Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8112,2,Mod(1,8112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8112, 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("8112.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8112.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: | \(64.7746461197\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1014) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8112.1 |
$q$-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 | ||||||||
\(5\) | −2.13706 | −0.955724 | −0.477862 | − | 0.878435i | \(-0.658588\pi\) | ||||
−0.477862 | + | 0.878435i | \(0.658588\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0489173 | −0.0184890 | −0.00924451 | − | 0.999957i | \(-0.502943\pi\) | ||||
−0.00924451 | + | 0.999957i | \(0.502943\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.29590 | 1.89828 | 0.949142 | − | 0.314848i | \(-0.101953\pi\) | ||||
0.949142 | + | 0.314848i | \(0.101953\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.13706 | −0.551787 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.89008 | −0.700948 | −0.350474 | − | 0.936572i | \(-0.613980\pi\) | ||||
−0.350474 | + | 0.936572i | \(0.613980\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.20775 | −1.65357 | −0.826786 | − | 0.562517i | \(-0.809833\pi\) | ||||
−0.826786 | + | 0.562517i | \(0.809833\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0489173 | −0.0106746 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.71379 | −0.565865 | −0.282932 | − | 0.959140i | \(-0.591307\pi\) | ||||
−0.282932 | + | 0.959140i | \(0.591307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.432960 | −0.0865921 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.91185 | 0.912108 | 0.456054 | − | 0.889952i | \(-0.349262\pi\) | ||||
0.456054 | + | 0.889952i | \(0.349262\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.00969 | 1.61819 | 0.809094 | − | 0.587679i | \(-0.199958\pi\) | ||||
0.809094 | + | 0.587679i | \(0.199958\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.29590 | 1.09597 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.104539 | 0.0176704 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.176292 | 0.0289822 | 0.0144911 | − | 0.999895i | \(-0.495387\pi\) | ||||
0.0144911 | + | 0.999895i | \(0.495387\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.59179 | 1.34181 | 0.670906 | − | 0.741542i | \(-0.265905\pi\) | ||||
0.670906 | + | 0.741542i | \(0.265905\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.71379 | −1.02384 | −0.511922 | − | 0.859032i | \(-0.671066\pi\) | ||||
−0.511922 | + | 0.859032i | \(0.671066\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.13706 | −0.318575 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.20775 | 1.05136 | 0.525679 | − | 0.850683i | \(-0.323811\pi\) | ||||
0.525679 | + | 0.850683i | \(0.323811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99761 | −0.999658 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.89008 | −0.404693 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.34481 | 1.28361 | 0.641804 | − | 0.766868i | \(-0.278186\pi\) | ||||
0.641804 | + | 0.766868i | \(0.278186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.4547 | −1.81424 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.20775 | −0.954690 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.26875 | −0.555744 | −0.277872 | − | 0.960618i | \(-0.589629\pi\) | ||||
−0.277872 | + | 0.960618i | \(0.589629\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.10992 | 0.910331 | 0.455166 | − | 0.890407i | \(-0.349580\pi\) | ||||
0.455166 | + | 0.890407i | \(0.349580\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0489173 | −0.00616301 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.38404 | 0.657766 | 0.328883 | − | 0.944371i | \(-0.393328\pi\) | ||||
0.328883 | + | 0.944371i | \(0.393328\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.71379 | −0.326702 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.71379 | −1.03414 | −0.517068 | − | 0.855944i | \(-0.672977\pi\) | ||||
−0.517068 | + | 0.855944i | \(0.672977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.9487 | 1.74961 | 0.874806 | − | 0.484474i | \(-0.160989\pi\) | ||||
0.874806 | + | 0.484474i | \(0.160989\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.432960 | −0.0499939 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.307979 | −0.0350974 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.8291 | −1.55589 | −0.777947 | − | 0.628330i | \(-0.783739\pi\) | ||||
−0.777947 | + | 0.628330i | \(0.783739\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.1347 | −1.22219 | −0.611094 | − | 0.791558i | \(-0.709270\pi\) | ||||
−0.611094 | + | 0.791558i | \(0.709270\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.17629 | 0.669913 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.91185 | 0.526606 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.92154 | −0.415683 | −0.207841 | − | 0.978163i | \(-0.566644\pi\) | ||||
−0.207841 | + | 0.978163i | \(0.566644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.00969 | 0.934261 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.4034 | 1.58036 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.47889 | 0.251694 | 0.125847 | − | 0.992050i | \(-0.459835\pi\) | ||||
0.125847 | + | 0.992050i | \(0.459835\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.29590 | 0.632761 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.65279 | 0.164459 | 0.0822295 | − | 0.996613i | \(-0.473796\pi\) | ||||
0.0822295 | + | 0.996613i | \(0.473796\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.23490 | 0.811409 | 0.405704 | − | 0.914004i | \(-0.367026\pi\) | ||||
0.405704 | + | 0.914004i | \(0.367026\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.104539 | 0.0102020 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.36658 | 0.808828 | 0.404414 | − | 0.914576i | \(-0.367475\pi\) | ||||
0.404414 | + | 0.914576i | \(0.367475\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4276 | 1.66926 | 0.834630 | − | 0.550811i | \(-0.185682\pi\) | ||||
0.834630 | + | 0.550811i | \(0.185682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.176292 | 0.0167329 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.9758 | −1.31474 | −0.657368 | − | 0.753570i | \(-0.728330\pi\) | ||||
−0.657368 | + | 0.753570i | \(0.728330\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.79954 | 0.540810 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.141375 | 0.0129598 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.6383 | 2.60348 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.59179 | 0.774696 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.6106 | 1.03848 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.52111 | 0.667390 | 0.333695 | − | 0.942681i | \(-0.391704\pi\) | ||||
0.333695 | + | 0.942681i | \(0.391704\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.71379 | −0.591116 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.12498 | −0.447772 | −0.223886 | − | 0.974615i | \(-0.571874\pi\) | ||||
−0.223886 | + | 0.974615i | \(0.571874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.352584 | 0.0305729 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.13706 | −0.183929 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.00000 | 0.341743 | 0.170872 | − | 0.985293i | \(-0.445342\pi\) | ||||
0.170872 | + | 0.985293i | \(0.445342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.68963 | −0.737045 | −0.368522 | − | 0.929619i | \(-0.620136\pi\) | ||||
−0.368522 | + | 0.929619i | \(0.620136\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.20775 | 0.607002 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4969 | −0.871724 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.99761 | −0.577153 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.86831 | 0.398828 | 0.199414 | − | 0.979915i | \(-0.436096\pi\) | ||||
0.199414 | + | 0.979915i | \(0.436096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7463 | 1.20004 | 0.600019 | − | 0.799986i | \(-0.295160\pi\) | ||||
0.600019 | + | 0.799986i | \(0.295160\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.89008 | −0.233649 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.2543 | −1.54654 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.7138 | −1.33391 | −0.666953 | − | 0.745100i | \(-0.732402\pi\) | ||||
−0.666953 | + | 0.745100i | \(0.732402\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.34481 | 0.741092 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.132751 | 0.0104623 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.54958 | 0.434677 | 0.217338 | − | 0.976096i | \(-0.430262\pi\) | ||||
0.217338 | + | 0.976096i | \(0.430262\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.4547 | −1.04745 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.92154 | −0.303458 | −0.151729 | − | 0.988422i | \(-0.548484\pi\) | ||||
−0.151729 | + | 0.988422i | \(0.548484\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.20775 | −0.551190 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.48427 | −0.264904 | −0.132452 | − | 0.991189i | \(-0.542285\pi\) | ||||
−0.132452 | + | 0.991189i | \(0.542285\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0211793 | 0.00160100 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.26875 | −0.320859 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.58881 | −0.268240 | −0.134120 | − | 0.990965i | \(-0.542821\pi\) | ||||
−0.134120 | + | 0.990965i | \(0.542821\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.50604 | 0.409261 | 0.204630 | − | 0.978839i | \(-0.434401\pi\) | ||||
0.204630 | + | 0.978839i | \(0.434401\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.10992 | 0.525580 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.376747 | −0.0276990 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.1957 | −1.33060 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.0489173 | −0.00355821 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.65817 | 0.409411 | 0.204705 | − | 0.978824i | \(-0.434376\pi\) | ||||
0.204705 | + | 0.978824i | \(0.434376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4034 | 0.964799 | 0.482400 | − | 0.875951i | \(-0.339765\pi\) | ||||
0.482400 | + | 0.875951i | \(0.339765\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.9812 | 1.42360 | 0.711801 | − | 0.702381i | \(-0.247880\pi\) | ||||
0.711801 | + | 0.702381i | \(0.247880\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.24160 | 0.442455 | 0.221228 | − | 0.975222i | \(-0.428994\pi\) | ||||
0.221228 | + | 0.975222i | \(0.428994\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.38404 | 0.379761 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.240275 | −0.0168640 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.3612 | −1.28240 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.71379 | −0.188622 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −45.3793 | −3.13895 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.08575 | 0.350118 | 0.175059 | − | 0.984558i | \(-0.443988\pi\) | ||||
0.175059 | + | 0.984558i | \(0.443988\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.71379 | −0.597059 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.3478 | 0.978512 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.440730 | −0.0299187 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.9487 | 1.01014 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5483 | 1.37601 | 0.688006 | − | 0.725705i | \(-0.258486\pi\) | ||||
0.688006 | + | 0.725705i | \(0.258486\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.432960 | −0.0288640 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.41119 | −0.292781 | −0.146390 | − | 0.989227i | \(-0.546766\pi\) | ||||
−0.146390 | + | 0.989227i | \(0.546766\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.230586 | 0.0152376 | 0.00761878 | − | 0.999971i | \(-0.497575\pi\) | ||||
0.00761878 | + | 0.999971i | \(0.497575\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.307979 | −0.0202635 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.82371 | −0.512548 | −0.256274 | − | 0.966604i | \(-0.582495\pi\) | ||||
−0.256274 | + | 0.966604i | \(0.582495\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.4034 | −1.00481 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.8291 | −0.898296 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1535 | −0.721457 | −0.360729 | − | 0.932671i | \(-0.617472\pi\) | ||||
−0.360729 | + | 0.932671i | \(0.617472\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.54527 | −0.228371 | −0.114185 | − | 0.993459i | \(-0.536426\pi\) | ||||
−0.114185 | + | 0.993459i | \(0.536426\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.9543 | 0.955397 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.1347 | −0.705631 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.17092 | 0.263266 | 0.131633 | − | 0.991299i | \(-0.457978\pi\) | ||||
0.131633 | + | 0.991299i | \(0.457978\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.0858 | −1.07417 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.17629 | 0.386774 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.8901 | −0.679305 | −0.339652 | − | 0.940551i | \(-0.610309\pi\) | ||||
−0.339652 | + | 0.940551i | \(0.610309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.00862374 | −0.000535853 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.91185 | 0.304036 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.2271 | 1.92555 | 0.962774 | − | 0.270309i | \(-0.0871259\pi\) | ||||
0.962774 | + | 0.270309i | \(0.0871259\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.9705 | −1.22678 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.92154 | −0.239995 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.9172 | 0.970491 | 0.485245 | − | 0.874378i | \(-0.338730\pi\) | ||||
0.485245 | + | 0.874378i | \(0.338730\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.52111 | −0.213892 | −0.106946 | − | 0.994265i | \(-0.534107\pi\) | ||||
−0.106946 | + | 0.994265i | \(0.534107\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.72587 | −0.164376 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.58104 | −0.515585 | −0.257792 | − | 0.966200i | \(-0.582995\pi\) | ||||
−0.257792 | + | 0.966200i | \(0.582995\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.00969 | 0.539396 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.07846 | −0.481920 | −0.240960 | − | 0.970535i | \(-0.577462\pi\) | ||||
−0.240960 | + | 0.970535i | \(0.577462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.4034 | 1.03453 | 0.517263 | − | 0.855827i | \(-0.326951\pi\) | ||||
0.517263 | + | 0.855827i | \(0.326951\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.4034 | 0.912420 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.420288 | −0.0248088 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.64742 | −0.508672 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.47889 | 0.145315 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.3709 | −1.13166 | −0.565830 | − | 0.824522i | \(-0.691444\pi\) | ||||
−0.565830 | + | 0.824522i | \(0.691444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.12259 | 0.531138 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.29590 | 0.365325 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.328421 | 0.0189299 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.65279 | 0.0949505 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.1943 | −0.870025 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4263 | 0.709204 | 0.354602 | − | 0.935017i | \(-0.384616\pi\) | ||||
0.354602 | + | 0.935017i | \(0.384616\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.23490 | 0.468467 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.71379 | −0.153885 | −0.0769425 | − | 0.997036i | \(-0.524516\pi\) | ||||
−0.0769425 | + | 0.997036i | \(0.524516\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.3884 | 0.869801 | 0.434901 | − | 0.900478i | \(-0.356783\pi\) | ||||
0.434901 | + | 0.900478i | \(0.356783\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.104539 | 0.00589013 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.6528 | 1.44080 | 0.720402 | − | 0.693557i | \(-0.243957\pi\) | ||||
0.720402 | + | 0.693557i | \(0.243957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.9245 | 1.73144 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.36658 | 0.466977 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.8310 | 1.15907 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.4276 | 0.963748 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.352584 | −0.0194386 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.82371 | 0.210170 | 0.105085 | − | 0.994463i | \(-0.466489\pi\) | ||||
0.105085 | + | 0.994463i | \(0.466489\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.176292 | 0.00966074 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.5060 | −0.628642 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.1304 | 1.09657 | 0.548285 | − | 0.836291i | \(-0.315281\pi\) | ||||
0.548285 | + | 0.836291i | \(0.315281\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.9758 | −0.759063 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 56.7241 | 3.07178 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.684726 | 0.0369717 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.79954 | 0.312237 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.93900 | −0.157774 | −0.0788869 | − | 0.996884i | \(-0.525137\pi\) | ||||
−0.0788869 | + | 0.996884i | \(0.525137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.37329 | 0.394683 | 0.197342 | − | 0.980335i | \(-0.436769\pi\) | ||||
0.197342 | + | 0.980335i | \(0.436769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.01075 | −0.107022 | −0.0535108 | − | 0.998567i | \(-0.517041\pi\) | ||||
−0.0535108 | + | 0.998567i | \(0.517041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.6219 | 0.988349 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.141375 | 0.00748237 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.4577 | −1.66027 | −0.830137 | − | 0.557559i | \(-0.811738\pi\) | ||||
−0.830137 | + | 0.557559i | \(0.811738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.9517 | 1.73430 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.6383 | 1.50312 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.9463 | −1.67215 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.49934 | 0.234863 | 0.117432 | − | 0.993081i | \(-0.462534\pi\) | ||||
0.117432 | + | 0.993081i | \(0.462534\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.59179 | 0.447271 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.457123 | −0.0237327 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.8297 | 1.95875 | 0.979373 | − | 0.202060i | \(-0.0647635\pi\) | ||||
0.979373 | + | 0.202060i | \(0.0647635\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.6106 | 0.599568 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.43967 | 0.433516 | 0.216758 | − | 0.976225i | \(-0.430452\pi\) | ||||
0.216758 | + | 0.976225i | \(0.430452\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.52111 | 0.385318 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.28621 | −0.0657222 | −0.0328611 | − | 0.999460i | \(-0.510462\pi\) | ||||
−0.0328611 | + | 0.999460i | \(0.510462\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.658170 | 0.0335434 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.71379 | −0.341281 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.3924 | 1.18604 | 0.593021 | − | 0.805187i | \(-0.297935\pi\) | ||||
0.593021 | + | 0.805187i | \(0.297935\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.84309 | 0.396642 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.12498 | −0.258521 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.5536 | 1.48700 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.0858 | 1.86128 | 0.930640 | − | 0.365935i | \(-0.119251\pi\) | ||||
0.930640 | + | 0.365935i | \(0.119251\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.352584 | 0.0176513 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.86592 | 0.242992 | 0.121496 | − | 0.992592i | \(-0.461231\pi\) | ||||
0.121496 | + | 0.992592i | \(0.461231\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.13706 | −0.106192 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.10992 | 0.0550165 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.445042 | −0.0220059 | −0.0110030 | − | 0.999939i | \(-0.503502\pi\) | ||||
−0.0110030 | + | 0.999939i | \(0.503502\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.00000 | 0.197305 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.208816 | 0.0102752 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.7955 | 1.16807 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.68963 | −0.425533 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.9869 | −0.878715 | −0.439358 | − | 0.898312i | \(-0.644794\pi\) | ||||
−0.439358 | + | 0.898312i | \(0.644794\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.2814 | −1.03719 | −0.518597 | − | 0.855019i | \(-0.673545\pi\) | ||||
−0.518597 | + | 0.855019i | \(0.673545\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.20775 | 0.350453 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.25129 | 0.0606966 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.347798 | −0.0168311 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.7138 | 1.19042 | 0.595211 | − | 0.803570i | \(-0.297069\pi\) | ||||
0.595211 | + | 0.803570i | \(0.297069\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.2174 | 1.54827 | 0.774136 | − | 0.633020i | \(-0.218185\pi\) | ||||
0.774136 | + | 0.633020i | \(0.218185\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.4969 | −0.503290 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.5603 | 0.935698 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.0877 | −1.53146 | −0.765731 | − | 0.643162i | \(-0.777622\pi\) | ||||
−0.765731 | + | 0.643162i | \(0.777622\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.99761 | −0.333219 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.5109 | −0.974504 | −0.487252 | − | 0.873261i | \(-0.662001\pi\) | ||||
−0.487252 | + | 0.873261i | \(0.662001\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.38059 | 0.397278 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.86831 | 0.230263 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.3163 | 0.722823 | 0.361411 | − | 0.932406i | \(-0.382295\pi\) | ||||
0.361411 | + | 0.932406i | \(0.382295\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 54.0930 | 2.54714 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.7463 | 0.692842 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.1860 | 0.897482 | 0.448741 | − | 0.893662i | \(-0.351873\pi\) | ||||
0.448741 | + | 0.893662i | \(0.351873\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.89008 | −0.134898 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.31229 | −0.387142 | −0.193571 | − | 0.981086i | \(-0.562007\pi\) | ||||
−0.193571 | + | 0.981086i | \(0.562007\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.32842 | −0.294107 | −0.147053 | − | 0.989129i | \(-0.546979\pi\) | ||||
−0.147053 | + | 0.989129i | \(0.546979\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.2543 | −0.892896 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.1879 | 1.44320 | 0.721602 | − | 0.692308i | \(-0.243406\pi\) | ||||
0.721602 | + | 0.692308i | \(0.243406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.263373 | −0.0121614 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.7138 | −0.770131 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −42.2693 | −1.94355 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.12067 | 0.143186 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.34481 | 0.427870 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.9323 | −0.819348 | −0.409674 | − | 0.912232i | \(-0.634357\pi\) | ||||
−0.409674 | + | 0.912232i | \(0.634357\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.132751 | 0.00604040 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.29755 | −0.240549 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.3279 | 1.37429 | 0.687145 | − | 0.726520i | \(-0.258864\pi\) | ||||
0.687145 | + | 0.726520i | \(0.258864\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.54958 | 0.250961 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0954 | −1.35819 | −0.679094 | − | 0.734051i | \(-0.737627\pi\) | ||||
−0.679094 | + | 0.734051i | \(0.737627\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.1957 | −0.639341 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.4547 | −0.604745 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.426256 | 0.0191202 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.92154 | −0.175202 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.7512 | −1.50489 | −0.752446 | − | 0.658654i | \(-0.771126\pi\) | ||||
−0.752446 | + | 0.658654i | \(0.771126\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.53212 | −0.157177 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.7439 | 0.653513 | 0.326756 | − | 0.945109i | \(-0.394044\pi\) | ||||
0.326756 | + | 0.945109i | \(0.394044\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.731250 | −0.0323486 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.20775 | −0.318230 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.5985 | −0.775483 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.3793 | 1.99578 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.48427 | −0.152943 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.1086 | 0.968595 | 0.484297 | − | 0.874903i | \(-0.339075\pi\) | ||||
0.484297 | + | 0.874903i | \(0.339075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3599 | 0.759095 | 0.379547 | − | 0.925172i | \(-0.376080\pi\) | ||||
0.379547 | + | 0.925172i | \(0.376080\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0211793 | 0.000924339 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.0388 | −1.13427 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.6353 | −0.679797 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.26875 | −0.185248 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.8799 | −0.773016 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.58881 | −0.154869 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −44.0562 | −1.89764 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.83579 | 0.379880 | 0.189940 | − | 0.981796i | \(-0.439171\pi\) | ||||
0.189940 | + | 0.981796i | \(0.439171\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.50604 | 0.236287 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −37.2438 | −1.59535 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.10859 | 0.346698 | 0.173349 | − | 0.984860i | \(-0.444541\pi\) | ||||
0.173349 | + | 0.984860i | \(0.444541\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.10992 | 0.303444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.4034 | −1.50824 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.676482 | 0.0287669 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.376747 | −0.0159920 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.56033 | 0.405084 | 0.202542 | − | 0.979274i | \(-0.435080\pi\) | ||||
0.202542 | + | 0.979274i | \(0.435080\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.1957 | −0.768222 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 45.1637 | 1.90342 | 0.951712 | − | 0.306991i | \(-0.0993223\pi\) | ||||
0.951712 | + | 0.306991i | \(0.0993223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.8672 | 1.25652 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.0489173 | −0.00205434 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.20775 | −0.134476 | −0.0672380 | − | 0.997737i | \(-0.521419\pi\) | ||||
−0.0672380 | + | 0.997737i | \(0.521419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0241632 | −0.00101120 | −0.000505599 | − | 1.00000i | \(-0.500161\pi\) | ||||
−0.000505599 | 1.00000i | \(0.500161\pi\) | ||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.65817 | 0.236373 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.17496 | 0.0489994 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −46.0200 | −1.91584 | −0.957918 | − | 0.287041i | \(-0.907328\pi\) | ||||
−0.957918 | + | 0.287041i | \(0.907328\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.4034 | 0.557027 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.544678 | 0.0225971 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 58.8340 | 2.43665 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.9385 | 1.07060 | 0.535299 | − | 0.844663i | \(-0.320199\pi\) | ||||
0.535299 | + | 0.844663i | \(0.320199\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −64.9396 | −2.67579 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.9812 | 0.821917 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.30691 | −0.341124 | −0.170562 | − | 0.985347i | \(-0.554558\pi\) | ||||
−0.170562 | + | 0.985347i | \(0.554558\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.302128 | −0.0123860 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.24160 | 0.255452 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.1702 | −1.51873 | −0.759366 | − | 0.650664i | \(-0.774491\pi\) | ||||
−0.759366 | + | 0.650664i | \(0.774491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5700 | −0.512742 | −0.256371 | − | 0.966578i | \(-0.582527\pi\) | ||||
−0.256371 | + | 0.966578i | \(0.582527\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.38404 | 0.219255 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −61.2019 | −2.48821 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.04892 | −0.326695 | −0.163348 | − | 0.986569i | \(-0.552229\pi\) | ||||
−0.163348 | + | 0.986569i | \(0.552229\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.240275 | −0.00973643 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.4590 | 1.23023 | 0.615115 | − | 0.788438i | \(-0.289110\pi\) | ||||
0.615115 | + | 0.788438i | \(0.289110\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.3612 | −0.740395 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.73317 | 0.190550 | 0.0952751 | − | 0.995451i | \(-0.469627\pi\) | ||||
0.0952751 | + | 0.995451i | \(0.469627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.9095 | 1.00120 | 0.500598 | − | 0.865680i | \(-0.333114\pi\) | ||||
0.500598 | + | 0.865680i | \(0.333114\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.71379 | −0.108901 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.191831 | 0.00768556 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.6477 | −0.905910 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −45.3793 | −1.81227 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.509499 | −0.0203150 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.4295 | −0.972523 | −0.486262 | − | 0.873813i | \(-0.661640\pi\) | ||||
−0.486262 | + | 0.873813i | \(0.661640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.08575 | 0.202141 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.0731 | −0.637841 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.71379 | −0.344712 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.7982 | 1.92741 | 0.963707 | − | 0.266963i | \(-0.0860201\pi\) | ||||
0.963707 | + | 0.266963i | \(0.0860201\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.2693 | 1.11483 | 0.557417 | − | 0.830233i | \(-0.311792\pi\) | ||||
0.557417 | + | 0.830233i | \(0.311792\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.3478 | 0.564944 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.8961 | −1.37191 | −0.685953 | − | 0.727646i | \(-0.740614\pi\) | ||||
−0.685953 | + | 0.727646i | \(0.740614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.8756 | −1.05496 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.440730 | −0.0172736 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.7157 | −0.458471 | −0.229236 | − | 0.973371i | \(-0.573623\pi\) | ||||
−0.229236 | + | 0.973371i | \(0.573623\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.9524 | 0.427946 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.9487 | 0.583204 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.13467 | 0.277927 | 0.138964 | − | 0.990297i | \(-0.455623\pi\) | ||||
0.138964 | + | 0.990297i | \(0.455623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.52888 | −0.331735 | −0.165867 | − | 0.986148i | \(-0.553042\pi\) | ||||
−0.165867 | + | 0.986148i | \(0.553042\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.753494 | −0.0292193 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.3297 | −0.516130 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.5483 | 0.794441 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.7633 | 1.72807 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.5937 | −1.21785 | −0.608924 | − | 0.793229i | \(-0.708399\pi\) | ||||
−0.608924 | + | 0.793229i | \(0.708399\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.432960 | −0.0166646 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.3002 | −0.664901 | −0.332451 | − | 0.943121i | \(-0.607875\pi\) | ||||
−0.332451 | + | 0.943121i | \(0.607875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.121261 | −0.00465357 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.41119 | −0.169037 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.3957 | −1.16306 | −0.581529 | − | 0.813526i | \(-0.697545\pi\) | ||||
−0.581529 | + | 0.813526i | \(0.697545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.54825 | −0.326612 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.230586 | 0.00879741 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.7318 | −1.35930 | −0.679652 | − | 0.733535i | \(-0.737869\pi\) | ||||
−0.679652 | + | 0.733535i | \(0.737869\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.307979 | −0.0116991 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.5703 | 0.704411 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.8310 | −0.940541 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.82371 | −0.295920 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.1328 | 0.760404 | 0.380202 | − | 0.924904i | \(-0.375855\pi\) | ||||
0.380202 | + | 0.924904i | \(0.375855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.27067 | −0.0479242 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.4034 | −0.580126 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0808502 | −0.00304069 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.6160 | 0.624025 | 0.312013 | − | 0.950078i | \(-0.398997\pi\) | ||||
0.312013 | + | 0.950078i | \(0.398997\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.8291 | −0.518631 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.4504 | −0.915675 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.1535 | −0.416533 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.04833 | −0.0763897 | −0.0381948 | − | 0.999270i | \(-0.512161\pi\) | ||||
−0.0381948 | + | 0.999270i | \(0.512161\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.402829 | −0.0150021 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.54527 | −0.131850 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.12664 | −0.0789813 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.9377 | −1.11033 | −0.555163 | − | 0.831741i | \(-0.687344\pi\) | ||||
−0.555163 | + | 0.831741i | \(0.687344\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.4034 | 0.717661 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.46250 | −0.0540187 | −0.0270093 | − | 0.999635i | \(-0.508598\pi\) | ||||
−0.0270093 | + | 0.999635i | \(0.508598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.9543 | 0.551599 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.8974 | 1.24863 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.3866 | −1.48564 | −0.742822 | − | 0.669489i | \(-0.766513\pi\) | ||||
−0.742822 | + | 0.669489i | \(0.766513\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.77538 | 0.358624 | 0.179312 | − | 0.983792i | \(-0.442613\pi\) | ||||
0.179312 | + | 0.983792i | \(0.442613\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.4039 | −0.381169 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.1347 | −0.407396 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.409271 | −0.0149544 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.5459 | −1.26060 | −0.630298 | − | 0.776353i | \(-0.717067\pi\) | ||||
−0.630298 | + | 0.776353i | \(0.717067\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.17092 | 0.151997 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.5138 | −1.14690 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.14483 | −0.186992 | −0.0934961 | − | 0.995620i | \(-0.529804\pi\) | ||||
−0.0934961 | + | 0.995620i | \(0.529804\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.0858 | −0.620174 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.5120 | −0.707310 | −0.353655 | − | 0.935376i | \(-0.615061\pi\) | ||||
−0.353655 | + | 0.935376i | \(0.615061\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.852511 | −0.0308630 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.17629 | 0.223304 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.75600 | 0.207567 | 0.103783 | − | 0.994600i | \(-0.466905\pi\) | ||||
0.103783 | + | 0.994600i | \(0.466905\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.8901 | −0.392197 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.12737 | −0.148451 | −0.0742257 | − | 0.997241i | \(-0.523649\pi\) | ||||
−0.0742257 | + | 0.997241i | \(0.523649\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.90084 | −0.140122 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.00862374 | −0.000309375 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −61.9275 | −2.21878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.8611 | −1.96309 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.91185 | 0.175535 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.7184 | 1.27485 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.2392 | 0.578865 | 0.289433 | − | 0.957198i | \(-0.406533\pi\) | ||||
0.289433 | + | 0.957198i | \(0.406533\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.2271 | 1.11172 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.683661 | 0.0243082 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.9705 | −0.708279 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.1148 | 0.570816 | 0.285408 | − | 0.958406i | \(-0.407871\pi\) | ||||
0.285408 | + | 0.958406i | \(0.407871\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.8310 | −0.736948 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.92154 | −0.138561 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 94.1154 | 3.32126 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.283698 | −0.00999905 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.9172 | 0.560313 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.1521 | 1.41167 | 0.705837 | − | 0.708374i | \(-0.250571\pi\) | ||||
0.705837 | + | 0.708374i | \(0.250571\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.8646 | −1.39984 | −0.699918 | − | 0.714224i | \(-0.746780\pi\) | ||||
−0.699918 | + | 0.714224i | \(0.746780\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.52111 | −0.123491 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.8598 | −0.415431 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.3913 | 1.69300 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.25428 | −0.218276 | −0.109138 | − | 0.994027i | \(-0.534809\pi\) | ||||
−0.109138 | + | 0.994027i | \(0.534809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.74333 | 0.165342 | 0.0826711 | − | 0.996577i | \(-0.473655\pi\) | ||||
0.0826711 | + | 0.996577i | \(0.473655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.72587 | −0.0949027 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.716185 | 0.0249042 | 0.0124521 | − | 0.999922i | \(-0.496036\pi\) | ||||
0.0124521 | + | 0.999922i | \(0.496036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.0060 | −1.25054 | −0.625269 | − | 0.780409i | \(-0.715011\pi\) | ||||
−0.625269 | + | 0.780409i | \(0.715011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.58104 | −0.297673 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.2237 | 0.700709 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.38059 | 0.290022 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.00969 | 0.311420 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.5555 | 0.744180 | 0.372090 | − | 0.928197i | \(-0.378641\pi\) | ||||
0.372090 | + | 0.928197i | \(0.378641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.87369 | −0.168058 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.07846 | −0.278237 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.40091 | −0.0481358 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.4034 | 0.597284 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.478420 | −0.0164000 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.8237 | 1.29506 | 0.647530 | − | 0.762040i | \(-0.275802\pi\) | ||||
0.647530 | + | 0.762040i | \(0.275802\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.4034 | 0.526786 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.58317 | −0.224877 | −0.112438 | − | 0.993659i | \(-0.535866\pi\) | ||||
−0.112438 | + | 0.993659i | \(0.535866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.6246 | 0.703702 | 0.351851 | − | 0.936056i | \(-0.385552\pi\) | ||||
0.351851 | + | 0.936056i | \(0.385552\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.420288 | −0.0143234 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.9081 | 0.541519 | 0.270760 | − | 0.962647i | \(-0.412725\pi\) | ||||
0.270760 | + | 0.962647i | \(0.412725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.44611 | 0.253175 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.64742 | −0.293682 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −87.0665 | −2.95353 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.47889 | 0.0838978 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.567959 | −0.0192005 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.6039 | 0.526905 | 0.263453 | − | 0.964672i | \(-0.415139\pi\) | ||||
0.263453 | + | 0.964672i | \(0.415139\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.3709 | −0.653364 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.2547 | −0.480255 | −0.240127 | − | 0.970741i | \(-0.577189\pi\) | ||||
−0.240127 | + | 0.970741i | \(0.577189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.65817 | −0.0558019 | −0.0279009 | − | 0.999611i | \(-0.508882\pi\) | ||||
−0.0279009 | + | 0.999611i | \(0.508882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.12259 | 0.306652 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.2030 | 0.644772 | 0.322386 | − | 0.946608i | \(-0.395515\pi\) | ||||
0.322386 | + | 0.946608i | \(0.395515\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.367913 | −0.0123394 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.29590 | 0.210920 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −51.9517 | −1.73850 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.66951 | 0.256364 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44.2543 | 1.47596 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.0073 | −0.899743 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.328421 | 0.0109292 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.7668 | −0.391140 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.3672 | 1.07473 | 0.537367 | − | 0.843348i | \(-0.319419\pi\) | ||||
0.537367 | + | 0.843348i | \(0.319419\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.65279 | 0.0548197 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.9624 | 1.12523 | 0.562613 | − | 0.826721i | \(-0.309796\pi\) | ||||
0.562613 | + | 0.826721i | \(0.309796\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −70.1027 | −2.32006 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.1943 | −0.502309 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.250700 | 0.00827886 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0780 | 0.662312 | 0.331156 | − | 0.943576i | \(-0.392561\pi\) | ||||
0.331156 | + | 0.943576i | \(0.392561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.4263 | 0.409459 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0763274 | −0.00250963 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.23490 | 0.270470 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.1280 | −1.84150 | −0.920749 | − | 0.390154i | \(-0.872422\pi\) | ||||
−0.920749 | + | 0.390154i | \(0.872422\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.4370 | 1.65301 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.71379 | −0.0888456 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 38.8853 | 1.27169 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0291 | 0.883001 | 0.441501 | − | 0.897261i | \(-0.354446\pi\) | ||||
0.441501 | + | 0.897261i | \(0.354446\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.3884 | 0.502180 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.0277 | 0.783282 | 0.391641 | − | 0.920118i | \(-0.371908\pi\) | ||||
0.391641 | + | 0.920118i | \(0.371908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.3163 | −0.759284 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.104539 | 0.00340067 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.7966 | −0.870771 | −0.435386 | − | 0.900244i | \(-0.643388\pi\) | ||||
−0.435386 | + | 0.900244i | \(0.643388\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.6528 | 0.831849 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.4215 | 1.11502 | 0.557510 | − | 0.830170i | \(-0.311757\pi\) | ||||
0.557510 | + | 0.830170i | \(0.311757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0919 | −0.391284 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.9245 | 0.999648 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.195669 | −0.00631849 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.1745 | 1.61853 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.36658 | 0.269609 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.6440 | −0.922082 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.2631 | 0.844565 | 0.422282 | − | 0.906464i | \(-0.361229\pi\) | ||||
0.422282 | + | 0.906464i | \(0.361229\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.8310 | 0.669188 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.9842 | 1.28315 | 0.641577 | − | 0.767059i | \(-0.278280\pi\) | ||||
0.641577 | + | 0.767059i | \(0.278280\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.425074 | 0.0136272 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.58317 | −0.146629 | −0.0733143 | − | 0.997309i | \(-0.523358\pi\) | ||||
−0.0733143 | + | 0.997309i | \(0.523358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.6896 | −0.789084 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.4276 | 0.556420 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.6848 | −0.340794 | −0.170397 | − | 0.985376i | \(-0.554505\pi\) | ||||
−0.170397 | + | 0.985376i | \(0.554505\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.7011 | −1.36057 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.352584 | −0.0112229 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.2198 | 0.579357 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.6021 | −1.60743 | −0.803714 | − | 0.595016i | \(-0.797146\pi\) | ||||
−0.803714 | + | 0.595016i | \(0.797146\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.82371 | 0.121342 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.3387 | −0.422865 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.9603 | −1.13887 | −0.569437 | − | 0.822035i | \(-0.692839\pi\) | ||||
−0.569437 | + | 0.822035i | \(0.692839\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.176292 | 0.00557763 |
(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 | 8112.2.a.cj.1.2 | 3 | ||
4.3 | odd | 2 | 1014.2.a.l.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 3042.2.a.bh.1.2 | 3 | |||
13.12 | even | 2 | 8112.2.a.cm.1.2 | 3 | |||
52.3 | odd | 6 | 1014.2.e.n.529.2 | 6 | |||
52.7 | even | 12 | 1014.2.i.h.361.2 | 12 | |||
52.11 | even | 12 | 1014.2.i.h.823.5 | 12 | |||
52.15 | even | 12 | 1014.2.i.h.823.2 | 12 | |||
52.19 | even | 12 | 1014.2.i.h.361.5 | 12 | |||
52.23 | odd | 6 | 1014.2.e.l.529.2 | 6 | |||
52.31 | even | 4 | 1014.2.b.f.337.5 | 6 | |||
52.35 | odd | 6 | 1014.2.e.n.991.2 | 6 | |||
52.43 | odd | 6 | 1014.2.e.l.991.2 | 6 | |||
52.47 | even | 4 | 1014.2.b.f.337.2 | 6 | |||
52.51 | odd | 2 | 1014.2.a.n.1.2 | yes | 3 | ||
156.47 | odd | 4 | 3042.2.b.o.1351.5 | 6 | |||
156.83 | odd | 4 | 3042.2.b.o.1351.2 | 6 | |||
156.155 | even | 2 | 3042.2.a.ba.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.l.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
1014.2.a.n.1.2 | yes | 3 | 52.51 | odd | 2 | ||
1014.2.b.f.337.2 | 6 | 52.47 | even | 4 | |||
1014.2.b.f.337.5 | 6 | 52.31 | even | 4 | |||
1014.2.e.l.529.2 | 6 | 52.23 | odd | 6 | |||
1014.2.e.l.991.2 | 6 | 52.43 | odd | 6 | |||
1014.2.e.n.529.2 | 6 | 52.3 | odd | 6 | |||
1014.2.e.n.991.2 | 6 | 52.35 | odd | 6 | |||
1014.2.i.h.361.2 | 12 | 52.7 | even | 12 | |||
1014.2.i.h.361.5 | 12 | 52.19 | even | 12 | |||
1014.2.i.h.823.2 | 12 | 52.15 | even | 12 | |||
1014.2.i.h.823.5 | 12 | 52.11 | even | 12 | |||
3042.2.a.ba.1.2 | 3 | 156.155 | even | 2 | |||
3042.2.a.bh.1.2 | 3 | 12.11 | even | 2 | |||
3042.2.b.o.1351.2 | 6 | 156.83 | odd | 4 | |||
3042.2.b.o.1351.5 | 6 | 156.47 | odd | 4 | |||
8112.2.a.cj.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8112.2.a.cm.1.2 | 3 | 13.12 | even | 2 |