i | \(-0.477444\pi\) | ||||
0.0708020 | + | 0.997490i | \(0.477444\pi\) | |||||||
\(74\) | 26.8865 | 3.12549 | ||||||||
\(75\) | −3.69842 | −0.427057 | ||||||||
\(76\) | −16.6040 | −1.90461 | ||||||||
\(77\) | −1.67374 | −0.190740 | ||||||||
\(78\) | 14.3459 | 1.62435 | ||||||||
\(79\) | −0.839614 | −0.0944639 | −0.0472320 | − | 0.998884i | \(-0.515040\pi\) | ||||
−0.0472320 | + | 0.998884i | \(0.515040\pi\) | |||||||
\(80\) | −50.4574 | −5.64131 | ||||||||
\(81\) | 3.86525 | 0.429472 | ||||||||
\(82\) | 22.4939 | 2.48404 | ||||||||
\(83\) | 14.3039 | 1.57006 | 0.785029 | − | 0.619459i | \(-0.212648\pi\) | ||||
0.785029 | + | 0.619459i | \(0.212648\pi\) | |||||||
\(84\) | −1.30251 | −0.142115 | ||||||||
\(85\) | 23.6185 | 2.56179 | ||||||||
\(86\) | −6.62709 | −0.714617 | ||||||||
\(87\) | −2.78445 | −0.298524 | ||||||||
\(88\) | 55.9364 | 5.96284 | ||||||||
\(89\) | 9.48423 | 1.00533 | 0.502663 | − | 0.864482i | \(-0.332354\pi\) | ||||
0.502663 | + | 0.864482i | \(0.332354\pi\) | |||||||
\(90\) | −20.5332 | −2.16439 | ||||||||
\(91\) | 1.97619 | 0.207161 | ||||||||
\(92\) | 36.8962 | 3.84669 | ||||||||
\(93\) | 2.22251 | 0.230464 | ||||||||
\(94\) | −27.4356 | −2.82977 | ||||||||
\(95\) | 9.24395 | 0.948409 | ||||||||
\(96\) | 19.3600 | 1.97592 | ||||||||
\(97\) | 2.46458 | 0.250241 | 0.125120 | − | 0.992142i | \(-0.460068\pi\) | ||||
0.125120 | + | 0.992142i | \(0.460068\pi\) | |||||||
\(98\) | 19.0567 | 1.92502 | ||||||||
\(99\) | 13.4490 | 1.35168 | ||||||||
\(100\) | 26.4804 | 2.64804 | ||||||||
\(101\) | 4.56191 | 0.453927 | 0.226963 | − | 0.973903i | \(-0.427120\pi\) | ||||
0.226963 | + | 0.973903i | \(0.427120\pi\) | |||||||
\(102\) | −16.3367 | −1.61757 | ||||||||
\(103\) | 0.204277 | 0.0201281 | 0.0100640 | − | 0.999949i | \(-0.496796\pi\) | ||||
0.0100640 | + | 0.999949i | \(0.496796\pi\) | |||||||
\(104\) | −66.0443 | −6.47618 | ||||||||
\(105\) | 0.725146 | 0.0707670 | ||||||||
\(106\) | −20.9146 | −2.03141 | ||||||||
\(107\) | −10.5970 | −1.02445 | −0.512223 | − | 0.858852i | \(-0.671178\pi\) | ||||
−0.512223 | + | 0.858852i | \(0.671178\pi\) | |||||||
\(108\) | 23.6152 | 2.27238 | ||||||||
\(109\) | 13.2752 | 1.27153 | 0.635766 | − | 0.771882i | \(-0.280684\pi\) | ||||
0.635766 | + | 0.771882i | \(0.280684\pi\) | |||||||
\(110\) | −48.4327 | −4.61787 | ||||||||
\(111\) | 7.62965 | 0.724174 | ||||||||
\(112\) | 4.80771 | 0.454286 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | −6.39393 | −0.598847 | ||||||||
\(115\) | −20.5412 | −1.91548 | ||||||||
\(116\) | 19.9365 | 1.85105 | ||||||||
\(117\) | −15.8793 | −1.46804 | ||||||||
\(118\) | 14.4887 | 1.33379 | ||||||||
\(119\) | −2.25043 | −0.206297 | ||||||||
\(120\) | −24.2344 | −2.21228 | ||||||||
\(121\) | 20.7228 | 1.88389 | ||||||||
\(122\) | −13.7778 | −1.24738 | ||||||||
\(123\) | 6.38316 | 0.575550 | ||||||||
\(124\) | −15.9130 | −1.42903 | ||||||||
\(125\) | 0.851581 | 0.0761677 | ||||||||
\(126\) | 1.95646 | 0.174295 | ||||||||
\(127\) | −9.70908 | −0.861541 | −0.430771 | − | 0.902461i | \(-0.641758\pi\) | ||||
−0.430771 | + | 0.902461i | \(0.641758\pi\) | |||||||
\(128\) | −49.4028 | −4.36664 | ||||||||
\(129\) | −1.88059 | −0.165576 | ||||||||
\(130\) | 57.1847 | 5.01543 | ||||||||
\(131\) | 5.59134 | 0.488517 | 0.244259 | − | 0.969710i | \(-0.421455\pi\) | ||||
0.244259 | + | 0.969710i | \(0.421455\pi\) | |||||||
\(132\) | 24.6868 | 2.14871 | ||||||||
\(133\) | −0.880788 | −0.0763740 | ||||||||
\(134\) | 38.0867 | 3.29019 | ||||||||
\(135\) | −13.1473 | −1.13154 | ||||||||
\(136\) | 75.2095 | 6.44916 | ||||||||
\(137\) | 11.4113 | 0.974931 | 0.487466 | − | 0.873142i | \(-0.337921\pi\) | ||||
0.487466 | + | 0.873142i | \(0.337921\pi\) | |||||||
\(138\) | 14.2081 | 1.20948 | ||||||||
\(139\) | 15.9263 | 1.35085 | 0.675426 | − | 0.737427i | \(-0.263960\pi\) | ||||
0.675426 | + | 0.737427i | \(0.263960\pi\) | |||||||
\(140\) | −5.19199 | −0.438803 | ||||||||
\(141\) | −7.78548 | −0.655655 | ||||||||
\(142\) | 2.75717 | 0.231377 | ||||||||
\(143\) | −37.4553 | −3.13217 | ||||||||
\(144\) | −38.6314 | −3.21929 | ||||||||
\(145\) | −11.0992 | −0.921741 | ||||||||
\(146\) | −3.33581 | −0.276073 | ||||||||
\(147\) | 5.40778 | 0.446026 | ||||||||
\(148\) | −54.6277 | −4.49037 | ||||||||
\(149\) | 8.32701 | 0.682175 | 0.341087 | − | 0.940032i | \(-0.389205\pi\) | ||||
0.341087 | + | 0.940032i | \(0.389205\pi\) | |||||||
\(150\) | 10.1972 | 0.832596 | ||||||||
\(151\) | 8.15113 | 0.663329 | 0.331665 | − | 0.943397i | \(-0.392390\pi\) | ||||
0.331665 | + | 0.943397i | \(0.392390\pi\) | |||||||
\(152\) | 29.4359 | 2.38757 | ||||||||
\(153\) | 18.0829 | 1.46192 | ||||||||
\(154\) | 4.61479 | 0.371870 | ||||||||
\(155\) | 8.85926 | 0.711593 | ||||||||
\(156\) | −29.1478 | −2.33369 | ||||||||
\(157\) | −7.31229 | −0.583584 | −0.291792 | − | 0.956482i | \(-0.594252\pi\) | ||||
−0.291792 | + | 0.956482i | \(0.594252\pi\) | |||||||
\(158\) | 2.31496 | 0.184168 | ||||||||
\(159\) | −5.93501 | −0.470677 | ||||||||
\(160\) | 77.1720 | 6.10098 | ||||||||
\(161\) | 1.95722 | 0.154251 | ||||||||
\(162\) | −10.6572 | −0.837305 | ||||||||
\(163\) | −9.24543 | −0.724158 | −0.362079 | − | 0.932147i | \(-0.617933\pi\) | ||||
−0.362079 | + | 0.932147i | \(0.617933\pi\) | |||||||
\(164\) | −45.7030 | −3.56880 | ||||||||
\(165\) | −13.7439 | −1.06996 | ||||||||
\(166\) | −39.4384 | −3.06101 | ||||||||
\(167\) | 9.29877 | 0.719560 | 0.359780 | − | 0.933037i | \(-0.382852\pi\) | ||||
0.359780 | + | 0.933037i | \(0.382852\pi\) | |||||||
\(168\) | 2.30911 | 0.178152 | ||||||||
\(169\) | 31.2237 | 2.40182 | ||||||||
\(170\) | −65.1203 | −4.99450 | ||||||||
\(171\) | 7.07739 | 0.541222 | ||||||||
\(172\) | 13.4649 | 1.02669 | ||||||||
\(173\) | 6.52736 | 0.496266 | 0.248133 | − | 0.968726i | \(-0.420183\pi\) | ||||
0.248133 | + | 0.968726i | \(0.420183\pi\) | |||||||
\(174\) | 7.67721 | 0.582008 | ||||||||
\(175\) | 1.40470 | 0.106185 | ||||||||
\(176\) | −91.1219 | −6.86857 | ||||||||
\(177\) | 4.11150 | 0.309039 | ||||||||
\(178\) | −26.1497 | −1.96000 | ||||||||
\(179\) | −16.2808 | −1.21688 | −0.608442 | − | 0.793599i | \(-0.708205\pi\) | ||||
−0.608442 | + | 0.793599i | \(0.708205\pi\) | |||||||
\(180\) | 41.7192 | 3.10956 | ||||||||
\(181\) | −7.40722 | −0.550575 | −0.275287 | − | 0.961362i | \(-0.588773\pi\) | ||||
−0.275287 | + | 0.961362i | \(0.588773\pi\) | |||||||
\(182\) | −5.44871 | −0.403885 | ||||||||
\(183\) | −3.90976 | −0.289017 | ||||||||
\(184\) | −65.4103 | −4.82211 | ||||||||
\(185\) | 30.4129 | 2.23600 | ||||||||
\(186\) | −6.12785 | −0.449316 | ||||||||
\(187\) | 42.6531 | 3.11910 | ||||||||
\(188\) | 55.7434 | 4.06551 | ||||||||
\(189\) | 1.25271 | 0.0911213 | ||||||||
\(190\) | −25.4872 | −1.84903 | ||||||||
\(191\) | −2.29571 | −0.166112 | −0.0830560 | − | 0.996545i | \(-0.526468\pi\) | ||||
−0.0830560 | + | 0.996545i | \(0.526468\pi\) | |||||||
\(192\) | −28.0626 | −2.02524 | ||||||||
\(193\) | −15.3589 | −1.10555 | −0.552777 | − | 0.833329i | \(-0.686432\pi\) | ||||
−0.552777 | + | 0.833329i | \(0.686432\pi\) | |||||||
\(194\) | −6.79528 | −0.487873 | ||||||||
\(195\) | 16.2275 | 1.16207 | ||||||||
\(196\) | −38.7193 | −2.76567 | ||||||||
\(197\) | 3.57093 | 0.254418 | 0.127209 | − | 0.991876i | \(-0.459398\pi\) | ||||
0.127209 | + | 0.991876i | \(0.459398\pi\) | |||||||
\(198\) | −37.0812 | −2.63525 | ||||||||
\(199\) | 26.6931 | 1.89222 | 0.946111 | − | 0.323844i | \(-0.104975\pi\) | ||||
0.946111 | + | 0.323844i | \(0.104975\pi\) | |||||||
\(200\) | −46.9450 | −3.31951 | ||||||||
\(201\) | 10.8080 | 0.762335 | ||||||||
\(202\) | −12.5780 | −0.884983 | ||||||||
\(203\) | 1.05756 | 0.0742264 | ||||||||
\(204\) | 33.1927 | 2.32395 | ||||||||
\(205\) | 25.4442 | 1.77710 | ||||||||
\(206\) | −0.563228 | −0.0392420 | ||||||||
\(207\) | −15.7269 | −1.09309 | ||||||||
\(208\) | 107.588 | 7.45989 | ||||||||
\(209\) | 16.6938 | 1.15473 | ||||||||
\(210\) | −1.99935 | −0.137968 | ||||||||
\(211\) | −9.61000 | −0.661580 | −0.330790 | − | 0.943704i | \(-0.607315\pi\) | ||||
−0.330790 | + | 0.943704i | \(0.607315\pi\) | |||||||
\(212\) | 42.4942 | 2.91851 | ||||||||
\(213\) | 0.782411 | 0.0536099 | ||||||||
\(214\) | 29.2177 | 1.99728 | ||||||||
\(215\) | −7.49630 | −0.511243 | ||||||||
\(216\) | −41.8656 | −2.84859 | ||||||||
\(217\) | −0.844133 | −0.0573035 | ||||||||
\(218\) | −36.6020 | −2.47900 | ||||||||
\(219\) | −0.946611 | −0.0639660 | ||||||||
\(220\) | 98.4052 | 6.63447 | ||||||||
\(221\) | −50.3607 | −3.38763 | ||||||||
\(222\) | −21.0363 | −1.41186 | ||||||||
\(223\) | −3.27501 | −0.219311 | −0.109655 | − | 0.993970i | \(-0.534975\pi\) | ||||
−0.109655 | + | 0.993970i | \(0.534975\pi\) | |||||||
\(224\) | −7.35314 | −0.491303 | ||||||||
\(225\) | −11.2872 | −0.752478 | ||||||||
\(226\) | 2.75717 | 0.183404 | ||||||||
\(227\) | −0.152049 | −0.0100918 | −0.00504591 | − | 0.999987i | \(-0.501606\pi\) | ||||
−0.00504591 | + | 0.999987i | \(0.501606\pi\) | |||||||
\(228\) | 12.9911 | 0.860360 | ||||||||
\(229\) | 3.54503 | 0.234262 | 0.117131 | − | 0.993116i | \(-0.462630\pi\) | ||||
0.117131 | + | 0.993116i | \(0.462630\pi\) | |||||||
\(230\) | 56.6357 | 3.73445 | ||||||||
\(231\) | 1.30955 | 0.0861622 | ||||||||
\(232\) | −35.3438 | −2.32043 | ||||||||
\(233\) | −23.8614 | −1.56321 | −0.781605 | − | 0.623774i | \(-0.785599\pi\) | ||||
−0.781605 | + | 0.623774i | \(0.785599\pi\) | |||||||
\(234\) | 43.7820 | 2.86212 | ||||||||
\(235\) | −31.0341 | −2.02444 | ||||||||
\(236\) | −29.4380 | −1.91625 | ||||||||
\(237\) | 0.656923 | 0.0426717 | ||||||||
\(238\) | 6.20483 | 0.402200 | ||||||||
\(239\) | 15.3049 | 0.989991 | 0.494996 | − | 0.868895i | \(-0.335170\pi\) | ||||
0.494996 | + | 0.868895i | \(0.335170\pi\) | |||||||
\(240\) | 39.4784 | 2.54832 | ||||||||
\(241\) | 10.7640 | 0.693370 | 0.346685 | − | 0.937982i | \(-0.387307\pi\) | ||||
0.346685 | + | 0.937982i | \(0.387307\pi\) | |||||||
\(242\) | −57.1365 | −3.67287 | ||||||||
\(243\) | −15.6707 | −1.00528 | ||||||||
\(244\) | 27.9936 | 1.79210 | ||||||||
\(245\) | 21.5562 | 1.37718 | ||||||||
\(246\) | −17.5995 | −1.12210 | ||||||||
\(247\) | −19.7105 | −1.25415 | ||||||||
\(248\) | 28.2109 | 1.79140 | ||||||||
\(249\) | −11.1915 | −0.709235 | ||||||||
\(250\) | −2.34796 | −0.148498 | ||||||||
\(251\) | 5.25145 | 0.331469 | 0.165734 | − | 0.986170i | \(-0.447001\pi\) | ||||
0.165734 | + | 0.986170i | \(0.447001\pi\) | |||||||
\(252\) | −3.97511 | −0.250409 | ||||||||
\(253\) | −37.0957 | −2.33219 | ||||||||
\(254\) | 26.7696 | 1.67967 | ||||||||
\(255\) | −18.4794 | −1.15722 | ||||||||
\(256\) | 64.4786 | 4.02991 | ||||||||
\(257\) | 6.51007 | 0.406087 | 0.203044 | − | 0.979170i | \(-0.434917\pi\) | ||||
0.203044 | + | 0.979170i | \(0.434917\pi\) | |||||||
\(258\) | 5.18510 | 0.322810 | ||||||||
\(259\) | −2.89782 | −0.180062 | ||||||||
\(260\) | −116.187 | −7.20564 | ||||||||
\(261\) | −8.49784 | −0.526003 | ||||||||
\(262\) | −15.4163 | −0.952421 | ||||||||
\(263\) | 15.8869 | 0.979629 | 0.489815 | − | 0.871827i | \(-0.337064\pi\) | ||||
0.489815 | + | 0.871827i | \(0.337064\pi\) | |||||||
\(264\) | −43.7652 | −2.69356 | ||||||||
\(265\) | −23.6578 | −1.45329 | ||||||||
\(266\) | 2.42848 | 0.148900 | ||||||||
\(267\) | −7.42057 | −0.454131 | ||||||||
\(268\) | −77.3842 | −4.72699 | ||||||||
\(269\) | 18.9275 | 1.15403 | 0.577015 | − | 0.816733i | \(-0.304217\pi\) | ||||
0.577015 | + | 0.816733i | \(0.304217\pi\) | |||||||
\(270\) | 36.2495 | 2.20607 | ||||||||
\(271\) | −25.4497 | −1.54596 | −0.772978 | − | 0.634433i | \(-0.781234\pi\) | ||||
−0.772978 | + | 0.634433i | \(0.781234\pi\) | |||||||
\(272\) | −122.518 | −7.42876 | ||||||||
\(273\) | −1.54619 | −0.0935800 | ||||||||
\(274\) | −31.4629 | −1.90074 | ||||||||
\(275\) | −26.6236 | −1.60547 | ||||||||
\(276\) | −28.8680 | −1.73765 | ||||||||
\(277\) | −4.25098 | −0.255417 | −0.127708 | − | 0.991812i | \(-0.540762\pi\) | ||||
−0.127708 | + | 0.991812i | \(0.540762\pi\) | |||||||
\(278\) | −43.9116 | −2.63364 | ||||||||
\(279\) | 6.78286 | 0.406079 | ||||||||
\(280\) | 9.20447 | 0.550072 | ||||||||
\(281\) | −10.6744 | −0.636781 | −0.318390 | − | 0.947960i | \(-0.603142\pi\) | ||||
−0.318390 | + | 0.947960i | \(0.603142\pi\) | |||||||
\(282\) | 21.4659 | 1.27828 | ||||||||
\(283\) | 8.95397 | 0.532258 | 0.266129 | − | 0.963937i | \(-0.414255\pi\) | ||||
0.266129 | + | 0.963937i | \(0.414255\pi\) | |||||||
\(284\) | −5.60200 | −0.332418 | ||||||||
\(285\) | −7.23257 | −0.428420 | ||||||||
\(286\) | 103.271 | 6.10653 | ||||||||
\(287\) | −2.42439 | −0.143107 | ||||||||
\(288\) | 59.0847 | 3.48160 | ||||||||
\(289\) | 40.3493 | 2.37349 | ||||||||
\(290\) | 30.6025 | 1.79704 | ||||||||
\(291\) | −1.92832 | −0.113040 | ||||||||
\(292\) | 6.77767 | 0.396633 | ||||||||
\(293\) | −9.95699 | −0.581694 | −0.290847 | − | 0.956770i | \(-0.593937\pi\) | ||||
−0.290847 | + | 0.956770i | \(0.593937\pi\) | |||||||
\(294\) | −14.9102 | −0.869580 | ||||||||
\(295\) | 16.3890 | 0.954207 | ||||||||
\(296\) | 96.8452 | 5.62901 | ||||||||
\(297\) | −23.7430 | −1.37771 | ||||||||
\(298\) | −22.9590 | −1.32998 | ||||||||
\(299\) | 43.7991 | 2.53297 | ||||||||
\(300\) | −20.7186 | −1.19619 | ||||||||
\(301\) | 0.714267 | 0.0411697 | ||||||||
\(302\) | −22.4741 | −1.29324 | ||||||||
\(303\) | −3.56928 | −0.205050 | ||||||||
\(304\) | −47.9519 | −2.75023 | ||||||||
\(305\) | −15.5849 | −0.892387 | ||||||||
\(306\) | −49.8577 | −2.85017 | ||||||||
\(307\) | 1.19316 | 0.0680971 | 0.0340486 | − | 0.999420i | \(-0.489160\pi\) | ||||
0.0340486 | + | 0.999420i | \(0.489160\pi\) | |||||||
\(308\) | −9.37630 | −0.534264 | ||||||||
\(309\) | −0.159829 | −0.00909235 | ||||||||
\(310\) | −24.4265 | −1.38733 | ||||||||
\(311\) | 9.91575 | 0.562271 | 0.281135 | − | 0.959668i | \(-0.409289\pi\) | ||||
0.281135 | + | 0.959668i | \(0.409289\pi\) | |||||||
\(312\) | 51.6738 | 2.92545 | ||||||||
\(313\) | 8.01406 | 0.452982 | 0.226491 | − | 0.974013i | \(-0.427275\pi\) | ||||
0.226491 | + | 0.974013i | \(0.427275\pi\) | |||||||
\(314\) | 20.1613 | 1.13777 | ||||||||
\(315\) | 2.21307 | 0.124692 | ||||||||
\(316\) | −4.70352 | −0.264594 | ||||||||
\(317\) | −5.64777 | −0.317210 | −0.158605 | − | 0.987342i | \(-0.550700\pi\) | ||||
−0.158605 | + | 0.987342i | \(0.550700\pi\) | |||||||
\(318\) | 16.3638 | 0.917639 | ||||||||
\(319\) | −20.0443 | −1.12226 | ||||||||
\(320\) | −111.862 | −6.25325 | ||||||||
\(321\) | 8.29118 | 0.462768 | ||||||||
\(322\) | −5.39640 | −0.300730 | ||||||||
\(323\) | 22.4457 | 1.24891 | ||||||||
\(324\) | 21.6531 | 1.20295 | ||||||||
\(325\) | 31.4347 | 1.74368 | ||||||||
\(326\) | 25.4913 | 1.41183 | ||||||||
\(327\) | −10.3866 | −0.574383 | ||||||||
\(328\) | 81.0232 | 4.47376 | ||||||||
\(329\) | 2.95701 | 0.163025 | ||||||||
\(330\) | 37.8943 | 2.08601 | ||||||||
\(331\) | −11.1549 | −0.613131 | −0.306566 | − | 0.951850i | \(-0.599180\pi\) | ||||
−0.306566 | + | 0.951850i | \(0.599180\pi\) | |||||||
\(332\) | 80.1306 | 4.39774 | ||||||||
\(333\) | 23.2849 | 1.27600 | ||||||||
\(334\) | −25.6383 | −1.40287 | ||||||||
\(335\) | 43.0821 | 2.35383 | ||||||||
\(336\) | −3.76161 | −0.205213 | ||||||||
\(337\) | 31.9195 | 1.73876 | 0.869382 | − | 0.494140i | \(-0.164517\pi\) | ||||
0.869382 | + | 0.494140i | \(0.164517\pi\) | |||||||
\(338\) | −86.0891 | −4.68263 | ||||||||
\(339\) | 0.782411 | 0.0424947 | ||||||||
\(340\) | 132.311 | 7.17557 | ||||||||
\(341\) | 15.9991 | 0.866399 | ||||||||
\(342\) | −19.5136 | −1.05517 | ||||||||
\(343\) | −4.13411 | −0.223221 | ||||||||
\(344\) | −23.8708 | −1.28703 | ||||||||
\(345\) | 16.0717 | 0.865270 | ||||||||
\(346\) | −17.9971 | −0.967528 | ||||||||
\(347\) | −13.1891 | −0.708030 | −0.354015 | − | 0.935240i | \(-0.615184\pi\) | ||||
−0.354015 | + | 0.935240i | \(0.615184\pi\) | |||||||
\(348\) | −15.5985 | −0.836167 | ||||||||
\(349\) | −28.7273 | −1.53774 | −0.768868 | − | 0.639408i | \(-0.779180\pi\) | ||||
−0.768868 | + | 0.639408i | \(0.779180\pi\) | |||||||
\(350\) | −3.87300 | −0.207020 | ||||||||
\(351\) | 28.0334 | 1.49631 | ||||||||
\(352\) | 139.366 | 7.42824 | ||||||||
\(353\) | −18.1119 | −0.964001 | −0.482000 | − | 0.876171i | \(-0.660090\pi\) | ||||
−0.482000 | + | 0.876171i | \(0.660090\pi\) | |||||||
\(354\) | −11.3361 | −0.602508 | ||||||||
\(355\) | 3.11881 | 0.165529 | ||||||||
\(356\) | 53.1307 | 2.81592 | ||||||||
\(357\) | 1.76076 | 0.0931895 | ||||||||
\(358\) | 44.8890 | 2.37245 | ||||||||
\(359\) | −21.9575 | −1.15887 | −0.579435 | − | 0.815018i | \(-0.696727\pi\) | ||||
−0.579435 | + | 0.815018i | \(0.696727\pi\) | |||||||
\(360\) | −73.9606 | −3.89807 | ||||||||
\(361\) | −10.2151 | −0.537635 | ||||||||
\(362\) | 20.4230 | 1.07341 | ||||||||
\(363\) | −16.2138 | −0.851002 | ||||||||
\(364\) | 11.0706 | 0.580259 | ||||||||
\(365\) | −3.77333 | −0.197505 | ||||||||
\(366\) | 10.7799 | 0.563473 | ||||||||
\(367\) | −0.403663 | −0.0210710 | −0.0105355 | − | 0.999944i | \(-0.503354\pi\) | ||||
−0.0105355 | + | 0.999944i | \(0.503354\pi\) | |||||||
\(368\) | 106.555 | 5.55458 | ||||||||
\(369\) | 19.4807 | 1.01413 | ||||||||
\(370\) | −83.8537 | −4.35934 | ||||||||
\(371\) | 2.25418 | 0.117031 | ||||||||
\(372\) | 12.4505 | 0.645529 | ||||||||
\(373\) | 24.4449 | 1.26571 | 0.632856 | − | 0.774270i | \(-0.281883\pi\) | ||||
0.632856 | + | 0.774270i | \(0.281883\pi\) | |||||||
\(374\) | −117.602 | −6.08105 | ||||||||
\(375\) | −0.666286 | −0.0344069 | ||||||||
\(376\) | −98.8231 | −5.09641 | ||||||||
\(377\) | 23.6664 | 1.21888 | ||||||||
\(378\) | −3.45394 | −0.177652 | ||||||||
\(379\) | 37.0498 | 1.90312 | 0.951561 | − | 0.307460i | \(-0.0994792\pi\) | ||||
0.951561 | + | 0.307460i | \(0.0994792\pi\) | |||||||
\(380\) | 51.7847 | 2.65650 | ||||||||
\(381\) | 7.59649 | 0.389180 | ||||||||
\(382\) | 6.32968 | 0.323855 | ||||||||
\(383\) | −12.9141 | −0.659878 | −0.329939 | − | 0.944002i | \(-0.607028\pi\) | ||||
−0.329939 | + | 0.944002i | \(0.607028\pi\) | |||||||
\(384\) | 38.6533 | 1.97252 | ||||||||
\(385\) | 5.22007 | 0.266039 | ||||||||
\(386\) | 42.3470 | 2.15541 | ||||||||
\(387\) | −5.73935 | −0.291747 | ||||||||
\(388\) | 13.8066 | 0.700924 | ||||||||
\(389\) | −23.9694 | −1.21530 | −0.607648 | − | 0.794207i | \(-0.707887\pi\) | ||||
−0.607648 | + | 0.794207i | \(0.707887\pi\) | |||||||
\(390\) | −44.7419 | −2.26560 | ||||||||
\(391\) | −49.8772 | −2.52240 | ||||||||
\(392\) | 68.6424 | 3.46697 | ||||||||
\(393\) | −4.37472 | −0.220676 | ||||||||
\(394\) | −9.84568 | −0.496018 | ||||||||
\(395\) | 2.61859 | 0.131756 | ||||||||
\(396\) | 75.3414 | 3.78605 | ||||||||
\(397\) | −22.8014 | −1.14437 | −0.572184 | − | 0.820125i | \(-0.693904\pi\) | ||||
−0.572184 | + | 0.820125i | \(0.693904\pi\) | |||||||
\(398\) | −73.5974 | −3.68910 | ||||||||
\(399\) | 0.689138 | 0.0345000 | ||||||||
\(400\) | 76.4747 | 3.82374 | ||||||||
\(401\) | 36.2381 | 1.80965 | 0.904823 | − | 0.425789i | \(-0.140003\pi\) | ||||
0.904823 | + | 0.425789i | \(0.140003\pi\) | |||||||
\(402\) | −29.7994 | −1.48626 | ||||||||
\(403\) | −18.8902 | −0.940988 | ||||||||
\(404\) | 25.5558 | 1.27145 | ||||||||
\(405\) | −12.0550 | −0.599016 | ||||||||
\(406\) | −2.91589 | −0.144713 | ||||||||
\(407\) | 54.9232 | 2.72244 | ||||||||
\(408\) | −58.8447 | −2.91325 | ||||||||
\(409\) | −4.06412 | −0.200958 | −0.100479 | − | 0.994939i | \(-0.532038\pi\) | ||||
−0.100479 | + | 0.994939i | \(0.532038\pi\) | |||||||
\(410\) | −70.1542 | −3.46467 | ||||||||
\(411\) | −8.92831 | −0.440401 | ||||||||
\(412\) | 1.14436 | 0.0563787 | ||||||||
\(413\) | −1.56159 | −0.0768409 | ||||||||
\(414\) | 43.3617 | 2.13111 | ||||||||
\(415\) | −44.6111 | −2.18987 | ||||||||
\(416\) | −164.550 | −8.06774 | ||||||||
\(417\) | −12.4609 | −0.610214 | ||||||||
\(418\) | −46.0277 | −2.25129 | ||||||||
\(419\) | 32.8570 | 1.60517 | 0.802585 | − | 0.596538i | \(-0.203457\pi\) | ||||
0.802585 | + | 0.596538i | \(0.203457\pi\) | |||||||
\(420\) | 4.06227 | 0.198218 | ||||||||
\(421\) | 14.2195 | 0.693016 | 0.346508 | − | 0.938047i | \(-0.387367\pi\) | ||||
0.346508 | + | 0.938047i | \(0.387367\pi\) | |||||||
\(422\) | 26.4964 | 1.28983 | ||||||||
\(423\) | −23.7604 | −1.15527 | ||||||||
\(424\) | −75.3346 | −3.65857 | ||||||||
\(425\) | −35.7969 | −1.73640 | ||||||||
\(426\) | −2.15724 | −0.104519 | ||||||||
\(427\) | 1.48497 | 0.0718626 | ||||||||
\(428\) | −59.3642 | −2.86948 | ||||||||
\(429\) | 29.3054 | 1.41488 | ||||||||
\(430\) | 20.6686 | 0.996728 | ||||||||
\(431\) | −21.4224 | −1.03188 | −0.515940 | − | 0.856625i | \(-0.672557\pi\) | ||||
−0.515940 | + | 0.856625i | \(0.672557\pi\) | |||||||
\(432\) | 68.2002 | 3.28128 | ||||||||
\(433\) | −30.7602 | −1.47824 | −0.739121 | − | 0.673573i | \(-0.764759\pi\) | ||||
−0.739121 | + | 0.673573i | \(0.764759\pi\) | |||||||
\(434\) | 2.32742 | 0.111720 | ||||||||
\(435\) | 8.68416 | 0.416374 | ||||||||
\(436\) | 74.3676 | 3.56156 | ||||||||
\(437\) | −19.5212 | −0.933827 | ||||||||
\(438\) | 2.60997 | 0.124709 | ||||||||
\(439\) | 38.1935 | 1.82288 | 0.911439 | − | 0.411436i | \(-0.134973\pi\) | ||||
0.911439 | + | 0.411436i | \(0.134973\pi\) | |||||||
\(440\) | −174.455 | −8.31680 | ||||||||
\(441\) | 16.5040 | 0.785903 | ||||||||
\(442\) | 138.853 | 6.60457 | ||||||||
\(443\) | 37.6101 | 1.78691 | 0.893456 | − | 0.449151i | \(-0.148273\pi\) | ||||
0.893456 | + | 0.449151i | \(0.148273\pi\) | |||||||
\(444\) | 42.7413 | 2.02841 | ||||||||
\(445\) | −29.5795 | −1.40220 | ||||||||
\(446\) | 9.02976 | 0.427571 | ||||||||
\(447\) | −6.51514 | −0.308156 | ||||||||
\(448\) | 10.6585 | 0.503565 | ||||||||
\(449\) | 24.0310 | 1.13409 | 0.567046 | − | 0.823686i | \(-0.308086\pi\) | ||||
0.567046 | + | 0.823686i | \(0.308086\pi\) | |||||||
\(450\) | 31.1207 | 1.46704 | ||||||||
\(451\) | 45.9502 | 2.16371 | ||||||||
\(452\) | −5.60200 | −0.263496 | ||||||||
\(453\) | −6.37753 | −0.299643 | ||||||||
\(454\) | 0.419224 | 0.0196752 | ||||||||
\(455\) | −6.16336 | −0.288943 | ||||||||
\(456\) | −23.0310 | −1.07852 | ||||||||
\(457\) | 28.1669 | 1.31759 | 0.658796 | − | 0.752322i | \(-0.271066\pi\) | ||||
0.658796 | + | 0.752322i | \(0.271066\pi\) | |||||||
\(458\) | −9.77427 | −0.456722 | ||||||||
\(459\) | −31.9237 | −1.49007 | ||||||||
\(460\) | −115.072 | −5.36526 | ||||||||
\(461\) | 2.14843 | 0.100062 | 0.0500312 | − | 0.998748i | \(-0.484068\pi\) | ||||
0.0500312 | + | 0.998748i | \(0.484068\pi\) | |||||||
\(462\) | −3.61066 | −0.167983 | ||||||||
\(463\) | 3.20776 | 0.149077 | 0.0745387 | − | 0.997218i | \(-0.476252\pi\) | ||||
0.0745387 | + | 0.997218i | \(0.476252\pi\) | |||||||
\(464\) | 57.5760 | 2.67290 | ||||||||
\(465\) | −6.93158 | −0.321444 | ||||||||
\(466\) | 65.7899 | 3.04766 | ||||||||
\(467\) | 17.8017 | 0.823763 | 0.411881 | − | 0.911238i | \(-0.364872\pi\) | ||||
0.411881 | + | 0.911238i | \(0.364872\pi\) | |||||||
\(468\) | −88.9559 | −4.11199 | ||||||||
\(469\) | −4.10498 | −0.189550 | ||||||||
\(470\) | 85.5663 | 3.94688 | ||||||||
\(471\) | 5.72122 | 0.263620 | ||||||||
\(472\) | 52.1884 | 2.40216 | ||||||||
\(473\) | −13.5377 | −0.622464 | ||||||||
\(474\) | −1.81125 | −0.0831935 | ||||||||
\(475\) | −14.0104 | −0.642841 | ||||||||
\(476\) | −12.6069 | −0.577838 | ||||||||
\(477\) | −18.1130 | −0.829337 | ||||||||
\(478\) | −42.1982 | −1.93010 | ||||||||
\(479\) | 10.0196 | 0.457807 | 0.228903 | − | 0.973449i | \(-0.426486\pi\) | ||||
0.228903 | + | 0.973449i | \(0.426486\pi\) | |||||||
\(480\) | −60.3802 | −2.75597 | ||||||||
\(481\) | −64.8481 | −2.95682 | ||||||||
\(482\) | −29.6782 | −1.35180 | ||||||||
\(483\) | −1.53135 | −0.0696789 | ||||||||
\(484\) | 116.089 | 5.27679 | ||||||||
\(485\) | −7.68656 | −0.349029 | ||||||||
\(486\) | 43.2069 | 1.95990 | ||||||||
\(487\) | 17.4777 | 0.791991 | 0.395996 | − | 0.918252i | \(-0.370400\pi\) | ||||
0.395996 | + | 0.918252i | \(0.370400\pi\) | |||||||
\(488\) | −49.6276 | −2.24653 | ||||||||
\(489\) | 7.23373 | 0.327120 | ||||||||
\(490\) | −59.4342 | −2.68497 | ||||||||
\(491\) | −34.4502 | −1.55472 | −0.777358 | − | 0.629058i | \(-0.783441\pi\) | ||||
−0.777358 | + | 0.629058i | \(0.783441\pi\) | |||||||
\(492\) | 35.7585 | 1.61212 | ||||||||
\(493\) | −26.9506 | −1.21379 | ||||||||
\(494\) | 54.3451 | 2.44510 | ||||||||
\(495\) | −41.9448 | −1.88528 | ||||||||
\(496\) | −45.9564 | −2.06350 | ||||||||
\(497\) | −0.297168 | −0.0133298 | ||||||||
\(498\) | 30.8570 | 1.38274 | ||||||||
\(499\) | −23.7730 | −1.06423 | −0.532113 | − | 0.846673i | \(-0.678602\pi\) | ||||
−0.532113 | + | 0.846673i | \(0.678602\pi\) | |||||||
\(500\) | 4.77056 | 0.213346 | ||||||||
\(501\) | −7.27546 | −0.325043 | ||||||||
\(502\) | −14.4792 | −0.646237 | ||||||||
\(503\) | 5.95730 | 0.265623 | 0.132812 | − | 0.991141i | \(-0.457600\pi\) | ||||
0.132812 | + | 0.991141i | \(0.457600\pi\) | |||||||
\(504\) | 7.04716 | 0.313905 | ||||||||
\(505\) | −14.2277 | −0.633124 | ||||||||
\(506\) | 102.279 | 4.54687 | ||||||||
\(507\) | −24.4297 | −1.08496 | ||||||||
\(508\) | −54.3903 | −2.41318 | ||||||||
\(509\) | −4.05798 | −0.179867 | −0.0899334 | − | 0.995948i | \(-0.528665\pi\) | ||||
−0.0899334 | + | 0.995948i | \(0.528665\pi\) | |||||||
\(510\) | 50.9509 | 2.25614 | ||||||||
\(511\) | 0.359533 | 0.0159048 | ||||||||
\(512\) | −78.9729 | −3.49014 | ||||||||
\(513\) | −12.4945 | −0.551645 | ||||||||
\(514\) | −17.9494 | −0.791714 | ||||||||
\(515\) | −0.637102 | −0.0280741 | ||||||||
\(516\) | −10.5351 | −0.463780 | ||||||||
\(517\) | −56.0449 | −2.46485 | ||||||||
\(518\) | 7.98979 | 0.351051 | ||||||||
\(519\) | −5.10708 | −0.224176 | ||||||||
\(520\) | 205.980 | 9.03280 | ||||||||
\(521\) | 16.7688 | 0.734656 | 0.367328 | − | 0.930091i | \(-0.380273\pi\) | ||||
0.367328 | + | 0.930091i | \(0.380273\pi\) | |||||||
\(522\) | 23.4300 | 1.02550 | ||||||||
\(523\) | 17.9611 | 0.785385 | 0.392693 | − | 0.919670i | \(-0.371544\pi\) | ||||
0.392693 | + | 0.919670i | \(0.371544\pi\) | |||||||
\(524\) | 31.3227 | 1.36834 | ||||||||
\(525\) | −1.09905 | −0.0479665 | ||||||||
\(526\) | −43.8030 | −1.90990 | ||||||||
\(527\) | 21.5116 | 0.937061 | ||||||||
\(528\) | 71.2948 | 3.10271 | ||||||||
\(529\) | 20.3787 | 0.886029 | ||||||||
\(530\) | 65.2287 | 2.83335 | ||||||||
\(531\) | 12.5478 | 0.544530 | ||||||||
\(532\) | −4.93418 | −0.213924 | ||||||||
\(533\) | −54.2536 | −2.34998 | ||||||||
\(534\) | 20.4598 | 0.885382 | ||||||||
\(535\) | 33.0499 | 1.42887 | ||||||||
\(536\) | 137.188 | 5.92563 | ||||||||
\(537\) | 12.7383 | 0.549697 | ||||||||
\(538\) | −52.1864 | −2.24992 | ||||||||
\(539\) | 38.9287 | 1.67678 | ||||||||
\(540\) | −73.6514 | −3.16945 | ||||||||
\(541\) | 15.7597 | 0.677563 | 0.338782 | − | 0.940865i | \(-0.389985\pi\) | ||||
0.338782 | + | 0.940865i | \(0.389985\pi\) | |||||||
\(542\) | 70.1691 | 3.01402 | ||||||||
\(543\) | 5.79549 | 0.248708 | ||||||||
\(544\) | 187.385 | 8.03407 | ||||||||
\(545\) | −41.4027 | −1.77350 | ||||||||
\(546\) | 4.26313 | 0.182445 | ||||||||
\(547\) | −17.2707 | −0.738441 | −0.369220 | − | 0.929342i | \(-0.620375\pi\) | ||||
−0.369220 | + | 0.929342i | \(0.620375\pi\) | |||||||
\(548\) | 63.9260 | 2.73078 | ||||||||
\(549\) | −11.9322 | −0.509252 | ||||||||
\(550\) | 73.4060 | 3.13004 | ||||||||
\(551\) | −10.5481 | −0.449364 | ||||||||
\(552\) | 51.1778 | 2.17827 | ||||||||
\(553\) | −0.249506 | −0.0106101 | ||||||||
\(554\) | 11.7207 | 0.497965 | ||||||||
\(555\) | −23.7954 | −1.01006 | ||||||||
\(556\) | 89.2193 | 3.78374 | ||||||||
\(557\) | −19.1217 | −0.810212 | −0.405106 | − | 0.914270i | \(-0.632765\pi\) | ||||
−0.405106 | + | 0.914270i | \(0.632765\pi\) | |||||||
\(558\) | −18.7015 | −0.791699 | ||||||||
\(559\) | 15.9840 | 0.676052 | ||||||||
\(560\) | −14.9943 | −0.633626 | ||||||||
\(561\) | −33.3722 | −1.40898 | ||||||||
\(562\) | 29.4312 | 1.24148 | ||||||||
\(563\) | −9.56993 | −0.403325 | −0.201662 | − | 0.979455i | \(-0.564634\pi\) | ||||
−0.201662 | + | 0.979455i | \(0.564634\pi\) | |||||||
\(564\) | −43.6143 | −1.83649 | ||||||||
\(565\) | 3.11881 | 0.131209 | ||||||||
\(566\) | −24.6876 | −1.03770 | ||||||||
\(567\) | 1.14863 | 0.0482378 | ||||||||
\(568\) | 9.93135 | 0.416710 | ||||||||
\(569\) | 1.79930 | 0.0754304 | 0.0377152 | − | 0.999289i | \(-0.487992\pi\) | ||||
0.0377152 | + | 0.999289i | \(0.487992\pi\) | |||||||
\(570\) | 19.9414 | 0.835255 | ||||||||
\(571\) | 19.9181 | 0.833548 | 0.416774 | − | 0.909010i | \(-0.363161\pi\) | ||||
0.416774 | + | 0.909010i | \(0.363161\pi\) | |||||||
\(572\) | −209.825 | −8.77322 | ||||||||
\(573\) | 1.79619 | 0.0750370 | ||||||||
\(574\) | 6.68447 | 0.279004 | ||||||||
\(575\) | 31.1329 | 1.29833 | ||||||||
\(576\) | −85.6439 | −3.56850 | ||||||||
\(577\) | 23.8184 | 0.991573 | 0.495786 | − | 0.868444i | \(-0.334880\pi\) | ||||
0.495786 | + | 0.868444i | \(0.334880\pi\) | |||||||
\(578\) | −111.250 | −4.62739 | ||||||||
\(579\) | 12.0169 | 0.499407 | ||||||||
\(580\) | −62.1779 | −2.58180 | ||||||||
\(581\) | 4.25066 | 0.176347 | ||||||||
\(582\) | 5.31670 | 0.220384 | ||||||||
\(583\) | −42.7240 | −1.76945 | ||||||||
\(584\) | −12.0156 | −0.497208 | ||||||||
\(585\) | 49.5245 | 2.04758 | ||||||||
\(586\) | 27.4532 | 1.13408 | ||||||||
\(587\) | 3.31009 | 0.136622 | 0.0683111 | − | 0.997664i | \(-0.478239\pi\) | ||||
0.0683111 | + | 0.997664i | \(0.478239\pi\) | |||||||
\(588\) | 30.2944 | 1.24932 | ||||||||
\(589\) | 8.41934 | 0.346913 | ||||||||
\(590\) | −45.1874 | −1.86034 | ||||||||
\(591\) | −2.79394 | −0.114927 | ||||||||
\(592\) | −157.763 | −6.48404 | ||||||||
\(593\) | −19.4542 | −0.798889 | −0.399445 | − | 0.916757i | \(-0.630797\pi\) | ||||
−0.399445 | + | 0.916757i | \(0.630797\pi\) | |||||||
\(594\) | 65.4635 | 2.68600 | ||||||||
\(595\) | 7.01866 | 0.287737 | ||||||||
\(596\) | 46.6479 | 1.91077 | ||||||||
\(597\) | −20.8849 | −0.854764 | ||||||||
\(598\) | −120.762 | −4.93832 | ||||||||
\(599\) | −37.9356 | −1.55001 | −0.775003 | − | 0.631957i | \(-0.782252\pi\) | ||||
−0.775003 | + | 0.631957i | \(0.782252\pi\) | |||||||
\(600\) | 36.7303 | 1.49951 | ||||||||
\(601\) | −6.22632 | −0.253977 | −0.126989 | − | 0.991904i | \(-0.540531\pi\) | ||||
−0.126989 | + | 0.991904i | \(0.540531\pi\) | |||||||
\(602\) | −1.96936 | −0.0802650 | ||||||||
\(603\) | 32.9847 | 1.34324 | ||||||||
\(604\) | 45.6627 | 1.85799 | ||||||||
\(605\) | −64.6305 | −2.62760 | ||||||||
\(606\) | 9.84114 | 0.399769 | ||||||||
\(607\) | −27.3757 | −1.11115 | −0.555573 | − | 0.831468i | \(-0.687501\pi\) | ||||
−0.555573 | + | 0.831468i | \(0.687501\pi\) | |||||||
\(608\) | 73.3399 | 2.97433 | ||||||||
\(609\) | −0.827449 | −0.0335299 | ||||||||
\(610\) | 42.9702 | 1.73981 | ||||||||
\(611\) | 66.1725 | 2.67705 | ||||||||
\(612\) | 101.301 | 4.09483 | ||||||||
\(613\) | −24.8765 | −1.00475 | −0.502376 | − | 0.864650i | \(-0.667540\pi\) | ||||
−0.502376 | + | 0.864650i | \(0.667540\pi\) | |||||||
\(614\) | −3.28974 | −0.132763 | ||||||||
\(615\) | −19.9079 | −0.802762 | ||||||||
\(616\) | 16.6225 | 0.669739 | ||||||||
\(617\) | 13.8557 | 0.557809 | 0.278905 | − | 0.960319i | \(-0.410029\pi\) | ||||
0.278905 | + | 0.960319i | \(0.410029\pi\) | |||||||
\(618\) | 0.440676 | 0.0177266 | ||||||||
\(619\) | −32.7066 | −1.31459 | −0.657295 | − | 0.753633i | \(-0.728300\pi\) | ||||
−0.657295 | + | 0.753633i | \(0.728300\pi\) | |||||||
\(620\) | 49.6296 | 1.99317 | ||||||||
\(621\) | 27.7643 | 1.11414 | ||||||||
\(622\) | −27.3395 | −1.09621 | ||||||||
\(623\) | 2.81841 | 0.112917 | ||||||||
\(624\) | −84.1781 | −3.36982 | ||||||||
\(625\) | −26.2907 | −1.05163 | ||||||||
\(626\) | −22.0962 | −0.883140 | ||||||||
\(627\) | −13.0614 | −0.521623 | ||||||||
\(628\) | −40.9635 | −1.63462 | ||||||||
\(629\) | 73.8472 | 2.94448 | ||||||||
\(630\) | −6.10181 | −0.243102 | ||||||||
\(631\) | −8.04559 | −0.320290 | −0.160145 | − | 0.987094i | \(-0.551196\pi\) | ||||
−0.160145 | + | 0.987094i | \(0.551196\pi\) | |||||||
\(632\) | 8.33850 | 0.331688 | ||||||||
\(633\) | 7.51897 | 0.298852 | ||||||||
\(634\) | 15.5719 | 0.618438 | ||||||||
\(635\) | 30.2807 | 1.20165 | ||||||||
\(636\) | −33.2479 | −1.31837 | ||||||||
\(637\) | −45.9634 | −1.82113 | ||||||||
\(638\) | 55.2656 | 2.18798 | ||||||||
\(639\) | 2.38783 | 0.0944612 | ||||||||
\(640\) | 154.078 | 6.09046 | ||||||||
\(641\) | −16.0524 | −0.634030 | −0.317015 | − | 0.948420i | \(-0.602681\pi\) | ||||
−0.317015 | + | 0.948420i | \(0.602681\pi\) | |||||||
\(642\) | −22.8602 | −0.902221 | ||||||||
\(643\) | −16.9250 | −0.667456 | −0.333728 | − | 0.942669i | \(-0.608307\pi\) | ||||
−0.333728 | + | 0.942669i | \(0.608307\pi\) | |||||||
\(644\) | 10.9644 | 0.432056 | ||||||||
\(645\) | 5.86519 | 0.230941 | ||||||||
\(646\) | −61.8867 | −2.43490 | ||||||||
\(647\) | −42.6738 | −1.67768 | −0.838840 | − | 0.544377i | \(-0.816766\pi\) | ||||
−0.838840 | + | 0.544377i | \(0.816766\pi\) | |||||||
\(648\) | −38.3871 | −1.50799 | ||||||||
\(649\) | 29.5972 | 1.16179 | ||||||||
\(650\) | −86.6708 | −3.39951 | ||||||||
\(651\) | 0.660459 | 0.0258854 | ||||||||
\(652\) | −51.7930 | −2.02837 | ||||||||
\(653\) | 37.6729 | 1.47425 | 0.737127 | − | 0.675754i | \(-0.236182\pi\) | ||||
0.737127 | + | 0.675754i | \(0.236182\pi\) | |||||||
\(654\) | 28.6378 | 1.11983 | ||||||||
\(655\) | −17.4383 | −0.681371 | ||||||||
\(656\) | −131.989 | −5.15331 | ||||||||
\(657\) | −2.88895 | −0.112709 | ||||||||
\(658\) | −8.15298 | −0.317836 | ||||||||
\(659\) | 29.8693 | 1.16354 | 0.581771 | − | 0.813353i | \(-0.302360\pi\) | ||||
0.581771 | + | 0.813353i | \(0.302360\pi\) | |||||||
\(660\) | −76.9933 | −2.99696 | ||||||||
\(661\) | −22.9212 | −0.891530 | −0.445765 | − | 0.895150i | \(-0.647068\pi\) | ||||
−0.445765 | + | 0.895150i | \(0.647068\pi\) | |||||||
\(662\) | 30.7561 | 1.19537 | ||||||||
\(663\) | 39.4027 | 1.53028 | ||||||||
\(664\) | −142.057 | −5.51289 | ||||||||
\(665\) | 2.74701 | 0.106524 | ||||||||
\(666\) | −64.2004 | −2.48771 | ||||||||
\(667\) | 23.4392 | 0.907569 | ||||||||
\(668\) | 52.0917 | 2.01549 | ||||||||
\(669\) | 2.56240 | 0.0990681 | ||||||||
\(670\) | −118.785 | −4.58906 | ||||||||
\(671\) | −28.1450 | −1.08652 | ||||||||
\(672\) | 5.75318 | 0.221934 | ||||||||
\(673\) | −16.2700 | −0.627163 | −0.313581 | − | 0.949561i | \(-0.601529\pi\) | ||||
−0.313581 | + | 0.949561i | \(0.601529\pi\) | |||||||
\(674\) | −88.0075 | −3.38992 | ||||||||
\(675\) | 19.9265 | 0.766970 | ||||||||
\(676\) | 174.915 | 6.72751 | ||||||||
\(677\) | −34.7188 | −1.33435 | −0.667176 | − | 0.744900i | \(-0.732497\pi\) | ||||
−0.667176 | + | 0.744900i | \(0.732497\pi\) | |||||||
\(678\) | −2.15724 | −0.0828484 | ||||||||
\(679\) | 0.732395 | 0.0281068 | ||||||||
\(680\) | −234.564 | −8.99511 | ||||||||
\(681\) | 0.118964 | 0.00455873 | ||||||||
\(682\) | −44.1122 | −1.68914 | ||||||||
\(683\) | 7.98992 | 0.305726 | 0.152863 | − | 0.988247i | \(-0.451151\pi\) | ||||
0.152863 | + | 0.988247i | \(0.451151\pi\) | |||||||
\(684\) | 39.6476 | 1.51596 | ||||||||
\(685\) | −35.5896 | −1.35981 | ||||||||
\(686\) | 11.3985 | 0.435195 | ||||||||
\(687\) | −2.77367 | −0.105822 | ||||||||
\(688\) | 38.8862 | 1.48252 | ||||||||
\(689\) | 50.4445 | 1.92178 | ||||||||
\(690\) | −44.3124 | −1.68694 | ||||||||
\(691\) | 6.88017 | 0.261734 | 0.130867 | − | 0.991400i | \(-0.458224\pi\) | ||||
0.130867 | + | 0.991400i | \(0.458224\pi\) | |||||||
\(692\) | 36.5663 | 1.39004 | ||||||||
\(693\) | 3.99661 | 0.151819 | ||||||||
\(694\) | 36.3647 | 1.38039 | ||||||||
\(695\) | −49.6711 | −1.88413 | ||||||||
\(696\) | 27.6533 | 1.04820 | ||||||||
\(697\) | 61.7825 | 2.34018 | ||||||||
\(698\) | 79.2061 | 2.99799 | ||||||||
\(699\) | 18.6694 | 0.706141 | ||||||||
\(700\) | 7.86913 | 0.297425 | ||||||||
\(701\) | 11.5530 | 0.436350 | 0.218175 | − | 0.975910i | \(-0.429990\pi\) | ||||
0.218175 | + | 0.975910i | \(0.429990\pi\) | |||||||
\(702\) | −77.2931 | −2.91724 | ||||||||
\(703\) | 28.9027 | 1.09009 | ||||||||
\(704\) | −202.013 | −7.61364 | ||||||||
\(705\) | 24.2814 | 0.914490 | ||||||||
\(706\) | 49.9377 | 1.87943 | ||||||||
\(707\) | 1.35565 | 0.0509845 | ||||||||
\(708\) | 23.0326 | 0.865619 | ||||||||
\(709\) | 34.0414 | 1.27845 | 0.639226 | − | 0.769019i | \(-0.279255\pi\) | ||||
0.639226 | + | 0.769019i | \(0.279255\pi\) | |||||||
\(710\) | −8.59909 | −0.322718 | ||||||||
\(711\) | 2.00486 | 0.0751880 | ||||||||
\(712\) | −94.1912 | −3.52997 | ||||||||
\(713\) | −18.7088 | −0.700652 | ||||||||
\(714\) | −4.85473 | −0.181684 | ||||||||
\(715\) | 116.816 | 4.36867 | ||||||||
\(716\) | −91.2050 | −3.40849 | ||||||||
\(717\) | −11.9747 | −0.447204 | ||||||||
\(718\) | 60.5406 | 2.25935 | ||||||||
\(719\) | 23.7192 | 0.884578 | 0.442289 | − | 0.896873i | \(-0.354167\pi\) | ||||
0.442289 | + | 0.896873i | \(0.354167\pi\) | |||||||
\(720\) | 120.484 | 4.49017 | ||||||||
\(721\) | 0.0607047 | 0.00226076 | ||||||||
\(722\) | 28.1647 | 1.04818 | ||||||||
\(723\) | −8.42187 | −0.313213 | ||||||||
\(724\) | −41.4953 | −1.54216 | ||||||||
\(725\) | 16.8223 | 0.624765 | ||||||||
\(726\) | 44.7042 | 1.65913 | ||||||||
\(727\) | 1.96085 | 0.0727240 | 0.0363620 | − | 0.999339i | \(-0.488423\pi\) | ||||
0.0363620 | + | 0.999339i | \(0.488423\pi\) | |||||||
\(728\) | −19.6263 | −0.727398 | ||||||||
\(729\) | 0.665190 | 0.0246367 | ||||||||
\(730\) | 10.4037 | 0.385059 | ||||||||
\(731\) | −18.2022 | −0.673231 | ||||||||
\(732\) | −21.9025 | −0.809539 | ||||||||
\(733\) | 1.98250 | 0.0732254 | 0.0366127 | − | 0.999330i | \(-0.488343\pi\) | ||||
0.0366127 | + | 0.999330i | \(0.488343\pi\) | |||||||
\(734\) | 1.11297 | 0.0410804 | ||||||||
\(735\) | −16.8658 | −0.622105 | ||||||||
\(736\) | −162.971 | −6.00717 | ||||||||
\(737\) | 77.8027 | 2.86590 | ||||||||
\(738\) | −53.7117 | −1.97716 | ||||||||
\(739\) | −28.9271 | −1.06410 | −0.532051 | − | 0.846712i | \(-0.678579\pi\) | ||||
−0.532051 | + | 0.846712i | \(0.678579\pi\) | |||||||
\(740\) | 170.373 | 6.26305 | ||||||||
\(741\) | 15.4217 | 0.566529 | ||||||||
\(742\) | −6.21516 | −0.228166 | ||||||||
\(743\) | 8.08169 | 0.296488 | 0.148244 | − | 0.988951i | \(-0.452638\pi\) | ||||
0.148244 | + | 0.988951i | \(0.452638\pi\) | |||||||
\(744\) | −22.0725 | −0.809218 | ||||||||
\(745\) | −25.9703 | −0.951479 | ||||||||
\(746\) | −67.3989 | −2.46765 | ||||||||
\(747\) | −34.1554 | −1.24968 | ||||||||
\(748\) | 238.943 | 8.73661 | ||||||||
\(749\) | −3.14908 | −0.115065 | ||||||||
\(750\) | 1.83707 | 0.0670802 | ||||||||
\(751\) | −47.3577 | −1.72811 | −0.864053 | − | 0.503401i | \(-0.832082\pi\) | ||||
−0.864053 | + | 0.503401i | \(0.832082\pi\) | |||||||
\(752\) | 160.986 | 5.87054 | ||||||||
\(753\) | −4.10879 | −0.149733 | ||||||||
\(754\) | −65.2523 | −2.37635 | ||||||||
\(755\) | −25.4218 | −0.925194 | ||||||||
\(756\) | 7.01769 | 0.255231 | ||||||||
\(757\) | −34.5284 | −1.25496 | −0.627478 | − | 0.778634i | \(-0.715913\pi\) | ||||
−0.627478 | + | 0.778634i | \(0.715913\pi\) | |||||||
\(758\) | −102.153 | −3.71036 | ||||||||
\(759\) | 29.0241 | 1.05351 | ||||||||
\(760\) | −91.8049 | −3.33011 | ||||||||
\(761\) | 9.60438 | 0.348158 | 0.174079 | − | 0.984732i | \(-0.444305\pi\) | ||||
0.174079 | + | 0.984732i | \(0.444305\pi\) | |||||||
\(762\) | −20.9448 | −0.758751 | ||||||||
\(763\) | 3.94496 | 0.142817 | ||||||||
\(764\) | −12.8606 | −0.465280 | ||||||||
\(765\) | −56.3971 | −2.03904 | ||||||||
\(766\) | 35.6063 | 1.28651 | ||||||||
\(767\) | −34.9456 | −1.26181 | ||||||||
\(768\) | −50.4487 | −1.82041 | ||||||||
\(769\) | −16.3484 | −0.589537 | −0.294768 | − | 0.955569i | \(-0.595243\pi\) | ||||
−0.294768 | + | 0.955569i | \(0.595243\pi\) | |||||||
\(770\) | −14.3926 | −0.518675 | ||||||||
\(771\) | −5.09355 | −0.183440 | ||||||||
\(772\) | −86.0404 | −3.09666 | ||||||||
\(773\) | 0.519158 | 0.0186728 | 0.00933641 | − | 0.999956i | \(-0.497028\pi\) | ||||
0.00933641 | + | 0.999956i | \(0.497028\pi\) | |||||||
\(774\) | 15.8244 | 0.568795 | ||||||||
\(775\) | −13.4273 | −0.482325 | ||||||||
\(776\) | −24.4766 | −0.878660 | ||||||||
\(777\) | 2.26729 | 0.0813385 | ||||||||
\(778\) | 66.0877 | 2.36936 | ||||||||
\(779\) | 24.1808 | 0.866367 | ||||||||
\(780\) | 90.9063 | 3.25497 | ||||||||
\(781\) | 5.63230 | 0.201540 | ||||||||
\(782\) | 137.520 | 4.91771 | ||||||||
\(783\) | 15.0021 | 0.536133 | ||||||||
\(784\) | −111.820 | −3.99359 | ||||||||
\(785\) | 22.8056 | 0.813967 | ||||||||
\(786\) | 12.0619 | 0.430232 | ||||||||
\(787\) | −41.5213 | −1.48008 | −0.740038 | − | 0.672565i | \(-0.765193\pi\) | ||||
−0.740038 | + | 0.672565i | \(0.765193\pi\) | |||||||
\(788\) | 20.0044 | 0.712627 | ||||||||
\(789\) | −12.4301 | −0.442523 | ||||||||
\(790\) | −7.21991 | −0.256873 | ||||||||
\(791\) | −0.297168 | −0.0105661 | ||||||||
\(792\) | −133.567 | −4.74609 | ||||||||
\(793\) | 33.2309 | 1.18006 | ||||||||
\(794\) | 62.8673 | 2.23108 | ||||||||
\(795\) | 18.5101 | 0.656487 | ||||||||
\(796\) | 149.535 | 5.30012 | ||||||||
\(797\) | −38.3748 | −1.35930 | −0.679652 | − | 0.733534i | \(-0.737869\pi\) | ||||
−0.679652 | + | 0.733534i | \(0.737869\pi\) | |||||||
\(798\) | −1.90007 | −0.0672618 | ||||||||
\(799\) | −75.3554 | −2.66588 | ||||||||
\(800\) | −116.964 | −4.13530 | ||||||||
\(801\) | −22.6468 | −0.800184 | ||||||||
\(802\) | −99.9148 | −3.52811 | ||||||||
\(803\) | −6.81432 | −0.240472 | ||||||||
\(804\) | 60.5462 | 2.13530 | ||||||||
\(805\) | −6.10420 | −0.215145 | ||||||||
\(806\) | 52.0835 | 1.83456 | ||||||||
\(807\) | −14.8091 | −0.521305 | ||||||||
\(808\) | −45.3059 | −1.59386 | ||||||||
\(809\) | −41.5785 | −1.46182 | −0.730911 | − | 0.682473i | \(-0.760905\pi\) | ||||
−0.730911 | + | 0.682473i | \(0.760905\pi\) | |||||||
\(810\) | 33.2376 | 1.16785 | ||||||||
\(811\) | 27.4236 | 0.962973 | 0.481486 | − | 0.876454i | \(-0.340097\pi\) | ||||
0.481486 | + | 0.876454i | \(0.340097\pi\) | |||||||
\(812\) | 5.92447 | 0.207908 | ||||||||
\(813\) | 19.9121 | 0.698347 | ||||||||
\(814\) | −151.433 | −5.30771 | ||||||||
\(815\) | 28.8347 | 1.01004 | ||||||||
\(816\) | 95.8596 | 3.35576 | ||||||||
\(817\) | −7.12406 | −0.249239 | ||||||||
\(818\) | 11.2055 | 0.391791 | ||||||||
\(819\) | −4.71882 | −0.164889 | ||||||||
\(820\) | 142.539 | 4.97767 | ||||||||
\(821\) | −46.4167 | −1.61995 | −0.809977 | − | 0.586461i | \(-0.800521\pi\) | ||||
−0.809977 | + | 0.586461i | \(0.800521\pi\) | |||||||
\(822\) | 24.6169 | 0.858612 | ||||||||
\(823\) | 47.4686 | 1.65465 | 0.827326 | − | 0.561722i | \(-0.189861\pi\) | ||||
0.827326 | + | 0.561722i | \(0.189861\pi\) | |||||||
\(824\) | −2.02875 | −0.0706749 | ||||||||
\(825\) | 20.8306 | 0.725229 | ||||||||
\(826\) | 4.30558 | 0.149810 | ||||||||
\(827\) | −38.3495 | −1.33354 | −0.666771 | − | 0.745263i | \(-0.732324\pi\) | ||||
−0.666771 | + | 0.745263i | \(0.732324\pi\) | |||||||
\(828\) | −88.1019 | −3.06175 | ||||||||
\(829\) | 14.5194 | 0.504279 | 0.252140 | − | 0.967691i | \(-0.418866\pi\) | ||||
0.252140 | + | 0.967691i | \(0.418866\pi\) | |||||||
\(830\) | 123.001 | 4.26941 | ||||||||
\(831\) | 3.32601 | 0.115378 | ||||||||
\(832\) | 238.517 | 8.26910 | ||||||||
\(833\) | 52.3418 | 1.81354 | ||||||||
\(834\) | 34.3569 | 1.18968 | ||||||||
\(835\) | −29.0011 | −1.00362 | ||||||||
\(836\) | 93.5188 | 3.23441 | ||||||||
\(837\) | −11.9745 | −0.413900 | ||||||||
\(838\) | −90.5925 | −3.12946 | ||||||||
\(839\) | −35.0695 | −1.21073 | −0.605367 | − | 0.795947i | \(-0.706974\pi\) | ||||
−0.605367 | + | 0.795947i | \(0.706974\pi\) | |||||||
\(840\) | −7.20167 | −0.248481 | ||||||||
\(841\) | −16.3349 | −0.563272 | ||||||||
\(842\) | −39.2056 | −1.35112 | ||||||||
\(843\) | 8.35176 | 0.287650 | ||||||||
\(844\) | −53.8353 | −1.85309 | ||||||||
\(845\) | −97.3806 | −3.34999 | ||||||||
\(846\) | 65.5116 | 2.25234 | ||||||||
\(847\) | 6.15816 | 0.211597 | ||||||||
\(848\) | 122.722 | 4.21430 | ||||||||
\(849\) | −7.00568 | −0.240434 | ||||||||
\(850\) | 98.6983 | 3.38532 | ||||||||
\(851\) | −64.2255 | −2.20162 | ||||||||
\(852\) | 4.38307 | 0.150161 | ||||||||
\(853\) | −28.1269 | −0.963048 | −0.481524 | − | 0.876433i | \(-0.659917\pi\) | ||||
−0.481524 | + | 0.876433i | \(0.659917\pi\) | |||||||
\(854\) | −4.09431 | −0.140104 | ||||||||
\(855\) | −22.0730 | −0.754881 | ||||||||
\(856\) | 105.242 | 3.59710 | ||||||||
\(857\) | −47.7875 | −1.63239 | −0.816194 | − | 0.577777i | \(-0.803920\pi\) | ||||
−0.816194 | + | 0.577777i | \(0.803920\pi\) | |||||||
\(858\) | −80.8002 | −2.75847 | ||||||||
\(859\) | 35.5209 | 1.21196 | 0.605979 | − | 0.795481i | \(-0.292782\pi\) | ||||
0.605979 | + | 0.795481i | \(0.292782\pi\) | |||||||
\(860\) | −41.9943 | −1.43199 | ||||||||
\(861\) | 1.89687 | 0.0646452 | ||||||||
\(862\) | 59.0653 | 2.01177 | ||||||||
\(863\) | −37.7729 | −1.28580 | −0.642902 | − | 0.765948i | \(-0.722270\pi\) | ||||
−0.642902 | + | 0.765948i | \(0.722270\pi\) | |||||||
\(864\) | −104.309 | −3.54865 | ||||||||
\(865\) | −20.3576 | −0.692178 | ||||||||
\(866\) | 84.8112 | 2.88200 | ||||||||
\(867\) | −31.5698 | −1.07217 | ||||||||
\(868\) | −4.72884 | −0.160507 | ||||||||
\(869\) | 4.72896 | 0.160419 | ||||||||
\(870\) | −23.9437 | −0.811768 | ||||||||
\(871\) | −91.8621 | −3.11263 | ||||||||
\(872\) | −131.840 | −4.46468 | ||||||||
\(873\) | −5.88502 | −0.199178 | ||||||||
\(874\) | 53.8234 | 1.82060 | ||||||||
\(875\) | 0.253063 | 0.00855508 | ||||||||
\(876\) | −5.30292 | −0.179169 | ||||||||
\(877\) | 38.2179 | 1.29053 | 0.645263 | − | 0.763960i | \(-0.276748\pi\) | ||||
0.645263 | + | 0.763960i | \(0.276748\pi\) | |||||||
\(878\) | −105.306 | −3.55391 | ||||||||
\(879\) | 7.79046 | 0.262766 | ||||||||
\(880\) | 284.192 | 9.58009 | ||||||||
\(881\) | 9.22324 | 0.310739 | 0.155369 | − | 0.987856i | \(-0.450343\pi\) | ||||
0.155369 | + | 0.987856i | \(0.450343\pi\) | |||||||
\(882\) | −45.5043 | −1.53221 | ||||||||
\(883\) | −24.3652 | −0.819956 | −0.409978 | − | 0.912095i | \(-0.634464\pi\) | ||||
−0.409978 | + | 0.912095i | \(0.634464\pi\) | |||||||
\(884\) | −282.121 | −9.48875 | ||||||||
\(885\) | −12.8230 | −0.431039 | ||||||||
\(886\) | −103.698 | −3.48379 | ||||||||
\(887\) | −28.0237 | −0.940945 | −0.470473 | − | 0.882415i | \(-0.655917\pi\) | ||||
−0.470473 | + | 0.882415i | \(0.655917\pi\) | |||||||
\(888\) | −75.7727 | −2.54277 | ||||||||
\(889\) | −2.88523 | −0.0967674 | ||||||||
\(890\) | 81.5558 | 2.73376 | ||||||||
\(891\) | −21.7702 | −0.729331 | ||||||||
\(892\) | −18.3466 | −0.614289 | ||||||||
\(893\) | −29.4930 | −0.986947 | ||||||||
\(894\) | 17.9634 | 0.600785 | ||||||||
\(895\) | 50.7766 | 1.69728 | ||||||||
\(896\) | −14.6809 | −0.490456 | ||||||||
\(897\) | −34.2689 | −1.14421 | ||||||||
\(898\) | −66.2575 | −2.21104 | ||||||||
\(899\) | −10.1091 | −0.337158 | ||||||||
\(900\) | −63.2308 | −2.10769 | ||||||||
\(901\) | −57.4448 | −1.91376 | ||||||||
\(902\) | −126.693 | −4.21840 | ||||||||
\(903\) | −0.558850 | −0.0185974 | ||||||||
\(904\) | 9.93135 | 0.330312 | ||||||||
\(905\) | 23.1017 | 0.767926 | ||||||||
\(906\) | 17.5840 | 0.584188 | ||||||||
\(907\) | −43.4622 | −1.44314 | −0.721569 | − | 0.692343i | \(-0.756579\pi\) | ||||
−0.721569 | + | 0.692343i | \(0.756579\pi\) | |||||||
\(908\) | −0.851777 | −0.0282672 | ||||||||
\(909\) | −10.8931 | −0.361300 | ||||||||
\(910\) | 16.9935 | 0.563328 | ||||||||
\(911\) | 39.6579 | 1.31393 | 0.656963 | − | 0.753923i | \(-0.271841\pi\) | ||||
0.656963 | + | 0.753923i | \(0.271841\pi\) | |||||||
\(912\) | 37.5181 | 1.24235 | ||||||||
\(913\) | −80.5640 | −2.66628 | ||||||||
\(914\) | −77.6610 | −2.56880 | ||||||||
\(915\) | 12.1938 | 0.403114 | ||||||||
\(916\) | 19.8593 | 0.656170 | ||||||||
\(917\) | 1.66157 | 0.0548697 | ||||||||
\(918\) | 88.0192 | 2.90507 | ||||||||
\(919\) | 23.0385 | 0.759970 | 0.379985 | − | 0.924993i | \(-0.375929\pi\) | ||||
0.379985 | + | 0.924993i | \(0.375929\pi\) | |||||||
\(920\) | 204.002 | 6.72575 | ||||||||
\(921\) | −0.933539 | −0.0307612 | ||||||||
\(922\) | −5.92359 | −0.195083 | ||||||||
\(923\) | −6.65009 | −0.218890 | ||||||||
\(924\) | 7.33612 | 0.241341 | ||||||||
\(925\) | −46.0947 | −1.51558 | ||||||||
\(926\) | −8.84436 | −0.290644 | ||||||||
\(927\) | −0.487781 | −0.0160208 | ||||||||
\(928\) | −88.0594 | −2.89069 | ||||||||
\(929\) | −19.0999 | −0.626648 | −0.313324 | − | 0.949646i | \(-0.601443\pi\) | ||||
−0.313324 | + | 0.949646i | \(0.601443\pi\) | |||||||
\(930\) | 19.1116 | 0.626693 | ||||||||
\(931\) | 20.4858 | 0.671396 | ||||||||
\(932\) | −133.671 | −4.37855 | ||||||||
\(933\) | −7.75819 | −0.253992 | ||||||||
\(934\) | −49.0823 | −1.60602 | ||||||||
\(935\) | −133.027 | −4.35044 | ||||||||
\(936\) | 157.703 | 5.15468 | ||||||||
\(937\) | 5.83484 | 0.190616 | 0.0953079 | − | 0.995448i | \(-0.469616\pi\) | ||||
0.0953079 | + | 0.995448i | \(0.469616\pi\) | |||||||
\(938\) | 11.3181 | 0.369550 | ||||||||
\(939\) | −6.27029 | −0.204623 | ||||||||
\(940\) | −173.853 | −5.67046 | ||||||||
\(941\) | −0.133144 | −0.00434038 | −0.00217019 | − | 0.999998i | \(-0.500691\pi\) | ||||
−0.00217019 | + | 0.999998i | \(0.500691\pi\) | |||||||
\(942\) | −15.7744 | −0.513957 | ||||||||
\(943\) | −53.7328 | −1.74978 | ||||||||
\(944\) | −85.0163 | −2.76704 | ||||||||
\(945\) | −3.90696 | −0.127094 | ||||||||
\(946\) | 37.3258 | 1.21356 | ||||||||
\(947\) | 11.1991 | 0.363923 | 0.181961 | − | 0.983306i | \(-0.441755\pi\) | ||||
0.181961 | + | 0.983306i | \(0.441755\pi\) | |||||||
\(948\) | 3.68008 | 0.119524 | ||||||||
\(949\) | 8.04571 | 0.261175 | ||||||||
\(950\) | 38.6291 | 1.25329 | ||||||||
\(951\) | 4.41887 | 0.143292 | ||||||||
\(952\) | 22.3498 | 0.724362 | ||||||||
\(953\) | 21.9641 | 0.711487 | 0.355744 | − | 0.934584i | \(-0.384228\pi\) | ||||
0.355744 | + | 0.934584i | \(0.384228\pi\) | |||||||
\(954\) | 49.9407 | 1.61689 | ||||||||
\(955\) | 7.15989 | 0.231689 | ||||||||
\(956\) | 85.7381 | 2.77297 | ||||||||
\(957\) | 15.6829 | 0.506955 | ||||||||
\(958\) | −27.6257 | −0.892547 | ||||||||
\(959\) | 3.39107 | 0.109503 | ||||||||
\(960\) | 87.5217 | 2.82475 | ||||||||
\(961\) | −22.9310 | −0.739711 | ||||||||
\(962\) | 178.797 | 5.76466 | ||||||||
\(963\) | 25.3038 | 0.815403 | ||||||||
\(964\) | 60.2999 | 1.94213 | ||||||||
\(965\) | 47.9013 | 1.54200 | ||||||||
\(966\) | 4.22220 | 0.135847 | ||||||||
\(967\) | 5.15613 | 0.165810 | 0.0829049 | − | 0.996557i | \(-0.473580\pi\) | ||||
0.0829049 | + | 0.996557i | \(0.473580\pi\) | |||||||
\(968\) | −205.806 | −6.61485 | ||||||||
\(969\) | −17.5618 | −0.564165 | ||||||||
\(970\) | 21.1932 | 0.680472 | ||||||||
\(971\) | 55.4784 | 1.78039 | 0.890194 | − | 0.455582i | \(-0.150569\pi\) | ||||
0.890194 | + | 0.455582i | \(0.150569\pi\) | |||||||
\(972\) | −87.7874 | −2.81578 | ||||||||
\(973\) | 4.73279 | 0.151726 | ||||||||
\(974\) | −48.1891 | −1.54408 | ||||||||
\(975\) | −24.5948 | −0.787664 | ||||||||
\(976\) | 80.8447 | 2.58778 | ||||||||
\(977\) | −43.1137 | −1.37933 | −0.689664 | − | 0.724129i | \(-0.742242\pi\) | ||||
−0.689664 | + | 0.724129i | \(0.742242\pi\) | |||||||
\(978\) | −19.9446 | −0.637759 | ||||||||
\(979\) | −53.4181 | −1.70725 | ||||||||
\(980\) | 120.758 | 3.85747 | ||||||||
\(981\) | −31.6989 | −1.01207 | ||||||||
\(982\) | 94.9852 | 3.03110 | ||||||||
\(983\) | 28.3694 | 0.904842 | 0.452421 | − | 0.891804i | \(-0.350560\pi\) | ||||
0.452421 | + | 0.891804i | \(0.350560\pi\) | |||||||
\(984\) | −63.3934 | −2.02091 | ||||||||
\(985\) | −11.1370 | −0.354856 | ||||||||
\(986\) | 74.3075 | 2.36643 | ||||||||
\(987\) | −2.31359 | −0.0736425 | ||||||||
\(988\) | −110.418 | −3.51287 | ||||||||
\(989\) | 15.8306 | 0.503383 | ||||||||
\(990\) | 115.649 | 3.67557 | ||||||||
\(991\) | −59.2003 | −1.88056 | −0.940280 | − | 0.340403i | \(-0.889436\pi\) | ||||
−0.940280 | + | 0.340403i | \(0.889436\pi\) | |||||||
\(992\) | 70.2878 | 2.23164 | ||||||||
\(993\) | 8.72775 | 0.276967 | ||||||||
\(994\) | 0.819343 | 0.0259880 | ||||||||
\(995\) | −83.2505 | −2.63922 | ||||||||
\(996\) | −62.6950 | −1.98657 | ||||||||
\(997\) | 27.9110 | 0.883950 | 0.441975 | − | 0.897027i | \(-0.354278\pi\) | ||||
0.441975 | + | 0.897027i | \(0.354278\pi\) | |||||||
\(998\) | 65.5463 | 2.07483 | ||||||||
\(999\) | −41.1073 | −1.30058 |
(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 | 8023.2.a.c.1.3 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.3 | ✓ | 158 | 1.1 | even | 1 | trivial |