Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.79904 | −1.97922 | −0.989610 | − | 0.143779i | \(-0.954075\pi\) | ||||
−0.989610 | + | 0.143779i | \(0.954075\pi\) | |||||||
\(3\) | −0.951830 | −0.549540 | −0.274770 | − | 0.961510i | \(-0.588602\pi\) | ||||
−0.274770 | + | 0.961510i | \(0.588602\pi\) | |||||||
\(4\) | 5.83462 | 2.91731 | ||||||||
\(5\) | 2.72456 | 1.21846 | 0.609231 | − | 0.792993i | \(-0.291478\pi\) | ||||
0.609231 | + | 0.792993i | \(0.291478\pi\) | |||||||
\(6\) | 2.66421 | 1.08766 | ||||||||
\(7\) | 1.55879 | 0.589169 | 0.294584 | − | 0.955625i | \(-0.404819\pi\) | ||||
0.294584 | + | 0.955625i | \(0.404819\pi\) | |||||||
\(8\) | −10.7333 | −3.79478 | ||||||||
\(9\) | −2.09402 | −0.698006 | ||||||||
\(10\) | −7.62616 | −2.41160 | ||||||||
\(11\) | 4.52022 | 1.36290 | 0.681450 | − | 0.731865i | \(-0.261350\pi\) | ||||
0.681450 | + | 0.731865i | \(0.261350\pi\) | |||||||
\(12\) | −5.55357 | −1.60318 | ||||||||
\(13\) | −4.81472 | −1.33536 | −0.667682 | − | 0.744447i | \(-0.732713\pi\) | ||||
−0.667682 | + | 0.744447i | \(0.732713\pi\) | |||||||
\(14\) | −4.36313 | −1.16609 | ||||||||
\(15\) | −2.59332 | −0.669593 | ||||||||
\(16\) | 18.3736 | 4.59339 | ||||||||
\(17\) | 4.93209 | 1.19621 | 0.598104 | − | 0.801419i | \(-0.295921\pi\) | ||||
0.598104 | + | 0.801419i | \(0.295921\pi\) | |||||||
\(18\) | 5.86124 | 1.38151 | ||||||||
\(19\) | −6.45811 | −1.48159 | −0.740796 | − | 0.671730i | \(-0.765551\pi\) | ||||
−0.740796 | + | 0.671730i | \(0.765551\pi\) | |||||||
\(20\) | 15.8968 | 3.55463 | ||||||||
\(21\) | −1.48371 | −0.323772 | ||||||||
\(22\) | −12.6523 | −2.69748 | ||||||||
\(23\) | −0.588724 | −0.122757 | −0.0613787 | − | 0.998115i | \(-0.519550\pi\) | ||||
−0.0613787 | + | 0.998115i | \(0.519550\pi\) | |||||||
\(24\) | 10.2162 | 2.08538 | ||||||||
\(25\) | 2.42324 | 0.484647 | ||||||||
\(26\) | 13.4766 | 2.64298 | ||||||||
\(27\) | 4.84864 | 0.933122 | ||||||||
\(28\) | 9.09497 | 1.71879 | ||||||||
\(29\) | −7.40239 | −1.37459 | −0.687295 | − | 0.726379i | \(-0.741202\pi\) | ||||
−0.687295 | + | 0.726379i | \(0.741202\pi\) | |||||||
\(30\) | 7.25881 | 1.32527 | ||||||||
\(31\) | 4.71218 | 0.846332 | 0.423166 | − | 0.906052i | \(-0.360919\pi\) | ||||
0.423166 | + | 0.906052i | \(0.360919\pi\) | |||||||
\(32\) | −29.9618 | −5.29655 | ||||||||
\(33\) | −4.30249 | −0.748967 | ||||||||
\(34\) | −13.8051 | −2.36756 | ||||||||
\(35\) | 4.24703 | 0.717879 | ||||||||
\(36\) | −12.2178 | −2.03630 | ||||||||
\(37\) | −9.59806 | −1.57791 | −0.788955 | − | 0.614451i | \(-0.789378\pi\) | ||||
−0.788955 | + | 0.614451i | \(0.789378\pi\) | |||||||
\(38\) | 18.0765 | 2.93239 | ||||||||
\(39\) | 4.58280 | 0.733835 | ||||||||
\(40\) | −29.2434 | −4.62379 | ||||||||
\(41\) | 3.80683 | 0.594527 | 0.297264 | − | 0.954795i | \(-0.403926\pi\) | ||||
0.297264 | + | 0.954795i | \(0.403926\pi\) | |||||||
\(42\) | 4.15296 | 0.640815 | ||||||||
\(43\) | −3.38931 | −0.516865 | −0.258432 | − | 0.966029i | \(-0.583206\pi\) | ||||
−0.258432 | + | 0.966029i | \(0.583206\pi\) | |||||||
\(44\) | 26.3738 | 3.97600 | ||||||||
\(45\) | −5.70528 | −0.850493 | ||||||||
\(46\) | 1.64786 | 0.242964 | ||||||||
\(47\) | −2.11515 | −0.308526 | −0.154263 | − | 0.988030i | \(-0.549300\pi\) | ||||
−0.154263 | + | 0.988030i | \(0.549300\pi\) | |||||||
\(48\) | −17.4885 | −2.52425 | ||||||||
\(49\) | −4.57016 | −0.652880 | ||||||||
\(50\) | −6.78273 | −0.959224 | ||||||||
\(51\) | −4.69451 | −0.657363 | ||||||||
\(52\) | −28.0921 | −3.89567 | ||||||||
\(53\) | 7.56236 | 1.03877 | 0.519385 | − | 0.854540i | \(-0.326161\pi\) | ||||
0.519385 | + | 0.854540i | \(0.326161\pi\) | |||||||
\(54\) | −13.5715 | −1.84685 | ||||||||
\(55\) | 12.3156 | 1.66064 | ||||||||
\(56\) | −16.7309 | −2.23577 | ||||||||
\(57\) | 6.14702 | 0.814193 | ||||||||
\(58\) | 20.7196 | 2.72061 | ||||||||
\(59\) | −0.485115 | −0.0631566 | −0.0315783 | − | 0.999501i | \(-0.510053\pi\) | ||||
−0.0315783 | + | 0.999501i | \(0.510053\pi\) | |||||||
\(60\) | −15.1310 | −1.95341 | ||||||||
\(61\) | 11.8614 | 1.51869 | 0.759345 | − | 0.650688i | \(-0.225519\pi\) | ||||
0.759345 | + | 0.650688i | \(0.225519\pi\) | |||||||
\(62\) | −13.1896 | −1.67508 | ||||||||
\(63\) | −3.26414 | −0.411244 | ||||||||
\(64\) | 47.1172 | 5.88965 | ||||||||
\(65\) | −13.1180 | −1.62709 | ||||||||
\(66\) | 12.0428 | 1.48237 | ||||||||
\(67\) | −1.53815 | −0.187915 | −0.0939575 | − | 0.995576i | \(-0.529952\pi\) | ||||
−0.0939575 | + | 0.995576i | \(0.529952\pi\) | |||||||
\(68\) | 28.7769 | 3.48971 | ||||||||
\(69\) | 0.560365 | 0.0674601 | ||||||||
\(70\) | −11.8876 | −1.42084 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | 22.4756 | 2.64878 | ||||||||
\(73\) | 9.26795 | 1.08473 | 0.542366 | − | 0.840143i | \(-0.317529\pi\) | ||||
0.542366 | + | 0.840143i | \(0.317529\pi\) | |||||||
\(74\) | 26.8653 | 3.12303 | ||||||||
\(75\) | −2.30651 | −0.266333 | ||||||||
\(76\) | −37.6806 | −4.32226 | ||||||||
\(77\) | 7.04610 | 0.802978 | ||||||||
\(78\) | −12.8274 | −1.45242 | ||||||||
\(79\) | 1.69346 | 0.190529 | 0.0952647 | − | 0.995452i | \(-0.469630\pi\) | ||||
0.0952647 | + | 0.995452i | \(0.469630\pi\) | |||||||
\(80\) | 50.0599 | 5.59687 | ||||||||
\(81\) | 1.66697 | 0.185219 | ||||||||
\(82\) | −10.6555 | −1.17670 | ||||||||
\(83\) | −14.2688 | −1.56621 | −0.783104 | − | 0.621891i | \(-0.786365\pi\) | ||||
−0.783104 | + | 0.621891i | \(0.786365\pi\) | |||||||
\(84\) | −8.65687 | −0.944542 | ||||||||
\(85\) | 13.4378 | 1.45753 | ||||||||
\(86\) | 9.48681 | 1.02299 | ||||||||
\(87\) | 7.04582 | 0.755391 | ||||||||
\(88\) | −48.5167 | −5.17190 | ||||||||
\(89\) | −4.19505 | −0.444675 | −0.222337 | − | 0.974970i | \(-0.571369\pi\) | ||||
−0.222337 | + | 0.974970i | \(0.571369\pi\) | |||||||
\(90\) | 15.9693 | 1.68331 | ||||||||
\(91\) | −7.50516 | −0.786754 | ||||||||
\(92\) | −3.43498 | −0.358122 | ||||||||
\(93\) | −4.48519 | −0.465093 | ||||||||
\(94\) | 5.92038 | 0.610640 | ||||||||
\(95\) | −17.5955 | −1.80526 | ||||||||
\(96\) | 28.5186 | 2.91066 | ||||||||
\(97\) | 16.9329 | 1.71927 | 0.859636 | − | 0.510908i | \(-0.170691\pi\) | ||||
0.859636 | + | 0.510908i | \(0.170691\pi\) | |||||||
\(98\) | 12.7921 | 1.29219 | ||||||||
\(99\) | −9.46544 | −0.951312 | ||||||||
\(100\) | 14.1387 | 1.41387 | ||||||||
\(101\) | 3.60427 | 0.358638 | 0.179319 | − | 0.983791i | \(-0.442611\pi\) | ||||
0.179319 | + | 0.983791i | \(0.442611\pi\) | |||||||
\(102\) | 13.1401 | 1.30107 | ||||||||
\(103\) | 7.52131 | 0.741097 | 0.370548 | − | 0.928813i | \(-0.379170\pi\) | ||||
0.370548 | + | 0.928813i | \(0.379170\pi\) | |||||||
\(104\) | 51.6776 | 5.06741 | ||||||||
\(105\) | −4.04245 | −0.394503 | ||||||||
\(106\) | −21.1674 | −2.05595 | ||||||||
\(107\) | 7.78789 | 0.752884 | 0.376442 | − | 0.926440i | \(-0.377147\pi\) | ||||
0.376442 | + | 0.926440i | \(0.377147\pi\) | |||||||
\(108\) | 28.2900 | 2.72221 | ||||||||
\(109\) | −6.68192 | −0.640012 | −0.320006 | − | 0.947416i | \(-0.603685\pi\) | ||||
−0.320006 | + | 0.947416i | \(0.603685\pi\) | |||||||
\(110\) | −34.4719 | −3.28677 | ||||||||
\(111\) | 9.13572 | 0.867124 | ||||||||
\(112\) | 28.6406 | 2.70628 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | −17.2058 | −1.61147 | ||||||||
\(115\) | −1.60401 | −0.149575 | ||||||||
\(116\) | −43.1901 | −4.01010 | ||||||||
\(117\) | 10.0821 | 0.932092 | ||||||||
\(118\) | 1.35786 | 0.125001 | ||||||||
\(119\) | 7.68811 | 0.704768 | ||||||||
\(120\) | 27.8348 | 2.54096 | ||||||||
\(121\) | 9.43243 | 0.857494 | ||||||||
\(122\) | −33.2004 | −3.00582 | ||||||||
\(123\) | −3.62346 | −0.326716 | ||||||||
\(124\) | 27.4938 | 2.46901 | ||||||||
\(125\) | −7.02055 | −0.627937 | ||||||||
\(126\) | 9.13647 | 0.813941 | ||||||||
\(127\) | −10.6704 | −0.946848 | −0.473424 | − | 0.880835i | \(-0.656982\pi\) | ||||
−0.473424 | + | 0.880835i | \(0.656982\pi\) | |||||||
\(128\) | −71.9592 | −6.36035 | ||||||||
\(129\) | 3.22605 | 0.284038 | ||||||||
\(130\) | 36.7178 | 3.22037 | ||||||||
\(131\) | −17.7640 | −1.55205 | −0.776026 | − | 0.630701i | \(-0.782767\pi\) | ||||
−0.776026 | + | 0.630701i | \(0.782767\pi\) | |||||||
\(132\) | −25.1034 | −2.18497 | ||||||||
\(133\) | −10.0669 | −0.872907 | ||||||||
\(134\) | 4.30534 | 0.371925 | ||||||||
\(135\) | 13.2104 | 1.13697 | ||||||||
\(136\) | −52.9374 | −4.53934 | ||||||||
\(137\) | −13.2043 | −1.12812 | −0.564061 | − | 0.825733i | \(-0.690762\pi\) | ||||
−0.564061 | + | 0.825733i | \(0.690762\pi\) | |||||||
\(138\) | −1.56848 | −0.133518 | ||||||||
\(139\) | 14.0241 | 1.18951 | 0.594754 | − | 0.803908i | \(-0.297249\pi\) | ||||
0.594754 | + | 0.803908i | \(0.297249\pi\) | |||||||
\(140\) | 24.7798 | 2.09428 | ||||||||
\(141\) | 2.01326 | 0.169547 | ||||||||
\(142\) | 2.79904 | 0.234890 | ||||||||
\(143\) | −21.7636 | −1.81997 | ||||||||
\(144\) | −38.4746 | −3.20622 | ||||||||
\(145\) | −20.1683 | −1.67488 | ||||||||
\(146\) | −25.9414 | −2.14692 | ||||||||
\(147\) | 4.35002 | 0.358783 | ||||||||
\(148\) | −56.0010 | −4.60326 | ||||||||
\(149\) | 18.7475 | 1.53586 | 0.767928 | − | 0.640537i | \(-0.221288\pi\) | ||||
0.767928 | + | 0.640537i | \(0.221288\pi\) | |||||||
\(150\) | 6.45601 | 0.527131 | ||||||||
\(151\) | −10.2197 | −0.831671 | −0.415836 | − | 0.909440i | \(-0.636511\pi\) | ||||
−0.415836 | + | 0.909440i | \(0.636511\pi\) | |||||||
\(152\) | 69.3165 | 5.62231 | ||||||||
\(153\) | −10.3279 | −0.834960 | ||||||||
\(154\) | −19.7223 | −1.58927 | ||||||||
\(155\) | 12.8386 | 1.03122 | ||||||||
\(156\) | 26.7389 | 2.14082 | ||||||||
\(157\) | 2.27234 | 0.181352 | 0.0906761 | − | 0.995880i | \(-0.471097\pi\) | ||||
0.0906761 | + | 0.995880i | \(0.471097\pi\) | |||||||
\(158\) | −4.74007 | −0.377099 | ||||||||
\(159\) | −7.19809 | −0.570845 | ||||||||
\(160\) | −81.6328 | −6.45364 | ||||||||
\(161\) | −0.917699 | −0.0723248 | ||||||||
\(162\) | −4.66592 | −0.366589 | ||||||||
\(163\) | −18.6264 | −1.45893 | −0.729465 | − | 0.684019i | \(-0.760231\pi\) | ||||
−0.729465 | + | 0.684019i | \(0.760231\pi\) | |||||||
\(164\) | 22.2114 | 1.73442 | ||||||||
\(165\) | −11.7224 | −0.912587 | ||||||||
\(166\) | 39.9390 | 3.09987 | ||||||||
\(167\) | −23.1945 | −1.79484 | −0.897422 | − | 0.441173i | \(-0.854563\pi\) | ||||
−0.897422 | + | 0.441173i | \(0.854563\pi\) | |||||||
\(168\) | 15.9250 | 1.22864 | ||||||||
\(169\) | 10.1815 | 0.783195 | ||||||||
\(170\) | −37.6129 | −2.88478 | ||||||||
\(171\) | 13.5234 | 1.03416 | ||||||||
\(172\) | −19.7753 | −1.50785 | ||||||||
\(173\) | −18.9370 | −1.43975 | −0.719876 | − | 0.694103i | \(-0.755801\pi\) | ||||
−0.719876 | + | 0.694103i | \(0.755801\pi\) | |||||||
\(174\) | −19.7215 | −1.49509 | ||||||||
\(175\) | 3.77733 | 0.285539 | ||||||||
\(176\) | 83.0526 | 6.26033 | ||||||||
\(177\) | 0.461747 | 0.0347070 | ||||||||
\(178\) | 11.7421 | 0.880109 | ||||||||
\(179\) | −10.2103 | −0.763153 | −0.381577 | − | 0.924337i | \(-0.624619\pi\) | ||||
−0.381577 | + | 0.924337i | \(0.624619\pi\) | |||||||
\(180\) | −33.2882 | −2.48115 | ||||||||
\(181\) | 3.78721 | 0.281501 | 0.140751 | − | 0.990045i | \(-0.455048\pi\) | ||||
0.140751 | + | 0.990045i | \(0.455048\pi\) | |||||||
\(182\) | 21.0072 | 1.55716 | ||||||||
\(183\) | −11.2900 | −0.834580 | ||||||||
\(184\) | 6.31892 | 0.465837 | ||||||||
\(185\) | −26.1505 | −1.92262 | ||||||||
\(186\) | 12.5542 | 0.920521 | ||||||||
\(187\) | 22.2942 | 1.63031 | ||||||||
\(188\) | −12.3411 | −0.900065 | ||||||||
\(189\) | 7.55804 | 0.549766 | ||||||||
\(190\) | 49.2505 | 3.57301 | ||||||||
\(191\) | 17.7306 | 1.28294 | 0.641471 | − | 0.767147i | \(-0.278324\pi\) | ||||
0.641471 | + | 0.767147i | \(0.278324\pi\) | |||||||
\(192\) | −44.8476 | −3.23659 | ||||||||
\(193\) | −6.63178 | −0.477366 | −0.238683 | − | 0.971098i | \(-0.576716\pi\) | ||||
−0.238683 | + | 0.971098i | \(0.576716\pi\) | |||||||
\(194\) | −47.3957 | −3.40282 | ||||||||
\(195\) | 12.4861 | 0.894149 | ||||||||
\(196\) | −26.6652 | −1.90465 | ||||||||
\(197\) | −26.1932 | −1.86619 | −0.933094 | − | 0.359633i | \(-0.882902\pi\) | ||||
−0.933094 | + | 0.359633i | \(0.882902\pi\) | |||||||
\(198\) | 26.4941 | 1.88286 | ||||||||
\(199\) | −5.79633 | −0.410891 | −0.205445 | − | 0.978669i | \(-0.565864\pi\) | ||||
−0.205445 | + | 0.978669i | \(0.565864\pi\) | |||||||
\(200\) | −26.0092 | −1.83913 | ||||||||
\(201\) | 1.46406 | 0.103267 | ||||||||
\(202\) | −10.0885 | −0.709824 | ||||||||
\(203\) | −11.5388 | −0.809865 | ||||||||
\(204\) | −27.3907 | −1.91773 | ||||||||
\(205\) | 10.3719 | 0.724408 | ||||||||
\(206\) | −21.0524 | −1.46679 | ||||||||
\(207\) | 1.23280 | 0.0856854 | ||||||||
\(208\) | −88.4636 | −6.13385 | ||||||||
\(209\) | −29.1921 | −2.01926 | ||||||||
\(210\) | 11.3150 | 0.780808 | ||||||||
\(211\) | 21.4352 | 1.47566 | 0.737830 | − | 0.674987i | \(-0.235851\pi\) | ||||
0.737830 | + | 0.674987i | \(0.235851\pi\) | |||||||
\(212\) | 44.1235 | 3.03042 | ||||||||
\(213\) | 0.951830 | 0.0652183 | ||||||||
\(214\) | −21.7986 | −1.49012 | ||||||||
\(215\) | −9.23438 | −0.629779 | ||||||||
\(216\) | −52.0417 | −3.54099 | ||||||||
\(217\) | 7.34531 | 0.498632 | ||||||||
\(218\) | 18.7029 | 1.26672 | ||||||||
\(219\) | −8.82152 | −0.596103 | ||||||||
\(220\) | 71.8570 | 4.84460 | ||||||||
\(221\) | −23.7466 | −1.59737 | ||||||||
\(222\) | −25.5712 | −1.71623 | ||||||||
\(223\) | −7.28428 | −0.487791 | −0.243896 | − | 0.969801i | \(-0.578425\pi\) | ||||
−0.243896 | + | 0.969801i | \(0.578425\pi\) | |||||||
\(224\) | −46.7043 | −3.12056 | ||||||||
\(225\) | −5.07430 | −0.338287 | ||||||||
\(226\) | 2.79904 | 0.186189 | ||||||||
\(227\) | −0.774392 | −0.0513982 | −0.0256991 | − | 0.999670i | \(-0.508181\pi\) | ||||
−0.0256991 | + | 0.999670i | \(0.508181\pi\) | |||||||
\(228\) | 35.8655 | 2.37525 | ||||||||
\(229\) | 3.83151 | 0.253193 | 0.126597 | − | 0.991954i | \(-0.459595\pi\) | ||||
0.126597 | + | 0.991954i | \(0.459595\pi\) | |||||||
\(230\) | 4.48970 | 0.296042 | ||||||||
\(231\) | −6.70669 | −0.441268 | ||||||||
\(232\) | 79.4518 | 5.21626 | ||||||||
\(233\) | −22.4638 | −1.47165 | −0.735825 | − | 0.677171i | \(-0.763206\pi\) | ||||
−0.735825 | + | 0.677171i | \(0.763206\pi\) | |||||||
\(234\) | −28.2202 | −1.84481 | ||||||||
\(235\) | −5.76285 | −0.375927 | ||||||||
\(236\) | −2.83046 | −0.184247 | ||||||||
\(237\) | −1.61189 | −0.104703 | ||||||||
\(238\) | −21.5193 | −1.39489 | ||||||||
\(239\) | −8.61463 | −0.557234 | −0.278617 | − | 0.960402i | \(-0.589876\pi\) | ||||
−0.278617 | + | 0.960402i | \(0.589876\pi\) | |||||||
\(240\) | −47.6485 | −3.07570 | ||||||||
\(241\) | 13.2008 | 0.850341 | 0.425171 | − | 0.905113i | \(-0.360214\pi\) | ||||
0.425171 | + | 0.905113i | \(0.360214\pi\) | |||||||
\(242\) | −26.4017 | −1.69717 | ||||||||
\(243\) | −16.1326 | −1.03491 | ||||||||
\(244\) | 69.2065 | 4.43049 | ||||||||
\(245\) | −12.4517 | −0.795509 | ||||||||
\(246\) | 10.1422 | 0.646643 | ||||||||
\(247\) | 31.0940 | 1.97846 | ||||||||
\(248\) | −50.5770 | −3.21164 | ||||||||
\(249\) | 13.5815 | 0.860693 | ||||||||
\(250\) | 19.6508 | 1.24283 | ||||||||
\(251\) | 19.2217 | 1.21327 | 0.606633 | − | 0.794982i | \(-0.292520\pi\) | ||||
0.606633 | + | 0.794982i | \(0.292520\pi\) | |||||||
\(252\) | −19.0450 | −1.19973 | ||||||||
\(253\) | −2.66116 | −0.167306 | ||||||||
\(254\) | 29.8670 | 1.87402 | ||||||||
\(255\) | −12.7905 | −0.800972 | ||||||||
\(256\) | 107.182 | 6.69889 | ||||||||
\(257\) | −28.6703 | −1.78840 | −0.894202 | − | 0.447663i | \(-0.852257\pi\) | ||||
−0.894202 | + | 0.447663i | \(0.852257\pi\) | |||||||
\(258\) | −9.02983 | −0.562173 | ||||||||
\(259\) | −14.9614 | −0.929656 | ||||||||
\(260\) | −76.5386 | −4.74672 | ||||||||
\(261\) | 15.5007 | 0.959472 | ||||||||
\(262\) | 49.7223 | 3.07185 | ||||||||
\(263\) | −4.38944 | −0.270665 | −0.135332 | − | 0.990800i | \(-0.543210\pi\) | ||||
−0.135332 | + | 0.990800i | \(0.543210\pi\) | |||||||
\(264\) | 46.1797 | 2.84216 | ||||||||
\(265\) | 20.6041 | 1.26570 | ||||||||
\(266\) | 28.1775 | 1.72768 | ||||||||
\(267\) | 3.99298 | 0.244366 | ||||||||
\(268\) | −8.97452 | −0.548206 | ||||||||
\(269\) | 2.28116 | 0.139085 | 0.0695423 | − | 0.997579i | \(-0.477846\pi\) | ||||
0.0695423 | + | 0.997579i | \(0.477846\pi\) | |||||||
\(270\) | −36.9765 | −2.25032 | ||||||||
\(271\) | −28.3719 | −1.72347 | −0.861736 | − | 0.507357i | \(-0.830622\pi\) | ||||
−0.861736 | + | 0.507357i | \(0.830622\pi\) | |||||||
\(272\) | 90.6201 | 5.49465 | ||||||||
\(273\) | 7.14364 | 0.432353 | ||||||||
\(274\) | 36.9594 | 2.23280 | ||||||||
\(275\) | 10.9536 | 0.660525 | ||||||||
\(276\) | 3.26952 | 0.196802 | ||||||||
\(277\) | −9.90508 | −0.595139 | −0.297569 | − | 0.954700i | \(-0.596176\pi\) | ||||
−0.297569 | + | 0.954700i | \(0.596176\pi\) | |||||||
\(278\) | −39.2540 | −2.35430 | ||||||||
\(279\) | −9.86738 | −0.590745 | ||||||||
\(280\) | −45.5845 | −2.72419 | ||||||||
\(281\) | 22.5145 | 1.34310 | 0.671550 | − | 0.740959i | \(-0.265629\pi\) | ||||
0.671550 | + | 0.740959i | \(0.265629\pi\) | |||||||
\(282\) | −5.63519 | −0.335571 | ||||||||
\(283\) | −12.9633 | −0.770588 | −0.385294 | − | 0.922794i | \(-0.625900\pi\) | ||||
−0.385294 | + | 0.922794i | \(0.625900\pi\) | |||||||
\(284\) | −5.83462 | −0.346221 | ||||||||
\(285\) | 16.7479 | 0.992062 | ||||||||
\(286\) | 60.9172 | 3.60211 | ||||||||
\(287\) | 5.93406 | 0.350277 | ||||||||
\(288\) | 62.7406 | 3.69703 | ||||||||
\(289\) | 7.32551 | 0.430912 | ||||||||
\(290\) | 56.4518 | 3.31496 | ||||||||
\(291\) | −16.1172 | −0.944807 | ||||||||
\(292\) | 54.0750 | 3.16450 | ||||||||
\(293\) | −5.78203 | −0.337790 | −0.168895 | − | 0.985634i | \(-0.554020\pi\) | ||||
−0.168895 | + | 0.985634i | \(0.554020\pi\) | |||||||
\(294\) | −12.1759 | −0.710111 | ||||||||
\(295\) | −1.32173 | −0.0769538 | ||||||||
\(296\) | 103.018 | 5.98782 | ||||||||
\(297\) | 21.9170 | 1.27175 | ||||||||
\(298\) | −52.4750 | −3.03980 | ||||||||
\(299\) | 2.83454 | 0.163926 | ||||||||
\(300\) | −13.4576 | −0.776976 | ||||||||
\(301\) | −5.28323 | −0.304521 | ||||||||
\(302\) | 28.6055 | 1.64606 | ||||||||
\(303\) | −3.43065 | −0.197086 | ||||||||
\(304\) | −118.658 | −6.80553 | ||||||||
\(305\) | 32.3170 | 1.85046 | ||||||||
\(306\) | 28.9082 | 1.65257 | ||||||||
\(307\) | 9.45478 | 0.539613 | 0.269806 | − | 0.962915i | \(-0.413040\pi\) | ||||
0.269806 | + | 0.962915i | \(0.413040\pi\) | |||||||
\(308\) | 41.1113 | 2.34253 | ||||||||
\(309\) | −7.15901 | −0.407262 | ||||||||
\(310\) | −35.9358 | −2.04102 | ||||||||
\(311\) | −0.299660 | −0.0169922 | −0.00849609 | − | 0.999964i | \(-0.502704\pi\) | ||||
−0.00849609 | + | 0.999964i | \(0.502704\pi\) | |||||||
\(312\) | −49.1883 | −2.78474 | ||||||||
\(313\) | 21.1267 | 1.19415 | 0.597077 | − | 0.802184i | \(-0.296329\pi\) | ||||
0.597077 | + | 0.802184i | \(0.296329\pi\) | |||||||
\(314\) | −6.36036 | −0.358936 | ||||||||
\(315\) | −8.89336 | −0.501084 | ||||||||
\(316\) | 9.88071 | 0.555833 | ||||||||
\(317\) | 17.0324 | 0.956635 | 0.478318 | − | 0.878187i | \(-0.341247\pi\) | ||||
0.478318 | + | 0.878187i | \(0.341247\pi\) | |||||||
\(318\) | 20.1477 | 1.12983 | ||||||||
\(319\) | −33.4605 | −1.87343 | ||||||||
\(320\) | 128.374 | 7.17630 | ||||||||
\(321\) | −7.41275 | −0.413740 | ||||||||
\(322\) | 2.56868 | 0.143147 | ||||||||
\(323\) | −31.8520 | −1.77229 | ||||||||
\(324\) | 9.72614 | 0.540341 | ||||||||
\(325\) | −11.6672 | −0.647180 | ||||||||
\(326\) | 52.1359 | 2.88754 | ||||||||
\(327\) | 6.36005 | 0.351712 | ||||||||
\(328\) | −40.8597 | −2.25610 | ||||||||
\(329\) | −3.29708 | −0.181774 | ||||||||
\(330\) | 32.8114 | 1.80621 | ||||||||
\(331\) | −18.6341 | −1.02422 | −0.512112 | − | 0.858918i | \(-0.671137\pi\) | ||||
−0.512112 | + | 0.858918i | \(0.671137\pi\) | |||||||
\(332\) | −83.2532 | −4.56911 | ||||||||
\(333\) | 20.0985 | 1.10139 | ||||||||
\(334\) | 64.9223 | 3.55239 | ||||||||
\(335\) | −4.19078 | −0.228967 | ||||||||
\(336\) | −27.2610 | −1.48721 | ||||||||
\(337\) | −0.878329 | −0.0478456 | −0.0239228 | − | 0.999714i | \(-0.507616\pi\) | ||||
−0.0239228 | + | 0.999714i | \(0.507616\pi\) | |||||||
\(338\) | −28.4985 | −1.55012 | ||||||||
\(339\) | 0.951830 | 0.0516963 | ||||||||
\(340\) | 78.4044 | 4.25207 | ||||||||
\(341\) | 21.3001 | 1.15346 | ||||||||
\(342\) | −37.8525 | −2.04683 | ||||||||
\(343\) | −18.0355 | −0.973825 | ||||||||
\(344\) | 36.3783 | 1.96139 | ||||||||
\(345\) | 1.52675 | 0.0821975 | ||||||||
\(346\) | 53.0053 | 2.84958 | ||||||||
\(347\) | 1.55446 | 0.0834477 | 0.0417239 | − | 0.999129i | \(-0.486715\pi\) | ||||
0.0417239 | + | 0.999129i | \(0.486715\pi\) | |||||||
\(348\) | 41.1097 | 2.20371 | ||||||||
\(349\) | −10.4934 | −0.561700 | −0.280850 | − | 0.959752i | \(-0.590616\pi\) | ||||
−0.280850 | + | 0.959752i | \(0.590616\pi\) | |||||||
\(350\) | −10.5729 | −0.565145 | ||||||||
\(351\) | −23.3449 | −1.24606 | ||||||||
\(352\) | −135.434 | −7.21866 | ||||||||
\(353\) | −19.9786 | −1.06335 | −0.531677 | − | 0.846947i | \(-0.678438\pi\) | ||||
−0.531677 | + | 0.846947i | \(0.678438\pi\) | |||||||
\(354\) | −1.29245 | −0.0686929 | ||||||||
\(355\) | −2.72456 | −0.144605 | ||||||||
\(356\) | −24.4765 | −1.29725 | ||||||||
\(357\) | −7.31778 | −0.387298 | ||||||||
\(358\) | 28.5790 | 1.51045 | ||||||||
\(359\) | −14.7281 | −0.777318 | −0.388659 | − | 0.921382i | \(-0.627062\pi\) | ||||
−0.388659 | + | 0.921382i | \(0.627062\pi\) | |||||||
\(360\) | 61.2363 | 3.22743 | ||||||||
\(361\) | 22.7071 | 1.19511 | ||||||||
\(362\) | −10.6006 | −0.557153 | ||||||||
\(363\) | −8.97808 | −0.471227 | ||||||||
\(364\) | −43.7898 | −2.29521 | ||||||||
\(365\) | 25.2511 | 1.32170 | ||||||||
\(366\) | 31.6011 | 1.65182 | ||||||||
\(367\) | −21.7557 | −1.13564 | −0.567820 | − | 0.823153i | \(-0.692213\pi\) | ||||
−0.567820 | + | 0.823153i | \(0.692213\pi\) | |||||||
\(368\) | −10.8170 | −0.563873 | ||||||||
\(369\) | −7.97157 | −0.414984 | ||||||||
\(370\) | 73.1963 | 3.80529 | ||||||||
\(371\) | 11.7882 | 0.612011 | ||||||||
\(372\) | −26.1694 | −1.35682 | ||||||||
\(373\) | 12.0515 | 0.624004 | 0.312002 | − | 0.950081i | \(-0.399000\pi\) | ||||
0.312002 | + | 0.950081i | \(0.399000\pi\) | |||||||
\(374\) | −62.4022 | −3.22674 | ||||||||
\(375\) | 6.68237 | 0.345076 | ||||||||
\(376\) | 22.7024 | 1.17079 | ||||||||
\(377\) | 35.6404 | 1.83558 | ||||||||
\(378\) | −21.1552 | −1.08811 | ||||||||
\(379\) | 24.9294 | 1.28054 | 0.640268 | − | 0.768151i | \(-0.278823\pi\) | ||||
0.640268 | + | 0.768151i | \(0.278823\pi\) | |||||||
\(380\) | −102.663 | −5.26651 | ||||||||
\(381\) | 10.1564 | 0.520330 | ||||||||
\(382\) | −49.6287 | −2.53922 | ||||||||
\(383\) | −18.3164 | −0.935925 | −0.467963 | − | 0.883748i | \(-0.655012\pi\) | ||||
−0.467963 | + | 0.883748i | \(0.655012\pi\) | |||||||
\(384\) | 68.4929 | 3.49527 | ||||||||
\(385\) | 19.1975 | 0.978397 | ||||||||
\(386\) | 18.5626 | 0.944812 | ||||||||
\(387\) | 7.09728 | 0.360775 | ||||||||
\(388\) | 98.7968 | 5.01565 | ||||||||
\(389\) | −1.38101 | −0.0700199 | −0.0350099 | − | 0.999387i | \(-0.511146\pi\) | ||||
−0.0350099 | + | 0.999387i | \(0.511146\pi\) | |||||||
\(390\) | −34.9491 | −1.76972 | ||||||||
\(391\) | −2.90364 | −0.146843 | ||||||||
\(392\) | 49.0527 | 2.47754 | ||||||||
\(393\) | 16.9084 | 0.852914 | ||||||||
\(394\) | 73.3158 | 3.69359 | ||||||||
\(395\) | 4.61394 | 0.232153 | ||||||||
\(396\) | −55.2272 | −2.77527 | ||||||||
\(397\) | 21.9907 | 1.10368 | 0.551841 | − | 0.833950i | \(-0.313926\pi\) | ||||
0.551841 | + | 0.833950i | \(0.313926\pi\) | |||||||
\(398\) | 16.2241 | 0.813243 | ||||||||
\(399\) | 9.58194 | 0.479697 | ||||||||
\(400\) | 44.5235 | 2.22617 | ||||||||
\(401\) | −32.5599 | −1.62597 | −0.812983 | − | 0.582288i | \(-0.802158\pi\) | ||||
−0.812983 | + | 0.582288i | \(0.802158\pi\) | |||||||
\(402\) | −4.09796 | −0.204387 | ||||||||
\(403\) | −22.6878 | −1.13016 | ||||||||
\(404\) | 21.0295 | 1.04626 | ||||||||
\(405\) | 4.54177 | 0.225682 | ||||||||
\(406\) | 32.2976 | 1.60290 | ||||||||
\(407\) | −43.3854 | −2.15053 | ||||||||
\(408\) | 50.3874 | 2.49455 | ||||||||
\(409\) | −32.5465 | −1.60932 | −0.804660 | − | 0.593736i | \(-0.797652\pi\) | ||||
−0.804660 | + | 0.593736i | \(0.797652\pi\) | |||||||
\(410\) | −29.0315 | −1.43376 | ||||||||
\(411\) | 12.5683 | 0.619948 | ||||||||
\(412\) | 43.8840 | 2.16201 | ||||||||
\(413\) | −0.756194 | −0.0372099 | ||||||||
\(414\) | −3.45065 | −0.169590 | ||||||||
\(415\) | −38.8763 | −1.90836 | ||||||||
\(416\) | 144.258 | 7.07282 | ||||||||
\(417\) | −13.3486 | −0.653682 | ||||||||
\(418\) | 81.7098 | 3.99656 | ||||||||
\(419\) | 34.5682 | 1.68877 | 0.844384 | − | 0.535738i | \(-0.179966\pi\) | ||||
0.844384 | + | 0.535738i | \(0.179966\pi\) | |||||||
\(420\) | −23.5862 | −1.15089 | ||||||||
\(421\) | −0.364949 | −0.0177865 | −0.00889325 | − | 0.999960i | \(-0.502831\pi\) | ||||
−0.00889325 | + | 0.999960i | \(0.502831\pi\) | |||||||
\(422\) | −59.9979 | −2.92065 | ||||||||
\(423\) | 4.42916 | 0.215353 | ||||||||
\(424\) | −81.1688 | −3.94190 | ||||||||
\(425\) | 11.9516 | 0.579739 | ||||||||
\(426\) | −2.66421 | −0.129081 | ||||||||
\(427\) | 18.4894 | 0.894765 | ||||||||
\(428\) | 45.4394 | 2.19640 | ||||||||
\(429\) | 20.7153 | 1.00014 | ||||||||
\(430\) | 25.8474 | 1.24647 | ||||||||
\(431\) | −17.8486 | −0.859736 | −0.429868 | − | 0.902892i | \(-0.641440\pi\) | ||||
−0.429868 | + | 0.902892i | \(0.641440\pi\) | |||||||
\(432\) | 89.0868 | 4.28619 | ||||||||
\(433\) | −30.9228 | −1.48605 | −0.743027 | − | 0.669262i | \(-0.766610\pi\) | ||||
−0.743027 | + | 0.669262i | \(0.766610\pi\) | |||||||
\(434\) | −20.5598 | −0.986903 | ||||||||
\(435\) | 19.1968 | 0.920415 | ||||||||
\(436\) | −38.9865 | −1.86711 | ||||||||
\(437\) | 3.80204 | 0.181876 | ||||||||
\(438\) | 24.6918 | 1.17982 | ||||||||
\(439\) | 35.1753 | 1.67882 | 0.839412 | − | 0.543495i | \(-0.182899\pi\) | ||||
0.839412 | + | 0.543495i | \(0.182899\pi\) | |||||||
\(440\) | −132.187 | −6.30176 | ||||||||
\(441\) | 9.57000 | 0.455714 | ||||||||
\(442\) | 66.4678 | 3.16155 | ||||||||
\(443\) | 8.21427 | 0.390272 | 0.195136 | − | 0.980776i | \(-0.437485\pi\) | ||||
0.195136 | + | 0.980776i | \(0.437485\pi\) | |||||||
\(444\) | 53.3035 | 2.52967 | ||||||||
\(445\) | −11.4297 | −0.541819 | ||||||||
\(446\) | 20.3890 | 0.965446 | ||||||||
\(447\) | −17.8444 | −0.844013 | ||||||||
\(448\) | 73.4460 | 3.47000 | ||||||||
\(449\) | −5.35415 | −0.252678 | −0.126339 | − | 0.991987i | \(-0.540323\pi\) | ||||
−0.126339 | + | 0.991987i | \(0.540323\pi\) | |||||||
\(450\) | 14.2032 | 0.669544 | ||||||||
\(451\) | 17.2077 | 0.810280 | ||||||||
\(452\) | −5.83462 | −0.274437 | ||||||||
\(453\) | 9.72746 | 0.457036 | ||||||||
\(454\) | 2.16755 | 0.101728 | ||||||||
\(455\) | −20.4483 | −0.958630 | ||||||||
\(456\) | −65.9776 | −3.08968 | ||||||||
\(457\) | 5.39398 | 0.252320 | 0.126160 | − | 0.992010i | \(-0.459735\pi\) | ||||
0.126160 | + | 0.992010i | \(0.459735\pi\) | |||||||
\(458\) | −10.7245 | −0.501125 | ||||||||
\(459\) | 23.9139 | 1.11621 | ||||||||
\(460\) | −9.35882 | −0.436357 | ||||||||
\(461\) | −14.9094 | −0.694401 | −0.347200 | − | 0.937791i | \(-0.612868\pi\) | ||||
−0.347200 | + | 0.937791i | \(0.612868\pi\) | |||||||
\(462\) | 18.7723 | 0.873366 | ||||||||
\(463\) | 30.7873 | 1.43081 | 0.715405 | − | 0.698710i | \(-0.246242\pi\) | ||||
0.715405 | + | 0.698710i | \(0.246242\pi\) | |||||||
\(464\) | −136.008 | −6.31403 | ||||||||
\(465\) | −12.2202 | −0.566697 | ||||||||
\(466\) | 62.8770 | 2.91272 | ||||||||
\(467\) | 15.3885 | 0.712096 | 0.356048 | − | 0.934468i | \(-0.384124\pi\) | ||||
0.356048 | + | 0.934468i | \(0.384124\pi\) | |||||||
\(468\) | 58.8253 | 2.71920 | ||||||||
\(469\) | −2.39766 | −0.110714 | ||||||||
\(470\) | 16.1304 | 0.744041 | ||||||||
\(471\) | −2.16288 | −0.0996603 | ||||||||
\(472\) | 5.20686 | 0.239665 | ||||||||
\(473\) | −15.3204 | −0.704434 | ||||||||
\(474\) | 4.51174 | 0.207231 | ||||||||
\(475\) | −15.6495 | −0.718049 | ||||||||
\(476\) | 44.8572 | 2.05603 | ||||||||
\(477\) | −15.8357 | −0.725068 | ||||||||
\(478\) | 24.1127 | 1.10289 | ||||||||
\(479\) | 31.2711 | 1.42881 | 0.714407 | − | 0.699731i | \(-0.246697\pi\) | ||||
0.714407 | + | 0.699731i | \(0.246697\pi\) | |||||||
\(480\) | 77.7006 | 3.54653 | ||||||||
\(481\) | 46.2120 | 2.10708 | ||||||||
\(482\) | −36.9497 | −1.68301 | ||||||||
\(483\) | 0.873494 | 0.0397454 | ||||||||
\(484\) | 55.0347 | 2.50158 | ||||||||
\(485\) | 46.1346 | 2.09486 | ||||||||
\(486\) | 45.1558 | 2.04831 | ||||||||
\(487\) | −28.2574 | −1.28047 | −0.640233 | − | 0.768181i | \(-0.721162\pi\) | ||||
−0.640233 | + | 0.768181i | \(0.721162\pi\) | |||||||
\(488\) | −127.311 | −5.76309 | ||||||||
\(489\) | 17.7291 | 0.801739 | ||||||||
\(490\) | 34.8528 | 1.57449 | ||||||||
\(491\) | −24.1233 | −1.08867 | −0.544335 | − | 0.838868i | \(-0.683218\pi\) | ||||
−0.544335 | + | 0.838868i | \(0.683218\pi\) | |||||||
\(492\) | −21.1415 | −0.953132 | ||||||||
\(493\) | −36.5093 | −1.64429 | ||||||||
\(494\) | −87.0333 | −3.91581 | ||||||||
\(495\) | −25.7892 | −1.15914 | ||||||||
\(496\) | 86.5795 | 3.88753 | ||||||||
\(497\) | −1.55879 | −0.0699215 | ||||||||
\(498\) | −38.0152 | −1.70350 | ||||||||
\(499\) | 24.8489 | 1.11239 | 0.556195 | − | 0.831052i | \(-0.312261\pi\) | ||||
0.556195 | + | 0.831052i | \(0.312261\pi\) | |||||||
\(500\) | −40.9623 | −1.83189 | ||||||||
\(501\) | 22.0772 | 0.986338 | ||||||||
\(502\) | −53.8024 | −2.40132 | ||||||||
\(503\) | 16.9000 | 0.753532 | 0.376766 | − | 0.926308i | \(-0.377036\pi\) | ||||
0.376766 | + | 0.926308i | \(0.377036\pi\) | |||||||
\(504\) | 35.0349 | 1.56058 | ||||||||
\(505\) | 9.82005 | 0.436987 | ||||||||
\(506\) | 7.44870 | 0.331135 | ||||||||
\(507\) | −9.69110 | −0.430397 | ||||||||
\(508\) | −62.2579 | −2.76225 | ||||||||
\(509\) | 6.06807 | 0.268962 | 0.134481 | − | 0.990916i | \(-0.457063\pi\) | ||||
0.134481 | + | 0.990916i | \(0.457063\pi\) | |||||||
\(510\) | 35.8011 | 1.58530 | ||||||||
\(511\) | 14.4468 | 0.639090 | ||||||||
\(512\) | −156.089 | −6.89822 | ||||||||
\(513\) | −31.3130 | −1.38250 | ||||||||
\(514\) | 80.2493 | 3.53965 | ||||||||
\(515\) | 20.4923 | 0.902997 | ||||||||
\(516\) | 18.8228 | 0.828626 | ||||||||
\(517\) | −9.56093 | −0.420489 | ||||||||
\(518\) | 41.8775 | 1.83999 | ||||||||
\(519\) | 18.0248 | 0.791200 | ||||||||
\(520\) | 140.799 | 6.17444 | ||||||||
\(521\) | −1.40716 | −0.0616487 | −0.0308243 | − | 0.999525i | \(-0.509813\pi\) | ||||
−0.0308243 | + | 0.999525i | \(0.509813\pi\) | |||||||
\(522\) | −43.3872 | −1.89901 | ||||||||
\(523\) | 12.8262 | 0.560851 | 0.280425 | − | 0.959876i | \(-0.409524\pi\) | ||||
0.280425 | + | 0.959876i | \(0.409524\pi\) | |||||||
\(524\) | −103.646 | −4.52782 | ||||||||
\(525\) | −3.59537 | −0.156915 | ||||||||
\(526\) | 12.2862 | 0.535705 | ||||||||
\(527\) | 23.2409 | 1.01239 | ||||||||
\(528\) | −79.0520 | −3.44030 | ||||||||
\(529\) | −22.6534 | −0.984931 | ||||||||
\(530\) | −57.6718 | −2.50510 | ||||||||
\(531\) | 1.01584 | 0.0440837 | ||||||||
\(532\) | −58.7363 | −2.54654 | ||||||||
\(533\) | −18.3288 | −0.793910 | ||||||||
\(534\) | −11.1765 | −0.483655 | ||||||||
\(535\) | 21.2186 | 0.917360 | ||||||||
\(536\) | 16.5094 | 0.713096 | ||||||||
\(537\) | 9.71847 | 0.419383 | ||||||||
\(538\) | −6.38505 | −0.275279 | ||||||||
\(539\) | −20.6582 | −0.889810 | ||||||||
\(540\) | 77.0778 | 3.31690 | ||||||||
\(541\) | −7.38366 | −0.317448 | −0.158724 | − | 0.987323i | \(-0.550738\pi\) | ||||
−0.158724 | + | 0.987323i | \(0.550738\pi\) | |||||||
\(542\) | 79.4141 | 3.41113 | ||||||||
\(543\) | −3.60478 | −0.154696 | ||||||||
\(544\) | −147.774 | −6.33577 | ||||||||
\(545\) | −18.2053 | −0.779829 | ||||||||
\(546\) | −19.9953 | −0.855721 | ||||||||
\(547\) | 20.7782 | 0.888412 | 0.444206 | − | 0.895925i | \(-0.353486\pi\) | ||||
0.444206 | + | 0.895925i | \(0.353486\pi\) | |||||||
\(548\) | −77.0423 | −3.29108 | ||||||||
\(549\) | −24.8379 | −1.06006 | ||||||||
\(550\) | −30.6595 | −1.30732 | ||||||||
\(551\) | 47.8054 | 2.03658 | ||||||||
\(552\) | −6.01454 | −0.255996 | ||||||||
\(553\) | 2.63976 | 0.112254 | ||||||||
\(554\) | 27.7247 | 1.17791 | ||||||||
\(555\) | 24.8908 | 1.05656 | ||||||||
\(556\) | 81.8253 | 3.47017 | ||||||||
\(557\) | 38.4553 | 1.62941 | 0.814703 | − | 0.579879i | \(-0.196900\pi\) | ||||
0.814703 | + | 0.579879i | \(0.196900\pi\) | |||||||
\(558\) | 27.6192 | 1.16921 | ||||||||
\(559\) | 16.3186 | 0.690202 | ||||||||
\(560\) | 78.0331 | 3.29750 | ||||||||
\(561\) | −21.2203 | −0.895920 | ||||||||
\(562\) | −63.0189 | −2.65829 | ||||||||
\(563\) | −16.6860 | −0.703229 | −0.351615 | − | 0.936145i | \(-0.614367\pi\) | ||||
−0.351615 | + | 0.936145i | \(0.614367\pi\) | |||||||
\(564\) | 11.7466 | 0.494622 | ||||||||
\(565\) | −2.72456 | −0.114623 | ||||||||
\(566\) | 36.2848 | 1.52516 | ||||||||
\(567\) | 2.59846 | 0.109125 | ||||||||
\(568\) | 10.7333 | 0.450357 | ||||||||
\(569\) | −41.0491 | −1.72087 | −0.860433 | − | 0.509563i | \(-0.829807\pi\) | ||||
−0.860433 | + | 0.509563i | \(0.829807\pi\) | |||||||
\(570\) | −46.8781 | −1.96351 | ||||||||
\(571\) | −31.3959 | −1.31388 | −0.656938 | − | 0.753945i | \(-0.728149\pi\) | ||||
−0.656938 | + | 0.753945i | \(0.728149\pi\) | |||||||
\(572\) | −126.982 | −5.30940 | ||||||||
\(573\) | −16.8765 | −0.705027 | ||||||||
\(574\) | −16.6097 | −0.693275 | ||||||||
\(575\) | −1.42662 | −0.0594941 | ||||||||
\(576\) | −98.6642 | −4.11101 | ||||||||
\(577\) | −35.2447 | −1.46726 | −0.733629 | − | 0.679550i | \(-0.762175\pi\) | ||||
−0.733629 | + | 0.679550i | \(0.762175\pi\) | |||||||
\(578\) | −20.5044 | −0.852870 | ||||||||
\(579\) | 6.31233 | 0.262331 | ||||||||
\(580\) | −117.674 | −4.88616 | ||||||||
\(581\) | −22.2422 | −0.922761 | ||||||||
\(582\) | 45.1127 | 1.86998 | ||||||||
\(583\) | 34.1836 | 1.41574 | ||||||||
\(584\) | −99.4753 | −4.11632 | ||||||||
\(585\) | 27.4693 | 1.13572 | ||||||||
\(586\) | 16.1841 | 0.668561 | ||||||||
\(587\) | 7.02358 | 0.289894 | 0.144947 | − | 0.989439i | \(-0.453699\pi\) | ||||
0.144947 | + | 0.989439i | \(0.453699\pi\) | |||||||
\(588\) | 25.3807 | 1.04668 | ||||||||
\(589\) | −30.4317 | −1.25392 | ||||||||
\(590\) | 3.69956 | 0.152309 | ||||||||
\(591\) | 24.9315 | 1.02554 | ||||||||
\(592\) | −176.350 | −7.24796 | ||||||||
\(593\) | 0.588708 | 0.0241754 | 0.0120877 | − | 0.999927i | \(-0.496152\pi\) | ||||
0.0120877 | + | 0.999927i | \(0.496152\pi\) | |||||||
\(594\) | −61.3464 | −2.51707 | ||||||||
\(595\) | 20.9467 | 0.858732 | ||||||||
\(596\) | 109.385 | 4.48057 | ||||||||
\(597\) | 5.51712 | 0.225801 | ||||||||
\(598\) | −7.93399 | −0.324445 | ||||||||
\(599\) | −25.6346 | −1.04740 | −0.523702 | − | 0.851902i | \(-0.675449\pi\) | ||||
−0.523702 | + | 0.851902i | \(0.675449\pi\) | |||||||
\(600\) | 24.7564 | 1.01067 | ||||||||
\(601\) | 15.1624 | 0.618486 | 0.309243 | − | 0.950983i | \(-0.399924\pi\) | ||||
0.309243 | + | 0.950983i | \(0.399924\pi\) | |||||||
\(602\) | 14.7880 | 0.602713 | ||||||||
\(603\) | 3.22091 | 0.131166 | ||||||||
\(604\) | −59.6283 | −2.42624 | ||||||||
\(605\) | 25.6992 | 1.04482 | ||||||||
\(606\) | 9.60253 | 0.390076 | ||||||||
\(607\) | 2.47771 | 0.100567 | 0.0502835 | − | 0.998735i | \(-0.483987\pi\) | ||||
0.0502835 | + | 0.998735i | \(0.483987\pi\) | |||||||
\(608\) | 193.497 | 7.84732 | ||||||||
\(609\) | 10.9830 | 0.445053 | ||||||||
\(610\) | −90.4565 | −3.66248 | ||||||||
\(611\) | 10.1838 | 0.411994 | ||||||||
\(612\) | −60.2593 | −2.43584 | ||||||||
\(613\) | −30.1231 | −1.21666 | −0.608330 | − | 0.793684i | \(-0.708160\pi\) | ||||
−0.608330 | + | 0.793684i | \(0.708160\pi\) | |||||||
\(614\) | −26.4643 | −1.06801 | ||||||||
\(615\) | −9.87233 | −0.398091 | ||||||||
\(616\) | −75.6276 | −3.04712 | ||||||||
\(617\) | 3.17681 | 0.127894 | 0.0639468 | − | 0.997953i | \(-0.479631\pi\) | ||||
0.0639468 | + | 0.997953i | \(0.479631\pi\) | |||||||
\(618\) | 20.0384 | 0.806061 | ||||||||
\(619\) | 44.6994 | 1.79662 | 0.898311 | − | 0.439360i | \(-0.144795\pi\) | ||||
0.898311 | + | 0.439360i | \(0.144795\pi\) | |||||||
\(620\) | 74.9084 | 3.00840 | ||||||||
\(621\) | −2.85451 | −0.114548 | ||||||||
\(622\) | 0.838761 | 0.0336312 | ||||||||
\(623\) | −6.53922 | −0.261988 | ||||||||
\(624\) | 84.2023 | 3.37079 | ||||||||
\(625\) | −31.2441 | −1.24976 | ||||||||
\(626\) | −59.1346 | −2.36349 | ||||||||
\(627\) | 27.7859 | 1.10966 | ||||||||
\(628\) | 13.2582 | 0.529061 | ||||||||
\(629\) | −47.3385 | −1.88751 | ||||||||
\(630\) | 24.8929 | 0.991756 | ||||||||
\(631\) | −22.7524 | −0.905758 | −0.452879 | − | 0.891572i | \(-0.649603\pi\) | ||||
−0.452879 | + | 0.891572i | \(0.649603\pi\) | |||||||
\(632\) | −18.1764 | −0.723017 | ||||||||
\(633\) | −20.4027 | −0.810933 | ||||||||
\(634\) | −47.6744 | −1.89339 | ||||||||
\(635\) | −29.0722 | −1.15370 | ||||||||
\(636\) | −41.9981 | −1.66533 | ||||||||
\(637\) | 22.0041 | 0.871832 | ||||||||
\(638\) | 93.6572 | 3.70792 | ||||||||
\(639\) | 2.09402 | 0.0828381 | ||||||||
\(640\) | −196.057 | −7.74984 | ||||||||
\(641\) | −20.3231 | −0.802714 | −0.401357 | − | 0.915922i | \(-0.631461\pi\) | ||||
−0.401357 | + | 0.915922i | \(0.631461\pi\) | |||||||
\(642\) | 20.7486 | 0.818882 | ||||||||
\(643\) | 6.90125 | 0.272159 | 0.136079 | − | 0.990698i | \(-0.456550\pi\) | ||||
0.136079 | + | 0.990698i | \(0.456550\pi\) | |||||||
\(644\) | −5.35443 | −0.210994 | ||||||||
\(645\) | 8.78956 | 0.346089 | ||||||||
\(646\) | 89.1549 | 3.50775 | ||||||||
\(647\) | −2.92065 | −0.114822 | −0.0574112 | − | 0.998351i | \(-0.518285\pi\) | ||||
−0.0574112 | + | 0.998351i | \(0.518285\pi\) | |||||||
\(648\) | −17.8920 | −0.702865 | ||||||||
\(649\) | −2.19283 | −0.0860760 | ||||||||
\(650\) | 32.6570 | 1.28091 | ||||||||
\(651\) | −6.99149 | −0.274018 | ||||||||
\(652\) | −108.678 | −4.25615 | ||||||||
\(653\) | 2.59117 | 0.101400 | 0.0507002 | − | 0.998714i | \(-0.483855\pi\) | ||||
0.0507002 | + | 0.998714i | \(0.483855\pi\) | |||||||
\(654\) | −17.8020 | −0.696115 | ||||||||
\(655\) | −48.3992 | −1.89111 | ||||||||
\(656\) | 69.9450 | 2.73089 | ||||||||
\(657\) | −19.4073 | −0.757149 | ||||||||
\(658\) | 9.22865 | 0.359770 | ||||||||
\(659\) | −35.4851 | −1.38230 | −0.691152 | − | 0.722710i | \(-0.742896\pi\) | ||||
−0.691152 | + | 0.722710i | \(0.742896\pi\) | |||||||
\(660\) | −68.3957 | −2.66230 | ||||||||
\(661\) | 16.9763 | 0.660303 | 0.330152 | − | 0.943928i | \(-0.392900\pi\) | ||||
0.330152 | + | 0.943928i | \(0.392900\pi\) | |||||||
\(662\) | 52.1577 | 2.02717 | ||||||||
\(663\) | 22.6028 | 0.877819 | ||||||||
\(664\) | 153.151 | 5.94341 | ||||||||
\(665\) | −27.4278 | −1.06360 | ||||||||
\(666\) | −56.2565 | −2.17990 | ||||||||
\(667\) | 4.35796 | 0.168741 | ||||||||
\(668\) | −135.331 | −5.23612 | ||||||||
\(669\) | 6.93340 | 0.268061 | ||||||||
\(670\) | 11.7302 | 0.453176 | ||||||||
\(671\) | 53.6160 | 2.06982 | ||||||||
\(672\) | 44.4546 | 1.71487 | ||||||||
\(673\) | 3.46985 | 0.133753 | 0.0668765 | − | 0.997761i | \(-0.478697\pi\) | ||||
0.0668765 | + | 0.997761i | \(0.478697\pi\) | |||||||
\(674\) | 2.45848 | 0.0946970 | ||||||||
\(675\) | 11.7494 | 0.452235 | ||||||||
\(676\) | 59.4054 | 2.28482 | ||||||||
\(677\) | 47.3242 | 1.81882 | 0.909409 | − | 0.415903i | \(-0.136534\pi\) | ||||
0.909409 | + | 0.415903i | \(0.136534\pi\) | |||||||
\(678\) | −2.66421 | −0.102318 | ||||||||
\(679\) | 26.3948 | 1.01294 | ||||||||
\(680\) | −144.231 | −5.53101 | ||||||||
\(681\) | 0.737090 | 0.0282453 | ||||||||
\(682\) | −59.6198 | −2.28296 | ||||||||
\(683\) | −13.9532 | −0.533904 | −0.266952 | − | 0.963710i | \(-0.586017\pi\) | ||||
−0.266952 | + | 0.963710i | \(0.586017\pi\) | |||||||
\(684\) | 78.9039 | 3.01697 | ||||||||
\(685\) | −35.9760 | −1.37457 | ||||||||
\(686\) | 50.4821 | 1.92741 | ||||||||
\(687\) | −3.64695 | −0.139140 | ||||||||
\(688\) | −62.2737 | −2.37416 | ||||||||
\(689\) | −36.4107 | −1.38714 | ||||||||
\(690\) | −4.27343 | −0.162687 | ||||||||
\(691\) | 44.1286 | 1.67873 | 0.839365 | − | 0.543568i | \(-0.182927\pi\) | ||||
0.839365 | + | 0.543568i | \(0.182927\pi\) | |||||||
\(692\) | −110.490 | −4.20020 | ||||||||
\(693\) | −14.7547 | −0.560483 | ||||||||
\(694\) | −4.35099 | −0.165161 | ||||||||
\(695\) | 38.2095 | 1.44937 | ||||||||
\(696\) | −75.6246 | −2.86654 | ||||||||
\(697\) | 18.7756 | 0.711178 | ||||||||
\(698\) | 29.3715 | 1.11173 | ||||||||
\(699\) | 21.3817 | 0.808730 | ||||||||
\(700\) | 22.0393 | 0.833006 | ||||||||
\(701\) | 10.7832 | 0.407276 | 0.203638 | − | 0.979046i | \(-0.434723\pi\) | ||||
0.203638 | + | 0.979046i | \(0.434723\pi\) | |||||||
\(702\) | 65.3432 | 2.46622 | ||||||||
\(703\) | 61.9853 | 2.33782 | ||||||||
\(704\) | 212.980 | 8.02699 | ||||||||
\(705\) | 5.48525 | 0.206587 | ||||||||
\(706\) | 55.9210 | 2.10461 | ||||||||
\(707\) | 5.61831 | 0.211298 | ||||||||
\(708\) | 2.69412 | 0.101251 | ||||||||
\(709\) | 30.7319 | 1.15416 | 0.577080 | − | 0.816687i | \(-0.304192\pi\) | ||||
0.577080 | + | 0.816687i | \(0.304192\pi\) | |||||||
\(710\) | 7.62616 | 0.286205 | ||||||||
\(711\) | −3.54614 | −0.132991 | ||||||||
\(712\) | 45.0266 | 1.68744 | ||||||||
\(713\) | −2.77417 | −0.103894 | ||||||||
\(714\) | 20.4828 | 0.766548 | ||||||||
\(715\) | −59.2963 | −2.21756 | ||||||||
\(716\) | −59.5732 | −2.22636 | ||||||||
\(717\) | 8.19967 | 0.306222 | ||||||||
\(718\) | 41.2245 | 1.53848 | ||||||||
\(719\) | 32.1913 | 1.20053 | 0.600267 | − | 0.799800i | \(-0.295061\pi\) | ||||
0.600267 | + | 0.799800i | \(0.295061\pi\) | |||||||
\(720\) | −104.826 | −3.90665 | ||||||||
\(721\) | 11.7242 | 0.436631 | ||||||||
\(722\) | −63.5582 | −2.36539 | ||||||||
\(723\) | −12.5650 | −0.467296 | ||||||||
\(724\) | 22.0969 | 0.821227 | ||||||||
\(725\) | −17.9377 | −0.666191 | ||||||||
\(726\) | 25.1300 | 0.932661 | ||||||||
\(727\) | −21.6385 | −0.802529 | −0.401265 | − | 0.915962i | \(-0.631429\pi\) | ||||
−0.401265 | + | 0.915962i | \(0.631429\pi\) | |||||||
\(728\) | 80.5548 | 2.98556 | ||||||||
\(729\) | 10.3546 | 0.383503 | ||||||||
\(730\) | −70.6788 | −2.61594 | ||||||||
\(731\) | −16.7164 | −0.618277 | ||||||||
\(732\) | −65.8728 | −2.43473 | ||||||||
\(733\) | 28.6036 | 1.05650 | 0.528248 | − | 0.849090i | \(-0.322849\pi\) | ||||
0.528248 | + | 0.849090i | \(0.322849\pi\) | |||||||
\(734\) | 60.8951 | 2.24768 | ||||||||
\(735\) | 11.8519 | 0.437164 | ||||||||
\(736\) | 17.6392 | 0.650191 | ||||||||
\(737\) | −6.95278 | −0.256109 | ||||||||
\(738\) | 22.3127 | 0.821344 | ||||||||
\(739\) | −29.2269 | −1.07513 | −0.537564 | − | 0.843223i | \(-0.680655\pi\) | ||||
−0.537564 | + | 0.843223i | \(0.680655\pi\) | |||||||
\(740\) | −152.578 | −5.60889 | ||||||||
\(741\) | −29.5962 | −1.08724 | ||||||||
\(742\) | −32.9955 | −1.21130 | ||||||||
\(743\) | −3.07880 | −0.112950 | −0.0564751 | − | 0.998404i | \(-0.517986\pi\) | ||||
−0.0564751 | + | 0.998404i | \(0.517986\pi\) | |||||||
\(744\) | 48.1407 | 1.76492 | ||||||||
\(745\) | 51.0787 | 1.87138 | ||||||||
\(746\) | −33.7327 | −1.23504 | ||||||||
\(747\) | 29.8792 | 1.09322 | ||||||||
\(748\) | 130.078 | 4.75612 | ||||||||
\(749\) | 12.1397 | 0.443576 | ||||||||
\(750\) | −18.7042 | −0.682982 | ||||||||
\(751\) | −28.3789 | −1.03556 | −0.517780 | − | 0.855514i | \(-0.673241\pi\) | ||||
−0.517780 | + | 0.855514i | \(0.673241\pi\) | |||||||
\(752\) | −38.8628 | −1.41718 | ||||||||
\(753\) | −18.2958 | −0.666738 | ||||||||
\(754\) | −99.7590 | −3.63301 | ||||||||
\(755\) | −27.8443 | −1.01336 | ||||||||
\(756\) | 44.0983 | 1.60384 | ||||||||
\(757\) | 5.51550 | 0.200464 | 0.100232 | − | 0.994964i | \(-0.468041\pi\) | ||||
0.100232 | + | 0.994964i | \(0.468041\pi\) | |||||||
\(758\) | −69.7783 | −2.53446 | ||||||||
\(759\) | 2.53298 | 0.0919413 | ||||||||
\(760\) | 188.857 | 6.85057 | ||||||||
\(761\) | −42.0455 | −1.52415 | −0.762074 | − | 0.647490i | \(-0.775819\pi\) | ||||
−0.762074 | + | 0.647490i | \(0.775819\pi\) | |||||||
\(762\) | −28.4283 | −1.02985 | ||||||||
\(763\) | −10.4157 | −0.377075 | ||||||||
\(764\) | 103.451 | 3.74274 | ||||||||
\(765\) | −28.1390 | −1.01737 | ||||||||
\(766\) | 51.2684 | 1.85240 | ||||||||
\(767\) | 2.33569 | 0.0843370 | ||||||||
\(768\) | −102.019 | −3.68130 | ||||||||
\(769\) | −51.2803 | −1.84921 | −0.924607 | − | 0.380923i | \(-0.875606\pi\) | ||||
−0.924607 | + | 0.380923i | \(0.875606\pi\) | |||||||
\(770\) | −53.7347 | −1.93646 | ||||||||
\(771\) | 27.2893 | 0.982799 | ||||||||
\(772\) | −38.6939 | −1.39262 | ||||||||
\(773\) | −19.7305 | −0.709656 | −0.354828 | − | 0.934932i | \(-0.615461\pi\) | ||||
−0.354828 | + | 0.934932i | \(0.615461\pi\) | |||||||
\(774\) | −19.8656 | −0.714053 | ||||||||
\(775\) | 11.4187 | 0.410172 | ||||||||
\(776\) | −181.745 | −6.52425 | ||||||||
\(777\) | 14.2407 | 0.510883 | ||||||||
\(778\) | 3.86550 | 0.138585 | ||||||||
\(779\) | −24.5849 | −0.880846 | ||||||||
\(780\) | 72.8518 | 2.60851 | ||||||||
\(781\) | −4.52022 | −0.161746 | ||||||||
\(782\) | 8.12740 | 0.290635 | ||||||||
\(783\) | −35.8915 | −1.28266 | ||||||||
\(784\) | −83.9701 | −2.99893 | ||||||||
\(785\) | 6.19112 | 0.220971 | ||||||||
\(786\) | −47.3272 | −1.68810 | ||||||||
\(787\) | −1.76911 | −0.0630620 | −0.0315310 | − | 0.999503i | \(-0.510038\pi\) | ||||
−0.0315310 | + | 0.999503i | \(0.510038\pi\) | |||||||
\(788\) | −152.827 | −5.44425 | ||||||||
\(789\) | 4.17801 | 0.148741 | ||||||||
\(790\) | −12.9146 | −0.459481 | ||||||||
\(791\) | −1.55879 | −0.0554243 | ||||||||
\(792\) | 101.595 | 3.61002 | ||||||||
\(793\) | −57.1091 | −2.02800 | ||||||||
\(794\) | −61.5528 | −2.18443 | ||||||||
\(795\) | −19.6116 | −0.695553 | ||||||||
\(796\) | −33.8194 | −1.19870 | ||||||||
\(797\) | −37.9826 | −1.34541 | −0.672707 | − | 0.739909i | \(-0.734869\pi\) | ||||
−0.672707 | + | 0.739909i | \(0.734869\pi\) | |||||||
\(798\) | −26.8202 | −0.949426 | ||||||||
\(799\) | −10.4321 | −0.369061 | ||||||||
\(800\) | −72.6046 | −2.56696 | ||||||||
\(801\) | 8.78452 | 0.310386 | ||||||||
\(802\) | 91.1365 | 3.21814 | ||||||||
\(803\) | 41.8932 | 1.47838 | ||||||||
\(804\) | 8.54222 | 0.301261 | ||||||||
\(805\) | −2.50033 | −0.0881250 | ||||||||
\(806\) | 63.5041 | 2.23684 | ||||||||
\(807\) | −2.17127 | −0.0764325 | ||||||||
\(808\) | −38.6855 | −1.36095 | ||||||||
\(809\) | −25.7544 | −0.905475 | −0.452738 | − | 0.891644i | \(-0.649553\pi\) | ||||
−0.452738 | + | 0.891644i | \(0.649553\pi\) | |||||||
\(810\) | −12.7126 | −0.446674 | ||||||||
\(811\) | 16.1452 | 0.566935 | 0.283468 | − | 0.958982i | \(-0.408515\pi\) | ||||
0.283468 | + | 0.958982i | \(0.408515\pi\) | |||||||
\(812\) | −67.3245 | −2.36263 | ||||||||
\(813\) | 27.0053 | 0.947116 | ||||||||
\(814\) | 121.437 | 4.25638 | ||||||||
\(815\) | −50.7487 | −1.77765 | ||||||||
\(816\) | −86.2549 | −3.01953 | ||||||||
\(817\) | 21.8885 | 0.765782 | ||||||||
\(818\) | 91.0989 | 3.18520 | ||||||||
\(819\) | 15.7159 | 0.549160 | ||||||||
\(820\) | 60.5164 | 2.11332 | ||||||||
\(821\) | 29.6913 | 1.03623 | 0.518117 | − | 0.855310i | \(-0.326633\pi\) | ||||
0.518117 | + | 0.855310i | \(0.326633\pi\) | |||||||
\(822\) | −35.1791 | −1.22701 | ||||||||
\(823\) | −6.58582 | −0.229567 | −0.114784 | − | 0.993391i | \(-0.536617\pi\) | ||||
−0.114784 | + | 0.993391i | \(0.536617\pi\) | |||||||
\(824\) | −80.7281 | −2.81230 | ||||||||
\(825\) | −10.4259 | −0.362985 | ||||||||
\(826\) | 2.11662 | 0.0736465 | ||||||||
\(827\) | −7.11821 | −0.247525 | −0.123762 | − | 0.992312i | \(-0.539496\pi\) | ||||
−0.123762 | + | 0.992312i | \(0.539496\pi\) | |||||||
\(828\) | 7.19291 | 0.249971 | ||||||||
\(829\) | −16.4817 | −0.572433 | −0.286217 | − | 0.958165i | \(-0.592398\pi\) | ||||
−0.286217 | + | 0.958165i | \(0.592398\pi\) | |||||||
\(830\) | 108.816 | 3.77707 | ||||||||
\(831\) | 9.42796 | 0.327052 | ||||||||
\(832\) | −226.856 | −7.86482 | ||||||||
\(833\) | −22.5404 | −0.780980 | ||||||||
\(834\) | 37.3632 | 1.29378 | ||||||||
\(835\) | −63.1949 | −2.18695 | ||||||||
\(836\) | −170.325 | −5.89081 | ||||||||
\(837\) | 22.8477 | 0.789730 | ||||||||
\(838\) | −96.7579 | −3.34244 | ||||||||
\(839\) | −29.1410 | −1.00606 | −0.503029 | − | 0.864269i | \(-0.667781\pi\) | ||||
−0.503029 | + | 0.864269i | \(0.667781\pi\) | |||||||
\(840\) | 43.3887 | 1.49705 | ||||||||
\(841\) | 25.7954 | 0.889496 | ||||||||
\(842\) | 1.02151 | 0.0352034 | ||||||||
\(843\) | −21.4299 | −0.738087 | ||||||||
\(844\) | 125.066 | 4.30496 | ||||||||
\(845\) | 27.7402 | 0.954293 | ||||||||
\(846\) | −12.3974 | −0.426231 | ||||||||
\(847\) | 14.7032 | 0.505209 | ||||||||
\(848\) | 138.948 | 4.77148 | ||||||||
\(849\) | 12.3389 | 0.423469 | ||||||||
\(850\) | −33.4531 | −1.14743 | ||||||||
\(851\) | 5.65060 | 0.193700 | ||||||||
\(852\) | 5.55357 | 0.190262 | ||||||||
\(853\) | −57.0947 | −1.95489 | −0.977443 | − | 0.211199i | \(-0.932263\pi\) | ||||
−0.977443 | + | 0.211199i | \(0.932263\pi\) | |||||||
\(854\) | −51.7526 | −1.77094 | ||||||||
\(855\) | 36.8453 | 1.26008 | ||||||||
\(856\) | −83.5894 | −2.85703 | ||||||||
\(857\) | 6.64210 | 0.226890 | 0.113445 | − | 0.993544i | \(-0.463811\pi\) | ||||
0.113445 | + | 0.993544i | \(0.463811\pi\) | |||||||
\(858\) | −57.9829 | −1.97950 | ||||||||
\(859\) | −5.22720 | −0.178350 | −0.0891748 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891748 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(860\) | −53.8791 | −1.83726 | ||||||||
\(861\) | −5.64822 | −0.192491 | ||||||||
\(862\) | 49.9589 | 1.70161 | ||||||||
\(863\) | 29.1300 | 0.991595 | 0.495798 | − | 0.868438i | \(-0.334876\pi\) | ||||
0.495798 | + | 0.868438i | \(0.334876\pi\) | |||||||
\(864\) | −145.274 | −4.94233 | ||||||||
\(865\) | −51.5950 | −1.75428 | ||||||||
\(866\) | 86.5540 | 2.94123 | ||||||||
\(867\) | −6.97264 | −0.236803 | ||||||||
\(868\) | 42.8571 | 1.45467 | ||||||||
\(869\) | 7.65483 | 0.259672 | ||||||||
\(870\) | −53.7325 | −1.82170 | ||||||||
\(871\) | 7.40576 | 0.250935 | ||||||||
\(872\) | 71.7187 | 2.42870 | ||||||||
\(873\) | −35.4577 | −1.20006 | ||||||||
\(874\) | −10.6421 | −0.359973 | ||||||||
\(875\) | −10.9436 | −0.369961 | ||||||||
\(876\) | −51.4702 | −1.73902 | ||||||||
\(877\) | −46.0981 | −1.55662 | −0.778311 | − | 0.627879i | \(-0.783923\pi\) | ||||
−0.778311 | + | 0.627879i | \(0.783923\pi\) | |||||||
\(878\) | −98.4570 | −3.32276 | ||||||||
\(879\) | 5.50352 | 0.185629 | ||||||||
\(880\) | 226.282 | 7.62797 | ||||||||
\(881\) | −35.3559 | −1.19117 | −0.595585 | − | 0.803292i | \(-0.703080\pi\) | ||||
−0.595585 | + | 0.803292i | \(0.703080\pi\) | |||||||
\(882\) | −26.7868 | −0.901959 | ||||||||
\(883\) | 2.32888 | 0.0783730 | 0.0391865 | − | 0.999232i | \(-0.487523\pi\) | ||||
0.0391865 | + | 0.999232i | \(0.487523\pi\) | |||||||
\(884\) | −138.553 | −4.66003 | ||||||||
\(885\) | 1.25806 | 0.0422892 | ||||||||
\(886\) | −22.9921 | −0.772433 | ||||||||
\(887\) | −22.8493 | −0.767205 | −0.383602 | − | 0.923498i | \(-0.625317\pi\) | ||||
−0.383602 | + | 0.923498i | \(0.625317\pi\) | |||||||
\(888\) | −98.0560 | −3.29055 | ||||||||
\(889\) | −16.6330 | −0.557853 | ||||||||
\(890\) | 31.9921 | 1.07238 | ||||||||
\(891\) | 7.53508 | 0.252435 | ||||||||
\(892\) | −42.5010 | −1.42304 | ||||||||
\(893\) | 13.6598 | 0.457109 | ||||||||
\(894\) | 49.9473 | 1.67049 | ||||||||
\(895\) | −27.8186 | −0.929873 | ||||||||
\(896\) | −112.170 | −3.74732 | ||||||||
\(897\) | −2.69800 | −0.0900837 | ||||||||
\(898\) | 14.9865 | 0.500105 | ||||||||
\(899\) | −34.8814 | −1.16336 | ||||||||
\(900\) | −29.6066 | −0.986888 | ||||||||
\(901\) | 37.2983 | 1.24258 | ||||||||
\(902\) | −48.1651 | −1.60372 | ||||||||
\(903\) | 5.02874 | 0.167346 | ||||||||
\(904\) | 10.7333 | 0.356983 | ||||||||
\(905\) | 10.3185 | 0.342998 | ||||||||
\(906\) | −27.2276 | −0.904575 | ||||||||
\(907\) | 40.7286 | 1.35237 | 0.676186 | − | 0.736731i | \(-0.263632\pi\) | ||||
0.676186 | + | 0.736731i | \(0.263632\pi\) | |||||||
\(908\) | −4.51828 | −0.149944 | ||||||||
\(909\) | −7.54741 | −0.250332 | ||||||||
\(910\) | 57.2355 | 1.89734 | ||||||||
\(911\) | 5.42463 | 0.179726 | 0.0898629 | − | 0.995954i | \(-0.471357\pi\) | ||||
0.0898629 | + | 0.995954i | \(0.471357\pi\) | |||||||
\(912\) | 112.943 | 3.73991 | ||||||||
\(913\) | −64.4983 | −2.13458 | ||||||||
\(914\) | −15.0979 | −0.499396 | ||||||||
\(915\) | −30.7603 | −1.01690 | ||||||||
\(916\) | 22.3554 | 0.738643 | ||||||||
\(917\) | −27.6905 | −0.914421 | ||||||||
\(918\) | −66.9361 | −2.20922 | ||||||||
\(919\) | 18.1092 | 0.597366 | 0.298683 | − | 0.954352i | \(-0.403453\pi\) | ||||
0.298683 | + | 0.954352i | \(0.403453\pi\) | |||||||
\(920\) | 17.2163 | 0.567605 | ||||||||
\(921\) | −8.99935 | −0.296539 | ||||||||
\(922\) | 41.7320 | 1.37437 | ||||||||
\(923\) | 4.81472 | 0.158478 | ||||||||
\(924\) | −39.1310 | −1.28732 | ||||||||
\(925\) | −23.2584 | −0.764730 | ||||||||
\(926\) | −86.1750 | −2.83189 | ||||||||
\(927\) | −15.7498 | −0.517290 | ||||||||
\(928\) | 221.789 | 7.28058 | ||||||||
\(929\) | 21.8749 | 0.717692 | 0.358846 | − | 0.933397i | \(-0.383170\pi\) | ||||
0.358846 | + | 0.933397i | \(0.383170\pi\) | |||||||
\(930\) | 34.2048 | 1.12162 | ||||||||
\(931\) | 29.5146 | 0.967301 | ||||||||
\(932\) | −131.068 | −4.29326 | ||||||||
\(933\) | 0.285226 | 0.00933787 | ||||||||
\(934\) | −43.0731 | −1.40939 | ||||||||
\(935\) | 60.7418 | 1.98647 | ||||||||
\(936\) | −108.214 | −3.53708 | ||||||||
\(937\) | −3.82510 | −0.124961 | −0.0624803 | − | 0.998046i | \(-0.519901\pi\) | ||||
−0.0624803 | + | 0.998046i | \(0.519901\pi\) | |||||||
\(938\) | 6.71114 | 0.219127 | ||||||||
\(939\) | −20.1091 | −0.656235 | ||||||||
\(940\) | −33.6240 | −1.09669 | ||||||||
\(941\) | 36.1146 | 1.17730 | 0.588652 | − | 0.808387i | \(-0.299659\pi\) | ||||
0.588652 | + | 0.808387i | \(0.299659\pi\) | |||||||
\(942\) | 6.05399 | 0.197250 | ||||||||
\(943\) | −2.24117 | −0.0729826 | ||||||||
\(944\) | −8.91329 | −0.290103 | ||||||||
\(945\) | 20.5923 | 0.669869 | ||||||||
\(946\) | 42.8825 | 1.39423 | ||||||||
\(947\) | 4.53975 | 0.147522 | 0.0737610 | − | 0.997276i | \(-0.476500\pi\) | ||||
0.0737610 | + | 0.997276i | \(0.476500\pi\) | |||||||
\(948\) | −9.40476 | −0.305452 | ||||||||
\(949\) | −44.6226 | −1.44851 | ||||||||
\(950\) | 43.8036 | 1.42118 | ||||||||
\(951\) | −16.2120 | −0.525709 | ||||||||
\(952\) | −82.5185 | −2.67444 | ||||||||
\(953\) | 3.20087 | 0.103686 | 0.0518432 | − | 0.998655i | \(-0.483490\pi\) | ||||
0.0518432 | + | 0.998655i | \(0.483490\pi\) | |||||||
\(954\) | 44.3248 | 1.43507 | ||||||||
\(955\) | 48.3081 | 1.56322 | ||||||||
\(956\) | −50.2631 | −1.62563 | ||||||||
\(957\) | 31.8487 | 1.02952 | ||||||||
\(958\) | −87.5291 | −2.82794 | ||||||||
\(959\) | −20.5828 | −0.664654 | ||||||||
\(960\) | −122.190 | −3.94366 | ||||||||
\(961\) | −8.79540 | −0.283723 | ||||||||
\(962\) | −129.349 | −4.17038 | ||||||||
\(963\) | −16.3080 | −0.525518 | ||||||||
\(964\) | 77.0219 | 2.48071 | ||||||||
\(965\) | −18.0687 | −0.581652 | ||||||||
\(966\) | −2.44494 | −0.0786648 | ||||||||
\(967\) | −19.5764 | −0.629535 | −0.314768 | − | 0.949169i | \(-0.601927\pi\) | ||||
−0.314768 | + | 0.949169i | \(0.601927\pi\) | |||||||
\(968\) | −101.241 | −3.25400 | ||||||||
\(969\) | 30.3177 | 0.973944 | ||||||||
\(970\) | −129.133 | −4.14620 | ||||||||
\(971\) | 31.7144 | 1.01776 | 0.508881 | − | 0.860837i | \(-0.330059\pi\) | ||||
0.508881 | + | 0.860837i | \(0.330059\pi\) | |||||||
\(972\) | −94.1276 | −3.01914 | ||||||||
\(973\) | 21.8607 | 0.700821 | ||||||||
\(974\) | 79.0936 | 2.53432 | ||||||||
\(975\) | 11.1052 | 0.355651 | ||||||||
\(976\) | 217.935 | 6.97594 | ||||||||
\(977\) | −18.4518 | −0.590326 | −0.295163 | − | 0.955447i | \(-0.595374\pi\) | ||||
−0.295163 | + | 0.955447i | \(0.595374\pi\) | |||||||
\(978\) | −49.6246 | −1.58682 | ||||||||
\(979\) | −18.9626 | −0.606047 | ||||||||
\(980\) | −72.6509 | −2.32075 | ||||||||
\(981\) | 13.9921 | 0.446732 | ||||||||
\(982\) | 67.5221 | 2.15472 | ||||||||
\(983\) | 16.7406 | 0.533941 | 0.266970 | − | 0.963705i | \(-0.413977\pi\) | ||||
0.266970 | + | 0.963705i | \(0.413977\pi\) | |||||||
\(984\) | 38.8915 | 1.23982 | ||||||||
\(985\) | −71.3650 | −2.27388 | ||||||||
\(986\) | 102.191 | 3.25442 | ||||||||
\(987\) | 3.13826 | 0.0998919 | ||||||||
\(988\) | 181.422 | 5.77179 | ||||||||
\(989\) | 1.99537 | 0.0634490 | ||||||||
\(990\) | 72.1849 | 2.29419 | ||||||||
\(991\) | 5.27862 | 0.167681 | 0.0838405 | − | 0.996479i | \(-0.473281\pi\) | ||||
0.0838405 | + | 0.996479i | \(0.473281\pi\) | |||||||
\(992\) | −141.185 | −4.48264 | ||||||||
\(993\) | 17.7365 | 0.562852 | ||||||||
\(994\) | 4.36313 | 0.138390 | ||||||||
\(995\) | −15.7925 | −0.500654 | ||||||||
\(996\) | 79.2430 | 2.51091 | ||||||||
\(997\) | 4.99832 | 0.158298 | 0.0791491 | − | 0.996863i | \(-0.474780\pi\) | ||||
0.0791491 | + | 0.996863i | \(0.474780\pi\) | |||||||
\(998\) | −69.5531 | −2.20166 | ||||||||
\(999\) | −46.5375 | −1.47238 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8023.2.a.c.1.1 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.1 | ✓ | 158 | 1.1 | even | 1 | trivial |