Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63224 | −1.86128 | −0.930638 | − | 0.365941i | \(-0.880747\pi\) | ||||
−0.930638 | + | 0.365941i | \(0.880747\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.92870 | 2.46435 | ||||||||
\(5\) | 3.86633 | 1.72907 | 0.864537 | − | 0.502569i | \(-0.167612\pi\) | ||||
0.864537 | + | 0.502569i | \(0.167612\pi\) | |||||||
\(6\) | 2.63224 | 1.07461 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −7.70903 | −2.72555 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −10.1771 | −3.21828 | ||||||||
\(11\) | −3.94955 | −1.19083 | −0.595417 | − | 0.803417i | \(-0.703013\pi\) | ||||
−0.595417 | + | 0.803417i | \(0.703013\pi\) | |||||||
\(12\) | −4.92870 | −1.42279 | ||||||||
\(13\) | 0.666715 | 0.184913 | 0.0924567 | − | 0.995717i | \(-0.470528\pi\) | ||||
0.0924567 | + | 0.995717i | \(0.470528\pi\) | |||||||
\(14\) | 2.63224 | 0.703496 | ||||||||
\(15\) | −3.86633 | −0.998282 | ||||||||
\(16\) | 10.4346 | 2.60866 | ||||||||
\(17\) | −4.28337 | −1.03887 | −0.519435 | − | 0.854510i | \(-0.673857\pi\) | ||||
−0.519435 | + | 0.854510i | \(0.673857\pi\) | |||||||
\(18\) | −2.63224 | −0.620425 | ||||||||
\(19\) | 0.176483 | 0.0404879 | 0.0202440 | − | 0.999795i | \(-0.493556\pi\) | ||||
0.0202440 | + | 0.999795i | \(0.493556\pi\) | |||||||
\(20\) | 19.0560 | 4.26104 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 10.3962 | 2.21647 | ||||||||
\(23\) | −5.36716 | −1.11913 | −0.559566 | − | 0.828786i | \(-0.689032\pi\) | ||||
−0.559566 | + | 0.828786i | \(0.689032\pi\) | |||||||
\(24\) | 7.70903 | 1.57360 | ||||||||
\(25\) | 9.94849 | 1.98970 | ||||||||
\(26\) | −1.75495 | −0.344175 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.92870 | −0.931436 | ||||||||
\(29\) | −2.72687 | −0.506367 | −0.253184 | − | 0.967418i | \(-0.581478\pi\) | ||||
−0.253184 | + | 0.967418i | \(0.581478\pi\) | |||||||
\(30\) | 10.1771 | 1.85808 | ||||||||
\(31\) | −7.79297 | −1.39966 | −0.699830 | − | 0.714310i | \(-0.746741\pi\) | ||||
−0.699830 | + | 0.714310i | \(0.746741\pi\) | |||||||
\(32\) | −12.0484 | −2.12988 | ||||||||
\(33\) | 3.94955 | 0.687528 | ||||||||
\(34\) | 11.2749 | 1.93362 | ||||||||
\(35\) | −3.86633 | −0.653529 | ||||||||
\(36\) | 4.92870 | 0.821449 | ||||||||
\(37\) | 9.69422 | 1.59372 | 0.796860 | − | 0.604164i | \(-0.206493\pi\) | ||||
0.796860 | + | 0.604164i | \(0.206493\pi\) | |||||||
\(38\) | −0.464545 | −0.0753592 | ||||||||
\(39\) | −0.666715 | −0.106760 | ||||||||
\(40\) | −29.8056 | −4.71269 | ||||||||
\(41\) | 6.28096 | 0.980920 | 0.490460 | − | 0.871464i | \(-0.336829\pi\) | ||||
0.490460 | + | 0.871464i | \(0.336829\pi\) | |||||||
\(42\) | −2.63224 | −0.406164 | ||||||||
\(43\) | 3.37422 | 0.514564 | 0.257282 | − | 0.966336i | \(-0.417173\pi\) | ||||
0.257282 | + | 0.966336i | \(0.417173\pi\) | |||||||
\(44\) | −19.4661 | −2.93463 | ||||||||
\(45\) | 3.86633 | 0.576358 | ||||||||
\(46\) | 14.1277 | 2.08301 | ||||||||
\(47\) | 13.0088 | 1.89753 | 0.948764 | − | 0.315985i | \(-0.102335\pi\) | ||||
0.948764 | + | 0.315985i | \(0.102335\pi\) | |||||||
\(48\) | −10.4346 | −1.50611 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −26.1868 | −3.70338 | ||||||||
\(51\) | 4.28337 | 0.599791 | ||||||||
\(52\) | 3.28603 | 0.455691 | ||||||||
\(53\) | −5.03862 | −0.692107 | −0.346054 | − | 0.938215i | \(-0.612479\pi\) | ||||
−0.346054 | + | 0.938215i | \(0.612479\pi\) | |||||||
\(54\) | 2.63224 | 0.358203 | ||||||||
\(55\) | −15.2703 | −2.05904 | ||||||||
\(56\) | 7.70903 | 1.03016 | ||||||||
\(57\) | −0.176483 | −0.0233757 | ||||||||
\(58\) | 7.17778 | 0.942489 | ||||||||
\(59\) | −4.21767 | −0.549094 | −0.274547 | − | 0.961574i | \(-0.588528\pi\) | ||||
−0.274547 | + | 0.961574i | \(0.588528\pi\) | |||||||
\(60\) | −19.0560 | −2.46011 | ||||||||
\(61\) | −6.76710 | −0.866438 | −0.433219 | − | 0.901289i | \(-0.642622\pi\) | ||||
−0.433219 | + | 0.901289i | \(0.642622\pi\) | |||||||
\(62\) | 20.5130 | 2.60515 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 10.8451 | 1.35564 | ||||||||
\(65\) | 2.57774 | 0.319729 | ||||||||
\(66\) | −10.3962 | −1.27968 | ||||||||
\(67\) | −11.2998 | −1.38049 | −0.690244 | − | 0.723577i | \(-0.742497\pi\) | ||||
−0.690244 | + | 0.723577i | \(0.742497\pi\) | |||||||
\(68\) | −21.1114 | −2.56013 | ||||||||
\(69\) | 5.36716 | 0.646131 | ||||||||
\(70\) | 10.1771 | 1.21640 | ||||||||
\(71\) | −3.54238 | −0.420403 | −0.210202 | − | 0.977658i | \(-0.567412\pi\) | ||||
−0.210202 | + | 0.977658i | \(0.567412\pi\) | |||||||
\(72\) | −7.70903 | −0.908518 | ||||||||
\(73\) | 1.67029 | 0.195493 | 0.0977466 | − | 0.995211i | \(-0.468837\pi\) | ||||
0.0977466 | + | 0.995211i | \(0.468837\pi\) | |||||||
\(74\) | −25.5175 | −2.96635 | ||||||||
\(75\) | −9.94849 | −1.14875 | ||||||||
\(76\) | 0.869830 | 0.0997763 | ||||||||
\(77\) | 3.94955 | 0.450093 | ||||||||
\(78\) | 1.75495 | 0.198709 | ||||||||
\(79\) | −5.00173 | −0.562739 | −0.281369 | − | 0.959600i | \(-0.590789\pi\) | ||||
−0.281369 | + | 0.959600i | \(0.590789\pi\) | |||||||
\(80\) | 40.3438 | 4.51057 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −16.5330 | −1.82576 | ||||||||
\(83\) | −2.95616 | −0.324480 | −0.162240 | − | 0.986751i | \(-0.551872\pi\) | ||||
−0.162240 | + | 0.986751i | \(0.551872\pi\) | |||||||
\(84\) | 4.92870 | 0.537765 | ||||||||
\(85\) | −16.5609 | −1.79628 | ||||||||
\(86\) | −8.88177 | −0.957746 | ||||||||
\(87\) | 2.72687 | 0.292351 | ||||||||
\(88\) | 30.4472 | 3.24568 | ||||||||
\(89\) | 4.67991 | 0.496070 | 0.248035 | − | 0.968751i | \(-0.420215\pi\) | ||||
0.248035 | + | 0.968751i | \(0.420215\pi\) | |||||||
\(90\) | −10.1771 | −1.07276 | ||||||||
\(91\) | −0.666715 | −0.0698907 | ||||||||
\(92\) | −26.4531 | −2.75793 | ||||||||
\(93\) | 7.79297 | 0.808094 | ||||||||
\(94\) | −34.2423 | −3.53182 | ||||||||
\(95\) | 0.682340 | 0.0700066 | ||||||||
\(96\) | 12.0484 | 1.22969 | ||||||||
\(97\) | 10.6954 | 1.08595 | 0.542976 | − | 0.839748i | \(-0.317297\pi\) | ||||
0.542976 | + | 0.839748i | \(0.317297\pi\) | |||||||
\(98\) | −2.63224 | −0.265897 | ||||||||
\(99\) | −3.94955 | −0.396945 | ||||||||
\(100\) | 49.0331 | 4.90331 | ||||||||
\(101\) | −16.9439 | −1.68598 | −0.842989 | − | 0.537930i | \(-0.819206\pi\) | ||||
−0.842989 | + | 0.537930i | \(0.819206\pi\) | |||||||
\(102\) | −11.2749 | −1.11638 | ||||||||
\(103\) | 3.87998 | 0.382306 | 0.191153 | − | 0.981560i | \(-0.438777\pi\) | ||||
0.191153 | + | 0.981560i | \(0.438777\pi\) | |||||||
\(104\) | −5.13973 | −0.503992 | ||||||||
\(105\) | 3.86633 | 0.377315 | ||||||||
\(106\) | 13.2629 | 1.28820 | ||||||||
\(107\) | −0.943279 | −0.0911902 | −0.0455951 | − | 0.998960i | \(-0.514518\pi\) | ||||
−0.0455951 | + | 0.998960i | \(0.514518\pi\) | |||||||
\(108\) | −4.92870 | −0.474264 | ||||||||
\(109\) | 6.46672 | 0.619399 | 0.309700 | − | 0.950834i | \(-0.399772\pi\) | ||||
0.309700 | + | 0.950834i | \(0.399772\pi\) | |||||||
\(110\) | 40.1950 | 3.83244 | ||||||||
\(111\) | −9.69422 | −0.920135 | ||||||||
\(112\) | −10.4346 | −0.985981 | ||||||||
\(113\) | 16.1795 | 1.52204 | 0.761020 | − | 0.648728i | \(-0.224699\pi\) | ||||
0.761020 | + | 0.648728i | \(0.224699\pi\) | |||||||
\(114\) | 0.464545 | 0.0435087 | ||||||||
\(115\) | −20.7512 | −1.93506 | ||||||||
\(116\) | −13.4399 | −1.24787 | ||||||||
\(117\) | 0.666715 | 0.0616378 | ||||||||
\(118\) | 11.1019 | 1.02202 | ||||||||
\(119\) | 4.28337 | 0.392656 | ||||||||
\(120\) | 29.8056 | 2.72087 | ||||||||
\(121\) | 4.59894 | 0.418086 | ||||||||
\(122\) | 17.8126 | 1.61268 | ||||||||
\(123\) | −6.28096 | −0.566335 | ||||||||
\(124\) | −38.4092 | −3.44925 | ||||||||
\(125\) | 19.1325 | 1.71126 | ||||||||
\(126\) | 2.63224 | 0.234499 | ||||||||
\(127\) | 14.6315 | 1.29833 | 0.649166 | − | 0.760647i | \(-0.275118\pi\) | ||||
0.649166 | + | 0.760647i | \(0.275118\pi\) | |||||||
\(128\) | −4.45008 | −0.393336 | ||||||||
\(129\) | −3.37422 | −0.297084 | ||||||||
\(130\) | −6.78523 | −0.595104 | ||||||||
\(131\) | −14.1269 | −1.23427 | −0.617135 | − | 0.786858i | \(-0.711707\pi\) | ||||
−0.617135 | + | 0.786858i | \(0.711707\pi\) | |||||||
\(132\) | 19.4661 | 1.69431 | ||||||||
\(133\) | −0.176483 | −0.0153030 | ||||||||
\(134\) | 29.7438 | 2.56947 | ||||||||
\(135\) | −3.86633 | −0.332761 | ||||||||
\(136\) | 33.0206 | 2.83149 | ||||||||
\(137\) | −8.36703 | −0.714844 | −0.357422 | − | 0.933943i | \(-0.616344\pi\) | ||||
−0.357422 | + | 0.933943i | \(0.616344\pi\) | |||||||
\(138\) | −14.1277 | −1.20263 | ||||||||
\(139\) | 19.6508 | 1.66676 | 0.833380 | − | 0.552700i | \(-0.186403\pi\) | ||||
0.833380 | + | 0.552700i | \(0.186403\pi\) | |||||||
\(140\) | −19.0560 | −1.61052 | ||||||||
\(141\) | −13.0088 | −1.09554 | ||||||||
\(142\) | 9.32440 | 0.782486 | ||||||||
\(143\) | −2.63322 | −0.220201 | ||||||||
\(144\) | 10.4346 | 0.869554 | ||||||||
\(145\) | −10.5430 | −0.875547 | ||||||||
\(146\) | −4.39662 | −0.363867 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 47.7799 | 3.92748 | ||||||||
\(149\) | 17.7764 | 1.45630 | 0.728149 | − | 0.685419i | \(-0.240381\pi\) | ||||
0.728149 | + | 0.685419i | \(0.240381\pi\) | |||||||
\(150\) | 26.1868 | 2.13815 | ||||||||
\(151\) | −16.9037 | −1.37560 | −0.687800 | − | 0.725900i | \(-0.741423\pi\) | ||||
−0.687800 | + | 0.725900i | \(0.741423\pi\) | |||||||
\(152\) | −1.36051 | −0.110352 | ||||||||
\(153\) | −4.28337 | −0.346290 | ||||||||
\(154\) | −10.3962 | −0.837747 | ||||||||
\(155\) | −30.1302 | −2.42012 | ||||||||
\(156\) | −3.28603 | −0.263093 | ||||||||
\(157\) | 22.6283 | 1.80594 | 0.902968 | − | 0.429708i | \(-0.141384\pi\) | ||||
0.902968 | + | 0.429708i | \(0.141384\pi\) | |||||||
\(158\) | 13.1658 | 1.04741 | ||||||||
\(159\) | 5.03862 | 0.399588 | ||||||||
\(160\) | −46.5832 | −3.68273 | ||||||||
\(161\) | 5.36716 | 0.422992 | ||||||||
\(162\) | −2.63224 | −0.206808 | ||||||||
\(163\) | 8.38183 | 0.656516 | 0.328258 | − | 0.944588i | \(-0.393538\pi\) | ||||
0.328258 | + | 0.944588i | \(0.393538\pi\) | |||||||
\(164\) | 30.9569 | 2.41733 | ||||||||
\(165\) | 15.2703 | 1.18879 | ||||||||
\(166\) | 7.78131 | 0.603947 | ||||||||
\(167\) | 4.36978 | 0.338144 | 0.169072 | − | 0.985604i | \(-0.445923\pi\) | ||||
0.169072 | + | 0.985604i | \(0.445923\pi\) | |||||||
\(168\) | −7.70903 | −0.594765 | ||||||||
\(169\) | −12.5555 | −0.965807 | ||||||||
\(170\) | 43.5923 | 3.34338 | ||||||||
\(171\) | 0.176483 | 0.0134960 | ||||||||
\(172\) | 16.6305 | 1.26807 | ||||||||
\(173\) | −23.2721 | −1.76934 | −0.884671 | − | 0.466215i | \(-0.845617\pi\) | ||||
−0.884671 | + | 0.466215i | \(0.845617\pi\) | |||||||
\(174\) | −7.17778 | −0.544146 | ||||||||
\(175\) | −9.94849 | −0.752035 | ||||||||
\(176\) | −41.2122 | −3.10648 | ||||||||
\(177\) | 4.21767 | 0.317020 | ||||||||
\(178\) | −12.3187 | −0.923323 | ||||||||
\(179\) | 12.5286 | 0.936429 | 0.468215 | − | 0.883615i | \(-0.344897\pi\) | ||||
0.468215 | + | 0.883615i | \(0.344897\pi\) | |||||||
\(180\) | 19.0560 | 1.42035 | ||||||||
\(181\) | 17.5228 | 1.30246 | 0.651228 | − | 0.758882i | \(-0.274254\pi\) | ||||
0.651228 | + | 0.758882i | \(0.274254\pi\) | |||||||
\(182\) | 1.75495 | 0.130086 | ||||||||
\(183\) | 6.76710 | 0.500238 | ||||||||
\(184\) | 41.3756 | 3.05025 | ||||||||
\(185\) | 37.4810 | 2.75566 | ||||||||
\(186\) | −20.5130 | −1.50409 | ||||||||
\(187\) | 16.9174 | 1.23712 | ||||||||
\(188\) | 64.1164 | 4.67617 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −1.79608 | −0.130302 | ||||||||
\(191\) | −6.05464 | −0.438098 | −0.219049 | − | 0.975714i | \(-0.570296\pi\) | ||||
−0.219049 | + | 0.975714i | \(0.570296\pi\) | |||||||
\(192\) | −10.8451 | −0.782679 | ||||||||
\(193\) | 2.29469 | 0.165175 | 0.0825876 | − | 0.996584i | \(-0.473682\pi\) | ||||
0.0825876 | + | 0.996584i | \(0.473682\pi\) | |||||||
\(194\) | −28.1528 | −2.02126 | ||||||||
\(195\) | −2.57774 | −0.184596 | ||||||||
\(196\) | 4.92870 | 0.352050 | ||||||||
\(197\) | 8.17623 | 0.582532 | 0.291266 | − | 0.956642i | \(-0.405923\pi\) | ||||
0.291266 | + | 0.956642i | \(0.405923\pi\) | |||||||
\(198\) | 10.3962 | 0.738824 | ||||||||
\(199\) | 7.67703 | 0.544210 | 0.272105 | − | 0.962268i | \(-0.412280\pi\) | ||||
0.272105 | + | 0.962268i | \(0.412280\pi\) | |||||||
\(200\) | −76.6932 | −5.42303 | ||||||||
\(201\) | 11.2998 | 0.797025 | ||||||||
\(202\) | 44.6004 | 3.13807 | ||||||||
\(203\) | 2.72687 | 0.191389 | ||||||||
\(204\) | 21.1114 | 1.47809 | ||||||||
\(205\) | 24.2842 | 1.69608 | ||||||||
\(206\) | −10.2130 | −0.711576 | ||||||||
\(207\) | −5.36716 | −0.373044 | ||||||||
\(208\) | 6.95693 | 0.482376 | ||||||||
\(209\) | −0.697028 | −0.0482144 | ||||||||
\(210\) | −10.1771 | −0.702287 | ||||||||
\(211\) | 26.3071 | 1.81106 | 0.905528 | − | 0.424287i | \(-0.139475\pi\) | ||||
0.905528 | + | 0.424287i | \(0.139475\pi\) | |||||||
\(212\) | −24.8338 | −1.70559 | ||||||||
\(213\) | 3.54238 | 0.242720 | ||||||||
\(214\) | 2.48294 | 0.169730 | ||||||||
\(215\) | 13.0459 | 0.889720 | ||||||||
\(216\) | 7.70903 | 0.524533 | ||||||||
\(217\) | 7.79297 | 0.529022 | ||||||||
\(218\) | −17.0220 | −1.15287 | ||||||||
\(219\) | −1.67029 | −0.112868 | ||||||||
\(220\) | −75.2624 | −5.07419 | ||||||||
\(221\) | −2.85578 | −0.192101 | ||||||||
\(222\) | 25.5175 | 1.71262 | ||||||||
\(223\) | 5.55368 | 0.371902 | 0.185951 | − | 0.982559i | \(-0.440463\pi\) | ||||
0.185951 | + | 0.982559i | \(0.440463\pi\) | |||||||
\(224\) | 12.0484 | 0.805020 | ||||||||
\(225\) | 9.94849 | 0.663233 | ||||||||
\(226\) | −42.5884 | −2.83294 | ||||||||
\(227\) | 11.8103 | 0.783879 | 0.391940 | − | 0.919991i | \(-0.371804\pi\) | ||||
0.391940 | + | 0.919991i | \(0.371804\pi\) | |||||||
\(228\) | −0.869830 | −0.0576059 | ||||||||
\(229\) | 10.8487 | 0.716900 | 0.358450 | − | 0.933549i | \(-0.383305\pi\) | ||||
0.358450 | + | 0.933549i | \(0.383305\pi\) | |||||||
\(230\) | 54.6222 | 3.60168 | ||||||||
\(231\) | −3.94955 | −0.259861 | ||||||||
\(232\) | 21.0215 | 1.38013 | ||||||||
\(233\) | 23.5182 | 1.54073 | 0.770364 | − | 0.637605i | \(-0.220075\pi\) | ||||
0.770364 | + | 0.637605i | \(0.220075\pi\) | |||||||
\(234\) | −1.75495 | −0.114725 | ||||||||
\(235\) | 50.2963 | 3.28097 | ||||||||
\(236\) | −20.7876 | −1.35316 | ||||||||
\(237\) | 5.00173 | 0.324897 | ||||||||
\(238\) | −11.2749 | −0.730840 | ||||||||
\(239\) | −26.3356 | −1.70351 | −0.851755 | − | 0.523941i | \(-0.824461\pi\) | ||||
−0.851755 | + | 0.523941i | \(0.824461\pi\) | |||||||
\(240\) | −40.3438 | −2.60418 | ||||||||
\(241\) | −8.03504 | −0.517582 | −0.258791 | − | 0.965933i | \(-0.583324\pi\) | ||||
−0.258791 | + | 0.965933i | \(0.583324\pi\) | |||||||
\(242\) | −12.1055 | −0.778173 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −33.3529 | −2.13520 | ||||||||
\(245\) | 3.86633 | 0.247011 | ||||||||
\(246\) | 16.5330 | 1.05411 | ||||||||
\(247\) | 0.117664 | 0.00748676 | ||||||||
\(248\) | 60.0763 | 3.81485 | ||||||||
\(249\) | 2.95616 | 0.187339 | ||||||||
\(250\) | −50.3613 | −3.18513 | ||||||||
\(251\) | 20.9598 | 1.32297 | 0.661486 | − | 0.749957i | \(-0.269926\pi\) | ||||
0.661486 | + | 0.749957i | \(0.269926\pi\) | |||||||
\(252\) | −4.92870 | −0.310479 | ||||||||
\(253\) | 21.1979 | 1.33270 | ||||||||
\(254\) | −38.5135 | −2.41655 | ||||||||
\(255\) | 16.5609 | 1.03708 | ||||||||
\(256\) | −9.97654 | −0.623534 | ||||||||
\(257\) | −0.394153 | −0.0245866 | −0.0122933 | − | 0.999924i | \(-0.503913\pi\) | ||||
−0.0122933 | + | 0.999924i | \(0.503913\pi\) | |||||||
\(258\) | 8.88177 | 0.552955 | ||||||||
\(259\) | −9.69422 | −0.602370 | ||||||||
\(260\) | 12.7049 | 0.787923 | ||||||||
\(261\) | −2.72687 | −0.168789 | ||||||||
\(262\) | 37.1853 | 2.29732 | ||||||||
\(263\) | 10.9986 | 0.678206 | 0.339103 | − | 0.940749i | \(-0.389877\pi\) | ||||
0.339103 | + | 0.940749i | \(0.389877\pi\) | |||||||
\(264\) | −30.4472 | −1.87390 | ||||||||
\(265\) | −19.4809 | −1.19671 | ||||||||
\(266\) | 0.464545 | 0.0284831 | ||||||||
\(267\) | −4.67991 | −0.286406 | ||||||||
\(268\) | −55.6932 | −3.40200 | ||||||||
\(269\) | 8.27868 | 0.504760 | 0.252380 | − | 0.967628i | \(-0.418787\pi\) | ||||
0.252380 | + | 0.967628i | \(0.418787\pi\) | |||||||
\(270\) | 10.1771 | 0.619359 | ||||||||
\(271\) | −4.70752 | −0.285961 | −0.142981 | − | 0.989725i | \(-0.545669\pi\) | ||||
−0.142981 | + | 0.989725i | \(0.545669\pi\) | |||||||
\(272\) | −44.6954 | −2.71006 | ||||||||
\(273\) | 0.666715 | 0.0403514 | ||||||||
\(274\) | 22.0240 | 1.33052 | ||||||||
\(275\) | −39.2921 | −2.36940 | ||||||||
\(276\) | 26.4531 | 1.59229 | ||||||||
\(277\) | 27.9629 | 1.68013 | 0.840064 | − | 0.542487i | \(-0.182517\pi\) | ||||
0.840064 | + | 0.542487i | \(0.182517\pi\) | |||||||
\(278\) | −51.7257 | −3.10230 | ||||||||
\(279\) | −7.79297 | −0.466553 | ||||||||
\(280\) | 29.8056 | 1.78123 | ||||||||
\(281\) | −25.2794 | −1.50804 | −0.754022 | − | 0.656849i | \(-0.771889\pi\) | ||||
−0.754022 | + | 0.656849i | \(0.771889\pi\) | |||||||
\(282\) | 34.2423 | 2.03910 | ||||||||
\(283\) | −18.2811 | −1.08670 | −0.543351 | − | 0.839506i | \(-0.682845\pi\) | ||||
−0.543351 | + | 0.839506i | \(0.682845\pi\) | |||||||
\(284\) | −17.4593 | −1.03602 | ||||||||
\(285\) | −0.682340 | −0.0404184 | ||||||||
\(286\) | 6.93128 | 0.409855 | ||||||||
\(287\) | −6.28096 | −0.370753 | ||||||||
\(288\) | −12.0484 | −0.709961 | ||||||||
\(289\) | 1.34724 | 0.0792492 | ||||||||
\(290\) | 27.7517 | 1.62963 | ||||||||
\(291\) | −10.6954 | −0.626975 | ||||||||
\(292\) | 8.23237 | 0.481763 | ||||||||
\(293\) | −28.4042 | −1.65939 | −0.829696 | − | 0.558215i | \(-0.811486\pi\) | ||||
−0.829696 | + | 0.558215i | \(0.811486\pi\) | |||||||
\(294\) | 2.63224 | 0.153515 | ||||||||
\(295\) | −16.3069 | −0.949425 | ||||||||
\(296\) | −74.7331 | −4.34377 | ||||||||
\(297\) | 3.94955 | 0.229176 | ||||||||
\(298\) | −46.7917 | −2.71057 | ||||||||
\(299\) | −3.57837 | −0.206942 | ||||||||
\(300\) | −49.0331 | −2.83093 | ||||||||
\(301\) | −3.37422 | −0.194487 | ||||||||
\(302\) | 44.4945 | 2.56037 | ||||||||
\(303\) | 16.9439 | 0.973400 | ||||||||
\(304\) | 1.84154 | 0.105619 | ||||||||
\(305\) | −26.1638 | −1.49814 | ||||||||
\(306\) | 11.2749 | 0.644541 | ||||||||
\(307\) | 28.0680 | 1.60192 | 0.800962 | − | 0.598715i | \(-0.204322\pi\) | ||||
0.800962 | + | 0.598715i | \(0.204322\pi\) | |||||||
\(308\) | 19.4661 | 1.10919 | ||||||||
\(309\) | −3.87998 | −0.220724 | ||||||||
\(310\) | 79.3099 | 4.50450 | ||||||||
\(311\) | −19.3118 | −1.09507 | −0.547537 | − | 0.836782i | \(-0.684434\pi\) | ||||
−0.547537 | + | 0.836782i | \(0.684434\pi\) | |||||||
\(312\) | 5.13973 | 0.290980 | ||||||||
\(313\) | −22.7937 | −1.28838 | −0.644188 | − | 0.764867i | \(-0.722805\pi\) | ||||
−0.644188 | + | 0.764867i | \(0.722805\pi\) | |||||||
\(314\) | −59.5632 | −3.36134 | ||||||||
\(315\) | −3.86633 | −0.217843 | ||||||||
\(316\) | −24.6520 | −1.38678 | ||||||||
\(317\) | 3.41287 | 0.191686 | 0.0958429 | − | 0.995396i | \(-0.469445\pi\) | ||||
0.0958429 | + | 0.995396i | \(0.469445\pi\) | |||||||
\(318\) | −13.2629 | −0.743744 | ||||||||
\(319\) | 10.7699 | 0.602999 | ||||||||
\(320\) | 41.9308 | 2.34400 | ||||||||
\(321\) | 0.943279 | 0.0526487 | ||||||||
\(322\) | −14.1277 | −0.787304 | ||||||||
\(323\) | −0.755941 | −0.0420617 | ||||||||
\(324\) | 4.92870 | 0.273816 | ||||||||
\(325\) | 6.63280 | 0.367922 | ||||||||
\(326\) | −22.0630 | −1.22196 | ||||||||
\(327\) | −6.46672 | −0.357610 | ||||||||
\(328\) | −48.4201 | −2.67355 | ||||||||
\(329\) | −13.0088 | −0.717198 | ||||||||
\(330\) | −40.1950 | −2.21266 | ||||||||
\(331\) | 15.7570 | 0.866084 | 0.433042 | − | 0.901374i | \(-0.357440\pi\) | ||||
0.433042 | + | 0.901374i | \(0.357440\pi\) | |||||||
\(332\) | −14.5700 | −0.799632 | ||||||||
\(333\) | 9.69422 | 0.531240 | ||||||||
\(334\) | −11.5023 | −0.629379 | ||||||||
\(335\) | −43.6887 | −2.38697 | ||||||||
\(336\) | 10.4346 | 0.569257 | ||||||||
\(337\) | −14.9115 | −0.812282 | −0.406141 | − | 0.913810i | \(-0.633126\pi\) | ||||
−0.406141 | + | 0.913810i | \(0.633126\pi\) | |||||||
\(338\) | 33.0491 | 1.79763 | ||||||||
\(339\) | −16.1795 | −0.878751 | ||||||||
\(340\) | −81.6236 | −4.42666 | ||||||||
\(341\) | 30.7787 | 1.66676 | ||||||||
\(342\) | −0.464545 | −0.0251197 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −26.0120 | −1.40247 | ||||||||
\(345\) | 20.7512 | 1.11721 | ||||||||
\(346\) | 61.2577 | 3.29323 | ||||||||
\(347\) | −1.76998 | −0.0950177 | −0.0475088 | − | 0.998871i | \(-0.515128\pi\) | ||||
−0.0475088 | + | 0.998871i | \(0.515128\pi\) | |||||||
\(348\) | 13.4399 | 0.720455 | ||||||||
\(349\) | 6.92509 | 0.370691 | 0.185346 | − | 0.982673i | \(-0.440660\pi\) | ||||
0.185346 | + | 0.982673i | \(0.440660\pi\) | |||||||
\(350\) | 26.1868 | 1.39974 | ||||||||
\(351\) | −0.666715 | −0.0355866 | ||||||||
\(352\) | 47.5859 | 2.53634 | ||||||||
\(353\) | 2.25271 | 0.119900 | 0.0599498 | − | 0.998201i | \(-0.480906\pi\) | ||||
0.0599498 | + | 0.998201i | \(0.480906\pi\) | |||||||
\(354\) | −11.1019 | −0.590061 | ||||||||
\(355\) | −13.6960 | −0.726908 | ||||||||
\(356\) | 23.0659 | 1.22249 | ||||||||
\(357\) | −4.28337 | −0.226700 | ||||||||
\(358\) | −32.9782 | −1.74295 | ||||||||
\(359\) | 4.90316 | 0.258779 | 0.129389 | − | 0.991594i | \(-0.458698\pi\) | ||||
0.129389 | + | 0.991594i | \(0.458698\pi\) | |||||||
\(360\) | −29.8056 | −1.57090 | ||||||||
\(361\) | −18.9689 | −0.998361 | ||||||||
\(362\) | −46.1241 | −2.42423 | ||||||||
\(363\) | −4.59894 | −0.241382 | ||||||||
\(364\) | −3.28603 | −0.172235 | ||||||||
\(365\) | 6.45790 | 0.338022 | ||||||||
\(366\) | −17.8126 | −0.931081 | ||||||||
\(367\) | 26.5141 | 1.38403 | 0.692013 | − | 0.721885i | \(-0.256724\pi\) | ||||
0.692013 | + | 0.721885i | \(0.256724\pi\) | |||||||
\(368\) | −56.0045 | −2.91943 | ||||||||
\(369\) | 6.28096 | 0.326973 | ||||||||
\(370\) | −98.6591 | −5.12904 | ||||||||
\(371\) | 5.03862 | 0.261592 | ||||||||
\(372\) | 38.4092 | 1.99142 | ||||||||
\(373\) | 1.63684 | 0.0847525 | 0.0423762 | − | 0.999102i | \(-0.486507\pi\) | ||||
0.0423762 | + | 0.999102i | \(0.486507\pi\) | |||||||
\(374\) | −44.5306 | −2.30262 | ||||||||
\(375\) | −19.1325 | −0.987997 | ||||||||
\(376\) | −100.285 | −5.17182 | ||||||||
\(377\) | −1.81805 | −0.0936341 | ||||||||
\(378\) | −2.63224 | −0.135388 | ||||||||
\(379\) | −11.5065 | −0.591050 | −0.295525 | − | 0.955335i | \(-0.595495\pi\) | ||||
−0.295525 | + | 0.955335i | \(0.595495\pi\) | |||||||
\(380\) | 3.36305 | 0.172521 | ||||||||
\(381\) | −14.6315 | −0.749593 | ||||||||
\(382\) | 15.9373 | 0.815422 | ||||||||
\(383\) | 1.00000 | 0.0510976 | ||||||||
\(384\) | 4.45008 | 0.227092 | ||||||||
\(385\) | 15.2703 | 0.778244 | ||||||||
\(386\) | −6.04017 | −0.307437 | ||||||||
\(387\) | 3.37422 | 0.171521 | ||||||||
\(388\) | 52.7143 | 2.67616 | ||||||||
\(389\) | −1.38743 | −0.0703455 | −0.0351727 | − | 0.999381i | \(-0.511198\pi\) | ||||
−0.0351727 | + | 0.999381i | \(0.511198\pi\) | |||||||
\(390\) | 6.78523 | 0.343583 | ||||||||
\(391\) | 22.9895 | 1.16263 | ||||||||
\(392\) | −7.70903 | −0.389365 | ||||||||
\(393\) | 14.1269 | 0.712606 | ||||||||
\(394\) | −21.5218 | −1.08425 | ||||||||
\(395\) | −19.3383 | −0.973017 | ||||||||
\(396\) | −19.4661 | −0.978210 | ||||||||
\(397\) | 14.3893 | 0.722180 | 0.361090 | − | 0.932531i | \(-0.382405\pi\) | ||||
0.361090 | + | 0.932531i | \(0.382405\pi\) | |||||||
\(398\) | −20.2078 | −1.01292 | ||||||||
\(399\) | 0.176483 | 0.00883519 | ||||||||
\(400\) | 103.809 | 5.19045 | ||||||||
\(401\) | 27.9566 | 1.39609 | 0.698044 | − | 0.716055i | \(-0.254054\pi\) | ||||
0.698044 | + | 0.716055i | \(0.254054\pi\) | |||||||
\(402\) | −29.7438 | −1.48348 | ||||||||
\(403\) | −5.19569 | −0.258816 | ||||||||
\(404\) | −83.5112 | −4.15484 | ||||||||
\(405\) | 3.86633 | 0.192119 | ||||||||
\(406\) | −7.17778 | −0.356227 | ||||||||
\(407\) | −38.2878 | −1.89786 | ||||||||
\(408\) | −33.0206 | −1.63476 | ||||||||
\(409\) | 5.04556 | 0.249487 | 0.124744 | − | 0.992189i | \(-0.460189\pi\) | ||||
0.124744 | + | 0.992189i | \(0.460189\pi\) | |||||||
\(410\) | −63.9220 | −3.15688 | ||||||||
\(411\) | 8.36703 | 0.412715 | ||||||||
\(412\) | 19.1232 | 0.942134 | ||||||||
\(413\) | 4.21767 | 0.207538 | ||||||||
\(414\) | 14.1277 | 0.694337 | ||||||||
\(415\) | −11.4295 | −0.561050 | ||||||||
\(416\) | −8.03287 | −0.393844 | ||||||||
\(417\) | −19.6508 | −0.962304 | ||||||||
\(418\) | 1.83474 | 0.0897403 | ||||||||
\(419\) | −27.8679 | −1.36144 | −0.680719 | − | 0.732544i | \(-0.738333\pi\) | ||||
−0.680719 | + | 0.732544i | \(0.738333\pi\) | |||||||
\(420\) | 19.0560 | 0.929835 | ||||||||
\(421\) | 12.6543 | 0.616732 | 0.308366 | − | 0.951268i | \(-0.400218\pi\) | ||||
0.308366 | + | 0.951268i | \(0.400218\pi\) | |||||||
\(422\) | −69.2466 | −3.37087 | ||||||||
\(423\) | 13.0088 | 0.632509 | ||||||||
\(424\) | 38.8429 | 1.88638 | ||||||||
\(425\) | −42.6130 | −2.06704 | ||||||||
\(426\) | −9.32440 | −0.451769 | ||||||||
\(427\) | 6.76710 | 0.327483 | ||||||||
\(428\) | −4.64914 | −0.224724 | ||||||||
\(429\) | 2.63322 | 0.127133 | ||||||||
\(430\) | −34.3398 | −1.65601 | ||||||||
\(431\) | 32.0464 | 1.54362 | 0.771811 | − | 0.635853i | \(-0.219351\pi\) | ||||
0.771811 | + | 0.635853i | \(0.219351\pi\) | |||||||
\(432\) | −10.4346 | −0.502037 | ||||||||
\(433\) | 34.9609 | 1.68011 | 0.840056 | − | 0.542500i | \(-0.182522\pi\) | ||||
0.840056 | + | 0.542500i | \(0.182522\pi\) | |||||||
\(434\) | −20.5130 | −0.984655 | ||||||||
\(435\) | 10.5430 | 0.505497 | ||||||||
\(436\) | 31.8725 | 1.52641 | ||||||||
\(437\) | −0.947212 | −0.0453113 | ||||||||
\(438\) | 4.39662 | 0.210079 | ||||||||
\(439\) | 6.88854 | 0.328772 | 0.164386 | − | 0.986396i | \(-0.447436\pi\) | ||||
0.164386 | + | 0.986396i | \(0.447436\pi\) | |||||||
\(440\) | 117.719 | 5.61203 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 7.51711 | 0.357553 | ||||||||
\(443\) | −30.9414 | −1.47007 | −0.735035 | − | 0.678029i | \(-0.762834\pi\) | ||||
−0.735035 | + | 0.678029i | \(0.762834\pi\) | |||||||
\(444\) | −47.7799 | −2.26753 | ||||||||
\(445\) | 18.0941 | 0.857742 | ||||||||
\(446\) | −14.6186 | −0.692211 | ||||||||
\(447\) | −17.7764 | −0.840794 | ||||||||
\(448\) | −10.8451 | −0.512384 | ||||||||
\(449\) | 20.2572 | 0.955995 | 0.477997 | − | 0.878361i | \(-0.341363\pi\) | ||||
0.477997 | + | 0.878361i | \(0.341363\pi\) | |||||||
\(450\) | −26.1868 | −1.23446 | ||||||||
\(451\) | −24.8069 | −1.16811 | ||||||||
\(452\) | 79.7439 | 3.75084 | ||||||||
\(453\) | 16.9037 | 0.794203 | ||||||||
\(454\) | −31.0876 | −1.45902 | ||||||||
\(455\) | −2.57774 | −0.120846 | ||||||||
\(456\) | 1.36051 | 0.0637118 | ||||||||
\(457\) | 17.8905 | 0.836880 | 0.418440 | − | 0.908244i | \(-0.362577\pi\) | ||||
0.418440 | + | 0.908244i | \(0.362577\pi\) | |||||||
\(458\) | −28.5563 | −1.33435 | ||||||||
\(459\) | 4.28337 | 0.199930 | ||||||||
\(460\) | −102.276 | −4.76866 | ||||||||
\(461\) | 11.9886 | 0.558364 | 0.279182 | − | 0.960238i | \(-0.409937\pi\) | ||||
0.279182 | + | 0.960238i | \(0.409937\pi\) | |||||||
\(462\) | 10.3962 | 0.483674 | ||||||||
\(463\) | 21.1581 | 0.983299 | 0.491649 | − | 0.870793i | \(-0.336394\pi\) | ||||
0.491649 | + | 0.870793i | \(0.336394\pi\) | |||||||
\(464\) | −28.4539 | −1.32094 | ||||||||
\(465\) | 30.1302 | 1.39725 | ||||||||
\(466\) | −61.9055 | −2.86772 | ||||||||
\(467\) | 29.7910 | 1.37856 | 0.689281 | − | 0.724494i | \(-0.257926\pi\) | ||||
0.689281 | + | 0.724494i | \(0.257926\pi\) | |||||||
\(468\) | 3.28603 | 0.151897 | ||||||||
\(469\) | 11.2998 | 0.521775 | ||||||||
\(470\) | −132.392 | −6.10678 | ||||||||
\(471\) | −22.6283 | −1.04266 | ||||||||
\(472\) | 32.5142 | 1.49659 | ||||||||
\(473\) | −13.3267 | −0.612761 | ||||||||
\(474\) | −13.1658 | −0.604723 | ||||||||
\(475\) | 1.75574 | 0.0805588 | ||||||||
\(476\) | 21.1114 | 0.967640 | ||||||||
\(477\) | −5.03862 | −0.230702 | ||||||||
\(478\) | 69.3217 | 3.17070 | ||||||||
\(479\) | 20.4078 | 0.932455 | 0.466228 | − | 0.884665i | \(-0.345613\pi\) | ||||
0.466228 | + | 0.884665i | \(0.345613\pi\) | |||||||
\(480\) | 46.5832 | 2.12622 | ||||||||
\(481\) | 6.46328 | 0.294700 | ||||||||
\(482\) | 21.1502 | 0.963363 | ||||||||
\(483\) | −5.36716 | −0.244214 | ||||||||
\(484\) | 22.6668 | 1.03031 | ||||||||
\(485\) | 41.3519 | 1.87769 | ||||||||
\(486\) | 2.63224 | 0.119401 | ||||||||
\(487\) | 3.69399 | 0.167391 | 0.0836954 | − | 0.996491i | \(-0.473328\pi\) | ||||
0.0836954 | + | 0.996491i | \(0.473328\pi\) | |||||||
\(488\) | 52.1678 | 2.36152 | ||||||||
\(489\) | −8.38183 | −0.379040 | ||||||||
\(490\) | −10.1771 | −0.459755 | ||||||||
\(491\) | −14.7016 | −0.663472 | −0.331736 | − | 0.943372i | \(-0.607634\pi\) | ||||
−0.331736 | + | 0.943372i | \(0.607634\pi\) | |||||||
\(492\) | −30.9569 | −1.39565 | ||||||||
\(493\) | 11.6802 | 0.526049 | ||||||||
\(494\) | −0.309719 | −0.0139349 | ||||||||
\(495\) | −15.2703 | −0.686347 | ||||||||
\(496\) | −81.3169 | −3.65124 | ||||||||
\(497\) | 3.54238 | 0.158897 | ||||||||
\(498\) | −7.78131 | −0.348689 | ||||||||
\(499\) | 22.7557 | 1.01869 | 0.509343 | − | 0.860564i | \(-0.329889\pi\) | ||||
0.509343 | + | 0.860564i | \(0.329889\pi\) | |||||||
\(500\) | 94.2982 | 4.21714 | ||||||||
\(501\) | −4.36978 | −0.195227 | ||||||||
\(502\) | −55.1713 | −2.46242 | ||||||||
\(503\) | −40.9223 | −1.82463 | −0.912317 | − | 0.409484i | \(-0.865709\pi\) | ||||
−0.912317 | + | 0.409484i | \(0.865709\pi\) | |||||||
\(504\) | 7.70903 | 0.343388 | ||||||||
\(505\) | −65.5106 | −2.91518 | ||||||||
\(506\) | −55.7979 | −2.48052 | ||||||||
\(507\) | 12.5555 | 0.557609 | ||||||||
\(508\) | 72.1140 | 3.19954 | ||||||||
\(509\) | 20.4399 | 0.905984 | 0.452992 | − | 0.891515i | \(-0.350357\pi\) | ||||
0.452992 | + | 0.891515i | \(0.350357\pi\) | |||||||
\(510\) | −43.5923 | −1.93030 | ||||||||
\(511\) | −1.67029 | −0.0738895 | ||||||||
\(512\) | 35.1608 | 1.55390 | ||||||||
\(513\) | −0.176483 | −0.00779191 | ||||||||
\(514\) | 1.03751 | 0.0457625 | ||||||||
\(515\) | 15.0013 | 0.661035 | ||||||||
\(516\) | −16.6305 | −0.732118 | ||||||||
\(517\) | −51.3789 | −2.25964 | ||||||||
\(518\) | 25.5175 | 1.12118 | ||||||||
\(519\) | 23.2721 | 1.02153 | ||||||||
\(520\) | −19.8719 | −0.871439 | ||||||||
\(521\) | −30.3007 | −1.32750 | −0.663750 | − | 0.747955i | \(-0.731036\pi\) | ||||
−0.663750 | + | 0.747955i | \(0.731036\pi\) | |||||||
\(522\) | 7.17778 | 0.314163 | ||||||||
\(523\) | 2.41888 | 0.105770 | 0.0528851 | − | 0.998601i | \(-0.483158\pi\) | ||||
0.0528851 | + | 0.998601i | \(0.483158\pi\) | |||||||
\(524\) | −69.6270 | −3.04167 | ||||||||
\(525\) | 9.94849 | 0.434188 | ||||||||
\(526\) | −28.9511 | −1.26233 | ||||||||
\(527\) | 33.3802 | 1.45406 | ||||||||
\(528\) | 41.2122 | 1.79353 | ||||||||
\(529\) | 5.80645 | 0.252454 | ||||||||
\(530\) | 51.2786 | 2.22740 | ||||||||
\(531\) | −4.21767 | −0.183031 | ||||||||
\(532\) | −0.869830 | −0.0377119 | ||||||||
\(533\) | 4.18761 | 0.181385 | ||||||||
\(534\) | 12.3187 | 0.533081 | ||||||||
\(535\) | −3.64703 | −0.157675 | ||||||||
\(536\) | 87.1104 | 3.76260 | ||||||||
\(537\) | −12.5286 | −0.540648 | ||||||||
\(538\) | −21.7915 | −0.939498 | ||||||||
\(539\) | −3.94955 | −0.170119 | ||||||||
\(540\) | −19.0560 | −0.820038 | ||||||||
\(541\) | −6.44495 | −0.277090 | −0.138545 | − | 0.990356i | \(-0.544243\pi\) | ||||
−0.138545 | + | 0.990356i | \(0.544243\pi\) | |||||||
\(542\) | 12.3913 | 0.532253 | ||||||||
\(543\) | −17.5228 | −0.751973 | ||||||||
\(544\) | 51.6079 | 2.21267 | ||||||||
\(545\) | 25.0024 | 1.07099 | ||||||||
\(546\) | −1.75495 | −0.0751051 | ||||||||
\(547\) | −20.2807 | −0.867138 | −0.433569 | − | 0.901120i | \(-0.642746\pi\) | ||||
−0.433569 | + | 0.901120i | \(0.642746\pi\) | |||||||
\(548\) | −41.2385 | −1.76162 | ||||||||
\(549\) | −6.76710 | −0.288813 | ||||||||
\(550\) | 103.426 | 4.41011 | ||||||||
\(551\) | −0.481246 | −0.0205018 | ||||||||
\(552\) | −41.3756 | −1.76106 | ||||||||
\(553\) | 5.00173 | 0.212695 | ||||||||
\(554\) | −73.6051 | −3.12718 | ||||||||
\(555\) | −37.4810 | −1.59098 | ||||||||
\(556\) | 96.8529 | 4.10748 | ||||||||
\(557\) | 2.40730 | 0.102000 | 0.0510002 | − | 0.998699i | \(-0.483759\pi\) | ||||
0.0510002 | + | 0.998699i | \(0.483759\pi\) | |||||||
\(558\) | 20.5130 | 0.868384 | ||||||||
\(559\) | 2.24964 | 0.0951498 | ||||||||
\(560\) | −40.3438 | −1.70484 | ||||||||
\(561\) | −16.9174 | −0.714252 | ||||||||
\(562\) | 66.5415 | 2.80688 | ||||||||
\(563\) | −9.70373 | −0.408963 | −0.204482 | − | 0.978870i | \(-0.565551\pi\) | ||||
−0.204482 | + | 0.978870i | \(0.565551\pi\) | |||||||
\(564\) | −64.1164 | −2.69979 | ||||||||
\(565\) | 62.5553 | 2.63172 | ||||||||
\(566\) | 48.1204 | 2.02265 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 27.3083 | 1.14583 | ||||||||
\(569\) | 21.6908 | 0.909326 | 0.454663 | − | 0.890663i | \(-0.349760\pi\) | ||||
0.454663 | + | 0.890663i | \(0.349760\pi\) | |||||||
\(570\) | 1.79608 | 0.0752297 | ||||||||
\(571\) | −17.6964 | −0.740571 | −0.370286 | − | 0.928918i | \(-0.620740\pi\) | ||||
−0.370286 | + | 0.928918i | \(0.620740\pi\) | |||||||
\(572\) | −12.9784 | −0.542652 | ||||||||
\(573\) | 6.05464 | 0.252936 | ||||||||
\(574\) | 16.5330 | 0.690074 | ||||||||
\(575\) | −53.3952 | −2.22673 | ||||||||
\(576\) | 10.8451 | 0.451880 | ||||||||
\(577\) | −9.89506 | −0.411937 | −0.205968 | − | 0.978559i | \(-0.566034\pi\) | ||||
−0.205968 | + | 0.978559i | \(0.566034\pi\) | |||||||
\(578\) | −3.54625 | −0.147505 | ||||||||
\(579\) | −2.29469 | −0.0953640 | ||||||||
\(580\) | −51.9631 | −2.15765 | ||||||||
\(581\) | 2.95616 | 0.122642 | ||||||||
\(582\) | 28.1528 | 1.16697 | ||||||||
\(583\) | 19.9003 | 0.824185 | ||||||||
\(584\) | −12.8764 | −0.532827 | ||||||||
\(585\) | 2.57774 | 0.106576 | ||||||||
\(586\) | 74.7668 | 3.08859 | ||||||||
\(587\) | −13.5376 | −0.558758 | −0.279379 | − | 0.960181i | \(-0.590129\pi\) | ||||
−0.279379 | + | 0.960181i | \(0.590129\pi\) | |||||||
\(588\) | −4.92870 | −0.203256 | ||||||||
\(589\) | −1.37533 | −0.0566693 | ||||||||
\(590\) | 42.9237 | 1.76714 | ||||||||
\(591\) | −8.17623 | −0.336325 | ||||||||
\(592\) | 101.156 | 4.15748 | ||||||||
\(593\) | 21.2673 | 0.873342 | 0.436671 | − | 0.899621i | \(-0.356157\pi\) | ||||
0.436671 | + | 0.899621i | \(0.356157\pi\) | |||||||
\(594\) | −10.3962 | −0.426560 | ||||||||
\(595\) | 16.5609 | 0.678931 | ||||||||
\(596\) | 87.6144 | 3.58882 | ||||||||
\(597\) | −7.67703 | −0.314200 | ||||||||
\(598\) | 9.41913 | 0.385177 | ||||||||
\(599\) | 14.0614 | 0.574534 | 0.287267 | − | 0.957851i | \(-0.407253\pi\) | ||||
0.287267 | + | 0.957851i | \(0.407253\pi\) | |||||||
\(600\) | 76.6932 | 3.13099 | ||||||||
\(601\) | −6.04380 | −0.246532 | −0.123266 | − | 0.992374i | \(-0.539337\pi\) | ||||
−0.123266 | + | 0.992374i | \(0.539337\pi\) | |||||||
\(602\) | 8.88177 | 0.361994 | ||||||||
\(603\) | −11.2998 | −0.460163 | ||||||||
\(604\) | −83.3130 | −3.38996 | ||||||||
\(605\) | 17.7810 | 0.722901 | ||||||||
\(606\) | −44.6004 | −1.81177 | ||||||||
\(607\) | −13.8956 | −0.564007 | −0.282003 | − | 0.959413i | \(-0.590999\pi\) | ||||
−0.282003 | + | 0.959413i | \(0.590999\pi\) | |||||||
\(608\) | −2.12634 | −0.0862346 | ||||||||
\(609\) | −2.72687 | −0.110498 | ||||||||
\(610\) | 68.8695 | 2.78844 | ||||||||
\(611\) | 8.67316 | 0.350878 | ||||||||
\(612\) | −21.1114 | −0.853378 | ||||||||
\(613\) | −4.66681 | −0.188491 | −0.0942454 | − | 0.995549i | \(-0.530044\pi\) | ||||
−0.0942454 | + | 0.995549i | \(0.530044\pi\) | |||||||
\(614\) | −73.8817 | −2.98162 | ||||||||
\(615\) | −24.2842 | −0.979235 | ||||||||
\(616\) | −30.4472 | −1.22675 | ||||||||
\(617\) | 21.1660 | 0.852110 | 0.426055 | − | 0.904697i | \(-0.359903\pi\) | ||||
0.426055 | + | 0.904697i | \(0.359903\pi\) | |||||||
\(618\) | 10.2130 | 0.410829 | ||||||||
\(619\) | 10.3794 | 0.417183 | 0.208591 | − | 0.978003i | \(-0.433112\pi\) | ||||
0.208591 | + | 0.978003i | \(0.433112\pi\) | |||||||
\(620\) | −148.503 | −5.96401 | ||||||||
\(621\) | 5.36716 | 0.215377 | ||||||||
\(622\) | 50.8334 | 2.03823 | ||||||||
\(623\) | −4.67991 | −0.187497 | ||||||||
\(624\) | −6.95693 | −0.278500 | ||||||||
\(625\) | 24.2300 | 0.969200 | ||||||||
\(626\) | 59.9985 | 2.39802 | ||||||||
\(627\) | 0.697028 | 0.0278366 | ||||||||
\(628\) | 111.528 | 4.45045 | ||||||||
\(629\) | −41.5239 | −1.65567 | ||||||||
\(630\) | 10.1771 | 0.405466 | ||||||||
\(631\) | 38.9154 | 1.54920 | 0.774598 | − | 0.632454i | \(-0.217952\pi\) | ||||
0.774598 | + | 0.632454i | \(0.217952\pi\) | |||||||
\(632\) | 38.5585 | 1.53377 | ||||||||
\(633\) | −26.3071 | −1.04561 | ||||||||
\(634\) | −8.98350 | −0.356780 | ||||||||
\(635\) | 56.5700 | 2.24491 | ||||||||
\(636\) | 24.8338 | 0.984725 | ||||||||
\(637\) | 0.666715 | 0.0264162 | ||||||||
\(638\) | −28.3490 | −1.12235 | ||||||||
\(639\) | −3.54238 | −0.140134 | ||||||||
\(640\) | −17.2055 | −0.680106 | ||||||||
\(641\) | 29.9437 | 1.18271 | 0.591353 | − | 0.806413i | \(-0.298594\pi\) | ||||
0.591353 | + | 0.806413i | \(0.298594\pi\) | |||||||
\(642\) | −2.48294 | −0.0979938 | ||||||||
\(643\) | 18.9275 | 0.746427 | 0.373214 | − | 0.927745i | \(-0.378256\pi\) | ||||
0.373214 | + | 0.927745i | \(0.378256\pi\) | |||||||
\(644\) | 26.4531 | 1.04240 | ||||||||
\(645\) | −13.0459 | −0.513680 | ||||||||
\(646\) | 1.98982 | 0.0782884 | ||||||||
\(647\) | −35.7508 | −1.40551 | −0.702755 | − | 0.711432i | \(-0.748047\pi\) | ||||
−0.702755 | + | 0.711432i | \(0.748047\pi\) | |||||||
\(648\) | −7.70903 | −0.302839 | ||||||||
\(649\) | 16.6579 | 0.653880 | ||||||||
\(650\) | −17.4591 | −0.684804 | ||||||||
\(651\) | −7.79297 | −0.305431 | ||||||||
\(652\) | 41.3115 | 1.61788 | ||||||||
\(653\) | 1.81891 | 0.0711794 | 0.0355897 | − | 0.999366i | \(-0.488669\pi\) | ||||
0.0355897 | + | 0.999366i | \(0.488669\pi\) | |||||||
\(654\) | 17.0220 | 0.665611 | ||||||||
\(655\) | −54.6191 | −2.13414 | ||||||||
\(656\) | 65.5395 | 2.55889 | ||||||||
\(657\) | 1.67029 | 0.0651644 | ||||||||
\(658\) | 34.2423 | 1.33490 | ||||||||
\(659\) | 10.2583 | 0.399606 | 0.199803 | − | 0.979836i | \(-0.435970\pi\) | ||||
0.199803 | + | 0.979836i | \(0.435970\pi\) | |||||||
\(660\) | 75.2624 | 2.92959 | ||||||||
\(661\) | 0.799759 | 0.0311070 | 0.0155535 | − | 0.999879i | \(-0.495049\pi\) | ||||
0.0155535 | + | 0.999879i | \(0.495049\pi\) | |||||||
\(662\) | −41.4763 | −1.61202 | ||||||||
\(663\) | 2.85578 | 0.110909 | ||||||||
\(664\) | 22.7891 | 0.884389 | ||||||||
\(665\) | −0.682340 | −0.0264600 | ||||||||
\(666\) | −25.5175 | −0.988784 | ||||||||
\(667\) | 14.6356 | 0.566691 | ||||||||
\(668\) | 21.5373 | 0.833303 | ||||||||
\(669\) | −5.55368 | −0.214717 | ||||||||
\(670\) | 114.999 | 4.44280 | ||||||||
\(671\) | 26.7270 | 1.03178 | ||||||||
\(672\) | −12.0484 | −0.464779 | ||||||||
\(673\) | 20.6600 | 0.796384 | 0.398192 | − | 0.917302i | \(-0.369638\pi\) | ||||
0.398192 | + | 0.917302i | \(0.369638\pi\) | |||||||
\(674\) | 39.2507 | 1.51188 | ||||||||
\(675\) | −9.94849 | −0.382918 | ||||||||
\(676\) | −61.8822 | −2.38008 | ||||||||
\(677\) | −11.0619 | −0.425145 | −0.212573 | − | 0.977145i | \(-0.568184\pi\) | ||||
−0.212573 | + | 0.977145i | \(0.568184\pi\) | |||||||
\(678\) | 42.5884 | 1.63560 | ||||||||
\(679\) | −10.6954 | −0.410451 | ||||||||
\(680\) | 127.669 | 4.89587 | ||||||||
\(681\) | −11.8103 | −0.452573 | ||||||||
\(682\) | −81.0171 | −3.10230 | ||||||||
\(683\) | 4.15426 | 0.158958 | 0.0794791 | − | 0.996837i | \(-0.474674\pi\) | ||||
0.0794791 | + | 0.996837i | \(0.474674\pi\) | |||||||
\(684\) | 0.869830 | 0.0332588 | ||||||||
\(685\) | −32.3497 | −1.23602 | ||||||||
\(686\) | 2.63224 | 0.100499 | ||||||||
\(687\) | −10.8487 | −0.413902 | ||||||||
\(688\) | 35.2088 | 1.34232 | ||||||||
\(689\) | −3.35932 | −0.127980 | ||||||||
\(690\) | −54.6222 | −2.07943 | ||||||||
\(691\) | 25.5928 | 0.973597 | 0.486799 | − | 0.873514i | \(-0.338165\pi\) | ||||
0.486799 | + | 0.873514i | \(0.338165\pi\) | |||||||
\(692\) | −114.701 | −4.36028 | ||||||||
\(693\) | 3.94955 | 0.150031 | ||||||||
\(694\) | 4.65902 | 0.176854 | ||||||||
\(695\) | 75.9765 | 2.88195 | ||||||||
\(696\) | −21.0215 | −0.796820 | ||||||||
\(697\) | −26.9036 | −1.01905 | ||||||||
\(698\) | −18.2285 | −0.689959 | ||||||||
\(699\) | −23.5182 | −0.889539 | ||||||||
\(700\) | −49.0331 | −1.85328 | ||||||||
\(701\) | −13.2617 | −0.500886 | −0.250443 | − | 0.968131i | \(-0.580576\pi\) | ||||
−0.250443 | + | 0.968131i | \(0.580576\pi\) | |||||||
\(702\) | 1.75495 | 0.0662365 | ||||||||
\(703\) | 1.71086 | 0.0645264 | ||||||||
\(704\) | −42.8333 | −1.61434 | ||||||||
\(705\) | −50.2963 | −1.89427 | ||||||||
\(706\) | −5.92967 | −0.223166 | ||||||||
\(707\) | 16.9439 | 0.637240 | ||||||||
\(708\) | 20.7876 | 0.781247 | ||||||||
\(709\) | −8.39250 | −0.315187 | −0.157593 | − | 0.987504i | \(-0.550374\pi\) | ||||
−0.157593 | + | 0.987504i | \(0.550374\pi\) | |||||||
\(710\) | 36.0512 | 1.35298 | ||||||||
\(711\) | −5.00173 | −0.187580 | ||||||||
\(712\) | −36.0776 | −1.35207 | ||||||||
\(713\) | 41.8262 | 1.56640 | ||||||||
\(714\) | 11.2749 | 0.421951 | ||||||||
\(715\) | −10.1809 | −0.380744 | ||||||||
\(716\) | 61.7495 | 2.30769 | ||||||||
\(717\) | 26.3356 | 0.983522 | ||||||||
\(718\) | −12.9063 | −0.481659 | ||||||||
\(719\) | 3.55060 | 0.132415 | 0.0662075 | − | 0.997806i | \(-0.478910\pi\) | ||||
0.0662075 | + | 0.997806i | \(0.478910\pi\) | |||||||
\(720\) | 40.3438 | 1.50352 | ||||||||
\(721\) | −3.87998 | −0.144498 | ||||||||
\(722\) | 49.9306 | 1.85822 | ||||||||
\(723\) | 8.03504 | 0.298826 | ||||||||
\(724\) | 86.3643 | 3.20970 | ||||||||
\(725\) | −27.1283 | −1.00752 | ||||||||
\(726\) | 12.1055 | 0.449278 | ||||||||
\(727\) | 43.6733 | 1.61975 | 0.809877 | − | 0.586599i | \(-0.199534\pi\) | ||||
0.809877 | + | 0.586599i | \(0.199534\pi\) | |||||||
\(728\) | 5.13973 | 0.190491 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −16.9988 | −0.629152 | ||||||||
\(731\) | −14.4530 | −0.534565 | ||||||||
\(732\) | 33.3529 | 1.23276 | ||||||||
\(733\) | −31.9478 | −1.18002 | −0.590010 | − | 0.807396i | \(-0.700876\pi\) | ||||
−0.590010 | + | 0.807396i | \(0.700876\pi\) | |||||||
\(734\) | −69.7916 | −2.57606 | ||||||||
\(735\) | −3.86633 | −0.142612 | ||||||||
\(736\) | 64.6660 | 2.38362 | ||||||||
\(737\) | 44.6290 | 1.64393 | ||||||||
\(738\) | −16.5330 | −0.608588 | ||||||||
\(739\) | 51.6325 | 1.89933 | 0.949666 | − | 0.313265i | \(-0.101423\pi\) | ||||
0.949666 | + | 0.313265i | \(0.101423\pi\) | |||||||
\(740\) | 184.733 | 6.79090 | ||||||||
\(741\) | −0.117664 | −0.00432248 | ||||||||
\(742\) | −13.2629 | −0.486895 | ||||||||
\(743\) | 34.2545 | 1.25667 | 0.628337 | − | 0.777941i | \(-0.283736\pi\) | ||||
0.628337 | + | 0.777941i | \(0.283736\pi\) | |||||||
\(744\) | −60.0763 | −2.20250 | ||||||||
\(745\) | 68.7293 | 2.51805 | ||||||||
\(746\) | −4.30856 | −0.157748 | ||||||||
\(747\) | −2.95616 | −0.108160 | ||||||||
\(748\) | 83.3806 | 3.04870 | ||||||||
\(749\) | 0.943279 | 0.0344667 | ||||||||
\(750\) | 50.3613 | 1.83894 | ||||||||
\(751\) | −34.8550 | −1.27188 | −0.635938 | − | 0.771740i | \(-0.719387\pi\) | ||||
−0.635938 | + | 0.771740i | \(0.719387\pi\) | |||||||
\(752\) | 135.742 | 4.95001 | ||||||||
\(753\) | −20.9598 | −0.763818 | ||||||||
\(754\) | 4.78553 | 0.174279 | ||||||||
\(755\) | −65.3551 | −2.37851 | ||||||||
\(756\) | 4.92870 | 0.179255 | ||||||||
\(757\) | 9.08748 | 0.330290 | 0.165145 | − | 0.986269i | \(-0.447191\pi\) | ||||
0.165145 | + | 0.986269i | \(0.447191\pi\) | |||||||
\(758\) | 30.2879 | 1.10011 | ||||||||
\(759\) | −21.1979 | −0.769434 | ||||||||
\(760\) | −5.26018 | −0.190807 | ||||||||
\(761\) | 33.6896 | 1.22125 | 0.610624 | − | 0.791921i | \(-0.290919\pi\) | ||||
0.610624 | + | 0.791921i | \(0.290919\pi\) | |||||||
\(762\) | 38.5135 | 1.39520 | ||||||||
\(763\) | −6.46672 | −0.234111 | ||||||||
\(764\) | −29.8415 | −1.07963 | ||||||||
\(765\) | −16.5609 | −0.598761 | ||||||||
\(766\) | −2.63224 | −0.0951068 | ||||||||
\(767\) | −2.81199 | −0.101535 | ||||||||
\(768\) | 9.97654 | 0.359997 | ||||||||
\(769\) | −29.3529 | −1.05849 | −0.529246 | − | 0.848469i | \(-0.677525\pi\) | ||||
−0.529246 | + | 0.848469i | \(0.677525\pi\) | |||||||
\(770\) | −40.1950 | −1.44853 | ||||||||
\(771\) | 0.394153 | 0.0141951 | ||||||||
\(772\) | 11.3098 | 0.407049 | ||||||||
\(773\) | 37.3234 | 1.34243 | 0.671214 | − | 0.741264i | \(-0.265773\pi\) | ||||
0.671214 | + | 0.741264i | \(0.265773\pi\) | |||||||
\(774\) | −8.88177 | −0.319249 | ||||||||
\(775\) | −77.5283 | −2.78490 | ||||||||
\(776\) | −82.4511 | −2.95982 | ||||||||
\(777\) | 9.69422 | 0.347778 | ||||||||
\(778\) | 3.65205 | 0.130932 | ||||||||
\(779\) | 1.10848 | 0.0397154 | ||||||||
\(780\) | −12.7049 | −0.454908 | ||||||||
\(781\) | 13.9908 | 0.500630 | ||||||||
\(782\) | −60.5140 | −2.16398 | ||||||||
\(783\) | 2.72687 | 0.0974504 | ||||||||
\(784\) | 10.4346 | 0.372666 | ||||||||
\(785\) | 87.4885 | 3.12260 | ||||||||
\(786\) | −37.1853 | −1.32636 | ||||||||
\(787\) | −5.71479 | −0.203710 | −0.101855 | − | 0.994799i | \(-0.532478\pi\) | ||||
−0.101855 | + | 0.994799i | \(0.532478\pi\) | |||||||
\(788\) | 40.2981 | 1.43556 | ||||||||
\(789\) | −10.9986 | −0.391562 | ||||||||
\(790\) | 50.9031 | 1.81105 | ||||||||
\(791\) | −16.1795 | −0.575277 | ||||||||
\(792\) | 30.4472 | 1.08189 | ||||||||
\(793\) | −4.51172 | −0.160216 | ||||||||
\(794\) | −37.8762 | −1.34418 | ||||||||
\(795\) | 19.4809 | 0.690918 | ||||||||
\(796\) | 37.8377 | 1.34112 | ||||||||
\(797\) | 4.80861 | 0.170330 | 0.0851649 | − | 0.996367i | \(-0.472858\pi\) | ||||
0.0851649 | + | 0.996367i | \(0.472858\pi\) | |||||||
\(798\) | −0.464545 | −0.0164447 | ||||||||
\(799\) | −55.7215 | −1.97128 | ||||||||
\(800\) | −119.864 | −4.23783 | ||||||||
\(801\) | 4.67991 | 0.165357 | ||||||||
\(802\) | −73.5886 | −2.59850 | ||||||||
\(803\) | −6.59691 | −0.232800 | ||||||||
\(804\) | 55.6932 | 1.96415 | ||||||||
\(805\) | 20.7512 | 0.731384 | ||||||||
\(806\) | 13.6763 | 0.481727 | ||||||||
\(807\) | −8.27868 | −0.291423 | ||||||||
\(808\) | 130.621 | 4.59523 | ||||||||
\(809\) | −24.0899 | −0.846957 | −0.423479 | − | 0.905906i | \(-0.639191\pi\) | ||||
−0.423479 | + | 0.905906i | \(0.639191\pi\) | |||||||
\(810\) | −10.1771 | −0.357587 | ||||||||
\(811\) | −39.1445 | −1.37455 | −0.687274 | − | 0.726398i | \(-0.741193\pi\) | ||||
−0.687274 | + | 0.726398i | \(0.741193\pi\) | |||||||
\(812\) | 13.4399 | 0.471649 | ||||||||
\(813\) | 4.70752 | 0.165100 | ||||||||
\(814\) | 100.783 | 3.53243 | ||||||||
\(815\) | 32.4069 | 1.13516 | ||||||||
\(816\) | 44.6954 | 1.56465 | ||||||||
\(817\) | 0.595492 | 0.0208336 | ||||||||
\(818\) | −13.2811 | −0.464364 | ||||||||
\(819\) | −0.666715 | −0.0232969 | ||||||||
\(820\) | 119.690 | 4.17974 | ||||||||
\(821\) | −46.4994 | −1.62284 | −0.811420 | − | 0.584464i | \(-0.801305\pi\) | ||||
−0.811420 | + | 0.584464i | \(0.801305\pi\) | |||||||
\(822\) | −22.0240 | −0.768177 | ||||||||
\(823\) | 51.1841 | 1.78417 | 0.892083 | − | 0.451871i | \(-0.149243\pi\) | ||||
0.892083 | + | 0.451871i | \(0.149243\pi\) | |||||||
\(824\) | −29.9109 | −1.04199 | ||||||||
\(825\) | 39.2921 | 1.36797 | ||||||||
\(826\) | −11.1019 | −0.386286 | ||||||||
\(827\) | 20.5583 | 0.714884 | 0.357442 | − | 0.933935i | \(-0.383649\pi\) | ||||
0.357442 | + | 0.933935i | \(0.383649\pi\) | |||||||
\(828\) | −26.4531 | −0.919309 | ||||||||
\(829\) | −18.7428 | −0.650963 | −0.325482 | − | 0.945548i | \(-0.605526\pi\) | ||||
−0.325482 | + | 0.945548i | \(0.605526\pi\) | |||||||
\(830\) | 30.0851 | 1.04427 | ||||||||
\(831\) | −27.9629 | −0.970022 | ||||||||
\(832\) | 7.23060 | 0.250676 | ||||||||
\(833\) | −4.28337 | −0.148410 | ||||||||
\(834\) | 51.7257 | 1.79111 | ||||||||
\(835\) | 16.8950 | 0.584675 | ||||||||
\(836\) | −3.43544 | −0.118817 | ||||||||
\(837\) | 7.79297 | 0.269365 | ||||||||
\(838\) | 73.3552 | 2.53401 | ||||||||
\(839\) | 16.1626 | 0.557996 | 0.278998 | − | 0.960292i | \(-0.409998\pi\) | ||||
0.278998 | + | 0.960292i | \(0.409998\pi\) | |||||||
\(840\) | −29.8056 | −1.02839 | ||||||||
\(841\) | −21.5642 | −0.743592 | ||||||||
\(842\) | −33.3091 | −1.14791 | ||||||||
\(843\) | 25.2794 | 0.870669 | ||||||||
\(844\) | 129.660 | 4.46307 | ||||||||
\(845\) | −48.5436 | −1.66995 | ||||||||
\(846\) | −34.2423 | −1.17727 | ||||||||
\(847\) | −4.59894 | −0.158022 | ||||||||
\(848\) | −52.5762 | −1.80547 | ||||||||
\(849\) | 18.2811 | 0.627407 | ||||||||
\(850\) | 112.168 | 3.84732 | ||||||||
\(851\) | −52.0305 | −1.78358 | ||||||||
\(852\) | 17.4593 | 0.598146 | ||||||||
\(853\) | −54.0201 | −1.84961 | −0.924807 | − | 0.380437i | \(-0.875774\pi\) | ||||
−0.924807 | + | 0.380437i | \(0.875774\pi\) | |||||||
\(854\) | −17.8126 | −0.609536 | ||||||||
\(855\) | 0.682340 | 0.0233355 | ||||||||
\(856\) | 7.27177 | 0.248544 | ||||||||
\(857\) | −6.78512 | −0.231775 | −0.115888 | − | 0.993262i | \(-0.536971\pi\) | ||||
−0.115888 | + | 0.993262i | \(0.536971\pi\) | |||||||
\(858\) | −6.93128 | −0.236630 | ||||||||
\(859\) | −55.7660 | −1.90271 | −0.951356 | − | 0.308094i | \(-0.900309\pi\) | ||||
−0.951356 | + | 0.308094i | \(0.900309\pi\) | |||||||
\(860\) | 64.2990 | 2.19258 | ||||||||
\(861\) | 6.28096 | 0.214054 | ||||||||
\(862\) | −84.3539 | −2.87310 | ||||||||
\(863\) | −0.624497 | −0.0212581 | −0.0106291 | − | 0.999944i | \(-0.503383\pi\) | ||||
−0.0106291 | + | 0.999944i | \(0.503383\pi\) | |||||||
\(864\) | 12.0484 | 0.409896 | ||||||||
\(865\) | −89.9774 | −3.05933 | ||||||||
\(866\) | −92.0254 | −3.12715 | ||||||||
\(867\) | −1.34724 | −0.0457545 | ||||||||
\(868\) | 38.4092 | 1.30369 | ||||||||
\(869\) | 19.7546 | 0.670128 | ||||||||
\(870\) | −27.7517 | −0.940870 | ||||||||
\(871\) | −7.53373 | −0.255271 | ||||||||
\(872\) | −49.8521 | −1.68821 | ||||||||
\(873\) | 10.6954 | 0.361984 | ||||||||
\(874\) | 2.49329 | 0.0843368 | ||||||||
\(875\) | −19.1325 | −0.646796 | ||||||||
\(876\) | −8.23237 | −0.278146 | ||||||||
\(877\) | −4.26994 | −0.144186 | −0.0720929 | − | 0.997398i | \(-0.522968\pi\) | ||||
−0.0720929 | + | 0.997398i | \(0.522968\pi\) | |||||||
\(878\) | −18.1323 | −0.611936 | ||||||||
\(879\) | 28.4042 | 0.958051 | ||||||||
\(880\) | −159.340 | −5.37134 | ||||||||
\(881\) | −12.5768 | −0.423725 | −0.211862 | − | 0.977300i | \(-0.567953\pi\) | ||||
−0.211862 | + | 0.977300i | \(0.567953\pi\) | |||||||
\(882\) | −2.63224 | −0.0886322 | ||||||||
\(883\) | −50.3970 | −1.69599 | −0.847997 | − | 0.530001i | \(-0.822192\pi\) | ||||
−0.847997 | + | 0.530001i | \(0.822192\pi\) | |||||||
\(884\) | −14.0753 | −0.473403 | ||||||||
\(885\) | 16.3069 | 0.548151 | ||||||||
\(886\) | 81.4452 | 2.73621 | ||||||||
\(887\) | 24.5216 | 0.823356 | 0.411678 | − | 0.911329i | \(-0.364943\pi\) | ||||
0.411678 | + | 0.911329i | \(0.364943\pi\) | |||||||
\(888\) | 74.7331 | 2.50788 | ||||||||
\(889\) | −14.6315 | −0.490723 | ||||||||
\(890\) | −47.6280 | −1.59649 | ||||||||
\(891\) | −3.94955 | −0.132315 | ||||||||
\(892\) | 27.3724 | 0.916495 | ||||||||
\(893\) | 2.29583 | 0.0768270 | ||||||||
\(894\) | 46.7917 | 1.56495 | ||||||||
\(895\) | 48.4395 | 1.61916 | ||||||||
\(896\) | 4.45008 | 0.148667 | ||||||||
\(897\) | 3.57837 | 0.119478 | ||||||||
\(898\) | −53.3217 | −1.77937 | ||||||||
\(899\) | 21.2504 | 0.708742 | ||||||||
\(900\) | 49.0331 | 1.63444 | ||||||||
\(901\) | 21.5823 | 0.719009 | ||||||||
\(902\) | 65.2979 | 2.17418 | ||||||||
\(903\) | 3.37422 | 0.112287 | ||||||||
\(904\) | −124.728 | −4.14841 | ||||||||
\(905\) | 67.7487 | 2.25204 | ||||||||
\(906\) | −44.4945 | −1.47823 | ||||||||
\(907\) | −13.8610 | −0.460245 | −0.230123 | − | 0.973162i | \(-0.573913\pi\) | ||||
−0.230123 | + | 0.973162i | \(0.573913\pi\) | |||||||
\(908\) | 58.2095 | 1.93175 | ||||||||
\(909\) | −16.9439 | −0.561993 | ||||||||
\(910\) | 6.78523 | 0.224928 | ||||||||
\(911\) | 25.8502 | 0.856456 | 0.428228 | − | 0.903671i | \(-0.359138\pi\) | ||||
0.428228 | + | 0.903671i | \(0.359138\pi\) | |||||||
\(912\) | −1.84154 | −0.0609793 | ||||||||
\(913\) | 11.6755 | 0.386402 | ||||||||
\(914\) | −47.0920 | −1.55766 | ||||||||
\(915\) | 26.1638 | 0.864949 | ||||||||
\(916\) | 53.4698 | 1.76669 | ||||||||
\(917\) | 14.1269 | 0.466510 | ||||||||
\(918\) | −11.2749 | −0.372126 | ||||||||
\(919\) | 19.6521 | 0.648264 | 0.324132 | − | 0.946012i | \(-0.394928\pi\) | ||||
0.324132 | + | 0.946012i | \(0.394928\pi\) | |||||||
\(920\) | 159.972 | 5.27411 | ||||||||
\(921\) | −28.0680 | −0.924872 | ||||||||
\(922\) | −31.5568 | −1.03927 | ||||||||
\(923\) | −2.36176 | −0.0777382 | ||||||||
\(924\) | −19.4661 | −0.640389 | ||||||||
\(925\) | 96.4428 | 3.17102 | ||||||||
\(926\) | −55.6931 | −1.83019 | ||||||||
\(927\) | 3.87998 | 0.127435 | ||||||||
\(928\) | 32.8546 | 1.07850 | ||||||||
\(929\) | −9.75732 | −0.320127 | −0.160064 | − | 0.987107i | \(-0.551170\pi\) | ||||
−0.160064 | + | 0.987107i | \(0.551170\pi\) | |||||||
\(930\) | −79.3099 | −2.60068 | ||||||||
\(931\) | 0.176483 | 0.00578399 | ||||||||
\(932\) | 115.914 | 3.79689 | ||||||||
\(933\) | 19.3118 | 0.632241 | ||||||||
\(934\) | −78.4171 | −2.56589 | ||||||||
\(935\) | 65.4081 | 2.13907 | ||||||||
\(936\) | −5.13973 | −0.167997 | ||||||||
\(937\) | −37.5499 | −1.22670 | −0.613351 | − | 0.789811i | \(-0.710179\pi\) | ||||
−0.613351 | + | 0.789811i | \(0.710179\pi\) | |||||||
\(938\) | −29.7438 | −0.971168 | ||||||||
\(939\) | 22.7937 | 0.743844 | ||||||||
\(940\) | 247.895 | 8.08544 | ||||||||
\(941\) | −7.93812 | −0.258775 | −0.129388 | − | 0.991594i | \(-0.541301\pi\) | ||||
−0.129388 | + | 0.991594i | \(0.541301\pi\) | |||||||
\(942\) | 59.5632 | 1.94067 | ||||||||
\(943\) | −33.7109 | −1.09778 | ||||||||
\(944\) | −44.0099 | −1.43240 | ||||||||
\(945\) | 3.86633 | 0.125772 | ||||||||
\(946\) | 35.0790 | 1.14052 | ||||||||
\(947\) | −18.4299 | −0.598891 | −0.299446 | − | 0.954113i | \(-0.596802\pi\) | ||||
−0.299446 | + | 0.954113i | \(0.596802\pi\) | |||||||
\(948\) | 24.6520 | 0.800660 | ||||||||
\(949\) | 1.11361 | 0.0361493 | ||||||||
\(950\) | −4.62152 | −0.149942 | ||||||||
\(951\) | −3.41287 | −0.110670 | ||||||||
\(952\) | −33.0206 | −1.07020 | ||||||||
\(953\) | 26.6089 | 0.861947 | 0.430973 | − | 0.902365i | \(-0.358170\pi\) | ||||
0.430973 | + | 0.902365i | \(0.358170\pi\) | |||||||
\(954\) | 13.2629 | 0.429401 | ||||||||
\(955\) | −23.4092 | −0.757505 | ||||||||
\(956\) | −129.800 | −4.19804 | ||||||||
\(957\) | −10.7699 | −0.348142 | ||||||||
\(958\) | −53.7182 | −1.73556 | ||||||||
\(959\) | 8.36703 | 0.270186 | ||||||||
\(960\) | −41.9308 | −1.35331 | ||||||||
\(961\) | 29.7304 | 0.959047 | ||||||||
\(962\) | −17.0129 | −0.548518 | ||||||||
\(963\) | −0.943279 | −0.0303967 | ||||||||
\(964\) | −39.6022 | −1.27550 | ||||||||
\(965\) | 8.87202 | 0.285600 | ||||||||
\(966\) | 14.1277 | 0.454550 | ||||||||
\(967\) | 53.2422 | 1.71215 | 0.856077 | − | 0.516849i | \(-0.172895\pi\) | ||||
0.856077 | + | 0.516849i | \(0.172895\pi\) | |||||||
\(968\) | −35.4534 | −1.13952 | ||||||||
\(969\) | 0.755941 | 0.0242843 | ||||||||
\(970\) | −108.848 | −3.49490 | ||||||||
\(971\) | 55.6755 | 1.78671 | 0.893357 | − | 0.449348i | \(-0.148344\pi\) | ||||
0.893357 | + | 0.449348i | \(0.148344\pi\) | |||||||
\(972\) | −4.92870 | −0.158088 | ||||||||
\(973\) | −19.6508 | −0.629976 | ||||||||
\(974\) | −9.72348 | −0.311560 | ||||||||
\(975\) | −6.63280 | −0.212420 | ||||||||
\(976\) | −70.6122 | −2.26024 | ||||||||
\(977\) | −28.2024 | −0.902273 | −0.451137 | − | 0.892455i | \(-0.648981\pi\) | ||||
−0.451137 | + | 0.892455i | \(0.648981\pi\) | |||||||
\(978\) | 22.0630 | 0.705497 | ||||||||
\(979\) | −18.4836 | −0.590737 | ||||||||
\(980\) | 19.0560 | 0.608720 | ||||||||
\(981\) | 6.46672 | 0.206466 | ||||||||
\(982\) | 38.6980 | 1.23490 | ||||||||
\(983\) | −44.6311 | −1.42351 | −0.711756 | − | 0.702427i | \(-0.752100\pi\) | ||||
−0.711756 | + | 0.702427i | \(0.752100\pi\) | |||||||
\(984\) | 48.4201 | 1.54358 | ||||||||
\(985\) | 31.6120 | 1.00724 | ||||||||
\(986\) | −30.7451 | −0.979123 | ||||||||
\(987\) | 13.0088 | 0.414075 | ||||||||
\(988\) | 0.579928 | 0.0184500 | ||||||||
\(989\) | −18.1100 | −0.575865 | ||||||||
\(990\) | 40.1950 | 1.27748 | ||||||||
\(991\) | 41.2610 | 1.31070 | 0.655350 | − | 0.755325i | \(-0.272521\pi\) | ||||
0.655350 | + | 0.755325i | \(0.272521\pi\) | |||||||
\(992\) | 93.8932 | 2.98111 | ||||||||
\(993\) | −15.7570 | −0.500034 | ||||||||
\(994\) | −9.32440 | −0.295752 | ||||||||
\(995\) | 29.6819 | 0.940980 | ||||||||
\(996\) | 14.5700 | 0.461668 | ||||||||
\(997\) | 51.0344 | 1.61628 | 0.808138 | − | 0.588993i | \(-0.200475\pi\) | ||||
0.808138 | + | 0.588993i | \(0.200475\pi\) | |||||||
\(998\) | −59.8985 | −1.89605 | ||||||||
\(999\) | −9.69422 | −0.306712 |
(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 | 8043.2.a.s.1.2 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.s.1.2 | ✓ | 50 | 1.1 | even | 1 | trivial |