Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, 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("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 15x^{6} + 11x^{5} + 75x^{4} - 35x^{3} - 141x^{2} + 37x + 80 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.818544\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.818544 | −0.578798 | −0.289399 | − | 0.957209i | \(-0.593455\pi\) | ||||
−0.289399 | + | 0.957209i | \(0.593455\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.32999 | −0.664993 | ||||||||
\(5\) | −3.72041 | −1.66382 | −0.831908 | − | 0.554913i | \(-0.812751\pi\) | ||||
−0.831908 | + | 0.554913i | \(0.812751\pi\) | |||||||
\(6\) | 0.818544 | 0.334169 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.72574 | 0.963695 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.04532 | 0.963014 | ||||||||
\(11\) | 3.70004 | 1.11560 | 0.557802 | − | 0.829974i | \(-0.311645\pi\) | ||||
0.557802 | + | 0.829974i | \(0.311645\pi\) | |||||||
\(12\) | 1.32999 | 0.383934 | ||||||||
\(13\) | 6.90735 | 1.91575 | 0.957877 | − | 0.287179i | \(-0.0927174\pi\) | ||||
0.957877 | + | 0.287179i | \(0.0927174\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.72041 | 0.960605 | ||||||||
\(16\) | 0.428834 | 0.107208 | ||||||||
\(17\) | 3.21772 | 0.780411 | 0.390206 | − | 0.920728i | \(-0.372404\pi\) | ||||
0.390206 | + | 0.920728i | \(0.372404\pi\) | |||||||
\(18\) | −0.818544 | −0.192933 | ||||||||
\(19\) | −6.07700 | −1.39416 | −0.697080 | − | 0.716994i | \(-0.745518\pi\) | ||||
−0.697080 | + | 0.716994i | \(0.745518\pi\) | |||||||
\(20\) | 4.94809 | 1.10643 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.02865 | −0.645710 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −2.72574 | −0.556389 | ||||||||
\(25\) | 8.84143 | 1.76829 | ||||||||
\(26\) | −5.65397 | −1.10883 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.33137 | −0.618619 | −0.309310 | − | 0.950961i | \(-0.600098\pi\) | ||||
−0.309310 | + | 0.950961i | \(0.600098\pi\) | |||||||
\(30\) | −3.04532 | −0.555996 | ||||||||
\(31\) | −0.638468 | −0.114672 | −0.0573362 | − | 0.998355i | \(-0.518261\pi\) | ||||
−0.0573362 | + | 0.998355i | \(0.518261\pi\) | |||||||
\(32\) | −5.80250 | −1.02575 | ||||||||
\(33\) | −3.70004 | −0.644094 | ||||||||
\(34\) | −2.63384 | −0.451700 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.32999 | −0.221664 | ||||||||
\(37\) | 7.78032 | 1.27908 | 0.639539 | − | 0.768759i | \(-0.279125\pi\) | ||||
0.639539 | + | 0.768759i | \(0.279125\pi\) | |||||||
\(38\) | 4.97429 | 0.806937 | ||||||||
\(39\) | −6.90735 | −1.10606 | ||||||||
\(40\) | −10.1409 | −1.60341 | ||||||||
\(41\) | −10.4188 | −1.62714 | −0.813571 | − | 0.581466i | \(-0.802479\pi\) | ||||
−0.813571 | + | 0.581466i | \(0.802479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.34017 | 0.661870 | 0.330935 | − | 0.943654i | \(-0.392636\pi\) | ||||
0.330935 | + | 0.943654i | \(0.392636\pi\) | |||||||
\(44\) | −4.92100 | −0.741869 | ||||||||
\(45\) | −3.72041 | −0.554606 | ||||||||
\(46\) | 0.818544 | 0.120688 | ||||||||
\(47\) | 6.02770 | 0.879230 | 0.439615 | − | 0.898186i | \(-0.355115\pi\) | ||||
0.439615 | + | 0.898186i | \(0.355115\pi\) | |||||||
\(48\) | −0.428834 | −0.0618968 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.23710 | −1.02348 | ||||||||
\(51\) | −3.21772 | −0.450571 | ||||||||
\(52\) | −9.18668 | −1.27396 | ||||||||
\(53\) | 7.27207 | 0.998896 | 0.499448 | − | 0.866344i | \(-0.333536\pi\) | ||||
0.499448 | + | 0.866344i | \(0.333536\pi\) | |||||||
\(54\) | 0.818544 | 0.111390 | ||||||||
\(55\) | −13.7657 | −1.85616 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.07700 | 0.804918 | ||||||||
\(58\) | 2.72687 | 0.358056 | ||||||||
\(59\) | 5.29661 | 0.689560 | 0.344780 | − | 0.938683i | \(-0.387953\pi\) | ||||
0.344780 | + | 0.938683i | \(0.387953\pi\) | |||||||
\(60\) | −4.94809 | −0.638795 | ||||||||
\(61\) | −8.11466 | −1.03898 | −0.519488 | − | 0.854478i | \(-0.673877\pi\) | ||||
−0.519488 | + | 0.854478i | \(0.673877\pi\) | |||||||
\(62\) | 0.522615 | 0.0663721 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.89193 | 0.486492 | ||||||||
\(65\) | −25.6981 | −3.18746 | ||||||||
\(66\) | 3.02865 | 0.372801 | ||||||||
\(67\) | −4.01771 | −0.490841 | −0.245420 | − | 0.969417i | \(-0.578926\pi\) | ||||
−0.245420 | + | 0.969417i | \(0.578926\pi\) | |||||||
\(68\) | −4.27952 | −0.518968 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.92567 | −0.347213 | −0.173606 | − | 0.984815i | \(-0.555542\pi\) | ||||
−0.173606 | + | 0.984815i | \(0.555542\pi\) | |||||||
\(72\) | 2.72574 | 0.321232 | ||||||||
\(73\) | −9.14983 | −1.07091 | −0.535453 | − | 0.844565i | \(-0.679859\pi\) | ||||
−0.535453 | + | 0.844565i | \(0.679859\pi\) | |||||||
\(74\) | −6.36854 | −0.740327 | ||||||||
\(75\) | −8.84143 | −1.02092 | ||||||||
\(76\) | 8.08232 | 0.927106 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.65397 | 0.640186 | ||||||||
\(79\) | 8.17142 | 0.919357 | 0.459678 | − | 0.888085i | \(-0.347965\pi\) | ||||
0.459678 | + | 0.888085i | \(0.347965\pi\) | |||||||
\(80\) | −1.59544 | −0.178375 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.52824 | 0.941786 | ||||||||
\(83\) | −6.01247 | −0.659954 | −0.329977 | − | 0.943989i | \(-0.607041\pi\) | ||||
−0.329977 | + | 0.943989i | \(0.607041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.9712 | −1.29846 | ||||||||
\(86\) | −3.55262 | −0.383089 | ||||||||
\(87\) | 3.33137 | 0.357160 | ||||||||
\(88\) | 10.0853 | 1.07510 | ||||||||
\(89\) | −14.4303 | −1.52961 | −0.764805 | − | 0.644262i | \(-0.777165\pi\) | ||||
−0.764805 | + | 0.644262i | \(0.777165\pi\) | |||||||
\(90\) | 3.04532 | 0.321005 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.32999 | 0.138661 | ||||||||
\(93\) | 0.638468 | 0.0662061 | ||||||||
\(94\) | −4.93394 | −0.508897 | ||||||||
\(95\) | 22.6089 | 2.31963 | ||||||||
\(96\) | 5.80250 | 0.592215 | ||||||||
\(97\) | 14.8716 | 1.50998 | 0.754991 | − | 0.655735i | \(-0.227641\pi\) | ||||
0.754991 | + | 0.655735i | \(0.227641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.70004 | 0.371868 | ||||||||
\(100\) | −11.7590 | −1.17590 | ||||||||
\(101\) | −4.20008 | −0.417924 | −0.208962 | − | 0.977924i | \(-0.567008\pi\) | ||||
−0.208962 | + | 0.977924i | \(0.567008\pi\) | |||||||
\(102\) | 2.63384 | 0.260789 | ||||||||
\(103\) | 17.4541 | 1.71980 | 0.859900 | − | 0.510462i | \(-0.170526\pi\) | ||||
0.859900 | + | 0.510462i | \(0.170526\pi\) | |||||||
\(104\) | 18.8276 | 1.84620 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.95251 | −0.578159 | ||||||||
\(107\) | −0.974217 | −0.0941811 | −0.0470905 | − | 0.998891i | \(-0.514995\pi\) | ||||
−0.0470905 | + | 0.998891i | \(0.514995\pi\) | |||||||
\(108\) | 1.32999 | 0.127978 | ||||||||
\(109\) | 0.186541 | 0.0178674 | 0.00893371 | − | 0.999960i | \(-0.497156\pi\) | ||||
0.00893371 | + | 0.999960i | \(0.497156\pi\) | |||||||
\(110\) | 11.2678 | 1.07434 | ||||||||
\(111\) | −7.78032 | −0.738476 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.70857 | 0.254801 | 0.127400 | − | 0.991851i | \(-0.459337\pi\) | ||||
0.127400 | + | 0.991851i | \(0.459337\pi\) | |||||||
\(114\) | −4.97429 | −0.465885 | ||||||||
\(115\) | 3.72041 | 0.346930 | ||||||||
\(116\) | 4.43067 | 0.411377 | ||||||||
\(117\) | 6.90735 | 0.638585 | ||||||||
\(118\) | −4.33551 | −0.399116 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.1409 | 0.925730 | ||||||||
\(121\) | 2.69030 | 0.244573 | ||||||||
\(122\) | 6.64220 | 0.601357 | ||||||||
\(123\) | 10.4188 | 0.939431 | ||||||||
\(124\) | 0.849154 | 0.0762563 | ||||||||
\(125\) | −14.2917 | −1.27829 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.67778 | 0.592557 | 0.296278 | − | 0.955102i | \(-0.404254\pi\) | ||||
0.296278 | + | 0.955102i | \(0.404254\pi\) | |||||||
\(128\) | 8.41928 | 0.744166 | ||||||||
\(129\) | −4.34017 | −0.382131 | ||||||||
\(130\) | 21.0351 | 1.84490 | ||||||||
\(131\) | −7.70604 | −0.673280 | −0.336640 | − | 0.941633i | \(-0.609291\pi\) | ||||
−0.336640 | + | 0.941633i | \(0.609291\pi\) | |||||||
\(132\) | 4.92100 | 0.428318 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.28867 | 0.284098 | ||||||||
\(135\) | 3.72041 | 0.320202 | ||||||||
\(136\) | 8.77066 | 0.752078 | ||||||||
\(137\) | −20.3951 | −1.74247 | −0.871234 | − | 0.490867i | \(-0.836680\pi\) | ||||
−0.871234 | + | 0.490867i | \(0.836680\pi\) | |||||||
\(138\) | −0.818544 | −0.0696791 | ||||||||
\(139\) | 12.1820 | 1.03326 | 0.516632 | − | 0.856208i | \(-0.327186\pi\) | ||||
0.516632 | + | 0.856208i | \(0.327186\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.02770 | −0.507624 | ||||||||
\(142\) | 2.39479 | 0.200966 | ||||||||
\(143\) | 25.5575 | 2.13722 | ||||||||
\(144\) | 0.428834 | 0.0357361 | ||||||||
\(145\) | 12.3940 | 1.02927 | ||||||||
\(146\) | 7.48953 | 0.619838 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.3477 | −0.850577 | ||||||||
\(149\) | −1.00394 | −0.0822459 | −0.0411229 | − | 0.999154i | \(-0.513094\pi\) | ||||
−0.0411229 | + | 0.999154i | \(0.513094\pi\) | |||||||
\(150\) | 7.23710 | 0.590907 | ||||||||
\(151\) | −2.71063 | −0.220588 | −0.110294 | − | 0.993899i | \(-0.535179\pi\) | ||||
−0.110294 | + | 0.993899i | \(0.535179\pi\) | |||||||
\(152\) | −16.5643 | −1.34354 | ||||||||
\(153\) | 3.21772 | 0.260137 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.37536 | 0.190794 | ||||||||
\(156\) | 9.18668 | 0.735523 | ||||||||
\(157\) | −3.02533 | −0.241448 | −0.120724 | − | 0.992686i | \(-0.538522\pi\) | ||||
−0.120724 | + | 0.992686i | \(0.538522\pi\) | |||||||
\(158\) | −6.68867 | −0.532122 | ||||||||
\(159\) | −7.27207 | −0.576713 | ||||||||
\(160\) | 21.5877 | 1.70665 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.818544 | −0.0643109 | ||||||||
\(163\) | 7.68199 | 0.601700 | 0.300850 | − | 0.953671i | \(-0.402730\pi\) | ||||
0.300850 | + | 0.953671i | \(0.402730\pi\) | |||||||
\(164\) | 13.8568 | 1.08204 | ||||||||
\(165\) | 13.7657 | 1.07166 | ||||||||
\(166\) | 4.92147 | 0.381980 | ||||||||
\(167\) | −4.58319 | −0.354658 | −0.177329 | − | 0.984152i | \(-0.556746\pi\) | ||||
−0.177329 | + | 0.984152i | \(0.556746\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.7115 | 2.67011 | ||||||||
\(170\) | 9.79897 | 0.751547 | ||||||||
\(171\) | −6.07700 | −0.464720 | ||||||||
\(172\) | −5.77237 | −0.440139 | ||||||||
\(173\) | 20.0190 | 1.52201 | 0.761006 | − | 0.648744i | \(-0.224706\pi\) | ||||
0.761006 | + | 0.648744i | \(0.224706\pi\) | |||||||
\(174\) | −2.72687 | −0.206723 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.58670 | 0.119602 | ||||||||
\(177\) | −5.29661 | −0.398118 | ||||||||
\(178\) | 11.8118 | 0.885336 | ||||||||
\(179\) | −4.71460 | −0.352385 | −0.176193 | − | 0.984356i | \(-0.556378\pi\) | ||||
−0.176193 | + | 0.984356i | \(0.556378\pi\) | |||||||
\(180\) | 4.94809 | 0.368809 | ||||||||
\(181\) | 1.17108 | 0.0870460 | 0.0435230 | − | 0.999052i | \(-0.486142\pi\) | ||||
0.0435230 | + | 0.999052i | \(0.486142\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.11466 | 0.599853 | ||||||||
\(184\) | −2.72574 | −0.200944 | ||||||||
\(185\) | −28.9460 | −2.12815 | ||||||||
\(186\) | −0.522615 | −0.0383200 | ||||||||
\(187\) | 11.9057 | 0.870630 | ||||||||
\(188\) | −8.01676 | −0.584682 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.5064 | −1.34259 | ||||||||
\(191\) | 24.1866 | 1.75008 | 0.875039 | − | 0.484052i | \(-0.160836\pi\) | ||||
0.875039 | + | 0.484052i | \(0.160836\pi\) | |||||||
\(192\) | −3.89193 | −0.280876 | ||||||||
\(193\) | 12.3253 | 0.887194 | 0.443597 | − | 0.896226i | \(-0.353702\pi\) | ||||
0.443597 | + | 0.896226i | \(0.353702\pi\) | |||||||
\(194\) | −12.1731 | −0.873975 | ||||||||
\(195\) | 25.6981 | 1.84028 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.76210 | −0.196792 | −0.0983958 | − | 0.995147i | \(-0.531371\pi\) | ||||
−0.0983958 | + | 0.995147i | \(0.531371\pi\) | |||||||
\(198\) | −3.02865 | −0.215237 | ||||||||
\(199\) | −16.5812 | −1.17541 | −0.587704 | − | 0.809076i | \(-0.699968\pi\) | ||||
−0.587704 | + | 0.809076i | \(0.699968\pi\) | |||||||
\(200\) | 24.0994 | 1.70409 | ||||||||
\(201\) | 4.01771 | 0.283387 | ||||||||
\(202\) | 3.43795 | 0.241893 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.27952 | 0.299626 | ||||||||
\(205\) | 38.7621 | 2.70727 | ||||||||
\(206\) | −14.2869 | −0.995417 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 2.96210 | 0.205385 | ||||||||
\(209\) | −22.4851 | −1.55533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.75812 | 0.189877 | 0.0949386 | − | 0.995483i | \(-0.469735\pi\) | ||||
0.0949386 | + | 0.995483i | \(0.469735\pi\) | |||||||
\(212\) | −9.67175 | −0.664259 | ||||||||
\(213\) | 2.92567 | 0.200463 | ||||||||
\(214\) | 0.797439 | 0.0545118 | ||||||||
\(215\) | −16.1472 | −1.10123 | ||||||||
\(216\) | −2.72574 | −0.185463 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.152692 | −0.0103416 | ||||||||
\(219\) | 9.14983 | 0.618288 | ||||||||
\(220\) | 18.3081 | 1.23433 | ||||||||
\(221\) | 22.2259 | 1.49508 | ||||||||
\(222\) | 6.36854 | 0.427428 | ||||||||
\(223\) | 25.8192 | 1.72898 | 0.864490 | − | 0.502650i | \(-0.167642\pi\) | ||||
0.864490 | + | 0.502650i | \(0.167642\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.84143 | 0.589429 | ||||||||
\(226\) | −2.21708 | −0.147478 | ||||||||
\(227\) | −8.37096 | −0.555600 | −0.277800 | − | 0.960639i | \(-0.589605\pi\) | ||||
−0.277800 | + | 0.960639i | \(0.589605\pi\) | |||||||
\(228\) | −8.08232 | −0.535265 | ||||||||
\(229\) | −19.5187 | −1.28983 | −0.644915 | − | 0.764254i | \(-0.723107\pi\) | ||||
−0.644915 | + | 0.764254i | \(0.723107\pi\) | |||||||
\(230\) | −3.04532 | −0.200802 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.08044 | −0.596160 | ||||||||
\(233\) | 6.25868 | 0.410020 | 0.205010 | − | 0.978760i | \(-0.434277\pi\) | ||||
0.205010 | + | 0.978760i | \(0.434277\pi\) | |||||||
\(234\) | −5.65397 | −0.369612 | ||||||||
\(235\) | −22.4255 | −1.46288 | ||||||||
\(236\) | −7.04442 | −0.458553 | ||||||||
\(237\) | −8.17142 | −0.530791 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.53876 | −0.293588 | −0.146794 | − | 0.989167i | \(-0.546895\pi\) | ||||
−0.146794 | + | 0.989167i | \(0.546895\pi\) | |||||||
\(240\) | 1.59544 | 0.102985 | ||||||||
\(241\) | 19.6771 | 1.26751 | 0.633756 | − | 0.773533i | \(-0.281512\pi\) | ||||
0.633756 | + | 0.773533i | \(0.281512\pi\) | |||||||
\(242\) | −2.20213 | −0.141558 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.7924 | 0.690911 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.52824 | −0.543741 | ||||||||
\(247\) | −41.9760 | −2.67087 | ||||||||
\(248\) | −1.74030 | −0.110509 | ||||||||
\(249\) | 6.01247 | 0.381025 | ||||||||
\(250\) | 11.6984 | 0.739869 | ||||||||
\(251\) | 10.3015 | 0.650226 | 0.325113 | − | 0.945675i | \(-0.394598\pi\) | ||||
0.325113 | + | 0.945675i | \(0.394598\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.70004 | −0.232620 | ||||||||
\(254\) | −5.46606 | −0.342971 | ||||||||
\(255\) | 11.9712 | 0.749667 | ||||||||
\(256\) | −14.6754 | −0.917214 | ||||||||
\(257\) | −15.3148 | −0.955312 | −0.477656 | − | 0.878547i | \(-0.658513\pi\) | ||||
−0.477656 | + | 0.878547i | \(0.658513\pi\) | |||||||
\(258\) | 3.55262 | 0.221177 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 34.1782 | 2.11964 | ||||||||
\(261\) | −3.33137 | −0.206206 | ||||||||
\(262\) | 6.30773 | 0.389693 | ||||||||
\(263\) | −5.31749 | −0.327891 | −0.163945 | − | 0.986469i | \(-0.552422\pi\) | ||||
−0.163945 | + | 0.986469i | \(0.552422\pi\) | |||||||
\(264\) | −10.0853 | −0.620710 | ||||||||
\(265\) | −27.0551 | −1.66198 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.4303 | 0.883121 | ||||||||
\(268\) | 5.34349 | 0.326406 | ||||||||
\(269\) | 1.76465 | 0.107592 | 0.0537962 | − | 0.998552i | \(-0.482868\pi\) | ||||
0.0537962 | + | 0.998552i | \(0.482868\pi\) | |||||||
\(270\) | −3.04532 | −0.185332 | ||||||||
\(271\) | −16.6166 | −1.00938 | −0.504692 | − | 0.863300i | \(-0.668394\pi\) | ||||
−0.504692 | + | 0.863300i | \(0.668394\pi\) | |||||||
\(272\) | 1.37987 | 0.0836666 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.6943 | 1.00854 | ||||||||
\(275\) | 32.7136 | 1.97271 | ||||||||
\(276\) | −1.32999 | −0.0800557 | ||||||||
\(277\) | 1.95295 | 0.117342 | 0.0586708 | − | 0.998277i | \(-0.481314\pi\) | ||||
0.0586708 | + | 0.998277i | \(0.481314\pi\) | |||||||
\(278\) | −9.97150 | −0.598051 | ||||||||
\(279\) | −0.638468 | −0.0382241 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.1183 | 0.782575 | 0.391287 | − | 0.920268i | \(-0.372030\pi\) | ||||
0.391287 | + | 0.920268i | \(0.372030\pi\) | |||||||
\(282\) | 4.93394 | 0.293812 | ||||||||
\(283\) | −0.979872 | −0.0582473 | −0.0291237 | − | 0.999576i | \(-0.509272\pi\) | ||||
−0.0291237 | + | 0.999576i | \(0.509272\pi\) | |||||||
\(284\) | 3.89110 | 0.230894 | ||||||||
\(285\) | −22.6089 | −1.33924 | ||||||||
\(286\) | −20.9199 | −1.23702 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.80250 | −0.341916 | ||||||||
\(289\) | −6.64630 | −0.390959 | ||||||||
\(290\) | −10.1451 | −0.595739 | ||||||||
\(291\) | −14.8716 | −0.871789 | ||||||||
\(292\) | 12.1691 | 0.712145 | ||||||||
\(293\) | 22.4505 | 1.31157 | 0.655786 | − | 0.754947i | \(-0.272337\pi\) | ||||
0.655786 | + | 0.754947i | \(0.272337\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.7056 | −1.14730 | ||||||||
\(296\) | 21.2071 | 1.23264 | ||||||||
\(297\) | −3.70004 | −0.214698 | ||||||||
\(298\) | 0.821768 | 0.0476038 | ||||||||
\(299\) | −6.90735 | −0.399462 | ||||||||
\(300\) | 11.7590 | 0.678905 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.21877 | 0.127676 | ||||||||
\(303\) | 4.20008 | 0.241288 | ||||||||
\(304\) | −2.60602 | −0.149466 | ||||||||
\(305\) | 30.1898 | 1.72866 | ||||||||
\(306\) | −2.63384 | −0.150567 | ||||||||
\(307\) | −29.2019 | −1.66664 | −0.833322 | − | 0.552789i | \(-0.813564\pi\) | ||||
−0.833322 | + | 0.552789i | \(0.813564\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.4541 | −0.992927 | ||||||||
\(310\) | −1.94434 | −0.110431 | ||||||||
\(311\) | −1.79193 | −0.101611 | −0.0508055 | − | 0.998709i | \(-0.516179\pi\) | ||||
−0.0508055 | + | 0.998709i | \(0.516179\pi\) | |||||||
\(312\) | −18.8276 | −1.06591 | ||||||||
\(313\) | 8.83165 | 0.499194 | 0.249597 | − | 0.968350i | \(-0.419702\pi\) | ||||
0.249597 | + | 0.968350i | \(0.419702\pi\) | |||||||
\(314\) | 2.47637 | 0.139750 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.8679 | −0.611366 | ||||||||
\(317\) | −21.5495 | −1.21034 | −0.605170 | − | 0.796096i | \(-0.706895\pi\) | ||||
−0.605170 | + | 0.796096i | \(0.706895\pi\) | |||||||
\(318\) | 5.95251 | 0.333800 | ||||||||
\(319\) | −12.3262 | −0.690134 | ||||||||
\(320\) | −14.4796 | −0.809433 | ||||||||
\(321\) | 0.974217 | 0.0543755 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5541 | −1.08802 | ||||||||
\(324\) | −1.32999 | −0.0738881 | ||||||||
\(325\) | 61.0708 | 3.38760 | ||||||||
\(326\) | −6.28805 | −0.348263 | ||||||||
\(327\) | −0.186541 | −0.0103158 | ||||||||
\(328\) | −28.3989 | −1.56807 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −11.2678 | −0.620272 | ||||||||
\(331\) | 23.1086 | 1.27016 | 0.635082 | − | 0.772444i | \(-0.280966\pi\) | ||||
0.635082 | + | 0.772444i | \(0.280966\pi\) | |||||||
\(332\) | 7.99650 | 0.438865 | ||||||||
\(333\) | 7.78032 | 0.426359 | ||||||||
\(334\) | 3.75154 | 0.205275 | ||||||||
\(335\) | 14.9475 | 0.816669 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.83315 | 0.263279 | 0.131639 | − | 0.991298i | \(-0.457976\pi\) | ||||
0.131639 | + | 0.991298i | \(0.457976\pi\) | |||||||
\(338\) | −28.4129 | −1.54546 | ||||||||
\(339\) | −2.70857 | −0.147109 | ||||||||
\(340\) | 15.9215 | 0.863467 | ||||||||
\(341\) | −2.36236 | −0.127929 | ||||||||
\(342\) | 4.97429 | 0.268979 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.8302 | 0.637841 | ||||||||
\(345\) | −3.72041 | −0.200300 | ||||||||
\(346\) | −16.3864 | −0.880938 | ||||||||
\(347\) | 2.31584 | 0.124321 | 0.0621605 | − | 0.998066i | \(-0.480201\pi\) | ||||
0.0621605 | + | 0.998066i | \(0.480201\pi\) | |||||||
\(348\) | −4.43067 | −0.237509 | ||||||||
\(349\) | −2.05541 | −0.110024 | −0.0550119 | − | 0.998486i | \(-0.517520\pi\) | ||||
−0.0550119 | + | 0.998486i | \(0.517520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.90735 | −0.368687 | ||||||||
\(352\) | −21.4695 | −1.14433 | ||||||||
\(353\) | −18.5639 | −0.988058 | −0.494029 | − | 0.869445i | \(-0.664476\pi\) | ||||
−0.494029 | + | 0.869445i | \(0.664476\pi\) | |||||||
\(354\) | 4.33551 | 0.230430 | ||||||||
\(355\) | 10.8847 | 0.577698 | ||||||||
\(356\) | 19.1921 | 1.01718 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.85910 | 0.203960 | ||||||||
\(359\) | −7.27408 | −0.383911 | −0.191956 | − | 0.981404i | \(-0.561483\pi\) | ||||
−0.191956 | + | 0.981404i | \(0.561483\pi\) | |||||||
\(360\) | −10.1409 | −0.534470 | ||||||||
\(361\) | 17.9299 | 0.943681 | ||||||||
\(362\) | −0.958584 | −0.0503821 | ||||||||
\(363\) | −2.69030 | −0.141204 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.0411 | 1.78179 | ||||||||
\(366\) | −6.64220 | −0.347194 | ||||||||
\(367\) | 20.2397 | 1.05651 | 0.528253 | − | 0.849087i | \(-0.322847\pi\) | ||||
0.528253 | + | 0.849087i | \(0.322847\pi\) | |||||||
\(368\) | −0.428834 | −0.0223545 | ||||||||
\(369\) | −10.4188 | −0.542381 | ||||||||
\(370\) | 23.6935 | 1.23177 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.849154 | −0.0440266 | ||||||||
\(373\) | 13.3237 | 0.689876 | 0.344938 | − | 0.938626i | \(-0.387900\pi\) | ||||
0.344938 | + | 0.938626i | \(0.387900\pi\) | |||||||
\(374\) | −9.74533 | −0.503919 | ||||||||
\(375\) | 14.2917 | 0.738019 | ||||||||
\(376\) | 16.4299 | 0.847310 | ||||||||
\(377\) | −23.0109 | −1.18512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.15684 | 0.470355 | 0.235178 | − | 0.971952i | \(-0.424433\pi\) | ||||
0.235178 | + | 0.971952i | \(0.424433\pi\) | |||||||
\(380\) | −30.0695 | −1.54253 | ||||||||
\(381\) | −6.67778 | −0.342113 | ||||||||
\(382\) | −19.7978 | −1.01294 | ||||||||
\(383\) | −8.98554 | −0.459140 | −0.229570 | − | 0.973292i | \(-0.573732\pi\) | ||||
−0.229570 | + | 0.973292i | \(0.573732\pi\) | |||||||
\(384\) | −8.41928 | −0.429645 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0888 | −0.513506 | ||||||||
\(387\) | 4.34017 | 0.220623 | ||||||||
\(388\) | −19.7790 | −1.00413 | ||||||||
\(389\) | −16.3724 | −0.830115 | −0.415057 | − | 0.909795i | \(-0.636238\pi\) | ||||
−0.415057 | + | 0.909795i | \(0.636238\pi\) | |||||||
\(390\) | −21.0351 | −1.06515 | ||||||||
\(391\) | −3.21772 | −0.162727 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.70604 | 0.388718 | ||||||||
\(394\) | 2.26090 | 0.113903 | ||||||||
\(395\) | −30.4010 | −1.52964 | ||||||||
\(396\) | −4.92100 | −0.247290 | ||||||||
\(397\) | −9.68491 | −0.486072 | −0.243036 | − | 0.970017i | \(-0.578143\pi\) | ||||
−0.243036 | + | 0.970017i | \(0.578143\pi\) | |||||||
\(398\) | 13.5724 | 0.680323 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.79150 | 0.189575 | ||||||||
\(401\) | 11.4662 | 0.572593 | 0.286297 | − | 0.958141i | \(-0.407576\pi\) | ||||
0.286297 | + | 0.958141i | \(0.407576\pi\) | |||||||
\(402\) | −3.28867 | −0.164024 | ||||||||
\(403\) | −4.41012 | −0.219684 | ||||||||
\(404\) | 5.58605 | 0.277916 | ||||||||
\(405\) | −3.72041 | −0.184869 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.7875 | 1.42694 | ||||||||
\(408\) | −8.77066 | −0.434212 | ||||||||
\(409\) | 38.6532 | 1.91128 | 0.955639 | − | 0.294541i | \(-0.0951666\pi\) | ||||
0.955639 | + | 0.294541i | \(0.0951666\pi\) | |||||||
\(410\) | −31.7285 | −1.56696 | ||||||||
\(411\) | 20.3951 | 1.00601 | ||||||||
\(412\) | −23.2137 | −1.14365 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.818544 | 0.0402292 | ||||||||
\(415\) | 22.3688 | 1.09804 | ||||||||
\(416\) | −40.0799 | −1.96508 | ||||||||
\(417\) | −12.1820 | −0.596555 | ||||||||
\(418\) | 18.4051 | 0.900222 | ||||||||
\(419\) | 6.70860 | 0.327736 | 0.163868 | − | 0.986482i | \(-0.447603\pi\) | ||||
0.163868 | + | 0.986482i | \(0.447603\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0515 | −1.65957 | −0.829783 | − | 0.558086i | \(-0.811536\pi\) | ||||
−0.829783 | + | 0.558086i | \(0.811536\pi\) | |||||||
\(422\) | −2.25765 | −0.109900 | ||||||||
\(423\) | 6.02770 | 0.293077 | ||||||||
\(424\) | 19.8218 | 0.962630 | ||||||||
\(425\) | 28.4492 | 1.37999 | ||||||||
\(426\) | −2.39479 | −0.116028 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.29569 | 0.0626298 | ||||||||
\(429\) | −25.5575 | −1.23393 | ||||||||
\(430\) | 13.2172 | 0.637390 | ||||||||
\(431\) | 7.46897 | 0.359768 | 0.179884 | − | 0.983688i | \(-0.442428\pi\) | ||||
0.179884 | + | 0.983688i | \(0.442428\pi\) | |||||||
\(432\) | −0.428834 | −0.0206323 | ||||||||
\(433\) | 25.8698 | 1.24322 | 0.621611 | − | 0.783326i | \(-0.286478\pi\) | ||||
0.621611 | + | 0.783326i | \(0.286478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.3940 | −0.594249 | ||||||||
\(436\) | −0.248097 | −0.0118817 | ||||||||
\(437\) | 6.07700 | 0.290702 | ||||||||
\(438\) | −7.48953 | −0.357864 | ||||||||
\(439\) | 15.9723 | 0.762318 | 0.381159 | − | 0.924509i | \(-0.375525\pi\) | ||||
0.381159 | + | 0.924509i | \(0.375525\pi\) | |||||||
\(440\) | −37.5216 | −1.78877 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.1929 | −0.865347 | ||||||||
\(443\) | 30.6283 | 1.45520 | 0.727598 | − | 0.686004i | \(-0.240637\pi\) | ||||
0.727598 | + | 0.686004i | \(0.240637\pi\) | |||||||
\(444\) | 10.3477 | 0.491081 | ||||||||
\(445\) | 53.6867 | 2.54499 | ||||||||
\(446\) | −21.1341 | −1.00073 | ||||||||
\(447\) | 1.00394 | 0.0474847 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.12584 | −0.336289 | −0.168144 | − | 0.985762i | \(-0.553778\pi\) | ||||
−0.168144 | + | 0.985762i | \(0.553778\pi\) | |||||||
\(450\) | −7.23710 | −0.341160 | ||||||||
\(451\) | −38.5500 | −1.81525 | ||||||||
\(452\) | −3.60236 | −0.169441 | ||||||||
\(453\) | 2.71063 | 0.127357 | ||||||||
\(454\) | 6.85200 | 0.321580 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.5643 | 0.775695 | ||||||||
\(457\) | 20.6851 | 0.967609 | 0.483805 | − | 0.875176i | \(-0.339254\pi\) | ||||
0.483805 | + | 0.875176i | \(0.339254\pi\) | |||||||
\(458\) | 15.9769 | 0.746551 | ||||||||
\(459\) | −3.21772 | −0.150190 | ||||||||
\(460\) | −4.94809 | −0.230706 | ||||||||
\(461\) | −12.1611 | −0.566401 | −0.283200 | − | 0.959061i | \(-0.591396\pi\) | ||||
−0.283200 | + | 0.959061i | \(0.591396\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.96022 | −0.0910992 | −0.0455496 | − | 0.998962i | \(-0.514504\pi\) | ||||
−0.0455496 | + | 0.998962i | \(0.514504\pi\) | |||||||
\(464\) | −1.42860 | −0.0663212 | ||||||||
\(465\) | −2.37536 | −0.110155 | ||||||||
\(466\) | −5.12301 | −0.237319 | ||||||||
\(467\) | 39.3922 | 1.82285 | 0.911427 | − | 0.411463i | \(-0.134982\pi\) | ||||
0.911427 | + | 0.411463i | \(0.134982\pi\) | |||||||
\(468\) | −9.18668 | −0.424654 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 18.3563 | 0.846711 | ||||||||
\(471\) | 3.02533 | 0.139400 | ||||||||
\(472\) | 14.4372 | 0.664525 | ||||||||
\(473\) | 16.0588 | 0.738385 | ||||||||
\(474\) | 6.68867 | 0.307221 | ||||||||
\(475\) | −53.7294 | −2.46527 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.27207 | 0.332965 | ||||||||
\(478\) | 3.71517 | 0.169928 | ||||||||
\(479\) | 2.82732 | 0.129183 | 0.0645917 | − | 0.997912i | \(-0.479425\pi\) | ||||
0.0645917 | + | 0.997912i | \(0.479425\pi\) | |||||||
\(480\) | −21.5877 | −0.985337 | ||||||||
\(481\) | 53.7414 | 2.45040 | ||||||||
\(482\) | −16.1066 | −0.733634 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.57806 | −0.162639 | ||||||||
\(485\) | −55.3284 | −2.51233 | ||||||||
\(486\) | 0.818544 | 0.0371299 | ||||||||
\(487\) | −24.7848 | −1.12311 | −0.561554 | − | 0.827440i | \(-0.689796\pi\) | ||||
−0.561554 | + | 0.827440i | \(0.689796\pi\) | |||||||
\(488\) | −22.1184 | −1.00125 | ||||||||
\(489\) | −7.68199 | −0.347392 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.1356 | 0.592802 | 0.296401 | − | 0.955064i | \(-0.404214\pi\) | ||||
0.296401 | + | 0.955064i | \(0.404214\pi\) | |||||||
\(492\) | −13.8568 | −0.624715 | ||||||||
\(493\) | −10.7194 | −0.482777 | ||||||||
\(494\) | 34.3592 | 1.54589 | ||||||||
\(495\) | −13.7657 | −0.618720 | ||||||||
\(496\) | −0.273797 | −0.0122938 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.92147 | −0.220536 | ||||||||
\(499\) | 16.4810 | 0.737790 | 0.368895 | − | 0.929471i | \(-0.379736\pi\) | ||||
0.368895 | + | 0.929471i | \(0.379736\pi\) | |||||||
\(500\) | 19.0077 | 0.850051 | ||||||||
\(501\) | 4.58319 | 0.204762 | ||||||||
\(502\) | −8.43224 | −0.376349 | ||||||||
\(503\) | −17.3522 | −0.773696 | −0.386848 | − | 0.922144i | \(-0.626436\pi\) | ||||
−0.386848 | + | 0.922144i | \(0.626436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.6260 | 0.695348 | ||||||||
\(506\) | 3.02865 | 0.134640 | ||||||||
\(507\) | −34.7115 | −1.54159 | ||||||||
\(508\) | −8.88135 | −0.394046 | ||||||||
\(509\) | 34.8099 | 1.54292 | 0.771461 | − | 0.636277i | \(-0.219527\pi\) | ||||
0.771461 | + | 0.636277i | \(0.219527\pi\) | |||||||
\(510\) | −9.79897 | −0.433906 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4.82609 | −0.213285 | ||||||||
\(513\) | 6.07700 | 0.268306 | ||||||||
\(514\) | 12.5358 | 0.552933 | ||||||||
\(515\) | −64.9362 | −2.86143 | ||||||||
\(516\) | 5.77237 | 0.254114 | ||||||||
\(517\) | 22.3027 | 0.980873 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.0190 | −0.878735 | ||||||||
\(520\) | −70.0465 | −3.07174 | ||||||||
\(521\) | −16.9148 | −0.741052 | −0.370526 | − | 0.928822i | \(-0.620823\pi\) | ||||
−0.370526 | + | 0.928822i | \(0.620823\pi\) | |||||||
\(522\) | 2.72687 | 0.119352 | ||||||||
\(523\) | 29.0471 | 1.27014 | 0.635071 | − | 0.772454i | \(-0.280971\pi\) | ||||
0.635071 | + | 0.772454i | \(0.280971\pi\) | |||||||
\(524\) | 10.2489 | 0.447726 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.35260 | 0.189783 | ||||||||
\(527\) | −2.05441 | −0.0894915 | ||||||||
\(528\) | −1.58670 | −0.0690524 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 22.1458 | 0.961950 | ||||||||
\(531\) | 5.29661 | 0.229853 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −71.9662 | −3.11720 | ||||||||
\(534\) | −11.8118 | −0.511149 | ||||||||
\(535\) | 3.62448 | 0.156700 | ||||||||
\(536\) | −10.9512 | −0.473021 | ||||||||
\(537\) | 4.71460 | 0.203450 | ||||||||
\(538\) | −1.44444 | −0.0622743 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.94809 | −0.212932 | ||||||||
\(541\) | −3.79565 | −0.163188 | −0.0815938 | − | 0.996666i | \(-0.526001\pi\) | ||||
−0.0815938 | + | 0.996666i | \(0.526001\pi\) | |||||||
\(542\) | 13.6014 | 0.584229 | ||||||||
\(543\) | −1.17108 | −0.0502560 | ||||||||
\(544\) | −18.6708 | −0.800504 | ||||||||
\(545\) | −0.694010 | −0.0297281 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.31002 | 0.141526 | 0.0707630 | − | 0.997493i | \(-0.477457\pi\) | ||||
0.0707630 | + | 0.997493i | \(0.477457\pi\) | |||||||
\(548\) | 27.1252 | 1.15873 | ||||||||
\(549\) | −8.11466 | −0.346325 | ||||||||
\(550\) | −26.7776 | −1.14180 | ||||||||
\(551\) | 20.2447 | 0.862454 | ||||||||
\(552\) | 2.72574 | 0.116015 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.59858 | −0.0679171 | ||||||||
\(555\) | 28.9460 | 1.22869 | ||||||||
\(556\) | −16.2019 | −0.687113 | ||||||||
\(557\) | −7.75267 | −0.328491 | −0.164246 | − | 0.986419i | \(-0.552519\pi\) | ||||
−0.164246 | + | 0.986419i | \(0.552519\pi\) | |||||||
\(558\) | 0.522615 | 0.0221240 | ||||||||
\(559\) | 29.9791 | 1.26798 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.9057 | −0.502658 | ||||||||
\(562\) | −10.7379 | −0.452953 | ||||||||
\(563\) | 16.2180 | 0.683508 | 0.341754 | − | 0.939789i | \(-0.388979\pi\) | ||||
0.341754 | + | 0.939789i | \(0.388979\pi\) | |||||||
\(564\) | 8.01676 | 0.337566 | ||||||||
\(565\) | −10.0770 | −0.423942 | ||||||||
\(566\) | 0.802068 | 0.0337134 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.97461 | −0.334607 | ||||||||
\(569\) | −24.0539 | −1.00839 | −0.504196 | − | 0.863589i | \(-0.668211\pi\) | ||||
−0.504196 | + | 0.863589i | \(0.668211\pi\) | |||||||
\(570\) | 18.5064 | 0.775147 | ||||||||
\(571\) | 43.9333 | 1.83855 | 0.919276 | − | 0.393613i | \(-0.128775\pi\) | ||||
0.919276 | + | 0.393613i | \(0.128775\pi\) | |||||||
\(572\) | −33.9911 | −1.42124 | ||||||||
\(573\) | −24.1866 | −1.01041 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.84143 | −0.368713 | ||||||||
\(576\) | 3.89193 | 0.162164 | ||||||||
\(577\) | 18.0483 | 0.751359 | 0.375679 | − | 0.926750i | \(-0.377409\pi\) | ||||
0.375679 | + | 0.926750i | \(0.377409\pi\) | |||||||
\(578\) | 5.44029 | 0.226286 | ||||||||
\(579\) | −12.3253 | −0.512222 | ||||||||
\(580\) | −16.4839 | −0.684456 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 12.1731 | 0.504590 | ||||||||
\(583\) | 26.9070 | 1.11437 | ||||||||
\(584\) | −24.9400 | −1.03203 | ||||||||
\(585\) | −25.6981 | −1.06249 | ||||||||
\(586\) | −18.3767 | −0.759136 | ||||||||
\(587\) | 0.826642 | 0.0341192 | 0.0170596 | − | 0.999854i | \(-0.494569\pi\) | ||||
0.0170596 | + | 0.999854i | \(0.494569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.87997 | 0.159871 | ||||||||
\(590\) | 16.1299 | 0.664056 | ||||||||
\(591\) | 2.76210 | 0.113618 | ||||||||
\(592\) | 3.33646 | 0.137128 | ||||||||
\(593\) | 0.685463 | 0.0281486 | 0.0140743 | − | 0.999901i | \(-0.495520\pi\) | ||||
0.0140743 | + | 0.999901i | \(0.495520\pi\) | |||||||
\(594\) | 3.02865 | 0.124267 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.33522 | 0.0546929 | ||||||||
\(597\) | 16.5812 | 0.678622 | ||||||||
\(598\) | 5.65397 | 0.231208 | ||||||||
\(599\) | −27.3692 | −1.11827 | −0.559137 | − | 0.829075i | \(-0.688867\pi\) | ||||
−0.559137 | + | 0.829075i | \(0.688867\pi\) | |||||||
\(600\) | −24.0994 | −0.983855 | ||||||||
\(601\) | 10.3969 | 0.424096 | 0.212048 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212048 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.01771 | −0.163614 | ||||||||
\(604\) | 3.60510 | 0.146689 | ||||||||
\(605\) | −10.0090 | −0.406925 | ||||||||
\(606\) | −3.43795 | −0.139657 | ||||||||
\(607\) | −15.8582 | −0.643663 | −0.321832 | − | 0.946797i | \(-0.604299\pi\) | ||||
−0.321832 | + | 0.946797i | \(0.604299\pi\) | |||||||
\(608\) | 35.2618 | 1.43005 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.7117 | −1.00055 | ||||||||
\(611\) | 41.6354 | 1.68439 | ||||||||
\(612\) | −4.27952 | −0.172989 | ||||||||
\(613\) | 8.49341 | 0.343046 | 0.171523 | − | 0.985180i | \(-0.445131\pi\) | ||||
0.171523 | + | 0.985180i | \(0.445131\pi\) | |||||||
\(614\) | 23.9031 | 0.964650 | ||||||||
\(615\) | −38.7621 | −1.56304 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.0404 | −0.806797 | −0.403399 | − | 0.915024i | \(-0.632171\pi\) | ||||
−0.403399 | + | 0.915024i | \(0.632171\pi\) | |||||||
\(618\) | 14.2869 | 0.574704 | ||||||||
\(619\) | 27.3390 | 1.09885 | 0.549424 | − | 0.835544i | \(-0.314847\pi\) | ||||
0.549424 | + | 0.835544i | \(0.314847\pi\) | |||||||
\(620\) | −3.15920 | −0.126876 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 1.46677 | 0.0588123 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.96210 | −0.118579 | ||||||||
\(625\) | 8.96370 | 0.358548 | ||||||||
\(626\) | −7.22909 | −0.288933 | ||||||||
\(627\) | 22.4851 | 0.897970 | ||||||||
\(628\) | 4.02365 | 0.160561 | ||||||||
\(629\) | 25.0349 | 0.998206 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.7286 | −0.506717 | −0.253358 | − | 0.967373i | \(-0.581535\pi\) | ||||
−0.253358 | + | 0.967373i | \(0.581535\pi\) | |||||||
\(632\) | 22.2732 | 0.885979 | ||||||||
\(633\) | −2.75812 | −0.109626 | ||||||||
\(634\) | 17.6392 | 0.700543 | ||||||||
\(635\) | −24.8441 | −0.985906 | ||||||||
\(636\) | 9.67175 | 0.383510 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.0895 | 0.399448 | ||||||||
\(639\) | −2.92567 | −0.115738 | ||||||||
\(640\) | −31.3231 | −1.23816 | ||||||||
\(641\) | 14.0195 | 0.553738 | 0.276869 | − | 0.960908i | \(-0.410703\pi\) | ||||
0.276869 | + | 0.960908i | \(0.410703\pi\) | |||||||
\(642\) | −0.797439 | −0.0314724 | ||||||||
\(643\) | −10.2819 | −0.405477 | −0.202738 | − | 0.979233i | \(-0.564984\pi\) | ||||
−0.202738 | + | 0.979233i | \(0.564984\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.1472 | 0.635796 | ||||||||
\(646\) | 16.0059 | 0.629742 | ||||||||
\(647\) | −35.5195 | −1.39641 | −0.698207 | − | 0.715896i | \(-0.746018\pi\) | ||||
−0.698207 | + | 0.715896i | \(0.746018\pi\) | |||||||
\(648\) | 2.72574 | 0.107077 | ||||||||
\(649\) | 19.5977 | 0.769276 | ||||||||
\(650\) | −49.9892 | −1.96074 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.2169 | −0.400126 | ||||||||
\(653\) | 27.4136 | 1.07278 | 0.536389 | − | 0.843971i | \(-0.319788\pi\) | ||||
0.536389 | + | 0.843971i | \(0.319788\pi\) | |||||||
\(654\) | 0.152692 | 0.00597074 | ||||||||
\(655\) | 28.6696 | 1.12021 | ||||||||
\(656\) | −4.46793 | −0.174443 | ||||||||
\(657\) | −9.14983 | −0.356969 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.7484 | 1.27570 | 0.637848 | − | 0.770162i | \(-0.279825\pi\) | ||||
0.637848 | + | 0.770162i | \(0.279825\pi\) | |||||||
\(660\) | −18.3081 | −0.712643 | ||||||||
\(661\) | 38.3045 | 1.48987 | 0.744936 | − | 0.667136i | \(-0.232480\pi\) | ||||
0.744936 | + | 0.667136i | \(0.232480\pi\) | |||||||
\(662\) | −18.9154 | −0.735169 | ||||||||
\(663\) | −22.2259 | −0.863182 | ||||||||
\(664\) | −16.3884 | −0.635994 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.36854 | −0.246776 | ||||||||
\(667\) | 3.33137 | 0.128991 | ||||||||
\(668\) | 6.09557 | 0.235845 | ||||||||
\(669\) | −25.8192 | −0.998227 | ||||||||
\(670\) | −12.2352 | −0.472686 | ||||||||
\(671\) | −30.0246 | −1.15909 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.487689 | −0.0187990 | −0.00939951 | − | 0.999956i | \(-0.502992\pi\) | ||||
−0.00939951 | + | 0.999956i | \(0.502992\pi\) | |||||||
\(674\) | −3.95615 | −0.152385 | ||||||||
\(675\) | −8.84143 | −0.340307 | ||||||||
\(676\) | −46.1658 | −1.77561 | ||||||||
\(677\) | 47.3426 | 1.81953 | 0.909763 | − | 0.415129i | \(-0.136264\pi\) | ||||
0.909763 | + | 0.415129i | \(0.136264\pi\) | |||||||
\(678\) | 2.21708 | 0.0851466 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −32.6304 | −1.25132 | ||||||||
\(681\) | 8.37096 | 0.320776 | ||||||||
\(682\) | 1.93370 | 0.0740450 | ||||||||
\(683\) | 38.7091 | 1.48116 | 0.740582 | − | 0.671966i | \(-0.234550\pi\) | ||||
0.740582 | + | 0.671966i | \(0.234550\pi\) | |||||||
\(684\) | 8.08232 | 0.309035 | ||||||||
\(685\) | 75.8780 | 2.89915 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.5187 | 0.744684 | ||||||||
\(688\) | 1.86121 | 0.0709581 | ||||||||
\(689\) | 50.2307 | 1.91364 | ||||||||
\(690\) | 3.04532 | 0.115933 | ||||||||
\(691\) | 21.9568 | 0.835277 | 0.417639 | − | 0.908613i | \(-0.362858\pi\) | ||||
0.417639 | + | 0.908613i | \(0.362858\pi\) | |||||||
\(692\) | −26.6249 | −1.01213 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.89562 | −0.0719567 | ||||||||
\(695\) | −45.3220 | −1.71916 | ||||||||
\(696\) | 9.08044 | 0.344193 | ||||||||
\(697\) | −33.5247 | −1.26984 | ||||||||
\(698\) | 1.68245 | 0.0636815 | ||||||||
\(699\) | −6.25868 | −0.236725 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.52091 | 0.284061 | 0.142031 | − | 0.989862i | \(-0.454637\pi\) | ||||
0.142031 | + | 0.989862i | \(0.454637\pi\) | |||||||
\(702\) | 5.65397 | 0.213395 | ||||||||
\(703\) | −47.2810 | −1.78324 | ||||||||
\(704\) | 14.4003 | 0.542732 | ||||||||
\(705\) | 22.4255 | 0.844593 | ||||||||
\(706\) | 15.1954 | 0.571886 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.04442 | 0.264745 | ||||||||
\(709\) | 0.693914 | 0.0260605 | 0.0130302 | − | 0.999915i | \(-0.495852\pi\) | ||||
0.0130302 | + | 0.999915i | \(0.495852\pi\) | |||||||
\(710\) | −8.90958 | −0.334371 | ||||||||
\(711\) | 8.17142 | 0.306452 | ||||||||
\(712\) | −39.3333 | −1.47408 | ||||||||
\(713\) | 0.638468 | 0.0239108 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −95.0842 | −3.55595 | ||||||||
\(716\) | 6.27034 | 0.234334 | ||||||||
\(717\) | 4.53876 | 0.169503 | ||||||||
\(718\) | 5.95415 | 0.222207 | ||||||||
\(719\) | 9.37630 | 0.349677 | 0.174838 | − | 0.984597i | \(-0.444060\pi\) | ||||
0.174838 | + | 0.984597i | \(0.444060\pi\) | |||||||
\(720\) | −1.59544 | −0.0594584 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −14.6764 | −0.546200 | ||||||||
\(723\) | −19.6771 | −0.731799 | ||||||||
\(724\) | −1.55753 | −0.0578850 | ||||||||
\(725\) | −29.4540 | −1.09390 | ||||||||
\(726\) | 2.20213 | 0.0817288 | ||||||||
\(727\) | 18.9568 | 0.703069 | 0.351535 | − | 0.936175i | \(-0.385660\pi\) | ||||
0.351535 | + | 0.936175i | \(0.385660\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.8641 | −1.03130 | ||||||||
\(731\) | 13.9654 | 0.516531 | ||||||||
\(732\) | −10.7924 | −0.398898 | ||||||||
\(733\) | 6.39615 | 0.236247 | 0.118124 | − | 0.992999i | \(-0.462312\pi\) | ||||
0.118124 | + | 0.992999i | \(0.462312\pi\) | |||||||
\(734\) | −16.5671 | −0.611504 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.80250 | 0.213883 | ||||||||
\(737\) | −14.8657 | −0.547584 | ||||||||
\(738\) | 8.52824 | 0.313929 | ||||||||
\(739\) | 29.8857 | 1.09936 | 0.549682 | − | 0.835374i | \(-0.314749\pi\) | ||||
0.549682 | + | 0.835374i | \(0.314749\pi\) | |||||||
\(740\) | 38.4977 | 1.41520 | ||||||||
\(741\) | 41.9760 | 1.54203 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.7564 | 0.614731 | 0.307366 | − | 0.951591i | \(-0.400553\pi\) | ||||
0.307366 | + | 0.951591i | \(0.400553\pi\) | |||||||
\(744\) | 1.74030 | 0.0638025 | ||||||||
\(745\) | 3.73506 | 0.136842 | ||||||||
\(746\) | −10.9060 | −0.399299 | ||||||||
\(747\) | −6.01247 | −0.219985 | ||||||||
\(748\) | −15.8344 | −0.578963 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −11.6984 | −0.427164 | ||||||||
\(751\) | −19.1378 | −0.698348 | −0.349174 | − | 0.937058i | \(-0.613538\pi\) | ||||
−0.349174 | + | 0.937058i | \(0.613538\pi\) | |||||||
\(752\) | 2.58488 | 0.0942609 | ||||||||
\(753\) | −10.3015 | −0.375408 | ||||||||
\(754\) | 18.8354 | 0.685946 | ||||||||
\(755\) | 10.0846 | 0.367018 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.3744 | −1.57647 | −0.788234 | − | 0.615376i | \(-0.789004\pi\) | ||||
−0.788234 | + | 0.615376i | \(0.789004\pi\) | |||||||
\(758\) | −7.49527 | −0.272241 | ||||||||
\(759\) | 3.70004 | 0.134303 | ||||||||
\(760\) | 61.6260 | 2.23541 | ||||||||
\(761\) | −6.16432 | −0.223456 | −0.111728 | − | 0.993739i | \(-0.535639\pi\) | ||||
−0.111728 | + | 0.993739i | \(0.535639\pi\) | |||||||
\(762\) | 5.46606 | 0.198014 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −32.1678 | −1.16379 | ||||||||
\(765\) | −11.9712 | −0.432820 | ||||||||
\(766\) | 7.35506 | 0.265749 | ||||||||
\(767\) | 36.5855 | 1.32103 | ||||||||
\(768\) | 14.6754 | 0.529553 | ||||||||
\(769\) | −2.61523 | −0.0943076 | −0.0471538 | − | 0.998888i | \(-0.515015\pi\) | ||||
−0.0471538 | + | 0.998888i | \(0.515015\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.3148 | 0.551550 | ||||||||
\(772\) | −16.3925 | −0.589977 | ||||||||
\(773\) | 52.4555 | 1.88669 | 0.943346 | − | 0.331810i | \(-0.107659\pi\) | ||||
0.943346 | + | 0.331810i | \(0.107659\pi\) | |||||||
\(774\) | −3.55262 | −0.127696 | ||||||||
\(775\) | −5.64497 | −0.202773 | ||||||||
\(776\) | 40.5361 | 1.45516 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.4015 | 0.480469 | ||||||||
\(779\) | 63.3150 | 2.26850 | ||||||||
\(780\) | −34.1782 | −1.22377 | ||||||||
\(781\) | −10.8251 | −0.387352 | ||||||||
\(782\) | 2.63384 | 0.0941860 | ||||||||
\(783\) | 3.33137 | 0.119053 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.2555 | 0.401725 | ||||||||
\(786\) | −6.30773 | −0.224989 | ||||||||
\(787\) | 33.2853 | 1.18649 | 0.593246 | − | 0.805021i | \(-0.297846\pi\) | ||||
0.593246 | + | 0.805021i | \(0.297846\pi\) | |||||||
\(788\) | 3.67356 | 0.130865 | ||||||||
\(789\) | 5.31749 | 0.189308 | ||||||||
\(790\) | 24.8846 | 0.885353 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 10.0853 | 0.358367 | ||||||||
\(793\) | −56.0508 | −1.99042 | ||||||||
\(794\) | 7.92752 | 0.281337 | ||||||||
\(795\) | 27.0551 | 0.959544 | ||||||||
\(796\) | 22.0527 | 0.781638 | ||||||||
\(797\) | 26.0207 | 0.921702 | 0.460851 | − | 0.887477i | \(-0.347544\pi\) | ||||
0.460851 | + | 0.887477i | \(0.347544\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.3954 | 0.686161 | ||||||||
\(800\) | −51.3024 | −1.81381 | ||||||||
\(801\) | −14.4303 | −0.509870 | ||||||||
\(802\) | −9.38557 | −0.331416 | ||||||||
\(803\) | −33.8547 | −1.19471 | ||||||||
\(804\) | −5.34349 | −0.188450 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.60988 | 0.127153 | ||||||||
\(807\) | −1.76465 | −0.0621185 | ||||||||
\(808\) | −11.4483 | −0.402751 | ||||||||
\(809\) | −41.8504 | −1.47138 | −0.735691 | − | 0.677317i | \(-0.763142\pi\) | ||||
−0.735691 | + | 0.677317i | \(0.763142\pi\) | |||||||
\(810\) | 3.04532 | 0.107002 | ||||||||
\(811\) | 17.1370 | 0.601760 | 0.300880 | − | 0.953662i | \(-0.402720\pi\) | ||||
0.300880 | + | 0.953662i | \(0.402720\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.6166 | 0.582768 | ||||||||
\(814\) | −23.5638 | −0.825912 | ||||||||
\(815\) | −28.5801 | −1.00112 | ||||||||
\(816\) | −1.37987 | −0.0483050 | ||||||||
\(817\) | −26.3752 | −0.922752 | ||||||||
\(818\) | −31.6393 | −1.10624 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −51.5531 | −1.80031 | ||||||||
\(821\) | −4.76075 | −0.166151 | −0.0830757 | − | 0.996543i | \(-0.526474\pi\) | ||||
−0.0830757 | + | 0.996543i | \(0.526474\pi\) | |||||||
\(822\) | −16.6943 | −0.582279 | ||||||||
\(823\) | −46.9815 | −1.63767 | −0.818835 | − | 0.574029i | \(-0.805380\pi\) | ||||
−0.818835 | + | 0.574029i | \(0.805380\pi\) | |||||||
\(824\) | 47.5752 | 1.65736 | ||||||||
\(825\) | −32.7136 | −1.13894 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.3820 | −0.465336 | −0.232668 | − | 0.972556i | \(-0.574746\pi\) | ||||
−0.232668 | + | 0.972556i | \(0.574746\pi\) | |||||||
\(828\) | 1.32999 | 0.0462202 | ||||||||
\(829\) | 0.371697 | 0.0129096 | 0.00645478 | − | 0.999979i | \(-0.497945\pi\) | ||||
0.00645478 | + | 0.999979i | \(0.497945\pi\) | |||||||
\(830\) | −18.3099 | −0.635545 | ||||||||
\(831\) | −1.95295 | −0.0677472 | ||||||||
\(832\) | 26.8829 | 0.931998 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9.97150 | 0.345285 | ||||||||
\(835\) | 17.0513 | 0.590085 | ||||||||
\(836\) | 29.9049 | 1.03428 | ||||||||
\(837\) | 0.638468 | 0.0220687 | ||||||||
\(838\) | −5.49128 | −0.189693 | ||||||||
\(839\) | −45.6631 | −1.57647 | −0.788233 | − | 0.615377i | \(-0.789004\pi\) | ||||
−0.788233 | + | 0.615377i | \(0.789004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9020 | −0.617310 | ||||||||
\(842\) | 27.8726 | 0.960554 | ||||||||
\(843\) | −13.1183 | −0.451820 | ||||||||
\(844\) | −3.66827 | −0.126267 | ||||||||
\(845\) | −129.141 | −4.44258 | ||||||||
\(846\) | −4.93394 | −0.169632 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.11851 | 0.107090 | ||||||||
\(849\) | 0.979872 | 0.0336291 | ||||||||
\(850\) | −23.2869 | −0.798735 | ||||||||
\(851\) | −7.78032 | −0.266706 | ||||||||
\(852\) | −3.89110 | −0.133307 | ||||||||
\(853\) | −42.5768 | −1.45780 | −0.728901 | − | 0.684619i | \(-0.759969\pi\) | ||||
−0.728901 | + | 0.684619i | \(0.759969\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.6089 | 0.773209 | ||||||||
\(856\) | −2.65546 | −0.0907618 | ||||||||
\(857\) | −41.3922 | −1.41393 | −0.706965 | − | 0.707248i | \(-0.749936\pi\) | ||||
−0.706965 | + | 0.707248i | \(0.749936\pi\) | |||||||
\(858\) | 20.9199 | 0.714194 | ||||||||
\(859\) | 52.7547 | 1.79997 | 0.899984 | − | 0.435923i | \(-0.143578\pi\) | ||||
0.899984 | + | 0.435923i | \(0.143578\pi\) | |||||||
\(860\) | 21.4756 | 0.732310 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.11368 | −0.208233 | ||||||||
\(863\) | 22.7441 | 0.774217 | 0.387109 | − | 0.922034i | \(-0.373474\pi\) | ||||
0.387109 | + | 0.922034i | \(0.373474\pi\) | |||||||
\(864\) | 5.80250 | 0.197405 | ||||||||
\(865\) | −74.4787 | −2.53235 | ||||||||
\(866\) | −21.1756 | −0.719575 | ||||||||
\(867\) | 6.64630 | 0.225720 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.2346 | 1.02564 | ||||||||
\(870\) | 10.1451 | 0.343950 | ||||||||
\(871\) | −27.7517 | −0.940330 | ||||||||
\(872\) | 0.508463 | 0.0172187 | ||||||||
\(873\) | 14.8716 | 0.503328 | ||||||||
\(874\) | −4.97429 | −0.168258 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.1691 | −0.411157 | ||||||||
\(877\) | 5.28592 | 0.178493 | 0.0892464 | − | 0.996010i | \(-0.471554\pi\) | ||||
0.0892464 | + | 0.996010i | \(0.471554\pi\) | |||||||
\(878\) | −13.0741 | −0.441228 | ||||||||
\(879\) | −22.4505 | −0.757237 | ||||||||
\(880\) | −5.90318 | −0.198996 | ||||||||
\(881\) | 51.9769 | 1.75115 | 0.875573 | − | 0.483086i | \(-0.160484\pi\) | ||||
0.875573 | + | 0.483086i | \(0.160484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.0607 | 0.439526 | 0.219763 | − | 0.975553i | \(-0.429472\pi\) | ||||
0.219763 | + | 0.975553i | \(0.429472\pi\) | |||||||
\(884\) | −29.5601 | −0.994215 | ||||||||
\(885\) | 19.7056 | 0.662395 | ||||||||
\(886\) | −25.0706 | −0.842264 | ||||||||
\(887\) | 49.1688 | 1.65093 | 0.825464 | − | 0.564455i | \(-0.190913\pi\) | ||||
0.825464 | + | 0.564455i | \(0.190913\pi\) | |||||||
\(888\) | −21.2071 | −0.711665 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −43.9449 | −1.47304 | ||||||||
\(891\) | 3.70004 | 0.123956 | ||||||||
\(892\) | −34.3391 | −1.14976 | ||||||||
\(893\) | −36.6303 | −1.22579 | ||||||||
\(894\) | −0.821768 | −0.0274840 | ||||||||
\(895\) | 17.5402 | 0.586305 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.90735 | 0.230630 | ||||||||
\(898\) | 5.83281 | 0.194643 | ||||||||
\(899\) | 2.12697 | 0.0709385 | ||||||||
\(900\) | −11.7590 | −0.391966 | ||||||||
\(901\) | 23.3995 | 0.779549 | ||||||||
\(902\) | 31.5548 | 1.05066 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.38286 | 0.245550 | ||||||||
\(905\) | −4.35691 | −0.144829 | ||||||||
\(906\) | −2.21877 | −0.0737137 | ||||||||
\(907\) | −51.1121 | −1.69715 | −0.848575 | − | 0.529074i | \(-0.822539\pi\) | ||||
−0.848575 | + | 0.529074i | \(0.822539\pi\) | |||||||
\(908\) | 11.1333 | 0.369470 | ||||||||
\(909\) | −4.20008 | −0.139308 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.9073 | 0.361376 | 0.180688 | − | 0.983540i | \(-0.442168\pi\) | ||||
0.180688 | + | 0.983540i | \(0.442168\pi\) | |||||||
\(912\) | 2.60602 | 0.0862940 | ||||||||
\(913\) | −22.2464 | −0.736248 | ||||||||
\(914\) | −16.9317 | −0.560050 | ||||||||
\(915\) | −30.1898 | −0.998045 | ||||||||
\(916\) | 25.9596 | 0.857728 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.63384 | 0.0869298 | ||||||||
\(919\) | −34.8033 | −1.14805 | −0.574027 | − | 0.818836i | \(-0.694619\pi\) | ||||
−0.574027 | + | 0.818836i | \(0.694619\pi\) | |||||||
\(920\) | 10.1409 | 0.334334 | ||||||||
\(921\) | 29.2019 | 0.962237 | ||||||||
\(922\) | 9.95443 | 0.327832 | ||||||||
\(923\) | −20.2086 | −0.665174 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 68.7892 | 2.26177 | ||||||||
\(926\) | 1.60453 | 0.0527280 | ||||||||
\(927\) | 17.4541 | 0.573267 | ||||||||
\(928\) | 19.3302 | 0.634547 | ||||||||
\(929\) | 7.12498 | 0.233763 | 0.116882 | − | 0.993146i | \(-0.462710\pi\) | ||||
0.116882 | + | 0.993146i | \(0.462710\pi\) | |||||||
\(930\) | 1.94434 | 0.0637574 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.32396 | −0.272660 | ||||||||
\(933\) | 1.79193 | 0.0586652 | ||||||||
\(934\) | −32.2442 | −1.05506 | ||||||||
\(935\) | −44.2940 | −1.44857 | ||||||||
\(936\) | 18.8276 | 0.615401 | ||||||||
\(937\) | 2.12786 | 0.0695142 | 0.0347571 | − | 0.999396i | \(-0.488934\pi\) | ||||
0.0347571 | + | 0.999396i | \(0.488934\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.83165 | −0.288210 | ||||||||
\(940\) | 29.8256 | 0.972804 | ||||||||
\(941\) | 46.7565 | 1.52422 | 0.762109 | − | 0.647449i | \(-0.224164\pi\) | ||||
0.762109 | + | 0.647449i | \(0.224164\pi\) | |||||||
\(942\) | −2.47637 | −0.0806844 | ||||||||
\(943\) | 10.4188 | 0.339283 | ||||||||
\(944\) | 2.27137 | 0.0739267 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.1448 | −0.427376 | ||||||||
\(947\) | 29.9575 | 0.973487 | 0.486744 | − | 0.873545i | \(-0.338185\pi\) | ||||
0.486744 | + | 0.873545i | \(0.338185\pi\) | |||||||
\(948\) | 10.8679 | 0.352972 | ||||||||
\(949\) | −63.2010 | −2.05159 | ||||||||
\(950\) | 43.9798 | 1.42689 | ||||||||
\(951\) | 21.5495 | 0.698791 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.6214 | 1.96372 | 0.981860 | − | 0.189605i | \(-0.0607207\pi\) | ||||
0.981860 | + | 0.189605i | \(0.0607207\pi\) | |||||||
\(954\) | −5.95251 | −0.192720 | ||||||||
\(955\) | −89.9838 | −2.91181 | ||||||||
\(956\) | 6.03648 | 0.195234 | ||||||||
\(957\) | 12.3262 | 0.398449 | ||||||||
\(958\) | −2.31428 | −0.0747711 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 14.4796 | 0.467326 | ||||||||
\(961\) | −30.5924 | −0.986850 | ||||||||
\(962\) | −43.9897 | −1.41828 | ||||||||
\(963\) | −0.974217 | −0.0313937 | ||||||||
\(964\) | −26.1703 | −0.842887 | ||||||||
\(965\) | −45.8551 | −1.47613 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.34634 | 0.204084 | 0.102042 | − | 0.994780i | \(-0.467462\pi\) | ||||
0.102042 | + | 0.994780i | \(0.467462\pi\) | |||||||
\(968\) | 7.33307 | 0.235694 | ||||||||
\(969\) | 19.5541 | 0.628167 | ||||||||
\(970\) | 45.2888 | 1.45413 | ||||||||
\(971\) | 31.3344 | 1.00557 | 0.502784 | − | 0.864412i | \(-0.332309\pi\) | ||||
0.502784 | + | 0.864412i | \(0.332309\pi\) | |||||||
\(972\) | 1.32999 | 0.0426593 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20.2875 | 0.650052 | ||||||||
\(975\) | −61.0708 | −1.95583 | ||||||||
\(976\) | −3.47984 | −0.111387 | ||||||||
\(977\) | −17.6550 | −0.564833 | −0.282417 | − | 0.959292i | \(-0.591136\pi\) | ||||
−0.282417 | + | 0.959292i | \(0.591136\pi\) | |||||||
\(978\) | 6.28805 | 0.201070 | ||||||||
\(979\) | −53.3928 | −1.70644 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.186541 | 0.00595581 | ||||||||
\(982\) | −10.7521 | −0.343113 | ||||||||
\(983\) | −3.40755 | −0.108684 | −0.0543420 | − | 0.998522i | \(-0.517306\pi\) | ||||
−0.0543420 | + | 0.998522i | \(0.517306\pi\) | |||||||
\(984\) | 28.3989 | 0.905324 | ||||||||
\(985\) | 10.2761 | 0.327425 | ||||||||
\(986\) | 8.77430 | 0.279431 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 55.8274 | 1.77611 | ||||||||
\(989\) | −4.34017 | −0.138009 | ||||||||
\(990\) | 11.2678 | 0.358114 | ||||||||
\(991\) | 1.05296 | 0.0334485 | 0.0167242 | − | 0.999860i | \(-0.494676\pi\) | ||||
0.0167242 | + | 0.999860i | \(0.494676\pi\) | |||||||
\(992\) | 3.70471 | 0.117625 | ||||||||
\(993\) | −23.1086 | −0.733330 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 61.6887 | 1.95566 | ||||||||
\(996\) | −7.99650 | −0.253379 | ||||||||
\(997\) | 54.9471 | 1.74019 | 0.870095 | − | 0.492883i | \(-0.164057\pi\) | ||||
0.870095 | + | 0.492883i | \(0.164057\pi\) | |||||||
\(998\) | −13.4904 | −0.427032 | ||||||||
\(999\) | −7.78032 | −0.246159 |
(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 | 3381.2.a.be.1.4 | 8 | ||
7.3 | odd | 6 | 483.2.i.g.415.5 | yes | 16 | ||
7.5 | odd | 6 | 483.2.i.g.277.5 | ✓ | 16 | ||
7.6 | odd | 2 | 3381.2.a.bf.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.g.277.5 | ✓ | 16 | 7.5 | odd | 6 | ||
483.2.i.g.415.5 | yes | 16 | 7.3 | odd | 6 | ||
3381.2.a.be.1.4 | 8 | 1.1 | even | 1 | trivial | ||
3381.2.a.bf.1.4 | 8 | 7.6 | odd | 2 |