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: | \(1\) |
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 | 1.11 | ||
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 | \(-0.510006\pi\) | ||||
−0.0314308 | + | 0.999506i | \(0.510006\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99210 | −0.996048 | ||||||||
\(5\) | −0.674348 | −0.301578 | −0.150789 | − | 0.988566i | \(-0.548181\pi\) | ||||
−0.150789 | + | 0.988566i | \(0.548181\pi\) | |||||||
\(6\) | 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 | \(-0.525795\pi\) | ||||
−0.0809492 | + | 0.996718i | \(0.525795\pi\) | |||||||
\(12\) | 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 | \(-0.289873\pi\) | ||||
0.613222 | + | 0.789911i | \(0.289873\pi\) | |||||||
\(18\) | 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 | \(-0.778498\pi\) | ||||
−0.767496 | + | 0.641053i | \(0.778498\pi\) | |||||||
\(24\) | 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 | \(-0.608961\pi\) | ||||
−0.335666 | + | 0.941981i | \(0.608961\pi\) | |||||||
\(30\) | 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 | \(-0.283548\pi\) | ||||
0.628796 | + | 0.777571i | \(0.283548\pi\) | |||||||
\(42\) | 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 | \(-0.465407\pi\) | ||||
0.108465 | + | 0.994100i | \(0.465407\pi\) | |||||||
\(48\) | 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 | \(-0.657720\pi\) | ||||
−0.475464 | + | 0.879735i | \(0.657720\pi\) | |||||||
\(54\) | 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 | \(-0.720717\pi\) | ||||
−0.639158 | + | 0.769076i | \(0.720717\pi\) | |||||||
\(60\) | 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 | \(-0.684235\pi\) | ||||
−0.547013 | + | 0.837124i | \(0.684235\pi\) | |||||||
\(72\) | 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 | \(-0.646734\pi\) | ||||
−0.444825 | + | 0.895617i | \(0.646734\pi\) | |||||||
\(84\) | 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 | \(-0.745257\pi\) | ||||
−0.696492 | + | 0.717564i | \(0.745257\pi\) | |||||||
\(90\) | 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 | \(-0.731765\pi\) | ||||
−0.665462 | + | 0.746432i | \(0.731765\pi\) | |||||||
\(102\) | 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 | \(-0.687617\pi\) | ||||
−0.555877 | + | 0.831265i | \(0.687617\pi\) | |||||||
\(108\) | 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 | \(-0.940961\pi\) | ||||
−0.982848 | + | 0.184415i | \(0.940961\pi\) | |||||||
\(114\) | 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 | \(-0.608916\pi\) | ||||
−0.335532 | + | 0.942029i | \(0.608916\pi\) | |||||||
\(132\) | 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 | \(-0.336526\pi\) | ||||
0.491289 | + | 0.870996i | \(0.336526\pi\) | |||||||
\(138\) | 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 | \(-0.917339\pi\) | ||||
−0.966470 | + | 0.256778i | \(0.917339\pi\) | |||||||
\(150\) | 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 | \(-0.687269\pi\) | ||||
−0.554965 | + | 0.831873i | \(0.687269\pi\) | |||||||
\(168\) | 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 | \(-0.412044\pi\) | ||||
0.272819 | + | 0.962065i | \(0.412044\pi\) | |||||||
\(174\) | 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 | \(-0.248797\pi\) | ||||
0.709774 | + | 0.704429i | \(0.248797\pi\) | |||||||
\(180\) | 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 | \(-0.414294\pi\) | ||||
0.266012 | + | 0.963970i | \(0.414294\pi\) | |||||||
\(192\) | 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 | \(-0.814742\pi\) | ||||
−0.835362 | + | 0.549700i | \(0.814742\pi\) | |||||||
\(198\) | 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 | \(-0.219272\pi\) | ||||
0.771968 | + | 0.635661i | \(0.219272\pi\) | |||||||
\(228\) | 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 | \(-0.453767\pi\) | ||||
0.144736 | + | 0.989470i | \(0.453767\pi\) | |||||||
\(234\) | 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 | \(-0.224170\pi\) | ||||
0.762096 | + | 0.647464i | \(0.224170\pi\) | |||||||
\(252\) | 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 | \(-0.764842\pi\) | ||||
−0.739297 | + | 0.673379i | \(0.764842\pi\) | |||||||
\(258\) | 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 | \(-0.289883\pi\) | ||||
0.613198 | + | 0.789929i | \(0.289883\pi\) | |||||||
\(264\) | 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 | \(-0.670109\pi\) | ||||
−0.509335 | + | 0.860568i | \(0.670109\pi\) | |||||||
\(270\) | 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 | \(-0.413802\pi\) | ||||
0.267501 | + | 0.963557i | \(0.413802\pi\) | |||||||
\(282\) | 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 | \(-0.218135\pi\) | ||||
0.774235 | + | 0.632898i | \(0.218135\pi\) | |||||||
\(294\) | 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 | \(-0.409665\pi\) | ||||
0.280001 | + | 0.960000i | \(0.409665\pi\) | |||||||
\(312\) | 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 | \(-0.311549\pi\) | ||||
0.558052 | + | 0.829806i | \(0.311549\pi\) | |||||||
\(318\) | 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 | \(-0.519867\pi\) | ||||
−0.0623726 | + | 0.998053i | \(0.519867\pi\) | |||||||
\(348\) | 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 | \(-0.689021\pi\) | ||||
−0.559537 | + | 0.828805i | \(0.689021\pi\) | |||||||
\(354\) | 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 | \(-0.805425\pi\) | ||||
−0.818917 | + | 0.573912i | \(0.805425\pi\) | |||||||
\(360\) | 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 | \(-0.583417\pi\) | ||||
−0.259072 | + | 0.965858i | \(0.583417\pi\) | |||||||
\(384\) | 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 | \(-0.424961\pi\) | ||||
0.233564 | + | 0.972341i | \(0.424961\pi\) | |||||||
\(390\) | 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 | \(-0.170987\pi\) | ||||
0.859160 | + | 0.511707i | \(0.170987\pi\) | |||||||
\(402\) | 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 | \(-0.530777\pi\) | ||||
−0.0965375 | + | 0.995329i | \(0.530777\pi\) | |||||||
\(420\) | 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 | \(-0.567985\pi\) | ||||
−0.211961 | + | 0.977278i | \(0.567985\pi\) | |||||||
\(432\) | 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 | \(-0.388053\pi\) | ||||
0.344486 | + | 0.938792i | \(0.388053\pi\) | |||||||
\(444\) | 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 | \(-0.564963\pi\) | ||||
−0.202673 | + | 0.979247i | \(0.564963\pi\) | |||||||
\(450\) | 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 | \(-0.344735\pi\) | ||||
0.468666 | + | 0.883375i | \(0.344735\pi\) | |||||||
\(462\) | 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 | \(-0.365210\pi\) | ||||
0.410914 | + | 0.911674i | \(0.365210\pi\) | |||||||
\(468\) | 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 | \(-0.270476\pi\) | ||||
0.660189 | + | 0.751100i | \(0.270476\pi\) | |||||||
\(480\) | 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 | \(-0.687942\pi\) | ||||
−0.556725 | + | 0.830697i | \(0.687942\pi\) | |||||||
\(492\) | 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 | \(-0.767375\pi\) | ||||
−0.744632 | + | 0.667476i | \(0.767375\pi\) | |||||||
\(504\) | 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 | \(-0.786787\pi\) | ||||
−0.783929 | + | 0.620851i | \(0.786787\pi\) | |||||||
\(510\) | 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 | \(-0.420133\pi\) | ||||
0.248286 | + | 0.968687i | \(0.420133\pi\) | |||||||
\(522\) | 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 | \(-0.185295\pi\) | ||||
0.835298 | + | 0.549798i | \(0.185295\pi\) | |||||||
\(558\) | 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 | \(-0.579610\pi\) | ||||
−0.247502 | + | 0.968887i | \(0.579610\pi\) | |||||||
\(564\) | 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 | \(-0.389109\pi\) | ||||
0.341371 | + | 0.939928i | \(0.389109\pi\) | |||||||
\(570\) | 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 | \(-0.448094\pi\) | ||||
0.162347 | + | 0.986734i | \(0.448094\pi\) | |||||||
\(588\) | 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 | \(-0.543221\pi\) | ||||
−0.135365 | + | 0.990796i | \(0.543221\pi\) | |||||||
\(594\) | 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 | \(-0.270451\pi\) | ||||
0.660248 | + | 0.751048i | \(0.270451\pi\) | |||||||
\(600\) | 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 | \(-0.736240\pi\) | ||||
−0.675889 | + | 0.737004i | \(0.736240\pi\) | |||||||
\(618\) | 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 | \(-0.626036\pi\) | ||||
−0.385688 | + | 0.922629i | \(0.626036\pi\) | |||||||
\(642\) | 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 | \(-0.668591\pi\) | ||||
−0.505228 | + | 0.862986i | \(0.668591\pi\) | |||||||
\(648\) | 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 | \(-0.534191\pi\) | ||||
−0.107209 | + | 0.994236i | \(0.534191\pi\) | |||||||
\(654\) | 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 | \(-0.204809\pi\) | ||||
0.800044 | + | 0.599941i | \(0.204809\pi\) | |||||||
\(660\) | 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 | \(-0.688095\pi\) | ||||
−0.557124 | + | 0.830429i | \(0.688095\pi\) | |||||||
\(678\) | 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 | \(-0.692920\pi\) | ||||
−0.569646 | + | 0.821890i | \(0.692920\pi\) | |||||||
\(684\) | 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 | \(-0.516835\pi\) | ||||
−0.0528649 | + | 0.998602i | \(0.516835\pi\) | |||||||
\(702\) | 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 | \(-0.537372\pi\) | ||||
−0.117137 | + | 0.993116i | \(0.537372\pi\) | |||||||
\(720\) | 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 | \(-0.502832\pi\) | ||||
−0.00889560 | + | 0.999960i | \(0.502832\pi\) | |||||||
\(744\) | 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 | \(-0.417143\pi\) | ||||
0.257374 | + | 0.966312i | \(0.417143\pi\) | |||||||
\(762\) | 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 | \(-0.241280\pi\) | ||||
0.726210 | + | 0.687473i | \(0.241280\pi\) | |||||||
\(774\) | 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 | \(-0.331050\pi\) | ||||
0.506200 | + | 0.862416i | \(0.331050\pi\) | |||||||
\(798\) | 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 | \(-0.770063\pi\) | ||||
−0.750241 | + | 0.661164i | \(0.770063\pi\) | |||||||
\(810\) | 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 | \(-0.649094\pi\) | ||||
−0.451452 | + | 0.892295i | \(0.649094\pi\) | |||||||
\(822\) | 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 | \(-0.233236\pi\) | ||||
0.743349 | + | 0.668903i | \(0.233236\pi\) | |||||||
\(828\) | 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 | \(-0.121017\pi\) | ||||
0.928595 | + | 0.371095i | \(0.121017\pi\) | |||||||
\(840\) | 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 | \(-0.569518\pi\) | ||||
−0.216665 | + | 0.976246i | \(0.569518\pi\) | |||||||
\(858\) | 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 | \(-0.654610\pi\) | ||||
−0.466846 | + | 0.884339i | \(0.654610\pi\) | |||||||
\(864\) | 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 | \(-0.561754\pi\) | ||||
−0.192792 | + | 0.981240i | \(0.561754\pi\) | |||||||
\(882\) | 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 | \(-0.237472\pi\) | ||||
0.734382 | + | 0.678737i | \(0.237472\pi\) | |||||||
\(888\) | 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 | \(-0.810941\pi\) | ||||
−0.828738 | + | 0.559637i | \(0.810941\pi\) | |||||||
\(912\) | 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 | \(-0.797474\pi\) | ||||
−0.804327 | + | 0.594186i | \(0.797474\pi\) | |||||||
\(930\) | 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 | \(-0.435005\pi\) | ||||
0.202771 | + | 0.979226i | \(0.435005\pi\) | |||||||
\(942\) | 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 | \(-0.289783\pi\) | ||||
0.613445 | + | 0.789738i | \(0.289783\pi\) | |||||||
\(948\) | 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 | \(-0.467570\pi\) | ||||
0.101704 | + | 0.994815i | \(0.467570\pi\) | |||||||
\(954\) | 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 | \(-0.379269\pi\) | ||||
0.370258 | + | 0.928929i | \(0.379269\pi\) | |||||||
\(972\) | 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 | \(-0.421317\pi\) | ||||
0.244682 | + | 0.969603i | \(0.421317\pi\) | |||||||
\(978\) | 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 | \(-0.744567\pi\) | ||||
−0.694935 | + | 0.719073i | \(0.744567\pi\) | |||||||
\(984\) | 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.j.1.11 | ✓ | 20 | |
3.2 | odd | 2 | 2151.2.a.k.1.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.11 | ✓ | 20 | 1.1 | even | 1 | trivial | |
2151.2.a.k.1.10 | yes | 20 | 3.2 | odd | 2 |