Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + 678 x^{6} - 39390 x^{5} - 3280 x^{4} + 42456 x^{3} + 10816 x^{2} + \cdots - 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.290663\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.290663 | 0.129988 | 0.0649942 | − | 0.997886i | \(-0.479297\pi\) | ||||
0.0649942 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −3.15490 | −1.19244 | −0.596220 | − | 0.802821i | \(-0.703331\pi\) | ||||
−0.596220 | + | 0.802821i | \(0.703331\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.290663 | −0.0919156 | ||||||||
\(11\) | 5.57708 | 1.68155 | 0.840776 | − | 0.541383i | \(-0.182099\pi\) | ||||
0.840776 | + | 0.541383i | \(0.182099\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 3.15490 | 0.843182 | ||||||||
\(15\) | 0.290663 | 0.0750488 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.13717 | −0.518339 | −0.259169 | − | 0.965832i | \(-0.583449\pi\) | ||||
−0.259169 | + | 0.965832i | \(0.583449\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −5.05516 | −1.15973 | −0.579867 | − | 0.814711i | \(-0.696895\pi\) | ||||
−0.579867 | + | 0.814711i | \(0.696895\pi\) | |||||||
\(20\) | 0.290663 | 0.0649942 | ||||||||
\(21\) | −3.15490 | −0.688455 | ||||||||
\(22\) | −5.57708 | −1.18904 | ||||||||
\(23\) | 1.96903 | 0.410571 | 0.205286 | − | 0.978702i | \(-0.434188\pi\) | ||||
0.205286 | + | 0.978702i | \(0.434188\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.91552 | −0.983103 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.15490 | −0.596220 | ||||||||
\(29\) | −0.444744 | −0.0825870 | −0.0412935 | − | 0.999147i | \(-0.513148\pi\) | ||||
−0.0412935 | + | 0.999147i | \(0.513148\pi\) | |||||||
\(30\) | −0.290663 | −0.0530675 | ||||||||
\(31\) | 2.60815 | 0.468438 | 0.234219 | − | 0.972184i | \(-0.424747\pi\) | ||||
0.234219 | + | 0.972184i | \(0.424747\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.57708 | 0.970845 | ||||||||
\(34\) | 2.13717 | 0.366521 | ||||||||
\(35\) | −0.917011 | −0.155003 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.55167 | −1.24149 | −0.620743 | − | 0.784014i | \(-0.713169\pi\) | ||||
−0.620743 | + | 0.784014i | \(0.713169\pi\) | |||||||
\(38\) | 5.05516 | 0.820055 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −0.290663 | −0.0459578 | ||||||||
\(41\) | 8.43427 | 1.31721 | 0.658606 | − | 0.752488i | \(-0.271147\pi\) | ||||
0.658606 | + | 0.752488i | \(0.271147\pi\) | |||||||
\(42\) | 3.15490 | 0.486811 | ||||||||
\(43\) | −1.60263 | −0.244399 | −0.122199 | − | 0.992506i | \(-0.538995\pi\) | ||||
−0.122199 | + | 0.992506i | \(0.538995\pi\) | |||||||
\(44\) | 5.57708 | 0.840776 | ||||||||
\(45\) | 0.290663 | 0.0433294 | ||||||||
\(46\) | −1.96903 | −0.290318 | ||||||||
\(47\) | 9.45661 | 1.37939 | 0.689694 | − | 0.724101i | \(-0.257745\pi\) | ||||
0.689694 | + | 0.724101i | \(0.257745\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 2.95338 | 0.421911 | ||||||||
\(50\) | 4.91552 | 0.695159 | ||||||||
\(51\) | −2.13717 | −0.299263 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 13.2019 | 1.81342 | 0.906708 | − | 0.421758i | \(-0.138587\pi\) | ||||
0.906708 | + | 0.421758i | \(0.138587\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 1.62105 | 0.218582 | ||||||||
\(56\) | 3.15490 | 0.421591 | ||||||||
\(57\) | −5.05516 | −0.669572 | ||||||||
\(58\) | 0.444744 | 0.0583978 | ||||||||
\(59\) | −10.9582 | −1.42663 | −0.713317 | − | 0.700841i | \(-0.752808\pi\) | ||||
−0.713317 | + | 0.700841i | \(0.752808\pi\) | |||||||
\(60\) | 0.290663 | 0.0375244 | ||||||||
\(61\) | −0.462620 | −0.0592324 | −0.0296162 | − | 0.999561i | \(-0.509429\pi\) | ||||
−0.0296162 | + | 0.999561i | \(0.509429\pi\) | |||||||
\(62\) | −2.60815 | −0.331236 | ||||||||
\(63\) | −3.15490 | −0.397480 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.290663 | −0.0360523 | ||||||||
\(66\) | −5.57708 | −0.686491 | ||||||||
\(67\) | 13.6224 | 1.66424 | 0.832118 | − | 0.554599i | \(-0.187128\pi\) | ||||
0.832118 | + | 0.554599i | \(0.187128\pi\) | |||||||
\(68\) | −2.13717 | −0.259169 | ||||||||
\(69\) | 1.96903 | 0.237043 | ||||||||
\(70\) | 0.917011 | 0.109604 | ||||||||
\(71\) | −8.17349 | −0.970014 | −0.485007 | − | 0.874510i | \(-0.661183\pi\) | ||||
−0.485007 | + | 0.874510i | \(0.661183\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −15.1964 | −1.77860 | −0.889302 | − | 0.457320i | \(-0.848809\pi\) | ||||
−0.889302 | + | 0.457320i | \(0.848809\pi\) | |||||||
\(74\) | 7.55167 | 0.877863 | ||||||||
\(75\) | −4.91552 | −0.567595 | ||||||||
\(76\) | −5.05516 | −0.579867 | ||||||||
\(77\) | −17.5951 | −2.00515 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −14.5749 | −1.63980 | −0.819901 | − | 0.572505i | \(-0.805972\pi\) | ||||
−0.819901 | + | 0.572505i | \(0.805972\pi\) | |||||||
\(80\) | 0.290663 | 0.0324971 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.43427 | −0.931409 | ||||||||
\(83\) | −12.2435 | −1.34389 | −0.671947 | − | 0.740599i | \(-0.734542\pi\) | ||||
−0.671947 | + | 0.740599i | \(0.734542\pi\) | |||||||
\(84\) | −3.15490 | −0.344228 | ||||||||
\(85\) | −0.621194 | −0.0673780 | ||||||||
\(86\) | 1.60263 | 0.172816 | ||||||||
\(87\) | −0.444744 | −0.0476816 | ||||||||
\(88\) | −5.57708 | −0.594519 | ||||||||
\(89\) | −7.96168 | −0.843937 | −0.421968 | − | 0.906611i | \(-0.638661\pi\) | ||||
−0.421968 | + | 0.906611i | \(0.638661\pi\) | |||||||
\(90\) | −0.290663 | −0.0306385 | ||||||||
\(91\) | 3.15490 | 0.330723 | ||||||||
\(92\) | 1.96903 | 0.205286 | ||||||||
\(93\) | 2.60815 | 0.270453 | ||||||||
\(94\) | −9.45661 | −0.975374 | ||||||||
\(95\) | −1.46935 | −0.150752 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 17.9490 | 1.82244 | 0.911222 | − | 0.411916i | \(-0.135140\pi\) | ||||
0.911222 | + | 0.411916i | \(0.135140\pi\) | |||||||
\(98\) | −2.95338 | −0.298336 | ||||||||
\(99\) | 5.57708 | 0.560518 | ||||||||
\(100\) | −4.91552 | −0.491552 | ||||||||
\(101\) | −5.29560 | −0.526932 | −0.263466 | − | 0.964669i | \(-0.584866\pi\) | ||||
−0.263466 | + | 0.964669i | \(0.584866\pi\) | |||||||
\(102\) | 2.13717 | 0.211611 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −0.917011 | −0.0894911 | ||||||||
\(106\) | −13.2019 | −1.28228 | ||||||||
\(107\) | 1.03117 | 0.0996867 | 0.0498433 | − | 0.998757i | \(-0.484128\pi\) | ||||
0.0498433 | + | 0.998757i | \(0.484128\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −9.95257 | −0.953284 | −0.476642 | − | 0.879098i | \(-0.658146\pi\) | ||||
−0.476642 | + | 0.879098i | \(0.658146\pi\) | |||||||
\(110\) | −1.62105 | −0.154561 | ||||||||
\(111\) | −7.55167 | −0.716772 | ||||||||
\(112\) | −3.15490 | −0.298110 | ||||||||
\(113\) | −8.67226 | −0.815818 | −0.407909 | − | 0.913023i | \(-0.633742\pi\) | ||||
−0.407909 | + | 0.913023i | \(0.633742\pi\) | |||||||
\(114\) | 5.05516 | 0.473459 | ||||||||
\(115\) | 0.572324 | 0.0533695 | ||||||||
\(116\) | −0.444744 | −0.0412935 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 10.9582 | 1.00878 | ||||||||
\(119\) | 6.74254 | 0.618088 | ||||||||
\(120\) | −0.290663 | −0.0265338 | ||||||||
\(121\) | 20.1038 | 1.82762 | ||||||||
\(122\) | 0.462620 | 0.0418836 | ||||||||
\(123\) | 8.43427 | 0.760492 | ||||||||
\(124\) | 2.60815 | 0.234219 | ||||||||
\(125\) | −2.88207 | −0.257780 | ||||||||
\(126\) | 3.15490 | 0.281061 | ||||||||
\(127\) | −1.72805 | −0.153340 | −0.0766699 | − | 0.997057i | \(-0.524429\pi\) | ||||
−0.0766699 | + | 0.997057i | \(0.524429\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.60263 | −0.141104 | ||||||||
\(130\) | 0.290663 | 0.0254928 | ||||||||
\(131\) | −13.9485 | −1.21869 | −0.609343 | − | 0.792907i | \(-0.708567\pi\) | ||||
−0.609343 | + | 0.792907i | \(0.708567\pi\) | |||||||
\(132\) | 5.57708 | 0.485422 | ||||||||
\(133\) | 15.9485 | 1.38291 | ||||||||
\(134\) | −13.6224 | −1.17679 | ||||||||
\(135\) | 0.290663 | 0.0250163 | ||||||||
\(136\) | 2.13717 | 0.183260 | ||||||||
\(137\) | −7.85127 | −0.670779 | −0.335390 | − | 0.942079i | \(-0.608868\pi\) | ||||
−0.335390 | + | 0.942079i | \(0.608868\pi\) | |||||||
\(138\) | −1.96903 | −0.167615 | ||||||||
\(139\) | 15.4944 | 1.31422 | 0.657108 | − | 0.753796i | \(-0.271779\pi\) | ||||
0.657108 | + | 0.753796i | \(0.271779\pi\) | |||||||
\(140\) | −0.917011 | −0.0775016 | ||||||||
\(141\) | 9.45661 | 0.796390 | ||||||||
\(142\) | 8.17349 | 0.685904 | ||||||||
\(143\) | −5.57708 | −0.466379 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.129271 | −0.0107353 | ||||||||
\(146\) | 15.1964 | 1.25766 | ||||||||
\(147\) | 2.95338 | 0.243591 | ||||||||
\(148\) | −7.55167 | −0.620743 | ||||||||
\(149\) | −17.7998 | −1.45822 | −0.729109 | − | 0.684398i | \(-0.760065\pi\) | ||||
−0.729109 | + | 0.684398i | \(0.760065\pi\) | |||||||
\(150\) | 4.91552 | 0.401350 | ||||||||
\(151\) | −6.49777 | −0.528781 | −0.264391 | − | 0.964416i | \(-0.585171\pi\) | ||||
−0.264391 | + | 0.964416i | \(0.585171\pi\) | |||||||
\(152\) | 5.05516 | 0.410028 | ||||||||
\(153\) | −2.13717 | −0.172780 | ||||||||
\(154\) | 17.5951 | 1.41785 | ||||||||
\(155\) | 0.758093 | 0.0608915 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −11.9055 | −0.950165 | −0.475082 | − | 0.879941i | \(-0.657582\pi\) | ||||
−0.475082 | + | 0.879941i | \(0.657582\pi\) | |||||||
\(158\) | 14.5749 | 1.15952 | ||||||||
\(159\) | 13.2019 | 1.04698 | ||||||||
\(160\) | −0.290663 | −0.0229789 | ||||||||
\(161\) | −6.21209 | −0.489581 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 3.87572 | 0.303570 | 0.151785 | − | 0.988414i | \(-0.451498\pi\) | ||||
0.151785 | + | 0.988414i | \(0.451498\pi\) | |||||||
\(164\) | 8.43427 | 0.658606 | ||||||||
\(165\) | 1.62105 | 0.126199 | ||||||||
\(166\) | 12.2435 | 0.950277 | ||||||||
\(167\) | 4.93497 | 0.381880 | 0.190940 | − | 0.981602i | \(-0.438846\pi\) | ||||
0.190940 | + | 0.981602i | \(0.438846\pi\) | |||||||
\(168\) | 3.15490 | 0.243406 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.621194 | 0.0476434 | ||||||||
\(171\) | −5.05516 | −0.386578 | ||||||||
\(172\) | −1.60263 | −0.122199 | ||||||||
\(173\) | 24.0000 | 1.82469 | 0.912345 | − | 0.409422i | \(-0.134270\pi\) | ||||
0.912345 | + | 0.409422i | \(0.134270\pi\) | |||||||
\(174\) | 0.444744 | 0.0337160 | ||||||||
\(175\) | 15.5079 | 1.17229 | ||||||||
\(176\) | 5.57708 | 0.420388 | ||||||||
\(177\) | −10.9582 | −0.823668 | ||||||||
\(178\) | 7.96168 | 0.596753 | ||||||||
\(179\) | 18.1673 | 1.35789 | 0.678946 | − | 0.734189i | \(-0.262437\pi\) | ||||
0.678946 | + | 0.734189i | \(0.262437\pi\) | |||||||
\(180\) | 0.290663 | 0.0216647 | ||||||||
\(181\) | −7.40216 | −0.550198 | −0.275099 | − | 0.961416i | \(-0.588711\pi\) | ||||
−0.275099 | + | 0.961416i | \(0.588711\pi\) | |||||||
\(182\) | −3.15490 | −0.233857 | ||||||||
\(183\) | −0.462620 | −0.0341978 | ||||||||
\(184\) | −1.96903 | −0.145159 | ||||||||
\(185\) | −2.19499 | −0.161379 | ||||||||
\(186\) | −2.60815 | −0.191239 | ||||||||
\(187\) | −11.9191 | −0.871614 | ||||||||
\(188\) | 9.45661 | 0.689694 | ||||||||
\(189\) | −3.15490 | −0.229485 | ||||||||
\(190\) | 1.46935 | 0.106598 | ||||||||
\(191\) | 1.61795 | 0.117071 | 0.0585354 | − | 0.998285i | \(-0.481357\pi\) | ||||
0.0585354 | + | 0.998285i | \(0.481357\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −2.89904 | −0.208677 | −0.104339 | − | 0.994542i | \(-0.533273\pi\) | ||||
−0.104339 | + | 0.994542i | \(0.533273\pi\) | |||||||
\(194\) | −17.9490 | −1.28866 | ||||||||
\(195\) | −0.290663 | −0.0208148 | ||||||||
\(196\) | 2.95338 | 0.210956 | ||||||||
\(197\) | −5.32513 | −0.379400 | −0.189700 | − | 0.981842i | \(-0.560751\pi\) | ||||
−0.189700 | + | 0.981842i | \(0.560751\pi\) | |||||||
\(198\) | −5.57708 | −0.396346 | ||||||||
\(199\) | −15.2964 | −1.08433 | −0.542167 | − | 0.840271i | \(-0.682396\pi\) | ||||
−0.542167 | + | 0.840271i | \(0.682396\pi\) | |||||||
\(200\) | 4.91552 | 0.347579 | ||||||||
\(201\) | 13.6224 | 0.960847 | ||||||||
\(202\) | 5.29560 | 0.372597 | ||||||||
\(203\) | 1.40312 | 0.0984799 | ||||||||
\(204\) | −2.13717 | −0.149632 | ||||||||
\(205\) | 2.45153 | 0.171222 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 1.96903 | 0.136857 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −28.1930 | −1.95015 | ||||||||
\(210\) | 0.917011 | 0.0632798 | ||||||||
\(211\) | −5.18412 | −0.356890 | −0.178445 | − | 0.983950i | \(-0.557107\pi\) | ||||
−0.178445 | + | 0.983950i | \(0.557107\pi\) | |||||||
\(212\) | 13.2019 | 0.906708 | ||||||||
\(213\) | −8.17349 | −0.560038 | ||||||||
\(214\) | −1.03117 | −0.0704891 | ||||||||
\(215\) | −0.465824 | −0.0317690 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −8.22846 | −0.558584 | ||||||||
\(218\) | 9.95257 | 0.674073 | ||||||||
\(219\) | −15.1964 | −1.02688 | ||||||||
\(220\) | 1.62105 | 0.109291 | ||||||||
\(221\) | 2.13717 | 0.143761 | ||||||||
\(222\) | 7.55167 | 0.506835 | ||||||||
\(223\) | 18.0617 | 1.20950 | 0.604749 | − | 0.796416i | \(-0.293273\pi\) | ||||
0.604749 | + | 0.796416i | \(0.293273\pi\) | |||||||
\(224\) | 3.15490 | 0.210795 | ||||||||
\(225\) | −4.91552 | −0.327701 | ||||||||
\(226\) | 8.67226 | 0.576870 | ||||||||
\(227\) | 8.33048 | 0.552913 | 0.276457 | − | 0.961026i | \(-0.410840\pi\) | ||||
0.276457 | + | 0.961026i | \(0.410840\pi\) | |||||||
\(228\) | −5.05516 | −0.334786 | ||||||||
\(229\) | −1.04971 | −0.0693666 | −0.0346833 | − | 0.999398i | \(-0.511042\pi\) | ||||
−0.0346833 | + | 0.999398i | \(0.511042\pi\) | |||||||
\(230\) | −0.572324 | −0.0377379 | ||||||||
\(231\) | −17.5951 | −1.15767 | ||||||||
\(232\) | 0.444744 | 0.0291989 | ||||||||
\(233\) | −17.9285 | −1.17454 | −0.587268 | − | 0.809392i | \(-0.699797\pi\) | ||||
−0.587268 | + | 0.809392i | \(0.699797\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 2.74868 | 0.179304 | ||||||||
\(236\) | −10.9582 | −0.713317 | ||||||||
\(237\) | −14.5749 | −0.946740 | ||||||||
\(238\) | −6.74254 | −0.437054 | ||||||||
\(239\) | −28.4472 | −1.84010 | −0.920049 | − | 0.391803i | \(-0.871851\pi\) | ||||
−0.920049 | + | 0.391803i | \(0.871851\pi\) | |||||||
\(240\) | 0.290663 | 0.0187622 | ||||||||
\(241\) | −23.7447 | −1.52953 | −0.764766 | − | 0.644309i | \(-0.777145\pi\) | ||||
−0.764766 | + | 0.644309i | \(0.777145\pi\) | |||||||
\(242\) | −20.1038 | −1.29232 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.462620 | −0.0296162 | ||||||||
\(245\) | 0.858438 | 0.0548436 | ||||||||
\(246\) | −8.43427 | −0.537749 | ||||||||
\(247\) | 5.05516 | 0.321652 | ||||||||
\(248\) | −2.60815 | −0.165618 | ||||||||
\(249\) | −12.2435 | −0.775898 | ||||||||
\(250\) | 2.88207 | 0.182278 | ||||||||
\(251\) | 2.69531 | 0.170127 | 0.0850634 | − | 0.996376i | \(-0.472891\pi\) | ||||
0.0850634 | + | 0.996376i | \(0.472891\pi\) | |||||||
\(252\) | −3.15490 | −0.198740 | ||||||||
\(253\) | 10.9814 | 0.690397 | ||||||||
\(254\) | 1.72805 | 0.108428 | ||||||||
\(255\) | −0.621194 | −0.0389007 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.5475 | 1.84312 | 0.921562 | − | 0.388230i | \(-0.126913\pi\) | ||||
0.921562 | + | 0.388230i | \(0.126913\pi\) | |||||||
\(258\) | 1.60263 | 0.0997753 | ||||||||
\(259\) | 23.8247 | 1.48040 | ||||||||
\(260\) | −0.290663 | −0.0180261 | ||||||||
\(261\) | −0.444744 | −0.0275290 | ||||||||
\(262\) | 13.9485 | 0.861740 | ||||||||
\(263\) | −8.69529 | −0.536175 | −0.268087 | − | 0.963395i | \(-0.586392\pi\) | ||||
−0.268087 | + | 0.963395i | \(0.586392\pi\) | |||||||
\(264\) | −5.57708 | −0.343245 | ||||||||
\(265\) | 3.83729 | 0.235723 | ||||||||
\(266\) | −15.9485 | −0.977866 | ||||||||
\(267\) | −7.96168 | −0.487247 | ||||||||
\(268\) | 13.6224 | 0.832118 | ||||||||
\(269\) | 2.38908 | 0.145665 | 0.0728323 | − | 0.997344i | \(-0.476796\pi\) | ||||
0.0728323 | + | 0.997344i | \(0.476796\pi\) | |||||||
\(270\) | −0.290663 | −0.0176892 | ||||||||
\(271\) | −27.3531 | −1.66158 | −0.830790 | − | 0.556586i | \(-0.812111\pi\) | ||||
−0.830790 | + | 0.556586i | \(0.812111\pi\) | |||||||
\(272\) | −2.13717 | −0.129585 | ||||||||
\(273\) | 3.15490 | 0.190943 | ||||||||
\(274\) | 7.85127 | 0.474313 | ||||||||
\(275\) | −27.4142 | −1.65314 | ||||||||
\(276\) | 1.96903 | 0.118522 | ||||||||
\(277\) | 7.20989 | 0.433200 | 0.216600 | − | 0.976260i | \(-0.430503\pi\) | ||||
0.216600 | + | 0.976260i | \(0.430503\pi\) | |||||||
\(278\) | −15.4944 | −0.929292 | ||||||||
\(279\) | 2.60815 | 0.156146 | ||||||||
\(280\) | 0.917011 | 0.0548019 | ||||||||
\(281\) | 9.84747 | 0.587451 | 0.293725 | − | 0.955890i | \(-0.405105\pi\) | ||||
0.293725 | + | 0.955890i | \(0.405105\pi\) | |||||||
\(282\) | −9.45661 | −0.563133 | ||||||||
\(283\) | −11.7273 | −0.697116 | −0.348558 | − | 0.937287i | \(-0.613329\pi\) | ||||
−0.348558 | + | 0.937287i | \(0.613329\pi\) | |||||||
\(284\) | −8.17349 | −0.485007 | ||||||||
\(285\) | −1.46935 | −0.0870366 | ||||||||
\(286\) | 5.57708 | 0.329780 | ||||||||
\(287\) | −26.6092 | −1.57069 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −12.4325 | −0.731325 | ||||||||
\(290\) | 0.129271 | 0.00759103 | ||||||||
\(291\) | 17.9490 | 1.05219 | ||||||||
\(292\) | −15.1964 | −0.889302 | ||||||||
\(293\) | −23.3098 | −1.36177 | −0.680887 | − | 0.732388i | \(-0.738406\pi\) | ||||
−0.680887 | + | 0.732388i | \(0.738406\pi\) | |||||||
\(294\) | −2.95338 | −0.172245 | ||||||||
\(295\) | −3.18514 | −0.185446 | ||||||||
\(296\) | 7.55167 | 0.438932 | ||||||||
\(297\) | 5.57708 | 0.323615 | ||||||||
\(298\) | 17.7998 | 1.03112 | ||||||||
\(299\) | −1.96903 | −0.113872 | ||||||||
\(300\) | −4.91552 | −0.283797 | ||||||||
\(301\) | 5.05613 | 0.291430 | ||||||||
\(302\) | 6.49777 | 0.373905 | ||||||||
\(303\) | −5.29560 | −0.304224 | ||||||||
\(304\) | −5.05516 | −0.289933 | ||||||||
\(305\) | −0.134466 | −0.00769952 | ||||||||
\(306\) | 2.13717 | 0.122174 | ||||||||
\(307\) | 14.8883 | 0.849718 | 0.424859 | − | 0.905260i | \(-0.360324\pi\) | ||||
0.424859 | + | 0.905260i | \(0.360324\pi\) | |||||||
\(308\) | −17.5951 | −1.00257 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −0.758093 | −0.0430568 | ||||||||
\(311\) | 32.4727 | 1.84136 | 0.920679 | − | 0.390321i | \(-0.127636\pi\) | ||||
0.920679 | + | 0.390321i | \(0.127636\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 21.6485 | 1.22365 | 0.611824 | − | 0.790994i | \(-0.290436\pi\) | ||||
0.611824 | + | 0.790994i | \(0.290436\pi\) | |||||||
\(314\) | 11.9055 | 0.671868 | ||||||||
\(315\) | −0.917011 | −0.0516677 | ||||||||
\(316\) | −14.5749 | −0.819901 | ||||||||
\(317\) | −11.4084 | −0.640762 | −0.320381 | − | 0.947289i | \(-0.603811\pi\) | ||||
−0.320381 | + | 0.947289i | \(0.603811\pi\) | |||||||
\(318\) | −13.2019 | −0.740324 | ||||||||
\(319\) | −2.48037 | −0.138874 | ||||||||
\(320\) | 0.290663 | 0.0162485 | ||||||||
\(321\) | 1.03117 | 0.0575541 | ||||||||
\(322\) | 6.21209 | 0.346186 | ||||||||
\(323\) | 10.8037 | 0.601135 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.91552 | 0.272664 | ||||||||
\(326\) | −3.87572 | −0.214656 | ||||||||
\(327\) | −9.95257 | −0.550379 | ||||||||
\(328\) | −8.43427 | −0.465704 | ||||||||
\(329\) | −29.8346 | −1.64484 | ||||||||
\(330\) | −1.62105 | −0.0892358 | ||||||||
\(331\) | −15.1788 | −0.834300 | −0.417150 | − | 0.908838i | \(-0.636971\pi\) | ||||
−0.417150 | + | 0.908838i | \(0.636971\pi\) | |||||||
\(332\) | −12.2435 | −0.671947 | ||||||||
\(333\) | −7.55167 | −0.413829 | ||||||||
\(334\) | −4.93497 | −0.270030 | ||||||||
\(335\) | 3.95951 | 0.216331 | ||||||||
\(336\) | −3.15490 | −0.172114 | ||||||||
\(337\) | −2.69714 | −0.146923 | −0.0734614 | − | 0.997298i | \(-0.523405\pi\) | ||||
−0.0734614 | + | 0.997298i | \(0.523405\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −8.67226 | −0.471013 | ||||||||
\(340\) | −0.621194 | −0.0336890 | ||||||||
\(341\) | 14.5459 | 0.787703 | ||||||||
\(342\) | 5.05516 | 0.273352 | ||||||||
\(343\) | 12.7667 | 0.689336 | ||||||||
\(344\) | 1.60263 | 0.0864079 | ||||||||
\(345\) | 0.572324 | 0.0308129 | ||||||||
\(346\) | −24.0000 | −1.29025 | ||||||||
\(347\) | 10.1270 | 0.543647 | 0.271824 | − | 0.962347i | \(-0.412373\pi\) | ||||
0.271824 | + | 0.962347i | \(0.412373\pi\) | |||||||
\(348\) | −0.444744 | −0.0238408 | ||||||||
\(349\) | −17.6111 | −0.942698 | −0.471349 | − | 0.881947i | \(-0.656233\pi\) | ||||
−0.471349 | + | 0.881947i | \(0.656233\pi\) | |||||||
\(350\) | −15.5079 | −0.828935 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −5.57708 | −0.297259 | ||||||||
\(353\) | −7.45823 | −0.396961 | −0.198481 | − | 0.980105i | \(-0.563601\pi\) | ||||
−0.198481 | + | 0.980105i | \(0.563601\pi\) | |||||||
\(354\) | 10.9582 | 0.582421 | ||||||||
\(355\) | −2.37573 | −0.126091 | ||||||||
\(356\) | −7.96168 | −0.421968 | ||||||||
\(357\) | 6.74254 | 0.356853 | ||||||||
\(358\) | −18.1673 | −0.960174 | ||||||||
\(359\) | −0.109489 | −0.00577861 | −0.00288931 | − | 0.999996i | \(-0.500920\pi\) | ||||
−0.00288931 | + | 0.999996i | \(0.500920\pi\) | |||||||
\(360\) | −0.290663 | −0.0153193 | ||||||||
\(361\) | 6.55465 | 0.344982 | ||||||||
\(362\) | 7.40216 | 0.389049 | ||||||||
\(363\) | 20.1038 | 1.05518 | ||||||||
\(364\) | 3.15490 | 0.165362 | ||||||||
\(365\) | −4.41703 | −0.231198 | ||||||||
\(366\) | 0.462620 | 0.0241815 | ||||||||
\(367\) | −23.9306 | −1.24916 | −0.624582 | − | 0.780959i | \(-0.714731\pi\) | ||||
−0.624582 | + | 0.780959i | \(0.714731\pi\) | |||||||
\(368\) | 1.96903 | 0.102643 | ||||||||
\(369\) | 8.43427 | 0.439070 | ||||||||
\(370\) | 2.19499 | 0.114112 | ||||||||
\(371\) | −41.6506 | −2.16239 | ||||||||
\(372\) | 2.60815 | 0.135226 | ||||||||
\(373\) | 2.83392 | 0.146735 | 0.0733673 | − | 0.997305i | \(-0.476625\pi\) | ||||
0.0733673 | + | 0.997305i | \(0.476625\pi\) | |||||||
\(374\) | 11.9191 | 0.616324 | ||||||||
\(375\) | −2.88207 | −0.148830 | ||||||||
\(376\) | −9.45661 | −0.487687 | ||||||||
\(377\) | 0.444744 | 0.0229055 | ||||||||
\(378\) | 3.15490 | 0.162270 | ||||||||
\(379\) | 2.43968 | 0.125318 | 0.0626590 | − | 0.998035i | \(-0.480042\pi\) | ||||
0.0626590 | + | 0.998035i | \(0.480042\pi\) | |||||||
\(380\) | −1.46935 | −0.0753759 | ||||||||
\(381\) | −1.72805 | −0.0885308 | ||||||||
\(382\) | −1.61795 | −0.0827815 | ||||||||
\(383\) | 7.68470 | 0.392670 | 0.196335 | − | 0.980537i | \(-0.437096\pi\) | ||||
0.196335 | + | 0.980537i | \(0.437096\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −5.11424 | −0.260646 | ||||||||
\(386\) | 2.89904 | 0.147557 | ||||||||
\(387\) | −1.60263 | −0.0814662 | ||||||||
\(388\) | 17.9490 | 0.911222 | ||||||||
\(389\) | −15.0757 | −0.764370 | −0.382185 | − | 0.924086i | \(-0.624828\pi\) | ||||
−0.382185 | + | 0.924086i | \(0.624828\pi\) | |||||||
\(390\) | 0.290663 | 0.0147183 | ||||||||
\(391\) | −4.20814 | −0.212815 | ||||||||
\(392\) | −2.95338 | −0.149168 | ||||||||
\(393\) | −13.9485 | −0.703608 | ||||||||
\(394\) | 5.32513 | 0.268276 | ||||||||
\(395\) | −4.23638 | −0.213155 | ||||||||
\(396\) | 5.57708 | 0.280259 | ||||||||
\(397\) | −19.8678 | −0.997138 | −0.498569 | − | 0.866850i | \(-0.666141\pi\) | ||||
−0.498569 | + | 0.866850i | \(0.666141\pi\) | |||||||
\(398\) | 15.2964 | 0.766740 | ||||||||
\(399\) | 15.9485 | 0.798424 | ||||||||
\(400\) | −4.91552 | −0.245776 | ||||||||
\(401\) | 8.07833 | 0.403412 | 0.201706 | − | 0.979446i | \(-0.435351\pi\) | ||||
0.201706 | + | 0.979446i | \(0.435351\pi\) | |||||||
\(402\) | −13.6224 | −0.679421 | ||||||||
\(403\) | −2.60815 | −0.129921 | ||||||||
\(404\) | −5.29560 | −0.263466 | ||||||||
\(405\) | 0.290663 | 0.0144431 | ||||||||
\(406\) | −1.40312 | −0.0696358 | ||||||||
\(407\) | −42.1162 | −2.08762 | ||||||||
\(408\) | 2.13717 | 0.105805 | ||||||||
\(409\) | −1.67295 | −0.0827219 | −0.0413609 | − | 0.999144i | \(-0.513169\pi\) | ||||
−0.0413609 | + | 0.999144i | \(0.513169\pi\) | |||||||
\(410\) | −2.45153 | −0.121072 | ||||||||
\(411\) | −7.85127 | −0.387275 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 34.5720 | 1.70118 | ||||||||
\(414\) | −1.96903 | −0.0967725 | ||||||||
\(415\) | −3.55872 | −0.174691 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 15.4944 | 0.758764 | ||||||||
\(418\) | 28.1930 | 1.37897 | ||||||||
\(419\) | −29.6169 | −1.44688 | −0.723439 | − | 0.690388i | \(-0.757440\pi\) | ||||
−0.723439 | + | 0.690388i | \(0.757440\pi\) | |||||||
\(420\) | −0.917011 | −0.0447456 | ||||||||
\(421\) | 21.6503 | 1.05517 | 0.527586 | − | 0.849502i | \(-0.323097\pi\) | ||||
0.527586 | + | 0.849502i | \(0.323097\pi\) | |||||||
\(422\) | 5.18412 | 0.252359 | ||||||||
\(423\) | 9.45661 | 0.459796 | ||||||||
\(424\) | −13.2019 | −0.641140 | ||||||||
\(425\) | 10.5053 | 0.509580 | ||||||||
\(426\) | 8.17349 | 0.396007 | ||||||||
\(427\) | 1.45952 | 0.0706310 | ||||||||
\(428\) | 1.03117 | 0.0498433 | ||||||||
\(429\) | −5.57708 | −0.269264 | ||||||||
\(430\) | 0.465824 | 0.0224640 | ||||||||
\(431\) | −12.8563 | −0.619267 | −0.309633 | − | 0.950856i | \(-0.600206\pi\) | ||||
−0.309633 | + | 0.950856i | \(0.600206\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 5.64923 | 0.271485 | 0.135742 | − | 0.990744i | \(-0.456658\pi\) | ||||
0.135742 | + | 0.990744i | \(0.456658\pi\) | |||||||
\(434\) | 8.22846 | 0.394978 | ||||||||
\(435\) | −0.129271 | −0.00619805 | ||||||||
\(436\) | −9.95257 | −0.476642 | ||||||||
\(437\) | −9.95376 | −0.476153 | ||||||||
\(438\) | 15.1964 | 0.726112 | ||||||||
\(439\) | −3.24402 | −0.154829 | −0.0774144 | − | 0.996999i | \(-0.524666\pi\) | ||||
−0.0774144 | + | 0.996999i | \(0.524666\pi\) | |||||||
\(440\) | −1.62105 | −0.0772805 | ||||||||
\(441\) | 2.95338 | 0.140637 | ||||||||
\(442\) | −2.13717 | −0.101655 | ||||||||
\(443\) | 3.93720 | 0.187062 | 0.0935309 | − | 0.995616i | \(-0.470185\pi\) | ||||
0.0935309 | + | 0.995616i | \(0.470185\pi\) | |||||||
\(444\) | −7.55167 | −0.358386 | ||||||||
\(445\) | −2.31416 | −0.109702 | ||||||||
\(446\) | −18.0617 | −0.855245 | ||||||||
\(447\) | −17.7998 | −0.841902 | ||||||||
\(448\) | −3.15490 | −0.149055 | ||||||||
\(449\) | −32.6440 | −1.54056 | −0.770282 | − | 0.637703i | \(-0.779885\pi\) | ||||
−0.770282 | + | 0.637703i | \(0.779885\pi\) | |||||||
\(450\) | 4.91552 | 0.231720 | ||||||||
\(451\) | 47.0386 | 2.21496 | ||||||||
\(452\) | −8.67226 | −0.407909 | ||||||||
\(453\) | −6.49777 | −0.305292 | ||||||||
\(454\) | −8.33048 | −0.390969 | ||||||||
\(455\) | 0.917011 | 0.0429902 | ||||||||
\(456\) | 5.05516 | 0.236730 | ||||||||
\(457\) | 30.0476 | 1.40557 | 0.702784 | − | 0.711403i | \(-0.251940\pi\) | ||||
0.702784 | + | 0.711403i | \(0.251940\pi\) | |||||||
\(458\) | 1.04971 | 0.0490496 | ||||||||
\(459\) | −2.13717 | −0.0997543 | ||||||||
\(460\) | 0.572324 | 0.0266847 | ||||||||
\(461\) | −28.1535 | −1.31124 | −0.655621 | − | 0.755090i | \(-0.727593\pi\) | ||||
−0.655621 | + | 0.755090i | \(0.727593\pi\) | |||||||
\(462\) | 17.5951 | 0.818599 | ||||||||
\(463\) | −28.2939 | −1.31493 | −0.657464 | − | 0.753486i | \(-0.728371\pi\) | ||||
−0.657464 | + | 0.753486i | \(0.728371\pi\) | |||||||
\(464\) | −0.444744 | −0.0206467 | ||||||||
\(465\) | 0.758093 | 0.0351557 | ||||||||
\(466\) | 17.9285 | 0.830523 | ||||||||
\(467\) | −17.8245 | −0.824821 | −0.412410 | − | 0.910998i | \(-0.635313\pi\) | ||||
−0.412410 | + | 0.910998i | \(0.635313\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −42.9771 | −1.98450 | ||||||||
\(470\) | −2.74868 | −0.126787 | ||||||||
\(471\) | −11.9055 | −0.548578 | ||||||||
\(472\) | 10.9582 | 0.504392 | ||||||||
\(473\) | −8.93798 | −0.410969 | ||||||||
\(474\) | 14.5749 | 0.669446 | ||||||||
\(475\) | 24.8487 | 1.14014 | ||||||||
\(476\) | 6.74254 | 0.309044 | ||||||||
\(477\) | 13.2019 | 0.604472 | ||||||||
\(478\) | 28.4472 | 1.30115 | ||||||||
\(479\) | −3.47708 | −0.158872 | −0.0794359 | − | 0.996840i | \(-0.525312\pi\) | ||||
−0.0794359 | + | 0.996840i | \(0.525312\pi\) | |||||||
\(480\) | −0.290663 | −0.0132669 | ||||||||
\(481\) | 7.55167 | 0.344326 | ||||||||
\(482\) | 23.7447 | 1.08154 | ||||||||
\(483\) | −6.21209 | −0.282660 | ||||||||
\(484\) | 20.1038 | 0.913809 | ||||||||
\(485\) | 5.21710 | 0.236896 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −11.5461 | −0.523205 | −0.261602 | − | 0.965176i | \(-0.584251\pi\) | ||||
−0.261602 | + | 0.965176i | \(0.584251\pi\) | |||||||
\(488\) | 0.462620 | 0.0209418 | ||||||||
\(489\) | 3.87572 | 0.175266 | ||||||||
\(490\) | −0.858438 | −0.0387803 | ||||||||
\(491\) | −7.19621 | −0.324761 | −0.162380 | − | 0.986728i | \(-0.551917\pi\) | ||||
−0.162380 | + | 0.986728i | \(0.551917\pi\) | |||||||
\(492\) | 8.43427 | 0.380246 | ||||||||
\(493\) | 0.950492 | 0.0428080 | ||||||||
\(494\) | −5.05516 | −0.227442 | ||||||||
\(495\) | 1.62105 | 0.0728607 | ||||||||
\(496\) | 2.60815 | 0.117110 | ||||||||
\(497\) | 25.7865 | 1.15668 | ||||||||
\(498\) | 12.2435 | 0.548643 | ||||||||
\(499\) | −6.96624 | −0.311852 | −0.155926 | − | 0.987769i | \(-0.549836\pi\) | ||||
−0.155926 | + | 0.987769i | \(0.549836\pi\) | |||||||
\(500\) | −2.88207 | −0.128890 | ||||||||
\(501\) | 4.93497 | 0.220478 | ||||||||
\(502\) | −2.69531 | −0.120298 | ||||||||
\(503\) | −14.9610 | −0.667078 | −0.333539 | − | 0.942736i | \(-0.608243\pi\) | ||||
−0.333539 | + | 0.942736i | \(0.608243\pi\) | |||||||
\(504\) | 3.15490 | 0.140530 | ||||||||
\(505\) | −1.53923 | −0.0684950 | ||||||||
\(506\) | −10.9814 | −0.488184 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −1.72805 | −0.0766699 | ||||||||
\(509\) | 4.23418 | 0.187677 | 0.0938384 | − | 0.995587i | \(-0.470086\pi\) | ||||
0.0938384 | + | 0.995587i | \(0.470086\pi\) | |||||||
\(510\) | 0.621194 | 0.0275070 | ||||||||
\(511\) | 47.9431 | 2.12088 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.05516 | −0.223191 | ||||||||
\(514\) | −29.5475 | −1.30329 | ||||||||
\(515\) | 0.290663 | 0.0128081 | ||||||||
\(516\) | −1.60263 | −0.0705518 | ||||||||
\(517\) | 52.7402 | 2.31951 | ||||||||
\(518\) | −23.8247 | −1.04680 | ||||||||
\(519\) | 24.0000 | 1.05349 | ||||||||
\(520\) | 0.290663 | 0.0127464 | ||||||||
\(521\) | −30.4410 | −1.33364 | −0.666822 | − | 0.745217i | \(-0.732346\pi\) | ||||
−0.666822 | + | 0.745217i | \(0.732346\pi\) | |||||||
\(522\) | 0.444744 | 0.0194659 | ||||||||
\(523\) | 4.86408 | 0.212691 | 0.106346 | − | 0.994329i | \(-0.466085\pi\) | ||||
0.106346 | + | 0.994329i | \(0.466085\pi\) | |||||||
\(524\) | −13.9485 | −0.609343 | ||||||||
\(525\) | 15.5079 | 0.676822 | ||||||||
\(526\) | 8.69529 | 0.379133 | ||||||||
\(527\) | −5.57405 | −0.242810 | ||||||||
\(528\) | 5.57708 | 0.242711 | ||||||||
\(529\) | −19.1229 | −0.831431 | ||||||||
\(530\) | −3.83729 | −0.166681 | ||||||||
\(531\) | −10.9582 | −0.475545 | ||||||||
\(532\) | 15.9485 | 0.691456 | ||||||||
\(533\) | −8.43427 | −0.365329 | ||||||||
\(534\) | 7.96168 | 0.344536 | ||||||||
\(535\) | 0.299722 | 0.0129581 | ||||||||
\(536\) | −13.6224 | −0.588396 | ||||||||
\(537\) | 18.1673 | 0.783979 | ||||||||
\(538\) | −2.38908 | −0.103000 | ||||||||
\(539\) | 16.4712 | 0.709466 | ||||||||
\(540\) | 0.290663 | 0.0125081 | ||||||||
\(541\) | −11.0402 | −0.474656 | −0.237328 | − | 0.971430i | \(-0.576272\pi\) | ||||
−0.237328 | + | 0.971430i | \(0.576272\pi\) | |||||||
\(542\) | 27.3531 | 1.17491 | ||||||||
\(543\) | −7.40216 | −0.317657 | ||||||||
\(544\) | 2.13717 | 0.0916302 | ||||||||
\(545\) | −2.89284 | −0.123916 | ||||||||
\(546\) | −3.15490 | −0.135017 | ||||||||
\(547\) | 14.7243 | 0.629564 | 0.314782 | − | 0.949164i | \(-0.398069\pi\) | ||||
0.314782 | + | 0.949164i | \(0.398069\pi\) | |||||||
\(548\) | −7.85127 | −0.335390 | ||||||||
\(549\) | −0.462620 | −0.0197441 | ||||||||
\(550\) | 27.4142 | 1.16895 | ||||||||
\(551\) | 2.24825 | 0.0957789 | ||||||||
\(552\) | −1.96903 | −0.0838075 | ||||||||
\(553\) | 45.9823 | 1.95536 | ||||||||
\(554\) | −7.20989 | −0.306319 | ||||||||
\(555\) | −2.19499 | −0.0931721 | ||||||||
\(556\) | 15.4944 | 0.657108 | ||||||||
\(557\) | −20.3026 | −0.860251 | −0.430125 | − | 0.902769i | \(-0.641531\pi\) | ||||
−0.430125 | + | 0.902769i | \(0.641531\pi\) | |||||||
\(558\) | −2.60815 | −0.110412 | ||||||||
\(559\) | 1.60263 | 0.0677840 | ||||||||
\(560\) | −0.917011 | −0.0387508 | ||||||||
\(561\) | −11.9191 | −0.503227 | ||||||||
\(562\) | −9.84747 | −0.415390 | ||||||||
\(563\) | 5.06971 | 0.213663 | 0.106831 | − | 0.994277i | \(-0.465929\pi\) | ||||
0.106831 | + | 0.994277i | \(0.465929\pi\) | |||||||
\(564\) | 9.45661 | 0.398195 | ||||||||
\(565\) | −2.52070 | −0.106047 | ||||||||
\(566\) | 11.7273 | 0.492936 | ||||||||
\(567\) | −3.15490 | −0.132493 | ||||||||
\(568\) | 8.17349 | 0.342952 | ||||||||
\(569\) | 12.9588 | 0.543262 | 0.271631 | − | 0.962401i | \(-0.412437\pi\) | ||||
0.271631 | + | 0.962401i | \(0.412437\pi\) | |||||||
\(570\) | 1.46935 | 0.0615442 | ||||||||
\(571\) | 3.92266 | 0.164158 | 0.0820791 | − | 0.996626i | \(-0.473844\pi\) | ||||
0.0820791 | + | 0.996626i | \(0.473844\pi\) | |||||||
\(572\) | −5.57708 | −0.233189 | ||||||||
\(573\) | 1.61795 | 0.0675908 | ||||||||
\(574\) | 26.6092 | 1.11065 | ||||||||
\(575\) | −9.67880 | −0.403634 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −34.3669 | −1.43071 | −0.715356 | − | 0.698760i | \(-0.753735\pi\) | ||||
−0.715356 | + | 0.698760i | \(0.753735\pi\) | |||||||
\(578\) | 12.4325 | 0.517125 | ||||||||
\(579\) | −2.89904 | −0.120480 | ||||||||
\(580\) | −0.129271 | −0.00536767 | ||||||||
\(581\) | 38.6269 | 1.60251 | ||||||||
\(582\) | −17.9490 | −0.744009 | ||||||||
\(583\) | 73.6279 | 3.04936 | ||||||||
\(584\) | 15.1964 | 0.628831 | ||||||||
\(585\) | −0.290663 | −0.0120174 | ||||||||
\(586\) | 23.3098 | 0.962920 | ||||||||
\(587\) | −33.4509 | −1.38066 | −0.690332 | − | 0.723492i | \(-0.742536\pi\) | ||||
−0.690332 | + | 0.723492i | \(0.742536\pi\) | |||||||
\(588\) | 2.95338 | 0.121795 | ||||||||
\(589\) | −13.1846 | −0.543263 | ||||||||
\(590\) | 3.18514 | 0.131130 | ||||||||
\(591\) | −5.32513 | −0.219047 | ||||||||
\(592\) | −7.55167 | −0.310372 | ||||||||
\(593\) | 16.7073 | 0.686085 | 0.343043 | − | 0.939320i | \(-0.388542\pi\) | ||||
0.343043 | + | 0.939320i | \(0.388542\pi\) | |||||||
\(594\) | −5.57708 | −0.228830 | ||||||||
\(595\) | 1.95981 | 0.0803442 | ||||||||
\(596\) | −17.7998 | −0.729109 | ||||||||
\(597\) | −15.2964 | −0.626041 | ||||||||
\(598\) | 1.96903 | 0.0805196 | ||||||||
\(599\) | 0.588732 | 0.0240549 | 0.0120275 | − | 0.999928i | \(-0.496171\pi\) | ||||
0.0120275 | + | 0.999928i | \(0.496171\pi\) | |||||||
\(600\) | 4.91552 | 0.200675 | ||||||||
\(601\) | 13.9648 | 0.569636 | 0.284818 | − | 0.958582i | \(-0.408067\pi\) | ||||
0.284818 | + | 0.958582i | \(0.408067\pi\) | |||||||
\(602\) | −5.05613 | −0.206072 | ||||||||
\(603\) | 13.6224 | 0.554745 | ||||||||
\(604\) | −6.49777 | −0.264391 | ||||||||
\(605\) | 5.84343 | 0.237569 | ||||||||
\(606\) | 5.29560 | 0.215119 | ||||||||
\(607\) | 19.5716 | 0.794388 | 0.397194 | − | 0.917735i | \(-0.369984\pi\) | ||||
0.397194 | + | 0.917735i | \(0.369984\pi\) | |||||||
\(608\) | 5.05516 | 0.205014 | ||||||||
\(609\) | 1.40312 | 0.0568574 | ||||||||
\(610\) | 0.134466 | 0.00544438 | ||||||||
\(611\) | −9.45661 | −0.382573 | ||||||||
\(612\) | −2.13717 | −0.0863898 | ||||||||
\(613\) | 19.0031 | 0.767529 | 0.383764 | − | 0.923431i | \(-0.374627\pi\) | ||||
0.383764 | + | 0.923431i | \(0.374627\pi\) | |||||||
\(614\) | −14.8883 | −0.600841 | ||||||||
\(615\) | 2.45153 | 0.0988551 | ||||||||
\(616\) | 17.5951 | 0.708927 | ||||||||
\(617\) | 6.22176 | 0.250479 | 0.125239 | − | 0.992127i | \(-0.460030\pi\) | ||||
0.125239 | + | 0.992127i | \(0.460030\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 25.4935 | 1.02467 | 0.512335 | − | 0.858786i | \(-0.328781\pi\) | ||||
0.512335 | + | 0.858786i | \(0.328781\pi\) | |||||||
\(620\) | 0.758093 | 0.0304457 | ||||||||
\(621\) | 1.96903 | 0.0790145 | ||||||||
\(622\) | −32.4727 | −1.30204 | ||||||||
\(623\) | 25.1183 | 1.00634 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 23.7399 | 0.949595 | ||||||||
\(626\) | −21.6485 | −0.865250 | ||||||||
\(627\) | −28.1930 | −1.12592 | ||||||||
\(628\) | −11.9055 | −0.475082 | ||||||||
\(629\) | 16.1392 | 0.643511 | ||||||||
\(630\) | 0.917011 | 0.0365346 | ||||||||
\(631\) | 11.1486 | 0.443819 | 0.221910 | − | 0.975067i | \(-0.428771\pi\) | ||||
0.221910 | + | 0.975067i | \(0.428771\pi\) | |||||||
\(632\) | 14.5749 | 0.579758 | ||||||||
\(633\) | −5.18412 | −0.206050 | ||||||||
\(634\) | 11.4084 | 0.453087 | ||||||||
\(635\) | −0.502280 | −0.0199324 | ||||||||
\(636\) | 13.2019 | 0.523488 | ||||||||
\(637\) | −2.95338 | −0.117017 | ||||||||
\(638\) | 2.48037 | 0.0981990 | ||||||||
\(639\) | −8.17349 | −0.323338 | ||||||||
\(640\) | −0.290663 | −0.0114895 | ||||||||
\(641\) | 10.9535 | 0.432636 | 0.216318 | − | 0.976323i | \(-0.430595\pi\) | ||||
0.216318 | + | 0.976323i | \(0.430595\pi\) | |||||||
\(642\) | −1.03117 | −0.0406969 | ||||||||
\(643\) | −41.6162 | −1.64118 | −0.820592 | − | 0.571514i | \(-0.806356\pi\) | ||||
−0.820592 | + | 0.571514i | \(0.806356\pi\) | |||||||
\(644\) | −6.21209 | −0.244791 | ||||||||
\(645\) | −0.465824 | −0.0183418 | ||||||||
\(646\) | −10.8037 | −0.425067 | ||||||||
\(647\) | −32.9026 | −1.29354 | −0.646768 | − | 0.762687i | \(-0.723880\pi\) | ||||
−0.646768 | + | 0.762687i | \(0.723880\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −61.1147 | −2.39896 | ||||||||
\(650\) | −4.91552 | −0.192802 | ||||||||
\(651\) | −8.22846 | −0.322499 | ||||||||
\(652\) | 3.87572 | 0.151785 | ||||||||
\(653\) | 10.7035 | 0.418861 | 0.209430 | − | 0.977824i | \(-0.432839\pi\) | ||||
0.209430 | + | 0.977824i | \(0.432839\pi\) | |||||||
\(654\) | 9.95257 | 0.389176 | ||||||||
\(655\) | −4.05431 | −0.158415 | ||||||||
\(656\) | 8.43427 | 0.329303 | ||||||||
\(657\) | −15.1964 | −0.592868 | ||||||||
\(658\) | 29.8346 | 1.16307 | ||||||||
\(659\) | −8.40362 | −0.327359 | −0.163679 | − | 0.986514i | \(-0.552336\pi\) | ||||
−0.163679 | + | 0.986514i | \(0.552336\pi\) | |||||||
\(660\) | 1.62105 | 0.0630993 | ||||||||
\(661\) | 14.7129 | 0.572267 | 0.286133 | − | 0.958190i | \(-0.407630\pi\) | ||||
0.286133 | + | 0.958190i | \(0.407630\pi\) | |||||||
\(662\) | 15.1788 | 0.589939 | ||||||||
\(663\) | 2.13717 | 0.0830006 | ||||||||
\(664\) | 12.2435 | 0.475138 | ||||||||
\(665\) | 4.63564 | 0.179762 | ||||||||
\(666\) | 7.55167 | 0.292621 | ||||||||
\(667\) | −0.875715 | −0.0339078 | ||||||||
\(668\) | 4.93497 | 0.190940 | ||||||||
\(669\) | 18.0617 | 0.698304 | ||||||||
\(670\) | −3.95951 | −0.152969 | ||||||||
\(671\) | −2.58007 | −0.0996024 | ||||||||
\(672\) | 3.15490 | 0.121703 | ||||||||
\(673\) | 25.7263 | 0.991676 | 0.495838 | − | 0.868415i | \(-0.334861\pi\) | ||||
0.495838 | + | 0.868415i | \(0.334861\pi\) | |||||||
\(674\) | 2.69714 | 0.103890 | ||||||||
\(675\) | −4.91552 | −0.189198 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 39.5284 | 1.51920 | 0.759601 | − | 0.650390i | \(-0.225394\pi\) | ||||
0.759601 | + | 0.650390i | \(0.225394\pi\) | |||||||
\(678\) | 8.67226 | 0.333056 | ||||||||
\(679\) | −56.6272 | −2.17315 | ||||||||
\(680\) | 0.621194 | 0.0238217 | ||||||||
\(681\) | 8.33048 | 0.319225 | ||||||||
\(682\) | −14.5459 | −0.556990 | ||||||||
\(683\) | −43.2833 | −1.65619 | −0.828095 | − | 0.560588i | \(-0.810575\pi\) | ||||
−0.828095 | + | 0.560588i | \(0.810575\pi\) | |||||||
\(684\) | −5.05516 | −0.193289 | ||||||||
\(685\) | −2.28207 | −0.0871935 | ||||||||
\(686\) | −12.7667 | −0.487434 | ||||||||
\(687\) | −1.04971 | −0.0400488 | ||||||||
\(688\) | −1.60263 | −0.0610996 | ||||||||
\(689\) | −13.2019 | −0.502951 | ||||||||
\(690\) | −0.572324 | −0.0217880 | ||||||||
\(691\) | 18.0548 | 0.686838 | 0.343419 | − | 0.939182i | \(-0.388415\pi\) | ||||
0.343419 | + | 0.939182i | \(0.388415\pi\) | |||||||
\(692\) | 24.0000 | 0.912345 | ||||||||
\(693\) | −17.5951 | −0.668383 | ||||||||
\(694\) | −10.1270 | −0.384417 | ||||||||
\(695\) | 4.50364 | 0.170833 | ||||||||
\(696\) | 0.444744 | 0.0168580 | ||||||||
\(697\) | −18.0254 | −0.682762 | ||||||||
\(698\) | 17.6111 | 0.666588 | ||||||||
\(699\) | −17.9285 | −0.678119 | ||||||||
\(700\) | 15.5079 | 0.586145 | ||||||||
\(701\) | 12.7773 | 0.482591 | 0.241296 | − | 0.970452i | \(-0.422428\pi\) | ||||
0.241296 | + | 0.970452i | \(0.422428\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 38.1749 | 1.43979 | ||||||||
\(704\) | 5.57708 | 0.210194 | ||||||||
\(705\) | 2.74868 | 0.103521 | ||||||||
\(706\) | 7.45823 | 0.280694 | ||||||||
\(707\) | 16.7071 | 0.628334 | ||||||||
\(708\) | −10.9582 | −0.411834 | ||||||||
\(709\) | −24.2744 | −0.911644 | −0.455822 | − | 0.890071i | \(-0.650655\pi\) | ||||
−0.455822 | + | 0.890071i | \(0.650655\pi\) | |||||||
\(710\) | 2.37573 | 0.0891595 | ||||||||
\(711\) | −14.5749 | −0.546601 | ||||||||
\(712\) | 7.96168 | 0.298377 | ||||||||
\(713\) | 5.13553 | 0.192327 | ||||||||
\(714\) | −6.74254 | −0.252333 | ||||||||
\(715\) | −1.62105 | −0.0606238 | ||||||||
\(716\) | 18.1673 | 0.678946 | ||||||||
\(717\) | −28.4472 | −1.06238 | ||||||||
\(718\) | 0.109489 | 0.00408609 | ||||||||
\(719\) | −20.4853 | −0.763973 | −0.381987 | − | 0.924168i | \(-0.624760\pi\) | ||||
−0.381987 | + | 0.924168i | \(0.624760\pi\) | |||||||
\(720\) | 0.290663 | 0.0108324 | ||||||||
\(721\) | −3.15490 | −0.117495 | ||||||||
\(722\) | −6.55465 | −0.243939 | ||||||||
\(723\) | −23.7447 | −0.883075 | ||||||||
\(724\) | −7.40216 | −0.275099 | ||||||||
\(725\) | 2.18615 | 0.0811915 | ||||||||
\(726\) | −20.1038 | −0.746122 | ||||||||
\(727\) | −18.8760 | −0.700073 | −0.350037 | − | 0.936736i | \(-0.613831\pi\) | ||||
−0.350037 | + | 0.936736i | \(0.613831\pi\) | |||||||
\(728\) | −3.15490 | −0.116928 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.41703 | 0.163482 | ||||||||
\(731\) | 3.42508 | 0.126681 | ||||||||
\(732\) | −0.462620 | −0.0170989 | ||||||||
\(733\) | 16.0005 | 0.590991 | 0.295496 | − | 0.955344i | \(-0.404515\pi\) | ||||
0.295496 | + | 0.955344i | \(0.404515\pi\) | |||||||
\(734\) | 23.9306 | 0.883293 | ||||||||
\(735\) | 0.858438 | 0.0316639 | ||||||||
\(736\) | −1.96903 | −0.0725794 | ||||||||
\(737\) | 75.9729 | 2.79850 | ||||||||
\(738\) | −8.43427 | −0.310470 | ||||||||
\(739\) | 27.2275 | 1.00158 | 0.500789 | − | 0.865569i | \(-0.333043\pi\) | ||||
0.500789 | + | 0.865569i | \(0.333043\pi\) | |||||||
\(740\) | −2.19499 | −0.0806894 | ||||||||
\(741\) | 5.05516 | 0.185706 | ||||||||
\(742\) | 41.6506 | 1.52904 | ||||||||
\(743\) | 0.764203 | 0.0280359 | 0.0140180 | − | 0.999902i | \(-0.495538\pi\) | ||||
0.0140180 | + | 0.999902i | \(0.495538\pi\) | |||||||
\(744\) | −2.60815 | −0.0956195 | ||||||||
\(745\) | −5.17374 | −0.189551 | ||||||||
\(746\) | −2.83392 | −0.103757 | ||||||||
\(747\) | −12.2435 | −0.447965 | ||||||||
\(748\) | −11.9191 | −0.435807 | ||||||||
\(749\) | −3.25323 | −0.118870 | ||||||||
\(750\) | 2.88207 | 0.105238 | ||||||||
\(751\) | −17.1952 | −0.627462 | −0.313731 | − | 0.949512i | \(-0.601579\pi\) | ||||
−0.313731 | + | 0.949512i | \(0.601579\pi\) | |||||||
\(752\) | 9.45661 | 0.344847 | ||||||||
\(753\) | 2.69531 | 0.0982227 | ||||||||
\(754\) | −0.444744 | −0.0161966 | ||||||||
\(755\) | −1.88866 | −0.0687354 | ||||||||
\(756\) | −3.15490 | −0.114743 | ||||||||
\(757\) | 42.9856 | 1.56234 | 0.781169 | − | 0.624320i | \(-0.214624\pi\) | ||||
0.781169 | + | 0.624320i | \(0.214624\pi\) | |||||||
\(758\) | −2.43968 | −0.0886133 | ||||||||
\(759\) | 10.9814 | 0.398601 | ||||||||
\(760\) | 1.46935 | 0.0532988 | ||||||||
\(761\) | 9.75380 | 0.353575 | 0.176788 | − | 0.984249i | \(-0.443429\pi\) | ||||
0.176788 | + | 0.984249i | \(0.443429\pi\) | |||||||
\(762\) | 1.72805 | 0.0626007 | ||||||||
\(763\) | 31.3994 | 1.13673 | ||||||||
\(764\) | 1.61795 | 0.0585354 | ||||||||
\(765\) | −0.621194 | −0.0224593 | ||||||||
\(766\) | −7.68470 | −0.277660 | ||||||||
\(767\) | 10.9582 | 0.395677 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 23.2481 | 0.838349 | 0.419174 | − | 0.907906i | \(-0.362320\pi\) | ||||
0.419174 | + | 0.907906i | \(0.362320\pi\) | |||||||
\(770\) | 5.11424 | 0.184305 | ||||||||
\(771\) | 29.5475 | 1.06413 | ||||||||
\(772\) | −2.89904 | −0.104339 | ||||||||
\(773\) | 40.8722 | 1.47007 | 0.735036 | − | 0.678028i | \(-0.237165\pi\) | ||||
0.735036 | + | 0.678028i | \(0.237165\pi\) | |||||||
\(774\) | 1.60263 | 0.0576053 | ||||||||
\(775\) | −12.8204 | −0.460523 | ||||||||
\(776\) | −17.9490 | −0.644331 | ||||||||
\(777\) | 23.8247 | 0.854708 | ||||||||
\(778\) | 15.0757 | 0.540491 | ||||||||
\(779\) | −42.6366 | −1.52761 | ||||||||
\(780\) | −0.290663 | −0.0104074 | ||||||||
\(781\) | −45.5842 | −1.63113 | ||||||||
\(782\) | 4.20814 | 0.150483 | ||||||||
\(783\) | −0.444744 | −0.0158939 | ||||||||
\(784\) | 2.95338 | 0.105478 | ||||||||
\(785\) | −3.46050 | −0.123510 | ||||||||
\(786\) | 13.9485 | 0.497526 | ||||||||
\(787\) | −21.5873 | −0.769503 | −0.384751 | − | 0.923020i | \(-0.625713\pi\) | ||||
−0.384751 | + | 0.923020i | \(0.625713\pi\) | |||||||
\(788\) | −5.32513 | −0.189700 | ||||||||
\(789\) | −8.69529 | −0.309561 | ||||||||
\(790\) | 4.23638 | 0.150723 | ||||||||
\(791\) | 27.3601 | 0.972813 | ||||||||
\(792\) | −5.57708 | −0.198173 | ||||||||
\(793\) | 0.462620 | 0.0164281 | ||||||||
\(794\) | 19.8678 | 0.705083 | ||||||||
\(795\) | 3.83729 | 0.136095 | ||||||||
\(796\) | −15.2964 | −0.542167 | ||||||||
\(797\) | 21.6888 | 0.768256 | 0.384128 | − | 0.923280i | \(-0.374502\pi\) | ||||
0.384128 | + | 0.923280i | \(0.374502\pi\) | |||||||
\(798\) | −15.9485 | −0.564571 | ||||||||
\(799\) | −20.2103 | −0.714990 | ||||||||
\(800\) | 4.91552 | 0.173790 | ||||||||
\(801\) | −7.96168 | −0.281312 | ||||||||
\(802\) | −8.07833 | −0.285256 | ||||||||
\(803\) | −84.7515 | −2.99082 | ||||||||
\(804\) | 13.6224 | 0.480423 | ||||||||
\(805\) | −1.80562 | −0.0636398 | ||||||||
\(806\) | 2.60815 | 0.0918683 | ||||||||
\(807\) | 2.38908 | 0.0840994 | ||||||||
\(808\) | 5.29560 | 0.186299 | ||||||||
\(809\) | −9.87247 | −0.347098 | −0.173549 | − | 0.984825i | \(-0.555523\pi\) | ||||
−0.173549 | + | 0.984825i | \(0.555523\pi\) | |||||||
\(810\) | −0.290663 | −0.0102128 | ||||||||
\(811\) | 14.8157 | 0.520248 | 0.260124 | − | 0.965575i | \(-0.416236\pi\) | ||||
0.260124 | + | 0.965575i | \(0.416236\pi\) | |||||||
\(812\) | 1.40312 | 0.0492400 | ||||||||
\(813\) | −27.3531 | −0.959314 | ||||||||
\(814\) | 42.1162 | 1.47617 | ||||||||
\(815\) | 1.12653 | 0.0394605 | ||||||||
\(816\) | −2.13717 | −0.0748158 | ||||||||
\(817\) | 8.10154 | 0.283437 | ||||||||
\(818\) | 1.67295 | 0.0584932 | ||||||||
\(819\) | 3.15490 | 0.110241 | ||||||||
\(820\) | 2.45153 | 0.0856110 | ||||||||
\(821\) | −23.7220 | −0.827903 | −0.413951 | − | 0.910299i | \(-0.635852\pi\) | ||||
−0.413951 | + | 0.910299i | \(0.635852\pi\) | |||||||
\(822\) | 7.85127 | 0.273845 | ||||||||
\(823\) | −21.7641 | −0.758649 | −0.379325 | − | 0.925264i | \(-0.623844\pi\) | ||||
−0.379325 | + | 0.925264i | \(0.623844\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −27.4142 | −0.954440 | ||||||||
\(826\) | −34.5720 | −1.20291 | ||||||||
\(827\) | −21.9738 | −0.764105 | −0.382053 | − | 0.924141i | \(-0.624783\pi\) | ||||
−0.382053 | + | 0.924141i | \(0.624783\pi\) | |||||||
\(828\) | 1.96903 | 0.0684285 | ||||||||
\(829\) | −50.6407 | −1.75883 | −0.879413 | − | 0.476060i | \(-0.842064\pi\) | ||||
−0.879413 | + | 0.476060i | \(0.842064\pi\) | |||||||
\(830\) | 3.55872 | 0.123525 | ||||||||
\(831\) | 7.20989 | 0.250108 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −6.31186 | −0.218693 | ||||||||
\(834\) | −15.4944 | −0.536527 | ||||||||
\(835\) | 1.43441 | 0.0496399 | ||||||||
\(836\) | −28.1930 | −0.975076 | ||||||||
\(837\) | 2.60815 | 0.0901509 | ||||||||
\(838\) | 29.6169 | 1.02310 | ||||||||
\(839\) | −40.9488 | −1.41371 | −0.706855 | − | 0.707358i | \(-0.749887\pi\) | ||||
−0.706855 | + | 0.707358i | \(0.749887\pi\) | |||||||
\(840\) | 0.917011 | 0.0316399 | ||||||||
\(841\) | −28.8022 | −0.993179 | ||||||||
\(842\) | −21.6503 | −0.746119 | ||||||||
\(843\) | 9.84747 | 0.339165 | ||||||||
\(844\) | −5.18412 | −0.178445 | ||||||||
\(845\) | 0.290663 | 0.00999910 | ||||||||
\(846\) | −9.45661 | −0.325125 | ||||||||
\(847\) | −63.4255 | −2.17932 | ||||||||
\(848\) | 13.2019 | 0.453354 | ||||||||
\(849\) | −11.7273 | −0.402480 | ||||||||
\(850\) | −10.5053 | −0.360328 | ||||||||
\(851\) | −14.8695 | −0.509718 | ||||||||
\(852\) | −8.17349 | −0.280019 | ||||||||
\(853\) | −39.2025 | −1.34227 | −0.671134 | − | 0.741336i | \(-0.734193\pi\) | ||||
−0.671134 | + | 0.741336i | \(0.734193\pi\) | |||||||
\(854\) | −1.45952 | −0.0499437 | ||||||||
\(855\) | −1.46935 | −0.0502506 | ||||||||
\(856\) | −1.03117 | −0.0352446 | ||||||||
\(857\) | 31.1171 | 1.06294 | 0.531470 | − | 0.847077i | \(-0.321640\pi\) | ||||
0.531470 | + | 0.847077i | \(0.321640\pi\) | |||||||
\(858\) | 5.57708 | 0.190398 | ||||||||
\(859\) | 3.08785 | 0.105356 | 0.0526780 | − | 0.998612i | \(-0.483224\pi\) | ||||
0.0526780 | + | 0.998612i | \(0.483224\pi\) | |||||||
\(860\) | −0.465824 | −0.0158845 | ||||||||
\(861\) | −26.6092 | −0.906841 | ||||||||
\(862\) | 12.8563 | 0.437888 | ||||||||
\(863\) | −18.3232 | −0.623729 | −0.311864 | − | 0.950127i | \(-0.600953\pi\) | ||||
−0.311864 | + | 0.950127i | \(0.600953\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 6.97592 | 0.237188 | ||||||||
\(866\) | −5.64923 | −0.191969 | ||||||||
\(867\) | −12.4325 | −0.422231 | ||||||||
\(868\) | −8.22846 | −0.279292 | ||||||||
\(869\) | −81.2853 | −2.75741 | ||||||||
\(870\) | 0.129271 | 0.00438269 | ||||||||
\(871\) | −13.6224 | −0.461576 | ||||||||
\(872\) | 9.95257 | 0.337037 | ||||||||
\(873\) | 17.9490 | 0.607481 | ||||||||
\(874\) | 9.95376 | 0.336691 | ||||||||
\(875\) | 9.09264 | 0.307387 | ||||||||
\(876\) | −15.1964 | −0.513439 | ||||||||
\(877\) | −49.1191 | −1.65863 | −0.829317 | − | 0.558778i | \(-0.811270\pi\) | ||||
−0.829317 | + | 0.558778i | \(0.811270\pi\) | |||||||
\(878\) | 3.24402 | 0.109480 | ||||||||
\(879\) | −23.3098 | −0.786221 | ||||||||
\(880\) | 1.62105 | 0.0546456 | ||||||||
\(881\) | 39.1803 | 1.32002 | 0.660009 | − | 0.751258i | \(-0.270552\pi\) | ||||
0.660009 | + | 0.751258i | \(0.270552\pi\) | |||||||
\(882\) | −2.95338 | −0.0994455 | ||||||||
\(883\) | −4.99667 | −0.168151 | −0.0840756 | − | 0.996459i | \(-0.526794\pi\) | ||||
−0.0840756 | + | 0.996459i | \(0.526794\pi\) | |||||||
\(884\) | 2.13717 | 0.0718807 | ||||||||
\(885\) | −3.18514 | −0.107067 | ||||||||
\(886\) | −3.93720 | −0.132273 | ||||||||
\(887\) | −51.7082 | −1.73619 | −0.868096 | − | 0.496396i | \(-0.834656\pi\) | ||||
−0.868096 | + | 0.496396i | \(0.834656\pi\) | |||||||
\(888\) | 7.55167 | 0.253417 | ||||||||
\(889\) | 5.45183 | 0.182848 | ||||||||
\(890\) | 2.31416 | 0.0775710 | ||||||||
\(891\) | 5.57708 | 0.186839 | ||||||||
\(892\) | 18.0617 | 0.604749 | ||||||||
\(893\) | −47.8047 | −1.59972 | ||||||||
\(894\) | 17.7998 | 0.595315 | ||||||||
\(895\) | 5.28057 | 0.176510 | ||||||||
\(896\) | 3.15490 | 0.105398 | ||||||||
\(897\) | −1.96903 | −0.0657440 | ||||||||
\(898\) | 32.6440 | 1.08934 | ||||||||
\(899\) | −1.15996 | −0.0386869 | ||||||||
\(900\) | −4.91552 | −0.163851 | ||||||||
\(901\) | −28.2146 | −0.939964 | ||||||||
\(902\) | −47.0386 | −1.56621 | ||||||||
\(903\) | 5.05613 | 0.168257 | ||||||||
\(904\) | 8.67226 | 0.288435 | ||||||||
\(905\) | −2.15153 | −0.0715194 | ||||||||
\(906\) | 6.49777 | 0.215874 | ||||||||
\(907\) | 45.2516 | 1.50255 | 0.751277 | − | 0.659987i | \(-0.229438\pi\) | ||||
0.751277 | + | 0.659987i | \(0.229438\pi\) | |||||||
\(908\) | 8.33048 | 0.276457 | ||||||||
\(909\) | −5.29560 | −0.175644 | ||||||||
\(910\) | −0.917011 | −0.0303986 | ||||||||
\(911\) | −51.2211 | −1.69703 | −0.848516 | − | 0.529170i | \(-0.822503\pi\) | ||||
−0.848516 | + | 0.529170i | \(0.822503\pi\) | |||||||
\(912\) | −5.05516 | −0.167393 | ||||||||
\(913\) | −68.2827 | −2.25983 | ||||||||
\(914\) | −30.0476 | −0.993887 | ||||||||
\(915\) | −0.134466 | −0.00444532 | ||||||||
\(916\) | −1.04971 | −0.0346833 | ||||||||
\(917\) | 44.0061 | 1.45321 | ||||||||
\(918\) | 2.13717 | 0.0705370 | ||||||||
\(919\) | 49.3019 | 1.62632 | 0.813160 | − | 0.582040i | \(-0.197745\pi\) | ||||
0.813160 | + | 0.582040i | \(0.197745\pi\) | |||||||
\(920\) | −0.572324 | −0.0188690 | ||||||||
\(921\) | 14.8883 | 0.490585 | ||||||||
\(922\) | 28.1535 | 0.927188 | ||||||||
\(923\) | 8.17349 | 0.269034 | ||||||||
\(924\) | −17.5951 | −0.578837 | ||||||||
\(925\) | 37.1203 | 1.22051 | ||||||||
\(926\) | 28.2939 | 0.929794 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 0.444744 | 0.0145995 | ||||||||
\(929\) | −37.4227 | −1.22780 | −0.613899 | − | 0.789385i | \(-0.710400\pi\) | ||||
−0.613899 | + | 0.789385i | \(0.710400\pi\) | |||||||
\(930\) | −0.758093 | −0.0248588 | ||||||||
\(931\) | −14.9298 | −0.489305 | ||||||||
\(932\) | −17.9285 | −0.587268 | ||||||||
\(933\) | 32.4727 | 1.06311 | ||||||||
\(934\) | 17.8245 | 0.583236 | ||||||||
\(935\) | −3.46445 | −0.113300 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 4.00375 | 0.130797 | 0.0653984 | − | 0.997859i | \(-0.479168\pi\) | ||||
0.0653984 | + | 0.997859i | \(0.479168\pi\) | |||||||
\(938\) | 42.9771 | 1.40325 | ||||||||
\(939\) | 21.6485 | 0.706474 | ||||||||
\(940\) | 2.74868 | 0.0896522 | ||||||||
\(941\) | 27.1284 | 0.884362 | 0.442181 | − | 0.896926i | \(-0.354205\pi\) | ||||
0.442181 | + | 0.896926i | \(0.354205\pi\) | |||||||
\(942\) | 11.9055 | 0.387903 | ||||||||
\(943\) | 16.6073 | 0.540809 | ||||||||
\(944\) | −10.9582 | −0.356659 | ||||||||
\(945\) | −0.917011 | −0.0298304 | ||||||||
\(946\) | 8.93798 | 0.290599 | ||||||||
\(947\) | −1.79919 | −0.0584658 | −0.0292329 | − | 0.999573i | \(-0.509306\pi\) | ||||
−0.0292329 | + | 0.999573i | \(0.509306\pi\) | |||||||
\(948\) | −14.5749 | −0.473370 | ||||||||
\(949\) | 15.1964 | 0.493296 | ||||||||
\(950\) | −24.8487 | −0.806199 | ||||||||
\(951\) | −11.4084 | −0.369944 | ||||||||
\(952\) | −6.74254 | −0.218527 | ||||||||
\(953\) | 41.8700 | 1.35630 | 0.678151 | − | 0.734923i | \(-0.262782\pi\) | ||||
0.678151 | + | 0.734923i | \(0.262782\pi\) | |||||||
\(954\) | −13.2019 | −0.427426 | ||||||||
\(955\) | 0.470278 | 0.0152178 | ||||||||
\(956\) | −28.4472 | −0.920049 | ||||||||
\(957\) | −2.48037 | −0.0801791 | ||||||||
\(958\) | 3.47708 | 0.112339 | ||||||||
\(959\) | 24.7700 | 0.799864 | ||||||||
\(960\) | 0.290663 | 0.00938110 | ||||||||
\(961\) | −24.1975 | −0.780566 | ||||||||
\(962\) | −7.55167 | −0.243476 | ||||||||
\(963\) | 1.03117 | 0.0332289 | ||||||||
\(964\) | −23.7447 | −0.764766 | ||||||||
\(965\) | −0.842643 | −0.0271256 | ||||||||
\(966\) | 6.21209 | 0.199871 | ||||||||
\(967\) | 0.719652 | 0.0231424 | 0.0115712 | − | 0.999933i | \(-0.496317\pi\) | ||||
0.0115712 | + | 0.999933i | \(0.496317\pi\) | |||||||
\(968\) | −20.1038 | −0.646161 | ||||||||
\(969\) | 10.8037 | 0.347065 | ||||||||
\(970\) | −5.21710 | −0.167511 | ||||||||
\(971\) | 19.1042 | 0.613083 | 0.306541 | − | 0.951857i | \(-0.400828\pi\) | ||||
0.306541 | + | 0.951857i | \(0.400828\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −48.8832 | −1.56712 | ||||||||
\(974\) | 11.5461 | 0.369962 | ||||||||
\(975\) | 4.91552 | 0.157422 | ||||||||
\(976\) | −0.462620 | −0.0148081 | ||||||||
\(977\) | 11.2186 | 0.358915 | 0.179458 | − | 0.983766i | \(-0.442566\pi\) | ||||
0.179458 | + | 0.983766i | \(0.442566\pi\) | |||||||
\(978\) | −3.87572 | −0.123932 | ||||||||
\(979\) | −44.4029 | −1.41912 | ||||||||
\(980\) | 0.858438 | 0.0274218 | ||||||||
\(981\) | −9.95257 | −0.317761 | ||||||||
\(982\) | 7.19621 | 0.229640 | ||||||||
\(983\) | −3.27103 | −0.104330 | −0.0521648 | − | 0.998638i | \(-0.516612\pi\) | ||||
−0.0521648 | + | 0.998638i | \(0.516612\pi\) | |||||||
\(984\) | −8.43427 | −0.268875 | ||||||||
\(985\) | −1.54782 | −0.0493175 | ||||||||
\(986\) | −0.950492 | −0.0302698 | ||||||||
\(987\) | −29.8346 | −0.949647 | ||||||||
\(988\) | 5.05516 | 0.160826 | ||||||||
\(989\) | −3.15562 | −0.100343 | ||||||||
\(990\) | −1.62105 | −0.0515203 | ||||||||
\(991\) | −23.3751 | −0.742534 | −0.371267 | − | 0.928526i | \(-0.621076\pi\) | ||||
−0.371267 | + | 0.928526i | \(0.621076\pi\) | |||||||
\(992\) | −2.60815 | −0.0828089 | ||||||||
\(993\) | −15.1788 | −0.481683 | ||||||||
\(994\) | −25.7865 | −0.817899 | ||||||||
\(995\) | −4.44610 | −0.140951 | ||||||||
\(996\) | −12.2435 | −0.387949 | ||||||||
\(997\) | 48.6147 | 1.53964 | 0.769822 | − | 0.638259i | \(-0.220345\pi\) | ||||
0.769822 | + | 0.638259i | \(0.220345\pi\) | |||||||
\(998\) | 6.96624 | 0.220512 | ||||||||
\(999\) | −7.55167 | −0.238924 |
(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 | 8034.2.a.bb.1.8 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bb.1.8 | ✓ | 14 | 1.1 | even | 1 | trivial |