Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2576,2,Mod(1,2576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2576.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2576 = 2^{4} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2576.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: | \(20.5694635607\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 161) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2576.1 |
$q$-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 | 0 | ||||||||
\(3\) | −0.688892 | −0.397732 | −0.198866 | − | 0.980027i | \(-0.563726\pi\) | ||||
−0.198866 | + | 0.980027i | \(0.563726\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.688892 | 0.308082 | 0.154041 | − | 0.988064i | \(-0.450771\pi\) | ||||
0.154041 | + | 0.988064i | \(0.450771\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.52543 | −0.841809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.903212 | 0.272329 | 0.136164 | − | 0.990686i | \(-0.456522\pi\) | ||||
0.136164 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.622216 | 0.172572 | 0.0862858 | − | 0.996270i | \(-0.472500\pi\) | ||||
0.0862858 | + | 0.996270i | \(0.472500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.474572 | −0.122534 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.31111 | 0.317990 | 0.158995 | − | 0.987279i | \(-0.449175\pi\) | ||||
0.158995 | + | 0.987279i | \(0.449175\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.05086 | −1.61758 | −0.808789 | − | 0.588100i | \(-0.799876\pi\) | ||||
−0.808789 | + | 0.588100i | \(0.799876\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.688892 | −0.150329 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.52543 | −0.905086 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.80642 | 0.732547 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.52543 | 0.283265 | 0.141632 | − | 0.989919i | \(-0.454765\pi\) | ||||
0.141632 | + | 0.989919i | \(0.454765\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.54617 | 0.636911 | 0.318456 | − | 0.947938i | \(-0.396836\pi\) | ||||
0.318456 | + | 0.947938i | \(0.396836\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.622216 | −0.108314 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.688892 | 0.116444 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.42864 | 0.399266 | 0.199633 | − | 0.979871i | \(-0.436025\pi\) | ||||
0.199633 | + | 0.979871i | \(0.436025\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.428639 | −0.0686372 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.75557 | −0.742695 | −0.371348 | − | 0.928494i | \(-0.621104\pi\) | ||||
−0.371348 | + | 0.928494i | \(0.621104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.23506 | −0.950838 | −0.475419 | − | 0.879759i | \(-0.657704\pi\) | ||||
−0.475419 | + | 0.879759i | \(0.657704\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.73975 | −0.259346 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.73975 | −1.42069 | −0.710344 | − | 0.703855i | \(-0.751461\pi\) | ||||
−0.710344 | + | 0.703855i | \(0.751461\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.903212 | −0.126475 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.85728 | −0.941920 | −0.470960 | − | 0.882155i | \(-0.656092\pi\) | ||||
−0.470960 | + | 0.882155i | \(0.656092\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.622216 | 0.0838995 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.85728 | 0.643362 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.97481 | −1.29861 | −0.649305 | − | 0.760528i | \(-0.724940\pi\) | ||||
−0.649305 | + | 0.760528i | \(0.724940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.87310 | 1.00805 | 0.504024 | − | 0.863690i | \(-0.331852\pi\) | ||||
0.504024 | + | 0.863690i | \(0.331852\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.52543 | −0.318174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.428639 | 0.0531662 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.76049 | 0.703756 | 0.351878 | − | 0.936046i | \(-0.385543\pi\) | ||||
0.351878 | + | 0.936046i | \(0.385543\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.688892 | 0.0829329 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.61285 | 0.903479 | 0.451739 | − | 0.892150i | \(-0.350804\pi\) | ||||
0.451739 | + | 0.892150i | \(0.350804\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.86665 | −0.218474 | −0.109237 | − | 0.994016i | \(-0.534841\pi\) | ||||
−0.109237 | + | 0.994016i | \(0.534841\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.11753 | 0.359982 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.903212 | 0.102931 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.65878 | −0.861680 | −0.430840 | − | 0.902428i | \(-0.641783\pi\) | ||||
−0.430840 | + | 0.902428i | \(0.641783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.95407 | 0.550452 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.0923 | 1.21754 | 0.608771 | − | 0.793346i | \(-0.291663\pi\) | ||||
0.608771 | + | 0.793346i | \(0.291663\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.903212 | 0.0979671 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.05086 | −0.112663 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.98418 | −0.316322 | −0.158161 | − | 0.987413i | \(-0.550557\pi\) | ||||
−0.158161 | + | 0.987413i | \(0.550557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.622216 | 0.0652259 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.44293 | −0.253320 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.85728 | −0.498346 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.49532 | −0.253361 | −0.126680 | − | 0.991944i | \(-0.540432\pi\) | ||||
−0.126680 | + | 0.991944i | \(0.540432\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.28100 | −0.229249 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.4286 | −1.03769 | −0.518844 | − | 0.854869i | \(-0.673638\pi\) | ||||
−0.518844 | + | 0.854869i | \(0.673638\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.24443 | −0.910881 | −0.455440 | − | 0.890266i | \(-0.650518\pi\) | ||||
−0.455440 | + | 0.890266i | \(0.650518\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.474572 | −0.0463135 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.8479 | −1.72542 | −0.862711 | − | 0.505697i | \(-0.831235\pi\) | ||||
−0.862711 | + | 0.505697i | \(0.831235\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.9906 | 1.05271 | 0.526356 | − | 0.850264i | \(-0.323558\pi\) | ||||
0.526356 | + | 0.850264i | \(0.323558\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.67307 | −0.158801 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.3684 | −1.16352 | −0.581761 | − | 0.813360i | \(-0.697636\pi\) | ||||
−0.581761 | + | 0.813360i | \(0.697636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.688892 | −0.0642395 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.57136 | −0.145272 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.31111 | 0.120189 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1842 | −0.925837 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.27607 | 0.295394 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.56199 | −0.586922 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.42864 | −0.747921 | −0.373960 | − | 0.927445i | \(-0.622000\pi\) | ||||
−0.373960 | + | 0.927445i | \(0.622000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.29529 | 0.378179 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.2192 | 1.50445 | 0.752226 | − | 0.658905i | \(-0.228980\pi\) | ||||
0.752226 | + | 0.658905i | \(0.228980\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.05086 | −0.611387 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.62222 | 0.225684 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.18421 | −0.442917 | −0.221458 | − | 0.975170i | \(-0.571082\pi\) | ||||
−0.221458 | + | 0.975170i | \(0.571082\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.8731 | −1.00706 | −0.503532 | − | 0.863977i | \(-0.667966\pi\) | ||||
−0.503532 | + | 0.863977i | \(0.667966\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.70964 | 0.565053 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.561993 | 0.0469962 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.05086 | 0.0872688 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.688892 | −0.0568189 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6128 | −1.44290 | −0.721450 | − | 0.692466i | \(-0.756524\pi\) | ||||
−0.721450 | + | 0.692466i | \(0.756524\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.04149 | 0.654407 | 0.327203 | − | 0.944954i | \(-0.393894\pi\) | ||||
0.327203 | + | 0.944954i | \(0.393894\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.31111 | −0.267687 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.44293 | 0.196221 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.31111 | −0.743107 | −0.371554 | − | 0.928411i | \(-0.621175\pi\) | ||||
−0.371554 | + | 0.928411i | \(0.621175\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.72393 | 0.374632 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.53972 | −0.120600 | −0.0603000 | − | 0.998180i | \(-0.519206\pi\) | ||||
−0.0603000 | + | 0.998180i | \(0.519206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.428639 | −0.0333695 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.3017 | 1.10670 | 0.553351 | − | 0.832948i | \(-0.313349\pi\) | ||||
0.553351 | + | 0.832948i | \(0.313349\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6128 | −0.970219 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.8064 | 1.36169 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.56199 | −0.194785 | −0.0973923 | − | 0.995246i | \(-0.531050\pi\) | ||||
−0.0973923 | + | 0.995246i | \(0.531050\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.52543 | −0.342090 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.87157 | 0.516499 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.7748 | 1.47804 | 0.739018 | − | 0.673685i | \(-0.235290\pi\) | ||||
0.739018 | + | 0.673685i | \(0.235290\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.3620 | 0.918857 | 0.459429 | − | 0.888215i | \(-0.348054\pi\) | ||||
0.459429 | + | 0.888215i | \(0.348054\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.42372 | −0.400933 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.67307 | 0.123007 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.18421 | 0.0865979 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.80642 | 0.276877 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.72393 | 0.341811 | 0.170906 | − | 0.985287i | \(-0.445331\pi\) | ||||
0.170906 | + | 0.985287i | \(0.445331\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.714082 | −0.0514007 | −0.0257004 | − | 0.999670i | \(-0.508182\pi\) | ||||
−0.0257004 | + | 0.999670i | \(0.508182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.295286 | −0.0211459 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.1017 | −1.14720 | −0.573600 | − | 0.819136i | \(-0.694453\pi\) | ||||
−0.573600 | + | 0.819136i | \(0.694453\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.6128 | −1.39032 | −0.695159 | − | 0.718856i | \(-0.744666\pi\) | ||||
−0.695159 | + | 0.718856i | \(0.744666\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.96836 | −0.279906 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.52543 | 0.107064 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.27607 | −0.228811 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.52543 | 0.175529 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.36842 | −0.440513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.2859 | −1.46538 | −0.732692 | − | 0.680561i | \(-0.761736\pi\) | ||||
−0.732692 | + | 0.680561i | \(0.761736\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.24443 | −0.359343 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.29529 | −0.292936 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.54617 | 0.240730 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.28592 | 0.0868943 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.815792 | 0.0548761 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.8129 | −0.924979 | −0.462489 | − | 0.886625i | \(-0.653044\pi\) | ||||
−0.462489 | + | 0.886625i | \(0.653044\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.4286 | 0.761909 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.8573 | 1.11886 | 0.559428 | − | 0.828879i | \(-0.311021\pi\) | ||||
0.559428 | + | 0.828879i | \(0.311021\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.0257 | 1.52158 | 0.760789 | − | 0.648999i | \(-0.224812\pi\) | ||||
0.760789 | + | 0.648999i | \(0.224812\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.622216 | −0.0409388 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.61729 | −0.105952 | −0.0529762 | − | 0.998596i | \(-0.516871\pi\) | ||||
−0.0529762 | + | 0.998596i | \(0.516871\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.70964 | −0.437688 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.27607 | 0.342718 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.2859 | −1.37687 | −0.688436 | − | 0.725297i | \(-0.741702\pi\) | ||||
−0.688436 | + | 0.725297i | \(0.741702\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.8736 | −1.85991 | −0.929955 | − | 0.367673i | \(-0.880155\pi\) | ||||
−0.929955 | + | 0.367673i | \(0.880155\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.8321 | −0.951479 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.688892 | 0.0440117 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.38715 | −0.279148 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.64143 | −0.484256 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.41927 | −0.0895836 | −0.0447918 | − | 0.998996i | \(-0.514262\pi\) | ||||
−0.0447918 | + | 0.998996i | \(0.514262\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.903212 | −0.0567844 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.622216 | −0.0389647 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.8573 | 1.17628 | 0.588142 | − | 0.808757i | \(-0.299859\pi\) | ||||
0.588142 | + | 0.808757i | \(0.299859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.42864 | 0.150908 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.85236 | −0.238455 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.44293 | −0.150637 | −0.0753187 | − | 0.997160i | \(-0.523997\pi\) | ||||
−0.0753187 | + | 0.997160i | \(0.523997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.72393 | −0.290188 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.05578 | 0.125812 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.6637 | 1.01600 | 0.508002 | − | 0.861356i | \(-0.330384\pi\) | ||||
0.508002 | + | 0.861356i | \(0.330384\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.6385 | −1.98265 | −0.991324 | − | 0.131439i | \(-0.958040\pi\) | ||||
−0.991324 | + | 0.131439i | \(0.958040\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.428639 | −0.0259424 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.08742 | −0.246481 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.76986 | −0.406761 | −0.203381 | − | 0.979100i | \(-0.565193\pi\) | ||||
−0.203381 | + | 0.979100i | \(0.565193\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.95560 | −0.536158 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.1941 | 1.62226 | 0.811131 | − | 0.584865i | \(-0.198853\pi\) | ||||
0.811131 | + | 0.584865i | \(0.198853\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.2257 | 1.38062 | 0.690312 | − | 0.723512i | \(-0.257473\pi\) | ||||
0.690312 | + | 0.723512i | \(0.257473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.34614 | 0.198208 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.75557 | −0.280712 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2810 | −0.898882 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.71900 | 0.100770 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.25088 | 0.306760 | 0.153380 | − | 0.988167i | \(-0.450984\pi\) | ||||
0.153380 | + | 0.988167i | \(0.450984\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.87157 | −0.400078 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.43801 | 0.199493 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.622216 | −0.0359837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.23506 | −0.359383 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.18421 | 0.412722 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.42372 | 0.310561 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.9333 | 0.681071 | 0.340535 | − | 0.940232i | \(-0.389392\pi\) | ||||
0.340535 | + | 0.940232i | \(0.389392\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.36842 | 0.362287 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.0350337 | −0.00198658 | −0.000993289 | − | 1.00000i | \(-0.500316\pi\) | ||||
−0.000993289 | 1.00000i | \(0.500316\pi\) | ||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.3116 | −1.37417 | −0.687086 | − | 0.726576i | \(-0.741110\pi\) | ||||
−0.687086 | + | 0.726576i | \(0.741110\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.73975 | −0.0980237 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.84299 | 0.272009 | 0.136005 | − | 0.990708i | \(-0.456574\pi\) | ||||
0.136005 | + | 0.990708i | \(0.456574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.37778 | 0.0771411 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.2953 | 0.686256 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.24443 | −0.514374 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.81579 | −0.156192 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.57136 | −0.418697 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.73975 | −0.536970 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.5812 | 0.966350 | 0.483175 | − | 0.875524i | \(-0.339483\pi\) | ||||
0.483175 | + | 0.875524i | \(0.339483\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.13335 | −0.336106 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.96836 | 0.216815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.8666 | −0.973258 | −0.486629 | − | 0.873609i | \(-0.661774\pi\) | ||||
−0.486629 | + | 0.873609i | \(0.661774\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.52051 | 0.462770 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.20294 | 0.173449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.474572 | 0.0255501 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.1842 | 1.67406 | 0.837028 | − | 0.547160i | \(-0.184291\pi\) | ||||
0.837028 | + | 0.547160i | \(0.184291\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.9813 | 1.92603 | 0.963016 | − | 0.269443i | \(-0.0868394\pi\) | ||||
0.963016 | + | 0.269443i | \(0.0868394\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.36842 | 0.126417 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.2672 | 1.55773 | 0.778867 | − | 0.627189i | \(-0.215794\pi\) | ||||
0.778867 | + | 0.627189i | \(0.215794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.24443 | 0.278346 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.903212 | −0.0478030 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.2208 | −1.27832 | −0.639162 | − | 0.769072i | \(-0.720719\pi\) | ||||
−0.639162 | + | 0.769072i | \(0.720719\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.7146 | 1.61656 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.01582 | 0.368235 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.28592 | −0.0673080 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.6543 | −1.23475 | −0.617373 | − | 0.786670i | \(-0.711803\pi\) | ||||
−0.617373 | + | 0.786670i | \(0.711803\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.0098 | 0.625208 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.85728 | −0.356012 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.8385 | −1.70032 | −0.850158 | − | 0.526528i | \(-0.823493\pi\) | ||||
−0.850158 | + | 0.526528i | \(0.823493\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.52051 | 0.233438 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.949145 | 0.0488834 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.63651 | 0.238161 | 0.119081 | − | 0.992885i | \(-0.462005\pi\) | ||||
0.119081 | + | 0.992885i | \(0.462005\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.80642 | 0.297472 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.28592 | 0.0657074 | 0.0328537 | − | 0.999460i | \(-0.489540\pi\) | ||||
0.0328537 | + | 0.999460i | \(0.489540\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.622216 | 0.0317110 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.7462 | 0.800424 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.8256 | 1.25871 | 0.629355 | − | 0.777118i | \(-0.283319\pi\) | ||||
0.629355 | + | 0.777118i | \(0.283319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.31111 | −0.0663056 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.8622 | −0.598369 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.27607 | −0.265468 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.09234 | −0.255577 | −0.127789 | − | 0.991801i | \(-0.540788\pi\) | ||||
−0.127789 | + | 0.991801i | \(0.540788\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.85728 | 0.243168 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.6222 | 1.02982 | 0.514912 | − | 0.857243i | \(-0.327825\pi\) | ||||
0.514912 | + | 0.857243i | \(0.327825\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.20648 | 0.109913 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.41282 | 0.169584 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.19358 | 0.108732 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.3876 | 1.84870 | 0.924350 | − | 0.381547i | \(-0.124608\pi\) | ||||
0.924350 | + | 0.381547i | \(0.124608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.57136 | 0.176162 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.97481 | −0.490828 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.64143 | 0.375103 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.17929 | 0.400541 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.7654 | −1.01446 | −0.507228 | − | 0.861812i | \(-0.669330\pi\) | ||||
−0.507228 | + | 0.861812i | \(0.669330\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.59057 | 0.126257 | 0.0631284 | − | 0.998005i | \(-0.479892\pi\) | ||||
0.0631284 | + | 0.998005i | \(0.479892\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.5970 | 1.19595 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.93332 | −0.287808 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.87310 | 0.381006 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.387152 | −0.0186919 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.3461 | −0.546524 | −0.273262 | − | 0.961940i | \(-0.588103\pi\) | ||||
−0.273262 | + | 0.961940i | \(0.588103\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.0257 | 1.58711 | 0.793556 | − | 0.608497i | \(-0.208227\pi\) | ||||
0.793556 | + | 0.608497i | \(0.208227\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.723926 | −0.0347096 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.05086 | 0.337288 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.8321 | 0.707897 | 0.353949 | − | 0.935265i | \(-0.384839\pi\) | ||||
0.353949 | + | 0.935265i | \(0.384839\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.52543 | −0.120258 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.58073 | 0.122614 | 0.0613071 | − | 0.998119i | \(-0.480473\pi\) | ||||
0.0613071 | + | 0.998119i | \(0.480473\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.05578 | −0.0974532 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.1334 | 0.573888 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −42.1990 | −1.99149 | −0.995746 | − | 0.0921366i | \(-0.970630\pi\) | ||||
−0.995746 | + | 0.0921366i | \(0.970630\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.29529 | −0.202257 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.53972 | −0.260279 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.428639 | 0.0200949 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.07313 | −0.377645 | −0.188823 | − | 0.982011i | \(-0.560467\pi\) | ||||
−0.188823 | + | 0.982011i | \(0.560467\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.99063 | 0.232943 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.8064 | 0.736179 | 0.368089 | − | 0.929790i | \(-0.380012\pi\) | ||||
0.368089 | + | 0.929790i | \(0.380012\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.6035 | 0.957525 | 0.478762 | − | 0.877944i | \(-0.341086\pi\) | ||||
0.478762 | + | 0.877944i | \(0.341086\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.68292 | −0.0780433 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.0731 | 0.466129 | 0.233064 | − | 0.972461i | \(-0.425125\pi\) | ||||
0.233064 | + | 0.972461i | \(0.425125\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.76049 | 0.265995 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.41435 | 0.295558 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.63158 | −0.258940 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.9081 | 1.46405 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.3176 | 0.792917 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.2543 | 1.06251 | 0.531257 | − | 0.847210i | \(-0.321720\pi\) | ||||
0.531257 | + | 0.847210i | \(0.321720\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.51114 | 0.0689019 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.688892 | 0.0313457 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.71900 | −0.0780559 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.51114 | −0.430991 | −0.215495 | − | 0.976505i | \(-0.569137\pi\) | ||||
−0.215495 | + | 0.976505i | \(0.569137\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.06070 | 0.0479665 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.4701 | 0.923804 | 0.461902 | − | 0.886931i | \(-0.347167\pi\) | ||||
0.461902 | + | 0.886931i | \(0.347167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.00000 | 0.0900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.57136 | −0.0706274 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.61285 | 0.341483 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.3368 | −0.910399 | −0.455200 | − | 0.890389i | \(-0.650432\pi\) | ||||
−0.455200 | + | 0.890389i | \(0.650432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.85236 | −0.440171 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.27655 | −0.279858 | −0.139929 | − | 0.990162i | \(-0.544687\pi\) | ||||
−0.139929 | + | 0.990162i | \(0.544687\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.18421 | −0.319693 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.68889 | 0.385887 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.3684 | −1.61200 | −0.806001 | − | 0.591914i | \(-0.798372\pi\) | ||||
−0.806001 | + | 0.591914i | \(0.798372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.86665 | −0.0825756 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −26.8385 | −1.18495 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.36842 | −0.280626 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.79706 | −0.386894 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.76494 | 0.0774721 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.0988 | 1.18722 | 0.593610 | − | 0.804753i | \(-0.297702\pi\) | ||||
0.593610 | + | 0.804753i | \(0.297702\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.1240 | 0.923687 | 0.461844 | − | 0.886961i | \(-0.347188\pi\) | ||||
0.461844 | + | 0.886961i | \(0.347188\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.11753 | 0.136060 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.64941 | 0.202532 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.1907 | 1.09318 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.95899 | −0.128168 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.2953 | −0.531572 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.6227 | −0.587863 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.903212 | 0.0389041 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.61729 | 0.241506 | 0.120753 | − | 0.992683i | \(-0.461469\pi\) | ||||
0.120753 | + | 0.992683i | \(0.461469\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.51606 | −0.365459 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.57136 | 0.324321 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.7971 | 0.803704 | 0.401852 | − | 0.915705i | \(-0.368367\pi\) | ||||
0.401852 | + | 0.915705i | \(0.368367\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.8829 | −0.848583 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.7556 | −0.458203 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.65878 | −0.325684 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.15257 | −0.0489237 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.8385 | 1.22193 | 0.610964 | − | 0.791658i | \(-0.290782\pi\) | ||||
0.610964 | + | 0.791658i | \(0.290782\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.87955 | −0.164088 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.815792 | −0.0344428 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.2034 | 1.02005 | 0.510026 | − | 0.860159i | \(-0.329636\pi\) | ||||
0.510026 | + | 0.860159i | \(0.329636\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.52051 | −0.358460 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.95407 | 0.208051 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.69535 | 0.112995 | 0.0564974 | − | 0.998403i | \(-0.482007\pi\) | ||||
0.0564974 | + | 0.998403i | \(0.482007\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.6035 | −1.19702 | −0.598509 | − | 0.801116i | \(-0.704240\pi\) | ||||
−0.598509 | + | 0.801116i | \(0.704240\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.25428 | −0.135949 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.52543 | 0.188723 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.1655 | 1.96352 | 0.981762 | − | 0.190113i | \(-0.0608855\pi\) | ||||
0.981762 | + | 0.190113i | \(0.0608855\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.491925 | 0.0204437 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.0923 | 0.460188 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.19358 | −0.256512 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.08250 | −0.0447558 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.88247 | 0.284070 | 0.142035 | − | 0.989862i | \(-0.454635\pi\) | ||||
0.142035 | + | 0.989862i | \(0.454635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.0035 | −1.03025 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0923 | 0.456278 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.41927 | 0.304673 | 0.152336 | − | 0.988329i | \(-0.451320\pi\) | ||||
0.152336 | + | 0.988329i | \(0.451320\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.903212 | 0.0370281 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.5111 | 0.552974 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.71408 | 0.110894 | 0.0554472 | − | 0.998462i | \(-0.482342\pi\) | ||||
0.0554472 | + | 0.998462i | \(0.482342\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.4099 | 1.15886 | 0.579432 | − | 0.815021i | \(-0.303274\pi\) | ||||
0.579432 | + | 0.815021i | \(0.303274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.5477 | −0.592428 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.01582 | −0.285234 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.8508 | 0.927486 | 0.463743 | − | 0.885970i | \(-0.346506\pi\) | ||||
0.463743 | + | 0.885970i | \(0.346506\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.05086 | −0.0425828 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.06022 | −0.245170 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.3590 | −1.34736 | −0.673680 | − | 0.739024i | \(-0.735287\pi\) | ||||
−0.673680 | + | 0.739024i | \(0.735287\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.25686 | 0.0910055 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.7748 | 0.554552 | 0.277276 | − | 0.960790i | \(-0.410568\pi\) | ||||
0.277276 | + | 0.960790i | \(0.410568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.6035 | −1.14967 | −0.574835 | − | 0.818269i | \(-0.694934\pi\) | ||||
−0.574835 | + | 0.818269i | \(0.694934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.80642 | −0.152747 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.98418 | −0.119559 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.1066 | 0.724265 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.38715 | 0.175206 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.18421 | 0.126963 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.4143 | −1.21078 | −0.605388 | − | 0.795930i | \(-0.706982\pi\) | ||||
−0.605388 | + | 0.795930i | \(0.706982\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.6637 | 0.582830 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.80642 | −0.230421 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.622216 | 0.0246531 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.2257 | −0.760557 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.30465 | −0.209521 | −0.104761 | − | 0.994497i | \(-0.533408\pi\) | ||||
−0.104761 | + | 0.994497i | \(0.533408\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 50.5718 | 1.99436 | 0.997179 | − | 0.0750565i | \(-0.0239137\pi\) | ||||
0.997179 | + | 0.0750565i | \(0.0239137\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.95899 | 0.116510 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.3936 | 0.565871 | 0.282936 | − | 0.959139i | \(-0.408692\pi\) | ||||
0.282936 | + | 0.959139i | \(0.408692\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00937 | −0.353649 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.44293 | −0.0957460 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.98126 | 0.312331 | 0.156166 | − | 0.987731i | \(-0.450087\pi\) | ||||
0.156166 | + | 0.987731i | \(0.450087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.8622 | 0.463495 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.71408 | 0.183914 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.5111 | 0.682137 | 0.341069 | − | 0.940038i | \(-0.389211\pi\) | ||||
0.341069 | + | 0.940038i | \(0.389211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.7719 | −1.11910 | −0.559548 | − | 0.828798i | \(-0.689025\pi\) | ||||
−0.559548 | + | 0.828798i | \(0.689025\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.561993 | −0.0218260 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.85728 | −0.188357 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.52543 | −0.0590648 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.51558 | 0.367894 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.11108 | 0.274520 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.0651 | −1.50585 | −0.752925 | − | 0.658106i | \(-0.771358\pi\) | ||||
−0.752925 | + | 0.658106i | \(0.771358\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.2257 | −0.663017 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.3749 | −0.398739 | −0.199369 | − | 0.979924i | \(-0.563889\pi\) | ||||
−0.199369 | + | 0.979924i | \(0.563889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.49532 | −0.0957614 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.6128 | −0.445005 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.41927 | −0.0543069 | −0.0271535 | − | 0.999631i | \(-0.508644\pi\) | ||||
−0.0271535 | + | 0.999631i | \(0.508644\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.57136 | −0.136455 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.8622 | −0.605181 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.26671 | −0.162549 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0350 | 0.381751 | 0.190875 | − | 0.981614i | \(-0.438867\pi\) | ||||
0.190875 | + | 0.981614i | \(0.438867\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.28100 | −0.0866479 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.17929 | −0.310258 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.23506 | −0.236170 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.11414 | 0.0421407 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.8765 | 1.50611 | 0.753057 | − | 0.657955i | \(-0.228578\pi\) | ||||
0.753057 | + | 0.657955i | \(0.228578\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.1240 | −0.645843 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.62222 | 0.174083 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.4286 | −0.392209 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.3778 | 0.427302 | 0.213651 | − | 0.976910i | \(-0.431465\pi\) | ||||
0.213651 | + | 0.976910i | \(0.431465\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.3417 | 0.725370 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.54617 | −0.132805 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.387152 | 0.0144787 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.6637 | 0.547626 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.5783 | 1.36414 | 0.682070 | − | 0.731287i | \(-0.261080\pi\) | ||||
0.682070 | + | 0.731287i | \(0.261080\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.24443 | −0.344281 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.8908 | 0.739746 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.90321 | −0.256379 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.3872 | −0.607766 | −0.303883 | − | 0.952709i | \(-0.598283\pi\) | ||||
−0.303883 | + | 0.952709i | \(0.598283\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.64449 | −0.172018 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.17484 | −0.302357 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.9976 | 1.77283 | 0.886415 | − | 0.462891i | \(-0.153188\pi\) | ||||
0.886415 | + | 0.462891i | \(0.153188\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.474572 | −0.0175049 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.20294 | 0.191653 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.4514 | −0.825888 | −0.412944 | − | 0.910756i | \(-0.635499\pi\) | ||||
−0.412944 | + | 0.910756i | \(0.635499\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.02227 | 0.111026 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.5892 | 1.70919 | 0.854596 | − | 0.519294i | \(-0.173805\pi\) | ||||
0.854596 | + | 0.519294i | \(0.173805\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1334 | −0.444532 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −28.0129 | −1.02494 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.8479 | −0.652148 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.8113 | −1.48923 | −0.744614 | − | 0.667496i | \(-0.767366\pi\) | ||||
−0.744614 | + | 0.667496i | \(0.767366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.977725 | 0.0356303 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.53972 | 0.201611 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.30465 | −0.0474185 | −0.0237092 | − | 0.999719i | \(-0.507548\pi\) | ||||
−0.0237092 | + | 0.999719i | \(0.507548\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.622216 | 0.0225850 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.4795 | −0.633631 | −0.316816 | − | 0.948487i | \(-0.602614\pi\) | ||||
−0.316816 | + | 0.948487i | \(0.602614\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.9906 | 0.397888 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.28100 | −0.0824696 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.20648 | −0.224103 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.361963 | 0.0130527 | 0.00652636 | − | 0.999979i | \(-0.497923\pi\) | ||||
0.00652636 | + | 0.999979i | \(0.497923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.9906 | −0.467846 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.5970 | 0.525019 | 0.262509 | − | 0.964929i | \(-0.415450\pi\) | ||||
0.262509 | + | 0.964929i | \(0.415450\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0479 | −0.576459 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.67307 | −0.0600211 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.5308 | 1.20137 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.87601 | 0.246043 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.80642 | 0.207505 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.41435 | −0.228938 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.00048 | 0.249540 | 0.124770 | − | 0.992186i | \(-0.460181\pi\) | ||||
0.124770 | + | 0.992186i | \(0.460181\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.68292 | 0.0599134 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.3684 | −0.439770 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.89877 | 0.173960 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.25428 | 0.115417 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.5841 | 0.516596 | 0.258298 | − | 0.966065i | \(-0.416838\pi\) | ||||
0.258298 | + | 0.966065i | \(0.416838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.7699 | −0.451765 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.53633 | 0.266283 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.68598 | −0.0594969 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.688892 | −0.0242803 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.4795 | −0.404097 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.0602 | 0.845912 | 0.422956 | − | 0.906150i | \(-0.360992\pi\) | ||||
0.422956 | + | 0.906150i | \(0.360992\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.7081 | 0.692045 | 0.346023 | − | 0.938226i | \(-0.387532\pi\) | ||||
0.346023 | + | 0.938226i | \(0.387532\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.4844 | 0.788563 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.06070 | −0.0371547 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43.9625 | 1.53805 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.57136 | −0.0549078 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.7797 | −0.864818 | −0.432409 | − | 0.901678i | \(-0.642336\pi\) | ||||
−0.432409 | + | 0.901678i | \(0.642336\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.2578 | 1.82159 | 0.910796 | − | 0.412856i | \(-0.135469\pi\) | ||||
0.910796 | + | 0.412856i | \(0.135469\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.81579 | 0.0980333 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.8385 | −1.07236 | −0.536181 | − | 0.844103i | \(-0.680133\pi\) | ||||
−0.536181 | + | 0.844103i | \(0.680133\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.3497 | −0.915162 | −0.457581 | − | 0.889168i | \(-0.651284\pi\) | ||||
−0.457581 | + | 0.889168i | \(0.651284\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.66370 | 0.161782 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.31111 | 0.0454272 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.85236 | 0.340955 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.4982 | 0.466567 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.1432 | −0.764468 | −0.382234 | − | 0.924066i | \(-0.624845\pi\) | ||||
−0.382234 | + | 0.924066i | \(0.624845\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.6731 | −0.919761 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.7338 | −0.645225 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.68889 | −0.298907 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.1842 | −0.349934 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.0000 | −0.549119 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.42864 | −0.0832527 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.8479 | 1.09045 | 0.545226 | − | 0.838289i | \(-0.316444\pi\) | ||||
0.545226 | + | 0.838289i | \(0.316444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.2667 | 0.419513 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.5308 | −1.21371 | −0.606855 | − | 0.794813i | \(-0.707569\pi\) | ||||
−0.606855 | + | 0.794813i | \(0.707569\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.53326 | −0.0523143 | −0.0261571 | − | 0.999658i | \(-0.508327\pi\) | ||||
−0.0261571 | + | 0.999658i | \(0.508327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.27607 | 0.111648 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.4068 | −1.64779 | −0.823894 | − | 0.566744i | \(-0.808203\pi\) | ||||
−0.823894 | + | 0.566744i | \(0.808203\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.76494 | −0.0600096 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.5270 | 0.357514 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.91750 | −0.234660 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.58427 | 0.121448 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.30174 | 0.213282 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.56199 | −0.221836 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.6780 | −0.900852 | −0.450426 | − | 0.892814i | \(-0.648728\pi\) | ||||
−0.450426 | + | 0.892814i | \(0.648728\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.61729 | −0.122008 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.3749 | 0.551683 | 0.275842 | − | 0.961203i | \(-0.411043\pi\) | ||||
0.275842 | + | 0.961203i | \(0.411043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0415 | 0.539839 | 0.269920 | − | 0.962883i | \(-0.413003\pi\) | ||||
0.269920 | + | 0.962883i | \(0.413003\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.73377 | 0.159124 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.8637 | −0.969149 | −0.484575 | − | 0.874750i | \(-0.661026\pi\) | ||||
−0.484575 | + | 0.874750i | \(0.661026\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.42864 | −0.282687 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.47457 | 0.149904 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 68.6735 | 2.29807 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.6227 | 0.455356 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.428639 | 0.0143119 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.40943 | 0.180414 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.99063 | −0.299521 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.29529 | 0.142938 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.51606 | 0.283083 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.387152 | 0.0128552 | 0.00642759 | − | 0.999979i | \(-0.497954\pi\) | ||||
0.00642759 | + | 0.999979i | \(0.497954\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.3368 | 0.873536 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.3921 | −0.775014 | −0.387507 | − | 0.921867i | \(-0.626664\pi\) | ||||
−0.387507 | + | 0.921867i | \(0.626664\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.0187 | 0.331572 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.73636 | −0.123520 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.2192 | 0.568629 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.4839 | −0.642716 | −0.321358 | − | 0.946958i | \(-0.604139\pi\) | ||||
−0.321358 | + | 0.946958i | \(0.604139\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.22077 | −0.270884 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.73683 | 0.155915 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.9906 | −0.361370 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.3461 | 0.766788 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.6548 | −1.46508 | −0.732538 | − | 0.680726i | \(-0.761665\pi\) | ||||
−0.732538 | + | 0.680726i | \(0.761665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.05086 | −0.231082 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.0241344 | 0.000790126 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.815792 | 0.0266792 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.5368 | −0.932257 | −0.466128 | − | 0.884717i | \(-0.654352\pi\) | ||||
−0.466128 | + | 0.884717i | \(0.654352\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.7481 | 0.546552 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.2607 | −1.21467 | −0.607333 | − | 0.794448i | \(-0.707760\pi\) | ||||
−0.607333 | + | 0.794448i | \(0.707760\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.75557 | 0.154863 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.62222 | 0.0853007 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.9906 | 0.682104 | 0.341052 | − | 0.940044i | \(-0.389217\pi\) | ||||
0.341052 | + | 0.940044i | \(0.389217\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.16146 | −0.0377025 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.33630 | −0.108187 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.8859 | −0.482200 | −0.241100 | − | 0.970500i | \(-0.577508\pi\) | ||||
−0.241100 | + | 0.970500i | \(0.577508\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.25428 | 0.105306 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.949145 | −0.0306815 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.18421 | −0.167407 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.4247 | −0.594344 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.0736 | 1.45248 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.491925 | −0.0158356 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.5397 | −0.949933 | −0.474967 | − | 0.880004i | \(-0.657540\pi\) | ||||
−0.474967 | + | 0.880004i | \(0.657540\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.36842 | 0.204583 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.5491 | −0.659452 | −0.329726 | − | 0.944077i | \(-0.606956\pi\) | ||||
−0.329726 | + | 0.944077i | \(0.606956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.8731 | −0.380634 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.93978 | 0.0621226 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.2128 | 1.19054 | 0.595271 | − | 0.803525i | \(-0.297045\pi\) | ||||
0.595271 | + | 0.803525i | \(0.297045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.69535 | −0.0861436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.7560 | −0.886182 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.2859 | 1.06166 | 0.530828 | − | 0.847480i | \(-0.321881\pi\) | ||||
0.530828 | + | 0.847480i | \(0.321881\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.0923 | −0.353431 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.70964 | 0.213570 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.23506 | 0.198263 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7368 | −0.404599 | −0.202299 | − | 0.979324i | \(-0.564841\pi\) | ||||
−0.202299 | + | 0.979324i | \(0.564841\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.1116 | −0.384349 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.5111 | −0.428332 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0509 | −0.413325 | −0.206662 | − | 0.978412i | \(-0.566260\pi\) | ||||
−0.206662 | + | 0.978412i | \(0.566260\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.24443 | 0.292481 |
(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 | 2576.2.a.v.1.2 | 3 | ||
4.3 | odd | 2 | 161.2.a.c.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 1449.2.a.m.1.1 | 3 | |||
20.19 | odd | 2 | 4025.2.a.j.1.1 | 3 | |||
28.27 | even | 2 | 1127.2.a.f.1.3 | 3 | |||
92.91 | even | 2 | 3703.2.a.c.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
161.2.a.c.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
1127.2.a.f.1.3 | 3 | 28.27 | even | 2 | |||
1449.2.a.m.1.1 | 3 | 12.11 | even | 2 | |||
2576.2.a.v.1.2 | 3 | 1.1 | even | 1 | trivial | ||
3703.2.a.c.1.3 | 3 | 92.91 | even | 2 | |||
4025.2.a.j.1.1 | 3 | 20.19 | odd | 2 |