Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 42x^{14} + 641x^{12} - 4448x^{10} + 14076x^{8} - 17900x^{6} + 6960x^{4} - 416x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 637) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(2.93761\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52340 | 1.07720 | 0.538602 | − | 0.842561i | \(-0.318953\pi\) | ||||
0.538602 | + | 0.842561i | \(0.318953\pi\) | |||||||
\(3\) | −2.99510 | −1.72922 | −0.864611 | − | 0.502442i | \(-0.832435\pi\) | ||||
−0.864611 | + | 0.502442i | \(0.832435\pi\) | |||||||
\(4\) | 0.320733 | 0.160367 | ||||||||
\(5\) | 2.94606 | 1.31752 | 0.658759 | − | 0.752354i | \(-0.271082\pi\) | ||||
0.658759 | + | 0.752354i | \(0.271082\pi\) | |||||||
\(6\) | −4.56272 | −1.86272 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.55819 | −0.904456 | ||||||||
\(9\) | 5.97063 | 1.99021 | ||||||||
\(10\) | 4.48801 | 1.41923 | ||||||||
\(11\) | −2.37108 | −0.714908 | −0.357454 | − | 0.933931i | \(-0.616355\pi\) | ||||
−0.357454 | + | 0.933931i | \(0.616355\pi\) | |||||||
\(12\) | −0.960628 | −0.277309 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.82374 | −2.27828 | ||||||||
\(16\) | −4.53860 | −1.13465 | ||||||||
\(17\) | −5.36994 | −1.30240 | −0.651201 | − | 0.758905i | \(-0.725735\pi\) | ||||
−0.651201 | + | 0.758905i | \(0.725735\pi\) | |||||||
\(18\) | 9.09563 | 2.14386 | ||||||||
\(19\) | 5.35438 | 1.22838 | 0.614189 | − | 0.789159i | \(-0.289483\pi\) | ||||
0.614189 | + | 0.789159i | \(0.289483\pi\) | |||||||
\(20\) | 0.944899 | 0.211286 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.61209 | −0.770101 | ||||||||
\(23\) | 2.79056 | 0.581873 | 0.290936 | − | 0.956742i | \(-0.406033\pi\) | ||||
0.290936 | + | 0.956742i | \(0.406033\pi\) | |||||||
\(24\) | 7.66203 | 1.56400 | ||||||||
\(25\) | 3.67927 | 0.735853 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.89733 | −1.71229 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.585818 | 0.108784 | 0.0543918 | − | 0.998520i | \(-0.482678\pi\) | ||||
0.0543918 | + | 0.998520i | \(0.482678\pi\) | |||||||
\(30\) | −13.4421 | −2.45417 | ||||||||
\(31\) | −8.33379 | −1.49679 | −0.748397 | − | 0.663252i | \(-0.769176\pi\) | ||||
−0.748397 | + | 0.663252i | \(0.769176\pi\) | |||||||
\(32\) | −1.79770 | −0.317792 | ||||||||
\(33\) | 7.10163 | 1.23623 | ||||||||
\(34\) | −8.18054 | −1.40295 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.91498 | 0.319163 | ||||||||
\(37\) | 0.675710 | 0.111086 | 0.0555430 | − | 0.998456i | \(-0.482311\pi\) | ||||
0.0555430 | + | 0.998456i | \(0.482311\pi\) | |||||||
\(38\) | 8.15683 | 1.32321 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.53657 | −1.19164 | ||||||||
\(41\) | −11.2799 | −1.76162 | −0.880808 | − | 0.473473i | \(-0.843000\pi\) | ||||
−0.880808 | + | 0.473473i | \(0.843000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5271 | 1.60536 | 0.802682 | − | 0.596408i | \(-0.203406\pi\) | ||||
0.802682 | + | 0.596408i | \(0.203406\pi\) | |||||||
\(44\) | −0.760484 | −0.114647 | ||||||||
\(45\) | 17.5898 | 2.62214 | ||||||||
\(46\) | 4.25113 | 0.626795 | ||||||||
\(47\) | −0.537744 | −0.0784380 | −0.0392190 | − | 0.999231i | \(-0.512487\pi\) | ||||
−0.0392190 | + | 0.999231i | \(0.512487\pi\) | |||||||
\(48\) | 13.5936 | 1.96206 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.60498 | 0.792664 | ||||||||
\(51\) | 16.0835 | 2.25214 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.90345 | 1.08562 | 0.542811 | − | 0.839855i | \(-0.317360\pi\) | ||||
0.542811 | + | 0.839855i | \(0.317360\pi\) | |||||||
\(54\) | −13.5541 | −1.84449 | ||||||||
\(55\) | −6.98535 | −0.941904 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.0369 | −2.12414 | ||||||||
\(58\) | 0.892432 | 0.117182 | ||||||||
\(59\) | 6.14603 | 0.800145 | 0.400072 | − | 0.916484i | \(-0.368985\pi\) | ||||
0.400072 | + | 0.916484i | \(0.368985\pi\) | |||||||
\(60\) | −2.83007 | −0.365360 | ||||||||
\(61\) | 2.78689 | 0.356824 | 0.178412 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178412 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(62\) | −12.6957 | −1.61235 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.33858 | 0.792323 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.8186 | 1.33168 | ||||||||
\(67\) | 4.21353 | 0.514765 | 0.257382 | − | 0.966310i | \(-0.417140\pi\) | ||||
0.257382 | + | 0.966310i | \(0.417140\pi\) | |||||||
\(68\) | −1.72232 | −0.208862 | ||||||||
\(69\) | −8.35802 | −1.00619 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.25151 | 0.148527 | 0.0742637 | − | 0.997239i | \(-0.476339\pi\) | ||||
0.0742637 | + | 0.997239i | \(0.476339\pi\) | |||||||
\(72\) | −15.2740 | −1.80006 | ||||||||
\(73\) | −10.8620 | −1.27130 | −0.635650 | − | 0.771977i | \(-0.719268\pi\) | ||||
−0.635650 | + | 0.771977i | \(0.719268\pi\) | |||||||
\(74\) | 1.02937 | 0.119662 | ||||||||
\(75\) | −11.0198 | −1.27245 | ||||||||
\(76\) | 1.71733 | 0.196991 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.29136 | 0.707833 | 0.353917 | − | 0.935277i | \(-0.384850\pi\) | ||||
0.353917 | + | 0.935277i | \(0.384850\pi\) | |||||||
\(80\) | −13.3710 | −1.49492 | ||||||||
\(81\) | 8.73651 | 0.970723 | ||||||||
\(82\) | −17.1837 | −1.89762 | ||||||||
\(83\) | 1.74725 | 0.191786 | 0.0958928 | − | 0.995392i | \(-0.469429\pi\) | ||||
0.0958928 | + | 0.995392i | \(0.469429\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.8202 | −1.71594 | ||||||||
\(86\) | 16.0369 | 1.72930 | ||||||||
\(87\) | −1.75458 | −0.188111 | ||||||||
\(88\) | 6.06567 | 0.646602 | ||||||||
\(89\) | −10.2343 | −1.08483 | −0.542416 | − | 0.840110i | \(-0.682490\pi\) | ||||
−0.542416 | + | 0.840110i | \(0.682490\pi\) | |||||||
\(90\) | 26.7963 | 2.82457 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.895027 | 0.0933130 | ||||||||
\(93\) | 24.9605 | 2.58829 | ||||||||
\(94\) | −0.819196 | −0.0844936 | ||||||||
\(95\) | 15.7743 | 1.61841 | ||||||||
\(96\) | 5.38430 | 0.549533 | ||||||||
\(97\) | 9.90640 | 1.00584 | 0.502921 | − | 0.864332i | \(-0.332259\pi\) | ||||
0.502921 | + | 0.864332i | \(0.332259\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.1568 | −1.42282 | ||||||||
\(100\) | 1.18006 | 0.118006 | ||||||||
\(101\) | 2.05077 | 0.204059 | 0.102030 | − | 0.994781i | \(-0.467466\pi\) | ||||
0.102030 | + | 0.994781i | \(0.467466\pi\) | |||||||
\(102\) | 24.5016 | 2.42602 | ||||||||
\(103\) | 3.02962 | 0.298517 | 0.149259 | − | 0.988798i | \(-0.452311\pi\) | ||||
0.149259 | + | 0.988798i | \(0.452311\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0401 | 1.16944 | ||||||||
\(107\) | −12.4305 | −1.20170 | −0.600852 | − | 0.799360i | \(-0.705172\pi\) | ||||
−0.600852 | + | 0.799360i | \(0.705172\pi\) | |||||||
\(108\) | −2.85367 | −0.274594 | ||||||||
\(109\) | −3.53782 | −0.338862 | −0.169431 | − | 0.985542i | \(-0.554193\pi\) | ||||
−0.169431 | + | 0.985542i | \(0.554193\pi\) | |||||||
\(110\) | −10.6414 | −1.01462 | ||||||||
\(111\) | −2.02382 | −0.192092 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3848 | 0.976921 | 0.488460 | − | 0.872586i | \(-0.337559\pi\) | ||||
0.488460 | + | 0.872586i | \(0.337559\pi\) | |||||||
\(114\) | −24.4305 | −2.28813 | ||||||||
\(115\) | 8.22117 | 0.766628 | ||||||||
\(116\) | 0.187891 | 0.0174453 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.36283 | 0.861918 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 22.5728 | 2.06060 | ||||||||
\(121\) | −5.37797 | −0.488907 | ||||||||
\(122\) | 4.24553 | 0.384372 | ||||||||
\(123\) | 33.7843 | 3.04623 | ||||||||
\(124\) | −2.67292 | −0.240036 | ||||||||
\(125\) | −3.89096 | −0.348018 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.09504 | 0.452112 | 0.226056 | − | 0.974114i | \(-0.427417\pi\) | ||||
0.226056 | + | 0.974114i | \(0.427417\pi\) | |||||||
\(128\) | 13.2516 | 1.17128 | ||||||||
\(129\) | −31.5296 | −2.77603 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.5443 | 1.96971 | 0.984854 | − | 0.173386i | \(-0.0554707\pi\) | ||||
0.984854 | + | 0.173386i | \(0.0554707\pi\) | |||||||
\(132\) | 2.27773 | 0.198251 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.41887 | 0.554506 | ||||||||
\(135\) | −26.2121 | −2.25597 | ||||||||
\(136\) | 13.7373 | 1.17797 | ||||||||
\(137\) | 1.03479 | 0.0884082 | 0.0442041 | − | 0.999023i | \(-0.485925\pi\) | ||||
0.0442041 | + | 0.999023i | \(0.485925\pi\) | |||||||
\(138\) | −12.7326 | −1.08387 | ||||||||
\(139\) | 8.49456 | 0.720499 | 0.360249 | − | 0.932856i | \(-0.382692\pi\) | ||||
0.360249 | + | 0.932856i | \(0.382692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.61060 | 0.135637 | ||||||||
\(142\) | 1.90655 | 0.159994 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −27.0983 | −2.25819 | ||||||||
\(145\) | 1.72585 | 0.143324 | ||||||||
\(146\) | −16.5471 | −1.36945 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.216723 | 0.0178145 | ||||||||
\(149\) | 4.31343 | 0.353370 | 0.176685 | − | 0.984267i | \(-0.443463\pi\) | ||||
0.176685 | + | 0.984267i | \(0.443463\pi\) | |||||||
\(150\) | −16.7875 | −1.37069 | ||||||||
\(151\) | 12.2447 | 0.996463 | 0.498232 | − | 0.867044i | \(-0.333983\pi\) | ||||
0.498232 | + | 0.867044i | \(0.333983\pi\) | |||||||
\(152\) | −13.6975 | −1.11101 | ||||||||
\(153\) | −32.0619 | −2.59205 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.5518 | −1.97205 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.2040 | −1.77207 | −0.886035 | − | 0.463619i | \(-0.846551\pi\) | ||||
−0.886035 | + | 0.463619i | \(0.846551\pi\) | |||||||
\(158\) | 9.58423 | 0.762480 | ||||||||
\(159\) | −23.6716 | −1.87728 | ||||||||
\(160\) | −5.29614 | −0.418697 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 13.3092 | 1.04567 | ||||||||
\(163\) | 11.3644 | 0.890127 | 0.445063 | − | 0.895499i | \(-0.353181\pi\) | ||||
0.445063 | + | 0.895499i | \(0.353181\pi\) | |||||||
\(164\) | −3.61782 | −0.282505 | ||||||||
\(165\) | 20.9218 | 1.62876 | ||||||||
\(166\) | 2.66175 | 0.206592 | ||||||||
\(167\) | −1.88127 | −0.145577 | −0.0727885 | − | 0.997347i | \(-0.523190\pi\) | ||||
−0.0727885 | + | 0.997347i | \(0.523190\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −24.1004 | −1.84841 | ||||||||
\(171\) | 31.9690 | 2.44473 | ||||||||
\(172\) | 3.37638 | 0.257447 | ||||||||
\(173\) | −5.57113 | −0.423565 | −0.211783 | − | 0.977317i | \(-0.567927\pi\) | ||||
−0.211783 | + | 0.977317i | \(0.567927\pi\) | |||||||
\(174\) | −2.67292 | −0.202634 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.7614 | 0.811170 | ||||||||
\(177\) | −18.4080 | −1.38363 | ||||||||
\(178\) | −15.5909 | −1.16858 | ||||||||
\(179\) | −4.66142 | −0.348411 | −0.174205 | − | 0.984709i | \(-0.555736\pi\) | ||||
−0.174205 | + | 0.984709i | \(0.555736\pi\) | |||||||
\(180\) | 5.64164 | 0.420503 | ||||||||
\(181\) | 12.5360 | 0.931794 | 0.465897 | − | 0.884839i | \(-0.345732\pi\) | ||||
0.465897 | + | 0.884839i | \(0.345732\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.34701 | −0.617029 | ||||||||
\(184\) | −7.13879 | −0.526278 | ||||||||
\(185\) | 1.99068 | 0.146358 | ||||||||
\(186\) | 38.0248 | 2.78811 | ||||||||
\(187\) | 12.7326 | 0.931098 | ||||||||
\(188\) | −0.172472 | −0.0125788 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.0305 | 1.74336 | ||||||||
\(191\) | −1.31764 | −0.0953408 | −0.0476704 | − | 0.998863i | \(-0.515180\pi\) | ||||
−0.0476704 | + | 0.998863i | \(0.515180\pi\) | |||||||
\(192\) | −18.9847 | −1.37010 | ||||||||
\(193\) | −15.1445 | −1.09012 | −0.545061 | − | 0.838396i | \(-0.683494\pi\) | ||||
−0.545061 | + | 0.838396i | \(0.683494\pi\) | |||||||
\(194\) | 15.0914 | 1.08350 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.90571 | 0.705753 | 0.352876 | − | 0.935670i | \(-0.385204\pi\) | ||||
0.352876 | + | 0.935670i | \(0.385204\pi\) | |||||||
\(198\) | −21.5665 | −1.53266 | ||||||||
\(199\) | −8.57326 | −0.607742 | −0.303871 | − | 0.952713i | \(-0.598279\pi\) | ||||
−0.303871 | + | 0.952713i | \(0.598279\pi\) | |||||||
\(200\) | −9.41225 | −0.665547 | ||||||||
\(201\) | −12.6199 | −0.890142 | ||||||||
\(202\) | 3.12413 | 0.219813 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.15852 | 0.361169 | ||||||||
\(205\) | −33.2311 | −2.32096 | ||||||||
\(206\) | 4.61530 | 0.321564 | ||||||||
\(207\) | 16.6614 | 1.15805 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.6957 | −0.878177 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.44515 | −0.0994881 | −0.0497440 | − | 0.998762i | \(-0.515841\pi\) | ||||
−0.0497440 | + | 0.998762i | \(0.515841\pi\) | |||||||
\(212\) | 2.53490 | 0.174098 | ||||||||
\(213\) | −3.74841 | −0.256837 | ||||||||
\(214\) | −18.9366 | −1.29448 | ||||||||
\(215\) | 31.0134 | 2.11510 | ||||||||
\(216\) | 22.7610 | 1.54869 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.38950 | −0.365023 | ||||||||
\(219\) | 32.5328 | 2.19836 | ||||||||
\(220\) | −2.24043 | −0.151050 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.08307 | −0.206922 | ||||||||
\(223\) | 14.9949 | 1.00413 | 0.502067 | − | 0.864829i | \(-0.332573\pi\) | ||||
0.502067 | + | 0.864829i | \(0.332573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.9675 | 1.46450 | ||||||||
\(226\) | 15.8202 | 1.05234 | ||||||||
\(227\) | 1.14220 | 0.0758105 | 0.0379052 | − | 0.999281i | \(-0.487932\pi\) | ||||
0.0379052 | + | 0.999281i | \(0.487932\pi\) | |||||||
\(228\) | −5.14356 | −0.340641 | ||||||||
\(229\) | 6.26935 | 0.414290 | 0.207145 | − | 0.978310i | \(-0.433583\pi\) | ||||
0.207145 | + | 0.978310i | \(0.433583\pi\) | |||||||
\(230\) | 12.5241 | 0.825814 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.49863 | −0.0983900 | ||||||||
\(233\) | −6.16695 | −0.404010 | −0.202005 | − | 0.979384i | \(-0.564746\pi\) | ||||
−0.202005 | + | 0.979384i | \(0.564746\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.58423 | −0.103343 | ||||||||
\(236\) | 1.97124 | 0.128317 | ||||||||
\(237\) | −18.8433 | −1.22400 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.4589 | 1.77617 | 0.888083 | − | 0.459684i | \(-0.152037\pi\) | ||||
0.888083 | + | 0.459684i | \(0.152037\pi\) | |||||||
\(240\) | 40.0474 | 2.58505 | ||||||||
\(241\) | −9.79378 | −0.630873 | −0.315436 | − | 0.948947i | \(-0.602151\pi\) | ||||
−0.315436 | + | 0.948947i | \(0.602151\pi\) | |||||||
\(242\) | −8.19278 | −0.526652 | ||||||||
\(243\) | 0.525262 | 0.0336956 | ||||||||
\(244\) | 0.893848 | 0.0572227 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 51.4668 | 3.28140 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 21.3194 | 1.35378 | ||||||||
\(249\) | −5.23319 | −0.331640 | ||||||||
\(250\) | −5.92747 | −0.374886 | ||||||||
\(251\) | 12.4945 | 0.788644 | 0.394322 | − | 0.918972i | \(-0.370979\pi\) | ||||
0.394322 | + | 0.918972i | \(0.370979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.61665 | −0.415985 | ||||||||
\(254\) | 7.76176 | 0.487016 | ||||||||
\(255\) | 47.3830 | 2.96724 | ||||||||
\(256\) | 7.51022 | 0.469389 | ||||||||
\(257\) | 19.1929 | 1.19722 | 0.598610 | − | 0.801040i | \(-0.295720\pi\) | ||||
0.598610 | + | 0.801040i | \(0.295720\pi\) | |||||||
\(258\) | −48.0321 | −2.99035 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.49770 | 0.216502 | ||||||||
\(262\) | 34.3439 | 2.12178 | ||||||||
\(263\) | 28.8153 | 1.77683 | 0.888415 | − | 0.459041i | \(-0.151807\pi\) | ||||
0.888415 | + | 0.459041i | \(0.151807\pi\) | |||||||
\(264\) | −18.1673 | −1.11812 | ||||||||
\(265\) | 23.2840 | 1.43033 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.6527 | 1.87592 | ||||||||
\(268\) | 1.35142 | 0.0825511 | ||||||||
\(269\) | 8.15419 | 0.497170 | 0.248585 | − | 0.968610i | \(-0.420035\pi\) | ||||
0.248585 | + | 0.968610i | \(0.420035\pi\) | |||||||
\(270\) | −39.9313 | −2.43014 | ||||||||
\(271\) | −18.5788 | −1.12858 | −0.564290 | − | 0.825577i | \(-0.690850\pi\) | ||||
−0.564290 | + | 0.825577i | \(0.690850\pi\) | |||||||
\(272\) | 24.3720 | 1.47777 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.57640 | 0.0952336 | ||||||||
\(275\) | −8.72384 | −0.526067 | ||||||||
\(276\) | −2.68069 | −0.161359 | ||||||||
\(277\) | −17.2342 | −1.03550 | −0.517752 | − | 0.855531i | \(-0.673231\pi\) | ||||
−0.517752 | + | 0.855531i | \(0.673231\pi\) | |||||||
\(278\) | 12.9406 | 0.776124 | ||||||||
\(279\) | −49.7580 | −2.97893 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.4691 | 0.684191 | 0.342096 | − | 0.939665i | \(-0.388863\pi\) | ||||
0.342096 | + | 0.939665i | \(0.388863\pi\) | |||||||
\(282\) | 2.45358 | 0.146108 | ||||||||
\(283\) | 1.45575 | 0.0865355 | 0.0432678 | − | 0.999064i | \(-0.486223\pi\) | ||||
0.0432678 | + | 0.999064i | \(0.486223\pi\) | |||||||
\(284\) | 0.401402 | 0.0238188 | ||||||||
\(285\) | −47.2456 | −2.79859 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −10.7334 | −0.632472 | ||||||||
\(289\) | 11.8363 | 0.696252 | ||||||||
\(290\) | 2.62916 | 0.154389 | ||||||||
\(291\) | −29.6707 | −1.73932 | ||||||||
\(292\) | −3.48380 | −0.203874 | ||||||||
\(293\) | 30.6962 | 1.79329 | 0.896645 | − | 0.442750i | \(-0.145997\pi\) | ||||
0.896645 | + | 0.442750i | \(0.145997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.1066 | 1.05421 | ||||||||
\(296\) | −1.72859 | −0.100472 | ||||||||
\(297\) | 21.0963 | 1.22413 | ||||||||
\(298\) | 6.57107 | 0.380652 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.53441 | −0.204059 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.6536 | 1.07339 | ||||||||
\(303\) | −6.14226 | −0.352864 | ||||||||
\(304\) | −24.3013 | −1.39378 | ||||||||
\(305\) | 8.21034 | 0.470123 | ||||||||
\(306\) | −48.8430 | −2.79217 | ||||||||
\(307\) | 21.2602 | 1.21339 | 0.606693 | − | 0.794936i | \(-0.292496\pi\) | ||||
0.606693 | + | 0.794936i | \(0.292496\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.07401 | −0.516202 | ||||||||
\(310\) | −37.4022 | −2.12430 | ||||||||
\(311\) | 4.44647 | 0.252136 | 0.126068 | − | 0.992022i | \(-0.459764\pi\) | ||||
0.126068 | + | 0.992022i | \(0.459764\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.28687 | −0.129261 | −0.0646307 | − | 0.997909i | \(-0.520587\pi\) | ||||
−0.0646307 | + | 0.997909i | \(0.520587\pi\) | |||||||
\(314\) | −33.8254 | −1.90888 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.01785 | 0.113513 | ||||||||
\(317\) | 8.10086 | 0.454990 | 0.227495 | − | 0.973779i | \(-0.426947\pi\) | ||||
0.227495 | + | 0.973779i | \(0.426947\pi\) | |||||||
\(318\) | −36.0613 | −2.02222 | ||||||||
\(319\) | −1.38902 | −0.0777703 | ||||||||
\(320\) | 18.6738 | 1.04390 | ||||||||
\(321\) | 37.2307 | 2.07801 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.7527 | −1.59984 | ||||||||
\(324\) | 2.80209 | 0.155672 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.3124 | 0.958847 | ||||||||
\(327\) | 10.5961 | 0.585967 | ||||||||
\(328\) | 28.8560 | 1.59330 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 31.8722 | 1.75451 | ||||||||
\(331\) | 11.7858 | 0.647804 | 0.323902 | − | 0.946091i | \(-0.395005\pi\) | ||||
0.323902 | + | 0.946091i | \(0.395005\pi\) | |||||||
\(332\) | 0.560401 | 0.0307560 | ||||||||
\(333\) | 4.03441 | 0.221084 | ||||||||
\(334\) | −2.86592 | −0.156816 | ||||||||
\(335\) | 12.4133 | 0.678212 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.63045 | 0.143290 | 0.0716450 | − | 0.997430i | \(-0.477175\pi\) | ||||
0.0716450 | + | 0.997430i | \(0.477175\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.1035 | −1.68931 | ||||||||
\(340\) | −5.07405 | −0.275179 | ||||||||
\(341\) | 19.7601 | 1.07007 | ||||||||
\(342\) | 48.7014 | 2.63347 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −26.9302 | −1.45198 | ||||||||
\(345\) | −24.6232 | −1.32567 | ||||||||
\(346\) | −8.48704 | −0.456266 | ||||||||
\(347\) | 4.82463 | 0.259000 | 0.129500 | − | 0.991579i | \(-0.458663\pi\) | ||||
0.129500 | + | 0.991579i | \(0.458663\pi\) | |||||||
\(348\) | −0.562753 | −0.0301667 | ||||||||
\(349\) | 17.5231 | 0.937991 | 0.468995 | − | 0.883201i | \(-0.344616\pi\) | ||||
0.468995 | + | 0.883201i | \(0.344616\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.26250 | 0.227192 | ||||||||
\(353\) | 6.59724 | 0.351136 | 0.175568 | − | 0.984467i | \(-0.443824\pi\) | ||||
0.175568 | + | 0.984467i | \(0.443824\pi\) | |||||||
\(354\) | −28.0426 | −1.49045 | ||||||||
\(355\) | 3.68704 | 0.195688 | ||||||||
\(356\) | −3.28248 | −0.173971 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.10118 | −0.375309 | ||||||||
\(359\) | −23.0484 | −1.21645 | −0.608225 | − | 0.793764i | \(-0.708118\pi\) | ||||
−0.608225 | + | 0.793764i | \(0.708118\pi\) | |||||||
\(360\) | −44.9981 | −2.37161 | ||||||||
\(361\) | 9.66934 | 0.508912 | ||||||||
\(362\) | 19.0973 | 1.00373 | ||||||||
\(363\) | 16.1076 | 0.845428 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.0001 | −1.67496 | ||||||||
\(366\) | −12.7158 | −0.664665 | ||||||||
\(367\) | −15.9318 | −0.831631 | −0.415815 | − | 0.909449i | \(-0.636504\pi\) | ||||
−0.415815 | + | 0.909449i | \(0.636504\pi\) | |||||||
\(368\) | −12.6652 | −0.660222 | ||||||||
\(369\) | −67.3478 | −3.50599 | ||||||||
\(370\) | 3.03259 | 0.157657 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.00568 | 0.415075 | ||||||||
\(373\) | 23.4289 | 1.21310 | 0.606552 | − | 0.795044i | \(-0.292552\pi\) | ||||
0.606552 | + | 0.795044i | \(0.292552\pi\) | |||||||
\(374\) | 19.3967 | 1.00298 | ||||||||
\(375\) | 11.6538 | 0.601800 | ||||||||
\(376\) | 1.37565 | 0.0709437 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.1041 | 1.54634 | 0.773172 | − | 0.634196i | \(-0.218669\pi\) | ||||
0.773172 | + | 0.634196i | \(0.218669\pi\) | |||||||
\(380\) | 5.05934 | 0.259539 | ||||||||
\(381\) | −15.2602 | −0.781802 | ||||||||
\(382\) | −2.00728 | −0.102701 | ||||||||
\(383\) | −12.8597 | −0.657101 | −0.328551 | − | 0.944486i | \(-0.606560\pi\) | ||||
−0.328551 | + | 0.944486i | \(0.606560\pi\) | |||||||
\(384\) | −39.6898 | −2.02541 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.0710 | −1.17428 | ||||||||
\(387\) | 62.8532 | 3.19501 | ||||||||
\(388\) | 3.17731 | 0.161304 | ||||||||
\(389\) | 36.8531 | 1.86853 | 0.934264 | − | 0.356582i | \(-0.116058\pi\) | ||||
0.934264 | + | 0.356582i | \(0.116058\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.9852 | −0.757833 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −67.5226 | −3.40606 | ||||||||
\(394\) | 15.0903 | 0.760239 | ||||||||
\(395\) | 18.5347 | 0.932583 | ||||||||
\(396\) | −4.54057 | −0.228172 | ||||||||
\(397\) | −20.3087 | −1.01926 | −0.509631 | − | 0.860393i | \(-0.670218\pi\) | ||||
−0.509631 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(398\) | −13.0605 | −0.654662 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.6987 | −0.834935 | ||||||||
\(401\) | 19.6699 | 0.982268 | 0.491134 | − | 0.871084i | \(-0.336583\pi\) | ||||
0.491134 | + | 0.871084i | \(0.336583\pi\) | |||||||
\(402\) | −19.2252 | −0.958864 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.657750 | 0.0327243 | ||||||||
\(405\) | 25.7383 | 1.27895 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.60216 | −0.0794162 | ||||||||
\(408\) | −41.1446 | −2.03696 | ||||||||
\(409\) | 23.1755 | 1.14595 | 0.572976 | − | 0.819572i | \(-0.305789\pi\) | ||||
0.572976 | + | 0.819572i | \(0.305789\pi\) | |||||||
\(410\) | −50.6241 | −2.50015 | ||||||||
\(411\) | −3.09931 | −0.152877 | ||||||||
\(412\) | 0.971699 | 0.0478722 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 25.3819 | 1.24745 | ||||||||
\(415\) | 5.14750 | 0.252681 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.4421 | −1.24590 | ||||||||
\(418\) | −19.3405 | −0.945975 | ||||||||
\(419\) | 28.6478 | 1.39953 | 0.699767 | − | 0.714371i | \(-0.253287\pi\) | ||||
0.699767 | + | 0.714371i | \(0.253287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.3249 | −1.77037 | −0.885184 | − | 0.465241i | \(-0.845968\pi\) | ||||
−0.885184 | + | 0.465241i | \(0.845968\pi\) | |||||||
\(422\) | −2.20153 | −0.107169 | ||||||||
\(423\) | −3.21067 | −0.156108 | ||||||||
\(424\) | −20.2185 | −0.981898 | ||||||||
\(425\) | −19.7575 | −0.958377 | ||||||||
\(426\) | −5.71031 | −0.276666 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.98688 | −0.192713 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 47.2456 | 2.27839 | ||||||||
\(431\) | 7.93131 | 0.382038 | 0.191019 | − | 0.981586i | \(-0.438821\pi\) | ||||
0.191019 | + | 0.981586i | \(0.438821\pi\) | |||||||
\(432\) | 40.3814 | 1.94285 | ||||||||
\(433\) | 9.60994 | 0.461824 | 0.230912 | − | 0.972975i | \(-0.425829\pi\) | ||||
0.230912 | + | 0.972975i | \(0.425829\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.16911 | −0.247840 | ||||||||
\(436\) | −1.13470 | −0.0543421 | ||||||||
\(437\) | 14.9417 | 0.714760 | ||||||||
\(438\) | 49.5603 | 2.36808 | ||||||||
\(439\) | 3.46690 | 0.165466 | 0.0827332 | − | 0.996572i | \(-0.473635\pi\) | ||||
0.0827332 | + | 0.996572i | \(0.473635\pi\) | |||||||
\(440\) | 17.8698 | 0.851910 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.45667 | 0.116720 | 0.0583600 | − | 0.998296i | \(-0.481413\pi\) | ||||
0.0583600 | + | 0.998296i | \(0.481413\pi\) | |||||||
\(444\) | −0.649106 | −0.0308052 | ||||||||
\(445\) | −30.1508 | −1.42929 | ||||||||
\(446\) | 22.8432 | 1.08166 | ||||||||
\(447\) | −12.9192 | −0.611056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.7487 | −1.07358 | −0.536790 | − | 0.843716i | \(-0.680363\pi\) | ||||
−0.536790 | + | 0.843716i | \(0.680363\pi\) | |||||||
\(450\) | 33.4652 | 1.57757 | ||||||||
\(451\) | 26.7454 | 1.25939 | ||||||||
\(452\) | 3.33075 | 0.156665 | ||||||||
\(453\) | −36.6742 | −1.72311 | ||||||||
\(454\) | 1.74002 | 0.0816633 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 41.0254 | 1.92119 | ||||||||
\(457\) | 12.2568 | 0.573349 | 0.286675 | − | 0.958028i | \(-0.407450\pi\) | ||||
0.286675 | + | 0.958028i | \(0.407450\pi\) | |||||||
\(458\) | 9.55070 | 0.446275 | ||||||||
\(459\) | 47.7781 | 2.23009 | ||||||||
\(460\) | 2.63680 | 0.122942 | ||||||||
\(461\) | 24.0650 | 1.12082 | 0.560409 | − | 0.828216i | \(-0.310644\pi\) | ||||
0.560409 | + | 0.828216i | \(0.310644\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.3956 | 0.901390 | 0.450695 | − | 0.892678i | \(-0.351176\pi\) | ||||
0.450695 | + | 0.892678i | \(0.351176\pi\) | |||||||
\(464\) | −2.65879 | −0.123431 | ||||||||
\(465\) | 73.5352 | 3.41012 | ||||||||
\(466\) | −9.39470 | −0.435201 | ||||||||
\(467\) | 17.8782 | 0.827307 | 0.413653 | − | 0.910434i | \(-0.364253\pi\) | ||||
0.413653 | + | 0.910434i | \(0.364253\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.41340 | −0.111322 | ||||||||
\(471\) | 66.5031 | 3.06430 | ||||||||
\(472\) | −15.7227 | −0.723696 | ||||||||
\(473\) | −24.9605 | −1.14769 | ||||||||
\(474\) | −28.7057 | −1.31850 | ||||||||
\(475\) | 19.7002 | 0.903906 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 47.1886 | 2.16062 | ||||||||
\(478\) | 41.8307 | 1.91329 | ||||||||
\(479\) | −20.7671 | −0.948875 | −0.474437 | − | 0.880289i | \(-0.657348\pi\) | ||||
−0.474437 | + | 0.880289i | \(0.657348\pi\) | |||||||
\(480\) | 15.8625 | 0.724019 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −14.9198 | −0.679578 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.72490 | −0.0784043 | ||||||||
\(485\) | 29.1848 | 1.32522 | ||||||||
\(486\) | 0.800181 | 0.0362970 | ||||||||
\(487\) | −19.1987 | −0.869977 | −0.434988 | − | 0.900436i | \(-0.643248\pi\) | ||||
−0.434988 | + | 0.900436i | \(0.643248\pi\) | |||||||
\(488\) | −7.12938 | −0.322732 | ||||||||
\(489\) | −34.0374 | −1.53923 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.91648 | 0.357266 | 0.178633 | − | 0.983916i | \(-0.442833\pi\) | ||||
0.178633 | + | 0.983916i | \(0.442833\pi\) | |||||||
\(492\) | 10.8357 | 0.488513 | ||||||||
\(493\) | −3.14581 | −0.141680 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −41.7069 | −1.87459 | ||||||||
\(496\) | 37.8237 | 1.69833 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.97222 | −0.357244 | ||||||||
\(499\) | 39.1750 | 1.75371 | 0.876856 | − | 0.480753i | \(-0.159637\pi\) | ||||
0.876856 | + | 0.480753i | \(0.159637\pi\) | |||||||
\(500\) | −1.24796 | −0.0558105 | ||||||||
\(501\) | 5.63459 | 0.251735 | ||||||||
\(502\) | 19.0340 | 0.849530 | ||||||||
\(503\) | −16.1533 | −0.720239 | −0.360120 | − | 0.932906i | \(-0.617264\pi\) | ||||
−0.360120 | + | 0.932906i | \(0.617264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.04169 | 0.268852 | ||||||||
\(506\) | −10.0798 | −0.448101 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.63415 | 0.0725036 | ||||||||
\(509\) | 24.3177 | 1.07786 | 0.538930 | − | 0.842350i | \(-0.318829\pi\) | ||||
0.538930 | + | 0.842350i | \(0.318829\pi\) | |||||||
\(510\) | 72.1830 | 3.19632 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −15.0621 | −0.665658 | ||||||||
\(513\) | −47.6396 | −2.10334 | ||||||||
\(514\) | 29.2384 | 1.28965 | ||||||||
\(515\) | 8.92543 | 0.393302 | ||||||||
\(516\) | −10.1126 | −0.445183 | ||||||||
\(517\) | 1.27503 | 0.0560759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.6861 | 0.732439 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4550 | 1.50950 | 0.754750 | − | 0.656012i | \(-0.227758\pi\) | ||||
0.754750 | + | 0.656012i | \(0.227758\pi\) | |||||||
\(522\) | 5.32838 | 0.233217 | ||||||||
\(523\) | −34.6865 | −1.51674 | −0.758368 | − | 0.651827i | \(-0.774003\pi\) | ||||
−0.758368 | + | 0.651827i | \(0.774003\pi\) | |||||||
\(524\) | 7.23072 | 0.315875 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 43.8971 | 1.91401 | ||||||||
\(527\) | 44.7520 | 1.94943 | ||||||||
\(528\) | −32.2314 | −1.40269 | ||||||||
\(529\) | −15.2128 | −0.661424 | ||||||||
\(530\) | 35.4708 | 1.54075 | ||||||||
\(531\) | 36.6956 | 1.59246 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 46.6962 | 2.02074 | ||||||||
\(535\) | −36.6211 | −1.58327 | ||||||||
\(536\) | −10.7790 | −0.465582 | ||||||||
\(537\) | 13.9614 | 0.602480 | ||||||||
\(538\) | 12.4221 | 0.535553 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.40708 | −0.361783 | ||||||||
\(541\) | −12.2568 | −0.526961 | −0.263481 | − | 0.964665i | \(-0.584871\pi\) | ||||
−0.263481 | + | 0.964665i | \(0.584871\pi\) | |||||||
\(542\) | −28.3028 | −1.21571 | ||||||||
\(543\) | −37.5466 | −1.61128 | ||||||||
\(544\) | 9.65356 | 0.413893 | ||||||||
\(545\) | −10.4226 | −0.446456 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4110 | −0.701686 | −0.350843 | − | 0.936434i | \(-0.614105\pi\) | ||||
−0.350843 | + | 0.936434i | \(0.614105\pi\) | |||||||
\(548\) | 0.331892 | 0.0141777 | ||||||||
\(549\) | 16.6395 | 0.710155 | ||||||||
\(550\) | −13.2899 | −0.566681 | ||||||||
\(551\) | 3.13669 | 0.133627 | ||||||||
\(552\) | 21.3814 | 0.910052 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −26.2545 | −1.11545 | ||||||||
\(555\) | −5.96229 | −0.253085 | ||||||||
\(556\) | 2.72449 | 0.115544 | ||||||||
\(557\) | 35.6541 | 1.51071 | 0.755356 | − | 0.655315i | \(-0.227464\pi\) | ||||
0.755356 | + | 0.655315i | \(0.227464\pi\) | |||||||
\(558\) | −75.8010 | −3.20891 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38.1353 | −1.61007 | ||||||||
\(562\) | 17.4720 | 0.737013 | ||||||||
\(563\) | −10.7748 | −0.454103 | −0.227052 | − | 0.973883i | \(-0.572909\pi\) | ||||
−0.227052 | + | 0.973883i | \(0.572909\pi\) | |||||||
\(564\) | 0.516572 | 0.0217516 | ||||||||
\(565\) | 30.5943 | 1.28711 | ||||||||
\(566\) | 2.21769 | 0.0932163 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.20161 | −0.134336 | ||||||||
\(569\) | 20.9328 | 0.877550 | 0.438775 | − | 0.898597i | \(-0.355413\pi\) | ||||
0.438775 | + | 0.898597i | \(0.355413\pi\) | |||||||
\(570\) | −71.9738 | −3.01465 | ||||||||
\(571\) | 32.2668 | 1.35032 | 0.675161 | − | 0.737670i | \(-0.264074\pi\) | ||||
0.675161 | + | 0.737670i | \(0.264074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.94645 | 0.164865 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2672 | 0.428173 | ||||||||
\(576\) | 37.8453 | 1.57689 | ||||||||
\(577\) | −0.197896 | −0.00823851 | −0.00411925 | − | 0.999992i | \(-0.501311\pi\) | ||||
−0.00411925 | + | 0.999992i | \(0.501311\pi\) | |||||||
\(578\) | 18.0313 | 0.750005 | ||||||||
\(579\) | 45.3592 | 1.88506 | ||||||||
\(580\) | 0.553539 | 0.0229844 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −45.2001 | −1.87361 | ||||||||
\(583\) | −18.7397 | −0.776120 | ||||||||
\(584\) | 27.7870 | 1.14984 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.7624 | 1.93174 | ||||||||
\(587\) | −10.1251 | −0.417907 | −0.208954 | − | 0.977926i | \(-0.567006\pi\) | ||||
−0.208954 | + | 0.977926i | \(0.567006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.6222 | −1.83863 | ||||||||
\(590\) | 27.5835 | 1.13559 | ||||||||
\(591\) | −29.6686 | −1.22040 | ||||||||
\(592\) | −3.06677 | −0.126044 | ||||||||
\(593\) | −29.9345 | −1.22926 | −0.614631 | − | 0.788815i | \(-0.710695\pi\) | ||||
−0.614631 | + | 0.788815i | \(0.710695\pi\) | |||||||
\(594\) | 32.1380 | 1.31864 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.38346 | 0.0566688 | ||||||||
\(597\) | 25.6778 | 1.05092 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.8872 | 1.09858 | 0.549291 | − | 0.835631i | \(-0.314898\pi\) | ||||
0.549291 | + | 0.835631i | \(0.314898\pi\) | |||||||
\(600\) | 28.1906 | 1.15088 | ||||||||
\(601\) | −24.7432 | −1.00930 | −0.504649 | − | 0.863325i | \(-0.668378\pi\) | ||||
−0.504649 | + | 0.863325i | \(0.668378\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.1574 | 1.02449 | ||||||||
\(604\) | 3.92730 | 0.159799 | ||||||||
\(605\) | −15.8438 | −0.644143 | ||||||||
\(606\) | −9.35709 | −0.380106 | ||||||||
\(607\) | 3.09235 | 0.125515 | 0.0627573 | − | 0.998029i | \(-0.480011\pi\) | ||||
0.0627573 | + | 0.998029i | \(0.480011\pi\) | |||||||
\(608\) | −9.62557 | −0.390369 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.5076 | 0.506417 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −10.2833 | −0.415679 | ||||||||
\(613\) | 31.3605 | 1.26664 | 0.633319 | − | 0.773891i | \(-0.281692\pi\) | ||||
0.633319 | + | 0.773891i | \(0.281692\pi\) | |||||||
\(614\) | 32.3877 | 1.30706 | ||||||||
\(615\) | 99.5305 | 4.01346 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.5311 | 0.504484 | 0.252242 | − | 0.967664i | \(-0.418832\pi\) | ||||
0.252242 | + | 0.967664i | \(0.418832\pi\) | |||||||
\(618\) | −13.8233 | −0.556055 | ||||||||
\(619\) | −11.6112 | −0.466692 | −0.233346 | − | 0.972394i | \(-0.574968\pi\) | ||||
−0.233346 | + | 0.972394i | \(0.574968\pi\) | |||||||
\(620\) | −7.87459 | −0.316251 | ||||||||
\(621\) | −24.8286 | −0.996336 | ||||||||
\(622\) | 6.77374 | 0.271602 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.8593 | −1.19437 | ||||||||
\(626\) | −3.48380 | −0.139241 | ||||||||
\(627\) | 38.0248 | 1.51856 | ||||||||
\(628\) | −7.12155 | −0.284181 | ||||||||
\(629\) | −3.62852 | −0.144679 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.7037 | −0.505728 | −0.252864 | − | 0.967502i | \(-0.581372\pi\) | ||||
−0.252864 | + | 0.967502i | \(0.581372\pi\) | |||||||
\(632\) | −16.0945 | −0.640204 | ||||||||
\(633\) | 4.32836 | 0.172037 | ||||||||
\(634\) | 12.3408 | 0.490116 | ||||||||
\(635\) | 15.0103 | 0.595665 | ||||||||
\(636\) | −7.59228 | −0.301054 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.11603 | −0.0837744 | ||||||||
\(639\) | 7.47233 | 0.295601 | ||||||||
\(640\) | 39.0399 | 1.54319 | ||||||||
\(641\) | −40.3015 | −1.59181 | −0.795906 | − | 0.605420i | \(-0.793005\pi\) | ||||
−0.795906 | + | 0.605420i | \(0.793005\pi\) | |||||||
\(642\) | 56.7170 | 2.23844 | ||||||||
\(643\) | 11.6643 | 0.459997 | 0.229998 | − | 0.973191i | \(-0.426128\pi\) | ||||
0.229998 | + | 0.973191i | \(0.426128\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −92.8882 | −3.65747 | ||||||||
\(646\) | −43.8017 | −1.72336 | ||||||||
\(647\) | −11.0387 | −0.433977 | −0.216988 | − | 0.976174i | \(-0.569623\pi\) | ||||
−0.216988 | + | 0.976174i | \(0.569623\pi\) | |||||||
\(648\) | −22.3496 | −0.877976 | ||||||||
\(649\) | −14.5727 | −0.572030 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.64493 | 0.142747 | ||||||||
\(653\) | 19.1260 | 0.748458 | 0.374229 | − | 0.927336i | \(-0.377907\pi\) | ||||
0.374229 | + | 0.927336i | \(0.377907\pi\) | |||||||
\(654\) | 16.1421 | 0.631206 | ||||||||
\(655\) | 66.4170 | 2.59513 | ||||||||
\(656\) | 51.1947 | 1.99882 | ||||||||
\(657\) | −64.8529 | −2.53015 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.8233 | 1.12279 | 0.561397 | − | 0.827546i | \(-0.310264\pi\) | ||||
0.561397 | + | 0.827546i | \(0.310264\pi\) | |||||||
\(660\) | 6.71032 | 0.261199 | ||||||||
\(661\) | 48.2385 | 1.87626 | 0.938131 | − | 0.346281i | \(-0.112556\pi\) | ||||
0.938131 | + | 0.346281i | \(0.112556\pi\) | |||||||
\(662\) | 17.9544 | 0.697816 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.46979 | −0.173462 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.14600 | 0.238153 | ||||||||
\(667\) | 1.63476 | 0.0632982 | ||||||||
\(668\) | −0.603386 | −0.0233457 | ||||||||
\(669\) | −44.9112 | −1.73637 | ||||||||
\(670\) | 18.9104 | 0.730572 | ||||||||
\(671\) | −6.60794 | −0.255097 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.0426 | −1.27370 | −0.636849 | − | 0.770989i | \(-0.719762\pi\) | ||||
−0.636849 | + | 0.770989i | \(0.719762\pi\) | |||||||
\(674\) | 4.00722 | 0.154352 | ||||||||
\(675\) | −32.7356 | −1.26000 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.7186 | 0.604117 | 0.302058 | − | 0.953289i | \(-0.402326\pi\) | ||||
0.302058 | + | 0.953289i | \(0.402326\pi\) | |||||||
\(678\) | −47.3830 | −1.81973 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 40.4710 | 1.55199 | ||||||||
\(681\) | −3.42100 | −0.131093 | ||||||||
\(682\) | 30.1024 | 1.15268 | ||||||||
\(683\) | 33.3629 | 1.27660 | 0.638298 | − | 0.769789i | \(-0.279639\pi\) | ||||
0.638298 | + | 0.769789i | \(0.279639\pi\) | |||||||
\(684\) | 10.2535 | 0.392053 | ||||||||
\(685\) | 3.04856 | 0.116479 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.7773 | −0.716400 | ||||||||
\(688\) | −47.7781 | −1.82152 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −37.5109 | −1.42802 | ||||||||
\(691\) | −45.3507 | −1.72522 | −0.862610 | − | 0.505869i | \(-0.831172\pi\) | ||||
−0.862610 | + | 0.505869i | \(0.831172\pi\) | |||||||
\(692\) | −1.78685 | −0.0679257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.34981 | 0.278995 | ||||||||
\(695\) | 25.0255 | 0.949270 | ||||||||
\(696\) | 4.48855 | 0.170138 | ||||||||
\(697\) | 60.5721 | 2.29433 | ||||||||
\(698\) | 26.6946 | 1.01041 | ||||||||
\(699\) | 18.4706 | 0.698623 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.5681 | 0.890155 | 0.445077 | − | 0.895492i | \(-0.353176\pi\) | ||||
0.445077 | + | 0.895492i | \(0.353176\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.61800 | 0.136456 | ||||||||
\(704\) | −15.0293 | −0.566438 | ||||||||
\(705\) | 4.74491 | 0.178704 | ||||||||
\(706\) | 10.0502 | 0.378244 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.90405 | −0.221888 | ||||||||
\(709\) | 8.66932 | 0.325583 | 0.162792 | − | 0.986660i | \(-0.447950\pi\) | ||||
0.162792 | + | 0.986660i | \(0.447950\pi\) | |||||||
\(710\) | 5.61681 | 0.210795 | ||||||||
\(711\) | 37.5634 | 1.40874 | ||||||||
\(712\) | 26.1812 | 0.981183 | ||||||||
\(713\) | −23.2560 | −0.870943 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.49507 | −0.0558735 | ||||||||
\(717\) | −82.2420 | −3.07138 | ||||||||
\(718\) | −35.1119 | −1.31036 | ||||||||
\(719\) | 11.0038 | 0.410373 | 0.205186 | − | 0.978723i | \(-0.434220\pi\) | ||||
0.205186 | + | 0.978723i | \(0.434220\pi\) | |||||||
\(720\) | −79.8331 | −2.97520 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.7302 | 0.548202 | ||||||||
\(723\) | 29.3333 | 1.09092 | ||||||||
\(724\) | 4.02071 | 0.149429 | ||||||||
\(725\) | 2.15538 | 0.0800488 | ||||||||
\(726\) | 24.5382 | 0.910698 | ||||||||
\(727\) | −40.7049 | −1.50966 | −0.754831 | − | 0.655919i | \(-0.772281\pi\) | ||||
−0.754831 | + | 0.655919i | \(0.772281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.7827 | −1.02899 | ||||||||
\(730\) | −48.7488 | −1.80427 | ||||||||
\(731\) | −56.5298 | −2.09083 | ||||||||
\(732\) | −2.67716 | −0.0989508 | ||||||||
\(733\) | −10.3536 | −0.382418 | −0.191209 | − | 0.981549i | \(-0.561241\pi\) | ||||
−0.191209 | + | 0.981549i | \(0.561241\pi\) | |||||||
\(734\) | −24.2704 | −0.895835 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.01660 | −0.184914 | ||||||||
\(737\) | −9.99062 | −0.368009 | ||||||||
\(738\) | −102.597 | −3.77666 | ||||||||
\(739\) | −48.5321 | −1.78528 | −0.892640 | − | 0.450770i | \(-0.851150\pi\) | ||||
−0.892640 | + | 0.450770i | \(0.851150\pi\) | |||||||
\(740\) | 0.638477 | 0.0234709 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.5215 | −0.899608 | −0.449804 | − | 0.893127i | \(-0.648506\pi\) | ||||
−0.449804 | + | 0.893127i | \(0.648506\pi\) | |||||||
\(744\) | −63.8537 | −2.34099 | ||||||||
\(745\) | 12.7076 | 0.465572 | ||||||||
\(746\) | 35.6915 | 1.30676 | ||||||||
\(747\) | 10.4322 | 0.381694 | ||||||||
\(748\) | 4.08376 | 0.149317 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17.7534 | 0.648261 | ||||||||
\(751\) | −28.0663 | −1.02415 | −0.512077 | − | 0.858939i | \(-0.671124\pi\) | ||||
−0.512077 | + | 0.858939i | \(0.671124\pi\) | |||||||
\(752\) | 2.44060 | 0.0889996 | ||||||||
\(753\) | −37.4222 | −1.36374 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.0738 | 1.31286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.70864 | 0.207484 | 0.103742 | − | 0.994604i | \(-0.466918\pi\) | ||||
0.103742 | + | 0.994604i | \(0.466918\pi\) | |||||||
\(758\) | 45.8605 | 1.66573 | ||||||||
\(759\) | 19.8175 | 0.719331 | ||||||||
\(760\) | −40.3536 | −1.46378 | ||||||||
\(761\) | 7.69598 | 0.278979 | 0.139490 | − | 0.990224i | \(-0.455454\pi\) | ||||
0.139490 | + | 0.990224i | \(0.455454\pi\) | |||||||
\(762\) | −23.2473 | −0.842159 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.422610 | −0.0152895 | ||||||||
\(765\) | −94.4563 | −3.41508 | ||||||||
\(766\) | −19.5904 | −0.707832 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −22.4939 | −0.811677 | ||||||||
\(769\) | −15.0754 | −0.543634 | −0.271817 | − | 0.962349i | \(-0.587625\pi\) | ||||
−0.271817 | + | 0.962349i | \(0.587625\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −57.4847 | −2.07026 | ||||||||
\(772\) | −4.85733 | −0.174819 | ||||||||
\(773\) | −21.2624 | −0.764755 | −0.382378 | − | 0.924006i | \(-0.624895\pi\) | ||||
−0.382378 | + | 0.924006i | \(0.624895\pi\) | |||||||
\(774\) | 95.7503 | 3.44167 | ||||||||
\(775\) | −30.6622 | −1.10142 | ||||||||
\(776\) | −25.3424 | −0.909740 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 56.1419 | 2.01278 | ||||||||
\(779\) | −60.3966 | −2.16393 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.96744 | −0.106183 | ||||||||
\(782\) | −22.8283 | −0.816340 | ||||||||
\(783\) | −5.21221 | −0.186269 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −65.4142 | −2.33473 | ||||||||
\(786\) | −102.864 | −3.66902 | ||||||||
\(787\) | −9.28939 | −0.331131 | −0.165565 | − | 0.986199i | \(-0.552945\pi\) | ||||
−0.165565 | + | 0.986199i | \(0.552945\pi\) | |||||||
\(788\) | 3.17709 | 0.113179 | ||||||||
\(789\) | −86.3048 | −3.07253 | ||||||||
\(790\) | 28.2357 | 1.00458 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 36.2158 | 1.28687 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −30.9381 | −1.09795 | ||||||||
\(795\) | −69.7381 | −2.47335 | ||||||||
\(796\) | −2.74973 | −0.0974615 | ||||||||
\(797\) | −49.7686 | −1.76289 | −0.881447 | − | 0.472283i | \(-0.843430\pi\) | ||||
−0.881447 | + | 0.472283i | \(0.843430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.88765 | 0.102158 | ||||||||
\(800\) | −6.61423 | −0.233848 | ||||||||
\(801\) | −61.1051 | −2.15904 | ||||||||
\(802\) | 29.9650 | 1.05810 | ||||||||
\(803\) | 25.7547 | 0.908863 | ||||||||
\(804\) | −4.04764 | −0.142749 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.4226 | −0.859717 | ||||||||
\(808\) | −5.24625 | −0.184563 | ||||||||
\(809\) | −9.59433 | −0.337319 | −0.168659 | − | 0.985674i | \(-0.553944\pi\) | ||||
−0.168659 | + | 0.985674i | \(0.553944\pi\) | |||||||
\(810\) | 39.2096 | 1.37768 | ||||||||
\(811\) | 35.6060 | 1.25030 | 0.625148 | − | 0.780506i | \(-0.285038\pi\) | ||||
0.625148 | + | 0.780506i | \(0.285038\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 55.6453 | 1.95157 | ||||||||
\(814\) | −2.44073 | −0.0855474 | ||||||||
\(815\) | 33.4801 | 1.17276 | ||||||||
\(816\) | −72.9966 | −2.55539 | ||||||||
\(817\) | 56.3659 | 1.97199 | ||||||||
\(818\) | 35.3054 | 1.23442 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.6583 | −0.372205 | ||||||||
\(821\) | 0.296780 | 0.0103577 | 0.00517884 | − | 0.999987i | \(-0.498352\pi\) | ||||
0.00517884 | + | 0.999987i | \(0.498352\pi\) | |||||||
\(822\) | −4.72147 | −0.164680 | ||||||||
\(823\) | 22.9119 | 0.798658 | 0.399329 | − | 0.916808i | \(-0.369243\pi\) | ||||
0.399329 | + | 0.916808i | \(0.369243\pi\) | |||||||
\(824\) | −7.75033 | −0.269995 | ||||||||
\(825\) | 26.1288 | 0.909687 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.50142 | −0.295623 | −0.147812 | − | 0.989016i | \(-0.547223\pi\) | ||||
−0.147812 | + | 0.989016i | \(0.547223\pi\) | |||||||
\(828\) | 5.34387 | 0.185712 | ||||||||
\(829\) | 54.3605 | 1.88802 | 0.944009 | − | 0.329919i | \(-0.107022\pi\) | ||||
0.944009 | + | 0.329919i | \(0.107022\pi\) | |||||||
\(830\) | 7.84168 | 0.272189 | ||||||||
\(831\) | 51.6182 | 1.79061 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −38.7583 | −1.34209 | ||||||||
\(835\) | −5.54233 | −0.191800 | ||||||||
\(836\) | −4.07192 | −0.140830 | ||||||||
\(837\) | 74.1485 | 2.56295 | ||||||||
\(838\) | 43.6419 | 1.50758 | ||||||||
\(839\) | −17.0486 | −0.588585 | −0.294292 | − | 0.955715i | \(-0.595084\pi\) | ||||
−0.294292 | + | 0.955715i | \(0.595084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6568 | −0.988166 | ||||||||
\(842\) | −55.3372 | −1.90705 | ||||||||
\(843\) | −34.3512 | −1.18312 | ||||||||
\(844\) | −0.463507 | −0.0159546 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.89112 | −0.168160 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −35.8706 | −1.23180 | ||||||||
\(849\) | −4.36013 | −0.149639 | ||||||||
\(850\) | −30.0984 | −1.03237 | ||||||||
\(851\) | 1.88561 | 0.0646379 | ||||||||
\(852\) | −1.20224 | −0.0411881 | ||||||||
\(853\) | 45.0401 | 1.54214 | 0.771072 | − | 0.636747i | \(-0.219721\pi\) | ||||
0.771072 | + | 0.636747i | \(0.219721\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 94.1825 | 3.22097 | ||||||||
\(856\) | 31.7996 | 1.08689 | ||||||||
\(857\) | −39.7927 | −1.35929 | −0.679646 | − | 0.733541i | \(-0.737866\pi\) | ||||
−0.679646 | + | 0.733541i | \(0.737866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.3379 | 0.762158 | 0.381079 | − | 0.924542i | \(-0.375553\pi\) | ||||
0.381079 | + | 0.924542i | \(0.375553\pi\) | |||||||
\(860\) | 9.94702 | 0.339191 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0825 | 0.411532 | ||||||||
\(863\) | −14.1624 | −0.482094 | −0.241047 | − | 0.970513i | \(-0.577491\pi\) | ||||
−0.241047 | + | 0.970513i | \(0.577491\pi\) | |||||||
\(864\) | 15.9947 | 0.544152 | ||||||||
\(865\) | −16.4129 | −0.558055 | ||||||||
\(866\) | 14.6397 | 0.497479 | ||||||||
\(867\) | −35.4509 | −1.20397 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.9173 | −0.506036 | ||||||||
\(870\) | −7.87459 | −0.266974 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 9.05041 | 0.306485 | ||||||||
\(873\) | 59.1474 | 2.00184 | ||||||||
\(874\) | 22.7622 | 0.769941 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.4343 | 0.352544 | ||||||||
\(877\) | −43.9546 | −1.48424 | −0.742121 | − | 0.670266i | \(-0.766180\pi\) | ||||
−0.742121 | + | 0.670266i | \(0.766180\pi\) | |||||||
\(878\) | 5.28147 | 0.178241 | ||||||||
\(879\) | −91.9382 | −3.10100 | ||||||||
\(880\) | 31.7037 | 1.06873 | ||||||||
\(881\) | 15.3849 | 0.518331 | 0.259165 | − | 0.965833i | \(-0.416553\pi\) | ||||
0.259165 | + | 0.965833i | \(0.416553\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.5262 | −1.49842 | −0.749212 | − | 0.662330i | \(-0.769568\pi\) | ||||
−0.749212 | + | 0.662330i | \(0.769568\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −54.2310 | −1.82295 | ||||||||
\(886\) | 3.74248 | 0.125731 | ||||||||
\(887\) | 16.1072 | 0.540826 | 0.270413 | − | 0.962744i | \(-0.412840\pi\) | ||||
0.270413 | + | 0.962744i | \(0.412840\pi\) | |||||||
\(888\) | 5.17731 | 0.173739 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −45.9316 | −1.53963 | ||||||||
\(891\) | −20.7150 | −0.693978 | ||||||||
\(892\) | 4.80936 | 0.161029 | ||||||||
\(893\) | −2.87928 | −0.0963515 | ||||||||
\(894\) | −19.6810 | −0.658231 | ||||||||
\(895\) | −13.7328 | −0.459037 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34.6553 | −1.15646 | ||||||||
\(899\) | −4.88208 | −0.162827 | ||||||||
\(900\) | 7.04572 | 0.234857 | ||||||||
\(901\) | −42.4411 | −1.41392 | ||||||||
\(902\) | 40.7439 | 1.35662 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −26.5663 | −0.883582 | ||||||||
\(905\) | 36.9318 | 1.22766 | ||||||||
\(906\) | −55.8694 | −1.85614 | ||||||||
\(907\) | 18.6037 | 0.617725 | 0.308862 | − | 0.951107i | \(-0.400052\pi\) | ||||
0.308862 | + | 0.951107i | \(0.400052\pi\) | |||||||
\(908\) | 0.366341 | 0.0121575 | ||||||||
\(909\) | 12.2444 | 0.406121 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.1801 | 1.26496 | 0.632481 | − | 0.774576i | \(-0.282037\pi\) | ||||
0.632481 | + | 0.774576i | \(0.282037\pi\) | |||||||
\(912\) | 72.7850 | 2.41015 | ||||||||
\(913\) | −4.14287 | −0.137109 | ||||||||
\(914\) | 18.6720 | 0.617614 | ||||||||
\(915\) | −24.5908 | −0.812946 | ||||||||
\(916\) | 2.01079 | 0.0664383 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 72.7850 | 2.40226 | ||||||||
\(919\) | −16.7629 | −0.552956 | −0.276478 | − | 0.961020i | \(-0.589167\pi\) | ||||
−0.276478 | + | 0.961020i | \(0.589167\pi\) | |||||||
\(920\) | −21.0313 | −0.693381 | ||||||||
\(921\) | −63.6765 | −2.09821 | ||||||||
\(922\) | 36.6605 | 1.20735 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.48612 | 0.0817430 | ||||||||
\(926\) | 29.5472 | 0.970980 | ||||||||
\(927\) | 18.0887 | 0.594111 | ||||||||
\(928\) | −1.05313 | −0.0345706 | ||||||||
\(929\) | −6.58871 | −0.216169 | −0.108084 | − | 0.994142i | \(-0.534472\pi\) | ||||
−0.108084 | + | 0.994142i | \(0.534472\pi\) | |||||||
\(930\) | 112.023 | 3.67339 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.97794 | −0.0647897 | ||||||||
\(933\) | −13.3176 | −0.436000 | ||||||||
\(934\) | 27.2356 | 0.891177 | ||||||||
\(935\) | 37.5109 | 1.22674 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.0958 | 1.27721 | 0.638603 | − | 0.769537i | \(-0.279513\pi\) | ||||
0.638603 | + | 0.769537i | \(0.279513\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.84940 | 0.223522 | ||||||||
\(940\) | −0.508114 | −0.0165728 | ||||||||
\(941\) | 13.2351 | 0.431452 | 0.215726 | − | 0.976454i | \(-0.430788\pi\) | ||||
0.215726 | + | 0.976454i | \(0.430788\pi\) | |||||||
\(942\) | 101.311 | 3.30088 | ||||||||
\(943\) | −31.4771 | −1.02504 | ||||||||
\(944\) | −27.8943 | −0.907884 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.0248 | −1.23629 | ||||||||
\(947\) | −50.1427 | −1.62942 | −0.814709 | − | 0.579870i | \(-0.803103\pi\) | ||||
−0.814709 | + | 0.579870i | \(0.803103\pi\) | |||||||
\(948\) | −6.04366 | −0.196289 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 30.0112 | 0.973690 | ||||||||
\(951\) | −24.2629 | −0.786778 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.9832 | 0.971252 | 0.485626 | − | 0.874167i | \(-0.338592\pi\) | ||||
0.485626 | + | 0.874167i | \(0.338592\pi\) | |||||||
\(954\) | 71.8869 | 2.32742 | ||||||||
\(955\) | −3.88184 | −0.125613 | ||||||||
\(956\) | 8.80697 | 0.284838 | ||||||||
\(957\) | 4.16026 | 0.134482 | ||||||||
\(958\) | −31.6366 | −1.02213 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −55.9300 | −1.80513 | ||||||||
\(961\) | 38.4521 | 1.24039 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −74.2180 | −2.39164 | ||||||||
\(964\) | −3.14119 | −0.101171 | ||||||||
\(965\) | −44.6165 | −1.43626 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.8356 | −1.21671 | −0.608356 | − | 0.793665i | \(-0.708171\pi\) | ||||
−0.608356 | + | 0.793665i | \(0.708171\pi\) | |||||||
\(968\) | 13.7579 | 0.442195 | ||||||||
\(969\) | 86.1172 | 2.76648 | ||||||||
\(970\) | 44.4600 | 1.42753 | ||||||||
\(971\) | −15.3432 | −0.492388 | −0.246194 | − | 0.969221i | \(-0.579180\pi\) | ||||
−0.246194 | + | 0.969221i | \(0.579180\pi\) | |||||||
\(972\) | 0.168469 | 0.00540364 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.2472 | −0.937142 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.6486 | −0.404871 | ||||||||
\(977\) | −26.5487 | −0.849367 | −0.424684 | − | 0.905342i | \(-0.639615\pi\) | ||||
−0.424684 | + | 0.905342i | \(0.639615\pi\) | |||||||
\(978\) | −51.8525 | −1.65806 | ||||||||
\(979\) | 24.2663 | 0.775555 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.1230 | −0.674406 | ||||||||
\(982\) | 12.0599 | 0.384848 | ||||||||
\(983\) | −8.02003 | −0.255799 | −0.127900 | − | 0.991787i | \(-0.540824\pi\) | ||||
−0.127900 | + | 0.991787i | \(0.540824\pi\) | |||||||
\(984\) | −86.4265 | −2.75518 | ||||||||
\(985\) | 29.1828 | 0.929842 | ||||||||
\(986\) | −4.79231 | −0.152618 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.3765 | 0.934117 | ||||||||
\(990\) | −63.5361 | −2.01931 | ||||||||
\(991\) | 49.0958 | 1.55958 | 0.779789 | − | 0.626042i | \(-0.215326\pi\) | ||||
0.779789 | + | 0.626042i | \(0.215326\pi\) | |||||||
\(992\) | 14.9817 | 0.475669 | ||||||||
\(993\) | −35.2995 | −1.12020 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.2573 | −0.800711 | ||||||||
\(996\) | −1.67846 | −0.0531840 | ||||||||
\(997\) | −19.9476 | −0.631746 | −0.315873 | − | 0.948801i | \(-0.602297\pi\) | ||||
−0.315873 | + | 0.948801i | \(0.602297\pi\) | |||||||
\(998\) | 59.6790 | 1.88910 | ||||||||
\(999\) | −6.01201 | −0.190212 |
(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 | 8281.2.a.cs.1.11 | 16 | ||
7.6 | odd | 2 | inner | 8281.2.a.cs.1.12 | 16 | ||
13.5 | odd | 4 | 637.2.c.g.246.5 | ✓ | 16 | ||
13.8 | odd | 4 | 637.2.c.g.246.11 | yes | 16 | ||
13.12 | even | 2 | inner | 8281.2.a.cs.1.5 | 16 | ||
91.5 | even | 12 | 637.2.r.g.116.5 | 32 | |||
91.18 | odd | 12 | 637.2.r.g.324.12 | 32 | |||
91.31 | even | 12 | 637.2.r.g.324.11 | 32 | |||
91.34 | even | 4 | 637.2.c.g.246.12 | yes | 16 | ||
91.44 | odd | 12 | 637.2.r.g.116.6 | 32 | |||
91.47 | even | 12 | 637.2.r.g.116.11 | 32 | |||
91.60 | odd | 12 | 637.2.r.g.324.6 | 32 | |||
91.73 | even | 12 | 637.2.r.g.324.5 | 32 | |||
91.83 | even | 4 | 637.2.c.g.246.6 | yes | 16 | ||
91.86 | odd | 12 | 637.2.r.g.116.12 | 32 | |||
91.90 | odd | 2 | inner | 8281.2.a.cs.1.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.g.246.5 | ✓ | 16 | 13.5 | odd | 4 | ||
637.2.c.g.246.6 | yes | 16 | 91.83 | even | 4 | ||
637.2.c.g.246.11 | yes | 16 | 13.8 | odd | 4 | ||
637.2.c.g.246.12 | yes | 16 | 91.34 | even | 4 | ||
637.2.r.g.116.5 | 32 | 91.5 | even | 12 | |||
637.2.r.g.116.6 | 32 | 91.44 | odd | 12 | |||
637.2.r.g.116.11 | 32 | 91.47 | even | 12 | |||
637.2.r.g.116.12 | 32 | 91.86 | odd | 12 | |||
637.2.r.g.324.5 | 32 | 91.73 | even | 12 | |||
637.2.r.g.324.6 | 32 | 91.60 | odd | 12 | |||
637.2.r.g.324.11 | 32 | 91.31 | even | 12 | |||
637.2.r.g.324.12 | 32 | 91.18 | odd | 12 | |||
8281.2.a.cs.1.5 | 16 | 13.12 | even | 2 | inner | ||
8281.2.a.cs.1.6 | 16 | 91.90 | odd | 2 | inner | ||
8281.2.a.cs.1.11 | 16 | 1.1 | even | 1 | trivial | ||
8281.2.a.cs.1.12 | 16 | 7.6 | odd | 2 | inner |