Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 24 x^{10} + 68 x^{9} + 213 x^{8} - 555 x^{7} - 814 x^{6} + 1911 x^{5} + 1005 x^{4} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 266) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.767178\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.767178 | −0.442930 | −0.221465 | − | 0.975168i | \(-0.571084\pi\) | ||||
−0.221465 | + | 0.975168i | \(0.571084\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.24084 | 1.00213 | 0.501066 | − | 0.865409i | \(-0.332941\pi\) | ||||
0.501066 | + | 0.865409i | \(0.332941\pi\) | |||||||
\(6\) | 0.767178 | 0.313199 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.41144 | −0.803813 | ||||||||
\(10\) | −2.24084 | −0.708614 | ||||||||
\(11\) | −4.92248 | −1.48418 | −0.742092 | − | 0.670298i | \(-0.766166\pi\) | ||||
−0.742092 | + | 0.670298i | \(0.766166\pi\) | |||||||
\(12\) | −0.767178 | −0.221465 | ||||||||
\(13\) | −2.23142 | −0.618885 | −0.309442 | − | 0.950918i | \(-0.600142\pi\) | ||||
−0.309442 | + | 0.950918i | \(0.600142\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.71912 | −0.443875 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.78296 | 0.674967 | 0.337484 | − | 0.941331i | \(-0.390424\pi\) | ||||
0.337484 | + | 0.941331i | \(0.390424\pi\) | |||||||
\(18\) | 2.41144 | 0.568382 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.24084 | 0.501066 | ||||||||
\(21\) | −0.767178 | −0.167412 | ||||||||
\(22\) | 4.92248 | 1.04948 | ||||||||
\(23\) | 7.55262 | 1.57483 | 0.787415 | − | 0.616424i | \(-0.211419\pi\) | ||||
0.787415 | + | 0.616424i | \(0.211419\pi\) | |||||||
\(24\) | 0.767178 | 0.156599 | ||||||||
\(25\) | 0.0213433 | 0.00426867 | ||||||||
\(26\) | 2.23142 | 0.437618 | ||||||||
\(27\) | 4.15153 | 0.798963 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −4.83046 | −0.896994 | −0.448497 | − | 0.893784i | \(-0.648041\pi\) | ||||
−0.448497 | + | 0.893784i | \(0.648041\pi\) | |||||||
\(30\) | 1.71912 | 0.313867 | ||||||||
\(31\) | −9.15931 | −1.64506 | −0.822530 | − | 0.568722i | \(-0.807438\pi\) | ||||
−0.822530 | + | 0.568722i | \(0.807438\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.77642 | 0.657390 | ||||||||
\(34\) | −2.78296 | −0.477274 | ||||||||
\(35\) | 2.24084 | 0.378770 | ||||||||
\(36\) | −2.41144 | −0.401906 | ||||||||
\(37\) | 0.687197 | 0.112974 | 0.0564872 | − | 0.998403i | \(-0.482010\pi\) | ||||
0.0564872 | + | 0.998403i | \(0.482010\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.71190 | 0.274123 | ||||||||
\(40\) | −2.24084 | −0.354307 | ||||||||
\(41\) | −4.47639 | −0.699095 | −0.349547 | − | 0.936919i | \(-0.613665\pi\) | ||||
−0.349547 | + | 0.936919i | \(0.613665\pi\) | |||||||
\(42\) | 0.767178 | 0.118378 | ||||||||
\(43\) | −9.26471 | −1.41286 | −0.706428 | − | 0.707785i | \(-0.749694\pi\) | ||||
−0.706428 | + | 0.707785i | \(0.749694\pi\) | |||||||
\(44\) | −4.92248 | −0.742092 | ||||||||
\(45\) | −5.40364 | −0.805527 | ||||||||
\(46\) | −7.55262 | −1.11357 | ||||||||
\(47\) | 11.2047 | 1.63437 | 0.817183 | − | 0.576378i | \(-0.195534\pi\) | ||||
0.817183 | + | 0.576378i | \(0.195534\pi\) | |||||||
\(48\) | −0.767178 | −0.110733 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.0213433 | −0.00301841 | ||||||||
\(51\) | −2.13502 | −0.298963 | ||||||||
\(52\) | −2.23142 | −0.309442 | ||||||||
\(53\) | 11.3485 | 1.55884 | 0.779420 | − | 0.626502i | \(-0.215514\pi\) | ||||
0.779420 | + | 0.626502i | \(0.215514\pi\) | |||||||
\(54\) | −4.15153 | −0.564952 | ||||||||
\(55\) | −11.0305 | −1.48735 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.83046 | 0.634271 | ||||||||
\(59\) | 2.50451 | 0.326059 | 0.163030 | − | 0.986621i | \(-0.447873\pi\) | ||||
0.163030 | + | 0.986621i | \(0.447873\pi\) | |||||||
\(60\) | −1.71912 | −0.221937 | ||||||||
\(61\) | 8.72488 | 1.11711 | 0.558553 | − | 0.829469i | \(-0.311357\pi\) | ||||
0.558553 | + | 0.829469i | \(0.311357\pi\) | |||||||
\(62\) | 9.15931 | 1.16323 | ||||||||
\(63\) | −2.41144 | −0.303813 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.00025 | −0.620204 | ||||||||
\(66\) | −3.77642 | −0.464845 | ||||||||
\(67\) | 2.20808 | 0.269759 | 0.134880 | − | 0.990862i | \(-0.456935\pi\) | ||||
0.134880 | + | 0.990862i | \(0.456935\pi\) | |||||||
\(68\) | 2.78296 | 0.337484 | ||||||||
\(69\) | −5.79420 | −0.697539 | ||||||||
\(70\) | −2.24084 | −0.267831 | ||||||||
\(71\) | −10.5960 | −1.25752 | −0.628759 | − | 0.777600i | \(-0.716437\pi\) | ||||
−0.628759 | + | 0.777600i | \(0.716437\pi\) | |||||||
\(72\) | 2.41144 | 0.284191 | ||||||||
\(73\) | 5.63116 | 0.659077 | 0.329539 | − | 0.944142i | \(-0.393107\pi\) | ||||
0.329539 | + | 0.944142i | \(0.393107\pi\) | |||||||
\(74\) | −0.687197 | −0.0798850 | ||||||||
\(75\) | −0.0163741 | −0.00189072 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.92248 | −0.560969 | ||||||||
\(78\) | −1.71190 | −0.193834 | ||||||||
\(79\) | 3.82937 | 0.430838 | 0.215419 | − | 0.976522i | \(-0.430888\pi\) | ||||
0.215419 | + | 0.976522i | \(0.430888\pi\) | |||||||
\(80\) | 2.24084 | 0.250533 | ||||||||
\(81\) | 4.04935 | 0.449928 | ||||||||
\(82\) | 4.47639 | 0.494335 | ||||||||
\(83\) | 15.6091 | 1.71332 | 0.856662 | − | 0.515878i | \(-0.172534\pi\) | ||||
0.856662 | + | 0.515878i | \(0.172534\pi\) | |||||||
\(84\) | −0.767178 | −0.0837059 | ||||||||
\(85\) | 6.23616 | 0.676406 | ||||||||
\(86\) | 9.26471 | 0.999040 | ||||||||
\(87\) | 3.70582 | 0.397306 | ||||||||
\(88\) | 4.92248 | 0.524738 | ||||||||
\(89\) | −2.39245 | −0.253599 | −0.126800 | − | 0.991928i | \(-0.540470\pi\) | ||||
−0.126800 | + | 0.991928i | \(0.540470\pi\) | |||||||
\(90\) | 5.40364 | 0.569593 | ||||||||
\(91\) | −2.23142 | −0.233916 | ||||||||
\(92\) | 7.55262 | 0.787415 | ||||||||
\(93\) | 7.02681 | 0.728647 | ||||||||
\(94\) | −11.2047 | −1.15567 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.767178 | 0.0782997 | ||||||||
\(97\) | 5.96881 | 0.606041 | 0.303021 | − | 0.952984i | \(-0.402005\pi\) | ||||
0.303021 | + | 0.952984i | \(0.402005\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 11.8703 | 1.19301 | ||||||||
\(100\) | 0.0213433 | 0.00213433 | ||||||||
\(101\) | 14.7081 | 1.46351 | 0.731757 | − | 0.681566i | \(-0.238701\pi\) | ||||
0.731757 | + | 0.681566i | \(0.238701\pi\) | |||||||
\(102\) | 2.13502 | 0.211399 | ||||||||
\(103\) | −0.138444 | −0.0136413 | −0.00682065 | − | 0.999977i | \(-0.502171\pi\) | ||||
−0.00682065 | + | 0.999977i | \(0.502171\pi\) | |||||||
\(104\) | 2.23142 | 0.218809 | ||||||||
\(105\) | −1.71912 | −0.167769 | ||||||||
\(106\) | −11.3485 | −1.10227 | ||||||||
\(107\) | −14.8536 | −1.43595 | −0.717975 | − | 0.696068i | \(-0.754931\pi\) | ||||
−0.717975 | + | 0.696068i | \(0.754931\pi\) | |||||||
\(108\) | 4.15153 | 0.399482 | ||||||||
\(109\) | 0.937456 | 0.0897920 | 0.0448960 | − | 0.998992i | \(-0.485704\pi\) | ||||
0.0448960 | + | 0.998992i | \(0.485704\pi\) | |||||||
\(110\) | 11.0305 | 1.05171 | ||||||||
\(111\) | −0.527202 | −0.0500398 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 12.2493 | 1.15232 | 0.576160 | − | 0.817337i | \(-0.304550\pi\) | ||||
0.576160 | + | 0.817337i | \(0.304550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.9242 | 1.57819 | ||||||||
\(116\) | −4.83046 | −0.448497 | ||||||||
\(117\) | 5.38093 | 0.497467 | ||||||||
\(118\) | −2.50451 | −0.230559 | ||||||||
\(119\) | 2.78296 | 0.255114 | ||||||||
\(120\) | 1.71912 | 0.156933 | ||||||||
\(121\) | 13.2308 | 1.20280 | ||||||||
\(122\) | −8.72488 | −0.789914 | ||||||||
\(123\) | 3.43419 | 0.309650 | ||||||||
\(124\) | −9.15931 | −0.822530 | ||||||||
\(125\) | −11.1564 | −0.997854 | ||||||||
\(126\) | 2.41144 | 0.214828 | ||||||||
\(127\) | 17.9233 | 1.59044 | 0.795220 | − | 0.606321i | \(-0.207355\pi\) | ||||
0.795220 | + | 0.606321i | \(0.207355\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.10768 | 0.625796 | ||||||||
\(130\) | 5.00025 | 0.438551 | ||||||||
\(131\) | −7.61516 | −0.665340 | −0.332670 | − | 0.943043i | \(-0.607950\pi\) | ||||
−0.332670 | + | 0.943043i | \(0.607950\pi\) | |||||||
\(132\) | 3.77642 | 0.328695 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.20808 | −0.190749 | ||||||||
\(135\) | 9.30291 | 0.800667 | ||||||||
\(136\) | −2.78296 | −0.238637 | ||||||||
\(137\) | −2.37425 | −0.202846 | −0.101423 | − | 0.994843i | \(-0.532339\pi\) | ||||
−0.101423 | + | 0.994843i | \(0.532339\pi\) | |||||||
\(138\) | 5.79420 | 0.493235 | ||||||||
\(139\) | 9.25763 | 0.785222 | 0.392611 | − | 0.919705i | \(-0.371572\pi\) | ||||
0.392611 | + | 0.919705i | \(0.371572\pi\) | |||||||
\(140\) | 2.24084 | 0.189385 | ||||||||
\(141\) | −8.59596 | −0.723910 | ||||||||
\(142\) | 10.5960 | 0.889199 | ||||||||
\(143\) | 10.9841 | 0.918538 | ||||||||
\(144\) | −2.41144 | −0.200953 | ||||||||
\(145\) | −10.8243 | −0.898907 | ||||||||
\(146\) | −5.63116 | −0.466038 | ||||||||
\(147\) | −0.767178 | −0.0632757 | ||||||||
\(148\) | 0.687197 | 0.0564872 | ||||||||
\(149\) | −18.4306 | −1.50989 | −0.754946 | − | 0.655787i | \(-0.772337\pi\) | ||||
−0.754946 | + | 0.655787i | \(0.772337\pi\) | |||||||
\(150\) | 0.0163741 | 0.00133694 | ||||||||
\(151\) | 19.3209 | 1.57231 | 0.786157 | − | 0.618027i | \(-0.212068\pi\) | ||||
0.786157 | + | 0.618027i | \(0.212068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.71094 | −0.542547 | ||||||||
\(154\) | 4.92248 | 0.396665 | ||||||||
\(155\) | −20.5245 | −1.64857 | ||||||||
\(156\) | 1.71190 | 0.137061 | ||||||||
\(157\) | 13.4990 | 1.07733 | 0.538667 | − | 0.842518i | \(-0.318928\pi\) | ||||
0.538667 | + | 0.842518i | \(0.318928\pi\) | |||||||
\(158\) | −3.82937 | −0.304648 | ||||||||
\(159\) | −8.70633 | −0.690457 | ||||||||
\(160\) | −2.24084 | −0.177154 | ||||||||
\(161\) | 7.55262 | 0.595230 | ||||||||
\(162\) | −4.04935 | −0.318147 | ||||||||
\(163\) | 8.27250 | 0.647952 | 0.323976 | − | 0.946065i | \(-0.394980\pi\) | ||||
0.323976 | + | 0.946065i | \(0.394980\pi\) | |||||||
\(164\) | −4.47639 | −0.349547 | ||||||||
\(165\) | 8.46233 | 0.658791 | ||||||||
\(166\) | −15.6091 | −1.21150 | ||||||||
\(167\) | 1.73675 | 0.134394 | 0.0671968 | − | 0.997740i | \(-0.478594\pi\) | ||||
0.0671968 | + | 0.997740i | \(0.478594\pi\) | |||||||
\(168\) | 0.767178 | 0.0591890 | ||||||||
\(169\) | −8.02076 | −0.616982 | ||||||||
\(170\) | −6.23616 | −0.478291 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.26471 | −0.706428 | ||||||||
\(173\) | 18.2806 | 1.38985 | 0.694923 | − | 0.719084i | \(-0.255439\pi\) | ||||
0.694923 | + | 0.719084i | \(0.255439\pi\) | |||||||
\(174\) | −3.70582 | −0.280938 | ||||||||
\(175\) | 0.0213433 | 0.00161341 | ||||||||
\(176\) | −4.92248 | −0.371046 | ||||||||
\(177\) | −1.92140 | −0.144422 | ||||||||
\(178\) | 2.39245 | 0.179322 | ||||||||
\(179\) | −6.65867 | −0.497693 | −0.248846 | − | 0.968543i | \(-0.580051\pi\) | ||||
−0.248846 | + | 0.968543i | \(0.580051\pi\) | |||||||
\(180\) | −5.40364 | −0.402763 | ||||||||
\(181\) | 1.36047 | 0.101123 | 0.0505613 | − | 0.998721i | \(-0.483899\pi\) | ||||
0.0505613 | + | 0.998721i | \(0.483899\pi\) | |||||||
\(182\) | 2.23142 | 0.165404 | ||||||||
\(183\) | −6.69353 | −0.494800 | ||||||||
\(184\) | −7.55262 | −0.556786 | ||||||||
\(185\) | 1.53990 | 0.113215 | ||||||||
\(186\) | −7.02681 | −0.515231 | ||||||||
\(187\) | −13.6991 | −1.00178 | ||||||||
\(188\) | 11.2047 | 0.817183 | ||||||||
\(189\) | 4.15153 | 0.301980 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.51380 | −0.616037 | −0.308019 | − | 0.951380i | \(-0.599666\pi\) | ||||
−0.308019 | + | 0.951380i | \(0.599666\pi\) | |||||||
\(192\) | −0.767178 | −0.0553663 | ||||||||
\(193\) | 9.54610 | 0.687143 | 0.343572 | − | 0.939126i | \(-0.388363\pi\) | ||||
0.343572 | + | 0.939126i | \(0.388363\pi\) | |||||||
\(194\) | −5.96881 | −0.428536 | ||||||||
\(195\) | 3.83608 | 0.274707 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −19.4294 | −1.38428 | −0.692142 | − | 0.721761i | \(-0.743333\pi\) | ||||
−0.692142 | + | 0.721761i | \(0.743333\pi\) | |||||||
\(198\) | −11.8703 | −0.843582 | ||||||||
\(199\) | −9.73734 | −0.690262 | −0.345131 | − | 0.938555i | \(-0.612165\pi\) | ||||
−0.345131 | + | 0.938555i | \(0.612165\pi\) | |||||||
\(200\) | −0.0213433 | −0.00150920 | ||||||||
\(201\) | −1.69399 | −0.119485 | ||||||||
\(202\) | −14.7081 | −1.03486 | ||||||||
\(203\) | −4.83046 | −0.339032 | ||||||||
\(204\) | −2.13502 | −0.149482 | ||||||||
\(205\) | −10.0309 | −0.700585 | ||||||||
\(206\) | 0.138444 | 0.00964586 | ||||||||
\(207\) | −18.2127 | −1.26587 | ||||||||
\(208\) | −2.23142 | −0.154721 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.71912 | 0.118630 | ||||||||
\(211\) | 5.62207 | 0.387040 | 0.193520 | − | 0.981096i | \(-0.438010\pi\) | ||||
0.193520 | + | 0.981096i | \(0.438010\pi\) | |||||||
\(212\) | 11.3485 | 0.779420 | ||||||||
\(213\) | 8.12904 | 0.556993 | ||||||||
\(214\) | 14.8536 | 1.01537 | ||||||||
\(215\) | −20.7607 | −1.41587 | ||||||||
\(216\) | −4.15153 | −0.282476 | ||||||||
\(217\) | −9.15931 | −0.621774 | ||||||||
\(218\) | −0.937456 | −0.0634926 | ||||||||
\(219\) | −4.32010 | −0.291925 | ||||||||
\(220\) | −11.0305 | −0.743674 | ||||||||
\(221\) | −6.20996 | −0.417727 | ||||||||
\(222\) | 0.527202 | 0.0353835 | ||||||||
\(223\) | 0.463833 | 0.0310606 | 0.0155303 | − | 0.999879i | \(-0.495056\pi\) | ||||
0.0155303 | + | 0.999879i | \(0.495056\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −0.0514682 | −0.00343121 | ||||||||
\(226\) | −12.2493 | −0.814814 | ||||||||
\(227\) | −20.6434 | −1.37015 | −0.685077 | − | 0.728471i | \(-0.740231\pi\) | ||||
−0.685077 | + | 0.728471i | \(0.740231\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.21473 | 0.410681 | 0.205340 | − | 0.978691i | \(-0.434170\pi\) | ||||
0.205340 | + | 0.978691i | \(0.434170\pi\) | |||||||
\(230\) | −16.9242 | −1.11595 | ||||||||
\(231\) | 3.77642 | 0.248470 | ||||||||
\(232\) | 4.83046 | 0.317135 | ||||||||
\(233\) | 3.87941 | 0.254148 | 0.127074 | − | 0.991893i | \(-0.459441\pi\) | ||||
0.127074 | + | 0.991893i | \(0.459441\pi\) | |||||||
\(234\) | −5.38093 | −0.351763 | ||||||||
\(235\) | 25.1078 | 1.63785 | ||||||||
\(236\) | 2.50451 | 0.163030 | ||||||||
\(237\) | −2.93781 | −0.190831 | ||||||||
\(238\) | −2.78296 | −0.180393 | ||||||||
\(239\) | −15.5680 | −1.00701 | −0.503506 | − | 0.863992i | \(-0.667957\pi\) | ||||
−0.503506 | + | 0.863992i | \(0.667957\pi\) | |||||||
\(240\) | −1.71912 | −0.110969 | ||||||||
\(241\) | 6.80945 | 0.438635 | 0.219317 | − | 0.975654i | \(-0.429617\pi\) | ||||
0.219317 | + | 0.975654i | \(0.429617\pi\) | |||||||
\(242\) | −13.2308 | −0.850508 | ||||||||
\(243\) | −15.5612 | −0.998250 | ||||||||
\(244\) | 8.72488 | 0.558553 | ||||||||
\(245\) | 2.24084 | 0.143162 | ||||||||
\(246\) | −3.43419 | −0.218956 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.15931 | 0.581616 | ||||||||
\(249\) | −11.9750 | −0.758883 | ||||||||
\(250\) | 11.1564 | 0.705590 | ||||||||
\(251\) | 4.79201 | 0.302469 | 0.151235 | − | 0.988498i | \(-0.451675\pi\) | ||||
0.151235 | + | 0.988498i | \(0.451675\pi\) | |||||||
\(252\) | −2.41144 | −0.151906 | ||||||||
\(253\) | −37.1776 | −2.33734 | ||||||||
\(254\) | −17.9233 | −1.12461 | ||||||||
\(255\) | −4.78424 | −0.299601 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.3341 | 0.894134 | 0.447067 | − | 0.894500i | \(-0.352469\pi\) | ||||
0.447067 | + | 0.894500i | \(0.352469\pi\) | |||||||
\(258\) | −7.10768 | −0.442505 | ||||||||
\(259\) | 0.687197 | 0.0427003 | ||||||||
\(260\) | −5.00025 | −0.310102 | ||||||||
\(261\) | 11.6484 | 0.721016 | ||||||||
\(262\) | 7.61516 | 0.470466 | ||||||||
\(263\) | 4.03546 | 0.248837 | 0.124419 | − | 0.992230i | \(-0.460293\pi\) | ||||
0.124419 | + | 0.992230i | \(0.460293\pi\) | |||||||
\(264\) | −3.77642 | −0.232422 | ||||||||
\(265\) | 25.4302 | 1.56216 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.83543 | 0.112327 | ||||||||
\(268\) | 2.20808 | 0.134880 | ||||||||
\(269\) | 1.28737 | 0.0784921 | 0.0392461 | − | 0.999230i | \(-0.487504\pi\) | ||||
0.0392461 | + | 0.999230i | \(0.487504\pi\) | |||||||
\(270\) | −9.30291 | −0.566157 | ||||||||
\(271\) | 16.6508 | 1.01146 | 0.505731 | − | 0.862691i | \(-0.331223\pi\) | ||||
0.505731 | + | 0.862691i | \(0.331223\pi\) | |||||||
\(272\) | 2.78296 | 0.168742 | ||||||||
\(273\) | 1.71190 | 0.103609 | ||||||||
\(274\) | 2.37425 | 0.143434 | ||||||||
\(275\) | −0.105062 | −0.00633549 | ||||||||
\(276\) | −5.79420 | −0.348770 | ||||||||
\(277\) | 24.4658 | 1.47001 | 0.735005 | − | 0.678062i | \(-0.237180\pi\) | ||||
0.735005 | + | 0.678062i | \(0.237180\pi\) | |||||||
\(278\) | −9.25763 | −0.555236 | ||||||||
\(279\) | 22.0871 | 1.32232 | ||||||||
\(280\) | −2.24084 | −0.133916 | ||||||||
\(281\) | 15.9467 | 0.951302 | 0.475651 | − | 0.879634i | \(-0.342213\pi\) | ||||
0.475651 | + | 0.879634i | \(0.342213\pi\) | |||||||
\(282\) | 8.59596 | 0.511882 | ||||||||
\(283\) | 5.09977 | 0.303150 | 0.151575 | − | 0.988446i | \(-0.451566\pi\) | ||||
0.151575 | + | 0.988446i | \(0.451566\pi\) | |||||||
\(284\) | −10.5960 | −0.628759 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.9841 | −0.649505 | ||||||||
\(287\) | −4.47639 | −0.264233 | ||||||||
\(288\) | 2.41144 | 0.142095 | ||||||||
\(289\) | −9.25513 | −0.544419 | ||||||||
\(290\) | 10.8243 | 0.635623 | ||||||||
\(291\) | −4.57914 | −0.268434 | ||||||||
\(292\) | 5.63116 | 0.329539 | ||||||||
\(293\) | 25.5743 | 1.49406 | 0.747032 | − | 0.664788i | \(-0.231478\pi\) | ||||
0.747032 | + | 0.664788i | \(0.231478\pi\) | |||||||
\(294\) | 0.767178 | 0.0447427 | ||||||||
\(295\) | 5.61219 | 0.326755 | ||||||||
\(296\) | −0.687197 | −0.0399425 | ||||||||
\(297\) | −20.4358 | −1.18581 | ||||||||
\(298\) | 18.4306 | 1.06766 | ||||||||
\(299\) | −16.8531 | −0.974638 | ||||||||
\(300\) | −0.0163741 | −0.000945361 0 | ||||||||
\(301\) | −9.26471 | −0.534009 | ||||||||
\(302\) | −19.3209 | −1.11179 | ||||||||
\(303\) | −11.2837 | −0.648234 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.5510 | 1.11949 | ||||||||
\(306\) | 6.71094 | 0.383639 | ||||||||
\(307\) | 17.5777 | 1.00321 | 0.501605 | − | 0.865097i | \(-0.332743\pi\) | ||||
0.501605 | + | 0.865097i | \(0.332743\pi\) | |||||||
\(308\) | −4.92248 | −0.280484 | ||||||||
\(309\) | 0.106211 | 0.00604215 | ||||||||
\(310\) | 20.5245 | 1.16571 | ||||||||
\(311\) | −9.64139 | −0.546713 | −0.273357 | − | 0.961913i | \(-0.588134\pi\) | ||||
−0.273357 | + | 0.961913i | \(0.588134\pi\) | |||||||
\(312\) | −1.71190 | −0.0969170 | ||||||||
\(313\) | −6.60921 | −0.373575 | −0.186787 | − | 0.982400i | \(-0.559808\pi\) | ||||
−0.186787 | + | 0.982400i | \(0.559808\pi\) | |||||||
\(314\) | −13.4990 | −0.761791 | ||||||||
\(315\) | −5.40364 | −0.304460 | ||||||||
\(316\) | 3.82937 | 0.215419 | ||||||||
\(317\) | 18.8621 | 1.05940 | 0.529700 | − | 0.848185i | \(-0.322305\pi\) | ||||
0.529700 | + | 0.848185i | \(0.322305\pi\) | |||||||
\(318\) | 8.70633 | 0.488227 | ||||||||
\(319\) | 23.7779 | 1.33130 | ||||||||
\(320\) | 2.24084 | 0.125267 | ||||||||
\(321\) | 11.3953 | 0.636026 | ||||||||
\(322\) | −7.55262 | −0.420891 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 4.04935 | 0.224964 | ||||||||
\(325\) | −0.0476260 | −0.00264181 | ||||||||
\(326\) | −8.27250 | −0.458171 | ||||||||
\(327\) | −0.719195 | −0.0397716 | ||||||||
\(328\) | 4.47639 | 0.247167 | ||||||||
\(329\) | 11.2047 | 0.617732 | ||||||||
\(330\) | −8.46233 | −0.465836 | ||||||||
\(331\) | −33.3366 | −1.83234 | −0.916172 | − | 0.400785i | \(-0.868737\pi\) | ||||
−0.916172 | + | 0.400785i | \(0.868737\pi\) | |||||||
\(332\) | 15.6091 | 0.856662 | ||||||||
\(333\) | −1.65713 | −0.0908103 | ||||||||
\(334\) | −1.73675 | −0.0950307 | ||||||||
\(335\) | 4.94793 | 0.270334 | ||||||||
\(336\) | −0.767178 | −0.0418530 | ||||||||
\(337\) | 20.5528 | 1.11958 | 0.559791 | − | 0.828634i | \(-0.310882\pi\) | ||||
0.559791 | + | 0.828634i | \(0.310882\pi\) | |||||||
\(338\) | 8.02076 | 0.436272 | ||||||||
\(339\) | −9.39741 | −0.510398 | ||||||||
\(340\) | 6.23616 | 0.338203 | ||||||||
\(341\) | 45.0865 | 2.44157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.26471 | 0.499520 | ||||||||
\(345\) | −12.9838 | −0.699027 | ||||||||
\(346\) | −18.2806 | −0.982769 | ||||||||
\(347\) | −9.82334 | −0.527344 | −0.263672 | − | 0.964612i | \(-0.584934\pi\) | ||||
−0.263672 | + | 0.964612i | \(0.584934\pi\) | |||||||
\(348\) | 3.70582 | 0.198653 | ||||||||
\(349\) | 33.8548 | 1.81221 | 0.906103 | − | 0.423057i | \(-0.139043\pi\) | ||||
0.906103 | + | 0.423057i | \(0.139043\pi\) | |||||||
\(350\) | −0.0213433 | −0.00114085 | ||||||||
\(351\) | −9.26382 | −0.494466 | ||||||||
\(352\) | 4.92248 | 0.262369 | ||||||||
\(353\) | −17.5725 | −0.935292 | −0.467646 | − | 0.883916i | \(-0.654898\pi\) | ||||
−0.467646 | + | 0.883916i | \(0.654898\pi\) | |||||||
\(354\) | 1.92140 | 0.102121 | ||||||||
\(355\) | −23.7440 | −1.26020 | ||||||||
\(356\) | −2.39245 | −0.126800 | ||||||||
\(357\) | −2.13502 | −0.112998 | ||||||||
\(358\) | 6.65867 | 0.351922 | ||||||||
\(359\) | −1.36696 | −0.0721454 | −0.0360727 | − | 0.999349i | \(-0.511485\pi\) | ||||
−0.0360727 | + | 0.999349i | \(0.511485\pi\) | |||||||
\(360\) | 5.40364 | 0.284797 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −1.36047 | −0.0715045 | ||||||||
\(363\) | −10.1504 | −0.532757 | ||||||||
\(364\) | −2.23142 | −0.116958 | ||||||||
\(365\) | 12.6185 | 0.660483 | ||||||||
\(366\) | 6.69353 | 0.349877 | ||||||||
\(367\) | −3.24763 | −0.169525 | −0.0847623 | − | 0.996401i | \(-0.527013\pi\) | ||||
−0.0847623 | + | 0.996401i | \(0.527013\pi\) | |||||||
\(368\) | 7.55262 | 0.393707 | ||||||||
\(369\) | 10.7945 | 0.561941 | ||||||||
\(370\) | −1.53990 | −0.0800553 | ||||||||
\(371\) | 11.3485 | 0.589186 | ||||||||
\(372\) | 7.02681 | 0.364323 | ||||||||
\(373\) | −14.7858 | −0.765581 | −0.382790 | − | 0.923835i | \(-0.625037\pi\) | ||||
−0.382790 | + | 0.923835i | \(0.625037\pi\) | |||||||
\(374\) | 13.6991 | 0.708362 | ||||||||
\(375\) | 8.55890 | 0.441980 | ||||||||
\(376\) | −11.2047 | −0.577836 | ||||||||
\(377\) | 10.7788 | 0.555136 | ||||||||
\(378\) | −4.15153 | −0.213532 | ||||||||
\(379\) | −28.2426 | −1.45073 | −0.725363 | − | 0.688366i | \(-0.758328\pi\) | ||||
−0.725363 | + | 0.688366i | \(0.758328\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.7504 | −0.704454 | ||||||||
\(382\) | 8.51380 | 0.435604 | ||||||||
\(383\) | −9.35499 | −0.478017 | −0.239009 | − | 0.971017i | \(-0.576822\pi\) | ||||
−0.239009 | + | 0.971017i | \(0.576822\pi\) | |||||||
\(384\) | 0.767178 | 0.0391499 | ||||||||
\(385\) | −11.0305 | −0.562165 | ||||||||
\(386\) | −9.54610 | −0.485884 | ||||||||
\(387\) | 22.3413 | 1.13567 | ||||||||
\(388\) | 5.96881 | 0.303021 | ||||||||
\(389\) | −3.13976 | −0.159192 | −0.0795960 | − | 0.996827i | \(-0.525363\pi\) | ||||
−0.0795960 | + | 0.996827i | \(0.525363\pi\) | |||||||
\(390\) | −3.83608 | −0.194247 | ||||||||
\(391\) | 21.0186 | 1.06296 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 5.84218 | 0.294699 | ||||||||
\(394\) | 19.4294 | 0.978837 | ||||||||
\(395\) | 8.58098 | 0.431756 | ||||||||
\(396\) | 11.8703 | 0.596503 | ||||||||
\(397\) | 22.6080 | 1.13466 | 0.567332 | − | 0.823489i | \(-0.307976\pi\) | ||||
0.567332 | + | 0.823489i | \(0.307976\pi\) | |||||||
\(398\) | 9.73734 | 0.488089 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0213433 | 0.00106717 | ||||||||
\(401\) | 38.5295 | 1.92407 | 0.962035 | − | 0.272925i | \(-0.0879910\pi\) | ||||
0.962035 | + | 0.272925i | \(0.0879910\pi\) | |||||||
\(402\) | 1.69399 | 0.0844883 | ||||||||
\(403\) | 20.4383 | 1.01810 | ||||||||
\(404\) | 14.7081 | 0.731757 | ||||||||
\(405\) | 9.07393 | 0.450887 | ||||||||
\(406\) | 4.83046 | 0.239732 | ||||||||
\(407\) | −3.38271 | −0.167675 | ||||||||
\(408\) | 2.13502 | 0.105699 | ||||||||
\(409\) | 3.91368 | 0.193519 | 0.0967594 | − | 0.995308i | \(-0.469152\pi\) | ||||
0.0967594 | + | 0.995308i | \(0.469152\pi\) | |||||||
\(410\) | 10.0309 | 0.495389 | ||||||||
\(411\) | 1.82147 | 0.0898465 | ||||||||
\(412\) | −0.138444 | −0.00682065 | ||||||||
\(413\) | 2.50451 | 0.123239 | ||||||||
\(414\) | 18.2127 | 0.895104 | ||||||||
\(415\) | 34.9775 | 1.71698 | ||||||||
\(416\) | 2.23142 | 0.109404 | ||||||||
\(417\) | −7.10225 | −0.347799 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.3819 | 1.53310 | 0.766552 | − | 0.642182i | \(-0.221971\pi\) | ||||
0.766552 | + | 0.642182i | \(0.221971\pi\) | |||||||
\(420\) | −1.71912 | −0.0838844 | ||||||||
\(421\) | 2.68280 | 0.130752 | 0.0653758 | − | 0.997861i | \(-0.479175\pi\) | ||||
0.0653758 | + | 0.997861i | \(0.479175\pi\) | |||||||
\(422\) | −5.62207 | −0.273678 | ||||||||
\(423\) | −27.0193 | −1.31372 | ||||||||
\(424\) | −11.3485 | −0.551133 | ||||||||
\(425\) | 0.0593977 | 0.00288121 | ||||||||
\(426\) | −8.12904 | −0.393853 | ||||||||
\(427\) | 8.72488 | 0.422227 | ||||||||
\(428\) | −14.8536 | −0.717975 | ||||||||
\(429\) | −8.42677 | −0.406848 | ||||||||
\(430\) | 20.7607 | 1.00117 | ||||||||
\(431\) | 6.16930 | 0.297164 | 0.148582 | − | 0.988900i | \(-0.452529\pi\) | ||||
0.148582 | + | 0.988900i | \(0.452529\pi\) | |||||||
\(432\) | 4.15153 | 0.199741 | ||||||||
\(433\) | 4.43698 | 0.213228 | 0.106614 | − | 0.994301i | \(-0.465999\pi\) | ||||
0.106614 | + | 0.994301i | \(0.465999\pi\) | |||||||
\(434\) | 9.15931 | 0.439661 | ||||||||
\(435\) | 8.30414 | 0.398153 | ||||||||
\(436\) | 0.937456 | 0.0448960 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 4.32010 | 0.206422 | ||||||||
\(439\) | 24.9968 | 1.19303 | 0.596516 | − | 0.802601i | \(-0.296551\pi\) | ||||
0.596516 | + | 0.802601i | \(0.296551\pi\) | |||||||
\(440\) | 11.0305 | 0.525857 | ||||||||
\(441\) | −2.41144 | −0.114830 | ||||||||
\(442\) | 6.20996 | 0.295377 | ||||||||
\(443\) | −9.40949 | −0.447058 | −0.223529 | − | 0.974697i | \(-0.571758\pi\) | ||||
−0.223529 | + | 0.974697i | \(0.571758\pi\) | |||||||
\(444\) | −0.527202 | −0.0250199 | ||||||||
\(445\) | −5.36108 | −0.254140 | ||||||||
\(446\) | −0.463833 | −0.0219631 | ||||||||
\(447\) | 14.1395 | 0.668777 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −21.7369 | −1.02583 | −0.512914 | − | 0.858440i | \(-0.671434\pi\) | ||||
−0.512914 | + | 0.858440i | \(0.671434\pi\) | |||||||
\(450\) | 0.0514682 | 0.00242623 | ||||||||
\(451\) | 22.0349 | 1.03759 | ||||||||
\(452\) | 12.2493 | 0.576160 | ||||||||
\(453\) | −14.8226 | −0.696425 | ||||||||
\(454\) | 20.6434 | 0.968845 | ||||||||
\(455\) | −5.00025 | −0.234415 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.0692620 | −0.00323994 | −0.00161997 | − | 0.999999i | \(-0.500516\pi\) | ||||
−0.00161997 | + | 0.999999i | \(0.500516\pi\) | |||||||
\(458\) | −6.21473 | −0.290395 | ||||||||
\(459\) | 11.5536 | 0.539274 | ||||||||
\(460\) | 16.9242 | 0.789093 | ||||||||
\(461\) | −9.55596 | −0.445065 | −0.222533 | − | 0.974925i | \(-0.571432\pi\) | ||||
−0.222533 | + | 0.974925i | \(0.571432\pi\) | |||||||
\(462\) | −3.77642 | −0.175695 | ||||||||
\(463\) | 3.08288 | 0.143273 | 0.0716367 | − | 0.997431i | \(-0.477178\pi\) | ||||
0.0716367 | + | 0.997431i | \(0.477178\pi\) | |||||||
\(464\) | −4.83046 | −0.224249 | ||||||||
\(465\) | 15.7459 | 0.730200 | ||||||||
\(466\) | −3.87941 | −0.179710 | ||||||||
\(467\) | −23.6336 | −1.09363 | −0.546817 | − | 0.837252i | \(-0.684161\pi\) | ||||
−0.546817 | + | 0.837252i | \(0.684161\pi\) | |||||||
\(468\) | 5.38093 | 0.248734 | ||||||||
\(469\) | 2.20808 | 0.101959 | ||||||||
\(470\) | −25.1078 | −1.15814 | ||||||||
\(471\) | −10.3561 | −0.477184 | ||||||||
\(472\) | −2.50451 | −0.115279 | ||||||||
\(473\) | 45.6054 | 2.09694 | ||||||||
\(474\) | 2.93781 | 0.134938 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.78296 | 0.127557 | ||||||||
\(477\) | −27.3663 | −1.25301 | ||||||||
\(478\) | 15.5680 | 0.712064 | ||||||||
\(479\) | −9.42310 | −0.430552 | −0.215276 | − | 0.976553i | \(-0.569065\pi\) | ||||
−0.215276 | + | 0.976553i | \(0.569065\pi\) | |||||||
\(480\) | 1.71912 | 0.0784667 | ||||||||
\(481\) | −1.53343 | −0.0699182 | ||||||||
\(482\) | −6.80945 | −0.310162 | ||||||||
\(483\) | −5.79420 | −0.263645 | ||||||||
\(484\) | 13.2308 | 0.601400 | ||||||||
\(485\) | 13.3751 | 0.607333 | ||||||||
\(486\) | 15.5612 | 0.705869 | ||||||||
\(487\) | 26.8713 | 1.21765 | 0.608826 | − | 0.793304i | \(-0.291641\pi\) | ||||
0.608826 | + | 0.793304i | \(0.291641\pi\) | |||||||
\(488\) | −8.72488 | −0.394957 | ||||||||
\(489\) | −6.34647 | −0.286997 | ||||||||
\(490\) | −2.24084 | −0.101231 | ||||||||
\(491\) | −21.2384 | −0.958477 | −0.479238 | − | 0.877685i | \(-0.659087\pi\) | ||||
−0.479238 | + | 0.877685i | \(0.659087\pi\) | |||||||
\(492\) | 3.43419 | 0.154825 | ||||||||
\(493\) | −13.4430 | −0.605442 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 26.5993 | 1.19555 | ||||||||
\(496\) | −9.15931 | −0.411265 | ||||||||
\(497\) | −10.5960 | −0.475297 | ||||||||
\(498\) | 11.9750 | 0.536611 | ||||||||
\(499\) | −6.88937 | −0.308410 | −0.154205 | − | 0.988039i | \(-0.549282\pi\) | ||||
−0.154205 | + | 0.988039i | \(0.549282\pi\) | |||||||
\(500\) | −11.1564 | −0.498927 | ||||||||
\(501\) | −1.33240 | −0.0595270 | ||||||||
\(502\) | −4.79201 | −0.213878 | ||||||||
\(503\) | 16.6555 | 0.742631 | 0.371315 | − | 0.928507i | \(-0.378907\pi\) | ||||
0.371315 | + | 0.928507i | \(0.378907\pi\) | |||||||
\(504\) | 2.41144 | 0.107414 | ||||||||
\(505\) | 32.9585 | 1.46663 | ||||||||
\(506\) | 37.1776 | 1.65275 | ||||||||
\(507\) | 6.15335 | 0.273280 | ||||||||
\(508\) | 17.9233 | 0.795220 | ||||||||
\(509\) | −34.7015 | −1.53812 | −0.769059 | − | 0.639178i | \(-0.779275\pi\) | ||||
−0.769059 | + | 0.639178i | \(0.779275\pi\) | |||||||
\(510\) | 4.78424 | 0.211850 | ||||||||
\(511\) | 5.63116 | 0.249108 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.3341 | −0.632248 | ||||||||
\(515\) | −0.310231 | −0.0136704 | ||||||||
\(516\) | 7.10768 | 0.312898 | ||||||||
\(517\) | −55.1547 | −2.42570 | ||||||||
\(518\) | −0.687197 | −0.0301937 | ||||||||
\(519\) | −14.0244 | −0.615605 | ||||||||
\(520\) | 5.00025 | 0.219275 | ||||||||
\(521\) | 27.8746 | 1.22121 | 0.610605 | − | 0.791935i | \(-0.290926\pi\) | ||||
0.610605 | + | 0.791935i | \(0.290926\pi\) | |||||||
\(522\) | −11.6484 | −0.509835 | ||||||||
\(523\) | −8.50066 | −0.371708 | −0.185854 | − | 0.982577i | \(-0.559505\pi\) | ||||
−0.185854 | + | 0.982577i | \(0.559505\pi\) | |||||||
\(524\) | −7.61516 | −0.332670 | ||||||||
\(525\) | −0.0163741 | −0.000714626 0 | ||||||||
\(526\) | −4.03546 | −0.175955 | ||||||||
\(527\) | −25.4900 | −1.11036 | ||||||||
\(528\) | 3.77642 | 0.164347 | ||||||||
\(529\) | 34.0420 | 1.48009 | ||||||||
\(530\) | −25.4302 | −1.10462 | ||||||||
\(531\) | −6.03947 | −0.262091 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.98871 | 0.432659 | ||||||||
\(534\) | −1.83543 | −0.0794269 | ||||||||
\(535\) | −33.2845 | −1.43901 | ||||||||
\(536\) | −2.20808 | −0.0953743 | ||||||||
\(537\) | 5.10839 | 0.220443 | ||||||||
\(538\) | −1.28737 | −0.0555023 | ||||||||
\(539\) | −4.92248 | −0.212026 | ||||||||
\(540\) | 9.30291 | 0.400333 | ||||||||
\(541\) | 36.6901 | 1.57743 | 0.788715 | − | 0.614758i | \(-0.210746\pi\) | ||||
0.788715 | + | 0.614758i | \(0.210746\pi\) | |||||||
\(542\) | −16.6508 | −0.715211 | ||||||||
\(543\) | −1.04372 | −0.0447903 | ||||||||
\(544\) | −2.78296 | −0.119318 | ||||||||
\(545\) | 2.10069 | 0.0899835 | ||||||||
\(546\) | −1.71190 | −0.0732624 | ||||||||
\(547\) | −38.0793 | −1.62815 | −0.814076 | − | 0.580758i | \(-0.802756\pi\) | ||||
−0.814076 | + | 0.580758i | \(0.802756\pi\) | |||||||
\(548\) | −2.37425 | −0.101423 | ||||||||
\(549\) | −21.0395 | −0.897945 | ||||||||
\(550\) | 0.105062 | 0.00447987 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 5.79420 | 0.246617 | ||||||||
\(553\) | 3.82937 | 0.162841 | ||||||||
\(554\) | −24.4658 | −1.03945 | ||||||||
\(555\) | −1.18137 | −0.0501465 | ||||||||
\(556\) | 9.25763 | 0.392611 | ||||||||
\(557\) | 17.0710 | 0.723320 | 0.361660 | − | 0.932310i | \(-0.382210\pi\) | ||||
0.361660 | + | 0.932310i | \(0.382210\pi\) | |||||||
\(558\) | −22.0871 | −0.935022 | ||||||||
\(559\) | 20.6735 | 0.874395 | ||||||||
\(560\) | 2.24084 | 0.0946926 | ||||||||
\(561\) | 10.5096 | 0.443716 | ||||||||
\(562\) | −15.9467 | −0.672672 | ||||||||
\(563\) | 5.81848 | 0.245220 | 0.122610 | − | 0.992455i | \(-0.460874\pi\) | ||||
0.122610 | + | 0.992455i | \(0.460874\pi\) | |||||||
\(564\) | −8.59596 | −0.361955 | ||||||||
\(565\) | 27.4487 | 1.15478 | ||||||||
\(566\) | −5.09977 | −0.214359 | ||||||||
\(567\) | 4.04935 | 0.170057 | ||||||||
\(568\) | 10.5960 | 0.444600 | ||||||||
\(569\) | −20.0422 | −0.840212 | −0.420106 | − | 0.907475i | \(-0.638007\pi\) | ||||
−0.420106 | + | 0.907475i | \(0.638007\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.2489 | −0.679996 | −0.339998 | − | 0.940426i | \(-0.610426\pi\) | ||||
−0.339998 | + | 0.940426i | \(0.610426\pi\) | |||||||
\(572\) | 10.9841 | 0.459269 | ||||||||
\(573\) | 6.53160 | 0.272861 | ||||||||
\(574\) | 4.47639 | 0.186841 | ||||||||
\(575\) | 0.161198 | 0.00672243 | ||||||||
\(576\) | −2.41144 | −0.100477 | ||||||||
\(577\) | 29.3423 | 1.22153 | 0.610767 | − | 0.791810i | \(-0.290861\pi\) | ||||
0.610767 | + | 0.791810i | \(0.290861\pi\) | |||||||
\(578\) | 9.25513 | 0.384963 | ||||||||
\(579\) | −7.32355 | −0.304356 | ||||||||
\(580\) | −10.8243 | −0.449453 | ||||||||
\(581\) | 15.6091 | 0.647576 | ||||||||
\(582\) | 4.57914 | 0.189811 | ||||||||
\(583\) | −55.8629 | −2.31360 | ||||||||
\(584\) | −5.63116 | −0.233019 | ||||||||
\(585\) | 12.0578 | 0.498528 | ||||||||
\(586\) | −25.5743 | −1.05646 | ||||||||
\(587\) | 14.3364 | 0.591728 | 0.295864 | − | 0.955230i | \(-0.404392\pi\) | ||||
0.295864 | + | 0.955230i | \(0.404392\pi\) | |||||||
\(588\) | −0.767178 | −0.0316379 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −5.61219 | −0.231050 | ||||||||
\(591\) | 14.9058 | 0.613142 | ||||||||
\(592\) | 0.687197 | 0.0282436 | ||||||||
\(593\) | 13.7730 | 0.565587 | 0.282794 | − | 0.959181i | \(-0.408739\pi\) | ||||
0.282794 | + | 0.959181i | \(0.408739\pi\) | |||||||
\(594\) | 20.4358 | 0.838493 | ||||||||
\(595\) | 6.23616 | 0.255657 | ||||||||
\(596\) | −18.4306 | −0.754946 | ||||||||
\(597\) | 7.47027 | 0.305738 | ||||||||
\(598\) | 16.8531 | 0.689173 | ||||||||
\(599\) | 32.0580 | 1.30986 | 0.654928 | − | 0.755691i | \(-0.272699\pi\) | ||||
0.654928 | + | 0.755691i | \(0.272699\pi\) | |||||||
\(600\) | 0.0163741 | 0.000668471 0 | ||||||||
\(601\) | −22.7544 | −0.928170 | −0.464085 | − | 0.885791i | \(-0.653617\pi\) | ||||
−0.464085 | + | 0.885791i | \(0.653617\pi\) | |||||||
\(602\) | 9.26471 | 0.377602 | ||||||||
\(603\) | −5.32464 | −0.216836 | ||||||||
\(604\) | 19.3209 | 0.786157 | ||||||||
\(605\) | 29.6481 | 1.20537 | ||||||||
\(606\) | 11.2837 | 0.458371 | ||||||||
\(607\) | 36.7702 | 1.49246 | 0.746228 | − | 0.665690i | \(-0.231863\pi\) | ||||
0.746228 | + | 0.665690i | \(0.231863\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.70582 | 0.150167 | ||||||||
\(610\) | −19.5510 | −0.791598 | ||||||||
\(611\) | −25.0023 | −1.01148 | ||||||||
\(612\) | −6.71094 | −0.271274 | ||||||||
\(613\) | −2.55526 | −0.103206 | −0.0516030 | − | 0.998668i | \(-0.516433\pi\) | ||||
−0.0516030 | + | 0.998668i | \(0.516433\pi\) | |||||||
\(614\) | −17.5777 | −0.709376 | ||||||||
\(615\) | 7.69545 | 0.310310 | ||||||||
\(616\) | 4.92248 | 0.198332 | ||||||||
\(617\) | −14.8360 | −0.597275 | −0.298638 | − | 0.954367i | \(-0.596532\pi\) | ||||
−0.298638 | + | 0.954367i | \(0.596532\pi\) | |||||||
\(618\) | −0.106211 | −0.00427244 | ||||||||
\(619\) | −22.4387 | −0.901889 | −0.450945 | − | 0.892552i | \(-0.648913\pi\) | ||||
−0.450945 | + | 0.892552i | \(0.648913\pi\) | |||||||
\(620\) | −20.5245 | −0.824284 | ||||||||
\(621\) | 31.3549 | 1.25823 | ||||||||
\(622\) | 9.64139 | 0.386585 | ||||||||
\(623\) | −2.39245 | −0.0958514 | ||||||||
\(624\) | 1.71190 | 0.0685307 | ||||||||
\(625\) | −25.1063 | −1.00425 | ||||||||
\(626\) | 6.60921 | 0.264157 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.4990 | 0.538667 | ||||||||
\(629\) | 1.91244 | 0.0762541 | ||||||||
\(630\) | 5.40364 | 0.215286 | ||||||||
\(631\) | 38.7200 | 1.54142 | 0.770709 | − | 0.637188i | \(-0.219902\pi\) | ||||
0.770709 | + | 0.637188i | \(0.219902\pi\) | |||||||
\(632\) | −3.82937 | −0.152324 | ||||||||
\(633\) | −4.31313 | −0.171432 | ||||||||
\(634\) | −18.8621 | −0.749108 | ||||||||
\(635\) | 40.1633 | 1.59383 | ||||||||
\(636\) | −8.70633 | −0.345228 | ||||||||
\(637\) | −2.23142 | −0.0884121 | ||||||||
\(638\) | −23.7779 | −0.941374 | ||||||||
\(639\) | 25.5517 | 1.01081 | ||||||||
\(640\) | −2.24084 | −0.0885768 | ||||||||
\(641\) | 18.3340 | 0.724151 | 0.362075 | − | 0.932149i | \(-0.382068\pi\) | ||||
0.362075 | + | 0.932149i | \(0.382068\pi\) | |||||||
\(642\) | −11.3953 | −0.449738 | ||||||||
\(643\) | −47.0310 | −1.85472 | −0.927361 | − | 0.374169i | \(-0.877928\pi\) | ||||
−0.927361 | + | 0.374169i | \(0.877928\pi\) | |||||||
\(644\) | 7.55262 | 0.297615 | ||||||||
\(645\) | 15.9271 | 0.627131 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.5945 | 0.573770 | 0.286885 | − | 0.957965i | \(-0.407380\pi\) | ||||
0.286885 | + | 0.957965i | \(0.407380\pi\) | |||||||
\(648\) | −4.04935 | −0.159074 | ||||||||
\(649\) | −12.3284 | −0.483932 | ||||||||
\(650\) | 0.0476260 | 0.00186804 | ||||||||
\(651\) | 7.02681 | 0.275403 | ||||||||
\(652\) | 8.27250 | 0.323976 | ||||||||
\(653\) | 2.83040 | 0.110762 | 0.0553810 | − | 0.998465i | \(-0.482363\pi\) | ||||
0.0553810 | + | 0.998465i | \(0.482363\pi\) | |||||||
\(654\) | 0.719195 | 0.0281228 | ||||||||
\(655\) | −17.0643 | −0.666759 | ||||||||
\(656\) | −4.47639 | −0.174774 | ||||||||
\(657\) | −13.5792 | −0.529775 | ||||||||
\(658\) | −11.2047 | −0.436803 | ||||||||
\(659\) | 36.2563 | 1.41235 | 0.706173 | − | 0.708039i | \(-0.250420\pi\) | ||||
0.706173 | + | 0.708039i | \(0.250420\pi\) | |||||||
\(660\) | 8.46233 | 0.329396 | ||||||||
\(661\) | 3.83355 | 0.149108 | 0.0745539 | − | 0.997217i | \(-0.476247\pi\) | ||||
0.0745539 | + | 0.997217i | \(0.476247\pi\) | |||||||
\(662\) | 33.3366 | 1.29566 | ||||||||
\(663\) | 4.76414 | 0.185024 | ||||||||
\(664\) | −15.6091 | −0.605752 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.65713 | 0.0642126 | ||||||||
\(667\) | −36.4826 | −1.41261 | ||||||||
\(668\) | 1.73675 | 0.0671968 | ||||||||
\(669\) | −0.355843 | −0.0137577 | ||||||||
\(670\) | −4.94793 | −0.191155 | ||||||||
\(671\) | −42.9481 | −1.65799 | ||||||||
\(672\) | 0.767178 | 0.0295945 | ||||||||
\(673\) | 43.6954 | 1.68433 | 0.842167 | − | 0.539216i | \(-0.181280\pi\) | ||||
0.842167 | + | 0.539216i | \(0.181280\pi\) | |||||||
\(674\) | −20.5528 | −0.791663 | ||||||||
\(675\) | 0.0886076 | 0.00341051 | ||||||||
\(676\) | −8.02076 | −0.308491 | ||||||||
\(677\) | 45.1162 | 1.73395 | 0.866977 | − | 0.498348i | \(-0.166060\pi\) | ||||
0.866977 | + | 0.498348i | \(0.166060\pi\) | |||||||
\(678\) | 9.39741 | 0.360906 | ||||||||
\(679\) | 5.96881 | 0.229062 | ||||||||
\(680\) | −6.23616 | −0.239146 | ||||||||
\(681\) | 15.8372 | 0.606882 | ||||||||
\(682\) | −45.0865 | −1.72645 | ||||||||
\(683\) | −8.93101 | −0.341736 | −0.170868 | − | 0.985294i | \(-0.554657\pi\) | ||||
−0.170868 | + | 0.985294i | \(0.554657\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.32030 | −0.203278 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −4.76780 | −0.181903 | ||||||||
\(688\) | −9.26471 | −0.353214 | ||||||||
\(689\) | −25.3233 | −0.964742 | ||||||||
\(690\) | 12.9838 | 0.494286 | ||||||||
\(691\) | −25.5005 | −0.970086 | −0.485043 | − | 0.874490i | \(-0.661196\pi\) | ||||
−0.485043 | + | 0.874490i | \(0.661196\pi\) | |||||||
\(692\) | 18.2806 | 0.694923 | ||||||||
\(693\) | 11.8703 | 0.450914 | ||||||||
\(694\) | 9.82334 | 0.372889 | ||||||||
\(695\) | 20.7448 | 0.786896 | ||||||||
\(696\) | −3.70582 | −0.140469 | ||||||||
\(697\) | −12.4576 | −0.471866 | ||||||||
\(698\) | −33.8548 | −1.28142 | ||||||||
\(699\) | −2.97619 | −0.112570 | ||||||||
\(700\) | 0.0213433 | 0.000806703 0 | ||||||||
\(701\) | −30.2238 | −1.14154 | −0.570769 | − | 0.821111i | \(-0.693355\pi\) | ||||
−0.570769 | + | 0.821111i | \(0.693355\pi\) | |||||||
\(702\) | 9.26382 | 0.349640 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −4.92248 | −0.185523 | ||||||||
\(705\) | −19.2621 | −0.725454 | ||||||||
\(706\) | 17.5725 | 0.661351 | ||||||||
\(707\) | 14.7081 | 0.553156 | ||||||||
\(708\) | −1.92140 | −0.0722108 | ||||||||
\(709\) | 15.3392 | 0.576076 | 0.288038 | − | 0.957619i | \(-0.406997\pi\) | ||||
0.288038 | + | 0.957619i | \(0.406997\pi\) | |||||||
\(710\) | 23.7440 | 0.891095 | ||||||||
\(711\) | −9.23429 | −0.346313 | ||||||||
\(712\) | 2.39245 | 0.0896608 | ||||||||
\(713\) | −69.1767 | −2.59069 | ||||||||
\(714\) | 2.13502 | 0.0799013 | ||||||||
\(715\) | 24.6136 | 0.920497 | ||||||||
\(716\) | −6.65867 | −0.248846 | ||||||||
\(717\) | 11.9434 | 0.446036 | ||||||||
\(718\) | 1.36696 | 0.0510145 | ||||||||
\(719\) | −9.84213 | −0.367050 | −0.183525 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183525 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(720\) | −5.40364 | −0.201382 | ||||||||
\(721\) | −0.138444 | −0.00515593 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.22405 | −0.194285 | ||||||||
\(724\) | 1.36047 | 0.0505613 | ||||||||
\(725\) | −0.103098 | −0.00382897 | ||||||||
\(726\) | 10.1504 | 0.376716 | ||||||||
\(727\) | 9.91032 | 0.367553 | 0.183777 | − | 0.982968i | \(-0.441168\pi\) | ||||
0.183777 | + | 0.982968i | \(0.441168\pi\) | |||||||
\(728\) | 2.23142 | 0.0827019 | ||||||||
\(729\) | −0.209870 | −0.00777297 | ||||||||
\(730\) | −12.6185 | −0.467032 | ||||||||
\(731\) | −25.7833 | −0.953631 | ||||||||
\(732\) | −6.69353 | −0.247400 | ||||||||
\(733\) | −25.1343 | −0.928355 | −0.464177 | − | 0.885742i | \(-0.653650\pi\) | ||||
−0.464177 | + | 0.885742i | \(0.653650\pi\) | |||||||
\(734\) | 3.24763 | 0.119872 | ||||||||
\(735\) | −1.71912 | −0.0634106 | ||||||||
\(736\) | −7.55262 | −0.278393 | ||||||||
\(737\) | −10.8692 | −0.400372 | ||||||||
\(738\) | −10.7945 | −0.397353 | ||||||||
\(739\) | 18.5339 | 0.681779 | 0.340890 | − | 0.940103i | \(-0.389272\pi\) | ||||
0.340890 | + | 0.940103i | \(0.389272\pi\) | |||||||
\(740\) | 1.53990 | 0.0566077 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.3485 | −0.416617 | ||||||||
\(743\) | −17.4596 | −0.640530 | −0.320265 | − | 0.947328i | \(-0.603772\pi\) | ||||
−0.320265 | + | 0.947328i | \(0.603772\pi\) | |||||||
\(744\) | −7.02681 | −0.257615 | ||||||||
\(745\) | −41.2999 | −1.51311 | ||||||||
\(746\) | 14.7858 | 0.541347 | ||||||||
\(747\) | −37.6405 | −1.37719 | ||||||||
\(748\) | −13.6991 | −0.500888 | ||||||||
\(749\) | −14.8536 | −0.542738 | ||||||||
\(750\) | −8.55890 | −0.312527 | ||||||||
\(751\) | 36.1521 | 1.31921 | 0.659605 | − | 0.751612i | \(-0.270724\pi\) | ||||
0.659605 | + | 0.751612i | \(0.270724\pi\) | |||||||
\(752\) | 11.2047 | 0.408592 | ||||||||
\(753\) | −3.67633 | −0.133973 | ||||||||
\(754\) | −10.7788 | −0.392540 | ||||||||
\(755\) | 43.2950 | 1.57567 | ||||||||
\(756\) | 4.15153 | 0.150990 | ||||||||
\(757\) | −16.8441 | −0.612207 | −0.306104 | − | 0.951998i | \(-0.599025\pi\) | ||||
−0.306104 | + | 0.951998i | \(0.599025\pi\) | |||||||
\(758\) | 28.2426 | 1.02582 | ||||||||
\(759\) | 28.5218 | 1.03528 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.23858 | −0.117399 | −0.0586993 | − | 0.998276i | \(-0.518695\pi\) | ||||
−0.0586993 | + | 0.998276i | \(0.518695\pi\) | |||||||
\(762\) | 13.7504 | 0.498124 | ||||||||
\(763\) | 0.937456 | 0.0339382 | ||||||||
\(764\) | −8.51380 | −0.308019 | ||||||||
\(765\) | −15.0381 | −0.543704 | ||||||||
\(766\) | 9.35499 | 0.338009 | ||||||||
\(767\) | −5.58861 | −0.201793 | ||||||||
\(768\) | −0.767178 | −0.0276831 | ||||||||
\(769\) | −19.1200 | −0.689485 | −0.344743 | − | 0.938697i | \(-0.612034\pi\) | ||||
−0.344743 | + | 0.938697i | \(0.612034\pi\) | |||||||
\(770\) | 11.0305 | 0.397510 | ||||||||
\(771\) | −10.9968 | −0.396039 | ||||||||
\(772\) | 9.54610 | 0.343572 | ||||||||
\(773\) | −29.8050 | −1.07201 | −0.536005 | − | 0.844215i | \(-0.680067\pi\) | ||||
−0.536005 | + | 0.844215i | \(0.680067\pi\) | |||||||
\(774\) | −22.3413 | −0.803041 | ||||||||
\(775\) | −0.195490 | −0.00702222 | ||||||||
\(776\) | −5.96881 | −0.214268 | ||||||||
\(777\) | −0.527202 | −0.0189133 | ||||||||
\(778\) | 3.13976 | 0.112566 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 3.83608 | 0.137354 | ||||||||
\(781\) | 52.1588 | 1.86639 | ||||||||
\(782\) | −21.0186 | −0.751625 | ||||||||
\(783\) | −20.0538 | −0.716665 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 30.2490 | 1.07963 | ||||||||
\(786\) | −5.84218 | −0.208384 | ||||||||
\(787\) | −53.6969 | −1.91409 | −0.957044 | − | 0.289943i | \(-0.906364\pi\) | ||||
−0.957044 | + | 0.289943i | \(0.906364\pi\) | |||||||
\(788\) | −19.4294 | −0.692142 | ||||||||
\(789\) | −3.09592 | −0.110218 | ||||||||
\(790\) | −8.58098 | −0.305298 | ||||||||
\(791\) | 12.2493 | 0.435536 | ||||||||
\(792\) | −11.8703 | −0.421791 | ||||||||
\(793\) | −19.4689 | −0.691360 | ||||||||
\(794\) | −22.6080 | −0.802328 | ||||||||
\(795\) | −19.5095 | −0.691929 | ||||||||
\(796\) | −9.73734 | −0.345131 | ||||||||
\(797\) | −25.9399 | −0.918839 | −0.459419 | − | 0.888219i | \(-0.651943\pi\) | ||||
−0.459419 | + | 0.888219i | \(0.651943\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.1821 | 1.10314 | ||||||||
\(800\) | −0.0213433 | −0.000754601 0 | ||||||||
\(801\) | 5.76924 | 0.203846 | ||||||||
\(802\) | −38.5295 | −1.36052 | ||||||||
\(803\) | −27.7193 | −0.978192 | ||||||||
\(804\) | −1.69399 | −0.0597423 | ||||||||
\(805\) | 16.9242 | 0.596499 | ||||||||
\(806\) | −20.4383 | −0.719907 | ||||||||
\(807\) | −0.987639 | −0.0347665 | ||||||||
\(808\) | −14.7081 | −0.517430 | ||||||||
\(809\) | 46.5746 | 1.63748 | 0.818738 | − | 0.574167i | \(-0.194674\pi\) | ||||
0.818738 | + | 0.574167i | \(0.194674\pi\) | |||||||
\(810\) | −9.07393 | −0.318825 | ||||||||
\(811\) | 21.8755 | 0.768154 | 0.384077 | − | 0.923301i | \(-0.374520\pi\) | ||||
0.384077 | + | 0.923301i | \(0.374520\pi\) | |||||||
\(812\) | −4.83046 | −0.169516 | ||||||||
\(813\) | −12.7741 | −0.448007 | ||||||||
\(814\) | 3.38271 | 0.118564 | ||||||||
\(815\) | 18.5373 | 0.649333 | ||||||||
\(816\) | −2.13502 | −0.0747408 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3.91368 | −0.136839 | ||||||||
\(819\) | 5.38093 | 0.188025 | ||||||||
\(820\) | −10.0309 | −0.350293 | ||||||||
\(821\) | 13.2858 | 0.463676 | 0.231838 | − | 0.972754i | \(-0.425526\pi\) | ||||
0.231838 | + | 0.972754i | \(0.425526\pi\) | |||||||
\(822\) | −1.82147 | −0.0635311 | ||||||||
\(823\) | 34.3764 | 1.19829 | 0.599143 | − | 0.800642i | \(-0.295508\pi\) | ||||
0.599143 | + | 0.800642i | \(0.295508\pi\) | |||||||
\(824\) | 0.138444 | 0.00482293 | ||||||||
\(825\) | 0.0806014 | 0.00280618 | ||||||||
\(826\) | −2.50451 | −0.0871430 | ||||||||
\(827\) | −14.2154 | −0.494317 | −0.247159 | − | 0.968975i | \(-0.579497\pi\) | ||||
−0.247159 | + | 0.968975i | \(0.579497\pi\) | |||||||
\(828\) | −18.2127 | −0.632934 | ||||||||
\(829\) | 49.6009 | 1.72271 | 0.861355 | − | 0.508004i | \(-0.169617\pi\) | ||||
0.861355 | + | 0.508004i | \(0.169617\pi\) | |||||||
\(830\) | −34.9775 | −1.21409 | ||||||||
\(831\) | −18.7696 | −0.651111 | ||||||||
\(832\) | −2.23142 | −0.0773606 | ||||||||
\(833\) | 2.78296 | 0.0964239 | ||||||||
\(834\) | 7.10225 | 0.245931 | ||||||||
\(835\) | 3.89177 | 0.134680 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −38.0252 | −1.31434 | ||||||||
\(838\) | −31.3819 | −1.08407 | ||||||||
\(839\) | 36.3106 | 1.25358 | 0.626791 | − | 0.779187i | \(-0.284368\pi\) | ||||
0.626791 | + | 0.779187i | \(0.284368\pi\) | |||||||
\(840\) | 1.71912 | 0.0593152 | ||||||||
\(841\) | −5.66664 | −0.195401 | ||||||||
\(842\) | −2.68280 | −0.0924553 | ||||||||
\(843\) | −12.2340 | −0.421360 | ||||||||
\(844\) | 5.62207 | 0.193520 | ||||||||
\(845\) | −17.9732 | −0.618297 | ||||||||
\(846\) | 27.0193 | 0.928944 | ||||||||
\(847\) | 13.2308 | 0.454616 | ||||||||
\(848\) | 11.3485 | 0.389710 | ||||||||
\(849\) | −3.91243 | −0.134274 | ||||||||
\(850\) | −0.0593977 | −0.00203732 | ||||||||
\(851\) | 5.19013 | 0.177916 | ||||||||
\(852\) | 8.12904 | 0.278496 | ||||||||
\(853\) | −29.3726 | −1.00570 | −0.502849 | − | 0.864374i | \(-0.667715\pi\) | ||||
−0.502849 | + | 0.864374i | \(0.667715\pi\) | |||||||
\(854\) | −8.72488 | −0.298559 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.8536 | 0.507685 | ||||||||
\(857\) | 37.7950 | 1.29105 | 0.645527 | − | 0.763737i | \(-0.276638\pi\) | ||||
0.645527 | + | 0.763737i | \(0.276638\pi\) | |||||||
\(858\) | 8.42677 | 0.287685 | ||||||||
\(859\) | 10.1542 | 0.346456 | 0.173228 | − | 0.984882i | \(-0.444580\pi\) | ||||
0.173228 | + | 0.984882i | \(0.444580\pi\) | |||||||
\(860\) | −20.7607 | −0.707934 | ||||||||
\(861\) | 3.43419 | 0.117037 | ||||||||
\(862\) | −6.16930 | −0.210127 | ||||||||
\(863\) | −34.0657 | −1.15961 | −0.579806 | − | 0.814755i | \(-0.696872\pi\) | ||||
−0.579806 | + | 0.814755i | \(0.696872\pi\) | |||||||
\(864\) | −4.15153 | −0.141238 | ||||||||
\(865\) | 40.9637 | 1.39281 | ||||||||
\(866\) | −4.43698 | −0.150775 | ||||||||
\(867\) | 7.10033 | 0.241140 | ||||||||
\(868\) | −9.15931 | −0.310887 | ||||||||
\(869\) | −18.8500 | −0.639442 | ||||||||
\(870\) | −8.30414 | −0.281537 | ||||||||
\(871\) | −4.92714 | −0.166950 | ||||||||
\(872\) | −0.937456 | −0.0317463 | ||||||||
\(873\) | −14.3934 | −0.487144 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1564 | −0.377153 | ||||||||
\(876\) | −4.32010 | −0.145963 | ||||||||
\(877\) | −12.7587 | −0.430830 | −0.215415 | − | 0.976523i | \(-0.569110\pi\) | ||||
−0.215415 | + | 0.976523i | \(0.569110\pi\) | |||||||
\(878\) | −24.9968 | −0.843601 | ||||||||
\(879\) | −19.6200 | −0.661766 | ||||||||
\(880\) | −11.0305 | −0.371837 | ||||||||
\(881\) | −49.2726 | −1.66004 | −0.830018 | − | 0.557737i | \(-0.811670\pi\) | ||||
−0.830018 | + | 0.557737i | \(0.811670\pi\) | |||||||
\(882\) | 2.41144 | 0.0811974 | ||||||||
\(883\) | 28.6708 | 0.964851 | 0.482425 | − | 0.875937i | \(-0.339756\pi\) | ||||
0.482425 | + | 0.875937i | \(0.339756\pi\) | |||||||
\(884\) | −6.20996 | −0.208863 | ||||||||
\(885\) | −4.30555 | −0.144729 | ||||||||
\(886\) | 9.40949 | 0.316118 | ||||||||
\(887\) | −47.8088 | −1.60526 | −0.802632 | − | 0.596475i | \(-0.796568\pi\) | ||||
−0.802632 | + | 0.596475i | \(0.796568\pi\) | |||||||
\(888\) | 0.527202 | 0.0176917 | ||||||||
\(889\) | 17.9233 | 0.601130 | ||||||||
\(890\) | 5.36108 | 0.179704 | ||||||||
\(891\) | −19.9329 | −0.667776 | ||||||||
\(892\) | 0.463833 | 0.0155303 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −14.1395 | −0.472897 | ||||||||
\(895\) | −14.9210 | −0.498754 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 12.9293 | 0.431696 | ||||||||
\(898\) | 21.7369 | 0.725369 | ||||||||
\(899\) | 44.2437 | 1.47561 | ||||||||
\(900\) | −0.0514682 | −0.00171561 | ||||||||
\(901\) | 31.5825 | 1.05217 | ||||||||
\(902\) | −22.0349 | −0.733683 | ||||||||
\(903\) | 7.10768 | 0.236529 | ||||||||
\(904\) | −12.2493 | −0.407407 | ||||||||
\(905\) | 3.04858 | 0.101338 | ||||||||
\(906\) | 14.8226 | 0.492447 | ||||||||
\(907\) | 4.50782 | 0.149680 | 0.0748398 | − | 0.997196i | \(-0.476155\pi\) | ||||
0.0748398 | + | 0.997196i | \(0.476155\pi\) | |||||||
\(908\) | −20.6434 | −0.685077 | ||||||||
\(909\) | −35.4677 | −1.17639 | ||||||||
\(910\) | 5.00025 | 0.165757 | ||||||||
\(911\) | −32.4239 | −1.07425 | −0.537125 | − | 0.843502i | \(-0.680490\pi\) | ||||
−0.537125 | + | 0.843502i | \(0.680490\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −76.8356 | −2.54289 | ||||||||
\(914\) | 0.0692620 | 0.00229098 | ||||||||
\(915\) | −14.9991 | −0.495855 | ||||||||
\(916\) | 6.21473 | 0.205340 | ||||||||
\(917\) | −7.61516 | −0.251475 | ||||||||
\(918\) | −11.5536 | −0.381324 | ||||||||
\(919\) | −6.44421 | −0.212575 | −0.106287 | − | 0.994335i | \(-0.533896\pi\) | ||||
−0.106287 | + | 0.994335i | \(0.533896\pi\) | |||||||
\(920\) | −16.9242 | −0.557973 | ||||||||
\(921\) | −13.4852 | −0.444352 | ||||||||
\(922\) | 9.55596 | 0.314709 | ||||||||
\(923\) | 23.6442 | 0.778259 | ||||||||
\(924\) | 3.77642 | 0.124235 | ||||||||
\(925\) | 0.0146671 | 0.000482251 0 | ||||||||
\(926\) | −3.08288 | −0.101310 | ||||||||
\(927\) | 0.333850 | 0.0109651 | ||||||||
\(928\) | 4.83046 | 0.158568 | ||||||||
\(929\) | −48.0761 | −1.57733 | −0.788663 | − | 0.614826i | \(-0.789226\pi\) | ||||
−0.788663 | + | 0.614826i | \(0.789226\pi\) | |||||||
\(930\) | −15.7459 | −0.516329 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.87941 | 0.127074 | ||||||||
\(933\) | 7.39666 | 0.242156 | ||||||||
\(934\) | 23.6336 | 0.773316 | ||||||||
\(935\) | −30.6974 | −1.00391 | ||||||||
\(936\) | −5.38093 | −0.175881 | ||||||||
\(937\) | 36.8634 | 1.20427 | 0.602137 | − | 0.798393i | \(-0.294316\pi\) | ||||
0.602137 | + | 0.798393i | \(0.294316\pi\) | |||||||
\(938\) | −2.20808 | −0.0720962 | ||||||||
\(939\) | 5.07044 | 0.165467 | ||||||||
\(940\) | 25.1078 | 0.818926 | ||||||||
\(941\) | 22.7283 | 0.740921 | 0.370461 | − | 0.928848i | \(-0.379200\pi\) | ||||
0.370461 | + | 0.928848i | \(0.379200\pi\) | |||||||
\(942\) | 10.3561 | 0.337420 | ||||||||
\(943\) | −33.8085 | −1.10095 | ||||||||
\(944\) | 2.50451 | 0.0815148 | ||||||||
\(945\) | 9.30291 | 0.302624 | ||||||||
\(946\) | −45.6054 | −1.48276 | ||||||||
\(947\) | 44.1148 | 1.43354 | 0.716769 | − | 0.697311i | \(-0.245620\pi\) | ||||
0.716769 | + | 0.697311i | \(0.245620\pi\) | |||||||
\(948\) | −2.93781 | −0.0954155 | ||||||||
\(949\) | −12.5655 | −0.407893 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.4706 | −0.469240 | ||||||||
\(952\) | −2.78296 | −0.0901963 | ||||||||
\(953\) | 6.87332 | 0.222649 | 0.111324 | − | 0.993784i | \(-0.464491\pi\) | ||||
0.111324 | + | 0.993784i | \(0.464491\pi\) | |||||||
\(954\) | 27.3663 | 0.886015 | ||||||||
\(955\) | −19.0780 | −0.617351 | ||||||||
\(956\) | −15.5680 | −0.503506 | ||||||||
\(957\) | −18.2418 | −0.589675 | ||||||||
\(958\) | 9.42310 | 0.304447 | ||||||||
\(959\) | −2.37425 | −0.0766685 | ||||||||
\(960\) | −1.71912 | −0.0554843 | ||||||||
\(961\) | 52.8929 | 1.70622 | ||||||||
\(962\) | 1.53343 | 0.0494396 | ||||||||
\(963\) | 35.8185 | 1.15424 | ||||||||
\(964\) | 6.80945 | 0.219317 | ||||||||
\(965\) | 21.3912 | 0.688608 | ||||||||
\(966\) | 5.79420 | 0.186425 | ||||||||
\(967\) | 15.4955 | 0.498303 | 0.249152 | − | 0.968464i | \(-0.419848\pi\) | ||||
0.249152 | + | 0.968464i | \(0.419848\pi\) | |||||||
\(968\) | −13.2308 | −0.425254 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.3751 | −0.429449 | ||||||||
\(971\) | −40.7332 | −1.30719 | −0.653596 | − | 0.756844i | \(-0.726740\pi\) | ||||
−0.653596 | + | 0.756844i | \(0.726740\pi\) | |||||||
\(972\) | −15.5612 | −0.499125 | ||||||||
\(973\) | 9.25763 | 0.296786 | ||||||||
\(974\) | −26.8713 | −0.861011 | ||||||||
\(975\) | 0.0365376 | 0.00117014 | ||||||||
\(976\) | 8.72488 | 0.279277 | ||||||||
\(977\) | −7.89391 | −0.252549 | −0.126274 | − | 0.991995i | \(-0.540302\pi\) | ||||
−0.126274 | + | 0.991995i | \(0.540302\pi\) | |||||||
\(978\) | 6.34647 | 0.202938 | ||||||||
\(979\) | 11.7768 | 0.376387 | ||||||||
\(980\) | 2.24084 | 0.0715809 | ||||||||
\(981\) | −2.26062 | −0.0721760 | ||||||||
\(982\) | 21.2384 | 0.677745 | ||||||||
\(983\) | 36.4754 | 1.16338 | 0.581692 | − | 0.813409i | \(-0.302391\pi\) | ||||
0.581692 | + | 0.813409i | \(0.302391\pi\) | |||||||
\(984\) | −3.43419 | −0.109478 | ||||||||
\(985\) | −43.5380 | −1.38724 | ||||||||
\(986\) | 13.4430 | 0.428112 | ||||||||
\(987\) | −8.59596 | −0.273612 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −69.9728 | −2.22501 | ||||||||
\(990\) | −26.5993 | −0.845381 | ||||||||
\(991\) | 32.8951 | 1.04495 | 0.522474 | − | 0.852655i | \(-0.325009\pi\) | ||||
0.522474 | + | 0.852655i | \(0.325009\pi\) | |||||||
\(992\) | 9.15931 | 0.290808 | ||||||||
\(993\) | 25.5751 | 0.811601 | ||||||||
\(994\) | 10.5960 | 0.336086 | ||||||||
\(995\) | −21.8198 | −0.691733 | ||||||||
\(996\) | −11.9750 | −0.379442 | ||||||||
\(997\) | 30.0472 | 0.951604 | 0.475802 | − | 0.879552i | \(-0.342158\pi\) | ||||
0.475802 | + | 0.879552i | \(0.342158\pi\) | |||||||
\(998\) | 6.88937 | 0.218079 | ||||||||
\(999\) | 2.85292 | 0.0902624 |
(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 | 5054.2.a.bl.1.5 | 12 | ||
19.6 | even | 9 | 266.2.u.d.169.2 | yes | 24 | ||
19.16 | even | 9 | 266.2.u.d.85.2 | ✓ | 24 | ||
19.18 | odd | 2 | 5054.2.a.bm.1.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
266.2.u.d.85.2 | ✓ | 24 | 19.16 | even | 9 | ||
266.2.u.d.169.2 | yes | 24 | 19.6 | even | 9 | ||
5054.2.a.bl.1.5 | 12 | 1.1 | even | 1 | trivial | ||
5054.2.a.bm.1.8 | 12 | 19.18 | odd | 2 |