Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7872,2,Mod(1,7872)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7872, 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("7872.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7872 = 2^{6} \cdot 3 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7872.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: | \(62.8582364712\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 492) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7872.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.449490 | −0.201018 | −0.100509 | − | 0.994936i | \(-0.532047\pi\) | ||||
−0.100509 | + | 0.994936i | \(0.532047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.44949 | 1.68175 | 0.840875 | − | 0.541230i | \(-0.182041\pi\) | ||||
0.840875 | + | 0.541230i | \(0.182041\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.44949 | 1.04006 | 0.520030 | − | 0.854148i | \(-0.325921\pi\) | ||||
0.520030 | + | 0.854148i | \(0.325921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.449490 | 0.124666 | 0.0623330 | − | 0.998055i | \(-0.480146\pi\) | ||||
0.0623330 | + | 0.998055i | \(0.480146\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.449490 | −0.116058 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.44949 | −0.351553 | −0.175776 | − | 0.984430i | \(-0.556244\pi\) | ||||
−0.175776 | + | 0.984430i | \(0.556244\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.44949 | −1.47961 | −0.739807 | − | 0.672819i | \(-0.765083\pi\) | ||||
−0.739807 | + | 0.672819i | \(0.765083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.44949 | 0.970958 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.44949 | 1.34481 | 0.672406 | − | 0.740183i | \(-0.265261\pi\) | ||||
0.672406 | + | 0.740183i | \(0.265261\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.79796 | −0.959592 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.34847 | −1.55027 | −0.775136 | − | 0.631795i | \(-0.782319\pi\) | ||||
−0.775136 | + | 0.631795i | \(0.782319\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00000 | 1.25724 | 0.628619 | − | 0.777714i | \(-0.283621\pi\) | ||||
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.44949 | 0.600479 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.89898 | −0.640988 | −0.320494 | − | 0.947250i | \(-0.603849\pi\) | ||||
−0.320494 | + | 0.947250i | \(0.603849\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.449490 | 0.0719760 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.449490 | −0.0670060 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.55051 | 0.663760 | 0.331880 | − | 0.943322i | \(-0.392317\pi\) | ||||
0.331880 | + | 0.943322i | \(0.392317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.7980 | 1.82828 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.44949 | −0.202969 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.8990 | 1.77181 | 0.885906 | − | 0.463866i | \(-0.153538\pi\) | ||||
0.885906 | + | 0.463866i | \(0.153538\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.55051 | −0.209071 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.44949 | −0.854256 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.6969 | 1.91338 | 0.956689 | − | 0.291111i | \(-0.0940250\pi\) | ||||
0.956689 | + | 0.291111i | \(0.0940250\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.7980 | 1.63861 | 0.819305 | − | 0.573357i | \(-0.194359\pi\) | ||||
0.819305 | + | 0.573357i | \(0.194359\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.44949 | 0.560583 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.202041 | −0.0250601 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.89898 | 0.842844 | 0.421422 | − | 0.906865i | \(-0.361531\pi\) | ||||
0.421422 | + | 0.906865i | \(0.361531\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.44949 | 0.776427 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.34847 | 0.516068 | 0.258034 | − | 0.966136i | \(-0.416925\pi\) | ||||
0.258034 | + | 0.966136i | \(0.416925\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | 0.117041 | 0.0585206 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585206 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.79796 | −0.554021 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.3485 | 1.74912 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.55051 | −0.828776 | −0.414388 | − | 0.910100i | \(-0.636004\pi\) | ||||
−0.414388 | + | 0.910100i | \(0.636004\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.651531 | 0.0706684 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.34847 | −0.895050 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.7980 | −1.67458 | −0.837290 | − | 0.546759i | \(-0.815861\pi\) | ||||
−0.837290 | + | 0.546759i | \(0.815861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.00000 | 0.725866 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.89898 | 0.297429 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.34847 | −0.339986 | −0.169993 | − | 0.985445i | \(-0.554374\pi\) | ||||
−0.169993 | + | 0.985445i | \(0.554374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.44949 | 0.346687 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.34847 | −0.432689 | −0.216344 | − | 0.976317i | \(-0.569413\pi\) | ||||
−0.216344 | + | 0.976317i | \(0.569413\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0000 | 1.28093 | 0.640464 | − | 0.767988i | \(-0.278742\pi\) | ||||
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.00000 | 0.193347 | 0.0966736 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966736 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.34847 | −0.512290 | −0.256145 | − | 0.966638i | \(-0.582453\pi\) | ||||
−0.256145 | + | 0.966638i | \(0.582453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.89898 | −0.370075 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.34847 | −0.126853 | −0.0634267 | − | 0.997987i | \(-0.520203\pi\) | ||||
−0.0634267 | + | 0.997987i | \(0.520203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.89898 | −0.270331 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.449490 | 0.0415553 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.44949 | −0.591224 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.898979 | 0.0817254 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.40408 | 0.393913 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.0000 | −1.59724 | −0.798621 | − | 0.601834i | \(-0.794437\pi\) | ||||
−0.798621 | + | 0.601834i | \(0.794437\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00000 | −0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.2474 | 1.07006 | 0.535032 | − | 0.844832i | \(-0.320299\pi\) | ||||
0.535032 | + | 0.844832i | \(0.320299\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −28.6969 | −2.48834 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.449490 | −0.0386859 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.44949 | −0.294710 | −0.147355 | − | 0.989084i | \(-0.547076\pi\) | ||||
−0.147355 | + | 0.989084i | \(0.547076\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.202041 | 0.0171369 | 0.00856845 | − | 0.999963i | \(-0.497273\pi\) | ||||
0.00856845 | + | 0.999963i | \(0.497273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.55051 | 0.383222 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.55051 | 0.129660 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.75255 | 0.311632 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.7980 | 1.05556 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5959 | −1.59469 | −0.797347 | − | 0.603522i | \(-0.793764\pi\) | ||||
−0.797347 | + | 0.603522i | \(0.793764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.44949 | −0.117184 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.14643 | −0.252727 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.79796 | 0.622345 | 0.311172 | − | 0.950353i | \(-0.399278\pi\) | ||||
0.311172 | + | 0.950353i | \(0.399278\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.8990 | 1.02296 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.6969 | 2.26164 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.89898 | 0.618696 | 0.309348 | − | 0.950949i | \(-0.399889\pi\) | ||||
0.309348 | + | 0.950949i | \(0.399889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.55051 | −0.120707 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.5959 | 1.05208 | 0.526042 | − | 0.850459i | \(-0.323676\pi\) | ||||
0.526042 | + | 0.850459i | \(0.323676\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7980 | −0.984458 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.44949 | −0.493205 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.55051 | −0.574055 | −0.287027 | − | 0.957922i | \(-0.592667\pi\) | ||||
−0.287027 | + | 0.957922i | \(0.592667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.3485 | −1.61379 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.6969 | 1.10469 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.34847 | −0.474507 | −0.237253 | − | 0.971448i | \(-0.576247\pi\) | ||||
−0.237253 | + | 0.971448i | \(0.576247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.7980 | −1.02559 | −0.512797 | − | 0.858510i | \(-0.671391\pi\) | ||||
−0.512797 | + | 0.858510i | \(0.671391\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.7980 | 0.946052 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.75255 | 0.128850 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.00000 | −0.365636 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.44949 | 0.323653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.10102 | 0.224382 | 0.112191 | − | 0.993687i | \(-0.464213\pi\) | ||||
0.112191 | + | 0.993687i | \(0.464213\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.55051 | 0.543498 | 0.271749 | − | 0.962368i | \(-0.412398\pi\) | ||||
0.271749 | + | 0.962368i | \(0.412398\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.202041 | −0.0144685 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.0454 | 1.71316 | 0.856582 | − | 0.516011i | \(-0.172584\pi\) | ||||
0.856582 | + | 0.516011i | \(0.172584\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.4495 | −1.02430 | −0.512149 | − | 0.858897i | \(-0.671150\pi\) | ||||
−0.512149 | + | 0.858897i | \(0.671150\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.89898 | 0.486616 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −37.1464 | −2.60717 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.449490 | 0.0313937 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.44949 | 0.448271 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.2474 | −1.53889 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.89898 | 0.337260 | 0.168630 | − | 0.985679i | \(-0.446066\pi\) | ||||
0.168630 | + | 0.985679i | \(0.446066\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.34847 | 0.297952 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.449490 | 0.0306549 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 31.1464 | 2.11436 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.00000 | 0.0675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.651531 | −0.0438267 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.79796 | −0.120400 | −0.0602001 | − | 0.998186i | \(-0.519174\pi\) | ||||
−0.0602001 | + | 0.998186i | \(0.519174\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.79796 | −0.319864 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.5505 | −1.23124 | −0.615620 | − | 0.788043i | \(-0.711094\pi\) | ||||
−0.615620 | + | 0.788043i | \(0.711094\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.55051 | 0.631115 | 0.315558 | − | 0.948906i | \(-0.397808\pi\) | ||||
0.315558 | + | 0.948906i | \(0.397808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.3485 | 1.00986 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.04541 | −0.133428 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.0000 | 0.649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.89898 | −0.575627 | −0.287814 | − | 0.957686i | \(-0.592928\pi\) | ||||
−0.287814 | + | 0.957686i | \(0.592928\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.69694 | 0.238141 | 0.119070 | − | 0.992886i | \(-0.462009\pi\) | ||||
0.119070 | + | 0.992886i | \(0.462009\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.75255 | −0.367517 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.89898 | −0.184458 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.55051 | −0.478494 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.8990 | 1.19289 | 0.596447 | − | 0.802653i | \(-0.296579\pi\) | ||||
0.596447 | + | 0.802653i | \(0.296579\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.2474 | 1.39869 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.651531 | 0.0408004 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.1464 | 1.63097 | 0.815485 | − | 0.578779i | \(-0.196470\pi\) | ||||
0.815485 | + | 0.578779i | \(0.196470\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.3485 | −1.07798 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.34847 | −0.516757 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.2474 | −1.06352 | −0.531762 | − | 0.846894i | \(-0.678470\pi\) | ||||
−0.531762 | + | 0.846894i | \(0.678470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.79796 | −0.356166 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.7980 | −0.966819 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.8990 | 0.786465 | 0.393232 | − | 0.919439i | \(-0.371357\pi\) | ||||
0.393232 | + | 0.919439i | \(0.371357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.6969 | −1.07501 | −0.537506 | − | 0.843260i | \(-0.680634\pi\) | ||||
−0.537506 | + | 0.843260i | \(0.680634\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.00000 | 0.121046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.5505 | −0.998033 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.7980 | −0.648786 | −0.324393 | − | 0.945922i | \(-0.605160\pi\) | ||||
−0.324393 | + | 0.945922i | \(0.605160\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.00000 | 0.419079 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.4495 | 1.75681 | 0.878405 | − | 0.477918i | \(-0.158608\pi\) | ||||
0.878405 | + | 0.477918i | \(0.158608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.89898 | −0.588433 | −0.294217 | − | 0.955739i | \(-0.595059\pi\) | ||||
−0.294217 | + | 0.955739i | \(0.595059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.89898 | 0.171721 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.44949 | −0.262645 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8990 | −0.876411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.34847 | −0.196291 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.3485 | −0.838247 | −0.419123 | − | 0.907929i | \(-0.637662\pi\) | ||||
−0.419123 | + | 0.907929i | \(0.637662\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.60612 | −0.384623 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.44949 | 0.200160 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.89898 | 0.167652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.44949 | −0.256464 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.34847 | −0.249813 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.75255 | −0.329390 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.5959 | −1.40376 | −0.701882 | − | 0.712294i | \(-0.747656\pi\) | ||||
−0.701882 | + | 0.712294i | \(0.747656\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.0000 | 0.739544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.6969 | 1.74066 | 0.870332 | − | 0.492466i | \(-0.163904\pi\) | ||||
0.870332 | + | 0.492466i | \(0.163904\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.34847 | −0.528407 | −0.264203 | − | 0.964467i | \(-0.585109\pi\) | ||||
−0.264203 | + | 0.964467i | \(0.585109\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.00000 | −0.112687 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.24745 | 0.519388 | 0.259694 | − | 0.965691i | \(-0.416378\pi\) | ||||
0.259694 | + | 0.965691i | \(0.416378\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.7980 | −1.61238 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.00000 | 0.111629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.34847 | 0.520163 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.15663 | −0.119628 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.34847 | −0.295771 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.2474 | 1.11628 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.5505 | 1.40438 | 0.702192 | − | 0.711988i | \(-0.252205\pi\) | ||||
0.702192 | + | 0.711988i | \(0.252205\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.89898 | −0.213663 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.10102 | −0.169427 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.797959 | 0.0434676 | 0.0217338 | − | 0.999764i | \(-0.493081\pi\) | ||||
0.0217338 | + | 0.999764i | \(0.493081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.34847 | −0.0732388 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.1464 | 1.30760 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 25.7980 | 1.39296 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.89898 | −0.156076 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.6515 | −0.732853 | −0.366426 | − | 0.930447i | \(-0.619419\pi\) | ||||
−0.366426 | + | 0.930447i | \(0.619419\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8990 | −0.636938 | −0.318469 | − | 0.947933i | \(-0.603169\pi\) | ||||
−0.318469 | + | 0.947933i | \(0.603169\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.449490 | 0.0239920 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.7980 | 0.840841 | 0.420420 | − | 0.907329i | \(-0.361883\pi\) | ||||
0.420420 | + | 0.907329i | \(0.361883\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.95459 | −0.103739 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.44949 | −0.341343 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.6515 | 0.878834 | 0.439417 | − | 0.898283i | \(-0.355185\pi\) | ||||
0.439417 | + | 0.898283i | \(0.355185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5959 | 1.18926 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.898979 | 0.0471842 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.449490 | −0.0235274 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.79796 | 0.146052 | 0.0730261 | − | 0.997330i | \(-0.476734\pi\) | ||||
0.0730261 | + | 0.997330i | \(0.476734\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 57.3939 | 2.97974 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.4949 | −1.21652 | −0.608260 | − | 0.793738i | \(-0.708132\pi\) | ||||
−0.608260 | + | 0.793738i | \(0.708132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.40408 | 0.227426 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.75255 | −0.193266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.3939 | 1.40713 | 0.703564 | − | 0.710631i | \(-0.251591\pi\) | ||||
0.703564 | + | 0.710631i | \(0.251591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.0000 | −0.922168 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 38.1464 | 1.94919 | 0.974596 | − | 0.223971i | \(-0.0719022\pi\) | ||||
0.974596 | + | 0.223971i | \(0.0719022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.89898 | −0.351605 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.00000 | −0.0508329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.24745 | −0.316758 | −0.158379 | − | 0.987378i | \(-0.550627\pi\) | ||||
−0.158379 | + | 0.987378i | \(0.550627\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.34847 | −0.472772 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.2474 | 0.617802 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.49490 | −0.226163 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.853572 | 0.0428395 | 0.0214198 | − | 0.999771i | \(-0.493181\pi\) | ||||
0.0214198 | + | 0.999771i | \(0.493181\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −28.6969 | −1.43664 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000 | 0.599251 | 0.299626 | − | 0.954057i | \(-0.403138\pi\) | ||||
0.299626 | + | 0.954057i | \(0.403138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.14643 | 0.156735 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.449490 | −0.0223353 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.4495 | −0.666666 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.89898 | −0.489473 | −0.244737 | − | 0.969590i | \(-0.578701\pi\) | ||||
−0.244737 | + | 0.969590i | \(0.578701\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.44949 | −0.170151 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 65.3939 | 3.21782 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.39388 | 0.166599 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.202041 | 0.00989399 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.2474 | 0.793740 | 0.396870 | − | 0.917875i | \(-0.370096\pi\) | ||||
0.396870 | + | 0.917875i | \(0.370096\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.3939 | 1.04267 | 0.521337 | − | 0.853351i | \(-0.325434\pi\) | ||||
0.521337 | + | 0.853351i | \(0.325434\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.55051 | 0.221253 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.95459 | 0.337347 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 56.9444 | 2.75573 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.55051 | 0.0748593 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.1464 | −1.78928 | −0.894640 | − | 0.446787i | \(-0.852568\pi\) | ||||
−0.894640 | + | 0.446787i | \(0.852568\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.4949 | −1.12909 | −0.564546 | − | 0.825401i | \(-0.690949\pi\) | ||||
−0.564546 | + | 0.825401i | \(0.690949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.75255 | 0.179921 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −41.5959 | −1.98980 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.0000 | −1.62273 | −0.811366 | − | 0.584539i | \(-0.801275\pi\) | ||||
−0.811366 | + | 0.584539i | \(0.801275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.7980 | 0.609427 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.10102 | 0.336621 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.30306 | −0.250267 | −0.125133 | − | 0.992140i | \(-0.539936\pi\) | ||||
−0.125133 | + | 0.992140i | \(0.539936\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.44949 | −0.162430 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.5959 | −0.920697 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.898979 | −0.0421448 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.5959 | 1.10377 | 0.551885 | − | 0.833920i | \(-0.313909\pi\) | ||||
0.551885 | + | 0.833920i | \(0.313909\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.44949 | −0.0676564 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.3939 | −1.64846 | −0.824229 | − | 0.566257i | \(-0.808391\pi\) | ||||
−0.824229 | + | 0.566257i | \(0.808391\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1464 | 0.518018 | 0.259009 | − | 0.965875i | \(-0.416604\pi\) | ||||
0.259009 | + | 0.965875i | \(0.416604\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.14643 | −0.145912 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.5959 | −1.18444 | −0.592219 | − | 0.805777i | \(-0.701748\pi\) | ||||
−0.592219 | + | 0.805777i | \(0.701748\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.6969 | 1.41745 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.79796 | 0.359311 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.44949 | −0.158608 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.9444 | 1.41983 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.8990 | 0.590604 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.75255 | −0.217150 | −0.108575 | − | 0.994088i | \(-0.534629\pi\) | ||||
−0.108575 | + | 0.994088i | \(0.534629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.75255 | −0.0799095 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28.6969 | 1.30576 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.50510 | 0.0683432 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.7980 | −1.75810 | −0.879052 | − | 0.476727i | \(-0.841823\pi\) | ||||
−0.879052 | + | 0.476727i | \(0.841823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.89898 | 0.357204 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.5505 | 0.521267 | 0.260634 | − | 0.965438i | \(-0.416069\pi\) | ||||
0.260634 | + | 0.965438i | \(0.416069\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.1010 | 0.545003 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.55051 | −0.0696903 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.3485 | 0.867897 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.4949 | −1.27561 | −0.637803 | − | 0.770199i | \(-0.720157\pi\) | ||||
−0.637803 | + | 0.770199i | \(0.720157\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.5959 | 0.607421 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.1464 | 0.630758 | 0.315379 | − | 0.948966i | \(-0.397868\pi\) | ||||
0.315379 | + | 0.948966i | \(0.397868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.95459 | 0.0869782 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7980 | −0.568377 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.2474 | 1.56232 | 0.781158 | − | 0.624334i | \(-0.214629\pi\) | ||||
0.781158 | + | 0.624334i | \(0.214629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.44949 | 0.196834 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.44949 | −0.284752 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.84337 | −0.257489 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.6969 | 0.690351 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.55051 | −0.331431 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5505 | 0.549848 | 0.274924 | − | 0.961466i | \(-0.411347\pi\) | ||||
0.274924 | + | 0.961466i | \(0.411347\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.5959 | −1.64395 | −0.821977 | − | 0.569520i | \(-0.807129\pi\) | ||||
−0.821977 | + | 0.569520i | \(0.807129\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.3485 | −0.931724 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.1464 | −0.441985 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.5959 | 0.808518 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.6969 | 0.637793 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.449490 | −0.0194696 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.898979 | −0.0388663 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.34847 | −0.273957 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 44.1464 | 1.90152 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.3939 | 1.17775 | 0.588877 | − | 0.808222i | \(-0.299570\pi\) | ||||
0.588877 | + | 0.808222i | \(0.299570\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.7980 | −0.592127 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.40408 | 0.102980 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.8990 | −0.551521 | −0.275760 | − | 0.961226i | \(-0.588930\pi\) | ||||
−0.275760 | + | 0.961226i | \(0.588930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.7980 | 0.546204 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 53.8434 | 2.29380 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.4949 | 1.89212 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.75255 | 0.0743917 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.0454 | 0.468009 | 0.234004 | − | 0.972236i | \(-0.424817\pi\) | ||||
0.234004 | + | 0.972236i | \(0.424817\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.449490 | −0.0190114 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.00000 | −0.211100 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.6515 | −1.33395 | −0.666976 | − | 0.745079i | \(-0.732412\pi\) | ||||
−0.666976 | + | 0.745079i | \(0.732412\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.606123 | 0.0254998 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.44949 | 0.186861 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.4495 | −1.10882 | −0.554410 | − | 0.832244i | \(-0.687056\pi\) | ||||
−0.554410 | + | 0.832244i | \(0.687056\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.10102 | 0.129547 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.9444 | −1.29047 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.4949 | −0.520169 | −0.260085 | − | 0.965586i | \(-0.583750\pi\) | ||||
−0.260085 | + | 0.965586i | \(0.583750\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.55051 | 0.313788 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.5959 | −1.39379 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 44.4949 | 1.84279 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.202041 | −0.00835337 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.55051 | 0.270368 | 0.135184 | − | 0.990820i | \(-0.456837\pi\) | ||||
0.135184 | + | 0.990820i | \(0.456837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −45.1464 | −1.86023 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.0454 | 0.989096 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.0454 | −0.782101 | −0.391051 | − | 0.920369i | \(-0.627888\pi\) | ||||
−0.391051 | + | 0.920369i | \(0.627888\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.89898 | 0.118847 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.4495 | −0.591378 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.8434 | 1.13765 | 0.568825 | − | 0.822459i | \(-0.307398\pi\) | ||||
0.568825 | + | 0.822459i | \(0.307398\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.8990 | 1.42356 | 0.711780 | − | 0.702403i | \(-0.247890\pi\) | ||||
0.711780 | + | 0.702403i | \(0.247890\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.89898 | 0.280948 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.404082 | −0.0164283 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.8990 | −0.604731 | −0.302365 | − | 0.953192i | \(-0.597776\pi\) | ||||
−0.302365 | + | 0.953192i | \(0.597776\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −37.1464 | −1.50525 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.04541 | 0.0827483 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.1918 | 1.74450 | 0.872251 | − | 0.489059i | \(-0.162660\pi\) | ||||
0.872251 | + | 0.489059i | \(0.162660\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.449490 | 0.0181252 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.3485 | −1.50359 | −0.751796 | − | 0.659395i | \(-0.770812\pi\) | ||||
−0.751796 | + | 0.659395i | \(0.770812\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.5959 | 0.506273 | 0.253136 | − | 0.967431i | \(-0.418538\pi\) | ||||
0.253136 | + | 0.967431i | \(0.418538\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.44949 | 0.258809 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −70.2929 | −2.81622 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.0102 | 0.880408 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −22.2474 | −0.888478 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.65153 | 0.225341 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1010 | −0.481734 | −0.240867 | − | 0.970558i | \(-0.577432\pi\) | ||||
−0.240867 | + | 0.970558i | \(0.577432\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.89898 | 0.194717 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.09082 | 0.321074 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.75255 | 0.227924 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.34847 | 0.172023 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.1464 | −1.50669 | −0.753347 | − | 0.657624i | \(-0.771562\pi\) | ||||
−0.753347 | + | 0.657624i | \(0.771562\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.8990 | −1.29741 | −0.648705 | − | 0.761040i | \(-0.724689\pi\) | ||||
−0.648705 | + | 0.761040i | \(0.724689\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.449490 | 0.0176986 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.0454 | −1.33846 | −0.669232 | − | 0.743054i | \(-0.733377\pi\) | ||||
−0.669232 | + | 0.743054i | \(0.733377\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 50.6969 | 1.99003 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 31.1464 | 1.22072 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.85357 | −0.385600 | −0.192800 | − | 0.981238i | \(-0.561757\pi\) | ||||
−0.192800 | + | 0.981238i | \(0.561757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.50510 | −0.215102 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.00000 | 0.0390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.1010 | 0.744070 | 0.372035 | − | 0.928219i | \(-0.378660\pi\) | ||||
0.372035 | + | 0.928219i | \(0.378660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.30306 | −0.0506832 | −0.0253416 | − | 0.999679i | \(-0.508067\pi\) | ||||
−0.0253416 | + | 0.999679i | \(0.508067\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.651531 | −0.0253034 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.8990 | 0.500201 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −53.8434 | −2.08482 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.79796 | −0.0695131 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.1464 | 1.70425 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.4949 | 0.404549 | 0.202274 | − | 0.979329i | \(-0.435167\pi\) | ||||
0.202274 | + | 0.979329i | \(0.435167\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.79796 | −0.184674 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.1464 | −1.50452 | −0.752260 | − | 0.658867i | \(-0.771036\pi\) | ||||
−0.752260 | + | 0.658867i | \(0.771036\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.8990 | −0.571770 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.5505 | −0.710857 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.5959 | −1.59162 | −0.795812 | − | 0.605544i | \(-0.792956\pi\) | ||||
−0.795812 | + | 0.605544i | \(0.792956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.55051 | 0.0592420 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.55051 | 0.364375 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.79796 | 0.220885 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7423 | −1.16949 | −0.584747 | − | 0.811216i | \(-0.698806\pi\) | ||||
−0.584747 | + | 0.811216i | \(0.698806\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.3485 | 0.583040 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0908154 | −0.00344482 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.44949 | 0.0549033 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.8990 | −1.01596 | −0.507980 | − | 0.861369i | \(-0.669608\pi\) | ||||
−0.507980 | + | 0.861369i | \(0.669608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.1464 | 0.948416 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.04541 | −0.0770345 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.3485 | −0.727674 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.1010 | −1.39336 | −0.696679 | − | 0.717383i | \(-0.745340\pi\) | ||||
−0.696679 | + | 0.717383i | \(0.745340\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.0000 | 0.375029 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.1464 | 1.69075 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.696938 | −0.0260640 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.89898 | −0.332338 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.04541 | 0.337337 | 0.168668 | − | 0.985673i | \(-0.446053\pi\) | ||||
0.168668 | + | 0.985673i | \(0.446053\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 57.8434 | 2.15420 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.69694 | 0.137491 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.0556 | 1.48763 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1464 | −1.08098 | −0.540491 | − | 0.841350i | \(-0.681761\pi\) | ||||
−0.540491 | + | 0.841350i | \(0.681761\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.44949 | 0.0536113 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.3031 | 0.823782 | 0.411891 | − | 0.911233i | \(-0.364868\pi\) | ||||
0.411891 | + | 0.911233i | \(0.364868\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.75255 | −0.212186 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.7980 | 0.876609 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.7980 | −1.64792 | −0.823960 | − | 0.566648i | \(-0.808240\pi\) | ||||
−0.823960 | + | 0.566648i | \(0.808240\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.89898 | −0.106497 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.20204 | 0.154158 | 0.0770790 | − | 0.997025i | \(-0.475441\pi\) | ||||
0.0770790 | + | 0.997025i | \(0.475441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.49490 | −0.164680 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.55051 | −0.276259 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.89898 | 0.325162 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0000 | 0.802791 | 0.401396 | − | 0.915905i | \(-0.368525\pi\) | ||||
0.401396 | + | 0.915905i | \(0.368525\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.8990 | 0.688717 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.80816 | 0.320562 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.24745 | 0.299759 | 0.149879 | − | 0.988704i | \(-0.452111\pi\) | ||||
0.149879 | + | 0.988704i | \(0.452111\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.2474 | 0.807531 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.4949 | −1.90294 | −0.951469 | − | 0.307744i | \(-0.900426\pi\) | ||||
−0.951469 | + | 0.307744i | \(0.900426\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.7980 | −0.861544 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.651531 | 0.0235561 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.60612 | 0.238533 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.1010 | −1.01335 | −0.506674 | − | 0.862138i | \(-0.669125\pi\) | ||||
−0.506674 | + | 0.862138i | \(0.669125\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.1464 | 0.941641 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.0454 | −0.541146 | −0.270573 | − | 0.962700i | \(-0.587213\pi\) | ||||
−0.270573 | + | 0.962700i | \(0.587213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.5857 | −1.20643 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.3485 | −0.622373 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.44949 | 0.231077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.0000 | 0.536742 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.34847 | −0.298350 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.50510 | −0.125102 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.2020 | 0.470602 | 0.235301 | − | 0.971923i | \(-0.424392\pi\) | ||||
0.235301 | + | 0.971923i | \(0.424392\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17.2474 | −0.614025 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.75255 | 0.204279 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.79796 | −0.205632 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.4949 | −0.655123 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.59592 | −0.233347 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.7980 | −0.558193 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.44949 | 0.121730 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.8990 | −0.454629 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.8990 | 0.454066 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.89898 | −0.101923 | −0.0509613 | − | 0.998701i | \(-0.516229\pi\) | ||||
−0.0509613 | + | 0.998701i | \(0.516229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.9898 | 1.68515 | 0.842575 | − | 0.538579i | \(-0.181039\pi\) | ||||
0.842575 | + | 0.538579i | \(0.181039\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.6969 | −0.620659 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.55051 | −0.124369 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.44949 | 0.225639 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.4495 | −0.643892 | −0.321946 | − | 0.946758i | \(-0.604337\pi\) | ||||
−0.321946 | + | 0.946758i | \(0.604337\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.6969 | −0.721450 | −0.360725 | − | 0.932672i | \(-0.617471\pi\) | ||||
−0.360725 | + | 0.932672i | \(0.617471\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.5505 | −0.576215 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.1464 | 1.25693 | 0.628467 | − | 0.777836i | \(-0.283683\pi\) | ||||
0.628467 | + | 0.777836i | \(0.283683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.5959 | −1.13210 | −0.566052 | − | 0.824370i | \(-0.691530\pi\) | ||||
−0.566052 | + | 0.824370i | \(0.691530\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.7980 | −0.374577 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.5505 | −0.642737 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.11123 | −0.211488 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.00000 | 0.241955 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.8990 | 1.41199 | 0.705995 | − | 0.708217i | \(-0.250500\pi\) | ||||
0.705995 | + | 0.708217i | \(0.250500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40.6969 | 1.40334 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.4495 | 1.01429 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.75255 | 0.197894 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.00000 | 0.137442 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.89898 | −0.339732 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.1464 | −0.862008 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.0000 | −0.410872 | −0.205436 | − | 0.978671i | \(-0.565861\pi\) | ||||
−0.205436 | + | 0.978671i | \(0.565861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.89898 | 0.0991430 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.89898 | 0.167346 | 0.0836730 | − | 0.996493i | \(-0.473335\pi\) | ||||
0.0836730 | + | 0.996493i | \(0.473335\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.2020 | −0.791643 | −0.395822 | − | 0.918327i | \(-0.629540\pi\) | ||||
−0.395822 | + | 0.918327i | \(0.629540\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.44949 | −0.151638 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.4495 | −1.10459 | −0.552297 | − | 0.833648i | \(-0.686248\pi\) | ||||
−0.552297 | + | 0.833648i | \(0.686248\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.39388 | 0.115395 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.8990 | −0.505996 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.4949 | 1.17016 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.10102 | 0.105074 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.34847 | −0.113329 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.5959 | 0.662463 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.8990 | 1.27976 | 0.639879 | − | 0.768476i | \(-0.278985\pi\) | ||||
0.639879 | + | 0.768476i | \(0.278985\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.3485 | −0.483962 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.0000 | −0.404290 | −0.202145 | − | 0.979356i | \(-0.564791\pi\) | ||||
−0.202145 | + | 0.979356i | \(0.564791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.7423 | 1.23648 | 0.618239 | − | 0.785990i | \(-0.287846\pi\) | ||||
0.618239 | + | 0.785990i | \(0.287846\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.60612 | −0.222062 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.3485 | 0.951848 | 0.475924 | − | 0.879486i | \(-0.342114\pi\) | ||||
0.475924 | + | 0.879486i | \(0.342114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −80.0908 | −2.68616 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.44949 | 0.115562 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.3485 | −0.982109 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.85357 | 0.0953844 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.89898 | 0.0967941 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −58.4393 | −1.94906 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.6969 | −0.622885 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.44949 | −0.148070 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.20204 | 0.206163 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.7980 | 1.05583 | 0.527917 | − | 0.849296i | \(-0.322973\pi\) | ||||
0.527917 | + | 0.849296i | \(0.322973\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.34847 | −0.144230 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.9444 | 0.362604 | 0.181302 | − | 0.983427i | \(-0.441969\pi\) | ||||
0.181302 | + | 0.983427i | \(0.441969\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.0454 | −0.861977 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.75255 | −0.190173 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 54.4949 | 1.79958 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.2474 | 0.865823 | 0.432912 | − | 0.901436i | \(-0.357486\pi\) | ||||
0.432912 | + | 0.901436i | \(0.357486\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.5959 | −0.810463 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.95459 | 0.0643362 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.7071 | 0.615087 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.0000 | 0.426976 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.14643 | −0.0704220 | −0.0352110 | − | 0.999380i | \(-0.511210\pi\) | ||||
−0.0352110 | + | 0.999380i | \(0.511210\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −82.5403 | −2.70515 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.6969 | 1.00497 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.24745 | 0.0734994 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.0000 | −0.914720 | −0.457360 | − | 0.889282i | \(-0.651205\pi\) | ||||
−0.457360 | + | 0.889282i | \(0.651205\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.34847 | −0.305076 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.2020 | −0.788964 | −0.394482 | − | 0.918904i | \(-0.629076\pi\) | ||||
−0.394482 | + | 0.918904i | \(0.629076\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.44949 | −0.210024 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.00000 | −0.0650600 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.202041 | −0.00656545 | −0.00328273 | − | 0.999995i | \(-0.501045\pi\) | ||||
−0.00328273 | + | 0.999995i | \(0.501045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.449490 | 0.0145911 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.24745 | 0.299869 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.0454 | −0.454975 | −0.227488 | − | 0.973781i | \(-0.573051\pi\) | ||||
−0.227488 | + | 0.973781i | \(0.573051\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.39388 | −0.0451048 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −28.7980 | −0.930906 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.3485 | −0.495628 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.00000 | 0.0644491 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.39388 | −0.109253 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.0000 | 1.09337 | 0.546683 | − | 0.837340i | \(-0.315890\pi\) | ||||
0.546683 | + | 0.837340i | \(0.315890\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.34847 | 0.300316 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.5505 | 1.10878 | 0.554389 | − | 0.832257i | \(-0.312952\pi\) | ||||
0.554389 | + | 0.832257i | \(0.312952\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.898979 | 0.0288200 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.15663 | −0.0690675 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0454 | −0.673302 | −0.336651 | − | 0.941629i | \(-0.609294\pi\) | ||||
−0.336651 | + | 0.941629i | \(0.609294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −54.4949 | −1.74166 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.34847 | −0.170763 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.1464 | 1.12100 | 0.560498 | − | 0.828155i | \(-0.310610\pi\) | ||||
0.560498 | + | 0.828155i | \(0.310610\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.8082 | −0.344377 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.2474 | 0.644483 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.44949 | −0.205082 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.8888 | 1.58477 | 0.792385 | − | 0.610022i | \(-0.208839\pi\) | ||||
0.792385 | + | 0.610022i | \(0.208839\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.5505 | 0.810821 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.49490 | 0.205902 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.65153 | −0.210656 | −0.105328 | − | 0.994438i | \(-0.533589\pi\) | ||||
−0.105328 | + | 0.994438i | \(0.533589\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.89898 | −0.123358 |
(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 | 7872.2.a.bq.1.1 | 2 | ||
4.3 | odd | 2 | 7872.2.a.bm.1.1 | 2 | |||
8.3 | odd | 2 | 1968.2.a.s.1.2 | 2 | |||
8.5 | even | 2 | 492.2.a.c.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 1476.2.a.d.1.1 | 2 | |||
24.11 | even | 2 | 5904.2.a.ba.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
492.2.a.c.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
1476.2.a.d.1.1 | 2 | 24.5 | odd | 2 | |||
1968.2.a.s.1.2 | 2 | 8.3 | odd | 2 | |||
5904.2.a.ba.1.1 | 2 | 24.11 | even | 2 | |||
7872.2.a.bm.1.1 | 2 | 4.3 | odd | 2 | |||
7872.2.a.bq.1.1 | 2 | 1.1 | even | 1 | trivial |