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: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} - 372 x^{4} + 146 x^{3} + 116 x^{2} - 12 x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.27342\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27342 | −0.900447 | −0.450224 | − | 0.892916i | \(-0.648656\pi\) | ||||
−0.450224 | + | 0.892916i | \(0.648656\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.378389 | −0.189195 | ||||||||
\(5\) | 2.08575 | 0.932774 | 0.466387 | − | 0.884581i | \(-0.345555\pi\) | ||||
0.466387 | + | 0.884581i | \(0.345555\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.02870 | 1.07081 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.65604 | −0.839914 | ||||||||
\(11\) | 2.11092 | 0.636467 | 0.318233 | − | 0.948012i | \(-0.396910\pi\) | ||||
0.318233 | + | 0.948012i | \(0.396910\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46613 | −0.961331 | −0.480666 | − | 0.876904i | \(-0.659605\pi\) | ||||
−0.480666 | + | 0.876904i | \(0.659605\pi\) | |||||||
\(14\) | −1.27342 | −0.340337 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.10004 | −0.775011 | ||||||||
\(17\) | −5.03226 | −1.22050 | −0.610252 | − | 0.792208i | \(-0.708932\pi\) | ||||
−0.610252 | + | 0.792208i | \(0.708932\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.224274 | 0.0514520 | 0.0257260 | − | 0.999669i | \(-0.491810\pi\) | ||||
0.0257260 | + | 0.999669i | \(0.491810\pi\) | |||||||
\(20\) | −0.789224 | −0.176476 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.68810 | −0.573105 | ||||||||
\(23\) | 7.75804 | 1.61766 | 0.808832 | − | 0.588040i | \(-0.200100\pi\) | ||||
0.808832 | + | 0.588040i | \(0.200100\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.649667 | −0.129933 | ||||||||
\(26\) | 4.41385 | 0.865628 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.378389 | −0.0715088 | ||||||||
\(29\) | −5.57528 | −1.03530 | −0.517651 | − | 0.855592i | \(-0.673194\pi\) | ||||
−0.517651 | + | 0.855592i | \(0.673194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.678920 | −0.121938 | −0.0609688 | − | 0.998140i | \(-0.519419\pi\) | ||||
−0.0609688 | + | 0.998140i | \(0.519419\pi\) | |||||||
\(32\) | −2.10973 | −0.372951 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.40821 | 1.09900 | ||||||||
\(35\) | 2.08575 | 0.352555 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9322 | 1.79725 | 0.898625 | − | 0.438718i | \(-0.144567\pi\) | ||||
0.898625 | + | 0.438718i | \(0.144567\pi\) | |||||||
\(38\) | −0.285596 | −0.0463299 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.31710 | 0.998821 | ||||||||
\(41\) | −1.33740 | −0.208867 | −0.104433 | − | 0.994532i | \(-0.533303\pi\) | ||||
−0.104433 | + | 0.994532i | \(0.533303\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.86968 | −0.895118 | −0.447559 | − | 0.894254i | \(-0.647707\pi\) | ||||
−0.447559 | + | 0.894254i | \(0.647707\pi\) | |||||||
\(44\) | −0.798750 | −0.120416 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.87928 | −1.45662 | ||||||||
\(47\) | −0.612915 | −0.0894028 | −0.0447014 | − | 0.999000i | \(-0.514234\pi\) | ||||
−0.0447014 | + | 0.999000i | \(0.514234\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.827302 | 0.116998 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.31155 | 0.181879 | ||||||||
\(53\) | −9.19649 | −1.26324 | −0.631618 | − | 0.775280i | \(-0.717609\pi\) | ||||
−0.631618 | + | 0.775280i | \(0.717609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.40284 | 0.593679 | ||||||||
\(56\) | 3.02870 | 0.404727 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.09970 | 0.932236 | ||||||||
\(59\) | −9.06930 | −1.18072 | −0.590361 | − | 0.807139i | \(-0.701015\pi\) | ||||
−0.590361 | + | 0.807139i | \(0.701015\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.604535 | 0.0774028 | 0.0387014 | − | 0.999251i | \(-0.487678\pi\) | ||||
0.0387014 | + | 0.999251i | \(0.487678\pi\) | |||||||
\(62\) | 0.864553 | 0.109798 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.88667 | 1.11083 | ||||||||
\(65\) | −7.22946 | −0.896704 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.65675 | −0.202404 | −0.101202 | − | 0.994866i | \(-0.532269\pi\) | ||||
−0.101202 | + | 0.994866i | \(0.532269\pi\) | |||||||
\(68\) | 1.90415 | 0.230913 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.65604 | −0.317457 | ||||||||
\(71\) | 7.12563 | 0.845657 | 0.422829 | − | 0.906210i | \(-0.361037\pi\) | ||||
0.422829 | + | 0.906210i | \(0.361037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.49595 | −0.877335 | −0.438667 | − | 0.898650i | \(-0.644549\pi\) | ||||
−0.438667 | + | 0.898650i | \(0.644549\pi\) | |||||||
\(74\) | −13.9214 | −1.61833 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0848630 | −0.00973445 | ||||||||
\(77\) | 2.11092 | 0.240562 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.41599 | 0.609346 | 0.304673 | − | 0.952457i | \(-0.401453\pi\) | ||||
0.304673 | + | 0.952457i | \(0.401453\pi\) | |||||||
\(80\) | −6.46590 | −0.722910 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.70308 | 0.188074 | ||||||||
\(83\) | −5.01259 | −0.550204 | −0.275102 | − | 0.961415i | \(-0.588712\pi\) | ||||
−0.275102 | + | 0.961415i | \(0.588712\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.4960 | −1.13845 | ||||||||
\(86\) | 7.47460 | 0.806007 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.39335 | 0.681533 | ||||||||
\(89\) | −8.62166 | −0.913894 | −0.456947 | − | 0.889494i | \(-0.651057\pi\) | ||||
−0.456947 | + | 0.889494i | \(0.651057\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.46613 | −0.363349 | ||||||||
\(92\) | −2.93556 | −0.306053 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.780501 | 0.0805025 | ||||||||
\(95\) | 0.467779 | 0.0479931 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.43694 | 0.653572 | 0.326786 | − | 0.945098i | \(-0.394034\pi\) | ||||
0.326786 | + | 0.945098i | \(0.394034\pi\) | |||||||
\(98\) | −1.27342 | −0.128635 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.245827 | 0.0245827 | ||||||||
\(101\) | −12.0226 | −1.19629 | −0.598145 | − | 0.801388i | \(-0.704095\pi\) | ||||
−0.598145 | + | 0.801388i | \(0.704095\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.25231 | 0.911657 | 0.455829 | − | 0.890068i | \(-0.349343\pi\) | ||||
0.455829 | + | 0.890068i | \(0.349343\pi\) | |||||||
\(104\) | −10.4979 | −1.02940 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.7110 | 1.13748 | ||||||||
\(107\) | −10.2336 | −0.989324 | −0.494662 | − | 0.869085i | \(-0.664708\pi\) | ||||
−0.494662 | + | 0.869085i | \(0.664708\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.22482 | −0.883577 | −0.441789 | − | 0.897119i | \(-0.645656\pi\) | ||||
−0.441789 | + | 0.897119i | \(0.645656\pi\) | |||||||
\(110\) | −5.60669 | −0.534577 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.10004 | −0.292927 | ||||||||
\(113\) | −16.8813 | −1.58806 | −0.794032 | − | 0.607876i | \(-0.792022\pi\) | ||||
−0.794032 | + | 0.607876i | \(0.792022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.1813 | 1.50891 | ||||||||
\(116\) | 2.10962 | 0.195874 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.5491 | 1.06318 | ||||||||
\(119\) | −5.03226 | −0.461307 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.54401 | −0.594910 | ||||||||
\(122\) | −0.769830 | −0.0696971 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.256896 | 0.0230699 | ||||||||
\(125\) | −11.7838 | −1.05397 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −7.09705 | −0.627296 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.20618 | 0.807435 | ||||||||
\(131\) | −1.55514 | −0.135874 | −0.0679368 | − | 0.997690i | \(-0.521642\pi\) | ||||
−0.0679368 | + | 0.997690i | \(0.521642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.224274 | 0.0194470 | ||||||||
\(134\) | 2.10975 | 0.182254 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.2412 | −1.30692 | ||||||||
\(137\) | 6.31696 | 0.539694 | 0.269847 | − | 0.962903i | \(-0.413027\pi\) | ||||
0.269847 | + | 0.962903i | \(0.413027\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4399 | 1.39441 | 0.697205 | − | 0.716872i | \(-0.254427\pi\) | ||||
0.697205 | + | 0.716872i | \(0.254427\pi\) | |||||||
\(140\) | −0.789224 | −0.0667016 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.07396 | −0.761470 | ||||||||
\(143\) | −7.31672 | −0.611855 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6286 | −0.965703 | ||||||||
\(146\) | 9.54553 | 0.789994 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.13664 | −0.340030 | ||||||||
\(149\) | 8.62637 | 0.706700 | 0.353350 | − | 0.935491i | \(-0.385042\pi\) | ||||
0.353350 | + | 0.935491i | \(0.385042\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.7050 | −1.76632 | −0.883162 | − | 0.469068i | \(-0.844590\pi\) | ||||
−0.883162 | + | 0.469068i | \(0.844590\pi\) | |||||||
\(152\) | 0.679259 | 0.0550952 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.68810 | −0.216613 | ||||||||
\(155\) | −1.41605 | −0.113740 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.92251 | 0.791902 | 0.395951 | − | 0.918272i | \(-0.370415\pi\) | ||||
0.395951 | + | 0.918272i | \(0.370415\pi\) | |||||||
\(158\) | −6.89685 | −0.548684 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.40035 | −0.347879 | ||||||||
\(161\) | 7.75804 | 0.611419 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0861 | −0.790005 | −0.395003 | − | 0.918680i | \(-0.629256\pi\) | ||||
−0.395003 | + | 0.918680i | \(0.629256\pi\) | |||||||
\(164\) | 0.506058 | 0.0395165 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.38316 | 0.495429 | ||||||||
\(167\) | 2.52578 | 0.195451 | 0.0977254 | − | 0.995213i | \(-0.468843\pi\) | ||||
0.0977254 | + | 0.995213i | \(0.468843\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.985951 | −0.0758424 | ||||||||
\(170\) | 13.3659 | 1.02512 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.22102 | 0.169352 | ||||||||
\(173\) | −10.7804 | −0.819618 | −0.409809 | − | 0.912171i | \(-0.634405\pi\) | ||||
−0.409809 | + | 0.912171i | \(0.634405\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.649667 | −0.0491102 | ||||||||
\(176\) | −6.54394 | −0.493268 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.9790 | 0.822913 | ||||||||
\(179\) | 21.7204 | 1.62346 | 0.811728 | − | 0.584036i | \(-0.198527\pi\) | ||||
0.811728 | + | 0.584036i | \(0.198527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.87464 | 0.436659 | 0.218329 | − | 0.975875i | \(-0.429939\pi\) | ||||
0.218329 | + | 0.975875i | \(0.429939\pi\) | |||||||
\(182\) | 4.41385 | 0.327177 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 23.4968 | 1.73221 | ||||||||
\(185\) | 22.8019 | 1.67643 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.6227 | −0.776809 | ||||||||
\(188\) | 0.231920 | 0.0169145 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.595681 | −0.0432153 | ||||||||
\(191\) | −8.92458 | −0.645760 | −0.322880 | − | 0.946440i | \(-0.604651\pi\) | ||||
−0.322880 | + | 0.946440i | \(0.604651\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.3225 | −1.67879 | −0.839396 | − | 0.543521i | \(-0.817091\pi\) | ||||
−0.839396 | + | 0.543521i | \(0.817091\pi\) | |||||||
\(194\) | −8.19696 | −0.588507 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.378389 | −0.0270278 | ||||||||
\(197\) | −19.0659 | −1.35839 | −0.679195 | − | 0.733957i | \(-0.737671\pi\) | ||||
−0.679195 | + | 0.733957i | \(0.737671\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.14093 | 0.506207 | 0.253104 | − | 0.967439i | \(-0.418549\pi\) | ||||
0.253104 | + | 0.967439i | \(0.418549\pi\) | |||||||
\(200\) | −1.96765 | −0.139134 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.3098 | 1.07720 | ||||||||
\(203\) | −5.57528 | −0.391308 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.78948 | −0.194825 | ||||||||
\(206\) | −11.7821 | −0.820900 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.7451 | 0.745042 | ||||||||
\(209\) | 0.473425 | 0.0327475 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.8604 | 0.747664 | 0.373832 | − | 0.927496i | \(-0.378044\pi\) | ||||
0.373832 | + | 0.927496i | \(0.378044\pi\) | |||||||
\(212\) | 3.47985 | 0.238997 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.0318 | 0.890834 | ||||||||
\(215\) | −12.2427 | −0.834943 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.678920 | −0.0460881 | ||||||||
\(218\) | 11.7471 | 0.795615 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.66599 | −0.112321 | ||||||||
\(221\) | 17.4425 | 1.17331 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.1985 | 1.75438 | 0.877190 | − | 0.480144i | \(-0.159416\pi\) | ||||
0.877190 | + | 0.480144i | \(0.159416\pi\) | |||||||
\(224\) | −2.10973 | −0.140962 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.4971 | 1.42997 | ||||||||
\(227\) | 1.57740 | 0.104696 | 0.0523480 | − | 0.998629i | \(-0.483329\pi\) | ||||
0.0523480 | + | 0.998629i | \(0.483329\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.07326 | −0.401333 | −0.200666 | − | 0.979660i | \(-0.564311\pi\) | ||||
−0.200666 | + | 0.979660i | \(0.564311\pi\) | |||||||
\(230\) | −20.6057 | −1.35870 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.8858 | −1.10861 | ||||||||
\(233\) | 2.10427 | 0.137856 | 0.0689278 | − | 0.997622i | \(-0.478042\pi\) | ||||
0.0689278 | + | 0.997622i | \(0.478042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.27838 | −0.0833926 | ||||||||
\(236\) | 3.43173 | 0.223386 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.40821 | 0.415383 | ||||||||
\(239\) | −22.6997 | −1.46832 | −0.734161 | − | 0.678976i | \(-0.762424\pi\) | ||||
−0.734161 | + | 0.678976i | \(0.762424\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.8242 | 1.47023 | 0.735117 | − | 0.677941i | \(-0.237127\pi\) | ||||
0.735117 | + | 0.677941i | \(0.237127\pi\) | |||||||
\(242\) | 8.33331 | 0.535685 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.228750 | −0.0146442 | ||||||||
\(245\) | 2.08575 | 0.133253 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.777364 | −0.0494625 | ||||||||
\(248\) | −2.05624 | −0.130572 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.0057 | 0.949046 | ||||||||
\(251\) | −0.360572 | −0.0227591 | −0.0113795 | − | 0.999935i | \(-0.503622\pi\) | ||||
−0.0113795 | + | 0.999935i | \(0.503622\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.3766 | 1.02959 | ||||||||
\(254\) | 1.27342 | 0.0799018 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.73578 | −0.545986 | ||||||||
\(257\) | 11.3934 | 0.710700 | 0.355350 | − | 0.934733i | \(-0.384362\pi\) | ||||
0.355350 | + | 0.934733i | \(0.384362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.9322 | 0.679296 | ||||||||
\(260\) | 2.73555 | 0.169652 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.98036 | 0.122347 | ||||||||
\(263\) | 26.8294 | 1.65437 | 0.827187 | − | 0.561926i | \(-0.189940\pi\) | ||||
0.827187 | + | 0.561926i | \(0.189940\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.1815 | −1.17831 | ||||||||
\(266\) | −0.285596 | −0.0175110 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.626896 | 0.0382938 | ||||||||
\(269\) | 29.0339 | 1.77023 | 0.885113 | − | 0.465377i | \(-0.154081\pi\) | ||||
0.885113 | + | 0.465377i | \(0.154081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7987 | −0.777464 | −0.388732 | − | 0.921351i | \(-0.627087\pi\) | ||||
−0.388732 | + | 0.921351i | \(0.627087\pi\) | |||||||
\(272\) | 15.6002 | 0.945903 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.04417 | −0.485966 | ||||||||
\(275\) | −1.37140 | −0.0826983 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.1286 | −0.668655 | −0.334327 | − | 0.942457i | \(-0.608509\pi\) | ||||
−0.334327 | + | 0.942457i | \(0.608509\pi\) | |||||||
\(278\) | −20.9349 | −1.25559 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.31710 | 0.377519 | ||||||||
\(281\) | −26.3268 | −1.57052 | −0.785262 | − | 0.619164i | \(-0.787472\pi\) | ||||
−0.785262 | + | 0.619164i | \(0.787472\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.23400 | −0.192241 | −0.0961207 | − | 0.995370i | \(-0.530643\pi\) | ||||
−0.0961207 | + | 0.995370i | \(0.530643\pi\) | |||||||
\(284\) | −2.69626 | −0.159994 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.31730 | 0.550943 | ||||||||
\(287\) | −1.33740 | −0.0789442 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.32368 | 0.489628 | ||||||||
\(290\) | 14.8082 | 0.869565 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.83639 | 0.165987 | ||||||||
\(293\) | 23.3615 | 1.36479 | 0.682396 | − | 0.730982i | \(-0.260938\pi\) | ||||
0.682396 | + | 0.730982i | \(0.260938\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.9163 | −1.10135 | ||||||||
\(296\) | 33.1105 | 1.92451 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.9850 | −0.636346 | ||||||||
\(299\) | −26.8904 | −1.55511 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.86968 | −0.338323 | ||||||||
\(302\) | 27.6396 | 1.59048 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.695260 | −0.0398759 | ||||||||
\(305\) | 1.26091 | 0.0721993 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.9099 | 1.82119 | 0.910596 | − | 0.413297i | \(-0.135623\pi\) | ||||
0.910596 | + | 0.413297i | \(0.135623\pi\) | |||||||
\(308\) | −0.798750 | −0.0455130 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.80324 | 0.102417 | ||||||||
\(311\) | 27.5284 | 1.56099 | 0.780496 | − | 0.625160i | \(-0.214966\pi\) | ||||
0.780496 | + | 0.625160i | \(0.214966\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.7307 | −1.17177 | −0.585886 | − | 0.810394i | \(-0.699253\pi\) | ||||
−0.585886 | + | 0.810394i | \(0.699253\pi\) | |||||||
\(314\) | −12.6356 | −0.713066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.04935 | −0.115285 | ||||||||
\(317\) | −3.97581 | −0.223304 | −0.111652 | − | 0.993747i | \(-0.535614\pi\) | ||||
−0.111652 | + | 0.993747i | \(0.535614\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7690 | −0.658936 | ||||||||
\(320\) | 18.5353 | 1.03616 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.87928 | −0.550551 | ||||||||
\(323\) | −1.12861 | −0.0627974 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.25183 | 0.124909 | ||||||||
\(326\) | 12.8439 | 0.711358 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.05058 | −0.223656 | ||||||||
\(329\) | −0.612915 | −0.0337911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.45118 | −0.354589 | −0.177295 | − | 0.984158i | \(-0.556735\pi\) | ||||
−0.177295 | + | 0.984158i | \(0.556735\pi\) | |||||||
\(332\) | 1.89671 | 0.104096 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.21639 | −0.175993 | ||||||||
\(335\) | −3.45556 | −0.188797 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.4825 | −1.27917 | −0.639586 | − | 0.768720i | \(-0.720894\pi\) | ||||
−0.639586 | + | 0.768720i | \(0.720894\pi\) | |||||||
\(338\) | 1.25553 | 0.0682921 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.97158 | 0.215389 | ||||||||
\(341\) | −1.43315 | −0.0776092 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −17.7775 | −0.958499 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.7280 | 0.738023 | ||||||||
\(347\) | −19.3384 | −1.03814 | −0.519070 | − | 0.854732i | \(-0.673722\pi\) | ||||
−0.519070 | + | 0.854732i | \(0.673722\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.9941 | 0.963204 | 0.481602 | − | 0.876390i | \(-0.340055\pi\) | ||||
0.481602 | + | 0.876390i | \(0.340055\pi\) | |||||||
\(350\) | 0.827302 | 0.0442212 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.45347 | −0.237371 | ||||||||
\(353\) | −32.3822 | −1.72353 | −0.861765 | − | 0.507307i | \(-0.830641\pi\) | ||||
−0.861765 | + | 0.507307i | \(0.830641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.8623 | 0.788807 | ||||||||
\(356\) | 3.26234 | 0.172904 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −27.6592 | −1.46184 | ||||||||
\(359\) | 7.91949 | 0.417975 | 0.208987 | − | 0.977918i | \(-0.432983\pi\) | ||||
0.208987 | + | 0.977918i | \(0.432983\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9497 | −0.997353 | ||||||||
\(362\) | −7.48091 | −0.393188 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.31155 | 0.0687437 | ||||||||
\(365\) | −15.6346 | −0.818355 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.4206 | 1.43134 | 0.715672 | − | 0.698436i | \(-0.246120\pi\) | ||||
0.715672 | + | 0.698436i | \(0.246120\pi\) | |||||||
\(368\) | −24.0503 | −1.25371 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −29.0365 | −1.50953 | ||||||||
\(371\) | −9.19649 | −0.477458 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.79509 | 0.196502 | 0.0982511 | − | 0.995162i | \(-0.468675\pi\) | ||||
0.0982511 | + | 0.995162i | \(0.468675\pi\) | |||||||
\(374\) | 13.5272 | 0.699476 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.85633 | −0.0957331 | ||||||||
\(377\) | 19.3246 | 0.995269 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.9912 | −1.84874 | −0.924371 | − | 0.381494i | \(-0.875410\pi\) | ||||
−0.924371 | + | 0.381494i | \(0.875410\pi\) | |||||||
\(380\) | −0.177003 | −0.00908004 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.3648 | 0.581473 | ||||||||
\(383\) | 1.34990 | 0.0689768 | 0.0344884 | − | 0.999405i | \(-0.489020\pi\) | ||||
0.0344884 | + | 0.999405i | \(0.489020\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.40284 | 0.224390 | ||||||||
\(386\) | 29.6995 | 1.51166 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.43567 | −0.123652 | ||||||||
\(389\) | 3.58741 | 0.181889 | 0.0909445 | − | 0.995856i | \(-0.471011\pi\) | ||||
0.0909445 | + | 0.995856i | \(0.471011\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.0405 | −1.97436 | ||||||||
\(392\) | 3.02870 | 0.152972 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.2790 | 1.22316 | ||||||||
\(395\) | 11.2964 | 0.568382 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.38007 | 0.420584 | 0.210292 | − | 0.977639i | \(-0.432559\pi\) | ||||
0.210292 | + | 0.977639i | \(0.432559\pi\) | |||||||
\(398\) | −9.09344 | −0.455813 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.01400 | 0.100700 | ||||||||
\(401\) | −9.89210 | −0.493988 | −0.246994 | − | 0.969017i | \(-0.579443\pi\) | ||||
−0.246994 | + | 0.969017i | \(0.579443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.35322 | 0.117222 | ||||||||
\(404\) | 4.54921 | 0.226332 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.09970 | 0.352352 | ||||||||
\(407\) | 23.0771 | 1.14389 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.56659 | −0.225804 | −0.112902 | − | 0.993606i | \(-0.536015\pi\) | ||||
−0.112902 | + | 0.993606i | \(0.536015\pi\) | |||||||
\(410\) | 3.55219 | 0.175430 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.50098 | −0.172481 | ||||||||
\(413\) | −9.06930 | −0.446271 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.4550 | −0.513215 | ||||||||
\(416\) | 7.31259 | 0.358529 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.602871 | −0.0294874 | ||||||||
\(419\) | 0.445636 | 0.0217707 | 0.0108854 | − | 0.999941i | \(-0.496535\pi\) | ||||
0.0108854 | + | 0.999941i | \(0.496535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.72563 | 0.376524 | 0.188262 | − | 0.982119i | \(-0.439715\pi\) | ||||
0.188262 | + | 0.982119i | \(0.439715\pi\) | |||||||
\(422\) | −13.8300 | −0.673232 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −27.8534 | −1.35268 | ||||||||
\(425\) | 3.26930 | 0.158584 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.604535 | 0.0292555 | ||||||||
\(428\) | 3.87230 | 0.187175 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.5901 | 0.751822 | ||||||||
\(431\) | −33.6636 | −1.62152 | −0.810760 | − | 0.585379i | \(-0.800946\pi\) | ||||
−0.810760 | + | 0.585379i | \(0.800946\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.2388 | −1.06873 | −0.534364 | − | 0.845255i | \(-0.679449\pi\) | ||||
−0.534364 | + | 0.845255i | \(0.679449\pi\) | |||||||
\(434\) | 0.864553 | 0.0414999 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.49057 | 0.167168 | ||||||||
\(437\) | 1.73993 | 0.0832321 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.92254 | −0.139485 | −0.0697425 | − | 0.997565i | \(-0.522218\pi\) | ||||
−0.0697425 | + | 0.997565i | \(0.522218\pi\) | |||||||
\(440\) | 13.3349 | 0.635716 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.2117 | −1.05650 | ||||||||
\(443\) | −1.86532 | −0.0886242 | −0.0443121 | − | 0.999018i | \(-0.514110\pi\) | ||||
−0.0443121 | + | 0.999018i | \(0.514110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.9826 | −0.852456 | ||||||||
\(446\) | −33.3618 | −1.57973 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.88667 | 0.419856 | ||||||||
\(449\) | −8.85530 | −0.417908 | −0.208954 | − | 0.977926i | \(-0.567006\pi\) | ||||
−0.208954 | + | 0.977926i | \(0.567006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.82314 | −0.132937 | ||||||||
\(452\) | 6.38772 | 0.300453 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.00871 | −0.0942732 | ||||||||
\(455\) | −7.22946 | −0.338922 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.9290 | 1.54035 | 0.770177 | − | 0.637830i | \(-0.220168\pi\) | ||||
0.770177 | + | 0.637830i | \(0.220168\pi\) | |||||||
\(458\) | 7.73384 | 0.361379 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.12283 | −0.285478 | ||||||||
\(461\) | −24.4113 | −1.13695 | −0.568474 | − | 0.822701i | \(-0.692466\pi\) | ||||
−0.568474 | + | 0.822701i | \(0.692466\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.9222 | −1.39060 | −0.695300 | − | 0.718719i | \(-0.744729\pi\) | ||||
−0.695300 | + | 0.718719i | \(0.744729\pi\) | |||||||
\(464\) | 17.2836 | 0.802371 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.67963 | −0.124132 | ||||||||
\(467\) | −14.9090 | −0.689905 | −0.344952 | − | 0.938620i | \(-0.612105\pi\) | ||||
−0.344952 | + | 0.938620i | \(0.612105\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.65675 | −0.0765016 | ||||||||
\(470\) | 1.62793 | 0.0750906 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −27.4682 | −1.26433 | ||||||||
\(473\) | −12.3904 | −0.569713 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.145704 | −0.00668534 | ||||||||
\(476\) | 1.90415 | 0.0872768 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 28.9064 | 1.32215 | ||||||||
\(479\) | 10.2536 | 0.468497 | 0.234249 | − | 0.972177i | \(-0.424737\pi\) | ||||
0.234249 | + | 0.972177i | \(0.424737\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.8926 | −1.72775 | ||||||||
\(482\) | −29.0649 | −1.32387 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.47618 | 0.112554 | ||||||||
\(485\) | 13.4258 | 0.609635 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5403 | 0.613569 | 0.306784 | − | 0.951779i | \(-0.400747\pi\) | ||||
0.306784 | + | 0.951779i | \(0.400747\pi\) | |||||||
\(488\) | 1.83095 | 0.0828834 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.65604 | −0.119988 | ||||||||
\(491\) | −9.12846 | −0.411962 | −0.205981 | − | 0.978556i | \(-0.566038\pi\) | ||||
−0.205981 | + | 0.978556i | \(0.566038\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.0563 | 1.26359 | ||||||||
\(494\) | 0.989914 | 0.0445383 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.10468 | 0.0945029 | ||||||||
\(497\) | 7.12563 | 0.319628 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.3752 | 1.35978 | 0.679890 | − | 0.733314i | \(-0.262028\pi\) | ||||
0.679890 | + | 0.733314i | \(0.262028\pi\) | |||||||
\(500\) | 4.45885 | 0.199406 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.459161 | 0.0204934 | ||||||||
\(503\) | −34.1012 | −1.52050 | −0.760250 | − | 0.649631i | \(-0.774923\pi\) | ||||
−0.760250 | + | 0.649631i | \(0.774923\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.0760 | −1.11587 | ||||||||
\(506\) | −20.8544 | −0.927090 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.378389 | 0.0167883 | ||||||||
\(509\) | 28.9661 | 1.28390 | 0.641951 | − | 0.766746i | \(-0.278125\pi\) | ||||
0.641951 | + | 0.766746i | \(0.278125\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.49595 | −0.331601 | ||||||||
\(512\) | 25.3184 | 1.11893 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.5086 | −0.639948 | ||||||||
\(515\) | 19.2980 | 0.850370 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.29381 | −0.0569019 | ||||||||
\(518\) | −13.9214 | −0.611671 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −21.8959 | −0.960197 | ||||||||
\(521\) | −19.5947 | −0.858461 | −0.429231 | − | 0.903195i | \(-0.641215\pi\) | ||||
−0.429231 | + | 0.903195i | \(0.641215\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.2890 | 0.843448 | 0.421724 | − | 0.906724i | \(-0.361425\pi\) | ||||
0.421724 | + | 0.906724i | \(0.361425\pi\) | |||||||
\(524\) | 0.588450 | 0.0257066 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.1653 | −1.48968 | ||||||||
\(527\) | 3.41650 | 0.148825 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.1872 | 1.61684 | ||||||||
\(530\) | 24.4263 | 1.06101 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.0848630 | −0.00367928 | ||||||||
\(533\) | 4.63560 | 0.200790 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.3448 | −0.922815 | ||||||||
\(536\) | −5.01780 | −0.216736 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −36.9724 | −1.59399 | ||||||||
\(539\) | 2.11092 | 0.0909238 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.87389 | −0.123558 | −0.0617792 | − | 0.998090i | \(-0.519677\pi\) | ||||
−0.0617792 | + | 0.998090i | \(0.519677\pi\) | |||||||
\(542\) | 16.2981 | 0.700065 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.6167 | 0.455188 | ||||||||
\(545\) | −19.2406 | −0.824177 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.9189 | −1.10821 | −0.554105 | − | 0.832447i | \(-0.686939\pi\) | ||||
−0.554105 | + | 0.832447i | \(0.686939\pi\) | |||||||
\(548\) | −2.39027 | −0.102107 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.74637 | 0.0744654 | ||||||||
\(551\) | −1.25039 | −0.0532684 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.41599 | 0.230311 | ||||||||
\(554\) | 14.1715 | 0.602088 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.22066 | −0.263815 | ||||||||
\(557\) | −37.5358 | −1.59044 | −0.795222 | − | 0.606319i | \(-0.792646\pi\) | ||||
−0.795222 | + | 0.606319i | \(0.792646\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.3451 | 0.860505 | ||||||||
\(560\) | −6.46590 | −0.273234 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.5252 | 1.41417 | ||||||||
\(563\) | 39.2104 | 1.65252 | 0.826260 | − | 0.563289i | \(-0.190464\pi\) | ||||
0.826260 | + | 0.563289i | \(0.190464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.2102 | −1.48130 | ||||||||
\(566\) | 4.11826 | 0.173103 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.5814 | 0.905536 | ||||||||
\(569\) | −35.4013 | −1.48410 | −0.742050 | − | 0.670344i | \(-0.766146\pi\) | ||||
−0.742050 | + | 0.670344i | \(0.766146\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.89890 | −0.121315 | −0.0606576 | − | 0.998159i | \(-0.519320\pi\) | ||||
−0.0606576 | + | 0.998159i | \(0.519320\pi\) | |||||||
\(572\) | 2.76857 | 0.115760 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.70308 | 0.0710851 | ||||||||
\(575\) | −5.04014 | −0.210189 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.5791 | −0.939978 | −0.469989 | − | 0.882672i | \(-0.655742\pi\) | ||||
−0.469989 | + | 0.882672i | \(0.655742\pi\) | |||||||
\(578\) | −10.5996 | −0.440884 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.40014 | 0.182706 | ||||||||
\(581\) | −5.01259 | −0.207957 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.4131 | −0.804007 | ||||||||
\(584\) | −22.7030 | −0.939456 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.7491 | −1.22892 | ||||||||
\(587\) | −14.5897 | −0.602181 | −0.301091 | − | 0.953596i | \(-0.597351\pi\) | ||||
−0.301091 | + | 0.953596i | \(0.597351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.152264 | −0.00627394 | ||||||||
\(590\) | 24.0884 | 0.991705 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −33.8904 | −1.39289 | ||||||||
\(593\) | 16.4282 | 0.674627 | 0.337314 | − | 0.941392i | \(-0.390482\pi\) | ||||
0.337314 | + | 0.941392i | \(0.390482\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4960 | −0.430295 | ||||||||
\(596\) | −3.26413 | −0.133704 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34.2429 | 1.40030 | ||||||||
\(599\) | 22.5507 | 0.921395 | 0.460698 | − | 0.887557i | \(-0.347599\pi\) | ||||
0.460698 | + | 0.887557i | \(0.347599\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.7123 | −1.70148 | −0.850741 | − | 0.525586i | \(-0.823846\pi\) | ||||
−0.850741 | + | 0.525586i | \(0.823846\pi\) | |||||||
\(602\) | 7.47460 | 0.304642 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.21292 | 0.334179 | ||||||||
\(605\) | −13.6491 | −0.554917 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.02170 | 0.325591 | 0.162795 | − | 0.986660i | \(-0.447949\pi\) | ||||
0.162795 | + | 0.986660i | \(0.447949\pi\) | |||||||
\(608\) | −0.473158 | −0.0191891 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.60567 | −0.0650116 | ||||||||
\(611\) | 2.12444 | 0.0859457 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.1953 | 0.936848 | 0.468424 | − | 0.883504i | \(-0.344822\pi\) | ||||
0.468424 | + | 0.883504i | \(0.344822\pi\) | |||||||
\(614\) | −40.6348 | −1.63989 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.39335 | 0.257595 | ||||||||
\(617\) | −18.3473 | −0.738635 | −0.369317 | − | 0.929303i | \(-0.620408\pi\) | ||||
−0.369317 | + | 0.929303i | \(0.620408\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.2358 | −1.13489 | −0.567446 | − | 0.823411i | \(-0.692069\pi\) | ||||
−0.567446 | + | 0.823411i | \(0.692069\pi\) | |||||||
\(620\) | 0.535819 | 0.0215190 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −35.0554 | −1.40559 | ||||||||
\(623\) | −8.62166 | −0.345419 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.3296 | −0.853184 | ||||||||
\(626\) | 26.3990 | 1.05512 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.75457 | −0.149824 | ||||||||
\(629\) | −55.0139 | −2.19355 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.8484 | 1.46691 | 0.733455 | − | 0.679738i | \(-0.237907\pi\) | ||||
0.733455 | + | 0.679738i | \(0.237907\pi\) | |||||||
\(632\) | 16.4034 | 0.652492 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.06290 | 0.201073 | ||||||||
\(635\) | −2.08575 | −0.0827703 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.46613 | −0.137333 | ||||||||
\(638\) | 14.9869 | 0.593337 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14.8026 | −0.585125 | ||||||||
\(641\) | −36.0974 | −1.42576 | −0.712881 | − | 0.701285i | \(-0.752610\pi\) | ||||
−0.712881 | + | 0.701285i | \(0.752610\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.75159 | 0.0690760 | 0.0345380 | − | 0.999403i | \(-0.489004\pi\) | ||||
0.0345380 | + | 0.999403i | \(0.489004\pi\) | |||||||
\(644\) | −2.93556 | −0.115677 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.43720 | 0.0565457 | ||||||||
\(647\) | −5.69840 | −0.224027 | −0.112014 | − | 0.993707i | \(-0.535730\pi\) | ||||
−0.112014 | + | 0.993707i | \(0.535730\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.1446 | −0.751491 | ||||||||
\(650\) | −2.86754 | −0.112474 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.81648 | 0.149465 | ||||||||
\(653\) | −17.8696 | −0.699290 | −0.349645 | − | 0.936882i | \(-0.613698\pi\) | ||||
−0.349645 | + | 0.936882i | \(0.613698\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.24364 | −0.126739 | ||||||||
\(656\) | 4.14600 | 0.161874 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.780501 | 0.0304271 | ||||||||
\(659\) | −32.0714 | −1.24932 | −0.624662 | − | 0.780895i | \(-0.714763\pi\) | ||||
−0.624662 | + | 0.780895i | \(0.714763\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.79459 | −0.225383 | −0.112692 | − | 0.993630i | \(-0.535947\pi\) | ||||
−0.112692 | + | 0.993630i | \(0.535947\pi\) | |||||||
\(662\) | 8.21510 | 0.319289 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.1816 | −0.589162 | ||||||||
\(665\) | 0.467779 | 0.0181397 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43.2532 | −1.67477 | ||||||||
\(668\) | −0.955728 | −0.0369782 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.40039 | 0.170002 | ||||||||
\(671\) | 1.27613 | 0.0492643 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.3555 | −0.784648 | −0.392324 | − | 0.919827i | \(-0.628329\pi\) | ||||
−0.392324 | + | 0.919827i | \(0.628329\pi\) | |||||||
\(674\) | 29.9032 | 1.15183 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.373073 | 0.0143490 | ||||||||
\(677\) | −42.8044 | −1.64511 | −0.822553 | − | 0.568689i | \(-0.807451\pi\) | ||||
−0.822553 | + | 0.568689i | \(0.807451\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.43694 | 0.247027 | ||||||||
\(680\) | −31.7893 | −1.21906 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.82500 | 0.0698830 | ||||||||
\(683\) | −9.59767 | −0.367245 | −0.183622 | − | 0.982997i | \(-0.558782\pi\) | ||||
−0.183622 | + | 0.982997i | \(0.558782\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.1756 | 0.503412 | ||||||||
\(686\) | −1.27342 | −0.0486196 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.1963 | 0.693726 | ||||||||
\(689\) | 31.8762 | 1.21439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.2390 | −0.807969 | −0.403984 | − | 0.914766i | \(-0.632375\pi\) | ||||
−0.403984 | + | 0.914766i | \(0.632375\pi\) | |||||||
\(692\) | 4.07919 | 0.155067 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.6260 | 0.934791 | ||||||||
\(695\) | 34.2893 | 1.30067 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.73015 | 0.254923 | ||||||||
\(698\) | −22.9142 | −0.867315 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.245827 | 0.00929139 | ||||||||
\(701\) | −33.2723 | −1.25668 | −0.628338 | − | 0.777940i | \(-0.716265\pi\) | ||||
−0.628338 | + | 0.777940i | \(0.716265\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.45182 | 0.0924722 | ||||||||
\(704\) | 18.7590 | 0.707008 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 41.2363 | 1.55195 | ||||||||
\(707\) | −12.0226 | −0.452155 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.3845 | 1.10356 | 0.551779 | − | 0.833990i | \(-0.313949\pi\) | ||||
0.551779 | + | 0.833990i | \(0.313949\pi\) | |||||||
\(710\) | −18.9260 | −0.710279 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −26.1124 | −0.978604 | ||||||||
\(713\) | −5.26709 | −0.197254 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.2608 | −0.570722 | ||||||||
\(716\) | −8.21875 | −0.307149 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.0849 | −0.376364 | ||||||||
\(719\) | 10.3787 | 0.387059 | 0.193530 | − | 0.981094i | \(-0.438006\pi\) | ||||
0.193530 | + | 0.981094i | \(0.438006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.25231 | 0.344574 | ||||||||
\(722\) | 24.1310 | 0.898064 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.22290 | −0.0826135 | ||||||||
\(725\) | 3.62207 | 0.134520 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.7802 | 1.88333 | 0.941666 | − | 0.336549i | \(-0.109260\pi\) | ||||
0.941666 | + | 0.336549i | \(0.109260\pi\) | |||||||
\(728\) | −10.4979 | −0.389077 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19.9095 | 0.736885 | ||||||||
\(731\) | 29.5378 | 1.09249 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.5120 | 1.38554 | 0.692768 | − | 0.721161i | \(-0.256391\pi\) | ||||
0.692768 | + | 0.721161i | \(0.256391\pi\) | |||||||
\(734\) | −34.9181 | −1.28885 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.3674 | −0.603309 | ||||||||
\(737\) | −3.49727 | −0.128824 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.5500 | −1.01344 | −0.506722 | − | 0.862109i | \(-0.669143\pi\) | ||||
−0.506722 | + | 0.862109i | \(0.669143\pi\) | |||||||
\(740\) | −8.62798 | −0.317171 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.7110 | 0.429926 | ||||||||
\(743\) | 43.0316 | 1.57868 | 0.789338 | − | 0.613959i | \(-0.210424\pi\) | ||||
0.789338 | + | 0.613959i | \(0.210424\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.9924 | 0.659191 | ||||||||
\(746\) | −4.83276 | −0.176940 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.01952 | 0.146968 | ||||||||
\(749\) | −10.2336 | −0.373929 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.07746 | 0.185279 | 0.0926396 | − | 0.995700i | \(-0.470470\pi\) | ||||
0.0926396 | + | 0.995700i | \(0.470470\pi\) | |||||||
\(752\) | 1.90006 | 0.0692881 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −24.6085 | −0.896187 | ||||||||
\(755\) | −45.2710 | −1.64758 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1949 | 1.35187 | 0.675936 | − | 0.736961i | \(-0.263740\pi\) | ||||
0.675936 | + | 0.736961i | \(0.263740\pi\) | |||||||
\(758\) | 45.8321 | 1.66470 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.41676 | 0.0513914 | ||||||||
\(761\) | −33.4225 | −1.21156 | −0.605781 | − | 0.795631i | \(-0.707139\pi\) | ||||
−0.605781 | + | 0.795631i | \(0.707139\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.22482 | −0.333961 | ||||||||
\(764\) | 3.37697 | 0.122174 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.71900 | −0.0621100 | ||||||||
\(767\) | 31.4354 | 1.13507 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.3925 | 1.67296 | 0.836479 | − | 0.547999i | \(-0.184610\pi\) | ||||
0.836479 | + | 0.547999i | \(0.184610\pi\) | |||||||
\(770\) | −5.60669 | −0.202051 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.82499 | 0.317618 | ||||||||
\(773\) | −22.3827 | −0.805048 | −0.402524 | − | 0.915409i | \(-0.631867\pi\) | ||||
−0.402524 | + | 0.915409i | \(0.631867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.441072 | 0.0158438 | ||||||||
\(776\) | 19.4956 | 0.699850 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.56830 | −0.163781 | ||||||||
\(779\) | −0.299944 | −0.0107466 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.0416 | 0.538232 | ||||||||
\(782\) | 49.7152 | 1.77781 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.10004 | −0.110716 | ||||||||
\(785\) | 20.6958 | 0.738666 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.3014 | −1.25836 | −0.629179 | − | 0.777260i | \(-0.716609\pi\) | ||||
−0.629179 | + | 0.777260i | \(0.716609\pi\) | |||||||
\(788\) | 7.21434 | 0.257000 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.3851 | −0.511798 | ||||||||
\(791\) | −16.8813 | −0.600232 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.09540 | −0.0744097 | ||||||||
\(794\) | −10.6714 | −0.378713 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.70205 | −0.0957716 | ||||||||
\(797\) | 17.4912 | 0.619570 | 0.309785 | − | 0.950807i | \(-0.399743\pi\) | ||||
0.309785 | + | 0.950807i | \(0.399743\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.08435 | 0.109116 | ||||||||
\(800\) | 1.37062 | 0.0484588 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.5969 | 0.444810 | ||||||||
\(803\) | −15.8234 | −0.558394 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.1813 | 0.570316 | ||||||||
\(806\) | −2.99665 | −0.105553 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −36.4128 | −1.28100 | ||||||||
\(809\) | 52.4987 | 1.84575 | 0.922877 | − | 0.385094i | \(-0.125831\pi\) | ||||
0.922877 | + | 0.385094i | \(0.125831\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.96928 | 0.209610 | 0.104805 | − | 0.994493i | \(-0.466578\pi\) | ||||
0.104805 | + | 0.994493i | \(0.466578\pi\) | |||||||
\(812\) | 2.10962 | 0.0740333 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.3869 | −1.03001 | ||||||||
\(815\) | −21.0371 | −0.736896 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.31642 | −0.0460557 | ||||||||
\(818\) | 5.81521 | 0.203324 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.05551 | 0.0368599 | ||||||||
\(821\) | −20.6990 | −0.722399 | −0.361199 | − | 0.932489i | \(-0.617633\pi\) | ||||
−0.361199 | + | 0.932489i | \(0.617633\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.2152 | −1.33210 | −0.666050 | − | 0.745907i | \(-0.732016\pi\) | ||||
−0.666050 | + | 0.745907i | \(0.732016\pi\) | |||||||
\(824\) | 28.0225 | 0.976209 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.5491 | 0.401844 | ||||||||
\(827\) | 27.2185 | 0.946479 | 0.473239 | − | 0.880934i | \(-0.343085\pi\) | ||||
0.473239 | + | 0.880934i | \(0.343085\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.3121 | 0.392886 | 0.196443 | − | 0.980515i | \(-0.437061\pi\) | ||||
0.196443 | + | 0.980515i | \(0.437061\pi\) | |||||||
\(830\) | 13.3136 | 0.462123 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −30.8023 | −1.06788 | ||||||||
\(833\) | −5.03226 | −0.174358 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.26813 | 0.182311 | ||||||||
\(836\) | −0.179139 | −0.00619565 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.567483 | −0.0196034 | ||||||||
\(839\) | −18.7066 | −0.645824 | −0.322912 | − | 0.946429i | \(-0.604662\pi\) | ||||
−0.322912 | + | 0.946429i | \(0.604662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.08370 | 0.0718519 | ||||||||
\(842\) | −9.83800 | −0.339040 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.10948 | −0.141454 | ||||||||
\(845\) | −2.05644 | −0.0707438 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.54401 | −0.224855 | ||||||||
\(848\) | 28.5095 | 0.979021 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.16320 | −0.142797 | ||||||||
\(851\) | 84.8128 | 2.90734 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.1464 | 0.484365 | 0.242182 | − | 0.970231i | \(-0.422137\pi\) | ||||
0.242182 | + | 0.970231i | \(0.422137\pi\) | |||||||
\(854\) | −0.769830 | −0.0263430 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.9946 | −1.05938 | ||||||||
\(857\) | 7.84138 | 0.267857 | 0.133928 | − | 0.990991i | \(-0.457241\pi\) | ||||
0.133928 | + | 0.990991i | \(0.457241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.2444 | −0.724851 | −0.362426 | − | 0.932013i | \(-0.618051\pi\) | ||||
−0.362426 | + | 0.932013i | \(0.618051\pi\) | |||||||
\(860\) | 4.63249 | 0.157967 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.8681 | 1.46009 | ||||||||
\(863\) | −31.6439 | −1.07717 | −0.538586 | − | 0.842571i | \(-0.681041\pi\) | ||||
−0.538586 | + | 0.842571i | \(0.681041\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.4852 | −0.764518 | ||||||||
\(866\) | 28.3194 | 0.962333 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.256896 | 0.00871962 | ||||||||
\(869\) | 11.4327 | 0.387828 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.74251 | 0.194578 | ||||||||
\(872\) | −27.9392 | −0.946141 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.21567 | −0.0749461 | ||||||||
\(875\) | −11.7838 | −0.398364 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.23316 | 0.142944 | 0.0714718 | − | 0.997443i | \(-0.477230\pi\) | ||||
0.0714718 | + | 0.997443i | \(0.477230\pi\) | |||||||
\(878\) | 3.72163 | 0.125599 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.6490 | −0.460108 | ||||||||
\(881\) | −41.2980 | −1.39136 | −0.695682 | − | 0.718350i | \(-0.744898\pi\) | ||||
−0.695682 | + | 0.718350i | \(0.744898\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.9434 | 0.805761 | 0.402881 | − | 0.915253i | \(-0.368009\pi\) | ||||
0.402881 | + | 0.915253i | \(0.368009\pi\) | |||||||
\(884\) | −6.60004 | −0.221984 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.37535 | 0.0798015 | ||||||||
\(887\) | 0.000719418 0 | 2.41557e−5 0 | 1.20778e−5 | − | 1.00000i | \(-0.499996\pi\) | ||||
1.20778e−5 | 1.00000i | \(0.499996\pi\) | ||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 22.8995 | 0.767592 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.91322 | −0.331919 | ||||||||
\(893\) | −0.137461 | −0.00459996 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.3031 | 1.51432 | ||||||||
\(896\) | −7.09705 | −0.237096 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.2766 | 0.376304 | ||||||||
\(899\) | 3.78517 | 0.126242 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.2792 | 1.54178 | ||||||||
\(902\) | 3.59506 | 0.119702 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −51.1285 | −1.70051 | ||||||||
\(905\) | 12.2530 | 0.407304 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.5697 | 0.815822 | 0.407911 | − | 0.913022i | \(-0.366257\pi\) | ||||
0.407911 | + | 0.913022i | \(0.366257\pi\) | |||||||
\(908\) | −0.596873 | −0.0198079 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.20618 | 0.305182 | ||||||||
\(911\) | −12.3580 | −0.409440 | −0.204720 | − | 0.978821i | \(-0.565628\pi\) | ||||
−0.204720 | + | 0.978821i | \(0.565628\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5812 | −0.350186 | ||||||||
\(914\) | −41.9326 | −1.38701 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.29806 | 0.0759300 | ||||||||
\(917\) | −1.55514 | −0.0513554 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.0428 | −0.595178 | −0.297589 | − | 0.954694i | \(-0.596183\pi\) | ||||
−0.297589 | + | 0.954694i | \(0.596183\pi\) | |||||||
\(920\) | 49.0083 | 1.61576 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.0859 | 1.02376 | ||||||||
\(923\) | −24.6984 | −0.812957 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.10232 | −0.233523 | ||||||||
\(926\) | 38.1036 | 1.25216 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.7623 | 0.386117 | ||||||||
\(929\) | 36.3068 | 1.19119 | 0.595595 | − | 0.803285i | \(-0.296917\pi\) | ||||
0.595595 | + | 0.803285i | \(0.296917\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.224274 | 0.00735029 | ||||||||
\(932\) | −0.796234 | −0.0260815 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.9854 | 0.621223 | ||||||||
\(935\) | −22.1563 | −0.724587 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.0953 | −0.427804 | −0.213902 | − | 0.976855i | \(-0.568617\pi\) | ||||
−0.213902 | + | 0.976855i | \(0.568617\pi\) | |||||||
\(938\) | 2.10975 | 0.0688857 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.483727 | 0.0157774 | ||||||||
\(941\) | −7.84886 | −0.255866 | −0.127933 | − | 0.991783i | \(-0.540834\pi\) | ||||
−0.127933 | + | 0.991783i | \(0.540834\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.3756 | −0.337876 | ||||||||
\(944\) | 28.1152 | 0.915073 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.7783 | 0.512996 | ||||||||
\(947\) | −13.3476 | −0.433738 | −0.216869 | − | 0.976201i | \(-0.569584\pi\) | ||||
−0.216869 | + | 0.976201i | \(0.569584\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.9819 | 0.843409 | ||||||||
\(950\) | 0.185543 | 0.00601980 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.2412 | −0.493971 | ||||||||
\(953\) | 19.4366 | 0.629612 | 0.314806 | − | 0.949156i | \(-0.398061\pi\) | ||||
0.314806 | + | 0.949156i | \(0.398061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.6144 | −0.602348 | ||||||||
\(956\) | 8.58932 | 0.277799 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.0571 | −0.421857 | ||||||||
\(959\) | 6.31696 | 0.203985 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5391 | −0.985131 | ||||||||
\(962\) | 48.2533 | 1.55575 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.63642 | −0.278160 | ||||||||
\(965\) | −48.6448 | −1.56593 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.70164 | −0.215510 | −0.107755 | − | 0.994177i | \(-0.534366\pi\) | ||||
−0.107755 | + | 0.994177i | \(0.534366\pi\) | |||||||
\(968\) | −19.8199 | −0.637034 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.0968 | −0.548944 | ||||||||
\(971\) | −40.7514 | −1.30778 | −0.653888 | − | 0.756591i | \(-0.726863\pi\) | ||||
−0.653888 | + | 0.756591i | \(0.726863\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.4399 | 0.527037 | ||||||||
\(974\) | −17.2425 | −0.552486 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.87408 | −0.0599880 | ||||||||
\(977\) | 47.8398 | 1.53053 | 0.765266 | − | 0.643715i | \(-0.222608\pi\) | ||||
0.765266 | + | 0.643715i | \(0.222608\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.1996 | −0.581663 | ||||||||
\(980\) | −0.789224 | −0.0252108 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.6244 | 0.370950 | ||||||||
\(983\) | −44.1662 | −1.40868 | −0.704342 | − | 0.709861i | \(-0.748758\pi\) | ||||
−0.704342 | + | 0.709861i | \(0.748758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −39.7667 | −1.26707 | ||||||||
\(986\) | −35.7275 | −1.13780 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.294146 | 0.00935803 | ||||||||
\(989\) | −45.5372 | −1.44800 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.3201 | −0.645490 | −0.322745 | − | 0.946486i | \(-0.604606\pi\) | ||||
−0.322745 | + | 0.946486i | \(0.604606\pi\) | |||||||
\(992\) | 1.43234 | 0.0454767 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.07396 | −0.287809 | ||||||||
\(995\) | 14.8942 | 0.472177 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.1177 | 0.415443 | 0.207721 | − | 0.978188i | \(-0.433395\pi\) | ||||
0.207721 | + | 0.978188i | \(0.433395\pi\) | |||||||
\(998\) | −38.6805 | −1.22441 | ||||||||
\(999\) | 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.o.1.5 | 13 | ||
3.2 | odd | 2 | 2667.2.a.l.1.9 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.l.1.9 | ✓ | 13 | 3.2 | odd | 2 | ||
8001.2.a.o.1.5 | 13 | 1.1 | even | 1 | trivial |