Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 29 x^{10} + 76 x^{9} + 320 x^{8} - 724 x^{7} - 1643 x^{6} + 3265 x^{5} + 3921 x^{4} + \cdots + 423 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.51858\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.51858 | 0.679131 | 0.339565 | − | 0.940582i | \(-0.389720\pi\) | ||||
0.339565 | + | 0.940582i | \(0.389720\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.35237 | 1.64504 | 0.822521 | − | 0.568735i | \(-0.192567\pi\) | ||||
0.822521 | + | 0.568735i | \(0.192567\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.51858 | 0.480218 | ||||||||
\(11\) | 5.50747 | 1.66056 | 0.830282 | − | 0.557344i | \(-0.188180\pi\) | ||||
0.830282 | + | 0.557344i | \(0.188180\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.889028 | −0.246572 | −0.123286 | − | 0.992371i | \(-0.539343\pi\) | ||||
−0.123286 | + | 0.992371i | \(0.539343\pi\) | |||||||
\(14\) | 4.35237 | 1.16322 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.257830 | −0.0625330 | −0.0312665 | − | 0.999511i | \(-0.509954\pi\) | ||||
−0.0312665 | + | 0.999511i | \(0.509954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.48754 | −0.800097 | −0.400048 | − | 0.916494i | \(-0.631007\pi\) | ||||
−0.400048 | + | 0.916494i | \(0.631007\pi\) | |||||||
\(20\) | 1.51858 | 0.339565 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.50747 | 1.17420 | ||||||||
\(23\) | −2.69314 | −0.561559 | −0.280779 | − | 0.959772i | \(-0.590593\pi\) | ||||
−0.280779 | + | 0.959772i | \(0.590593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.69391 | −0.538781 | ||||||||
\(26\) | −0.889028 | −0.174353 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.35237 | 0.822521 | ||||||||
\(29\) | −1.61241 | −0.299418 | −0.149709 | − | 0.988730i | \(-0.547834\pi\) | ||||
−0.149709 | + | 0.988730i | \(0.547834\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.129803 | −0.0233134 | −0.0116567 | − | 0.999932i | \(-0.503711\pi\) | ||||
−0.0116567 | + | 0.999932i | \(0.503711\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.257830 | −0.0442175 | ||||||||
\(35\) | 6.60944 | 1.11720 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.62620 | 1.58254 | 0.791269 | − | 0.611468i | \(-0.209421\pi\) | ||||
0.791269 | + | 0.611468i | \(0.209421\pi\) | |||||||
\(38\) | −3.48754 | −0.565754 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.51858 | 0.240109 | ||||||||
\(41\) | 1.32208 | 0.206474 | 0.103237 | − | 0.994657i | \(-0.467080\pi\) | ||||
0.103237 | + | 0.994657i | \(0.467080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.65072 | 1.31922 | 0.659612 | − | 0.751607i | \(-0.270721\pi\) | ||||
0.659612 | + | 0.751607i | \(0.270721\pi\) | |||||||
\(44\) | 5.50747 | 0.830282 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.69314 | −0.397082 | ||||||||
\(47\) | 2.28763 | 0.333684 | 0.166842 | − | 0.985984i | \(-0.446643\pi\) | ||||
0.166842 | + | 0.985984i | \(0.446643\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.9431 | 1.70616 | ||||||||
\(50\) | −2.69391 | −0.380976 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.889028 | −0.123286 | ||||||||
\(53\) | −1.25633 | −0.172570 | −0.0862851 | − | 0.996270i | \(-0.527500\pi\) | ||||
−0.0862851 | + | 0.996270i | \(0.527500\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.36354 | 1.12774 | ||||||||
\(56\) | 4.35237 | 0.581610 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.61241 | −0.211720 | ||||||||
\(59\) | −7.39850 | −0.963202 | −0.481601 | − | 0.876390i | \(-0.659945\pi\) | ||||
−0.481601 | + | 0.876390i | \(0.659945\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.49418 | −0.447384 | −0.223692 | − | 0.974660i | \(-0.571811\pi\) | ||||
−0.223692 | + | 0.974660i | \(0.571811\pi\) | |||||||
\(62\) | −0.129803 | −0.0164851 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.35006 | −0.167455 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.45868 | −0.422545 | −0.211272 | − | 0.977427i | \(-0.567761\pi\) | ||||
−0.211272 | + | 0.977427i | \(0.567761\pi\) | |||||||
\(68\) | −0.257830 | −0.0312665 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.60944 | 0.789979 | ||||||||
\(71\) | 14.5730 | 1.72950 | 0.864751 | − | 0.502201i | \(-0.167476\pi\) | ||||
0.864751 | + | 0.502201i | \(0.167476\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.70403 | −0.433524 | −0.216762 | − | 0.976224i | \(-0.569550\pi\) | ||||
−0.216762 | + | 0.976224i | \(0.569550\pi\) | |||||||
\(74\) | 9.62620 | 1.11902 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.48754 | −0.400048 | ||||||||
\(77\) | 23.9705 | 2.73170 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.40799 | 1.05848 | 0.529241 | − | 0.848472i | \(-0.322477\pi\) | ||||
0.529241 | + | 0.848472i | \(0.322477\pi\) | |||||||
\(80\) | 1.51858 | 0.169783 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.32208 | 0.145999 | ||||||||
\(83\) | −16.5111 | −1.81233 | −0.906165 | − | 0.422924i | \(-0.861004\pi\) | ||||
−0.906165 | + | 0.422924i | \(0.861004\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.391536 | −0.0424681 | ||||||||
\(86\) | 8.65072 | 0.932832 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.50747 | 0.587098 | ||||||||
\(89\) | 12.8672 | 1.36392 | 0.681960 | − | 0.731390i | \(-0.261128\pi\) | ||||
0.681960 | + | 0.731390i | \(0.261128\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.86938 | −0.405621 | ||||||||
\(92\) | −2.69314 | −0.280779 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.28763 | 0.235951 | ||||||||
\(95\) | −5.29612 | −0.543370 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8784 | −1.20607 | −0.603037 | − | 0.797713i | \(-0.706043\pi\) | ||||
−0.603037 | + | 0.797713i | \(0.706043\pi\) | |||||||
\(98\) | 11.9431 | 1.20644 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.69391 | −0.269391 | ||||||||
\(101\) | −6.88141 | −0.684726 | −0.342363 | − | 0.939568i | \(-0.611227\pi\) | ||||
−0.342363 | + | 0.939568i | \(0.611227\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.5670 | −1.92800 | −0.963998 | − | 0.265911i | \(-0.914327\pi\) | ||||
−0.963998 | + | 0.265911i | \(0.914327\pi\) | |||||||
\(104\) | −0.889028 | −0.0871764 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.25633 | −0.122026 | ||||||||
\(107\) | 19.5947 | 1.89429 | 0.947147 | − | 0.320799i | \(-0.103951\pi\) | ||||
0.947147 | + | 0.320799i | \(0.103951\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.2902 | 1.46454 | 0.732269 | − | 0.681015i | \(-0.238461\pi\) | ||||
0.732269 | + | 0.681015i | \(0.238461\pi\) | |||||||
\(110\) | 8.36354 | 0.797432 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.35237 | 0.411261 | ||||||||
\(113\) | 3.27705 | 0.308279 | 0.154140 | − | 0.988049i | \(-0.450739\pi\) | ||||
0.154140 | + | 0.988049i | \(0.450739\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.08976 | −0.381372 | ||||||||
\(116\) | −1.61241 | −0.149709 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.39850 | −0.681087 | ||||||||
\(119\) | −1.12217 | −0.102869 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.3322 | 1.75747 | ||||||||
\(122\) | −3.49418 | −0.316348 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.129803 | −0.0116567 | ||||||||
\(125\) | −11.6838 | −1.04503 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.37983 | −0.211176 | −0.105588 | − | 0.994410i | \(-0.533672\pi\) | ||||
−0.105588 | + | 0.994410i | \(0.533672\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.35006 | −0.118408 | ||||||||
\(131\) | −9.93489 | −0.868015 | −0.434008 | − | 0.900909i | \(-0.642901\pi\) | ||||
−0.434008 | + | 0.900909i | \(0.642901\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.1791 | −1.31619 | ||||||||
\(134\) | −3.45868 | −0.298784 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.257830 | −0.0221087 | ||||||||
\(137\) | 21.3464 | 1.82374 | 0.911872 | − | 0.410474i | \(-0.134637\pi\) | ||||
0.911872 | + | 0.410474i | \(0.134637\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.04927 | −0.343455 | −0.171727 | − | 0.985145i | \(-0.554935\pi\) | ||||
−0.171727 | + | 0.985145i | \(0.554935\pi\) | |||||||
\(140\) | 6.60944 | 0.558599 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.5730 | 1.22294 | ||||||||
\(143\) | −4.89629 | −0.409449 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.44858 | −0.203344 | ||||||||
\(146\) | −3.70403 | −0.306548 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.62620 | 0.791269 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.65060 | −0.785355 | −0.392677 | − | 0.919676i | \(-0.628451\pi\) | ||||
−0.392677 | + | 0.919676i | \(0.628451\pi\) | |||||||
\(152\) | −3.48754 | −0.282877 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 23.9705 | 1.93160 | ||||||||
\(155\) | −0.197117 | −0.0158328 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.5773 | −1.72205 | −0.861027 | − | 0.508559i | \(-0.830179\pi\) | ||||
−0.861027 | + | 0.508559i | \(0.830179\pi\) | |||||||
\(158\) | 9.40799 | 0.748459 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.51858 | 0.120054 | ||||||||
\(161\) | −11.7216 | −0.923788 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4786 | 1.05573 | 0.527865 | − | 0.849329i | \(-0.322993\pi\) | ||||
0.527865 | + | 0.849329i | \(0.322993\pi\) | |||||||
\(164\) | 1.32208 | 0.103237 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.5111 | −1.28151 | ||||||||
\(167\) | −1.95084 | −0.150961 | −0.0754804 | − | 0.997147i | \(-0.524049\pi\) | ||||
−0.0754804 | + | 0.997147i | \(0.524049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2096 | −0.939202 | ||||||||
\(170\) | −0.391536 | −0.0300295 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.65072 | 0.659612 | ||||||||
\(173\) | −0.332976 | −0.0253157 | −0.0126578 | − | 0.999920i | \(-0.504029\pi\) | ||||
−0.0126578 | + | 0.999920i | \(0.504029\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.7249 | −0.886318 | ||||||||
\(176\) | 5.50747 | 0.415141 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.8672 | 0.964437 | ||||||||
\(179\) | 8.14115 | 0.608498 | 0.304249 | − | 0.952592i | \(-0.401594\pi\) | ||||
0.304249 | + | 0.952592i | \(0.401594\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.87618 | −0.585432 | −0.292716 | − | 0.956199i | \(-0.594559\pi\) | ||||
−0.292716 | + | 0.956199i | \(0.594559\pi\) | |||||||
\(182\) | −3.86938 | −0.286818 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.69314 | −0.198541 | ||||||||
\(185\) | 14.6182 | 1.07475 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.41999 | −0.103840 | ||||||||
\(188\) | 2.28763 | 0.166842 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.29612 | −0.384221 | ||||||||
\(191\) | −20.2488 | −1.46515 | −0.732577 | − | 0.680684i | \(-0.761683\pi\) | ||||
−0.732577 | + | 0.680684i | \(0.761683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.2272 | −0.952115 | −0.476058 | − | 0.879414i | \(-0.657935\pi\) | ||||
−0.476058 | + | 0.879414i | \(0.657935\pi\) | |||||||
\(194\) | −11.8784 | −0.852823 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.9431 | 0.853082 | ||||||||
\(197\) | 10.5773 | 0.753600 | 0.376800 | − | 0.926295i | \(-0.377024\pi\) | ||||
0.376800 | + | 0.926295i | \(0.377024\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0343 | −0.994863 | −0.497431 | − | 0.867503i | \(-0.665723\pi\) | ||||
−0.497431 | + | 0.867503i | \(0.665723\pi\) | |||||||
\(200\) | −2.69391 | −0.190488 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.88141 | −0.484174 | ||||||||
\(203\) | −7.01783 | −0.492555 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00768 | 0.140223 | ||||||||
\(206\) | −19.5670 | −1.36330 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.889028 | −0.0616430 | ||||||||
\(209\) | −19.2075 | −1.32861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.8982 | −1.78290 | −0.891452 | − | 0.453115i | \(-0.850313\pi\) | ||||
−0.891452 | + | 0.453115i | \(0.850313\pi\) | |||||||
\(212\) | −1.25633 | −0.0862851 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.5947 | 1.33947 | ||||||||
\(215\) | 13.1368 | 0.895925 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.564953 | −0.0383515 | ||||||||
\(218\) | 15.2902 | 1.03559 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.36354 | 0.563870 | ||||||||
\(221\) | 0.229218 | 0.0154189 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.9086 | −1.73497 | −0.867483 | − | 0.497467i | \(-0.834264\pi\) | ||||
−0.867483 | + | 0.497467i | \(0.834264\pi\) | |||||||
\(224\) | 4.35237 | 0.290805 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.27705 | 0.217986 | ||||||||
\(227\) | −19.7476 | −1.31069 | −0.655345 | − | 0.755329i | \(-0.727477\pi\) | ||||
−0.655345 | + | 0.755329i | \(0.727477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.8704 | 1.51132 | 0.755658 | − | 0.654966i | \(-0.227317\pi\) | ||||
0.755658 | + | 0.654966i | \(0.227317\pi\) | |||||||
\(230\) | −4.08976 | −0.269671 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.61241 | −0.105860 | ||||||||
\(233\) | 1.79710 | 0.117732 | 0.0588661 | − | 0.998266i | \(-0.481251\pi\) | ||||
0.0588661 | + | 0.998266i | \(0.481251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.47395 | 0.226615 | ||||||||
\(236\) | −7.39850 | −0.481601 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.12217 | −0.0727396 | ||||||||
\(239\) | −1.88863 | −0.122165 | −0.0610826 | − | 0.998133i | \(-0.519455\pi\) | ||||
−0.0610826 | + | 0.998133i | \(0.519455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.85516 | 0.570411 | 0.285205 | − | 0.958466i | \(-0.407938\pi\) | ||||
0.285205 | + | 0.958466i | \(0.407938\pi\) | |||||||
\(242\) | 19.3322 | 1.24272 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.49418 | −0.223692 | ||||||||
\(245\) | 18.1366 | 1.15871 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.10052 | 0.197281 | ||||||||
\(248\) | −0.129803 | −0.00824253 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.6838 | −0.738950 | ||||||||
\(251\) | 17.6848 | 1.11626 | 0.558128 | − | 0.829755i | \(-0.311520\pi\) | ||||
0.558128 | + | 0.829755i | \(0.311520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.8324 | −0.932504 | ||||||||
\(254\) | −2.37983 | −0.149324 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.8389 | −1.36227 | −0.681136 | − | 0.732157i | \(-0.738514\pi\) | ||||
−0.681136 | + | 0.732157i | \(0.738514\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 41.8968 | 2.60334 | ||||||||
\(260\) | −1.35006 | −0.0837274 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.93489 | −0.613779 | ||||||||
\(263\) | 15.4275 | 0.951302 | 0.475651 | − | 0.879634i | \(-0.342213\pi\) | ||||
0.475651 | + | 0.879634i | \(0.342213\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.90784 | −0.117198 | ||||||||
\(266\) | −15.1791 | −0.930689 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.45868 | −0.211272 | ||||||||
\(269\) | 8.22690 | 0.501603 | 0.250801 | − | 0.968039i | \(-0.419306\pi\) | ||||
0.250801 | + | 0.968039i | \(0.419306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.80919 | 0.595866 | 0.297933 | − | 0.954587i | \(-0.403703\pi\) | ||||
0.297933 | + | 0.954587i | \(0.403703\pi\) | |||||||
\(272\) | −0.257830 | −0.0156332 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.3464 | 1.28958 | ||||||||
\(275\) | −14.8366 | −0.894681 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.50186 | 0.0902379 | 0.0451189 | − | 0.998982i | \(-0.485633\pi\) | ||||
0.0451189 | + | 0.998982i | \(0.485633\pi\) | |||||||
\(278\) | −4.04927 | −0.242859 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.60944 | 0.394989 | ||||||||
\(281\) | −6.05893 | −0.361446 | −0.180723 | − | 0.983534i | \(-0.557844\pi\) | ||||
−0.180723 | + | 0.983534i | \(0.557844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.4994 | 0.861898 | 0.430949 | − | 0.902376i | \(-0.358179\pi\) | ||||
0.430949 | + | 0.902376i | \(0.358179\pi\) | |||||||
\(284\) | 14.5730 | 0.864751 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.89629 | −0.289524 | ||||||||
\(287\) | 5.75417 | 0.339658 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9335 | −0.996090 | ||||||||
\(290\) | −2.44858 | −0.143786 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.70403 | −0.216762 | ||||||||
\(293\) | 8.49809 | 0.496464 | 0.248232 | − | 0.968701i | \(-0.420150\pi\) | ||||
0.248232 | + | 0.968701i | \(0.420150\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2352 | −0.654140 | ||||||||
\(296\) | 9.62620 | 0.559512 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | 2.39428 | 0.138465 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 37.6512 | 2.17018 | ||||||||
\(302\) | −9.65060 | −0.555330 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.48754 | −0.200024 | ||||||||
\(305\) | −5.30620 | −0.303832 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.56218 | −0.146231 | −0.0731157 | − | 0.997323i | \(-0.523294\pi\) | ||||
−0.0731157 | + | 0.997323i | \(0.523294\pi\) | |||||||
\(308\) | 23.9705 | 1.36585 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.197117 | −0.0111955 | ||||||||
\(311\) | 5.29938 | 0.300500 | 0.150250 | − | 0.988648i | \(-0.451992\pi\) | ||||
0.150250 | + | 0.988648i | \(0.451992\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.8375 | 1.57347 | 0.786735 | − | 0.617291i | \(-0.211770\pi\) | ||||
0.786735 | + | 0.617291i | \(0.211770\pi\) | |||||||
\(314\) | −21.5773 | −1.21768 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.40799 | 0.529241 | ||||||||
\(317\) | 23.2519 | 1.30596 | 0.652979 | − | 0.757376i | \(-0.273519\pi\) | ||||
0.652979 | + | 0.757376i | \(0.273519\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.88032 | −0.497202 | ||||||||
\(320\) | 1.51858 | 0.0848914 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.7216 | −0.653217 | ||||||||
\(323\) | 0.899192 | 0.0500324 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.39496 | 0.132848 | ||||||||
\(326\) | 13.4786 | 0.746513 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.32208 | 0.0729994 | ||||||||
\(329\) | 9.95660 | 0.548925 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.5832 | 0.966458 | 0.483229 | − | 0.875494i | \(-0.339464\pi\) | ||||
0.483229 | + | 0.875494i | \(0.339464\pi\) | |||||||
\(332\) | −16.5111 | −0.906165 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.95084 | −0.106745 | ||||||||
\(335\) | −5.25229 | −0.286963 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.34833 | 0.182395 | 0.0911975 | − | 0.995833i | \(-0.470931\pi\) | ||||
0.0911975 | + | 0.995833i | \(0.470931\pi\) | |||||||
\(338\) | −12.2096 | −0.664116 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.391536 | −0.0212340 | ||||||||
\(341\) | −0.714888 | −0.0387133 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21.5144 | 1.16167 | ||||||||
\(344\) | 8.65072 | 0.466416 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.332976 | −0.0179009 | ||||||||
\(347\) | 10.0699 | 0.540578 | 0.270289 | − | 0.962779i | \(-0.412881\pi\) | ||||
0.270289 | + | 0.962779i | \(0.412881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.0001 | 0.909996 | 0.454998 | − | 0.890492i | \(-0.349640\pi\) | ||||
0.454998 | + | 0.890492i | \(0.349640\pi\) | |||||||
\(350\) | −11.7249 | −0.626721 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.50747 | 0.293549 | ||||||||
\(353\) | 2.55240 | 0.135850 | 0.0679252 | − | 0.997690i | \(-0.478362\pi\) | ||||
0.0679252 | + | 0.997690i | \(0.478362\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.1304 | 1.17456 | ||||||||
\(356\) | 12.8672 | 0.681960 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.14115 | 0.430273 | ||||||||
\(359\) | −11.4760 | −0.605683 | −0.302841 | − | 0.953041i | \(-0.597935\pi\) | ||||
−0.302841 | + | 0.953041i | \(0.597935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.83706 | −0.359845 | ||||||||
\(362\) | −7.87618 | −0.413963 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.86938 | −0.202811 | ||||||||
\(365\) | −5.62488 | −0.294420 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.93896 | −0.101213 | −0.0506065 | − | 0.998719i | \(-0.516115\pi\) | ||||
−0.0506065 | + | 0.998719i | \(0.516115\pi\) | |||||||
\(368\) | −2.69314 | −0.140390 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14.6182 | 0.759963 | ||||||||
\(371\) | −5.46801 | −0.283885 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.1484 | −0.784352 | −0.392176 | − | 0.919890i | \(-0.628278\pi\) | ||||
−0.392176 | + | 0.919890i | \(0.628278\pi\) | |||||||
\(374\) | −1.41999 | −0.0734259 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.28763 | 0.117975 | ||||||||
\(377\) | 1.43348 | 0.0738281 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.9218 | −1.02332 | −0.511658 | − | 0.859189i | \(-0.670969\pi\) | ||||
−0.511658 | + | 0.859189i | \(0.670969\pi\) | |||||||
\(380\) | −5.29612 | −0.271685 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.2488 | −1.03602 | ||||||||
\(383\) | 34.5336 | 1.76459 | 0.882293 | − | 0.470700i | \(-0.155998\pi\) | ||||
0.882293 | + | 0.470700i | \(0.155998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 36.4012 | 1.85518 | ||||||||
\(386\) | −13.2272 | −0.673247 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.8784 | −0.603037 | ||||||||
\(389\) | −5.95485 | −0.301923 | −0.150961 | − | 0.988540i | \(-0.548237\pi\) | ||||
−0.150961 | + | 0.988540i | \(0.548237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.694373 | 0.0351159 | ||||||||
\(392\) | 11.9431 | 0.603220 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.5773 | 0.532876 | ||||||||
\(395\) | 14.2868 | 0.718847 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.6111 | −1.33557 | −0.667786 | − | 0.744353i | \(-0.732758\pi\) | ||||
−0.667786 | + | 0.744353i | \(0.732758\pi\) | |||||||
\(398\) | −14.0343 | −0.703474 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.69391 | −0.134695 | ||||||||
\(401\) | −15.2785 | −0.762970 | −0.381485 | − | 0.924375i | \(-0.624587\pi\) | ||||
−0.381485 | + | 0.924375i | \(0.624587\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.115399 | 0.00574843 | ||||||||
\(404\) | −6.88141 | −0.342363 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.01783 | −0.348289 | ||||||||
\(407\) | 53.0160 | 2.62790 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.09083 | 0.449512 | 0.224756 | − | 0.974415i | \(-0.427841\pi\) | ||||
0.224756 | + | 0.974415i | \(0.427841\pi\) | |||||||
\(410\) | 2.00768 | 0.0991523 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −19.5670 | −0.963998 | ||||||||
\(413\) | −32.2010 | −1.58451 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.0735 | −1.23081 | ||||||||
\(416\) | −0.889028 | −0.0435882 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −19.2075 | −0.939470 | ||||||||
\(419\) | 17.4245 | 0.851242 | 0.425621 | − | 0.904902i | \(-0.360056\pi\) | ||||
0.425621 | + | 0.904902i | \(0.360056\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.1905 | −0.594126 | −0.297063 | − | 0.954858i | \(-0.596007\pi\) | ||||
−0.297063 | + | 0.954858i | \(0.596007\pi\) | |||||||
\(422\) | −25.8982 | −1.26070 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.25633 | −0.0610128 | ||||||||
\(425\) | 0.694570 | 0.0336916 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.2080 | −0.735966 | ||||||||
\(428\) | 19.5947 | 0.947147 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.1368 | 0.633515 | ||||||||
\(431\) | −11.9045 | −0.573421 | −0.286711 | − | 0.958017i | \(-0.592562\pi\) | ||||
−0.286711 | + | 0.958017i | \(0.592562\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.49961 | 0.312351 | 0.156176 | − | 0.987729i | \(-0.450083\pi\) | ||||
0.156176 | + | 0.987729i | \(0.450083\pi\) | |||||||
\(434\) | −0.564953 | −0.0271186 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.2902 | 0.732269 | ||||||||
\(437\) | 9.39244 | 0.449301 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.5085 | −0.883363 | −0.441682 | − | 0.897172i | \(-0.645618\pi\) | ||||
−0.441682 | + | 0.897172i | \(0.645618\pi\) | |||||||
\(440\) | 8.36354 | 0.398716 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.229218 | 0.0109028 | ||||||||
\(443\) | −19.5275 | −0.927780 | −0.463890 | − | 0.885893i | \(-0.653547\pi\) | ||||
−0.463890 | + | 0.885893i | \(0.653547\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.5399 | 0.926280 | ||||||||
\(446\) | −25.9086 | −1.22681 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.35237 | 0.205630 | ||||||||
\(449\) | 41.5708 | 1.96185 | 0.980923 | − | 0.194396i | \(-0.0622745\pi\) | ||||
0.980923 | + | 0.194396i | \(0.0622745\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.28129 | 0.342862 | ||||||||
\(452\) | 3.27705 | 0.154140 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.7476 | −0.926798 | ||||||||
\(455\) | −5.87598 | −0.275470 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.8990 | −0.696944 | −0.348472 | − | 0.937319i | \(-0.613299\pi\) | ||||
−0.348472 | + | 0.937319i | \(0.613299\pi\) | |||||||
\(458\) | 22.8704 | 1.06866 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.08976 | −0.190686 | ||||||||
\(461\) | −17.6770 | −0.823298 | −0.411649 | − | 0.911342i | \(-0.635047\pi\) | ||||
−0.411649 | + | 0.911342i | \(0.635047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.16756 | −0.379579 | −0.189789 | − | 0.981825i | \(-0.560781\pi\) | ||||
−0.189789 | + | 0.981825i | \(0.560781\pi\) | |||||||
\(464\) | −1.61241 | −0.0748545 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.79710 | 0.0832492 | ||||||||
\(467\) | 21.4875 | 0.994324 | 0.497162 | − | 0.867658i | \(-0.334375\pi\) | ||||
0.497162 | + | 0.867658i | \(0.334375\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0534 | −0.695103 | ||||||||
\(470\) | 3.47395 | 0.160241 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.39850 | −0.340543 | ||||||||
\(473\) | 47.6436 | 2.19065 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.39511 | 0.431077 | ||||||||
\(476\) | −1.12217 | −0.0514347 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.88863 | −0.0863839 | ||||||||
\(479\) | 16.0082 | 0.731433 | 0.365716 | − | 0.930726i | \(-0.380824\pi\) | ||||
0.365716 | + | 0.930726i | \(0.380824\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.55797 | −0.390210 | ||||||||
\(482\) | 8.85516 | 0.403341 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.3322 | 0.878735 | ||||||||
\(485\) | −18.0384 | −0.819082 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.3252 | 0.694452 | 0.347226 | − | 0.937782i | \(-0.387124\pi\) | ||||
0.347226 | + | 0.937782i | \(0.387124\pi\) | |||||||
\(488\) | −3.49418 | −0.158174 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.1366 | 0.819330 | ||||||||
\(491\) | 8.53751 | 0.385293 | 0.192646 | − | 0.981268i | \(-0.438293\pi\) | ||||
0.192646 | + | 0.981268i | \(0.438293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.415729 | 0.0187235 | ||||||||
\(494\) | 3.10052 | 0.139499 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.129803 | −0.00582835 | ||||||||
\(497\) | 63.4273 | 2.84510 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.1643 | −0.455018 | −0.227509 | − | 0.973776i | \(-0.573058\pi\) | ||||
−0.227509 | + | 0.973776i | \(0.573058\pi\) | |||||||
\(500\) | −11.6838 | −0.522517 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.6848 | 0.789312 | ||||||||
\(503\) | 18.8216 | 0.839215 | 0.419608 | − | 0.907706i | \(-0.362168\pi\) | ||||
0.419608 | + | 0.907706i | \(0.362168\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.4500 | −0.465018 | ||||||||
\(506\) | −14.8324 | −0.659380 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.37983 | −0.105588 | ||||||||
\(509\) | −27.8511 | −1.23448 | −0.617239 | − | 0.786776i | \(-0.711749\pi\) | ||||
−0.617239 | + | 0.786776i | \(0.711749\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.1213 | −0.713165 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.8389 | −0.963272 | ||||||||
\(515\) | −29.7141 | −1.30936 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.5990 | 0.554104 | ||||||||
\(518\) | 41.8968 | 1.84084 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.35006 | −0.0592042 | ||||||||
\(521\) | 24.9165 | 1.09161 | 0.545805 | − | 0.837912i | \(-0.316224\pi\) | ||||
0.545805 | + | 0.837912i | \(0.316224\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.3882 | −1.63487 | −0.817436 | − | 0.576019i | \(-0.804605\pi\) | ||||
−0.817436 | + | 0.576019i | \(0.804605\pi\) | |||||||
\(524\) | −9.93489 | −0.434008 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.4275 | 0.672672 | ||||||||
\(527\) | 0.0334672 | 0.00145785 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7470 | −0.684652 | ||||||||
\(530\) | −1.90784 | −0.0828713 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.1791 | −0.658096 | ||||||||
\(533\) | −1.17536 | −0.0509106 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.7562 | 1.28647 | ||||||||
\(536\) | −3.45868 | −0.149392 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.22690 | 0.354687 | ||||||||
\(539\) | 65.7764 | 2.83319 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8136 | 0.507908 | 0.253954 | − | 0.967216i | \(-0.418269\pi\) | ||||
0.253954 | + | 0.967216i | \(0.418269\pi\) | |||||||
\(542\) | 9.80919 | 0.421341 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.257830 | −0.0110544 | ||||||||
\(545\) | 23.2195 | 0.994613 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.7249 | −0.843375 | −0.421688 | − | 0.906741i | \(-0.638562\pi\) | ||||
−0.421688 | + | 0.906741i | \(0.638562\pi\) | |||||||
\(548\) | 21.3464 | 0.911872 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.8366 | −0.632635 | ||||||||
\(551\) | 5.62336 | 0.239563 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.9471 | 1.74125 | ||||||||
\(554\) | 1.50186 | 0.0638078 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.04927 | −0.171727 | ||||||||
\(557\) | −14.2105 | −0.602120 | −0.301060 | − | 0.953605i | \(-0.597340\pi\) | ||||
−0.301060 | + | 0.953605i | \(0.597340\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.69074 | −0.325284 | ||||||||
\(560\) | 6.60944 | 0.279300 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.05893 | −0.255581 | ||||||||
\(563\) | −24.2364 | −1.02144 | −0.510721 | − | 0.859746i | \(-0.670622\pi\) | ||||
−0.510721 | + | 0.859746i | \(0.670622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.97648 | 0.209362 | ||||||||
\(566\) | 14.4994 | 0.609454 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.5730 | 0.611471 | ||||||||
\(569\) | 9.53601 | 0.399770 | 0.199885 | − | 0.979819i | \(-0.435943\pi\) | ||||
0.199885 | + | 0.979819i | \(0.435943\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.958077 | −0.0400943 | −0.0200471 | − | 0.999799i | \(-0.506382\pi\) | ||||
−0.0200471 | + | 0.999799i | \(0.506382\pi\) | |||||||
\(572\) | −4.89629 | −0.204724 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.75417 | 0.240174 | ||||||||
\(575\) | 7.25507 | 0.302557 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.3502 | 1.01371 | 0.506856 | − | 0.862031i | \(-0.330807\pi\) | ||||
0.506856 | + | 0.862031i | \(0.330807\pi\) | |||||||
\(578\) | −16.9335 | −0.704342 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.44858 | −0.101672 | ||||||||
\(581\) | −71.8625 | −2.98136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.91919 | −0.286564 | ||||||||
\(584\) | −3.70403 | −0.153274 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.49809 | 0.351053 | ||||||||
\(587\) | −40.5631 | −1.67422 | −0.837108 | − | 0.547037i | \(-0.815756\pi\) | ||||
−0.837108 | + | 0.547037i | \(0.815756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.452695 | 0.0186530 | ||||||||
\(590\) | −11.2352 | −0.462547 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.62620 | 0.395635 | ||||||||
\(593\) | 1.78740 | 0.0733996 | 0.0366998 | − | 0.999326i | \(-0.488315\pi\) | ||||
0.0366998 | + | 0.999326i | \(0.488315\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.70411 | −0.0698617 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.39428 | 0.0979094 | ||||||||
\(599\) | 22.9380 | 0.937222 | 0.468611 | − | 0.883405i | \(-0.344755\pi\) | ||||
0.468611 | + | 0.883405i | \(0.344755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.77077 | 0.316976 | 0.158488 | − | 0.987361i | \(-0.449338\pi\) | ||||
0.158488 | + | 0.987361i | \(0.449338\pi\) | |||||||
\(602\) | 37.6512 | 1.53455 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.65060 | −0.392677 | ||||||||
\(605\) | 29.3575 | 1.19355 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.31561 | 0.0533990 | 0.0266995 | − | 0.999644i | \(-0.491500\pi\) | ||||
0.0266995 | + | 0.999644i | \(0.491500\pi\) | |||||||
\(608\) | −3.48754 | −0.141438 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.30620 | −0.214842 | ||||||||
\(611\) | −2.03376 | −0.0822773 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.8574 | −1.85216 | −0.926082 | − | 0.377321i | \(-0.876845\pi\) | ||||
−0.926082 | + | 0.377321i | \(0.876845\pi\) | |||||||
\(614\) | −2.56218 | −0.103401 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 23.9705 | 0.965801 | ||||||||
\(617\) | −23.6340 | −0.951470 | −0.475735 | − | 0.879589i | \(-0.657818\pi\) | ||||
−0.475735 | + | 0.879589i | \(0.657818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.4446 | −1.02270 | −0.511352 | − | 0.859371i | \(-0.670855\pi\) | ||||
−0.511352 | + | 0.859371i | \(0.670855\pi\) | |||||||
\(620\) | −0.197117 | −0.00791642 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.29938 | 0.212486 | ||||||||
\(623\) | 56.0028 | 2.24370 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.27333 | −0.170933 | ||||||||
\(626\) | 27.8375 | 1.11261 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.5773 | −0.861027 | ||||||||
\(629\) | −2.48192 | −0.0989608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.4428 | −1.76924 | −0.884620 | − | 0.466313i | \(-0.845582\pi\) | ||||
−0.884620 | + | 0.466313i | \(0.845582\pi\) | |||||||
\(632\) | 9.40799 | 0.374230 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.2519 | 0.923451 | ||||||||
\(635\) | −3.61398 | −0.143416 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.6178 | −0.420692 | ||||||||
\(638\) | −8.88032 | −0.351575 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.51858 | 0.0600272 | ||||||||
\(641\) | −41.7490 | −1.64899 | −0.824493 | − | 0.565872i | \(-0.808540\pi\) | ||||
−0.824493 | + | 0.565872i | \(0.808540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.60191 | −0.339226 | −0.169613 | − | 0.985511i | \(-0.554252\pi\) | ||||
−0.169613 | + | 0.985511i | \(0.554252\pi\) | |||||||
\(644\) | −11.7216 | −0.461894 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.899192 | 0.0353783 | ||||||||
\(647\) | 1.39668 | 0.0549093 | 0.0274546 | − | 0.999623i | \(-0.491260\pi\) | ||||
0.0274546 | + | 0.999623i | \(0.491260\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.7470 | −1.59946 | ||||||||
\(650\) | 2.39496 | 0.0939380 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.4786 | 0.527865 | ||||||||
\(653\) | −6.77316 | −0.265054 | −0.132527 | − | 0.991179i | \(-0.542309\pi\) | ||||
−0.132527 | + | 0.991179i | \(0.542309\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.0869 | −0.589496 | ||||||||
\(656\) | 1.32208 | 0.0516184 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.95660 | 0.388149 | ||||||||
\(659\) | −19.0173 | −0.740809 | −0.370405 | − | 0.928871i | \(-0.620781\pi\) | ||||
−0.370405 | + | 0.928871i | \(0.620781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.7130 | −0.727851 | −0.363925 | − | 0.931428i | \(-0.618564\pi\) | ||||
−0.363925 | + | 0.931428i | \(0.618564\pi\) | |||||||
\(662\) | 17.5832 | 0.683389 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.5111 | −0.640756 | ||||||||
\(665\) | −23.0507 | −0.893867 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.34246 | 0.168141 | ||||||||
\(668\) | −1.95084 | −0.0754804 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.25229 | −0.202913 | ||||||||
\(671\) | −19.2441 | −0.742910 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.16966 | 0.353464 | 0.176732 | − | 0.984259i | \(-0.443447\pi\) | ||||
0.176732 | + | 0.984259i | \(0.443447\pi\) | |||||||
\(674\) | 3.34833 | 0.128973 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.2096 | −0.469601 | ||||||||
\(677\) | 28.5767 | 1.09829 | 0.549145 | − | 0.835727i | \(-0.314953\pi\) | ||||
0.549145 | + | 0.835727i | \(0.314953\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −51.6994 | −1.98404 | ||||||||
\(680\) | −0.391536 | −0.0150147 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.714888 | −0.0273745 | ||||||||
\(683\) | 0.346634 | 0.0132636 | 0.00663179 | − | 0.999978i | \(-0.497889\pi\) | ||||
0.00663179 | + | 0.999978i | \(0.497889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.4162 | 1.23856 | ||||||||
\(686\) | 21.5144 | 0.821423 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.65072 | 0.329806 | ||||||||
\(689\) | 1.11691 | 0.0425510 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.90123 | 0.300577 | 0.150289 | − | 0.988642i | \(-0.451980\pi\) | ||||
0.150289 | + | 0.988642i | \(0.451980\pi\) | |||||||
\(692\) | −0.332976 | −0.0126578 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.0699 | 0.382247 | ||||||||
\(695\) | −6.14915 | −0.233251 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.340871 | −0.0129114 | ||||||||
\(698\) | 17.0001 | 0.643464 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.7249 | −0.443159 | ||||||||
\(701\) | 44.4543 | 1.67901 | 0.839507 | − | 0.543349i | \(-0.182844\pi\) | ||||
0.839507 | + | 0.543349i | \(0.182844\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.5718 | −1.26618 | ||||||||
\(704\) | 5.50747 | 0.207570 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.55240 | 0.0960607 | ||||||||
\(707\) | −29.9505 | −1.12640 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0815 | 0.491287 | 0.245644 | − | 0.969360i | \(-0.421001\pi\) | ||||
0.245644 | + | 0.969360i | \(0.421001\pi\) | |||||||
\(710\) | 22.1304 | 0.830538 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.8672 | 0.482218 | ||||||||
\(713\) | 0.349579 | 0.0130918 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.43543 | −0.278069 | ||||||||
\(716\) | 8.14115 | 0.304249 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.4760 | −0.428282 | ||||||||
\(719\) | 16.1980 | 0.604085 | 0.302042 | − | 0.953295i | \(-0.402332\pi\) | ||||
0.302042 | + | 0.953295i | \(0.402332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −85.1629 | −3.17163 | ||||||||
\(722\) | −6.83706 | −0.254449 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.87618 | −0.292716 | ||||||||
\(725\) | 4.34369 | 0.161321 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.9835 | 1.59417 | 0.797086 | − | 0.603866i | \(-0.206374\pi\) | ||||
0.797086 | + | 0.603866i | \(0.206374\pi\) | |||||||
\(728\) | −3.86938 | −0.143409 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.62488 | −0.208186 | ||||||||
\(731\) | −2.23042 | −0.0824949 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.9049 | −0.439719 | −0.219859 | − | 0.975532i | \(-0.570560\pi\) | ||||
−0.219859 | + | 0.975532i | \(0.570560\pi\) | |||||||
\(734\) | −1.93896 | −0.0715685 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.69314 | −0.0992705 | ||||||||
\(737\) | −19.0485 | −0.701662 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.31009 | 0.268906 | 0.134453 | − | 0.990920i | \(-0.457072\pi\) | ||||
0.134453 | + | 0.990920i | \(0.457072\pi\) | |||||||
\(740\) | 14.6182 | 0.537375 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.46801 | −0.200737 | ||||||||
\(743\) | −19.0299 | −0.698138 | −0.349069 | − | 0.937097i | \(-0.613502\pi\) | ||||
−0.349069 | + | 0.937097i | \(0.613502\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.51858 | 0.0556366 | ||||||||
\(746\) | −15.1484 | −0.554621 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.41999 | −0.0519200 | ||||||||
\(749\) | 85.2836 | 3.11619 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.70708 | 0.354216 | 0.177108 | − | 0.984191i | \(-0.443326\pi\) | ||||
0.177108 | + | 0.984191i | \(0.443326\pi\) | |||||||
\(752\) | 2.28763 | 0.0834211 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.43348 | 0.0522043 | ||||||||
\(755\) | −14.6552 | −0.533358 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.8281 | −1.12047 | −0.560233 | − | 0.828335i | \(-0.689288\pi\) | ||||
−0.560233 | + | 0.828335i | \(0.689288\pi\) | |||||||
\(758\) | −19.9218 | −0.723594 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.29612 | −0.192110 | ||||||||
\(761\) | −35.9356 | −1.30266 | −0.651332 | − | 0.758793i | \(-0.725789\pi\) | ||||
−0.651332 | + | 0.758793i | \(0.725789\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 66.5488 | 2.40923 | ||||||||
\(764\) | −20.2488 | −0.732577 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.5336 | 1.24775 | ||||||||
\(767\) | 6.57747 | 0.237499 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.3229 | 1.85075 | 0.925376 | − | 0.379051i | \(-0.123750\pi\) | ||||
0.925376 | + | 0.379051i | \(0.123750\pi\) | |||||||
\(770\) | 36.4012 | 1.31181 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.2272 | −0.476058 | ||||||||
\(773\) | 42.7957 | 1.53925 | 0.769627 | − | 0.638493i | \(-0.220442\pi\) | ||||
0.769627 | + | 0.638493i | \(0.220442\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.349678 | 0.0125608 | ||||||||
\(776\) | −11.8784 | −0.426411 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.95485 | −0.213492 | ||||||||
\(779\) | −4.61079 | −0.165199 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 80.2605 | 2.87195 | ||||||||
\(782\) | 0.694373 | 0.0248307 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.9431 | 0.426541 | ||||||||
\(785\) | −32.7669 | −1.16950 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 54.5692 | 1.94518 | 0.972590 | − | 0.232526i | \(-0.0746990\pi\) | ||||
0.972590 | + | 0.232526i | \(0.0746990\pi\) | |||||||
\(788\) | 10.5773 | 0.376800 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.2868 | 0.508302 | ||||||||
\(791\) | 14.2630 | 0.507132 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.10643 | 0.110312 | ||||||||
\(794\) | −26.6111 | −0.944392 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.0343 | −0.497431 | ||||||||
\(797\) | 32.8397 | 1.16324 | 0.581621 | − | 0.813460i | \(-0.302419\pi\) | ||||
0.581621 | + | 0.813460i | \(0.302419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.589818 | −0.0208663 | ||||||||
\(800\) | −2.69391 | −0.0952440 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.2785 | −0.539501 | ||||||||
\(803\) | −20.3998 | −0.719894 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.8001 | −0.627373 | ||||||||
\(806\) | 0.115399 | 0.00406475 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.88141 | −0.242087 | ||||||||
\(809\) | 12.8541 | 0.451926 | 0.225963 | − | 0.974136i | \(-0.427447\pi\) | ||||
0.225963 | + | 0.974136i | \(0.427447\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.6585 | −0.620074 | −0.310037 | − | 0.950724i | \(-0.600341\pi\) | ||||
−0.310037 | + | 0.950724i | \(0.600341\pi\) | |||||||
\(812\) | −7.01783 | −0.246277 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 53.0160 | 1.85821 | ||||||||
\(815\) | 20.4684 | 0.716978 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.1697 | −1.05551 | ||||||||
\(818\) | 9.09083 | 0.317853 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.00768 | 0.0701113 | ||||||||
\(821\) | −12.1988 | −0.425740 | −0.212870 | − | 0.977081i | \(-0.568281\pi\) | ||||
−0.212870 | + | 0.977081i | \(0.568281\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.87571 | −0.344245 | −0.172123 | − | 0.985076i | \(-0.555063\pi\) | ||||
−0.172123 | + | 0.985076i | \(0.555063\pi\) | |||||||
\(824\) | −19.5670 | −0.681649 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −32.2010 | −1.12042 | ||||||||
\(827\) | −30.5112 | −1.06098 | −0.530489 | − | 0.847692i | \(-0.677992\pi\) | ||||
−0.530489 | + | 0.847692i | \(0.677992\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.7400 | −1.62335 | −0.811674 | − | 0.584111i | \(-0.801443\pi\) | ||||
−0.811674 | + | 0.584111i | \(0.801443\pi\) | |||||||
\(830\) | −25.0735 | −0.870314 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.889028 | −0.0308215 | ||||||||
\(833\) | −3.07930 | −0.106691 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.96252 | −0.102522 | ||||||||
\(836\) | −19.2075 | −0.664306 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.4245 | 0.601919 | ||||||||
\(839\) | −21.5539 | −0.744123 | −0.372062 | − | 0.928208i | \(-0.621349\pi\) | ||||
−0.372062 | + | 0.928208i | \(0.621349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4001 | −0.910349 | ||||||||
\(842\) | −12.1905 | −0.420111 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.8982 | −0.891452 | ||||||||
\(845\) | −18.5413 | −0.637841 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 84.1408 | 2.89111 | ||||||||
\(848\) | −1.25633 | −0.0431425 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.694570 | 0.0238236 | ||||||||
\(851\) | −25.9247 | −0.888688 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.8218 | −0.404770 | −0.202385 | − | 0.979306i | \(-0.564869\pi\) | ||||
−0.202385 | + | 0.979306i | \(0.564869\pi\) | |||||||
\(854\) | −15.2080 | −0.520406 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.5947 | 0.669734 | ||||||||
\(857\) | −15.6430 | −0.534355 | −0.267178 | − | 0.963647i | \(-0.586091\pi\) | ||||
−0.267178 | + | 0.963647i | \(0.586091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.9286 | 0.406998 | 0.203499 | − | 0.979075i | \(-0.434769\pi\) | ||||
0.203499 | + | 0.979075i | \(0.434769\pi\) | |||||||
\(860\) | 13.1368 | 0.447963 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.9045 | −0.405470 | ||||||||
\(863\) | 43.6027 | 1.48425 | 0.742127 | − | 0.670260i | \(-0.233817\pi\) | ||||
0.742127 | + | 0.670260i | \(0.233817\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.505651 | −0.0171927 | ||||||||
\(866\) | 6.49961 | 0.220866 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.564953 | −0.0191757 | ||||||||
\(869\) | 51.8142 | 1.75768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.07486 | 0.104188 | ||||||||
\(872\) | 15.2902 | 0.517793 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.39244 | 0.317704 | ||||||||
\(875\) | −50.8524 | −1.71912 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.3603 | −0.755053 | −0.377527 | − | 0.925999i | \(-0.623225\pi\) | ||||
−0.377527 | + | 0.925999i | \(0.623225\pi\) | |||||||
\(878\) | −18.5085 | −0.624632 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.36354 | 0.281935 | ||||||||
\(881\) | −30.2108 | −1.01783 | −0.508914 | − | 0.860817i | \(-0.669953\pi\) | ||||
−0.508914 | + | 0.860817i | \(0.669953\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.4746 | 1.32843 | 0.664213 | − | 0.747544i | \(-0.268767\pi\) | ||||
0.664213 | + | 0.747544i | \(0.268767\pi\) | |||||||
\(884\) | 0.229218 | 0.00770944 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.5275 | −0.656039 | ||||||||
\(887\) | −12.9706 | −0.435511 | −0.217755 | − | 0.976003i | \(-0.569874\pi\) | ||||
−0.217755 | + | 0.976003i | \(0.569874\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.3579 | −0.347394 | ||||||||
\(890\) | 19.5399 | 0.654979 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.9086 | −0.867483 | ||||||||
\(893\) | −7.97818 | −0.266980 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.3630 | 0.413250 | ||||||||
\(896\) | 4.35237 | 0.145403 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 41.5708 | 1.38723 | ||||||||
\(899\) | 0.209297 | 0.00698044 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.323919 | 0.0107913 | ||||||||
\(902\) | 7.28129 | 0.242440 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.27705 | 0.108993 | ||||||||
\(905\) | −11.9606 | −0.397585 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.49042 | −0.215511 | −0.107755 | − | 0.994177i | \(-0.534366\pi\) | ||||
−0.107755 | + | 0.994177i | \(0.534366\pi\) | |||||||
\(908\) | −19.7476 | −0.655345 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.87598 | −0.194787 | ||||||||
\(911\) | 13.1414 | 0.435394 | 0.217697 | − | 0.976016i | \(-0.430146\pi\) | ||||
0.217697 | + | 0.976016i | \(0.430146\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −90.9344 | −3.00949 | ||||||||
\(914\) | −14.8990 | −0.492814 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.8704 | 0.755658 | ||||||||
\(917\) | −43.2403 | −1.42792 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.8602 | −0.984997 | −0.492498 | − | 0.870313i | \(-0.663916\pi\) | ||||
−0.492498 | + | 0.870313i | \(0.663916\pi\) | |||||||
\(920\) | −4.08976 | −0.134835 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.6770 | −0.582160 | ||||||||
\(923\) | −12.9558 | −0.426447 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.9321 | −0.852642 | ||||||||
\(926\) | −8.16756 | −0.268403 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.61241 | −0.0529301 | ||||||||
\(929\) | 51.0056 | 1.67344 | 0.836721 | − | 0.547630i | \(-0.184470\pi\) | ||||
0.836721 | + | 0.547630i | \(0.184470\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.6522 | −1.36510 | ||||||||
\(932\) | 1.79710 | 0.0588661 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.4875 | 0.703093 | ||||||||
\(935\) | −2.15637 | −0.0705209 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.1681 | −1.41024 | −0.705120 | − | 0.709088i | \(-0.749107\pi\) | ||||
−0.705120 | + | 0.709088i | \(0.749107\pi\) | |||||||
\(938\) | −15.0534 | −0.491512 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.47395 | 0.113308 | ||||||||
\(941\) | −19.2726 | −0.628270 | −0.314135 | − | 0.949378i | \(-0.601714\pi\) | ||||
−0.314135 | + | 0.949378i | \(0.601714\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.56054 | −0.115947 | ||||||||
\(944\) | −7.39850 | −0.240801 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 47.6436 | 1.54903 | ||||||||
\(947\) | 8.94475 | 0.290665 | 0.145333 | − | 0.989383i | \(-0.453575\pi\) | ||||
0.145333 | + | 0.989383i | \(0.453575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.29299 | 0.106895 | ||||||||
\(950\) | 9.39511 | 0.304818 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.12217 | −0.0363698 | ||||||||
\(953\) | 21.0275 | 0.681146 | 0.340573 | − | 0.940218i | \(-0.389379\pi\) | ||||
0.340573 | + | 0.940218i | \(0.389379\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.7495 | −0.995032 | ||||||||
\(956\) | −1.88863 | −0.0610826 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.0082 | 0.517201 | ||||||||
\(959\) | 92.9074 | 3.00014 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9832 | −0.999456 | ||||||||
\(962\) | −8.55797 | −0.275920 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.85516 | 0.285205 | ||||||||
\(965\) | −20.0866 | −0.646611 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.1986 | −1.16407 | −0.582034 | − | 0.813164i | \(-0.697743\pi\) | ||||
−0.582034 | + | 0.813164i | \(0.697743\pi\) | |||||||
\(968\) | 19.3322 | 0.621360 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.0384 | −0.579178 | ||||||||
\(971\) | 47.3120 | 1.51831 | 0.759157 | − | 0.650908i | \(-0.225612\pi\) | ||||
0.759157 | + | 0.650908i | \(0.225612\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.6239 | −0.564998 | ||||||||
\(974\) | 15.3252 | 0.491052 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.49418 | −0.111846 | ||||||||
\(977\) | −38.5262 | −1.23256 | −0.616282 | − | 0.787526i | \(-0.711362\pi\) | ||||
−0.616282 | + | 0.787526i | \(0.711362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 70.8656 | 2.26487 | ||||||||
\(980\) | 18.1366 | 0.579354 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.53751 | 0.272443 | ||||||||
\(983\) | 38.6141 | 1.23160 | 0.615799 | − | 0.787904i | \(-0.288833\pi\) | ||||
0.615799 | + | 0.787904i | \(0.288833\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0625 | 0.511793 | ||||||||
\(986\) | 0.415729 | 0.0132395 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.10052 | 0.0986407 | ||||||||
\(989\) | −23.2976 | −0.740821 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.397942 | 0.0126410 | 0.00632052 | − | 0.999980i | \(-0.497988\pi\) | ||||
0.00632052 | + | 0.999980i | \(0.497988\pi\) | |||||||
\(992\) | −0.129803 | −0.00412126 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 63.4273 | 2.01179 | ||||||||
\(995\) | −21.3122 | −0.675642 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.2177 | 1.14703 | 0.573513 | − | 0.819196i | \(-0.305580\pi\) | ||||
0.573513 | + | 0.819196i | \(0.305580\pi\) | |||||||
\(998\) | −10.1643 | −0.321746 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.o.1.8 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.j.1.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.j.1.5 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.o.1.8 | yes | 12 | 1.1 | even | 1 | trivial |