Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.691771 | −0.489156 | −0.244578 | − | 0.969630i | \(-0.578649\pi\) | ||||
−0.244578 | + | 0.969630i | \(0.578649\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.52145 | −0.760727 | ||||||||
\(5\) | −0.236679 | −0.105846 | −0.0529230 | − | 0.998599i | \(-0.516854\pi\) | ||||
−0.0529230 | + | 0.998599i | \(0.516854\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.43604 | 0.861270 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.163728 | 0.0517752 | ||||||||
\(11\) | −4.73037 | −1.42626 | −0.713130 | − | 0.701032i | \(-0.752723\pi\) | ||||
−0.713130 | + | 0.701032i | \(0.752723\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.51889 | −0.421264 | −0.210632 | − | 0.977565i | \(-0.567552\pi\) | ||||
−0.210632 | + | 0.977565i | \(0.567552\pi\) | |||||||
\(14\) | −0.691771 | −0.184884 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.35773 | 0.339431 | ||||||||
\(17\) | 4.88453 | 1.18467 | 0.592336 | − | 0.805691i | \(-0.298206\pi\) | ||||
0.592336 | + | 0.805691i | \(0.298206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.13777 | 0.490439 | 0.245219 | − | 0.969468i | \(-0.421140\pi\) | ||||
0.245219 | + | 0.969468i | \(0.421140\pi\) | |||||||
\(20\) | 0.360096 | 0.0805199 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.27233 | 0.697664 | ||||||||
\(23\) | 1.62008 | 0.337811 | 0.168905 | − | 0.985632i | \(-0.445977\pi\) | ||||
0.168905 | + | 0.985632i | \(0.445977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.94398 | −0.988797 | ||||||||
\(26\) | 1.05072 | 0.206064 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.52145 | −0.287528 | ||||||||
\(29\) | −0.481543 | −0.0894203 | −0.0447101 | − | 0.999000i | \(-0.514236\pi\) | ||||
−0.0447101 | + | 0.999000i | \(0.514236\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.10709 | −1.63568 | −0.817841 | − | 0.575445i | \(-0.804829\pi\) | ||||
−0.817841 | + | 0.575445i | \(0.804829\pi\) | |||||||
\(32\) | −5.81131 | −1.02730 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.37897 | −0.579489 | ||||||||
\(35\) | −0.236679 | −0.0400060 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9544 | 1.80089 | 0.900443 | − | 0.434974i | \(-0.143242\pi\) | ||||
0.900443 | + | 0.434974i | \(0.143242\pi\) | |||||||
\(38\) | −1.47885 | −0.239901 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.576559 | −0.0911620 | ||||||||
\(41\) | −4.78089 | −0.746650 | −0.373325 | − | 0.927701i | \(-0.621782\pi\) | ||||
−0.373325 | + | 0.927701i | \(0.621782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.26680 | 0.193185 | 0.0965927 | − | 0.995324i | \(-0.469206\pi\) | ||||
0.0965927 | + | 0.995324i | \(0.469206\pi\) | |||||||
\(44\) | 7.19704 | 1.08499 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.12073 | −0.165242 | ||||||||
\(47\) | 6.43162 | 0.938148 | 0.469074 | − | 0.883159i | \(-0.344588\pi\) | ||||
0.469074 | + | 0.883159i | \(0.344588\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.42010 | 0.483676 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.31092 | 0.320467 | ||||||||
\(53\) | 11.2045 | 1.53906 | 0.769531 | − | 0.638610i | \(-0.220490\pi\) | ||||
0.769531 | + | 0.638610i | \(0.220490\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.11958 | 0.150964 | ||||||||
\(56\) | 2.43604 | 0.325529 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.333117 | 0.0437405 | ||||||||
\(59\) | −7.68081 | −0.999956 | −0.499978 | − | 0.866038i | \(-0.666659\pi\) | ||||
−0.499978 | + | 0.866038i | \(0.666659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.26239 | 0.673780 | 0.336890 | − | 0.941544i | \(-0.390625\pi\) | ||||
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(62\) | 6.30002 | 0.800103 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.30465 | 0.163081 | ||||||||
\(65\) | 0.359489 | 0.0445891 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.1697 | −1.85327 | −0.926635 | − | 0.375963i | \(-0.877312\pi\) | ||||
−0.926635 | + | 0.375963i | \(0.877312\pi\) | |||||||
\(68\) | −7.43158 | −0.901211 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.163728 | 0.0195692 | ||||||||
\(71\) | 2.66621 | 0.316421 | 0.158210 | − | 0.987405i | \(-0.449428\pi\) | ||||
0.158210 | + | 0.987405i | \(0.449428\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5894 | 1.23939 | 0.619695 | − | 0.784843i | \(-0.287256\pi\) | ||||
0.619695 | + | 0.784843i | \(0.287256\pi\) | |||||||
\(74\) | −7.57791 | −0.880914 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.25252 | −0.373090 | ||||||||
\(77\) | −4.73037 | −0.539076 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.1527 | −1.47979 | −0.739895 | − | 0.672722i | \(-0.765125\pi\) | ||||
−0.739895 | + | 0.672722i | \(0.765125\pi\) | |||||||
\(80\) | −0.321345 | −0.0359275 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.30728 | 0.365228 | ||||||||
\(83\) | −11.1108 | −1.21957 | −0.609783 | − | 0.792568i | \(-0.708743\pi\) | ||||
−0.609783 | + | 0.792568i | \(0.708743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.15606 | −0.125393 | ||||||||
\(86\) | −0.876336 | −0.0944978 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.5234 | −1.22839 | ||||||||
\(89\) | 11.0913 | 1.17568 | 0.587838 | − | 0.808979i | \(-0.299979\pi\) | ||||
0.587838 | + | 0.808979i | \(0.299979\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.51889 | −0.159223 | ||||||||
\(92\) | −2.46488 | −0.256982 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.44921 | −0.458901 | ||||||||
\(95\) | −0.505966 | −0.0519110 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.66578 | −0.981411 | −0.490706 | − | 0.871325i | \(-0.663261\pi\) | ||||
−0.490706 | + | 0.871325i | \(0.663261\pi\) | |||||||
\(98\) | −0.691771 | −0.0698794 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.52204 | 0.752204 | ||||||||
\(101\) | 13.6540 | 1.35863 | 0.679314 | − | 0.733848i | \(-0.262277\pi\) | ||||
0.679314 | + | 0.733848i | \(0.262277\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.04299 | 0.595434 | 0.297717 | − | 0.954654i | \(-0.403775\pi\) | ||||
0.297717 | + | 0.954654i | \(0.403775\pi\) | |||||||
\(104\) | −3.70007 | −0.362822 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.75097 | −0.752841 | ||||||||
\(107\) | −6.94638 | −0.671532 | −0.335766 | − | 0.941945i | \(-0.608995\pi\) | ||||
−0.335766 | + | 0.941945i | \(0.608995\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.77730 | −0.744930 | −0.372465 | − | 0.928046i | \(-0.621487\pi\) | ||||
−0.372465 | + | 0.928046i | \(0.621487\pi\) | |||||||
\(110\) | −0.774492 | −0.0738449 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.35773 | 0.128293 | ||||||||
\(113\) | 5.69588 | 0.535823 | 0.267911 | − | 0.963444i | \(-0.413667\pi\) | ||||
0.267911 | + | 0.963444i | \(0.413667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.383440 | −0.0357559 | ||||||||
\(116\) | 0.732645 | 0.0680244 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.31336 | 0.489134 | ||||||||
\(119\) | 4.88453 | 0.447764 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3764 | 1.03422 | ||||||||
\(122\) | −3.64037 | −0.329583 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.8560 | 1.24431 | ||||||||
\(125\) | 2.35353 | 0.210506 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 10.7201 | 0.947533 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.248684 | −0.0218110 | ||||||||
\(131\) | −2.77660 | −0.242593 | −0.121296 | − | 0.992616i | \(-0.538705\pi\) | ||||
−0.121296 | + | 0.992616i | \(0.538705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.13777 | 0.185368 | ||||||||
\(134\) | 10.4939 | 0.906538 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.8989 | 1.02032 | ||||||||
\(137\) | −5.85349 | −0.500097 | −0.250048 | − | 0.968233i | \(-0.580447\pi\) | ||||
−0.250048 | + | 0.968233i | \(0.580447\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.8728 | 1.09186 | 0.545929 | − | 0.837832i | \(-0.316177\pi\) | ||||
0.545929 | + | 0.837832i | \(0.316177\pi\) | |||||||
\(140\) | 0.360096 | 0.0304337 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.84440 | −0.154779 | ||||||||
\(143\) | 7.18490 | 0.600832 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.113971 | 0.00946478 | ||||||||
\(146\) | −7.32541 | −0.606255 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16.6665 | −1.36998 | ||||||||
\(149\) | 22.2004 | 1.81873 | 0.909364 | − | 0.416001i | \(-0.136569\pi\) | ||||
0.909364 | + | 0.416001i | \(0.136569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5226 | 1.10045 | 0.550225 | − | 0.835016i | \(-0.314542\pi\) | ||||
0.550225 | + | 0.835016i | \(0.314542\pi\) | |||||||
\(152\) | 5.20770 | 0.422400 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.27233 | 0.263692 | ||||||||
\(155\) | 2.15546 | 0.173130 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.03369 | 0.0824973 | 0.0412487 | − | 0.999149i | \(-0.486866\pi\) | ||||
0.0412487 | + | 0.999149i | \(0.486866\pi\) | |||||||
\(158\) | 9.09863 | 0.723848 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.37542 | 0.108736 | ||||||||
\(161\) | 1.62008 | 0.127680 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.0280 | −1.64704 | −0.823519 | − | 0.567289i | \(-0.807992\pi\) | ||||
−0.823519 | + | 0.567289i | \(0.807992\pi\) | |||||||
\(164\) | 7.27391 | 0.567997 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.68611 | 0.596558 | ||||||||
\(167\) | −18.2548 | −1.41260 | −0.706300 | − | 0.707913i | \(-0.749637\pi\) | ||||
−0.706300 | + | 0.707913i | \(0.749637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6930 | −0.822537 | ||||||||
\(170\) | 0.799732 | 0.0613366 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.92738 | −0.146961 | ||||||||
\(173\) | −10.4129 | −0.791679 | −0.395840 | − | 0.918320i | \(-0.629546\pi\) | ||||
−0.395840 | + | 0.918320i | \(0.629546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.94398 | −0.373730 | ||||||||
\(176\) | −6.42254 | −0.484117 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.67264 | −0.575089 | ||||||||
\(179\) | −5.46552 | −0.408513 | −0.204256 | − | 0.978917i | \(-0.565478\pi\) | ||||
−0.204256 | + | 0.978917i | \(0.565478\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.91504 | 0.216673 | 0.108337 | − | 0.994114i | \(-0.465448\pi\) | ||||
0.108337 | + | 0.994114i | \(0.465448\pi\) | |||||||
\(182\) | 1.05072 | 0.0778848 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.94659 | 0.290946 | ||||||||
\(185\) | −2.59267 | −0.190617 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.1056 | −1.68965 | ||||||||
\(188\) | −9.78540 | −0.713674 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.350012 | 0.0253926 | ||||||||
\(191\) | 4.76963 | 0.345118 | 0.172559 | − | 0.984999i | \(-0.444796\pi\) | ||||
0.172559 | + | 0.984999i | \(0.444796\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.130634 | 0.00940327 | 0.00470163 | − | 0.999989i | \(-0.498503\pi\) | ||||
0.00470163 | + | 0.999989i | \(0.498503\pi\) | |||||||
\(194\) | 6.68651 | 0.480063 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.52145 | −0.108675 | ||||||||
\(197\) | 19.2367 | 1.37056 | 0.685280 | − | 0.728279i | \(-0.259680\pi\) | ||||
0.685280 | + | 0.728279i | \(0.259680\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8797 | −0.842128 | −0.421064 | − | 0.907031i | \(-0.638343\pi\) | ||||
−0.421064 | + | 0.907031i | \(0.638343\pi\) | |||||||
\(200\) | −12.0437 | −0.851621 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.44547 | −0.664581 | ||||||||
\(203\) | −0.481543 | −0.0337977 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.13154 | 0.0790300 | ||||||||
\(206\) | −4.18037 | −0.291260 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.06223 | −0.142990 | ||||||||
\(209\) | −10.1125 | −0.699493 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3794 | 0.989915 | 0.494958 | − | 0.868917i | \(-0.335184\pi\) | ||||
0.494958 | + | 0.868917i | \(0.335184\pi\) | |||||||
\(212\) | −17.0472 | −1.17080 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.80531 | 0.328484 | ||||||||
\(215\) | −0.299825 | −0.0204479 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.10709 | −0.618229 | ||||||||
\(218\) | 5.38011 | 0.364387 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.70339 | −0.114842 | ||||||||
\(221\) | −7.41905 | −0.499059 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.11238 | −0.543245 | −0.271623 | − | 0.962404i | \(-0.587560\pi\) | ||||
−0.271623 | + | 0.962404i | \(0.587560\pi\) | |||||||
\(224\) | −5.81131 | −0.388285 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.94024 | −0.262101 | ||||||||
\(227\) | 24.9231 | 1.65420 | 0.827101 | − | 0.562054i | \(-0.189989\pi\) | ||||
0.827101 | + | 0.562054i | \(0.189989\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.85102 | −0.650974 | −0.325487 | − | 0.945547i | \(-0.605528\pi\) | ||||
−0.325487 | + | 0.945547i | \(0.605528\pi\) | |||||||
\(230\) | 0.265252 | 0.0174902 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.17306 | −0.0770150 | ||||||||
\(233\) | −27.7502 | −1.81797 | −0.908987 | − | 0.416823i | \(-0.863143\pi\) | ||||
−0.908987 | + | 0.416823i | \(0.863143\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.52223 | −0.0992992 | ||||||||
\(236\) | 11.6860 | 0.760693 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.37897 | −0.219026 | ||||||||
\(239\) | 0.812448 | 0.0525529 | 0.0262765 | − | 0.999655i | \(-0.491635\pi\) | ||||
0.0262765 | + | 0.999655i | \(0.491635\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.39668 | −0.347631 | −0.173815 | − | 0.984778i | \(-0.555610\pi\) | ||||
−0.173815 | + | 0.984778i | \(0.555610\pi\) | |||||||
\(242\) | −7.86986 | −0.505894 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.00648 | −0.512562 | ||||||||
\(245\) | −0.236679 | −0.0151209 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.24704 | −0.206604 | ||||||||
\(248\) | −22.1852 | −1.40876 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.62810 | −0.102970 | ||||||||
\(251\) | −13.4081 | −0.846314 | −0.423157 | − | 0.906056i | \(-0.639078\pi\) | ||||
−0.423157 | + | 0.906056i | \(0.639078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.66359 | −0.481806 | ||||||||
\(254\) | −0.691771 | −0.0434056 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.0252 | −0.626572 | ||||||||
\(257\) | −23.1837 | −1.44616 | −0.723079 | − | 0.690765i | \(-0.757274\pi\) | ||||
−0.723079 | + | 0.690765i | \(0.757274\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.9544 | 0.680671 | ||||||||
\(260\) | −0.546946 | −0.0339201 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.92077 | 0.118666 | ||||||||
\(263\) | 29.6493 | 1.82825 | 0.914126 | − | 0.405430i | \(-0.132878\pi\) | ||||
0.914126 | + | 0.405430i | \(0.132878\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.65188 | −0.162904 | ||||||||
\(266\) | −1.47885 | −0.0906741 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 23.0799 | 1.40983 | ||||||||
\(269\) | 12.4588 | 0.759624 | 0.379812 | − | 0.925064i | \(-0.375989\pi\) | ||||
0.379812 | + | 0.925064i | \(0.375989\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.16036 | −0.434961 | −0.217481 | − | 0.976065i | \(-0.569784\pi\) | ||||
−0.217481 | + | 0.976065i | \(0.569784\pi\) | |||||||
\(272\) | 6.63185 | 0.402115 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.04927 | 0.244625 | ||||||||
\(275\) | 23.3869 | 1.41028 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.1691 | −1.75260 | −0.876299 | − | 0.481767i | \(-0.839995\pi\) | ||||
−0.876299 | + | 0.481767i | \(0.839995\pi\) | |||||||
\(278\) | −8.90504 | −0.534089 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.576559 | −0.0344560 | ||||||||
\(281\) | 2.42921 | 0.144914 | 0.0724572 | − | 0.997372i | \(-0.476916\pi\) | ||||
0.0724572 | + | 0.997372i | \(0.476916\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0816 | −0.777621 | −0.388810 | − | 0.921318i | \(-0.627114\pi\) | ||||
−0.388810 | + | 0.921318i | \(0.627114\pi\) | |||||||
\(284\) | −4.05651 | −0.240710 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.97031 | −0.293900 | ||||||||
\(287\) | −4.78089 | −0.282207 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.85859 | 0.403447 | ||||||||
\(290\) | −0.0788419 | −0.00462975 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.1112 | −0.942837 | ||||||||
\(293\) | −11.9508 | −0.698174 | −0.349087 | − | 0.937090i | \(-0.613508\pi\) | ||||
−0.349087 | + | 0.937090i | \(0.613508\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.81788 | 0.105841 | ||||||||
\(296\) | 26.6852 | 1.55105 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.3576 | −0.889642 | ||||||||
\(299\) | −2.46073 | −0.142307 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.26680 | 0.0730172 | ||||||||
\(302\) | −9.35451 | −0.538292 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.90251 | 0.166470 | ||||||||
\(305\) | −1.24550 | −0.0713169 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.3233 | −1.90186 | −0.950931 | − | 0.309402i | \(-0.899871\pi\) | ||||
−0.950931 | + | 0.309402i | \(0.899871\pi\) | |||||||
\(308\) | 7.19704 | 0.410089 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.49108 | −0.0846877 | ||||||||
\(311\) | 17.5249 | 0.993747 | 0.496874 | − | 0.867823i | \(-0.334481\pi\) | ||||
0.496874 | + | 0.867823i | \(0.334481\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.4399 | −0.590099 | −0.295050 | − | 0.955482i | \(-0.595336\pi\) | ||||
−0.295050 | + | 0.955482i | \(0.595336\pi\) | |||||||
\(314\) | −0.715076 | −0.0403540 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.0112 | 1.12572 | ||||||||
\(317\) | 17.5619 | 0.986377 | 0.493188 | − | 0.869923i | \(-0.335831\pi\) | ||||
0.493188 | + | 0.869923i | \(0.335831\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.27788 | 0.127537 | ||||||||
\(320\) | −0.308782 | −0.0172614 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.12073 | −0.0624556 | ||||||||
\(323\) | 10.4420 | 0.581009 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.50936 | 0.416544 | ||||||||
\(326\) | 14.5465 | 0.805658 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.6464 | −0.643067 | ||||||||
\(329\) | 6.43162 | 0.354587 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.3554 | −1.28373 | −0.641865 | − | 0.766818i | \(-0.721839\pi\) | ||||
−0.641865 | + | 0.766818i | \(0.721839\pi\) | |||||||
\(332\) | 16.9045 | 0.927756 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.6281 | 0.690981 | ||||||||
\(335\) | 3.59034 | 0.196161 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.90547 | −0.267218 | −0.133609 | − | 0.991034i | \(-0.542657\pi\) | ||||
−0.133609 | + | 0.991034i | \(0.542657\pi\) | |||||||
\(338\) | 7.39709 | 0.402349 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.75890 | 0.0953896 | ||||||||
\(341\) | 43.0799 | 2.33291 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 3.08598 | 0.166385 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.20335 | 0.387255 | ||||||||
\(347\) | 10.4466 | 0.560805 | 0.280403 | − | 0.959882i | \(-0.409532\pi\) | ||||
0.280403 | + | 0.959882i | \(0.409532\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.3334 | −1.03489 | −0.517446 | − | 0.855716i | \(-0.673117\pi\) | ||||
−0.517446 | + | 0.855716i | \(0.673117\pi\) | |||||||
\(350\) | 3.42010 | 0.182812 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 27.4897 | 1.46520 | ||||||||
\(353\) | −4.03886 | −0.214967 | −0.107483 | − | 0.994207i | \(-0.534279\pi\) | ||||
−0.107483 | + | 0.994207i | \(0.534279\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.631035 | −0.0334919 | ||||||||
\(356\) | −16.8749 | −0.894368 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.78089 | 0.199826 | ||||||||
\(359\) | −0.855429 | −0.0451478 | −0.0225739 | − | 0.999745i | \(-0.507186\pi\) | ||||
−0.0225739 | + | 0.999745i | \(0.507186\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4299 | −0.759470 | ||||||||
\(362\) | −2.01654 | −0.105987 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.31092 | 0.121125 | ||||||||
\(365\) | −2.50628 | −0.131185 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.7046 | 1.28957 | 0.644784 | − | 0.764365i | \(-0.276947\pi\) | ||||
0.644784 | + | 0.764365i | \(0.276947\pi\) | |||||||
\(368\) | 2.19963 | 0.114664 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.79353 | 0.0932412 | ||||||||
\(371\) | 11.2045 | 0.581711 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.282770 | 0.0146413 | 0.00732065 | − | 0.999973i | \(-0.497670\pi\) | ||||
0.00732065 | + | 0.999973i | \(0.497670\pi\) | |||||||
\(374\) | 15.9838 | 0.826502 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.6677 | 0.807998 | ||||||||
\(377\) | 0.731410 | 0.0376695 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.3555 | −0.634657 | −0.317329 | − | 0.948316i | \(-0.602786\pi\) | ||||
−0.317329 | + | 0.948316i | \(0.602786\pi\) | |||||||
\(380\) | 0.769803 | 0.0394901 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.29949 | −0.168817 | ||||||||
\(383\) | −22.1873 | −1.13372 | −0.566859 | − | 0.823815i | \(-0.691841\pi\) | ||||
−0.566859 | + | 0.823815i | \(0.691841\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.11958 | 0.0570590 | ||||||||
\(386\) | −0.0903691 | −0.00459966 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.7060 | 0.746586 | ||||||||
\(389\) | 27.5859 | 1.39866 | 0.699331 | − | 0.714798i | \(-0.253481\pi\) | ||||
0.699331 | + | 0.714798i | \(0.253481\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.91334 | 0.400195 | ||||||||
\(392\) | 2.43604 | 0.123039 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.3074 | −0.670418 | ||||||||
\(395\) | 3.11296 | 0.156630 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.4752 | −1.73026 | −0.865130 | − | 0.501547i | \(-0.832764\pi\) | ||||
−0.865130 | + | 0.501547i | \(0.832764\pi\) | |||||||
\(398\) | 8.21801 | 0.411932 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.71257 | −0.335629 | ||||||||
\(401\) | 18.3464 | 0.916174 | 0.458087 | − | 0.888907i | \(-0.348535\pi\) | ||||
0.458087 | + | 0.888907i | \(0.348535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.8327 | 0.689053 | ||||||||
\(404\) | −20.7740 | −1.03354 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.333117 | 0.0165323 | ||||||||
\(407\) | −51.8182 | −2.56853 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.2920 | −0.558355 | −0.279178 | − | 0.960239i | \(-0.590062\pi\) | ||||
−0.279178 | + | 0.960239i | \(0.590062\pi\) | |||||||
\(410\) | −0.782764 | −0.0386580 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.19413 | −0.452962 | ||||||||
\(413\) | −7.68081 | −0.377948 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.62969 | 0.129086 | ||||||||
\(416\) | 8.82674 | 0.432766 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.99550 | 0.342161 | ||||||||
\(419\) | −4.64156 | −0.226755 | −0.113377 | − | 0.993552i | \(-0.536167\pi\) | ||||
−0.113377 | + | 0.993552i | \(0.536167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.1742 | −0.885756 | −0.442878 | − | 0.896582i | \(-0.646042\pi\) | ||||
−0.442878 | + | 0.896582i | \(0.646042\pi\) | |||||||
\(422\) | −9.94722 | −0.484223 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 27.2947 | 1.32555 | ||||||||
\(425\) | −24.1490 | −1.17140 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.26239 | 0.254665 | ||||||||
\(428\) | 10.5686 | 0.510852 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.207410 | 0.0100022 | ||||||||
\(431\) | −13.9712 | −0.672969 | −0.336485 | − | 0.941689i | \(-0.609238\pi\) | ||||
−0.336485 | + | 0.941689i | \(0.609238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.48040 | −0.0711437 | −0.0355719 | − | 0.999367i | \(-0.511325\pi\) | ||||
−0.0355719 | + | 0.999367i | \(0.511325\pi\) | |||||||
\(434\) | 6.30002 | 0.302411 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.8328 | 0.566688 | ||||||||
\(437\) | 3.46337 | 0.165675 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.9084 | −1.95245 | −0.976225 | − | 0.216758i | \(-0.930452\pi\) | ||||
−0.976225 | + | 0.216758i | \(0.930452\pi\) | |||||||
\(440\) | 2.72734 | 0.130021 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.13228 | 0.244118 | ||||||||
\(443\) | −2.15526 | −0.102400 | −0.0511998 | − | 0.998688i | \(-0.516305\pi\) | ||||
−0.0511998 | + | 0.998688i | \(0.516305\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.62508 | −0.124441 | ||||||||
\(446\) | 5.61191 | 0.265732 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.30465 | 0.0616387 | ||||||||
\(449\) | −1.25094 | −0.0590356 | −0.0295178 | − | 0.999564i | \(-0.509397\pi\) | ||||
−0.0295178 | + | 0.999564i | \(0.509397\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.6154 | 1.06492 | ||||||||
\(452\) | −8.66601 | −0.407615 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.2410 | −0.809162 | ||||||||
\(455\) | 0.359489 | 0.0168531 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.33789 | −0.436808 | −0.218404 | − | 0.975858i | \(-0.570085\pi\) | ||||
−0.218404 | + | 0.975858i | \(0.570085\pi\) | |||||||
\(458\) | 6.81465 | 0.318428 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.583385 | 0.0272005 | ||||||||
\(461\) | 9.40350 | 0.437965 | 0.218982 | − | 0.975729i | \(-0.429726\pi\) | ||||
0.218982 | + | 0.975729i | \(0.429726\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.8889 | 1.66790 | 0.833950 | − | 0.551840i | \(-0.186074\pi\) | ||||
0.833950 | + | 0.551840i | \(0.186074\pi\) | |||||||
\(464\) | −0.653803 | −0.0303520 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.1968 | 0.889273 | ||||||||
\(467\) | 9.27065 | 0.428994 | 0.214497 | − | 0.976725i | \(-0.431189\pi\) | ||||
0.214497 | + | 0.976725i | \(0.431189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.1697 | −0.700470 | ||||||||
\(470\) | 1.05303 | 0.0485728 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.7107 | −0.861232 | ||||||||
\(473\) | −5.99244 | −0.275533 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.5691 | −0.484944 | ||||||||
\(476\) | −7.43158 | −0.340626 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.562028 | −0.0257066 | ||||||||
\(479\) | −23.0284 | −1.05220 | −0.526098 | − | 0.850424i | \(-0.676345\pi\) | ||||
−0.526098 | + | 0.850424i | \(0.676345\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.6385 | −0.758648 | ||||||||
\(482\) | 3.73327 | 0.170046 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.3087 | −0.786757 | ||||||||
\(485\) | 2.28769 | 0.103879 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.9762 | −0.542694 | −0.271347 | − | 0.962482i | \(-0.587469\pi\) | ||||
−0.271347 | + | 0.962482i | \(0.587469\pi\) | |||||||
\(488\) | 12.8194 | 0.580306 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.163728 | 0.00739646 | ||||||||
\(491\) | −42.2730 | −1.90775 | −0.953877 | − | 0.300199i | \(-0.902947\pi\) | ||||
−0.953877 | + | 0.300199i | \(0.902947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.35211 | −0.105934 | ||||||||
\(494\) | 2.24621 | 0.101062 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.3649 | −0.555201 | ||||||||
\(497\) | 2.66621 | 0.119596 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.88448 | 0.173893 | 0.0869465 | − | 0.996213i | \(-0.472289\pi\) | ||||
0.0869465 | + | 0.996213i | \(0.472289\pi\) | |||||||
\(500\) | −3.58079 | −0.160138 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.27536 | 0.413980 | ||||||||
\(503\) | 7.79134 | 0.347399 | 0.173699 | − | 0.984799i | \(-0.444428\pi\) | ||||
0.173699 | + | 0.984799i | \(0.444428\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.23162 | −0.143805 | ||||||||
\(506\) | 5.30145 | 0.235678 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.52145 | −0.0675036 | ||||||||
\(509\) | 25.8939 | 1.14773 | 0.573864 | − | 0.818951i | \(-0.305444\pi\) | ||||
0.573864 | + | 0.818951i | \(0.305444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.5894 | 0.468445 | ||||||||
\(512\) | −14.5051 | −0.641041 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.0378 | 0.707397 | ||||||||
\(515\) | −1.43025 | −0.0630243 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.4239 | −1.33804 | ||||||||
\(518\) | −7.57791 | −0.332954 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.875729 | 0.0384033 | ||||||||
\(521\) | −7.34696 | −0.321876 | −0.160938 | − | 0.986964i | \(-0.551452\pi\) | ||||
−0.160938 | + | 0.986964i | \(0.551452\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.81126 | 0.122928 | 0.0614639 | − | 0.998109i | \(-0.480423\pi\) | ||||
0.0614639 | + | 0.998109i | \(0.480423\pi\) | |||||||
\(524\) | 4.22447 | 0.184547 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.5105 | −0.894300 | ||||||||
\(527\) | −44.4838 | −1.93774 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.3753 | −0.885884 | ||||||||
\(530\) | 1.83449 | 0.0796852 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.25252 | −0.141015 | ||||||||
\(533\) | 7.26165 | 0.314537 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.64406 | 0.0710790 | ||||||||
\(536\) | −36.9539 | −1.59616 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.61860 | −0.371574 | ||||||||
\(539\) | −4.73037 | −0.203751 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.76871 | 0.205023 | 0.102511 | − | 0.994732i | \(-0.467312\pi\) | ||||
0.102511 | + | 0.994732i | \(0.467312\pi\) | |||||||
\(542\) | 4.95333 | 0.212764 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −28.3855 | −1.21702 | ||||||||
\(545\) | 1.84072 | 0.0788479 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.47547 | 0.191357 | 0.0956786 | − | 0.995412i | \(-0.469498\pi\) | ||||
0.0956786 | + | 0.995412i | \(0.469498\pi\) | |||||||
\(548\) | 8.90580 | 0.380437 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.1784 | −0.689847 | ||||||||
\(551\) | −1.02943 | −0.0438552 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.1527 | −0.559308 | ||||||||
\(554\) | 20.1783 | 0.857294 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.5854 | −0.830605 | ||||||||
\(557\) | −30.3570 | −1.28627 | −0.643135 | − | 0.765753i | \(-0.722366\pi\) | ||||
−0.643135 | + | 0.765753i | \(0.722366\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.92413 | −0.0813820 | ||||||||
\(560\) | −0.321345 | −0.0135793 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.68046 | −0.0708858 | ||||||||
\(563\) | −40.3405 | −1.70015 | −0.850076 | − | 0.526661i | \(-0.823444\pi\) | ||||
−0.850076 | + | 0.526661i | \(0.823444\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.34809 | −0.0567147 | ||||||||
\(566\) | 9.04947 | 0.380378 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.49499 | 0.272524 | ||||||||
\(569\) | 1.96447 | 0.0823550 | 0.0411775 | − | 0.999152i | \(-0.486889\pi\) | ||||
0.0411775 | + | 0.999152i | \(0.486889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.7620 | 0.743315 | 0.371658 | − | 0.928370i | \(-0.378790\pi\) | ||||
0.371658 | + | 0.928370i | \(0.378790\pi\) | |||||||
\(572\) | −10.9315 | −0.457069 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.30728 | 0.138043 | ||||||||
\(575\) | −8.00966 | −0.334026 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.06360 | 0.335692 | 0.167846 | − | 0.985813i | \(-0.446319\pi\) | ||||
0.167846 | + | 0.985813i | \(0.446319\pi\) | |||||||
\(578\) | −4.74457 | −0.197348 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.173402 | −0.00720011 | ||||||||
\(581\) | −11.1108 | −0.460953 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −53.0016 | −2.19510 | ||||||||
\(584\) | 25.7961 | 1.06745 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.26723 | 0.341516 | ||||||||
\(587\) | 2.82469 | 0.116588 | 0.0582938 | − | 0.998299i | \(-0.481434\pi\) | ||||
0.0582938 | + | 0.998299i | \(0.481434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.4689 | −0.802202 | ||||||||
\(590\) | −1.25756 | −0.0517729 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.8730 | 0.611277 | ||||||||
\(593\) | 25.7116 | 1.05585 | 0.527925 | − | 0.849291i | \(-0.322970\pi\) | ||||
0.527925 | + | 0.849291i | \(0.322970\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.15606 | −0.0473940 | ||||||||
\(596\) | −33.7769 | −1.38355 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.70226 | 0.0696105 | ||||||||
\(599\) | 34.6917 | 1.41746 | 0.708732 | − | 0.705478i | \(-0.249268\pi\) | ||||
0.708732 | + | 0.705478i | \(0.249268\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.8762 | 0.525230 | 0.262615 | − | 0.964901i | \(-0.415415\pi\) | ||||
0.262615 | + | 0.964901i | \(0.415415\pi\) | |||||||
\(602\) | −0.876336 | −0.0357168 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.5739 | −0.837142 | ||||||||
\(605\) | −2.69255 | −0.109468 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.8987 | 1.05120 | 0.525599 | − | 0.850733i | \(-0.323841\pi\) | ||||
0.525599 | + | 0.850733i | \(0.323841\pi\) | |||||||
\(608\) | −12.4233 | −0.503830 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.861598 | 0.0348851 | ||||||||
\(611\) | −9.76891 | −0.395208 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.6547 | −1.48047 | −0.740234 | − | 0.672349i | \(-0.765285\pi\) | ||||
−0.740234 | + | 0.672349i | \(0.765285\pi\) | |||||||
\(614\) | 23.0521 | 0.930307 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.5234 | −0.464290 | ||||||||
\(617\) | −49.5324 | −1.99410 | −0.997050 | − | 0.0767545i | \(-0.975544\pi\) | ||||
−0.997050 | + | 0.0767545i | \(0.975544\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.3703 | −1.74320 | −0.871599 | − | 0.490219i | \(-0.836917\pi\) | ||||
−0.871599 | + | 0.490219i | \(0.836917\pi\) | |||||||
\(620\) | −3.27942 | −0.131705 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.1232 | −0.486097 | ||||||||
\(623\) | 11.0913 | 0.444364 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.1629 | 0.966515 | ||||||||
\(626\) | 7.22203 | 0.288651 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.57271 | −0.0627579 | ||||||||
\(629\) | 53.5069 | 2.13346 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.7213 | −1.26280 | −0.631402 | − | 0.775455i | \(-0.717520\pi\) | ||||
−0.631402 | + | 0.775455i | \(0.717520\pi\) | |||||||
\(632\) | −32.0404 | −1.27450 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.1488 | −0.482492 | ||||||||
\(635\) | −0.236679 | −0.00939232 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.51889 | −0.0601806 | ||||||||
\(638\) | −1.57577 | −0.0623853 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.53722 | −0.100293 | ||||||||
\(641\) | 6.12263 | 0.241829 | 0.120915 | − | 0.992663i | \(-0.461417\pi\) | ||||
0.120915 | + | 0.992663i | \(0.461417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.36807 | −0.0539513 | −0.0269757 | − | 0.999636i | \(-0.508588\pi\) | ||||
−0.0269757 | + | 0.999636i | \(0.508588\pi\) | |||||||
\(644\) | −2.46488 | −0.0971299 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.22348 | −0.284204 | ||||||||
\(647\) | −23.2875 | −0.915525 | −0.457762 | − | 0.889075i | \(-0.651349\pi\) | ||||
−0.457762 | + | 0.889075i | \(0.651349\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.3330 | 1.42620 | ||||||||
\(650\) | −5.19476 | −0.203755 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 31.9931 | 1.25295 | ||||||||
\(653\) | −26.1315 | −1.02260 | −0.511302 | − | 0.859401i | \(-0.670836\pi\) | ||||
−0.511302 | + | 0.859401i | \(0.670836\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.657163 | 0.0256775 | ||||||||
\(656\) | −6.49114 | −0.253436 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.44921 | −0.173448 | ||||||||
\(659\) | −10.1531 | −0.395510 | −0.197755 | − | 0.980252i | \(-0.563365\pi\) | ||||
−0.197755 | + | 0.980252i | \(0.563365\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.42067 | 0.0941533 | 0.0470766 | − | 0.998891i | \(-0.485009\pi\) | ||||
0.0470766 | + | 0.998891i | \(0.485009\pi\) | |||||||
\(662\) | 16.1566 | 0.627944 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −27.0663 | −1.05038 | ||||||||
\(665\) | −0.505966 | −0.0196205 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.780140 | −0.0302071 | ||||||||
\(668\) | 27.7738 | 1.07460 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.48369 | −0.0959534 | ||||||||
\(671\) | −24.8930 | −0.960985 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0790 | −1.00527 | −0.502636 | − | 0.864498i | \(-0.667636\pi\) | ||||
−0.502636 | + | 0.864498i | \(0.667636\pi\) | |||||||
\(674\) | 3.39346 | 0.130711 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.2689 | 0.625725 | ||||||||
\(677\) | −45.3731 | −1.74383 | −0.871915 | − | 0.489657i | \(-0.837122\pi\) | ||||
−0.871915 | + | 0.489657i | \(0.837122\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.66578 | −0.370939 | ||||||||
\(680\) | −2.81622 | −0.107997 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −29.8014 | −1.14116 | ||||||||
\(683\) | 11.9507 | 0.457282 | 0.228641 | − | 0.973511i | \(-0.426572\pi\) | ||||
0.228641 | + | 0.973511i | \(0.426572\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.38540 | 0.0529333 | ||||||||
\(686\) | −0.691771 | −0.0264119 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.71997 | 0.0655732 | ||||||||
\(689\) | −17.0184 | −0.648351 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.9466 | −0.454469 | −0.227235 | − | 0.973840i | \(-0.572968\pi\) | ||||
−0.227235 | + | 0.973840i | \(0.572968\pi\) | |||||||
\(692\) | 15.8428 | 0.602251 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.22669 | −0.274321 | ||||||||
\(695\) | −3.04672 | −0.115569 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.3524 | −0.884535 | ||||||||
\(698\) | 13.3743 | 0.506223 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.52204 | 0.284306 | ||||||||
\(701\) | −11.7682 | −0.444478 | −0.222239 | − | 0.974992i | \(-0.571337\pi\) | ||||
−0.222239 | + | 0.974992i | \(0.571337\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.4179 | 0.883224 | ||||||||
\(704\) | −6.17146 | −0.232596 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.79396 | 0.105152 | ||||||||
\(707\) | 13.6540 | 0.513513 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.7838 | −0.818108 | −0.409054 | − | 0.912510i | \(-0.634141\pi\) | ||||
−0.409054 | + | 0.912510i | \(0.634141\pi\) | |||||||
\(710\) | 0.436532 | 0.0163827 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.0189 | 1.01257 | ||||||||
\(713\) | −14.7542 | −0.552551 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.70052 | −0.0635957 | ||||||||
\(716\) | 8.31554 | 0.310766 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.591761 | 0.0220843 | ||||||||
\(719\) | −49.2724 | −1.83755 | −0.918774 | − | 0.394783i | \(-0.870820\pi\) | ||||
−0.918774 | + | 0.394783i | \(0.870820\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.04299 | 0.225053 | ||||||||
\(722\) | 9.98220 | 0.371499 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.43510 | −0.164829 | ||||||||
\(725\) | 2.38074 | 0.0884185 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.7353 | 0.472327 | 0.236164 | − | 0.971713i | \(-0.424110\pi\) | ||||
0.236164 | + | 0.971713i | \(0.424110\pi\) | |||||||
\(728\) | −3.70007 | −0.137134 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.73377 | 0.0641697 | ||||||||
\(731\) | 6.18772 | 0.228861 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.6644 | 0.837130 | 0.418565 | − | 0.908187i | \(-0.362533\pi\) | ||||
0.418565 | + | 0.908187i | \(0.362533\pi\) | |||||||
\(734\) | −17.0899 | −0.630799 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.41481 | −0.347035 | ||||||||
\(737\) | 71.7581 | 2.64324 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.56804 | −0.278395 | −0.139197 | − | 0.990265i | \(-0.544452\pi\) | ||||
−0.139197 | + | 0.990265i | \(0.544452\pi\) | |||||||
\(740\) | 3.94462 | 0.145007 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.75097 | −0.284547 | ||||||||
\(743\) | 2.44813 | 0.0898132 | 0.0449066 | − | 0.998991i | \(-0.485701\pi\) | ||||
0.0449066 | + | 0.998991i | \(0.485701\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.25437 | −0.192505 | ||||||||
\(746\) | −0.195612 | −0.00716188 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 35.1541 | 1.28536 | ||||||||
\(749\) | −6.94638 | −0.253815 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3013 | 1.32465 | 0.662327 | − | 0.749215i | \(-0.269569\pi\) | ||||
0.662327 | + | 0.749215i | \(0.269569\pi\) | |||||||
\(752\) | 8.73237 | 0.318437 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.505968 | −0.0184263 | ||||||||
\(755\) | −3.20050 | −0.116478 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0015 | 0.690620 | 0.345310 | − | 0.938489i | \(-0.387774\pi\) | ||||
0.345310 | + | 0.938489i | \(0.387774\pi\) | |||||||
\(758\) | 8.54714 | 0.310446 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.23255 | −0.0447094 | ||||||||
\(761\) | −11.8346 | −0.429005 | −0.214503 | − | 0.976723i | \(-0.568813\pi\) | ||||
−0.214503 | + | 0.976723i | \(0.568813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.77730 | −0.281557 | ||||||||
\(764\) | −7.25677 | −0.262541 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.3485 | 0.554564 | ||||||||
\(767\) | 11.6663 | 0.421245 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.9124 | 0.465634 | 0.232817 | − | 0.972521i | \(-0.425206\pi\) | ||||
0.232817 | + | 0.972521i | \(0.425206\pi\) | |||||||
\(770\) | −0.774492 | −0.0279108 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.198754 | −0.00715332 | ||||||||
\(773\) | −44.8628 | −1.61360 | −0.806801 | − | 0.590823i | \(-0.798803\pi\) | ||||
−0.806801 | + | 0.590823i | \(0.798803\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.0253 | 1.61736 | ||||||||
\(776\) | −23.5462 | −0.845260 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.0832 | −0.684164 | ||||||||
\(779\) | −10.2205 | −0.366186 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6121 | −0.451298 | ||||||||
\(782\) | −5.47422 | −0.195758 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.35773 | 0.0484902 | ||||||||
\(785\) | −0.244652 | −0.00873201 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.5191 | 0.909658 | 0.454829 | − | 0.890579i | \(-0.349700\pi\) | ||||
0.454829 | + | 0.890579i | \(0.349700\pi\) | |||||||
\(788\) | −29.2678 | −1.04262 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.15345 | −0.0766165 | ||||||||
\(791\) | 5.69588 | 0.202522 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.99298 | −0.283839 | ||||||||
\(794\) | 23.8489 | 0.846367 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.0744 | 0.640629 | ||||||||
\(797\) | 35.4729 | 1.25651 | 0.628257 | − | 0.778006i | \(-0.283769\pi\) | ||||
0.628257 | + | 0.778006i | \(0.283769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.4154 | 1.11140 | ||||||||
\(800\) | 28.7310 | 1.01580 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.6915 | −0.448152 | ||||||||
\(803\) | −50.0916 | −1.76769 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.383440 | −0.0135145 | ||||||||
\(806\) | −9.56903 | −0.337055 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.2618 | 1.17015 | ||||||||
\(809\) | −39.9982 | −1.40626 | −0.703131 | − | 0.711061i | \(-0.748215\pi\) | ||||
−0.703131 | + | 0.711061i | \(0.748215\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.3383 | −0.749287 | −0.374644 | − | 0.927169i | \(-0.622235\pi\) | ||||
−0.374644 | + | 0.927169i | \(0.622235\pi\) | |||||||
\(812\) | 0.732645 | 0.0257108 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 35.8463 | 1.25641 | ||||||||
\(815\) | 4.97688 | 0.174332 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.70813 | 0.0947456 | ||||||||
\(818\) | 7.81150 | 0.273123 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.72158 | −0.0601202 | ||||||||
\(821\) | −0.612120 | −0.0213631 | −0.0106816 | − | 0.999943i | \(-0.503400\pi\) | ||||
−0.0106816 | + | 0.999943i | \(0.503400\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.7565 | −1.31611 | −0.658055 | − | 0.752970i | \(-0.728621\pi\) | ||||
−0.658055 | + | 0.752970i | \(0.728621\pi\) | |||||||
\(824\) | 14.7210 | 0.512829 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.31336 | 0.184875 | ||||||||
\(827\) | −38.2190 | −1.32900 | −0.664502 | − | 0.747287i | \(-0.731356\pi\) | ||||
−0.664502 | + | 0.747287i | \(0.731356\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0302 | −0.799871 | −0.399935 | − | 0.916543i | \(-0.630967\pi\) | ||||
−0.399935 | + | 0.916543i | \(0.630967\pi\) | |||||||
\(830\) | −1.81914 | −0.0631433 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.98161 | −0.0687000 | ||||||||
\(833\) | 4.88453 | 0.169239 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.32053 | 0.149518 | ||||||||
\(836\) | 15.3856 | 0.532123 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.21089 | 0.110919 | ||||||||
\(839\) | 34.5464 | 1.19268 | 0.596338 | − | 0.802734i | \(-0.296622\pi\) | ||||
0.596338 | + | 0.802734i | \(0.296622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7681 | −0.992004 | ||||||||
\(842\) | 12.5724 | 0.433273 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.8775 | −0.753055 | ||||||||
\(845\) | 2.53080 | 0.0870623 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.3764 | 0.390898 | ||||||||
\(848\) | 15.2127 | 0.522406 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.7056 | 0.572997 | ||||||||
\(851\) | 17.7470 | 0.608359 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.0512 | 1.16589 | 0.582946 | − | 0.812511i | \(-0.301900\pi\) | ||||
0.582946 | + | 0.812511i | \(0.301900\pi\) | |||||||
\(854\) | −3.64037 | −0.124571 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.9217 | −0.578370 | ||||||||
\(857\) | −33.3224 | −1.13827 | −0.569136 | − | 0.822243i | \(-0.692722\pi\) | ||||
−0.569136 | + | 0.822243i | \(0.692722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.3511 | 1.17204 | 0.586022 | − | 0.810295i | \(-0.300693\pi\) | ||||
0.586022 | + | 0.810295i | \(0.300693\pi\) | |||||||
\(860\) | 0.456170 | 0.0155553 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.66487 | 0.329187 | ||||||||
\(863\) | −0.252328 | −0.00858935 | −0.00429467 | − | 0.999991i | \(-0.501367\pi\) | ||||
−0.00429467 | + | 0.999991i | \(0.501367\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.46452 | 0.0837961 | ||||||||
\(866\) | 1.02410 | 0.0348004 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.8560 | 0.470303 | ||||||||
\(869\) | 62.2170 | 2.11057 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.0410 | 0.780715 | ||||||||
\(872\) | −18.9458 | −0.641586 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.39586 | −0.0810411 | ||||||||
\(875\) | 2.35353 | 0.0795639 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.6171 | 1.30401 | 0.652004 | − | 0.758216i | \(-0.273929\pi\) | ||||
0.652004 | + | 0.758216i | \(0.273929\pi\) | |||||||
\(878\) | 28.2992 | 0.955053 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.52008 | 0.0512419 | ||||||||
\(881\) | 0.798968 | 0.0269179 | 0.0134590 | − | 0.999909i | \(-0.495716\pi\) | ||||
0.0134590 | + | 0.999909i | \(0.495716\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.06536 | −0.271421 | −0.135711 | − | 0.990749i | \(-0.543332\pi\) | ||||
−0.135711 | + | 0.990749i | \(0.543332\pi\) | |||||||
\(884\) | 11.2877 | 0.379648 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.49095 | 0.0500894 | ||||||||
\(887\) | −16.3375 | −0.548559 | −0.274280 | − | 0.961650i | \(-0.588439\pi\) | ||||
−0.274280 | + | 0.961650i | \(0.588439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 1.81595 | 0.0608709 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.3426 | 0.413261 | ||||||||
\(893\) | 13.7493 | 0.460104 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.29357 | 0.0432394 | ||||||||
\(896\) | 10.7201 | 0.358134 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.865365 | 0.0288776 | ||||||||
\(899\) | 4.38545 | 0.146263 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.7289 | 1.82328 | ||||||||
\(902\) | −15.6447 | −0.520911 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.8754 | 0.461488 | ||||||||
\(905\) | −0.689928 | −0.0229340 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.06870 | −0.301121 | −0.150561 | − | 0.988601i | \(-0.548108\pi\) | ||||
−0.150561 | + | 0.988601i | \(0.548108\pi\) | |||||||
\(908\) | −37.9193 | −1.25839 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.248684 | −0.00824379 | ||||||||
\(911\) | −10.9544 | −0.362936 | −0.181468 | − | 0.983397i | \(-0.558085\pi\) | ||||
−0.181468 | + | 0.983397i | \(0.558085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.5581 | 1.73942 | ||||||||
\(914\) | 6.45968 | 0.213667 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.9879 | 0.495213 | ||||||||
\(917\) | −2.77660 | −0.0916914 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.67443 | −0.121208 | −0.0606041 | − | 0.998162i | \(-0.519303\pi\) | ||||
−0.0606041 | + | 0.998162i | \(0.519303\pi\) | |||||||
\(920\) | −0.934074 | −0.0307955 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.50507 | −0.214233 | ||||||||
\(923\) | −4.04967 | −0.133297 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −54.1582 | −1.78071 | ||||||||
\(926\) | −24.8269 | −0.815863 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.79840 | 0.0918619 | ||||||||
\(929\) | −44.8141 | −1.47030 | −0.735151 | − | 0.677903i | \(-0.762889\pi\) | ||||
−0.735151 | + | 0.677903i | \(0.762889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.13777 | 0.0700627 | ||||||||
\(932\) | 42.2206 | 1.38298 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.41316 | −0.209845 | ||||||||
\(935\) | 5.46861 | 0.178843 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.40715 | 0.241981 | 0.120990 | − | 0.992654i | \(-0.461393\pi\) | ||||
0.120990 | + | 0.992654i | \(0.461393\pi\) | |||||||
\(938\) | 10.4939 | 0.342639 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.31600 | 0.0755396 | ||||||||
\(941\) | −50.7499 | −1.65440 | −0.827199 | − | 0.561909i | \(-0.810067\pi\) | ||||
−0.827199 | + | 0.561909i | \(0.810067\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.74545 | −0.252226 | ||||||||
\(944\) | −10.4284 | −0.339416 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.14539 | 0.134778 | ||||||||
\(947\) | −40.3285 | −1.31050 | −0.655250 | − | 0.755412i | \(-0.727437\pi\) | ||||
−0.655250 | + | 0.755412i | \(0.727437\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.0840 | −0.522110 | ||||||||
\(950\) | 7.31141 | 0.237213 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.8989 | 0.385645 | ||||||||
\(953\) | 3.51760 | 0.113946 | 0.0569731 | − | 0.998376i | \(-0.481855\pi\) | ||||
0.0569731 | + | 0.998376i | \(0.481855\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.12887 | −0.0365294 | ||||||||
\(956\) | −1.23610 | −0.0399784 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.9304 | 0.514688 | ||||||||
\(959\) | −5.85349 | −0.189019 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.9390 | 1.67545 | ||||||||
\(962\) | 11.5100 | 0.371097 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.21080 | 0.264452 | ||||||||
\(965\) | −0.0309184 | −0.000995299 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.1545 | −1.45207 | −0.726035 | − | 0.687658i | \(-0.758639\pi\) | ||||
−0.726035 | + | 0.687658i | \(0.758639\pi\) | |||||||
\(968\) | 27.7133 | 0.890741 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.58256 | −0.0508128 | ||||||||
\(971\) | 38.2249 | 1.22669 | 0.613347 | − | 0.789813i | \(-0.289823\pi\) | ||||
0.613347 | + | 0.789813i | \(0.289823\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.8728 | 0.412683 | ||||||||
\(974\) | 8.28480 | 0.265462 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.14488 | 0.228702 | ||||||||
\(977\) | 32.0622 | 1.02576 | 0.512880 | − | 0.858460i | \(-0.328579\pi\) | ||||
0.512880 | + | 0.858460i | \(0.328579\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −52.4660 | −1.67682 | ||||||||
\(980\) | 0.360096 | 0.0115028 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 29.2432 | 0.933189 | ||||||||
\(983\) | −31.8590 | −1.01614 | −0.508072 | − | 0.861315i | \(-0.669642\pi\) | ||||
−0.508072 | + | 0.861315i | \(0.669642\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.55293 | −0.145068 | ||||||||
\(986\) | 1.62712 | 0.0518181 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.94022 | 0.157169 | ||||||||
\(989\) | 2.05232 | 0.0652601 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.9795 | 0.793500 | 0.396750 | − | 0.917927i | \(-0.370138\pi\) | ||||
0.396750 | + | 0.917927i | \(0.370138\pi\) | |||||||
\(992\) | 52.9241 | 1.68034 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.84440 | −0.0585010 | ||||||||
\(995\) | 2.81167 | 0.0891359 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.0534 | 1.07848 | 0.539241 | − | 0.842151i | \(-0.318711\pi\) | ||||
0.539241 | + | 0.842151i | \(0.318711\pi\) | |||||||
\(998\) | −2.68717 | −0.0850608 | ||||||||
\(999\) | 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 | 8001.2.a.x.1.8 | ✓ | 22 | |
3.2 | odd | 2 | inner | 8001.2.a.x.1.15 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.x.1.8 | ✓ | 22 | 1.1 | even | 1 | trivial | |
8001.2.a.x.1.15 | yes | 22 | 3.2 | odd | 2 | inner |