Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.84209 | −1.30255 | −0.651277 | − | 0.758840i | \(-0.725766\pi\) | ||||
−0.651277 | + | 0.758840i | \(0.725766\pi\) | |||||||
\(3\) | −1.69681 | −0.979652 | −0.489826 | − | 0.871820i | \(-0.662940\pi\) | ||||
−0.489826 | + | 0.871820i | \(0.662940\pi\) | |||||||
\(4\) | 1.39329 | 0.696645 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.12567 | 1.27605 | ||||||||
\(7\) | 1.54055 | 0.582274 | 0.291137 | − | 0.956681i | \(-0.405967\pi\) | ||||
0.291137 | + | 0.956681i | \(0.405967\pi\) | |||||||
\(8\) | 1.11761 | 0.395136 | ||||||||
\(9\) | −0.120844 | −0.0402812 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.53578 | 0.764566 | 0.382283 | − | 0.924045i | \(-0.375138\pi\) | ||||
0.382283 | + | 0.924045i | \(0.375138\pi\) | |||||||
\(12\) | −2.36415 | −0.682470 | ||||||||
\(13\) | 6.36889 | 1.76641 | 0.883207 | − | 0.468984i | \(-0.155380\pi\) | ||||
0.883207 | + | 0.468984i | \(0.155380\pi\) | |||||||
\(14\) | −2.83783 | −0.758442 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.84532 | −1.21133 | ||||||||
\(17\) | −3.54355 | −0.859437 | −0.429719 | − | 0.902963i | \(-0.641387\pi\) | ||||
−0.429719 | + | 0.902963i | \(0.641387\pi\) | |||||||
\(18\) | 0.222605 | 0.0524684 | ||||||||
\(19\) | 0.713569 | 0.163704 | 0.0818520 | − | 0.996644i | \(-0.473917\pi\) | ||||
0.0818520 | + | 0.996644i | \(0.473917\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.61402 | −0.570426 | ||||||||
\(22\) | −4.67113 | −0.995889 | ||||||||
\(23\) | 1.66453 | 0.347079 | 0.173540 | − | 0.984827i | \(-0.444480\pi\) | ||||
0.173540 | + | 0.984827i | \(0.444480\pi\) | |||||||
\(24\) | −1.89637 | −0.387095 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −11.7321 | −2.30085 | ||||||||
\(27\) | 5.29547 | 1.01911 | ||||||||
\(28\) | 2.14644 | 0.405638 | ||||||||
\(29\) | −8.23983 | −1.53010 | −0.765049 | − | 0.643972i | \(-0.777285\pi\) | ||||
−0.765049 | + | 0.643972i | \(0.777285\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.5697 | 1.89838 | 0.949188 | − | 0.314711i | \(-0.101908\pi\) | ||||
0.949188 | + | 0.314711i | \(0.101908\pi\) | |||||||
\(32\) | 6.69029 | 1.18269 | ||||||||
\(33\) | −4.30273 | −0.749009 | ||||||||
\(34\) | 6.52753 | 1.11946 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.168370 | −0.0280617 | ||||||||
\(37\) | −0.496832 | −0.0816787 | −0.0408393 | − | 0.999166i | \(-0.513003\pi\) | ||||
−0.0408393 | + | 0.999166i | \(0.513003\pi\) | |||||||
\(38\) | −1.31446 | −0.213233 | ||||||||
\(39\) | −10.8068 | −1.73047 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.92984 | −1.39461 | −0.697303 | − | 0.716776i | \(-0.745617\pi\) | ||||
−0.697303 | + | 0.716776i | \(0.745617\pi\) | |||||||
\(42\) | 4.81525 | 0.743010 | ||||||||
\(43\) | 1.50676 | 0.229778 | 0.114889 | − | 0.993378i | \(-0.463349\pi\) | ||||
0.114889 | + | 0.993378i | \(0.463349\pi\) | |||||||
\(44\) | 3.53308 | 0.532632 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.06622 | −0.452089 | ||||||||
\(47\) | 6.94849 | 1.01354 | 0.506771 | − | 0.862081i | \(-0.330839\pi\) | ||||
0.506771 | + | 0.862081i | \(0.330839\pi\) | |||||||
\(48\) | 8.22158 | 1.18668 | ||||||||
\(49\) | −4.62670 | −0.660958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.01272 | 0.841950 | ||||||||
\(52\) | 8.87372 | 1.23056 | ||||||||
\(53\) | −9.87593 | −1.35656 | −0.678281 | − | 0.734802i | \(-0.737275\pi\) | ||||
−0.678281 | + | 0.734802i | \(0.737275\pi\) | |||||||
\(54\) | −9.75473 | −1.32745 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.72174 | 0.230077 | ||||||||
\(57\) | −1.21079 | −0.160373 | ||||||||
\(58\) | 15.1785 | 1.99303 | ||||||||
\(59\) | −10.1744 | −1.32459 | −0.662296 | − | 0.749242i | \(-0.730418\pi\) | ||||
−0.662296 | + | 0.749242i | \(0.730418\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.13781 | −1.16998 | −0.584988 | − | 0.811042i | \(-0.698901\pi\) | ||||
−0.584988 | + | 0.811042i | \(0.698901\pi\) | |||||||
\(62\) | −19.4703 | −2.47273 | ||||||||
\(63\) | −0.186166 | −0.0234547 | ||||||||
\(64\) | −2.63346 | −0.329183 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.92601 | 0.975625 | ||||||||
\(67\) | −1.85057 | −0.226083 | −0.113041 | − | 0.993590i | \(-0.536059\pi\) | ||||
−0.113041 | + | 0.993590i | \(0.536059\pi\) | |||||||
\(68\) | −4.93720 | −0.598723 | ||||||||
\(69\) | −2.82439 | −0.340017 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.47485 | −1.12446 | −0.562229 | − | 0.826981i | \(-0.690056\pi\) | ||||
−0.562229 | + | 0.826981i | \(0.690056\pi\) | |||||||
\(72\) | −0.135056 | −0.0159165 | ||||||||
\(73\) | −8.88186 | −1.03954 | −0.519771 | − | 0.854305i | \(-0.673983\pi\) | ||||
−0.519771 | + | 0.854305i | \(0.673983\pi\) | |||||||
\(74\) | 0.915209 | 0.106391 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.994210 | 0.114044 | ||||||||
\(77\) | 3.90650 | 0.445187 | ||||||||
\(78\) | 19.9071 | 2.25403 | ||||||||
\(79\) | −6.12948 | −0.689621 | −0.344810 | − | 0.938672i | \(-0.612057\pi\) | ||||
−0.344810 | + | 0.938672i | \(0.612057\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.62287 | −0.958096 | ||||||||
\(82\) | 16.4496 | 1.81655 | ||||||||
\(83\) | −0.835537 | −0.0917122 | −0.0458561 | − | 0.998948i | \(-0.514602\pi\) | ||||
−0.0458561 | + | 0.998948i | \(0.514602\pi\) | |||||||
\(84\) | −3.64209 | −0.397384 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.77558 | −0.299299 | ||||||||
\(87\) | 13.9814 | 1.49896 | ||||||||
\(88\) | 2.83402 | 0.302107 | ||||||||
\(89\) | 2.27480 | 0.241129 | 0.120564 | − | 0.992706i | \(-0.461530\pi\) | ||||
0.120564 | + | 0.992706i | \(0.461530\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.81161 | 1.02854 | ||||||||
\(92\) | 2.31918 | 0.241791 | ||||||||
\(93\) | −17.9348 | −1.85975 | ||||||||
\(94\) | −12.7997 | −1.32019 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −11.3521 | −1.15862 | ||||||||
\(97\) | −7.56572 | −0.768182 | −0.384091 | − | 0.923295i | \(-0.625485\pi\) | ||||
−0.384091 | + | 0.923295i | \(0.625485\pi\) | |||||||
\(98\) | 8.52280 | 0.860933 | ||||||||
\(99\) | −0.306433 | −0.0307976 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.9324 | −1.68483 | −0.842417 | − | 0.538826i | \(-0.818868\pi\) | ||||
−0.842417 | + | 0.538826i | \(0.818868\pi\) | |||||||
\(102\) | −11.0760 | −1.09668 | ||||||||
\(103\) | 2.83252 | 0.279096 | 0.139548 | − | 0.990215i | \(-0.455435\pi\) | ||||
0.139548 | + | 0.990215i | \(0.455435\pi\) | |||||||
\(104\) | 7.11795 | 0.697973 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.1923 | 1.76700 | ||||||||
\(107\) | 4.86488 | 0.470306 | 0.235153 | − | 0.971958i | \(-0.424441\pi\) | ||||
0.235153 | + | 0.971958i | \(0.424441\pi\) | |||||||
\(108\) | 7.37813 | 0.709961 | ||||||||
\(109\) | 10.2870 | 0.985317 | 0.492658 | − | 0.870223i | \(-0.336025\pi\) | ||||
0.492658 | + | 0.870223i | \(0.336025\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.843029 | 0.0800167 | ||||||||
\(112\) | −7.46447 | −0.705326 | ||||||||
\(113\) | 12.6981 | 1.19454 | 0.597270 | − | 0.802041i | \(-0.296252\pi\) | ||||
0.597270 | + | 0.802041i | \(0.296252\pi\) | |||||||
\(114\) | 2.23038 | 0.208894 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.4805 | −1.06594 | ||||||||
\(117\) | −0.769640 | −0.0711532 | ||||||||
\(118\) | 18.7421 | 1.72535 | ||||||||
\(119\) | −5.45902 | −0.500427 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.56982 | −0.415438 | ||||||||
\(122\) | 16.8326 | 1.52396 | ||||||||
\(123\) | 15.1522 | 1.36623 | ||||||||
\(124\) | 14.7267 | 1.32249 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.342934 | 0.0305510 | ||||||||
\(127\) | 1.17595 | 0.104349 | 0.0521743 | − | 0.998638i | \(-0.483385\pi\) | ||||
0.0521743 | + | 0.998638i | \(0.483385\pi\) | |||||||
\(128\) | −8.52951 | −0.753909 | ||||||||
\(129\) | −2.55668 | −0.225103 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.7573 | 1.63884 | 0.819418 | − | 0.573196i | \(-0.194297\pi\) | ||||
0.819418 | + | 0.573196i | \(0.194297\pi\) | |||||||
\(132\) | −5.99496 | −0.521794 | ||||||||
\(133\) | 1.09929 | 0.0953205 | ||||||||
\(134\) | 3.40891 | 0.294485 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.96031 | −0.339594 | ||||||||
\(137\) | −5.04016 | −0.430610 | −0.215305 | − | 0.976547i | \(-0.569075\pi\) | ||||
−0.215305 | + | 0.976547i | \(0.569075\pi\) | |||||||
\(138\) | 5.20278 | 0.442890 | ||||||||
\(139\) | −0.226430 | −0.0192056 | −0.00960278 | − | 0.999954i | \(-0.503057\pi\) | ||||
−0.00960278 | + | 0.999954i | \(0.503057\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.7902 | −0.992918 | ||||||||
\(142\) | 17.4535 | 1.46467 | ||||||||
\(143\) | 16.1501 | 1.35054 | ||||||||
\(144\) | 0.585526 | 0.0487938 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.3612 | 1.35406 | ||||||||
\(147\) | 7.85063 | 0.647509 | ||||||||
\(148\) | −0.692232 | −0.0569011 | ||||||||
\(149\) | −4.00539 | −0.328134 | −0.164067 | − | 0.986449i | \(-0.552461\pi\) | ||||
−0.164067 | + | 0.986449i | \(0.552461\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.73080 | −0.466366 | −0.233183 | − | 0.972433i | \(-0.574914\pi\) | ||||
−0.233183 | + | 0.972433i | \(0.574914\pi\) | |||||||
\(152\) | 0.797494 | 0.0646853 | ||||||||
\(153\) | 0.428215 | 0.0346191 | ||||||||
\(154\) | −7.19612 | −0.579880 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −15.0570 | −1.20552 | ||||||||
\(157\) | 4.02238 | 0.321021 | 0.160510 | − | 0.987034i | \(-0.448686\pi\) | ||||
0.160510 | + | 0.987034i | \(0.448686\pi\) | |||||||
\(158\) | 11.2911 | 0.898268 | ||||||||
\(159\) | 16.7575 | 1.32896 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.56430 | 0.202095 | ||||||||
\(162\) | 15.8841 | 1.24797 | ||||||||
\(163\) | −2.51003 | −0.196601 | −0.0983004 | − | 0.995157i | \(-0.531341\pi\) | ||||
−0.0983004 | + | 0.995157i | \(0.531341\pi\) | |||||||
\(164\) | −12.4419 | −0.971546 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.53913 | 0.119460 | ||||||||
\(167\) | −25.3075 | −1.95835 | −0.979177 | − | 0.203008i | \(-0.934928\pi\) | ||||
−0.979177 | + | 0.203008i | \(0.934928\pi\) | |||||||
\(168\) | −2.92146 | −0.225395 | ||||||||
\(169\) | 27.5628 | 2.12022 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0862302 | −0.00659419 | ||||||||
\(172\) | 2.09935 | 0.160074 | ||||||||
\(173\) | 19.0394 | 1.44754 | 0.723769 | − | 0.690043i | \(-0.242408\pi\) | ||||
0.723769 | + | 0.690043i | \(0.242408\pi\) | |||||||
\(174\) | −25.7550 | −1.95248 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.2867 | −0.926143 | ||||||||
\(177\) | 17.2640 | 1.29764 | ||||||||
\(178\) | −4.19039 | −0.314083 | ||||||||
\(179\) | 12.3757 | 0.925007 | 0.462503 | − | 0.886618i | \(-0.346951\pi\) | ||||
0.462503 | + | 0.886618i | \(0.346951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.62774 | 0.418307 | 0.209153 | − | 0.977883i | \(-0.432929\pi\) | ||||
0.209153 | + | 0.977883i | \(0.432929\pi\) | |||||||
\(182\) | −18.0738 | −1.33972 | ||||||||
\(183\) | 15.5051 | 1.14617 | ||||||||
\(184\) | 1.86030 | 0.137143 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 33.0374 | 2.42242 | ||||||||
\(187\) | −8.98566 | −0.657097 | ||||||||
\(188\) | 9.68127 | 0.706079 | ||||||||
\(189\) | 8.15794 | 0.593403 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0108 | −1.15850 | −0.579251 | − | 0.815149i | \(-0.696655\pi\) | ||||
−0.579251 | + | 0.815149i | \(0.696655\pi\) | |||||||
\(192\) | 4.46848 | 0.322485 | ||||||||
\(193\) | −6.92078 | −0.498169 | −0.249084 | − | 0.968482i | \(-0.580130\pi\) | ||||
−0.249084 | + | 0.968482i | \(0.580130\pi\) | |||||||
\(194\) | 13.9367 | 1.00060 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.44634 | −0.460453 | ||||||||
\(197\) | 4.08208 | 0.290836 | 0.145418 | − | 0.989370i | \(-0.453547\pi\) | ||||
0.145418 | + | 0.989370i | \(0.453547\pi\) | |||||||
\(198\) | 0.564476 | 0.0401156 | ||||||||
\(199\) | 7.24353 | 0.513481 | 0.256740 | − | 0.966480i | \(-0.417352\pi\) | ||||
0.256740 | + | 0.966480i | \(0.417352\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.14006 | 0.221483 | ||||||||
\(202\) | 31.1909 | 2.19459 | ||||||||
\(203\) | −12.6939 | −0.890935 | ||||||||
\(204\) | 8.37747 | 0.586540 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.21775 | −0.363538 | ||||||||
\(207\) | −0.201148 | −0.0139808 | ||||||||
\(208\) | −30.8593 | −2.13971 | ||||||||
\(209\) | 1.80945 | 0.125163 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0986890 | 0.00679403 | 0.00339701 | − | 0.999994i | \(-0.498919\pi\) | ||||
0.00339701 | + | 0.999994i | \(0.498919\pi\) | |||||||
\(212\) | −13.7600 | −0.945043 | ||||||||
\(213\) | 16.0770 | 1.10158 | ||||||||
\(214\) | −8.96154 | −0.612598 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.91828 | 0.402688 | ||||||||
\(217\) | 16.2832 | 1.10537 | ||||||||
\(218\) | −18.9496 | −1.28343 | ||||||||
\(219\) | 15.0708 | 1.01839 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.5685 | −1.51812 | ||||||||
\(222\) | −1.55293 | −0.104226 | ||||||||
\(223\) | −15.5911 | −1.04406 | −0.522028 | − | 0.852928i | \(-0.674824\pi\) | ||||
−0.522028 | + | 0.852928i | \(0.674824\pi\) | |||||||
\(224\) | 10.3067 | 0.688647 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.3911 | −1.55595 | ||||||||
\(227\) | −24.7410 | −1.64212 | −0.821059 | − | 0.570843i | \(-0.806616\pi\) | ||||
−0.821059 | + | 0.570843i | \(0.806616\pi\) | |||||||
\(228\) | −1.68698 | −0.111723 | ||||||||
\(229\) | −21.0262 | −1.38945 | −0.694725 | − | 0.719275i | \(-0.744474\pi\) | ||||
−0.694725 | + | 0.719275i | \(0.744474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.62858 | −0.436128 | ||||||||
\(232\) | −9.20893 | −0.604596 | ||||||||
\(233\) | 8.57165 | 0.561548 | 0.280774 | − | 0.959774i | \(-0.409409\pi\) | ||||
0.280774 | + | 0.959774i | \(0.409409\pi\) | |||||||
\(234\) | 1.41774 | 0.0926809 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −14.1759 | −0.922771 | ||||||||
\(237\) | 10.4006 | 0.675589 | ||||||||
\(238\) | 10.0560 | 0.651833 | ||||||||
\(239\) | 22.7072 | 1.46880 | 0.734402 | − | 0.678715i | \(-0.237463\pi\) | ||||
0.734402 | + | 0.678715i | \(0.237463\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 8.41801 | 0.541130 | ||||||||
\(243\) | −1.25507 | −0.0805127 | ||||||||
\(244\) | −12.7316 | −0.815059 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −27.9117 | −1.77959 | ||||||||
\(247\) | 4.54465 | 0.289169 | ||||||||
\(248\) | 11.8128 | 0.750115 | ||||||||
\(249\) | 1.41775 | 0.0898460 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9356 | −0.816489 | −0.408244 | − | 0.912873i | \(-0.633859\pi\) | ||||
−0.408244 | + | 0.912873i | \(0.633859\pi\) | |||||||
\(252\) | −0.259383 | −0.0163396 | ||||||||
\(253\) | 4.22089 | 0.265365 | ||||||||
\(254\) | −2.16620 | −0.135920 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9790 | 1.31119 | ||||||||
\(257\) | 10.8510 | 0.676865 | 0.338432 | − | 0.940991i | \(-0.390103\pi\) | ||||
0.338432 | + | 0.940991i | \(0.390103\pi\) | |||||||
\(258\) | 4.70963 | 0.293209 | ||||||||
\(259\) | −0.765395 | −0.0475593 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.995730 | 0.0616341 | ||||||||
\(262\) | −34.5527 | −2.13467 | ||||||||
\(263\) | −14.1032 | −0.869638 | −0.434819 | − | 0.900518i | \(-0.643188\pi\) | ||||
−0.434819 | + | 0.900518i | \(0.643188\pi\) | |||||||
\(264\) | −4.80878 | −0.295960 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.02499 | −0.124160 | ||||||||
\(267\) | −3.85991 | −0.236222 | ||||||||
\(268\) | −2.57838 | −0.157500 | ||||||||
\(269\) | −7.55668 | −0.460739 | −0.230370 | − | 0.973103i | \(-0.573993\pi\) | ||||
−0.230370 | + | 0.973103i | \(0.573993\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.9578 | 1.27309 | 0.636546 | − | 0.771238i | \(-0.280362\pi\) | ||||
0.636546 | + | 0.771238i | \(0.280362\pi\) | |||||||
\(272\) | 17.1696 | 1.04106 | ||||||||
\(273\) | −16.6484 | −1.00761 | ||||||||
\(274\) | 9.28443 | 0.560893 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.93520 | −0.236871 | ||||||||
\(277\) | 14.9632 | 0.899052 | 0.449526 | − | 0.893267i | \(-0.351593\pi\) | ||||
0.449526 | + | 0.893267i | \(0.351593\pi\) | |||||||
\(278\) | 0.417105 | 0.0250163 | ||||||||
\(279\) | −1.27728 | −0.0764688 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.7490 | 1.83433 | 0.917165 | − | 0.398507i | \(-0.130471\pi\) | ||||
0.917165 | + | 0.398507i | \(0.130471\pi\) | |||||||
\(282\) | 21.7187 | 1.29333 | ||||||||
\(283\) | −4.06104 | −0.241404 | −0.120702 | − | 0.992689i | \(-0.538515\pi\) | ||||
−0.120702 | + | 0.992689i | \(0.538515\pi\) | |||||||
\(284\) | −13.2012 | −0.783349 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.7499 | −1.75915 | ||||||||
\(287\) | −13.7569 | −0.812043 | ||||||||
\(288\) | −0.808478 | −0.0476400 | ||||||||
\(289\) | −4.44326 | −0.261368 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.8376 | 0.752551 | ||||||||
\(292\) | −12.3750 | −0.724193 | ||||||||
\(293\) | 18.7249 | 1.09392 | 0.546961 | − | 0.837158i | \(-0.315785\pi\) | ||||
0.546961 | + | 0.837158i | \(0.315785\pi\) | |||||||
\(294\) | −14.4615 | −0.843415 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.555266 | −0.0322742 | ||||||||
\(297\) | 13.4282 | 0.779180 | ||||||||
\(298\) | 7.37828 | 0.427412 | ||||||||
\(299\) | 10.6012 | 0.613085 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.32124 | 0.133794 | ||||||||
\(302\) | 10.5566 | 0.607467 | ||||||||
\(303\) | 28.7310 | 1.65055 | ||||||||
\(304\) | −3.45747 | −0.198300 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.788810 | −0.0450933 | ||||||||
\(307\) | 2.41046 | 0.137572 | 0.0687860 | − | 0.997631i | \(-0.478087\pi\) | ||||
0.0687860 | + | 0.997631i | \(0.478087\pi\) | |||||||
\(308\) | 5.44289 | 0.310137 | ||||||||
\(309\) | −4.80624 | −0.273418 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0513 | −0.910183 | −0.455092 | − | 0.890445i | \(-0.650394\pi\) | ||||
−0.455092 | + | 0.890445i | \(0.650394\pi\) | |||||||
\(312\) | −12.0778 | −0.683771 | ||||||||
\(313\) | −6.01435 | −0.339951 | −0.169976 | − | 0.985448i | \(-0.554369\pi\) | ||||
−0.169976 | + | 0.985448i | \(0.554369\pi\) | |||||||
\(314\) | −7.40958 | −0.418147 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.54015 | −0.480421 | ||||||||
\(317\) | −27.5411 | −1.54686 | −0.773430 | − | 0.633881i | \(-0.781461\pi\) | ||||
−0.773430 | + | 0.633881i | \(0.781461\pi\) | |||||||
\(318\) | −30.8689 | −1.73104 | ||||||||
\(319\) | −20.8944 | −1.16986 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.25476 | −0.460736 | ||||||||
\(322\) | −4.72366 | −0.263240 | ||||||||
\(323\) | −2.52857 | −0.140693 | ||||||||
\(324\) | −12.0142 | −0.667453 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.62370 | 0.256083 | ||||||||
\(327\) | −17.4551 | −0.965268 | ||||||||
\(328\) | −9.98010 | −0.551059 | ||||||||
\(329\) | 10.7045 | 0.590158 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.248029 | 0.0136329 | 0.00681645 | − | 0.999977i | \(-0.497830\pi\) | ||||
0.00681645 | + | 0.999977i | \(0.497830\pi\) | |||||||
\(332\) | −1.16415 | −0.0638909 | ||||||||
\(333\) | 0.0600390 | 0.00329011 | ||||||||
\(334\) | 46.6187 | 2.55086 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.6658 | 0.690974 | ||||||||
\(337\) | 21.1908 | 1.15433 | 0.577167 | − | 0.816626i | \(-0.304158\pi\) | ||||
0.577167 | + | 0.816626i | \(0.304158\pi\) | |||||||
\(338\) | −50.7731 | −2.76169 | ||||||||
\(339\) | −21.5463 | −1.17023 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.8024 | 1.45143 | ||||||||
\(342\) | 0.158844 | 0.00858929 | ||||||||
\(343\) | −17.9115 | −0.967132 | ||||||||
\(344\) | 1.68397 | 0.0907936 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −35.0722 | −1.88549 | ||||||||
\(347\) | −17.9531 | −0.963775 | −0.481887 | − | 0.876233i | \(-0.660049\pi\) | ||||
−0.481887 | + | 0.876233i | \(0.660049\pi\) | |||||||
\(348\) | 19.4802 | 1.04425 | ||||||||
\(349\) | 7.68481 | 0.411358 | 0.205679 | − | 0.978619i | \(-0.434060\pi\) | ||||
0.205679 | + | 0.978619i | \(0.434060\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.7263 | 1.80018 | ||||||||
\(352\) | 16.9651 | 0.904243 | ||||||||
\(353\) | −25.0052 | −1.33089 | −0.665446 | − | 0.746446i | \(-0.731759\pi\) | ||||
−0.665446 | + | 0.746446i | \(0.731759\pi\) | |||||||
\(354\) | −31.8018 | −1.69025 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.16946 | 0.167981 | ||||||||
\(357\) | 9.26291 | 0.490245 | ||||||||
\(358\) | −22.7972 | −1.20487 | ||||||||
\(359\) | 7.21328 | 0.380703 | 0.190351 | − | 0.981716i | \(-0.439037\pi\) | ||||
0.190351 | + | 0.981716i | \(0.439037\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4908 | −0.973201 | ||||||||
\(362\) | −10.3668 | −0.544867 | ||||||||
\(363\) | 7.75410 | 0.406985 | ||||||||
\(364\) | 13.6704 | 0.716525 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −28.5618 | −1.49295 | ||||||||
\(367\) | −10.0531 | −0.524767 | −0.262383 | − | 0.964964i | \(-0.584509\pi\) | ||||
−0.262383 | + | 0.964964i | \(0.584509\pi\) | |||||||
\(368\) | −8.06520 | −0.420428 | ||||||||
\(369\) | 1.07911 | 0.0561764 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.2144 | −0.789891 | ||||||||
\(372\) | −24.9883 | −1.29558 | ||||||||
\(373\) | −31.7029 | −1.64151 | −0.820756 | − | 0.571279i | \(-0.806447\pi\) | ||||
−0.820756 | + | 0.571279i | \(0.806447\pi\) | |||||||
\(374\) | 16.5524 | 0.855904 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.76571 | 0.400486 | ||||||||
\(377\) | −52.4786 | −2.70278 | ||||||||
\(378\) | −15.0277 | −0.772939 | ||||||||
\(379\) | −8.44277 | −0.433676 | −0.216838 | − | 0.976208i | \(-0.569574\pi\) | ||||
−0.216838 | + | 0.976208i | \(0.569574\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.99536 | −0.102225 | ||||||||
\(382\) | 29.4933 | 1.50901 | ||||||||
\(383\) | 9.65154 | 0.493171 | 0.246585 | − | 0.969121i | \(-0.420691\pi\) | ||||
0.246585 | + | 0.969121i | \(0.420691\pi\) | |||||||
\(384\) | 14.4729 | 0.738569 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.7487 | 0.648891 | ||||||||
\(387\) | −0.182082 | −0.00925574 | ||||||||
\(388\) | −10.5412 | −0.535151 | ||||||||
\(389\) | 23.9535 | 1.21449 | 0.607246 | − | 0.794514i | \(-0.292274\pi\) | ||||
0.607246 | + | 0.794514i | \(0.292274\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.89836 | −0.298293 | ||||||||
\(392\) | −5.17086 | −0.261168 | ||||||||
\(393\) | −31.8276 | −1.60549 | ||||||||
\(394\) | −7.51955 | −0.378829 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.426950 | −0.0214550 | ||||||||
\(397\) | 26.7766 | 1.34388 | 0.671940 | − | 0.740606i | \(-0.265461\pi\) | ||||
0.671940 | + | 0.740606i | \(0.265461\pi\) | |||||||
\(398\) | −13.3432 | −0.668836 | ||||||||
\(399\) | −1.86528 | −0.0933810 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.2168 | −1.25927 | −0.629635 | − | 0.776891i | \(-0.716795\pi\) | ||||
−0.629635 | + | 0.776891i | \(0.716795\pi\) | |||||||
\(402\) | −5.78426 | −0.288493 | ||||||||
\(403\) | 67.3173 | 3.35331 | ||||||||
\(404\) | −23.5917 | −1.17373 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.3832 | 1.16049 | ||||||||
\(407\) | −1.25986 | −0.0624488 | ||||||||
\(408\) | 6.71989 | 0.332684 | ||||||||
\(409\) | −13.2389 | −0.654619 | −0.327310 | − | 0.944917i | \(-0.606142\pi\) | ||||
−0.327310 | + | 0.944917i | \(0.606142\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.55219 | 0.421848 | ||||||||
\(412\) | 3.94652 | 0.194431 | ||||||||
\(413\) | −15.6742 | −0.771275 | ||||||||
\(414\) | 0.370533 | 0.0182107 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 42.6097 | 2.08911 | ||||||||
\(417\) | 0.384209 | 0.0188148 | ||||||||
\(418\) | −3.33318 | −0.163031 | ||||||||
\(419\) | −18.5429 | −0.905880 | −0.452940 | − | 0.891541i | \(-0.649625\pi\) | ||||
−0.452940 | + | 0.891541i | \(0.649625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.9339 | −1.26394 | −0.631972 | − | 0.774992i | \(-0.717754\pi\) | ||||
−0.631972 | + | 0.774992i | \(0.717754\pi\) | |||||||
\(422\) | −0.181794 | −0.00884958 | ||||||||
\(423\) | −0.839680 | −0.0408266 | ||||||||
\(424\) | −11.0375 | −0.536026 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −29.6153 | −1.43486 | ||||||||
\(427\) | −14.0773 | −0.681246 | ||||||||
\(428\) | 6.77819 | 0.327636 | ||||||||
\(429\) | −27.4036 | −1.32306 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.5328 | 1.08537 | 0.542683 | − | 0.839937i | \(-0.317408\pi\) | ||||
0.542683 | + | 0.839937i | \(0.317408\pi\) | |||||||
\(432\) | −25.6583 | −1.23448 | ||||||||
\(433\) | 33.5776 | 1.61364 | 0.806818 | − | 0.590801i | \(-0.201188\pi\) | ||||
0.806818 | + | 0.590801i | \(0.201188\pi\) | |||||||
\(434\) | −29.9950 | −1.43981 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.3328 | 0.686416 | ||||||||
\(437\) | 1.18776 | 0.0568182 | ||||||||
\(438\) | −27.7618 | −1.32651 | ||||||||
\(439\) | −3.64200 | −0.173823 | −0.0869116 | − | 0.996216i | \(-0.527700\pi\) | ||||
−0.0869116 | + | 0.996216i | \(0.527700\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.559107 | 0.0266242 | ||||||||
\(442\) | 41.5732 | 1.97743 | ||||||||
\(443\) | −27.0746 | −1.28635 | −0.643177 | − | 0.765718i | \(-0.722384\pi\) | ||||
−0.643177 | + | 0.765718i | \(0.722384\pi\) | |||||||
\(444\) | 1.17458 | 0.0557433 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 28.7202 | 1.35994 | ||||||||
\(447\) | 6.79637 | 0.321457 | ||||||||
\(448\) | −4.05698 | −0.191674 | ||||||||
\(449\) | 40.1427 | 1.89445 | 0.947224 | − | 0.320571i | \(-0.103875\pi\) | ||||
0.947224 | + | 0.320571i | \(0.103875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.6441 | −1.06627 | ||||||||
\(452\) | 17.6922 | 0.832170 | ||||||||
\(453\) | 9.72407 | 0.456877 | ||||||||
\(454\) | 45.5751 | 2.13895 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.35319 | −0.0633691 | ||||||||
\(457\) | 22.3710 | 1.04647 | 0.523236 | − | 0.852188i | \(-0.324725\pi\) | ||||
0.523236 | + | 0.852188i | \(0.324725\pi\) | |||||||
\(458\) | 38.7321 | 1.80983 | ||||||||
\(459\) | −18.7648 | −0.875864 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.3342 | −1.45938 | −0.729689 | − | 0.683780i | \(-0.760335\pi\) | ||||
−0.729689 | + | 0.683780i | \(0.760335\pi\) | |||||||
\(462\) | 12.2104 | 0.568080 | ||||||||
\(463\) | 9.21061 | 0.428053 | 0.214027 | − | 0.976828i | \(-0.431342\pi\) | ||||
0.214027 | + | 0.976828i | \(0.431342\pi\) | |||||||
\(464\) | 39.9246 | 1.85345 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.7897 | −0.731446 | ||||||||
\(467\) | 1.38103 | 0.0639065 | 0.0319532 | − | 0.999489i | \(-0.489827\pi\) | ||||
0.0319532 | + | 0.999489i | \(0.489827\pi\) | |||||||
\(468\) | −1.07233 | −0.0495686 | ||||||||
\(469\) | −2.85089 | −0.131642 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.82520 | −0.314489 | ||||||||
\(472\) | −11.3710 | −0.523394 | ||||||||
\(473\) | 3.82081 | 0.175681 | ||||||||
\(474\) | −19.1587 | −0.879990 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.60600 | −0.348620 | ||||||||
\(477\) | 1.19344 | 0.0546440 | ||||||||
\(478\) | −41.8286 | −1.91320 | ||||||||
\(479\) | 1.68759 | 0.0771080 | 0.0385540 | − | 0.999257i | \(-0.487725\pi\) | ||||
0.0385540 | + | 0.999257i | \(0.487725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.16427 | −0.144278 | ||||||||
\(482\) | −1.84209 | −0.0839048 | ||||||||
\(483\) | −4.35112 | −0.197983 | ||||||||
\(484\) | −6.36709 | −0.289413 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.31195 | 0.104872 | ||||||||
\(487\) | 32.1394 | 1.45638 | 0.728188 | − | 0.685377i | \(-0.240363\pi\) | ||||
0.728188 | + | 0.685377i | \(0.240363\pi\) | |||||||
\(488\) | −10.2125 | −0.462299 | ||||||||
\(489\) | 4.25904 | 0.192600 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.6379 | −1.65345 | −0.826723 | − | 0.562608i | \(-0.809798\pi\) | ||||
−0.826723 | + | 0.562608i | \(0.809798\pi\) | |||||||
\(492\) | 21.1115 | 0.951778 | ||||||||
\(493\) | 29.1982 | 1.31502 | ||||||||
\(494\) | −8.37164 | −0.376658 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −51.2136 | −2.29956 | ||||||||
\(497\) | −14.5965 | −0.654742 | ||||||||
\(498\) | −2.61161 | −0.117029 | ||||||||
\(499\) | 38.2943 | 1.71429 | 0.857145 | − | 0.515076i | \(-0.172236\pi\) | ||||
0.857145 | + | 0.515076i | \(0.172236\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.9420 | 1.91851 | ||||||||
\(502\) | 23.8285 | 1.06352 | ||||||||
\(503\) | 36.2174 | 1.61485 | 0.807427 | − | 0.589967i | \(-0.200859\pi\) | ||||
0.807427 | + | 0.589967i | \(0.200859\pi\) | |||||||
\(504\) | −0.208061 | −0.00926777 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.77525 | −0.345652 | ||||||||
\(507\) | −46.7688 | −2.07707 | ||||||||
\(508\) | 1.63844 | 0.0726940 | ||||||||
\(509\) | 18.3681 | 0.814153 | 0.407076 | − | 0.913394i | \(-0.366548\pi\) | ||||
0.407076 | + | 0.913394i | \(0.366548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.6830 | −0.605298 | ||||||||
\(512\) | −21.5862 | −0.953985 | ||||||||
\(513\) | 3.77869 | 0.166833 | ||||||||
\(514\) | −19.9885 | −0.881653 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.56220 | −0.156817 | ||||||||
\(517\) | 17.6198 | 0.774920 | ||||||||
\(518\) | 1.40993 | 0.0619486 | ||||||||
\(519\) | −32.3062 | −1.41808 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.0378 | −1.62265 | −0.811327 | − | 0.584593i | \(-0.801254\pi\) | ||||
−0.811327 | + | 0.584593i | \(0.801254\pi\) | |||||||
\(522\) | −1.83422 | −0.0802817 | ||||||||
\(523\) | −20.9663 | −0.916791 | −0.458395 | − | 0.888748i | \(-0.651576\pi\) | ||||
−0.458395 | + | 0.888748i | \(0.651576\pi\) | |||||||
\(524\) | 26.1344 | 1.14169 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.9793 | 1.13275 | ||||||||
\(527\) | −37.4543 | −1.63153 | ||||||||
\(528\) | 20.8481 | 0.907298 | ||||||||
\(529\) | −20.2293 | −0.879536 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.22951 | 0.0533561 | ||||||||
\(532\) | 1.53163 | 0.0664046 | ||||||||
\(533\) | −56.8732 | −2.46345 | ||||||||
\(534\) | 7.11029 | 0.307692 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.06822 | −0.0893334 | ||||||||
\(537\) | −20.9993 | −0.906185 | ||||||||
\(538\) | 13.9201 | 0.600137 | ||||||||
\(539\) | −11.7323 | −0.505346 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.75202 | 0.419272 | 0.209636 | − | 0.977779i | \(-0.432772\pi\) | ||||
0.209636 | + | 0.977779i | \(0.432772\pi\) | |||||||
\(542\) | −38.6060 | −1.65827 | ||||||||
\(543\) | −9.54920 | −0.409795 | ||||||||
\(544\) | −23.7074 | −1.01645 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 30.6678 | 1.31246 | ||||||||
\(547\) | −30.8874 | −1.32065 | −0.660326 | − | 0.750979i | \(-0.729582\pi\) | ||||
−0.660326 | + | 0.750979i | \(0.729582\pi\) | |||||||
\(548\) | −7.02241 | −0.299983 | ||||||||
\(549\) | 1.10424 | 0.0471280 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.87969 | −0.250483 | ||||||||
\(552\) | −3.15658 | −0.134353 | ||||||||
\(553\) | −9.44278 | −0.401548 | ||||||||
\(554\) | −27.5636 | −1.17106 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.315483 | −0.0133795 | ||||||||
\(557\) | −25.1804 | −1.06693 | −0.533463 | − | 0.845823i | \(-0.679110\pi\) | ||||
−0.533463 | + | 0.845823i | \(0.679110\pi\) | |||||||
\(558\) | 2.35286 | 0.0996047 | ||||||||
\(559\) | 9.59638 | 0.405884 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.2469 | 0.643726 | ||||||||
\(562\) | −56.6424 | −2.38931 | ||||||||
\(563\) | −37.8072 | −1.59338 | −0.796692 | − | 0.604386i | \(-0.793419\pi\) | ||||
−0.796692 | + | 0.604386i | \(0.793419\pi\) | |||||||
\(564\) | −16.4272 | −0.691712 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.48080 | 0.314441 | ||||||||
\(567\) | −13.2840 | −0.557874 | ||||||||
\(568\) | −10.5892 | −0.444313 | ||||||||
\(569\) | −9.89011 | −0.414615 | −0.207307 | − | 0.978276i | \(-0.566470\pi\) | ||||
−0.207307 | + | 0.978276i | \(0.566470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.8124 | −0.870972 | −0.435486 | − | 0.900196i | \(-0.643423\pi\) | ||||
−0.435486 | + | 0.900196i | \(0.643423\pi\) | |||||||
\(572\) | 22.5018 | 0.940848 | ||||||||
\(573\) | 27.1673 | 1.13493 | ||||||||
\(574\) | 25.3414 | 1.05773 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.318237 | 0.0132599 | ||||||||
\(577\) | −22.7214 | −0.945906 | −0.472953 | − | 0.881088i | \(-0.656812\pi\) | ||||
−0.472953 | + | 0.881088i | \(0.656812\pi\) | |||||||
\(578\) | 8.18487 | 0.340446 | ||||||||
\(579\) | 11.7432 | 0.488032 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.28719 | −0.0534016 | ||||||||
\(582\) | −23.6479 | −0.980238 | ||||||||
\(583\) | −25.0432 | −1.03718 | ||||||||
\(584\) | −9.92647 | −0.410760 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −34.4930 | −1.42489 | ||||||||
\(587\) | −26.2568 | −1.08373 | −0.541866 | − | 0.840465i | \(-0.682282\pi\) | ||||
−0.541866 | + | 0.840465i | \(0.682282\pi\) | |||||||
\(588\) | 10.9382 | 0.451084 | ||||||||
\(589\) | 7.54222 | 0.310772 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.92650 | −0.284918 | ||||||||
\(592\) | 2.40731 | 0.0989399 | ||||||||
\(593\) | 16.3255 | 0.670406 | 0.335203 | − | 0.942146i | \(-0.391195\pi\) | ||||
0.335203 | + | 0.942146i | \(0.391195\pi\) | |||||||
\(594\) | −24.7358 | −1.01492 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.58067 | −0.228593 | ||||||||
\(597\) | −12.2909 | −0.503032 | ||||||||
\(598\) | −19.5284 | −0.798576 | ||||||||
\(599\) | −45.7396 | −1.86887 | −0.934436 | − | 0.356132i | \(-0.884095\pi\) | ||||
−0.934436 | + | 0.356132i | \(0.884095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.3734 | −0.708676 | −0.354338 | − | 0.935117i | \(-0.615294\pi\) | ||||
−0.354338 | + | 0.935117i | \(0.615294\pi\) | |||||||
\(602\) | −4.27592 | −0.174274 | ||||||||
\(603\) | 0.223629 | 0.00910688 | ||||||||
\(604\) | −7.98467 | −0.324892 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −52.9250 | −2.14993 | ||||||||
\(607\) | −4.48838 | −0.182178 | −0.0910890 | − | 0.995843i | \(-0.529035\pi\) | ||||
−0.0910890 | + | 0.995843i | \(0.529035\pi\) | |||||||
\(608\) | 4.77399 | 0.193611 | ||||||||
\(609\) | 21.5391 | 0.872807 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44.2542 | 1.79033 | ||||||||
\(612\) | 0.596628 | 0.0241173 | ||||||||
\(613\) | 29.9448 | 1.20946 | 0.604730 | − | 0.796430i | \(-0.293281\pi\) | ||||
0.604730 | + | 0.796430i | \(0.293281\pi\) | |||||||
\(614\) | −4.44028 | −0.179195 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.36595 | 0.175909 | ||||||||
\(617\) | 48.0028 | 1.93252 | 0.966261 | − | 0.257566i | \(-0.0829205\pi\) | ||||
0.966261 | + | 0.257566i | \(0.0829205\pi\) | |||||||
\(618\) | 8.85352 | 0.356141 | ||||||||
\(619\) | −6.70266 | −0.269403 | −0.134701 | − | 0.990886i | \(-0.543008\pi\) | ||||
−0.134701 | + | 0.990886i | \(0.543008\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.81449 | 0.353713 | ||||||||
\(622\) | 29.5678 | 1.18556 | ||||||||
\(623\) | 3.50445 | 0.140403 | ||||||||
\(624\) | 52.3624 | 2.09617 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11.0790 | 0.442805 | ||||||||
\(627\) | −3.07030 | −0.122616 | ||||||||
\(628\) | 5.60434 | 0.223638 | ||||||||
\(629\) | 1.76055 | 0.0701977 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.36072 | −0.293025 | −0.146513 | − | 0.989209i | \(-0.546805\pi\) | ||||
−0.146513 | + | 0.989209i | \(0.546805\pi\) | |||||||
\(632\) | −6.85039 | −0.272494 | ||||||||
\(633\) | −0.167456 | −0.00665579 | ||||||||
\(634\) | 50.7331 | 2.01487 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 23.3481 | 0.925814 | ||||||||
\(637\) | −29.4670 | −1.16752 | ||||||||
\(638\) | 38.4893 | 1.52381 | ||||||||
\(639\) | 1.14497 | 0.0452945 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.1888 | −1.46887 | −0.734434 | − | 0.678680i | \(-0.762552\pi\) | ||||
−0.734434 | + | 0.678680i | \(0.762552\pi\) | |||||||
\(642\) | 15.2060 | 0.600133 | ||||||||
\(643\) | −27.0935 | −1.06846 | −0.534232 | − | 0.845338i | \(-0.679399\pi\) | ||||
−0.534232 | + | 0.845338i | \(0.679399\pi\) | |||||||
\(644\) | 3.57281 | 0.140789 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.65785 | 0.183261 | ||||||||
\(647\) | −16.1175 | −0.633646 | −0.316823 | − | 0.948485i | \(-0.602616\pi\) | ||||
−0.316823 | + | 0.948485i | \(0.602616\pi\) | |||||||
\(648\) | −9.63702 | −0.378578 | ||||||||
\(649\) | −25.8000 | −1.01274 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.6294 | −1.08288 | ||||||||
\(652\) | −3.49720 | −0.136961 | ||||||||
\(653\) | 11.7529 | 0.459928 | 0.229964 | − | 0.973199i | \(-0.426139\pi\) | ||||
0.229964 | + | 0.973199i | \(0.426139\pi\) | |||||||
\(654\) | 32.1538 | 1.25731 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 43.2680 | 1.68933 | ||||||||
\(657\) | 1.07331 | 0.0418740 | ||||||||
\(658\) | −19.7186 | −0.768713 | ||||||||
\(659\) | −12.7347 | −0.496075 | −0.248038 | − | 0.968750i | \(-0.579786\pi\) | ||||
−0.248038 | + | 0.968750i | \(0.579786\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.32682 | −0.0905028 | −0.0452514 | − | 0.998976i | \(-0.514409\pi\) | ||||
−0.0452514 | + | 0.998976i | \(0.514409\pi\) | |||||||
\(662\) | −0.456891 | −0.0177576 | ||||||||
\(663\) | 38.2944 | 1.48723 | ||||||||
\(664\) | −0.933807 | −0.0362387 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.110597 | −0.00428555 | ||||||||
\(667\) | −13.7155 | −0.531065 | ||||||||
\(668\) | −35.2607 | −1.36428 | ||||||||
\(669\) | 26.4551 | 1.02281 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.1715 | −0.894525 | ||||||||
\(672\) | −17.4885 | −0.674635 | ||||||||
\(673\) | −21.2017 | −0.817267 | −0.408633 | − | 0.912699i | \(-0.633995\pi\) | ||||
−0.408633 | + | 0.912699i | \(0.633995\pi\) | |||||||
\(674\) | −39.0353 | −1.50358 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 38.4030 | 1.47704 | ||||||||
\(677\) | −51.8603 | −1.99315 | −0.996576 | − | 0.0826794i | \(-0.973652\pi\) | ||||
−0.996576 | + | 0.0826794i | \(0.973652\pi\) | |||||||
\(678\) | 39.6902 | 1.52429 | ||||||||
\(679\) | −11.6554 | −0.447292 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.9807 | 1.60870 | ||||||||
\(682\) | −49.3725 | −1.89057 | ||||||||
\(683\) | −22.4656 | −0.859621 | −0.429811 | − | 0.902919i | \(-0.641420\pi\) | ||||
−0.429811 | + | 0.902919i | \(0.641420\pi\) | |||||||
\(684\) | −0.120144 | −0.00459381 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 32.9946 | 1.25974 | ||||||||
\(687\) | 35.6774 | 1.36118 | ||||||||
\(688\) | −7.30073 | −0.278338 | ||||||||
\(689\) | −62.8987 | −2.39625 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.2504 | 1.94966 | 0.974829 | − | 0.222953i | \(-0.0715698\pi\) | ||||
0.974829 | + | 0.222953i | \(0.0715698\pi\) | |||||||
\(692\) | 26.5274 | 1.00842 | ||||||||
\(693\) | −0.472075 | −0.0179327 | ||||||||
\(694\) | 33.0713 | 1.25537 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 15.6258 | 0.592294 | ||||||||
\(697\) | 31.6433 | 1.19858 | ||||||||
\(698\) | −14.1561 | −0.535816 | ||||||||
\(699\) | −14.5444 | −0.550121 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.425393 | 0.0160669 | 0.00803344 | − | 0.999968i | \(-0.497443\pi\) | ||||
0.00803344 | + | 0.999968i | \(0.497443\pi\) | |||||||
\(702\) | −62.1268 | −2.34483 | ||||||||
\(703\) | −0.354524 | −0.0133711 | ||||||||
\(704\) | −6.67788 | −0.251682 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 46.0618 | 1.73356 | ||||||||
\(707\) | −26.0852 | −0.981035 | ||||||||
\(708\) | 24.0537 | 0.903995 | ||||||||
\(709\) | −15.9902 | −0.600523 | −0.300261 | − | 0.953857i | \(-0.597074\pi\) | ||||
−0.300261 | + | 0.953857i | \(0.597074\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.740709 | 0.0277787 | ||||||||
\(712\) | 2.54235 | 0.0952785 | ||||||||
\(713\) | 17.5936 | 0.658886 | ||||||||
\(714\) | −17.0631 | −0.638570 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17.2430 | 0.644402 | ||||||||
\(717\) | −38.5297 | −1.43892 | ||||||||
\(718\) | −13.2875 | −0.495885 | ||||||||
\(719\) | −26.2235 | −0.977973 | −0.488986 | − | 0.872291i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872291i | \(0.662633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.36364 | 0.162510 | ||||||||
\(722\) | 34.0617 | 1.26765 | ||||||||
\(723\) | −1.69681 | −0.0631050 | ||||||||
\(724\) | 7.84108 | 0.291412 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −14.2837 | −0.530120 | ||||||||
\(727\) | 25.2570 | 0.936730 | 0.468365 | − | 0.883535i | \(-0.344843\pi\) | ||||
0.468365 | + | 0.883535i | \(0.344843\pi\) | |||||||
\(728\) | 10.9656 | 0.406411 | ||||||||
\(729\) | 27.9982 | 1.03697 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.33927 | −0.197480 | ||||||||
\(732\) | 21.6031 | 0.798474 | ||||||||
\(733\) | −8.92252 | −0.329561 | −0.164780 | − | 0.986330i | \(-0.552692\pi\) | ||||
−0.164780 | + | 0.986330i | \(0.552692\pi\) | |||||||
\(734\) | 18.5187 | 0.683537 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.1362 | 0.410486 | ||||||||
\(737\) | −4.69263 | −0.172855 | ||||||||
\(738\) | −1.98782 | −0.0731728 | ||||||||
\(739\) | −14.2439 | −0.523970 | −0.261985 | − | 0.965072i | \(-0.584377\pi\) | ||||
−0.261985 | + | 0.965072i | \(0.584377\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.71139 | −0.283285 | ||||||||
\(742\) | 28.0262 | 1.02887 | ||||||||
\(743\) | −14.9854 | −0.549762 | −0.274881 | − | 0.961478i | \(-0.588638\pi\) | ||||
−0.274881 | + | 0.961478i | \(0.588638\pi\) | |||||||
\(744\) | −20.0441 | −0.734852 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 58.3995 | 2.13816 | ||||||||
\(747\) | 0.100969 | 0.00369427 | ||||||||
\(748\) | −12.5196 | −0.457763 | ||||||||
\(749\) | 7.49459 | 0.273847 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.1216 | −1.06266 | −0.531330 | − | 0.847165i | \(-0.678308\pi\) | ||||
−0.531330 | + | 0.847165i | \(0.678308\pi\) | |||||||
\(752\) | −33.6677 | −1.22773 | ||||||||
\(753\) | 21.9492 | 0.799875 | ||||||||
\(754\) | 96.6702 | 3.52052 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11.3664 | 0.413392 | ||||||||
\(757\) | 29.9865 | 1.08988 | 0.544940 | − | 0.838475i | \(-0.316553\pi\) | ||||
0.544940 | + | 0.838475i | \(0.316553\pi\) | |||||||
\(758\) | 15.5523 | 0.564886 | ||||||||
\(759\) | −7.16204 | −0.259966 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.01232 | 0.0729466 | 0.0364733 | − | 0.999335i | \(-0.488388\pi\) | ||||
0.0364733 | + | 0.999335i | \(0.488388\pi\) | |||||||
\(762\) | 3.67563 | 0.133154 | ||||||||
\(763\) | 15.8477 | 0.573724 | ||||||||
\(764\) | −22.3077 | −0.807065 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.7790 | −0.642381 | ||||||||
\(767\) | −64.7996 | −2.33978 | ||||||||
\(768\) | −35.5974 | −1.28451 | ||||||||
\(769\) | 46.1301 | 1.66350 | 0.831748 | − | 0.555154i | \(-0.187341\pi\) | ||||
0.831748 | + | 0.555154i | \(0.187341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.4120 | −0.663092 | ||||||||
\(772\) | −9.64266 | −0.347047 | ||||||||
\(773\) | 48.0505 | 1.72826 | 0.864128 | − | 0.503272i | \(-0.167870\pi\) | ||||
0.864128 | + | 0.503272i | \(0.167870\pi\) | |||||||
\(774\) | 0.335411 | 0.0120561 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.45554 | −0.303536 | ||||||||
\(777\) | 1.29873 | 0.0465916 | ||||||||
\(778\) | −44.1245 | −1.58194 | ||||||||
\(779\) | −6.37206 | −0.228303 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.0261 | −0.859723 | ||||||||
\(782\) | 10.8653 | 0.388542 | ||||||||
\(783\) | −43.6338 | −1.55934 | ||||||||
\(784\) | 22.4179 | 0.800638 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 58.6292 | 2.09124 | ||||||||
\(787\) | 36.3244 | 1.29482 | 0.647412 | − | 0.762140i | \(-0.275851\pi\) | ||||
0.647412 | + | 0.762140i | \(0.275851\pi\) | |||||||
\(788\) | 5.68752 | 0.202610 | ||||||||
\(789\) | 23.9303 | 0.851943 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.5621 | 0.695548 | ||||||||
\(792\) | −0.342473 | −0.0121692 | ||||||||
\(793\) | −58.1977 | −2.06666 | ||||||||
\(794\) | −49.3249 | −1.75048 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.0923 | 0.357714 | ||||||||
\(797\) | 36.6218 | 1.29721 | 0.648606 | − | 0.761124i | \(-0.275352\pi\) | ||||
0.648606 | + | 0.761124i | \(0.275352\pi\) | |||||||
\(798\) | 3.43602 | 0.121634 | ||||||||
\(799\) | −24.6223 | −0.871075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.274895 | −0.00971295 | ||||||||
\(802\) | 46.4517 | 1.64027 | ||||||||
\(803\) | −22.5224 | −0.794799 | ||||||||
\(804\) | 4.37501 | 0.154295 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −124.004 | −4.36787 | ||||||||
\(807\) | 12.8222 | 0.451364 | ||||||||
\(808\) | −18.9238 | −0.665738 | ||||||||
\(809\) | −34.5599 | −1.21506 | −0.607530 | − | 0.794297i | \(-0.707840\pi\) | ||||
−0.607530 | + | 0.794297i | \(0.707840\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.3270 | −0.608435 | −0.304217 | − | 0.952603i | \(-0.598395\pi\) | ||||
−0.304217 | + | 0.952603i | \(0.598395\pi\) | |||||||
\(812\) | −17.6863 | −0.620666 | ||||||||
\(813\) | −35.5613 | −1.24719 | ||||||||
\(814\) | 2.32077 | 0.0813429 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −29.1336 | −1.01988 | ||||||||
\(817\) | 1.07518 | 0.0376156 | ||||||||
\(818\) | 24.3871 | 0.852677 | ||||||||
\(819\) | −1.18567 | −0.0414306 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.5004 | 0.471169 | 0.235584 | − | 0.971854i | \(-0.424300\pi\) | ||||
0.235584 | + | 0.971854i | \(0.424300\pi\) | |||||||
\(822\) | −15.7539 | −0.549480 | ||||||||
\(823\) | 46.7783 | 1.63059 | 0.815295 | − | 0.579046i | \(-0.196575\pi\) | ||||
0.815295 | + | 0.579046i | \(0.196575\pi\) | |||||||
\(824\) | 3.16566 | 0.110281 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.8732 | 1.00463 | ||||||||
\(827\) | 44.0656 | 1.53231 | 0.766155 | − | 0.642656i | \(-0.222167\pi\) | ||||
0.766155 | + | 0.642656i | \(0.222167\pi\) | |||||||
\(828\) | −0.280258 | −0.00973963 | ||||||||
\(829\) | −4.27440 | −0.148456 | −0.0742280 | − | 0.997241i | \(-0.523649\pi\) | ||||
−0.0742280 | + | 0.997241i | \(0.523649\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.3897 | −0.880759 | ||||||||
\(832\) | −16.7722 | −0.581473 | ||||||||
\(833\) | 16.3950 | 0.568051 | ||||||||
\(834\) | −0.707746 | −0.0245073 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.52110 | 0.0871940 | ||||||||
\(837\) | 55.9716 | 1.93466 | ||||||||
\(838\) | 34.1577 | 1.17996 | ||||||||
\(839\) | −31.6115 | −1.09135 | −0.545675 | − | 0.837997i | \(-0.683727\pi\) | ||||
−0.545675 | + | 0.837997i | \(0.683727\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.8947 | 1.34120 | ||||||||
\(842\) | 47.7726 | 1.64635 | ||||||||
\(843\) | −52.1751 | −1.79701 | ||||||||
\(844\) | 0.137502 | 0.00473303 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.54677 | 0.0531789 | ||||||||
\(847\) | −7.04004 | −0.241899 | ||||||||
\(848\) | 47.8521 | 1.64325 | ||||||||
\(849\) | 6.89080 | 0.236492 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.826993 | −0.0283490 | ||||||||
\(852\) | 22.3999 | 0.767409 | ||||||||
\(853\) | 5.03330 | 0.172337 | 0.0861684 | − | 0.996281i | \(-0.472538\pi\) | ||||
0.0861684 | + | 0.996281i | \(0.472538\pi\) | |||||||
\(854\) | 25.9316 | 0.887359 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.43705 | 0.185834 | ||||||||
\(857\) | 17.8339 | 0.609195 | 0.304598 | − | 0.952481i | \(-0.401478\pi\) | ||||
0.304598 | + | 0.952481i | \(0.401478\pi\) | |||||||
\(858\) | 50.4799 | 1.72336 | ||||||||
\(859\) | 29.9247 | 1.02102 | 0.510509 | − | 0.859873i | \(-0.329457\pi\) | ||||
0.510509 | + | 0.859873i | \(0.329457\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.3428 | 0.795519 | ||||||||
\(862\) | −41.5074 | −1.41375 | ||||||||
\(863\) | 21.1041 | 0.718392 | 0.359196 | − | 0.933262i | \(-0.383051\pi\) | ||||
0.359196 | + | 0.933262i | \(0.383051\pi\) | |||||||
\(864\) | 35.4282 | 1.20529 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −61.8529 | −2.10185 | ||||||||
\(867\) | 7.53935 | 0.256050 | ||||||||
\(868\) | 22.6872 | 0.770053 | ||||||||
\(869\) | −15.5430 | −0.527261 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.7861 | −0.399356 | ||||||||
\(872\) | 11.4969 | 0.389334 | ||||||||
\(873\) | 0.914268 | 0.0309433 | ||||||||
\(874\) | −2.18796 | −0.0740088 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.9980 | 0.709457 | ||||||||
\(877\) | −12.0202 | −0.405892 | −0.202946 | − | 0.979190i | \(-0.565052\pi\) | ||||
−0.202946 | + | 0.979190i | \(0.565052\pi\) | |||||||
\(878\) | 6.70889 | 0.226414 | ||||||||
\(879\) | −31.7726 | −1.07166 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.0651 | −0.507556 | −0.253778 | − | 0.967263i | \(-0.581673\pi\) | ||||
−0.253778 | + | 0.967263i | \(0.581673\pi\) | |||||||
\(882\) | −1.02993 | −0.0346794 | ||||||||
\(883\) | 3.17468 | 0.106836 | 0.0534182 | − | 0.998572i | \(-0.482988\pi\) | ||||
0.0534182 | + | 0.998572i | \(0.482988\pi\) | |||||||
\(884\) | −31.4445 | −1.05759 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 49.8738 | 1.67554 | ||||||||
\(887\) | 33.6952 | 1.13137 | 0.565687 | − | 0.824620i | \(-0.308611\pi\) | ||||
0.565687 | + | 0.824620i | \(0.308611\pi\) | |||||||
\(888\) | 0.942179 | 0.0316175 | ||||||||
\(889\) | 1.81161 | 0.0607594 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.8657 | −0.732528 | ||||||||
\(892\) | −21.7229 | −0.727337 | ||||||||
\(893\) | 4.95823 | 0.165921 | ||||||||
\(894\) | −12.5195 | −0.418715 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.1401 | −0.438981 | ||||||||
\(897\) | −17.9883 | −0.600610 | ||||||||
\(898\) | −73.9463 | −2.46762 | ||||||||
\(899\) | −87.0925 | −2.90470 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.9958 | 1.16588 | ||||||||
\(902\) | 41.7125 | 1.38887 | ||||||||
\(903\) | −3.93869 | −0.131071 | ||||||||
\(904\) | 14.1916 | 0.472005 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −17.9126 | −0.595106 | ||||||||
\(907\) | −15.5495 | −0.516311 | −0.258156 | − | 0.966103i | \(-0.583115\pi\) | ||||
−0.258156 | + | 0.966103i | \(0.583115\pi\) | |||||||
\(908\) | −34.4714 | −1.14397 | ||||||||
\(909\) | 2.04617 | 0.0678671 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.4791 | 1.57305 | 0.786527 | − | 0.617556i | \(-0.211877\pi\) | ||||
0.786527 | + | 0.617556i | \(0.211877\pi\) | |||||||
\(912\) | 5.86667 | 0.194265 | ||||||||
\(913\) | −2.11874 | −0.0701200 | ||||||||
\(914\) | −41.2094 | −1.36309 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29.2956 | −0.967954 | ||||||||
\(917\) | 28.8966 | 0.954251 | ||||||||
\(918\) | 34.5664 | 1.14086 | ||||||||
\(919\) | −43.8093 | −1.44514 | −0.722568 | − | 0.691299i | \(-0.757039\pi\) | ||||
−0.722568 | + | 0.691299i | \(0.757039\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.09008 | −0.134773 | ||||||||
\(922\) | 57.7203 | 1.90092 | ||||||||
\(923\) | −60.3443 | −1.98626 | ||||||||
\(924\) | −9.23554 | −0.303827 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.9668 | −0.557562 | ||||||||
\(927\) | −0.342292 | −0.0112423 | ||||||||
\(928\) | −55.1268 | −1.80963 | ||||||||
\(929\) | −23.2341 | −0.762285 | −0.381143 | − | 0.924516i | \(-0.624469\pi\) | ||||
−0.381143 | + | 0.924516i | \(0.624469\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.30147 | −0.108201 | ||||||||
\(932\) | 11.9428 | 0.391200 | ||||||||
\(933\) | 27.2359 | 0.891663 | ||||||||
\(934\) | −2.54398 | −0.0832416 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.860159 | −0.0281152 | ||||||||
\(937\) | −26.0794 | −0.851975 | −0.425988 | − | 0.904729i | \(-0.640073\pi\) | ||||
−0.425988 | + | 0.904729i | \(0.640073\pi\) | |||||||
\(938\) | 5.25160 | 0.171471 | ||||||||
\(939\) | 10.2052 | 0.333034 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.0611 | −0.751771 | −0.375885 | − | 0.926666i | \(-0.622661\pi\) | ||||
−0.375885 | + | 0.926666i | \(0.622661\pi\) | |||||||
\(942\) | 12.5726 | 0.409638 | ||||||||
\(943\) | −14.8640 | −0.484039 | ||||||||
\(944\) | 49.2982 | 1.60452 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.03826 | −0.228834 | ||||||||
\(947\) | 37.2266 | 1.20970 | 0.604851 | − | 0.796339i | \(-0.293233\pi\) | ||||
0.604851 | + | 0.796339i | \(0.293233\pi\) | |||||||
\(948\) | 14.4910 | 0.470646 | ||||||||
\(949\) | −56.5676 | −1.83626 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 46.7319 | 1.51539 | ||||||||
\(952\) | −6.10107 | −0.197737 | ||||||||
\(953\) | −23.0528 | −0.746753 | −0.373377 | − | 0.927680i | \(-0.621800\pi\) | ||||
−0.373377 | + | 0.927680i | \(0.621800\pi\) | |||||||
\(954\) | −2.19843 | −0.0711767 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 31.6377 | 1.02324 | ||||||||
\(957\) | 35.4538 | 1.14606 | ||||||||
\(958\) | −3.10869 | −0.100437 | ||||||||
\(959\) | −7.76463 | −0.250733 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 80.7187 | 2.60383 | ||||||||
\(962\) | 5.82887 | 0.187930 | ||||||||
\(963\) | −0.587889 | −0.0189445 | ||||||||
\(964\) | 1.39329 | 0.0448749 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.01515 | 0.257883 | ||||||||
\(967\) | 29.7340 | 0.956181 | 0.478090 | − | 0.878311i | \(-0.341329\pi\) | ||||
0.478090 | + | 0.878311i | \(0.341329\pi\) | |||||||
\(968\) | −5.10729 | −0.164154 | ||||||||
\(969\) | 4.29049 | 0.137831 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0126 | −0.513868 | −0.256934 | − | 0.966429i | \(-0.582712\pi\) | ||||
−0.256934 | + | 0.966429i | \(0.582712\pi\) | |||||||
\(972\) | −1.74868 | −0.0560888 | ||||||||
\(973\) | −0.348827 | −0.0111829 | ||||||||
\(974\) | −59.2037 | −1.89701 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44.2756 | 1.41723 | ||||||||
\(977\) | 16.8004 | 0.537493 | 0.268747 | − | 0.963211i | \(-0.413391\pi\) | ||||
0.268747 | + | 0.963211i | \(0.413391\pi\) | |||||||
\(978\) | −7.84553 | −0.250872 | ||||||||
\(979\) | 5.76840 | 0.184359 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.24312 | −0.0396897 | ||||||||
\(982\) | 67.4903 | 2.15370 | ||||||||
\(983\) | −19.1223 | −0.609908 | −0.304954 | − | 0.952367i | \(-0.598641\pi\) | ||||
−0.304954 | + | 0.952367i | \(0.598641\pi\) | |||||||
\(984\) | 16.9343 | 0.539846 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −53.7857 | −1.71289 | ||||||||
\(987\) | −18.1635 | −0.578150 | ||||||||
\(988\) | 6.33202 | 0.201448 | ||||||||
\(989\) | 2.50805 | 0.0797513 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.1892 | −0.323670 | −0.161835 | − | 0.986818i | \(-0.551741\pi\) | ||||
−0.161835 | + | 0.986818i | \(0.551741\pi\) | |||||||
\(992\) | 70.7144 | 2.24518 | ||||||||
\(993\) | −0.420857 | −0.0133555 | ||||||||
\(994\) | 26.8880 | 0.852837 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.97533 | 0.0625908 | ||||||||
\(997\) | −16.0609 | −0.508652 | −0.254326 | − | 0.967118i | \(-0.581854\pi\) | ||||
−0.254326 | + | 0.967118i | \(0.581854\pi\) | |||||||
\(998\) | −70.5415 | −2.23295 | ||||||||
\(999\) | −2.63096 | −0.0832399 |
(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 | 6025.2.a.p.1.9 | 46 | ||
5.2 | odd | 4 | 1205.2.b.c.724.9 | ✓ | 46 | ||
5.3 | odd | 4 | 1205.2.b.c.724.38 | yes | 46 | ||
5.4 | even | 2 | inner | 6025.2.a.p.1.38 | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.c.724.9 | ✓ | 46 | 5.2 | odd | 4 | ||
1205.2.b.c.724.38 | yes | 46 | 5.3 | odd | 4 | ||
6025.2.a.p.1.9 | 46 | 1.1 | even | 1 | trivial | ||
6025.2.a.p.1.38 | 46 | 5.4 | even | 2 | inner |