Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} - 4372 x^{2} - 692 x + 1200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.25950\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(5\) | 2.25950 | 1.01048 | 0.505239 | − | 0.862980i | \(-0.331404\pi\) | ||||
0.505239 | + | 0.862980i | \(0.331404\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.73494 | 1.41167 | 0.705837 | − | 0.708375i | \(-0.250571\pi\) | ||||
0.705837 | + | 0.708375i | \(0.250571\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.25950 | 0.714515 | ||||||||
\(11\) | 3.84055 | 1.15797 | 0.578984 | − | 0.815339i | \(-0.303449\pi\) | ||||
0.578984 | + | 0.815339i | \(0.303449\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.08367 | −1.13261 | −0.566303 | − | 0.824197i | \(-0.691627\pi\) | ||||
−0.566303 | + | 0.824197i | \(0.691627\pi\) | |||||||
\(14\) | 3.73494 | 0.998204 | ||||||||
\(15\) | −2.25950 | −0.583399 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.16453 | −0.267162 | −0.133581 | − | 0.991038i | \(-0.542648\pi\) | ||||
−0.133581 | + | 0.991038i | \(0.542648\pi\) | |||||||
\(20\) | 2.25950 | 0.505239 | ||||||||
\(21\) | −3.73494 | −0.815030 | ||||||||
\(22\) | 3.84055 | 0.818807 | ||||||||
\(23\) | 5.03855 | 1.05061 | 0.525305 | − | 0.850914i | \(-0.323951\pi\) | ||||
0.525305 | + | 0.850914i | \(0.323951\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0.105322 | 0.0210645 | ||||||||
\(26\) | −4.08367 | −0.800873 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.73494 | 0.705837 | ||||||||
\(29\) | 6.70162 | 1.24446 | 0.622230 | − | 0.782835i | \(-0.286227\pi\) | ||||
0.622230 | + | 0.782835i | \(0.286227\pi\) | |||||||
\(30\) | −2.25950 | −0.412526 | ||||||||
\(31\) | −7.12027 | −1.27884 | −0.639419 | − | 0.768859i | \(-0.720825\pi\) | ||||
−0.639419 | + | 0.768859i | \(0.720825\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.84055 | −0.668553 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 8.43907 | 1.42646 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.75553 | −0.453006 | −0.226503 | − | 0.974011i | \(-0.572729\pi\) | ||||
−0.226503 | + | 0.974011i | \(0.572729\pi\) | |||||||
\(38\) | −1.16453 | −0.188912 | ||||||||
\(39\) | 4.08367 | 0.653910 | ||||||||
\(40\) | 2.25950 | 0.357258 | ||||||||
\(41\) | 8.36186 | 1.30590 | 0.652951 | − | 0.757400i | \(-0.273531\pi\) | ||||
0.652951 | + | 0.757400i | \(0.273531\pi\) | |||||||
\(42\) | −3.73494 | −0.576313 | ||||||||
\(43\) | 10.5441 | 1.60795 | 0.803976 | − | 0.594661i | \(-0.202714\pi\) | ||||
0.803976 | + | 0.594661i | \(0.202714\pi\) | |||||||
\(44\) | 3.84055 | 0.578984 | ||||||||
\(45\) | 2.25950 | 0.336826 | ||||||||
\(46\) | 5.03855 | 0.742893 | ||||||||
\(47\) | 0.0503609 | 0.00734589 | 0.00367294 | − | 0.999993i | \(-0.498831\pi\) | ||||
0.00367294 | + | 0.999993i | \(0.498831\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 6.94974 | 0.992821 | ||||||||
\(50\) | 0.105322 | 0.0148948 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −4.08367 | −0.566303 | ||||||||
\(53\) | −0.972069 | −0.133524 | −0.0667620 | − | 0.997769i | \(-0.521267\pi\) | ||||
−0.0667620 | + | 0.997769i | \(0.521267\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 8.67770 | 1.17010 | ||||||||
\(56\) | 3.73494 | 0.499102 | ||||||||
\(57\) | 1.16453 | 0.154246 | ||||||||
\(58\) | 6.70162 | 0.879966 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −2.25950 | −0.291700 | ||||||||
\(61\) | −6.11723 | −0.783231 | −0.391616 | − | 0.920129i | \(-0.628084\pi\) | ||||
−0.391616 | + | 0.920129i | \(0.628084\pi\) | |||||||
\(62\) | −7.12027 | −0.904275 | ||||||||
\(63\) | 3.73494 | 0.470558 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.22703 | −1.14447 | ||||||||
\(66\) | −3.84055 | −0.472739 | ||||||||
\(67\) | −0.356946 | −0.0436079 | −0.0218040 | − | 0.999762i | \(-0.506941\pi\) | ||||
−0.0218040 | + | 0.999762i | \(0.506941\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −5.03855 | −0.606570 | ||||||||
\(70\) | 8.43907 | 1.00866 | ||||||||
\(71\) | 5.02022 | 0.595791 | 0.297895 | − | 0.954599i | \(-0.403715\pi\) | ||||
0.297895 | + | 0.954599i | \(0.403715\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −5.24611 | −0.614010 | −0.307005 | − | 0.951708i | \(-0.599327\pi\) | ||||
−0.307005 | + | 0.951708i | \(0.599327\pi\) | |||||||
\(74\) | −2.75553 | −0.320323 | ||||||||
\(75\) | −0.105322 | −0.0121616 | ||||||||
\(76\) | −1.16453 | −0.133581 | ||||||||
\(77\) | 14.3442 | 1.63467 | ||||||||
\(78\) | 4.08367 | 0.462384 | ||||||||
\(79\) | 0.531164 | 0.0597606 | 0.0298803 | − | 0.999553i | \(-0.490487\pi\) | ||||
0.0298803 | + | 0.999553i | \(0.490487\pi\) | |||||||
\(80\) | 2.25950 | 0.252619 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.36186 | 0.923412 | ||||||||
\(83\) | 5.67224 | 0.622610 | 0.311305 | − | 0.950310i | \(-0.399234\pi\) | ||||
0.311305 | + | 0.950310i | \(0.399234\pi\) | |||||||
\(84\) | −3.73494 | −0.407515 | ||||||||
\(85\) | −2.25950 | −0.245077 | ||||||||
\(86\) | 10.5441 | 1.13699 | ||||||||
\(87\) | −6.70162 | −0.718489 | ||||||||
\(88\) | 3.84055 | 0.409404 | ||||||||
\(89\) | 13.4985 | 1.43084 | 0.715421 | − | 0.698693i | \(-0.246235\pi\) | ||||
0.715421 | + | 0.698693i | \(0.246235\pi\) | |||||||
\(90\) | 2.25950 | 0.238172 | ||||||||
\(91\) | −15.2522 | −1.59887 | ||||||||
\(92\) | 5.03855 | 0.525305 | ||||||||
\(93\) | 7.12027 | 0.738337 | ||||||||
\(94\) | 0.0503609 | 0.00519433 | ||||||||
\(95\) | −2.63126 | −0.269962 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −7.52852 | −0.764405 | −0.382203 | − | 0.924079i | \(-0.624834\pi\) | ||||
−0.382203 | + | 0.924079i | \(0.624834\pi\) | |||||||
\(98\) | 6.94974 | 0.702030 | ||||||||
\(99\) | 3.84055 | 0.385990 | ||||||||
\(100\) | 0.105322 | 0.0105322 | ||||||||
\(101\) | 7.36090 | 0.732437 | 0.366218 | − | 0.930529i | \(-0.380652\pi\) | ||||
0.366218 | + | 0.930529i | \(0.380652\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 16.9716 | 1.67226 | 0.836128 | − | 0.548534i | \(-0.184814\pi\) | ||||
0.836128 | + | 0.548534i | \(0.184814\pi\) | |||||||
\(104\) | −4.08367 | −0.400437 | ||||||||
\(105\) | −8.43907 | −0.823569 | ||||||||
\(106\) | −0.972069 | −0.0944157 | ||||||||
\(107\) | 6.02420 | 0.582381 | 0.291191 | − | 0.956665i | \(-0.405949\pi\) | ||||
0.291191 | + | 0.956665i | \(0.405949\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −10.5956 | −1.01487 | −0.507436 | − | 0.861689i | \(-0.669407\pi\) | ||||
−0.507436 | + | 0.861689i | \(0.669407\pi\) | |||||||
\(110\) | 8.67770 | 0.827386 | ||||||||
\(111\) | 2.75553 | 0.261543 | ||||||||
\(112\) | 3.73494 | 0.352918 | ||||||||
\(113\) | −20.2421 | −1.90421 | −0.952107 | − | 0.305766i | \(-0.901088\pi\) | ||||
−0.952107 | + | 0.305766i | \(0.901088\pi\) | |||||||
\(114\) | 1.16453 | 0.109069 | ||||||||
\(115\) | 11.3846 | 1.06162 | ||||||||
\(116\) | 6.70162 | 0.622230 | ||||||||
\(117\) | −4.08367 | −0.377535 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | −3.73494 | −0.342381 | ||||||||
\(120\) | −2.25950 | −0.206263 | ||||||||
\(121\) | 3.74980 | 0.340891 | ||||||||
\(122\) | −6.11723 | −0.553828 | ||||||||
\(123\) | −8.36186 | −0.753963 | ||||||||
\(124\) | −7.12027 | −0.639419 | ||||||||
\(125\) | −11.0595 | −0.989192 | ||||||||
\(126\) | 3.73494 | 0.332735 | ||||||||
\(127\) | −7.19680 | −0.638612 | −0.319306 | − | 0.947652i | \(-0.603450\pi\) | ||||
−0.319306 | + | 0.947652i | \(0.603450\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −10.5441 | −0.928352 | ||||||||
\(130\) | −9.22703 | −0.809264 | ||||||||
\(131\) | −10.3416 | −0.903550 | −0.451775 | − | 0.892132i | \(-0.649209\pi\) | ||||
−0.451775 | + | 0.892132i | \(0.649209\pi\) | |||||||
\(132\) | −3.84055 | −0.334277 | ||||||||
\(133\) | −4.34946 | −0.377146 | ||||||||
\(134\) | −0.356946 | −0.0308355 | ||||||||
\(135\) | −2.25950 | −0.194466 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 12.5181 | 1.06950 | 0.534748 | − | 0.845012i | \(-0.320407\pi\) | ||||
0.534748 | + | 0.845012i | \(0.320407\pi\) | |||||||
\(138\) | −5.03855 | −0.428910 | ||||||||
\(139\) | −0.485663 | −0.0411934 | −0.0205967 | − | 0.999788i | \(-0.506557\pi\) | ||||
−0.0205967 | + | 0.999788i | \(0.506557\pi\) | |||||||
\(140\) | 8.43907 | 0.713232 | ||||||||
\(141\) | −0.0503609 | −0.00424115 | ||||||||
\(142\) | 5.02022 | 0.421288 | ||||||||
\(143\) | −15.6835 | −1.31152 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 15.1423 | 1.25750 | ||||||||
\(146\) | −5.24611 | −0.434171 | ||||||||
\(147\) | −6.94974 | −0.573205 | ||||||||
\(148\) | −2.75553 | −0.226503 | ||||||||
\(149\) | −12.1194 | −0.992861 | −0.496431 | − | 0.868076i | \(-0.665356\pi\) | ||||
−0.496431 | + | 0.868076i | \(0.665356\pi\) | |||||||
\(150\) | −0.105322 | −0.00859954 | ||||||||
\(151\) | −12.0007 | −0.976600 | −0.488300 | − | 0.872676i | \(-0.662383\pi\) | ||||
−0.488300 | + | 0.872676i | \(0.662383\pi\) | |||||||
\(152\) | −1.16453 | −0.0944562 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 14.3442 | 1.15589 | ||||||||
\(155\) | −16.0882 | −1.29224 | ||||||||
\(156\) | 4.08367 | 0.326955 | ||||||||
\(157\) | 6.65132 | 0.530833 | 0.265417 | − | 0.964134i | \(-0.414490\pi\) | ||||
0.265417 | + | 0.964134i | \(0.414490\pi\) | |||||||
\(158\) | 0.531164 | 0.0422571 | ||||||||
\(159\) | 0.972069 | 0.0770901 | ||||||||
\(160\) | 2.25950 | 0.178629 | ||||||||
\(161\) | 18.8187 | 1.48312 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 15.2569 | 1.19501 | 0.597507 | − | 0.801864i | \(-0.296158\pi\) | ||||
0.597507 | + | 0.801864i | \(0.296158\pi\) | |||||||
\(164\) | 8.36186 | 0.652951 | ||||||||
\(165\) | −8.67770 | −0.675558 | ||||||||
\(166\) | 5.67224 | 0.440251 | ||||||||
\(167\) | −18.2500 | −1.41223 | −0.706114 | − | 0.708098i | \(-0.749554\pi\) | ||||
−0.706114 | + | 0.708098i | \(0.749554\pi\) | |||||||
\(168\) | −3.73494 | −0.288157 | ||||||||
\(169\) | 3.67634 | 0.282796 | ||||||||
\(170\) | −2.25950 | −0.173295 | ||||||||
\(171\) | −1.16453 | −0.0890541 | ||||||||
\(172\) | 10.5441 | 0.803976 | ||||||||
\(173\) | −5.65681 | −0.430079 | −0.215040 | − | 0.976605i | \(-0.568988\pi\) | ||||
−0.215040 | + | 0.976605i | \(0.568988\pi\) | |||||||
\(174\) | −6.70162 | −0.508048 | ||||||||
\(175\) | 0.393373 | 0.0297362 | ||||||||
\(176\) | 3.84055 | 0.289492 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 13.4985 | 1.01176 | ||||||||
\(179\) | −17.5859 | −1.31443 | −0.657216 | − | 0.753702i | \(-0.728266\pi\) | ||||
−0.657216 | + | 0.753702i | \(0.728266\pi\) | |||||||
\(180\) | 2.25950 | 0.168413 | ||||||||
\(181\) | 15.4875 | 1.15118 | 0.575589 | − | 0.817739i | \(-0.304773\pi\) | ||||
0.575589 | + | 0.817739i | \(0.304773\pi\) | |||||||
\(182\) | −15.2522 | −1.13057 | ||||||||
\(183\) | 6.11723 | 0.452199 | ||||||||
\(184\) | 5.03855 | 0.371447 | ||||||||
\(185\) | −6.22610 | −0.457752 | ||||||||
\(186\) | 7.12027 | 0.522083 | ||||||||
\(187\) | −3.84055 | −0.280849 | ||||||||
\(188\) | 0.0503609 | 0.00367294 | ||||||||
\(189\) | −3.73494 | −0.271677 | ||||||||
\(190\) | −2.63126 | −0.190892 | ||||||||
\(191\) | −5.98757 | −0.433245 | −0.216623 | − | 0.976255i | \(-0.569504\pi\) | ||||
−0.216623 | + | 0.976255i | \(0.569504\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 20.0576 | 1.44378 | 0.721888 | − | 0.692010i | \(-0.243274\pi\) | ||||
0.721888 | + | 0.692010i | \(0.243274\pi\) | |||||||
\(194\) | −7.52852 | −0.540516 | ||||||||
\(195\) | 9.22703 | 0.660761 | ||||||||
\(196\) | 6.94974 | 0.496410 | ||||||||
\(197\) | −1.62569 | −0.115826 | −0.0579129 | − | 0.998322i | \(-0.518445\pi\) | ||||
−0.0579129 | + | 0.998322i | \(0.518445\pi\) | |||||||
\(198\) | 3.84055 | 0.272936 | ||||||||
\(199\) | −10.9179 | −0.773952 | −0.386976 | − | 0.922090i | \(-0.626480\pi\) | ||||
−0.386976 | + | 0.922090i | \(0.626480\pi\) | |||||||
\(200\) | 0.105322 | 0.00744742 | ||||||||
\(201\) | 0.356946 | 0.0251771 | ||||||||
\(202\) | 7.36090 | 0.517911 | ||||||||
\(203\) | 25.0301 | 1.75677 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 18.8936 | 1.31958 | ||||||||
\(206\) | 16.9716 | 1.18246 | ||||||||
\(207\) | 5.03855 | 0.350203 | ||||||||
\(208\) | −4.08367 | −0.283151 | ||||||||
\(209\) | −4.47245 | −0.309366 | ||||||||
\(210\) | −8.43907 | −0.582351 | ||||||||
\(211\) | 24.7016 | 1.70053 | 0.850264 | − | 0.526357i | \(-0.176443\pi\) | ||||
0.850264 | + | 0.526357i | \(0.176443\pi\) | |||||||
\(212\) | −0.972069 | −0.0667620 | ||||||||
\(213\) | −5.02022 | −0.343980 | ||||||||
\(214\) | 6.02420 | 0.411806 | ||||||||
\(215\) | 23.8242 | 1.62480 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −26.5937 | −1.80530 | ||||||||
\(218\) | −10.5956 | −0.717623 | ||||||||
\(219\) | 5.24611 | 0.354499 | ||||||||
\(220\) | 8.67770 | 0.585051 | ||||||||
\(221\) | 4.08367 | 0.274697 | ||||||||
\(222\) | 2.75553 | 0.184939 | ||||||||
\(223\) | −17.9650 | −1.20303 | −0.601513 | − | 0.798863i | \(-0.705435\pi\) | ||||
−0.601513 | + | 0.798863i | \(0.705435\pi\) | |||||||
\(224\) | 3.73494 | 0.249551 | ||||||||
\(225\) | 0.105322 | 0.00702150 | ||||||||
\(226\) | −20.2421 | −1.34648 | ||||||||
\(227\) | −12.1520 | −0.806554 | −0.403277 | − | 0.915078i | \(-0.632129\pi\) | ||||
−0.403277 | + | 0.915078i | \(0.632129\pi\) | |||||||
\(228\) | 1.16453 | 0.0771231 | ||||||||
\(229\) | −10.5713 | −0.698571 | −0.349286 | − | 0.937016i | \(-0.613576\pi\) | ||||
−0.349286 | + | 0.937016i | \(0.613576\pi\) | |||||||
\(230\) | 11.3846 | 0.750677 | ||||||||
\(231\) | −14.3442 | −0.943779 | ||||||||
\(232\) | 6.70162 | 0.439983 | ||||||||
\(233\) | 13.9663 | 0.914961 | 0.457480 | − | 0.889220i | \(-0.348752\pi\) | ||||
0.457480 | + | 0.889220i | \(0.348752\pi\) | |||||||
\(234\) | −4.08367 | −0.266958 | ||||||||
\(235\) | 0.113790 | 0.00742285 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | −0.531164 | −0.0345028 | ||||||||
\(238\) | −3.73494 | −0.242100 | ||||||||
\(239\) | 28.5324 | 1.84561 | 0.922803 | − | 0.385273i | \(-0.125893\pi\) | ||||
0.922803 | + | 0.385273i | \(0.125893\pi\) | |||||||
\(240\) | −2.25950 | −0.145850 | ||||||||
\(241\) | −29.0203 | −1.86936 | −0.934682 | − | 0.355485i | \(-0.884316\pi\) | ||||
−0.934682 | + | 0.355485i | \(0.884316\pi\) | |||||||
\(242\) | 3.74980 | 0.241047 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.11723 | −0.391616 | ||||||||
\(245\) | 15.7029 | 1.00322 | ||||||||
\(246\) | −8.36186 | −0.533132 | ||||||||
\(247\) | 4.75557 | 0.302590 | ||||||||
\(248\) | −7.12027 | −0.452137 | ||||||||
\(249\) | −5.67224 | −0.359464 | ||||||||
\(250\) | −11.0595 | −0.699464 | ||||||||
\(251\) | 26.4706 | 1.67081 | 0.835404 | − | 0.549636i | \(-0.185234\pi\) | ||||
0.835404 | + | 0.549636i | \(0.185234\pi\) | |||||||
\(252\) | 3.73494 | 0.235279 | ||||||||
\(253\) | 19.3508 | 1.21657 | ||||||||
\(254\) | −7.19680 | −0.451567 | ||||||||
\(255\) | 2.25950 | 0.141495 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.5525 | −1.21965 | −0.609827 | − | 0.792534i | \(-0.708761\pi\) | ||||
−0.609827 | + | 0.792534i | \(0.708761\pi\) | |||||||
\(258\) | −10.5441 | −0.656444 | ||||||||
\(259\) | −10.2917 | −0.639496 | ||||||||
\(260\) | −9.22703 | −0.572236 | ||||||||
\(261\) | 6.70162 | 0.414820 | ||||||||
\(262\) | −10.3416 | −0.638906 | ||||||||
\(263\) | −20.1022 | −1.23956 | −0.619778 | − | 0.784777i | \(-0.712778\pi\) | ||||
−0.619778 | + | 0.784777i | \(0.712778\pi\) | |||||||
\(264\) | −3.84055 | −0.236369 | ||||||||
\(265\) | −2.19639 | −0.134923 | ||||||||
\(266\) | −4.34946 | −0.266682 | ||||||||
\(267\) | −13.4985 | −0.826097 | ||||||||
\(268\) | −0.356946 | −0.0218040 | ||||||||
\(269\) | −21.5907 | −1.31641 | −0.658205 | − | 0.752839i | \(-0.728684\pi\) | ||||
−0.658205 | + | 0.752839i | \(0.728684\pi\) | |||||||
\(270\) | −2.25950 | −0.137509 | ||||||||
\(271\) | 11.2670 | 0.684419 | 0.342209 | − | 0.939624i | \(-0.388825\pi\) | ||||
0.342209 | + | 0.939624i | \(0.388825\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 15.2522 | 0.923107 | ||||||||
\(274\) | 12.5181 | 0.756247 | ||||||||
\(275\) | 0.404496 | 0.0243920 | ||||||||
\(276\) | −5.03855 | −0.303285 | ||||||||
\(277\) | 10.0277 | 0.602503 | 0.301252 | − | 0.953545i | \(-0.402596\pi\) | ||||
0.301252 | + | 0.953545i | \(0.402596\pi\) | |||||||
\(278\) | −0.485663 | −0.0291281 | ||||||||
\(279\) | −7.12027 | −0.426279 | ||||||||
\(280\) | 8.43907 | 0.504331 | ||||||||
\(281\) | 29.8315 | 1.77960 | 0.889799 | − | 0.456354i | \(-0.150845\pi\) | ||||
0.889799 | + | 0.456354i | \(0.150845\pi\) | |||||||
\(282\) | −0.0503609 | −0.00299895 | ||||||||
\(283\) | 10.4024 | 0.618361 | 0.309180 | − | 0.951003i | \(-0.399945\pi\) | ||||
0.309180 | + | 0.951003i | \(0.399945\pi\) | |||||||
\(284\) | 5.02022 | 0.297895 | ||||||||
\(285\) | 2.63126 | 0.155862 | ||||||||
\(286\) | −15.6835 | −0.927386 | ||||||||
\(287\) | 31.2310 | 1.84351 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 15.1423 | 0.889186 | ||||||||
\(291\) | 7.52852 | 0.441329 | ||||||||
\(292\) | −5.24611 | −0.307005 | ||||||||
\(293\) | −12.9210 | −0.754850 | −0.377425 | − | 0.926040i | \(-0.623190\pi\) | ||||
−0.377425 | + | 0.926040i | \(0.623190\pi\) | |||||||
\(294\) | −6.94974 | −0.405317 | ||||||||
\(295\) | −2.25950 | −0.131553 | ||||||||
\(296\) | −2.75553 | −0.160162 | ||||||||
\(297\) | −3.84055 | −0.222851 | ||||||||
\(298\) | −12.1194 | −0.702059 | ||||||||
\(299\) | −20.5758 | −1.18993 | ||||||||
\(300\) | −0.105322 | −0.00608080 | ||||||||
\(301\) | 39.3814 | 2.26990 | ||||||||
\(302\) | −12.0007 | −0.690561 | ||||||||
\(303\) | −7.36090 | −0.422873 | ||||||||
\(304\) | −1.16453 | −0.0667906 | ||||||||
\(305\) | −13.8219 | −0.791437 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −2.59585 | −0.148153 | −0.0740766 | − | 0.997253i | \(-0.523601\pi\) | ||||
−0.0740766 | + | 0.997253i | \(0.523601\pi\) | |||||||
\(308\) | 14.3442 | 0.817337 | ||||||||
\(309\) | −16.9716 | −0.965478 | ||||||||
\(310\) | −16.0882 | −0.913749 | ||||||||
\(311\) | −18.7836 | −1.06512 | −0.532560 | − | 0.846392i | \(-0.678770\pi\) | ||||
−0.532560 | + | 0.846392i | \(0.678770\pi\) | |||||||
\(312\) | 4.08367 | 0.231192 | ||||||||
\(313\) | 6.07314 | 0.343274 | 0.171637 | − | 0.985160i | \(-0.445094\pi\) | ||||
0.171637 | + | 0.985160i | \(0.445094\pi\) | |||||||
\(314\) | 6.65132 | 0.375356 | ||||||||
\(315\) | 8.43907 | 0.475488 | ||||||||
\(316\) | 0.531164 | 0.0298803 | ||||||||
\(317\) | 17.1939 | 0.965706 | 0.482853 | − | 0.875701i | \(-0.339601\pi\) | ||||
0.482853 | + | 0.875701i | \(0.339601\pi\) | |||||||
\(318\) | 0.972069 | 0.0545109 | ||||||||
\(319\) | 25.7379 | 1.44105 | ||||||||
\(320\) | 2.25950 | 0.126310 | ||||||||
\(321\) | −6.02420 | −0.336238 | ||||||||
\(322\) | 18.8187 | 1.04872 | ||||||||
\(323\) | 1.16453 | 0.0647964 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −0.430102 | −0.0238578 | ||||||||
\(326\) | 15.2569 | 0.845002 | ||||||||
\(327\) | 10.5956 | 0.585937 | ||||||||
\(328\) | 8.36186 | 0.461706 | ||||||||
\(329\) | 0.188095 | 0.0103700 | ||||||||
\(330\) | −8.67770 | −0.477692 | ||||||||
\(331\) | −29.0385 | −1.59610 | −0.798049 | − | 0.602592i | \(-0.794135\pi\) | ||||
−0.798049 | + | 0.602592i | \(0.794135\pi\) | |||||||
\(332\) | 5.67224 | 0.311305 | ||||||||
\(333\) | −2.75553 | −0.151002 | ||||||||
\(334\) | −18.2500 | −0.998597 | ||||||||
\(335\) | −0.806519 | −0.0440648 | ||||||||
\(336\) | −3.73494 | −0.203757 | ||||||||
\(337\) | 25.9764 | 1.41503 | 0.707513 | − | 0.706701i | \(-0.249817\pi\) | ||||
0.707513 | + | 0.706701i | \(0.249817\pi\) | |||||||
\(338\) | 3.67634 | 0.199967 | ||||||||
\(339\) | 20.2421 | 1.09940 | ||||||||
\(340\) | −2.25950 | −0.122538 | ||||||||
\(341\) | −27.3457 | −1.48085 | ||||||||
\(342\) | −1.16453 | −0.0629708 | ||||||||
\(343\) | −0.187700 | −0.0101349 | ||||||||
\(344\) | 10.5441 | 0.568497 | ||||||||
\(345\) | −11.3846 | −0.612925 | ||||||||
\(346\) | −5.65681 | −0.304112 | ||||||||
\(347\) | 9.12812 | 0.490023 | 0.245012 | − | 0.969520i | \(-0.421208\pi\) | ||||
0.245012 | + | 0.969520i | \(0.421208\pi\) | |||||||
\(348\) | −6.70162 | −0.359245 | ||||||||
\(349\) | 13.1665 | 0.704787 | 0.352394 | − | 0.935852i | \(-0.385368\pi\) | ||||
0.352394 | + | 0.935852i | \(0.385368\pi\) | |||||||
\(350\) | 0.393373 | 0.0210267 | ||||||||
\(351\) | 4.08367 | 0.217970 | ||||||||
\(352\) | 3.84055 | 0.204702 | ||||||||
\(353\) | 26.8304 | 1.42804 | 0.714018 | − | 0.700128i | \(-0.246874\pi\) | ||||
0.714018 | + | 0.700128i | \(0.246874\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | 11.3432 | 0.602033 | ||||||||
\(356\) | 13.4985 | 0.715421 | ||||||||
\(357\) | 3.73494 | 0.197674 | ||||||||
\(358\) | −17.5859 | −0.929444 | ||||||||
\(359\) | 7.02028 | 0.370516 | 0.185258 | − | 0.982690i | \(-0.440688\pi\) | ||||
0.185258 | + | 0.982690i | \(0.440688\pi\) | |||||||
\(360\) | 2.25950 | 0.119086 | ||||||||
\(361\) | −17.6439 | −0.928624 | ||||||||
\(362\) | 15.4875 | 0.814006 | ||||||||
\(363\) | −3.74980 | −0.196814 | ||||||||
\(364\) | −15.2522 | −0.799434 | ||||||||
\(365\) | −11.8536 | −0.620444 | ||||||||
\(366\) | 6.11723 | 0.319753 | ||||||||
\(367\) | 16.5640 | 0.864632 | 0.432316 | − | 0.901722i | \(-0.357696\pi\) | ||||
0.432316 | + | 0.901722i | \(0.357696\pi\) | |||||||
\(368\) | 5.03855 | 0.262652 | ||||||||
\(369\) | 8.36186 | 0.435301 | ||||||||
\(370\) | −6.22610 | −0.323680 | ||||||||
\(371\) | −3.63062 | −0.188492 | ||||||||
\(372\) | 7.12027 | 0.369169 | ||||||||
\(373\) | 3.82633 | 0.198120 | 0.0990600 | − | 0.995081i | \(-0.468416\pi\) | ||||
0.0990600 | + | 0.995081i | \(0.468416\pi\) | |||||||
\(374\) | −3.84055 | −0.198590 | ||||||||
\(375\) | 11.0595 | 0.571110 | ||||||||
\(376\) | 0.0503609 | 0.00259716 | ||||||||
\(377\) | −27.3672 | −1.40948 | ||||||||
\(378\) | −3.73494 | −0.192104 | ||||||||
\(379\) | −7.12721 | −0.366100 | −0.183050 | − | 0.983104i | \(-0.558597\pi\) | ||||
−0.183050 | + | 0.983104i | \(0.558597\pi\) | |||||||
\(380\) | −2.63126 | −0.134981 | ||||||||
\(381\) | 7.19680 | 0.368703 | ||||||||
\(382\) | −5.98757 | −0.306351 | ||||||||
\(383\) | 19.2278 | 0.982494 | 0.491247 | − | 0.871020i | \(-0.336541\pi\) | ||||
0.491247 | + | 0.871020i | \(0.336541\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 32.4107 | 1.65180 | ||||||||
\(386\) | 20.0576 | 1.02090 | ||||||||
\(387\) | 10.5441 | 0.535984 | ||||||||
\(388\) | −7.52852 | −0.382203 | ||||||||
\(389\) | 19.0883 | 0.967815 | 0.483908 | − | 0.875119i | \(-0.339217\pi\) | ||||
0.483908 | + | 0.875119i | \(0.339217\pi\) | |||||||
\(390\) | 9.22703 | 0.467229 | ||||||||
\(391\) | −5.03855 | −0.254810 | ||||||||
\(392\) | 6.94974 | 0.351015 | ||||||||
\(393\) | 10.3416 | 0.521665 | ||||||||
\(394\) | −1.62569 | −0.0819013 | ||||||||
\(395\) | 1.20016 | 0.0603867 | ||||||||
\(396\) | 3.84055 | 0.192995 | ||||||||
\(397\) | 21.1370 | 1.06084 | 0.530418 | − | 0.847736i | \(-0.322035\pi\) | ||||
0.530418 | + | 0.847736i | \(0.322035\pi\) | |||||||
\(398\) | −10.9179 | −0.547267 | ||||||||
\(399\) | 4.34946 | 0.217745 | ||||||||
\(400\) | 0.105322 | 0.00526612 | ||||||||
\(401\) | 24.8782 | 1.24236 | 0.621180 | − | 0.783668i | \(-0.286654\pi\) | ||||
0.621180 | + | 0.783668i | \(0.286654\pi\) | |||||||
\(402\) | 0.356946 | 0.0178029 | ||||||||
\(403\) | 29.0768 | 1.44842 | ||||||||
\(404\) | 7.36090 | 0.366218 | ||||||||
\(405\) | 2.25950 | 0.112275 | ||||||||
\(406\) | 25.0301 | 1.24222 | ||||||||
\(407\) | −10.5827 | −0.524566 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −11.5738 | −0.572287 | −0.286144 | − | 0.958187i | \(-0.592373\pi\) | ||||
−0.286144 | + | 0.958187i | \(0.592373\pi\) | |||||||
\(410\) | 18.8936 | 0.933087 | ||||||||
\(411\) | −12.5181 | −0.617473 | ||||||||
\(412\) | 16.9716 | 0.836128 | ||||||||
\(413\) | −3.73494 | −0.183784 | ||||||||
\(414\) | 5.03855 | 0.247631 | ||||||||
\(415\) | 12.8164 | 0.629133 | ||||||||
\(416\) | −4.08367 | −0.200218 | ||||||||
\(417\) | 0.485663 | 0.0237830 | ||||||||
\(418\) | −4.47245 | −0.218755 | ||||||||
\(419\) | −6.59791 | −0.322329 | −0.161165 | − | 0.986928i | \(-0.551525\pi\) | ||||
−0.161165 | + | 0.986928i | \(0.551525\pi\) | |||||||
\(420\) | −8.43907 | −0.411785 | ||||||||
\(421\) | 1.87461 | 0.0913628 | 0.0456814 | − | 0.998956i | \(-0.485454\pi\) | ||||
0.0456814 | + | 0.998956i | \(0.485454\pi\) | |||||||
\(422\) | 24.7016 | 1.20245 | ||||||||
\(423\) | 0.0503609 | 0.00244863 | ||||||||
\(424\) | −0.972069 | −0.0472078 | ||||||||
\(425\) | −0.105322 | −0.00510889 | ||||||||
\(426\) | −5.02022 | −0.243231 | ||||||||
\(427\) | −22.8475 | −1.10567 | ||||||||
\(428\) | 6.02420 | 0.291191 | ||||||||
\(429\) | 15.6835 | 0.757207 | ||||||||
\(430\) | 23.8242 | 1.14891 | ||||||||
\(431\) | −22.9785 | −1.10684 | −0.553418 | − | 0.832904i | \(-0.686677\pi\) | ||||
−0.553418 | + | 0.832904i | \(0.686677\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 0.864790 | 0.0415591 | 0.0207796 | − | 0.999784i | \(-0.493385\pi\) | ||||
0.0207796 | + | 0.999784i | \(0.493385\pi\) | |||||||
\(434\) | −26.5937 | −1.27654 | ||||||||
\(435\) | −15.1423 | −0.726017 | ||||||||
\(436\) | −10.5956 | −0.507436 | ||||||||
\(437\) | −5.86756 | −0.280683 | ||||||||
\(438\) | 5.24611 | 0.250669 | ||||||||
\(439\) | −9.41071 | −0.449149 | −0.224574 | − | 0.974457i | \(-0.572099\pi\) | ||||
−0.224574 | + | 0.974457i | \(0.572099\pi\) | |||||||
\(440\) | 8.67770 | 0.413693 | ||||||||
\(441\) | 6.94974 | 0.330940 | ||||||||
\(442\) | 4.08367 | 0.194240 | ||||||||
\(443\) | −13.5800 | −0.645206 | −0.322603 | − | 0.946534i | \(-0.604558\pi\) | ||||
−0.322603 | + | 0.946534i | \(0.604558\pi\) | |||||||
\(444\) | 2.75553 | 0.130771 | ||||||||
\(445\) | 30.4999 | 1.44583 | ||||||||
\(446\) | −17.9650 | −0.850668 | ||||||||
\(447\) | 12.1194 | 0.573229 | ||||||||
\(448\) | 3.73494 | 0.176459 | ||||||||
\(449\) | 29.3480 | 1.38502 | 0.692510 | − | 0.721408i | \(-0.256505\pi\) | ||||
0.692510 | + | 0.721408i | \(0.256505\pi\) | |||||||
\(450\) | 0.105322 | 0.00496495 | ||||||||
\(451\) | 32.1141 | 1.51219 | ||||||||
\(452\) | −20.2421 | −0.952107 | ||||||||
\(453\) | 12.0007 | 0.563840 | ||||||||
\(454\) | −12.1520 | −0.570320 | ||||||||
\(455\) | −34.4624 | −1.61562 | ||||||||
\(456\) | 1.16453 | 0.0545343 | ||||||||
\(457\) | −37.0754 | −1.73431 | −0.867157 | − | 0.498035i | \(-0.834055\pi\) | ||||
−0.867157 | + | 0.498035i | \(0.834055\pi\) | |||||||
\(458\) | −10.5713 | −0.493965 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 11.3846 | 0.530809 | ||||||||
\(461\) | −34.0342 | −1.58513 | −0.792566 | − | 0.609786i | \(-0.791255\pi\) | ||||
−0.792566 | + | 0.609786i | \(0.791255\pi\) | |||||||
\(462\) | −14.3442 | −0.667352 | ||||||||
\(463\) | −1.56747 | −0.0728466 | −0.0364233 | − | 0.999336i | \(-0.511596\pi\) | ||||
−0.0364233 | + | 0.999336i | \(0.511596\pi\) | |||||||
\(464\) | 6.70162 | 0.311115 | ||||||||
\(465\) | 16.0882 | 0.746073 | ||||||||
\(466\) | 13.9663 | 0.646975 | ||||||||
\(467\) | −9.32331 | −0.431431 | −0.215716 | − | 0.976456i | \(-0.569208\pi\) | ||||
−0.215716 | + | 0.976456i | \(0.569208\pi\) | |||||||
\(468\) | −4.08367 | −0.188768 | ||||||||
\(469\) | −1.33317 | −0.0615601 | ||||||||
\(470\) | 0.113790 | 0.00524875 | ||||||||
\(471\) | −6.65132 | −0.306477 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | 40.4949 | 1.86196 | ||||||||
\(474\) | −0.531164 | −0.0243972 | ||||||||
\(475\) | −0.122652 | −0.00562764 | ||||||||
\(476\) | −3.73494 | −0.171190 | ||||||||
\(477\) | −0.972069 | −0.0445080 | ||||||||
\(478\) | 28.5324 | 1.30504 | ||||||||
\(479\) | −18.8986 | −0.863501 | −0.431750 | − | 0.901993i | \(-0.642104\pi\) | ||||
−0.431750 | + | 0.901993i | \(0.642104\pi\) | |||||||
\(480\) | −2.25950 | −0.103131 | ||||||||
\(481\) | 11.2527 | 0.513077 | ||||||||
\(482\) | −29.0203 | −1.32184 | ||||||||
\(483\) | −18.8187 | −0.856278 | ||||||||
\(484\) | 3.74980 | 0.170446 | ||||||||
\(485\) | −17.0107 | −0.772414 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −2.21739 | −0.100479 | −0.0502397 | − | 0.998737i | \(-0.515999\pi\) | ||||
−0.0502397 | + | 0.998737i | \(0.515999\pi\) | |||||||
\(488\) | −6.11723 | −0.276914 | ||||||||
\(489\) | −15.2569 | −0.689942 | ||||||||
\(490\) | 15.7029 | 0.709386 | ||||||||
\(491\) | −25.7217 | −1.16080 | −0.580401 | − | 0.814331i | \(-0.697104\pi\) | ||||
−0.580401 | + | 0.814331i | \(0.697104\pi\) | |||||||
\(492\) | −8.36186 | −0.376982 | ||||||||
\(493\) | −6.70162 | −0.301826 | ||||||||
\(494\) | 4.75557 | 0.213963 | ||||||||
\(495\) | 8.67770 | 0.390034 | ||||||||
\(496\) | −7.12027 | −0.319709 | ||||||||
\(497\) | 18.7502 | 0.841062 | ||||||||
\(498\) | −5.67224 | −0.254179 | ||||||||
\(499\) | 28.1068 | 1.25823 | 0.629116 | − | 0.777311i | \(-0.283417\pi\) | ||||
0.629116 | + | 0.777311i | \(0.283417\pi\) | |||||||
\(500\) | −11.0595 | −0.494596 | ||||||||
\(501\) | 18.2500 | 0.815351 | ||||||||
\(502\) | 26.4706 | 1.18144 | ||||||||
\(503\) | −23.9722 | −1.06887 | −0.534434 | − | 0.845210i | \(-0.679475\pi\) | ||||
−0.534434 | + | 0.845210i | \(0.679475\pi\) | |||||||
\(504\) | 3.73494 | 0.166367 | ||||||||
\(505\) | 16.6319 | 0.740111 | ||||||||
\(506\) | 19.3508 | 0.860247 | ||||||||
\(507\) | −3.67634 | −0.163272 | ||||||||
\(508\) | −7.19680 | −0.319306 | ||||||||
\(509\) | −32.5485 | −1.44269 | −0.721343 | − | 0.692578i | \(-0.756475\pi\) | ||||
−0.721343 | + | 0.692578i | \(0.756475\pi\) | |||||||
\(510\) | 2.25950 | 0.100052 | ||||||||
\(511\) | −19.5939 | −0.866782 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.16453 | 0.0514154 | ||||||||
\(514\) | −19.5525 | −0.862426 | ||||||||
\(515\) | 38.3472 | 1.68978 | ||||||||
\(516\) | −10.5441 | −0.464176 | ||||||||
\(517\) | 0.193413 | 0.00850630 | ||||||||
\(518\) | −10.2917 | −0.452192 | ||||||||
\(519\) | 5.65681 | 0.248306 | ||||||||
\(520\) | −9.22703 | −0.404632 | ||||||||
\(521\) | 26.6450 | 1.16734 | 0.583670 | − | 0.811991i | \(-0.301616\pi\) | ||||
0.583670 | + | 0.811991i | \(0.301616\pi\) | |||||||
\(522\) | 6.70162 | 0.293322 | ||||||||
\(523\) | −7.84479 | −0.343029 | −0.171514 | − | 0.985182i | \(-0.554866\pi\) | ||||
−0.171514 | + | 0.985182i | \(0.554866\pi\) | |||||||
\(524\) | −10.3416 | −0.451775 | ||||||||
\(525\) | −0.393373 | −0.0171682 | ||||||||
\(526\) | −20.1022 | −0.876499 | ||||||||
\(527\) | 7.12027 | 0.310164 | ||||||||
\(528\) | −3.84055 | −0.167138 | ||||||||
\(529\) | 2.38697 | 0.103781 | ||||||||
\(530\) | −2.19639 | −0.0954049 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | −4.34946 | −0.188573 | ||||||||
\(533\) | −34.1470 | −1.47907 | ||||||||
\(534\) | −13.4985 | −0.584139 | ||||||||
\(535\) | 13.6117 | 0.588483 | ||||||||
\(536\) | −0.356946 | −0.0154177 | ||||||||
\(537\) | 17.5859 | 0.758888 | ||||||||
\(538\) | −21.5907 | −0.930843 | ||||||||
\(539\) | 26.6908 | 1.14966 | ||||||||
\(540\) | −2.25950 | −0.0972332 | ||||||||
\(541\) | 14.3164 | 0.615511 | 0.307756 | − | 0.951465i | \(-0.400422\pi\) | ||||
0.307756 | + | 0.951465i | \(0.400422\pi\) | |||||||
\(542\) | 11.2670 | 0.483957 | ||||||||
\(543\) | −15.4875 | −0.664633 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −23.9407 | −1.02551 | ||||||||
\(546\) | 15.2522 | 0.652735 | ||||||||
\(547\) | 7.81064 | 0.333959 | 0.166979 | − | 0.985960i | \(-0.446599\pi\) | ||||
0.166979 | + | 0.985960i | \(0.446599\pi\) | |||||||
\(548\) | 12.5181 | 0.534748 | ||||||||
\(549\) | −6.11723 | −0.261077 | ||||||||
\(550\) | 0.404496 | 0.0172478 | ||||||||
\(551\) | −7.80426 | −0.332473 | ||||||||
\(552\) | −5.03855 | −0.214455 | ||||||||
\(553\) | 1.98386 | 0.0843624 | ||||||||
\(554\) | 10.0277 | 0.426034 | ||||||||
\(555\) | 6.22610 | 0.264283 | ||||||||
\(556\) | −0.485663 | −0.0205967 | ||||||||
\(557\) | 31.0526 | 1.31574 | 0.657871 | − | 0.753130i | \(-0.271457\pi\) | ||||
0.657871 | + | 0.753130i | \(0.271457\pi\) | |||||||
\(558\) | −7.12027 | −0.301425 | ||||||||
\(559\) | −43.0584 | −1.82118 | ||||||||
\(560\) | 8.43907 | 0.356616 | ||||||||
\(561\) | 3.84055 | 0.162148 | ||||||||
\(562\) | 29.8315 | 1.25837 | ||||||||
\(563\) | −23.7356 | −1.00034 | −0.500168 | − | 0.865928i | \(-0.666728\pi\) | ||||
−0.500168 | + | 0.865928i | \(0.666728\pi\) | |||||||
\(564\) | −0.0503609 | −0.00212057 | ||||||||
\(565\) | −45.7369 | −1.92416 | ||||||||
\(566\) | 10.4024 | 0.437247 | ||||||||
\(567\) | 3.73494 | 0.156853 | ||||||||
\(568\) | 5.02022 | 0.210644 | ||||||||
\(569\) | −18.0113 | −0.755072 | −0.377536 | − | 0.925995i | \(-0.623229\pi\) | ||||
−0.377536 | + | 0.925995i | \(0.623229\pi\) | |||||||
\(570\) | 2.63126 | 0.110211 | ||||||||
\(571\) | 13.2665 | 0.555185 | 0.277592 | − | 0.960699i | \(-0.410464\pi\) | ||||
0.277592 | + | 0.960699i | \(0.410464\pi\) | |||||||
\(572\) | −15.6835 | −0.655761 | ||||||||
\(573\) | 5.98757 | 0.250134 | ||||||||
\(574\) | 31.2310 | 1.30356 | ||||||||
\(575\) | 0.530672 | 0.0221306 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 6.08544 | 0.253340 | 0.126670 | − | 0.991945i | \(-0.459571\pi\) | ||||
0.126670 | + | 0.991945i | \(0.459571\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −20.0576 | −0.833565 | ||||||||
\(580\) | 15.1423 | 0.628749 | ||||||||
\(581\) | 21.1855 | 0.878921 | ||||||||
\(582\) | 7.52852 | 0.312067 | ||||||||
\(583\) | −3.73328 | −0.154617 | ||||||||
\(584\) | −5.24611 | −0.217085 | ||||||||
\(585\) | −9.22703 | −0.381491 | ||||||||
\(586\) | −12.9210 | −0.533760 | ||||||||
\(587\) | 8.53687 | 0.352354 | 0.176177 | − | 0.984358i | \(-0.443627\pi\) | ||||
0.176177 | + | 0.984358i | \(0.443627\pi\) | |||||||
\(588\) | −6.94974 | −0.286603 | ||||||||
\(589\) | 8.29179 | 0.341657 | ||||||||
\(590\) | −2.25950 | −0.0930220 | ||||||||
\(591\) | 1.62569 | 0.0668721 | ||||||||
\(592\) | −2.75553 | −0.113251 | ||||||||
\(593\) | 23.7012 | 0.973293 | 0.486647 | − | 0.873599i | \(-0.338220\pi\) | ||||
0.486647 | + | 0.873599i | \(0.338220\pi\) | |||||||
\(594\) | −3.84055 | −0.157580 | ||||||||
\(595\) | −8.43907 | −0.345968 | ||||||||
\(596\) | −12.1194 | −0.496431 | ||||||||
\(597\) | 10.9179 | 0.446841 | ||||||||
\(598\) | −20.5758 | −0.841405 | ||||||||
\(599\) | −2.08309 | −0.0851129 | −0.0425564 | − | 0.999094i | \(-0.513550\pi\) | ||||
−0.0425564 | + | 0.999094i | \(0.513550\pi\) | |||||||
\(600\) | −0.105322 | −0.00429977 | ||||||||
\(601\) | 4.30685 | 0.175680 | 0.0878401 | − | 0.996135i | \(-0.472004\pi\) | ||||
0.0878401 | + | 0.996135i | \(0.472004\pi\) | |||||||
\(602\) | 39.3814 | 1.60506 | ||||||||
\(603\) | −0.356946 | −0.0145360 | ||||||||
\(604\) | −12.0007 | −0.488300 | ||||||||
\(605\) | 8.47267 | 0.344463 | ||||||||
\(606\) | −7.36090 | −0.299016 | ||||||||
\(607\) | −1.62235 | −0.0658491 | −0.0329246 | − | 0.999458i | \(-0.510482\pi\) | ||||
−0.0329246 | + | 0.999458i | \(0.510482\pi\) | |||||||
\(608\) | −1.16453 | −0.0472281 | ||||||||
\(609\) | −25.0301 | −1.01427 | ||||||||
\(610\) | −13.8219 | −0.559631 | ||||||||
\(611\) | −0.205657 | −0.00831999 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −25.1016 | −1.01385 | −0.506923 | − | 0.861992i | \(-0.669217\pi\) | ||||
−0.506923 | + | 0.861992i | \(0.669217\pi\) | |||||||
\(614\) | −2.59585 | −0.104760 | ||||||||
\(615\) | −18.8936 | −0.761863 | ||||||||
\(616\) | 14.3442 | 0.577944 | ||||||||
\(617\) | 1.41959 | 0.0571505 | 0.0285753 | − | 0.999592i | \(-0.490903\pi\) | ||||
0.0285753 | + | 0.999592i | \(0.490903\pi\) | |||||||
\(618\) | −16.9716 | −0.682696 | ||||||||
\(619\) | −33.0372 | −1.32788 | −0.663938 | − | 0.747788i | \(-0.731116\pi\) | ||||
−0.663938 | + | 0.747788i | \(0.731116\pi\) | |||||||
\(620\) | −16.0882 | −0.646118 | ||||||||
\(621\) | −5.03855 | −0.202190 | ||||||||
\(622\) | −18.7836 | −0.753154 | ||||||||
\(623\) | 50.4162 | 2.01988 | ||||||||
\(624\) | 4.08367 | 0.163478 | ||||||||
\(625\) | −25.5155 | −1.02062 | ||||||||
\(626\) | 6.07314 | 0.242731 | ||||||||
\(627\) | 4.47245 | 0.178612 | ||||||||
\(628\) | 6.65132 | 0.265417 | ||||||||
\(629\) | 2.75553 | 0.109870 | ||||||||
\(630\) | 8.43907 | 0.336221 | ||||||||
\(631\) | −37.6015 | −1.49689 | −0.748446 | − | 0.663196i | \(-0.769200\pi\) | ||||
−0.748446 | + | 0.663196i | \(0.769200\pi\) | |||||||
\(632\) | 0.531164 | 0.0211286 | ||||||||
\(633\) | −24.7016 | −0.981800 | ||||||||
\(634\) | 17.1939 | 0.682857 | ||||||||
\(635\) | −16.2611 | −0.645303 | ||||||||
\(636\) | 0.972069 | 0.0385450 | ||||||||
\(637\) | −28.3804 | −1.12447 | ||||||||
\(638\) | 25.7379 | 1.01897 | ||||||||
\(639\) | 5.02022 | 0.198597 | ||||||||
\(640\) | 2.25950 | 0.0893144 | ||||||||
\(641\) | 0.103096 | 0.00407206 | 0.00203603 | − | 0.999998i | \(-0.499352\pi\) | ||||
0.00203603 | + | 0.999998i | \(0.499352\pi\) | |||||||
\(642\) | −6.02420 | −0.237756 | ||||||||
\(643\) | 17.7498 | 0.699986 | 0.349993 | − | 0.936752i | \(-0.386184\pi\) | ||||
0.349993 | + | 0.936752i | \(0.386184\pi\) | |||||||
\(644\) | 18.8187 | 0.741559 | ||||||||
\(645\) | −23.8242 | −0.938079 | ||||||||
\(646\) | 1.16453 | 0.0458180 | ||||||||
\(647\) | 26.9828 | 1.06080 | 0.530401 | − | 0.847747i | \(-0.322041\pi\) | ||||
0.530401 | + | 0.847747i | \(0.322041\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −3.84055 | −0.150755 | ||||||||
\(650\) | −0.430102 | −0.0168700 | ||||||||
\(651\) | 26.5937 | 1.04229 | ||||||||
\(652\) | 15.2569 | 0.597507 | ||||||||
\(653\) | −34.5877 | −1.35352 | −0.676761 | − | 0.736202i | \(-0.736617\pi\) | ||||
−0.676761 | + | 0.736202i | \(0.736617\pi\) | |||||||
\(654\) | 10.5956 | 0.414320 | ||||||||
\(655\) | −23.3668 | −0.913017 | ||||||||
\(656\) | 8.36186 | 0.326476 | ||||||||
\(657\) | −5.24611 | −0.204670 | ||||||||
\(658\) | 0.188095 | 0.00733269 | ||||||||
\(659\) | −9.03242 | −0.351853 | −0.175927 | − | 0.984403i | \(-0.556292\pi\) | ||||
−0.175927 | + | 0.984403i | \(0.556292\pi\) | |||||||
\(660\) | −8.67770 | −0.337779 | ||||||||
\(661\) | 14.1662 | 0.551003 | 0.275502 | − | 0.961301i | \(-0.411156\pi\) | ||||
0.275502 | + | 0.961301i | \(0.411156\pi\) | |||||||
\(662\) | −29.0385 | −1.12861 | ||||||||
\(663\) | −4.08367 | −0.158597 | ||||||||
\(664\) | 5.67224 | 0.220126 | ||||||||
\(665\) | −9.82758 | −0.381097 | ||||||||
\(666\) | −2.75553 | −0.106774 | ||||||||
\(667\) | 33.7664 | 1.30744 | ||||||||
\(668\) | −18.2500 | −0.706114 | ||||||||
\(669\) | 17.9650 | 0.694567 | ||||||||
\(670\) | −0.806519 | −0.0311585 | ||||||||
\(671\) | −23.4935 | −0.906957 | ||||||||
\(672\) | −3.73494 | −0.144078 | ||||||||
\(673\) | −45.0241 | −1.73555 | −0.867776 | − | 0.496955i | \(-0.834451\pi\) | ||||
−0.867776 | + | 0.496955i | \(0.834451\pi\) | |||||||
\(674\) | 25.9764 | 1.00057 | ||||||||
\(675\) | −0.105322 | −0.00405386 | ||||||||
\(676\) | 3.67634 | 0.141398 | ||||||||
\(677\) | 12.1851 | 0.468312 | 0.234156 | − | 0.972199i | \(-0.424767\pi\) | ||||
0.234156 | + | 0.972199i | \(0.424767\pi\) | |||||||
\(678\) | 20.2421 | 0.777392 | ||||||||
\(679\) | −28.1185 | −1.07909 | ||||||||
\(680\) | −2.25950 | −0.0866477 | ||||||||
\(681\) | 12.1520 | 0.465664 | ||||||||
\(682\) | −27.3457 | −1.04712 | ||||||||
\(683\) | −34.0667 | −1.30353 | −0.651763 | − | 0.758423i | \(-0.725970\pi\) | ||||
−0.651763 | + | 0.758423i | \(0.725970\pi\) | |||||||
\(684\) | −1.16453 | −0.0445271 | ||||||||
\(685\) | 28.2846 | 1.08070 | ||||||||
\(686\) | −0.187700 | −0.00716643 | ||||||||
\(687\) | 10.5713 | 0.403320 | ||||||||
\(688\) | 10.5441 | 0.401988 | ||||||||
\(689\) | 3.96961 | 0.151230 | ||||||||
\(690\) | −11.3846 | −0.433404 | ||||||||
\(691\) | 16.1644 | 0.614923 | 0.307461 | − | 0.951561i | \(-0.400520\pi\) | ||||
0.307461 | + | 0.951561i | \(0.400520\pi\) | |||||||
\(692\) | −5.65681 | −0.215040 | ||||||||
\(693\) | 14.3442 | 0.544891 | ||||||||
\(694\) | 9.12812 | 0.346499 | ||||||||
\(695\) | −1.09735 | −0.0416250 | ||||||||
\(696\) | −6.70162 | −0.254024 | ||||||||
\(697\) | −8.36186 | −0.316728 | ||||||||
\(698\) | 13.1665 | 0.498360 | ||||||||
\(699\) | −13.9663 | −0.528253 | ||||||||
\(700\) | 0.393373 | 0.0148681 | ||||||||
\(701\) | 35.3391 | 1.33474 | 0.667369 | − | 0.744727i | \(-0.267420\pi\) | ||||
0.667369 | + | 0.744727i | \(0.267420\pi\) | |||||||
\(702\) | 4.08367 | 0.154128 | ||||||||
\(703\) | 3.20890 | 0.121026 | ||||||||
\(704\) | 3.84055 | 0.144746 | ||||||||
\(705\) | −0.113790 | −0.00428558 | ||||||||
\(706\) | 26.8304 | 1.00977 | ||||||||
\(707\) | 27.4925 | 1.03396 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | −41.0406 | −1.54131 | −0.770656 | − | 0.637251i | \(-0.780071\pi\) | ||||
−0.770656 | + | 0.637251i | \(0.780071\pi\) | |||||||
\(710\) | 11.3432 | 0.425702 | ||||||||
\(711\) | 0.531164 | 0.0199202 | ||||||||
\(712\) | 13.4985 | 0.505879 | ||||||||
\(713\) | −35.8758 | −1.34356 | ||||||||
\(714\) | 3.73494 | 0.139776 | ||||||||
\(715\) | −35.4369 | −1.32526 | ||||||||
\(716\) | −17.5859 | −0.657216 | ||||||||
\(717\) | −28.5324 | −1.06556 | ||||||||
\(718\) | 7.02028 | 0.261995 | ||||||||
\(719\) | −17.1001 | −0.637728 | −0.318864 | − | 0.947800i | \(-0.603301\pi\) | ||||
−0.318864 | + | 0.947800i | \(0.603301\pi\) | |||||||
\(720\) | 2.25950 | 0.0842064 | ||||||||
\(721\) | 63.3877 | 2.36068 | ||||||||
\(722\) | −17.6439 | −0.656637 | ||||||||
\(723\) | 29.0203 | 1.07928 | ||||||||
\(724\) | 15.4875 | 0.575589 | ||||||||
\(725\) | 0.705831 | 0.0262139 | ||||||||
\(726\) | −3.74980 | −0.139168 | ||||||||
\(727\) | −17.2349 | −0.639205 | −0.319603 | − | 0.947552i | \(-0.603549\pi\) | ||||
−0.319603 | + | 0.947552i | \(0.603549\pi\) | |||||||
\(728\) | −15.2522 | −0.565285 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.8536 | −0.438720 | ||||||||
\(731\) | −10.5441 | −0.389986 | ||||||||
\(732\) | 6.11723 | 0.226099 | ||||||||
\(733\) | −39.5708 | −1.46158 | −0.730790 | − | 0.682602i | \(-0.760848\pi\) | ||||
−0.730790 | + | 0.682602i | \(0.760848\pi\) | |||||||
\(734\) | 16.5640 | 0.611387 | ||||||||
\(735\) | −15.7029 | −0.579211 | ||||||||
\(736\) | 5.03855 | 0.185723 | ||||||||
\(737\) | −1.37087 | −0.0504966 | ||||||||
\(738\) | 8.36186 | 0.307804 | ||||||||
\(739\) | 26.2005 | 0.963799 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(740\) | −6.22610 | −0.228876 | ||||||||
\(741\) | −4.75557 | −0.174700 | ||||||||
\(742\) | −3.63062 | −0.133284 | ||||||||
\(743\) | −25.0926 | −0.920559 | −0.460280 | − | 0.887774i | \(-0.652251\pi\) | ||||
−0.460280 | + | 0.887774i | \(0.652251\pi\) | |||||||
\(744\) | 7.12027 | 0.261042 | ||||||||
\(745\) | −27.3838 | −1.00326 | ||||||||
\(746\) | 3.82633 | 0.140092 | ||||||||
\(747\) | 5.67224 | 0.207537 | ||||||||
\(748\) | −3.84055 | −0.140424 | ||||||||
\(749\) | 22.5000 | 0.822132 | ||||||||
\(750\) | 11.0595 | 0.403836 | ||||||||
\(751\) | −25.1869 | −0.919082 | −0.459541 | − | 0.888157i | \(-0.651986\pi\) | ||||
−0.459541 | + | 0.888157i | \(0.651986\pi\) | |||||||
\(752\) | 0.0503609 | 0.00183647 | ||||||||
\(753\) | −26.4706 | −0.964642 | ||||||||
\(754\) | −27.3672 | −0.996654 | ||||||||
\(755\) | −27.1155 | −0.986833 | ||||||||
\(756\) | −3.73494 | −0.135838 | ||||||||
\(757\) | 42.0424 | 1.52806 | 0.764028 | − | 0.645183i | \(-0.223219\pi\) | ||||
0.764028 | + | 0.645183i | \(0.223219\pi\) | |||||||
\(758\) | −7.12721 | −0.258872 | ||||||||
\(759\) | −19.3508 | −0.702389 | ||||||||
\(760\) | −2.63126 | −0.0954458 | ||||||||
\(761\) | 40.5003 | 1.46814 | 0.734068 | − | 0.679076i | \(-0.237619\pi\) | ||||
0.734068 | + | 0.679076i | \(0.237619\pi\) | |||||||
\(762\) | 7.19680 | 0.260712 | ||||||||
\(763\) | −39.5738 | −1.43267 | ||||||||
\(764\) | −5.98757 | −0.216623 | ||||||||
\(765\) | −2.25950 | −0.0816923 | ||||||||
\(766\) | 19.2278 | 0.694728 | ||||||||
\(767\) | 4.08367 | 0.147453 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −47.3385 | −1.70707 | −0.853535 | − | 0.521036i | \(-0.825546\pi\) | ||||
−0.853535 | + | 0.521036i | \(0.825546\pi\) | |||||||
\(770\) | 32.4107 | 1.16800 | ||||||||
\(771\) | 19.5525 | 0.704168 | ||||||||
\(772\) | 20.0576 | 0.721888 | ||||||||
\(773\) | −20.0210 | −0.720105 | −0.360053 | − | 0.932932i | \(-0.617241\pi\) | ||||
−0.360053 | + | 0.932932i | \(0.617241\pi\) | |||||||
\(774\) | 10.5441 | 0.378998 | ||||||||
\(775\) | −0.749924 | −0.0269381 | ||||||||
\(776\) | −7.52852 | −0.270258 | ||||||||
\(777\) | 10.2917 | 0.369213 | ||||||||
\(778\) | 19.0883 | 0.684349 | ||||||||
\(779\) | −9.73766 | −0.348888 | ||||||||
\(780\) | 9.22703 | 0.330381 | ||||||||
\(781\) | 19.2804 | 0.689907 | ||||||||
\(782\) | −5.03855 | −0.180178 | ||||||||
\(783\) | −6.70162 | −0.239496 | ||||||||
\(784\) | 6.94974 | 0.248205 | ||||||||
\(785\) | 15.0286 | 0.536395 | ||||||||
\(786\) | 10.3416 | 0.368873 | ||||||||
\(787\) | 16.7688 | 0.597745 | 0.298872 | − | 0.954293i | \(-0.403390\pi\) | ||||
0.298872 | + | 0.954293i | \(0.403390\pi\) | |||||||
\(788\) | −1.62569 | −0.0579129 | ||||||||
\(789\) | 20.1022 | 0.715658 | ||||||||
\(790\) | 1.20016 | 0.0426999 | ||||||||
\(791\) | −75.6028 | −2.68813 | ||||||||
\(792\) | 3.84055 | 0.136468 | ||||||||
\(793\) | 24.9807 | 0.887092 | ||||||||
\(794\) | 21.1370 | 0.750124 | ||||||||
\(795\) | 2.19639 | 0.0778978 | ||||||||
\(796\) | −10.9179 | −0.386976 | ||||||||
\(797\) | 39.5968 | 1.40259 | 0.701296 | − | 0.712870i | \(-0.252605\pi\) | ||||
0.701296 | + | 0.712870i | \(0.252605\pi\) | |||||||
\(798\) | 4.34946 | 0.153969 | ||||||||
\(799\) | −0.0503609 | −0.00178164 | ||||||||
\(800\) | 0.105322 | 0.00372371 | ||||||||
\(801\) | 13.4985 | 0.476948 | ||||||||
\(802\) | 24.8782 | 0.878481 | ||||||||
\(803\) | −20.1479 | −0.711005 | ||||||||
\(804\) | 0.356946 | 0.0125885 | ||||||||
\(805\) | 42.5207 | 1.49866 | ||||||||
\(806\) | 29.0768 | 1.02419 | ||||||||
\(807\) | 21.5907 | 0.760030 | ||||||||
\(808\) | 7.36090 | 0.258956 | ||||||||
\(809\) | 49.7068 | 1.74760 | 0.873800 | − | 0.486286i | \(-0.161649\pi\) | ||||
0.873800 | + | 0.486286i | \(0.161649\pi\) | |||||||
\(810\) | 2.25950 | 0.0793906 | ||||||||
\(811\) | −51.6865 | −1.81496 | −0.907480 | − | 0.420095i | \(-0.861997\pi\) | ||||
−0.907480 | + | 0.420095i | \(0.861997\pi\) | |||||||
\(812\) | 25.0301 | 0.878385 | ||||||||
\(813\) | −11.2670 | −0.395149 | ||||||||
\(814\) | −10.5827 | −0.370924 | ||||||||
\(815\) | 34.4729 | 1.20753 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −12.2789 | −0.429584 | ||||||||
\(818\) | −11.5738 | −0.404668 | ||||||||
\(819\) | −15.2522 | −0.532956 | ||||||||
\(820\) | 18.8936 | 0.659792 | ||||||||
\(821\) | −31.8857 | −1.11282 | −0.556410 | − | 0.830908i | \(-0.687822\pi\) | ||||
−0.556410 | + | 0.830908i | \(0.687822\pi\) | |||||||
\(822\) | −12.5181 | −0.436620 | ||||||||
\(823\) | −38.7694 | −1.35142 | −0.675708 | − | 0.737170i | \(-0.736162\pi\) | ||||
−0.675708 | + | 0.737170i | \(0.736162\pi\) | |||||||
\(824\) | 16.9716 | 0.591232 | ||||||||
\(825\) | −0.404496 | −0.0140827 | ||||||||
\(826\) | −3.73494 | −0.129955 | ||||||||
\(827\) | −18.4879 | −0.642886 | −0.321443 | − | 0.946929i | \(-0.604168\pi\) | ||||
−0.321443 | + | 0.946929i | \(0.604168\pi\) | |||||||
\(828\) | 5.03855 | 0.175102 | ||||||||
\(829\) | 32.0706 | 1.11386 | 0.556928 | − | 0.830561i | \(-0.311980\pi\) | ||||
0.556928 | + | 0.830561i | \(0.311980\pi\) | |||||||
\(830\) | 12.8164 | 0.444864 | ||||||||
\(831\) | −10.0277 | −0.347855 | ||||||||
\(832\) | −4.08367 | −0.141576 | ||||||||
\(833\) | −6.94974 | −0.240794 | ||||||||
\(834\) | 0.485663 | 0.0168171 | ||||||||
\(835\) | −41.2358 | −1.42703 | ||||||||
\(836\) | −4.47245 | −0.154683 | ||||||||
\(837\) | 7.12027 | 0.246112 | ||||||||
\(838\) | −6.59791 | −0.227921 | ||||||||
\(839\) | 2.64124 | 0.0911857 | 0.0455928 | − | 0.998960i | \(-0.485482\pi\) | ||||
0.0455928 | + | 0.998960i | \(0.485482\pi\) | |||||||
\(840\) | −8.43907 | −0.291176 | ||||||||
\(841\) | 15.9117 | 0.548680 | ||||||||
\(842\) | 1.87461 | 0.0646033 | ||||||||
\(843\) | −29.8315 | −1.02745 | ||||||||
\(844\) | 24.7016 | 0.850264 | ||||||||
\(845\) | 8.30668 | 0.285759 | ||||||||
\(846\) | 0.0503609 | 0.00173144 | ||||||||
\(847\) | 14.0053 | 0.481227 | ||||||||
\(848\) | −0.972069 | −0.0333810 | ||||||||
\(849\) | −10.4024 | −0.357011 | ||||||||
\(850\) | −0.105322 | −0.00361253 | ||||||||
\(851\) | −13.8839 | −0.475932 | ||||||||
\(852\) | −5.02022 | −0.171990 | ||||||||
\(853\) | 22.5016 | 0.770440 | 0.385220 | − | 0.922825i | \(-0.374126\pi\) | ||||
0.385220 | + | 0.922825i | \(0.374126\pi\) | |||||||
\(854\) | −22.8475 | −0.781824 | ||||||||
\(855\) | −2.63126 | −0.0899872 | ||||||||
\(856\) | 6.02420 | 0.205903 | ||||||||
\(857\) | −47.8504 | −1.63454 | −0.817269 | − | 0.576256i | \(-0.804513\pi\) | ||||
−0.817269 | + | 0.576256i | \(0.804513\pi\) | |||||||
\(858\) | 15.6835 | 0.535427 | ||||||||
\(859\) | −7.48499 | −0.255385 | −0.127692 | − | 0.991814i | \(-0.540757\pi\) | ||||
−0.127692 | + | 0.991814i | \(0.540757\pi\) | |||||||
\(860\) | 23.8242 | 0.812400 | ||||||||
\(861\) | −31.2310 | −1.06435 | ||||||||
\(862\) | −22.9785 | −0.782651 | ||||||||
\(863\) | −14.7692 | −0.502748 | −0.251374 | − | 0.967890i | \(-0.580882\pi\) | ||||
−0.251374 | + | 0.967890i | \(0.580882\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −12.7815 | −0.434585 | ||||||||
\(866\) | 0.864790 | 0.0293868 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −26.5937 | −0.902650 | ||||||||
\(869\) | 2.03996 | 0.0692009 | ||||||||
\(870\) | −15.1423 | −0.513371 | ||||||||
\(871\) | 1.45765 | 0.0493906 | ||||||||
\(872\) | −10.5956 | −0.358811 | ||||||||
\(873\) | −7.52852 | −0.254802 | ||||||||
\(874\) | −5.86756 | −0.198473 | ||||||||
\(875\) | −41.3065 | −1.39642 | ||||||||
\(876\) | 5.24611 | 0.177250 | ||||||||
\(877\) | 37.6775 | 1.27228 | 0.636139 | − | 0.771574i | \(-0.280530\pi\) | ||||
0.636139 | + | 0.771574i | \(0.280530\pi\) | |||||||
\(878\) | −9.41071 | −0.317596 | ||||||||
\(879\) | 12.9210 | 0.435813 | ||||||||
\(880\) | 8.67770 | 0.292525 | ||||||||
\(881\) | 17.7856 | 0.599211 | 0.299606 | − | 0.954063i | \(-0.403145\pi\) | ||||
0.299606 | + | 0.954063i | \(0.403145\pi\) | |||||||
\(882\) | 6.94974 | 0.234010 | ||||||||
\(883\) | −13.1203 | −0.441533 | −0.220767 | − | 0.975327i | \(-0.570856\pi\) | ||||
−0.220767 | + | 0.975327i | \(0.570856\pi\) | |||||||
\(884\) | 4.08367 | 0.137349 | ||||||||
\(885\) | 2.25950 | 0.0759521 | ||||||||
\(886\) | −13.5800 | −0.456229 | ||||||||
\(887\) | −51.2070 | −1.71936 | −0.859681 | − | 0.510832i | \(-0.829337\pi\) | ||||
−0.859681 | + | 0.510832i | \(0.829337\pi\) | |||||||
\(888\) | 2.75553 | 0.0924694 | ||||||||
\(889\) | −26.8796 | −0.901512 | ||||||||
\(890\) | 30.4999 | 1.02236 | ||||||||
\(891\) | 3.84055 | 0.128663 | ||||||||
\(892\) | −17.9650 | −0.601513 | ||||||||
\(893\) | −0.0586469 | −0.00196254 | ||||||||
\(894\) | 12.1194 | 0.405334 | ||||||||
\(895\) | −39.7353 | −1.32820 | ||||||||
\(896\) | 3.73494 | 0.124775 | ||||||||
\(897\) | 20.5758 | 0.687005 | ||||||||
\(898\) | 29.3480 | 0.979357 | ||||||||
\(899\) | −47.7173 | −1.59146 | ||||||||
\(900\) | 0.105322 | 0.00351075 | ||||||||
\(901\) | 0.972069 | 0.0323843 | ||||||||
\(902\) | 32.1141 | 1.06928 | ||||||||
\(903\) | −39.3814 | −1.31053 | ||||||||
\(904\) | −20.2421 | −0.673241 | ||||||||
\(905\) | 34.9940 | 1.16324 | ||||||||
\(906\) | 12.0007 | 0.398695 | ||||||||
\(907\) | −4.09384 | −0.135934 | −0.0679669 | − | 0.997688i | \(-0.521651\pi\) | ||||
−0.0679669 | + | 0.997688i | \(0.521651\pi\) | |||||||
\(908\) | −12.1520 | −0.403277 | ||||||||
\(909\) | 7.36090 | 0.244146 | ||||||||
\(910\) | −34.4624 | −1.14242 | ||||||||
\(911\) | −32.0931 | −1.06329 | −0.531646 | − | 0.846967i | \(-0.678426\pi\) | ||||
−0.531646 | + | 0.846967i | \(0.678426\pi\) | |||||||
\(912\) | 1.16453 | 0.0385616 | ||||||||
\(913\) | 21.7845 | 0.720962 | ||||||||
\(914\) | −37.0754 | −1.22634 | ||||||||
\(915\) | 13.8219 | 0.456937 | ||||||||
\(916\) | −10.5713 | −0.349286 | ||||||||
\(917\) | −38.6252 | −1.27552 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −28.9217 | −0.954039 | −0.477019 | − | 0.878893i | \(-0.658283\pi\) | ||||
−0.477019 | + | 0.878893i | \(0.658283\pi\) | |||||||
\(920\) | 11.3846 | 0.375338 | ||||||||
\(921\) | 2.59585 | 0.0855363 | ||||||||
\(922\) | −34.0342 | −1.12086 | ||||||||
\(923\) | −20.5009 | −0.674796 | ||||||||
\(924\) | −14.3442 | −0.471889 | ||||||||
\(925\) | −0.290219 | −0.00954234 | ||||||||
\(926\) | −1.56747 | −0.0515103 | ||||||||
\(927\) | 16.9716 | 0.557419 | ||||||||
\(928\) | 6.70162 | 0.219991 | ||||||||
\(929\) | −57.8829 | −1.89908 | −0.949539 | − | 0.313650i | \(-0.898448\pi\) | ||||
−0.949539 | + | 0.313650i | \(0.898448\pi\) | |||||||
\(930\) | 16.0882 | 0.527553 | ||||||||
\(931\) | −8.09321 | −0.265244 | ||||||||
\(932\) | 13.9663 | 0.457480 | ||||||||
\(933\) | 18.7836 | 0.614948 | ||||||||
\(934\) | −9.32331 | −0.305068 | ||||||||
\(935\) | −8.67770 | −0.283791 | ||||||||
\(936\) | −4.08367 | −0.133479 | ||||||||
\(937\) | 19.6569 | 0.642162 | 0.321081 | − | 0.947052i | \(-0.395954\pi\) | ||||
0.321081 | + | 0.947052i | \(0.395954\pi\) | |||||||
\(938\) | −1.33317 | −0.0435296 | ||||||||
\(939\) | −6.07314 | −0.198189 | ||||||||
\(940\) | 0.113790 | 0.00371143 | ||||||||
\(941\) | 25.7217 | 0.838505 | 0.419252 | − | 0.907870i | \(-0.362292\pi\) | ||||
0.419252 | + | 0.907870i | \(0.362292\pi\) | |||||||
\(942\) | −6.65132 | −0.216712 | ||||||||
\(943\) | 42.1316 | 1.37199 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −8.43907 | −0.274523 | ||||||||
\(946\) | 40.4949 | 1.31660 | ||||||||
\(947\) | 21.6020 | 0.701971 | 0.350986 | − | 0.936381i | \(-0.385847\pi\) | ||||
0.350986 | + | 0.936381i | \(0.385847\pi\) | |||||||
\(948\) | −0.531164 | −0.0172514 | ||||||||
\(949\) | 21.4234 | 0.695432 | ||||||||
\(950\) | −0.122652 | −0.00397934 | ||||||||
\(951\) | −17.1939 | −0.557551 | ||||||||
\(952\) | −3.73494 | −0.121050 | ||||||||
\(953\) | 10.1110 | 0.327526 | 0.163763 | − | 0.986500i | \(-0.447637\pi\) | ||||
0.163763 | + | 0.986500i | \(0.447637\pi\) | |||||||
\(954\) | −0.972069 | −0.0314719 | ||||||||
\(955\) | −13.5289 | −0.437784 | ||||||||
\(956\) | 28.5324 | 0.922803 | ||||||||
\(957\) | −25.7379 | −0.831988 | ||||||||
\(958\) | −18.8986 | −0.610587 | ||||||||
\(959\) | 46.7544 | 1.50978 | ||||||||
\(960\) | −2.25950 | −0.0729249 | ||||||||
\(961\) | 19.6982 | 0.635425 | ||||||||
\(962\) | 11.2527 | 0.362800 | ||||||||
\(963\) | 6.02420 | 0.194127 | ||||||||
\(964\) | −29.0203 | −0.934682 | ||||||||
\(965\) | 45.3200 | 1.45890 | ||||||||
\(966\) | −18.8187 | −0.605480 | ||||||||
\(967\) | 56.0564 | 1.80265 | 0.901327 | − | 0.433139i | \(-0.142594\pi\) | ||||
0.901327 | + | 0.433139i | \(0.142594\pi\) | |||||||
\(968\) | 3.74980 | 0.120523 | ||||||||
\(969\) | −1.16453 | −0.0374102 | ||||||||
\(970\) | −17.0107 | −0.546179 | ||||||||
\(971\) | −13.8417 | −0.444203 | −0.222101 | − | 0.975024i | \(-0.571292\pi\) | ||||
−0.222101 | + | 0.975024i | \(0.571292\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −1.81392 | −0.0581516 | ||||||||
\(974\) | −2.21739 | −0.0710497 | ||||||||
\(975\) | 0.430102 | 0.0137743 | ||||||||
\(976\) | −6.11723 | −0.195808 | ||||||||
\(977\) | −35.7335 | −1.14322 | −0.571609 | − | 0.820526i | \(-0.693680\pi\) | ||||
−0.571609 | + | 0.820526i | \(0.693680\pi\) | |||||||
\(978\) | −15.2569 | −0.487862 | ||||||||
\(979\) | 51.8418 | 1.65687 | ||||||||
\(980\) | 15.7029 | 0.501611 | ||||||||
\(981\) | −10.5956 | −0.338291 | ||||||||
\(982\) | −25.7217 | −0.820811 | ||||||||
\(983\) | −40.9912 | −1.30742 | −0.653708 | − | 0.756747i | \(-0.726788\pi\) | ||||
−0.653708 | + | 0.756747i | \(0.726788\pi\) | |||||||
\(984\) | −8.36186 | −0.266566 | ||||||||
\(985\) | −3.67325 | −0.117039 | ||||||||
\(986\) | −6.70162 | −0.213423 | ||||||||
\(987\) | −0.188095 | −0.00598712 | ||||||||
\(988\) | 4.75557 | 0.151295 | ||||||||
\(989\) | 53.1267 | 1.68933 | ||||||||
\(990\) | 8.67770 | 0.275795 | ||||||||
\(991\) | 1.54052 | 0.0489361 | 0.0244680 | − | 0.999701i | \(-0.492211\pi\) | ||||
0.0244680 | + | 0.999701i | \(0.492211\pi\) | |||||||
\(992\) | −7.12027 | −0.226069 | ||||||||
\(993\) | 29.0385 | 0.921508 | ||||||||
\(994\) | 18.7502 | 0.594720 | ||||||||
\(995\) | −24.6690 | −0.782061 | ||||||||
\(996\) | −5.67224 | −0.179732 | ||||||||
\(997\) | 0.664495 | 0.0210448 | 0.0105224 | − | 0.999945i | \(-0.496651\pi\) | ||||
0.0105224 | + | 0.999945i | \(0.496651\pi\) | |||||||
\(998\) | 28.1068 | 0.889705 | ||||||||
\(999\) | 2.75553 | 0.0871810 |
(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 | 6018.2.a.z.1.9 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.z.1.9 | ✓ | 11 | 1.1 | even | 1 | trivial |