Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1287,2,Mod(1,1287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1287.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1287 = 3^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1287.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: | \(10.2767467401\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.194616205.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 10x^{4} - 2x^{3} + 24x^{2} + 7x - 12 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.23127\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1287.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23127 | −0.870640 | −0.435320 | − | 0.900276i | \(-0.643365\pi\) | ||||
−0.435320 | + | 0.900276i | \(0.643365\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.483971 | −0.241985 | ||||||||
\(5\) | −1.04428 | −0.467014 | −0.233507 | − | 0.972355i | \(-0.575020\pi\) | ||||
−0.233507 | + | 0.972355i | \(0.575020\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.82820 | 1.82489 | 0.912444 | − | 0.409202i | \(-0.134193\pi\) | ||||
0.912444 | + | 0.409202i | \(0.134193\pi\) | |||||||
\(8\) | 3.05844 | 1.08132 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.28579 | 0.406601 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −5.94482 | −1.58882 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.79783 | −0.699458 | ||||||||
\(17\) | 2.46254 | 0.597254 | 0.298627 | − | 0.954370i | \(-0.403471\pi\) | ||||
0.298627 | + | 0.954370i | \(0.403471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.68717 | −0.616479 | −0.308239 | − | 0.951309i | \(-0.599740\pi\) | ||||
−0.308239 | + | 0.951309i | \(0.599740\pi\) | |||||||
\(20\) | 0.505399 | 0.113011 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.23127 | −0.262508 | ||||||||
\(23\) | 6.84042 | 1.42633 | 0.713163 | − | 0.700999i | \(-0.247262\pi\) | ||||
0.713163 | + | 0.700999i | \(0.247262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.90949 | −0.781898 | ||||||||
\(26\) | −1.23127 | −0.241472 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.33671 | −0.441596 | ||||||||
\(29\) | −4.25373 | −0.789897 | −0.394949 | − | 0.918703i | \(-0.629238\pi\) | ||||
−0.394949 | + | 0.918703i | \(0.629238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.87743 | 1.77404 | 0.887019 | − | 0.461732i | \(-0.152772\pi\) | ||||
0.887019 | + | 0.461732i | \(0.152772\pi\) | |||||||
\(32\) | −2.67200 | −0.472347 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.03206 | −0.519994 | ||||||||
\(35\) | −5.04197 | −0.852248 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.450326 | 0.0740331 | 0.0370166 | − | 0.999315i | \(-0.488215\pi\) | ||||
0.0370166 | + | 0.999315i | \(0.488215\pi\) | |||||||
\(38\) | 3.30863 | 0.536731 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.19386 | −0.504993 | ||||||||
\(41\) | 0.139742 | 0.0218241 | 0.0109120 | − | 0.999940i | \(-0.496527\pi\) | ||||
0.0109120 | + | 0.999940i | \(0.496527\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8332 | −1.65204 | −0.826020 | − | 0.563640i | \(-0.809400\pi\) | ||||
−0.826020 | + | 0.563640i | \(0.809400\pi\) | |||||||
\(44\) | −0.483971 | −0.0729613 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.42241 | −1.24182 | ||||||||
\(47\) | −3.74833 | −0.546750 | −0.273375 | − | 0.961908i | \(-0.588140\pi\) | ||||
−0.273375 | + | 0.961908i | \(0.588140\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.3115 | 2.33022 | ||||||||
\(50\) | 4.81364 | 0.680752 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.483971 | −0.0671147 | ||||||||
\(53\) | −13.3115 | −1.82848 | −0.914238 | − | 0.405177i | \(-0.867210\pi\) | ||||
−0.914238 | + | 0.405177i | \(0.867210\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.04428 | −0.140810 | ||||||||
\(56\) | 14.7668 | 1.97329 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.23749 | 0.687717 | ||||||||
\(59\) | 6.19528 | 0.806556 | 0.403278 | − | 0.915077i | \(-0.367871\pi\) | ||||
0.403278 | + | 0.915077i | \(0.367871\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.87974 | 0.752823 | 0.376412 | − | 0.926453i | \(-0.377158\pi\) | ||||
0.376412 | + | 0.926453i | \(0.377158\pi\) | |||||||
\(62\) | −12.1618 | −1.54455 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.88561 | 1.11070 | ||||||||
\(65\) | −1.04428 | −0.129526 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.01222 | 0.734509 | 0.367255 | − | 0.930120i | \(-0.380298\pi\) | ||||
0.367255 | + | 0.930120i | \(0.380298\pi\) | |||||||
\(68\) | −1.19180 | −0.144527 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.20803 | 0.742002 | ||||||||
\(71\) | 8.95234 | 1.06245 | 0.531224 | − | 0.847231i | \(-0.321732\pi\) | ||||
0.531224 | + | 0.847231i | \(0.321732\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.06116 | 0.826446 | 0.413223 | − | 0.910630i | \(-0.364403\pi\) | ||||
0.413223 | + | 0.910630i | \(0.364403\pi\) | |||||||
\(74\) | −0.554473 | −0.0644562 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.30051 | 0.149179 | ||||||||
\(77\) | 4.82820 | 0.550224 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.25373 | 0.703599 | 0.351800 | − | 0.936075i | \(-0.385570\pi\) | ||||
0.351800 | + | 0.936075i | \(0.385570\pi\) | |||||||
\(80\) | 2.92171 | 0.326657 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.172061 | −0.0190009 | ||||||||
\(83\) | 11.6647 | 1.28037 | 0.640185 | − | 0.768220i | \(-0.278858\pi\) | ||||
0.640185 | + | 0.768220i | \(0.278858\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.57157 | −0.278926 | ||||||||
\(86\) | 13.3386 | 1.43833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.05844 | 0.326031 | ||||||||
\(89\) | −1.16116 | −0.123083 | −0.0615413 | − | 0.998105i | \(-0.519602\pi\) | ||||
−0.0615413 | + | 0.998105i | \(0.519602\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.82820 | 0.506133 | ||||||||
\(92\) | −3.31056 | −0.345150 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.61521 | 0.476023 | ||||||||
\(95\) | 2.80614 | 0.287904 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.16322 | −0.727314 | −0.363657 | − | 0.931533i | \(-0.618472\pi\) | ||||
−0.363657 | + | 0.931533i | \(0.618472\pi\) | |||||||
\(98\) | −20.0839 | −2.02878 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.89208 | 0.189208 | ||||||||
\(101\) | 6.32776 | 0.629635 | 0.314818 | − | 0.949152i | \(-0.398057\pi\) | ||||
0.314818 | + | 0.949152i | \(0.398057\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.6750 | 1.84010 | 0.920051 | − | 0.391799i | \(-0.128147\pi\) | ||||
0.920051 | + | 0.391799i | \(0.128147\pi\) | |||||||
\(104\) | 3.05844 | 0.299905 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.3901 | 1.59195 | ||||||||
\(107\) | 6.67136 | 0.644944 | 0.322472 | − | 0.946579i | \(-0.395486\pi\) | ||||
0.322472 | + | 0.946579i | \(0.395486\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.31318 | −0.221562 | −0.110781 | − | 0.993845i | \(-0.535335\pi\) | ||||
−0.110781 | + | 0.993845i | \(0.535335\pi\) | |||||||
\(110\) | 1.28579 | 0.122595 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13.5085 | −1.27643 | ||||||||
\(113\) | −3.80601 | −0.358040 | −0.179020 | − | 0.983845i | \(-0.557293\pi\) | ||||
−0.179020 | + | 0.983845i | \(0.557293\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.14328 | −0.666114 | ||||||||
\(116\) | 2.05868 | 0.191144 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.62807 | −0.702220 | ||||||||
\(119\) | 11.8896 | 1.08992 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −7.23955 | −0.655438 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.78039 | −0.429291 | ||||||||
\(125\) | 9.30396 | 0.832171 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.67136 | 0.237045 | 0.118522 | − | 0.992951i | \(-0.462184\pi\) | ||||
0.118522 | + | 0.992951i | \(0.462184\pi\) | |||||||
\(128\) | −5.59661 | −0.494675 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.28579 | 0.112771 | ||||||||
\(131\) | 9.34193 | 0.816209 | 0.408104 | − | 0.912935i | \(-0.366190\pi\) | ||||
0.408104 | + | 0.912935i | \(0.366190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.9742 | −1.12500 | ||||||||
\(134\) | −7.40267 | −0.639493 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.53154 | 0.645825 | ||||||||
\(137\) | −13.5034 | −1.15368 | −0.576838 | − | 0.816858i | \(-0.695714\pi\) | ||||
−0.576838 | + | 0.816858i | \(0.695714\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6987 | −1.50119 | −0.750593 | − | 0.660765i | \(-0.770232\pi\) | ||||
−0.750593 | + | 0.660765i | \(0.770232\pi\) | |||||||
\(140\) | 2.44017 | 0.206232 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.0228 | −0.925010 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.44206 | 0.368893 | ||||||||
\(146\) | −8.69420 | −0.719538 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.217945 | −0.0179149 | ||||||||
\(149\) | −5.51666 | −0.451942 | −0.225971 | − | 0.974134i | \(-0.572555\pi\) | ||||
−0.225971 | + | 0.974134i | \(0.572555\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.01080 | −0.407773 | −0.203886 | − | 0.978995i | \(-0.565357\pi\) | ||||
−0.203886 | + | 0.978995i | \(0.565357\pi\) | |||||||
\(152\) | −8.21855 | −0.666612 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.94482 | −0.479048 | ||||||||
\(155\) | −10.3148 | −0.828501 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.70901 | −0.375820 | −0.187910 | − | 0.982186i | \(-0.560171\pi\) | ||||
−0.187910 | + | 0.982186i | \(0.560171\pi\) | |||||||
\(158\) | −7.70004 | −0.612582 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.79030 | 0.220593 | ||||||||
\(161\) | 33.0269 | 2.60288 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.25284 | −0.724739 | −0.362369 | − | 0.932035i | \(-0.618032\pi\) | ||||
−0.362369 | + | 0.932035i | \(0.618032\pi\) | |||||||
\(164\) | −0.0676311 | −0.00528111 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.3625 | −1.11474 | ||||||||
\(167\) | 20.5061 | 1.58681 | 0.793407 | − | 0.608692i | \(-0.208305\pi\) | ||||
0.793407 | + | 0.608692i | \(0.208305\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 3.16630 | 0.242844 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.24293 | 0.399770 | ||||||||
\(173\) | 14.0548 | 1.06857 | 0.534284 | − | 0.845305i | \(-0.320581\pi\) | ||||
0.534284 | + | 0.845305i | \(0.320581\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.8758 | −1.42688 | ||||||||
\(176\) | −2.79783 | −0.210894 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.42970 | 0.107161 | ||||||||
\(179\) | −14.7568 | −1.10298 | −0.551488 | − | 0.834183i | \(-0.685940\pi\) | ||||
−0.551488 | + | 0.834183i | \(0.685940\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.23728 | 0.240625 | 0.120313 | − | 0.992736i | \(-0.461610\pi\) | ||||
0.120313 | + | 0.992736i | \(0.461610\pi\) | |||||||
\(182\) | −5.94482 | −0.440660 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 20.9210 | 1.54232 | ||||||||
\(185\) | −0.470264 | −0.0345745 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.46254 | 0.180079 | ||||||||
\(188\) | 1.81408 | 0.132306 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.45512 | −0.250661 | ||||||||
\(191\) | 9.09575 | 0.658146 | 0.329073 | − | 0.944305i | \(-0.393264\pi\) | ||||
0.329073 | + | 0.944305i | \(0.393264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.87478 | 0.566839 | 0.283420 | − | 0.958996i | \(-0.408531\pi\) | ||||
0.283420 | + | 0.958996i | \(0.408531\pi\) | |||||||
\(194\) | 8.81986 | 0.633229 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.89429 | −0.563878 | ||||||||
\(197\) | −9.71126 | −0.691898 | −0.345949 | − | 0.938253i | \(-0.612443\pi\) | ||||
−0.345949 | + | 0.938253i | \(0.612443\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1240 | 0.930332 | 0.465166 | − | 0.885223i | \(-0.345995\pi\) | ||||
0.465166 | + | 0.885223i | \(0.345995\pi\) | |||||||
\(200\) | −11.9569 | −0.845484 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.79119 | −0.548186 | ||||||||
\(203\) | −20.5378 | −1.44147 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.145929 | −0.0101921 | ||||||||
\(206\) | −22.9940 | −1.60207 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.79783 | −0.193995 | ||||||||
\(209\) | −2.68717 | −0.185875 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.85926 | 0.541054 | 0.270527 | − | 0.962712i | \(-0.412802\pi\) | ||||
0.270527 | + | 0.962712i | \(0.412802\pi\) | |||||||
\(212\) | 6.44238 | 0.442465 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.21425 | −0.561515 | ||||||||
\(215\) | 11.3128 | 0.771526 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 47.6902 | 3.23742 | ||||||||
\(218\) | 2.84815 | 0.192901 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.505399 | 0.0340740 | ||||||||
\(221\) | 2.46254 | 0.165649 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.07805 | −0.473981 | −0.236991 | − | 0.971512i | \(-0.576161\pi\) | ||||
−0.236991 | + | 0.971512i | \(0.576161\pi\) | |||||||
\(224\) | −12.9009 | −0.861979 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.68624 | 0.311724 | ||||||||
\(227\) | −20.6501 | −1.37059 | −0.685296 | − | 0.728264i | \(-0.740327\pi\) | ||||
−0.685296 | + | 0.728264i | \(0.740327\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.44402 | −0.0954238 | −0.0477119 | − | 0.998861i | \(-0.515193\pi\) | ||||
−0.0477119 | + | 0.998861i | \(0.515193\pi\) | |||||||
\(230\) | 8.79531 | 0.579946 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.0098 | −0.854134 | ||||||||
\(233\) | 0.537803 | 0.0352326 | 0.0176163 | − | 0.999845i | \(-0.494392\pi\) | ||||
0.0176163 | + | 0.999845i | \(0.494392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.91429 | 0.255340 | ||||||||
\(236\) | −2.99833 | −0.195175 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.6394 | −0.948930 | ||||||||
\(239\) | 5.48993 | 0.355114 | 0.177557 | − | 0.984110i | \(-0.443181\pi\) | ||||
0.177557 | + | 0.984110i | \(0.443181\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6463 | −1.26553 | −0.632765 | − | 0.774344i | \(-0.718080\pi\) | ||||
−0.632765 | + | 0.774344i | \(0.718080\pi\) | |||||||
\(242\) | −1.23127 | −0.0791491 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.84562 | −0.182172 | ||||||||
\(245\) | −17.0337 | −1.08824 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.68717 | −0.170980 | ||||||||
\(248\) | 30.2095 | 1.91831 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.4557 | −0.724522 | ||||||||
\(251\) | 7.10538 | 0.448487 | 0.224244 | − | 0.974533i | \(-0.428009\pi\) | ||||
0.224244 | + | 0.974533i | \(0.428009\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.84042 | 0.430053 | ||||||||
\(254\) | −3.28917 | −0.206381 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.8803 | −0.680017 | ||||||||
\(257\) | −4.33990 | −0.270716 | −0.135358 | − | 0.990797i | \(-0.543218\pi\) | ||||
−0.135358 | + | 0.990797i | \(0.543218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.17426 | 0.135102 | ||||||||
\(260\) | 0.505399 | 0.0313435 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.5025 | −0.710624 | ||||||||
\(263\) | 5.36105 | 0.330576 | 0.165288 | − | 0.986245i | \(-0.447145\pi\) | ||||
0.165288 | + | 0.986245i | \(0.447145\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.9009 | 0.853924 | ||||||||
\(266\) | 15.9747 | 0.979474 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.90974 | −0.177740 | ||||||||
\(269\) | −0.305701 | −0.0186389 | −0.00931946 | − | 0.999957i | \(-0.502967\pi\) | ||||
−0.00931946 | + | 0.999957i | \(0.502967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.89804 | 0.419026 | 0.209513 | − | 0.977806i | \(-0.432812\pi\) | ||||
0.209513 | + | 0.977806i | \(0.432812\pi\) | |||||||
\(272\) | −6.88978 | −0.417754 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.6264 | 1.00444 | ||||||||
\(275\) | −3.90949 | −0.235751 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.6001 | 1.89867 | 0.949334 | − | 0.314269i | \(-0.101759\pi\) | ||||
0.949334 | + | 0.314269i | \(0.101759\pi\) | |||||||
\(278\) | 21.7919 | 1.30699 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −15.4206 | −0.921555 | ||||||||
\(281\) | −26.8160 | −1.59971 | −0.799855 | − | 0.600193i | \(-0.795090\pi\) | ||||
−0.799855 | + | 0.600193i | \(0.795090\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.8032 | −1.65273 | −0.826363 | − | 0.563138i | \(-0.809594\pi\) | ||||
−0.826363 | + | 0.563138i | \(0.809594\pi\) | |||||||
\(284\) | −4.33267 | −0.257097 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.23127 | −0.0728066 | ||||||||
\(287\) | 0.674703 | 0.0398265 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.9359 | −0.643287 | ||||||||
\(290\) | −5.46939 | −0.321173 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.41740 | −0.199988 | ||||||||
\(293\) | 2.83370 | 0.165546 | 0.0827731 | − | 0.996568i | \(-0.473622\pi\) | ||||
0.0827731 | + | 0.996568i | \(0.473622\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.46957 | −0.376673 | ||||||||
\(296\) | 1.37730 | 0.0800537 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.79250 | 0.393479 | ||||||||
\(299\) | 6.84042 | 0.395591 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −52.3046 | −3.01479 | ||||||||
\(302\) | 6.16965 | 0.355024 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.51824 | 0.431201 | ||||||||
\(305\) | −6.14006 | −0.351579 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.417630 | −0.0238354 | −0.0119177 | − | 0.999929i | \(-0.503794\pi\) | ||||
−0.0119177 | + | 0.999929i | \(0.503794\pi\) | |||||||
\(308\) | −2.33671 | −0.133146 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.7003 | 0.721327 | ||||||||
\(311\) | −14.5524 | −0.825190 | −0.412595 | − | 0.910915i | \(-0.635377\pi\) | ||||
−0.412595 | + | 0.910915i | \(0.635377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.8588 | 0.613778 | 0.306889 | − | 0.951745i | \(-0.400712\pi\) | ||||
0.306889 | + | 0.951745i | \(0.400712\pi\) | |||||||
\(314\) | 5.79807 | 0.327204 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.02662 | −0.170261 | ||||||||
\(317\) | 30.8428 | 1.73230 | 0.866151 | − | 0.499782i | \(-0.166586\pi\) | ||||
0.866151 | + | 0.499782i | \(0.166586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.25373 | −0.238163 | ||||||||
\(320\) | −9.27903 | −0.518713 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −40.6651 | −2.26618 | ||||||||
\(323\) | −6.61727 | −0.368195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.90949 | −0.216859 | ||||||||
\(326\) | 11.3928 | 0.630987 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.427393 | 0.0235989 | ||||||||
\(329\) | −18.0977 | −0.997757 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4885 | 0.796359 | 0.398179 | − | 0.917308i | \(-0.369642\pi\) | ||||
0.398179 | + | 0.917308i | \(0.369642\pi\) | |||||||
\(332\) | −5.64539 | −0.309831 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.2486 | −1.38154 | ||||||||
\(335\) | −6.27841 | −0.343026 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.3856 | 0.729159 | 0.364579 | − | 0.931172i | \(-0.381213\pi\) | ||||
0.364579 | + | 0.931172i | \(0.381213\pi\) | |||||||
\(338\) | −1.23127 | −0.0669723 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.24457 | 0.0674961 | ||||||||
\(341\) | 9.87743 | 0.534893 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 44.9578 | 2.42749 | ||||||||
\(344\) | −33.1326 | −1.78639 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.3053 | −0.930339 | ||||||||
\(347\) | 12.0449 | 0.646605 | 0.323302 | − | 0.946296i | \(-0.395207\pi\) | ||||
0.323302 | + | 0.946296i | \(0.395207\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.9479 | −0.693086 | −0.346543 | − | 0.938034i | \(-0.612645\pi\) | ||||
−0.346543 | + | 0.938034i | \(0.612645\pi\) | |||||||
\(350\) | 23.2412 | 1.24230 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.67200 | −0.142418 | ||||||||
\(353\) | −32.4161 | −1.72533 | −0.862666 | − | 0.505773i | \(-0.831207\pi\) | ||||
−0.862666 | + | 0.505773i | \(0.831207\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.34871 | −0.496178 | ||||||||
\(356\) | 0.561967 | 0.0297842 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.1697 | 0.960296 | ||||||||
\(359\) | 12.0843 | 0.637787 | 0.318893 | − | 0.947791i | \(-0.396689\pi\) | ||||
0.318893 | + | 0.947791i | \(0.396689\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.7791 | −0.619954 | ||||||||
\(362\) | −3.98597 | −0.209498 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.33671 | −0.122477 | ||||||||
\(365\) | −7.37380 | −0.385962 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.69698 | −0.401779 | −0.200890 | − | 0.979614i | \(-0.564383\pi\) | ||||
−0.200890 | + | 0.979614i | \(0.564383\pi\) | |||||||
\(368\) | −19.1383 | −0.997654 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.579023 | 0.0301020 | ||||||||
\(371\) | −64.2706 | −3.33676 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.53373 | 0.338304 | 0.169152 | − | 0.985590i | \(-0.445897\pi\) | ||||
0.169152 | + | 0.985590i | \(0.445897\pi\) | |||||||
\(374\) | −3.03206 | −0.156784 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.4640 | −0.591213 | ||||||||
\(377\) | −4.25373 | −0.219078 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.7605 | −0.912298 | −0.456149 | − | 0.889903i | \(-0.650772\pi\) | ||||
−0.456149 | + | 0.889903i | \(0.650772\pi\) | |||||||
\(380\) | −1.35809 | −0.0696686 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.1993 | −0.573008 | ||||||||
\(383\) | −27.8411 | −1.42261 | −0.711307 | − | 0.702881i | \(-0.751896\pi\) | ||||
−0.711307 | + | 0.702881i | \(0.751896\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.04197 | −0.256963 | ||||||||
\(386\) | −9.69599 | −0.493513 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.46679 | 0.175999 | ||||||||
\(389\) | 18.0202 | 0.913658 | 0.456829 | − | 0.889555i | \(-0.348985\pi\) | ||||
0.456829 | + | 0.889555i | \(0.348985\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.8448 | 0.851879 | ||||||||
\(392\) | 49.8878 | 2.51971 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.9572 | 0.602395 | ||||||||
\(395\) | −6.53061 | −0.328591 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.40061 | −0.170672 | −0.0853360 | − | 0.996352i | \(-0.527196\pi\) | ||||
−0.0853360 | + | 0.996352i | \(0.527196\pi\) | |||||||
\(398\) | −16.1592 | −0.809985 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.9381 | 0.546904 | ||||||||
\(401\) | 12.4817 | 0.623306 | 0.311653 | − | 0.950196i | \(-0.399117\pi\) | ||||
0.311653 | + | 0.950196i | \(0.399117\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.87743 | 0.492030 | ||||||||
\(404\) | −3.06245 | −0.152363 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 25.2877 | 1.25501 | ||||||||
\(407\) | 0.450326 | 0.0223218 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.2077 | −1.54312 | −0.771561 | − | 0.636155i | \(-0.780524\pi\) | ||||
−0.771561 | + | 0.636155i | \(0.780524\pi\) | |||||||
\(410\) | 0.179679 | 0.00887370 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.03815 | −0.445278 | ||||||||
\(413\) | 29.9120 | 1.47187 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.1812 | −0.597951 | ||||||||
\(416\) | −2.67200 | −0.131005 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.30863 | 0.161831 | ||||||||
\(419\) | 22.6750 | 1.10775 | 0.553873 | − | 0.832601i | \(-0.313149\pi\) | ||||
0.553873 | + | 0.832601i | \(0.313149\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.9661 | −1.41172 | −0.705860 | − | 0.708351i | \(-0.749439\pi\) | ||||
−0.705860 | + | 0.708351i | \(0.749439\pi\) | |||||||
\(422\) | −9.67688 | −0.471063 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −40.7125 | −1.97717 | ||||||||
\(425\) | −9.62728 | −0.466992 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.3885 | 1.37382 | ||||||||
\(428\) | −3.22874 | −0.156067 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.9291 | −0.671722 | ||||||||
\(431\) | −12.8485 | −0.618891 | −0.309446 | − | 0.950917i | \(-0.600143\pi\) | ||||
−0.309446 | + | 0.950917i | \(0.600143\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.4007 | 0.595942 | 0.297971 | − | 0.954575i | \(-0.403690\pi\) | ||||
0.297971 | + | 0.954575i | \(0.403690\pi\) | |||||||
\(434\) | −58.7196 | −2.81863 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.11951 | 0.0536148 | ||||||||
\(437\) | −18.3814 | −0.879299 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8848 | −0.710414 | −0.355207 | − | 0.934788i | \(-0.615590\pi\) | ||||
−0.355207 | + | 0.934788i | \(0.615590\pi\) | |||||||
\(440\) | −3.19386 | −0.152261 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.03206 | −0.144220 | ||||||||
\(443\) | 12.4823 | 0.593052 | 0.296526 | − | 0.955025i | \(-0.404172\pi\) | ||||
0.296526 | + | 0.955025i | \(0.404172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.21257 | 0.0574814 | ||||||||
\(446\) | 8.71500 | 0.412667 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 42.9015 | 2.02691 | ||||||||
\(449\) | 14.4224 | 0.680636 | 0.340318 | − | 0.940310i | \(-0.389465\pi\) | ||||
0.340318 | + | 0.940310i | \(0.389465\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.139742 | 0.00658020 | ||||||||
\(452\) | 1.84200 | 0.0866404 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 25.4258 | 1.19329 | ||||||||
\(455\) | −5.04197 | −0.236371 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.7181 | −0.782041 | −0.391021 | − | 0.920382i | \(-0.627878\pi\) | ||||
−0.391021 | + | 0.920382i | \(0.627878\pi\) | |||||||
\(458\) | 1.77799 | 0.0830798 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.45714 | 0.161190 | ||||||||
\(461\) | 4.25625 | 0.198233 | 0.0991166 | − | 0.995076i | \(-0.468398\pi\) | ||||
0.0991166 | + | 0.995076i | \(0.468398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.0962 | 1.30574 | 0.652870 | − | 0.757470i | \(-0.273565\pi\) | ||||
0.652870 | + | 0.757470i | \(0.273565\pi\) | |||||||
\(464\) | 11.9012 | 0.552500 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.662181 | −0.0306749 | ||||||||
\(467\) | 5.37530 | 0.248739 | 0.124370 | − | 0.992236i | \(-0.460309\pi\) | ||||
0.124370 | + | 0.992236i | \(0.460309\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.0282 | 1.34040 | ||||||||
\(470\) | −4.81955 | −0.222309 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.9479 | 0.872147 | ||||||||
\(473\) | −10.8332 | −0.498109 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.5055 | 0.482023 | ||||||||
\(476\) | −5.75424 | −0.263745 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.75960 | −0.309177 | ||||||||
\(479\) | −28.8326 | −1.31740 | −0.658698 | − | 0.752408i | \(-0.728892\pi\) | ||||
−0.658698 | + | 0.752408i | \(0.728892\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.450326 | 0.0205331 | ||||||||
\(482\) | 24.1899 | 1.10182 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.483971 | −0.0219987 | ||||||||
\(485\) | 7.48037 | 0.339666 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.0821 | −1.27252 | −0.636260 | − | 0.771474i | \(-0.719520\pi\) | ||||
−0.636260 | + | 0.771474i | \(0.719520\pi\) | |||||||
\(488\) | 17.9828 | 0.814045 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 20.9731 | 0.947469 | ||||||||
\(491\) | 33.8170 | 1.52614 | 0.763069 | − | 0.646317i | \(-0.223692\pi\) | ||||
0.763069 | + | 0.646317i | \(0.223692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.4750 | −0.471770 | ||||||||
\(494\) | 3.30863 | 0.148862 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −27.6354 | −1.24087 | ||||||||
\(497\) | 43.2237 | 1.93885 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.05872 | −0.0921611 | −0.0460806 | − | 0.998938i | \(-0.514673\pi\) | ||||
−0.0460806 | + | 0.998938i | \(0.514673\pi\) | |||||||
\(500\) | −4.50284 | −0.201373 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.74865 | −0.390471 | ||||||||
\(503\) | −30.1771 | −1.34553 | −0.672766 | − | 0.739855i | \(-0.734894\pi\) | ||||
−0.672766 | + | 0.739855i | \(0.734894\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.60792 | −0.294049 | ||||||||
\(506\) | −8.42241 | −0.374422 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.29286 | −0.0573613 | ||||||||
\(509\) | 13.0536 | 0.578591 | 0.289296 | − | 0.957240i | \(-0.406579\pi\) | ||||
0.289296 | + | 0.957240i | \(0.406579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.0927 | 1.50817 | ||||||||
\(512\) | 24.5898 | 1.08673 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.34359 | 0.235696 | ||||||||
\(515\) | −19.5018 | −0.859353 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.74833 | −0.164851 | ||||||||
\(518\) | −2.67711 | −0.117625 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.19386 | −0.140060 | ||||||||
\(521\) | 0.881997 | 0.0386410 | 0.0193205 | − | 0.999813i | \(-0.493850\pi\) | ||||
0.0193205 | + | 0.999813i | \(0.493850\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.7936 | −0.996694 | −0.498347 | − | 0.866978i | \(-0.666059\pi\) | ||||
−0.498347 | + | 0.866978i | \(0.666059\pi\) | |||||||
\(524\) | −4.52122 | −0.197511 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.60090 | −0.287813 | ||||||||
\(527\) | 24.3236 | 1.05955 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.7913 | 1.03440 | ||||||||
\(530\) | −17.1158 | −0.743461 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.27913 | 0.272235 | ||||||||
\(533\) | 0.139742 | 0.00605291 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.96673 | −0.301198 | ||||||||
\(536\) | 18.3880 | 0.794241 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.376401 | 0.0162278 | ||||||||
\(539\) | 16.3115 | 0.702586 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.0273 | 1.63492 | 0.817460 | − | 0.575986i | \(-0.195382\pi\) | ||||
0.817460 | + | 0.575986i | \(0.195382\pi\) | |||||||
\(542\) | −8.49336 | −0.364821 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.57990 | −0.282111 | ||||||||
\(545\) | 2.41559 | 0.103473 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.9245 | 0.467100 | 0.233550 | − | 0.972345i | \(-0.424966\pi\) | ||||
0.233550 | + | 0.972345i | \(0.424966\pi\) | |||||||
\(548\) | 6.53527 | 0.279173 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.81364 | 0.205254 | ||||||||
\(551\) | 11.4305 | 0.486955 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.1942 | 1.28399 | ||||||||
\(554\) | −38.9083 | −1.65306 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.56566 | 0.363265 | ||||||||
\(557\) | −4.24090 | −0.179693 | −0.0898463 | − | 0.995956i | \(-0.528638\pi\) | ||||
−0.0898463 | + | 0.995956i | \(0.528638\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.8332 | −0.458194 | ||||||||
\(560\) | 14.1066 | 0.596112 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.0178 | 1.39277 | ||||||||
\(563\) | 35.4686 | 1.49482 | 0.747412 | − | 0.664361i | \(-0.231296\pi\) | ||||
0.747412 | + | 0.664361i | \(0.231296\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.97453 | 0.167210 | ||||||||
\(566\) | 34.2332 | 1.43893 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.3802 | 1.14885 | ||||||||
\(569\) | 32.8755 | 1.37821 | 0.689106 | − | 0.724661i | \(-0.258004\pi\) | ||||
0.689106 | + | 0.724661i | \(0.258004\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5303 | 0.566227 | 0.283114 | − | 0.959086i | \(-0.408633\pi\) | ||||
0.283114 | + | 0.959086i | \(0.408633\pi\) | |||||||
\(572\) | −0.483971 | −0.0202358 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.830743 | −0.0346745 | ||||||||
\(575\) | −26.7425 | −1.11524 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.1270 | 1.58725 | 0.793624 | − | 0.608409i | \(-0.208192\pi\) | ||||
0.793624 | + | 0.608409i | \(0.208192\pi\) | |||||||
\(578\) | 13.4650 | 0.560072 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.14983 | −0.0892668 | ||||||||
\(581\) | 56.3197 | 2.33653 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.3115 | −0.551306 | ||||||||
\(584\) | 21.5962 | 0.893655 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.48905 | −0.144131 | ||||||||
\(587\) | 0.611402 | 0.0252353 | 0.0126176 | − | 0.999920i | \(-0.495984\pi\) | ||||
0.0126176 | + | 0.999920i | \(0.495984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.5423 | −1.09366 | ||||||||
\(590\) | 7.96580 | 0.327947 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.25994 | −0.0517830 | ||||||||
\(593\) | 23.7963 | 0.977198 | 0.488599 | − | 0.872508i | \(-0.337508\pi\) | ||||
0.488599 | + | 0.872508i | \(0.337508\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.4161 | −0.509009 | ||||||||
\(596\) | 2.66990 | 0.109363 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.42241 | −0.344418 | ||||||||
\(599\) | 6.35281 | 0.259569 | 0.129784 | − | 0.991542i | \(-0.458571\pi\) | ||||
0.129784 | + | 0.991542i | \(0.458571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.0793 | 1.71645 | 0.858224 | − | 0.513275i | \(-0.171568\pi\) | ||||
0.858224 | + | 0.513275i | \(0.171568\pi\) | |||||||
\(602\) | 64.4012 | 2.62480 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.42508 | 0.0986751 | ||||||||
\(605\) | −1.04428 | −0.0424558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.2945 | −1.79786 | −0.898929 | − | 0.438093i | \(-0.855654\pi\) | ||||
−0.898929 | + | 0.438093i | \(0.855654\pi\) | |||||||
\(608\) | 7.18010 | 0.291192 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.56008 | 0.306099 | ||||||||
\(611\) | −3.74833 | −0.151641 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.69112 | 0.189473 | 0.0947363 | − | 0.995502i | \(-0.469799\pi\) | ||||
0.0947363 | + | 0.995502i | \(0.469799\pi\) | |||||||
\(614\) | 0.514215 | 0.0207520 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.7668 | 0.594970 | ||||||||
\(617\) | −2.55837 | −0.102996 | −0.0514981 | − | 0.998673i | \(-0.516400\pi\) | ||||
−0.0514981 | + | 0.998673i | \(0.516400\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.9375 | −0.881742 | −0.440871 | − | 0.897571i | \(-0.645330\pi\) | ||||
−0.440871 | + | 0.897571i | \(0.645330\pi\) | |||||||
\(620\) | 4.99204 | 0.200485 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.9179 | 0.718444 | ||||||||
\(623\) | −5.60631 | −0.224612 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.83155 | 0.393262 | ||||||||
\(626\) | −13.3702 | −0.534380 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.27902 | 0.0909429 | ||||||||
\(629\) | 1.10895 | 0.0442166 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.9394 | 0.714158 | 0.357079 | − | 0.934074i | \(-0.383773\pi\) | ||||
0.357079 | + | 0.934074i | \(0.383773\pi\) | |||||||
\(632\) | 19.1267 | 0.760818 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −37.9758 | −1.50821 | ||||||||
\(635\) | −2.78963 | −0.110703 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.3115 | 0.646286 | ||||||||
\(638\) | 5.23749 | 0.207354 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.84440 | 0.231020 | ||||||||
\(641\) | −29.1930 | −1.15306 | −0.576528 | − | 0.817078i | \(-0.695593\pi\) | ||||
−0.576528 | + | 0.817078i | \(0.695593\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −49.1335 | −1.93764 | −0.968819 | − | 0.247770i | \(-0.920302\pi\) | ||||
−0.968819 | + | 0.247770i | \(0.920302\pi\) | |||||||
\(644\) | −15.9841 | −0.629860 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.14765 | 0.320565 | ||||||||
\(647\) | −44.0511 | −1.73183 | −0.865914 | − | 0.500193i | \(-0.833262\pi\) | ||||
−0.865914 | + | 0.500193i | \(0.833262\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.19528 | 0.243186 | ||||||||
\(650\) | 4.81364 | 0.188807 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.47811 | 0.175376 | ||||||||
\(653\) | −31.6536 | −1.23870 | −0.619350 | − | 0.785115i | \(-0.712604\pi\) | ||||
−0.619350 | + | 0.785115i | \(0.712604\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.75555 | −0.381181 | ||||||||
\(656\) | −0.390975 | −0.0152650 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.2832 | 0.868688 | ||||||||
\(659\) | −41.1367 | −1.60246 | −0.801229 | − | 0.598358i | \(-0.795820\pi\) | ||||
−0.801229 | + | 0.598358i | \(0.795820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.3438 | −0.946863 | −0.473432 | − | 0.880831i | \(-0.656985\pi\) | ||||
−0.473432 | + | 0.880831i | \(0.656985\pi\) | |||||||
\(662\) | −17.8393 | −0.693342 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 35.6759 | 1.38449 | ||||||||
\(665\) | 13.5486 | 0.525393 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.0973 | −1.12665 | ||||||||
\(668\) | −9.92438 | −0.383986 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.73043 | 0.298652 | ||||||||
\(671\) | 5.87974 | 0.226985 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.7516 | −0.607178 | −0.303589 | − | 0.952803i | \(-0.598185\pi\) | ||||
−0.303589 | + | 0.952803i | \(0.598185\pi\) | |||||||
\(674\) | −16.4813 | −0.634835 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.483971 | −0.0186143 | ||||||||
\(677\) | 11.9285 | 0.458451 | 0.229226 | − | 0.973373i | \(-0.426381\pi\) | ||||
0.229226 | + | 0.973373i | \(0.426381\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.5854 | −1.32727 | ||||||||
\(680\) | −7.86501 | −0.301609 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.1618 | −0.465699 | ||||||||
\(683\) | −45.8727 | −1.75527 | −0.877636 | − | 0.479328i | \(-0.840880\pi\) | ||||
−0.877636 | + | 0.479328i | \(0.840880\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.1013 | 0.538783 | ||||||||
\(686\) | −55.3553 | −2.11347 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.3093 | 1.15553 | ||||||||
\(689\) | −13.3115 | −0.507128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.3374 | 0.393253 | 0.196627 | − | 0.980478i | \(-0.437001\pi\) | ||||
0.196627 | + | 0.980478i | \(0.437001\pi\) | |||||||
\(692\) | −6.80212 | −0.258578 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.8306 | −0.562960 | ||||||||
\(695\) | 18.4823 | 0.701075 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.344121 | 0.0130345 | ||||||||
\(698\) | 15.9424 | 0.603429 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.13533 | 0.345283 | ||||||||
\(701\) | −22.9944 | −0.868487 | −0.434243 | − | 0.900796i | \(-0.642984\pi\) | ||||
−0.434243 | + | 0.900796i | \(0.642984\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.21010 | −0.0456398 | ||||||||
\(704\) | 8.88561 | 0.334889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 39.9130 | 1.50214 | ||||||||
\(707\) | 30.5517 | 1.14901 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.6028 | −1.29954 | −0.649768 | − | 0.760132i | \(-0.725134\pi\) | ||||
−0.649768 | + | 0.760132i | \(0.725134\pi\) | |||||||
\(710\) | 11.5108 | 0.431993 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.55134 | −0.133092 | ||||||||
\(713\) | 67.5657 | 2.53036 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.04428 | −0.0390537 | ||||||||
\(716\) | 7.14187 | 0.266904 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.8791 | −0.555283 | ||||||||
\(719\) | −37.2446 | −1.38899 | −0.694495 | − | 0.719497i | \(-0.744372\pi\) | ||||
−0.694495 | + | 0.719497i | \(0.744372\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 90.1666 | 3.35798 | ||||||||
\(722\) | 14.5033 | 0.539757 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.56675 | −0.0582277 | ||||||||
\(725\) | 16.6299 | 0.617619 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0501 | −0.743619 | −0.371809 | − | 0.928309i | \(-0.621262\pi\) | ||||
−0.371809 | + | 0.928309i | \(0.621262\pi\) | |||||||
\(728\) | 14.7668 | 0.547293 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.07914 | 0.336034 | ||||||||
\(731\) | −26.6771 | −0.986688 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.8983 | 0.845769 | 0.422885 | − | 0.906184i | \(-0.361018\pi\) | ||||
0.422885 | + | 0.906184i | \(0.361018\pi\) | |||||||
\(734\) | 9.47708 | 0.349805 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.2776 | −0.673720 | ||||||||
\(737\) | 6.01222 | 0.221463 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0535 | −0.553751 | −0.276876 | − | 0.960906i | \(-0.589299\pi\) | ||||
−0.276876 | + | 0.960906i | \(0.589299\pi\) | |||||||
\(740\) | 0.227594 | 0.00836653 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 79.1346 | 2.90512 | ||||||||
\(743\) | −39.0967 | −1.43432 | −0.717159 | − | 0.696909i | \(-0.754558\pi\) | ||||
−0.717159 | + | 0.696909i | \(0.754558\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.76091 | 0.211063 | ||||||||
\(746\) | −8.04480 | −0.294541 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.19180 | −0.0435765 | ||||||||
\(749\) | 32.2106 | 1.17695 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.3300 | 0.741853 | 0.370927 | − | 0.928662i | \(-0.379040\pi\) | ||||
0.370927 | + | 0.928662i | \(0.379040\pi\) | |||||||
\(752\) | 10.4872 | 0.382428 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.23749 | 0.190738 | ||||||||
\(755\) | 5.23265 | 0.190436 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.5436 | 1.32820 | 0.664100 | − | 0.747644i | \(-0.268815\pi\) | ||||
0.664100 | + | 0.747644i | \(0.268815\pi\) | |||||||
\(758\) | 21.8681 | 0.794283 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.58243 | 0.311317 | ||||||||
\(761\) | −2.77210 | −0.100488 | −0.0502442 | − | 0.998737i | \(-0.516000\pi\) | ||||
−0.0502442 | + | 0.998737i | \(0.516000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.1685 | −0.404326 | ||||||||
\(764\) | −4.40208 | −0.159262 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.2800 | 1.23859 | ||||||||
\(767\) | 6.19528 | 0.223698 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.26336 | 0.153741 | 0.0768704 | − | 0.997041i | \(-0.475507\pi\) | ||||
0.0768704 | + | 0.997041i | \(0.475507\pi\) | |||||||
\(770\) | 6.20803 | 0.223722 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.81116 | −0.137167 | ||||||||
\(773\) | −41.2964 | −1.48533 | −0.742665 | − | 0.669663i | \(-0.766438\pi\) | ||||
−0.742665 | + | 0.669663i | \(0.766438\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.6157 | −1.38712 | ||||||||
\(776\) | −21.9083 | −0.786462 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.1877 | −0.795468 | ||||||||
\(779\) | −0.375511 | −0.0134541 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.95234 | 0.320340 | ||||||||
\(782\) | −20.7405 | −0.741680 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −45.6368 | −1.62989 | ||||||||
\(785\) | 4.91750 | 0.175513 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.706140 | −0.0251712 | −0.0125856 | − | 0.999921i | \(-0.504006\pi\) | ||||
−0.0125856 | + | 0.999921i | \(0.504006\pi\) | |||||||
\(788\) | 4.69996 | 0.167429 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.04096 | 0.286084 | ||||||||
\(791\) | −18.3762 | −0.653382 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.87974 | 0.208796 | ||||||||
\(794\) | 4.18708 | 0.148594 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.35161 | −0.225127 | ||||||||
\(797\) | −49.8834 | −1.76696 | −0.883481 | − | 0.468467i | \(-0.844807\pi\) | ||||
−0.883481 | + | 0.468467i | \(0.844807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.23042 | −0.326549 | ||||||||
\(800\) | 10.4461 | 0.369327 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.3684 | −0.542676 | ||||||||
\(803\) | 7.06116 | 0.249183 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34.4892 | −1.21558 | ||||||||
\(806\) | −12.1618 | −0.428381 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.3531 | 0.680839 | ||||||||
\(809\) | −3.29718 | −0.115923 | −0.0579613 | − | 0.998319i | \(-0.518460\pi\) | ||||
−0.0579613 | + | 0.998319i | \(0.518460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.9951 | −0.702123 | −0.351061 | − | 0.936352i | \(-0.614179\pi\) | ||||
−0.351061 | + | 0.936352i | \(0.614179\pi\) | |||||||
\(812\) | 9.93972 | 0.348816 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.554473 | −0.0194343 | ||||||||
\(815\) | 9.66252 | 0.338463 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.1105 | 1.01845 | ||||||||
\(818\) | 38.4252 | 1.34350 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0706255 | 0.00246635 | ||||||||
\(821\) | −12.4547 | −0.434671 | −0.217335 | − | 0.976097i | \(-0.569737\pi\) | ||||
−0.217335 | + | 0.976097i | \(0.569737\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.1636 | 0.772575 | 0.386288 | − | 0.922378i | \(-0.373757\pi\) | ||||
0.386288 | + | 0.922378i | \(0.373757\pi\) | |||||||
\(824\) | 57.1164 | 1.98974 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.8298 | −1.28147 | ||||||||
\(827\) | 46.4124 | 1.61392 | 0.806958 | − | 0.590609i | \(-0.201112\pi\) | ||||
0.806958 | + | 0.590609i | \(0.201112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.9506 | 0.831839 | 0.415920 | − | 0.909401i | \(-0.363460\pi\) | ||||
0.415920 | + | 0.909401i | \(0.363460\pi\) | |||||||
\(830\) | 14.9984 | 0.520601 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.88561 | 0.308053 | ||||||||
\(833\) | 40.1678 | 1.39173 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.4141 | −0.741064 | ||||||||
\(836\) | 1.30051 | 0.0449791 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.9191 | −0.964448 | ||||||||
\(839\) | −20.7000 | −0.714645 | −0.357322 | − | 0.933981i | \(-0.616310\pi\) | ||||
−0.357322 | + | 0.933981i | \(0.616310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.9058 | −0.376062 | ||||||||
\(842\) | 35.6651 | 1.22910 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.80365 | −0.130927 | ||||||||
\(845\) | −1.04428 | −0.0359242 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.82820 | 0.165899 | ||||||||
\(848\) | 37.2433 | 1.27894 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.8538 | 0.406582 | ||||||||
\(851\) | 3.08042 | 0.105595 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.3776 | −0.937390 | −0.468695 | − | 0.883360i | \(-0.655276\pi\) | ||||
−0.468695 | + | 0.883360i | \(0.655276\pi\) | |||||||
\(854\) | −34.9540 | −1.19610 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.4040 | 0.697393 | ||||||||
\(857\) | −1.98167 | −0.0676925 | −0.0338463 | − | 0.999427i | \(-0.510776\pi\) | ||||
−0.0338463 | + | 0.999427i | \(0.510776\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.7870 | −1.28928 | −0.644638 | − | 0.764488i | \(-0.722992\pi\) | ||||
−0.644638 | + | 0.764488i | \(0.722992\pi\) | |||||||
\(860\) | −5.47506 | −0.186698 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.8200 | 0.538832 | ||||||||
\(863\) | −21.4243 | −0.729290 | −0.364645 | − | 0.931147i | \(-0.618810\pi\) | ||||
−0.364645 | + | 0.931147i | \(0.618810\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.6771 | −0.499037 | ||||||||
\(866\) | −15.2687 | −0.518851 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −23.0807 | −0.783409 | ||||||||
\(869\) | 6.25373 | 0.212143 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.01222 | 0.203716 | ||||||||
\(872\) | −7.07472 | −0.239580 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22.6324 | 0.765553 | ||||||||
\(875\) | 44.9214 | 1.51862 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.165496 | −0.00558840 | −0.00279420 | − | 0.999996i | \(-0.500889\pi\) | ||||
−0.00279420 | + | 0.999996i | \(0.500889\pi\) | |||||||
\(878\) | 18.3273 | 0.618515 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.92171 | 0.0984907 | ||||||||
\(881\) | −30.7459 | −1.03586 | −0.517928 | − | 0.855424i | \(-0.673297\pi\) | ||||
−0.517928 | + | 0.855424i | \(0.673297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.5890 | 0.827485 | 0.413743 | − | 0.910394i | \(-0.364221\pi\) | ||||
0.413743 | + | 0.910394i | \(0.364221\pi\) | |||||||
\(884\) | −1.19180 | −0.0400845 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.3691 | −0.516335 | ||||||||
\(887\) | 13.5461 | 0.454833 | 0.227417 | − | 0.973798i | \(-0.426972\pi\) | ||||
0.227417 | + | 0.973798i | \(0.426972\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.8978 | 0.432580 | ||||||||
\(890\) | −1.49300 | −0.0500456 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.42557 | 0.114696 | ||||||||
\(893\) | 10.0724 | 0.337060 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4102 | 0.515106 | ||||||||
\(896\) | −27.0215 | −0.902727 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.7579 | −0.592589 | ||||||||
\(899\) | −42.0159 | −1.40131 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.7802 | −1.09207 | ||||||||
\(902\) | −0.172061 | −0.00572899 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.6405 | −0.387156 | ||||||||
\(905\) | −3.38061 | −0.112375 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.57868 | 0.284850 | 0.142425 | − | 0.989806i | \(-0.454510\pi\) | ||||
0.142425 | + | 0.989806i | \(0.454510\pi\) | |||||||
\(908\) | 9.99403 | 0.331663 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.20803 | 0.205794 | ||||||||
\(911\) | −38.6360 | −1.28007 | −0.640034 | − | 0.768346i | \(-0.721080\pi\) | ||||
−0.640034 | + | 0.768346i | \(0.721080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.6647 | 0.386046 | ||||||||
\(914\) | 20.5846 | 0.680877 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.698865 | 0.0230912 | ||||||||
\(917\) | 45.1047 | 1.48949 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.45847 | 0.0810975 | 0.0405488 | − | 0.999178i | \(-0.487089\pi\) | ||||
0.0405488 | + | 0.999178i | \(0.487089\pi\) | |||||||
\(920\) | −21.8473 | −0.720284 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.24060 | −0.172590 | ||||||||
\(923\) | 8.95234 | 0.294670 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.76054 | −0.0578863 | ||||||||
\(926\) | −34.5940 | −1.13683 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.3659 | 0.373105 | ||||||||
\(929\) | 18.0463 | 0.592079 | 0.296039 | − | 0.955176i | \(-0.404334\pi\) | ||||
0.296039 | + | 0.955176i | \(0.404334\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.8318 | −1.43653 | ||||||||
\(932\) | −0.260281 | −0.00852578 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.61845 | −0.216562 | ||||||||
\(935\) | −2.57157 | −0.0840994 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.3652 | −1.18800 | −0.594000 | − | 0.804465i | \(-0.702452\pi\) | ||||
−0.594000 | + | 0.804465i | \(0.702452\pi\) | |||||||
\(938\) | −35.7416 | −1.16700 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.89440 | −0.0617885 | ||||||||
\(941\) | 40.0377 | 1.30519 | 0.652596 | − | 0.757706i | \(-0.273680\pi\) | ||||
0.652596 | + | 0.757706i | \(0.273680\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.955895 | 0.0311282 | ||||||||
\(944\) | −17.3333 | −0.564152 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.3386 | 0.433674 | ||||||||
\(947\) | −22.2749 | −0.723836 | −0.361918 | − | 0.932210i | \(-0.617878\pi\) | ||||
−0.361918 | + | 0.932210i | \(0.617878\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.06116 | 0.229215 | ||||||||
\(950\) | −12.9351 | −0.419669 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 36.3638 | 1.17856 | ||||||||
\(953\) | −14.5545 | −0.471468 | −0.235734 | − | 0.971818i | \(-0.575749\pi\) | ||||
−0.235734 | + | 0.971818i | \(0.575749\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.49847 | −0.307363 | ||||||||
\(956\) | −2.65697 | −0.0859325 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.5008 | 1.14698 | ||||||||
\(959\) | −65.1973 | −2.10533 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66.5636 | 2.14721 | ||||||||
\(962\) | −0.554473 | −0.0178769 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.50824 | 0.306240 | ||||||||
\(965\) | −8.22344 | −0.264722 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7075 | 0.826697 | 0.413349 | − | 0.910573i | \(-0.364359\pi\) | ||||
0.413349 | + | 0.910573i | \(0.364359\pi\) | |||||||
\(968\) | 3.05844 | 0.0983021 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.21037 | −0.295727 | ||||||||
\(971\) | −24.2273 | −0.777492 | −0.388746 | − | 0.921345i | \(-0.627092\pi\) | ||||
−0.388746 | + | 0.921345i | \(0.627092\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −85.4529 | −2.73949 | ||||||||
\(974\) | 34.5767 | 1.10791 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.4505 | −0.526568 | ||||||||
\(977\) | −8.34241 | −0.266897 | −0.133449 | − | 0.991056i | \(-0.542605\pi\) | ||||
−0.133449 | + | 0.991056i | \(0.542605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.16116 | −0.0371108 | ||||||||
\(980\) | 8.24382 | 0.263339 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.6379 | −1.32872 | ||||||||
\(983\) | 14.6977 | 0.468784 | 0.234392 | − | 0.972142i | \(-0.424690\pi\) | ||||
0.234392 | + | 0.972142i | \(0.424690\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.1412 | 0.323126 | ||||||||
\(986\) | 12.8976 | 0.410742 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.30051 | 0.0413748 | ||||||||
\(989\) | −74.1033 | −2.35635 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4700 | −0.809082 | −0.404541 | − | 0.914520i | \(-0.632569\pi\) | ||||
−0.404541 | + | 0.914520i | \(0.632569\pi\) | |||||||
\(992\) | −26.3924 | −0.837961 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −53.2201 | −1.68804 | ||||||||
\(995\) | −13.7050 | −0.434478 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.8048 | 0.722236 | 0.361118 | − | 0.932520i | \(-0.382395\pi\) | ||||
0.361118 | + | 0.932520i | \(0.382395\pi\) | |||||||
\(998\) | 2.53485 | 0.0802392 | ||||||||
\(999\) | 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 | 1287.2.a.q.1.3 | 6 | ||
3.2 | odd | 2 | 143.2.a.c.1.4 | ✓ | 6 | ||
12.11 | even | 2 | 2288.2.a.z.1.4 | 6 | |||
15.14 | odd | 2 | 3575.2.a.p.1.3 | 6 | |||
21.20 | even | 2 | 7007.2.a.r.1.4 | 6 | |||
24.5 | odd | 2 | 9152.2.a.cm.1.4 | 6 | |||
24.11 | even | 2 | 9152.2.a.cs.1.3 | 6 | |||
33.32 | even | 2 | 1573.2.a.m.1.3 | 6 | |||
39.38 | odd | 2 | 1859.2.a.m.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.a.c.1.4 | ✓ | 6 | 3.2 | odd | 2 | ||
1287.2.a.q.1.3 | 6 | 1.1 | even | 1 | trivial | ||
1573.2.a.m.1.3 | 6 | 33.32 | even | 2 | |||
1859.2.a.m.1.3 | 6 | 39.38 | odd | 2 | |||
2288.2.a.z.1.4 | 6 | 12.11 | even | 2 | |||
3575.2.a.p.1.3 | 6 | 15.14 | odd | 2 | |||
7007.2.a.r.1.4 | 6 | 21.20 | even | 2 | |||
9152.2.a.cm.1.4 | 6 | 24.5 | odd | 2 | |||
9152.2.a.cs.1.3 | 6 | 24.11 | even | 2 |