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 | 1.16 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.775659 | 0.548473 | 0.274237 | − | 0.961662i | \(-0.411575\pi\) | ||||
0.274237 | + | 0.961662i | \(0.411575\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.39835 | −0.699177 | ||||||||
\(5\) | 0.833166 | 0.372603 | 0.186302 | − | 0.982493i | \(-0.440350\pi\) | ||||
0.186302 | + | 0.982493i | \(0.440350\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.63596 | −0.931953 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.646253 | 0.204363 | ||||||||
\(11\) | 0.821214 | 0.247605 | 0.123803 | − | 0.992307i | \(-0.460491\pi\) | ||||
0.123803 | + | 0.992307i | \(0.460491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.40878 | −0.945424 | −0.472712 | − | 0.881217i | \(-0.656725\pi\) | ||||
−0.472712 | + | 0.881217i | \(0.656725\pi\) | |||||||
\(14\) | 0.775659 | 0.207303 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.752101 | 0.188025 | ||||||||
\(17\) | −2.50310 | −0.607091 | −0.303546 | − | 0.952817i | \(-0.598170\pi\) | ||||
−0.303546 | + | 0.952817i | \(0.598170\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.40296 | 0.321861 | 0.160931 | − | 0.986966i | \(-0.448550\pi\) | ||||
0.160931 | + | 0.986966i | \(0.448550\pi\) | |||||||
\(20\) | −1.16506 | −0.260516 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.636982 | 0.135805 | ||||||||
\(23\) | 0.947115 | 0.197487 | 0.0987436 | − | 0.995113i | \(-0.468518\pi\) | ||||
0.0987436 | + | 0.995113i | \(0.468518\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.30583 | −0.861167 | ||||||||
\(26\) | −2.64405 | −0.518540 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.39835 | −0.264264 | ||||||||
\(29\) | 1.78577 | 0.331610 | 0.165805 | − | 0.986159i | \(-0.446978\pi\) | ||||
0.165805 | + | 0.986159i | \(0.446978\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.51944 | 1.53014 | 0.765068 | − | 0.643949i | \(-0.222705\pi\) | ||||
0.765068 | + | 0.643949i | \(0.222705\pi\) | |||||||
\(32\) | 5.85530 | 1.03508 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.94155 | −0.332973 | ||||||||
\(35\) | 0.833166 | 0.140831 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.89168 | −0.475390 | −0.237695 | − | 0.971340i | \(-0.576392\pi\) | ||||
−0.237695 | + | 0.971340i | \(0.576392\pi\) | |||||||
\(38\) | 1.08822 | 0.176532 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.19620 | −0.347249 | ||||||||
\(41\) | 2.30169 | 0.359464 | 0.179732 | − | 0.983716i | \(-0.442477\pi\) | ||||
0.179732 | + | 0.983716i | \(0.442477\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.58041 | 0.851004 | 0.425502 | − | 0.904957i | \(-0.360098\pi\) | ||||
0.425502 | + | 0.904957i | \(0.360098\pi\) | |||||||
\(44\) | −1.14835 | −0.173120 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.734638 | 0.108316 | ||||||||
\(47\) | 2.14718 | 0.313198 | 0.156599 | − | 0.987662i | \(-0.449947\pi\) | ||||
0.156599 | + | 0.987662i | \(0.449947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.33986 | −0.472327 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.76668 | 0.661019 | ||||||||
\(53\) | −0.992903 | −0.136386 | −0.0681929 | − | 0.997672i | \(-0.521723\pi\) | ||||
−0.0681929 | + | 0.997672i | \(0.521723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.684208 | 0.0922586 | ||||||||
\(56\) | −2.63596 | −0.352245 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.38515 | 0.181879 | ||||||||
\(59\) | −13.0882 | −1.70394 | −0.851971 | − | 0.523589i | \(-0.824593\pi\) | ||||
−0.851971 | + | 0.523589i | \(0.824593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.19849 | −0.921672 | −0.460836 | − | 0.887485i | \(-0.652450\pi\) | ||||
−0.460836 | + | 0.887485i | \(0.652450\pi\) | |||||||
\(62\) | 6.60817 | 0.839239 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.03751 | 0.379689 | ||||||||
\(65\) | −2.84008 | −0.352268 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.77977 | −0.706111 | −0.353056 | − | 0.935602i | \(-0.614857\pi\) | ||||
−0.353056 | + | 0.935602i | \(0.614857\pi\) | |||||||
\(68\) | 3.50022 | 0.424464 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.646253 | 0.0772420 | ||||||||
\(71\) | −0.675593 | −0.0801781 | −0.0400891 | − | 0.999196i | \(-0.512764\pi\) | ||||
−0.0400891 | + | 0.999196i | \(0.512764\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0038 | −1.17086 | −0.585429 | − | 0.810724i | \(-0.699074\pi\) | ||||
−0.585429 | + | 0.810724i | \(0.699074\pi\) | |||||||
\(74\) | −2.24296 | −0.260739 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.96183 | −0.225038 | ||||||||
\(77\) | 0.821214 | 0.0935860 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.57957 | 0.177716 | 0.0888578 | − | 0.996044i | \(-0.471678\pi\) | ||||
0.0888578 | + | 0.996044i | \(0.471678\pi\) | |||||||
\(80\) | 0.626625 | 0.0700589 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.78533 | 0.197156 | ||||||||
\(83\) | 3.31531 | 0.363902 | 0.181951 | − | 0.983308i | \(-0.441759\pi\) | ||||
0.181951 | + | 0.983308i | \(0.441759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.08550 | −0.226204 | ||||||||
\(86\) | 4.32849 | 0.466753 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.16469 | −0.230757 | ||||||||
\(89\) | −1.39169 | −0.147519 | −0.0737595 | − | 0.997276i | \(-0.523500\pi\) | ||||
−0.0737595 | + | 0.997276i | \(0.523500\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.40878 | −0.357337 | ||||||||
\(92\) | −1.32440 | −0.138078 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.66548 | 0.171781 | ||||||||
\(95\) | 1.16890 | 0.119927 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.55016 | −0.461999 | −0.230999 | − | 0.972954i | \(-0.574200\pi\) | ||||
−0.230999 | + | 0.972954i | \(0.574200\pi\) | |||||||
\(98\) | 0.775659 | 0.0783533 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.02108 | 0.602108 | ||||||||
\(101\) | 8.82048 | 0.877670 | 0.438835 | − | 0.898568i | \(-0.355391\pi\) | ||||
0.438835 | + | 0.898568i | \(0.355391\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.65003 | 0.556714 | 0.278357 | − | 0.960478i | \(-0.410210\pi\) | ||||
0.278357 | + | 0.960478i | \(0.410210\pi\) | |||||||
\(104\) | 8.98540 | 0.881091 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.770154 | −0.0748039 | ||||||||
\(107\) | −20.2463 | −1.95729 | −0.978643 | − | 0.205567i | \(-0.934096\pi\) | ||||
−0.978643 | + | 0.205567i | \(0.934096\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.369111 | −0.0353545 | −0.0176772 | − | 0.999844i | \(-0.505627\pi\) | ||||
−0.0176772 | + | 0.999844i | \(0.505627\pi\) | |||||||
\(110\) | 0.530712 | 0.0506014 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.752101 | 0.0710669 | ||||||||
\(113\) | −10.8983 | −1.02523 | −0.512613 | − | 0.858620i | \(-0.671323\pi\) | ||||
−0.512613 | + | 0.858620i | \(0.671323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.789105 | 0.0735844 | ||||||||
\(116\) | −2.49714 | −0.231854 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.1520 | −0.934567 | ||||||||
\(119\) | −2.50310 | −0.229459 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3256 | −0.938692 | ||||||||
\(122\) | −5.58357 | −0.505513 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.9132 | −1.06984 | ||||||||
\(125\) | −7.75331 | −0.693477 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −9.35453 | −0.826831 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.20293 | −0.193210 | ||||||||
\(131\) | −6.34339 | −0.554224 | −0.277112 | − | 0.960838i | \(-0.589377\pi\) | ||||
−0.277112 | + | 0.960838i | \(0.589377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.40296 | 0.121652 | ||||||||
\(134\) | −4.48313 | −0.387283 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.59808 | 0.565781 | ||||||||
\(137\) | −16.5664 | −1.41536 | −0.707682 | − | 0.706531i | \(-0.750259\pi\) | ||||
−0.707682 | + | 0.706531i | \(0.750259\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.6965 | −1.24654 | −0.623271 | − | 0.782006i | \(-0.714197\pi\) | ||||
−0.623271 | + | 0.782006i | \(0.714197\pi\) | |||||||
\(140\) | −1.16506 | −0.0984657 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.524029 | −0.0439756 | ||||||||
\(143\) | −2.79933 | −0.234092 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.48785 | 0.123559 | ||||||||
\(146\) | −7.75955 | −0.642185 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.04359 | 0.332381 | ||||||||
\(149\) | 12.6949 | 1.04001 | 0.520003 | − | 0.854164i | \(-0.325931\pi\) | ||||
0.520003 | + | 0.854164i | \(0.325931\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.318150 | −0.0258906 | −0.0129453 | − | 0.999916i | \(-0.504121\pi\) | ||||
−0.0129453 | + | 0.999916i | \(0.504121\pi\) | |||||||
\(152\) | −3.69815 | −0.299960 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.636982 | 0.0513294 | ||||||||
\(155\) | 7.09811 | 0.570134 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.24209 | 0.657790 | 0.328895 | − | 0.944366i | \(-0.393324\pi\) | ||||
0.328895 | + | 0.944366i | \(0.393324\pi\) | |||||||
\(158\) | 1.22521 | 0.0974723 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.87844 | 0.385674 | ||||||||
\(161\) | 0.947115 | 0.0746431 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7768 | 1.00076 | 0.500379 | − | 0.865806i | \(-0.333194\pi\) | ||||
0.500379 | + | 0.865806i | \(0.333194\pi\) | |||||||
\(164\) | −3.21858 | −0.251329 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.57155 | 0.199591 | ||||||||
\(167\) | 19.9015 | 1.54002 | 0.770010 | − | 0.638031i | \(-0.220251\pi\) | ||||
0.770010 | + | 0.638031i | \(0.220251\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.38025 | −0.106173 | ||||||||
\(170\) | −1.61764 | −0.124067 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.80338 | −0.595002 | ||||||||
\(173\) | 6.38620 | 0.485534 | 0.242767 | − | 0.970085i | \(-0.421945\pi\) | ||||
0.242767 | + | 0.970085i | \(0.421945\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.30583 | −0.325490 | ||||||||
\(176\) | 0.617636 | 0.0465561 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.07948 | −0.0809102 | ||||||||
\(179\) | −13.5632 | −1.01376 | −0.506879 | − | 0.862017i | \(-0.669201\pi\) | ||||
−0.506879 | + | 0.862017i | \(0.669201\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.27667 | −0.540871 | −0.270435 | − | 0.962738i | \(-0.587168\pi\) | ||||
−0.270435 | + | 0.962738i | \(0.587168\pi\) | |||||||
\(182\) | −2.64405 | −0.195990 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.49656 | −0.184049 | ||||||||
\(185\) | −2.40925 | −0.177132 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.05558 | −0.150319 | ||||||||
\(188\) | −3.00251 | −0.218981 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.906667 | 0.0657765 | ||||||||
\(191\) | −2.22153 | −0.160744 | −0.0803721 | − | 0.996765i | \(-0.525611\pi\) | ||||
−0.0803721 | + | 0.996765i | \(0.525611\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.4286 | −1.11057 | −0.555287 | − | 0.831659i | \(-0.687392\pi\) | ||||
−0.555287 | + | 0.831659i | \(0.687392\pi\) | |||||||
\(194\) | −3.52937 | −0.253394 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.39835 | −0.0998824 | ||||||||
\(197\) | 12.8028 | 0.912162 | 0.456081 | − | 0.889938i | \(-0.349253\pi\) | ||||
0.456081 | + | 0.889938i | \(0.349253\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.89117 | 0.275838 | 0.137919 | − | 0.990444i | \(-0.455959\pi\) | ||||
0.137919 | + | 0.990444i | \(0.455959\pi\) | |||||||
\(200\) | 11.3500 | 0.802567 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.84168 | 0.481379 | ||||||||
\(203\) | 1.78577 | 0.125337 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.91769 | 0.133937 | ||||||||
\(206\) | 4.38249 | 0.305343 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.56374 | −0.177764 | ||||||||
\(209\) | 1.15213 | 0.0796945 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.1279 | 1.59219 | 0.796095 | − | 0.605172i | \(-0.206896\pi\) | ||||
0.796095 | + | 0.605172i | \(0.206896\pi\) | |||||||
\(212\) | 1.38843 | 0.0953577 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.7042 | −1.07352 | ||||||||
\(215\) | 4.64941 | 0.317087 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.51944 | 0.578337 | ||||||||
\(218\) | −0.286304 | −0.0193910 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.956765 | −0.0645051 | ||||||||
\(221\) | 8.53251 | 0.573959 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.28503 | 0.420877 | 0.210438 | − | 0.977607i | \(-0.432511\pi\) | ||||
0.210438 | + | 0.977607i | \(0.432511\pi\) | |||||||
\(224\) | 5.85530 | 0.391224 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.45336 | −0.562309 | ||||||||
\(227\) | 7.52578 | 0.499503 | 0.249752 | − | 0.968310i | \(-0.419651\pi\) | ||||
0.249752 | + | 0.968310i | \(0.419651\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.0451 | −1.78719 | −0.893596 | − | 0.448872i | \(-0.851826\pi\) | ||||
−0.893596 | + | 0.448872i | \(0.851826\pi\) | |||||||
\(230\) | 0.612076 | 0.0403591 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.70723 | −0.309045 | ||||||||
\(233\) | −20.8606 | −1.36663 | −0.683313 | − | 0.730126i | \(-0.739461\pi\) | ||||
−0.683313 | + | 0.730126i | \(0.739461\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.78896 | 0.116699 | ||||||||
\(236\) | 18.3020 | 1.19136 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.94155 | −0.125852 | ||||||||
\(239\) | 20.7716 | 1.34360 | 0.671800 | − | 0.740732i | \(-0.265521\pi\) | ||||
0.671800 | + | 0.740732i | \(0.265521\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.7249 | −1.72150 | −0.860750 | − | 0.509028i | \(-0.830005\pi\) | ||||
−0.860750 | + | 0.509028i | \(0.830005\pi\) | |||||||
\(242\) | −8.00915 | −0.514847 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.0660 | 0.644412 | ||||||||
\(245\) | 0.833166 | 0.0532291 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.78238 | −0.304295 | ||||||||
\(248\) | −22.4569 | −1.42602 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.01392 | −0.380354 | ||||||||
\(251\) | −24.2026 | −1.52765 | −0.763827 | − | 0.645420i | \(-0.776682\pi\) | ||||
−0.763827 | + | 0.645420i | \(0.776682\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.777784 | 0.0488989 | ||||||||
\(254\) | 0.775659 | 0.0486691 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.3309 | −0.833184 | ||||||||
\(257\) | −29.2037 | −1.82168 | −0.910838 | − | 0.412765i | \(-0.864563\pi\) | ||||
−0.910838 | + | 0.412765i | \(0.864563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.89168 | −0.179680 | ||||||||
\(260\) | 3.97143 | 0.246298 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.92030 | −0.303977 | ||||||||
\(263\) | 8.46412 | 0.521920 | 0.260960 | − | 0.965350i | \(-0.415961\pi\) | ||||
0.260960 | + | 0.965350i | \(0.415961\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.827253 | −0.0508178 | ||||||||
\(266\) | 1.08822 | 0.0667229 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.08217 | 0.493697 | ||||||||
\(269\) | −25.1306 | −1.53224 | −0.766119 | − | 0.642699i | \(-0.777815\pi\) | ||||
−0.766119 | + | 0.642699i | \(0.777815\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.485582 | 0.0294970 | 0.0147485 | − | 0.999891i | \(-0.495305\pi\) | ||||
0.0147485 | + | 0.999891i | \(0.495305\pi\) | |||||||
\(272\) | −1.88259 | −0.114149 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.8499 | −0.776290 | ||||||||
\(275\) | −3.53601 | −0.213229 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.5162 | −0.752027 | −0.376013 | − | 0.926614i | \(-0.622705\pi\) | ||||
−0.376013 | + | 0.926614i | \(0.622705\pi\) | |||||||
\(278\) | −11.3995 | −0.683695 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.19620 | −0.131248 | ||||||||
\(281\) | 4.50129 | 0.268524 | 0.134262 | − | 0.990946i | \(-0.457134\pi\) | ||||
0.134262 | + | 0.990946i | \(0.457134\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.68047 | −0.278225 | −0.139112 | − | 0.990277i | \(-0.544425\pi\) | ||||
−0.139112 | + | 0.990277i | \(0.544425\pi\) | |||||||
\(284\) | 0.944718 | 0.0560587 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.17133 | −0.128393 | ||||||||
\(287\) | 2.30169 | 0.135865 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.7345 | −0.631440 | ||||||||
\(290\) | 1.15406 | 0.0677688 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.9889 | 0.818637 | ||||||||
\(293\) | 21.7063 | 1.26809 | 0.634047 | − | 0.773295i | \(-0.281393\pi\) | ||||
0.634047 | + | 0.773295i | \(0.281393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.9047 | −0.634894 | ||||||||
\(296\) | 7.62236 | 0.443041 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.84690 | 0.570416 | ||||||||
\(299\) | −3.22850 | −0.186709 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.58041 | 0.321649 | ||||||||
\(302\) | −0.246775 | −0.0142003 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.05517 | 0.0605180 | ||||||||
\(305\) | −5.99754 | −0.343418 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.76773 | 0.443328 | 0.221664 | − | 0.975123i | \(-0.428851\pi\) | ||||
0.221664 | + | 0.975123i | \(0.428851\pi\) | |||||||
\(308\) | −1.14835 | −0.0654332 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.50571 | 0.312703 | ||||||||
\(311\) | 3.35408 | 0.190192 | 0.0950961 | − | 0.995468i | \(-0.469684\pi\) | ||||
0.0950961 | + | 0.995468i | \(0.469684\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.56356 | 0.257948 | 0.128974 | − | 0.991648i | \(-0.458832\pi\) | ||||
0.128974 | + | 0.991648i | \(0.458832\pi\) | |||||||
\(314\) | 6.39305 | 0.360780 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.20880 | −0.124255 | ||||||||
\(317\) | 0.418733 | 0.0235184 | 0.0117592 | − | 0.999931i | \(-0.496257\pi\) | ||||
0.0117592 | + | 0.999931i | \(0.496257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.46650 | 0.0821083 | ||||||||
\(320\) | 2.53075 | 0.141473 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.734638 | 0.0409398 | ||||||||
\(323\) | −3.51175 | −0.195399 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.6776 | 0.814168 | ||||||||
\(326\) | 9.91046 | 0.548889 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.06717 | −0.335003 | ||||||||
\(329\) | 2.14718 | 0.118378 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.6681 | 0.751266 | 0.375633 | − | 0.926768i | \(-0.377425\pi\) | ||||
0.375633 | + | 0.926768i | \(0.377425\pi\) | |||||||
\(332\) | −4.63597 | −0.254432 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.4367 | 0.844660 | ||||||||
\(335\) | −4.81551 | −0.263099 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.1006 | −0.713637 | −0.356819 | − | 0.934174i | \(-0.616139\pi\) | ||||
−0.356819 | + | 0.934174i | \(0.616139\pi\) | |||||||
\(338\) | −1.07060 | −0.0582329 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.91627 | 0.158157 | ||||||||
\(341\) | 6.99628 | 0.378870 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −14.7097 | −0.793096 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.95351 | 0.266302 | ||||||||
\(347\) | −3.79071 | −0.203496 | −0.101748 | − | 0.994810i | \(-0.532444\pi\) | ||||
−0.101748 | + | 0.994810i | \(0.532444\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.5522 | −0.993075 | −0.496537 | − | 0.868015i | \(-0.665395\pi\) | ||||
−0.496537 | + | 0.868015i | \(0.665395\pi\) | |||||||
\(350\) | −3.33986 | −0.178523 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.80845 | 0.256291 | ||||||||
\(353\) | 3.95098 | 0.210289 | 0.105145 | − | 0.994457i | \(-0.466469\pi\) | ||||
0.105145 | + | 0.994457i | \(0.466469\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.562881 | −0.0298746 | ||||||||
\(356\) | 1.94608 | 0.103142 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.5204 | −0.556019 | ||||||||
\(359\) | −5.14938 | −0.271774 | −0.135887 | − | 0.990724i | \(-0.543388\pi\) | ||||
−0.135887 | + | 0.990724i | \(0.543388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0317 | −0.896405 | ||||||||
\(362\) | −5.64421 | −0.296653 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.76668 | 0.249842 | ||||||||
\(365\) | −8.33485 | −0.436266 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.8116 | −1.66055 | −0.830276 | − | 0.557353i | \(-0.811817\pi\) | ||||
−0.830276 | + | 0.557353i | \(0.811817\pi\) | |||||||
\(368\) | 0.712326 | 0.0371326 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.86876 | −0.0971521 | ||||||||
\(371\) | −0.992903 | −0.0515490 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.4919 | −0.905695 | −0.452848 | − | 0.891588i | \(-0.649592\pi\) | ||||
−0.452848 | + | 0.891588i | \(0.649592\pi\) | |||||||
\(374\) | −1.59443 | −0.0824460 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.65988 | −0.291886 | ||||||||
\(377\) | −6.08730 | −0.313512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.3687 | −1.20037 | −0.600185 | − | 0.799861i | \(-0.704906\pi\) | ||||
−0.600185 | + | 0.799861i | \(0.704906\pi\) | |||||||
\(380\) | −1.63453 | −0.0838499 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.72315 | −0.0881639 | ||||||||
\(383\) | 12.7842 | 0.653242 | 0.326621 | − | 0.945155i | \(-0.394090\pi\) | ||||
0.326621 | + | 0.945155i | \(0.394090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.684208 | 0.0348705 | ||||||||
\(386\) | −11.9673 | −0.609121 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.36273 | 0.323019 | ||||||||
\(389\) | −31.1873 | −1.58126 | −0.790630 | − | 0.612294i | \(-0.790247\pi\) | ||||
−0.790630 | + | 0.612294i | \(0.790247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.37073 | −0.119893 | ||||||||
\(392\) | −2.63596 | −0.133136 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.93060 | 0.500296 | ||||||||
\(395\) | 1.31605 | 0.0662174 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.1511 | 1.81437 | 0.907186 | − | 0.420729i | \(-0.138226\pi\) | ||||
0.907186 | + | 0.420729i | \(0.138226\pi\) | |||||||
\(398\) | 3.01822 | 0.151290 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.23842 | −0.161921 | ||||||||
\(401\) | 22.0119 | 1.09922 | 0.549611 | − | 0.835421i | \(-0.314776\pi\) | ||||
0.549611 | + | 0.835421i | \(0.314776\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.0409 | −1.44663 | ||||||||
\(404\) | −12.3341 | −0.613647 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.38515 | 0.0687438 | ||||||||
\(407\) | −2.37469 | −0.117709 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.7967 | −1.17667 | −0.588335 | − | 0.808617i | \(-0.700216\pi\) | ||||
−0.588335 | + | 0.808617i | \(0.700216\pi\) | |||||||
\(410\) | 1.48747 | 0.0734611 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.90074 | −0.389242 | ||||||||
\(413\) | −13.0882 | −0.644029 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.76220 | 0.135591 | ||||||||
\(416\) | −19.9594 | −0.978590 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.893660 | 0.0437103 | ||||||||
\(419\) | 19.9178 | 0.973048 | 0.486524 | − | 0.873667i | \(-0.338265\pi\) | ||||
0.486524 | + | 0.873667i | \(0.338265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.26730 | −0.354187 | −0.177093 | − | 0.984194i | \(-0.556669\pi\) | ||||
−0.177093 | + | 0.984194i | \(0.556669\pi\) | |||||||
\(422\) | 17.9393 | 0.873274 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.61725 | 0.127105 | ||||||||
\(425\) | 10.7779 | 0.522807 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.19849 | −0.348359 | ||||||||
\(428\) | 28.3115 | 1.36849 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.60635 | 0.173914 | ||||||||
\(431\) | 11.2632 | 0.542529 | 0.271264 | − | 0.962505i | \(-0.412558\pi\) | ||||
0.271264 | + | 0.962505i | \(0.412558\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.4552 | −1.79998 | −0.899992 | − | 0.435907i | \(-0.856428\pi\) | ||||
−0.899992 | + | 0.435907i | \(0.856428\pi\) | |||||||
\(434\) | 6.60817 | 0.317203 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.516148 | 0.0247190 | ||||||||
\(437\) | 1.32876 | 0.0635634 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.93341 | −0.378641 | −0.189321 | − | 0.981915i | \(-0.560629\pi\) | ||||
−0.189321 | + | 0.981915i | \(0.560629\pi\) | |||||||
\(440\) | −1.80355 | −0.0859807 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.61832 | 0.314801 | ||||||||
\(443\) | 8.55610 | 0.406513 | 0.203256 | − | 0.979126i | \(-0.434848\pi\) | ||||
0.203256 | + | 0.979126i | \(0.434848\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.15951 | −0.0549661 | ||||||||
\(446\) | 4.87504 | 0.230840 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.03751 | 0.143509 | ||||||||
\(449\) | 38.8738 | 1.83457 | 0.917285 | − | 0.398232i | \(-0.130376\pi\) | ||||
0.917285 | + | 0.398232i | \(0.130376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.89018 | 0.0890051 | ||||||||
\(452\) | 15.2397 | 0.716815 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.83743 | 0.273964 | ||||||||
\(455\) | −2.84008 | −0.133145 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.65559 | −0.217779 | −0.108890 | − | 0.994054i | \(-0.534730\pi\) | ||||
−0.108890 | + | 0.994054i | \(0.534730\pi\) | |||||||
\(458\) | −20.9778 | −0.980227 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.10345 | −0.0514485 | ||||||||
\(461\) | 0.338860 | 0.0157823 | 0.00789114 | − | 0.999969i | \(-0.497488\pi\) | ||||
0.00789114 | + | 0.999969i | \(0.497488\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.1206 | −1.58572 | −0.792858 | − | 0.609406i | \(-0.791408\pi\) | ||||
−0.792858 | + | 0.609406i | \(0.791408\pi\) | |||||||
\(464\) | 1.34308 | 0.0623510 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.1807 | −0.749558 | ||||||||
\(467\) | 15.2172 | 0.704166 | 0.352083 | − | 0.935969i | \(-0.385473\pi\) | ||||
0.352083 | + | 0.935969i | \(0.385473\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.77977 | −0.266885 | ||||||||
\(470\) | 1.38762 | 0.0640061 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 34.5001 | 1.58799 | ||||||||
\(473\) | 4.58271 | 0.210713 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.04091 | −0.277176 | ||||||||
\(476\) | 3.50022 | 0.160432 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.1116 | 0.736929 | ||||||||
\(479\) | −41.7641 | −1.90825 | −0.954126 | − | 0.299405i | \(-0.903212\pi\) | ||||
−0.954126 | + | 0.299405i | \(0.903212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.85710 | 0.449445 | ||||||||
\(482\) | −20.7294 | −0.944197 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.4389 | 0.656312 | ||||||||
\(485\) | −3.79104 | −0.172142 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0202 | 0.544689 | 0.272344 | − | 0.962200i | \(-0.412201\pi\) | ||||
0.272344 | + | 0.962200i | \(0.412201\pi\) | |||||||
\(488\) | 18.9749 | 0.858956 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.646253 | 0.0291947 | ||||||||
\(491\) | 20.4192 | 0.921506 | 0.460753 | − | 0.887528i | \(-0.347579\pi\) | ||||
0.460753 | + | 0.887528i | \(0.347579\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.46997 | −0.201317 | ||||||||
\(494\) | −3.70949 | −0.166898 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.40748 | 0.287704 | ||||||||
\(497\) | −0.675593 | −0.0303045 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.7661 | −1.06392 | −0.531958 | − | 0.846771i | \(-0.678544\pi\) | ||||
−0.531958 | + | 0.846771i | \(0.678544\pi\) | |||||||
\(500\) | 10.8419 | 0.484863 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.7730 | −0.837878 | ||||||||
\(503\) | 17.3725 | 0.774604 | 0.387302 | − | 0.921953i | \(-0.373407\pi\) | ||||
0.387302 | + | 0.921953i | \(0.373407\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.34892 | 0.327023 | ||||||||
\(506\) | 0.603295 | 0.0268197 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.39835 | −0.0620419 | ||||||||
\(509\) | −3.06618 | −0.135906 | −0.0679531 | − | 0.997689i | \(-0.521647\pi\) | ||||
−0.0679531 | + | 0.997689i | \(0.521647\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0038 | −0.442543 | ||||||||
\(512\) | 8.36880 | 0.369852 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.6521 | −0.999140 | ||||||||
\(515\) | 4.70742 | 0.207433 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.76329 | 0.0775495 | ||||||||
\(518\) | −2.24296 | −0.0985499 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.48634 | 0.328298 | ||||||||
\(521\) | −26.9322 | −1.17992 | −0.589961 | − | 0.807431i | \(-0.700857\pi\) | ||||
−0.589961 | + | 0.807431i | \(0.700857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.30944 | 0.319619 | 0.159810 | − | 0.987148i | \(-0.448912\pi\) | ||||
0.159810 | + | 0.987148i | \(0.448912\pi\) | |||||||
\(524\) | 8.87030 | 0.387501 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.56527 | 0.286259 | ||||||||
\(527\) | −21.3250 | −0.928932 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1030 | −0.960999 | ||||||||
\(530\) | −0.641666 | −0.0278722 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.96183 | −0.0850563 | ||||||||
\(533\) | −7.84595 | −0.339846 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.8686 | −0.729291 | ||||||||
\(536\) | 15.2353 | 0.658063 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.4927 | −0.840392 | ||||||||
\(539\) | 0.821214 | 0.0353722 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.5215 | −1.31222 | −0.656111 | − | 0.754664i | \(-0.727800\pi\) | ||||
−0.656111 | + | 0.754664i | \(0.727800\pi\) | |||||||
\(542\) | 0.376646 | 0.0161783 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.6564 | −0.628388 | ||||||||
\(545\) | −0.307531 | −0.0131732 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.3344 | −1.63906 | −0.819531 | − | 0.573035i | \(-0.805766\pi\) | ||||
−0.819531 | + | 0.573035i | \(0.805766\pi\) | |||||||
\(548\) | 23.1657 | 0.989590 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.74274 | −0.116951 | ||||||||
\(551\) | 2.50537 | 0.106732 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.57957 | 0.0671702 | ||||||||
\(554\) | −9.70831 | −0.412467 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.5509 | 0.871553 | ||||||||
\(557\) | 0.188070 | 0.00796880 | 0.00398440 | − | 0.999992i | \(-0.498732\pi\) | ||||
0.00398440 | + | 0.999992i | \(0.498732\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.0224 | −0.804560 | ||||||||
\(560\) | 0.626625 | 0.0264798 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.49146 | 0.147278 | ||||||||
\(563\) | 20.4436 | 0.861594 | 0.430797 | − | 0.902449i | \(-0.358232\pi\) | ||||
0.430797 | + | 0.902449i | \(0.358232\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.08010 | −0.382003 | ||||||||
\(566\) | −3.63045 | −0.152599 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.78084 | 0.0747223 | ||||||||
\(569\) | 27.1530 | 1.13831 | 0.569157 | − | 0.822229i | \(-0.307270\pi\) | ||||
0.569157 | + | 0.822229i | \(0.307270\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.65084 | 0.278329 | 0.139165 | − | 0.990269i | \(-0.455558\pi\) | ||||
0.139165 | + | 0.990269i | \(0.455558\pi\) | |||||||
\(572\) | 3.91446 | 0.163672 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.78533 | 0.0745181 | ||||||||
\(575\) | −4.07812 | −0.170069 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.7405 | 1.52953 | 0.764764 | − | 0.644310i | \(-0.222856\pi\) | ||||
0.764764 | + | 0.644310i | \(0.222856\pi\) | |||||||
\(578\) | −8.32629 | −0.346328 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.08054 | −0.0863895 | ||||||||
\(581\) | 3.31531 | 0.137542 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.815386 | −0.0337698 | ||||||||
\(584\) | 26.3697 | 1.09119 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.8366 | 0.695515 | ||||||||
\(587\) | 12.4810 | 0.515145 | 0.257572 | − | 0.966259i | \(-0.417077\pi\) | ||||
0.257572 | + | 0.966259i | \(0.417077\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.9524 | 0.492491 | ||||||||
\(590\) | −8.45830 | −0.348223 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.17484 | −0.0893853 | ||||||||
\(593\) | 44.7690 | 1.83844 | 0.919221 | − | 0.393742i | \(-0.128820\pi\) | ||||
0.919221 | + | 0.393742i | \(0.128820\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.08550 | −0.0854972 | ||||||||
\(596\) | −17.7519 | −0.727148 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.50422 | −0.102405 | ||||||||
\(599\) | −39.1831 | −1.60098 | −0.800490 | − | 0.599346i | \(-0.795427\pi\) | ||||
−0.800490 | + | 0.599346i | \(0.795427\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.78843 | −0.399279 | −0.199639 | − | 0.979869i | \(-0.563977\pi\) | ||||
−0.199639 | + | 0.979869i | \(0.563977\pi\) | |||||||
\(602\) | 4.32849 | 0.176416 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.444886 | 0.0181021 | ||||||||
\(605\) | −8.60295 | −0.349760 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.8224 | −0.479857 | −0.239929 | − | 0.970791i | \(-0.577124\pi\) | ||||
−0.239929 | + | 0.970791i | \(0.577124\pi\) | |||||||
\(608\) | 8.21475 | 0.333152 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.65204 | −0.188356 | ||||||||
\(611\) | −7.31924 | −0.296105 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.7346 | 0.837461 | 0.418730 | − | 0.908111i | \(-0.362475\pi\) | ||||
0.418730 | + | 0.908111i | \(0.362475\pi\) | |||||||
\(614\) | 6.02511 | 0.243154 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.16469 | −0.0872178 | ||||||||
\(617\) | −29.3288 | −1.18073 | −0.590367 | − | 0.807135i | \(-0.701017\pi\) | ||||
−0.590367 | + | 0.807135i | \(0.701017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.0032 | 0.603029 | 0.301515 | − | 0.953462i | \(-0.402508\pi\) | ||||
0.301515 | + | 0.953462i | \(0.402508\pi\) | |||||||
\(620\) | −9.92567 | −0.398624 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.60162 | 0.104315 | ||||||||
\(623\) | −1.39169 | −0.0557569 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.0694 | 0.602775 | ||||||||
\(626\) | 3.53977 | 0.141477 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.5254 | −0.459912 | ||||||||
\(629\) | 7.23817 | 0.288605 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.3359 | 0.451273 | 0.225637 | − | 0.974212i | \(-0.427554\pi\) | ||||
0.225637 | + | 0.974212i | \(0.427554\pi\) | |||||||
\(632\) | −4.16369 | −0.165623 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.324794 | 0.0128992 | ||||||||
\(635\) | 0.833166 | 0.0330632 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.40878 | −0.135061 | ||||||||
\(638\) | 1.13750 | 0.0450342 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.79388 | −0.308080 | ||||||||
\(641\) | 12.5109 | 0.494149 | 0.247074 | − | 0.968997i | \(-0.420531\pi\) | ||||
0.247074 | + | 0.968997i | \(0.420531\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.8249 | −0.624073 | −0.312037 | − | 0.950070i | \(-0.601011\pi\) | ||||
−0.312037 | + | 0.950070i | \(0.601011\pi\) | |||||||
\(644\) | −1.32440 | −0.0521888 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.72392 | −0.107171 | ||||||||
\(647\) | 17.2085 | 0.676534 | 0.338267 | − | 0.941050i | \(-0.390159\pi\) | ||||
0.338267 | + | 0.941050i | \(0.390159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.7482 | −0.421905 | ||||||||
\(650\) | 11.3848 | 0.446550 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.8665 | −0.699707 | ||||||||
\(653\) | 16.6436 | 0.651315 | 0.325657 | − | 0.945488i | \(-0.394414\pi\) | ||||
0.325657 | + | 0.945488i | \(0.394414\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.28510 | −0.206506 | ||||||||
\(656\) | 1.73110 | 0.0675883 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.66548 | 0.0649270 | ||||||||
\(659\) | 35.9180 | 1.39917 | 0.699583 | − | 0.714551i | \(-0.253369\pi\) | ||||
0.699583 | + | 0.714551i | \(0.253369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.3781 | 1.10378 | 0.551890 | − | 0.833917i | \(-0.313907\pi\) | ||||
0.551890 | + | 0.833917i | \(0.313907\pi\) | |||||||
\(662\) | 10.6018 | 0.412049 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.73903 | −0.339140 | ||||||||
\(665\) | 1.16890 | 0.0453280 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.69133 | 0.0654887 | ||||||||
\(668\) | −27.8293 | −1.07675 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.73519 | −0.144303 | ||||||||
\(671\) | −5.91150 | −0.228211 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.0138 | −1.73515 | −0.867577 | − | 0.497303i | \(-0.834324\pi\) | ||||
−0.867577 | + | 0.497303i | \(0.834324\pi\) | |||||||
\(674\) | −10.1616 | −0.391411 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.93007 | 0.0742335 | ||||||||
\(677\) | −24.6030 | −0.945570 | −0.472785 | − | 0.881178i | \(-0.656751\pi\) | ||||
−0.472785 | + | 0.881178i | \(0.656751\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.55016 | −0.174619 | ||||||||
\(680\) | 5.49730 | 0.210812 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.42673 | 0.207800 | ||||||||
\(683\) | 17.5156 | 0.670217 | 0.335109 | − | 0.942179i | \(-0.391227\pi\) | ||||
0.335109 | + | 0.942179i | \(0.391227\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.8026 | −0.527369 | ||||||||
\(686\) | 0.775659 | 0.0296148 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.19703 | 0.160010 | ||||||||
\(689\) | 3.38458 | 0.128942 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.1962 | 0.616132 | 0.308066 | − | 0.951365i | \(-0.400318\pi\) | ||||
0.308066 | + | 0.951365i | \(0.400318\pi\) | |||||||
\(692\) | −8.93017 | −0.339474 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.94029 | −0.111612 | ||||||||
\(695\) | −12.2446 | −0.464466 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.76136 | −0.218227 | ||||||||
\(698\) | −14.3901 | −0.544675 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.02108 | 0.227575 | ||||||||
\(701\) | 40.1314 | 1.51574 | 0.757871 | − | 0.652405i | \(-0.226240\pi\) | ||||
0.757871 | + | 0.652405i | \(0.226240\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.05691 | −0.153009 | ||||||||
\(704\) | 2.49444 | 0.0940129 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.06461 | 0.115338 | ||||||||
\(707\) | 8.82048 | 0.331728 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.6274 | −1.15024 | −0.575118 | − | 0.818070i | \(-0.695044\pi\) | ||||
−0.575118 | + | 0.818070i | \(0.695044\pi\) | |||||||
\(710\) | −0.436604 | −0.0163854 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.66844 | 0.137481 | ||||||||
\(713\) | 8.06889 | 0.302182 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.33231 | −0.0872235 | ||||||||
\(716\) | 18.9661 | 0.708796 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.99416 | −0.149061 | ||||||||
\(719\) | −31.6921 | −1.18192 | −0.590958 | − | 0.806702i | \(-0.701250\pi\) | ||||
−0.590958 | + | 0.806702i | \(0.701250\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.65003 | 0.210418 | ||||||||
\(722\) | −13.2108 | −0.491655 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.1754 | 0.378164 | ||||||||
\(725\) | −7.68924 | −0.285571 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.4231 | −0.905801 | −0.452901 | − | 0.891561i | \(-0.649611\pi\) | ||||
−0.452901 | + | 0.891561i | \(0.649611\pi\) | |||||||
\(728\) | 8.98540 | 0.333021 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.46499 | −0.239280 | ||||||||
\(731\) | −13.9683 | −0.516637 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.9558 | 0.441599 | 0.220800 | − | 0.975319i | \(-0.429133\pi\) | ||||
0.220800 | + | 0.975319i | \(0.429133\pi\) | |||||||
\(734\) | −24.6749 | −0.910769 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.54564 | 0.204415 | ||||||||
\(737\) | −4.74643 | −0.174837 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0507 | −0.553648 | −0.276824 | − | 0.960921i | \(-0.589282\pi\) | ||||
−0.276824 | + | 0.960921i | \(0.589282\pi\) | |||||||
\(740\) | 3.36899 | 0.123846 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.770154 | −0.0282732 | ||||||||
\(743\) | 53.7505 | 1.97191 | 0.985957 | − | 0.166999i | \(-0.0534075\pi\) | ||||
0.985957 | + | 0.166999i | \(0.0534075\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.5770 | 0.387510 | ||||||||
\(746\) | −13.5677 | −0.496750 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.87443 | 0.105100 | ||||||||
\(749\) | −20.2463 | −0.739785 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.76059 | 0.356169 | 0.178085 | − | 0.984015i | \(-0.443010\pi\) | ||||
0.178085 | + | 0.984015i | \(0.443010\pi\) | |||||||
\(752\) | 1.61489 | 0.0588891 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.72167 | −0.171953 | ||||||||
\(755\) | −0.265072 | −0.00964694 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.3529 | 1.17589 | 0.587944 | − | 0.808902i | \(-0.299938\pi\) | ||||
0.587944 | + | 0.808902i | \(0.299938\pi\) | |||||||
\(758\) | −18.1261 | −0.658371 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.08117 | −0.111766 | ||||||||
\(761\) | −29.5981 | −1.07293 | −0.536465 | − | 0.843923i | \(-0.680241\pi\) | ||||
−0.536465 | + | 0.843923i | \(0.680241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.369111 | −0.0133627 | ||||||||
\(764\) | 3.10648 | 0.112389 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.91617 | 0.358286 | ||||||||
\(767\) | 44.6148 | 1.61095 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.0353 | −0.830676 | −0.415338 | − | 0.909667i | \(-0.636337\pi\) | ||||
−0.415338 | + | 0.909667i | \(0.636337\pi\) | |||||||
\(770\) | 0.530712 | 0.0191255 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.5746 | 0.776488 | ||||||||
\(773\) | 22.4412 | 0.807154 | 0.403577 | − | 0.914946i | \(-0.367767\pi\) | ||||
0.403577 | + | 0.914946i | \(0.367767\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.6833 | −1.31770 | ||||||||
\(776\) | 11.9940 | 0.430561 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.1907 | −0.867279 | ||||||||
\(779\) | 3.22918 | 0.115697 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.554806 | −0.0198525 | ||||||||
\(782\) | −1.83887 | −0.0657580 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.752101 | 0.0268608 | ||||||||
\(785\) | 6.86703 | 0.245095 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2193 | 1.21979 | 0.609894 | − | 0.792483i | \(-0.291212\pi\) | ||||
0.609894 | + | 0.792483i | \(0.291212\pi\) | |||||||
\(788\) | −17.9028 | −0.637762 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.02080 | 0.0363185 | ||||||||
\(791\) | −10.8983 | −0.387499 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.5380 | 0.871371 | ||||||||
\(794\) | 28.0409 | 0.995135 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.44123 | −0.192859 | ||||||||
\(797\) | 37.5468 | 1.32998 | 0.664988 | − | 0.746854i | \(-0.268437\pi\) | ||||
0.664988 | + | 0.746854i | \(0.268437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.37460 | −0.190140 | ||||||||
\(800\) | −25.2119 | −0.891377 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.0737 | 0.602894 | ||||||||
\(803\) | −8.21527 | −0.289911 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.789105 | 0.0278123 | ||||||||
\(806\) | −22.5258 | −0.793437 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23.2504 | −0.817948 | ||||||||
\(809\) | 18.2474 | 0.641544 | 0.320772 | − | 0.947156i | \(-0.396058\pi\) | ||||
0.320772 | + | 0.947156i | \(0.396058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.7675 | −0.975048 | −0.487524 | − | 0.873110i | \(-0.662100\pi\) | ||||
−0.487524 | + | 0.873110i | \(0.662100\pi\) | |||||||
\(812\) | −2.49714 | −0.0876325 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.84195 | −0.0645602 | ||||||||
\(815\) | 10.6452 | 0.372886 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.82909 | 0.273905 | ||||||||
\(818\) | −18.4581 | −0.645372 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.68161 | −0.0936459 | ||||||||
\(821\) | −0.530588 | −0.0185176 | −0.00925882 | − | 0.999957i | \(-0.502947\pi\) | ||||
−0.00925882 | + | 0.999957i | \(0.502947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.3917 | 1.33825 | 0.669125 | − | 0.743150i | \(-0.266669\pi\) | ||||
0.669125 | + | 0.743150i | \(0.266669\pi\) | |||||||
\(824\) | −14.8933 | −0.518831 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.1520 | −0.353233 | ||||||||
\(827\) | −19.9999 | −0.695464 | −0.347732 | − | 0.937594i | \(-0.613048\pi\) | ||||
−0.347732 | + | 0.937594i | \(0.613048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.81614 | 0.306197 | 0.153099 | − | 0.988211i | \(-0.451075\pi\) | ||||
0.153099 | + | 0.988211i | \(0.451075\pi\) | |||||||
\(830\) | 2.14253 | 0.0743682 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.3542 | −0.358967 | ||||||||
\(833\) | −2.50310 | −0.0867273 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.5812 | 0.573817 | ||||||||
\(836\) | −1.61109 | −0.0557206 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.4494 | 0.533691 | ||||||||
\(839\) | −22.1358 | −0.764211 | −0.382106 | − | 0.924119i | \(-0.624801\pi\) | ||||
−0.382106 | + | 0.924119i | \(0.624801\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8110 | −0.890035 | ||||||||
\(842\) | −5.63695 | −0.194262 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −32.3410 | −1.11322 | ||||||||
\(845\) | −1.14997 | −0.0395603 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.3256 | −0.354792 | ||||||||
\(848\) | −0.746763 | −0.0256440 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.36000 | 0.286746 | ||||||||
\(851\) | −2.73876 | −0.0938833 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.56457 | −0.293245 | −0.146623 | − | 0.989192i | \(-0.546840\pi\) | ||||
−0.146623 | + | 0.989192i | \(0.546840\pi\) | |||||||
\(854\) | −5.58357 | −0.191066 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 53.3685 | 1.82410 | ||||||||
\(857\) | −6.57137 | −0.224474 | −0.112237 | − | 0.993681i | \(-0.535802\pi\) | ||||
−0.112237 | + | 0.993681i | \(0.535802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7406 | 0.502944 | 0.251472 | − | 0.967865i | \(-0.419085\pi\) | ||||
0.251472 | + | 0.967865i | \(0.419085\pi\) | |||||||
\(860\) | −6.50152 | −0.221700 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.73639 | 0.297563 | ||||||||
\(863\) | 20.0421 | 0.682242 | 0.341121 | − | 0.940019i | \(-0.389193\pi\) | ||||
0.341121 | + | 0.940019i | \(0.389193\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.32077 | 0.180912 | ||||||||
\(866\) | −29.0525 | −0.987243 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.9132 | −0.404360 | ||||||||
\(869\) | 1.29717 | 0.0440033 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.7019 | 0.667575 | ||||||||
\(872\) | 0.972964 | 0.0329487 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.03067 | 0.0348628 | ||||||||
\(875\) | −7.75331 | −0.262110 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.0175 | −1.04739 | −0.523694 | − | 0.851907i | \(-0.675446\pi\) | ||||
−0.523694 | + | 0.851907i | \(0.675446\pi\) | |||||||
\(878\) | −6.15362 | −0.207675 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.514594 | 0.0173469 | ||||||||
\(881\) | −4.04652 | −0.136331 | −0.0681654 | − | 0.997674i | \(-0.521715\pi\) | ||||
−0.0681654 | + | 0.997674i | \(0.521715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.7648 | 1.87663 | 0.938317 | − | 0.345777i | \(-0.112385\pi\) | ||||
0.938317 | + | 0.345777i | \(0.112385\pi\) | |||||||
\(884\) | −11.9315 | −0.401299 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.63661 | 0.222961 | ||||||||
\(887\) | 56.9316 | 1.91158 | 0.955788 | − | 0.294058i | \(-0.0950058\pi\) | ||||
0.955788 | + | 0.294058i | \(0.0950058\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −0.899384 | −0.0301474 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.78870 | −0.294267 | ||||||||
\(893\) | 3.01240 | 0.100806 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.3004 | −0.377730 | ||||||||
\(896\) | −9.35453 | −0.312513 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.1528 | 1.00621 | ||||||||
\(899\) | 15.2138 | 0.507408 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.48534 | 0.0827986 | ||||||||
\(902\) | 1.46613 | 0.0488169 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28.7275 | 0.955463 | ||||||||
\(905\) | −6.06268 | −0.201530 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.6800 | −0.520645 | −0.260323 | − | 0.965522i | \(-0.583829\pi\) | ||||
−0.260323 | + | 0.965522i | \(0.583829\pi\) | |||||||
\(908\) | −10.5237 | −0.349241 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.20293 | −0.0730264 | ||||||||
\(911\) | −23.8935 | −0.791627 | −0.395814 | − | 0.918331i | \(-0.629537\pi\) | ||||
−0.395814 | + | 0.918331i | \(0.629537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.72258 | 0.0901042 | ||||||||
\(914\) | −3.61115 | −0.119446 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 37.8186 | 1.24956 | ||||||||
\(917\) | −6.34339 | −0.209477 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.0890 | −0.596702 | −0.298351 | − | 0.954456i | \(-0.596437\pi\) | ||||
−0.298351 | + | 0.954456i | \(0.596437\pi\) | |||||||
\(920\) | −2.08005 | −0.0685772 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.262840 | 0.00865616 | ||||||||
\(923\) | 2.30294 | 0.0758024 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.4511 | 0.409390 | ||||||||
\(926\) | −26.4659 | −0.869723 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.4562 | 0.343243 | ||||||||
\(929\) | 10.9992 | 0.360873 | 0.180437 | − | 0.983587i | \(-0.442249\pi\) | ||||
0.180437 | + | 0.983587i | \(0.442249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.40296 | 0.0459802 | ||||||||
\(932\) | 29.1706 | 0.955513 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.8033 | 0.386216 | ||||||||
\(935\) | −1.71264 | −0.0560094 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.9182 | 1.69609 | 0.848046 | − | 0.529923i | \(-0.177779\pi\) | ||||
0.848046 | + | 0.529923i | \(0.177779\pi\) | |||||||
\(938\) | −4.48313 | −0.146379 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.50159 | −0.0815930 | ||||||||
\(941\) | −13.1964 | −0.430192 | −0.215096 | − | 0.976593i | \(-0.569006\pi\) | ||||
−0.215096 | + | 0.976593i | \(0.569006\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.17997 | 0.0709895 | ||||||||
\(944\) | −9.84367 | −0.320384 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.55462 | 0.115571 | ||||||||
\(947\) | −39.0756 | −1.26979 | −0.634893 | − | 0.772600i | \(-0.718956\pi\) | ||||
−0.634893 | + | 0.772600i | \(0.718956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.1008 | 1.10696 | ||||||||
\(950\) | −4.68568 | −0.152024 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.59808 | 0.213845 | ||||||||
\(953\) | 4.31917 | 0.139912 | 0.0699559 | − | 0.997550i | \(-0.477714\pi\) | ||||
0.0699559 | + | 0.997550i | \(0.477714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.85090 | −0.0598938 | ||||||||
\(956\) | −29.0460 | −0.939415 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32.3947 | −1.04663 | ||||||||
\(959\) | −16.5664 | −0.534957 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.5808 | 1.34132 | ||||||||
\(962\) | 7.64574 | 0.246509 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37.3708 | 1.20363 | ||||||||
\(965\) | −12.8546 | −0.413804 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.6032 | 1.72376 | 0.861881 | − | 0.507110i | \(-0.169286\pi\) | ||||
0.861881 | + | 0.507110i | \(0.169286\pi\) | |||||||
\(968\) | 27.2179 | 0.874817 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.94055 | −0.0944155 | ||||||||
\(971\) | 5.46228 | 0.175293 | 0.0876465 | − | 0.996152i | \(-0.472065\pi\) | ||||
0.0876465 | + | 0.996152i | \(0.472065\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.6965 | −0.471149 | ||||||||
\(974\) | 9.32359 | 0.298747 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.41399 | −0.173298 | ||||||||
\(977\) | 32.4956 | 1.03963 | 0.519813 | − | 0.854280i | \(-0.326001\pi\) | ||||
0.519813 | + | 0.854280i | \(0.326001\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.14288 | −0.0365265 | ||||||||
\(980\) | −1.16506 | −0.0372165 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.8383 | 0.505422 | ||||||||
\(983\) | 3.17977 | 0.101419 | 0.0507095 | − | 0.998713i | \(-0.483852\pi\) | ||||
0.0507095 | + | 0.998713i | \(0.483852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6669 | 0.339875 | ||||||||
\(986\) | −3.46717 | −0.110417 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.68745 | 0.212756 | ||||||||
\(989\) | 5.28529 | 0.168062 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.3965 | −1.21971 | −0.609853 | − | 0.792515i | \(-0.708771\pi\) | ||||
−0.609853 | + | 0.792515i | \(0.708771\pi\) | |||||||
\(992\) | 49.8838 | 1.58381 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.524029 | −0.0166212 | ||||||||
\(995\) | 3.24199 | 0.102778 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.5944 | 0.778912 | 0.389456 | − | 0.921045i | \(-0.372663\pi\) | ||||
0.389456 | + | 0.921045i | \(0.372663\pi\) | |||||||
\(998\) | −18.4344 | −0.583530 | ||||||||
\(999\) | 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.1.16 | yes | 22 | |
3.2 | odd | 2 | inner | 8001.2.a.x.1.7 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.x.1.7 | ✓ | 22 | 3.2 | odd | 2 | inner | |
8001.2.a.x.1.16 | yes | 22 | 1.1 | even | 1 | trivial |