Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.21265 | −1.85482 | −0.927412 | − | 0.374043i | \(-0.877971\pi\) | ||||
−0.927412 | + | 0.374043i | \(0.877971\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.26318 | 1.45934 | 0.729669 | − | 0.683801i | \(-0.239674\pi\) | ||||
0.729669 | + | 0.683801i | \(0.239674\pi\) | |||||||
\(6\) | 3.21265 | 1.31156 | ||||||||
\(7\) | −3.74888 | −1.41694 | −0.708472 | − | 0.705739i | \(-0.750615\pi\) | ||||
−0.708472 | + | 0.705739i | \(0.750615\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.32111 | 2.44037 | ||||||||
\(10\) | −3.26318 | −1.03191 | ||||||||
\(11\) | 2.74731 | 0.828346 | 0.414173 | − | 0.910198i | \(-0.364071\pi\) | ||||
0.414173 | + | 0.910198i | \(0.364071\pi\) | |||||||
\(12\) | −3.21265 | −0.927412 | ||||||||
\(13\) | 1.96912 | 0.546136 | 0.273068 | − | 0.961995i | \(-0.411962\pi\) | ||||
0.273068 | + | 0.961995i | \(0.411962\pi\) | |||||||
\(14\) | 3.74888 | 1.00193 | ||||||||
\(15\) | −10.4834 | −2.70681 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.78943 | 0.676536 | 0.338268 | − | 0.941050i | \(-0.390159\pi\) | ||||
0.338268 | + | 0.941050i | \(0.390159\pi\) | |||||||
\(18\) | −7.32111 | −1.72560 | ||||||||
\(19\) | 5.90910 | 1.35564 | 0.677821 | − | 0.735227i | \(-0.262925\pi\) | ||||
0.677821 | + | 0.735227i | \(0.262925\pi\) | |||||||
\(20\) | 3.26318 | 0.729669 | ||||||||
\(21\) | 12.0438 | 2.62818 | ||||||||
\(22\) | −2.74731 | −0.585729 | ||||||||
\(23\) | 0.836221 | 0.174364 | 0.0871821 | − | 0.996192i | \(-0.472214\pi\) | ||||
0.0871821 | + | 0.996192i | \(0.472214\pi\) | |||||||
\(24\) | 3.21265 | 0.655779 | ||||||||
\(25\) | 5.64833 | 1.12967 | ||||||||
\(26\) | −1.96912 | −0.386176 | ||||||||
\(27\) | −13.8822 | −2.67163 | ||||||||
\(28\) | −3.74888 | −0.708472 | ||||||||
\(29\) | 3.74478 | 0.695388 | 0.347694 | − | 0.937608i | \(-0.386965\pi\) | ||||
0.347694 | + | 0.937608i | \(0.386965\pi\) | |||||||
\(30\) | 10.4834 | 1.91401 | ||||||||
\(31\) | 6.96260 | 1.25052 | 0.625260 | − | 0.780417i | \(-0.284993\pi\) | ||||
0.625260 | + | 0.780417i | \(0.284993\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −8.82615 | −1.53644 | ||||||||
\(34\) | −2.78943 | −0.478383 | ||||||||
\(35\) | −12.2333 | −2.06780 | ||||||||
\(36\) | 7.32111 | 1.22018 | ||||||||
\(37\) | −9.58970 | −1.57654 | −0.788268 | − | 0.615331i | \(-0.789022\pi\) | ||||
−0.788268 | + | 0.615331i | \(0.789022\pi\) | |||||||
\(38\) | −5.90910 | −0.958583 | ||||||||
\(39\) | −6.32609 | −1.01299 | ||||||||
\(40\) | −3.26318 | −0.515954 | ||||||||
\(41\) | 11.2749 | 1.76085 | 0.880423 | − | 0.474189i | \(-0.157259\pi\) | ||||
0.880423 | + | 0.474189i | \(0.157259\pi\) | |||||||
\(42\) | −12.0438 | −1.85840 | ||||||||
\(43\) | 6.25743 | 0.954249 | 0.477124 | − | 0.878836i | \(-0.341679\pi\) | ||||
0.477124 | + | 0.878836i | \(0.341679\pi\) | |||||||
\(44\) | 2.74731 | 0.414173 | ||||||||
\(45\) | 23.8901 | 3.56132 | ||||||||
\(46\) | −0.836221 | −0.123294 | ||||||||
\(47\) | −7.60552 | −1.10938 | −0.554690 | − | 0.832057i | \(-0.687163\pi\) | ||||
−0.554690 | + | 0.832057i | \(0.687163\pi\) | |||||||
\(48\) | −3.21265 | −0.463706 | ||||||||
\(49\) | 7.05412 | 1.00773 | ||||||||
\(50\) | −5.64833 | −0.798794 | ||||||||
\(51\) | −8.96145 | −1.25485 | ||||||||
\(52\) | 1.96912 | 0.273068 | ||||||||
\(53\) | 13.6811 | 1.87925 | 0.939624 | − | 0.342207i | \(-0.111175\pi\) | ||||
0.939624 | + | 0.342207i | \(0.111175\pi\) | |||||||
\(54\) | 13.8822 | 1.88913 | ||||||||
\(55\) | 8.96497 | 1.20884 | ||||||||
\(56\) | 3.74888 | 0.500965 | ||||||||
\(57\) | −18.9839 | −2.51447 | ||||||||
\(58\) | −3.74478 | −0.491714 | ||||||||
\(59\) | −3.51087 | −0.457076 | −0.228538 | − | 0.973535i | \(-0.573395\pi\) | ||||
−0.228538 | + | 0.973535i | \(0.573395\pi\) | |||||||
\(60\) | −10.4834 | −1.35341 | ||||||||
\(61\) | 5.81031 | 0.743934 | 0.371967 | − | 0.928246i | \(-0.378684\pi\) | ||||
0.371967 | + | 0.928246i | \(0.378684\pi\) | |||||||
\(62\) | −6.96260 | −0.884251 | ||||||||
\(63\) | −27.4460 | −3.45787 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.42559 | 0.796996 | ||||||||
\(66\) | 8.82615 | 1.08642 | ||||||||
\(67\) | −0.257564 | −0.0314664 | −0.0157332 | − | 0.999876i | \(-0.505008\pi\) | ||||
−0.0157332 | + | 0.999876i | \(0.505008\pi\) | |||||||
\(68\) | 2.78943 | 0.338268 | ||||||||
\(69\) | −2.68648 | −0.323415 | ||||||||
\(70\) | 12.2333 | 1.46216 | ||||||||
\(71\) | −4.76765 | −0.565815 | −0.282908 | − | 0.959147i | \(-0.591299\pi\) | ||||
−0.282908 | + | 0.959147i | \(0.591299\pi\) | |||||||
\(72\) | −7.32111 | −0.862801 | ||||||||
\(73\) | 11.5717 | 1.35437 | 0.677185 | − | 0.735813i | \(-0.263200\pi\) | ||||
0.677185 | + | 0.735813i | \(0.263200\pi\) | |||||||
\(74\) | 9.58970 | 1.11478 | ||||||||
\(75\) | −18.1461 | −2.09533 | ||||||||
\(76\) | 5.90910 | 0.677821 | ||||||||
\(77\) | −10.2994 | −1.17372 | ||||||||
\(78\) | 6.32609 | 0.716289 | ||||||||
\(79\) | −7.34390 | −0.826253 | −0.413127 | − | 0.910674i | \(-0.635563\pi\) | ||||
−0.413127 | + | 0.910674i | \(0.635563\pi\) | |||||||
\(80\) | 3.26318 | 0.364834 | ||||||||
\(81\) | 22.6353 | 2.51503 | ||||||||
\(82\) | −11.2749 | −1.24511 | ||||||||
\(83\) | −11.0188 | −1.20947 | −0.604734 | − | 0.796428i | \(-0.706721\pi\) | ||||
−0.604734 | + | 0.796428i | \(0.706721\pi\) | |||||||
\(84\) | 12.0438 | 1.31409 | ||||||||
\(85\) | 9.10240 | 0.987294 | ||||||||
\(86\) | −6.25743 | −0.674756 | ||||||||
\(87\) | −12.0307 | −1.28982 | ||||||||
\(88\) | −2.74731 | −0.292865 | ||||||||
\(89\) | −11.4928 | −1.21823 | −0.609116 | − | 0.793081i | \(-0.708475\pi\) | ||||
−0.609116 | + | 0.793081i | \(0.708475\pi\) | |||||||
\(90\) | −23.8901 | −2.51823 | ||||||||
\(91\) | −7.38200 | −0.773844 | ||||||||
\(92\) | 0.836221 | 0.0871821 | ||||||||
\(93\) | −22.3684 | −2.31949 | ||||||||
\(94\) | 7.60552 | 0.784450 | ||||||||
\(95\) | 19.2825 | 1.97834 | ||||||||
\(96\) | 3.21265 | 0.327889 | ||||||||
\(97\) | −9.25349 | −0.939549 | −0.469775 | − | 0.882786i | \(-0.655665\pi\) | ||||
−0.469775 | + | 0.882786i | \(0.655665\pi\) | |||||||
\(98\) | −7.05412 | −0.712573 | ||||||||
\(99\) | 20.1134 | 2.02147 | ||||||||
\(100\) | 5.64833 | 0.564833 | ||||||||
\(101\) | −0.874535 | −0.0870195 | −0.0435097 | − | 0.999053i | \(-0.513854\pi\) | ||||
−0.0435097 | + | 0.999053i | \(0.513854\pi\) | |||||||
\(102\) | 8.96145 | 0.887316 | ||||||||
\(103\) | 6.62031 | 0.652318 | 0.326159 | − | 0.945315i | \(-0.394245\pi\) | ||||
0.326159 | + | 0.945315i | \(0.394245\pi\) | |||||||
\(104\) | −1.96912 | −0.193088 | ||||||||
\(105\) | 39.3012 | 3.83540 | ||||||||
\(106\) | −13.6811 | −1.32883 | ||||||||
\(107\) | 13.7276 | 1.32710 | 0.663550 | − | 0.748132i | \(-0.269049\pi\) | ||||
0.663550 | + | 0.748132i | \(0.269049\pi\) | |||||||
\(108\) | −13.8822 | −1.33581 | ||||||||
\(109\) | −8.01601 | −0.767794 | −0.383897 | − | 0.923376i | \(-0.625418\pi\) | ||||
−0.383897 | + | 0.923376i | \(0.625418\pi\) | |||||||
\(110\) | −8.96497 | −0.854776 | ||||||||
\(111\) | 30.8083 | 2.92420 | ||||||||
\(112\) | −3.74888 | −0.354236 | ||||||||
\(113\) | 9.74825 | 0.917039 | 0.458519 | − | 0.888684i | \(-0.348380\pi\) | ||||
0.458519 | + | 0.888684i | \(0.348380\pi\) | |||||||
\(114\) | 18.9839 | 1.77800 | ||||||||
\(115\) | 2.72874 | 0.254456 | ||||||||
\(116\) | 3.74478 | 0.347694 | ||||||||
\(117\) | 14.4161 | 1.33277 | ||||||||
\(118\) | 3.51087 | 0.323202 | ||||||||
\(119\) | −10.4572 | −0.958613 | ||||||||
\(120\) | 10.4834 | 0.957003 | ||||||||
\(121\) | −3.45227 | −0.313843 | ||||||||
\(122\) | −5.81031 | −0.526041 | ||||||||
\(123\) | −36.2223 | −3.26606 | ||||||||
\(124\) | 6.96260 | 0.625260 | ||||||||
\(125\) | 2.11561 | 0.189226 | ||||||||
\(126\) | 27.4460 | 2.44508 | ||||||||
\(127\) | 18.4658 | 1.63858 | 0.819288 | − | 0.573382i | \(-0.194369\pi\) | ||||
0.819288 | + | 0.573382i | \(0.194369\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −20.1029 | −1.76996 | ||||||||
\(130\) | −6.42559 | −0.563561 | ||||||||
\(131\) | −15.5116 | −1.35525 | −0.677627 | − | 0.735406i | \(-0.736991\pi\) | ||||
−0.677627 | + | 0.735406i | \(0.736991\pi\) | |||||||
\(132\) | −8.82615 | −0.768218 | ||||||||
\(133\) | −22.1525 | −1.92087 | ||||||||
\(134\) | 0.257564 | 0.0222501 | ||||||||
\(135\) | −45.3001 | −3.89881 | ||||||||
\(136\) | −2.78943 | −0.239191 | ||||||||
\(137\) | −18.8452 | −1.61005 | −0.805025 | − | 0.593241i | \(-0.797848\pi\) | ||||
−0.805025 | + | 0.593241i | \(0.797848\pi\) | |||||||
\(138\) | 2.68648 | 0.228689 | ||||||||
\(139\) | 0.0766866 | 0.00650448 | 0.00325224 | − | 0.999995i | \(-0.498965\pi\) | ||||
0.00325224 | + | 0.999995i | \(0.498965\pi\) | |||||||
\(140\) | −12.2333 | −1.03390 | ||||||||
\(141\) | 24.4339 | 2.05770 | ||||||||
\(142\) | 4.76765 | 0.400092 | ||||||||
\(143\) | 5.40979 | 0.452389 | ||||||||
\(144\) | 7.32111 | 0.610092 | ||||||||
\(145\) | 12.2199 | 1.01481 | ||||||||
\(146\) | −11.5717 | −0.957684 | ||||||||
\(147\) | −22.6624 | −1.86916 | ||||||||
\(148\) | −9.58970 | −0.788268 | ||||||||
\(149\) | −12.4778 | −1.02222 | −0.511110 | − | 0.859515i | \(-0.670766\pi\) | ||||
−0.511110 | + | 0.859515i | \(0.670766\pi\) | |||||||
\(150\) | 18.1461 | 1.48162 | ||||||||
\(151\) | 12.8308 | 1.04415 | 0.522076 | − | 0.852899i | \(-0.325158\pi\) | ||||
0.522076 | + | 0.852899i | \(0.325158\pi\) | |||||||
\(152\) | −5.90910 | −0.479292 | ||||||||
\(153\) | 20.4217 | 1.65100 | ||||||||
\(154\) | 10.2994 | 0.829946 | ||||||||
\(155\) | 22.7202 | 1.82493 | ||||||||
\(156\) | −6.32609 | −0.506493 | ||||||||
\(157\) | −6.42567 | −0.512824 | −0.256412 | − | 0.966568i | \(-0.582540\pi\) | ||||
−0.256412 | + | 0.966568i | \(0.582540\pi\) | |||||||
\(158\) | 7.34390 | 0.584249 | ||||||||
\(159\) | −43.9527 | −3.48567 | ||||||||
\(160\) | −3.26318 | −0.257977 | ||||||||
\(161\) | −3.13490 | −0.247064 | ||||||||
\(162\) | −22.6353 | −1.77839 | ||||||||
\(163\) | 4.69912 | 0.368063 | 0.184032 | − | 0.982920i | \(-0.441085\pi\) | ||||
0.184032 | + | 0.982920i | \(0.441085\pi\) | |||||||
\(164\) | 11.2749 | 0.880423 | ||||||||
\(165\) | −28.8013 | −2.24218 | ||||||||
\(166\) | 11.0188 | 0.855223 | ||||||||
\(167\) | −8.48757 | −0.656788 | −0.328394 | − | 0.944541i | \(-0.606507\pi\) | ||||
−0.328394 | + | 0.944541i | \(0.606507\pi\) | |||||||
\(168\) | −12.0438 | −0.929202 | ||||||||
\(169\) | −9.12256 | −0.701736 | ||||||||
\(170\) | −9.10240 | −0.698122 | ||||||||
\(171\) | 43.2612 | 3.30826 | ||||||||
\(172\) | 6.25743 | 0.477124 | ||||||||
\(173\) | −13.6661 | −1.03901 | −0.519505 | − | 0.854467i | \(-0.673884\pi\) | ||||
−0.519505 | + | 0.854467i | \(0.673884\pi\) | |||||||
\(174\) | 12.0307 | 0.912042 | ||||||||
\(175\) | −21.1749 | −1.60067 | ||||||||
\(176\) | 2.74731 | 0.207087 | ||||||||
\(177\) | 11.2792 | 0.847795 | ||||||||
\(178\) | 11.4928 | 0.861419 | ||||||||
\(179\) | 5.71596 | 0.427231 | 0.213616 | − | 0.976918i | \(-0.431476\pi\) | ||||
0.213616 | + | 0.976918i | \(0.431476\pi\) | |||||||
\(180\) | 23.8901 | 1.78066 | ||||||||
\(181\) | −7.17041 | −0.532972 | −0.266486 | − | 0.963839i | \(-0.585863\pi\) | ||||
−0.266486 | + | 0.963839i | \(0.585863\pi\) | |||||||
\(182\) | 7.38200 | 0.547190 | ||||||||
\(183\) | −18.6665 | −1.37987 | ||||||||
\(184\) | −0.836221 | −0.0616471 | ||||||||
\(185\) | −31.2929 | −2.30070 | ||||||||
\(186\) | 22.3684 | 1.64013 | ||||||||
\(187\) | 7.66343 | 0.560406 | ||||||||
\(188\) | −7.60552 | −0.554690 | ||||||||
\(189\) | 52.0427 | 3.78555 | ||||||||
\(190\) | −19.2825 | −1.39890 | ||||||||
\(191\) | −5.12685 | −0.370965 | −0.185483 | − | 0.982648i | \(-0.559385\pi\) | ||||
−0.185483 | + | 0.982648i | \(0.559385\pi\) | |||||||
\(192\) | −3.21265 | −0.231853 | ||||||||
\(193\) | 15.2315 | 1.09639 | 0.548193 | − | 0.836352i | \(-0.315316\pi\) | ||||
0.548193 | + | 0.836352i | \(0.315316\pi\) | |||||||
\(194\) | 9.25349 | 0.664362 | ||||||||
\(195\) | −20.6432 | −1.47829 | ||||||||
\(196\) | 7.05412 | 0.503865 | ||||||||
\(197\) | −24.6358 | −1.75523 | −0.877616 | − | 0.479365i | \(-0.840867\pi\) | ||||
−0.877616 | + | 0.479365i | \(0.840867\pi\) | |||||||
\(198\) | −20.1134 | −1.42940 | ||||||||
\(199\) | −11.8668 | −0.841215 | −0.420608 | − | 0.907243i | \(-0.638183\pi\) | ||||
−0.420608 | + | 0.907243i | \(0.638183\pi\) | |||||||
\(200\) | −5.64833 | −0.399397 | ||||||||
\(201\) | 0.827461 | 0.0583646 | ||||||||
\(202\) | 0.874535 | 0.0615321 | ||||||||
\(203\) | −14.0387 | −0.985326 | ||||||||
\(204\) | −8.96145 | −0.627427 | ||||||||
\(205\) | 36.7921 | 2.56967 | ||||||||
\(206\) | −6.62031 | −0.461259 | ||||||||
\(207\) | 6.12206 | 0.425513 | ||||||||
\(208\) | 1.96912 | 0.136534 | ||||||||
\(209\) | 16.2342 | 1.12294 | ||||||||
\(210\) | −39.3012 | −2.71204 | ||||||||
\(211\) | 15.7996 | 1.08769 | 0.543843 | − | 0.839187i | \(-0.316969\pi\) | ||||
0.543843 | + | 0.839187i | \(0.316969\pi\) | |||||||
\(212\) | 13.6811 | 0.939624 | ||||||||
\(213\) | 15.3168 | 1.04949 | ||||||||
\(214\) | −13.7276 | −0.938401 | ||||||||
\(215\) | 20.4191 | 1.39257 | ||||||||
\(216\) | 13.8822 | 0.944563 | ||||||||
\(217\) | −26.1020 | −1.77192 | ||||||||
\(218\) | 8.01601 | 0.542913 | ||||||||
\(219\) | −37.1759 | −2.51212 | ||||||||
\(220\) | 8.96497 | 0.604418 | ||||||||
\(221\) | 5.49272 | 0.369480 | ||||||||
\(222\) | −30.8083 | −2.06772 | ||||||||
\(223\) | 5.02473 | 0.336481 | 0.168241 | − | 0.985746i | \(-0.446191\pi\) | ||||
0.168241 | + | 0.985746i | \(0.446191\pi\) | |||||||
\(224\) | 3.74888 | 0.250483 | ||||||||
\(225\) | 41.3520 | 2.75680 | ||||||||
\(226\) | −9.74825 | −0.648444 | ||||||||
\(227\) | 13.3338 | 0.884994 | 0.442497 | − | 0.896770i | \(-0.354093\pi\) | ||||
0.442497 | + | 0.896770i | \(0.354093\pi\) | |||||||
\(228\) | −18.9839 | −1.25724 | ||||||||
\(229\) | 28.5085 | 1.88389 | 0.941947 | − | 0.335760i | \(-0.108993\pi\) | ||||
0.941947 | + | 0.335760i | \(0.108993\pi\) | |||||||
\(230\) | −2.72874 | −0.179928 | ||||||||
\(231\) | 33.0882 | 2.17704 | ||||||||
\(232\) | −3.74478 | −0.245857 | ||||||||
\(233\) | 17.7156 | 1.16059 | 0.580294 | − | 0.814407i | \(-0.302938\pi\) | ||||
0.580294 | + | 0.814407i | \(0.302938\pi\) | |||||||
\(234\) | −14.4161 | −0.942413 | ||||||||
\(235\) | −24.8182 | −1.61896 | ||||||||
\(236\) | −3.51087 | −0.228538 | ||||||||
\(237\) | 23.5934 | 1.53255 | ||||||||
\(238\) | 10.4572 | 0.677842 | ||||||||
\(239\) | 18.9752 | 1.22740 | 0.613701 | − | 0.789538i | \(-0.289680\pi\) | ||||
0.613701 | + | 0.789538i | \(0.289680\pi\) | |||||||
\(240\) | −10.4834 | −0.676703 | ||||||||
\(241\) | −16.4613 | −1.06037 | −0.530183 | − | 0.847883i | \(-0.677877\pi\) | ||||
−0.530183 | + | 0.847883i | \(0.677877\pi\) | |||||||
\(242\) | 3.45227 | 0.221920 | ||||||||
\(243\) | −31.0726 | −1.99331 | ||||||||
\(244\) | 5.81031 | 0.371967 | ||||||||
\(245\) | 23.0188 | 1.47062 | ||||||||
\(246\) | 36.2223 | 2.30945 | ||||||||
\(247\) | 11.6357 | 0.740364 | ||||||||
\(248\) | −6.96260 | −0.442125 | ||||||||
\(249\) | 35.3994 | 2.24335 | ||||||||
\(250\) | −2.11561 | −0.133803 | ||||||||
\(251\) | −23.6762 | −1.49443 | −0.747214 | − | 0.664584i | \(-0.768609\pi\) | ||||
−0.747214 | + | 0.664584i | \(0.768609\pi\) | |||||||
\(252\) | −27.4460 | −1.72893 | ||||||||
\(253\) | 2.29736 | 0.144434 | ||||||||
\(254\) | −18.4658 | −1.15865 | ||||||||
\(255\) | −29.2428 | −1.83126 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.8689 | 1.73841 | 0.869207 | − | 0.494449i | \(-0.164630\pi\) | ||||
0.869207 | + | 0.494449i | \(0.164630\pi\) | |||||||
\(258\) | 20.1029 | 1.25155 | ||||||||
\(259\) | 35.9507 | 2.23386 | ||||||||
\(260\) | 6.42559 | 0.398498 | ||||||||
\(261\) | 27.4159 | 1.69700 | ||||||||
\(262\) | 15.5116 | 0.958309 | ||||||||
\(263\) | −16.3752 | −1.00974 | −0.504868 | − | 0.863196i | \(-0.668459\pi\) | ||||
−0.504868 | + | 0.863196i | \(0.668459\pi\) | |||||||
\(264\) | 8.82615 | 0.543212 | ||||||||
\(265\) | 44.6440 | 2.74246 | ||||||||
\(266\) | 22.1525 | 1.35826 | ||||||||
\(267\) | 36.9222 | 2.25960 | ||||||||
\(268\) | −0.257564 | −0.0157332 | ||||||||
\(269\) | 12.7426 | 0.776931 | 0.388465 | − | 0.921463i | \(-0.373005\pi\) | ||||
0.388465 | + | 0.921463i | \(0.373005\pi\) | |||||||
\(270\) | 45.3001 | 2.75687 | ||||||||
\(271\) | 20.2797 | 1.23190 | 0.615951 | − | 0.787784i | \(-0.288772\pi\) | ||||
0.615951 | + | 0.787784i | \(0.288772\pi\) | |||||||
\(272\) | 2.78943 | 0.169134 | ||||||||
\(273\) | 23.7158 | 1.43534 | ||||||||
\(274\) | 18.8452 | 1.13848 | ||||||||
\(275\) | 15.5177 | 0.935754 | ||||||||
\(276\) | −2.68648 | −0.161707 | ||||||||
\(277\) | −5.78606 | −0.347651 | −0.173825 | − | 0.984776i | \(-0.555613\pi\) | ||||
−0.173825 | + | 0.984776i | \(0.555613\pi\) | |||||||
\(278\) | −0.0766866 | −0.00459936 | ||||||||
\(279\) | 50.9739 | 3.05173 | ||||||||
\(280\) | 12.2333 | 0.731078 | ||||||||
\(281\) | 16.5039 | 0.984540 | 0.492270 | − | 0.870443i | \(-0.336167\pi\) | ||||
0.492270 | + | 0.870443i | \(0.336167\pi\) | |||||||
\(282\) | −24.4339 | −1.45502 | ||||||||
\(283\) | −1.55336 | −0.0923378 | −0.0461689 | − | 0.998934i | \(-0.514701\pi\) | ||||
−0.0461689 | + | 0.998934i | \(0.514701\pi\) | |||||||
\(284\) | −4.76765 | −0.282908 | ||||||||
\(285\) | −61.9477 | −3.66947 | ||||||||
\(286\) | −5.40979 | −0.319888 | ||||||||
\(287\) | −42.2683 | −2.49502 | ||||||||
\(288\) | −7.32111 | −0.431400 | ||||||||
\(289\) | −9.21909 | −0.542300 | ||||||||
\(290\) | −12.2199 | −0.717576 | ||||||||
\(291\) | 29.7282 | 1.74270 | ||||||||
\(292\) | 11.5717 | 0.677185 | ||||||||
\(293\) | 26.8358 | 1.56776 | 0.783881 | − | 0.620911i | \(-0.213237\pi\) | ||||
0.783881 | + | 0.620911i | \(0.213237\pi\) | |||||||
\(294\) | 22.6624 | 1.32170 | ||||||||
\(295\) | −11.4566 | −0.667028 | ||||||||
\(296\) | 9.58970 | 0.557390 | ||||||||
\(297\) | −38.1387 | −2.21303 | ||||||||
\(298\) | 12.4778 | 0.722819 | ||||||||
\(299\) | 1.64662 | 0.0952265 | ||||||||
\(300\) | −18.1461 | −1.04766 | ||||||||
\(301\) | −23.4584 | −1.35212 | ||||||||
\(302\) | −12.8308 | −0.738327 | ||||||||
\(303\) | 2.80957 | 0.161406 | ||||||||
\(304\) | 5.90910 | 0.338910 | ||||||||
\(305\) | 18.9601 | 1.08565 | ||||||||
\(306\) | −20.4217 | −1.16743 | ||||||||
\(307\) | −6.60978 | −0.377240 | −0.188620 | − | 0.982050i | \(-0.560401\pi\) | ||||
−0.188620 | + | 0.982050i | \(0.560401\pi\) | |||||||
\(308\) | −10.2994 | −0.586860 | ||||||||
\(309\) | −21.2687 | −1.20994 | ||||||||
\(310\) | −22.7202 | −1.29042 | ||||||||
\(311\) | 9.25864 | 0.525009 | 0.262505 | − | 0.964931i | \(-0.415451\pi\) | ||||
0.262505 | + | 0.964931i | \(0.415451\pi\) | |||||||
\(312\) | 6.32609 | 0.358144 | ||||||||
\(313\) | 23.6357 | 1.33597 | 0.667983 | − | 0.744176i | \(-0.267158\pi\) | ||||
0.667983 | + | 0.744176i | \(0.267158\pi\) | |||||||
\(314\) | 6.42567 | 0.362621 | ||||||||
\(315\) | −89.5610 | −5.04619 | ||||||||
\(316\) | −7.34390 | −0.413127 | ||||||||
\(317\) | 26.1017 | 1.46602 | 0.733010 | − | 0.680218i | \(-0.238115\pi\) | ||||
0.733010 | + | 0.680218i | \(0.238115\pi\) | |||||||
\(318\) | 43.9527 | 2.46474 | ||||||||
\(319\) | 10.2881 | 0.576022 | ||||||||
\(320\) | 3.26318 | 0.182417 | ||||||||
\(321\) | −44.1020 | −2.46153 | ||||||||
\(322\) | 3.13490 | 0.174701 | ||||||||
\(323\) | 16.4830 | 0.917140 | ||||||||
\(324\) | 22.6353 | 1.25752 | ||||||||
\(325\) | 11.1222 | 0.616951 | ||||||||
\(326\) | −4.69912 | −0.260260 | ||||||||
\(327\) | 25.7526 | 1.42412 | ||||||||
\(328\) | −11.2749 | −0.622553 | ||||||||
\(329\) | 28.5122 | 1.57193 | ||||||||
\(330\) | 28.8013 | 1.58546 | ||||||||
\(331\) | −29.3754 | −1.61462 | −0.807309 | − | 0.590129i | \(-0.799077\pi\) | ||||
−0.807309 | + | 0.590129i | \(0.799077\pi\) | |||||||
\(332\) | −11.0188 | −0.604734 | ||||||||
\(333\) | −70.2072 | −3.84733 | ||||||||
\(334\) | 8.48757 | 0.464419 | ||||||||
\(335\) | −0.840476 | −0.0459201 | ||||||||
\(336\) | 12.0438 | 0.657045 | ||||||||
\(337\) | −25.5751 | −1.39316 | −0.696582 | − | 0.717477i | \(-0.745297\pi\) | ||||
−0.696582 | + | 0.717477i | \(0.745297\pi\) | |||||||
\(338\) | 9.12256 | 0.496202 | ||||||||
\(339\) | −31.3177 | −1.70094 | ||||||||
\(340\) | 9.10240 | 0.493647 | ||||||||
\(341\) | 19.1284 | 1.03586 | ||||||||
\(342\) | −43.2612 | −2.33930 | ||||||||
\(343\) | −0.202877 | −0.0109544 | ||||||||
\(344\) | −6.25743 | −0.337378 | ||||||||
\(345\) | −8.76648 | −0.471971 | ||||||||
\(346\) | 13.6661 | 0.734692 | ||||||||
\(347\) | 14.6545 | 0.786695 | 0.393347 | − | 0.919390i | \(-0.371317\pi\) | ||||
0.393347 | + | 0.919390i | \(0.371317\pi\) | |||||||
\(348\) | −12.0307 | −0.644911 | ||||||||
\(349\) | −12.8791 | −0.689402 | −0.344701 | − | 0.938713i | \(-0.612020\pi\) | ||||
−0.344701 | + | 0.938713i | \(0.612020\pi\) | |||||||
\(350\) | 21.1749 | 1.13185 | ||||||||
\(351\) | −27.3357 | −1.45907 | ||||||||
\(352\) | −2.74731 | −0.146432 | ||||||||
\(353\) | −0.410032 | −0.0218238 | −0.0109119 | − | 0.999940i | \(-0.503473\pi\) | ||||
−0.0109119 | + | 0.999940i | \(0.503473\pi\) | |||||||
\(354\) | −11.2792 | −0.599482 | ||||||||
\(355\) | −15.5577 | −0.825715 | ||||||||
\(356\) | −11.4928 | −0.609116 | ||||||||
\(357\) | 33.5954 | 1.77806 | ||||||||
\(358\) | −5.71596 | −0.302098 | ||||||||
\(359\) | 15.6921 | 0.828195 | 0.414097 | − | 0.910233i | \(-0.364097\pi\) | ||||
0.414097 | + | 0.910233i | \(0.364097\pi\) | |||||||
\(360\) | −23.8901 | −1.25912 | ||||||||
\(361\) | 15.9175 | 0.837763 | ||||||||
\(362\) | 7.17041 | 0.376868 | ||||||||
\(363\) | 11.0909 | 0.582122 | ||||||||
\(364\) | −7.38200 | −0.386922 | ||||||||
\(365\) | 37.7606 | 1.97648 | ||||||||
\(366\) | 18.6665 | 0.975712 | ||||||||
\(367\) | 29.7225 | 1.55150 | 0.775750 | − | 0.631040i | \(-0.217372\pi\) | ||||
0.775750 | + | 0.631040i | \(0.217372\pi\) | |||||||
\(368\) | 0.836221 | 0.0435911 | ||||||||
\(369\) | 82.5449 | 4.29711 | ||||||||
\(370\) | 31.2929 | 1.62684 | ||||||||
\(371\) | −51.2890 | −2.66279 | ||||||||
\(372\) | −22.3684 | −1.15975 | ||||||||
\(373\) | −0.737493 | −0.0381859 | −0.0190930 | − | 0.999818i | \(-0.506078\pi\) | ||||
−0.0190930 | + | 0.999818i | \(0.506078\pi\) | |||||||
\(374\) | −7.66343 | −0.396267 | ||||||||
\(375\) | −6.79670 | −0.350980 | ||||||||
\(376\) | 7.60552 | 0.392225 | ||||||||
\(377\) | 7.37392 | 0.379776 | ||||||||
\(378\) | −52.0427 | −2.67679 | ||||||||
\(379\) | 17.5835 | 0.903203 | 0.451602 | − | 0.892220i | \(-0.350853\pi\) | ||||
0.451602 | + | 0.892220i | \(0.350853\pi\) | |||||||
\(380\) | 19.2825 | 0.989169 | ||||||||
\(381\) | −59.3242 | −3.03927 | ||||||||
\(382\) | 5.12685 | 0.262312 | ||||||||
\(383\) | 13.0037 | 0.664456 | 0.332228 | − | 0.943199i | \(-0.392200\pi\) | ||||
0.332228 | + | 0.943199i | \(0.392200\pi\) | |||||||
\(384\) | 3.21265 | 0.163945 | ||||||||
\(385\) | −33.6086 | −1.71285 | ||||||||
\(386\) | −15.2315 | −0.775262 | ||||||||
\(387\) | 45.8113 | 2.32872 | ||||||||
\(388\) | −9.25349 | −0.469775 | ||||||||
\(389\) | −13.8361 | −0.701521 | −0.350760 | − | 0.936465i | \(-0.614077\pi\) | ||||
−0.350760 | + | 0.936465i | \(0.614077\pi\) | |||||||
\(390\) | 20.6432 | 1.04531 | ||||||||
\(391\) | 2.33258 | 0.117964 | ||||||||
\(392\) | −7.05412 | −0.356287 | ||||||||
\(393\) | 49.8332 | 2.51375 | ||||||||
\(394\) | 24.6358 | 1.24114 | ||||||||
\(395\) | −23.9645 | −1.20578 | ||||||||
\(396\) | 20.1134 | 1.01074 | ||||||||
\(397\) | 29.0131 | 1.45613 | 0.728064 | − | 0.685509i | \(-0.240420\pi\) | ||||
0.728064 | + | 0.685509i | \(0.240420\pi\) | |||||||
\(398\) | 11.8668 | 0.594829 | ||||||||
\(399\) | 71.1683 | 3.56287 | ||||||||
\(400\) | 5.64833 | 0.282416 | ||||||||
\(401\) | 35.9816 | 1.79684 | 0.898419 | − | 0.439140i | \(-0.144717\pi\) | ||||
0.898419 | + | 0.439140i | \(0.144717\pi\) | |||||||
\(402\) | −0.827461 | −0.0412700 | ||||||||
\(403\) | 13.7102 | 0.682953 | ||||||||
\(404\) | −0.874535 | −0.0435097 | ||||||||
\(405\) | 73.8629 | 3.67028 | ||||||||
\(406\) | 14.0387 | 0.696731 | ||||||||
\(407\) | −26.3459 | −1.30592 | ||||||||
\(408\) | 8.96145 | 0.443658 | ||||||||
\(409\) | −22.3444 | −1.10486 | −0.552429 | − | 0.833560i | \(-0.686299\pi\) | ||||
−0.552429 | + | 0.833560i | \(0.686299\pi\) | |||||||
\(410\) | −36.7921 | −1.81703 | ||||||||
\(411\) | 60.5428 | 2.98636 | ||||||||
\(412\) | 6.62031 | 0.326159 | ||||||||
\(413\) | 13.1618 | 0.647651 | ||||||||
\(414\) | −6.12206 | −0.300883 | ||||||||
\(415\) | −35.9562 | −1.76502 | ||||||||
\(416\) | −1.96912 | −0.0965441 | ||||||||
\(417\) | −0.246367 | −0.0120647 | ||||||||
\(418\) | −16.2342 | −0.794039 | ||||||||
\(419\) | −33.6052 | −1.64172 | −0.820860 | − | 0.571130i | \(-0.806505\pi\) | ||||
−0.820860 | + | 0.571130i | \(0.806505\pi\) | |||||||
\(420\) | 39.3012 | 1.91770 | ||||||||
\(421\) | −15.3383 | −0.747543 | −0.373772 | − | 0.927521i | \(-0.621936\pi\) | ||||
−0.373772 | + | 0.927521i | \(0.621936\pi\) | |||||||
\(422\) | −15.7996 | −0.769111 | ||||||||
\(423\) | −55.6808 | −2.70729 | ||||||||
\(424\) | −13.6811 | −0.664415 | ||||||||
\(425\) | 15.7556 | 0.764259 | ||||||||
\(426\) | −15.3168 | −0.742100 | ||||||||
\(427\) | −21.7822 | −1.05411 | ||||||||
\(428\) | 13.7276 | 0.663550 | ||||||||
\(429\) | −17.3798 | −0.839102 | ||||||||
\(430\) | −20.4191 | −0.984696 | ||||||||
\(431\) | 6.03095 | 0.290500 | 0.145250 | − | 0.989395i | \(-0.453601\pi\) | ||||
0.145250 | + | 0.989395i | \(0.453601\pi\) | |||||||
\(432\) | −13.8822 | −0.667907 | ||||||||
\(433\) | −16.2591 | −0.781361 | −0.390680 | − | 0.920526i | \(-0.627760\pi\) | ||||
−0.390680 | + | 0.920526i | \(0.627760\pi\) | |||||||
\(434\) | 26.1020 | 1.25293 | ||||||||
\(435\) | −39.2582 | −1.88229 | ||||||||
\(436\) | −8.01601 | −0.383897 | ||||||||
\(437\) | 4.94132 | 0.236375 | ||||||||
\(438\) | 37.1759 | 1.77633 | ||||||||
\(439\) | −1.63102 | −0.0778444 | −0.0389222 | − | 0.999242i | \(-0.512392\pi\) | ||||
−0.0389222 | + | 0.999242i | \(0.512392\pi\) | |||||||
\(440\) | −8.96497 | −0.427388 | ||||||||
\(441\) | 51.6439 | 2.45924 | ||||||||
\(442\) | −5.49272 | −0.261262 | ||||||||
\(443\) | −24.4638 | −1.16231 | −0.581154 | − | 0.813794i | \(-0.697399\pi\) | ||||
−0.581154 | + | 0.813794i | \(0.697399\pi\) | |||||||
\(444\) | 30.8083 | 1.46210 | ||||||||
\(445\) | −37.5029 | −1.77781 | ||||||||
\(446\) | −5.02473 | −0.237928 | ||||||||
\(447\) | 40.0868 | 1.89604 | ||||||||
\(448\) | −3.74888 | −0.177118 | ||||||||
\(449\) | 16.6981 | 0.788033 | 0.394016 | − | 0.919103i | \(-0.371085\pi\) | ||||
0.394016 | + | 0.919103i | \(0.371085\pi\) | |||||||
\(450\) | −41.3520 | −1.94935 | ||||||||
\(451\) | 30.9757 | 1.45859 | ||||||||
\(452\) | 9.74825 | 0.458519 | ||||||||
\(453\) | −41.2207 | −1.93672 | ||||||||
\(454\) | −13.3338 | −0.625785 | ||||||||
\(455\) | −24.0888 | −1.12930 | ||||||||
\(456\) | 18.9839 | 0.889001 | ||||||||
\(457\) | −16.7108 | −0.781699 | −0.390849 | − | 0.920455i | \(-0.627819\pi\) | ||||
−0.390849 | + | 0.920455i | \(0.627819\pi\) | |||||||
\(458\) | −28.5085 | −1.33211 | ||||||||
\(459\) | −38.7234 | −1.80745 | ||||||||
\(460\) | 2.72874 | 0.127228 | ||||||||
\(461\) | −11.0991 | −0.516937 | −0.258469 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258469 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(462\) | −33.0882 | −1.53940 | ||||||||
\(463\) | 27.1051 | 1.25968 | 0.629840 | − | 0.776725i | \(-0.283120\pi\) | ||||
0.629840 | + | 0.776725i | \(0.283120\pi\) | |||||||
\(464\) | 3.74478 | 0.173847 | ||||||||
\(465\) | −72.9920 | −3.38492 | ||||||||
\(466\) | −17.7156 | −0.820660 | ||||||||
\(467\) | 30.8905 | 1.42944 | 0.714722 | − | 0.699409i | \(-0.246553\pi\) | ||||
0.714722 | + | 0.699409i | \(0.246553\pi\) | |||||||
\(468\) | 14.4161 | 0.666386 | ||||||||
\(469\) | 0.965576 | 0.0445862 | ||||||||
\(470\) | 24.8182 | 1.14478 | ||||||||
\(471\) | 20.6434 | 0.951198 | ||||||||
\(472\) | 3.51087 | 0.161601 | ||||||||
\(473\) | 17.1911 | 0.790448 | ||||||||
\(474\) | −23.5934 | −1.08368 | ||||||||
\(475\) | 33.3765 | 1.53142 | ||||||||
\(476\) | −10.4572 | −0.479307 | ||||||||
\(477\) | 100.161 | 4.58606 | ||||||||
\(478\) | −18.9752 | −0.867905 | ||||||||
\(479\) | 0.270250 | 0.0123480 | 0.00617401 | − | 0.999981i | \(-0.498035\pi\) | ||||
0.00617401 | + | 0.999981i | \(0.498035\pi\) | |||||||
\(480\) | 10.4834 | 0.478501 | ||||||||
\(481\) | −18.8833 | −0.861003 | ||||||||
\(482\) | 16.4613 | 0.749792 | ||||||||
\(483\) | 10.0713 | 0.458261 | ||||||||
\(484\) | −3.45227 | −0.156921 | ||||||||
\(485\) | −30.1958 | −1.37112 | ||||||||
\(486\) | 31.0726 | 1.40948 | ||||||||
\(487\) | 32.3472 | 1.46579 | 0.732895 | − | 0.680342i | \(-0.238169\pi\) | ||||
0.732895 | + | 0.680342i | \(0.238169\pi\) | |||||||
\(488\) | −5.81031 | −0.263020 | ||||||||
\(489\) | −15.0966 | −0.682692 | ||||||||
\(490\) | −23.0188 | −1.03988 | ||||||||
\(491\) | 2.07595 | 0.0936863 | 0.0468432 | − | 0.998902i | \(-0.485084\pi\) | ||||
0.0468432 | + | 0.998902i | \(0.485084\pi\) | |||||||
\(492\) | −36.2223 | −1.63303 | ||||||||
\(493\) | 10.4458 | 0.470455 | ||||||||
\(494\) | −11.6357 | −0.523517 | ||||||||
\(495\) | 65.6335 | 2.95001 | ||||||||
\(496\) | 6.96260 | 0.312630 | ||||||||
\(497\) | 17.8733 | 0.801729 | ||||||||
\(498\) | −35.3994 | −1.58629 | ||||||||
\(499\) | 10.1670 | 0.455139 | 0.227570 | − | 0.973762i | \(-0.426922\pi\) | ||||
0.227570 | + | 0.973762i | \(0.426922\pi\) | |||||||
\(500\) | 2.11561 | 0.0946128 | ||||||||
\(501\) | 27.2676 | 1.21823 | ||||||||
\(502\) | 23.6762 | 1.05672 | ||||||||
\(503\) | −13.3630 | −0.595827 | −0.297914 | − | 0.954593i | \(-0.596291\pi\) | ||||
−0.297914 | + | 0.954593i | \(0.596291\pi\) | |||||||
\(504\) | 27.4460 | 1.22254 | ||||||||
\(505\) | −2.85376 | −0.126991 | ||||||||
\(506\) | −2.29736 | −0.102130 | ||||||||
\(507\) | 29.3076 | 1.30160 | ||||||||
\(508\) | 18.4658 | 0.819288 | ||||||||
\(509\) | 4.72767 | 0.209550 | 0.104775 | − | 0.994496i | \(-0.466588\pi\) | ||||
0.104775 | + | 0.994496i | \(0.466588\pi\) | |||||||
\(510\) | 29.2428 | 1.29489 | ||||||||
\(511\) | −43.3811 | −1.91907 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −82.0313 | −3.62177 | ||||||||
\(514\) | −27.8689 | −1.22924 | ||||||||
\(515\) | 21.6032 | 0.951953 | ||||||||
\(516\) | −20.1029 | −0.884981 | ||||||||
\(517\) | −20.8948 | −0.918950 | ||||||||
\(518\) | −35.9507 | −1.57958 | ||||||||
\(519\) | 43.9042 | 1.92718 | ||||||||
\(520\) | −6.42559 | −0.281781 | ||||||||
\(521\) | −26.9765 | −1.18186 | −0.590931 | − | 0.806722i | \(-0.701240\pi\) | ||||
−0.590931 | + | 0.806722i | \(0.701240\pi\) | |||||||
\(522\) | −27.4159 | −1.19996 | ||||||||
\(523\) | −0.542034 | −0.0237015 | −0.0118507 | − | 0.999930i | \(-0.503772\pi\) | ||||
−0.0118507 | + | 0.999930i | \(0.503772\pi\) | |||||||
\(524\) | −15.5116 | −0.677627 | ||||||||
\(525\) | 68.0275 | 2.96896 | ||||||||
\(526\) | 16.3752 | 0.713992 | ||||||||
\(527\) | 19.4217 | 0.846021 | ||||||||
\(528\) | −8.82615 | −0.384109 | ||||||||
\(529\) | −22.3007 | −0.969597 | ||||||||
\(530\) | −44.6440 | −1.93921 | ||||||||
\(531\) | −25.7034 | −1.11543 | ||||||||
\(532\) | −22.1525 | −0.960434 | ||||||||
\(533\) | 22.2017 | 0.961661 | ||||||||
\(534\) | −36.9222 | −1.59778 | ||||||||
\(535\) | 44.7957 | 1.93669 | ||||||||
\(536\) | 0.257564 | 0.0111251 | ||||||||
\(537\) | −18.3634 | −0.792438 | ||||||||
\(538\) | −12.7426 | −0.549373 | ||||||||
\(539\) | 19.3799 | 0.834750 | ||||||||
\(540\) | −45.3001 | −1.94940 | ||||||||
\(541\) | 21.2539 | 0.913776 | 0.456888 | − | 0.889524i | \(-0.348964\pi\) | ||||
0.456888 | + | 0.889524i | \(0.348964\pi\) | |||||||
\(542\) | −20.2797 | −0.871087 | ||||||||
\(543\) | 23.0360 | 0.988570 | ||||||||
\(544\) | −2.78943 | −0.119596 | ||||||||
\(545\) | −26.1577 | −1.12047 | ||||||||
\(546\) | −23.7158 | −1.01494 | ||||||||
\(547\) | −22.9263 | −0.980256 | −0.490128 | − | 0.871650i | \(-0.663050\pi\) | ||||
−0.490128 | + | 0.871650i | \(0.663050\pi\) | |||||||
\(548\) | −18.8452 | −0.805025 | ||||||||
\(549\) | 42.5379 | 1.81547 | ||||||||
\(550\) | −15.5177 | −0.661678 | ||||||||
\(551\) | 22.1283 | 0.942697 | ||||||||
\(552\) | 2.68648 | 0.114344 | ||||||||
\(553\) | 27.5314 | 1.17076 | ||||||||
\(554\) | 5.78606 | 0.245826 | ||||||||
\(555\) | 100.533 | 4.26739 | ||||||||
\(556\) | 0.0766866 | 0.00325224 | ||||||||
\(557\) | 16.9861 | 0.719724 | 0.359862 | − | 0.933006i | \(-0.382824\pi\) | ||||
0.359862 | + | 0.933006i | \(0.382824\pi\) | |||||||
\(558\) | −50.9739 | −2.15790 | ||||||||
\(559\) | 12.3216 | 0.521149 | ||||||||
\(560\) | −12.2333 | −0.516950 | ||||||||
\(561\) | −24.6199 | −1.03945 | ||||||||
\(562\) | −16.5039 | −0.696175 | ||||||||
\(563\) | −32.0473 | −1.35063 | −0.675316 | − | 0.737529i | \(-0.735993\pi\) | ||||
−0.675316 | + | 0.737529i | \(0.735993\pi\) | |||||||
\(564\) | 24.4339 | 1.02885 | ||||||||
\(565\) | 31.8103 | 1.33827 | ||||||||
\(566\) | 1.55336 | 0.0652926 | ||||||||
\(567\) | −84.8570 | −3.56366 | ||||||||
\(568\) | 4.76765 | 0.200046 | ||||||||
\(569\) | 5.74945 | 0.241030 | 0.120515 | − | 0.992712i | \(-0.461545\pi\) | ||||
0.120515 | + | 0.992712i | \(0.461545\pi\) | |||||||
\(570\) | 61.9477 | 2.59470 | ||||||||
\(571\) | −15.9260 | −0.666482 | −0.333241 | − | 0.942842i | \(-0.608142\pi\) | ||||
−0.333241 | + | 0.942842i | \(0.608142\pi\) | |||||||
\(572\) | 5.40979 | 0.226195 | ||||||||
\(573\) | 16.4707 | 0.688075 | ||||||||
\(574\) | 42.2683 | 1.76425 | ||||||||
\(575\) | 4.72325 | 0.196973 | ||||||||
\(576\) | 7.32111 | 0.305046 | ||||||||
\(577\) | −5.43332 | −0.226192 | −0.113096 | − | 0.993584i | \(-0.536077\pi\) | ||||
−0.113096 | + | 0.993584i | \(0.536077\pi\) | |||||||
\(578\) | 9.21909 | 0.383464 | ||||||||
\(579\) | −48.9334 | −2.03360 | ||||||||
\(580\) | 12.2199 | 0.507403 | ||||||||
\(581\) | 41.3081 | 1.71375 | ||||||||
\(582\) | −29.7282 | −1.23227 | ||||||||
\(583\) | 37.5864 | 1.55667 | ||||||||
\(584\) | −11.5717 | −0.478842 | ||||||||
\(585\) | 47.0424 | 1.94496 | ||||||||
\(586\) | −26.8358 | −1.10858 | ||||||||
\(587\) | 21.7465 | 0.897572 | 0.448786 | − | 0.893639i | \(-0.351856\pi\) | ||||
0.448786 | + | 0.893639i | \(0.351856\pi\) | |||||||
\(588\) | −22.6624 | −0.934581 | ||||||||
\(589\) | 41.1427 | 1.69526 | ||||||||
\(590\) | 11.4566 | 0.471660 | ||||||||
\(591\) | 79.1463 | 3.25564 | ||||||||
\(592\) | −9.58970 | −0.394134 | ||||||||
\(593\) | −20.1947 | −0.829298 | −0.414649 | − | 0.909981i | \(-0.636096\pi\) | ||||
−0.414649 | + | 0.909981i | \(0.636096\pi\) | |||||||
\(594\) | 38.1387 | 1.56485 | ||||||||
\(595\) | −34.1238 | −1.39894 | ||||||||
\(596\) | −12.4778 | −0.511110 | ||||||||
\(597\) | 38.1239 | 1.56031 | ||||||||
\(598\) | −1.64662 | −0.0673353 | ||||||||
\(599\) | 29.3853 | 1.20065 | 0.600326 | − | 0.799756i | \(-0.295038\pi\) | ||||
0.600326 | + | 0.799756i | \(0.295038\pi\) | |||||||
\(600\) | 18.1461 | 0.740811 | ||||||||
\(601\) | −16.5934 | −0.676860 | −0.338430 | − | 0.940992i | \(-0.609896\pi\) | ||||
−0.338430 | + | 0.940992i | \(0.609896\pi\) | |||||||
\(602\) | 23.4584 | 0.956091 | ||||||||
\(603\) | −1.88565 | −0.0767896 | ||||||||
\(604\) | 12.8308 | 0.522076 | ||||||||
\(605\) | −11.2654 | −0.458002 | ||||||||
\(606\) | −2.80957 | −0.114131 | ||||||||
\(607\) | −32.9796 | −1.33860 | −0.669300 | − | 0.742992i | \(-0.733406\pi\) | ||||
−0.669300 | + | 0.742992i | \(0.733406\pi\) | |||||||
\(608\) | −5.90910 | −0.239646 | ||||||||
\(609\) | 45.1015 | 1.82761 | ||||||||
\(610\) | −18.9601 | −0.767671 | ||||||||
\(611\) | −14.9762 | −0.605872 | ||||||||
\(612\) | 20.4217 | 0.825498 | ||||||||
\(613\) | −8.22018 | −0.332010 | −0.166005 | − | 0.986125i | \(-0.553087\pi\) | ||||
−0.166005 | + | 0.986125i | \(0.553087\pi\) | |||||||
\(614\) | 6.60978 | 0.266749 | ||||||||
\(615\) | −118.200 | −4.76628 | ||||||||
\(616\) | 10.2994 | 0.414973 | ||||||||
\(617\) | −19.8560 | −0.799371 | −0.399686 | − | 0.916652i | \(-0.630881\pi\) | ||||
−0.399686 | + | 0.916652i | \(0.630881\pi\) | |||||||
\(618\) | 21.2687 | 0.855553 | ||||||||
\(619\) | −32.0121 | −1.28668 | −0.643338 | − | 0.765582i | \(-0.722451\pi\) | ||||
−0.643338 | + | 0.765582i | \(0.722451\pi\) | |||||||
\(620\) | 22.7202 | 0.912465 | ||||||||
\(621\) | −11.6086 | −0.465836 | ||||||||
\(622\) | −9.25864 | −0.371238 | ||||||||
\(623\) | 43.0850 | 1.72617 | ||||||||
\(624\) | −6.32609 | −0.253246 | ||||||||
\(625\) | −21.3380 | −0.853522 | ||||||||
\(626\) | −23.6357 | −0.944671 | ||||||||
\(627\) | −52.1546 | −2.08286 | ||||||||
\(628\) | −6.42567 | −0.256412 | ||||||||
\(629\) | −26.7498 | −1.06658 | ||||||||
\(630\) | 89.5610 | 3.56820 | ||||||||
\(631\) | −16.4771 | −0.655942 | −0.327971 | − | 0.944688i | \(-0.606365\pi\) | ||||
−0.327971 | + | 0.944688i | \(0.606365\pi\) | |||||||
\(632\) | 7.34390 | 0.292125 | ||||||||
\(633\) | −50.7584 | −2.01747 | ||||||||
\(634\) | −26.1017 | −1.03663 | ||||||||
\(635\) | 60.2572 | 2.39124 | ||||||||
\(636\) | −43.9527 | −1.74284 | ||||||||
\(637\) | 13.8904 | 0.550358 | ||||||||
\(638\) | −10.2881 | −0.407309 | ||||||||
\(639\) | −34.9044 | −1.38080 | ||||||||
\(640\) | −3.26318 | −0.128988 | ||||||||
\(641\) | −4.88036 | −0.192762 | −0.0963812 | − | 0.995344i | \(-0.530727\pi\) | ||||
−0.0963812 | + | 0.995344i | \(0.530727\pi\) | |||||||
\(642\) | 44.1020 | 1.74057 | ||||||||
\(643\) | −2.80335 | −0.110553 | −0.0552766 | − | 0.998471i | \(-0.517604\pi\) | ||||
−0.0552766 | + | 0.998471i | \(0.517604\pi\) | |||||||
\(644\) | −3.13490 | −0.123532 | ||||||||
\(645\) | −65.5994 | −2.58297 | ||||||||
\(646\) | −16.4830 | −0.648516 | ||||||||
\(647\) | −34.3332 | −1.34978 | −0.674888 | − | 0.737920i | \(-0.735808\pi\) | ||||
−0.674888 | + | 0.737920i | \(0.735808\pi\) | |||||||
\(648\) | −22.6353 | −0.889197 | ||||||||
\(649\) | −9.64545 | −0.378617 | ||||||||
\(650\) | −11.1222 | −0.436250 | ||||||||
\(651\) | 83.8564 | 3.28659 | ||||||||
\(652\) | 4.69912 | 0.184032 | ||||||||
\(653\) | 39.6810 | 1.55284 | 0.776418 | − | 0.630218i | \(-0.217035\pi\) | ||||
0.776418 | + | 0.630218i | \(0.217035\pi\) | |||||||
\(654\) | −25.7526 | −1.00701 | ||||||||
\(655\) | −50.6170 | −1.97777 | ||||||||
\(656\) | 11.2749 | 0.440212 | ||||||||
\(657\) | 84.7179 | 3.30516 | ||||||||
\(658\) | −28.5122 | −1.11152 | ||||||||
\(659\) | −23.2122 | −0.904218 | −0.452109 | − | 0.891963i | \(-0.649328\pi\) | ||||
−0.452109 | + | 0.891963i | \(0.649328\pi\) | |||||||
\(660\) | −28.8013 | −1.12109 | ||||||||
\(661\) | 21.6905 | 0.843664 | 0.421832 | − | 0.906674i | \(-0.361387\pi\) | ||||
0.421832 | + | 0.906674i | \(0.361387\pi\) | |||||||
\(662\) | 29.3754 | 1.14171 | ||||||||
\(663\) | −17.6462 | −0.685321 | ||||||||
\(664\) | 11.0188 | 0.427611 | ||||||||
\(665\) | −72.2876 | −2.80319 | ||||||||
\(666\) | 70.2072 | 2.72047 | ||||||||
\(667\) | 3.13146 | 0.121251 | ||||||||
\(668\) | −8.48757 | −0.328394 | ||||||||
\(669\) | −16.1427 | −0.624113 | ||||||||
\(670\) | 0.840476 | 0.0324704 | ||||||||
\(671\) | 15.9627 | 0.616235 | ||||||||
\(672\) | −12.0438 | −0.464601 | ||||||||
\(673\) | −28.9665 | −1.11658 | −0.558288 | − | 0.829648i | \(-0.688541\pi\) | ||||
−0.558288 | + | 0.829648i | \(0.688541\pi\) | |||||||
\(674\) | 25.5751 | 0.985116 | ||||||||
\(675\) | −78.4112 | −3.01805 | ||||||||
\(676\) | −9.12256 | −0.350868 | ||||||||
\(677\) | 26.2490 | 1.00883 | 0.504416 | − | 0.863461i | \(-0.331708\pi\) | ||||
0.504416 | + | 0.863461i | \(0.331708\pi\) | |||||||
\(678\) | 31.3177 | 1.20275 | ||||||||
\(679\) | 34.6902 | 1.33129 | ||||||||
\(680\) | −9.10240 | −0.349061 | ||||||||
\(681\) | −42.8367 | −1.64151 | ||||||||
\(682\) | −19.1284 | −0.732466 | ||||||||
\(683\) | 31.6103 | 1.20953 | 0.604766 | − | 0.796403i | \(-0.293266\pi\) | ||||
0.604766 | + | 0.796403i | \(0.293266\pi\) | |||||||
\(684\) | 43.2612 | 1.65413 | ||||||||
\(685\) | −61.4951 | −2.34961 | ||||||||
\(686\) | 0.202877 | 0.00774590 | ||||||||
\(687\) | −91.5878 | −3.49429 | ||||||||
\(688\) | 6.25743 | 0.238562 | ||||||||
\(689\) | 26.9398 | 1.02633 | ||||||||
\(690\) | 8.76648 | 0.333734 | ||||||||
\(691\) | −30.5337 | −1.16156 | −0.580778 | − | 0.814062i | \(-0.697252\pi\) | ||||
−0.580778 | + | 0.814062i | \(0.697252\pi\) | |||||||
\(692\) | −13.6661 | −0.519505 | ||||||||
\(693\) | −75.4027 | −2.86431 | ||||||||
\(694\) | −14.6545 | −0.556277 | ||||||||
\(695\) | 0.250242 | 0.00949222 | ||||||||
\(696\) | 12.0307 | 0.456021 | ||||||||
\(697\) | 31.4506 | 1.19128 | ||||||||
\(698\) | 12.8791 | 0.487481 | ||||||||
\(699\) | −56.9140 | −2.15269 | ||||||||
\(700\) | −21.1749 | −0.800336 | ||||||||
\(701\) | 22.9239 | 0.865823 | 0.432912 | − | 0.901436i | \(-0.357486\pi\) | ||||
0.432912 | + | 0.901436i | \(0.357486\pi\) | |||||||
\(702\) | 27.3357 | 1.03172 | ||||||||
\(703\) | −56.6665 | −2.13722 | ||||||||
\(704\) | 2.74731 | 0.103543 | ||||||||
\(705\) | 79.7320 | 3.00288 | ||||||||
\(706\) | 0.410032 | 0.0154318 | ||||||||
\(707\) | 3.27853 | 0.123302 | ||||||||
\(708\) | 11.2792 | 0.423898 | ||||||||
\(709\) | −10.6309 | −0.399252 | −0.199626 | − | 0.979872i | \(-0.563973\pi\) | ||||
−0.199626 | + | 0.979872i | \(0.563973\pi\) | |||||||
\(710\) | 15.5577 | 0.583869 | ||||||||
\(711\) | −53.7655 | −2.01636 | ||||||||
\(712\) | 11.4928 | 0.430710 | ||||||||
\(713\) | 5.82227 | 0.218046 | ||||||||
\(714\) | −33.5954 | −1.25728 | ||||||||
\(715\) | 17.6531 | 0.660189 | ||||||||
\(716\) | 5.71596 | 0.213616 | ||||||||
\(717\) | −60.9606 | −2.27661 | ||||||||
\(718\) | −15.6921 | −0.585622 | ||||||||
\(719\) | 29.6106 | 1.10429 | 0.552144 | − | 0.833749i | \(-0.313810\pi\) | ||||
0.552144 | + | 0.833749i | \(0.313810\pi\) | |||||||
\(720\) | 23.8901 | 0.890330 | ||||||||
\(721\) | −24.8188 | −0.924299 | ||||||||
\(722\) | −15.9175 | −0.592388 | ||||||||
\(723\) | 52.8844 | 1.96679 | ||||||||
\(724\) | −7.17041 | −0.266486 | ||||||||
\(725\) | 21.1517 | 0.785556 | ||||||||
\(726\) | −11.0909 | −0.411623 | ||||||||
\(727\) | −9.68963 | −0.359369 | −0.179684 | − | 0.983724i | \(-0.557508\pi\) | ||||
−0.179684 | + | 0.983724i | \(0.557508\pi\) | |||||||
\(728\) | 7.38200 | 0.273595 | ||||||||
\(729\) | 31.9195 | 1.18220 | ||||||||
\(730\) | −37.7606 | −1.39758 | ||||||||
\(731\) | 17.4546 | 0.645583 | ||||||||
\(732\) | −18.6665 | −0.689933 | ||||||||
\(733\) | 2.86524 | 0.105830 | 0.0529151 | − | 0.998599i | \(-0.483149\pi\) | ||||
0.0529151 | + | 0.998599i | \(0.483149\pi\) | |||||||
\(734\) | −29.7225 | −1.09708 | ||||||||
\(735\) | −73.9514 | −2.72774 | ||||||||
\(736\) | −0.836221 | −0.0308235 | ||||||||
\(737\) | −0.707608 | −0.0260651 | ||||||||
\(738\) | −82.5449 | −3.03852 | ||||||||
\(739\) | −45.2734 | −1.66541 | −0.832705 | − | 0.553717i | \(-0.813209\pi\) | ||||
−0.832705 | + | 0.553717i | \(0.813209\pi\) | |||||||
\(740\) | −31.2929 | −1.15035 | ||||||||
\(741\) | −37.3815 | −1.37324 | ||||||||
\(742\) | 51.2890 | 1.88288 | ||||||||
\(743\) | −27.5709 | −1.01148 | −0.505739 | − | 0.862687i | \(-0.668780\pi\) | ||||
−0.505739 | + | 0.862687i | \(0.668780\pi\) | |||||||
\(744\) | 22.3684 | 0.820064 | ||||||||
\(745\) | −40.7173 | −1.49176 | ||||||||
\(746\) | 0.737493 | 0.0270015 | ||||||||
\(747\) | −80.6696 | −2.95155 | ||||||||
\(748\) | 7.66343 | 0.280203 | ||||||||
\(749\) | −51.4632 | −1.88043 | ||||||||
\(750\) | 6.79670 | 0.248180 | ||||||||
\(751\) | 21.5914 | 0.787882 | 0.393941 | − | 0.919136i | \(-0.371111\pi\) | ||||
0.393941 | + | 0.919136i | \(0.371111\pi\) | |||||||
\(752\) | −7.60552 | −0.277345 | ||||||||
\(753\) | 76.0632 | 2.77190 | ||||||||
\(754\) | −7.37392 | −0.268542 | ||||||||
\(755\) | 41.8690 | 1.52377 | ||||||||
\(756\) | 52.0427 | 1.89277 | ||||||||
\(757\) | 33.9685 | 1.23461 | 0.617303 | − | 0.786726i | \(-0.288225\pi\) | ||||
0.617303 | + | 0.786726i | \(0.288225\pi\) | |||||||
\(758\) | −17.5835 | −0.638661 | ||||||||
\(759\) | −7.38062 | −0.267899 | ||||||||
\(760\) | −19.2825 | −0.699448 | ||||||||
\(761\) | 46.4643 | 1.68433 | 0.842165 | − | 0.539220i | \(-0.181281\pi\) | ||||
0.842165 | + | 0.539220i | \(0.181281\pi\) | |||||||
\(762\) | 59.3242 | 2.14909 | ||||||||
\(763\) | 30.0511 | 1.08792 | ||||||||
\(764\) | −5.12685 | −0.185483 | ||||||||
\(765\) | 66.6396 | 2.40936 | ||||||||
\(766\) | −13.0037 | −0.469841 | ||||||||
\(767\) | −6.91332 | −0.249626 | ||||||||
\(768\) | −3.21265 | −0.115926 | ||||||||
\(769\) | −10.0527 | −0.362511 | −0.181256 | − | 0.983436i | \(-0.558016\pi\) | ||||
−0.181256 | + | 0.983436i | \(0.558016\pi\) | |||||||
\(770\) | 33.6086 | 1.21117 | ||||||||
\(771\) | −89.5329 | −3.22445 | ||||||||
\(772\) | 15.2315 | 0.548193 | ||||||||
\(773\) | 13.5930 | 0.488907 | 0.244453 | − | 0.969661i | \(-0.421392\pi\) | ||||
0.244453 | + | 0.969661i | \(0.421392\pi\) | |||||||
\(774\) | −45.8113 | −1.64665 | ||||||||
\(775\) | 39.3270 | 1.41267 | ||||||||
\(776\) | 9.25349 | 0.332181 | ||||||||
\(777\) | −115.497 | −4.14342 | ||||||||
\(778\) | 13.8361 | 0.496050 | ||||||||
\(779\) | 66.6246 | 2.38708 | ||||||||
\(780\) | −20.6432 | −0.739144 | ||||||||
\(781\) | −13.0982 | −0.468691 | ||||||||
\(782\) | −2.33258 | −0.0834129 | ||||||||
\(783\) | −51.9857 | −1.85782 | ||||||||
\(784\) | 7.05412 | 0.251933 | ||||||||
\(785\) | −20.9681 | −0.748383 | ||||||||
\(786\) | −49.8332 | −1.77749 | ||||||||
\(787\) | −16.0621 | −0.572553 | −0.286277 | − | 0.958147i | \(-0.592418\pi\) | ||||
−0.286277 | + | 0.958147i | \(0.592418\pi\) | |||||||
\(788\) | −24.6358 | −0.877616 | ||||||||
\(789\) | 52.6077 | 1.87288 | ||||||||
\(790\) | 23.9645 | 0.852617 | ||||||||
\(791\) | −36.5451 | −1.29939 | ||||||||
\(792\) | −20.1134 | −0.714698 | ||||||||
\(793\) | 11.4412 | 0.406289 | ||||||||
\(794\) | −29.0131 | −1.02964 | ||||||||
\(795\) | −143.425 | −5.08677 | ||||||||
\(796\) | −11.8668 | −0.420608 | ||||||||
\(797\) | 1.00246 | 0.0355088 | 0.0177544 | − | 0.999842i | \(-0.494348\pi\) | ||||
0.0177544 | + | 0.999842i | \(0.494348\pi\) | |||||||
\(798\) | −71.1683 | −2.51933 | ||||||||
\(799\) | −21.2151 | −0.750535 | ||||||||
\(800\) | −5.64833 | −0.199699 | ||||||||
\(801\) | −84.1398 | −2.97293 | ||||||||
\(802\) | −35.9816 | −1.27056 | ||||||||
\(803\) | 31.7912 | 1.12189 | ||||||||
\(804\) | 0.827461 | 0.0291823 | ||||||||
\(805\) | −10.2297 | −0.360550 | ||||||||
\(806\) | −13.7102 | −0.482921 | ||||||||
\(807\) | −40.9375 | −1.44107 | ||||||||
\(808\) | 0.874535 | 0.0307660 | ||||||||
\(809\) | −34.3337 | −1.20711 | −0.603555 | − | 0.797322i | \(-0.706249\pi\) | ||||
−0.603555 | + | 0.797322i | \(0.706249\pi\) | |||||||
\(810\) | −73.8629 | −2.59528 | ||||||||
\(811\) | 50.4335 | 1.77096 | 0.885479 | − | 0.464679i | \(-0.153830\pi\) | ||||
0.885479 | + | 0.464679i | \(0.153830\pi\) | |||||||
\(812\) | −14.0387 | −0.492663 | ||||||||
\(813\) | −65.1515 | −2.28496 | ||||||||
\(814\) | 26.3459 | 0.923424 | ||||||||
\(815\) | 15.3340 | 0.537128 | ||||||||
\(816\) | −8.96145 | −0.313713 | ||||||||
\(817\) | 36.9758 | 1.29362 | ||||||||
\(818\) | 22.3444 | 0.781252 | ||||||||
\(819\) | −54.0444 | −1.88846 | ||||||||
\(820\) | 36.7921 | 1.28483 | ||||||||
\(821\) | −1.52327 | −0.0531625 | −0.0265812 | − | 0.999647i | \(-0.508462\pi\) | ||||
−0.0265812 | + | 0.999647i | \(0.508462\pi\) | |||||||
\(822\) | −60.5428 | −2.11167 | ||||||||
\(823\) | −29.4844 | −1.02776 | −0.513881 | − | 0.857862i | \(-0.671793\pi\) | ||||
−0.513881 | + | 0.857862i | \(0.671793\pi\) | |||||||
\(824\) | −6.62031 | −0.230629 | ||||||||
\(825\) | −49.8530 | −1.73566 | ||||||||
\(826\) | −13.1618 | −0.457959 | ||||||||
\(827\) | 22.0399 | 0.766404 | 0.383202 | − | 0.923665i | \(-0.374821\pi\) | ||||
0.383202 | + | 0.923665i | \(0.374821\pi\) | |||||||
\(828\) | 6.12206 | 0.212756 | ||||||||
\(829\) | −39.3626 | −1.36712 | −0.683559 | − | 0.729895i | \(-0.739569\pi\) | ||||
−0.683559 | + | 0.729895i | \(0.739569\pi\) | |||||||
\(830\) | 35.9562 | 1.24806 | ||||||||
\(831\) | 18.5886 | 0.644831 | ||||||||
\(832\) | 1.96912 | 0.0682670 | ||||||||
\(833\) | 19.6770 | 0.681766 | ||||||||
\(834\) | 0.246367 | 0.00853100 | ||||||||
\(835\) | −27.6964 | −0.958475 | ||||||||
\(836\) | 16.2342 | 0.561470 | ||||||||
\(837\) | −96.6561 | −3.34092 | ||||||||
\(838\) | 33.6052 | 1.16087 | ||||||||
\(839\) | 36.6796 | 1.26632 | 0.633160 | − | 0.774021i | \(-0.281758\pi\) | ||||
0.633160 | + | 0.774021i | \(0.281758\pi\) | |||||||
\(840\) | −39.3012 | −1.35602 | ||||||||
\(841\) | −14.9766 | −0.516435 | ||||||||
\(842\) | 15.3383 | 0.528593 | ||||||||
\(843\) | −53.0212 | −1.82615 | ||||||||
\(844\) | 15.7996 | 0.543843 | ||||||||
\(845\) | −29.7685 | −1.02407 | ||||||||
\(846\) | 55.6808 | 1.91435 | ||||||||
\(847\) | 12.9421 | 0.444697 | ||||||||
\(848\) | 13.6811 | 0.469812 | ||||||||
\(849\) | 4.99040 | 0.171270 | ||||||||
\(850\) | −15.7556 | −0.540413 | ||||||||
\(851\) | −8.01911 | −0.274892 | ||||||||
\(852\) | 15.3168 | 0.524744 | ||||||||
\(853\) | 22.7441 | 0.778743 | 0.389371 | − | 0.921081i | \(-0.372692\pi\) | ||||
0.389371 | + | 0.921081i | \(0.372692\pi\) | |||||||
\(854\) | 21.7822 | 0.745370 | ||||||||
\(855\) | 141.169 | 4.82787 | ||||||||
\(856\) | −13.7276 | −0.469200 | ||||||||
\(857\) | −35.3073 | −1.20608 | −0.603038 | − | 0.797713i | \(-0.706043\pi\) | ||||
−0.603038 | + | 0.797713i | \(0.706043\pi\) | |||||||
\(858\) | 17.3798 | 0.593335 | ||||||||
\(859\) | 18.9037 | 0.644987 | 0.322493 | − | 0.946572i | \(-0.395479\pi\) | ||||
0.322493 | + | 0.946572i | \(0.395479\pi\) | |||||||
\(860\) | 20.4191 | 0.696285 | ||||||||
\(861\) | 135.793 | 4.62782 | ||||||||
\(862\) | −6.03095 | −0.205415 | ||||||||
\(863\) | −8.22936 | −0.280131 | −0.140065 | − | 0.990142i | \(-0.544731\pi\) | ||||
−0.140065 | + | 0.990142i | \(0.544731\pi\) | |||||||
\(864\) | 13.8822 | 0.472282 | ||||||||
\(865\) | −44.5948 | −1.51627 | ||||||||
\(866\) | 16.2591 | 0.552506 | ||||||||
\(867\) | 29.6177 | 1.00587 | ||||||||
\(868\) | −26.1020 | −0.885958 | ||||||||
\(869\) | −20.1760 | −0.684424 | ||||||||
\(870\) | 39.2582 | 1.33098 | ||||||||
\(871\) | −0.507174 | −0.0171849 | ||||||||
\(872\) | 8.01601 | 0.271456 | ||||||||
\(873\) | −67.7458 | −2.29285 | ||||||||
\(874\) | −4.94132 | −0.167143 | ||||||||
\(875\) | −7.93116 | −0.268122 | ||||||||
\(876\) | −37.1759 | −1.25606 | ||||||||
\(877\) | 3.72004 | 0.125617 | 0.0628084 | − | 0.998026i | \(-0.479994\pi\) | ||||
0.0628084 | + | 0.998026i | \(0.479994\pi\) | |||||||
\(878\) | 1.63102 | 0.0550443 | ||||||||
\(879\) | −86.2139 | −2.90792 | ||||||||
\(880\) | 8.96497 | 0.302209 | ||||||||
\(881\) | −8.46897 | −0.285327 | −0.142663 | − | 0.989771i | \(-0.545567\pi\) | ||||
−0.142663 | + | 0.989771i | \(0.545567\pi\) | |||||||
\(882\) | −51.6439 | −1.73894 | ||||||||
\(883\) | −32.5328 | −1.09481 | −0.547407 | − | 0.836866i | \(-0.684385\pi\) | ||||
−0.547407 | + | 0.836866i | \(0.684385\pi\) | |||||||
\(884\) | 5.49272 | 0.184740 | ||||||||
\(885\) | 36.8060 | 1.23722 | ||||||||
\(886\) | 24.4638 | 0.821876 | ||||||||
\(887\) | 39.4037 | 1.32305 | 0.661524 | − | 0.749924i | \(-0.269910\pi\) | ||||
0.661524 | + | 0.749924i | \(0.269910\pi\) | |||||||
\(888\) | −30.8083 | −1.03386 | ||||||||
\(889\) | −69.2262 | −2.32177 | ||||||||
\(890\) | 37.5029 | 1.25710 | ||||||||
\(891\) | 62.1862 | 2.08332 | ||||||||
\(892\) | 5.02473 | 0.168241 | ||||||||
\(893\) | −44.9418 | −1.50392 | ||||||||
\(894\) | −40.0868 | −1.34070 | ||||||||
\(895\) | 18.6522 | 0.623474 | ||||||||
\(896\) | 3.74888 | 0.125241 | ||||||||
\(897\) | −5.29001 | −0.176628 | ||||||||
\(898\) | −16.6981 | −0.557223 | ||||||||
\(899\) | 26.0734 | 0.869596 | ||||||||
\(900\) | 41.3520 | 1.37840 | ||||||||
\(901\) | 38.1625 | 1.27138 | ||||||||
\(902\) | −30.9757 | −1.03138 | ||||||||
\(903\) | 75.3635 | 2.50794 | ||||||||
\(904\) | −9.74825 | −0.324222 | ||||||||
\(905\) | −23.3983 | −0.777787 | ||||||||
\(906\) | 41.2207 | 1.36947 | ||||||||
\(907\) | −10.2299 | −0.339677 | −0.169839 | − | 0.985472i | \(-0.554325\pi\) | ||||
−0.169839 | + | 0.985472i | \(0.554325\pi\) | |||||||
\(908\) | 13.3338 | 0.442497 | ||||||||
\(909\) | −6.40256 | −0.212360 | ||||||||
\(910\) | 24.0888 | 0.798535 | ||||||||
\(911\) | −17.3354 | −0.574348 | −0.287174 | − | 0.957878i | \(-0.592716\pi\) | ||||
−0.287174 | + | 0.957878i | \(0.592716\pi\) | |||||||
\(912\) | −18.9839 | −0.628619 | ||||||||
\(913\) | −30.2720 | −1.00186 | ||||||||
\(914\) | 16.7108 | 0.552745 | ||||||||
\(915\) | −60.9120 | −2.01369 | ||||||||
\(916\) | 28.5085 | 0.941947 | ||||||||
\(917\) | 58.1511 | 1.92032 | ||||||||
\(918\) | 38.7234 | 1.27806 | ||||||||
\(919\) | −36.0779 | −1.19010 | −0.595050 | − | 0.803689i | \(-0.702868\pi\) | ||||
−0.595050 | + | 0.803689i | \(0.702868\pi\) | |||||||
\(920\) | −2.72874 | −0.0899638 | ||||||||
\(921\) | 21.2349 | 0.699714 | ||||||||
\(922\) | 11.0991 | 0.365530 | ||||||||
\(923\) | −9.38807 | −0.309012 | ||||||||
\(924\) | 33.0882 | 1.08852 | ||||||||
\(925\) | −54.1658 | −1.78096 | ||||||||
\(926\) | −27.1051 | −0.890728 | ||||||||
\(927\) | 48.4680 | 1.59190 | ||||||||
\(928\) | −3.74478 | −0.122928 | ||||||||
\(929\) | 20.5507 | 0.674246 | 0.337123 | − | 0.941461i | \(-0.390546\pi\) | ||||
0.337123 | + | 0.941461i | \(0.390546\pi\) | |||||||
\(930\) | 72.9920 | 2.39350 | ||||||||
\(931\) | 41.6835 | 1.36612 | ||||||||
\(932\) | 17.7156 | 0.580294 | ||||||||
\(933\) | −29.7448 | −0.973800 | ||||||||
\(934\) | −30.8905 | −1.01077 | ||||||||
\(935\) | 25.0071 | 0.817821 | ||||||||
\(936\) | −14.4161 | −0.471206 | ||||||||
\(937\) | −17.6871 | −0.577812 | −0.288906 | − | 0.957357i | \(-0.593291\pi\) | ||||
−0.288906 | + | 0.957357i | \(0.593291\pi\) | |||||||
\(938\) | −0.965576 | −0.0315272 | ||||||||
\(939\) | −75.9330 | −2.47798 | ||||||||
\(940\) | −24.8182 | −0.809479 | ||||||||
\(941\) | 8.13342 | 0.265142 | 0.132571 | − | 0.991174i | \(-0.457677\pi\) | ||||
0.132571 | + | 0.991174i | \(0.457677\pi\) | |||||||
\(942\) | −20.6434 | −0.672598 | ||||||||
\(943\) | 9.42833 | 0.307029 | ||||||||
\(944\) | −3.51087 | −0.114269 | ||||||||
\(945\) | 169.825 | 5.52439 | ||||||||
\(946\) | −17.1911 | −0.558931 | ||||||||
\(947\) | −50.5671 | −1.64321 | −0.821605 | − | 0.570057i | \(-0.806921\pi\) | ||||
−0.821605 | + | 0.570057i | \(0.806921\pi\) | |||||||
\(948\) | 23.5934 | 0.766277 | ||||||||
\(949\) | 22.7861 | 0.739669 | ||||||||
\(950\) | −33.3765 | −1.08288 | ||||||||
\(951\) | −83.8557 | −2.71921 | ||||||||
\(952\) | 10.4572 | 0.338921 | ||||||||
\(953\) | −26.8991 | −0.871347 | −0.435674 | − | 0.900105i | \(-0.643490\pi\) | ||||
−0.435674 | + | 0.900105i | \(0.643490\pi\) | |||||||
\(954\) | −100.161 | −3.24283 | ||||||||
\(955\) | −16.7298 | −0.541364 | ||||||||
\(956\) | 18.9752 | 0.613701 | ||||||||
\(957\) | −33.0520 | −1.06842 | ||||||||
\(958\) | −0.270250 | −0.00873137 | ||||||||
\(959\) | 70.6483 | 2.28135 | ||||||||
\(960\) | −10.4834 | −0.338352 | ||||||||
\(961\) | 17.4778 | 0.563799 | ||||||||
\(962\) | 18.8833 | 0.608821 | ||||||||
\(963\) | 100.501 | 3.23861 | ||||||||
\(964\) | −16.4613 | −0.530183 | ||||||||
\(965\) | 49.7030 | 1.60000 | ||||||||
\(966\) | −10.0713 | −0.324039 | ||||||||
\(967\) | 20.9466 | 0.673596 | 0.336798 | − | 0.941577i | \(-0.390656\pi\) | ||||
0.336798 | + | 0.941577i | \(0.390656\pi\) | |||||||
\(968\) | 3.45227 | 0.110960 | ||||||||
\(969\) | −52.9541 | −1.70113 | ||||||||
\(970\) | 30.1958 | 0.969528 | ||||||||
\(971\) | 47.4120 | 1.52152 | 0.760762 | − | 0.649031i | \(-0.224826\pi\) | ||||
0.760762 | + | 0.649031i | \(0.224826\pi\) | |||||||
\(972\) | −31.0726 | −0.996654 | ||||||||
\(973\) | −0.287489 | −0.00921648 | ||||||||
\(974\) | −32.3472 | −1.03647 | ||||||||
\(975\) | −35.7318 | −1.14433 | ||||||||
\(976\) | 5.81031 | 0.185983 | ||||||||
\(977\) | −2.69646 | −0.0862675 | −0.0431338 | − | 0.999069i | \(-0.513734\pi\) | ||||
−0.0431338 | + | 0.999069i | \(0.513734\pi\) | |||||||
\(978\) | 15.0966 | 0.482736 | ||||||||
\(979\) | −31.5742 | −1.00912 | ||||||||
\(980\) | 23.0188 | 0.735310 | ||||||||
\(981\) | −58.6861 | −1.87370 | ||||||||
\(982\) | −2.07595 | −0.0662462 | ||||||||
\(983\) | 19.7251 | 0.629132 | 0.314566 | − | 0.949236i | \(-0.398141\pi\) | ||||
0.314566 | + | 0.949236i | \(0.398141\pi\) | |||||||
\(984\) | 36.2223 | 1.15473 | ||||||||
\(985\) | −80.3911 | −2.56147 | ||||||||
\(986\) | −10.4458 | −0.332662 | ||||||||
\(987\) | −91.5997 | −2.91565 | ||||||||
\(988\) | 11.6357 | 0.370182 | ||||||||
\(989\) | 5.23260 | 0.166387 | ||||||||
\(990\) | −65.6335 | −2.08597 | ||||||||
\(991\) | −10.3904 | −0.330063 | −0.165031 | − | 0.986288i | \(-0.552773\pi\) | ||||
−0.165031 | + | 0.986288i | \(0.552773\pi\) | |||||||
\(992\) | −6.96260 | −0.221063 | ||||||||
\(993\) | 94.3728 | 2.99483 | ||||||||
\(994\) | −17.8733 | −0.566908 | ||||||||
\(995\) | −38.7235 | −1.22762 | ||||||||
\(996\) | 35.3994 | 1.12167 | ||||||||
\(997\) | 57.0048 | 1.80536 | 0.902680 | − | 0.430312i | \(-0.141596\pi\) | ||||
0.902680 | + | 0.430312i | \(0.141596\pi\) | |||||||
\(998\) | −10.1670 | −0.321832 | ||||||||
\(999\) | 133.126 | 4.21192 |
(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 | 4006.2.a.h.1.1 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.h.1.1 | ✓ | 42 | 1.1 | even | 1 | trivial |