Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 50x^{6} + 698x^{4} - 2653x^{2} + 2268 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.95827\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.95827 | −1.39946 | −0.699730 | − | 0.714408i | \(-0.746696\pi\) | ||||
−0.699730 | + | 0.714408i | \(0.746696\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.66789 | 0.958486 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 1.31458 | 0.0580966 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.4481 | −0.505666 | −0.252833 | − | 0.967510i | \(-0.581362\pi\) | ||||
−0.252833 | + | 0.967510i | \(0.581362\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 48.8596 | 1.04240 | 0.521201 | − | 0.853434i | \(-0.325484\pi\) | ||||
0.521201 | + | 0.853434i | \(0.325484\pi\) | |||||||
\(14\) | −27.7079 | −0.528946 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −66.5466 | −1.03979 | ||||||||
\(17\) | −124.724 | −1.77941 | −0.889703 | − | 0.456539i | \(-0.849089\pi\) | ||||
−0.889703 | + | 0.456539i | \(0.849089\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −122.717 | −1.48175 | −0.740874 | − | 0.671644i | \(-0.765588\pi\) | ||||
−0.740874 | + | 0.671644i | \(0.765588\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 73.0227 | 0.707659 | ||||||||
\(23\) | −140.628 | −1.27491 | −0.637456 | − | 0.770487i | \(-0.720013\pi\) | ||||
−0.637456 | + | 0.770487i | \(0.720013\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −193.400 | −1.45880 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 53.6752 | 0.362274 | ||||||||
\(29\) | 196.100 | 1.25569 | 0.627843 | − | 0.778340i | \(-0.283938\pi\) | ||||
0.627843 | + | 0.778340i | \(0.283938\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 289.591 | 1.67781 | 0.838905 | − | 0.544277i | \(-0.183196\pi\) | ||||
0.838905 | + | 0.544277i | \(0.183196\pi\) | |||||||
\(32\) | 252.893 | 1.39705 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 493.690 | 2.49021 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −401.649 | −1.78461 | −0.892307 | − | 0.451429i | \(-0.850914\pi\) | ||||
−0.892307 | + | 0.451429i | \(0.850914\pi\) | |||||||
\(38\) | 485.747 | 2.07365 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 303.093 | 1.15452 | 0.577258 | − | 0.816562i | \(-0.304123\pi\) | ||||
0.577258 | + | 0.816562i | \(0.304123\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 202.027 | 0.716485 | 0.358242 | − | 0.933629i | \(-0.383376\pi\) | ||||
0.358242 | + | 0.933629i | \(0.383376\pi\) | |||||||
\(44\) | −141.458 | −0.484674 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 556.643 | 1.78419 | ||||||||
\(47\) | −308.944 | −0.958811 | −0.479405 | − | 0.877594i | \(-0.659148\pi\) | ||||
−0.479405 | + | 0.877594i | \(0.659148\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 374.650 | 0.999128 | ||||||||
\(53\) | −461.082 | −1.19499 | −0.597495 | − | 0.801873i | \(-0.703837\pi\) | ||||
−0.597495 | + | 0.801873i | \(0.703837\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.20203 | 0.0219584 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −776.217 | −1.75728 | ||||||||
\(59\) | −111.900 | −0.246918 | −0.123459 | − | 0.992350i | \(-0.539399\pi\) | ||||
−0.123459 | + | 0.992350i | \(0.539399\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 416.658 | 0.874551 | 0.437276 | − | 0.899327i | \(-0.355943\pi\) | ||||
0.437276 | + | 0.899327i | \(0.355943\pi\) | |||||||
\(62\) | −1146.28 | −2.34803 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −468.644 | −0.915321 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 452.322 | 0.824775 | 0.412388 | − | 0.911009i | \(-0.364695\pi\) | ||||
0.412388 | + | 0.911009i | \(0.364695\pi\) | |||||||
\(68\) | −956.367 | −1.70554 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1008.59 | −1.68589 | −0.842944 | − | 0.538001i | \(-0.819180\pi\) | ||||
−0.842944 | + | 0.538001i | \(0.819180\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 669.043 | 1.07268 | 0.536339 | − | 0.844002i | \(-0.319807\pi\) | ||||
0.536339 | + | 0.844002i | \(0.319807\pi\) | |||||||
\(74\) | 1589.84 | 2.49749 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −940.980 | −1.42024 | ||||||||
\(77\) | −129.137 | −0.191124 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 517.398 | 0.736859 | 0.368429 | − | 0.929656i | \(-0.379896\pi\) | ||||
0.368429 | + | 0.929656i | \(0.379896\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1199.72 | −1.61570 | ||||||||
\(83\) | 35.3950 | 0.0468085 | 0.0234042 | − | 0.999726i | \(-0.492550\pi\) | ||||
0.0234042 | + | 0.999726i | \(0.492550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −799.677 | −1.00269 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −24.2515 | −0.0293775 | ||||||||
\(89\) | 1082.09 | 1.28878 | 0.644389 | − | 0.764698i | \(-0.277112\pi\) | ||||
0.644389 | + | 0.764698i | \(0.277112\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 342.018 | 0.393991 | ||||||||
\(92\) | −1078.32 | −1.22199 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1222.88 | 1.34182 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 203.138 | 0.212634 | 0.106317 | − | 0.994332i | \(-0.466094\pi\) | ||||
0.106317 | + | 0.994332i | \(0.466094\pi\) | |||||||
\(98\) | −193.955 | −0.199923 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1567.11 | −1.54390 | −0.771949 | − | 0.635684i | \(-0.780718\pi\) | ||||
−0.771949 | + | 0.635684i | \(0.780718\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −473.964 | −0.453409 | −0.226704 | − | 0.973964i | \(-0.572795\pi\) | ||||
−0.226704 | + | 0.973964i | \(0.572795\pi\) | |||||||
\(104\) | 64.2297 | 0.0605600 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1825.09 | 1.67234 | ||||||||
\(107\) | −496.898 | −0.448943 | −0.224472 | − | 0.974481i | \(-0.572066\pi\) | ||||
−0.224472 | + | 0.974481i | \(0.572066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1125.46 | 0.988983 | 0.494492 | − | 0.869182i | \(-0.335354\pi\) | ||||
0.494492 | + | 0.869182i | \(0.335354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −465.826 | −0.393004 | ||||||||
\(113\) | 184.508 | 0.153603 | 0.0768013 | − | 0.997046i | \(-0.475529\pi\) | ||||
0.0768013 | + | 0.997046i | \(0.475529\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1503.67 | 1.20356 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 442.931 | 0.345552 | ||||||||
\(119\) | −873.065 | −0.672553 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −990.666 | −0.744302 | ||||||||
\(122\) | −1649.25 | −1.22390 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2220.55 | 1.60816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2835.92 | 1.98148 | 0.990738 | − | 0.135784i | \(-0.0433553\pi\) | ||||
0.990738 | + | 0.135784i | \(0.0433553\pi\) | |||||||
\(128\) | −168.121 | −0.116093 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −189.998 | −0.126719 | −0.0633595 | − | 0.997991i | \(-0.520181\pi\) | ||||
−0.0633595 | + | 0.997991i | \(0.520181\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −859.019 | −0.560048 | ||||||||
\(134\) | −1790.41 | −1.15424 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −163.959 | −0.103377 | ||||||||
\(137\) | −2230.24 | −1.39082 | −0.695408 | − | 0.718615i | \(-0.744777\pi\) | ||||
−0.695408 | + | 0.718615i | \(0.744777\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −398.286 | −0.243037 | −0.121519 | − | 0.992589i | \(-0.538776\pi\) | ||||
−0.121519 | + | 0.992589i | \(0.538776\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3992.29 | 2.35933 | ||||||||
\(143\) | −901.370 | −0.527107 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2648.25 | −1.50117 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3079.80 | −1.71053 | ||||||||
\(149\) | 3556.30 | 1.95532 | 0.977662 | − | 0.210183i | \(-0.0674060\pi\) | ||||
0.977662 | + | 0.210183i | \(0.0674060\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −955.955 | −0.515196 | −0.257598 | − | 0.966252i | \(-0.582931\pi\) | ||||
−0.257598 | + | 0.966252i | \(0.582931\pi\) | |||||||
\(152\) | −161.321 | −0.0860845 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 511.159 | 0.267470 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3095.78 | −1.57370 | −0.786848 | − | 0.617147i | \(-0.788288\pi\) | ||||
−0.786848 | + | 0.617147i | \(0.788288\pi\) | |||||||
\(158\) | −2048.00 | −1.03120 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −984.396 | −0.481871 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2665.44 | −1.28082 | −0.640409 | − | 0.768034i | \(-0.721235\pi\) | ||||
−0.640409 | + | 0.768034i | \(0.721235\pi\) | |||||||
\(164\) | 2324.08 | 1.10659 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −140.103 | −0.0655065 | ||||||||
\(167\) | 967.998 | 0.448538 | 0.224269 | − | 0.974527i | \(-0.428000\pi\) | ||||
0.224269 | + | 0.974527i | \(0.428000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 190.265 | 0.0866023 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1549.12 | 0.686741 | ||||||||
\(173\) | 2793.34 | 1.22759 | 0.613796 | − | 0.789465i | \(-0.289642\pi\) | ||||
0.613796 | + | 0.789465i | \(0.289642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1227.66 | 0.525786 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4283.20 | −1.80359 | ||||||||
\(179\) | 449.319 | 0.187618 | 0.0938091 | − | 0.995590i | \(-0.470096\pi\) | ||||
0.0938091 | + | 0.995590i | \(0.470096\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2054.72 | 0.843790 | 0.421895 | − | 0.906645i | \(-0.361365\pi\) | ||||
0.421895 | + | 0.906645i | \(0.361365\pi\) | |||||||
\(182\) | −1353.80 | −0.551374 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −184.866 | −0.0740680 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2300.92 | 0.899785 | ||||||||
\(188\) | −2368.95 | −0.919007 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −42.1490 | −0.0159675 | −0.00798376 | − | 0.999968i | \(-0.502541\pi\) | ||||
−0.00798376 | + | 0.999968i | \(0.502541\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3613.73 | 1.34778 | 0.673890 | − | 0.738831i | \(-0.264622\pi\) | ||||
0.673890 | + | 0.738831i | \(0.264622\pi\) | |||||||
\(194\) | −804.074 | −0.297573 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 375.727 | 0.136927 | ||||||||
\(197\) | −2429.72 | −0.878733 | −0.439366 | − | 0.898308i | \(-0.644797\pi\) | ||||
−0.439366 | + | 0.898308i | \(0.644797\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3540.39 | 1.26116 | 0.630582 | − | 0.776123i | \(-0.282816\pi\) | ||||
0.630582 | + | 0.776123i | \(0.282816\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6203.06 | 2.16062 | ||||||||
\(203\) | 1372.70 | 0.474604 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1876.08 | 0.634527 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3251.44 | −1.08388 | ||||||||
\(209\) | 2263.90 | 0.749269 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2183.66 | −0.712461 | −0.356230 | − | 0.934398i | \(-0.615938\pi\) | ||||
−0.356230 | + | 0.934398i | \(0.615938\pi\) | |||||||
\(212\) | −3535.53 | −1.14538 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1966.85 | 0.628278 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2027.14 | 0.634153 | ||||||||
\(218\) | −4454.86 | −1.38404 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6093.95 | −1.85486 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5276.91 | −1.58461 | −0.792305 | − | 0.610126i | \(-0.791119\pi\) | ||||
−0.792305 | + | 0.610126i | \(0.791119\pi\) | |||||||
\(224\) | 1770.25 | 0.528034 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −730.334 | −0.214960 | ||||||||
\(227\) | 4472.50 | 1.30771 | 0.653855 | − | 0.756620i | \(-0.273151\pi\) | ||||
0.653855 | + | 0.756620i | \(0.273151\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1698.75 | 0.490202 | 0.245101 | − | 0.969498i | \(-0.421179\pi\) | ||||
0.245101 | + | 0.969498i | \(0.421179\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 257.788 | 0.0729510 | ||||||||
\(233\) | 4857.72 | 1.36583 | 0.682917 | − | 0.730496i | \(-0.260711\pi\) | ||||
0.682917 | + | 0.730496i | \(0.260711\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −858.039 | −0.236668 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3455.83 | 0.941210 | ||||||||
\(239\) | −375.571 | −0.101647 | −0.0508235 | − | 0.998708i | \(-0.516185\pi\) | ||||
−0.0508235 | + | 0.998708i | \(0.516185\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1005.92 | −0.268868 | −0.134434 | − | 0.990923i | \(-0.542922\pi\) | ||||
−0.134434 | + | 0.990923i | \(0.542922\pi\) | |||||||
\(242\) | 3921.32 | 1.04162 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3194.89 | 0.838246 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5995.91 | −1.54458 | ||||||||
\(248\) | 380.690 | 0.0974751 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5462.83 | 1.37375 | 0.686874 | − | 0.726776i | \(-0.258982\pi\) | ||||
0.686874 | + | 0.726776i | \(0.258982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2594.33 | 0.644679 | ||||||||
\(254\) | −11225.3 | −2.77300 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4414.62 | 1.07779 | ||||||||
\(257\) | 427.791 | 0.103832 | 0.0519161 | − | 0.998651i | \(-0.483467\pi\) | ||||
0.0519161 | + | 0.998651i | \(0.483467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2811.54 | −0.674521 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 752.062 | 0.177338 | ||||||||
\(263\) | 520.645 | 0.122070 | 0.0610349 | − | 0.998136i | \(-0.480560\pi\) | ||||
0.0610349 | + | 0.998136i | \(0.480560\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3400.23 | 0.783764 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3468.36 | 0.790536 | ||||||||
\(269\) | 1995.64 | 0.452328 | 0.226164 | − | 0.974089i | \(-0.427381\pi\) | ||||
0.226164 | + | 0.974089i | \(0.427381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5212.99 | 1.16851 | 0.584256 | − | 0.811569i | \(-0.301386\pi\) | ||||
0.584256 | + | 0.811569i | \(0.301386\pi\) | |||||||
\(272\) | 8299.93 | 1.85021 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8827.87 | 1.94639 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6338.81 | 1.37495 | 0.687477 | − | 0.726206i | \(-0.258718\pi\) | ||||
0.687477 | + | 0.726206i | \(0.258718\pi\) | |||||||
\(278\) | 1576.52 | 0.340121 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4861.28 | 1.03203 | 0.516014 | − | 0.856580i | \(-0.327415\pi\) | ||||
0.516014 | + | 0.856580i | \(0.327415\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1040.23 | −0.218499 | −0.109250 | − | 0.994014i | \(-0.534845\pi\) | ||||
−0.109250 | + | 0.994014i | \(0.534845\pi\) | |||||||
\(284\) | −7733.79 | −1.61590 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3567.86 | 0.737665 | ||||||||
\(287\) | 2121.65 | 0.436366 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10643.0 | 2.16629 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5130.15 | 1.02815 | ||||||||
\(293\) | −3807.01 | −0.759072 | −0.379536 | − | 0.925177i | \(-0.623916\pi\) | ||||
−0.379536 | + | 0.925177i | \(0.623916\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −527.998 | −0.103680 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14076.8 | −2.73640 | ||||||||
\(299\) | −6871.03 | −1.32897 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1414.19 | 0.270806 | ||||||||
\(302\) | 3783.93 | 0.720995 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8166.39 | 1.54071 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1313.26 | −0.244142 | −0.122071 | − | 0.992521i | \(-0.538954\pi\) | ||||
−0.122071 | + | 0.992521i | \(0.538954\pi\) | |||||||
\(308\) | −990.208 | −0.183189 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 566.183 | 0.103232 | 0.0516162 | − | 0.998667i | \(-0.483563\pi\) | ||||
0.0516162 | + | 0.998667i | \(0.483563\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1146.47 | −0.207036 | −0.103518 | − | 0.994628i | \(-0.533010\pi\) | ||||
−0.103518 | + | 0.994628i | \(0.533010\pi\) | |||||||
\(314\) | 12253.9 | 2.20232 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3967.35 | 0.706269 | ||||||||
\(317\) | 2562.45 | 0.454012 | 0.227006 | − | 0.973893i | \(-0.427106\pi\) | ||||
0.227006 | + | 0.973893i | \(0.427106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3617.68 | −0.634957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3896.50 | 0.674359 | ||||||||
\(323\) | 15305.7 | 2.63663 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10550.5 | 1.79245 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 398.438 | 0.0670734 | ||||||||
\(329\) | −2162.61 | −0.362396 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −917.092 | −0.152290 | −0.0761450 | − | 0.997097i | \(-0.524261\pi\) | ||||
−0.0761450 | + | 0.997097i | \(0.524261\pi\) | |||||||
\(332\) | 271.405 | 0.0448653 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3831.60 | −0.627711 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2446.17 | −0.395405 | −0.197702 | − | 0.980262i | \(-0.563348\pi\) | ||||
−0.197702 | + | 0.980262i | \(0.563348\pi\) | |||||||
\(338\) | −753.121 | −0.121196 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5342.42 | −0.848412 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 265.580 | 0.0416253 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11056.8 | −1.71796 | ||||||||
\(347\) | 3598.36 | 0.556687 | 0.278343 | − | 0.960482i | \(-0.410215\pi\) | ||||
0.278343 | + | 0.960482i | \(0.410215\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −247.567 | −0.0379712 | −0.0189856 | − | 0.999820i | \(-0.506044\pi\) | ||||
−0.0189856 | + | 0.999820i | \(0.506044\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4665.40 | −0.706439 | ||||||||
\(353\) | −81.3189 | −0.0122611 | −0.00613055 | − | 0.999981i | \(-0.501951\pi\) | ||||
−0.00613055 | + | 0.999981i | \(0.501951\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8297.35 | 1.23528 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1778.52 | −0.262564 | ||||||||
\(359\) | −4547.08 | −0.668483 | −0.334242 | − | 0.942487i | \(-0.608480\pi\) | ||||
−0.334242 | + | 0.942487i | \(0.608480\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8200.46 | 1.19558 | ||||||||
\(362\) | −8133.12 | −1.18085 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2622.55 | 0.377635 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11297.4 | −1.60686 | −0.803429 | − | 0.595401i | \(-0.796993\pi\) | ||||
−0.803429 | + | 0.595401i | \(0.796993\pi\) | |||||||
\(368\) | 9358.31 | 1.32564 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3227.57 | −0.451664 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2880.15 | 0.399808 | 0.199904 | − | 0.979816i | \(-0.435937\pi\) | ||||
0.199904 | + | 0.979816i | \(0.435937\pi\) | |||||||
\(374\) | −9107.65 | −1.25921 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −406.130 | −0.0557036 | ||||||||
\(377\) | 9581.38 | 1.30893 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10505.6 | −1.42384 | −0.711922 | − | 0.702259i | \(-0.752175\pi\) | ||||
−0.711922 | + | 0.702259i | \(0.752175\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 166.837 | 0.0223459 | ||||||||
\(383\) | −522.066 | −0.0696510 | −0.0348255 | − | 0.999393i | \(-0.511088\pi\) | ||||
−0.0348255 | + | 0.999393i | \(0.511088\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14304.1 | −1.88616 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1557.64 | 0.203807 | ||||||||
\(389\) | 6513.24 | 0.848932 | 0.424466 | − | 0.905444i | \(-0.360462\pi\) | ||||
0.424466 | + | 0.905444i | \(0.360462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17539.6 | 2.26859 | ||||||||
\(392\) | 64.4142 | 0.00829951 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9617.48 | 1.22975 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9106.98 | −1.15130 | −0.575650 | − | 0.817696i | \(-0.695251\pi\) | ||||
−0.575650 | + | 0.817696i | \(0.695251\pi\) | |||||||
\(398\) | −14013.8 | −1.76495 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3204.43 | 0.399056 | 0.199528 | − | 0.979892i | \(-0.436059\pi\) | ||||
0.199528 | + | 0.979892i | \(0.436059\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14149.3 | 1.74895 | ||||||||
\(404\) | −12016.5 | −1.47981 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5433.52 | −0.664190 | ||||||||
\(407\) | 7409.68 | 0.902418 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6396.33 | 0.773296 | 0.386648 | − | 0.922227i | \(-0.373633\pi\) | ||||
0.386648 | + | 0.922227i | \(0.373633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3634.31 | −0.434586 | ||||||||
\(413\) | −783.302 | −0.0933263 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12356.2 | 1.45629 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8961.13 | −1.04857 | ||||||||
\(419\) | 11046.1 | 1.28791 | 0.643956 | − | 0.765062i | \(-0.277292\pi\) | ||||
0.643956 | + | 0.765062i | \(0.277292\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15873.7 | 1.83762 | 0.918811 | − | 0.394698i | \(-0.129151\pi\) | ||||
0.918811 | + | 0.394698i | \(0.129151\pi\) | |||||||
\(422\) | 8643.51 | 0.997060 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −606.127 | −0.0694248 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2916.61 | 0.330549 | ||||||||
\(428\) | −3810.16 | −0.430306 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4878.52 | 0.545221 | 0.272611 | − | 0.962124i | \(-0.412113\pi\) | ||||
0.272611 | + | 0.962124i | \(0.412113\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8450.44 | 0.937880 | 0.468940 | − | 0.883230i | \(-0.344636\pi\) | ||||
0.468940 | + | 0.883230i | \(0.344636\pi\) | |||||||
\(434\) | −8023.96 | −0.887471 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8629.88 | 0.947927 | ||||||||
\(437\) | 17257.4 | 1.88910 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10996.0 | 1.19546 | 0.597732 | − | 0.801696i | \(-0.296069\pi\) | ||||
0.597732 | + | 0.801696i | \(0.296069\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24121.5 | 2.59580 | ||||||||
\(443\) | 13494.3 | 1.44725 | 0.723626 | − | 0.690193i | \(-0.242474\pi\) | ||||
0.723626 | + | 0.690193i | \(0.242474\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20887.4 | 2.21760 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3280.51 | −0.345959 | ||||||||
\(449\) | −15411.4 | −1.61984 | −0.809920 | − | 0.586540i | \(-0.800490\pi\) | ||||
−0.809920 | + | 0.586540i | \(0.800490\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5591.50 | −0.583799 | ||||||||
\(452\) | 1414.79 | 0.147226 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17703.3 | −1.83009 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11175.7 | 1.14393 | 0.571967 | − | 0.820277i | \(-0.306181\pi\) | ||||
0.571967 | + | 0.820277i | \(0.306181\pi\) | |||||||
\(458\) | −6724.10 | −0.686018 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6343.45 | 0.640876 | 0.320438 | − | 0.947270i | \(-0.396170\pi\) | ||||
0.320438 | + | 0.947270i | \(0.396170\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5947.99 | 0.597034 | 0.298517 | − | 0.954404i | \(-0.403508\pi\) | ||||
0.298517 | + | 0.954404i | \(0.403508\pi\) | |||||||
\(464\) | −13049.8 | −1.30565 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19228.1 | −1.91143 | ||||||||
\(467\) | 11775.8 | 1.16685 | 0.583424 | − | 0.812168i | \(-0.301713\pi\) | ||||
0.583424 | + | 0.812168i | \(0.301713\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3166.25 | 0.311736 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −147.101 | −0.0143451 | ||||||||
\(473\) | −3727.02 | −0.362302 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6694.57 | −0.644632 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1486.61 | 0.142251 | ||||||||
\(479\) | 18005.6 | 1.71753 | 0.858765 | − | 0.512370i | \(-0.171232\pi\) | ||||
0.858765 | + | 0.512370i | \(0.171232\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19624.4 | −1.86029 | ||||||||
\(482\) | 3981.71 | 0.376269 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7596.32 | −0.713403 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11098.4 | 1.03268 | 0.516340 | − | 0.856383i | \(-0.327294\pi\) | ||||
0.516340 | + | 0.856383i | \(0.327294\pi\) | |||||||
\(488\) | 547.729 | 0.0508085 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11253.9 | −1.03438 | −0.517191 | − | 0.855870i | \(-0.673022\pi\) | ||||
−0.517191 | + | 0.855870i | \(0.673022\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24458.3 | −2.23437 | ||||||||
\(494\) | 23733.4 | 2.16157 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19271.3 | −1.74457 | ||||||||
\(497\) | −7060.16 | −0.637206 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6099.94 | −0.547236 | −0.273618 | − | 0.961838i | \(-0.588220\pi\) | ||||
−0.273618 | + | 0.961838i | \(0.588220\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21623.3 | −1.92250 | ||||||||
\(503\) | 19384.4 | 1.71830 | 0.859152 | − | 0.511721i | \(-0.170992\pi\) | ||||
0.859152 | + | 0.511721i | \(0.170992\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10269.0 | −0.902202 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21745.6 | 1.89922 | ||||||||
\(509\) | 5257.46 | 0.457825 | 0.228912 | − | 0.973447i | \(-0.426483\pi\) | ||||
0.228912 | + | 0.973447i | \(0.426483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4683.30 | 0.405434 | ||||||||
\(512\) | −16129.3 | −1.39223 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1693.31 | −0.145309 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5699.44 | 0.484838 | ||||||||
\(518\) | 11128.8 | 0.943964 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7762.65 | −0.652760 | −0.326380 | − | 0.945239i | \(-0.605829\pi\) | ||||
−0.326380 | + | 0.945239i | \(0.605829\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9640.89 | −0.806055 | −0.403027 | − | 0.915188i | \(-0.632042\pi\) | ||||
−0.403027 | + | 0.915188i | \(0.632042\pi\) | |||||||
\(524\) | −1456.88 | −0.121458 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2060.85 | −0.170832 | ||||||||
\(527\) | −36118.9 | −2.98551 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7609.24 | 0.625399 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6586.86 | −0.536798 | ||||||||
\(533\) | 14809.0 | 1.20347 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 594.612 | 0.0479166 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7899.28 | −0.633015 | ||||||||
\(539\) | −903.959 | −0.0722380 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2039.89 | −0.162110 | −0.0810551 | − | 0.996710i | \(-0.525829\pi\) | ||||
−0.0810551 | + | 0.996710i | \(0.525829\pi\) | |||||||
\(542\) | −20634.4 | −1.63528 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −31541.7 | −2.48592 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1274.24 | 0.0996025 | 0.0498013 | − | 0.998759i | \(-0.484141\pi\) | ||||
0.0498013 | + | 0.998759i | \(0.484141\pi\) | |||||||
\(548\) | −17101.2 | −1.33308 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24064.8 | −1.86061 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3621.79 | 0.278506 | ||||||||
\(554\) | −25090.7 | −1.92419 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3054.01 | −0.232948 | ||||||||
\(557\) | 19965.7 | 1.51880 | 0.759402 | − | 0.650621i | \(-0.225492\pi\) | ||||
0.759402 | + | 0.650621i | \(0.225492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9870.97 | 0.746865 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19242.3 | −1.44428 | ||||||||
\(563\) | −13467.9 | −1.00818 | −0.504090 | − | 0.863651i | \(-0.668172\pi\) | ||||
−0.504090 | + | 0.863651i | \(0.668172\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4117.51 | 0.305781 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1325.87 | −0.0979444 | ||||||||
\(569\) | −8579.29 | −0.632096 | −0.316048 | − | 0.948743i | \(-0.602356\pi\) | ||||
−0.316048 | + | 0.948743i | \(0.602356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2146.06 | −0.157285 | −0.0786426 | − | 0.996903i | \(-0.525059\pi\) | ||||
−0.0786426 | + | 0.996903i | \(0.525059\pi\) | |||||||
\(572\) | −6911.61 | −0.505225 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8398.06 | −0.610676 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22451.1 | −1.61985 | −0.809925 | − | 0.586534i | \(-0.800492\pi\) | ||||
−0.809925 | + | 0.586534i | \(0.800492\pi\) | |||||||
\(578\) | −42127.8 | −3.03163 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 247.765 | 0.0176919 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8506.10 | 0.604266 | ||||||||
\(584\) | 879.508 | 0.0623190 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15069.2 | 1.06229 | ||||||||
\(587\) | 6015.40 | 0.422968 | 0.211484 | − | 0.977381i | \(-0.432170\pi\) | ||||
0.211484 | + | 0.977381i | \(0.432170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35537.8 | −2.48609 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 26728.4 | 1.85562 | ||||||||
\(593\) | 15737.3 | 1.08981 | 0.544903 | − | 0.838499i | \(-0.316566\pi\) | ||||
0.544903 | + | 0.838499i | \(0.316566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 27269.3 | 1.87415 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 27197.4 | 1.85984 | ||||||||
\(599\) | 25634.5 | 1.74858 | 0.874288 | − | 0.485407i | \(-0.161328\pi\) | ||||
0.874288 | + | 0.485407i | \(0.161328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6955.91 | −0.472109 | −0.236054 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236054 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(602\) | −5597.74 | −0.378982 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7330.16 | −0.493808 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −952.222 | −0.0636730 | −0.0318365 | − | 0.999493i | \(-0.510136\pi\) | ||||
−0.0318365 | + | 0.999493i | \(0.510136\pi\) | |||||||
\(608\) | −31034.2 | −2.07007 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15094.9 | −0.999466 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2962.98 | 0.195226 | 0.0976132 | − | 0.995224i | \(-0.468879\pi\) | ||||
0.0976132 | + | 0.995224i | \(0.468879\pi\) | |||||||
\(614\) | 5198.23 | 0.341667 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −169.760 | −0.0111036 | ||||||||
\(617\) | −28257.7 | −1.84378 | −0.921891 | − | 0.387449i | \(-0.873356\pi\) | ||||
−0.921891 | + | 0.387449i | \(0.873356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10708.5 | −0.695336 | −0.347668 | − | 0.937618i | \(-0.613026\pi\) | ||||
−0.347668 | + | 0.937618i | \(0.613026\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2241.10 | −0.144470 | ||||||||
\(623\) | 7574.63 | 0.487113 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4538.03 | 0.289738 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23738.1 | −1.50837 | ||||||||
\(629\) | 50095.1 | 3.17555 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17383.2 | 1.09669 | 0.548346 | − | 0.836251i | \(-0.315258\pi\) | ||||
0.548346 | + | 0.836251i | \(0.315258\pi\) | |||||||
\(632\) | 680.159 | 0.0428090 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10142.9 | −0.635371 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2394.12 | 0.148915 | ||||||||
\(638\) | 14319.8 | 0.888597 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8268.85 | −0.509516 | −0.254758 | − | 0.967005i | \(-0.581996\pi\) | ||||
−0.254758 | + | 0.967005i | \(0.581996\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1676.14 | 0.102800 | 0.0514000 | − | 0.998678i | \(-0.483632\pi\) | ||||
0.0514000 | + | 0.998678i | \(0.483632\pi\) | |||||||
\(644\) | −7548.24 | −0.461867 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −60584.1 | −3.68986 | ||||||||
\(647\) | −17319.8 | −1.05242 | −0.526208 | − | 0.850356i | \(-0.676387\pi\) | ||||
−0.526208 | + | 0.850356i | \(0.676387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2064.35 | 0.124858 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20438.3 | −1.22765 | ||||||||
\(653\) | 17191.7 | 1.03026 | 0.515132 | − | 0.857111i | \(-0.327743\pi\) | ||||
0.515132 | + | 0.857111i | \(0.327743\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −20169.8 | −1.20045 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8560.18 | 0.507159 | ||||||||
\(659\) | −1559.35 | −0.0921753 | −0.0460877 | − | 0.998937i | \(-0.514675\pi\) | ||||
−0.0460877 | + | 0.998937i | \(0.514675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17710.2 | −1.04213 | −0.521065 | − | 0.853517i | \(-0.674465\pi\) | ||||
−0.521065 | + | 0.853517i | \(0.674465\pi\) | |||||||
\(662\) | 3630.10 | 0.213124 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 46.5294 | 0.00271941 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27577.2 | −1.60089 | ||||||||
\(668\) | 7422.50 | 0.429918 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7686.57 | −0.442231 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15614.1 | −0.894322 | −0.447161 | − | 0.894453i | \(-0.647565\pi\) | ||||
−0.447161 | + | 0.894453i | \(0.647565\pi\) | |||||||
\(674\) | 9682.60 | 0.553353 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1458.93 | 0.0830071 | ||||||||
\(677\) | −1964.69 | −0.111535 | −0.0557675 | − | 0.998444i | \(-0.517761\pi\) | ||||
−0.0557675 | + | 0.998444i | \(0.517761\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1421.96 | 0.0803682 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 21146.7 | 1.18732 | ||||||||
\(683\) | −5230.81 | −0.293047 | −0.146524 | − | 0.989207i | \(-0.546808\pi\) | ||||
−0.146524 | + | 0.989207i | \(0.546808\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1357.69 | −0.0755637 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13444.2 | −0.744994 | ||||||||
\(689\) | −22528.3 | −1.24566 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28743.3 | 1.58241 | 0.791205 | − | 0.611551i | \(-0.209454\pi\) | ||||
0.791205 | + | 0.611551i | \(0.209454\pi\) | |||||||
\(692\) | 21419.0 | 1.17663 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14243.3 | −0.779061 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37802.8 | −2.05435 | ||||||||
\(698\) | 979.937 | 0.0531392 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15018.5 | −0.809188 | −0.404594 | − | 0.914497i | \(-0.632587\pi\) | ||||
−0.404594 | + | 0.914497i | \(0.632587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49289.2 | 2.64435 | ||||||||
\(704\) | 8645.62 | 0.462847 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 321.882 | 0.0171589 | ||||||||
\(707\) | −10969.8 | −0.583539 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2164.88 | 0.114674 | 0.0573368 | − | 0.998355i | \(-0.481739\pi\) | ||||
0.0573368 | + | 0.998355i | \(0.481739\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1422.49 | 0.0748737 | ||||||||
\(713\) | −40724.6 | −2.13906 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3445.33 | 0.179830 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17998.5 | 0.935515 | ||||||||
\(719\) | −16570.9 | −0.859516 | −0.429758 | − | 0.902944i | \(-0.641401\pi\) | ||||
−0.429758 | + | 0.902944i | \(0.641401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3317.75 | −0.171372 | ||||||||
\(722\) | −32459.6 | −1.67316 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15755.3 | 0.808761 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4179.50 | 0.213217 | 0.106609 | − | 0.994301i | \(-0.466001\pi\) | ||||
0.106609 | + | 0.994301i | \(0.466001\pi\) | |||||||
\(728\) | 449.608 | 0.0228895 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25197.5 | −1.27492 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24312.7 | 1.22511 | 0.612557 | − | 0.790426i | \(-0.290141\pi\) | ||||
0.612557 | + | 0.790426i | \(0.290141\pi\) | |||||||
\(734\) | 44717.9 | 2.24873 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35563.8 | −1.78111 | ||||||||
\(737\) | −8344.50 | −0.417061 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8812.62 | −0.438671 | −0.219335 | − | 0.975650i | \(-0.570389\pi\) | ||||
−0.219335 | + | 0.975650i | \(0.570389\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12775.6 | 0.632085 | ||||||||
\(743\) | −30132.1 | −1.48780 | −0.743902 | − | 0.668288i | \(-0.767027\pi\) | ||||
−0.743902 | + | 0.668288i | \(0.767027\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11400.4 | −0.559515 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17643.2 | 0.862432 | ||||||||
\(749\) | −3478.28 | −0.169685 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1000.93 | 0.0486343 | 0.0243172 | − | 0.999704i | \(-0.492259\pi\) | ||||
0.0243172 | + | 0.999704i | \(0.492259\pi\) | |||||||
\(752\) | 20559.2 | 0.996962 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −37925.7 | −1.83179 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21708.6 | −1.04229 | −0.521144 | − | 0.853469i | \(-0.674495\pi\) | ||||
−0.521144 | + | 0.853469i | \(0.674495\pi\) | |||||||
\(758\) | 41584.0 | 1.99261 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33904.7 | 1.61504 | 0.807520 | − | 0.589840i | \(-0.200809\pi\) | ||||
0.807520 | + | 0.589840i | \(0.200809\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7878.20 | 0.373801 | ||||||||
\(764\) | −323.194 | −0.0153047 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2066.48 | 0.0974738 | ||||||||
\(767\) | −5467.41 | −0.257388 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6114.14 | −0.286712 | −0.143356 | − | 0.989671i | \(-0.545789\pi\) | ||||
−0.143356 | + | 0.989671i | \(0.545789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 27709.7 | 1.29183 | ||||||||
\(773\) | 12350.0 | 0.574644 | 0.287322 | − | 0.957834i | \(-0.407235\pi\) | ||||
0.287322 | + | 0.957834i | \(0.407235\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 267.040 | 0.0123533 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25781.2 | −1.18805 | ||||||||
\(779\) | −37194.6 | −1.71070 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18606.7 | 0.852496 | ||||||||
\(782\) | −69426.6 | −3.17479 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3260.78 | −0.148541 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13597.6 | −0.615888 | −0.307944 | − | 0.951405i | \(-0.599641\pi\) | ||||
−0.307944 | + | 0.951405i | \(0.599641\pi\) | |||||||
\(788\) | −18630.8 | −0.842254 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1291.56 | 0.0580563 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20357.8 | 0.911634 | ||||||||
\(794\) | 36047.9 | 1.61120 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27147.3 | 1.20881 | ||||||||
\(797\) | 18951.1 | 0.842262 | 0.421131 | − | 0.907000i | \(-0.361633\pi\) | ||||
0.421131 | + | 0.907000i | \(0.361633\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38532.6 | 1.70611 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12684.0 | −0.558463 | ||||||||
\(803\) | −12342.6 | −0.542417 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −56006.9 | −2.44759 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2060.09 | −0.0896952 | ||||||||
\(809\) | 27695.1 | 1.20359 | 0.601797 | − | 0.798649i | \(-0.294451\pi\) | ||||
0.601797 | + | 0.798649i | \(0.294451\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1439.61 | 0.0623325 | 0.0311663 | − | 0.999514i | \(-0.490078\pi\) | ||||
0.0311663 | + | 0.999514i | \(0.490078\pi\) | |||||||
\(812\) | 10525.7 | 0.454902 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29329.5 | −1.26290 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24792.2 | −1.06165 | ||||||||
\(818\) | −25318.4 | −1.08220 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11212.2 | −0.476626 | −0.238313 | − | 0.971188i | \(-0.576594\pi\) | ||||
−0.238313 | + | 0.971188i | \(0.576594\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14736.8 | 0.624170 | 0.312085 | − | 0.950054i | \(-0.398973\pi\) | ||||
0.312085 | + | 0.950054i | \(0.398973\pi\) | |||||||
\(824\) | −623.062 | −0.0263415 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3100.52 | 0.130606 | ||||||||
\(827\) | 9129.69 | 0.383882 | 0.191941 | − | 0.981406i | \(-0.438522\pi\) | ||||
0.191941 | + | 0.981406i | \(0.438522\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13177.4 | 0.552074 | 0.276037 | − | 0.961147i | \(-0.410979\pi\) | ||||
0.276037 | + | 0.961147i | \(0.410979\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22897.8 | −0.954133 | ||||||||
\(833\) | −6111.46 | −0.254201 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17359.3 | 0.718164 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −43723.3 | −1.80238 | ||||||||
\(839\) | 40633.0 | 1.67200 | 0.835999 | − | 0.548731i | \(-0.184889\pi\) | ||||
0.835999 | + | 0.548731i | \(0.184889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14066.2 | 0.576746 | ||||||||
\(842\) | −62832.5 | −2.57168 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16744.1 | −0.682884 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6934.66 | −0.281320 | ||||||||
\(848\) | 30683.4 | 1.24254 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56483.1 | 2.27522 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16268.8 | 0.653027 | 0.326514 | − | 0.945192i | \(-0.394126\pi\) | ||||
0.326514 | + | 0.945192i | \(0.394126\pi\) | |||||||
\(854\) | −11544.7 | −0.462590 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −653.210 | −0.0260821 | ||||||||
\(857\) | 2376.68 | 0.0947325 | 0.0473663 | − | 0.998878i | \(-0.484917\pi\) | ||||
0.0473663 | + | 0.998878i | \(0.484917\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18821.4 | −0.747589 | −0.373794 | − | 0.927512i | \(-0.621943\pi\) | ||||
−0.373794 | + | 0.927512i | \(0.621943\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19310.5 | −0.763015 | ||||||||
\(863\) | 20478.1 | 0.807743 | 0.403871 | − | 0.914816i | \(-0.367664\pi\) | ||||
0.403871 | + | 0.914816i | \(0.367664\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −33449.1 | −1.31252 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15543.9 | 0.607827 | ||||||||
\(869\) | −9545.03 | −0.372604 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22100.3 | 0.859747 | ||||||||
\(872\) | 1479.50 | 0.0574566 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −68309.6 | −2.64371 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46886.5 | 1.80530 | 0.902648 | − | 0.430379i | \(-0.141620\pi\) | ||||
0.902648 | + | 0.430379i | \(0.141620\pi\) | |||||||
\(878\) | −43525.0 | −1.67300 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16858.4 | 0.644691 | 0.322346 | − | 0.946622i | \(-0.395529\pi\) | ||||
0.322346 | + | 0.946622i | \(0.395529\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38016.2 | 1.44886 | 0.724432 | − | 0.689346i | \(-0.242102\pi\) | ||||
0.724432 | + | 0.689346i | \(0.242102\pi\) | |||||||
\(884\) | −46727.8 | −1.77786 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −53414.0 | −2.02537 | ||||||||
\(887\) | −25246.2 | −0.955675 | −0.477838 | − | 0.878448i | \(-0.658579\pi\) | ||||
−0.477838 | + | 0.878448i | \(0.658579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19851.5 | 0.748928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −40462.7 | −1.51883 | ||||||||
\(893\) | 37912.7 | 1.42072 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1176.85 | −0.0438791 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 61002.4 | 2.26690 | ||||||||
\(899\) | 56788.9 | 2.10680 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 57507.8 | 2.12637 | ||||||||
\(902\) | 22132.7 | 0.817003 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 242.550 | 0.00892378 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11679.5 | −0.427576 | −0.213788 | − | 0.976880i | \(-0.568580\pi\) | ||||
−0.213788 | + | 0.976880i | \(0.568580\pi\) | |||||||
\(908\) | 34294.6 | 1.25342 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23655.6 | 0.860312 | 0.430156 | − | 0.902755i | \(-0.358459\pi\) | ||||
0.430156 | + | 0.902755i | \(0.358459\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −652.971 | −0.0236694 | ||||||||
\(914\) | −44236.4 | −1.60089 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13025.8 | 0.469852 | ||||||||
\(917\) | −1329.98 | −0.0478953 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19902.0 | 0.714371 | 0.357185 | − | 0.934033i | \(-0.383736\pi\) | ||||
0.357185 | + | 0.934033i | \(0.383736\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −25109.1 | −0.896880 | ||||||||
\(923\) | −49279.5 | −1.75737 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23543.8 | −0.835525 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 49592.3 | 1.75425 | ||||||||
\(929\) | −48903.6 | −1.72710 | −0.863550 | − | 0.504262i | \(-0.831764\pi\) | ||||
−0.863550 | + | 0.504262i | \(0.831764\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6013.13 | −0.211678 | ||||||||
\(932\) | 37248.4 | 1.30913 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −46611.7 | −1.63296 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1179.03 | −0.0411068 | −0.0205534 | − | 0.999789i | \(-0.506543\pi\) | ||||
−0.0205534 | + | 0.999789i | \(0.506543\pi\) | |||||||
\(938\) | −12532.9 | −0.436261 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6253.60 | −0.216643 | −0.108322 | − | 0.994116i | \(-0.534548\pi\) | ||||
−0.108322 | + | 0.994116i | \(0.534548\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42623.3 | −1.47191 | ||||||||
\(944\) | 7446.58 | 0.256743 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14752.6 | 0.507027 | ||||||||
\(947\) | 29027.3 | 0.996050 | 0.498025 | − | 0.867163i | \(-0.334059\pi\) | ||||
0.498025 | + | 0.867163i | \(0.334059\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32689.2 | 1.11816 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1147.71 | −0.0390730 | ||||||||
\(953\) | 47968.6 | 1.63049 | 0.815245 | − | 0.579116i | \(-0.196602\pi\) | ||||
0.815245 | + | 0.579116i | \(0.196602\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2879.83 | −0.0974273 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −71271.0 | −2.40361 | ||||||||
\(959\) | −15611.7 | −0.525679 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54072.1 | 1.81505 | ||||||||
\(962\) | 77678.8 | 2.60339 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7713.29 | −0.257706 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6940.06 | −0.230793 | −0.115397 | − | 0.993319i | \(-0.536814\pi\) | ||||
−0.115397 | + | 0.993319i | \(0.536814\pi\) | |||||||
\(968\) | −1302.31 | −0.0432414 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25930.9 | −0.857015 | −0.428507 | − | 0.903538i | \(-0.640960\pi\) | ||||
−0.428507 | + | 0.903538i | \(0.640960\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2788.00 | −0.0918594 | ||||||||
\(974\) | −43930.4 | −1.44519 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27727.2 | −0.909350 | ||||||||
\(977\) | −9361.03 | −0.306536 | −0.153268 | − | 0.988185i | \(-0.548980\pi\) | ||||
−0.153268 | + | 0.988185i | \(0.548980\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19962.6 | −0.651691 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 44546.0 | 1.44757 | ||||||||
\(983\) | 5317.34 | 0.172530 | 0.0862649 | − | 0.996272i | \(-0.472507\pi\) | ||||
0.0862649 | + | 0.996272i | \(0.472507\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 96812.6 | 3.12692 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −45976.0 | −1.48046 | ||||||||
\(989\) | −28410.7 | −0.913455 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38425.3 | −1.23170 | −0.615852 | − | 0.787862i | \(-0.711188\pi\) | ||||
−0.615852 | + | 0.787862i | \(0.711188\pi\) | |||||||
\(992\) | 73235.5 | 2.34398 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 27946.0 | 0.891744 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29596.3 | 0.940145 | 0.470073 | − | 0.882628i | \(-0.344228\pi\) | ||||
0.470073 | + | 0.882628i | \(0.344228\pi\) | |||||||
\(998\) | 24145.2 | 0.765835 | ||||||||
\(999\) | 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 | 1575.4.a.bs.1.2 | yes | 8 | |
3.2 | odd | 2 | inner | 1575.4.a.bs.1.7 | yes | 8 | |
5.4 | even | 2 | 1575.4.a.br.1.7 | yes | 8 | ||
15.14 | odd | 2 | 1575.4.a.br.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1575.4.a.br.1.2 | ✓ | 8 | 15.14 | odd | 2 | ||
1575.4.a.br.1.7 | yes | 8 | 5.4 | even | 2 | ||
1575.4.a.bs.1.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1575.4.a.bs.1.7 | yes | 8 | 3.2 | odd | 2 | inner |