Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(0\) |
Dimension: | \(179\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59548 | −1.83528 | −0.917640 | − | 0.397414i | \(-0.869908\pi\) | ||||
−0.917640 | + | 0.397414i | \(0.869908\pi\) | |||||||
\(3\) | −2.23952 | −1.29299 | −0.646493 | − | 0.762920i | \(-0.723765\pi\) | ||||
−0.646493 | + | 0.762920i | \(0.723765\pi\) | |||||||
\(4\) | 4.73650 | 2.36825 | ||||||||
\(5\) | −0.915423 | −0.409389 | −0.204695 | − | 0.978826i | \(-0.565620\pi\) | ||||
−0.204695 | + | 0.978826i | \(0.565620\pi\) | |||||||
\(6\) | 5.81261 | 2.37299 | ||||||||
\(7\) | −1.92878 | −0.729009 | −0.364504 | − | 0.931202i | \(-0.618762\pi\) | ||||
−0.364504 | + | 0.931202i | \(0.618762\pi\) | |||||||
\(8\) | −7.10252 | −2.51112 | ||||||||
\(9\) | 2.01543 | 0.671811 | ||||||||
\(10\) | 2.37596 | 0.751344 | ||||||||
\(11\) | −1.40497 | −0.423615 | −0.211807 | − | 0.977311i | \(-0.567935\pi\) | ||||
−0.211807 | + | 0.977311i | \(0.567935\pi\) | |||||||
\(12\) | −10.6075 | −3.06211 | ||||||||
\(13\) | −4.73029 | −1.31195 | −0.655974 | − | 0.754784i | \(-0.727742\pi\) | ||||
−0.655974 | + | 0.754784i | \(0.727742\pi\) | |||||||
\(14\) | 5.00609 | 1.33793 | ||||||||
\(15\) | 2.05010 | 0.529335 | ||||||||
\(16\) | 8.96142 | 2.24036 | ||||||||
\(17\) | 6.19564 | 1.50266 | 0.751332 | − | 0.659925i | \(-0.229412\pi\) | ||||
0.751332 | + | 0.659925i | \(0.229412\pi\) | |||||||
\(18\) | −5.23101 | −1.23296 | ||||||||
\(19\) | −5.43193 | −1.24617 | −0.623085 | − | 0.782154i | \(-0.714121\pi\) | ||||
−0.623085 | + | 0.782154i | \(0.714121\pi\) | |||||||
\(20\) | −4.33590 | −0.969536 | ||||||||
\(21\) | 4.31952 | 0.942597 | ||||||||
\(22\) | 3.64657 | 0.777451 | ||||||||
\(23\) | −1.13085 | −0.235798 | −0.117899 | − | 0.993026i | \(-0.537616\pi\) | ||||
−0.117899 | + | 0.993026i | \(0.537616\pi\) | |||||||
\(24\) | 15.9062 | 3.24684 | ||||||||
\(25\) | −4.16200 | −0.832400 | ||||||||
\(26\) | 12.2774 | 2.40779 | ||||||||
\(27\) | 2.20495 | 0.424343 | ||||||||
\(28\) | −9.13564 | −1.72647 | ||||||||
\(29\) | −0.475004 | −0.0882060 | −0.0441030 | − | 0.999027i | \(-0.514043\pi\) | ||||
−0.0441030 | + | 0.999027i | \(0.514043\pi\) | |||||||
\(30\) | −5.32100 | −0.971477 | ||||||||
\(31\) | 0.173094 | 0.0310886 | 0.0155443 | − | 0.999879i | \(-0.495052\pi\) | ||||
0.0155443 | + | 0.999879i | \(0.495052\pi\) | |||||||
\(32\) | −9.05412 | −1.60056 | ||||||||
\(33\) | 3.14646 | 0.547728 | ||||||||
\(34\) | −16.0806 | −2.75781 | ||||||||
\(35\) | 1.76564 | 0.298448 | ||||||||
\(36\) | 9.54610 | 1.59102 | ||||||||
\(37\) | 5.39098 | 0.886272 | 0.443136 | − | 0.896454i | \(-0.353866\pi\) | ||||
0.443136 | + | 0.896454i | \(0.353866\pi\) | |||||||
\(38\) | 14.0984 | 2.28707 | ||||||||
\(39\) | 10.5936 | 1.69633 | ||||||||
\(40\) | 6.50181 | 1.02803 | ||||||||
\(41\) | 1.13606 | 0.177422 | 0.0887112 | − | 0.996057i | \(-0.471725\pi\) | ||||
0.0887112 | + | 0.996057i | \(0.471725\pi\) | |||||||
\(42\) | −11.2112 | −1.72993 | ||||||||
\(43\) | 0.281797 | 0.0429737 | 0.0214868 | − | 0.999769i | \(-0.493160\pi\) | ||||
0.0214868 | + | 0.999769i | \(0.493160\pi\) | |||||||
\(44\) | −6.65464 | −1.00323 | ||||||||
\(45\) | −1.84497 | −0.275032 | ||||||||
\(46\) | 2.93508 | 0.432754 | ||||||||
\(47\) | −8.99914 | −1.31266 | −0.656330 | − | 0.754474i | \(-0.727892\pi\) | ||||
−0.656330 | + | 0.754474i | \(0.727892\pi\) | |||||||
\(48\) | −20.0693 | −2.89675 | ||||||||
\(49\) | −3.27983 | −0.468546 | ||||||||
\(50\) | 10.8024 | 1.52769 | ||||||||
\(51\) | −13.8752 | −1.94292 | ||||||||
\(52\) | −22.4050 | −3.10702 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | −5.72290 | −0.778788 | ||||||||
\(55\) | 1.28614 | 0.173423 | ||||||||
\(56\) | 13.6992 | 1.83063 | ||||||||
\(57\) | 12.1649 | 1.61128 | ||||||||
\(58\) | 1.23286 | 0.161883 | ||||||||
\(59\) | −11.2777 | −1.46823 | −0.734114 | − | 0.679026i | \(-0.762402\pi\) | ||||
−0.734114 | + | 0.679026i | \(0.762402\pi\) | |||||||
\(60\) | 9.71032 | 1.25360 | ||||||||
\(61\) | −0.0211009 | −0.00270169 | −0.00135084 | − | 0.999999i | \(-0.500430\pi\) | ||||
−0.00135084 | + | 0.999999i | \(0.500430\pi\) | |||||||
\(62\) | −0.449262 | −0.0570563 | ||||||||
\(63\) | −3.88732 | −0.489756 | ||||||||
\(64\) | 5.57692 | 0.697116 | ||||||||
\(65\) | 4.33022 | 0.537098 | ||||||||
\(66\) | −8.16655 | −1.00523 | ||||||||
\(67\) | 10.0137 | 1.22336 | 0.611681 | − | 0.791104i | \(-0.290493\pi\) | ||||
0.611681 | + | 0.791104i | \(0.290493\pi\) | |||||||
\(68\) | 29.3456 | 3.55868 | ||||||||
\(69\) | 2.53255 | 0.304883 | ||||||||
\(70\) | −4.58269 | −0.547736 | ||||||||
\(71\) | −12.2715 | −1.45636 | −0.728179 | − | 0.685387i | \(-0.759633\pi\) | ||||
−0.728179 | + | 0.685387i | \(0.759633\pi\) | |||||||
\(72\) | −14.3147 | −1.68700 | ||||||||
\(73\) | 10.5694 | 1.23706 | 0.618529 | − | 0.785762i | \(-0.287729\pi\) | ||||
0.618529 | + | 0.785762i | \(0.287729\pi\) | |||||||
\(74\) | −13.9922 | −1.62656 | ||||||||
\(75\) | 9.32087 | 1.07628 | ||||||||
\(76\) | −25.7283 | −2.95124 | ||||||||
\(77\) | 2.70987 | 0.308819 | ||||||||
\(78\) | −27.4954 | −3.11324 | ||||||||
\(79\) | −13.2834 | −1.49450 | −0.747252 | − | 0.664541i | \(-0.768627\pi\) | ||||
−0.747252 | + | 0.664541i | \(0.768627\pi\) | |||||||
\(80\) | −8.20349 | −0.917178 | ||||||||
\(81\) | −10.9843 | −1.22048 | ||||||||
\(82\) | −2.94861 | −0.325619 | ||||||||
\(83\) | −10.1607 | −1.11528 | −0.557642 | − | 0.830081i | \(-0.688294\pi\) | ||||
−0.557642 | + | 0.830081i | \(0.688294\pi\) | |||||||
\(84\) | 20.4594 | 2.23231 | ||||||||
\(85\) | −5.67163 | −0.615174 | ||||||||
\(86\) | −0.731398 | −0.0788687 | ||||||||
\(87\) | 1.06378 | 0.114049 | ||||||||
\(88\) | 9.97883 | 1.06375 | ||||||||
\(89\) | 0.0261827 | 0.00277537 | 0.00138768 | − | 0.999999i | \(-0.499558\pi\) | ||||
0.00138768 | + | 0.999999i | \(0.499558\pi\) | |||||||
\(90\) | 4.78859 | 0.504761 | ||||||||
\(91\) | 9.12368 | 0.956421 | ||||||||
\(92\) | −5.35625 | −0.558428 | ||||||||
\(93\) | −0.387647 | −0.0401972 | ||||||||
\(94\) | 23.3571 | 2.40910 | ||||||||
\(95\) | 4.97251 | 0.510169 | ||||||||
\(96\) | 20.2769 | 2.06950 | ||||||||
\(97\) | 9.24864 | 0.939057 | 0.469529 | − | 0.882917i | \(-0.344424\pi\) | ||||
0.469529 | + | 0.882917i | \(0.344424\pi\) | |||||||
\(98\) | 8.51271 | 0.859914 | ||||||||
\(99\) | −2.83163 | −0.284589 | ||||||||
\(100\) | −19.7133 | −1.97133 | ||||||||
\(101\) | −9.86776 | −0.981879 | −0.490939 | − | 0.871194i | \(-0.663346\pi\) | ||||
−0.490939 | + | 0.871194i | \(0.663346\pi\) | |||||||
\(102\) | 36.0128 | 3.56580 | ||||||||
\(103\) | −13.0108 | −1.28199 | −0.640996 | − | 0.767544i | \(-0.721478\pi\) | ||||
−0.640996 | + | 0.767544i | \(0.721478\pi\) | |||||||
\(104\) | 33.5970 | 3.29446 | ||||||||
\(105\) | −3.95419 | −0.385889 | ||||||||
\(106\) | −2.59548 | −0.252095 | ||||||||
\(107\) | 4.49778 | 0.434817 | 0.217409 | − | 0.976081i | \(-0.430240\pi\) | ||||
0.217409 | + | 0.976081i | \(0.430240\pi\) | |||||||
\(108\) | 10.4438 | 1.00495 | ||||||||
\(109\) | −15.7049 | −1.50426 | −0.752128 | − | 0.659016i | \(-0.770973\pi\) | ||||
−0.752128 | + | 0.659016i | \(0.770973\pi\) | |||||||
\(110\) | −3.33815 | −0.318280 | ||||||||
\(111\) | −12.0732 | −1.14594 | ||||||||
\(112\) | −17.2846 | −1.63324 | ||||||||
\(113\) | 2.90124 | 0.272926 | 0.136463 | − | 0.990645i | \(-0.456427\pi\) | ||||
0.136463 | + | 0.990645i | \(0.456427\pi\) | |||||||
\(114\) | −31.5737 | −2.95715 | ||||||||
\(115\) | 1.03520 | 0.0965331 | ||||||||
\(116\) | −2.24985 | −0.208894 | ||||||||
\(117\) | −9.53360 | −0.881381 | ||||||||
\(118\) | 29.2709 | 2.69461 | ||||||||
\(119\) | −11.9500 | −1.09545 | ||||||||
\(120\) | −14.5609 | −1.32922 | ||||||||
\(121\) | −9.02606 | −0.820551 | ||||||||
\(122\) | 0.0547668 | 0.00495835 | ||||||||
\(123\) | −2.54422 | −0.229404 | ||||||||
\(124\) | 0.819860 | 0.0736256 | ||||||||
\(125\) | 8.38710 | 0.750165 | ||||||||
\(126\) | 10.0894 | 0.898839 | ||||||||
\(127\) | 7.81813 | 0.693747 | 0.346873 | − | 0.937912i | \(-0.387243\pi\) | ||||
0.346873 | + | 0.937912i | \(0.387243\pi\) | |||||||
\(128\) | 3.63347 | 0.321157 | ||||||||
\(129\) | −0.631090 | −0.0555644 | ||||||||
\(130\) | −11.2390 | −0.985724 | ||||||||
\(131\) | −20.2337 | −1.76782 | −0.883912 | − | 0.467653i | \(-0.845100\pi\) | ||||
−0.883912 | + | 0.467653i | \(0.845100\pi\) | |||||||
\(132\) | 14.9032 | 1.29716 | ||||||||
\(133\) | 10.4770 | 0.908469 | ||||||||
\(134\) | −25.9902 | −2.24521 | ||||||||
\(135\) | −2.01846 | −0.173722 | ||||||||
\(136\) | −44.0046 | −3.77337 | ||||||||
\(137\) | −14.0223 | −1.19801 | −0.599005 | − | 0.800746i | \(-0.704437\pi\) | ||||
−0.599005 | + | 0.800746i | \(0.704437\pi\) | |||||||
\(138\) | −6.57317 | −0.559545 | ||||||||
\(139\) | 22.1859 | 1.88178 | 0.940890 | − | 0.338712i | \(-0.109991\pi\) | ||||
0.940890 | + | 0.338712i | \(0.109991\pi\) | |||||||
\(140\) | 8.36297 | 0.706800 | ||||||||
\(141\) | 20.1537 | 1.69725 | ||||||||
\(142\) | 31.8504 | 2.67282 | ||||||||
\(143\) | 6.64593 | 0.555760 | ||||||||
\(144\) | 18.0612 | 1.50510 | ||||||||
\(145\) | 0.434829 | 0.0361106 | ||||||||
\(146\) | −27.4327 | −2.27035 | ||||||||
\(147\) | 7.34522 | 0.605824 | ||||||||
\(148\) | 25.5344 | 2.09891 | ||||||||
\(149\) | 8.32775 | 0.682236 | 0.341118 | − | 0.940021i | \(-0.389194\pi\) | ||||
0.341118 | + | 0.940021i | \(0.389194\pi\) | |||||||
\(150\) | −24.1921 | −1.97528 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | 38.5804 | 3.12928 | ||||||||
\(153\) | 12.4869 | 1.00951 | ||||||||
\(154\) | −7.03341 | −0.566769 | ||||||||
\(155\) | −0.158454 | −0.0127274 | ||||||||
\(156\) | 50.1764 | 4.01733 | ||||||||
\(157\) | −6.00646 | −0.479368 | −0.239684 | − | 0.970851i | \(-0.577044\pi\) | ||||
−0.239684 | + | 0.970851i | \(0.577044\pi\) | |||||||
\(158\) | 34.4769 | 2.74283 | ||||||||
\(159\) | −2.23952 | −0.177605 | ||||||||
\(160\) | 8.28835 | 0.655252 | ||||||||
\(161\) | 2.18115 | 0.171899 | ||||||||
\(162\) | 28.5096 | 2.23992 | ||||||||
\(163\) | 12.7717 | 1.00036 | 0.500180 | − | 0.865921i | \(-0.333267\pi\) | ||||
0.500180 | + | 0.865921i | \(0.333267\pi\) | |||||||
\(164\) | 5.38093 | 0.420180 | ||||||||
\(165\) | −2.88034 | −0.224234 | ||||||||
\(166\) | 26.3719 | 2.04686 | ||||||||
\(167\) | −9.42386 | −0.729240 | −0.364620 | − | 0.931156i | \(-0.618801\pi\) | ||||
−0.364620 | + | 0.931156i | \(0.618801\pi\) | |||||||
\(168\) | −30.6795 | −2.36697 | ||||||||
\(169\) | 9.37569 | 0.721207 | ||||||||
\(170\) | 14.7206 | 1.12902 | ||||||||
\(171\) | −10.9477 | −0.837191 | ||||||||
\(172\) | 1.33473 | 0.101772 | ||||||||
\(173\) | −24.0964 | −1.83201 | −0.916007 | − | 0.401163i | \(-0.868606\pi\) | ||||
−0.916007 | + | 0.401163i | \(0.868606\pi\) | |||||||
\(174\) | −2.76101 | −0.209312 | ||||||||
\(175\) | 8.02757 | 0.606827 | ||||||||
\(176\) | −12.5905 | −0.949047 | ||||||||
\(177\) | 25.2565 | 1.89840 | ||||||||
\(178\) | −0.0679567 | −0.00509357 | ||||||||
\(179\) | −4.83894 | −0.361680 | −0.180840 | − | 0.983513i | \(-0.557882\pi\) | ||||
−0.180840 | + | 0.983513i | \(0.557882\pi\) | |||||||
\(180\) | −8.73872 | −0.651345 | ||||||||
\(181\) | 8.82661 | 0.656077 | 0.328039 | − | 0.944664i | \(-0.393612\pi\) | ||||
0.328039 | + | 0.944664i | \(0.393612\pi\) | |||||||
\(182\) | −23.6803 | −1.75530 | ||||||||
\(183\) | 0.0472557 | 0.00349325 | ||||||||
\(184\) | 8.03185 | 0.592116 | ||||||||
\(185\) | −4.93503 | −0.362830 | ||||||||
\(186\) | 1.00613 | 0.0737730 | ||||||||
\(187\) | −8.70469 | −0.636550 | ||||||||
\(188\) | −42.6244 | −3.10870 | ||||||||
\(189\) | −4.25286 | −0.309350 | ||||||||
\(190\) | −12.9060 | −0.936302 | ||||||||
\(191\) | −24.5905 | −1.77930 | −0.889652 | − | 0.456639i | \(-0.849053\pi\) | ||||
−0.889652 | + | 0.456639i | \(0.849053\pi\) | |||||||
\(192\) | −12.4896 | −0.901360 | ||||||||
\(193\) | −15.2749 | −1.09951 | −0.549755 | − | 0.835326i | \(-0.685279\pi\) | ||||
−0.549755 | + | 0.835326i | \(0.685279\pi\) | |||||||
\(194\) | −24.0046 | −1.72343 | ||||||||
\(195\) | −9.69760 | −0.694459 | ||||||||
\(196\) | −15.5349 | −1.10963 | ||||||||
\(197\) | 12.5708 | 0.895630 | 0.447815 | − | 0.894126i | \(-0.352202\pi\) | ||||
0.447815 | + | 0.894126i | \(0.352202\pi\) | |||||||
\(198\) | 7.34942 | 0.522300 | ||||||||
\(199\) | 2.69173 | 0.190812 | 0.0954058 | − | 0.995438i | \(-0.469585\pi\) | ||||
0.0954058 | + | 0.995438i | \(0.469585\pi\) | |||||||
\(200\) | 29.5607 | 2.09026 | ||||||||
\(201\) | −22.4257 | −1.58179 | ||||||||
\(202\) | 25.6115 | 1.80202 | ||||||||
\(203\) | 0.916175 | 0.0643029 | ||||||||
\(204\) | −65.7200 | −4.60132 | ||||||||
\(205\) | −1.03997 | −0.0726348 | ||||||||
\(206\) | 33.7692 | 2.35281 | ||||||||
\(207\) | −2.27914 | −0.158412 | ||||||||
\(208\) | −42.3902 | −2.93923 | ||||||||
\(209\) | 7.63170 | 0.527896 | ||||||||
\(210\) | 10.2630 | 0.708215 | ||||||||
\(211\) | −14.9066 | −1.02621 | −0.513105 | − | 0.858326i | \(-0.671505\pi\) | ||||
−0.513105 | + | 0.858326i | \(0.671505\pi\) | |||||||
\(212\) | 4.73650 | 0.325304 | ||||||||
\(213\) | 27.4822 | 1.88305 | ||||||||
\(214\) | −11.6739 | −0.798011 | ||||||||
\(215\) | −0.257964 | −0.0175930 | ||||||||
\(216\) | −15.6607 | −1.06558 | ||||||||
\(217\) | −0.333860 | −0.0226639 | ||||||||
\(218\) | 40.7617 | 2.76073 | ||||||||
\(219\) | −23.6704 | −1.59950 | ||||||||
\(220\) | 6.09181 | 0.410710 | ||||||||
\(221\) | −29.3072 | −1.97142 | ||||||||
\(222\) | 31.3357 | 2.10311 | ||||||||
\(223\) | 26.9242 | 1.80298 | 0.901488 | − | 0.432804i | \(-0.142476\pi\) | ||||
0.901488 | + | 0.432804i | \(0.142476\pi\) | |||||||
\(224\) | 17.4634 | 1.16682 | ||||||||
\(225\) | −8.38824 | −0.559216 | ||||||||
\(226\) | −7.53011 | −0.500895 | ||||||||
\(227\) | −11.7941 | −0.782803 | −0.391401 | − | 0.920220i | \(-0.628010\pi\) | ||||
−0.391401 | + | 0.920220i | \(0.628010\pi\) | |||||||
\(228\) | 57.6190 | 3.81591 | ||||||||
\(229\) | 15.5279 | 1.02611 | 0.513057 | − | 0.858355i | \(-0.328513\pi\) | ||||
0.513057 | + | 0.858355i | \(0.328513\pi\) | |||||||
\(230\) | −2.68684 | −0.177165 | ||||||||
\(231\) | −6.06881 | −0.399298 | ||||||||
\(232\) | 3.37372 | 0.221496 | ||||||||
\(233\) | −2.45302 | −0.160703 | −0.0803515 | − | 0.996767i | \(-0.525604\pi\) | ||||
−0.0803515 | + | 0.996767i | \(0.525604\pi\) | |||||||
\(234\) | 24.7442 | 1.61758 | ||||||||
\(235\) | 8.23802 | 0.537389 | ||||||||
\(236\) | −53.4167 | −3.47713 | ||||||||
\(237\) | 29.7485 | 1.93237 | ||||||||
\(238\) | 31.0159 | 2.01046 | ||||||||
\(239\) | −29.4889 | −1.90748 | −0.953738 | − | 0.300640i | \(-0.902800\pi\) | ||||
−0.953738 | + | 0.300640i | \(0.902800\pi\) | |||||||
\(240\) | 18.3718 | 1.18590 | ||||||||
\(241\) | −11.6183 | −0.748403 | −0.374201 | − | 0.927347i | \(-0.622083\pi\) | ||||
−0.374201 | + | 0.927347i | \(0.622083\pi\) | |||||||
\(242\) | 23.4269 | 1.50594 | ||||||||
\(243\) | 17.9847 | 1.15372 | ||||||||
\(244\) | −0.0999443 | −0.00639828 | ||||||||
\(245\) | 3.00243 | 0.191818 | ||||||||
\(246\) | 6.60346 | 0.421021 | ||||||||
\(247\) | 25.6946 | 1.63491 | ||||||||
\(248\) | −1.22940 | −0.0780673 | ||||||||
\(249\) | 22.7551 | 1.44205 | ||||||||
\(250\) | −21.7685 | −1.37676 | ||||||||
\(251\) | 8.14918 | 0.514372 | 0.257186 | − | 0.966362i | \(-0.417205\pi\) | ||||
0.257186 | + | 0.966362i | \(0.417205\pi\) | |||||||
\(252\) | −18.4123 | −1.15986 | ||||||||
\(253\) | 1.58881 | 0.0998873 | ||||||||
\(254\) | −20.2918 | −1.27322 | ||||||||
\(255\) | 12.7017 | 0.795412 | ||||||||
\(256\) | −20.5844 | −1.28653 | ||||||||
\(257\) | −23.9653 | −1.49491 | −0.747456 | − | 0.664311i | \(-0.768725\pi\) | ||||
−0.747456 | + | 0.664311i | \(0.768725\pi\) | |||||||
\(258\) | 1.63798 | 0.101976 | ||||||||
\(259\) | −10.3980 | −0.646100 | ||||||||
\(260\) | 20.5101 | 1.27198 | ||||||||
\(261\) | −0.957338 | −0.0592578 | ||||||||
\(262\) | 52.5160 | 3.24445 | ||||||||
\(263\) | 3.98244 | 0.245568 | 0.122784 | − | 0.992433i | \(-0.460818\pi\) | ||||
0.122784 | + | 0.992433i | \(0.460818\pi\) | |||||||
\(264\) | −22.3478 | −1.37541 | ||||||||
\(265\) | −0.915423 | −0.0562340 | ||||||||
\(266\) | −27.1927 | −1.66729 | ||||||||
\(267\) | −0.0586367 | −0.00358851 | ||||||||
\(268\) | 47.4297 | 2.89723 | ||||||||
\(269\) | 10.1580 | 0.619345 | 0.309672 | − | 0.950843i | \(-0.399781\pi\) | ||||
0.309672 | + | 0.950843i | \(0.399781\pi\) | |||||||
\(270\) | 5.23887 | 0.318828 | ||||||||
\(271\) | 2.39275 | 0.145349 | 0.0726746 | − | 0.997356i | \(-0.476847\pi\) | ||||
0.0726746 | + | 0.997356i | \(0.476847\pi\) | |||||||
\(272\) | 55.5217 | 3.36650 | ||||||||
\(273\) | −20.4326 | −1.23664 | ||||||||
\(274\) | 36.3947 | 2.19868 | ||||||||
\(275\) | 5.84749 | 0.352617 | ||||||||
\(276\) | 11.9954 | 0.722039 | ||||||||
\(277\) | −25.3491 | −1.52308 | −0.761539 | − | 0.648119i | \(-0.775556\pi\) | ||||
−0.761539 | + | 0.648119i | \(0.775556\pi\) | |||||||
\(278\) | −57.5829 | −3.45359 | ||||||||
\(279\) | 0.348860 | 0.0208857 | ||||||||
\(280\) | −12.5405 | −0.749440 | ||||||||
\(281\) | −13.5331 | −0.807314 | −0.403657 | − | 0.914910i | \(-0.632261\pi\) | ||||
−0.403657 | + | 0.914910i | \(0.632261\pi\) | |||||||
\(282\) | −52.3085 | −3.11493 | ||||||||
\(283\) | −22.5588 | −1.34098 | −0.670490 | − | 0.741919i | \(-0.733916\pi\) | ||||
−0.670490 | + | 0.741919i | \(0.733916\pi\) | |||||||
\(284\) | −58.1239 | −3.44902 | ||||||||
\(285\) | −11.1360 | −0.659641 | ||||||||
\(286\) | −17.2493 | −1.01998 | ||||||||
\(287\) | −2.19120 | −0.129342 | ||||||||
\(288\) | −18.2480 | −1.07527 | ||||||||
\(289\) | 21.3859 | 1.25800 | ||||||||
\(290\) | −1.12859 | −0.0662730 | ||||||||
\(291\) | −20.7125 | −1.21419 | ||||||||
\(292\) | 50.0621 | 2.92966 | ||||||||
\(293\) | 23.1877 | 1.35464 | 0.677320 | − | 0.735688i | \(-0.263141\pi\) | ||||
0.677320 | + | 0.735688i | \(0.263141\pi\) | |||||||
\(294\) | −19.0644 | −1.11186 | ||||||||
\(295\) | 10.3238 | 0.601077 | ||||||||
\(296\) | −38.2895 | −2.22553 | ||||||||
\(297\) | −3.09789 | −0.179758 | ||||||||
\(298\) | −21.6145 | −1.25209 | ||||||||
\(299\) | 5.34923 | 0.309354 | ||||||||
\(300\) | 44.1483 | 2.54890 | ||||||||
\(301\) | −0.543524 | −0.0313282 | ||||||||
\(302\) | 2.59548 | 0.149353 | ||||||||
\(303\) | 22.0990 | 1.26956 | ||||||||
\(304\) | −48.6778 | −2.79186 | ||||||||
\(305\) | 0.0193162 | 0.00110604 | ||||||||
\(306\) | −32.4095 | −1.85273 | ||||||||
\(307\) | −24.2096 | −1.38172 | −0.690858 | − | 0.722991i | \(-0.742767\pi\) | ||||
−0.690858 | + | 0.722991i | \(0.742767\pi\) | |||||||
\(308\) | 12.8353 | 0.731360 | ||||||||
\(309\) | 29.1379 | 1.65760 | ||||||||
\(310\) | 0.411265 | 0.0233583 | ||||||||
\(311\) | −11.5510 | −0.654998 | −0.327499 | − | 0.944851i | \(-0.606206\pi\) | ||||
−0.327499 | + | 0.944851i | \(0.606206\pi\) | |||||||
\(312\) | −75.2410 | −4.25969 | ||||||||
\(313\) | −28.5031 | −1.61109 | −0.805545 | − | 0.592535i | \(-0.798127\pi\) | ||||
−0.805545 | + | 0.592535i | \(0.798127\pi\) | |||||||
\(314\) | 15.5896 | 0.879774 | ||||||||
\(315\) | 3.55854 | 0.200501 | ||||||||
\(316\) | −62.9170 | −3.53936 | ||||||||
\(317\) | 0.750276 | 0.0421397 | 0.0210699 | − | 0.999778i | \(-0.493293\pi\) | ||||
0.0210699 | + | 0.999778i | \(0.493293\pi\) | |||||||
\(318\) | 5.81261 | 0.325955 | ||||||||
\(319\) | 0.667366 | 0.0373653 | ||||||||
\(320\) | −5.10524 | −0.285392 | ||||||||
\(321\) | −10.0729 | −0.562212 | ||||||||
\(322\) | −5.66112 | −0.315482 | ||||||||
\(323\) | −33.6543 | −1.87257 | ||||||||
\(324\) | −52.0273 | −2.89040 | ||||||||
\(325\) | 19.6875 | 1.09207 | ||||||||
\(326\) | −33.1488 | −1.83594 | ||||||||
\(327\) | 35.1714 | 1.94498 | ||||||||
\(328\) | −8.06887 | −0.445529 | ||||||||
\(329\) | 17.3573 | 0.956940 | ||||||||
\(330\) | 7.47585 | 0.411532 | ||||||||
\(331\) | −20.6983 | −1.13768 | −0.568842 | − | 0.822447i | \(-0.692608\pi\) | ||||
−0.568842 | + | 0.822447i | \(0.692608\pi\) | |||||||
\(332\) | −48.1263 | −2.64127 | ||||||||
\(333\) | 10.8652 | 0.595407 | ||||||||
\(334\) | 24.4594 | 1.33836 | ||||||||
\(335\) | −9.16673 | −0.500832 | ||||||||
\(336\) | 38.7091 | 2.11175 | ||||||||
\(337\) | −10.5763 | −0.576128 | −0.288064 | − | 0.957611i | \(-0.593012\pi\) | ||||
−0.288064 | + | 0.957611i | \(0.593012\pi\) | |||||||
\(338\) | −24.3344 | −1.32362 | ||||||||
\(339\) | −6.49738 | −0.352889 | ||||||||
\(340\) | −26.8637 | −1.45689 | ||||||||
\(341\) | −0.243192 | −0.0131696 | ||||||||
\(342\) | 28.4145 | 1.53648 | ||||||||
\(343\) | 19.8275 | 1.07058 | ||||||||
\(344\) | −2.00147 | −0.107912 | ||||||||
\(345\) | −2.31835 | −0.124816 | ||||||||
\(346\) | 62.5416 | 3.36226 | ||||||||
\(347\) | −3.64359 | −0.195598 | −0.0977991 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977991 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(348\) | 5.03859 | 0.270097 | ||||||||
\(349\) | 15.2532 | 0.816488 | 0.408244 | − | 0.912873i | \(-0.366141\pi\) | ||||
0.408244 | + | 0.912873i | \(0.366141\pi\) | |||||||
\(350\) | −20.8354 | −1.11370 | ||||||||
\(351\) | −10.4301 | −0.556716 | ||||||||
\(352\) | 12.7208 | 0.678020 | ||||||||
\(353\) | −6.88166 | −0.366274 | −0.183137 | − | 0.983087i | \(-0.558625\pi\) | ||||
−0.183137 | + | 0.983087i | \(0.558625\pi\) | |||||||
\(354\) | −65.5527 | −3.48409 | ||||||||
\(355\) | 11.2336 | 0.596218 | ||||||||
\(356\) | 0.124015 | 0.00657276 | ||||||||
\(357\) | 26.7622 | 1.41641 | ||||||||
\(358\) | 12.5594 | 0.663783 | ||||||||
\(359\) | −1.96041 | −0.103466 | −0.0517332 | − | 0.998661i | \(-0.516475\pi\) | ||||
−0.0517332 | + | 0.998661i | \(0.516475\pi\) | |||||||
\(360\) | 13.1040 | 0.690639 | ||||||||
\(361\) | 10.5059 | 0.552940 | ||||||||
\(362\) | −22.9093 | −1.20408 | ||||||||
\(363\) | 20.2140 | 1.06096 | ||||||||
\(364\) | 43.2143 | 2.26504 | ||||||||
\(365\) | −9.67550 | −0.506439 | ||||||||
\(366\) | −0.122651 | −0.00641108 | ||||||||
\(367\) | −12.6874 | −0.662279 | −0.331139 | − | 0.943582i | \(-0.607433\pi\) | ||||
−0.331139 | + | 0.943582i | \(0.607433\pi\) | |||||||
\(368\) | −10.1340 | −0.528271 | ||||||||
\(369\) | 2.28965 | 0.119194 | ||||||||
\(370\) | 12.8087 | 0.665895 | ||||||||
\(371\) | −1.92878 | −0.100137 | ||||||||
\(372\) | −1.83609 | −0.0951969 | ||||||||
\(373\) | −8.42879 | −0.436426 | −0.218213 | − | 0.975901i | \(-0.570023\pi\) | ||||
−0.218213 | + | 0.975901i | \(0.570023\pi\) | |||||||
\(374\) | 22.5928 | 1.16825 | ||||||||
\(375\) | −18.7831 | −0.969953 | ||||||||
\(376\) | 63.9166 | 3.29624 | ||||||||
\(377\) | 2.24691 | 0.115722 | ||||||||
\(378\) | 11.0382 | 0.567743 | ||||||||
\(379\) | 15.0186 | 0.771453 | 0.385726 | − | 0.922613i | \(-0.373951\pi\) | ||||
0.385726 | + | 0.922613i | \(0.373951\pi\) | |||||||
\(380\) | 23.5523 | 1.20821 | ||||||||
\(381\) | −17.5088 | −0.897004 | ||||||||
\(382\) | 63.8240 | 3.26552 | ||||||||
\(383\) | −15.9739 | −0.816229 | −0.408114 | − | 0.912931i | \(-0.633814\pi\) | ||||
−0.408114 | + | 0.912931i | \(0.633814\pi\) | |||||||
\(384\) | −8.13722 | −0.415251 | ||||||||
\(385\) | −2.48068 | −0.126427 | ||||||||
\(386\) | 39.6456 | 2.01791 | ||||||||
\(387\) | 0.567944 | 0.0288702 | ||||||||
\(388\) | 43.8062 | 2.22392 | ||||||||
\(389\) | −1.69938 | −0.0861621 | −0.0430810 | − | 0.999072i | \(-0.513717\pi\) | ||||
−0.0430810 | + | 0.999072i | \(0.513717\pi\) | |||||||
\(390\) | 25.1699 | 1.27453 | ||||||||
\(391\) | −7.00631 | −0.354324 | ||||||||
\(392\) | 23.2950 | 1.17658 | ||||||||
\(393\) | 45.3136 | 2.28577 | ||||||||
\(394\) | −32.6271 | −1.64373 | ||||||||
\(395\) | 12.1600 | 0.611834 | ||||||||
\(396\) | −13.4120 | −0.673978 | ||||||||
\(397\) | −14.3248 | −0.718943 | −0.359471 | − | 0.933156i | \(-0.617043\pi\) | ||||
−0.359471 | + | 0.933156i | \(0.617043\pi\) | |||||||
\(398\) | −6.98632 | −0.350193 | ||||||||
\(399\) | −23.4634 | −1.17464 | ||||||||
\(400\) | −37.2974 | −1.86487 | ||||||||
\(401\) | −35.2531 | −1.76045 | −0.880227 | − | 0.474553i | \(-0.842610\pi\) | ||||
−0.880227 | + | 0.474553i | \(0.842610\pi\) | |||||||
\(402\) | 58.2055 | 2.90303 | ||||||||
\(403\) | −0.818787 | −0.0407867 | ||||||||
\(404\) | −46.7386 | −2.32533 | ||||||||
\(405\) | 10.0553 | 0.499652 | ||||||||
\(406\) | −2.37791 | −0.118014 | ||||||||
\(407\) | −7.57417 | −0.375438 | ||||||||
\(408\) | 98.5491 | 4.87891 | ||||||||
\(409\) | −17.4175 | −0.861240 | −0.430620 | − | 0.902533i | \(-0.641705\pi\) | ||||
−0.430620 | + | 0.902533i | \(0.641705\pi\) | |||||||
\(410\) | 2.69922 | 0.133305 | ||||||||
\(411\) | 31.4033 | 1.54901 | ||||||||
\(412\) | −61.6256 | −3.03608 | ||||||||
\(413\) | 21.7521 | 1.07035 | ||||||||
\(414\) | 5.91547 | 0.290729 | ||||||||
\(415\) | 9.30136 | 0.456586 | ||||||||
\(416\) | 42.8287 | 2.09985 | ||||||||
\(417\) | −49.6856 | −2.43311 | ||||||||
\(418\) | −19.8079 | −0.968836 | ||||||||
\(419\) | −32.1615 | −1.57119 | −0.785597 | − | 0.618739i | \(-0.787644\pi\) | ||||
−0.785597 | + | 0.618739i | \(0.787644\pi\) | |||||||
\(420\) | −18.7290 | −0.913883 | ||||||||
\(421\) | 1.73999 | 0.0848019 | 0.0424009 | − | 0.999101i | \(-0.486499\pi\) | ||||
0.0424009 | + | 0.999101i | \(0.486499\pi\) | |||||||
\(422\) | 38.6897 | 1.88338 | ||||||||
\(423\) | −18.1372 | −0.881859 | ||||||||
\(424\) | −7.10252 | −0.344929 | ||||||||
\(425\) | −25.7863 | −1.25082 | ||||||||
\(426\) | −71.3294 | −3.45592 | ||||||||
\(427\) | 0.0406988 | 0.00196956 | ||||||||
\(428\) | 21.3037 | 1.02976 | ||||||||
\(429\) | −14.8837 | −0.718590 | ||||||||
\(430\) | 0.669539 | 0.0322880 | ||||||||
\(431\) | 13.9656 | 0.672700 | 0.336350 | − | 0.941737i | \(-0.390807\pi\) | ||||
0.336350 | + | 0.941737i | \(0.390807\pi\) | |||||||
\(432\) | 19.7595 | 0.950680 | ||||||||
\(433\) | −30.8270 | −1.48145 | −0.740727 | − | 0.671807i | \(-0.765519\pi\) | ||||
−0.740727 | + | 0.671807i | \(0.765519\pi\) | |||||||
\(434\) | 0.866525 | 0.0415946 | ||||||||
\(435\) | −0.973807 | −0.0466905 | ||||||||
\(436\) | −74.3863 | −3.56246 | ||||||||
\(437\) | 6.14267 | 0.293844 | ||||||||
\(438\) | 61.4360 | 2.93553 | ||||||||
\(439\) | 8.84366 | 0.422085 | 0.211042 | − | 0.977477i | \(-0.432314\pi\) | ||||
0.211042 | + | 0.977477i | \(0.432314\pi\) | |||||||
\(440\) | −9.13485 | −0.435487 | ||||||||
\(441\) | −6.61027 | −0.314775 | ||||||||
\(442\) | 76.0661 | 3.61810 | ||||||||
\(443\) | −29.9752 | −1.42416 | −0.712082 | − | 0.702097i | \(-0.752247\pi\) | ||||
−0.712082 | + | 0.702097i | \(0.752247\pi\) | |||||||
\(444\) | −57.1846 | −2.71386 | ||||||||
\(445\) | −0.0239683 | −0.00113621 | ||||||||
\(446\) | −69.8811 | −3.30897 | ||||||||
\(447\) | −18.6501 | −0.882121 | ||||||||
\(448\) | −10.7566 | −0.508203 | ||||||||
\(449\) | 16.6323 | 0.784929 | 0.392464 | − | 0.919767i | \(-0.371623\pi\) | ||||
0.392464 | + | 0.919767i | \(0.371623\pi\) | |||||||
\(450\) | 21.7715 | 1.02632 | ||||||||
\(451\) | −1.59613 | −0.0751587 | ||||||||
\(452\) | 13.7417 | 0.646357 | ||||||||
\(453\) | 2.23952 | 0.105222 | ||||||||
\(454\) | 30.6113 | 1.43666 | ||||||||
\(455\) | −8.35202 | −0.391549 | ||||||||
\(456\) | −86.4014 | −4.04612 | ||||||||
\(457\) | −2.95227 | −0.138101 | −0.0690506 | − | 0.997613i | \(-0.521997\pi\) | ||||
−0.0690506 | + | 0.997613i | \(0.521997\pi\) | |||||||
\(458\) | −40.3023 | −1.88320 | ||||||||
\(459\) | 13.6611 | 0.637645 | ||||||||
\(460\) | 4.90323 | 0.228614 | ||||||||
\(461\) | 7.26264 | 0.338255 | 0.169127 | − | 0.985594i | \(-0.445905\pi\) | ||||
0.169127 | + | 0.985594i | \(0.445905\pi\) | |||||||
\(462\) | 15.7514 | 0.732823 | ||||||||
\(463\) | −28.5288 | −1.32585 | −0.662923 | − | 0.748687i | \(-0.730685\pi\) | ||||
−0.662923 | + | 0.748687i | \(0.730685\pi\) | |||||||
\(464\) | −4.25671 | −0.197613 | ||||||||
\(465\) | 0.354861 | 0.0164563 | ||||||||
\(466\) | 6.36677 | 0.294935 | ||||||||
\(467\) | −29.1857 | −1.35055 | −0.675277 | − | 0.737564i | \(-0.735976\pi\) | ||||
−0.675277 | + | 0.737564i | \(0.735976\pi\) | |||||||
\(468\) | −45.1559 | −2.08733 | ||||||||
\(469\) | −19.3141 | −0.891842 | ||||||||
\(470\) | −21.3816 | −0.986259 | ||||||||
\(471\) | 13.4516 | 0.619816 | ||||||||
\(472\) | 80.0999 | 3.68689 | ||||||||
\(473\) | −0.395917 | −0.0182043 | ||||||||
\(474\) | −77.2115 | −3.54644 | ||||||||
\(475\) | 22.6077 | 1.03731 | ||||||||
\(476\) | −56.6011 | −2.59431 | ||||||||
\(477\) | 2.01543 | 0.0922804 | ||||||||
\(478\) | 76.5376 | 3.50075 | ||||||||
\(479\) | 38.9292 | 1.77872 | 0.889361 | − | 0.457205i | \(-0.151149\pi\) | ||||
0.889361 | + | 0.457205i | \(0.151149\pi\) | |||||||
\(480\) | −18.5619 | −0.847231 | ||||||||
\(481\) | −25.5009 | −1.16274 | ||||||||
\(482\) | 30.1551 | 1.37353 | ||||||||
\(483\) | −4.88472 | −0.222262 | ||||||||
\(484\) | −42.7519 | −1.94327 | ||||||||
\(485\) | −8.46642 | −0.384440 | ||||||||
\(486\) | −46.6789 | −2.11740 | ||||||||
\(487\) | 27.0210 | 1.22444 | 0.612218 | − | 0.790689i | \(-0.290277\pi\) | ||||
0.612218 | + | 0.790689i | \(0.290277\pi\) | |||||||
\(488\) | 0.149869 | 0.00678427 | ||||||||
\(489\) | −28.6025 | −1.29345 | ||||||||
\(490\) | −7.79273 | −0.352040 | ||||||||
\(491\) | 7.35559 | 0.331953 | 0.165977 | − | 0.986130i | \(-0.446922\pi\) | ||||
0.165977 | + | 0.986130i | \(0.446922\pi\) | |||||||
\(492\) | −12.0507 | −0.543287 | ||||||||
\(493\) | −2.94295 | −0.132544 | ||||||||
\(494\) | −66.6898 | −3.00052 | ||||||||
\(495\) | 2.59213 | 0.116508 | ||||||||
\(496\) | 1.55117 | 0.0696496 | ||||||||
\(497\) | 23.6689 | 1.06170 | ||||||||
\(498\) | −59.0604 | −2.64656 | ||||||||
\(499\) | 27.1308 | 1.21454 | 0.607271 | − | 0.794495i | \(-0.292264\pi\) | ||||
0.607271 | + | 0.794495i | \(0.292264\pi\) | |||||||
\(500\) | 39.7255 | 1.77658 | ||||||||
\(501\) | 21.1049 | 0.942897 | ||||||||
\(502\) | −21.1510 | −0.944015 | ||||||||
\(503\) | 0.324456 | 0.0144668 | 0.00723338 | − | 0.999974i | \(-0.497698\pi\) | ||||
0.00723338 | + | 0.999974i | \(0.497698\pi\) | |||||||
\(504\) | 27.6098 | 1.22984 | ||||||||
\(505\) | 9.03317 | 0.401971 | ||||||||
\(506\) | −4.12371 | −0.183321 | ||||||||
\(507\) | −20.9970 | −0.932510 | ||||||||
\(508\) | 37.0306 | 1.64297 | ||||||||
\(509\) | −12.4878 | −0.553510 | −0.276755 | − | 0.960941i | \(-0.589259\pi\) | ||||
−0.276755 | + | 0.960941i | \(0.589259\pi\) | |||||||
\(510\) | −32.9670 | −1.45980 | ||||||||
\(511\) | −20.3861 | −0.901826 | ||||||||
\(512\) | 46.1595 | 2.03998 | ||||||||
\(513\) | −11.9771 | −0.528804 | ||||||||
\(514\) | 62.2013 | 2.74358 | ||||||||
\(515\) | 11.9104 | 0.524834 | ||||||||
\(516\) | −2.98916 | −0.131590 | ||||||||
\(517\) | 12.6435 | 0.556062 | ||||||||
\(518\) | 26.9877 | 1.18577 | ||||||||
\(519\) | 53.9642 | 2.36877 | ||||||||
\(520\) | −30.7555 | −1.34872 | ||||||||
\(521\) | 14.6288 | 0.640899 | 0.320449 | − | 0.947266i | \(-0.396166\pi\) | ||||
0.320449 | + | 0.947266i | \(0.396166\pi\) | |||||||
\(522\) | 2.48475 | 0.108755 | ||||||||
\(523\) | −10.3413 | −0.452192 | −0.226096 | − | 0.974105i | \(-0.572596\pi\) | ||||
−0.226096 | + | 0.974105i | \(0.572596\pi\) | |||||||
\(524\) | −95.8368 | −4.18665 | ||||||||
\(525\) | −17.9779 | −0.784618 | ||||||||
\(526\) | −10.3363 | −0.450685 | ||||||||
\(527\) | 1.07243 | 0.0467157 | ||||||||
\(528\) | 28.1967 | 1.22710 | ||||||||
\(529\) | −21.7212 | −0.944399 | ||||||||
\(530\) | 2.37596 | 0.103205 | ||||||||
\(531\) | −22.7294 | −0.986372 | ||||||||
\(532\) | 49.6242 | 2.15148 | ||||||||
\(533\) | −5.37389 | −0.232769 | ||||||||
\(534\) | 0.152190 | 0.00658591 | ||||||||
\(535\) | −4.11737 | −0.178010 | ||||||||
\(536\) | −71.1222 | −3.07201 | ||||||||
\(537\) | 10.8369 | 0.467646 | ||||||||
\(538\) | −26.3649 | −1.13667 | ||||||||
\(539\) | 4.60806 | 0.198483 | ||||||||
\(540\) | −9.56045 | −0.411416 | ||||||||
\(541\) | 39.4200 | 1.69480 | 0.847400 | − | 0.530955i | \(-0.178167\pi\) | ||||
0.847400 | + | 0.530955i | \(0.178167\pi\) | |||||||
\(542\) | −6.21032 | −0.266756 | ||||||||
\(543\) | −19.7673 | −0.848298 | ||||||||
\(544\) | −56.0961 | −2.40510 | ||||||||
\(545\) | 14.3766 | 0.615827 | ||||||||
\(546\) | 53.0324 | 2.26958 | ||||||||
\(547\) | −12.7784 | −0.546363 | −0.273182 | − | 0.961962i | \(-0.588076\pi\) | ||||
−0.273182 | + | 0.961962i | \(0.588076\pi\) | |||||||
\(548\) | −66.4168 | −2.83718 | ||||||||
\(549\) | −0.0425274 | −0.00181503 | ||||||||
\(550\) | −15.1770 | −0.647150 | ||||||||
\(551\) | 2.58019 | 0.109920 | ||||||||
\(552\) | −17.9875 | −0.765597 | ||||||||
\(553\) | 25.6208 | 1.08951 | ||||||||
\(554\) | 65.7930 | 2.79527 | ||||||||
\(555\) | 11.0521 | 0.469134 | ||||||||
\(556\) | 105.083 | 4.45652 | ||||||||
\(557\) | −20.9673 | −0.888413 | −0.444206 | − | 0.895925i | \(-0.646514\pi\) | ||||
−0.444206 | + | 0.895925i | \(0.646514\pi\) | |||||||
\(558\) | −0.905458 | −0.0383311 | ||||||||
\(559\) | −1.33298 | −0.0563792 | ||||||||
\(560\) | 15.8227 | 0.668631 | ||||||||
\(561\) | 19.4943 | 0.823050 | ||||||||
\(562\) | 35.1247 | 1.48165 | ||||||||
\(563\) | −22.2170 | −0.936334 | −0.468167 | − | 0.883640i | \(-0.655085\pi\) | ||||
−0.468167 | + | 0.883640i | \(0.655085\pi\) | |||||||
\(564\) | 95.4581 | 4.01951 | ||||||||
\(565\) | −2.65586 | −0.111733 | ||||||||
\(566\) | 58.5507 | 2.46107 | ||||||||
\(567\) | 21.1863 | 0.889741 | ||||||||
\(568\) | 87.1585 | 3.65709 | ||||||||
\(569\) | −5.35056 | −0.224307 | −0.112153 | − | 0.993691i | \(-0.535775\pi\) | ||||
−0.112153 | + | 0.993691i | \(0.535775\pi\) | |||||||
\(570\) | 28.9033 | 1.21063 | ||||||||
\(571\) | −25.6917 | −1.07517 | −0.537583 | − | 0.843211i | \(-0.680662\pi\) | ||||
−0.537583 | + | 0.843211i | \(0.680662\pi\) | |||||||
\(572\) | 31.4784 | 1.31618 | ||||||||
\(573\) | 55.0708 | 2.30061 | ||||||||
\(574\) | 5.68721 | 0.237379 | ||||||||
\(575\) | 4.70658 | 0.196278 | ||||||||
\(576\) | 11.2399 | 0.468330 | ||||||||
\(577\) | −9.69911 | −0.403779 | −0.201890 | − | 0.979408i | \(-0.564708\pi\) | ||||
−0.201890 | + | 0.979408i | \(0.564708\pi\) | |||||||
\(578\) | −55.5067 | −2.30877 | ||||||||
\(579\) | 34.2084 | 1.42165 | ||||||||
\(580\) | 2.05957 | 0.0855189 | ||||||||
\(581\) | 19.5978 | 0.813052 | ||||||||
\(582\) | 53.7588 | 2.22837 | ||||||||
\(583\) | −1.40497 | −0.0581879 | ||||||||
\(584\) | −75.0696 | −3.10640 | ||||||||
\(585\) | 8.72727 | 0.360828 | ||||||||
\(586\) | −60.1831 | −2.48614 | ||||||||
\(587\) | −0.447424 | −0.0184672 | −0.00923358 | − | 0.999957i | \(-0.502939\pi\) | ||||
−0.00923358 | + | 0.999957i | \(0.502939\pi\) | |||||||
\(588\) | 34.7906 | 1.43474 | ||||||||
\(589\) | −0.940236 | −0.0387417 | ||||||||
\(590\) | −26.7953 | −1.10314 | ||||||||
\(591\) | −28.1524 | −1.15804 | ||||||||
\(592\) | 48.3109 | 1.98556 | ||||||||
\(593\) | −13.4924 | −0.554067 | −0.277034 | − | 0.960860i | \(-0.589351\pi\) | ||||
−0.277034 | + | 0.960860i | \(0.589351\pi\) | |||||||
\(594\) | 8.04051 | 0.329906 | ||||||||
\(595\) | 10.9393 | 0.448467 | ||||||||
\(596\) | 39.4444 | 1.61570 | ||||||||
\(597\) | −6.02817 | −0.246717 | ||||||||
\(598\) | −13.8838 | −0.567751 | ||||||||
\(599\) | −45.8820 | −1.87469 | −0.937343 | − | 0.348408i | \(-0.886722\pi\) | ||||
−0.937343 | + | 0.348408i | \(0.886722\pi\) | |||||||
\(600\) | −66.2016 | −2.70267 | ||||||||
\(601\) | 5.85474 | 0.238820 | 0.119410 | − | 0.992845i | \(-0.461900\pi\) | ||||
0.119410 | + | 0.992845i | \(0.461900\pi\) | |||||||
\(602\) | 1.41070 | 0.0574960 | ||||||||
\(603\) | 20.1819 | 0.821869 | ||||||||
\(604\) | −4.73650 | −0.192725 | ||||||||
\(605\) | 8.26266 | 0.335925 | ||||||||
\(606\) | −57.3575 | −2.32999 | ||||||||
\(607\) | 44.4328 | 1.80347 | 0.901735 | − | 0.432289i | \(-0.142294\pi\) | ||||
0.901735 | + | 0.432289i | \(0.142294\pi\) | |||||||
\(608\) | 49.1814 | 1.99457 | ||||||||
\(609\) | −2.05179 | −0.0831427 | ||||||||
\(610\) | −0.0501348 | −0.00202990 | ||||||||
\(611\) | 42.5686 | 1.72214 | ||||||||
\(612\) | 59.1442 | 2.39076 | ||||||||
\(613\) | 16.6245 | 0.671459 | 0.335729 | − | 0.941959i | \(-0.391017\pi\) | ||||
0.335729 | + | 0.941959i | \(0.391017\pi\) | |||||||
\(614\) | 62.8355 | 2.53583 | ||||||||
\(615\) | 2.32904 | 0.0939158 | ||||||||
\(616\) | −19.2469 | −0.775481 | ||||||||
\(617\) | 11.0852 | 0.446273 | 0.223136 | − | 0.974787i | \(-0.428371\pi\) | ||||
0.223136 | + | 0.974787i | \(0.428371\pi\) | |||||||
\(618\) | −75.6267 | −3.04215 | ||||||||
\(619\) | 48.2928 | 1.94105 | 0.970526 | − | 0.240997i | \(-0.0774743\pi\) | ||||
0.970526 | + | 0.240997i | \(0.0774743\pi\) | |||||||
\(620\) | −0.750519 | −0.0301416 | ||||||||
\(621\) | −2.49346 | −0.100059 | ||||||||
\(622\) | 29.9804 | 1.20210 | ||||||||
\(623\) | −0.0505006 | −0.00202327 | ||||||||
\(624\) | 94.9335 | 3.80038 | ||||||||
\(625\) | 13.1323 | 0.525290 | ||||||||
\(626\) | 73.9791 | 2.95680 | ||||||||
\(627\) | −17.0913 | −0.682562 | ||||||||
\(628\) | −28.4496 | −1.13526 | ||||||||
\(629\) | 33.4006 | 1.33177 | ||||||||
\(630\) | −9.23611 | −0.367975 | ||||||||
\(631\) | 4.18873 | 0.166751 | 0.0833754 | − | 0.996518i | \(-0.473430\pi\) | ||||
0.0833754 | + | 0.996518i | \(0.473430\pi\) | |||||||
\(632\) | 94.3459 | 3.75288 | ||||||||
\(633\) | 33.3835 | 1.32688 | ||||||||
\(634\) | −1.94732 | −0.0773381 | ||||||||
\(635\) | −7.15689 | −0.284013 | ||||||||
\(636\) | −10.6075 | −0.420613 | ||||||||
\(637\) | 15.5145 | 0.614708 | ||||||||
\(638\) | −1.73213 | −0.0685758 | ||||||||
\(639\) | −24.7324 | −0.978398 | ||||||||
\(640\) | −3.32616 | −0.131478 | ||||||||
\(641\) | 49.1571 | 1.94159 | 0.970794 | − | 0.239915i | \(-0.0771195\pi\) | ||||
0.970794 | + | 0.239915i | \(0.0771195\pi\) | |||||||
\(642\) | 26.1439 | 1.03182 | ||||||||
\(643\) | 4.24484 | 0.167400 | 0.0837001 | − | 0.996491i | \(-0.473326\pi\) | ||||
0.0837001 | + | 0.996491i | \(0.473326\pi\) | |||||||
\(644\) | 10.3310 | 0.407099 | ||||||||
\(645\) | 0.577714 | 0.0227475 | ||||||||
\(646\) | 87.3489 | 3.43670 | ||||||||
\(647\) | −4.44464 | −0.174737 | −0.0873683 | − | 0.996176i | \(-0.527846\pi\) | ||||
−0.0873683 | + | 0.996176i | \(0.527846\pi\) | |||||||
\(648\) | 78.0164 | 3.06477 | ||||||||
\(649\) | 15.8448 | 0.621963 | ||||||||
\(650\) | −51.0984 | −2.00425 | ||||||||
\(651\) | 0.747685 | 0.0293041 | ||||||||
\(652\) | 60.4934 | 2.36910 | ||||||||
\(653\) | −14.5703 | −0.570179 | −0.285089 | − | 0.958501i | \(-0.592023\pi\) | ||||
−0.285089 | + | 0.958501i | \(0.592023\pi\) | |||||||
\(654\) | −91.2865 | −3.56959 | ||||||||
\(655\) | 18.5224 | 0.723729 | ||||||||
\(656\) | 10.1807 | 0.397489 | ||||||||
\(657\) | 21.3020 | 0.831070 | ||||||||
\(658\) | −45.0505 | −1.75625 | ||||||||
\(659\) | 33.8578 | 1.31891 | 0.659456 | − | 0.751743i | \(-0.270787\pi\) | ||||
0.659456 | + | 0.751743i | \(0.270787\pi\) | |||||||
\(660\) | −13.6427 | −0.531042 | ||||||||
\(661\) | −4.68338 | −0.182162 | −0.0910812 | − | 0.995843i | \(-0.529032\pi\) | ||||
−0.0910812 | + | 0.995843i | \(0.529032\pi\) | |||||||
\(662\) | 53.7221 | 2.08797 | ||||||||
\(663\) | 65.6339 | 2.54901 | ||||||||
\(664\) | 72.1668 | 2.80061 | ||||||||
\(665\) | −9.59086 | −0.371918 | ||||||||
\(666\) | −28.2003 | −1.09274 | ||||||||
\(667\) | 0.537156 | 0.0207988 | ||||||||
\(668\) | −44.6361 | −1.72702 | ||||||||
\(669\) | −60.2971 | −2.33122 | ||||||||
\(670\) | 23.7920 | 0.919166 | ||||||||
\(671\) | 0.0296461 | 0.00114448 | ||||||||
\(672\) | −39.1095 | −1.50868 | ||||||||
\(673\) | 49.7267 | 1.91682 | 0.958412 | − | 0.285388i | \(-0.0921225\pi\) | ||||
0.958412 | + | 0.285388i | \(0.0921225\pi\) | |||||||
\(674\) | 27.4506 | 1.05736 | ||||||||
\(675\) | −9.17701 | −0.353223 | ||||||||
\(676\) | 44.4079 | 1.70800 | ||||||||
\(677\) | 35.6773 | 1.37119 | 0.685596 | − | 0.727982i | \(-0.259542\pi\) | ||||
0.685596 | + | 0.727982i | \(0.259542\pi\) | |||||||
\(678\) | 16.8638 | 0.647650 | ||||||||
\(679\) | −17.8386 | −0.684581 | ||||||||
\(680\) | 40.2828 | 1.54478 | ||||||||
\(681\) | 26.4131 | 1.01215 | ||||||||
\(682\) | 0.631200 | 0.0241699 | ||||||||
\(683\) | −3.57858 | −0.136930 | −0.0684652 | − | 0.997654i | \(-0.521810\pi\) | ||||
−0.0684652 | + | 0.997654i | \(0.521810\pi\) | |||||||
\(684\) | −51.8537 | −1.98268 | ||||||||
\(685\) | 12.8364 | 0.490452 | ||||||||
\(686\) | −51.4617 | −1.96482 | ||||||||
\(687\) | −34.7750 | −1.32675 | ||||||||
\(688\) | 2.52531 | 0.0962764 | ||||||||
\(689\) | −4.73029 | −0.180210 | ||||||||
\(690\) | 6.01723 | 0.229072 | ||||||||
\(691\) | 50.4774 | 1.92025 | 0.960125 | − | 0.279570i | \(-0.0901919\pi\) | ||||
0.960125 | + | 0.279570i | \(0.0901919\pi\) | |||||||
\(692\) | −114.132 | −4.33867 | ||||||||
\(693\) | 5.46157 | 0.207468 | ||||||||
\(694\) | 9.45685 | 0.358977 | ||||||||
\(695\) | −20.3094 | −0.770381 | ||||||||
\(696\) | −7.55551 | −0.286391 | ||||||||
\(697\) | 7.03860 | 0.266606 | ||||||||
\(698\) | −39.5894 | −1.49848 | ||||||||
\(699\) | 5.49359 | 0.207787 | ||||||||
\(700\) | 38.0226 | 1.43712 | ||||||||
\(701\) | −25.8321 | −0.975666 | −0.487833 | − | 0.872937i | \(-0.662213\pi\) | ||||
−0.487833 | + | 0.872937i | \(0.662213\pi\) | |||||||
\(702\) | 27.0710 | 1.02173 | ||||||||
\(703\) | −29.2834 | −1.10445 | ||||||||
\(704\) | −7.83542 | −0.295308 | ||||||||
\(705\) | −18.4492 | −0.694836 | ||||||||
\(706\) | 17.8612 | 0.672215 | ||||||||
\(707\) | 19.0327 | 0.715798 | ||||||||
\(708\) | 119.628 | 4.49588 | ||||||||
\(709\) | 37.7668 | 1.41836 | 0.709181 | − | 0.705026i | \(-0.249065\pi\) | ||||
0.709181 | + | 0.705026i | \(0.249065\pi\) | |||||||
\(710\) | −29.1565 | −1.09423 | ||||||||
\(711\) | −26.7719 | −1.00402 | ||||||||
\(712\) | −0.185963 | −0.00696927 | ||||||||
\(713\) | −0.195743 | −0.00733063 | ||||||||
\(714\) | −69.4607 | −2.59950 | ||||||||
\(715\) | −6.08383 | −0.227522 | ||||||||
\(716\) | −22.9196 | −0.856548 | ||||||||
\(717\) | 66.0408 | 2.46634 | ||||||||
\(718\) | 5.08820 | 0.189890 | ||||||||
\(719\) | 13.5118 | 0.503904 | 0.251952 | − | 0.967740i | \(-0.418928\pi\) | ||||
0.251952 | + | 0.967740i | \(0.418928\pi\) | |||||||
\(720\) | −16.5336 | −0.616170 | ||||||||
\(721\) | 25.0949 | 0.934583 | ||||||||
\(722\) | −27.2677 | −1.01480 | ||||||||
\(723\) | 26.0195 | 0.967674 | ||||||||
\(724\) | 41.8072 | 1.55375 | ||||||||
\(725\) | 1.97697 | 0.0734227 | ||||||||
\(726\) | −52.4650 | −1.94716 | ||||||||
\(727\) | −0.909933 | −0.0337476 | −0.0168738 | − | 0.999858i | \(-0.505371\pi\) | ||||
−0.0168738 | + | 0.999858i | \(0.505371\pi\) | |||||||
\(728\) | −64.8011 | −2.40169 | ||||||||
\(729\) | −7.32410 | −0.271263 | ||||||||
\(730\) | 25.1125 | 0.929456 | ||||||||
\(731\) | 1.74591 | 0.0645750 | ||||||||
\(732\) | 0.223827 | 0.00827288 | ||||||||
\(733\) | −11.1235 | −0.410857 | −0.205429 | − | 0.978672i | \(-0.565859\pi\) | ||||
−0.205429 | + | 0.978672i | \(0.565859\pi\) | |||||||
\(734\) | 32.9299 | 1.21547 | ||||||||
\(735\) | −6.72398 | −0.248018 | ||||||||
\(736\) | 10.2388 | 0.377408 | ||||||||
\(737\) | −14.0689 | −0.518234 | ||||||||
\(738\) | −5.94273 | −0.218755 | ||||||||
\(739\) | 38.7261 | 1.42456 | 0.712282 | − | 0.701894i | \(-0.247662\pi\) | ||||
0.712282 | + | 0.701894i | \(0.247662\pi\) | |||||||
\(740\) | −23.3747 | −0.859273 | ||||||||
\(741\) | −57.5435 | −2.11391 | ||||||||
\(742\) | 5.00609 | 0.183779 | ||||||||
\(743\) | 8.16600 | 0.299582 | 0.149791 | − | 0.988718i | \(-0.452140\pi\) | ||||
0.149791 | + | 0.988718i | \(0.452140\pi\) | |||||||
\(744\) | 2.75327 | 0.100940 | ||||||||
\(745\) | −7.62341 | −0.279300 | ||||||||
\(746\) | 21.8767 | 0.800964 | ||||||||
\(747\) | −20.4783 | −0.749261 | ||||||||
\(748\) | −41.2298 | −1.50751 | ||||||||
\(749\) | −8.67521 | −0.316985 | ||||||||
\(750\) | 48.7510 | 1.78013 | ||||||||
\(751\) | −5.06604 | −0.184863 | −0.0924313 | − | 0.995719i | \(-0.529464\pi\) | ||||
−0.0924313 | + | 0.995719i | \(0.529464\pi\) | |||||||
\(752\) | −80.6451 | −2.94082 | ||||||||
\(753\) | −18.2502 | −0.665075 | ||||||||
\(754\) | −5.83180 | −0.212381 | ||||||||
\(755\) | 0.915423 | 0.0333156 | ||||||||
\(756\) | −20.1437 | −0.732618 | ||||||||
\(757\) | −22.9193 | −0.833016 | −0.416508 | − | 0.909132i | \(-0.636746\pi\) | ||||
−0.416508 | + | 0.909132i | \(0.636746\pi\) | |||||||
\(758\) | −38.9804 | −1.41583 | ||||||||
\(759\) | −3.55816 | −0.129153 | ||||||||
\(760\) | −35.3174 | −1.28110 | ||||||||
\(761\) | −14.6692 | −0.531758 | −0.265879 | − | 0.964006i | \(-0.585662\pi\) | ||||
−0.265879 | + | 0.964006i | \(0.585662\pi\) | |||||||
\(762\) | 45.4437 | 1.64625 | ||||||||
\(763\) | 30.2912 | 1.09662 | ||||||||
\(764\) | −116.473 | −4.21383 | ||||||||
\(765\) | −11.4308 | −0.413281 | ||||||||
\(766\) | 41.4599 | 1.49801 | ||||||||
\(767\) | 53.3467 | 1.92624 | ||||||||
\(768\) | 46.0992 | 1.66346 | ||||||||
\(769\) | −30.3536 | −1.09458 | −0.547289 | − | 0.836944i | \(-0.684340\pi\) | ||||
−0.547289 | + | 0.836944i | \(0.684340\pi\) | |||||||
\(770\) | 6.43855 | 0.232029 | ||||||||
\(771\) | 53.6706 | 1.93290 | ||||||||
\(772\) | −72.3495 | −2.60391 | ||||||||
\(773\) | 7.24859 | 0.260714 | 0.130357 | − | 0.991467i | \(-0.458388\pi\) | ||||
0.130357 | + | 0.991467i | \(0.458388\pi\) | |||||||
\(774\) | −1.47409 | −0.0529849 | ||||||||
\(775\) | −0.720418 | −0.0258782 | ||||||||
\(776\) | −65.6887 | −2.35809 | ||||||||
\(777\) | 23.2865 | 0.835398 | ||||||||
\(778\) | 4.41071 | 0.158131 | ||||||||
\(779\) | −6.17098 | −0.221098 | ||||||||
\(780\) | −45.9327 | −1.64465 | ||||||||
\(781\) | 17.2411 | 0.616935 | ||||||||
\(782\) | 18.1847 | 0.650284 | ||||||||
\(783\) | −1.04736 | −0.0374296 | ||||||||
\(784\) | −29.3919 | −1.04971 | ||||||||
\(785\) | 5.49845 | 0.196248 | ||||||||
\(786\) | −117.610 | −4.19503 | ||||||||
\(787\) | −44.9306 | −1.60160 | −0.800802 | − | 0.598929i | \(-0.795593\pi\) | ||||
−0.800802 | + | 0.598929i | \(0.795593\pi\) | |||||||
\(788\) | 59.5414 | 2.12108 | ||||||||
\(789\) | −8.91873 | −0.317515 | ||||||||
\(790\) | −31.5609 | −1.12289 | ||||||||
\(791\) | −5.59585 | −0.198965 | ||||||||
\(792\) | 20.1117 | 0.714637 | ||||||||
\(793\) | 0.0998133 | 0.00354448 | ||||||||
\(794\) | 37.1798 | 1.31946 | ||||||||
\(795\) | 2.05010 | 0.0727097 | ||||||||
\(796\) | 12.7494 | 0.451890 | ||||||||
\(797\) | 19.7845 | 0.700803 | 0.350402 | − | 0.936600i | \(-0.386045\pi\) | ||||
0.350402 | + | 0.936600i | \(0.386045\pi\) | |||||||
\(798\) | 60.8986 | 2.15579 | ||||||||
\(799\) | −55.7554 | −1.97248 | ||||||||
\(800\) | 37.6833 | 1.33231 | ||||||||
\(801\) | 0.0527696 | 0.00186452 | ||||||||
\(802\) | 91.4985 | 3.23092 | ||||||||
\(803\) | −14.8497 | −0.524036 | ||||||||
\(804\) | −106.220 | −3.74607 | ||||||||
\(805\) | −1.99667 | −0.0703734 | ||||||||
\(806\) | 2.12514 | 0.0748549 | ||||||||
\(807\) | −22.7490 | −0.800804 | ||||||||
\(808\) | 70.0859 | 2.46561 | ||||||||
\(809\) | −15.8874 | −0.558570 | −0.279285 | − | 0.960208i | \(-0.590097\pi\) | ||||
−0.279285 | + | 0.960208i | \(0.590097\pi\) | |||||||
\(810\) | −26.0983 | −0.917001 | ||||||||
\(811\) | −31.5445 | −1.10768 | −0.553838 | − | 0.832625i | \(-0.686837\pi\) | ||||
−0.553838 | + | 0.832625i | \(0.686837\pi\) | |||||||
\(812\) | 4.33946 | 0.152285 | ||||||||
\(813\) | −5.35860 | −0.187934 | ||||||||
\(814\) | 19.6586 | 0.689033 | ||||||||
\(815\) | −11.6915 | −0.409537 | ||||||||
\(816\) | −124.342 | −4.35283 | ||||||||
\(817\) | −1.53070 | −0.0535525 | ||||||||
\(818\) | 45.2067 | 1.58062 | ||||||||
\(819\) | 18.3882 | 0.642534 | ||||||||
\(820\) | −4.92583 | −0.172017 | ||||||||
\(821\) | −40.0120 | −1.39643 | −0.698214 | − | 0.715889i | \(-0.746022\pi\) | ||||
−0.698214 | + | 0.715889i | \(0.746022\pi\) | |||||||
\(822\) | −81.5064 | −2.84286 | ||||||||
\(823\) | −4.38506 | −0.152854 | −0.0764268 | − | 0.997075i | \(-0.524351\pi\) | ||||
−0.0764268 | + | 0.997075i | \(0.524351\pi\) | |||||||
\(824\) | 92.4094 | 3.21923 | ||||||||
\(825\) | −13.0956 | −0.455929 | ||||||||
\(826\) | −56.4570 | −1.96439 | ||||||||
\(827\) | −21.3622 | −0.742836 | −0.371418 | − | 0.928466i | \(-0.621128\pi\) | ||||
−0.371418 | + | 0.928466i | \(0.621128\pi\) | |||||||
\(828\) | −10.7952 | −0.375158 | ||||||||
\(829\) | 8.39222 | 0.291474 | 0.145737 | − | 0.989323i | \(-0.453445\pi\) | ||||
0.145737 | + | 0.989323i | \(0.453445\pi\) | |||||||
\(830\) | −24.1415 | −0.837962 | ||||||||
\(831\) | 56.7697 | 1.96932 | ||||||||
\(832\) | −26.3805 | −0.914579 | ||||||||
\(833\) | −20.3206 | −0.704068 | ||||||||
\(834\) | 128.958 | 4.46544 | ||||||||
\(835\) | 8.62682 | 0.298543 | ||||||||
\(836\) | 36.1475 | 1.25019 | ||||||||
\(837\) | 0.381665 | 0.0131923 | ||||||||
\(838\) | 83.4745 | 2.88358 | ||||||||
\(839\) | 23.0943 | 0.797304 | 0.398652 | − | 0.917102i | \(-0.369478\pi\) | ||||
0.398652 | + | 0.917102i | \(0.369478\pi\) | |||||||
\(840\) | 28.0847 | 0.969015 | ||||||||
\(841\) | −28.7744 | −0.992220 | ||||||||
\(842\) | −4.51610 | −0.155635 | ||||||||
\(843\) | 30.3075 | 1.04385 | ||||||||
\(844\) | −70.6050 | −2.43032 | ||||||||
\(845\) | −8.58272 | −0.295255 | ||||||||
\(846\) | 47.0746 | 1.61846 | ||||||||
\(847\) | 17.4092 | 0.598188 | ||||||||
\(848\) | 8.96142 | 0.307736 | ||||||||
\(849\) | 50.5207 | 1.73387 | ||||||||
\(850\) | 66.9276 | 2.29560 | ||||||||
\(851\) | −6.09637 | −0.208981 | ||||||||
\(852\) | 130.169 | 4.45953 | ||||||||
\(853\) | 41.6724 | 1.42684 | 0.713418 | − | 0.700739i | \(-0.247146\pi\) | ||||
0.713418 | + | 0.700739i | \(0.247146\pi\) | |||||||
\(854\) | −0.105633 | −0.00361468 | ||||||||
\(855\) | 10.0218 | 0.342737 | ||||||||
\(856\) | −31.9456 | −1.09188 | ||||||||
\(857\) | 14.4831 | 0.494732 | 0.247366 | − | 0.968922i | \(-0.420435\pi\) | ||||
0.247366 | + | 0.968922i | \(0.420435\pi\) | |||||||
\(858\) | 38.6302 | 1.31881 | ||||||||
\(859\) | 25.6595 | 0.875490 | 0.437745 | − | 0.899099i | \(-0.355777\pi\) | ||||
0.437745 | + | 0.899099i | \(0.355777\pi\) | |||||||
\(860\) | −1.22184 | −0.0416646 | ||||||||
\(861\) | 4.90723 | 0.167238 | ||||||||
\(862\) | −36.2474 | −1.23459 | ||||||||
\(863\) | −12.2604 | −0.417347 | −0.208674 | − | 0.977985i | \(-0.566915\pi\) | ||||
−0.208674 | + | 0.977985i | \(0.566915\pi\) | |||||||
\(864\) | −19.9639 | −0.679186 | ||||||||
\(865\) | 22.0584 | 0.750007 | ||||||||
\(866\) | 80.0109 | 2.71888 | ||||||||
\(867\) | −47.8942 | −1.62657 | ||||||||
\(868\) | −1.58133 | −0.0536737 | ||||||||
\(869\) | 18.6629 | 0.633094 | ||||||||
\(870\) | 2.52749 | 0.0856900 | ||||||||
\(871\) | −47.3675 | −1.60499 | ||||||||
\(872\) | 111.544 | 3.77737 | ||||||||
\(873\) | 18.6400 | 0.630869 | ||||||||
\(874\) | −15.9432 | −0.539286 | ||||||||
\(875\) | −16.1768 | −0.546877 | ||||||||
\(876\) | −112.115 | −3.78801 | ||||||||
\(877\) | 18.7815 | 0.634208 | 0.317104 | − | 0.948391i | \(-0.397290\pi\) | ||||
0.317104 | + | 0.948391i | \(0.397290\pi\) | |||||||
\(878\) | −22.9535 | −0.774644 | ||||||||
\(879\) | −51.9292 | −1.75153 | ||||||||
\(880\) | 11.5257 | 0.388530 | ||||||||
\(881\) | 22.5324 | 0.759136 | 0.379568 | − | 0.925164i | \(-0.376073\pi\) | ||||
0.379568 | + | 0.925164i | \(0.376073\pi\) | |||||||
\(882\) | 17.1568 | 0.577700 | ||||||||
\(883\) | −38.6033 | −1.29911 | −0.649553 | − | 0.760317i | \(-0.725044\pi\) | ||||
−0.649553 | + | 0.760317i | \(0.725044\pi\) | |||||||
\(884\) | −138.813 | −4.66880 | ||||||||
\(885\) | −23.1204 | −0.777184 | ||||||||
\(886\) | 77.7999 | 2.61374 | ||||||||
\(887\) | −12.7037 | −0.426549 | −0.213275 | − | 0.976992i | \(-0.568413\pi\) | ||||
−0.213275 | + | 0.976992i | \(0.568413\pi\) | |||||||
\(888\) | 85.7501 | 2.87758 | ||||||||
\(889\) | −15.0794 | −0.505747 | ||||||||
\(890\) | 0.0622091 | 0.00208525 | ||||||||
\(891\) | 15.4327 | 0.517014 | ||||||||
\(892\) | 127.526 | 4.26990 | ||||||||
\(893\) | 48.8827 | 1.63580 | ||||||||
\(894\) | 48.4060 | 1.61894 | ||||||||
\(895\) | 4.42968 | 0.148068 | ||||||||
\(896\) | −7.00815 | −0.234126 | ||||||||
\(897\) | −11.9797 | −0.399990 | ||||||||
\(898\) | −43.1689 | −1.44056 | ||||||||
\(899\) | −0.0822204 | −0.00274220 | ||||||||
\(900\) | −39.7309 | −1.32436 | ||||||||
\(901\) | 6.19564 | 0.206407 | ||||||||
\(902\) | 4.14271 | 0.137937 | ||||||||
\(903\) | 1.21723 | 0.0405069 | ||||||||
\(904\) | −20.6061 | −0.685350 | ||||||||
\(905\) | −8.08008 | −0.268591 | ||||||||
\(906\) | −5.81261 | −0.193111 | ||||||||
\(907\) | 45.1381 | 1.49879 | 0.749393 | − | 0.662126i | \(-0.230346\pi\) | ||||
0.749393 | + | 0.662126i | \(0.230346\pi\) | |||||||
\(908\) | −55.8628 | −1.85387 | ||||||||
\(909\) | −19.8878 | −0.659637 | ||||||||
\(910\) | 21.6775 | 0.718601 | ||||||||
\(911\) | 13.1106 | 0.434373 | 0.217187 | − | 0.976130i | \(-0.430312\pi\) | ||||
0.217187 | + | 0.976130i | \(0.430312\pi\) | |||||||
\(912\) | 109.015 | 3.60984 | ||||||||
\(913\) | 14.2755 | 0.472451 | ||||||||
\(914\) | 7.66254 | 0.253454 | ||||||||
\(915\) | −0.0432590 | −0.00143010 | ||||||||
\(916\) | 73.5479 | 2.43009 | ||||||||
\(917\) | 39.0262 | 1.28876 | ||||||||
\(918\) | −35.4570 | −1.17026 | ||||||||
\(919\) | −12.4633 | −0.411127 | −0.205563 | − | 0.978644i | \(-0.565903\pi\) | ||||
−0.205563 | + | 0.978644i | \(0.565903\pi\) | |||||||
\(920\) | −7.35254 | −0.242406 | ||||||||
\(921\) | 54.2178 | 1.78654 | ||||||||
\(922\) | −18.8500 | −0.620792 | ||||||||
\(923\) | 58.0478 | 1.91067 | ||||||||
\(924\) | −28.7449 | −0.945637 | ||||||||
\(925\) | −22.4373 | −0.737733 | ||||||||
\(926\) | 74.0459 | 2.43330 | ||||||||
\(927\) | −26.2224 | −0.861256 | ||||||||
\(928\) | 4.30074 | 0.141179 | ||||||||
\(929\) | −22.9564 | −0.753174 | −0.376587 | − | 0.926381i | \(-0.622902\pi\) | ||||
−0.376587 | + | 0.926381i | \(0.622902\pi\) | |||||||
\(930\) | −0.921034 | −0.0302019 | ||||||||
\(931\) | 17.8158 | 0.583889 | ||||||||
\(932\) | −11.6187 | −0.380585 | ||||||||
\(933\) | 25.8687 | 0.846903 | ||||||||
\(934\) | 75.7508 | 2.47864 | ||||||||
\(935\) | 7.96847 | 0.260597 | ||||||||
\(936\) | 67.7125 | 2.21325 | ||||||||
\(937\) | 39.3761 | 1.28636 | 0.643181 | − | 0.765714i | \(-0.277614\pi\) | ||||
0.643181 | + | 0.765714i | \(0.277614\pi\) | |||||||
\(938\) | 50.1293 | 1.63678 | ||||||||
\(939\) | 63.8331 | 2.08311 | ||||||||
\(940\) | 39.0194 | 1.27267 | ||||||||
\(941\) | 48.8973 | 1.59401 | 0.797004 | − | 0.603974i | \(-0.206417\pi\) | ||||
0.797004 | + | 0.603974i | \(0.206417\pi\) | |||||||
\(942\) | −34.9132 | −1.13753 | ||||||||
\(943\) | −1.28471 | −0.0418358 | ||||||||
\(944\) | −101.064 | −3.28935 | ||||||||
\(945\) | 3.89316 | 0.126645 | ||||||||
\(946\) | 1.02759 | 0.0334099 | ||||||||
\(947\) | −11.7124 | −0.380603 | −0.190302 | − | 0.981726i | \(-0.560947\pi\) | ||||
−0.190302 | + | 0.981726i | \(0.560947\pi\) | |||||||
\(948\) | 140.904 | 4.57634 | ||||||||
\(949\) | −49.9965 | −1.62296 | ||||||||
\(950\) | −58.6777 | −1.90376 | ||||||||
\(951\) | −1.68026 | −0.0544860 | ||||||||
\(952\) | 84.8751 | 2.75082 | ||||||||
\(953\) | 5.80969 | 0.188194 | 0.0940972 | − | 0.995563i | \(-0.470004\pi\) | ||||
0.0940972 | + | 0.995563i | \(0.470004\pi\) | |||||||
\(954\) | −5.23101 | −0.169360 | ||||||||
\(955\) | 22.5107 | 0.728428 | ||||||||
\(956\) | −139.674 | −4.51738 | ||||||||
\(957\) | −1.49458 | −0.0483128 | ||||||||
\(958\) | −101.040 | −3.26445 | ||||||||
\(959\) | 27.0459 | 0.873359 | ||||||||
\(960\) | 11.4333 | 0.369007 | ||||||||
\(961\) | −30.9700 | −0.999033 | ||||||||
\(962\) | 66.1871 | 2.13396 | ||||||||
\(963\) | 9.06498 | 0.292115 | ||||||||
\(964\) | −55.0302 | −1.77240 | ||||||||
\(965\) | 13.9830 | 0.450128 | ||||||||
\(966\) | 12.6782 | 0.407913 | ||||||||
\(967\) | 25.3804 | 0.816179 | 0.408089 | − | 0.912942i | \(-0.366195\pi\) | ||||
0.408089 | + | 0.912942i | \(0.366195\pi\) | |||||||
\(968\) | 64.1077 | 2.06050 | ||||||||
\(969\) | 75.3693 | 2.42121 | ||||||||
\(970\) | 21.9744 | 0.705555 | ||||||||
\(971\) | 49.4845 | 1.58803 | 0.794016 | − | 0.607896i | \(-0.207986\pi\) | ||||
0.794016 | + | 0.607896i | \(0.207986\pi\) | |||||||
\(972\) | 85.1846 | 2.73230 | ||||||||
\(973\) | −42.7915 | −1.37183 | ||||||||
\(974\) | −70.1323 | −2.24718 | ||||||||
\(975\) | −44.0905 | −1.41202 | ||||||||
\(976\) | −0.189094 | −0.00605275 | ||||||||
\(977\) | 52.9016 | 1.69247 | 0.846237 | − | 0.532807i | \(-0.178863\pi\) | ||||
0.846237 | + | 0.532807i | \(0.178863\pi\) | |||||||
\(978\) | 74.2372 | 2.37384 | ||||||||
\(979\) | −0.0367860 | −0.00117569 | ||||||||
\(980\) | 14.2210 | 0.454273 | ||||||||
\(981\) | −31.6522 | −1.01058 | ||||||||
\(982\) | −19.0913 | −0.609227 | ||||||||
\(983\) | −24.5416 | −0.782757 | −0.391378 | − | 0.920230i | \(-0.628002\pi\) | ||||
−0.391378 | + | 0.920230i | \(0.628002\pi\) | |||||||
\(984\) | 18.0704 | 0.576062 | ||||||||
\(985\) | −11.5076 | −0.366662 | ||||||||
\(986\) | 7.63836 | 0.243255 | ||||||||
\(987\) | −38.8720 | −1.23731 | ||||||||
\(988\) | 121.703 | 3.87187 | ||||||||
\(989\) | −0.318669 | −0.0101331 | ||||||||
\(990\) | −6.72782 | −0.213824 | ||||||||
\(991\) | −46.9471 | −1.49132 | −0.745661 | − | 0.666325i | \(-0.767866\pi\) | ||||
−0.745661 | + | 0.666325i | \(0.767866\pi\) | |||||||
\(992\) | −1.56722 | −0.0497592 | ||||||||
\(993\) | 46.3543 | 1.47101 | ||||||||
\(994\) | −61.4322 | −1.94851 | ||||||||
\(995\) | −2.46407 | −0.0781163 | ||||||||
\(996\) | 107.780 | 3.41513 | ||||||||
\(997\) | 25.9911 | 0.823146 | 0.411573 | − | 0.911377i | \(-0.364979\pi\) | ||||
0.411573 | + | 0.911377i | \(0.364979\pi\) | |||||||
\(998\) | −70.4174 | −2.22902 | ||||||||
\(999\) | 11.8869 | 0.376083 |
(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 | 8003.2.a.d.1.10 | ✓ | 179 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.d.1.10 | ✓ | 179 | 1.1 | even | 1 | trivial |