Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4913.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.04948\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-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 | ||||||||
\(3\) | 3.04948 | 1.76062 | 0.880309 | − | 0.474400i | \(-0.157335\pi\) | ||||
0.880309 | + | 0.474400i | \(0.157335\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.48793 | 0.665422 | 0.332711 | − | 0.943029i | \(-0.392037\pi\) | ||||
0.332711 | + | 0.943029i | \(0.392037\pi\) | |||||||
\(6\) | −3.04948 | −1.24495 | ||||||||
\(7\) | 0.344151 | 0.130077 | 0.0650384 | − | 0.997883i | \(-0.479283\pi\) | ||||
0.0650384 | + | 0.997883i | \(0.479283\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.29934 | 2.09978 | ||||||||
\(10\) | −1.48793 | −0.470524 | ||||||||
\(11\) | −0.905704 | −0.273080 | −0.136540 | − | 0.990635i | \(-0.543598\pi\) | ||||
−0.136540 | + | 0.990635i | \(0.543598\pi\) | |||||||
\(12\) | 3.04948 | 0.880309 | ||||||||
\(13\) | −2.24985 | −0.623997 | −0.311999 | − | 0.950083i | \(-0.600998\pi\) | ||||
−0.311999 | + | 0.950083i | \(0.600998\pi\) | |||||||
\(14\) | −0.344151 | −0.0919782 | ||||||||
\(15\) | 4.53741 | 1.17155 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.58570 | 0.627123 | 0.313562 | − | 0.949568i | \(-0.398478\pi\) | ||||
0.313562 | + | 0.949568i | \(0.398478\pi\) | |||||||
\(18\) | −6.29934 | −1.48477 | ||||||||
\(19\) | −0.688301 | −0.157907 | −0.0789536 | − | 0.996878i | \(-0.525158\pi\) | ||||
−0.0789536 | + | 0.996878i | \(0.525158\pi\) | |||||||
\(20\) | 1.48793 | 0.332711 | ||||||||
\(21\) | 1.04948 | 0.229016 | ||||||||
\(22\) | 0.905704 | 0.193097 | ||||||||
\(23\) | 1.46259 | 0.304971 | 0.152486 | − | 0.988306i | \(-0.451272\pi\) | ||||
0.152486 | + | 0.988306i | \(0.451272\pi\) | |||||||
\(24\) | −3.04948 | −0.622473 | ||||||||
\(25\) | −2.78607 | −0.557214 | ||||||||
\(26\) | 2.24985 | 0.441233 | ||||||||
\(27\) | 10.0613 | 1.93629 | ||||||||
\(28\) | 0.344151 | 0.0650384 | ||||||||
\(29\) | −4.24274 | −0.787857 | −0.393929 | − | 0.919141i | \(-0.628884\pi\) | ||||
−0.393929 | + | 0.919141i | \(0.628884\pi\) | |||||||
\(30\) | −4.53741 | −0.828414 | ||||||||
\(31\) | 1.92985 | 0.346611 | 0.173305 | − | 0.984868i | \(-0.444555\pi\) | ||||
0.173305 | + | 0.984868i | \(0.444555\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.76193 | −0.480790 | ||||||||
\(34\) | −2.58570 | −0.443443 | ||||||||
\(35\) | 0.512072 | 0.0865559 | ||||||||
\(36\) | 6.29934 | 1.04989 | ||||||||
\(37\) | −1.84911 | −0.303991 | −0.151996 | − | 0.988381i | \(-0.548570\pi\) | ||||
−0.151996 | + | 0.988381i | \(0.548570\pi\) | |||||||
\(38\) | 0.688301 | 0.111657 | ||||||||
\(39\) | −6.86089 | −1.09862 | ||||||||
\(40\) | −1.48793 | −0.235262 | ||||||||
\(41\) | 1.21740 | 0.190126 | 0.0950631 | − | 0.995471i | \(-0.469695\pi\) | ||||
0.0950631 | + | 0.995471i | \(0.469695\pi\) | |||||||
\(42\) | −1.04948 | −0.161938 | ||||||||
\(43\) | −6.59036 | −1.00502 | −0.502510 | − | 0.864571i | \(-0.667590\pi\) | ||||
−0.502510 | + | 0.864571i | \(0.667590\pi\) | |||||||
\(44\) | −0.905704 | −0.136540 | ||||||||
\(45\) | 9.37296 | 1.39724 | ||||||||
\(46\) | −1.46259 | −0.215647 | ||||||||
\(47\) | −6.42244 | −0.936809 | −0.468405 | − | 0.883514i | \(-0.655171\pi\) | ||||
−0.468405 | + | 0.883514i | \(0.655171\pi\) | |||||||
\(48\) | 3.04948 | 0.440155 | ||||||||
\(49\) | −6.88156 | −0.983080 | ||||||||
\(50\) | 2.78607 | 0.394010 | ||||||||
\(51\) | 7.88503 | 1.10413 | ||||||||
\(52\) | −2.24985 | −0.311999 | ||||||||
\(53\) | 2.87689 | 0.395172 | 0.197586 | − | 0.980286i | \(-0.436690\pi\) | ||||
0.197586 | + | 0.980286i | \(0.436690\pi\) | |||||||
\(54\) | −10.0613 | −1.36916 | ||||||||
\(55\) | −1.34762 | −0.181713 | ||||||||
\(56\) | −0.344151 | −0.0459891 | ||||||||
\(57\) | −2.09896 | −0.278014 | ||||||||
\(58\) | 4.24274 | 0.557099 | ||||||||
\(59\) | 11.0118 | 1.43361 | 0.716806 | − | 0.697273i | \(-0.245603\pi\) | ||||
0.716806 | + | 0.697273i | \(0.245603\pi\) | |||||||
\(60\) | 4.53741 | 0.585777 | ||||||||
\(61\) | −1.75015 | −0.224083 | −0.112042 | − | 0.993704i | \(-0.535739\pi\) | ||||
−0.112042 | + | 0.993704i | \(0.535739\pi\) | |||||||
\(62\) | −1.92985 | −0.245091 | ||||||||
\(63\) | 2.16792 | 0.273132 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.34762 | −0.415221 | ||||||||
\(66\) | 2.76193 | 0.339970 | ||||||||
\(67\) | 4.34415 | 0.530722 | 0.265361 | − | 0.964149i | \(-0.414509\pi\) | ||||
0.265361 | + | 0.964149i | \(0.414509\pi\) | |||||||
\(68\) | 2.58570 | 0.313562 | ||||||||
\(69\) | 4.46014 | 0.536938 | ||||||||
\(70\) | −0.512072 | −0.0612043 | ||||||||
\(71\) | 5.29586 | 0.628503 | 0.314252 | − | 0.949340i | \(-0.398246\pi\) | ||||
0.314252 | + | 0.949340i | \(0.398246\pi\) | |||||||
\(72\) | −6.29934 | −0.742384 | ||||||||
\(73\) | 5.90206 | 0.690784 | 0.345392 | − | 0.938459i | \(-0.387746\pi\) | ||||
0.345392 | + | 0.938459i | \(0.387746\pi\) | |||||||
\(74\) | 1.84911 | 0.214954 | ||||||||
\(75\) | −8.49607 | −0.981041 | ||||||||
\(76\) | −0.688301 | −0.0789536 | ||||||||
\(77\) | −0.311699 | −0.0355213 | ||||||||
\(78\) | 6.86089 | 0.776843 | ||||||||
\(79\) | −15.1107 | −1.70009 | −0.850046 | − | 0.526709i | \(-0.823426\pi\) | ||||
−0.850046 | + | 0.526709i | \(0.823426\pi\) | |||||||
\(80\) | 1.48793 | 0.166355 | ||||||||
\(81\) | 11.7836 | 1.30929 | ||||||||
\(82\) | −1.21740 | −0.134440 | ||||||||
\(83\) | 15.7701 | 1.73099 | 0.865495 | − | 0.500918i | \(-0.167004\pi\) | ||||
0.865495 | + | 0.500918i | \(0.167004\pi\) | |||||||
\(84\) | 1.04948 | 0.114508 | ||||||||
\(85\) | 3.84733 | 0.417302 | ||||||||
\(86\) | 6.59036 | 0.710657 | ||||||||
\(87\) | −12.9382 | −1.38712 | ||||||||
\(88\) | 0.905704 | 0.0965483 | ||||||||
\(89\) | −1.61934 | −0.171650 | −0.0858250 | − | 0.996310i | \(-0.527353\pi\) | ||||
−0.0858250 | + | 0.996310i | \(0.527353\pi\) | |||||||
\(90\) | −9.37296 | −0.987997 | ||||||||
\(91\) | −0.774289 | −0.0811675 | ||||||||
\(92\) | 1.46259 | 0.152486 | ||||||||
\(93\) | 5.88503 | 0.610249 | ||||||||
\(94\) | 6.42244 | 0.662424 | ||||||||
\(95\) | −1.02414 | −0.105075 | ||||||||
\(96\) | −3.04948 | −0.311236 | ||||||||
\(97\) | 14.3436 | 1.45637 | 0.728184 | − | 0.685381i | \(-0.240364\pi\) | ||||
0.728184 | + | 0.685381i | \(0.240364\pi\) | |||||||
\(98\) | 6.88156 | 0.695143 | ||||||||
\(99\) | −5.70533 | −0.573407 | ||||||||
\(100\) | −2.78607 | −0.278607 | ||||||||
\(101\) | 2.90690 | 0.289247 | 0.144624 | − | 0.989487i | \(-0.453803\pi\) | ||||
0.144624 | + | 0.989487i | \(0.453803\pi\) | |||||||
\(102\) | −7.88503 | −0.780734 | ||||||||
\(103\) | −12.0866 | −1.19093 | −0.595464 | − | 0.803382i | \(-0.703032\pi\) | ||||
−0.595464 | + | 0.803382i | \(0.703032\pi\) | |||||||
\(104\) | 2.24985 | 0.220616 | ||||||||
\(105\) | 1.56155 | 0.152392 | ||||||||
\(106\) | −2.87689 | −0.279429 | ||||||||
\(107\) | −7.03712 | −0.680304 | −0.340152 | − | 0.940370i | \(-0.610479\pi\) | ||||
−0.340152 | + | 0.940370i | \(0.610479\pi\) | |||||||
\(108\) | 10.0613 | 0.968145 | ||||||||
\(109\) | −4.91926 | −0.471180 | −0.235590 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235590 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(110\) | 1.34762 | 0.128491 | ||||||||
\(111\) | −5.63882 | −0.535213 | ||||||||
\(112\) | 0.344151 | 0.0325192 | ||||||||
\(113\) | 10.5108 | 0.988775 | 0.494387 | − | 0.869242i | \(-0.335392\pi\) | ||||
0.494387 | + | 0.869242i | \(0.335392\pi\) | |||||||
\(114\) | 2.09896 | 0.196586 | ||||||||
\(115\) | 2.17623 | 0.202934 | ||||||||
\(116\) | −4.24274 | −0.393929 | ||||||||
\(117\) | −14.1726 | −1.31026 | ||||||||
\(118\) | −11.0118 | −1.01372 | ||||||||
\(119\) | 0.889869 | 0.0815742 | ||||||||
\(120\) | −4.53741 | −0.414207 | ||||||||
\(121\) | −10.1797 | −0.925427 | ||||||||
\(122\) | 1.75015 | 0.158451 | ||||||||
\(123\) | 3.71244 | 0.334740 | ||||||||
\(124\) | 1.92985 | 0.173305 | ||||||||
\(125\) | −11.5851 | −1.03620 | ||||||||
\(126\) | −2.16792 | −0.193134 | ||||||||
\(127\) | −20.0830 | −1.78207 | −0.891037 | − | 0.453930i | \(-0.850021\pi\) | ||||
−0.891037 | + | 0.453930i | \(0.850021\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −20.0972 | −1.76946 | ||||||||
\(130\) | 3.34762 | 0.293606 | ||||||||
\(131\) | −8.54572 | −0.746643 | −0.373321 | − | 0.927702i | \(-0.621781\pi\) | ||||
−0.373321 | + | 0.927702i | \(0.621781\pi\) | |||||||
\(132\) | −2.76193 | −0.240395 | ||||||||
\(133\) | −0.236879 | −0.0205401 | ||||||||
\(134\) | −4.34415 | −0.375277 | ||||||||
\(135\) | 14.9704 | 1.28845 | ||||||||
\(136\) | −2.58570 | −0.221722 | ||||||||
\(137\) | −15.0625 | −1.28687 | −0.643436 | − | 0.765500i | \(-0.722492\pi\) | ||||
−0.643436 | + | 0.765500i | \(0.722492\pi\) | |||||||
\(138\) | −4.46014 | −0.379673 | ||||||||
\(139\) | −2.85030 | −0.241760 | −0.120880 | − | 0.992667i | \(-0.538572\pi\) | ||||
−0.120880 | + | 0.992667i | \(0.538572\pi\) | |||||||
\(140\) | 0.512072 | 0.0432780 | ||||||||
\(141\) | −19.5851 | −1.64936 | ||||||||
\(142\) | −5.29586 | −0.444419 | ||||||||
\(143\) | 2.03770 | 0.170401 | ||||||||
\(144\) | 6.29934 | 0.524945 | ||||||||
\(145\) | −6.31289 | −0.524257 | ||||||||
\(146\) | −5.90206 | −0.488458 | ||||||||
\(147\) | −20.9852 | −1.73083 | ||||||||
\(148\) | −1.84911 | −0.151996 | ||||||||
\(149\) | −5.24502 | −0.429689 | −0.214844 | − | 0.976648i | \(-0.568924\pi\) | ||||
−0.214844 | + | 0.976648i | \(0.568924\pi\) | |||||||
\(150\) | 8.49607 | 0.693701 | ||||||||
\(151\) | 12.0613 | 0.981532 | 0.490766 | − | 0.871292i | \(-0.336717\pi\) | ||||
0.490766 | + | 0.871292i | \(0.336717\pi\) | |||||||
\(152\) | 0.688301 | 0.0558286 | ||||||||
\(153\) | 16.2882 | 1.31682 | ||||||||
\(154\) | 0.311699 | 0.0251174 | ||||||||
\(155\) | 2.87147 | 0.230642 | ||||||||
\(156\) | −6.86089 | −0.549311 | ||||||||
\(157\) | −14.4190 | −1.15076 | −0.575380 | − | 0.817887i | \(-0.695146\pi\) | ||||
−0.575380 | + | 0.817887i | \(0.695146\pi\) | |||||||
\(158\) | 15.1107 | 1.20215 | ||||||||
\(159\) | 8.77304 | 0.695747 | ||||||||
\(160\) | −1.48793 | −0.117631 | ||||||||
\(161\) | 0.503352 | 0.0396697 | ||||||||
\(162\) | −11.7836 | −0.925809 | ||||||||
\(163\) | 20.9562 | 1.64142 | 0.820708 | − | 0.571347i | \(-0.193579\pi\) | ||||
0.820708 | + | 0.571347i | \(0.193579\pi\) | |||||||
\(164\) | 1.21740 | 0.0950631 | ||||||||
\(165\) | −4.10955 | −0.319928 | ||||||||
\(166\) | −15.7701 | −1.22399 | ||||||||
\(167\) | −2.59520 | −0.200823 | −0.100411 | − | 0.994946i | \(-0.532016\pi\) | ||||
−0.100411 | + | 0.994946i | \(0.532016\pi\) | |||||||
\(168\) | −1.04948 | −0.0809692 | ||||||||
\(169\) | −7.93816 | −0.610627 | ||||||||
\(170\) | −3.84733 | −0.295077 | ||||||||
\(171\) | −4.33584 | −0.331570 | ||||||||
\(172\) | −6.59036 | −0.502510 | ||||||||
\(173\) | −15.6629 | −1.19083 | −0.595414 | − | 0.803419i | \(-0.703012\pi\) | ||||
−0.595414 | + | 0.803419i | \(0.703012\pi\) | |||||||
\(174\) | 12.9382 | 0.980839 | ||||||||
\(175\) | −0.958828 | −0.0724806 | ||||||||
\(176\) | −0.905704 | −0.0682700 | ||||||||
\(177\) | 33.5802 | 2.52404 | ||||||||
\(178\) | 1.61934 | 0.121375 | ||||||||
\(179\) | 25.1868 | 1.88255 | 0.941273 | − | 0.337646i | \(-0.109631\pi\) | ||||
0.941273 | + | 0.337646i | \(0.109631\pi\) | |||||||
\(180\) | 9.37296 | 0.698619 | ||||||||
\(181\) | 6.06957 | 0.451148 | 0.225574 | − | 0.974226i | \(-0.427574\pi\) | ||||
0.225574 | + | 0.974226i | \(0.427574\pi\) | |||||||
\(182\) | 0.774289 | 0.0573941 | ||||||||
\(183\) | −5.33704 | −0.394525 | ||||||||
\(184\) | −1.46259 | −0.107824 | ||||||||
\(185\) | −2.75134 | −0.202283 | ||||||||
\(186\) | −5.88503 | −0.431511 | ||||||||
\(187\) | −2.34187 | −0.171255 | ||||||||
\(188\) | −6.42244 | −0.468405 | ||||||||
\(189\) | 3.46259 | 0.251866 | ||||||||
\(190\) | 1.02414 | 0.0742992 | ||||||||
\(191\) | 8.11319 | 0.587050 | 0.293525 | − | 0.955951i | \(-0.405172\pi\) | ||||
0.293525 | + | 0.955951i | \(0.405172\pi\) | |||||||
\(192\) | 3.04948 | 0.220077 | ||||||||
\(193\) | −12.8968 | −0.928333 | −0.464166 | − | 0.885748i | \(-0.653646\pi\) | ||||
−0.464166 | + | 0.885748i | \(0.653646\pi\) | |||||||
\(194\) | −14.3436 | −1.02981 | ||||||||
\(195\) | −10.2085 | −0.731047 | ||||||||
\(196\) | −6.88156 | −0.491540 | ||||||||
\(197\) | 14.4920 | 1.03251 | 0.516257 | − | 0.856434i | \(-0.327325\pi\) | ||||
0.516257 | + | 0.856434i | \(0.327325\pi\) | |||||||
\(198\) | 5.70533 | 0.405460 | ||||||||
\(199\) | 20.5344 | 1.45564 | 0.727822 | − | 0.685766i | \(-0.240533\pi\) | ||||
0.727822 | + | 0.685766i | \(0.240533\pi\) | |||||||
\(200\) | 2.78607 | 0.197005 | ||||||||
\(201\) | 13.2474 | 0.934400 | ||||||||
\(202\) | −2.90690 | −0.204529 | ||||||||
\(203\) | −1.46014 | −0.102482 | ||||||||
\(204\) | 7.88503 | 0.552063 | ||||||||
\(205\) | 1.81141 | 0.126514 | ||||||||
\(206\) | 12.0866 | 0.842113 | ||||||||
\(207\) | 9.21335 | 0.640372 | ||||||||
\(208\) | −2.24985 | −0.155999 | ||||||||
\(209\) | 0.623397 | 0.0431213 | ||||||||
\(210\) | −1.56155 | −0.107757 | ||||||||
\(211\) | −6.99356 | −0.481456 | −0.240728 | − | 0.970593i | \(-0.577386\pi\) | ||||
−0.240728 | + | 0.970593i | \(0.577386\pi\) | |||||||
\(212\) | 2.87689 | 0.197586 | ||||||||
\(213\) | 16.1496 | 1.10655 | ||||||||
\(214\) | 7.03712 | 0.481047 | ||||||||
\(215\) | −9.80599 | −0.668763 | ||||||||
\(216\) | −10.0613 | −0.684582 | ||||||||
\(217\) | 0.664158 | 0.0450860 | ||||||||
\(218\) | 4.91926 | 0.333174 | ||||||||
\(219\) | 17.9982 | 1.21621 | ||||||||
\(220\) | −1.34762 | −0.0908567 | ||||||||
\(221\) | −5.81744 | −0.391323 | ||||||||
\(222\) | 5.63882 | 0.378453 | ||||||||
\(223\) | −8.26630 | −0.553552 | −0.276776 | − | 0.960934i | \(-0.589266\pi\) | ||||
−0.276776 | + | 0.960934i | \(0.589266\pi\) | |||||||
\(224\) | −0.344151 | −0.0229945 | ||||||||
\(225\) | −17.5504 | −1.17003 | ||||||||
\(226\) | −10.5108 | −0.699169 | ||||||||
\(227\) | −3.27586 | −0.217427 | −0.108713 | − | 0.994073i | \(-0.534673\pi\) | ||||
−0.108713 | + | 0.994073i | \(0.534673\pi\) | |||||||
\(228\) | −2.09896 | −0.139007 | ||||||||
\(229\) | −3.04601 | −0.201286 | −0.100643 | − | 0.994923i | \(-0.532090\pi\) | ||||
−0.100643 | + | 0.994923i | \(0.532090\pi\) | |||||||
\(230\) | −2.17623 | −0.143496 | ||||||||
\(231\) | −0.950519 | −0.0625395 | ||||||||
\(232\) | 4.24274 | 0.278550 | ||||||||
\(233\) | 12.9540 | 0.848644 | 0.424322 | − | 0.905511i | \(-0.360512\pi\) | ||||
0.424322 | + | 0.905511i | \(0.360512\pi\) | |||||||
\(234\) | 14.1726 | 0.926491 | ||||||||
\(235\) | −9.55613 | −0.623373 | ||||||||
\(236\) | 11.0118 | 0.716806 | ||||||||
\(237\) | −46.0799 | −2.99321 | ||||||||
\(238\) | −0.889869 | −0.0576817 | ||||||||
\(239\) | 8.68652 | 0.561885 | 0.280942 | − | 0.959725i | \(-0.409353\pi\) | ||||
0.280942 | + | 0.959725i | \(0.409353\pi\) | |||||||
\(240\) | 4.53741 | 0.292889 | ||||||||
\(241\) | −15.8491 | −1.02093 | −0.510465 | − | 0.859898i | \(-0.670527\pi\) | ||||
−0.510465 | + | 0.859898i | \(0.670527\pi\) | |||||||
\(242\) | 10.1797 | 0.654376 | ||||||||
\(243\) | 5.75015 | 0.368872 | ||||||||
\(244\) | −1.75015 | −0.112042 | ||||||||
\(245\) | −10.2393 | −0.654163 | ||||||||
\(246\) | −3.71244 | −0.236697 | ||||||||
\(247\) | 1.54858 | 0.0985337 | ||||||||
\(248\) | −1.92985 | −0.122545 | ||||||||
\(249\) | 48.0905 | 3.04761 | ||||||||
\(250\) | 11.5851 | 0.732707 | ||||||||
\(251\) | 4.61103 | 0.291046 | 0.145523 | − | 0.989355i | \(-0.453514\pi\) | ||||
0.145523 | + | 0.989355i | \(0.453514\pi\) | |||||||
\(252\) | 2.16792 | 0.136566 | ||||||||
\(253\) | −1.32467 | −0.0832815 | ||||||||
\(254\) | 20.0830 | 1.26012 | ||||||||
\(255\) | 11.7324 | 0.734709 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.2182 | 1.26118 | 0.630588 | − | 0.776118i | \(-0.282814\pi\) | ||||
0.630588 | + | 0.776118i | \(0.282814\pi\) | |||||||
\(258\) | 20.0972 | 1.25120 | ||||||||
\(259\) | −0.636372 | −0.0395422 | ||||||||
\(260\) | −3.34762 | −0.207611 | ||||||||
\(261\) | −26.7264 | −1.65433 | ||||||||
\(262\) | 8.54572 | 0.527956 | ||||||||
\(263\) | 15.7471 | 0.971009 | 0.485504 | − | 0.874234i | \(-0.338636\pi\) | ||||
0.485504 | + | 0.874234i | \(0.338636\pi\) | |||||||
\(264\) | 2.76193 | 0.169985 | ||||||||
\(265\) | 4.28061 | 0.262956 | ||||||||
\(266\) | 0.236879 | 0.0145240 | ||||||||
\(267\) | −4.93816 | −0.302210 | ||||||||
\(268\) | 4.34415 | 0.265361 | ||||||||
\(269\) | 1.00000 | 0.0609711 | ||||||||
\(270\) | −14.9704 | −0.911072 | ||||||||
\(271\) | 17.3316 | 1.05282 | 0.526410 | − | 0.850231i | \(-0.323538\pi\) | ||||
0.526410 | + | 0.850231i | \(0.323538\pi\) | |||||||
\(272\) | 2.58570 | 0.156781 | ||||||||
\(273\) | −2.36118 | −0.142905 | ||||||||
\(274\) | 15.0625 | 0.909956 | ||||||||
\(275\) | 2.52335 | 0.152164 | ||||||||
\(276\) | 4.46014 | 0.268469 | ||||||||
\(277\) | −23.1578 | −1.39142 | −0.695708 | − | 0.718325i | \(-0.744909\pi\) | ||||
−0.695708 | + | 0.718325i | \(0.744909\pi\) | |||||||
\(278\) | 2.85030 | 0.170950 | ||||||||
\(279\) | 12.1568 | 0.727806 | ||||||||
\(280\) | −0.512072 | −0.0306021 | ||||||||
\(281\) | −14.0106 | −0.835801 | −0.417901 | − | 0.908493i | \(-0.637234\pi\) | ||||
−0.417901 | + | 0.908493i | \(0.637234\pi\) | |||||||
\(282\) | 19.5851 | 1.16628 | ||||||||
\(283\) | 26.1135 | 1.55229 | 0.776145 | − | 0.630555i | \(-0.217173\pi\) | ||||
0.776145 | + | 0.630555i | \(0.217173\pi\) | |||||||
\(284\) | 5.29586 | 0.314252 | ||||||||
\(285\) | −3.12311 | −0.184997 | ||||||||
\(286\) | −2.03770 | −0.120492 | ||||||||
\(287\) | 0.418970 | 0.0247310 | ||||||||
\(288\) | −6.29934 | −0.371192 | ||||||||
\(289\) | −10.3142 | −0.606716 | ||||||||
\(290\) | 6.31289 | 0.370706 | ||||||||
\(291\) | 43.7404 | 2.56411 | ||||||||
\(292\) | 5.90206 | 0.345392 | ||||||||
\(293\) | −8.14964 | −0.476107 | −0.238053 | − | 0.971252i | \(-0.576509\pi\) | ||||
−0.238053 | + | 0.971252i | \(0.576509\pi\) | |||||||
\(294\) | 20.9852 | 1.22388 | ||||||||
\(295\) | 16.3847 | 0.953956 | ||||||||
\(296\) | 1.84911 | 0.107477 | ||||||||
\(297\) | −9.11252 | −0.528762 | ||||||||
\(298\) | 5.24502 | 0.303836 | ||||||||
\(299\) | −3.29062 | −0.190301 | ||||||||
\(300\) | −8.49607 | −0.490521 | ||||||||
\(301\) | −2.26808 | −0.130730 | ||||||||
\(302\) | −12.0613 | −0.694048 | ||||||||
\(303\) | 8.86453 | 0.509254 | ||||||||
\(304\) | −0.688301 | −0.0394768 | ||||||||
\(305\) | −2.60409 | −0.149110 | ||||||||
\(306\) | −16.2882 | −0.931133 | ||||||||
\(307\) | 0.809130 | 0.0461795 | 0.0230898 | − | 0.999733i | \(-0.492650\pi\) | ||||
0.0230898 | + | 0.999733i | \(0.492650\pi\) | |||||||
\(308\) | −0.311699 | −0.0177607 | ||||||||
\(309\) | −36.8579 | −2.09677 | ||||||||
\(310\) | −2.87147 | −0.163089 | ||||||||
\(311\) | −0.444367 | −0.0251977 | −0.0125989 | − | 0.999921i | \(-0.504010\pi\) | ||||
−0.0125989 | + | 0.999921i | \(0.504010\pi\) | |||||||
\(312\) | 6.86089 | 0.388421 | ||||||||
\(313\) | 1.05085 | 0.0593974 | 0.0296987 | − | 0.999559i | \(-0.490545\pi\) | ||||
0.0296987 | + | 0.999559i | \(0.490545\pi\) | |||||||
\(314\) | 14.4190 | 0.813710 | ||||||||
\(315\) | 3.22571 | 0.181748 | ||||||||
\(316\) | −15.1107 | −0.850046 | ||||||||
\(317\) | 6.46784 | 0.363270 | 0.181635 | − | 0.983366i | \(-0.441861\pi\) | ||||
0.181635 | + | 0.983366i | \(0.441861\pi\) | |||||||
\(318\) | −8.77304 | −0.491967 | ||||||||
\(319\) | 3.84266 | 0.215148 | ||||||||
\(320\) | 1.48793 | 0.0831777 | ||||||||
\(321\) | −21.4596 | −1.19776 | ||||||||
\(322\) | −0.503352 | −0.0280507 | ||||||||
\(323\) | −1.77974 | −0.0990273 | ||||||||
\(324\) | 11.7836 | 0.654646 | ||||||||
\(325\) | 6.26825 | 0.347700 | ||||||||
\(326\) | −20.9562 | −1.16066 | ||||||||
\(327\) | −15.0012 | −0.829568 | ||||||||
\(328\) | −1.21740 | −0.0672198 | ||||||||
\(329\) | −2.21029 | −0.121857 | ||||||||
\(330\) | 4.10955 | 0.226223 | ||||||||
\(331\) | 22.0153 | 1.21007 | 0.605034 | − | 0.796200i | \(-0.293160\pi\) | ||||
0.605034 | + | 0.796200i | \(0.293160\pi\) | |||||||
\(332\) | 15.7701 | 0.865495 | ||||||||
\(333\) | −11.6482 | −0.638315 | ||||||||
\(334\) | 2.59520 | 0.142003 | ||||||||
\(335\) | 6.46379 | 0.353154 | ||||||||
\(336\) | 1.04948 | 0.0572539 | ||||||||
\(337\) | 14.2647 | 0.777047 | 0.388524 | − | 0.921439i | \(-0.372985\pi\) | ||||
0.388524 | + | 0.921439i | \(0.372985\pi\) | |||||||
\(338\) | 7.93816 | 0.431779 | ||||||||
\(339\) | 32.0525 | 1.74086 | ||||||||
\(340\) | 3.84733 | 0.208651 | ||||||||
\(341\) | −1.74787 | −0.0946524 | ||||||||
\(342\) | 4.33584 | 0.234455 | ||||||||
\(343\) | −4.77735 | −0.257953 | ||||||||
\(344\) | 6.59036 | 0.355329 | ||||||||
\(345\) | 6.63637 | 0.357290 | ||||||||
\(346\) | 15.6629 | 0.842043 | ||||||||
\(347\) | 26.0825 | 1.40018 | 0.700092 | − | 0.714052i | \(-0.253142\pi\) | ||||
0.700092 | + | 0.714052i | \(0.253142\pi\) | |||||||
\(348\) | −12.9382 | −0.693558 | ||||||||
\(349\) | 24.5684 | 1.31512 | 0.657559 | − | 0.753403i | \(-0.271589\pi\) | ||||
0.657559 | + | 0.753403i | \(0.271589\pi\) | |||||||
\(350\) | 0.958828 | 0.0512515 | ||||||||
\(351\) | −22.6364 | −1.20824 | ||||||||
\(352\) | 0.905704 | 0.0482742 | ||||||||
\(353\) | 8.36823 | 0.445396 | 0.222698 | − | 0.974887i | \(-0.428514\pi\) | ||||
0.222698 | + | 0.974887i | \(0.428514\pi\) | |||||||
\(354\) | −33.5802 | −1.78477 | ||||||||
\(355\) | 7.87987 | 0.418220 | ||||||||
\(356\) | −1.61934 | −0.0858250 | ||||||||
\(357\) | 2.71364 | 0.143621 | ||||||||
\(358\) | −25.1868 | −1.33116 | ||||||||
\(359\) | −2.12835 | −0.112330 | −0.0561651 | − | 0.998421i | \(-0.517887\pi\) | ||||
−0.0561651 | + | 0.998421i | \(0.517887\pi\) | |||||||
\(360\) | −9.37296 | −0.493998 | ||||||||
\(361\) | −18.5262 | −0.975065 | ||||||||
\(362\) | −6.06957 | −0.319010 | ||||||||
\(363\) | −31.0428 | −1.62932 | ||||||||
\(364\) | −0.774289 | −0.0405838 | ||||||||
\(365\) | 8.78184 | 0.459663 | ||||||||
\(366\) | 5.33704 | 0.278971 | ||||||||
\(367\) | 9.53496 | 0.497721 | 0.248860 | − | 0.968539i | \(-0.419944\pi\) | ||||
0.248860 | + | 0.968539i | \(0.419944\pi\) | |||||||
\(368\) | 1.46259 | 0.0762428 | ||||||||
\(369\) | 7.66882 | 0.399223 | ||||||||
\(370\) | 2.75134 | 0.143035 | ||||||||
\(371\) | 0.990085 | 0.0514027 | ||||||||
\(372\) | 5.88503 | 0.305125 | ||||||||
\(373\) | 16.7808 | 0.868875 | 0.434437 | − | 0.900702i | \(-0.356947\pi\) | ||||
0.434437 | + | 0.900702i | \(0.356947\pi\) | |||||||
\(374\) | 2.34187 | 0.121095 | ||||||||
\(375\) | −35.3286 | −1.82436 | ||||||||
\(376\) | 6.42244 | 0.331212 | ||||||||
\(377\) | 9.54555 | 0.491621 | ||||||||
\(378\) | −3.46259 | −0.178096 | ||||||||
\(379\) | −29.0341 | −1.49138 | −0.745690 | − | 0.666293i | \(-0.767880\pi\) | ||||
−0.745690 | + | 0.666293i | \(0.767880\pi\) | |||||||
\(380\) | −1.02414 | −0.0525374 | ||||||||
\(381\) | −61.2426 | −3.13755 | ||||||||
\(382\) | −8.11319 | −0.415107 | ||||||||
\(383\) | 35.5798 | 1.81804 | 0.909022 | − | 0.416749i | \(-0.136831\pi\) | ||||
0.909022 | + | 0.416749i | \(0.136831\pi\) | |||||||
\(384\) | −3.04948 | −0.155618 | ||||||||
\(385\) | −0.463785 | −0.0236367 | ||||||||
\(386\) | 12.8968 | 0.656430 | ||||||||
\(387\) | −41.5149 | −2.11032 | ||||||||
\(388\) | 14.3436 | 0.728184 | ||||||||
\(389\) | −37.5839 | −1.90558 | −0.952789 | − | 0.303634i | \(-0.901800\pi\) | ||||
−0.952789 | + | 0.303634i | \(0.901800\pi\) | |||||||
\(390\) | 10.2085 | 0.516928 | ||||||||
\(391\) | 3.78181 | 0.191255 | ||||||||
\(392\) | 6.88156 | 0.347571 | ||||||||
\(393\) | −26.0600 | −1.31455 | ||||||||
\(394\) | −14.4920 | −0.730097 | ||||||||
\(395\) | −22.4837 | −1.13128 | ||||||||
\(396\) | −5.70533 | −0.286704 | ||||||||
\(397\) | −16.8913 | −0.847750 | −0.423875 | − | 0.905721i | \(-0.639330\pi\) | ||||
−0.423875 | + | 0.905721i | \(0.639330\pi\) | |||||||
\(398\) | −20.5344 | −1.02930 | ||||||||
\(399\) | −0.722359 | −0.0361632 | ||||||||
\(400\) | −2.78607 | −0.139303 | ||||||||
\(401\) | 3.68585 | 0.184063 | 0.0920314 | − | 0.995756i | \(-0.470664\pi\) | ||||
0.0920314 | + | 0.995756i | \(0.470664\pi\) | |||||||
\(402\) | −13.2474 | −0.660721 | ||||||||
\(403\) | −4.34187 | −0.216284 | ||||||||
\(404\) | 2.90690 | 0.144624 | ||||||||
\(405\) | 17.5332 | 0.871231 | ||||||||
\(406\) | 1.46014 | 0.0724656 | ||||||||
\(407\) | 1.67474 | 0.0830140 | ||||||||
\(408\) | −7.88503 | −0.390367 | ||||||||
\(409\) | 18.5784 | 0.918643 | 0.459322 | − | 0.888270i | \(-0.348093\pi\) | ||||
0.459322 | + | 0.888270i | \(0.348093\pi\) | |||||||
\(410\) | −1.81141 | −0.0894590 | ||||||||
\(411\) | −45.9327 | −2.26569 | ||||||||
\(412\) | −12.0866 | −0.595464 | ||||||||
\(413\) | 3.78971 | 0.186480 | ||||||||
\(414\) | −9.21335 | −0.452811 | ||||||||
\(415\) | 23.4647 | 1.15184 | ||||||||
\(416\) | 2.24985 | 0.110308 | ||||||||
\(417\) | −8.69194 | −0.425646 | ||||||||
\(418\) | −0.623397 | −0.0304913 | ||||||||
\(419\) | 3.30890 | 0.161650 | 0.0808251 | − | 0.996728i | \(-0.474244\pi\) | ||||
0.0808251 | + | 0.996728i | \(0.474244\pi\) | |||||||
\(420\) | 1.56155 | 0.0761960 | ||||||||
\(421\) | 7.23994 | 0.352853 | 0.176427 | − | 0.984314i | \(-0.443546\pi\) | ||||
0.176427 | + | 0.984314i | \(0.443546\pi\) | |||||||
\(422\) | 6.99356 | 0.340441 | ||||||||
\(423\) | −40.4571 | −1.96709 | ||||||||
\(424\) | −2.87689 | −0.139714 | ||||||||
\(425\) | −7.20393 | −0.349442 | ||||||||
\(426\) | −16.1496 | −0.782453 | ||||||||
\(427\) | −0.602314 | −0.0291480 | ||||||||
\(428\) | −7.03712 | −0.340152 | ||||||||
\(429\) | 6.21393 | 0.300011 | ||||||||
\(430\) | 9.80599 | 0.472887 | ||||||||
\(431\) | −11.1645 | −0.537777 | −0.268888 | − | 0.963171i | \(-0.586656\pi\) | ||||
−0.268888 | + | 0.963171i | \(0.586656\pi\) | |||||||
\(432\) | 10.0613 | 0.484073 | ||||||||
\(433\) | 28.8143 | 1.38473 | 0.692363 | − | 0.721549i | \(-0.256570\pi\) | ||||
0.692363 | + | 0.721549i | \(0.256570\pi\) | |||||||
\(434\) | −0.664158 | −0.0318806 | ||||||||
\(435\) | −19.2510 | −0.923017 | ||||||||
\(436\) | −4.91926 | −0.235590 | ||||||||
\(437\) | −1.00670 | −0.0481571 | ||||||||
\(438\) | −17.9982 | −0.859988 | ||||||||
\(439\) | 20.4897 | 0.977922 | 0.488961 | − | 0.872306i | \(-0.337376\pi\) | ||||
0.488961 | + | 0.872306i | \(0.337376\pi\) | |||||||
\(440\) | 1.34762 | 0.0642454 | ||||||||
\(441\) | −43.3493 | −2.06425 | ||||||||
\(442\) | 5.81744 | 0.276707 | ||||||||
\(443\) | 9.58503 | 0.455398 | 0.227699 | − | 0.973732i | \(-0.426880\pi\) | ||||
0.227699 | + | 0.973732i | \(0.426880\pi\) | |||||||
\(444\) | −5.63882 | −0.267607 | ||||||||
\(445\) | −2.40947 | −0.114220 | ||||||||
\(446\) | 8.26630 | 0.391421 | ||||||||
\(447\) | −15.9946 | −0.756518 | ||||||||
\(448\) | 0.344151 | 0.0162596 | ||||||||
\(449\) | −21.4476 | −1.01218 | −0.506088 | − | 0.862482i | \(-0.668909\pi\) | ||||
−0.506088 | + | 0.862482i | \(0.668909\pi\) | |||||||
\(450\) | 17.5504 | 0.827333 | ||||||||
\(451\) | −1.10261 | −0.0519197 | ||||||||
\(452\) | 10.5108 | 0.494387 | ||||||||
\(453\) | 36.7806 | 1.72810 | ||||||||
\(454\) | 3.27586 | 0.153744 | ||||||||
\(455\) | −1.15209 | −0.0540107 | ||||||||
\(456\) | 2.09896 | 0.0982929 | ||||||||
\(457\) | 10.7176 | 0.501350 | 0.250675 | − | 0.968071i | \(-0.419347\pi\) | ||||
0.250675 | + | 0.968071i | \(0.419347\pi\) | |||||||
\(458\) | 3.04601 | 0.142331 | ||||||||
\(459\) | 26.0154 | 1.21429 | ||||||||
\(460\) | 2.17623 | 0.101467 | ||||||||
\(461\) | −19.6658 | −0.915926 | −0.457963 | − | 0.888971i | \(-0.651421\pi\) | ||||
−0.457963 | + | 0.888971i | \(0.651421\pi\) | |||||||
\(462\) | 0.950519 | 0.0442221 | ||||||||
\(463\) | 22.6226 | 1.05136 | 0.525682 | − | 0.850681i | \(-0.323810\pi\) | ||||
0.525682 | + | 0.850681i | \(0.323810\pi\) | |||||||
\(464\) | −4.24274 | −0.196964 | ||||||||
\(465\) | 8.75651 | 0.406073 | ||||||||
\(466\) | −12.9540 | −0.600082 | ||||||||
\(467\) | 30.0503 | 1.39056 | 0.695282 | − | 0.718737i | \(-0.255280\pi\) | ||||
0.695282 | + | 0.718737i | \(0.255280\pi\) | |||||||
\(468\) | −14.1726 | −0.655128 | ||||||||
\(469\) | 1.49504 | 0.0690347 | ||||||||
\(470\) | 9.55613 | 0.440792 | ||||||||
\(471\) | −43.9704 | −2.02605 | ||||||||
\(472\) | −11.0118 | −0.506858 | ||||||||
\(473\) | 5.96891 | 0.274451 | ||||||||
\(474\) | 46.0799 | 2.11652 | ||||||||
\(475\) | 1.91766 | 0.0879881 | ||||||||
\(476\) | 0.889869 | 0.0407871 | ||||||||
\(477\) | 18.1225 | 0.829773 | ||||||||
\(478\) | −8.68652 | −0.397312 | ||||||||
\(479\) | −32.6251 | −1.49068 | −0.745339 | − | 0.666685i | \(-0.767712\pi\) | ||||
−0.745339 | + | 0.666685i | \(0.767712\pi\) | |||||||
\(480\) | −4.53741 | −0.207103 | ||||||||
\(481\) | 4.16022 | 0.189690 | ||||||||
\(482\) | 15.8491 | 0.721907 | ||||||||
\(483\) | 1.53496 | 0.0698432 | ||||||||
\(484\) | −10.1797 | −0.462714 | ||||||||
\(485\) | 21.3422 | 0.969099 | ||||||||
\(486\) | −5.75015 | −0.260832 | ||||||||
\(487\) | −4.12981 | −0.187139 | −0.0935697 | − | 0.995613i | \(-0.529828\pi\) | ||||
−0.0935697 | + | 0.995613i | \(0.529828\pi\) | |||||||
\(488\) | 1.75015 | 0.0792254 | ||||||||
\(489\) | 63.9056 | 2.88991 | ||||||||
\(490\) | 10.2393 | 0.462563 | ||||||||
\(491\) | −35.2225 | −1.58957 | −0.794785 | − | 0.606891i | \(-0.792416\pi\) | ||||
−0.794785 | + | 0.606891i | \(0.792416\pi\) | |||||||
\(492\) | 3.71244 | 0.167370 | ||||||||
\(493\) | −10.9704 | −0.494084 | ||||||||
\(494\) | −1.54858 | −0.0696738 | ||||||||
\(495\) | −8.48912 | −0.381558 | ||||||||
\(496\) | 1.92985 | 0.0866527 | ||||||||
\(497\) | 1.82258 | 0.0817537 | ||||||||
\(498\) | −48.0905 | −2.15499 | ||||||||
\(499\) | 16.3253 | 0.730819 | 0.365409 | − | 0.930847i | \(-0.380929\pi\) | ||||
0.365409 | + | 0.930847i | \(0.380929\pi\) | |||||||
\(500\) | −11.5851 | −0.518102 | ||||||||
\(501\) | −7.91401 | −0.353572 | ||||||||
\(502\) | −4.61103 | −0.205801 | ||||||||
\(503\) | 39.0571 | 1.74147 | 0.870736 | − | 0.491751i | \(-0.163643\pi\) | ||||
0.870736 | + | 0.491751i | \(0.163643\pi\) | |||||||
\(504\) | −2.16792 | −0.0965669 | ||||||||
\(505\) | 4.32526 | 0.192471 | ||||||||
\(506\) | 1.32467 | 0.0588889 | ||||||||
\(507\) | −24.2073 | −1.07508 | ||||||||
\(508\) | −20.0830 | −0.891037 | ||||||||
\(509\) | 8.19139 | 0.363077 | 0.181539 | − | 0.983384i | \(-0.441892\pi\) | ||||
0.181539 | + | 0.983384i | \(0.441892\pi\) | |||||||
\(510\) | −11.7324 | −0.519518 | ||||||||
\(511\) | 2.03120 | 0.0898549 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.92518 | −0.305754 | ||||||||
\(514\) | −20.2182 | −0.891786 | ||||||||
\(515\) | −17.9840 | −0.792469 | ||||||||
\(516\) | −20.0972 | −0.884729 | ||||||||
\(517\) | 5.81683 | 0.255824 | ||||||||
\(518\) | 0.636372 | 0.0279606 | ||||||||
\(519\) | −47.7637 | −2.09660 | ||||||||
\(520\) | 3.34762 | 0.146803 | ||||||||
\(521\) | −9.81960 | −0.430205 | −0.215102 | − | 0.976592i | \(-0.569009\pi\) | ||||
−0.215102 | + | 0.976592i | \(0.569009\pi\) | |||||||
\(522\) | 26.7264 | 1.16978 | ||||||||
\(523\) | 4.42973 | 0.193698 | 0.0968492 | − | 0.995299i | \(-0.469124\pi\) | ||||
0.0968492 | + | 0.995299i | \(0.469124\pi\) | |||||||
\(524\) | −8.54572 | −0.373321 | ||||||||
\(525\) | −2.92393 | −0.127611 | ||||||||
\(526\) | −15.7471 | −0.686607 | ||||||||
\(527\) | 4.99000 | 0.217368 | ||||||||
\(528\) | −2.76193 | −0.120197 | ||||||||
\(529\) | −20.8608 | −0.906993 | ||||||||
\(530\) | −4.28061 | −0.185938 | ||||||||
\(531\) | 69.3669 | 3.01027 | ||||||||
\(532\) | −0.236879 | −0.0102700 | ||||||||
\(533\) | −2.73898 | −0.118638 | ||||||||
\(534\) | 4.93816 | 0.213695 | ||||||||
\(535\) | −10.4707 | −0.452689 | ||||||||
\(536\) | −4.34415 | −0.187639 | ||||||||
\(537\) | 76.8065 | 3.31445 | ||||||||
\(538\) | −1.00000 | −0.0431131 | ||||||||
\(539\) | 6.23265 | 0.268459 | ||||||||
\(540\) | 14.9704 | 0.644225 | ||||||||
\(541\) | 3.01458 | 0.129607 | 0.0648035 | − | 0.997898i | \(-0.479358\pi\) | ||||
0.0648035 | + | 0.997898i | \(0.479358\pi\) | |||||||
\(542\) | −17.3316 | −0.744457 | ||||||||
\(543\) | 18.5090 | 0.794299 | ||||||||
\(544\) | −2.58570 | −0.110861 | ||||||||
\(545\) | −7.31951 | −0.313533 | ||||||||
\(546\) | 2.36118 | 0.101049 | ||||||||
\(547\) | 35.5411 | 1.51963 | 0.759813 | − | 0.650141i | \(-0.225290\pi\) | ||||
0.759813 | + | 0.650141i | \(0.225290\pi\) | |||||||
\(548\) | −15.0625 | −0.643436 | ||||||||
\(549\) | −11.0248 | −0.470525 | ||||||||
\(550\) | −2.52335 | −0.107596 | ||||||||
\(551\) | 2.92028 | 0.124408 | ||||||||
\(552\) | −4.46014 | −0.189836 | ||||||||
\(553\) | −5.20037 | −0.221142 | ||||||||
\(554\) | 23.1578 | 0.983880 | ||||||||
\(555\) | −8.39016 | −0.356142 | ||||||||
\(556\) | −2.85030 | −0.120880 | ||||||||
\(557\) | 21.5510 | 0.913144 | 0.456572 | − | 0.889687i | \(-0.349077\pi\) | ||||
0.456572 | + | 0.889687i | \(0.349077\pi\) | |||||||
\(558\) | −12.1568 | −0.514636 | ||||||||
\(559\) | 14.8274 | 0.627130 | ||||||||
\(560\) | 0.512072 | 0.0216390 | ||||||||
\(561\) | −7.14150 | −0.301514 | ||||||||
\(562\) | 14.0106 | 0.591001 | ||||||||
\(563\) | 30.3310 | 1.27830 | 0.639150 | − | 0.769082i | \(-0.279286\pi\) | ||||
0.639150 | + | 0.769082i | \(0.279286\pi\) | |||||||
\(564\) | −19.5851 | −0.824682 | ||||||||
\(565\) | 15.6393 | 0.657952 | ||||||||
\(566\) | −26.1135 | −1.09763 | ||||||||
\(567\) | 4.05534 | 0.170308 | ||||||||
\(568\) | −5.29586 | −0.222210 | ||||||||
\(569\) | 3.78038 | 0.158482 | 0.0792409 | − | 0.996855i | \(-0.474750\pi\) | ||||
0.0792409 | + | 0.996855i | \(0.474750\pi\) | |||||||
\(570\) | 3.12311 | 0.130812 | ||||||||
\(571\) | 18.4336 | 0.771424 | 0.385712 | − | 0.922619i | \(-0.373956\pi\) | ||||
0.385712 | + | 0.922619i | \(0.373956\pi\) | |||||||
\(572\) | 2.03770 | 0.0852006 | ||||||||
\(573\) | 24.7410 | 1.03357 | ||||||||
\(574\) | −0.418970 | −0.0174875 | ||||||||
\(575\) | −4.07488 | −0.169934 | ||||||||
\(576\) | 6.29934 | 0.262472 | ||||||||
\(577\) | 30.3922 | 1.26524 | 0.632622 | − | 0.774461i | \(-0.281979\pi\) | ||||
0.632622 | + | 0.774461i | \(0.281979\pi\) | |||||||
\(578\) | 10.3142 | 0.429013 | ||||||||
\(579\) | −39.3286 | −1.63444 | ||||||||
\(580\) | −6.31289 | −0.262129 | ||||||||
\(581\) | 5.42728 | 0.225161 | ||||||||
\(582\) | −43.7404 | −1.81310 | ||||||||
\(583\) | −2.60561 | −0.107913 | ||||||||
\(584\) | −5.90206 | −0.244229 | ||||||||
\(585\) | −21.0878 | −0.871873 | ||||||||
\(586\) | 8.14964 | 0.336658 | ||||||||
\(587\) | −38.4248 | −1.58596 | −0.792981 | − | 0.609246i | \(-0.791472\pi\) | ||||
−0.792981 | + | 0.609246i | \(0.791472\pi\) | |||||||
\(588\) | −20.9852 | −0.865415 | ||||||||
\(589\) | −1.32832 | −0.0547323 | ||||||||
\(590\) | −16.3847 | −0.674549 | ||||||||
\(591\) | 44.1931 | 1.81786 | ||||||||
\(592\) | −1.84911 | −0.0759979 | ||||||||
\(593\) | 15.0010 | 0.616018 | 0.308009 | − | 0.951383i | \(-0.400337\pi\) | ||||
0.308009 | + | 0.951383i | \(0.400337\pi\) | |||||||
\(594\) | 9.11252 | 0.373891 | ||||||||
\(595\) | 1.32406 | 0.0542812 | ||||||||
\(596\) | −5.24502 | −0.214844 | ||||||||
\(597\) | 62.6192 | 2.56283 | ||||||||
\(598\) | 3.29062 | 0.134563 | ||||||||
\(599\) | −8.67407 | −0.354413 | −0.177207 | − | 0.984174i | \(-0.556706\pi\) | ||||
−0.177207 | + | 0.984174i | \(0.556706\pi\) | |||||||
\(600\) | 8.49607 | 0.346850 | ||||||||
\(601\) | −20.1244 | −0.820891 | −0.410445 | − | 0.911885i | \(-0.634627\pi\) | ||||
−0.410445 | + | 0.911885i | \(0.634627\pi\) | |||||||
\(602\) | 2.26808 | 0.0924400 | ||||||||
\(603\) | 27.3653 | 1.11440 | ||||||||
\(604\) | 12.0613 | 0.490766 | ||||||||
\(605\) | −15.1467 | −0.615800 | ||||||||
\(606\) | −8.86453 | −0.360097 | ||||||||
\(607\) | 5.35730 | 0.217446 | 0.108723 | − | 0.994072i | \(-0.465324\pi\) | ||||
0.108723 | + | 0.994072i | \(0.465324\pi\) | |||||||
\(608\) | 0.688301 | 0.0279143 | ||||||||
\(609\) | −4.45268 | −0.180432 | ||||||||
\(610\) | 2.60409 | 0.105437 | ||||||||
\(611\) | 14.4496 | 0.584566 | ||||||||
\(612\) | 16.2882 | 0.658410 | ||||||||
\(613\) | 21.6009 | 0.872454 | 0.436227 | − | 0.899837i | \(-0.356314\pi\) | ||||
0.436227 | + | 0.899837i | \(0.356314\pi\) | |||||||
\(614\) | −0.809130 | −0.0326538 | ||||||||
\(615\) | 5.52385 | 0.222743 | ||||||||
\(616\) | 0.311699 | 0.0125587 | ||||||||
\(617\) | −36.2231 | −1.45829 | −0.729144 | − | 0.684360i | \(-0.760082\pi\) | ||||
−0.729144 | + | 0.684360i | \(0.760082\pi\) | |||||||
\(618\) | 36.8579 | 1.48264 | ||||||||
\(619\) | 31.9927 | 1.28590 | 0.642948 | − | 0.765910i | \(-0.277711\pi\) | ||||
0.642948 | + | 0.765910i | \(0.277711\pi\) | |||||||
\(620\) | 2.87147 | 0.115321 | ||||||||
\(621\) | 14.7155 | 0.590513 | ||||||||
\(622\) | 0.444367 | 0.0178175 | ||||||||
\(623\) | −0.557298 | −0.0223277 | ||||||||
\(624\) | −6.86089 | −0.274655 | ||||||||
\(625\) | −3.30747 | −0.132299 | ||||||||
\(626\) | −1.05085 | −0.0420003 | ||||||||
\(627\) | 1.90104 | 0.0759201 | ||||||||
\(628\) | −14.4190 | −0.575380 | ||||||||
\(629\) | −4.78123 | −0.190640 | ||||||||
\(630\) | −3.22571 | −0.128515 | ||||||||
\(631\) | −22.3539 | −0.889894 | −0.444947 | − | 0.895557i | \(-0.646778\pi\) | ||||
−0.444947 | + | 0.895557i | \(0.646778\pi\) | |||||||
\(632\) | 15.1107 | 0.601073 | ||||||||
\(633\) | −21.3267 | −0.847661 | ||||||||
\(634\) | −6.46784 | −0.256871 | ||||||||
\(635\) | −29.8820 | −1.18583 | ||||||||
\(636\) | 8.77304 | 0.347873 | ||||||||
\(637\) | 15.4825 | 0.613439 | ||||||||
\(638\) | −3.84266 | −0.152133 | ||||||||
\(639\) | 33.3604 | 1.31972 | ||||||||
\(640\) | −1.48793 | −0.0588155 | ||||||||
\(641\) | −8.18573 | −0.323317 | −0.161659 | − | 0.986847i | \(-0.551684\pi\) | ||||
−0.161659 | + | 0.986847i | \(0.551684\pi\) | |||||||
\(642\) | 21.4596 | 0.846941 | ||||||||
\(643\) | 17.4703 | 0.688961 | 0.344480 | − | 0.938793i | \(-0.388055\pi\) | ||||
0.344480 | + | 0.938793i | \(0.388055\pi\) | |||||||
\(644\) | 0.503352 | 0.0198348 | ||||||||
\(645\) | −29.9032 | −1.17744 | ||||||||
\(646\) | 1.77974 | 0.0700229 | ||||||||
\(647\) | −44.5260 | −1.75050 | −0.875249 | − | 0.483673i | \(-0.839303\pi\) | ||||
−0.875249 | + | 0.483673i | \(0.839303\pi\) | |||||||
\(648\) | −11.7836 | −0.462904 | ||||||||
\(649\) | −9.97341 | −0.391491 | ||||||||
\(650\) | −6.26825 | −0.245861 | ||||||||
\(651\) | 2.02534 | 0.0793793 | ||||||||
\(652\) | 20.9562 | 0.820708 | ||||||||
\(653\) | 37.0875 | 1.45134 | 0.725672 | − | 0.688041i | \(-0.241529\pi\) | ||||
0.725672 | + | 0.688041i | \(0.241529\pi\) | |||||||
\(654\) | 15.0012 | 0.586593 | ||||||||
\(655\) | −12.7154 | −0.496832 | ||||||||
\(656\) | 1.21740 | 0.0475316 | ||||||||
\(657\) | 37.1791 | 1.45049 | ||||||||
\(658\) | 2.21029 | 0.0861660 | ||||||||
\(659\) | 15.6928 | 0.611305 | 0.305652 | − | 0.952143i | \(-0.401126\pi\) | ||||
0.305652 | + | 0.952143i | \(0.401126\pi\) | |||||||
\(660\) | −4.10955 | −0.159964 | ||||||||
\(661\) | 4.10083 | 0.159504 | 0.0797519 | − | 0.996815i | \(-0.474587\pi\) | ||||
0.0797519 | + | 0.996815i | \(0.474587\pi\) | |||||||
\(662\) | −22.0153 | −0.855647 | ||||||||
\(663\) | −17.7402 | −0.688971 | ||||||||
\(664\) | −15.7701 | −0.611997 | ||||||||
\(665\) | −0.352460 | −0.0136678 | ||||||||
\(666\) | 11.6482 | 0.451357 | ||||||||
\(667\) | −6.20539 | −0.240274 | ||||||||
\(668\) | −2.59520 | −0.100411 | ||||||||
\(669\) | −25.2079 | −0.974595 | ||||||||
\(670\) | −6.46379 | −0.249718 | ||||||||
\(671\) | 1.58511 | 0.0611926 | ||||||||
\(672\) | −1.04948 | −0.0404846 | ||||||||
\(673\) | 8.56587 | 0.330190 | 0.165095 | − | 0.986278i | \(-0.447207\pi\) | ||||
0.165095 | + | 0.986278i | \(0.447207\pi\) | |||||||
\(674\) | −14.2647 | −0.549456 | ||||||||
\(675\) | −28.0314 | −1.07893 | ||||||||
\(676\) | −7.93816 | −0.305314 | ||||||||
\(677\) | 15.2255 | 0.585165 | 0.292583 | − | 0.956240i | \(-0.405485\pi\) | ||||
0.292583 | + | 0.956240i | \(0.405485\pi\) | |||||||
\(678\) | −32.0525 | −1.23097 | ||||||||
\(679\) | 4.93635 | 0.189440 | ||||||||
\(680\) | −3.84733 | −0.147538 | ||||||||
\(681\) | −9.98968 | −0.382805 | ||||||||
\(682\) | 1.74787 | 0.0669294 | ||||||||
\(683\) | −34.5265 | −1.32112 | −0.660560 | − | 0.750774i | \(-0.729681\pi\) | ||||
−0.660560 | + | 0.750774i | \(0.729681\pi\) | |||||||
\(684\) | −4.33584 | −0.165785 | ||||||||
\(685\) | −22.4119 | −0.856313 | ||||||||
\(686\) | 4.77735 | 0.182400 | ||||||||
\(687\) | −9.28875 | −0.354388 | ||||||||
\(688\) | −6.59036 | −0.251255 | ||||||||
\(689\) | −6.47259 | −0.246586 | ||||||||
\(690\) | −6.63637 | −0.252642 | ||||||||
\(691\) | 32.7649 | 1.24644 | 0.623218 | − | 0.782048i | \(-0.285825\pi\) | ||||
0.623218 | + | 0.782048i | \(0.285825\pi\) | |||||||
\(692\) | −15.6629 | −0.595414 | ||||||||
\(693\) | −1.96349 | −0.0745870 | ||||||||
\(694\) | −26.0825 | −0.990080 | ||||||||
\(695\) | −4.24105 | −0.160872 | ||||||||
\(696\) | 12.9382 | 0.490420 | ||||||||
\(697\) | 3.14783 | 0.119233 | ||||||||
\(698\) | −24.5684 | −0.929929 | ||||||||
\(699\) | 39.5029 | 1.49414 | ||||||||
\(700\) | −0.958828 | −0.0362403 | ||||||||
\(701\) | −4.80166 | −0.181356 | −0.0906782 | − | 0.995880i | \(-0.528903\pi\) | ||||
−0.0906782 | + | 0.995880i | \(0.528903\pi\) | |||||||
\(702\) | 22.6364 | 0.854355 | ||||||||
\(703\) | 1.27274 | 0.0480024 | ||||||||
\(704\) | −0.905704 | −0.0341350 | ||||||||
\(705\) | −29.1412 | −1.09752 | ||||||||
\(706\) | −8.36823 | −0.314943 | ||||||||
\(707\) | 1.00041 | 0.0376243 | ||||||||
\(708\) | 33.5802 | 1.26202 | ||||||||
\(709\) | −34.4618 | −1.29424 | −0.647120 | − | 0.762389i | \(-0.724027\pi\) | ||||
−0.647120 | + | 0.762389i | \(0.724027\pi\) | |||||||
\(710\) | −7.87987 | −0.295726 | ||||||||
\(711\) | −95.1876 | −3.56982 | ||||||||
\(712\) | 1.61934 | 0.0606874 | ||||||||
\(713\) | 2.82258 | 0.105706 | ||||||||
\(714\) | −2.71364 | −0.101555 | ||||||||
\(715\) | 3.03195 | 0.113389 | ||||||||
\(716\) | 25.1868 | 0.941273 | ||||||||
\(717\) | 26.4894 | 0.989264 | ||||||||
\(718\) | 2.12835 | 0.0794295 | ||||||||
\(719\) | −41.1653 | −1.53521 | −0.767604 | − | 0.640925i | \(-0.778551\pi\) | ||||
−0.767604 | + | 0.640925i | \(0.778551\pi\) | |||||||
\(720\) | 9.37296 | 0.349310 | ||||||||
\(721\) | −4.15961 | −0.154912 | ||||||||
\(722\) | 18.5262 | 0.689475 | ||||||||
\(723\) | −48.3316 | −1.79747 | ||||||||
\(724\) | 6.06957 | 0.225574 | ||||||||
\(725\) | 11.8206 | 0.439005 | ||||||||
\(726\) | 31.0428 | 1.15211 | ||||||||
\(727\) | −50.5549 | −1.87498 | −0.937489 | − | 0.348015i | \(-0.886856\pi\) | ||||
−0.937489 | + | 0.348015i | \(0.886856\pi\) | |||||||
\(728\) | 0.774289 | 0.0286971 | ||||||||
\(729\) | −17.8159 | −0.659848 | ||||||||
\(730\) | −8.78184 | −0.325031 | ||||||||
\(731\) | −17.0407 | −0.630272 | ||||||||
\(732\) | −5.33704 | −0.197263 | ||||||||
\(733\) | −29.3797 | −1.08516 | −0.542581 | − | 0.840003i | \(-0.682553\pi\) | ||||
−0.542581 | + | 0.840003i | \(0.682553\pi\) | |||||||
\(734\) | −9.53496 | −0.351942 | ||||||||
\(735\) | −31.2245 | −1.15173 | ||||||||
\(736\) | −1.46259 | −0.0539118 | ||||||||
\(737\) | −3.93451 | −0.144930 | ||||||||
\(738\) | −7.66882 | −0.282293 | ||||||||
\(739\) | −22.4975 | −0.827584 | −0.413792 | − | 0.910371i | \(-0.635796\pi\) | ||||
−0.413792 | + | 0.910371i | \(0.635796\pi\) | |||||||
\(740\) | −2.75134 | −0.101141 | ||||||||
\(741\) | 4.72236 | 0.173480 | ||||||||
\(742\) | −0.990085 | −0.0363472 | ||||||||
\(743\) | −7.49123 | −0.274826 | −0.137413 | − | 0.990514i | \(-0.543879\pi\) | ||||
−0.137413 | + | 0.990514i | \(0.543879\pi\) | |||||||
\(744\) | −5.88503 | −0.215756 | ||||||||
\(745\) | −7.80421 | −0.285924 | ||||||||
\(746\) | −16.7808 | −0.614387 | ||||||||
\(747\) | 99.3409 | 3.63469 | ||||||||
\(748\) | −2.34187 | −0.0856274 | ||||||||
\(749\) | −2.42183 | −0.0884917 | ||||||||
\(750\) | 35.3286 | 1.29002 | ||||||||
\(751\) | 31.3441 | 1.14376 | 0.571881 | − | 0.820337i | \(-0.306214\pi\) | ||||
0.571881 | + | 0.820337i | \(0.306214\pi\) | |||||||
\(752\) | −6.42244 | −0.234202 | ||||||||
\(753\) | 14.0613 | 0.512421 | ||||||||
\(754\) | −9.54555 | −0.347628 | ||||||||
\(755\) | 17.9463 | 0.653132 | ||||||||
\(756\) | 3.46259 | 0.125933 | ||||||||
\(757\) | −44.8626 | −1.63056 | −0.815280 | − | 0.579067i | \(-0.803417\pi\) | ||||
−0.815280 | + | 0.579067i | \(0.803417\pi\) | |||||||
\(758\) | 29.0341 | 1.05457 | ||||||||
\(759\) | −4.03957 | −0.146627 | ||||||||
\(760\) | 1.02414 | 0.0371496 | ||||||||
\(761\) | −18.5983 | −0.674189 | −0.337094 | − | 0.941471i | \(-0.609444\pi\) | ||||
−0.337094 | + | 0.941471i | \(0.609444\pi\) | |||||||
\(762\) | 61.2426 | 2.21859 | ||||||||
\(763\) | −1.69297 | −0.0612895 | ||||||||
\(764\) | 8.11319 | 0.293525 | ||||||||
\(765\) | 24.2356 | 0.876241 | ||||||||
\(766\) | −35.5798 | −1.28555 | ||||||||
\(767\) | −24.7749 | −0.894570 | ||||||||
\(768\) | 3.04948 | 0.110039 | ||||||||
\(769\) | 52.1929 | 1.88213 | 0.941063 | − | 0.338232i | \(-0.109829\pi\) | ||||
0.941063 | + | 0.338232i | \(0.109829\pi\) | |||||||
\(770\) | 0.463785 | 0.0167137 | ||||||||
\(771\) | 61.6550 | 2.22045 | ||||||||
\(772\) | −12.8968 | −0.464166 | ||||||||
\(773\) | 41.7206 | 1.50059 | 0.750293 | − | 0.661105i | \(-0.229912\pi\) | ||||
0.750293 | + | 0.661105i | \(0.229912\pi\) | |||||||
\(774\) | 41.5149 | 1.49222 | ||||||||
\(775\) | −5.37669 | −0.193136 | ||||||||
\(776\) | −14.3436 | −0.514904 | ||||||||
\(777\) | −1.94060 | −0.0696188 | ||||||||
\(778\) | 37.5839 | 1.34745 | ||||||||
\(779\) | −0.837940 | −0.0300223 | ||||||||
\(780\) | −10.2085 | −0.365523 | ||||||||
\(781\) | −4.79648 | −0.171632 | ||||||||
\(782\) | −3.78181 | −0.135237 | ||||||||
\(783\) | −42.6873 | −1.52552 | ||||||||
\(784\) | −6.88156 | −0.245770 | ||||||||
\(785\) | −21.4544 | −0.765740 | ||||||||
\(786\) | 26.0600 | 0.929530 | ||||||||
\(787\) | 20.8879 | 0.744574 | 0.372287 | − | 0.928118i | \(-0.378574\pi\) | ||||
0.372287 | + | 0.928118i | \(0.378574\pi\) | |||||||
\(788\) | 14.4920 | 0.516257 | ||||||||
\(789\) | 48.0205 | 1.70958 | ||||||||
\(790\) | 22.4837 | 0.799934 | ||||||||
\(791\) | 3.61731 | 0.128617 | ||||||||
\(792\) | 5.70533 | 0.202730 | ||||||||
\(793\) | 3.93757 | 0.139827 | ||||||||
\(794\) | 16.8913 | 0.599450 | ||||||||
\(795\) | 13.0536 | 0.462965 | ||||||||
\(796\) | 20.5344 | 0.727822 | ||||||||
\(797\) | 20.6075 | 0.729955 | 0.364978 | − | 0.931016i | \(-0.381077\pi\) | ||||
0.364978 | + | 0.931016i | \(0.381077\pi\) | |||||||
\(798\) | 0.722359 | 0.0255712 | ||||||||
\(799\) | −16.6065 | −0.587495 | ||||||||
\(800\) | 2.78607 | 0.0985024 | ||||||||
\(801\) | −10.2008 | −0.360427 | ||||||||
\(802\) | −3.68585 | −0.130152 | ||||||||
\(803\) | −5.34552 | −0.188639 | ||||||||
\(804\) | 13.2474 | 0.467200 | ||||||||
\(805\) | 0.748951 | 0.0263971 | ||||||||
\(806\) | 4.34187 | 0.152936 | ||||||||
\(807\) | 3.04948 | 0.107347 | ||||||||
\(808\) | −2.90690 | −0.102264 | ||||||||
\(809\) | 8.27012 | 0.290762 | 0.145381 | − | 0.989376i | \(-0.453559\pi\) | ||||
0.145381 | + | 0.989376i | \(0.453559\pi\) | |||||||
\(810\) | −17.5332 | −0.616053 | ||||||||
\(811\) | 26.6200 | 0.934753 | 0.467377 | − | 0.884058i | \(-0.345199\pi\) | ||||
0.467377 | + | 0.884058i | \(0.345199\pi\) | |||||||
\(812\) | −1.46014 | −0.0512409 | ||||||||
\(813\) | 52.8524 | 1.85362 | ||||||||
\(814\) | −1.67474 | −0.0586997 | ||||||||
\(815\) | 31.1813 | 1.09223 | ||||||||
\(816\) | 7.88503 | 0.276031 | ||||||||
\(817\) | 4.53616 | 0.158700 | ||||||||
\(818\) | −18.5784 | −0.649579 | ||||||||
\(819\) | −4.87751 | −0.170434 | ||||||||
\(820\) | 1.81141 | 0.0632571 | ||||||||
\(821\) | 29.4026 | 1.02616 | 0.513078 | − | 0.858342i | \(-0.328505\pi\) | ||||
0.513078 | + | 0.858342i | \(0.328505\pi\) | |||||||
\(822\) | 45.9327 | 1.60209 | ||||||||
\(823\) | 15.4716 | 0.539305 | 0.269653 | − | 0.962958i | \(-0.413091\pi\) | ||||
0.269653 | + | 0.962958i | \(0.413091\pi\) | |||||||
\(824\) | 12.0866 | 0.421057 | ||||||||
\(825\) | 7.69492 | 0.267903 | ||||||||
\(826\) | −3.78971 | −0.131861 | ||||||||
\(827\) | −24.5579 | −0.853963 | −0.426982 | − | 0.904260i | \(-0.640423\pi\) | ||||
−0.426982 | + | 0.904260i | \(0.640423\pi\) | |||||||
\(828\) | 9.21335 | 0.320186 | ||||||||
\(829\) | 20.1760 | 0.700741 | 0.350371 | − | 0.936611i | \(-0.386056\pi\) | ||||
0.350371 | + | 0.936611i | \(0.386056\pi\) | |||||||
\(830\) | −23.4647 | −0.814472 | ||||||||
\(831\) | −70.6192 | −2.44975 | ||||||||
\(832\) | −2.24985 | −0.0779997 | ||||||||
\(833\) | −17.7936 | −0.616513 | ||||||||
\(834\) | 8.69194 | 0.300977 | ||||||||
\(835\) | −3.86147 | −0.133632 | ||||||||
\(836\) | 0.623397 | 0.0215606 | ||||||||
\(837\) | 19.4167 | 0.671139 | ||||||||
\(838\) | −3.30890 | −0.114304 | ||||||||
\(839\) | −39.9874 | −1.38052 | −0.690259 | − | 0.723562i | \(-0.742504\pi\) | ||||
−0.690259 | + | 0.723562i | \(0.742504\pi\) | |||||||
\(840\) | −1.56155 | −0.0538787 | ||||||||
\(841\) | −10.9992 | −0.379281 | ||||||||
\(842\) | −7.23994 | −0.249505 | ||||||||
\(843\) | −42.7250 | −1.47153 | ||||||||
\(844\) | −6.99356 | −0.240728 | ||||||||
\(845\) | −11.8114 | −0.406325 | ||||||||
\(846\) | 40.4571 | 1.39094 | ||||||||
\(847\) | −3.50335 | −0.120377 | ||||||||
\(848\) | 2.87689 | 0.0987930 | ||||||||
\(849\) | 79.6328 | 2.73299 | ||||||||
\(850\) | 7.20393 | 0.247093 | ||||||||
\(851\) | −2.70449 | −0.0927086 | ||||||||
\(852\) | 16.1496 | 0.553277 | ||||||||
\(853\) | −38.2866 | −1.31091 | −0.655453 | − | 0.755236i | \(-0.727522\pi\) | ||||
−0.655453 | + | 0.755236i | \(0.727522\pi\) | |||||||
\(854\) | 0.602314 | 0.0206108 | ||||||||
\(855\) | −6.45142 | −0.220634 | ||||||||
\(856\) | 7.03712 | 0.240524 | ||||||||
\(857\) | 10.4287 | 0.356239 | 0.178120 | − | 0.984009i | \(-0.442999\pi\) | ||||
0.178120 | + | 0.984009i | \(0.442999\pi\) | |||||||
\(858\) | −6.21393 | −0.212140 | ||||||||
\(859\) | −31.3752 | −1.07051 | −0.535254 | − | 0.844691i | \(-0.679784\pi\) | ||||
−0.535254 | + | 0.844691i | \(0.679784\pi\) | |||||||
\(860\) | −9.80599 | −0.334381 | ||||||||
\(861\) | 1.27764 | 0.0435419 | ||||||||
\(862\) | 11.1645 | 0.380266 | ||||||||
\(863\) | 22.9420 | 0.780954 | 0.390477 | − | 0.920613i | \(-0.372310\pi\) | ||||
0.390477 | + | 0.920613i | \(0.372310\pi\) | |||||||
\(864\) | −10.0613 | −0.342291 | ||||||||
\(865\) | −23.3053 | −0.792403 | ||||||||
\(866\) | −28.8143 | −0.979150 | ||||||||
\(867\) | −31.4529 | −1.06820 | ||||||||
\(868\) | 0.664158 | 0.0225430 | ||||||||
\(869\) | 13.6859 | 0.464261 | ||||||||
\(870\) | 19.2510 | 0.652672 | ||||||||
\(871\) | −9.77371 | −0.331169 | ||||||||
\(872\) | 4.91926 | 0.166587 | ||||||||
\(873\) | 90.3549 | 3.05805 | ||||||||
\(874\) | 1.00670 | 0.0340522 | ||||||||
\(875\) | −3.98703 | −0.134786 | ||||||||
\(876\) | 17.9982 | 0.608104 | ||||||||
\(877\) | 13.8521 | 0.467754 | 0.233877 | − | 0.972266i | \(-0.424859\pi\) | ||||
0.233877 | + | 0.972266i | \(0.424859\pi\) | |||||||
\(878\) | −20.4897 | −0.691495 | ||||||||
\(879\) | −24.8522 | −0.838243 | ||||||||
\(880\) | −1.34762 | −0.0454283 | ||||||||
\(881\) | 20.0782 | 0.676451 | 0.338225 | − | 0.941065i | \(-0.390173\pi\) | ||||
0.338225 | + | 0.941065i | \(0.390173\pi\) | |||||||
\(882\) | 43.3493 | 1.45965 | ||||||||
\(883\) | 55.3481 | 1.86261 | 0.931306 | − | 0.364237i | \(-0.118670\pi\) | ||||
0.931306 | + | 0.364237i | \(0.118670\pi\) | |||||||
\(884\) | −5.81744 | −0.195662 | ||||||||
\(885\) | 49.9650 | 1.67955 | ||||||||
\(886\) | −9.58503 | −0.322015 | ||||||||
\(887\) | 1.28823 | 0.0432544 | 0.0216272 | − | 0.999766i | \(-0.493115\pi\) | ||||
0.0216272 | + | 0.999766i | \(0.493115\pi\) | |||||||
\(888\) | 5.63882 | 0.189226 | ||||||||
\(889\) | −6.91156 | −0.231806 | ||||||||
\(890\) | 2.40947 | 0.0807655 | ||||||||
\(891\) | −10.6725 | −0.357541 | ||||||||
\(892\) | −8.26630 | −0.276776 | ||||||||
\(893\) | 4.42058 | 0.147929 | ||||||||
\(894\) | 15.9946 | 0.534939 | ||||||||
\(895\) | 37.4761 | 1.25269 | ||||||||
\(896\) | −0.344151 | −0.0114973 | ||||||||
\(897\) | −10.0347 | −0.335048 | ||||||||
\(898\) | 21.4476 | 0.715716 | ||||||||
\(899\) | −8.18784 | −0.273080 | ||||||||
\(900\) | −17.5504 | −0.585013 | ||||||||
\(901\) | 7.43877 | 0.247822 | ||||||||
\(902\) | 1.10261 | 0.0367127 | ||||||||
\(903\) | −6.91646 | −0.230165 | ||||||||
\(904\) | −10.5108 | −0.349585 | ||||||||
\(905\) | 9.03109 | 0.300203 | ||||||||
\(906\) | −36.7806 | −1.22195 | ||||||||
\(907\) | 11.6760 | 0.387695 | 0.193848 | − | 0.981032i | \(-0.437903\pi\) | ||||
0.193848 | + | 0.981032i | \(0.437903\pi\) | |||||||
\(908\) | −3.27586 | −0.108713 | ||||||||
\(909\) | 18.3115 | 0.607355 | ||||||||
\(910\) | 1.15209 | 0.0381913 | ||||||||
\(911\) | 31.6479 | 1.04854 | 0.524271 | − | 0.851551i | \(-0.324338\pi\) | ||||
0.524271 | + | 0.851551i | \(0.324338\pi\) | |||||||
\(912\) | −2.09896 | −0.0695036 | ||||||||
\(913\) | −14.2830 | −0.472698 | ||||||||
\(914\) | −10.7176 | −0.354508 | ||||||||
\(915\) | −7.94113 | −0.262526 | ||||||||
\(916\) | −3.04601 | −0.100643 | ||||||||
\(917\) | −2.94102 | −0.0971209 | ||||||||
\(918\) | −26.0154 | −0.858635 | ||||||||
\(919\) | −49.3145 | −1.62674 | −0.813368 | − | 0.581749i | \(-0.802368\pi\) | ||||
−0.813368 | + | 0.581749i | \(0.802368\pi\) | |||||||
\(920\) | −2.17623 | −0.0717482 | ||||||||
\(921\) | 2.46743 | 0.0813045 | ||||||||
\(922\) | 19.6658 | 0.647657 | ||||||||
\(923\) | −11.9149 | −0.392184 | ||||||||
\(924\) | −0.950519 | −0.0312698 | ||||||||
\(925\) | 5.15174 | 0.169388 | ||||||||
\(926\) | −22.6226 | −0.743426 | ||||||||
\(927\) | −76.1375 | −2.50069 | ||||||||
\(928\) | 4.24274 | 0.139275 | ||||||||
\(929\) | −25.7689 | −0.845450 | −0.422725 | − | 0.906258i | \(-0.638926\pi\) | ||||
−0.422725 | + | 0.906258i | \(0.638926\pi\) | |||||||
\(930\) | −8.75651 | −0.287137 | ||||||||
\(931\) | 4.73659 | 0.155235 | ||||||||
\(932\) | 12.9540 | 0.424322 | ||||||||
\(933\) | −1.35509 | −0.0443636 | ||||||||
\(934\) | −30.0503 | −0.983277 | ||||||||
\(935\) | −3.48454 | −0.113957 | ||||||||
\(936\) | 14.1726 | 0.463245 | ||||||||
\(937\) | −6.22816 | −0.203465 | −0.101733 | − | 0.994812i | \(-0.532439\pi\) | ||||
−0.101733 | + | 0.994812i | \(0.532439\pi\) | |||||||
\(938\) | −1.49504 | −0.0488149 | ||||||||
\(939\) | 3.20454 | 0.104576 | ||||||||
\(940\) | −9.55613 | −0.311687 | ||||||||
\(941\) | 15.3930 | 0.501799 | 0.250900 | − | 0.968013i | \(-0.419274\pi\) | ||||
0.250900 | + | 0.968013i | \(0.419274\pi\) | |||||||
\(942\) | 43.9704 | 1.43263 | ||||||||
\(943\) | 1.78056 | 0.0579830 | ||||||||
\(944\) | 11.0118 | 0.358403 | ||||||||
\(945\) | 5.15209 | 0.167597 | ||||||||
\(946\) | −5.96891 | −0.194066 | ||||||||
\(947\) | −19.0683 | −0.619635 | −0.309818 | − | 0.950796i | \(-0.600268\pi\) | ||||
−0.309818 | + | 0.950796i | \(0.600268\pi\) | |||||||
\(948\) | −46.0799 | −1.49661 | ||||||||
\(949\) | −13.2788 | −0.431047 | ||||||||
\(950\) | −1.91766 | −0.0622170 | ||||||||
\(951\) | 19.7236 | 0.639580 | ||||||||
\(952\) | −0.889869 | −0.0288408 | ||||||||
\(953\) | −39.7141 | −1.28647 | −0.643234 | − | 0.765670i | \(-0.722408\pi\) | ||||
−0.643234 | + | 0.765670i | \(0.722408\pi\) | |||||||
\(954\) | −18.1225 | −0.586738 | ||||||||
\(955\) | 12.0718 | 0.390636 | ||||||||
\(956\) | 8.68652 | 0.280942 | ||||||||
\(957\) | 11.7181 | 0.378793 | ||||||||
\(958\) | 32.6251 | 1.05407 | ||||||||
\(959\) | −5.18376 | −0.167392 | ||||||||
\(960\) | 4.53741 | 0.146444 | ||||||||
\(961\) | −27.2757 | −0.879861 | ||||||||
\(962\) | −4.16022 | −0.134131 | ||||||||
\(963\) | −44.3292 | −1.42849 | ||||||||
\(964\) | −15.8491 | −0.510465 | ||||||||
\(965\) | −19.1895 | −0.617733 | ||||||||
\(966\) | −1.53496 | −0.0493866 | ||||||||
\(967\) | −54.5429 | −1.75398 | −0.876991 | − | 0.480507i | \(-0.840453\pi\) | ||||
−0.876991 | + | 0.480507i | \(0.840453\pi\) | |||||||
\(968\) | 10.1797 | 0.327188 | ||||||||
\(969\) | −5.42728 | −0.174349 | ||||||||
\(970\) | −21.3422 | −0.685257 | ||||||||
\(971\) | −20.6894 | −0.663955 | −0.331977 | − | 0.943287i | \(-0.607716\pi\) | ||||
−0.331977 | + | 0.943287i | \(0.607716\pi\) | |||||||
\(972\) | 5.75015 | 0.184436 | ||||||||
\(973\) | −0.980934 | −0.0314473 | ||||||||
\(974\) | 4.12981 | 0.132328 | ||||||||
\(975\) | 19.1149 | 0.612167 | ||||||||
\(976\) | −1.75015 | −0.0560208 | ||||||||
\(977\) | 3.49749 | 0.111895 | 0.0559473 | − | 0.998434i | \(-0.482182\pi\) | ||||
0.0559473 | + | 0.998434i | \(0.482182\pi\) | |||||||
\(978\) | −63.9056 | −2.04347 | ||||||||
\(979\) | 1.46664 | 0.0468742 | ||||||||
\(980\) | −10.2393 | −0.327081 | ||||||||
\(981\) | −30.9881 | −0.989373 | ||||||||
\(982\) | 35.2225 | 1.12400 | ||||||||
\(983\) | 16.5884 | 0.529086 | 0.264543 | − | 0.964374i | \(-0.414779\pi\) | ||||
0.264543 | + | 0.964374i | \(0.414779\pi\) | |||||||
\(984\) | −3.71244 | −0.118348 | ||||||||
\(985\) | 21.5631 | 0.687057 | ||||||||
\(986\) | 10.9704 | 0.349370 | ||||||||
\(987\) | −6.74023 | −0.214544 | ||||||||
\(988\) | 1.54858 | 0.0492668 | ||||||||
\(989\) | −9.63900 | −0.306502 | ||||||||
\(990\) | 8.48912 | 0.269802 | ||||||||
\(991\) | −27.1297 | −0.861805 | −0.430902 | − | 0.902399i | \(-0.641805\pi\) | ||||
−0.430902 | + | 0.902399i | \(0.641805\pi\) | |||||||
\(992\) | −1.92985 | −0.0612727 | ||||||||
\(993\) | 67.1351 | 2.13047 | ||||||||
\(994\) | −1.82258 | −0.0578086 | ||||||||
\(995\) | 30.5537 | 0.968617 | ||||||||
\(996\) | 48.0905 | 1.52381 | ||||||||
\(997\) | 56.5029 | 1.78946 | 0.894732 | − | 0.446603i | \(-0.147366\pi\) | ||||
0.894732 | + | 0.446603i | \(0.147366\pi\) | |||||||
\(998\) | −16.3253 | −0.516767 | ||||||||
\(999\) | −18.6044 | −0.588616 |
(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 | 538.2.a.c.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 4842.2.a.j.1.2 | 4 | |||
4.3 | odd | 2 | 4304.2.a.e.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.c.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4304.2.a.e.1.1 | 4 | 4.3 | odd | 2 | |||
4842.2.a.j.1.2 | 4 | 3.2 | odd | 2 |