Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6525,2,Mod(1,6525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6525, 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("6525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6525.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: | \(52.1023873189\) |
Analytic rank: | \(1\) |
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: | \( x^{8} - 2x^{7} - 12x^{6} + 23x^{5} + 36x^{4} - 62x^{3} - 15x^{2} + 14x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2175) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-2.72810\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.72810 | 1.92906 | 0.964528 | − | 0.263981i | \(-0.0850357\pi\) | ||||
0.964528 | + | 0.263981i | \(0.0850357\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.44251 | 2.72126 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.61695 | −1.74504 | −0.872521 | − | 0.488577i | \(-0.837516\pi\) | ||||
−0.872521 | + | 0.488577i | \(0.837516\pi\) | |||||||
\(8\) | 9.39150 | 3.32040 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.87758 | 0.566110 | 0.283055 | − | 0.959104i | \(-0.408652\pi\) | ||||
0.283055 | + | 0.959104i | \(0.408652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.48400 | −1.52099 | −0.760494 | − | 0.649345i | \(-0.775043\pi\) | ||||
−0.760494 | + | 0.649345i | \(0.775043\pi\) | |||||||
\(14\) | −12.5955 | −3.36628 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.7359 | 3.68398 | ||||||||
\(17\) | −5.74056 | −1.39229 | −0.696145 | − | 0.717901i | \(-0.745103\pi\) | ||||
−0.696145 | + | 0.717901i | \(0.745103\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.40455 | −1.23989 | −0.619944 | − | 0.784646i | \(-0.712845\pi\) | ||||
−0.619944 | + | 0.784646i | \(0.712845\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.12221 | 1.09206 | ||||||||
\(23\) | −0.137016 | −0.0285698 | −0.0142849 | − | 0.999898i | \(-0.504547\pi\) | ||||
−0.0142849 | + | 0.999898i | \(0.504547\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −14.9609 | −2.93407 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −25.1278 | −4.74870 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.18167 | −1.46947 | −0.734736 | − | 0.678353i | \(-0.762694\pi\) | ||||
−0.734736 | + | 0.678353i | \(0.762694\pi\) | |||||||
\(32\) | 21.4180 | 3.78620 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −15.6608 | −2.68581 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.45785 | 0.732866 | 0.366433 | − | 0.930444i | \(-0.380579\pi\) | ||||
0.366433 | + | 0.930444i | \(0.380579\pi\) | |||||||
\(38\) | −14.7441 | −2.39181 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.215243 | 0.0336153 | 0.0168076 | − | 0.999859i | \(-0.494650\pi\) | ||||
0.0168076 | + | 0.999859i | \(0.494650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.17115 | −1.09359 | −0.546795 | − | 0.837266i | \(-0.684152\pi\) | ||||
−0.546795 | + | 0.837266i | \(0.684152\pi\) | |||||||
\(44\) | 10.2187 | 1.54053 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.373793 | −0.0551128 | ||||||||
\(47\) | −9.91293 | −1.44595 | −0.722975 | − | 0.690874i | \(-0.757226\pi\) | ||||
−0.722975 | + | 0.690874i | \(0.757226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.3162 | 2.04517 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −29.8467 | −4.13899 | ||||||||
\(53\) | −1.14754 | −0.157627 | −0.0788134 | − | 0.996889i | \(-0.525113\pi\) | ||||
−0.0788134 | + | 0.996889i | \(0.525113\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −43.3601 | −5.79423 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.72810 | −0.358217 | ||||||||
\(59\) | 0.244913 | 0.0318849 | 0.0159425 | − | 0.999873i | \(-0.494925\pi\) | ||||
0.0159425 | + | 0.999873i | \(0.494925\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.75284 | 1.12069 | 0.560343 | − | 0.828260i | \(-0.310669\pi\) | ||||
0.560343 | + | 0.828260i | \(0.310669\pi\) | |||||||
\(62\) | −22.3204 | −2.83469 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 28.9585 | 3.61981 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.53295 | 0.798127 | 0.399064 | − | 0.916923i | \(-0.369335\pi\) | ||||
0.399064 | + | 0.916923i | \(0.369335\pi\) | |||||||
\(68\) | −31.2431 | −3.78878 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.277412 | 0.0329227 | 0.0164614 | − | 0.999865i | \(-0.494760\pi\) | ||||
0.0164614 | + | 0.999865i | \(0.494760\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.4933 | 1.34519 | 0.672594 | − | 0.740011i | \(-0.265180\pi\) | ||||
0.672594 | + | 0.740011i | \(0.265180\pi\) | |||||||
\(74\) | 12.1614 | 1.41374 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −29.4143 | −3.37405 | ||||||||
\(77\) | −8.66866 | −0.987886 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.66223 | 0.187015 | 0.0935076 | − | 0.995619i | \(-0.470192\pi\) | ||||
0.0935076 | + | 0.995619i | \(0.470192\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.587203 | 0.0648457 | ||||||||
\(83\) | 9.58514 | 1.05211 | 0.526053 | − | 0.850452i | \(-0.323671\pi\) | ||||
0.526053 | + | 0.850452i | \(0.323671\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −19.5636 | −2.10960 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 17.6333 | 1.87971 | ||||||||
\(89\) | −16.3332 | −1.73132 | −0.865659 | − | 0.500634i | \(-0.833100\pi\) | ||||
−0.865659 | + | 0.500634i | \(0.833100\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.3193 | 2.65419 | ||||||||
\(92\) | −0.745712 | −0.0777458 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −27.0434 | −2.78932 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.04128 | −0.816468 | −0.408234 | − | 0.912877i | \(-0.633855\pi\) | ||||
−0.408234 | + | 0.912877i | \(0.633855\pi\) | |||||||
\(98\) | 39.0559 | 3.94525 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3239 | 1.22627 | 0.613135 | − | 0.789978i | \(-0.289908\pi\) | ||||
0.613135 | + | 0.789978i | \(0.289908\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.660912 | 0.0651216 | 0.0325608 | − | 0.999470i | \(-0.489634\pi\) | ||||
0.0325608 | + | 0.999470i | \(0.489634\pi\) | |||||||
\(104\) | −51.5030 | −5.05028 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.13060 | −0.304071 | ||||||||
\(107\) | −14.5868 | −1.41016 | −0.705079 | − | 0.709128i | \(-0.749089\pi\) | ||||
−0.705079 | + | 0.709128i | \(0.749089\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.5050 | 1.48511 | 0.742557 | − | 0.669783i | \(-0.233613\pi\) | ||||
0.742557 | + | 0.669783i | \(0.233613\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −68.0349 | −6.42869 | ||||||||
\(113\) | −7.80660 | −0.734383 | −0.367191 | − | 0.930145i | \(-0.619681\pi\) | ||||
−0.367191 | + | 0.930145i | \(0.619681\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.44251 | −0.505325 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.668145 | 0.0615078 | ||||||||
\(119\) | 26.5038 | 2.42960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.47471 | −0.679519 | ||||||||
\(122\) | 23.8786 | 2.16187 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −44.5289 | −3.99881 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.7106 | −1.74903 | −0.874515 | − | 0.484999i | \(-0.838820\pi\) | ||||
−0.874515 | + | 0.484999i | \(0.838820\pi\) | |||||||
\(128\) | 36.1656 | 3.19662 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.05738 | 0.0923834 | 0.0461917 | − | 0.998933i | \(-0.485291\pi\) | ||||
0.0461917 | + | 0.998933i | \(0.485291\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.9525 | 2.16366 | ||||||||
\(134\) | 17.8225 | 1.53963 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −53.9125 | −4.62296 | ||||||||
\(137\) | 3.21467 | 0.274648 | 0.137324 | − | 0.990526i | \(-0.456150\pi\) | ||||
0.137324 | + | 0.990526i | \(0.456150\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.48410 | 0.719612 | 0.359806 | − | 0.933027i | \(-0.382843\pi\) | ||||
0.359806 | + | 0.933027i | \(0.382843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.756807 | 0.0635098 | ||||||||
\(143\) | −10.2966 | −0.861046 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 31.3548 | 2.59494 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 24.2619 | 1.99432 | ||||||||
\(149\) | 5.93205 | 0.485972 | 0.242986 | − | 0.970030i | \(-0.421873\pi\) | ||||
0.242986 | + | 0.970030i | \(0.421873\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.06281 | 0.656142 | 0.328071 | − | 0.944653i | \(-0.393601\pi\) | ||||
0.328071 | + | 0.944653i | \(0.393601\pi\) | |||||||
\(152\) | −50.7568 | −4.11692 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −23.6490 | −1.90569 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.87127 | 0.787813 | 0.393906 | − | 0.919151i | \(-0.371123\pi\) | ||||
0.393906 | + | 0.919151i | \(0.371123\pi\) | |||||||
\(158\) | 4.53472 | 0.360763 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.632596 | 0.0498555 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.25711 | −0.0984643 | −0.0492321 | − | 0.998787i | \(-0.515677\pi\) | ||||
−0.0492321 | + | 0.998787i | \(0.515677\pi\) | |||||||
\(164\) | 1.17146 | 0.0914757 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 26.1492 | 2.02957 | ||||||||
\(167\) | −15.1462 | −1.17205 | −0.586024 | − | 0.810294i | \(-0.699308\pi\) | ||||
−0.586024 | + | 0.810294i | \(0.699308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.0742 | 1.31340 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −39.0291 | −2.97594 | ||||||||
\(173\) | 2.34929 | 0.178613 | 0.0893065 | − | 0.996004i | \(-0.471535\pi\) | ||||
0.0893065 | + | 0.996004i | \(0.471535\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 27.6678 | 2.08554 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −44.5586 | −3.33981 | ||||||||
\(179\) | 17.7814 | 1.32904 | 0.664520 | − | 0.747270i | \(-0.268636\pi\) | ||||
0.664520 | + | 0.747270i | \(0.268636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.69871 | −0.200594 | −0.100297 | − | 0.994958i | \(-0.531979\pi\) | ||||
−0.100297 | + | 0.994958i | \(0.531979\pi\) | |||||||
\(182\) | 69.0735 | 5.12007 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.28679 | −0.0948632 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.7783 | −0.788190 | ||||||||
\(188\) | −53.9512 | −3.93480 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.7997 | −0.781442 | −0.390721 | − | 0.920509i | \(-0.627774\pi\) | ||||
−0.390721 | + | 0.920509i | \(0.627774\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.18447 | 0.301205 | 0.150602 | − | 0.988594i | \(-0.451879\pi\) | ||||
0.150602 | + | 0.988594i | \(0.451879\pi\) | |||||||
\(194\) | −21.9374 | −1.57501 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 77.9160 | 5.56543 | ||||||||
\(197\) | 5.76856 | 0.410993 | 0.205496 | − | 0.978658i | \(-0.434119\pi\) | ||||
0.205496 | + | 0.978658i | \(0.434119\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.45094 | −0.386407 | −0.193203 | − | 0.981159i | \(-0.561888\pi\) | ||||
−0.193203 | + | 0.981159i | \(0.561888\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 33.6207 | 2.36554 | ||||||||
\(203\) | 4.61695 | 0.324046 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.80303 | 0.125623 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −80.8117 | −5.60328 | ||||||||
\(209\) | −10.1474 | −0.701914 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.863332 | 0.0594342 | 0.0297171 | − | 0.999558i | \(-0.490539\pi\) | ||||
0.0297171 | + | 0.999558i | \(0.490539\pi\) | |||||||
\(212\) | −6.24550 | −0.428943 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −39.7942 | −2.72027 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 37.7743 | 2.56429 | ||||||||
\(218\) | 42.2993 | 2.86487 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.4812 | 2.11766 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.615197 | 0.0411967 | 0.0205983 | − | 0.999788i | \(-0.493443\pi\) | ||||
0.0205983 | + | 0.999788i | \(0.493443\pi\) | |||||||
\(224\) | −98.8856 | −6.60707 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.2972 | −1.41667 | ||||||||
\(227\) | −23.7230 | −1.57455 | −0.787275 | − | 0.616602i | \(-0.788509\pi\) | ||||
−0.787275 | + | 0.616602i | \(0.788509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.9808 | −1.38645 | −0.693226 | − | 0.720721i | \(-0.743811\pi\) | ||||
−0.693226 | + | 0.720721i | \(0.743811\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.39150 | −0.616582 | ||||||||
\(233\) | −7.95482 | −0.521138 | −0.260569 | − | 0.965455i | \(-0.583910\pi\) | ||||
−0.260569 | + | 0.965455i | \(0.583910\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.33294 | 0.0867670 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 72.3051 | 4.68684 | ||||||||
\(239\) | −17.4888 | −1.13125 | −0.565627 | − | 0.824661i | \(-0.691366\pi\) | ||||
−0.565627 | + | 0.824661i | \(0.691366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.7743 | −0.951699 | −0.475849 | − | 0.879527i | \(-0.657859\pi\) | ||||
−0.475849 | + | 0.879527i | \(0.657859\pi\) | |||||||
\(242\) | −20.3917 | −1.31083 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 47.6375 | 3.04968 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.6385 | 1.88585 | ||||||||
\(248\) | −76.8382 | −4.87923 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.30996 | 0.208923 | 0.104461 | − | 0.994529i | \(-0.466688\pi\) | ||||
0.104461 | + | 0.994529i | \(0.466688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.257258 | −0.0161737 | ||||||||
\(254\) | −53.7723 | −3.37398 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 40.7463 | 2.54664 | ||||||||
\(257\) | −30.8668 | −1.92542 | −0.962709 | − | 0.270539i | \(-0.912798\pi\) | ||||
−0.962709 | + | 0.270539i | \(0.912798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.5816 | −1.27888 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.88463 | 0.178213 | ||||||||
\(263\) | 19.4833 | 1.20139 | 0.600697 | − | 0.799477i | \(-0.294890\pi\) | ||||
0.600697 | + | 0.799477i | \(0.294890\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 68.0728 | 4.17381 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 35.5557 | 2.17191 | ||||||||
\(269\) | −20.8385 | −1.27055 | −0.635273 | − | 0.772287i | \(-0.719113\pi\) | ||||
−0.635273 | + | 0.772287i | \(0.719113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.5849 | 1.49343 | 0.746713 | − | 0.665146i | \(-0.231631\pi\) | ||||
0.746713 | + | 0.665146i | \(0.231631\pi\) | |||||||
\(272\) | −84.5924 | −5.12916 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.76994 | 0.529811 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.89904 | −0.114102 | −0.0570510 | − | 0.998371i | \(-0.518170\pi\) | ||||
−0.0570510 | + | 0.998371i | \(0.518170\pi\) | |||||||
\(278\) | 23.1455 | 1.38817 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.4916 | −1.93828 | −0.969142 | − | 0.246503i | \(-0.920719\pi\) | ||||
−0.969142 | + | 0.246503i | \(0.920719\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.9151 | 0.708279 | 0.354140 | − | 0.935193i | \(-0.384774\pi\) | ||||
0.354140 | + | 0.935193i | \(0.384774\pi\) | |||||||
\(284\) | 1.50982 | 0.0895912 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −28.0902 | −1.66101 | ||||||||
\(287\) | −0.993764 | −0.0586600 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.9540 | 0.938472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 62.5524 | 3.66060 | ||||||||
\(293\) | 20.7359 | 1.21140 | 0.605702 | − | 0.795692i | \(-0.292892\pi\) | ||||
0.605702 | + | 0.795692i | \(0.292892\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 41.8659 | 2.43341 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.1832 | 0.937467 | ||||||||
\(299\) | 0.751396 | 0.0434544 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.1088 | 1.90836 | ||||||||
\(302\) | 21.9961 | 1.26574 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −79.6409 | −4.56772 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.9755 | 0.968842 | 0.484421 | − | 0.874835i | \(-0.339030\pi\) | ||||
0.484421 | + | 0.874835i | \(0.339030\pi\) | |||||||
\(308\) | −47.1793 | −2.68829 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.9019 | 1.18524 | 0.592619 | − | 0.805483i | \(-0.298094\pi\) | ||||
0.592619 | + | 0.805483i | \(0.298094\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7754 | −0.722110 | −0.361055 | − | 0.932545i | \(-0.617583\pi\) | ||||
−0.361055 | + | 0.932545i | \(0.617583\pi\) | |||||||
\(314\) | 26.9298 | 1.51973 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.04669 | 0.508916 | ||||||||
\(317\) | 15.0552 | 0.845582 | 0.422791 | − | 0.906227i | \(-0.361050\pi\) | ||||
0.422791 | + | 0.906227i | \(0.361050\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.87758 | −0.105124 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.72578 | 0.0961741 | ||||||||
\(323\) | 31.0251 | 1.72628 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.42951 | −0.189943 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.02145 | 0.111616 | ||||||||
\(329\) | 45.7675 | 2.52324 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.7325 | −0.974668 | −0.487334 | − | 0.873216i | \(-0.662031\pi\) | ||||
−0.487334 | + | 0.873216i | \(0.662031\pi\) | |||||||
\(332\) | 52.1672 | 2.86305 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −41.3203 | −2.26095 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.5905 | 0.958217 | 0.479108 | − | 0.877756i | \(-0.340960\pi\) | ||||
0.479108 | + | 0.877756i | \(0.340960\pi\) | |||||||
\(338\) | 46.5801 | 2.53363 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.3617 | −0.831883 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −33.7784 | −1.82386 | ||||||||
\(344\) | −67.3479 | −3.63115 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.40909 | 0.344555 | ||||||||
\(347\) | −21.0789 | −1.13157 | −0.565787 | − | 0.824552i | \(-0.691427\pi\) | ||||
−0.565787 | + | 0.824552i | \(0.691427\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.723154 | −0.0387096 | −0.0193548 | − | 0.999813i | \(-0.506161\pi\) | ||||
−0.0193548 | + | 0.999813i | \(0.506161\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 40.2139 | 2.14341 | ||||||||
\(353\) | 5.93891 | 0.316096 | 0.158048 | − | 0.987431i | \(-0.449480\pi\) | ||||
0.158048 | + | 0.987431i | \(0.449480\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −88.8938 | −4.71136 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 48.5092 | 2.56379 | ||||||||
\(359\) | 2.30973 | 0.121903 | 0.0609514 | − | 0.998141i | \(-0.480587\pi\) | ||||
0.0609514 | + | 0.998141i | \(0.480587\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.2091 | 0.537323 | ||||||||
\(362\) | −7.36234 | −0.386956 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 137.801 | 7.22272 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.9235 | −1.19660 | −0.598298 | − | 0.801274i | \(-0.704156\pi\) | ||||
−0.598298 | + | 0.801274i | \(0.704156\pi\) | |||||||
\(368\) | −2.01906 | −0.105251 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.29813 | 0.275065 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.83182 | 0.146626 | 0.0733129 | − | 0.997309i | \(-0.476643\pi\) | ||||
0.0733129 | + | 0.997309i | \(0.476643\pi\) | |||||||
\(374\) | −29.4043 | −1.52046 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −93.0973 | −4.80113 | ||||||||
\(377\) | 5.48400 | 0.282440 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.2539 | −1.50267 | −0.751335 | − | 0.659921i | \(-0.770590\pi\) | ||||
−0.751335 | + | 0.659921i | \(0.770590\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −29.4627 | −1.50744 | ||||||||
\(383\) | −2.99063 | −0.152814 | −0.0764070 | − | 0.997077i | \(-0.524345\pi\) | ||||
−0.0764070 | + | 0.997077i | \(0.524345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.4156 | 0.581040 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −43.7648 | −2.22182 | ||||||||
\(389\) | 8.57339 | 0.434688 | 0.217344 | − | 0.976095i | \(-0.430261\pi\) | ||||
0.217344 | + | 0.976095i | \(0.430261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.786549 | 0.0397775 | ||||||||
\(392\) | 134.451 | 6.79078 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.7372 | 0.792828 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.29605 | −0.466556 | −0.233278 | − | 0.972410i | \(-0.574945\pi\) | ||||
−0.233278 | + | 0.972410i | \(0.574945\pi\) | |||||||
\(398\) | −14.8707 | −0.745400 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.5392 | −0.975739 | −0.487870 | − | 0.872916i | \(-0.662226\pi\) | ||||
−0.487870 | + | 0.872916i | \(0.662226\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 44.8683 | 2.23505 | ||||||||
\(404\) | 67.0728 | 3.33700 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.5955 | 0.625103 | ||||||||
\(407\) | 8.36995 | 0.414883 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.9582 | 1.87691 | 0.938456 | − | 0.345398i | \(-0.112256\pi\) | ||||
0.938456 | + | 0.345398i | \(0.112256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.59702 | 0.177213 | ||||||||
\(413\) | −1.13075 | −0.0556405 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −117.456 | −5.75876 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −27.6832 | −1.35403 | ||||||||
\(419\) | 10.0952 | 0.493184 | 0.246592 | − | 0.969119i | \(-0.420689\pi\) | ||||
0.246592 | + | 0.969119i | \(0.420689\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8521 | 0.675111 | 0.337556 | − | 0.941306i | \(-0.390400\pi\) | ||||
0.337556 | + | 0.941306i | \(0.390400\pi\) | |||||||
\(422\) | 2.35525 | 0.114652 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.7771 | −0.523384 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.4114 | −1.95565 | ||||||||
\(428\) | −79.3888 | −3.83740 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.2149 | −0.877380 | −0.438690 | − | 0.898638i | \(-0.644557\pi\) | ||||
−0.438690 | + | 0.898638i | \(0.644557\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.73476 | −0.323652 | −0.161826 | − | 0.986819i | \(-0.551738\pi\) | ||||
−0.161826 | + | 0.986819i | \(0.551738\pi\) | |||||||
\(434\) | 103.052 | 4.94666 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 84.3864 | 4.04137 | ||||||||
\(437\) | 0.740510 | 0.0354234 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.9590 | 1.47759 | 0.738795 | − | 0.673930i | \(-0.235395\pi\) | ||||
0.738795 | + | 0.673930i | \(0.235395\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 85.8838 | 4.08508 | ||||||||
\(443\) | 21.4432 | 1.01880 | 0.509398 | − | 0.860531i | \(-0.329868\pi\) | ||||
0.509398 | + | 0.860531i | \(0.329868\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.67832 | 0.0794707 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −133.700 | −6.31672 | ||||||||
\(449\) | −25.6895 | −1.21236 | −0.606180 | − | 0.795327i | \(-0.707299\pi\) | ||||
−0.606180 | + | 0.795327i | \(0.707299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.404134 | 0.0190299 | ||||||||
\(452\) | −42.4875 | −1.99844 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −64.7186 | −3.03739 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.3278 | −1.41868 | −0.709338 | − | 0.704868i | \(-0.751006\pi\) | ||||
−0.709338 | + | 0.704868i | \(0.751006\pi\) | |||||||
\(458\) | −57.2377 | −2.67454 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.0026 | 1.44393 | 0.721967 | − | 0.691928i | \(-0.243238\pi\) | ||||
0.721967 | + | 0.691928i | \(0.243238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.6990 | 1.28728 | 0.643640 | − | 0.765328i | \(-0.277423\pi\) | ||||
0.643640 | + | 0.765328i | \(0.277423\pi\) | |||||||
\(464\) | −14.7359 | −0.684097 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.7015 | −1.00530 | ||||||||
\(467\) | −4.03243 | −0.186598 | −0.0932992 | − | 0.995638i | \(-0.529741\pi\) | ||||
−0.0932992 | + | 0.995638i | \(0.529741\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.1623 | −1.39277 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.30010 | 0.105871 | ||||||||
\(473\) | −13.4644 | −0.619093 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 144.248 | 6.61157 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −47.7110 | −2.18225 | ||||||||
\(479\) | −1.32186 | −0.0603973 | −0.0301986 | − | 0.999544i | \(-0.509614\pi\) | ||||
−0.0301986 | + | 0.999544i | \(0.509614\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.4468 | −1.11468 | ||||||||
\(482\) | −40.3058 | −1.83588 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −40.6812 | −1.84915 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.89390 | 0.448335 | 0.224168 | − | 0.974551i | \(-0.428034\pi\) | ||||
0.224168 | + | 0.974551i | \(0.428034\pi\) | |||||||
\(488\) | 82.2024 | 3.72113 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.1305 | −0.773089 | −0.386545 | − | 0.922271i | \(-0.626331\pi\) | ||||
−0.386545 | + | 0.922271i | \(0.626331\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.74056 | 0.258542 | ||||||||
\(494\) | 80.8568 | 3.63792 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −120.564 | −5.41350 | ||||||||
\(497\) | −1.28080 | −0.0574516 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.95477 | −0.356104 | −0.178052 | − | 0.984021i | \(-0.556980\pi\) | ||||
−0.178052 | + | 0.984021i | \(0.556980\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.02989 | 0.403024 | ||||||||
\(503\) | 13.3471 | 0.595119 | 0.297559 | − | 0.954703i | \(-0.403827\pi\) | ||||
0.297559 | + | 0.954703i | \(0.403827\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.701825 | −0.0311999 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −107.275 | −4.75956 | ||||||||
\(509\) | 5.55324 | 0.246143 | 0.123071 | − | 0.992398i | \(-0.460726\pi\) | ||||
0.123071 | + | 0.992398i | \(0.460726\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −53.0639 | −2.34741 | ||||||||
\(512\) | 38.8286 | 1.71600 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −84.2076 | −3.71424 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.6123 | −0.818567 | ||||||||
\(518\) | −56.1487 | −2.46703 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.5095 | −1.81857 | −0.909283 | − | 0.416179i | \(-0.863369\pi\) | ||||
−0.909283 | + | 0.416179i | \(0.863369\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.6261 | 0.508375 | 0.254188 | − | 0.967155i | \(-0.418192\pi\) | ||||
0.254188 | + | 0.967155i | \(0.418192\pi\) | |||||||
\(524\) | 5.75479 | 0.251399 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 53.1525 | 2.31756 | ||||||||
\(527\) | 46.9674 | 2.04593 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9812 | −0.999184 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 135.804 | 5.88786 | ||||||||
\(533\) | −1.18039 | −0.0511284 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 61.3543 | 2.65010 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −56.8495 | −2.45096 | ||||||||
\(539\) | 26.8797 | 1.15779 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.29830 | −0.227792 | −0.113896 | − | 0.993493i | \(-0.536333\pi\) | ||||
−0.113896 | + | 0.993493i | \(0.536333\pi\) | |||||||
\(542\) | 67.0700 | 2.88090 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −122.951 | −5.27149 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.78093 | 0.289932 | 0.144966 | − | 0.989437i | \(-0.453693\pi\) | ||||
0.144966 | + | 0.989437i | \(0.453693\pi\) | |||||||
\(548\) | 17.4959 | 0.747387 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.40455 | 0.230241 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.67441 | −0.326349 | ||||||||
\(554\) | −5.18076 | −0.220109 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 46.1748 | 1.95825 | ||||||||
\(557\) | 0.186307 | 0.00789410 | 0.00394705 | − | 0.999992i | \(-0.498744\pi\) | ||||
0.00394705 | + | 0.999992i | \(0.498744\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.3266 | 1.66334 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −88.6401 | −3.73906 | ||||||||
\(563\) | −27.1382 | −1.14374 | −0.571869 | − | 0.820345i | \(-0.693781\pi\) | ||||
−0.571869 | + | 0.820345i | \(0.693781\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 32.5056 | 1.36631 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.60532 | 0.109317 | ||||||||
\(569\) | −22.8795 | −0.959157 | −0.479578 | − | 0.877499i | \(-0.659210\pi\) | ||||
−0.479578 | + | 0.877499i | \(0.659210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.3621 | 1.60541 | 0.802703 | − | 0.596379i | \(-0.203394\pi\) | ||||
0.802703 | + | 0.596379i | \(0.203394\pi\) | |||||||
\(572\) | −56.0395 | −2.34313 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.71108 | −0.113158 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.0497 | 0.501637 | 0.250818 | − | 0.968034i | \(-0.419300\pi\) | ||||
0.250818 | + | 0.968034i | \(0.419300\pi\) | |||||||
\(578\) | 43.5241 | 1.81036 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −44.2541 | −1.83597 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.15459 | −0.0892341 | ||||||||
\(584\) | 107.939 | 4.46656 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 56.5695 | 2.33687 | ||||||||
\(587\) | −23.6704 | −0.976982 | −0.488491 | − | 0.872569i | \(-0.662453\pi\) | ||||
−0.488491 | + | 0.872569i | \(0.662453\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.2183 | 1.82198 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 65.6905 | 2.69986 | ||||||||
\(593\) | 25.9414 | 1.06529 | 0.532643 | − | 0.846340i | \(-0.321199\pi\) | ||||
0.532643 | + | 0.846340i | \(0.321199\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 32.2852 | 1.32245 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.04988 | 0.0838259 | ||||||||
\(599\) | 17.2886 | 0.706393 | 0.353196 | − | 0.935549i | \(-0.385095\pi\) | ||||
0.353196 | + | 0.935549i | \(0.385095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.8997 | −1.26042 | −0.630212 | − | 0.776423i | \(-0.717032\pi\) | ||||
−0.630212 | + | 0.776423i | \(0.717032\pi\) | |||||||
\(602\) | 90.3240 | 3.68133 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 43.8820 | 1.78553 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.07152 | −0.165258 | −0.0826290 | − | 0.996580i | \(-0.526332\pi\) | ||||
−0.0826290 | + | 0.996580i | \(0.526332\pi\) | |||||||
\(608\) | −115.754 | −4.69446 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 54.3625 | 2.19927 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.3595 | −1.30699 | −0.653494 | − | 0.756931i | \(-0.726698\pi\) | ||||
−0.653494 | + | 0.756931i | \(0.726698\pi\) | |||||||
\(614\) | 46.3108 | 1.86895 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −81.4118 | −3.28017 | ||||||||
\(617\) | −33.4957 | −1.34849 | −0.674243 | − | 0.738509i | \(-0.735530\pi\) | ||||
−0.674243 | + | 0.738509i | \(0.735530\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.6857 | −0.670656 | −0.335328 | − | 0.942101i | \(-0.608847\pi\) | ||||
−0.335328 | + | 0.942101i | \(0.608847\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 57.0224 | 2.28639 | ||||||||
\(623\) | 75.4096 | 3.02122 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −34.8526 | −1.39299 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 53.7245 | 2.14384 | ||||||||
\(629\) | −25.5905 | −1.02036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.91590 | 0.394746 | 0.197373 | − | 0.980328i | \(-0.436759\pi\) | ||||
0.197373 | + | 0.980328i | \(0.436759\pi\) | |||||||
\(632\) | 15.6108 | 0.620965 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 41.0719 | 1.63118 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −78.5099 | −3.11068 | ||||||||
\(638\) | −5.12221 | −0.202790 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.9862 | 0.907902 | 0.453951 | − | 0.891027i | \(-0.350014\pi\) | ||||
0.453951 | + | 0.891027i | \(0.350014\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.9117 | 0.509190 | 0.254595 | − | 0.967048i | \(-0.418058\pi\) | ||||
0.254595 | + | 0.967048i | \(0.418058\pi\) | |||||||
\(644\) | 3.44291 | 0.135670 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 84.6395 | 3.33010 | ||||||||
\(647\) | 16.6096 | 0.652989 | 0.326494 | − | 0.945199i | \(-0.394133\pi\) | ||||
0.326494 | + | 0.945199i | \(0.394133\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.459842 | 0.0180504 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.84182 | −0.267947 | ||||||||
\(653\) | −21.5638 | −0.843858 | −0.421929 | − | 0.906629i | \(-0.638647\pi\) | ||||
−0.421929 | + | 0.906629i | \(0.638647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.17180 | 0.123838 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 124.858 | 4.86747 | ||||||||
\(659\) | −31.7863 | −1.23822 | −0.619110 | − | 0.785305i | \(-0.712506\pi\) | ||||
−0.619110 | + | 0.785305i | \(0.712506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.0046 | 1.16704 | 0.583521 | − | 0.812098i | \(-0.301674\pi\) | ||||
0.583521 | + | 0.812098i | \(0.301674\pi\) | |||||||
\(662\) | −48.3760 | −1.88019 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 90.0189 | 3.49341 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.137016 | 0.00530529 | ||||||||
\(668\) | −82.4334 | −3.18944 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.4341 | 0.634432 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.0842 | 1.35240 | 0.676199 | − | 0.736719i | \(-0.263626\pi\) | ||||
0.676199 | + | 0.736719i | \(0.263626\pi\) | |||||||
\(674\) | 47.9886 | 1.84845 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 92.9267 | 3.57410 | ||||||||
\(677\) | 42.1433 | 1.61970 | 0.809849 | − | 0.586638i | \(-0.199549\pi\) | ||||
0.809849 | + | 0.586638i | \(0.199549\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.1261 | 1.42477 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −41.9082 | −1.60475 | ||||||||
\(683\) | −31.8895 | −1.22022 | −0.610109 | − | 0.792318i | \(-0.708874\pi\) | ||||
−0.610109 | + | 0.792318i | \(0.708874\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −92.1508 | −3.51833 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −105.673 | −4.02876 | ||||||||
\(689\) | 6.29311 | 0.239748 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.2963 | 0.429732 | 0.214866 | − | 0.976644i | \(-0.431069\pi\) | ||||
0.214866 | + | 0.976644i | \(0.431069\pi\) | |||||||
\(692\) | 12.7860 | 0.486052 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −57.5052 | −2.18287 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.23561 | −0.0468022 | ||||||||
\(698\) | −1.97283 | −0.0746729 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.39354 | 0.0526332 | 0.0263166 | − | 0.999654i | \(-0.491622\pi\) | ||||
0.0263166 | + | 0.999654i | \(0.491622\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.0927 | −0.908672 | ||||||||
\(704\) | 54.3717 | 2.04921 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.2019 | 0.609767 | ||||||||
\(707\) | −56.8986 | −2.13989 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.24967 | 0.197156 | 0.0985778 | − | 0.995129i | \(-0.468571\pi\) | ||||
0.0985778 | + | 0.995129i | \(0.468571\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −153.394 | −5.74867 | ||||||||
\(713\) | 1.12102 | 0.0419826 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 96.7752 | 3.61666 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.30116 | 0.235157 | ||||||||
\(719\) | −46.4801 | −1.73341 | −0.866707 | − | 0.498817i | \(-0.833768\pi\) | ||||
−0.866707 | + | 0.498817i | \(0.833768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.05140 | −0.113640 | ||||||||
\(722\) | 27.8515 | 1.03653 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.6878 | −0.545866 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.3101 | −1.60628 | −0.803141 | − | 0.595790i | \(-0.796839\pi\) | ||||
−0.803141 | + | 0.595790i | \(0.796839\pi\) | |||||||
\(728\) | 237.786 | 8.81295 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.1664 | 1.52259 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.6793 | −0.689936 | −0.344968 | − | 0.938614i | \(-0.612110\pi\) | ||||
−0.344968 | + | 0.938614i | \(0.612110\pi\) | |||||||
\(734\) | −62.5375 | −2.30830 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.93461 | −0.108171 | ||||||||
\(737\) | 12.2661 | 0.451828 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.3256 | 1.52019 | 0.760093 | − | 0.649815i | \(-0.225153\pi\) | ||||
0.760093 | + | 0.649815i | \(0.225153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.4538 | 0.530616 | ||||||||
\(743\) | 32.3390 | 1.18640 | 0.593202 | − | 0.805054i | \(-0.297864\pi\) | ||||
0.593202 | + | 0.805054i | \(0.297864\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.72547 | 0.282849 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −58.6612 | −2.14487 | ||||||||
\(749\) | 67.3464 | 2.46078 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.34454 | −0.340987 | −0.170494 | − | 0.985359i | \(-0.554536\pi\) | ||||
−0.170494 | + | 0.985359i | \(0.554536\pi\) | |||||||
\(752\) | −146.076 | −5.32685 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.9609 | 0.544843 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.01932 | −0.182430 | −0.0912151 | − | 0.995831i | \(-0.529075\pi\) | ||||
−0.0912151 | + | 0.995831i | \(0.529075\pi\) | |||||||
\(758\) | −79.8074 | −2.89873 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.9103 | 1.26550 | 0.632748 | − | 0.774358i | \(-0.281927\pi\) | ||||
0.632748 | + | 0.774358i | \(0.281927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −71.5859 | −2.59159 | ||||||||
\(764\) | −58.7777 | −2.12650 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.15872 | −0.294787 | ||||||||
\(767\) | −1.34310 | −0.0484965 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.4889 | 1.35189 | 0.675943 | − | 0.736954i | \(-0.263737\pi\) | ||||
0.675943 | + | 0.736954i | \(0.263737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.7740 | 0.819655 | ||||||||
\(773\) | 33.7332 | 1.21330 | 0.606649 | − | 0.794970i | \(-0.292513\pi\) | ||||
0.606649 | + | 0.794970i | \(0.292513\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −75.5197 | −2.71100 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.3890 | 0.838538 | ||||||||
\(779\) | −1.16329 | −0.0416792 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.520862 | 0.0186379 | ||||||||
\(782\) | 2.14578 | 0.0767330 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 210.962 | 7.53436 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.5508 | 0.411740 | 0.205870 | − | 0.978579i | \(-0.433998\pi\) | ||||
0.205870 | + | 0.978579i | \(0.433998\pi\) | |||||||
\(788\) | 31.3955 | 1.11842 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.0426 | 1.28153 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.0006 | −1.70455 | ||||||||
\(794\) | −25.3605 | −0.900012 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29.6668 | −1.05151 | ||||||||
\(797\) | −9.11795 | −0.322974 | −0.161487 | − | 0.986875i | \(-0.551629\pi\) | ||||
−0.161487 | + | 0.986875i | \(0.551629\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 56.9058 | 2.01318 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −53.3047 | −1.88226 | ||||||||
\(803\) | 21.5795 | 0.761525 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 122.405 | 4.31153 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 115.740 | 4.07171 | ||||||||
\(809\) | 11.9809 | 0.421227 | 0.210613 | − | 0.977569i | \(-0.432454\pi\) | ||||
0.210613 | + | 0.977569i | \(0.432454\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.2172 | −0.674807 | −0.337403 | − | 0.941360i | \(-0.609549\pi\) | ||||
−0.337403 | + | 0.941360i | \(0.609549\pi\) | |||||||
\(812\) | 25.1278 | 0.881812 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.8340 | 0.800332 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.7568 | 1.35593 | ||||||||
\(818\) | 103.554 | 3.62067 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.5611 | 0.368585 | 0.184292 | − | 0.982871i | \(-0.441001\pi\) | ||||
0.184292 | + | 0.982871i | \(0.441001\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.1655 | −1.01665 | −0.508323 | − | 0.861166i | \(-0.669734\pi\) | ||||
−0.508323 | + | 0.861166i | \(0.669734\pi\) | |||||||
\(824\) | 6.20696 | 0.216230 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.08479 | −0.107334 | ||||||||
\(827\) | −40.5140 | −1.40881 | −0.704405 | − | 0.709798i | \(-0.748786\pi\) | ||||
−0.704405 | + | 0.709798i | \(0.748786\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.3925 | 1.78494 | 0.892468 | − | 0.451111i | \(-0.148972\pi\) | ||||
0.892468 | + | 0.451111i | \(0.148972\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −158.808 | −5.50569 | ||||||||
\(833\) | −82.1829 | −2.84747 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −55.2276 | −1.91009 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.5407 | 0.951379 | ||||||||
\(839\) | 30.2352 | 1.04383 | 0.521917 | − | 0.852996i | \(-0.325217\pi\) | ||||
0.521917 | + | 0.852996i | \(0.325217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 37.7899 | 1.30233 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.69869 | 0.161736 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.5103 | 1.18579 | ||||||||
\(848\) | −16.9100 | −0.580693 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.610797 | −0.0209379 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.163336 | 0.00559252 | 0.00279626 | − | 0.999996i | \(-0.499110\pi\) | ||||
0.00279626 | + | 0.999996i | \(0.499110\pi\) | |||||||
\(854\) | −110.246 | −3.77255 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −136.992 | −4.68229 | ||||||||
\(857\) | 0.869730 | 0.0297094 | 0.0148547 | − | 0.999890i | \(-0.495271\pi\) | ||||
0.0148547 | + | 0.999890i | \(0.495271\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.5362 | −1.72427 | −0.862136 | − | 0.506677i | \(-0.830874\pi\) | ||||
−0.862136 | + | 0.506677i | \(0.830874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −49.6920 | −1.69251 | ||||||||
\(863\) | −43.1139 | −1.46761 | −0.733807 | − | 0.679358i | \(-0.762258\pi\) | ||||
−0.733807 | + | 0.679358i | \(0.762258\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.3731 | −0.624342 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 205.587 | 6.97809 | ||||||||
\(869\) | 3.12096 | 0.105871 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.8267 | −1.21394 | ||||||||
\(872\) | 145.616 | 4.93117 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.02018 | 0.0683337 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.23901 | 0.109374 | 0.0546868 | − | 0.998504i | \(-0.482584\pi\) | ||||
0.0546868 | + | 0.998504i | \(0.482584\pi\) | |||||||
\(878\) | 84.4590 | 2.85035 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.49218 | −0.319800 | −0.159900 | − | 0.987133i | \(-0.551117\pi\) | ||||
−0.159900 | + | 0.987133i | \(0.551117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.4268 | 1.36047 | 0.680235 | − | 0.732994i | \(-0.261878\pi\) | ||||
0.680235 | + | 0.732994i | \(0.261878\pi\) | |||||||
\(884\) | 171.337 | 5.76268 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 58.4991 | 1.96532 | ||||||||
\(887\) | 17.5249 | 0.588430 | 0.294215 | − | 0.955739i | \(-0.404942\pi\) | ||||
0.294215 | + | 0.955739i | \(0.404942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 91.0026 | 3.05213 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.34822 | 0.112107 | ||||||||
\(893\) | 53.5749 | 1.79282 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −166.975 | −5.57823 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −70.0833 | −2.33871 | ||||||||
\(899\) | 8.18167 | 0.272874 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.58752 | 0.219462 | ||||||||
\(902\) | 1.10252 | 0.0367098 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −73.3157 | −2.43844 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.8878 | −1.15843 | −0.579216 | − | 0.815174i | \(-0.696641\pi\) | ||||
−0.579216 | + | 0.815174i | \(0.696641\pi\) | |||||||
\(908\) | −129.113 | −4.28475 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.5212 | −1.44192 | −0.720960 | − | 0.692976i | \(-0.756299\pi\) | ||||
−0.720960 | + | 0.692976i | \(0.756299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.9968 | 0.595608 | ||||||||
\(914\) | −82.7373 | −2.73671 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −114.188 | −3.77289 | ||||||||
\(917\) | −4.88185 | −0.161213 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.2543 | −1.26189 | −0.630946 | − | 0.775827i | \(-0.717333\pi\) | ||||
−0.630946 | + | 0.775827i | \(0.717333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 84.5780 | 2.78543 | ||||||||
\(923\) | −1.52133 | −0.0500751 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 75.5655 | 2.48324 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −21.4180 | −0.703079 | ||||||||
\(929\) | −40.3492 | −1.32381 | −0.661906 | − | 0.749586i | \(-0.730252\pi\) | ||||
−0.661906 | + | 0.749586i | \(0.730252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −77.3725 | −2.53578 | ||||||||
\(932\) | −43.2942 | −1.41815 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.0009 | −0.359959 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.95384 | 0.161835 | 0.0809174 | − | 0.996721i | \(-0.474215\pi\) | ||||
0.0809174 | + | 0.996721i | \(0.474215\pi\) | |||||||
\(938\) | −82.2857 | −2.68672 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.5220 | 1.54917 | 0.774587 | − | 0.632467i | \(-0.217958\pi\) | ||||
0.774587 | + | 0.632467i | \(0.217958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0294917 | −0.000960383 0 | ||||||||
\(944\) | 3.60901 | 0.117463 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.7321 | −1.19426 | ||||||||
\(947\) | −37.1547 | −1.20736 | −0.603682 | − | 0.797225i | \(-0.706300\pi\) | ||||
−0.603682 | + | 0.797225i | \(0.706300\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −63.0292 | −2.04601 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 248.911 | 8.06725 | ||||||||
\(953\) | 44.5351 | 1.44263 | 0.721316 | − | 0.692606i | \(-0.243537\pi\) | ||||
0.721316 | + | 0.692606i | \(0.243537\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −95.1828 | −3.07843 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.60616 | −0.116510 | ||||||||
\(959\) | −14.8420 | −0.479272 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.9398 | 1.15935 | ||||||||
\(962\) | −66.6933 | −2.15028 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −80.4095 | −2.58982 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.7291 | −1.56702 | −0.783511 | − | 0.621379i | \(-0.786573\pi\) | ||||
−0.783511 | + | 0.621379i | \(0.786573\pi\) | |||||||
\(968\) | −70.1988 | −2.25627 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.7448 | 1.66057 | 0.830285 | − | 0.557339i | \(-0.188178\pi\) | ||||
0.830285 | + | 0.557339i | \(0.188178\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39.1706 | −1.25575 | ||||||||
\(974\) | 26.9915 | 0.864864 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 128.981 | 4.12858 | ||||||||
\(977\) | 37.7726 | 1.20845 | 0.604227 | − | 0.796813i | \(-0.293482\pi\) | ||||
0.604227 | + | 0.796813i | \(0.293482\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.6669 | −0.980117 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −46.7337 | −1.49133 | ||||||||
\(983\) | −21.1318 | −0.673999 | −0.336999 | − | 0.941505i | \(-0.609412\pi\) | ||||
−0.336999 | + | 0.941505i | \(0.609412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.6608 | 0.498742 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 161.308 | 5.13189 | ||||||||
\(989\) | 0.982563 | 0.0312437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0241 | 0.350191 | 0.175096 | − | 0.984551i | \(-0.443977\pi\) | ||||
0.175096 | + | 0.984551i | \(0.443977\pi\) | |||||||
\(992\) | −175.235 | −5.56371 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.49414 | −0.110827 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.2785 | −0.895589 | −0.447795 | − | 0.894136i | \(-0.647790\pi\) | ||||
−0.447795 | + | 0.894136i | \(0.647790\pi\) | |||||||
\(998\) | −21.7014 | −0.686945 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6525.2.a.by.1.8 | 8 | ||
3.2 | odd | 2 | 2175.2.a.bd.1.1 | yes | 8 | ||
5.4 | even | 2 | 6525.2.a.bz.1.1 | 8 | |||
15.2 | even | 4 | 2175.2.c.p.349.1 | 16 | |||
15.8 | even | 4 | 2175.2.c.p.349.16 | 16 | |||
15.14 | odd | 2 | 2175.2.a.bc.1.8 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2175.2.a.bc.1.8 | ✓ | 8 | 15.14 | odd | 2 | ||
2175.2.a.bd.1.1 | yes | 8 | 3.2 | odd | 2 | ||
2175.2.c.p.349.1 | 16 | 15.2 | even | 4 | |||
2175.2.c.p.349.16 | 16 | 15.8 | even | 4 | |||
6525.2.a.by.1.8 | 8 | 1.1 | even | 1 | trivial | ||
6525.2.a.bz.1.1 | 8 | 5.4 | even | 2 |