Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 21 x^{18} + 96 x^{17} + 164 x^{16} - 936 x^{15} - 540 x^{14} + 4804 x^{13} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.0888996\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0888996 | 0.0628615 | 0.0314308 | − | 0.999506i | \(-0.489994\pi\) | ||||
0.0314308 | + | 0.999506i | \(0.489994\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99210 | −0.996048 | ||||||||
\(5\) | 0.674348 | 0.301578 | 0.150789 | − | 0.988566i | \(-0.451819\pi\) | ||||
0.150789 | + | 0.988566i | \(0.451819\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.687902 | 0.260002 | 0.130001 | − | 0.991514i | \(-0.458502\pi\) | ||||
0.130001 | + | 0.991514i | \(0.458502\pi\) | |||||||
\(8\) | −0.354896 | −0.125475 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.0599493 | 0.0189576 | ||||||||
\(11\) | 0.536956 | 0.161898 | 0.0809492 | − | 0.996718i | \(-0.474205\pi\) | ||||
0.0809492 | + | 0.996718i | \(0.474205\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.628799 | −0.174397 | −0.0871987 | − | 0.996191i | \(-0.527792\pi\) | ||||
−0.0871987 | + | 0.996191i | \(0.527792\pi\) | |||||||
\(14\) | 0.0611542 | 0.0163441 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.95264 | 0.988161 | ||||||||
\(17\) | −5.05676 | −1.22644 | −0.613222 | − | 0.789911i | \(-0.710127\pi\) | ||||
−0.613222 | + | 0.789911i | \(0.710127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.724853 | −0.166293 | −0.0831463 | − | 0.996537i | \(-0.526497\pi\) | ||||
−0.0831463 | + | 0.996537i | \(0.526497\pi\) | |||||||
\(20\) | −1.34337 | −0.300386 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0477352 | 0.0101772 | ||||||||
\(23\) | 7.36157 | 1.53499 | 0.767496 | − | 0.641053i | \(-0.221502\pi\) | ||||
0.767496 | + | 0.641053i | \(0.221502\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.54525 | −0.909051 | ||||||||
\(26\) | −0.0559000 | −0.0109629 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.37037 | −0.258975 | ||||||||
\(29\) | 3.61524 | 0.671332 | 0.335666 | − | 0.941981i | \(-0.391039\pi\) | ||||
0.335666 | + | 0.941981i | \(0.391039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.74731 | 1.03225 | 0.516124 | − | 0.856514i | \(-0.327374\pi\) | ||||
0.516124 | + | 0.856514i | \(0.327374\pi\) | |||||||
\(32\) | 1.06118 | 0.187592 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.449544 | −0.0770961 | ||||||||
\(35\) | 0.463885 | 0.0784109 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.110957 | −0.0182413 | −0.00912063 | − | 0.999958i | \(-0.502903\pi\) | ||||
−0.00912063 | + | 0.999958i | \(0.502903\pi\) | |||||||
\(38\) | −0.0644391 | −0.0104534 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.239323 | −0.0378403 | ||||||||
\(41\) | −8.05251 | −1.25759 | −0.628796 | − | 0.777571i | \(-0.716452\pi\) | ||||
−0.628796 | + | 0.777571i | \(0.716452\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.2197 | 1.86349 | 0.931746 | − | 0.363111i | \(-0.118285\pi\) | ||||
0.931746 | + | 0.363111i | \(0.118285\pi\) | |||||||
\(44\) | −1.06967 | −0.161259 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.654440 | 0.0964919 | ||||||||
\(47\) | −1.48719 | −0.216929 | −0.108465 | − | 0.994100i | \(-0.534593\pi\) | ||||
−0.108465 | + | 0.994100i | \(0.534593\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.52679 | −0.932399 | ||||||||
\(50\) | −0.404071 | −0.0571443 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.25263 | 0.173708 | ||||||||
\(53\) | 6.92286 | 0.950927 | 0.475464 | − | 0.879735i | \(-0.342280\pi\) | ||||
0.475464 | + | 0.879735i | \(0.342280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.362095 | 0.0488249 | ||||||||
\(56\) | −0.244133 | −0.0326237 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.321393 | 0.0422010 | ||||||||
\(59\) | 9.81893 | 1.27832 | 0.639158 | − | 0.769076i | \(-0.279283\pi\) | ||||
0.639158 | + | 0.769076i | \(0.279283\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.30376 | 0.807113 | 0.403557 | − | 0.914955i | \(-0.367774\pi\) | ||||
0.403557 | + | 0.914955i | \(0.367774\pi\) | |||||||
\(62\) | 0.510934 | 0.0648886 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.81095 | −0.976369 | ||||||||
\(65\) | −0.424030 | −0.0525944 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.02929 | −0.858764 | −0.429382 | − | 0.903123i | \(-0.641269\pi\) | ||||
−0.429382 | + | 0.903123i | \(0.641269\pi\) | |||||||
\(68\) | 10.0736 | 1.22160 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0412392 | 0.00492903 | ||||||||
\(71\) | 9.21843 | 1.09403 | 0.547013 | − | 0.837124i | \(-0.315765\pi\) | ||||
0.547013 | + | 0.837124i | \(0.315765\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1931 | −1.42710 | −0.713548 | − | 0.700606i | \(-0.752913\pi\) | ||||
−0.713548 | + | 0.700606i | \(0.752913\pi\) | |||||||
\(74\) | −0.00986406 | −0.00114667 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.44398 | 0.165636 | ||||||||
\(77\) | 0.369373 | 0.0420940 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.71164 | −0.755118 | −0.377559 | − | 0.925985i | \(-0.623236\pi\) | ||||
−0.377559 | + | 0.925985i | \(0.623236\pi\) | |||||||
\(80\) | 2.66546 | 0.298007 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.715865 | −0.0790541 | ||||||||
\(83\) | 8.10511 | 0.889651 | 0.444825 | − | 0.895617i | \(-0.353266\pi\) | ||||
0.444825 | + | 0.895617i | \(0.353266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.41002 | −0.369868 | ||||||||
\(86\) | 1.08633 | 0.117142 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.190563 | −0.0203141 | ||||||||
\(89\) | 13.1414 | 1.39298 | 0.696492 | − | 0.717564i | \(-0.254743\pi\) | ||||
0.696492 | + | 0.717564i | \(0.254743\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.432552 | −0.0453438 | ||||||||
\(92\) | −14.6650 | −1.52893 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.132211 | −0.0136365 | ||||||||
\(95\) | −0.488803 | −0.0501502 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.31742 | 0.844506 | 0.422253 | − | 0.906478i | \(-0.361239\pi\) | ||||
0.422253 | + | 0.906478i | \(0.361239\pi\) | |||||||
\(98\) | −0.580229 | −0.0586120 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.05459 | 0.905459 | ||||||||
\(101\) | 13.3756 | 1.33092 | 0.665462 | − | 0.746432i | \(-0.268235\pi\) | ||||
0.665462 | + | 0.746432i | \(0.268235\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.09332 | 0.304794 | 0.152397 | − | 0.988319i | \(-0.451301\pi\) | ||||
0.152397 | + | 0.988319i | \(0.451301\pi\) | |||||||
\(104\) | 0.223158 | 0.0218825 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.615439 | 0.0597767 | ||||||||
\(107\) | 11.5001 | 1.11175 | 0.555877 | − | 0.831265i | \(-0.312383\pi\) | ||||
0.555877 | + | 0.831265i | \(0.312383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0986 | 0.967275 | 0.483637 | − | 0.875268i | \(-0.339315\pi\) | ||||
0.483637 | + | 0.875268i | \(0.339315\pi\) | |||||||
\(110\) | 0.0321901 | 0.00306921 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.71903 | 0.256924 | ||||||||
\(113\) | 20.8956 | 1.96570 | 0.982848 | − | 0.184415i | \(-0.0590392\pi\) | ||||
0.982848 | + | 0.184415i | \(0.0590392\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.96426 | 0.462920 | ||||||||
\(116\) | −7.20190 | −0.668679 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.872898 | 0.0803568 | ||||||||
\(119\) | −3.47855 | −0.318878 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7117 | −0.973789 | ||||||||
\(122\) | 0.560401 | 0.0507364 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.4492 | −1.02817 | ||||||||
\(125\) | −6.43683 | −0.575727 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.25364 | 0.466185 | 0.233092 | − | 0.972455i | \(-0.425116\pi\) | ||||
0.233092 | + | 0.972455i | \(0.425116\pi\) | |||||||
\(128\) | −2.81675 | −0.248968 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0376961 | −0.00330616 | ||||||||
\(131\) | 7.68069 | 0.671065 | 0.335532 | − | 0.942029i | \(-0.391084\pi\) | ||||
0.335532 | + | 0.942029i | \(0.391084\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.498628 | −0.0432365 | ||||||||
\(134\) | −0.624901 | −0.0539832 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.79462 | 0.153888 | ||||||||
\(137\) | −11.5008 | −0.982578 | −0.491289 | − | 0.870996i | \(-0.663474\pi\) | ||||
−0.491289 | + | 0.870996i | \(0.663474\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.1077 | 1.45106 | 0.725529 | − | 0.688192i | \(-0.241595\pi\) | ||||
0.725529 | + | 0.688192i | \(0.241595\pi\) | |||||||
\(140\) | −0.924105 | −0.0781011 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.819514 | 0.0687721 | ||||||||
\(143\) | −0.337638 | −0.0282347 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.43793 | 0.202459 | ||||||||
\(146\) | −1.08396 | −0.0897094 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.221038 | 0.0181692 | ||||||||
\(149\) | 23.5946 | 1.93294 | 0.966470 | − | 0.256778i | \(-0.0826609\pi\) | ||||
0.966470 | + | 0.256778i | \(0.0826609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.3698 | −0.925263 | −0.462631 | − | 0.886551i | \(-0.653095\pi\) | ||||
−0.462631 | + | 0.886551i | \(0.653095\pi\) | |||||||
\(152\) | 0.257247 | 0.0208655 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0328371 | 0.00264609 | ||||||||
\(155\) | 3.87569 | 0.311303 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.914383 | −0.0729757 | −0.0364878 | − | 0.999334i | \(-0.511617\pi\) | ||||
−0.0364878 | + | 0.999334i | \(0.511617\pi\) | |||||||
\(158\) | −0.596662 | −0.0474679 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.715605 | 0.0565735 | ||||||||
\(161\) | 5.06403 | 0.399102 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.90233 | −0.775610 | −0.387805 | − | 0.921741i | \(-0.626767\pi\) | ||||
−0.387805 | + | 0.921741i | \(0.626767\pi\) | |||||||
\(164\) | 16.0414 | 1.25262 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.720541 | 0.0559248 | ||||||||
\(167\) | 14.3435 | 1.10993 | 0.554965 | − | 0.831873i | \(-0.312731\pi\) | ||||
0.554965 | + | 0.831873i | \(0.312731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6046 | −0.969586 | ||||||||
\(170\) | −0.303149 | −0.0232505 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −24.3429 | −1.85613 | ||||||||
\(173\) | −7.17674 | −0.545637 | −0.272819 | − | 0.962065i | \(-0.587956\pi\) | ||||
−0.272819 | + | 0.962065i | \(0.587956\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.12669 | −0.236355 | ||||||||
\(176\) | 2.12240 | 0.159982 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.16826 | 0.0875651 | ||||||||
\(179\) | −18.9923 | −1.41955 | −0.709774 | − | 0.704429i | \(-0.751203\pi\) | ||||
−0.709774 | + | 0.704429i | \(0.751203\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1558 | 1.49817 | 0.749086 | − | 0.662473i | \(-0.230493\pi\) | ||||
0.749086 | + | 0.662473i | \(0.230493\pi\) | |||||||
\(182\) | −0.0384537 | −0.00285038 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.61259 | −0.192603 | ||||||||
\(185\) | −0.0748239 | −0.00550116 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.71526 | −0.198559 | ||||||||
\(188\) | 2.96263 | 0.216072 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0434544 | −0.00315251 | ||||||||
\(191\) | −7.35271 | −0.532023 | −0.266012 | − | 0.963970i | \(-0.585706\pi\) | ||||
−0.266012 | + | 0.963970i | \(0.585706\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.59970 | 0.403076 | 0.201538 | − | 0.979481i | \(-0.435406\pi\) | ||||
0.201538 | + | 0.979481i | \(0.435406\pi\) | |||||||
\(194\) | 0.739415 | 0.0530869 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.0020 | 0.928714 | ||||||||
\(197\) | 23.4497 | 1.67072 | 0.835362 | − | 0.549700i | \(-0.185258\pi\) | ||||
0.835362 | + | 0.549700i | \(0.185258\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.09735 | 0.574006 | 0.287003 | − | 0.957930i | \(-0.407341\pi\) | ||||
0.287003 | + | 0.957930i | \(0.407341\pi\) | |||||||
\(200\) | 1.61309 | 0.114063 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.18909 | 0.0836639 | ||||||||
\(203\) | 2.48693 | 0.174548 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.43020 | −0.379261 | ||||||||
\(206\) | 0.274995 | 0.0191598 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.48542 | −0.172333 | ||||||||
\(209\) | −0.389214 | −0.0269225 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.2444 | −1.80674 | −0.903371 | − | 0.428860i | \(-0.858915\pi\) | ||||
−0.903371 | + | 0.428860i | \(0.858915\pi\) | |||||||
\(212\) | −13.7910 | −0.947170 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.02235 | 0.0698865 | ||||||||
\(215\) | 8.24036 | 0.561988 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.95359 | 0.268387 | ||||||||
\(218\) | 0.897765 | 0.0608044 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.721329 | −0.0486320 | ||||||||
\(221\) | 3.17968 | 0.213889 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.41208 | 0.362420 | 0.181210 | − | 0.983444i | \(-0.441999\pi\) | ||||
0.181210 | + | 0.983444i | \(0.441999\pi\) | |||||||
\(224\) | 0.729987 | 0.0487743 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.85761 | 0.123567 | ||||||||
\(227\) | −23.2617 | −1.54394 | −0.771968 | − | 0.635661i | \(-0.780728\pi\) | ||||
−0.771968 | + | 0.635661i | \(0.780728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.9483 | 1.45039 | 0.725193 | − | 0.688546i | \(-0.241751\pi\) | ||||
0.725193 | + | 0.688546i | \(0.241751\pi\) | |||||||
\(230\) | 0.441321 | 0.0290998 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.28303 | −0.0842352 | ||||||||
\(233\) | −4.41858 | −0.289471 | −0.144736 | − | 0.989470i | \(-0.546233\pi\) | ||||
−0.144736 | + | 0.989470i | \(0.546233\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.00289 | −0.0654210 | ||||||||
\(236\) | −19.5603 | −1.27326 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.309242 | −0.0200452 | ||||||||
\(239\) | 1.00000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2098 | −0.722087 | −0.361044 | − | 0.932549i | \(-0.617579\pi\) | ||||
−0.361044 | + | 0.932549i | \(0.617579\pi\) | |||||||
\(242\) | −0.952264 | −0.0612138 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.5577 | −0.803924 | ||||||||
\(245\) | −4.40133 | −0.281191 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.455787 | 0.0290010 | ||||||||
\(248\) | −2.03970 | −0.129521 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.572231 | −0.0361911 | ||||||||
\(251\) | −24.1478 | −1.52419 | −0.762096 | − | 0.647464i | \(-0.775830\pi\) | ||||
−0.762096 | + | 0.647464i | \(0.775830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.95284 | 0.248513 | ||||||||
\(254\) | 0.467046 | 0.0293051 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.3715 | 0.960718 | ||||||||
\(257\) | 23.7037 | 1.47859 | 0.739297 | − | 0.673379i | \(-0.235158\pi\) | ||||
0.739297 | + | 0.673379i | \(0.235158\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0763277 | −0.00474277 | ||||||||
\(260\) | 0.844708 | 0.0523866 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.682810 | 0.0421841 | ||||||||
\(263\) | −19.8888 | −1.22640 | −0.613198 | − | 0.789929i | \(-0.710117\pi\) | ||||
−0.613198 | + | 0.789929i | \(0.710117\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.66842 | 0.286779 | ||||||||
\(266\) | −0.0443278 | −0.00271791 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.0030 | 0.855371 | ||||||||
\(269\) | 16.7074 | 1.01867 | 0.509335 | − | 0.860568i | \(-0.329891\pi\) | ||||
0.509335 | + | 0.860568i | \(0.329891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0253 | 1.09496 | 0.547481 | − | 0.836818i | \(-0.315587\pi\) | ||||
0.547481 | + | 0.836818i | \(0.315587\pi\) | |||||||
\(272\) | −19.9876 | −1.21192 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.02242 | −0.0617664 | ||||||||
\(275\) | −2.44060 | −0.147174 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.7188 | −1.42513 | −0.712563 | − | 0.701608i | \(-0.752466\pi\) | ||||
−0.712563 | + | 0.701608i | \(0.752466\pi\) | |||||||
\(278\) | 1.52087 | 0.0912157 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.164631 | −0.00983858 | ||||||||
\(281\) | −8.96828 | −0.535003 | −0.267501 | − | 0.963557i | \(-0.586198\pi\) | ||||
−0.267501 | + | 0.963557i | \(0.586198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.74613 | 0.163240 | 0.0816201 | − | 0.996664i | \(-0.473991\pi\) | ||||
0.0816201 | + | 0.996664i | \(0.473991\pi\) | |||||||
\(284\) | −18.3640 | −1.08970 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0300158 | −0.00177487 | ||||||||
\(287\) | −5.53934 | −0.326977 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.57079 | 0.504164 | ||||||||
\(290\) | 0.216731 | 0.0127269 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 24.2899 | 1.42146 | ||||||||
\(293\) | −26.5055 | −1.54847 | −0.774235 | − | 0.632898i | \(-0.781865\pi\) | ||||
−0.774235 | + | 0.632898i | \(0.781865\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.62138 | 0.385511 | ||||||||
\(296\) | 0.0393783 | 0.00228882 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.09755 | 0.121508 | ||||||||
\(299\) | −4.62895 | −0.267699 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.40598 | 0.484512 | ||||||||
\(302\) | −1.01077 | −0.0581634 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.86509 | −0.164324 | ||||||||
\(305\) | 4.25093 | 0.243407 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.6982 | −1.58082 | −0.790410 | − | 0.612578i | \(-0.790133\pi\) | ||||
−0.790410 | + | 0.612578i | \(0.790133\pi\) | |||||||
\(308\) | −0.735827 | −0.0419276 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.344547 | 0.0195690 | ||||||||
\(311\) | −9.87576 | −0.560003 | −0.280001 | − | 0.960000i | \(-0.590335\pi\) | ||||
−0.280001 | + | 0.960000i | \(0.590335\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.8397 | −0.838792 | −0.419396 | − | 0.907803i | \(-0.637758\pi\) | ||||
−0.419396 | + | 0.907803i | \(0.637758\pi\) | |||||||
\(314\) | −0.0812883 | −0.00458736 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.3702 | 0.752134 | ||||||||
\(317\) | −19.8717 | −1.11610 | −0.558052 | − | 0.829806i | \(-0.688451\pi\) | ||||
−0.558052 | + | 0.829806i | \(0.688451\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.94122 | 0.108688 | ||||||||
\(320\) | −5.26730 | −0.294451 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.450190 | 0.0250881 | ||||||||
\(323\) | 3.66541 | 0.203949 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.85805 | 0.158536 | ||||||||
\(326\) | −0.880313 | −0.0487560 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.85780 | 0.157796 | ||||||||
\(329\) | −1.02304 | −0.0564021 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.2217 | −0.836658 | −0.418329 | − | 0.908296i | \(-0.637384\pi\) | ||||
−0.418329 | + | 0.908296i | \(0.637384\pi\) | |||||||
\(332\) | −16.1462 | −0.886135 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.27513 | 0.0697719 | ||||||||
\(335\) | −4.74019 | −0.258984 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.2836 | −1.70413 | −0.852063 | − | 0.523440i | \(-0.824648\pi\) | ||||
−0.852063 | + | 0.523440i | \(0.824648\pi\) | |||||||
\(338\) | −1.12054 | −0.0609496 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.79308 | 0.368407 | ||||||||
\(341\) | 3.08605 | 0.167119 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.30510 | −0.502428 | ||||||||
\(344\) | −4.33673 | −0.233821 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.638009 | −0.0342996 | ||||||||
\(347\) | 2.32374 | 0.124745 | 0.0623726 | − | 0.998053i | \(-0.480133\pi\) | ||||
0.0623726 | + | 0.998053i | \(0.480133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1644 | 0.918788 | 0.459394 | − | 0.888233i | \(-0.348067\pi\) | ||||
0.459394 | + | 0.888233i | \(0.348067\pi\) | |||||||
\(350\) | −0.277961 | −0.0148577 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.569807 | 0.0303708 | ||||||||
\(353\) | 21.0255 | 1.11907 | 0.559537 | − | 0.828805i | \(-0.310979\pi\) | ||||
0.559537 | + | 0.828805i | \(0.310979\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.21643 | 0.329934 | ||||||||
\(356\) | −26.1789 | −1.38748 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.68840 | −0.0892350 | ||||||||
\(359\) | 31.0325 | 1.63783 | 0.818917 | − | 0.573912i | \(-0.194575\pi\) | ||||
0.818917 | + | 0.573912i | \(0.194575\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4746 | −0.972347 | ||||||||
\(362\) | 1.79185 | 0.0941773 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.861685 | 0.0451646 | ||||||||
\(365\) | −8.22240 | −0.430380 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.316706 | −0.0165319 | −0.00826595 | − | 0.999966i | \(-0.502631\pi\) | ||||
−0.00826595 | + | 0.999966i | \(0.502631\pi\) | |||||||
\(368\) | 29.0976 | 1.51682 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.00665181 | −0.000345811 0 | ||||||||
\(371\) | 4.76224 | 0.247243 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.67698 | −0.138609 | −0.0693045 | − | 0.997596i | \(-0.522078\pi\) | ||||
−0.0693045 | + | 0.997596i | \(0.522078\pi\) | |||||||
\(374\) | −0.241385 | −0.0124817 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.527798 | 0.0272191 | ||||||||
\(377\) | −2.27326 | −0.117079 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.6822 | −0.908275 | −0.454137 | − | 0.890932i | \(-0.650052\pi\) | ||||
−0.454137 | + | 0.890932i | \(0.650052\pi\) | |||||||
\(380\) | 0.973744 | 0.0499520 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.653653 | −0.0334438 | ||||||||
\(383\) | 10.1403 | 0.518145 | 0.259072 | − | 0.965858i | \(-0.416583\pi\) | ||||
0.259072 | + | 0.965858i | \(0.416583\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.249086 | 0.0126946 | ||||||||
\(386\) | 0.497811 | 0.0253379 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.5691 | −0.841169 | ||||||||
\(389\) | −9.21319 | −0.467127 | −0.233564 | − | 0.972341i | \(-0.575039\pi\) | ||||
−0.233564 | + | 0.972341i | \(0.575039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.2256 | −1.88258 | ||||||||
\(392\) | 2.31633 | 0.116992 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.08467 | 0.105024 | ||||||||
\(395\) | −4.52598 | −0.227727 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.4727 | 1.52938 | 0.764689 | − | 0.644399i | \(-0.222892\pi\) | ||||
0.764689 | + | 0.644399i | \(0.222892\pi\) | |||||||
\(398\) | 0.719851 | 0.0360829 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.9658 | −0.898289 | ||||||||
\(401\) | −34.4093 | −1.71832 | −0.859160 | − | 0.511707i | \(-0.829013\pi\) | ||||
−0.859160 | + | 0.511707i | \(0.829013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.61391 | −0.180021 | ||||||||
\(404\) | −26.6455 | −1.32566 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.221087 | 0.0109724 | ||||||||
\(407\) | −0.0595792 | −0.00295323 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.0633 | −0.942618 | −0.471309 | − | 0.881968i | \(-0.656218\pi\) | ||||
−0.471309 | + | 0.881968i | \(0.656218\pi\) | |||||||
\(410\) | −0.482742 | −0.0238409 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.16219 | −0.303589 | ||||||||
\(413\) | 6.75446 | 0.332365 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.46566 | 0.268299 | ||||||||
\(416\) | −0.667269 | −0.0327156 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0346010 | −0.00169239 | ||||||||
\(419\) | 3.95215 | 0.193075 | 0.0965375 | − | 0.995329i | \(-0.469223\pi\) | ||||
0.0965375 | + | 0.995329i | \(0.469223\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8805 | 1.35881 | 0.679406 | − | 0.733762i | \(-0.262237\pi\) | ||||
0.679406 | + | 0.733762i | \(0.262237\pi\) | |||||||
\(422\) | −2.33312 | −0.113574 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.45689 | −0.119317 | ||||||||
\(425\) | 22.9842 | 1.11490 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.33637 | 0.209851 | ||||||||
\(428\) | −22.9093 | −1.10736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.732564 | 0.0353274 | ||||||||
\(431\) | 8.80087 | 0.423923 | 0.211961 | − | 0.977278i | \(-0.432015\pi\) | ||||
0.211961 | + | 0.977278i | \(0.432015\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.8304 | 1.86607 | 0.933034 | − | 0.359788i | \(-0.117151\pi\) | ||||
0.933034 | + | 0.359788i | \(0.117151\pi\) | |||||||
\(434\) | 0.351472 | 0.0168712 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.1175 | −0.963453 | ||||||||
\(437\) | −5.33605 | −0.255258 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.9487 | 1.28619 | 0.643095 | − | 0.765786i | \(-0.277650\pi\) | ||||
0.643095 | + | 0.765786i | \(0.277650\pi\) | |||||||
\(440\) | −0.128506 | −0.00612629 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.282673 | 0.0134454 | ||||||||
\(443\) | −14.5012 | −0.688972 | −0.344486 | − | 0.938792i | \(-0.611947\pi\) | ||||
−0.344486 | + | 0.938792i | \(0.611947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.86187 | 0.420093 | ||||||||
\(446\) | 0.481132 | 0.0227823 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.37316 | −0.253858 | ||||||||
\(449\) | 8.58911 | 0.405345 | 0.202673 | − | 0.979247i | \(-0.435037\pi\) | ||||
0.202673 | + | 0.979247i | \(0.435037\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.32385 | −0.203602 | ||||||||
\(452\) | −41.6261 | −1.95793 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.06796 | −0.0970541 | ||||||||
\(455\) | −0.291691 | −0.0136747 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.4901 | 0.631040 | 0.315520 | − | 0.948919i | \(-0.397821\pi\) | ||||
0.315520 | + | 0.948919i | \(0.397821\pi\) | |||||||
\(458\) | 1.95120 | 0.0911734 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.88929 | −0.461090 | ||||||||
\(461\) | −20.1254 | −0.937332 | −0.468666 | − | 0.883375i | \(-0.655265\pi\) | ||||
−0.468666 | + | 0.883375i | \(0.655265\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.2303 | 0.893709 | 0.446855 | − | 0.894607i | \(-0.352544\pi\) | ||||
0.446855 | + | 0.894607i | \(0.352544\pi\) | |||||||
\(464\) | 14.2897 | 0.663384 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.392810 | −0.0181966 | ||||||||
\(467\) | −17.7598 | −0.821828 | −0.410914 | − | 0.911674i | \(-0.634790\pi\) | ||||
−0.410914 | + | 0.911674i | \(0.634790\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.83546 | −0.223281 | ||||||||
\(470\) | −0.0891561 | −0.00411246 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.48470 | −0.160396 | ||||||||
\(473\) | 6.56146 | 0.301696 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.29464 | 0.151168 | ||||||||
\(476\) | 6.92961 | 0.317618 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.0888996 | 0.00406617 | ||||||||
\(479\) | −28.8979 | −1.32038 | −0.660189 | − | 0.751100i | \(-0.729524\pi\) | ||||
−0.660189 | + | 0.751100i | \(0.729524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0697698 | 0.00318123 | ||||||||
\(482\) | −0.996548 | −0.0453915 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.3387 | 0.969941 | ||||||||
\(485\) | 5.60884 | 0.254684 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.62899 | −0.391017 | −0.195508 | − | 0.980702i | \(-0.562636\pi\) | ||||
−0.195508 | + | 0.980702i | \(0.562636\pi\) | |||||||
\(488\) | −2.23718 | −0.101272 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.391276 | −0.0176761 | ||||||||
\(491\) | 24.6724 | 1.11345 | 0.556725 | − | 0.830697i | \(-0.312058\pi\) | ||||
0.556725 | + | 0.830697i | \(0.312058\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.2814 | −0.823351 | ||||||||
\(494\) | 0.0405193 | 0.00182305 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.7171 | 1.02003 | ||||||||
\(497\) | 6.34137 | 0.284449 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.336524 | −0.0150649 | −0.00753244 | − | 0.999972i | \(-0.502398\pi\) | ||||
−0.00753244 | + | 0.999972i | \(0.502398\pi\) | |||||||
\(500\) | 12.8228 | 0.573452 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.14673 | −0.0958131 | ||||||||
\(503\) | 33.4007 | 1.48926 | 0.744632 | − | 0.667476i | \(-0.232625\pi\) | ||||
0.744632 | + | 0.667476i | \(0.232625\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.01983 | 0.401377 | ||||||||
\(506\) | 0.351406 | 0.0156219 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.4658 | −0.464343 | ||||||||
\(509\) | 35.3725 | 1.56786 | 0.783929 | − | 0.620851i | \(-0.213213\pi\) | ||||
0.783929 | + | 0.620851i | \(0.213213\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.38766 | −0.371048 | ||||||||
\(512\) | 7.00002 | 0.309360 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.10725 | 0.0929466 | ||||||||
\(515\) | 2.08598 | 0.0919191 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.798557 | −0.0351205 | ||||||||
\(518\) | −0.00678550 | −0.000298138 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.150486 | 0.00659926 | ||||||||
\(521\) | −11.3345 | −0.496572 | −0.248286 | − | 0.968687i | \(-0.579867\pi\) | ||||
−0.248286 | + | 0.968687i | \(0.579867\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.7825 | −1.78329 | −0.891646 | − | 0.452733i | \(-0.850449\pi\) | ||||
−0.891646 | + | 0.452733i | \(0.850449\pi\) | |||||||
\(524\) | −15.3007 | −0.668413 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.76811 | −0.0770931 | ||||||||
\(527\) | −29.0628 | −1.26599 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.1926 | 1.35620 | ||||||||
\(530\) | 0.415020 | 0.0180273 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.993314 | 0.0430656 | ||||||||
\(533\) | 5.06341 | 0.219321 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.75505 | 0.335280 | ||||||||
\(536\) | 2.49466 | 0.107753 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.48528 | 0.0640352 | ||||||||
\(539\) | −3.50460 | −0.150954 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.1438 | 0.651082 | 0.325541 | − | 0.945528i | \(-0.394454\pi\) | ||||
0.325541 | + | 0.945528i | \(0.394454\pi\) | |||||||
\(542\) | 1.60245 | 0.0688310 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.36613 | −0.230071 | ||||||||
\(545\) | 6.81000 | 0.291709 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0014 | 1.19725 | 0.598627 | − | 0.801028i | \(-0.295713\pi\) | ||||
0.598627 | + | 0.801028i | \(0.295713\pi\) | |||||||
\(548\) | 22.9107 | 0.978696 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.216969 | −0.00925157 | ||||||||
\(551\) | −2.62051 | −0.111638 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.61695 | −0.196333 | ||||||||
\(554\) | −2.10859 | −0.0895855 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −34.0802 | −1.44532 | ||||||||
\(557\) | −39.4275 | −1.67060 | −0.835298 | − | 0.549798i | \(-0.814705\pi\) | ||||
−0.835298 | + | 0.549798i | \(0.814705\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.68376 | −0.324988 | ||||||||
\(560\) | 1.83357 | 0.0774826 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.797276 | −0.0336311 | ||||||||
\(563\) | 11.7452 | 0.495003 | 0.247502 | − | 0.968887i | \(-0.420390\pi\) | ||||
0.247502 | + | 0.968887i | \(0.420390\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0909 | 0.592810 | ||||||||
\(566\) | 0.244129 | 0.0102615 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.27158 | −0.137272 | ||||||||
\(569\) | −16.2860 | −0.682743 | −0.341371 | − | 0.939928i | \(-0.610891\pi\) | ||||
−0.341371 | + | 0.939928i | \(0.610891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.21609 | 0.134589 | 0.0672946 | − | 0.997733i | \(-0.478563\pi\) | ||||
0.0672946 | + | 0.997733i | \(0.478563\pi\) | |||||||
\(572\) | 0.672607 | 0.0281231 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.492445 | −0.0205542 | ||||||||
\(575\) | −33.4602 | −1.39539 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.9258 | 0.954412 | 0.477206 | − | 0.878792i | \(-0.341650\pi\) | ||||
0.477206 | + | 0.878792i | \(0.341650\pi\) | |||||||
\(578\) | 0.761940 | 0.0316925 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.85659 | −0.201659 | ||||||||
\(581\) | 5.57552 | 0.231311 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.71727 | 0.153954 | ||||||||
\(584\) | 4.32728 | 0.179064 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.35633 | −0.0973392 | ||||||||
\(587\) | −7.86672 | −0.324694 | −0.162347 | − | 0.986734i | \(-0.551906\pi\) | ||||
−0.162347 | + | 0.986734i | \(0.551906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.16596 | −0.171655 | ||||||||
\(590\) | 0.588638 | 0.0242338 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.438575 | −0.0180253 | ||||||||
\(593\) | 6.59271 | 0.270730 | 0.135365 | − | 0.990796i | \(-0.456779\pi\) | ||||
0.135365 | + | 0.990796i | \(0.456779\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.34576 | −0.0961666 | ||||||||
\(596\) | −47.0026 | −1.92530 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.411511 | −0.0168280 | ||||||||
\(599\) | −32.3184 | −1.32050 | −0.660248 | − | 0.751048i | \(-0.729549\pi\) | ||||
−0.660248 | + | 0.751048i | \(0.729549\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.1450 | −1.39280 | −0.696402 | − | 0.717652i | \(-0.745217\pi\) | ||||
−0.696402 | + | 0.717652i | \(0.745217\pi\) | |||||||
\(602\) | 0.747288 | 0.0304572 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22.6498 | 0.921606 | ||||||||
\(605\) | −7.22340 | −0.293673 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.5667 | −0.794186 | −0.397093 | − | 0.917778i | \(-0.629981\pi\) | ||||
−0.397093 | + | 0.917778i | \(0.629981\pi\) | |||||||
\(608\) | −0.769199 | −0.0311952 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.377906 | 0.0153010 | ||||||||
\(611\) | 0.935145 | 0.0378319 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.3571 | −1.87235 | −0.936174 | − | 0.351538i | \(-0.885659\pi\) | ||||
−0.936174 | + | 0.351538i | \(0.885659\pi\) | |||||||
\(614\) | −2.46236 | −0.0993728 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.131089 | −0.00528172 | ||||||||
\(617\) | 33.5775 | 1.35178 | 0.675889 | − | 0.737004i | \(-0.263760\pi\) | ||||
0.675889 | + | 0.737004i | \(0.263760\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.59081 | −0.385487 | −0.192744 | − | 0.981249i | \(-0.561739\pi\) | ||||
−0.192744 | + | 0.981249i | \(0.561739\pi\) | |||||||
\(620\) | −7.72075 | −0.310073 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.877951 | −0.0352026 | ||||||||
\(623\) | 9.03998 | 0.362179 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.3856 | 0.735424 | ||||||||
\(626\) | −1.31925 | −0.0527277 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.82154 | 0.0726873 | ||||||||
\(629\) | 0.561084 | 0.0223719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.4228 | −1.21111 | −0.605556 | − | 0.795803i | \(-0.707049\pi\) | ||||
−0.605556 | + | 0.795803i | \(0.707049\pi\) | |||||||
\(632\) | 2.38193 | 0.0947482 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.76658 | −0.0701600 | ||||||||
\(635\) | 3.54278 | 0.140591 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.10404 | 0.162608 | ||||||||
\(638\) | 0.172574 | 0.00683227 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.89947 | −0.0750832 | ||||||||
\(641\) | 19.5297 | 0.771376 | 0.385688 | − | 0.922629i | \(-0.373964\pi\) | ||||
0.385688 | + | 0.922629i | \(0.373964\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.7587 | 1.64680 | 0.823401 | − | 0.567460i | \(-0.192074\pi\) | ||||
0.823401 | + | 0.567460i | \(0.192074\pi\) | |||||||
\(644\) | −10.0880 | −0.397525 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.325853 | 0.0128205 | ||||||||
\(647\) | 25.7021 | 1.01046 | 0.505228 | − | 0.862986i | \(-0.331409\pi\) | ||||
0.505228 | + | 0.862986i | \(0.331409\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.27233 | 0.206957 | ||||||||
\(650\) | 0.254080 | 0.00996582 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.7264 | 0.772545 | ||||||||
\(653\) | 5.47922 | 0.214418 | 0.107209 | − | 0.994236i | \(-0.465809\pi\) | ||||
0.107209 | + | 0.994236i | \(0.465809\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.17946 | 0.202378 | ||||||||
\(656\) | −31.8287 | −1.24270 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.0909480 | −0.00354552 | ||||||||
\(659\) | −41.0759 | −1.60009 | −0.800044 | − | 0.599941i | \(-0.795191\pi\) | ||||
−0.800044 | + | 0.599941i | \(0.795191\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.166915 | 0.00649225 | 0.00324612 | − | 0.999995i | \(-0.498967\pi\) | ||||
0.00324612 | + | 0.999995i | \(0.498967\pi\) | |||||||
\(662\) | −1.35320 | −0.0525936 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.87647 | −0.111629 | ||||||||
\(665\) | −0.336249 | −0.0130392 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.6138 | 1.03049 | ||||||||
\(668\) | −28.5736 | −1.10554 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.421401 | −0.0162801 | ||||||||
\(671\) | 3.38484 | 0.130670 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.5591 | −1.21651 | −0.608257 | − | 0.793741i | \(-0.708131\pi\) | ||||
−0.608257 | + | 0.793741i | \(0.708131\pi\) | |||||||
\(674\) | −2.78110 | −0.107124 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.1096 | 0.965754 | ||||||||
\(677\) | 28.9919 | 1.11425 | 0.557124 | − | 0.830429i | \(-0.311905\pi\) | ||||
0.557124 | + | 0.830429i | \(0.311905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.72157 | 0.219574 | ||||||||
\(680\) | 1.21020 | 0.0464091 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.274349 | 0.0105054 | ||||||||
\(683\) | 29.7746 | 1.13929 | 0.569646 | − | 0.821890i | \(-0.307080\pi\) | ||||
0.569646 | + | 0.821890i | \(0.307080\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.75554 | −0.296324 | ||||||||
\(686\) | −0.827220 | −0.0315834 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 48.3003 | 1.84143 | ||||||||
\(689\) | −4.35309 | −0.165839 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.5776 | −0.820852 | −0.410426 | − | 0.911894i | \(-0.634620\pi\) | ||||
−0.410426 | + | 0.911894i | \(0.634620\pi\) | |||||||
\(692\) | 14.2968 | 0.543481 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.206580 | 0.00784167 | ||||||||
\(695\) | 11.5366 | 0.437607 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.7196 | 1.54236 | ||||||||
\(698\) | 1.52591 | 0.0577564 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.22867 | 0.235421 | ||||||||
\(701\) | 2.79934 | 0.105730 | 0.0528649 | − | 0.998602i | \(-0.483165\pi\) | ||||
0.0528649 | + | 0.998602i | \(0.483165\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0804277 | 0.00303339 | ||||||||
\(704\) | −4.19414 | −0.158072 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.86916 | 0.0703467 | ||||||||
\(707\) | 9.20111 | 0.346043 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.7987 | −1.75756 | −0.878781 | − | 0.477225i | \(-0.841643\pi\) | ||||
−0.878781 | + | 0.477225i | \(0.841643\pi\) | |||||||
\(710\) | 0.552638 | 0.0207401 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.66382 | −0.174784 | ||||||||
\(713\) | 42.3092 | 1.58449 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.227685 | −0.00851495 | ||||||||
\(716\) | 37.8344 | 1.41394 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.75878 | 0.102957 | ||||||||
\(719\) | 6.28186 | 0.234274 | 0.117137 | − | 0.993116i | \(-0.462628\pi\) | ||||
0.117137 | + | 0.993116i | \(0.462628\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.12790 | 0.0792471 | ||||||||
\(722\) | −1.64238 | −0.0611232 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −40.1524 | −1.49225 | ||||||||
\(725\) | −16.4322 | −0.610275 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.34229 | 0.198135 | 0.0990673 | − | 0.995081i | \(-0.468414\pi\) | ||||
0.0990673 | + | 0.995081i | \(0.468414\pi\) | |||||||
\(728\) | 0.153511 | 0.00568949 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.730968 | −0.0270544 | ||||||||
\(731\) | −61.7922 | −2.28547 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.43108 | −0.126730 | −0.0633650 | − | 0.997990i | \(-0.520183\pi\) | ||||
−0.0633650 | + | 0.997990i | \(0.520183\pi\) | |||||||
\(734\) | −0.0281550 | −0.00103922 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.81195 | 0.287952 | ||||||||
\(737\) | −3.77442 | −0.139033 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.0227 | 1.65619 | 0.828093 | − | 0.560591i | \(-0.189426\pi\) | ||||
0.828093 | + | 0.560591i | \(0.189426\pi\) | |||||||
\(740\) | 0.149056 | 0.00547942 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.423362 | 0.0155421 | ||||||||
\(743\) | 0.484953 | 0.0177912 | 0.00889560 | − | 0.999960i | \(-0.497168\pi\) | ||||
0.00889560 | + | 0.999960i | \(0.497168\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.9109 | 0.582932 | ||||||||
\(746\) | −0.237983 | −0.00871317 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.40905 | 0.197775 | ||||||||
\(749\) | 7.91092 | 0.289059 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.09423 | 0.112910 | 0.0564550 | − | 0.998405i | \(-0.482020\pi\) | ||||
0.0564550 | + | 0.998405i | \(0.482020\pi\) | |||||||
\(752\) | −5.87834 | −0.214361 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.202092 | −0.00735974 | ||||||||
\(755\) | −7.66722 | −0.279039 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.9908 | −0.799271 | −0.399635 | − | 0.916674i | \(-0.630863\pi\) | ||||
−0.399635 | + | 0.916674i | \(0.630863\pi\) | |||||||
\(758\) | −1.57194 | −0.0570955 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.173474 | 0.00629257 | ||||||||
\(761\) | −14.2000 | −0.514748 | −0.257374 | − | 0.966312i | \(-0.582857\pi\) | ||||
−0.257374 | + | 0.966312i | \(0.582857\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.94688 | 0.251494 | ||||||||
\(764\) | 14.6473 | 0.529921 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.901468 | 0.0325713 | ||||||||
\(767\) | −6.17413 | −0.222935 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.78312 | −0.208545 | −0.104272 | − | 0.994549i | \(-0.533251\pi\) | ||||
−0.104272 | + | 0.994549i | \(0.533251\pi\) | |||||||
\(770\) | 0.0221437 | 0.000798002 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.1552 | −0.401483 | ||||||||
\(773\) | −40.3814 | −1.45242 | −0.726210 | − | 0.687473i | \(-0.758720\pi\) | ||||
−0.726210 | + | 0.687473i | \(0.758720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.1230 | −0.938366 | ||||||||
\(776\) | −2.95182 | −0.105964 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.819049 | −0.0293643 | ||||||||
\(779\) | 5.83689 | 0.209128 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.94989 | 0.177121 | ||||||||
\(782\) | −3.30935 | −0.118342 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25.7981 | −0.921360 | ||||||||
\(785\) | −0.616612 | −0.0220078 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.2097 | 1.07686 | 0.538430 | − | 0.842670i | \(-0.319017\pi\) | ||||
0.538430 | + | 0.842670i | \(0.319017\pi\) | |||||||
\(788\) | −46.7141 | −1.66412 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.402358 | −0.0143153 | ||||||||
\(791\) | 14.3741 | 0.511086 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.96380 | −0.140759 | ||||||||
\(794\) | 2.70901 | 0.0961390 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.1307 | −0.571738 | ||||||||
\(797\) | −28.5813 | −1.01240 | −0.506200 | − | 0.862416i | \(-0.668950\pi\) | ||||
−0.506200 | + | 0.862416i | \(0.668950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.52037 | 0.266052 | ||||||||
\(800\) | −4.82333 | −0.170531 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.05898 | −0.108016 | ||||||||
\(803\) | −6.54717 | −0.231044 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.41492 | 0.120360 | ||||||||
\(806\) | −0.321275 | −0.0113164 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.74695 | −0.166997 | ||||||||
\(809\) | 42.6781 | 1.50048 | 0.750241 | − | 0.661164i | \(-0.229937\pi\) | ||||
0.750241 | + | 0.661164i | \(0.229937\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.9127 | −0.523655 | −0.261828 | − | 0.965115i | \(-0.584325\pi\) | ||||
−0.261828 | + | 0.965115i | \(0.584325\pi\) | |||||||
\(812\) | −4.95420 | −0.173858 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.00529657 | −0.000185645 0 | ||||||||
\(815\) | −6.67762 | −0.233907 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.85751 | −0.309885 | ||||||||
\(818\) | −1.69472 | −0.0592544 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.8175 | 0.377763 | ||||||||
\(821\) | 25.8710 | 0.902905 | 0.451452 | − | 0.892295i | \(-0.350906\pi\) | ||||
0.451452 | + | 0.892295i | \(0.350906\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.4859 | 0.679236 | 0.339618 | − | 0.940563i | \(-0.389702\pi\) | ||||
0.339618 | + | 0.940563i | \(0.389702\pi\) | |||||||
\(824\) | −1.09781 | −0.0382439 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.600468 | 0.0208930 | ||||||||
\(827\) | −42.7539 | −1.48670 | −0.743349 | − | 0.668903i | \(-0.766764\pi\) | ||||
−0.743349 | + | 0.668903i | \(0.766764\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.6962 | −0.753542 | −0.376771 | − | 0.926307i | \(-0.622966\pi\) | ||||
−0.376771 | + | 0.926307i | \(0.622966\pi\) | |||||||
\(830\) | 0.485895 | 0.0168657 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.91152 | 0.170276 | ||||||||
\(833\) | 33.0044 | 1.14353 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.67249 | 0.334730 | ||||||||
\(836\) | 0.775352 | 0.0268161 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.351344 | 0.0121370 | ||||||||
\(839\) | −53.7944 | −1.85719 | −0.928595 | − | 0.371095i | \(-0.878983\pi\) | ||||
−0.928595 | + | 0.371095i | \(0.878983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9301 | −0.549313 | ||||||||
\(842\) | 2.47857 | 0.0854170 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 52.2815 | 1.79960 | ||||||||
\(845\) | −8.49990 | −0.292405 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.36858 | −0.253187 | ||||||||
\(848\) | 27.3636 | 0.939669 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.04329 | 0.0700843 | ||||||||
\(851\) | −0.816819 | −0.0280002 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.311946 | −0.0106808 | −0.00534041 | − | 0.999986i | \(-0.501700\pi\) | ||||
−0.00534041 | + | 0.999986i | \(0.501700\pi\) | |||||||
\(854\) | 0.385501 | 0.0131916 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.08133 | −0.139497 | ||||||||
\(857\) | 12.6856 | 0.433330 | 0.216665 | − | 0.976246i | \(-0.430482\pi\) | ||||
0.216665 | + | 0.976246i | \(0.430482\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.87231 | −0.0638823 | −0.0319411 | − | 0.999490i | \(-0.510169\pi\) | ||||
−0.0319411 | + | 0.999490i | \(0.510169\pi\) | |||||||
\(860\) | −16.4156 | −0.559767 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.782394 | 0.0266484 | ||||||||
\(863\) | 27.4289 | 0.933692 | 0.466846 | − | 0.884339i | \(-0.345390\pi\) | ||||
0.466846 | + | 0.884339i | \(0.345390\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.83962 | −0.164552 | ||||||||
\(866\) | 3.45200 | 0.117304 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.87593 | −0.267326 | ||||||||
\(869\) | −3.60385 | −0.122252 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.42001 | 0.149766 | ||||||||
\(872\) | −3.58397 | −0.121368 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.474373 | −0.0160459 | ||||||||
\(875\) | −4.42790 | −0.149690 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.8318 | −0.703441 | −0.351720 | − | 0.936105i | \(-0.614403\pi\) | ||||
−0.351720 | + | 0.936105i | \(0.614403\pi\) | |||||||
\(878\) | 2.39573 | 0.0808519 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.43123 | 0.0482469 | ||||||||
\(881\) | 11.4448 | 0.385584 | 0.192792 | − | 0.981240i | \(-0.438246\pi\) | ||||
0.192792 | + | 0.981240i | \(0.438246\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.46065 | 0.0828076 | 0.0414038 | − | 0.999142i | \(-0.486817\pi\) | ||||
0.0414038 | + | 0.999142i | \(0.486817\pi\) | |||||||
\(884\) | −6.33424 | −0.213044 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.28915 | −0.0433098 | ||||||||
\(887\) | −43.7435 | −1.46876 | −0.734382 | − | 0.678737i | \(-0.762528\pi\) | ||||
−0.734382 | + | 0.678737i | \(0.762528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.61399 | 0.121209 | ||||||||
\(890\) | 0.787817 | 0.0264077 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.7814 | −0.360988 | ||||||||
\(893\) | 1.07800 | 0.0360737 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.8074 | −0.428104 | ||||||||
\(896\) | −1.93765 | −0.0647322 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.763568 | 0.0254806 | ||||||||
\(899\) | 20.7779 | 0.692981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.0072 | −1.16626 | ||||||||
\(902\) | −0.384388 | −0.0127987 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.41578 | −0.246645 | ||||||||
\(905\) | 13.5921 | 0.451815 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.9761 | −0.995339 | −0.497669 | − | 0.867367i | \(-0.665811\pi\) | ||||
−0.497669 | + | 0.867367i | \(0.665811\pi\) | |||||||
\(908\) | 46.3396 | 1.53784 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.0259312 | −0.000859610 0 | ||||||||
\(911\) | 50.0272 | 1.65748 | 0.828738 | − | 0.559637i | \(-0.189059\pi\) | ||||
0.828738 | + | 0.559637i | \(0.189059\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.35209 | 0.144033 | ||||||||
\(914\) | 1.19926 | 0.0396682 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −43.7232 | −1.44465 | ||||||||
\(917\) | 5.28356 | 0.174478 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.1329 | 0.796070 | 0.398035 | − | 0.917370i | \(-0.369692\pi\) | ||||
0.398035 | + | 0.917370i | \(0.369692\pi\) | |||||||
\(920\) | −1.76179 | −0.0580846 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.78914 | −0.0589221 | ||||||||
\(923\) | −5.79654 | −0.190795 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.504329 | 0.0165822 | ||||||||
\(926\) | 1.70957 | 0.0561799 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.83641 | 0.125936 | ||||||||
\(929\) | 49.0310 | 1.60865 | 0.804327 | − | 0.594186i | \(-0.202526\pi\) | ||||
0.804327 | + | 0.594186i | \(0.202526\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.73096 | 0.155051 | ||||||||
\(932\) | 8.80225 | 0.288327 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.57884 | −0.0516613 | ||||||||
\(935\) | −1.83103 | −0.0598810 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.755623 | 0.0246851 | 0.0123426 | − | 0.999924i | \(-0.496071\pi\) | ||||
0.0123426 | + | 0.999924i | \(0.496071\pi\) | |||||||
\(938\) | −0.429870 | −0.0140358 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.99784 | 0.0651625 | ||||||||
\(941\) | −12.4403 | −0.405542 | −0.202771 | − | 0.979226i | \(-0.564995\pi\) | ||||
−0.202771 | + | 0.979226i | \(0.564995\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −59.2791 | −1.93039 | ||||||||
\(944\) | 38.8107 | 1.26318 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.583311 | 0.0189651 | ||||||||
\(947\) | −37.7555 | −1.22689 | −0.613445 | − | 0.789738i | \(-0.710217\pi\) | ||||
−0.613445 | + | 0.789738i | \(0.710217\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.66702 | 0.248882 | ||||||||
\(950\) | 0.292892 | 0.00950268 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.23452 | 0.0400111 | ||||||||
\(953\) | −6.27937 | −0.203409 | −0.101704 | − | 0.994815i | \(-0.532430\pi\) | ||||
−0.101704 | + | 0.994815i | \(0.532430\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.95829 | −0.160446 | ||||||||
\(956\) | −1.99210 | −0.0644290 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.56901 | −0.0830009 | ||||||||
\(959\) | −7.91141 | −0.255473 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.03160 | 0.0655355 | ||||||||
\(962\) | 0.00620251 | 0.000199977 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.3310 | 0.719234 | ||||||||
\(965\) | 3.77615 | 0.121559 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.8287 | 1.34512 | 0.672560 | − | 0.740042i | \(-0.265195\pi\) | ||||
0.672560 | + | 0.740042i | \(0.265195\pi\) | |||||||
\(968\) | 3.80153 | 0.122186 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.498623 | 0.0160098 | ||||||||
\(971\) | −23.0751 | −0.740515 | −0.370258 | − | 0.928929i | \(-0.620731\pi\) | ||||
−0.370258 | + | 0.928929i | \(0.620731\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.7684 | 0.377278 | ||||||||
\(974\) | −0.767114 | −0.0245799 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.9165 | 0.797558 | ||||||||
\(977\) | −15.2960 | −0.489363 | −0.244682 | − | 0.969603i | \(-0.578683\pi\) | ||||
−0.244682 | + | 0.969603i | \(0.578683\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.05635 | 0.225522 | ||||||||
\(980\) | 8.76788 | 0.280080 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.19337 | 0.0699931 | ||||||||
\(983\) | 43.5763 | 1.38987 | 0.694935 | − | 0.719073i | \(-0.255433\pi\) | ||||
0.694935 | + | 0.719073i | \(0.255433\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.8133 | 0.503853 | ||||||||
\(986\) | −1.62521 | −0.0517571 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.907972 | −0.0288864 | ||||||||
\(989\) | 89.9564 | 2.86045 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.3453 | 1.05925 | 0.529624 | − | 0.848232i | \(-0.322333\pi\) | ||||
0.529624 | + | 0.848232i | \(0.322333\pi\) | |||||||
\(992\) | 6.09893 | 0.193641 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.563745 | 0.0178809 | ||||||||
\(995\) | 5.46044 | 0.173107 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.7971 | 1.35540 | 0.677699 | − | 0.735340i | \(-0.262977\pi\) | ||||
0.677699 | + | 0.735340i | \(0.262977\pi\) | |||||||
\(998\) | −0.0299168 | −0.000947001 0 | ||||||||
\(999\) | 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 | 2151.2.a.k.1.10 | yes | 20 | |
3.2 | odd | 2 | 2151.2.a.j.1.11 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.11 | ✓ | 20 | 3.2 | odd | 2 | ||
2151.2.a.k.1.10 | yes | 20 | 1.1 | even | 1 | trivial |