Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 57 x^{10} + 28 x^{9} - 290 x^{8} + 51 x^{7} + 644 x^{6} - 259 x^{5} - 640 x^{4} + 274 x^{3} + 256 x^{2} - 74 x - 35 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.931518\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.931518 | 0.658683 | 0.329341 | − | 0.944211i | \(-0.393173\pi\) | ||||
0.329341 | + | 0.944211i | \(0.393173\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.13227 | −0.566137 | ||||||||
\(5\) | 1.13816 | 0.509001 | 0.254500 | − | 0.967073i | \(-0.418089\pi\) | ||||
0.254500 | + | 0.967073i | \(0.418089\pi\) | |||||||
\(6\) | 0.931518 | 0.380291 | ||||||||
\(7\) | −2.87358 | −1.08611 | −0.543055 | − | 0.839697i | \(-0.682733\pi\) | ||||
−0.543055 | + | 0.839697i | \(0.682733\pi\) | |||||||
\(8\) | −2.91777 | −1.03159 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.06022 | 0.335270 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.13227 | −0.326859 | ||||||||
\(13\) | 1.40430 | 0.389484 | 0.194742 | − | 0.980854i | \(-0.437613\pi\) | ||||
0.194742 | + | 0.980854i | \(0.437613\pi\) | |||||||
\(14\) | −2.67679 | −0.715402 | ||||||||
\(15\) | 1.13816 | 0.293872 | ||||||||
\(16\) | −0.453408 | −0.113352 | ||||||||
\(17\) | −0.846049 | −0.205197 | −0.102599 | − | 0.994723i | \(-0.532716\pi\) | ||||
−0.102599 | + | 0.994723i | \(0.532716\pi\) | |||||||
\(18\) | 0.931518 | 0.219561 | ||||||||
\(19\) | 4.27664 | 0.981130 | 0.490565 | − | 0.871405i | \(-0.336790\pi\) | ||||
0.490565 | + | 0.871405i | \(0.336790\pi\) | |||||||
\(20\) | −1.28871 | −0.288164 | ||||||||
\(21\) | −2.87358 | −0.627066 | ||||||||
\(22\) | 0.931518 | 0.198600 | ||||||||
\(23\) | 5.20869 | 1.08609 | 0.543043 | − | 0.839705i | \(-0.317272\pi\) | ||||
0.543043 | + | 0.839705i | \(0.317272\pi\) | |||||||
\(24\) | −2.91777 | −0.595587 | ||||||||
\(25\) | −3.70459 | −0.740918 | ||||||||
\(26\) | 1.30814 | 0.256546 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.25368 | 0.614887 | ||||||||
\(29\) | 8.20744 | 1.52408 | 0.762042 | − | 0.647528i | \(-0.224197\pi\) | ||||
0.762042 | + | 0.647528i | \(0.224197\pi\) | |||||||
\(30\) | 1.06022 | 0.193568 | ||||||||
\(31\) | 7.18706 | 1.29083 | 0.645417 | − | 0.763830i | \(-0.276684\pi\) | ||||
0.645417 | + | 0.763830i | \(0.276684\pi\) | |||||||
\(32\) | 5.41318 | 0.956924 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −0.788110 | −0.135160 | ||||||||
\(35\) | −3.27059 | −0.552831 | ||||||||
\(36\) | −1.13227 | −0.188712 | ||||||||
\(37\) | 4.15083 | 0.682392 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(38\) | 3.98377 | 0.646253 | ||||||||
\(39\) | 1.40430 | 0.224869 | ||||||||
\(40\) | −3.32089 | −0.525079 | ||||||||
\(41\) | 0.166336 | 0.0259773 | 0.0129886 | − | 0.999916i | \(-0.495865\pi\) | ||||
0.0129886 | + | 0.999916i | \(0.495865\pi\) | |||||||
\(42\) | −2.67679 | −0.413038 | ||||||||
\(43\) | 6.54819 | 0.998590 | 0.499295 | − | 0.866432i | \(-0.333592\pi\) | ||||
0.499295 | + | 0.866432i | \(0.333592\pi\) | |||||||
\(44\) | −1.13227 | −0.170697 | ||||||||
\(45\) | 1.13816 | 0.169667 | ||||||||
\(46\) | 4.85199 | 0.715387 | ||||||||
\(47\) | 0.378293 | 0.0551797 | 0.0275899 | − | 0.999619i | \(-0.491217\pi\) | ||||
0.0275899 | + | 0.999619i | \(0.491217\pi\) | |||||||
\(48\) | −0.453408 | −0.0654438 | ||||||||
\(49\) | 1.25745 | 0.179635 | ||||||||
\(50\) | −3.45089 | −0.488030 | ||||||||
\(51\) | −0.846049 | −0.118471 | ||||||||
\(52\) | −1.59006 | −0.220501 | ||||||||
\(53\) | −0.923656 | −0.126874 | −0.0634370 | − | 0.997986i | \(-0.520206\pi\) | ||||
−0.0634370 | + | 0.997986i | \(0.520206\pi\) | |||||||
\(54\) | 0.931518 | 0.126764 | ||||||||
\(55\) | 1.13816 | 0.153469 | ||||||||
\(56\) | 8.38444 | 1.12042 | ||||||||
\(57\) | 4.27664 | 0.566455 | ||||||||
\(58\) | 7.64538 | 1.00389 | ||||||||
\(59\) | −1.30403 | −0.169770 | −0.0848852 | − | 0.996391i | \(-0.527052\pi\) | ||||
−0.0848852 | + | 0.996391i | \(0.527052\pi\) | |||||||
\(60\) | −1.28871 | −0.166372 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 6.69488 | 0.850250 | ||||||||
\(63\) | −2.87358 | −0.362037 | ||||||||
\(64\) | 5.94929 | 0.743662 | ||||||||
\(65\) | 1.59832 | 0.198248 | ||||||||
\(66\) | 0.931518 | 0.114662 | ||||||||
\(67\) | −6.07605 | −0.742308 | −0.371154 | − | 0.928571i | \(-0.621038\pi\) | ||||
−0.371154 | + | 0.928571i | \(0.621038\pi\) | |||||||
\(68\) | 0.957959 | 0.116170 | ||||||||
\(69\) | 5.20869 | 0.627052 | ||||||||
\(70\) | −3.04661 | −0.364140 | ||||||||
\(71\) | −13.3483 | −1.58415 | −0.792075 | − | 0.610424i | \(-0.790999\pi\) | ||||
−0.792075 | + | 0.610424i | \(0.790999\pi\) | |||||||
\(72\) | −2.91777 | −0.343862 | ||||||||
\(73\) | 3.93967 | 0.461104 | 0.230552 | − | 0.973060i | \(-0.425947\pi\) | ||||
0.230552 | + | 0.973060i | \(0.425947\pi\) | |||||||
\(74\) | 3.86657 | 0.449480 | ||||||||
\(75\) | −3.70459 | −0.427769 | ||||||||
\(76\) | −4.84233 | −0.555454 | ||||||||
\(77\) | −2.87358 | −0.327475 | ||||||||
\(78\) | 1.30814 | 0.148117 | ||||||||
\(79\) | 7.00809 | 0.788472 | 0.394236 | − | 0.919009i | \(-0.371009\pi\) | ||||
0.394236 | + | 0.919009i | \(0.371009\pi\) | |||||||
\(80\) | −0.516051 | −0.0576962 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.154945 | 0.0171108 | ||||||||
\(83\) | 2.26262 | 0.248355 | 0.124177 | − | 0.992260i | \(-0.460371\pi\) | ||||
0.124177 | + | 0.992260i | \(0.460371\pi\) | |||||||
\(84\) | 3.25368 | 0.355005 | ||||||||
\(85\) | −0.962939 | −0.104445 | ||||||||
\(86\) | 6.09976 | 0.657754 | ||||||||
\(87\) | 8.20744 | 0.879930 | ||||||||
\(88\) | −2.91777 | −0.311035 | ||||||||
\(89\) | 2.22445 | 0.235791 | 0.117896 | − | 0.993026i | \(-0.462385\pi\) | ||||
0.117896 | + | 0.993026i | \(0.462385\pi\) | |||||||
\(90\) | 1.06022 | 0.111757 | ||||||||
\(91\) | −4.03538 | −0.423023 | ||||||||
\(92\) | −5.89766 | −0.614874 | ||||||||
\(93\) | 7.18706 | 0.745263 | ||||||||
\(94\) | 0.352387 | 0.0363459 | ||||||||
\(95\) | 4.86751 | 0.499396 | ||||||||
\(96\) | 5.41318 | 0.552481 | ||||||||
\(97\) | 10.6596 | 1.08231 | 0.541157 | − | 0.840922i | \(-0.317986\pi\) | ||||
0.541157 | + | 0.840922i | \(0.317986\pi\) | |||||||
\(98\) | 1.17133 | 0.118323 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 4.19461 | 0.419461 | ||||||||
\(101\) | −3.11381 | −0.309836 | −0.154918 | − | 0.987927i | \(-0.549511\pi\) | ||||
−0.154918 | + | 0.987927i | \(0.549511\pi\) | |||||||
\(102\) | −0.788110 | −0.0780345 | ||||||||
\(103\) | −0.547424 | −0.0539393 | −0.0269697 | − | 0.999636i | \(-0.508586\pi\) | ||||
−0.0269697 | + | 0.999636i | \(0.508586\pi\) | |||||||
\(104\) | −4.09744 | −0.401787 | ||||||||
\(105\) | −3.27059 | −0.319177 | ||||||||
\(106\) | −0.860402 | −0.0835697 | ||||||||
\(107\) | −4.67778 | −0.452219 | −0.226109 | − | 0.974102i | \(-0.572601\pi\) | ||||
−0.226109 | + | 0.974102i | \(0.572601\pi\) | |||||||
\(108\) | −1.13227 | −0.108953 | ||||||||
\(109\) | 15.4885 | 1.48353 | 0.741764 | − | 0.670661i | \(-0.233989\pi\) | ||||
0.741764 | + | 0.670661i | \(0.233989\pi\) | |||||||
\(110\) | 1.06022 | 0.101088 | ||||||||
\(111\) | 4.15083 | 0.393979 | ||||||||
\(112\) | 1.30290 | 0.123113 | ||||||||
\(113\) | −4.79624 | −0.451192 | −0.225596 | − | 0.974221i | \(-0.572433\pi\) | ||||
−0.225596 | + | 0.974221i | \(0.572433\pi\) | |||||||
\(114\) | 3.98377 | 0.373114 | ||||||||
\(115\) | 5.92832 | 0.552819 | ||||||||
\(116\) | −9.29307 | −0.862840 | ||||||||
\(117\) | 1.40430 | 0.129828 | ||||||||
\(118\) | −1.21473 | −0.111825 | ||||||||
\(119\) | 2.43119 | 0.222867 | ||||||||
\(120\) | −3.32089 | −0.303154 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.931518 | 0.0843357 | ||||||||
\(123\) | 0.166336 | 0.0149980 | ||||||||
\(124\) | −8.13772 | −0.730789 | ||||||||
\(125\) | −9.90722 | −0.886129 | ||||||||
\(126\) | −2.67679 | −0.238467 | ||||||||
\(127\) | 2.84301 | 0.252276 | 0.126138 | − | 0.992013i | \(-0.459742\pi\) | ||||
0.126138 | + | 0.992013i | \(0.459742\pi\) | |||||||
\(128\) | −5.28449 | −0.467087 | ||||||||
\(129\) | 6.54819 | 0.576536 | ||||||||
\(130\) | 1.48887 | 0.130582 | ||||||||
\(131\) | 5.03902 | 0.440262 | 0.220131 | − | 0.975470i | \(-0.429352\pi\) | ||||
0.220131 | + | 0.975470i | \(0.429352\pi\) | |||||||
\(132\) | −1.13227 | −0.0985518 | ||||||||
\(133\) | −12.2893 | −1.06561 | ||||||||
\(134\) | −5.65995 | −0.488945 | ||||||||
\(135\) | 1.13816 | 0.0979572 | ||||||||
\(136\) | 2.46858 | 0.211679 | ||||||||
\(137\) | −14.5240 | −1.24087 | −0.620436 | − | 0.784257i | \(-0.713044\pi\) | ||||
−0.620436 | + | 0.784257i | \(0.713044\pi\) | |||||||
\(138\) | 4.85199 | 0.413029 | ||||||||
\(139\) | −20.5839 | −1.74590 | −0.872951 | − | 0.487807i | \(-0.837797\pi\) | ||||
−0.872951 | + | 0.487807i | \(0.837797\pi\) | |||||||
\(140\) | 3.70320 | 0.312978 | ||||||||
\(141\) | 0.378293 | 0.0318580 | ||||||||
\(142\) | −12.4342 | −1.04345 | ||||||||
\(143\) | 1.40430 | 0.117434 | ||||||||
\(144\) | −0.453408 | −0.0377840 | ||||||||
\(145\) | 9.34138 | 0.775759 | ||||||||
\(146\) | 3.66988 | 0.303721 | ||||||||
\(147\) | 1.25745 | 0.103712 | ||||||||
\(148\) | −4.69987 | −0.386327 | ||||||||
\(149\) | 4.64026 | 0.380145 | 0.190073 | − | 0.981770i | \(-0.439128\pi\) | ||||
0.190073 | + | 0.981770i | \(0.439128\pi\) | |||||||
\(150\) | −3.45089 | −0.281764 | ||||||||
\(151\) | −20.0189 | −1.62912 | −0.814558 | − | 0.580083i | \(-0.803020\pi\) | ||||
−0.814558 | + | 0.580083i | \(0.803020\pi\) | |||||||
\(152\) | −12.4783 | −1.01212 | ||||||||
\(153\) | −0.846049 | −0.0683990 | ||||||||
\(154\) | −2.67679 | −0.215702 | ||||||||
\(155\) | 8.18002 | 0.657035 | ||||||||
\(156\) | −1.59006 | −0.127306 | ||||||||
\(157\) | 18.2010 | 1.45260 | 0.726299 | − | 0.687379i | \(-0.241239\pi\) | ||||
0.726299 | + | 0.687379i | \(0.241239\pi\) | |||||||
\(158\) | 6.52817 | 0.519353 | ||||||||
\(159\) | −0.923656 | −0.0732507 | ||||||||
\(160\) | 6.16107 | 0.487075 | ||||||||
\(161\) | −14.9676 | −1.17961 | ||||||||
\(162\) | 0.931518 | 0.0731870 | ||||||||
\(163\) | −10.2340 | −0.801589 | −0.400794 | − | 0.916168i | \(-0.631266\pi\) | ||||
−0.400794 | + | 0.916168i | \(0.631266\pi\) | |||||||
\(164\) | −0.188338 | −0.0147067 | ||||||||
\(165\) | 1.13816 | 0.0886056 | ||||||||
\(166\) | 2.10767 | 0.163587 | ||||||||
\(167\) | 22.1101 | 1.71093 | 0.855466 | − | 0.517859i | \(-0.173271\pi\) | ||||
0.855466 | + | 0.517859i | \(0.173271\pi\) | |||||||
\(168\) | 8.38444 | 0.646873 | ||||||||
\(169\) | −11.0279 | −0.848302 | ||||||||
\(170\) | −0.896995 | −0.0687964 | ||||||||
\(171\) | 4.27664 | 0.327043 | ||||||||
\(172\) | −7.41434 | −0.565338 | ||||||||
\(173\) | −3.68124 | −0.279880 | −0.139940 | − | 0.990160i | \(-0.544691\pi\) | ||||
−0.139940 | + | 0.990160i | \(0.544691\pi\) | |||||||
\(174\) | 7.64538 | 0.579595 | ||||||||
\(175\) | 10.6454 | 0.804719 | ||||||||
\(176\) | −0.453408 | −0.0341769 | ||||||||
\(177\) | −1.30403 | −0.0980170 | ||||||||
\(178\) | 2.07212 | 0.155312 | ||||||||
\(179\) | 25.7165 | 1.92214 | 0.961070 | − | 0.276304i | \(-0.0891098\pi\) | ||||
0.961070 | + | 0.276304i | \(0.0891098\pi\) | |||||||
\(180\) | −1.28871 | −0.0960547 | ||||||||
\(181\) | −22.6825 | −1.68597 | −0.842987 | − | 0.537934i | \(-0.819205\pi\) | ||||
−0.842987 | + | 0.537934i | \(0.819205\pi\) | |||||||
\(182\) | −3.75903 | −0.278638 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −15.1978 | −1.12039 | ||||||||
\(185\) | 4.72430 | 0.347338 | ||||||||
\(186\) | 6.69488 | 0.490892 | ||||||||
\(187\) | −0.846049 | −0.0618692 | ||||||||
\(188\) | −0.428332 | −0.0312393 | ||||||||
\(189\) | −2.87358 | −0.209022 | ||||||||
\(190\) | 4.53417 | 0.328943 | ||||||||
\(191\) | −7.49696 | −0.542461 | −0.271230 | − | 0.962514i | \(-0.587431\pi\) | ||||
−0.271230 | + | 0.962514i | \(0.587431\pi\) | |||||||
\(192\) | 5.94929 | 0.429353 | ||||||||
\(193\) | 0.393089 | 0.0282952 | 0.0141476 | − | 0.999900i | \(-0.495497\pi\) | ||||
0.0141476 | + | 0.999900i | \(0.495497\pi\) | |||||||
\(194\) | 9.92957 | 0.712902 | ||||||||
\(195\) | 1.59832 | 0.114458 | ||||||||
\(196\) | −1.42377 | −0.101698 | ||||||||
\(197\) | −7.27055 | −0.518005 | −0.259003 | − | 0.965877i | \(-0.583394\pi\) | ||||
−0.259003 | + | 0.965877i | \(0.583394\pi\) | |||||||
\(198\) | 0.931518 | 0.0662001 | ||||||||
\(199\) | −9.86046 | −0.698989 | −0.349495 | − | 0.936938i | \(-0.613647\pi\) | ||||
−0.349495 | + | 0.936938i | \(0.613647\pi\) | |||||||
\(200\) | 10.8091 | 0.764322 | ||||||||
\(201\) | −6.07605 | −0.428572 | ||||||||
\(202\) | −2.90058 | −0.204084 | ||||||||
\(203\) | −23.5847 | −1.65532 | ||||||||
\(204\) | 0.957959 | 0.0670706 | ||||||||
\(205\) | 0.189317 | 0.0132224 | ||||||||
\(206\) | −0.509936 | −0.0355289 | ||||||||
\(207\) | 5.20869 | 0.362029 | ||||||||
\(208\) | −0.636723 | −0.0441488 | ||||||||
\(209\) | 4.27664 | 0.295822 | ||||||||
\(210\) | −3.04661 | −0.210236 | ||||||||
\(211\) | 22.7443 | 1.56578 | 0.782890 | − | 0.622160i | \(-0.213744\pi\) | ||||
0.782890 | + | 0.622160i | \(0.213744\pi\) | |||||||
\(212\) | 1.04583 | 0.0718280 | ||||||||
\(213\) | −13.3483 | −0.914610 | ||||||||
\(214\) | −4.35744 | −0.297869 | ||||||||
\(215\) | 7.45289 | 0.508283 | ||||||||
\(216\) | −2.91777 | −0.198529 | ||||||||
\(217\) | −20.6526 | −1.40199 | ||||||||
\(218\) | 14.4278 | 0.977174 | ||||||||
\(219\) | 3.93967 | 0.266218 | ||||||||
\(220\) | −1.28871 | −0.0868847 | ||||||||
\(221\) | −1.18811 | −0.0799210 | ||||||||
\(222\) | 3.86657 | 0.259507 | ||||||||
\(223\) | 6.37218 | 0.426712 | 0.213356 | − | 0.976974i | \(-0.431561\pi\) | ||||
0.213356 | + | 0.976974i | \(0.431561\pi\) | |||||||
\(224\) | −15.5552 | −1.03933 | ||||||||
\(225\) | −3.70459 | −0.246973 | ||||||||
\(226\) | −4.46778 | −0.297192 | ||||||||
\(227\) | 17.5489 | 1.16476 | 0.582379 | − | 0.812917i | \(-0.302122\pi\) | ||||
0.582379 | + | 0.812917i | \(0.302122\pi\) | |||||||
\(228\) | −4.84233 | −0.320691 | ||||||||
\(229\) | −8.33291 | −0.550654 | −0.275327 | − | 0.961351i | \(-0.588786\pi\) | ||||
−0.275327 | + | 0.961351i | \(0.588786\pi\) | |||||||
\(230\) | 5.52234 | 0.364132 | ||||||||
\(231\) | −2.87358 | −0.189068 | ||||||||
\(232\) | −23.9474 | −1.57223 | ||||||||
\(233\) | 22.9485 | 1.50341 | 0.751704 | − | 0.659501i | \(-0.229232\pi\) | ||||
0.751704 | + | 0.659501i | \(0.229232\pi\) | |||||||
\(234\) | 1.30814 | 0.0855155 | ||||||||
\(235\) | 0.430558 | 0.0280865 | ||||||||
\(236\) | 1.47652 | 0.0961133 | ||||||||
\(237\) | 7.00809 | 0.455225 | ||||||||
\(238\) | 2.26470 | 0.146798 | ||||||||
\(239\) | 5.29702 | 0.342636 | 0.171318 | − | 0.985216i | \(-0.445197\pi\) | ||||
0.171318 | + | 0.985216i | \(0.445197\pi\) | |||||||
\(240\) | −0.516051 | −0.0333109 | ||||||||
\(241\) | 1.49502 | 0.0963030 | 0.0481515 | − | 0.998840i | \(-0.484667\pi\) | ||||
0.0481515 | + | 0.998840i | \(0.484667\pi\) | |||||||
\(242\) | 0.931518 | 0.0598803 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.13227 | −0.0724864 | ||||||||
\(245\) | 1.43117 | 0.0914344 | ||||||||
\(246\) | 0.154945 | 0.00987892 | ||||||||
\(247\) | 6.00571 | 0.382134 | ||||||||
\(248\) | −20.9702 | −1.33161 | ||||||||
\(249\) | 2.26262 | 0.143388 | ||||||||
\(250\) | −9.22875 | −0.583678 | ||||||||
\(251\) | −11.0035 | −0.694534 | −0.347267 | − | 0.937766i | \(-0.612890\pi\) | ||||
−0.347267 | + | 0.937766i | \(0.612890\pi\) | |||||||
\(252\) | 3.25368 | 0.204962 | ||||||||
\(253\) | 5.20869 | 0.327467 | ||||||||
\(254\) | 2.64831 | 0.166170 | ||||||||
\(255\) | −0.962939 | −0.0603016 | ||||||||
\(256\) | −16.8212 | −1.05132 | ||||||||
\(257\) | 20.5640 | 1.28275 | 0.641375 | − | 0.767228i | \(-0.278364\pi\) | ||||
0.641375 | + | 0.767228i | \(0.278364\pi\) | |||||||
\(258\) | 6.09976 | 0.379754 | ||||||||
\(259\) | −11.9277 | −0.741152 | ||||||||
\(260\) | −1.80974 | −0.112235 | ||||||||
\(261\) | 8.20744 | 0.508028 | ||||||||
\(262\) | 4.69394 | 0.289993 | ||||||||
\(263\) | 25.0818 | 1.54661 | 0.773306 | − | 0.634034i | \(-0.218602\pi\) | ||||
0.773306 | + | 0.634034i | \(0.218602\pi\) | |||||||
\(264\) | −2.91777 | −0.179576 | ||||||||
\(265\) | −1.05127 | −0.0645789 | ||||||||
\(266\) | −11.4477 | −0.701902 | ||||||||
\(267\) | 2.22445 | 0.136134 | ||||||||
\(268\) | 6.87975 | 0.420248 | ||||||||
\(269\) | −19.5174 | −1.19000 | −0.595000 | − | 0.803726i | \(-0.702848\pi\) | ||||
−0.595000 | + | 0.803726i | \(0.702848\pi\) | |||||||
\(270\) | 1.06022 | 0.0645227 | ||||||||
\(271\) | −5.00015 | −0.303737 | −0.151869 | − | 0.988401i | \(-0.548529\pi\) | ||||
−0.151869 | + | 0.988401i | \(0.548529\pi\) | |||||||
\(272\) | 0.383605 | 0.0232595 | ||||||||
\(273\) | −4.03538 | −0.244232 | ||||||||
\(274\) | −13.5294 | −0.817341 | ||||||||
\(275\) | −3.70459 | −0.223395 | ||||||||
\(276\) | −5.89766 | −0.354998 | ||||||||
\(277\) | −15.9275 | −0.956993 | −0.478497 | − | 0.878089i | \(-0.658818\pi\) | ||||
−0.478497 | + | 0.878089i | \(0.658818\pi\) | |||||||
\(278\) | −19.1743 | −1.15000 | ||||||||
\(279\) | 7.18706 | 0.430278 | ||||||||
\(280\) | 9.54283 | 0.570293 | ||||||||
\(281\) | 5.48295 | 0.327085 | 0.163543 | − | 0.986536i | \(-0.447708\pi\) | ||||
0.163543 | + | 0.986536i | \(0.447708\pi\) | |||||||
\(282\) | 0.352387 | 0.0209843 | ||||||||
\(283\) | −4.22686 | −0.251261 | −0.125630 | − | 0.992077i | \(-0.540095\pi\) | ||||
−0.125630 | + | 0.992077i | \(0.540095\pi\) | |||||||
\(284\) | 15.1139 | 0.896846 | ||||||||
\(285\) | 4.86751 | 0.288326 | ||||||||
\(286\) | 1.30814 | 0.0773517 | ||||||||
\(287\) | −0.477979 | −0.0282142 | ||||||||
\(288\) | 5.41318 | 0.318975 | ||||||||
\(289\) | −16.2842 | −0.957894 | ||||||||
\(290\) | 8.70166 | 0.510979 | ||||||||
\(291\) | 10.6596 | 0.624874 | ||||||||
\(292\) | −4.46079 | −0.261048 | ||||||||
\(293\) | −15.7392 | −0.919494 | −0.459747 | − | 0.888050i | \(-0.652060\pi\) | ||||
−0.459747 | + | 0.888050i | \(0.652060\pi\) | |||||||
\(294\) | 1.17133 | 0.0683136 | ||||||||
\(295\) | −1.48420 | −0.0864132 | ||||||||
\(296\) | −12.1112 | −0.703947 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 4.32249 | 0.250395 | ||||||||
\(299\) | 7.31459 | 0.423013 | ||||||||
\(300\) | 4.19461 | 0.242176 | ||||||||
\(301\) | −18.8167 | −1.08458 | ||||||||
\(302\) | −18.6480 | −1.07307 | ||||||||
\(303\) | −3.11381 | −0.178884 | ||||||||
\(304\) | −1.93906 | −0.111213 | ||||||||
\(305\) | 1.13816 | 0.0651709 | ||||||||
\(306\) | −0.788110 | −0.0450533 | ||||||||
\(307\) | 22.6377 | 1.29200 | 0.646001 | − | 0.763337i | \(-0.276440\pi\) | ||||
0.646001 | + | 0.763337i | \(0.276440\pi\) | |||||||
\(308\) | 3.25368 | 0.185395 | ||||||||
\(309\) | −0.547424 | −0.0311419 | ||||||||
\(310\) | 7.61984 | 0.432778 | ||||||||
\(311\) | 8.40924 | 0.476844 | 0.238422 | − | 0.971162i | \(-0.423370\pi\) | ||||
0.238422 | + | 0.971162i | \(0.423370\pi\) | |||||||
\(312\) | −4.09744 | −0.231972 | ||||||||
\(313\) | −7.39027 | −0.417723 | −0.208861 | − | 0.977945i | \(-0.566976\pi\) | ||||
−0.208861 | + | 0.977945i | \(0.566976\pi\) | |||||||
\(314\) | 16.9546 | 0.956801 | ||||||||
\(315\) | −3.27059 | −0.184277 | ||||||||
\(316\) | −7.93508 | −0.446383 | ||||||||
\(317\) | 16.1084 | 0.904738 | 0.452369 | − | 0.891831i | \(-0.350579\pi\) | ||||
0.452369 | + | 0.891831i | \(0.350579\pi\) | |||||||
\(318\) | −0.860402 | −0.0482490 | ||||||||
\(319\) | 8.20744 | 0.459528 | ||||||||
\(320\) | 6.77125 | 0.378524 | ||||||||
\(321\) | −4.67778 | −0.261088 | ||||||||
\(322\) | −13.9426 | −0.776989 | ||||||||
\(323\) | −3.61825 | −0.201325 | ||||||||
\(324\) | −1.13227 | −0.0629041 | ||||||||
\(325\) | −5.20238 | −0.288576 | ||||||||
\(326\) | −9.53316 | −0.527993 | ||||||||
\(327\) | 15.4885 | 0.856515 | ||||||||
\(328\) | −0.485329 | −0.0267978 | ||||||||
\(329\) | −1.08705 | −0.0599313 | ||||||||
\(330\) | 1.06022 | 0.0583630 | ||||||||
\(331\) | 23.9924 | 1.31874 | 0.659371 | − | 0.751818i | \(-0.270823\pi\) | ||||
0.659371 | + | 0.751818i | \(0.270823\pi\) | |||||||
\(332\) | −2.56191 | −0.140603 | ||||||||
\(333\) | 4.15083 | 0.227464 | ||||||||
\(334\) | 20.5960 | 1.12696 | ||||||||
\(335\) | −6.91552 | −0.377835 | ||||||||
\(336\) | 1.30290 | 0.0710792 | ||||||||
\(337\) | −2.36611 | −0.128890 | −0.0644452 | − | 0.997921i | \(-0.520528\pi\) | ||||
−0.0644452 | + | 0.997921i | \(0.520528\pi\) | |||||||
\(338\) | −10.2727 | −0.558762 | ||||||||
\(339\) | −4.79624 | −0.260496 | ||||||||
\(340\) | 1.09031 | 0.0591304 | ||||||||
\(341\) | 7.18706 | 0.389201 | ||||||||
\(342\) | 3.98377 | 0.215418 | ||||||||
\(343\) | 16.5017 | 0.891007 | ||||||||
\(344\) | −19.1061 | −1.03013 | ||||||||
\(345\) | 5.92832 | 0.319170 | ||||||||
\(346\) | −3.42914 | −0.184352 | ||||||||
\(347\) | −3.62961 | −0.194848 | −0.0974238 | − | 0.995243i | \(-0.531060\pi\) | ||||
−0.0974238 | + | 0.995243i | \(0.531060\pi\) | |||||||
\(348\) | −9.29307 | −0.498161 | ||||||||
\(349\) | −9.39190 | −0.502737 | −0.251368 | − | 0.967892i | \(-0.580881\pi\) | ||||
−0.251368 | + | 0.967892i | \(0.580881\pi\) | |||||||
\(350\) | 9.91641 | 0.530055 | ||||||||
\(351\) | 1.40430 | 0.0749562 | ||||||||
\(352\) | 5.41318 | 0.288524 | ||||||||
\(353\) | −1.21621 | −0.0647324 | −0.0323662 | − | 0.999476i | \(-0.510304\pi\) | ||||
−0.0323662 | + | 0.999476i | \(0.510304\pi\) | |||||||
\(354\) | −1.21473 | −0.0645621 | ||||||||
\(355\) | −15.1925 | −0.806334 | ||||||||
\(356\) | −2.51869 | −0.133490 | ||||||||
\(357\) | 2.43119 | 0.128672 | ||||||||
\(358\) | 23.9554 | 1.26608 | ||||||||
\(359\) | 10.9139 | 0.576016 | 0.288008 | − | 0.957628i | \(-0.407007\pi\) | ||||
0.288008 | + | 0.957628i | \(0.407007\pi\) | |||||||
\(360\) | −3.32089 | −0.175026 | ||||||||
\(361\) | −0.710310 | −0.0373847 | ||||||||
\(362\) | −21.1291 | −1.11052 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 4.56915 | 0.239489 | ||||||||
\(365\) | 4.48398 | 0.234702 | ||||||||
\(366\) | 0.931518 | 0.0486912 | ||||||||
\(367\) | −17.3256 | −0.904390 | −0.452195 | − | 0.891919i | \(-0.649359\pi\) | ||||
−0.452195 | + | 0.891919i | \(0.649359\pi\) | |||||||
\(368\) | −2.36166 | −0.123110 | ||||||||
\(369\) | 0.166336 | 0.00865909 | ||||||||
\(370\) | 4.40078 | 0.228785 | ||||||||
\(371\) | 2.65420 | 0.137799 | ||||||||
\(372\) | −8.13772 | −0.421921 | ||||||||
\(373\) | −26.9978 | −1.39789 | −0.698946 | − | 0.715174i | \(-0.746347\pi\) | ||||
−0.698946 | + | 0.715174i | \(0.746347\pi\) | |||||||
\(374\) | −0.788110 | −0.0407522 | ||||||||
\(375\) | −9.90722 | −0.511607 | ||||||||
\(376\) | −1.10377 | −0.0569227 | ||||||||
\(377\) | 11.5257 | 0.593606 | ||||||||
\(378\) | −2.67679 | −0.137679 | ||||||||
\(379\) | −13.0855 | −0.672156 | −0.336078 | − | 0.941834i | \(-0.609101\pi\) | ||||
−0.336078 | + | 0.941834i | \(0.609101\pi\) | |||||||
\(380\) | −5.51135 | −0.282726 | ||||||||
\(381\) | 2.84301 | 0.145652 | ||||||||
\(382\) | −6.98355 | −0.357310 | ||||||||
\(383\) | −7.46685 | −0.381538 | −0.190769 | − | 0.981635i | \(-0.561098\pi\) | ||||
−0.190769 | + | 0.981635i | \(0.561098\pi\) | |||||||
\(384\) | −5.28449 | −0.269673 | ||||||||
\(385\) | −3.27059 | −0.166685 | ||||||||
\(386\) | 0.366169 | 0.0186375 | ||||||||
\(387\) | 6.54819 | 0.332863 | ||||||||
\(388\) | −12.0695 | −0.612738 | ||||||||
\(389\) | −0.429291 | −0.0217659 | −0.0108830 | − | 0.999941i | \(-0.503464\pi\) | ||||
−0.0108830 | + | 0.999941i | \(0.503464\pi\) | |||||||
\(390\) | 1.48887 | 0.0753917 | ||||||||
\(391\) | −4.40681 | −0.222862 | ||||||||
\(392\) | −3.66894 | −0.185309 | ||||||||
\(393\) | 5.03902 | 0.254185 | ||||||||
\(394\) | −6.77265 | −0.341201 | ||||||||
\(395\) | 7.97633 | 0.401333 | ||||||||
\(396\) | −1.13227 | −0.0568989 | ||||||||
\(397\) | −32.2072 | −1.61643 | −0.808217 | − | 0.588885i | \(-0.799567\pi\) | ||||
−0.808217 | + | 0.588885i | \(0.799567\pi\) | |||||||
\(398\) | −9.18519 | −0.460412 | ||||||||
\(399\) | −12.2893 | −0.615233 | ||||||||
\(400\) | 1.67969 | 0.0839846 | ||||||||
\(401\) | −13.0892 | −0.653643 | −0.326821 | − | 0.945086i | \(-0.605978\pi\) | ||||
−0.326821 | + | 0.945086i | \(0.605978\pi\) | |||||||
\(402\) | −5.65995 | −0.282293 | ||||||||
\(403\) | 10.0928 | 0.502759 | ||||||||
\(404\) | 3.52569 | 0.175410 | ||||||||
\(405\) | 1.13816 | 0.0565556 | ||||||||
\(406\) | −21.9696 | −1.09033 | ||||||||
\(407\) | 4.15083 | 0.205749 | ||||||||
\(408\) | 2.46858 | 0.122213 | ||||||||
\(409\) | −26.5459 | −1.31261 | −0.656304 | − | 0.754496i | \(-0.727881\pi\) | ||||
−0.656304 | + | 0.754496i | \(0.727881\pi\) | |||||||
\(410\) | 0.176352 | 0.00870940 | ||||||||
\(411\) | −14.5240 | −0.716418 | ||||||||
\(412\) | 0.619834 | 0.0305370 | ||||||||
\(413\) | 3.74723 | 0.184389 | ||||||||
\(414\) | 4.85199 | 0.238462 | ||||||||
\(415\) | 2.57522 | 0.126413 | ||||||||
\(416\) | 7.60176 | 0.372707 | ||||||||
\(417\) | −20.5839 | −1.00800 | ||||||||
\(418\) | 3.98377 | 0.194853 | ||||||||
\(419\) | −24.8530 | −1.21415 | −0.607073 | − | 0.794646i | \(-0.707657\pi\) | ||||
−0.607073 | + | 0.794646i | \(0.707657\pi\) | |||||||
\(420\) | 3.70320 | 0.180698 | ||||||||
\(421\) | −19.4476 | −0.947817 | −0.473908 | − | 0.880574i | \(-0.657157\pi\) | ||||
−0.473908 | + | 0.880574i | \(0.657157\pi\) | |||||||
\(422\) | 21.1867 | 1.03135 | ||||||||
\(423\) | 0.378293 | 0.0183932 | ||||||||
\(424\) | 2.69502 | 0.130882 | ||||||||
\(425\) | 3.13427 | 0.152034 | ||||||||
\(426\) | −12.4342 | −0.602438 | ||||||||
\(427\) | −2.87358 | −0.139062 | ||||||||
\(428\) | 5.29653 | 0.256018 | ||||||||
\(429\) | 1.40430 | 0.0678005 | ||||||||
\(430\) | 6.94250 | 0.334797 | ||||||||
\(431\) | −32.3889 | −1.56012 | −0.780058 | − | 0.625707i | \(-0.784811\pi\) | ||||
−0.780058 | + | 0.625707i | \(0.784811\pi\) | |||||||
\(432\) | −0.453408 | −0.0218146 | ||||||||
\(433\) | −20.8652 | −1.00272 | −0.501359 | − | 0.865239i | \(-0.667166\pi\) | ||||
−0.501359 | + | 0.865239i | \(0.667166\pi\) | |||||||
\(434\) | −19.2382 | −0.923465 | ||||||||
\(435\) | 9.34138 | 0.447885 | ||||||||
\(436\) | −17.5372 | −0.839880 | ||||||||
\(437\) | 22.2757 | 1.06559 | ||||||||
\(438\) | 3.66988 | 0.175354 | ||||||||
\(439\) | 12.5132 | 0.597224 | 0.298612 | − | 0.954375i | \(-0.403476\pi\) | ||||
0.298612 | + | 0.954375i | \(0.403476\pi\) | |||||||
\(440\) | −3.32089 | −0.158317 | ||||||||
\(441\) | 1.25745 | 0.0598784 | ||||||||
\(442\) | −1.10675 | −0.0526426 | ||||||||
\(443\) | 28.5951 | 1.35859 | 0.679297 | − | 0.733863i | \(-0.262285\pi\) | ||||
0.679297 | + | 0.733863i | \(0.262285\pi\) | |||||||
\(444\) | −4.69987 | −0.223046 | ||||||||
\(445\) | 2.53178 | 0.120018 | ||||||||
\(446\) | 5.93580 | 0.281068 | ||||||||
\(447\) | 4.64026 | 0.219477 | ||||||||
\(448\) | −17.0958 | −0.807698 | ||||||||
\(449\) | 13.9163 | 0.656751 | 0.328376 | − | 0.944547i | \(-0.393499\pi\) | ||||
0.328376 | + | 0.944547i | \(0.393499\pi\) | |||||||
\(450\) | −3.45089 | −0.162677 | ||||||||
\(451\) | 0.166336 | 0.00783244 | ||||||||
\(452\) | 5.43065 | 0.255436 | ||||||||
\(453\) | −20.0189 | −0.940570 | ||||||||
\(454\) | 16.3471 | 0.767207 | ||||||||
\(455\) | −4.59291 | −0.215319 | ||||||||
\(456\) | −12.4783 | −0.584348 | ||||||||
\(457\) | 26.4741 | 1.23841 | 0.619204 | − | 0.785230i | \(-0.287455\pi\) | ||||
0.619204 | + | 0.785230i | \(0.287455\pi\) | |||||||
\(458\) | −7.76226 | −0.362706 | ||||||||
\(459\) | −0.846049 | −0.0394902 | ||||||||
\(460\) | −6.71248 | −0.312971 | ||||||||
\(461\) | −34.1329 | −1.58973 | −0.794864 | − | 0.606787i | \(-0.792458\pi\) | ||||
−0.794864 | + | 0.606787i | \(0.792458\pi\) | |||||||
\(462\) | −2.67679 | −0.124536 | ||||||||
\(463\) | 24.5877 | 1.14269 | 0.571344 | − | 0.820711i | \(-0.306422\pi\) | ||||
0.571344 | + | 0.820711i | \(0.306422\pi\) | |||||||
\(464\) | −3.72132 | −0.172758 | ||||||||
\(465\) | 8.18002 | 0.379340 | ||||||||
\(466\) | 21.3770 | 0.990269 | ||||||||
\(467\) | −4.21020 | −0.194825 | −0.0974124 | − | 0.995244i | \(-0.531057\pi\) | ||||
−0.0974124 | + | 0.995244i | \(0.531057\pi\) | |||||||
\(468\) | −1.59006 | −0.0735004 | ||||||||
\(469\) | 17.4600 | 0.806228 | ||||||||
\(470\) | 0.401073 | 0.0185001 | ||||||||
\(471\) | 18.2010 | 0.838658 | ||||||||
\(472\) | 3.80486 | 0.175133 | ||||||||
\(473\) | 6.54819 | 0.301086 | ||||||||
\(474\) | 6.52817 | 0.299849 | ||||||||
\(475\) | −15.8432 | −0.726937 | ||||||||
\(476\) | −2.75277 | −0.126173 | ||||||||
\(477\) | −0.923656 | −0.0422913 | ||||||||
\(478\) | 4.93427 | 0.225688 | ||||||||
\(479\) | 25.1877 | 1.15086 | 0.575428 | − | 0.817853i | \(-0.304836\pi\) | ||||
0.575428 | + | 0.817853i | \(0.304836\pi\) | |||||||
\(480\) | 6.16107 | 0.281213 | ||||||||
\(481\) | 5.82902 | 0.265781 | ||||||||
\(482\) | 1.39264 | 0.0634331 | ||||||||
\(483\) | −14.9676 | −0.681048 | ||||||||
\(484\) | −1.13227 | −0.0514670 | ||||||||
\(485\) | 12.1323 | 0.550899 | ||||||||
\(486\) | 0.931518 | 0.0422545 | ||||||||
\(487\) | 21.0131 | 0.952194 | 0.476097 | − | 0.879393i | \(-0.342051\pi\) | ||||
0.476097 | + | 0.879393i | \(0.342051\pi\) | |||||||
\(488\) | −2.91777 | −0.132081 | ||||||||
\(489\) | −10.2340 | −0.462798 | ||||||||
\(490\) | 1.33317 | 0.0602263 | ||||||||
\(491\) | −4.29368 | −0.193771 | −0.0968856 | − | 0.995296i | \(-0.530888\pi\) | ||||
−0.0968856 | + | 0.995296i | \(0.530888\pi\) | |||||||
\(492\) | −0.188338 | −0.00849091 | ||||||||
\(493\) | −6.94390 | −0.312737 | ||||||||
\(494\) | 5.59443 | 0.251705 | ||||||||
\(495\) | 1.13816 | 0.0511565 | ||||||||
\(496\) | −3.25867 | −0.146319 | ||||||||
\(497\) | 38.3573 | 1.72056 | ||||||||
\(498\) | 2.10767 | 0.0944470 | ||||||||
\(499\) | −16.7576 | −0.750173 | −0.375087 | − | 0.926990i | \(-0.622387\pi\) | ||||
−0.375087 | + | 0.926990i | \(0.622387\pi\) | |||||||
\(500\) | 11.2177 | 0.501670 | ||||||||
\(501\) | 22.1101 | 0.987807 | ||||||||
\(502\) | −10.2499 | −0.457477 | ||||||||
\(503\) | −20.7558 | −0.925456 | −0.462728 | − | 0.886500i | \(-0.653129\pi\) | ||||
−0.462728 | + | 0.886500i | \(0.653129\pi\) | |||||||
\(504\) | 8.38444 | 0.373473 | ||||||||
\(505\) | −3.54402 | −0.157707 | ||||||||
\(506\) | 4.85199 | 0.215697 | ||||||||
\(507\) | −11.0279 | −0.489767 | ||||||||
\(508\) | −3.21906 | −0.142823 | ||||||||
\(509\) | 14.7620 | 0.654315 | 0.327158 | − | 0.944970i | \(-0.393909\pi\) | ||||
0.327158 | + | 0.944970i | \(0.393909\pi\) | |||||||
\(510\) | −0.896995 | −0.0397196 | ||||||||
\(511\) | −11.3210 | −0.500810 | ||||||||
\(512\) | −5.10026 | −0.225402 | ||||||||
\(513\) | 4.27664 | 0.188818 | ||||||||
\(514\) | 19.1558 | 0.844925 | ||||||||
\(515\) | −0.623056 | −0.0274551 | ||||||||
\(516\) | −7.41434 | −0.326398 | ||||||||
\(517\) | 0.378293 | 0.0166373 | ||||||||
\(518\) | −11.1109 | −0.488184 | ||||||||
\(519\) | −3.68124 | −0.161589 | ||||||||
\(520\) | −4.66354 | −0.204510 | ||||||||
\(521\) | 3.40170 | 0.149031 | 0.0745155 | − | 0.997220i | \(-0.476259\pi\) | ||||
0.0745155 | + | 0.997220i | \(0.476259\pi\) | |||||||
\(522\) | 7.64538 | 0.334629 | ||||||||
\(523\) | 24.0147 | 1.05009 | 0.525045 | − | 0.851074i | \(-0.324048\pi\) | ||||
0.525045 | + | 0.851074i | \(0.324048\pi\) | |||||||
\(524\) | −5.70556 | −0.249248 | ||||||||
\(525\) | 10.6454 | 0.464605 | ||||||||
\(526\) | 23.3642 | 1.01873 | ||||||||
\(527\) | −6.08061 | −0.264875 | ||||||||
\(528\) | −0.453408 | −0.0197320 | ||||||||
\(529\) | 4.13044 | 0.179584 | ||||||||
\(530\) | −0.979276 | −0.0425370 | ||||||||
\(531\) | −1.30403 | −0.0565901 | ||||||||
\(532\) | 13.9148 | 0.603284 | ||||||||
\(533\) | 0.233586 | 0.0101177 | ||||||||
\(534\) | 2.07212 | 0.0896692 | ||||||||
\(535\) | −5.32407 | −0.230180 | ||||||||
\(536\) | 17.7285 | 0.765755 | ||||||||
\(537\) | 25.7165 | 1.10975 | ||||||||
\(538\) | −18.1809 | −0.783832 | ||||||||
\(539\) | 1.25745 | 0.0541620 | ||||||||
\(540\) | −1.28871 | −0.0554572 | ||||||||
\(541\) | −23.7949 | −1.02302 | −0.511512 | − | 0.859276i | \(-0.670914\pi\) | ||||
−0.511512 | + | 0.859276i | \(0.670914\pi\) | |||||||
\(542\) | −4.65773 | −0.200067 | ||||||||
\(543\) | −22.6825 | −0.973397 | ||||||||
\(544\) | −4.57982 | −0.196358 | ||||||||
\(545\) | 17.6284 | 0.755117 | ||||||||
\(546\) | −3.75903 | −0.160872 | ||||||||
\(547\) | −15.3604 | −0.656763 | −0.328382 | − | 0.944545i | \(-0.606503\pi\) | ||||
−0.328382 | + | 0.944545i | \(0.606503\pi\) | |||||||
\(548\) | 16.4452 | 0.702504 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −3.45089 | −0.147147 | ||||||||
\(551\) | 35.1003 | 1.49532 | ||||||||
\(552\) | −15.1978 | −0.646859 | ||||||||
\(553\) | −20.1383 | −0.856367 | ||||||||
\(554\) | −14.8368 | −0.630355 | ||||||||
\(555\) | 4.72430 | 0.200536 | ||||||||
\(556\) | 23.3066 | 0.988420 | ||||||||
\(557\) | −19.2009 | −0.813567 | −0.406783 | − | 0.913525i | \(-0.633350\pi\) | ||||
−0.406783 | + | 0.913525i | \(0.633350\pi\) | |||||||
\(558\) | 6.69488 | 0.283417 | ||||||||
\(559\) | 9.19565 | 0.388935 | ||||||||
\(560\) | 1.48291 | 0.0626645 | ||||||||
\(561\) | −0.846049 | −0.0357202 | ||||||||
\(562\) | 5.10747 | 0.215446 | ||||||||
\(563\) | −8.35263 | −0.352021 | −0.176011 | − | 0.984388i | \(-0.556319\pi\) | ||||
−0.176011 | + | 0.984388i | \(0.556319\pi\) | |||||||
\(564\) | −0.428332 | −0.0180360 | ||||||||
\(565\) | −5.45888 | −0.229657 | ||||||||
\(566\) | −3.93740 | −0.165501 | ||||||||
\(567\) | −2.87358 | −0.120679 | ||||||||
\(568\) | 38.9472 | 1.63419 | ||||||||
\(569\) | 39.5884 | 1.65963 | 0.829817 | − | 0.558036i | \(-0.188445\pi\) | ||||
0.829817 | + | 0.558036i | \(0.188445\pi\) | |||||||
\(570\) | 4.53417 | 0.189915 | ||||||||
\(571\) | −22.6971 | −0.949843 | −0.474921 | − | 0.880028i | \(-0.657523\pi\) | ||||
−0.474921 | + | 0.880028i | \(0.657523\pi\) | |||||||
\(572\) | −1.59006 | −0.0664837 | ||||||||
\(573\) | −7.49696 | −0.313190 | ||||||||
\(574\) | −0.445246 | −0.0185842 | ||||||||
\(575\) | −19.2961 | −0.804702 | ||||||||
\(576\) | 5.94929 | 0.247887 | ||||||||
\(577\) | 17.7404 | 0.738541 | 0.369271 | − | 0.929322i | \(-0.379608\pi\) | ||||
0.369271 | + | 0.929322i | \(0.379608\pi\) | |||||||
\(578\) | −15.1690 | −0.630948 | ||||||||
\(579\) | 0.393089 | 0.0163362 | ||||||||
\(580\) | −10.5770 | −0.439186 | ||||||||
\(581\) | −6.50181 | −0.269741 | ||||||||
\(582\) | 9.92957 | 0.411594 | ||||||||
\(583\) | −0.923656 | −0.0382539 | ||||||||
\(584\) | −11.4951 | −0.475669 | ||||||||
\(585\) | 1.59832 | 0.0660825 | ||||||||
\(586\) | −14.6613 | −0.605655 | ||||||||
\(587\) | 45.4916 | 1.87764 | 0.938820 | − | 0.344408i | \(-0.111920\pi\) | ||||
0.938820 | + | 0.344408i | \(0.111920\pi\) | |||||||
\(588\) | −1.42377 | −0.0587154 | ||||||||
\(589\) | 30.7365 | 1.26648 | ||||||||
\(590\) | −1.38256 | −0.0569189 | ||||||||
\(591\) | −7.27055 | −0.299071 | ||||||||
\(592\) | −1.88202 | −0.0773504 | ||||||||
\(593\) | 0.631502 | 0.0259327 | 0.0129663 | − | 0.999916i | \(-0.495873\pi\) | ||||
0.0129663 | + | 0.999916i | \(0.495873\pi\) | |||||||
\(594\) | 0.931518 | 0.0382207 | ||||||||
\(595\) | 2.76708 | 0.113439 | ||||||||
\(596\) | −5.25405 | −0.215214 | ||||||||
\(597\) | −9.86046 | −0.403562 | ||||||||
\(598\) | 6.81367 | 0.278632 | ||||||||
\(599\) | 7.97573 | 0.325880 | 0.162940 | − | 0.986636i | \(-0.447902\pi\) | ||||
0.162940 | + | 0.986636i | \(0.447902\pi\) | |||||||
\(600\) | 10.8091 | 0.441282 | ||||||||
\(601\) | −42.1385 | −1.71886 | −0.859432 | − | 0.511249i | \(-0.829183\pi\) | ||||
−0.859432 | + | 0.511249i | \(0.829183\pi\) | |||||||
\(602\) | −17.5281 | −0.714393 | ||||||||
\(603\) | −6.07605 | −0.247436 | ||||||||
\(604\) | 22.6669 | 0.922302 | ||||||||
\(605\) | 1.13816 | 0.0462728 | ||||||||
\(606\) | −2.90058 | −0.117828 | ||||||||
\(607\) | 5.96984 | 0.242308 | 0.121154 | − | 0.992634i | \(-0.461340\pi\) | ||||
0.121154 | + | 0.992634i | \(0.461340\pi\) | |||||||
\(608\) | 23.1503 | 0.938867 | ||||||||
\(609\) | −23.5847 | −0.955701 | ||||||||
\(610\) | 1.06022 | 0.0429269 | ||||||||
\(611\) | 0.531239 | 0.0214916 | ||||||||
\(612\) | 0.957959 | 0.0387232 | ||||||||
\(613\) | −19.5289 | −0.788767 | −0.394383 | − | 0.918946i | \(-0.629042\pi\) | ||||
−0.394383 | + | 0.918946i | \(0.629042\pi\) | |||||||
\(614\) | 21.0874 | 0.851019 | ||||||||
\(615\) | 0.189317 | 0.00763398 | ||||||||
\(616\) | 8.38444 | 0.337819 | ||||||||
\(617\) | −40.6362 | −1.63595 | −0.817975 | − | 0.575254i | \(-0.804903\pi\) | ||||
−0.817975 | + | 0.575254i | \(0.804903\pi\) | |||||||
\(618\) | −0.509936 | −0.0205126 | ||||||||
\(619\) | 27.3664 | 1.09995 | 0.549974 | − | 0.835181i | \(-0.314637\pi\) | ||||
0.549974 | + | 0.835181i | \(0.314637\pi\) | |||||||
\(620\) | −9.26203 | −0.371972 | ||||||||
\(621\) | 5.20869 | 0.209017 | ||||||||
\(622\) | 7.83336 | 0.314089 | ||||||||
\(623\) | −6.39213 | −0.256095 | ||||||||
\(624\) | −0.636723 | −0.0254893 | ||||||||
\(625\) | 7.24696 | 0.289878 | ||||||||
\(626\) | −6.88417 | −0.275147 | ||||||||
\(627\) | 4.27664 | 0.170793 | ||||||||
\(628\) | −20.6085 | −0.822370 | ||||||||
\(629\) | −3.51180 | −0.140025 | ||||||||
\(630\) | −3.04661 | −0.121380 | ||||||||
\(631\) | 1.65053 | 0.0657067 | 0.0328534 | − | 0.999460i | \(-0.489541\pi\) | ||||
0.0328534 | + | 0.999460i | \(0.489541\pi\) | |||||||
\(632\) | −20.4480 | −0.813378 | ||||||||
\(633\) | 22.7443 | 0.904004 | ||||||||
\(634\) | 15.0053 | 0.595935 | ||||||||
\(635\) | 3.23580 | 0.128409 | ||||||||
\(636\) | 1.04583 | 0.0414699 | ||||||||
\(637\) | 1.76584 | 0.0699650 | ||||||||
\(638\) | 7.64538 | 0.302683 | ||||||||
\(639\) | −13.3483 | −0.528050 | ||||||||
\(640\) | −6.01459 | −0.237748 | ||||||||
\(641\) | −24.2765 | −0.958866 | −0.479433 | − | 0.877579i | \(-0.659158\pi\) | ||||
−0.479433 | + | 0.877579i | \(0.659158\pi\) | |||||||
\(642\) | −4.35744 | −0.171974 | ||||||||
\(643\) | −27.9072 | −1.10055 | −0.550277 | − | 0.834982i | \(-0.685478\pi\) | ||||
−0.550277 | + | 0.834982i | \(0.685478\pi\) | |||||||
\(644\) | 16.9474 | 0.667821 | ||||||||
\(645\) | 7.45289 | 0.293457 | ||||||||
\(646\) | −3.37047 | −0.132609 | ||||||||
\(647\) | 35.0312 | 1.37722 | 0.688609 | − | 0.725133i | \(-0.258222\pi\) | ||||
0.688609 | + | 0.725133i | \(0.258222\pi\) | |||||||
\(648\) | −2.91777 | −0.114621 | ||||||||
\(649\) | −1.30403 | −0.0511877 | ||||||||
\(650\) | −4.84611 | −0.190080 | ||||||||
\(651\) | −20.6526 | −0.809438 | ||||||||
\(652\) | 11.5877 | 0.453809 | ||||||||
\(653\) | −10.2826 | −0.402390 | −0.201195 | − | 0.979551i | \(-0.564483\pi\) | ||||
−0.201195 | + | 0.979551i | \(0.564483\pi\) | |||||||
\(654\) | 14.4278 | 0.564172 | ||||||||
\(655\) | 5.73522 | 0.224093 | ||||||||
\(656\) | −0.0754179 | −0.00294458 | ||||||||
\(657\) | 3.93967 | 0.153701 | ||||||||
\(658\) | −1.01261 | −0.0394757 | ||||||||
\(659\) | 16.9607 | 0.660697 | 0.330348 | − | 0.943859i | \(-0.392834\pi\) | ||||
0.330348 | + | 0.943859i | \(0.392834\pi\) | |||||||
\(660\) | −1.28871 | −0.0501629 | ||||||||
\(661\) | −15.7229 | −0.611551 | −0.305776 | − | 0.952104i | \(-0.598916\pi\) | ||||
−0.305776 | + | 0.952104i | \(0.598916\pi\) | |||||||
\(662\) | 22.3494 | 0.868632 | ||||||||
\(663\) | −1.18811 | −0.0461424 | ||||||||
\(664\) | −6.60180 | −0.256200 | ||||||||
\(665\) | −13.9872 | −0.542399 | ||||||||
\(666\) | 3.86657 | 0.149827 | ||||||||
\(667\) | 42.7500 | 1.65529 | ||||||||
\(668\) | −25.0347 | −0.968622 | ||||||||
\(669\) | 6.37218 | 0.246363 | ||||||||
\(670\) | −6.44193 | −0.248873 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | −15.5552 | −0.600055 | ||||||||
\(673\) | 8.19652 | 0.315953 | 0.157976 | − | 0.987443i | \(-0.449503\pi\) | ||||
0.157976 | + | 0.987443i | \(0.449503\pi\) | |||||||
\(674\) | −2.20408 | −0.0848979 | ||||||||
\(675\) | −3.70459 | −0.142590 | ||||||||
\(676\) | 12.4866 | 0.480255 | ||||||||
\(677\) | 4.86904 | 0.187133 | 0.0935663 | − | 0.995613i | \(-0.470173\pi\) | ||||
0.0935663 | + | 0.995613i | \(0.470173\pi\) | |||||||
\(678\) | −4.46778 | −0.171584 | ||||||||
\(679\) | −30.6311 | −1.17551 | ||||||||
\(680\) | 2.80964 | 0.107745 | ||||||||
\(681\) | 17.5489 | 0.672474 | ||||||||
\(682\) | 6.69488 | 0.256360 | ||||||||
\(683\) | 19.5539 | 0.748208 | 0.374104 | − | 0.927387i | \(-0.377950\pi\) | ||||
0.374104 | + | 0.927387i | \(0.377950\pi\) | |||||||
\(684\) | −4.84233 | −0.185151 | ||||||||
\(685\) | −16.5307 | −0.631605 | ||||||||
\(686\) | 15.3716 | 0.586891 | ||||||||
\(687\) | −8.33291 | −0.317920 | ||||||||
\(688\) | −2.96900 | −0.113192 | ||||||||
\(689\) | −1.29709 | −0.0494154 | ||||||||
\(690\) | 5.52234 | 0.210232 | ||||||||
\(691\) | −3.37313 | −0.128320 | −0.0641600 | − | 0.997940i | \(-0.520437\pi\) | ||||
−0.0641600 | + | 0.997940i | \(0.520437\pi\) | |||||||
\(692\) | 4.16817 | 0.158450 | ||||||||
\(693\) | −2.87358 | −0.109158 | ||||||||
\(694\) | −3.38105 | −0.128343 | ||||||||
\(695\) | −23.4278 | −0.888665 | ||||||||
\(696\) | −23.9474 | −0.907725 | ||||||||
\(697\) | −0.140728 | −0.00533046 | ||||||||
\(698\) | −8.74872 | −0.331144 | ||||||||
\(699\) | 22.9485 | 0.867993 | ||||||||
\(700\) | −12.0535 | −0.455581 | ||||||||
\(701\) | −19.2156 | −0.725765 | −0.362882 | − | 0.931835i | \(-0.618207\pi\) | ||||
−0.362882 | + | 0.931835i | \(0.618207\pi\) | |||||||
\(702\) | 1.30814 | 0.0493724 | ||||||||
\(703\) | 17.7516 | 0.669515 | ||||||||
\(704\) | 5.94929 | 0.224222 | ||||||||
\(705\) | 0.430558 | 0.0162158 | ||||||||
\(706\) | −1.13292 | −0.0426381 | ||||||||
\(707\) | 8.94779 | 0.336516 | ||||||||
\(708\) | 1.47652 | 0.0554910 | ||||||||
\(709\) | 16.3974 | 0.615817 | 0.307908 | − | 0.951416i | \(-0.400371\pi\) | ||||
0.307908 | + | 0.951416i | \(0.400371\pi\) | |||||||
\(710\) | −14.1521 | −0.531118 | ||||||||
\(711\) | 7.00809 | 0.262824 | ||||||||
\(712\) | −6.49043 | −0.243239 | ||||||||
\(713\) | 37.4352 | 1.40196 | ||||||||
\(714\) | 2.26470 | 0.0847541 | ||||||||
\(715\) | 1.59832 | 0.0597739 | ||||||||
\(716\) | −29.1181 | −1.08819 | ||||||||
\(717\) | 5.29702 | 0.197821 | ||||||||
\(718\) | 10.1665 | 0.379412 | ||||||||
\(719\) | −44.2474 | −1.65015 | −0.825075 | − | 0.565024i | \(-0.808867\pi\) | ||||
−0.825075 | + | 0.565024i | \(0.808867\pi\) | |||||||
\(720\) | −0.516051 | −0.0192321 | ||||||||
\(721\) | 1.57307 | 0.0585840 | ||||||||
\(722\) | −0.661667 | −0.0246247 | ||||||||
\(723\) | 1.49502 | 0.0556006 | ||||||||
\(724\) | 25.6828 | 0.954492 | ||||||||
\(725\) | −30.4052 | −1.12922 | ||||||||
\(726\) | 0.931518 | 0.0345719 | ||||||||
\(727\) | 8.20387 | 0.304265 | 0.152132 | − | 0.988360i | \(-0.451386\pi\) | ||||
0.152132 | + | 0.988360i | \(0.451386\pi\) | |||||||
\(728\) | 11.7743 | 0.436385 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.17691 | 0.154594 | ||||||||
\(731\) | −5.54009 | −0.204908 | ||||||||
\(732\) | −1.13227 | −0.0418500 | ||||||||
\(733\) | 1.42155 | 0.0525062 | 0.0262531 | − | 0.999655i | \(-0.491642\pi\) | ||||
0.0262531 | + | 0.999655i | \(0.491642\pi\) | |||||||
\(734\) | −16.1391 | −0.595706 | ||||||||
\(735\) | 1.43117 | 0.0527897 | ||||||||
\(736\) | 28.1956 | 1.03930 | ||||||||
\(737\) | −6.07605 | −0.223814 | ||||||||
\(738\) | 0.154945 | 0.00570359 | ||||||||
\(739\) | −15.8808 | −0.584184 | −0.292092 | − | 0.956390i | \(-0.594351\pi\) | ||||
−0.292092 | + | 0.956390i | \(0.594351\pi\) | |||||||
\(740\) | −5.34921 | −0.196641 | ||||||||
\(741\) | 6.00571 | 0.220625 | ||||||||
\(742\) | 2.47243 | 0.0907659 | ||||||||
\(743\) | −43.9673 | −1.61300 | −0.806502 | − | 0.591231i | \(-0.798642\pi\) | ||||
−0.806502 | + | 0.591231i | \(0.798642\pi\) | |||||||
\(744\) | −20.9702 | −0.768804 | ||||||||
\(745\) | 5.28136 | 0.193494 | ||||||||
\(746\) | −25.1489 | −0.920768 | ||||||||
\(747\) | 2.26262 | 0.0827849 | ||||||||
\(748\) | 0.957959 | 0.0350265 | ||||||||
\(749\) | 13.4420 | 0.491159 | ||||||||
\(750\) | −9.22875 | −0.336986 | ||||||||
\(751\) | 7.36604 | 0.268791 | 0.134395 | − | 0.990928i | \(-0.457091\pi\) | ||||
0.134395 | + | 0.990928i | \(0.457091\pi\) | |||||||
\(752\) | −0.171521 | −0.00625473 | ||||||||
\(753\) | −11.0035 | −0.400989 | ||||||||
\(754\) | 10.7364 | 0.390998 | ||||||||
\(755\) | −22.7847 | −0.829221 | ||||||||
\(756\) | 3.25368 | 0.118335 | ||||||||
\(757\) | 12.7893 | 0.464835 | 0.232418 | − | 0.972616i | \(-0.425336\pi\) | ||||
0.232418 | + | 0.972616i | \(0.425336\pi\) | |||||||
\(758\) | −12.1894 | −0.442738 | ||||||||
\(759\) | 5.20869 | 0.189063 | ||||||||
\(760\) | −14.2023 | −0.515170 | ||||||||
\(761\) | −24.5790 | −0.890988 | −0.445494 | − | 0.895285i | \(-0.646972\pi\) | ||||
−0.445494 | + | 0.895285i | \(0.646972\pi\) | |||||||
\(762\) | 2.64831 | 0.0959382 | ||||||||
\(763\) | −44.5074 | −1.61127 | ||||||||
\(764\) | 8.48861 | 0.307107 | ||||||||
\(765\) | −0.962939 | −0.0348151 | ||||||||
\(766\) | −6.95550 | −0.251313 | ||||||||
\(767\) | −1.83126 | −0.0661229 | ||||||||
\(768\) | −16.8212 | −0.606982 | ||||||||
\(769\) | −21.8219 | −0.786918 | −0.393459 | − | 0.919342i | \(-0.628722\pi\) | ||||
−0.393459 | + | 0.919342i | \(0.628722\pi\) | |||||||
\(770\) | −3.04661 | −0.109792 | ||||||||
\(771\) | 20.5640 | 0.740596 | ||||||||
\(772\) | −0.445084 | −0.0160189 | ||||||||
\(773\) | 44.0296 | 1.58363 | 0.791817 | − | 0.610758i | \(-0.209135\pi\) | ||||
0.791817 | + | 0.610758i | \(0.209135\pi\) | |||||||
\(774\) | 6.09976 | 0.219251 | ||||||||
\(775\) | −26.6251 | −0.956403 | ||||||||
\(776\) | −31.1021 | −1.11650 | ||||||||
\(777\) | −11.9277 | −0.427905 | ||||||||
\(778\) | −0.399892 | −0.0143368 | ||||||||
\(779\) | 0.711359 | 0.0254871 | ||||||||
\(780\) | −1.80974 | −0.0647991 | ||||||||
\(781\) | −13.3483 | −0.477639 | ||||||||
\(782\) | −4.10502 | −0.146795 | ||||||||
\(783\) | 8.20744 | 0.293310 | ||||||||
\(784\) | −0.570136 | −0.0203620 | ||||||||
\(785\) | 20.7157 | 0.739373 | ||||||||
\(786\) | 4.69394 | 0.167427 | ||||||||
\(787\) | 0.872256 | 0.0310926 | 0.0155463 | − | 0.999879i | \(-0.495051\pi\) | ||||
0.0155463 | + | 0.999879i | \(0.495051\pi\) | |||||||
\(788\) | 8.23226 | 0.293262 | ||||||||
\(789\) | 25.0818 | 0.892936 | ||||||||
\(790\) | 7.43010 | 0.264351 | ||||||||
\(791\) | 13.7824 | 0.490044 | ||||||||
\(792\) | −2.91777 | −0.103678 | ||||||||
\(793\) | 1.40430 | 0.0498683 | ||||||||
\(794\) | −30.0016 | −1.06472 | ||||||||
\(795\) | −1.05127 | −0.0372847 | ||||||||
\(796\) | 11.1647 | 0.395724 | ||||||||
\(797\) | 18.0615 | 0.639771 | 0.319886 | − | 0.947456i | \(-0.396356\pi\) | ||||
0.319886 | + | 0.947456i | \(0.396356\pi\) | |||||||
\(798\) | −11.4477 | −0.405243 | ||||||||
\(799\) | −0.320055 | −0.0113227 | ||||||||
\(800\) | −20.0536 | −0.709003 | ||||||||
\(801\) | 2.22445 | 0.0785971 | ||||||||
\(802\) | −12.1928 | −0.430543 | ||||||||
\(803\) | 3.93967 | 0.139028 | ||||||||
\(804\) | 6.87975 | 0.242630 | ||||||||
\(805\) | −17.0355 | −0.600422 | ||||||||
\(806\) | 9.40165 | 0.331159 | ||||||||
\(807\) | −19.5174 | −0.687046 | ||||||||
\(808\) | 9.08540 | 0.319623 | ||||||||
\(809\) | 47.4599 | 1.66860 | 0.834300 | − | 0.551310i | \(-0.185872\pi\) | ||||
0.834300 | + | 0.551310i | \(0.185872\pi\) | |||||||
\(810\) | 1.06022 | 0.0372522 | ||||||||
\(811\) | 17.9421 | 0.630034 | 0.315017 | − | 0.949086i | \(-0.397990\pi\) | ||||
0.315017 | + | 0.949086i | \(0.397990\pi\) | |||||||
\(812\) | 26.7043 | 0.937139 | ||||||||
\(813\) | −5.00015 | −0.175363 | ||||||||
\(814\) | 3.86657 | 0.135523 | ||||||||
\(815\) | −11.6479 | −0.408009 | ||||||||
\(816\) | 0.383605 | 0.0134289 | ||||||||
\(817\) | 28.0043 | 0.979746 | ||||||||
\(818\) | −24.7280 | −0.864593 | ||||||||
\(819\) | −4.03538 | −0.141008 | ||||||||
\(820\) | −0.214358 | −0.00748572 | ||||||||
\(821\) | 18.7155 | 0.653176 | 0.326588 | − | 0.945167i | \(-0.394101\pi\) | ||||
0.326588 | + | 0.945167i | \(0.394101\pi\) | |||||||
\(822\) | −13.5294 | −0.471892 | ||||||||
\(823\) | −15.1782 | −0.529079 | −0.264539 | − | 0.964375i | \(-0.585220\pi\) | ||||
−0.264539 | + | 0.964375i | \(0.585220\pi\) | |||||||
\(824\) | 1.59726 | 0.0556431 | ||||||||
\(825\) | −3.70459 | −0.128977 | ||||||||
\(826\) | 3.49062 | 0.121454 | ||||||||
\(827\) | 7.54528 | 0.262375 | 0.131188 | − | 0.991358i | \(-0.458121\pi\) | ||||
0.131188 | + | 0.991358i | \(0.458121\pi\) | |||||||
\(828\) | −5.89766 | −0.204958 | ||||||||
\(829\) | −38.8988 | −1.35101 | −0.675505 | − | 0.737355i | \(-0.736074\pi\) | ||||
−0.675505 | + | 0.737355i | \(0.736074\pi\) | |||||||
\(830\) | 2.39887 | 0.0832659 | ||||||||
\(831\) | −15.9275 | −0.552520 | ||||||||
\(832\) | 8.35462 | 0.289644 | ||||||||
\(833\) | −1.06386 | −0.0368606 | ||||||||
\(834\) | −19.1743 | −0.663950 | ||||||||
\(835\) | 25.1648 | 0.870865 | ||||||||
\(836\) | −4.84233 | −0.167476 | ||||||||
\(837\) | 7.18706 | 0.248421 | ||||||||
\(838\) | −23.1510 | −0.799737 | ||||||||
\(839\) | −43.1046 | −1.48814 | −0.744068 | − | 0.668104i | \(-0.767106\pi\) | ||||
−0.744068 | + | 0.668104i | \(0.767106\pi\) | |||||||
\(840\) | 9.54283 | 0.329259 | ||||||||
\(841\) | 38.3620 | 1.32283 | ||||||||
\(842\) | −18.1158 | −0.624311 | ||||||||
\(843\) | 5.48295 | 0.188843 | ||||||||
\(844\) | −25.7528 | −0.886446 | ||||||||
\(845\) | −12.5515 | −0.431786 | ||||||||
\(846\) | 0.352387 | 0.0121153 | ||||||||
\(847\) | −2.87358 | −0.0987373 | ||||||||
\(848\) | 0.418793 | 0.0143814 | ||||||||
\(849\) | −4.22686 | −0.145066 | ||||||||
\(850\) | 2.91963 | 0.100142 | ||||||||
\(851\) | 21.6204 | 0.741136 | ||||||||
\(852\) | 15.1139 | 0.517794 | ||||||||
\(853\) | −38.9132 | −1.33236 | −0.666181 | − | 0.745790i | \(-0.732072\pi\) | ||||
−0.666181 | + | 0.745790i | \(0.732072\pi\) | |||||||
\(854\) | −2.67679 | −0.0915978 | ||||||||
\(855\) | 4.86751 | 0.166465 | ||||||||
\(856\) | 13.6487 | 0.466503 | ||||||||
\(857\) | −19.4681 | −0.665018 | −0.332509 | − | 0.943100i | \(-0.607895\pi\) | ||||
−0.332509 | + | 0.943100i | \(0.607895\pi\) | |||||||
\(858\) | 1.30814 | 0.0446590 | ||||||||
\(859\) | −46.4664 | −1.58541 | −0.792707 | − | 0.609603i | \(-0.791329\pi\) | ||||
−0.792707 | + | 0.609603i | \(0.791329\pi\) | |||||||
\(860\) | −8.43871 | −0.287758 | ||||||||
\(861\) | −0.477979 | −0.0162895 | ||||||||
\(862\) | −30.1708 | −1.02762 | ||||||||
\(863\) | −6.69874 | −0.228028 | −0.114014 | − | 0.993479i | \(-0.536371\pi\) | ||||
−0.114014 | + | 0.993479i | \(0.536371\pi\) | |||||||
\(864\) | 5.41318 | 0.184160 | ||||||||
\(865\) | −4.18984 | −0.142459 | ||||||||
\(866\) | −19.4363 | −0.660473 | ||||||||
\(867\) | −16.2842 | −0.553040 | ||||||||
\(868\) | 23.3844 | 0.793717 | ||||||||
\(869\) | 7.00809 | 0.237733 | ||||||||
\(870\) | 8.70166 | 0.295014 | ||||||||
\(871\) | −8.53263 | −0.289117 | ||||||||
\(872\) | −45.1918 | −1.53039 | ||||||||
\(873\) | 10.6596 | 0.360771 | ||||||||
\(874\) | 20.7502 | 0.701887 | ||||||||
\(875\) | 28.4692 | 0.962433 | ||||||||
\(876\) | −4.46079 | −0.150716 | ||||||||
\(877\) | −2.94494 | −0.0994436 | −0.0497218 | − | 0.998763i | \(-0.515833\pi\) | ||||
−0.0497218 | + | 0.998763i | \(0.515833\pi\) | |||||||
\(878\) | 11.6563 | 0.393381 | ||||||||
\(879\) | −15.7392 | −0.530870 | ||||||||
\(880\) | −0.516051 | −0.0173961 | ||||||||
\(881\) | 52.7814 | 1.77825 | 0.889126 | − | 0.457663i | \(-0.151313\pi\) | ||||
0.889126 | + | 0.457663i | \(0.151313\pi\) | |||||||
\(882\) | 1.17133 | 0.0394409 | ||||||||
\(883\) | −13.1341 | −0.441998 | −0.220999 | − | 0.975274i | \(-0.570932\pi\) | ||||
−0.220999 | + | 0.975274i | \(0.570932\pi\) | |||||||
\(884\) | 1.34527 | 0.0452462 | ||||||||
\(885\) | −1.48420 | −0.0498907 | ||||||||
\(886\) | 26.6369 | 0.894883 | ||||||||
\(887\) | −11.6115 | −0.389875 | −0.194938 | − | 0.980816i | \(-0.562450\pi\) | ||||
−0.194938 | + | 0.980816i | \(0.562450\pi\) | |||||||
\(888\) | −12.1112 | −0.406424 | ||||||||
\(889\) | −8.16960 | −0.274000 | ||||||||
\(890\) | 2.35840 | 0.0790537 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −7.21505 | −0.241578 | ||||||||
\(893\) | 1.61783 | 0.0541385 | ||||||||
\(894\) | 4.32249 | 0.144566 | ||||||||
\(895\) | 29.2695 | 0.978371 | ||||||||
\(896\) | 15.1854 | 0.507308 | ||||||||
\(897\) | 7.31459 | 0.244227 | ||||||||
\(898\) | 12.9633 | 0.432591 | ||||||||
\(899\) | 58.9874 | 1.96734 | ||||||||
\(900\) | 4.19461 | 0.139820 | ||||||||
\(901\) | 0.781459 | 0.0260342 | ||||||||
\(902\) | 0.154945 | 0.00515910 | ||||||||
\(903\) | −18.8167 | −0.626182 | ||||||||
\(904\) | 13.9943 | 0.465444 | ||||||||
\(905\) | −25.8163 | −0.858162 | ||||||||
\(906\) | −18.6480 | −0.619537 | ||||||||
\(907\) | 17.2320 | 0.572179 | 0.286089 | − | 0.958203i | \(-0.407645\pi\) | ||||
0.286089 | + | 0.958203i | \(0.407645\pi\) | |||||||
\(908\) | −19.8701 | −0.659413 | ||||||||
\(909\) | −3.11381 | −0.103279 | ||||||||
\(910\) | −4.27838 | −0.141827 | ||||||||
\(911\) | 7.53148 | 0.249529 | 0.124765 | − | 0.992186i | \(-0.460182\pi\) | ||||
0.124765 | + | 0.992186i | \(0.460182\pi\) | |||||||
\(912\) | −1.93906 | −0.0642089 | ||||||||
\(913\) | 2.26262 | 0.0748818 | ||||||||
\(914\) | 24.6611 | 0.815718 | ||||||||
\(915\) | 1.13816 | 0.0376264 | ||||||||
\(916\) | 9.43514 | 0.311746 | ||||||||
\(917\) | −14.4800 | −0.478173 | ||||||||
\(918\) | −0.788110 | −0.0260115 | ||||||||
\(919\) | 34.0656 | 1.12372 | 0.561860 | − | 0.827232i | \(-0.310086\pi\) | ||||
0.561860 | + | 0.827232i | \(0.310086\pi\) | |||||||
\(920\) | −17.2975 | −0.570281 | ||||||||
\(921\) | 22.6377 | 0.745937 | ||||||||
\(922\) | −31.7954 | −1.04713 | ||||||||
\(923\) | −18.7451 | −0.617001 | ||||||||
\(924\) | 3.25368 | 0.107038 | ||||||||
\(925\) | −15.3771 | −0.505596 | ||||||||
\(926\) | 22.9039 | 0.752669 | ||||||||
\(927\) | −0.547424 | −0.0179798 | ||||||||
\(928\) | 44.4284 | 1.45843 | ||||||||
\(929\) | 37.7346 | 1.23803 | 0.619015 | − | 0.785379i | \(-0.287532\pi\) | ||||
0.619015 | + | 0.785379i | \(0.287532\pi\) | |||||||
\(930\) | 7.61984 | 0.249864 | ||||||||
\(931\) | 5.37765 | 0.176245 | ||||||||
\(932\) | −25.9840 | −0.851135 | ||||||||
\(933\) | 8.40924 | 0.275306 | ||||||||
\(934\) | −3.92188 | −0.128328 | ||||||||
\(935\) | −0.962939 | −0.0314915 | ||||||||
\(936\) | −4.09744 | −0.133929 | ||||||||
\(937\) | −14.3169 | −0.467713 | −0.233856 | − | 0.972271i | \(-0.575135\pi\) | ||||
−0.233856 | + | 0.972271i | \(0.575135\pi\) | |||||||
\(938\) | 16.2643 | 0.531048 | ||||||||
\(939\) | −7.39027 | −0.241172 | ||||||||
\(940\) | −0.487510 | −0.0159008 | ||||||||
\(941\) | 16.2025 | 0.528187 | 0.264093 | − | 0.964497i | \(-0.414927\pi\) | ||||
0.264093 | + | 0.964497i | \(0.414927\pi\) | |||||||
\(942\) | 16.9546 | 0.552410 | ||||||||
\(943\) | 0.866391 | 0.0282136 | ||||||||
\(944\) | 0.591258 | 0.0192438 | ||||||||
\(945\) | −3.27059 | −0.106392 | ||||||||
\(946\) | 6.09976 | 0.198320 | ||||||||
\(947\) | 22.4697 | 0.730166 | 0.365083 | − | 0.930975i | \(-0.381041\pi\) | ||||
0.365083 | + | 0.930975i | \(0.381041\pi\) | |||||||
\(948\) | −7.93508 | −0.257719 | ||||||||
\(949\) | 5.53250 | 0.179593 | ||||||||
\(950\) | −14.7582 | −0.478821 | ||||||||
\(951\) | 16.1084 | 0.522351 | ||||||||
\(952\) | −7.09365 | −0.229906 | ||||||||
\(953\) | 23.0493 | 0.746639 | 0.373319 | − | 0.927703i | \(-0.378220\pi\) | ||||
0.373319 | + | 0.927703i | \(0.378220\pi\) | |||||||
\(954\) | −0.860402 | −0.0278566 | ||||||||
\(955\) | −8.53274 | −0.276113 | ||||||||
\(956\) | −5.99768 | −0.193979 | ||||||||
\(957\) | 8.20744 | 0.265309 | ||||||||
\(958\) | 23.4628 | 0.758049 | ||||||||
\(959\) | 41.7359 | 1.34772 | ||||||||
\(960\) | 6.77125 | 0.218541 | ||||||||
\(961\) | 20.6538 | 0.666253 | ||||||||
\(962\) | 5.42984 | 0.175065 | ||||||||
\(963\) | −4.67778 | −0.150740 | ||||||||
\(964\) | −1.69278 | −0.0545207 | ||||||||
\(965\) | 0.447398 | 0.0144023 | ||||||||
\(966\) | −13.9426 | −0.448595 | ||||||||
\(967\) | 53.4375 | 1.71843 | 0.859217 | − | 0.511611i | \(-0.170951\pi\) | ||||
0.859217 | + | 0.511611i | \(0.170951\pi\) | |||||||
\(968\) | −2.91777 | −0.0937807 | ||||||||
\(969\) | −3.61825 | −0.116235 | ||||||||
\(970\) | 11.3014 | 0.362867 | ||||||||
\(971\) | 19.8254 | 0.636227 | 0.318113 | − | 0.948053i | \(-0.396951\pi\) | ||||
0.318113 | + | 0.948053i | \(0.396951\pi\) | |||||||
\(972\) | −1.13227 | −0.0363177 | ||||||||
\(973\) | 59.1494 | 1.89624 | ||||||||
\(974\) | 19.5741 | 0.627194 | ||||||||
\(975\) | −5.20238 | −0.166609 | ||||||||
\(976\) | −0.453408 | −0.0145132 | ||||||||
\(977\) | 46.6622 | 1.49286 | 0.746428 | − | 0.665466i | \(-0.231767\pi\) | ||||
0.746428 | + | 0.665466i | \(0.231767\pi\) | |||||||
\(978\) | −9.53316 | −0.304837 | ||||||||
\(979\) | 2.22445 | 0.0710937 | ||||||||
\(980\) | −1.62048 | −0.0517644 | ||||||||
\(981\) | 15.4885 | 0.494509 | ||||||||
\(982\) | −3.99964 | −0.127634 | ||||||||
\(983\) | −23.3443 | −0.744568 | −0.372284 | − | 0.928119i | \(-0.621425\pi\) | ||||
−0.372284 | + | 0.928119i | \(0.621425\pi\) | |||||||
\(984\) | −0.485329 | −0.0154717 | ||||||||
\(985\) | −8.27505 | −0.263665 | ||||||||
\(986\) | −6.46837 | −0.205995 | ||||||||
\(987\) | −1.08705 | −0.0346013 | ||||||||
\(988\) | −6.80011 | −0.216340 | ||||||||
\(989\) | 34.1075 | 1.08455 | ||||||||
\(990\) | 1.06022 | 0.0336959 | ||||||||
\(991\) | −32.4785 | −1.03171 | −0.515857 | − | 0.856675i | \(-0.672526\pi\) | ||||
−0.515857 | + | 0.856675i | \(0.672526\pi\) | |||||||
\(992\) | 38.9049 | 1.23523 | ||||||||
\(993\) | 23.9924 | 0.761376 | ||||||||
\(994\) | 35.7306 | 1.13330 | ||||||||
\(995\) | −11.2228 | −0.355786 | ||||||||
\(996\) | −2.56191 | −0.0811771 | ||||||||
\(997\) | −58.9975 | −1.86847 | −0.934234 | − | 0.356660i | \(-0.883915\pi\) | ||||
−0.934234 | + | 0.356660i | \(0.883915\pi\) | |||||||
\(998\) | −15.6100 | −0.494126 | ||||||||
\(999\) | 4.15083 | 0.131326 |
(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 | 2013.2.a.g.1.8 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.h.1.6 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.g.1.8 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.h.1.6 | 13 | 3.2 | odd | 2 |