Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(2.15119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.15119 | 1.24199 | 0.620996 | − | 0.783814i | \(-0.286728\pi\) | ||||
0.620996 | + | 0.783814i | \(0.286728\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.75581 | −1.67965 | −0.839825 | − | 0.542857i | \(-0.817343\pi\) | ||||
−0.839825 | + | 0.542857i | \(0.817343\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.62763 | 0.542544 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.89580 | 1.47614 | 0.738069 | − | 0.674725i | \(-0.235738\pi\) | ||||
0.738069 | + | 0.674725i | \(0.235738\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.80162 | 0.499678 | 0.249839 | − | 0.968287i | \(-0.419622\pi\) | ||||
0.249839 | + | 0.968287i | \(0.419622\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.07948 | −2.08611 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.27358 | 1.03649 | 0.518247 | − | 0.855231i | \(-0.326585\pi\) | ||||
0.518247 | + | 0.855231i | \(0.326585\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.31507 | 1.21936 | 0.609681 | − | 0.792647i | \(-0.291298\pi\) | ||||
0.609681 | + | 0.792647i | \(0.291298\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.795860 | 0.165948 | 0.0829742 | − | 0.996552i | \(-0.473558\pi\) | ||||
0.0829742 | + | 0.996552i | \(0.473558\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.10613 | 1.82123 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.95223 | −0.568157 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.466132 | 0.0865585 | 0.0432792 | − | 0.999063i | \(-0.486219\pi\) | ||||
0.0432792 | + | 0.999063i | \(0.486219\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.71538 | −0.487696 | −0.243848 | − | 0.969813i | \(-0.578410\pi\) | ||||
−0.243848 | + | 0.969813i | \(0.578410\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.5318 | 1.83335 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1055 | −1.66133 | −0.830667 | − | 0.556769i | \(-0.812041\pi\) | ||||
−0.830667 | + | 0.556769i | \(0.812041\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.87562 | 0.620597 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.98724 | −0.608048 | −0.304024 | − | 0.952664i | \(-0.598330\pi\) | ||||
−0.304024 | + | 0.952664i | \(0.598330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.11308 | −0.911284 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.29800 | 0.335197 | 0.167599 | − | 0.985855i | \(-0.446399\pi\) | ||||
0.167599 | + | 0.985855i | \(0.446399\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.19329 | 1.28732 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.15028 | −0.158003 | −0.0790015 | − | 0.996874i | \(-0.525173\pi\) | ||||
−0.0790015 | + | 0.996874i | \(0.525173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.3877 | −2.47940 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.4338 | 1.51444 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.87226 | 0.894692 | 0.447346 | − | 0.894361i | \(-0.352369\pi\) | ||||
0.447346 | + | 0.894361i | \(0.352369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.97900 | 1.14964 | 0.574821 | − | 0.818279i | \(-0.305072\pi\) | ||||
0.574821 | + | 0.818279i | \(0.305072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.76653 | −0.839285 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.33631 | −0.407595 | −0.203797 | − | 0.979013i | \(-0.565328\pi\) | ||||
−0.203797 | + | 0.979013i | \(0.565328\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.71205 | 0.206107 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.810480 | 0.0961863 | 0.0480931 | − | 0.998843i | \(-0.484686\pi\) | ||||
0.0480931 | + | 0.998843i | \(0.484686\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.12535 | −0.248753 | −0.124376 | − | 0.992235i | \(-0.539693\pi\) | ||||
−0.124376 | + | 0.992235i | \(0.539693\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 19.5890 | 2.26195 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00504 | −0.675619 | −0.337810 | − | 0.941214i | \(-0.609686\pi\) | ||||
−0.337810 | + | 0.941214i | \(0.609686\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2337 | −1.24819 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.93699 | −0.541905 | −0.270952 | − | 0.962593i | \(-0.587339\pi\) | ||||
−0.270952 | + | 0.962593i | \(0.587339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.0507 | −1.74095 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00274 | 0.107505 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.0344 | 1.38165 | 0.690824 | − | 0.723023i | \(-0.257248\pi\) | ||||
0.690824 | + | 0.723023i | \(0.257248\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.84130 | −0.605715 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.9624 | −2.04810 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0806 | 1.22660 | 0.613298 | − | 0.789852i | \(-0.289843\pi\) | ||||
0.613298 | + | 0.789852i | \(0.289843\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.96856 | 0.800870 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.5725 | 1.64903 | 0.824513 | − | 0.565843i | \(-0.191449\pi\) | ||||
0.824513 | + | 0.565843i | \(0.191449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.30586 | 0.325736 | 0.162868 | − | 0.986648i | \(-0.447926\pi\) | ||||
0.162868 | + | 0.986648i | \(0.447926\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.64267 | 0.642171 | 0.321085 | − | 0.947050i | \(-0.395952\pi\) | ||||
0.321085 | + | 0.947050i | \(0.395952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.65846 | −0.254634 | −0.127317 | − | 0.991862i | \(-0.540637\pi\) | ||||
−0.127317 | + | 0.991862i | \(0.540637\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.7389 | −2.06336 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.59350 | −0.432120 | −0.216060 | − | 0.976380i | \(-0.569321\pi\) | ||||
−0.216060 | + | 0.976380i | \(0.569321\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.98910 | −0.278735 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.93237 | 0.271098 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.9688 | 1.17899 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.15119 | −0.193967 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15.4218 | −1.37937 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.9912 | 1.41899 | 0.709494 | − | 0.704711i | \(-0.248924\pi\) | ||||
0.709494 | + | 0.704711i | \(0.248924\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.57731 | −0.755190 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.20712 | 0.454948 | 0.227474 | − | 0.973784i | \(-0.426953\pi\) | ||||
0.227474 | + | 0.973784i | \(0.426953\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.0880 | 0.954304 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.66661 | 0.398696 | 0.199348 | − | 0.979929i | \(-0.436118\pi\) | ||||
0.199348 | + | 0.979929i | \(0.436118\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.46110 | 0.548023 | 0.274012 | − | 0.961726i | \(-0.411649\pi\) | ||||
0.274012 | + | 0.961726i | \(0.411649\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.94343 | 0.416312 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.82035 | 0.737595 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.75070 | −0.145388 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.41639 | −0.607574 | −0.303787 | − | 0.952740i | \(-0.598251\pi\) | ||||
−0.303787 | + | 0.952740i | \(0.598251\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.87902 | 0.559806 | 0.279903 | − | 0.960028i | \(-0.409698\pi\) | ||||
0.279903 | + | 0.960028i | \(0.409698\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.95581 | 0.562344 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.1985 | 0.819159 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.9637 | −1.11443 | −0.557214 | − | 0.830369i | \(-0.688130\pi\) | ||||
−0.557214 | + | 0.830369i | \(0.688130\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.47447 | −0.196239 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.5670 | 1.68926 | 0.844628 | − | 0.535353i | \(-0.179822\pi\) | ||||
0.844628 | + | 0.535353i | \(0.179822\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −39.5555 | −3.07939 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.2690 | −1.02679 | −0.513394 | − | 0.858153i | \(-0.671612\pi\) | ||||
−0.513394 | + | 0.858153i | \(0.671612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.75418 | −0.750321 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.65099 | 0.661557 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.58266 | −0.272384 | −0.136192 | − | 0.990682i | \(-0.543486\pi\) | ||||
−0.136192 | + | 0.990682i | \(0.543486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.7836 | 1.11120 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.682622 | −0.0510216 | −0.0255108 | − | 0.999675i | \(-0.508121\pi\) | ||||
−0.0255108 | + | 0.999675i | \(0.508121\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.20632 | 0.461312 | 0.230656 | − | 0.973035i | \(-0.425913\pi\) | ||||
0.230656 | + | 0.973035i | \(0.425913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.3156 | 1.42785 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 37.9544 | 2.79046 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.9226 | 1.53001 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.9415 | −1.15349 | −0.576745 | − | 0.816924i | \(-0.695677\pi\) | ||||
−0.576745 | + | 0.816924i | \(0.695677\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.9740 | 1.43776 | 0.718880 | − | 0.695134i | \(-0.244655\pi\) | ||||
0.718880 | + | 0.695134i | \(0.244655\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.5561 | −1.04239 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.46343 | 0.602994 | 0.301497 | − | 0.953467i | \(-0.402514\pi\) | ||||
0.301497 | + | 0.953467i | \(0.402514\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.7937 | 1.89935 | 0.949677 | − | 0.313231i | \(-0.101411\pi\) | ||||
0.949677 | + | 0.313231i | \(0.101411\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.17704 | −0.506229 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.75581 | 0.262317 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.29537 | 0.0900343 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.0215 | 1.79995 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.86401 | 0.679066 | 0.339533 | − | 0.940594i | \(-0.389731\pi\) | ||||
0.339533 | + | 0.940594i | \(0.389731\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.74350 | 0.119463 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.9753 | 1.02131 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.57203 | −0.308949 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.69934 | 0.517914 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.6007 | −1.91524 | −0.957622 | − | 0.288028i | \(-0.907000\pi\) | ||||
−0.957622 | + | 0.288028i | \(0.907000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.8214 | 0.988095 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.9504 | −1.05867 | −0.529333 | − | 0.848414i | \(-0.677558\pi\) | ||||
−0.529333 | + | 0.848414i | \(0.677558\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.0736 | 1.32650 | 0.663249 | − | 0.748399i | \(-0.269177\pi\) | ||||
0.663249 | + | 0.748399i | \(0.269177\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.0841 | −1.83985 | −0.919926 | − | 0.392093i | \(-0.871751\pi\) | ||||
−0.919926 | + | 0.392093i | \(0.871751\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.63084 | −0.563014 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.9180 | −0.839114 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.35261 | 0.281547 | 0.140773 | − | 0.990042i | \(-0.455041\pi\) | ||||
0.140773 | + | 0.990042i | \(0.455041\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0638 | 1.29243 | 0.646213 | − | 0.763157i | \(-0.276352\pi\) | ||||
0.646213 | + | 0.763157i | \(0.276352\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.3092 | −0.982085 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.57572 | 0.609289 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.6204 | −0.673041 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6468 | 0.924495 | 0.462248 | − | 0.886751i | \(-0.347043\pi\) | ||||
0.462248 | + | 0.886751i | \(0.347043\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.89637 | 0.244963 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −34.5283 | −2.16224 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −31.3870 | −1.95787 | −0.978935 | − | 0.204174i | \(-0.934549\pi\) | ||||
−0.978935 | + | 0.204174i | \(0.934549\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.758691 | 0.0469618 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.23273 | 0.384327 | 0.192163 | − | 0.981363i | \(-0.438450\pi\) | ||||
0.192163 | + | 0.981363i | \(0.438450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.32024 | 0.265390 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28.0396 | 1.71600 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.7736 | −0.839793 | −0.419897 | − | 0.907572i | \(-0.637934\pi\) | ||||
−0.419897 | + | 0.907572i | \(0.637934\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4987 | 1.48819 | 0.744096 | − | 0.668073i | \(-0.232880\pi\) | ||||
0.744096 | + | 0.668073i | \(0.232880\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 44.5818 | 2.68838 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.3534 | 1.70359 | 0.851794 | − | 0.523876i | \(-0.175515\pi\) | ||||
0.851794 | + | 0.523876i | \(0.175515\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.41964 | −0.264597 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7300 | −0.998026 | −0.499013 | − | 0.866595i | \(-0.666304\pi\) | ||||
−0.499013 | + | 0.866595i | \(0.666304\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.592314 | 0.0352094 | 0.0176047 | − | 0.999845i | \(-0.494396\pi\) | ||||
0.0176047 | + | 0.999845i | \(0.494396\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −42.9430 | −2.54373 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.26345 | 0.0743206 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.9876 | 1.52342 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.47237 | 0.494961 | 0.247480 | − | 0.968893i | \(-0.420397\pi\) | ||||
0.247480 | + | 0.968893i | \(0.420397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.8109 | −1.50277 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.4535 | −0.838678 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.43384 | 0.0829208 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 35.6507 | 2.04808 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.7234 | −1.93100 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.7488 | 1.41249 | 0.706245 | − | 0.707967i | \(-0.250388\pi\) | ||||
0.706245 | + | 0.707967i | \(0.250388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.11154 | 0.404561 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.6463 | 1.62438 | 0.812190 | − | 0.583393i | \(-0.198275\pi\) | ||||
0.812190 | + | 0.583393i | \(0.198275\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.17226 | −0.405400 | −0.202700 | − | 0.979241i | \(-0.564972\pi\) | ||||
−0.202700 | + | 0.979241i | \(0.564972\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.8823 | −1.79069 | −0.895343 | − | 0.445377i | \(-0.853070\pi\) | ||||
−0.895343 | + | 0.445377i | \(0.853070\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.28209 | 0.127772 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.2897 | 0.797571 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.7144 | 1.26386 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.4057 | 0.910027 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.71886 | −0.316254 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 36.1504 | 1.98700 | 0.993501 | − | 0.113819i | \(-0.0363084\pi\) | ||||
0.993501 | + | 0.113819i | \(0.0363084\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.4480 | −0.901347 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.5305 | 0.684617 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.03769 | −0.328894 | −0.164447 | − | 0.986386i | \(-0.552584\pi\) | ||||
−0.164447 | + | 0.986386i | \(0.552584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.88150 | −0.536689 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.2939 | −0.719907 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.43014 | −0.346187 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.13405 | −0.0608790 | −0.0304395 | − | 0.999537i | \(-0.509691\pi\) | ||||
−0.0304395 | + | 0.999537i | \(0.509691\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.5719 | −1.63648 | −0.818239 | − | 0.574878i | \(-0.805049\pi\) | ||||
−0.818239 | + | 0.574878i | \(0.805049\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.31878 | −0.283896 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.97272 | −0.317896 | −0.158948 | − | 0.987287i | \(-0.550810\pi\) | ||||
−0.158948 | + | 0.987287i | \(0.550810\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.04401 | −0.161559 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.4602 | 0.974290 | 0.487145 | − | 0.873321i | \(-0.338038\pi\) | ||||
0.487145 | + | 0.873321i | \(0.338038\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.25001 | 0.486843 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.8985 | 1.46429 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.98240 | 0.417818 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.6502 | −0.712536 | −0.356268 | − | 0.934384i | \(-0.615951\pi\) | ||||
−0.356268 | + | 0.934384i | \(0.615951\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.62763 | −0.0847311 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.5757 | 0.858255 | 0.429128 | − | 0.903244i | \(-0.358821\pi\) | ||||
0.429128 | + | 0.903244i | \(0.358821\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −33.1754 | −1.71317 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.839790 | 0.0432514 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.3549 | 1.04556 | 0.522781 | − | 0.852467i | \(-0.324895\pi\) | ||||
0.522781 | + | 0.852467i | \(0.324895\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.4001 | 1.76237 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.13617 | −0.0580554 | −0.0290277 | − | 0.999579i | \(-0.509241\pi\) | ||||
−0.0290277 | + | 0.999579i | \(0.509241\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.48975 | −0.329893 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.8476 | −1.76684 | −0.883421 | − | 0.468580i | \(-0.844766\pi\) | ||||
−0.883421 | + | 0.468580i | \(0.844766\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.40117 | 0.172005 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.2015 | 0.565042 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.5538 | 1.13480 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.0264 | 1.75792 | 0.878962 | − | 0.476892i | \(-0.158237\pi\) | ||||
0.878962 | + | 0.476892i | \(0.158237\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.52844 | 0.0763268 | 0.0381634 | − | 0.999272i | \(-0.487849\pi\) | ||||
0.0381634 | + | 0.999272i | \(0.487849\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.89207 | −0.243691 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 42.1917 | 2.09652 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −49.4745 | −2.45236 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.0186 | 1.33599 | 0.667993 | − | 0.744168i | \(-0.267154\pi\) | ||||
0.667993 | + | 0.744168i | \(0.267154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.0388 | 0.495177 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.5424 | 0.910211 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.8991 | 0.680640 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0427 | 1.46768 | 0.733841 | − | 0.679321i | \(-0.237726\pi\) | ||||
0.733841 | + | 0.679321i | \(0.237726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.97506 | 0.388681 | 0.194340 | − | 0.980934i | \(-0.437743\pi\) | ||||
0.194340 | + | 0.980934i | \(0.437743\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.74029 | 0.181859 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.9157 | 1.88769 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.9743 | 0.916087 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0717 | 0.485136 | 0.242568 | − | 0.970134i | \(-0.422010\pi\) | ||||
0.242568 | + | 0.970134i | \(0.422010\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.6295 | 0.943332 | 0.471666 | − | 0.881777i | \(-0.343653\pi\) | ||||
0.471666 | + | 0.881777i | \(0.343653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.76610 | −0.180571 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.23006 | 0.202351 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.3190 | −0.922048 | −0.461024 | − | 0.887388i | \(-0.652518\pi\) | ||||
−0.461024 | + | 0.887388i | \(0.652518\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.5851 | −1.07305 | −0.536526 | − | 0.843884i | \(-0.680264\pi\) | ||||
−0.536526 | + | 0.843884i | \(0.680264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −48.9549 | −2.32068 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.9541 | −0.754602 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.3860 | 1.15085 | 0.575424 | − | 0.817855i | \(-0.304837\pi\) | ||||
0.575424 | + | 0.817855i | \(0.304837\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.89580 | −0.230534 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.7981 | 0.695275 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.6503 | 1.19987 | 0.599935 | − | 0.800049i | \(-0.295193\pi\) | ||||
0.599935 | + | 0.800049i | \(0.295193\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.6166 | −0.588891 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.4123 | −1.55617 | −0.778084 | − | 0.628161i | \(-0.783808\pi\) | ||||
−0.778084 | + | 0.628161i | \(0.783808\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.7774 | 0.593816 | 0.296908 | − | 0.954906i | \(-0.404044\pi\) | ||||
0.296908 | + | 0.954906i | \(0.404044\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.9388 | 1.01739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.1333 | 1.34813 | 0.674063 | − | 0.738674i | \(-0.264547\pi\) | ||||
0.674063 | + | 0.738674i | \(0.264547\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.0387 | −1.38411 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.5207 | −0.897563 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 48.3997 | 2.22073 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.87223 | −0.0857236 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.5993 | 1.48950 | 0.744751 | − | 0.667343i | \(-0.232568\pi\) | ||||
0.744751 | + | 0.667343i | \(0.232568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.2062 | −0.830133 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −45.3723 | −2.06025 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.16540 | −0.415324 | −0.207662 | − | 0.978201i | \(-0.566585\pi\) | ||||
−0.207662 | + | 0.978201i | \(0.566585\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 46.3947 | 2.09804 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.8127 | 0.487970 | 0.243985 | − | 0.969779i | \(-0.421545\pi\) | ||||
0.243985 | + | 0.969779i | \(0.421545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.99205 | 0.0897174 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −29.9284 | −1.34518 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −41.0860 | −1.83926 | −0.919632 | − | 0.392782i | \(-0.871513\pi\) | ||||
−0.919632 | + | 0.392782i | \(0.871513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.5442 | −1.27526 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 40.6226 | 1.81127 | 0.905637 | − | 0.424054i | \(-0.139393\pi\) | ||||
0.905637 | + | 0.424054i | \(0.139393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −62.2432 | −2.76979 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.9831 | −0.931893 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.0824 | −0.491218 | −0.245609 | − | 0.969369i | \(-0.578988\pi\) | ||||
−0.245609 | + | 0.969369i | \(0.578988\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.6913 | −0.692788 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.4162 | −0.547122 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.2505 | 0.494798 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.70699 | −0.338299 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.97583 | −0.261806 | −0.130903 | − | 0.991395i | \(-0.541788\pi\) | ||||
−0.130903 | + | 0.991395i | \(0.541788\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.8554 | 1.56785 | 0.783925 | − | 0.620856i | \(-0.213215\pi\) | ||||
0.783925 | + | 0.620856i | \(0.213215\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.6044 | −0.505494 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3666 | −0.972461 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.1855 | 0.485410 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.80162 | −0.0780367 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.9486 | −1.07862 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.46845 | −0.0633684 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.4848 | 1.86956 | 0.934780 | − | 0.355228i | \(-0.115597\pi\) | ||||
0.934780 | + | 0.355228i | \(0.115597\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.3510 | 0.572946 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.98468 | 0.427697 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0946 | −0.859183 | −0.429592 | − | 0.903023i | \(-0.641342\pi\) | ||||
−0.429592 | + | 0.903023i | \(0.641342\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.6145 | 0.623732 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.47752 | 0.105546 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 81.6472 | 3.46573 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.9467 | 0.463826 | 0.231913 | − | 0.972736i | \(-0.425501\pi\) | ||||
0.231913 | + | 0.972736i | \(0.425501\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.18347 | −0.303828 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 45.0085 | 1.90026 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.1109 | −0.510413 | −0.255207 | − | 0.966887i | \(-0.582144\pi\) | ||||
−0.255207 | + | 0.966887i | \(0.582144\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.2523 | 0.725810 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.9522 | −1.33950 | −0.669752 | − | 0.742584i | \(-0.733600\pi\) | ||||
−0.669752 | + | 0.742584i | \(0.733600\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.7625 | −0.785185 | −0.392593 | − | 0.919712i | \(-0.628422\pi\) | ||||
−0.392593 | + | 0.919712i | \(0.628422\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −34.2933 | −1.43262 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.24721 | 0.302229 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.53985 | −0.105736 | −0.0528678 | − | 0.998602i | \(-0.516836\pi\) | ||||
−0.0528678 | + | 0.998602i | \(0.516836\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 42.9679 | 1.78569 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.63154 | −0.233235 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.0134 | −0.455349 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.3984 | −1.62615 | −0.813073 | − | 0.582162i | \(-0.802207\pi\) | ||||
−0.813073 | + | 0.582162i | \(0.802207\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.4324 | −0.594678 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.2065 | 0.748914 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.8084 | 0.813434 | 0.406717 | − | 0.913554i | \(-0.366674\pi\) | ||||
0.406717 | + | 0.913554i | \(0.366674\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 57.6384 | 2.35898 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.58948 | −0.350957 | −0.175478 | − | 0.984483i | \(-0.556147\pi\) | ||||
−0.175478 | + | 0.984483i | \(0.556147\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9096 | 0.975295 | 0.487647 | − | 0.873041i | \(-0.337855\pi\) | ||||
0.487647 | + | 0.873041i | \(0.337855\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.43028 | −0.221138 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −48.7086 | −1.98028 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.4089 | −1.51838 | −0.759190 | − | 0.650869i | \(-0.774405\pi\) | ||||
−0.759190 | + | 0.650869i | \(0.774405\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.14011 | 0.167491 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.5834 | −1.71993 | −0.859964 | − | 0.510355i | \(-0.829514\pi\) | ||||
−0.859964 | + | 0.510355i | \(0.829514\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.07948 | 0.325796 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.0073 | −0.805463 | −0.402731 | − | 0.915318i | \(-0.631939\pi\) | ||||
−0.402731 | + | 0.915318i | \(0.631939\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.3030 | −1.45914 | −0.729571 | − | 0.683905i | \(-0.760280\pi\) | ||||
−0.729571 | + | 0.683905i | \(0.760280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.34956 | −0.0942847 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.3909 | 0.495637 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 55.9773 | 2.23552 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.1866 | −1.72196 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.2166 | 1.52138 | 0.760690 | − | 0.649115i | \(-0.224861\pi\) | ||||
0.760690 | + | 0.649115i | \(0.224861\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.2194 | 0.843395 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −60.0599 | −2.38340 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.31916 | 0.0521853 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.65170 | 0.144233 | 0.0721167 | − | 0.997396i | \(-0.477025\pi\) | ||||
0.0721167 | + | 0.997396i | \(0.477025\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.9103 | −0.509132 | −0.254566 | − | 0.967055i | \(-0.581933\pi\) | ||||
−0.254566 | + | 0.967055i | \(0.581933\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.2148 | 1.26846 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.5774 | 1.39869 | 0.699345 | − | 0.714784i | \(-0.253475\pi\) | ||||
0.699345 | + | 0.714784i | \(0.253475\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.6452 | 1.32069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.3469 | −0.991899 | −0.495950 | − | 0.868351i | \(-0.665180\pi\) | ||||
−0.495950 | + | 0.868351i | \(0.665180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.5570 | −0.764153 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.45928 | −0.134959 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.6083 | −0.569059 | −0.284530 | − | 0.958667i | \(-0.591837\pi\) | ||||
−0.284530 | + | 0.958667i | \(0.591837\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.5466 | −0.915855 | −0.457928 | − | 0.888989i | \(-0.651408\pi\) | ||||
−0.457928 | + | 0.888989i | \(0.651408\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.5628 | 0.643245 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.370976 | 0.0143642 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −61.5256 | −2.37872 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.9594 | 1.69703 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.9476 | 0.691827 | 0.345914 | − | 0.938266i | \(-0.387569\pi\) | ||||
0.345914 | + | 0.938266i | \(0.387569\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −26.8834 | −1.03474 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.41360 | −0.0543291 | −0.0271645 | − | 0.999631i | \(-0.508648\pi\) | ||||
−0.0271645 | + | 0.999631i | \(0.508648\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.3124 | −1.31485 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.7811 | −1.02475 | −0.512374 | − | 0.858762i | \(-0.671234\pi\) | ||||
−0.512374 | + | 0.858762i | \(0.671234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.5269 | −0.669669 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 43.1821 | 1.64750 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.07236 | −0.0789507 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.5061 | −1.16050 | −0.580252 | − | 0.814437i | \(-0.697046\pi\) | ||||
−0.580252 | + | 0.814437i | \(0.697046\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.2667 | −0.920487 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.27358 | −0.161873 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −60.4143 | −2.28508 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.524271 | 0.0198014 | 0.00990072 | − | 0.999951i | \(-0.496848\pi\) | ||||
0.00990072 | + | 0.999951i | \(0.496848\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −53.7115 | −2.02577 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.5666 | −0.699259 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.2384 | −1.58630 | −0.793148 | − | 0.609029i | \(-0.791559\pi\) | ||||
−0.793148 | + | 0.609029i | \(0.791559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.77399 | −0.366553 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.16106 | −0.0809324 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.1276 | −1.23890 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.36330 | 0.349679 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.6669 | −0.397807 | −0.198904 | − | 0.980019i | \(-0.563738\pi\) | ||||
−0.198904 | + | 0.980019i | \(0.563738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.1612 | 1.60518 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.24465 | 0.157643 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.1863 | −0.859931 | −0.429965 | − | 0.902845i | \(-0.641474\pi\) | ||||
−0.429965 | + | 0.902845i | \(0.641474\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.768094 | 0.0284479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.0398 | −0.630238 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.143539 | −0.00530173 | −0.00265086 | − | 0.999996i | \(-0.500844\pi\) | ||||
−0.00265086 | + | 0.999996i | \(0.500844\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.3339 | −0.601667 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.0099 | 0.772863 | 0.386431 | − | 0.922318i | \(-0.373708\pi\) | ||||
0.386431 | + | 0.922318i | \(0.373708\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.5992 | 0.756732 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.99529 | 0.219946 | 0.109973 | − | 0.993935i | \(-0.464924\pi\) | ||||
0.109973 | + | 0.993935i | \(0.464924\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.8546 | 1.02051 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.03560 | −0.294007 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.5741 | −0.933213 | −0.466607 | − | 0.884465i | \(-0.654524\pi\) | ||||
−0.466607 | + | 0.884465i | \(0.654524\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.5080 | 1.14822 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.8363 | −0.940279 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.9799 | −1.56213 | −0.781066 | − | 0.624449i | \(-0.785324\pi\) | ||||
−0.781066 | + | 0.624449i | \(0.785324\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.38185 | 0.304242 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.1201 | 0.729352 | 0.364676 | − | 0.931134i | \(-0.381180\pi\) | ||||
0.364676 | + | 0.931134i | \(0.381180\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −26.1247 | −0.944541 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.3812 | 0.447058 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.03102 | 0.181423 | 0.0907116 | − | 0.995877i | \(-0.471086\pi\) | ||||
0.0907116 | + | 0.995877i | \(0.471086\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −67.5196 | −2.43166 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5637 | 0.487851 | 0.243925 | − | 0.969794i | \(-0.421565\pi\) | ||||
0.243925 | + | 0.969794i | \(0.421565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.7266 | −0.888205 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.31507 | −0.190432 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.96795 | 0.141984 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.37613 | −0.0491788 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52.4452 | 1.87185 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.03110 | 0.321924 | 0.160962 | − | 0.986961i | \(-0.448540\pi\) | ||||
0.160962 | + | 0.986961i | \(0.448540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.4078 | 0.477331 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1767 | 0.574452 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.29366 | 0.329612 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.18087 | −0.183516 | −0.0917579 | − | 0.995781i | \(-0.529249\pi\) | ||||
−0.0917579 | + | 0.995781i | \(0.529249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.82066 | 0.347430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.2153 | 0.749605 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.4053 | −0.367194 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.6297 | −1.04302 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.1674 | −1.55284 | −0.776421 | − | 0.630214i | \(-0.782967\pi\) | ||||
−0.776421 | + | 0.630214i | \(0.782967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.6464 | −1.21660 | −0.608300 | − | 0.793707i | \(-0.708148\pi\) | ||||
−0.608300 | + | 0.793707i | \(0.708148\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 52.7015 | 1.84832 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −81.0015 | −2.83736 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.1925 | −0.741430 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.0119 | −1.36152 | −0.680762 | − | 0.732505i | \(-0.738351\pi\) | ||||
−0.680762 | + | 0.732505i | \(0.738351\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.9152 | 0.659343 | 0.329672 | − | 0.944096i | \(-0.393062\pi\) | ||||
0.329672 | + | 0.944096i | \(0.393062\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 95.9040 | 3.33895 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.9323 | −0.658339 | −0.329169 | − | 0.944271i | \(-0.606769\pi\) | ||||
−0.329169 | + | 0.944271i | \(0.606769\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.3111 | −0.497046 | −0.248523 | − | 0.968626i | \(-0.579945\pi\) | ||||
−0.248523 | + | 0.968626i | \(0.579945\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 60.9936 | 2.11584 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.8360 | 1.72464 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.01642 | 0.277088 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.1176 | −1.76478 | −0.882388 | − | 0.470522i | \(-0.844066\pi\) | ||||
−0.882388 | + | 0.470522i | \(0.844066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7827 | −0.992508 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.9894 | −1.23954 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.6349 | 1.26028 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.27418 | 0.0437298 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.04257 | −0.275696 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.6010 | 1.69831 | 0.849153 | − | 0.528147i | \(-0.177113\pi\) | ||||
0.849153 | + | 0.528147i | \(0.177113\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.4915 | −1.11119 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −51.3659 | −1.75463 | −0.877313 | − | 0.479919i | \(-0.840666\pi\) | ||||
−0.877313 | + | 0.479919i | \(0.840666\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.1818 | 1.37099 | 0.685493 | − | 0.728080i | \(-0.259587\pi\) | ||||
0.685493 | + | 0.728080i | \(0.259587\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.8413 | −0.641367 | −0.320683 | − | 0.947186i | \(-0.603913\pi\) | ||||
−0.320683 | + | 0.947186i | \(0.603913\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.4558 | 0.457511 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.71792 | 0.0923056 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.3994 | −0.997308 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.01075 | −0.203666 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.6627 | 0.665482 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.08184 | −0.205369 | −0.102685 | − | 0.994714i | \(-0.532743\pi\) | ||||
−0.102685 | + | 0.994714i | \(0.532743\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.2257 | 0.614738 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.8074 | −1.30745 | −0.653727 | − | 0.756731i | \(-0.726795\pi\) | ||||
−0.653727 | + | 0.756731i | \(0.726795\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.4610 | −1.46258 | −0.731289 | − | 0.682068i | \(-0.761081\pi\) | ||||
−0.731289 | + | 0.682068i | \(0.761081\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −55.5243 | −1.86643 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.92458 | 0.266081 | 0.133041 | − | 0.991111i | \(-0.457526\pi\) | ||||
0.133041 | + | 0.991111i | \(0.457526\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −54.9980 | −1.84250 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.2140 | 0.408727 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.56380 | 0.0856984 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.08446 | 0.102987 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.26572 | −0.0422143 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.91581 | −0.163769 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.3098 | −0.774843 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.7983 | 0.823415 | 0.411707 | − | 0.911316i | \(-0.364933\pi\) | ||||
0.411707 | + | 0.911316i | \(0.364933\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.9739 | 0.894669 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.4131 | −0.643185 | −0.321592 | − | 0.946878i | \(-0.604218\pi\) | ||||
−0.321592 | + | 0.946878i | \(0.604218\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.1705 | −0.799927 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −72.5456 | −2.39828 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.6399 | 0.548898 | 0.274449 | − | 0.961602i | \(-0.411505\pi\) | ||||
0.274449 | + | 0.961602i | \(0.411505\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 53.2395 | 1.75430 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.46017 | 0.0480622 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −92.0220 | −3.02566 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.38072 | 0.176726 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.3751 | 1.32467 | 0.662333 | − | 0.749210i | \(-0.269567\pi\) | ||||
0.662333 | + | 0.749210i | \(0.269567\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 61.6236 | 2.01747 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −78.5812 | −2.56988 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.0533 | −1.01447 | −0.507234 | − | 0.861809i | \(-0.669332\pi\) | ||||
−0.507234 | + | 0.861809i | \(0.669332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.4289 | −0.503504 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.3305 | 1.24954 | 0.624769 | − | 0.780810i | \(-0.285193\pi\) | ||||
0.624769 | + | 0.780810i | \(0.285193\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.795860 | −0.0259168 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.77100 | 0.155037 | 0.0775183 | − | 0.996991i | \(-0.475300\pi\) | ||||
0.0775183 | + | 0.996991i | \(0.475300\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.82906 | −0.124297 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −68.5849 | −2.22402 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.73083 | −0.218033 | −0.109016 | − | 0.994040i | \(-0.534770\pi\) | ||||
−0.109016 | + | 0.994040i | \(0.534770\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 59.8734 | 1.93746 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.90921 | 0.158692 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.6267 | −0.762152 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.8118 | 0.348406 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −75.0186 | −2.41493 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.8582 | −1.34607 | −0.673034 | − | 0.739611i | \(-0.735009\pi\) | ||||
−0.673034 | + | 0.739611i | \(0.735009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.8630 | 1.56971 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.8108 | 1.05295 | 0.526475 | − | 0.850191i | \(-0.323513\pi\) | ||||
0.526475 | + | 0.850191i | \(0.323513\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 35.2919 | 1.13025 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.6724 | 0.661368 | 0.330684 | − | 0.943741i | \(-0.392720\pi\) | ||||
0.330684 | + | 0.943741i | \(0.392720\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63.8140 | 2.03950 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.32700 | −0.138150 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.71927 | −0.0867313 | −0.0433657 | − | 0.999059i | \(-0.513808\pi\) | ||||
−0.0433657 | + | 0.999059i | \(0.513808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.7870 | −1.01282 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.17328 | −0.100905 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.32195 | 0.264356 | 0.132178 | − | 0.991226i | \(-0.457803\pi\) | ||||
0.132178 | + | 0.991226i | \(0.457803\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 77.7664 | 2.46784 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −100.632 | −3.19025 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.74009 | −0.150120 | −0.0750600 | − | 0.997179i | \(-0.523915\pi\) | ||||
−0.0750600 | + | 0.997179i | \(0.523915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.8338 | 0.943898 |
(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 | 8036.2.a.t.1.16 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.5 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.16 | yes | 20 | 1.1 | even | 1 | trivial |