Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 2012) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.301406 | −0.174017 | −0.0870083 | − | 0.996208i | \(-0.527731\pi\) | ||||
−0.0870083 | + | 0.996208i | \(0.527731\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.72608 | 1.66635 | 0.833177 | − | 0.553006i | \(-0.186519\pi\) | ||||
0.833177 | + | 0.553006i | \(0.186519\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.06802 | 1.15960 | 0.579800 | − | 0.814759i | \(-0.303131\pi\) | ||||
0.579800 | + | 0.814759i | \(0.303131\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.90915 | −0.969718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.17363 | −0.353864 | −0.176932 | − | 0.984223i | \(-0.556617\pi\) | ||||
−0.176932 | + | 0.984223i | \(0.556617\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.64937 | −1.28950 | −0.644752 | − | 0.764392i | \(-0.723039\pi\) | ||||
−0.644752 | + | 0.764392i | \(0.723039\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.12306 | −0.289973 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.45150 | −0.352041 | −0.176020 | − | 0.984387i | \(-0.556322\pi\) | ||||
−0.176020 | + | 0.984387i | \(0.556322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.85726 | 0.884916 | 0.442458 | − | 0.896789i | \(-0.354106\pi\) | ||||
0.442458 | + | 0.896789i | \(0.354106\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.924717 | −0.201790 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.40909 | 1.12787 | 0.563936 | − | 0.825818i | \(-0.309286\pi\) | ||||
0.563936 | + | 0.825818i | \(0.309286\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.88368 | 1.77674 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.78105 | 0.342764 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.63184 | 1.04581 | 0.522903 | − | 0.852392i | \(-0.324849\pi\) | ||||
0.522903 | + | 0.852392i | \(0.324849\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.49372 | 0.807096 | 0.403548 | − | 0.914958i | \(-0.367777\pi\) | ||||
0.403548 | + | 0.914958i | \(0.367777\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.353740 | 0.0615783 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.4317 | 1.93231 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.33783 | −1.20633 | −0.603166 | − | 0.797616i | \(-0.706094\pi\) | ||||
−0.603166 | + | 0.797616i | \(0.706094\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.40135 | 0.224395 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.3803 | −1.77730 | −0.888648 | − | 0.458589i | \(-0.848355\pi\) | ||||
−0.888648 | + | 0.458589i | \(0.848355\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.68116 | −0.256374 | −0.128187 | − | 0.991750i | \(-0.540916\pi\) | ||||
−0.128187 | + | 0.991750i | \(0.540916\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.8397 | −1.61589 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.152534 | 0.0222494 | 0.0111247 | − | 0.999938i | \(-0.496459\pi\) | ||||
0.0111247 | + | 0.999938i | \(0.496459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.41272 | 0.344674 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.437491 | 0.0612609 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.85851 | 0.942088 | 0.471044 | − | 0.882110i | \(-0.343877\pi\) | ||||
0.471044 | + | 0.882110i | \(0.343877\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.37306 | −0.589663 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.16260 | −0.153990 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8204 | 1.40870 | 0.704348 | − | 0.709855i | \(-0.251240\pi\) | ||||
0.704348 | + | 0.709855i | \(0.251240\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.25765 | 0.417099 | 0.208550 | − | 0.978012i | \(-0.433126\pi\) | ||||
0.208550 | + | 0.978012i | \(0.433126\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.92533 | −1.12449 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17.3239 | −2.14877 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.34459 | −1.01945 | −0.509727 | − | 0.860336i | \(-0.670254\pi\) | ||||
−0.509727 | + | 0.860336i | \(0.670254\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.63033 | −0.196269 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.5490 | 1.84533 | 0.922665 | − | 0.385601i | \(-0.126006\pi\) | ||||
0.922665 | + | 0.385601i | \(0.126006\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.3257 | 1.91078 | 0.955392 | − | 0.295341i | \(-0.0954332\pi\) | ||||
0.955392 | + | 0.295341i | \(0.0954332\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.67759 | −0.309182 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.60073 | −0.410341 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.8536 | −1.33363 | −0.666814 | − | 0.745224i | \(-0.732343\pi\) | ||||
−0.666814 | + | 0.745224i | \(0.732343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.19064 | 0.910072 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.33359 | −0.146381 | −0.0731903 | − | 0.997318i | \(-0.523318\pi\) | ||||
−0.0731903 | + | 0.997318i | \(0.523318\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.40841 | −0.586624 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.69747 | −0.181988 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.98475 | 0.740382 | 0.370191 | − | 0.928956i | \(-0.379292\pi\) | ||||
0.370191 | + | 0.928956i | \(0.379292\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.2644 | −1.49531 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.35443 | −0.140448 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.3725 | 1.47458 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.18127 | 0.729147 | 0.364574 | − | 0.931175i | \(-0.381215\pi\) | ||||
0.364574 | + | 0.931175i | \(0.381215\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.41428 | 0.343149 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.9931 | 1.49186 | 0.745932 | − | 0.666022i | \(-0.232004\pi\) | ||||
0.745932 | + | 0.666022i | \(0.232004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.3974 | 1.71422 | 0.857110 | − | 0.515133i | \(-0.172258\pi\) | ||||
0.857110 | + | 0.515133i | \(0.172258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.44557 | −0.336253 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.06215 | 0.682724 | 0.341362 | − | 0.939932i | \(-0.389112\pi\) | ||||
0.341362 | + | 0.939932i | \(0.389112\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.91081 | −0.470370 | −0.235185 | − | 0.971951i | \(-0.575570\pi\) | ||||
−0.235185 | + | 0.971951i | \(0.575570\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.21166 | 0.209922 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.9925 | −1.78666 | −0.893332 | − | 0.449398i | \(-0.851639\pi\) | ||||
−0.893332 | + | 0.449398i | \(0.851639\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.1547 | 1.87944 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.5257 | 1.25046 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.45323 | −0.408227 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.62258 | −0.874780 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.43007 | 0.309279 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14.4709 | 1.29432 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.7997 | 0.958315 | 0.479157 | − | 0.877729i | \(-0.340942\pi\) | ||||
0.479157 | + | 0.877729i | \(0.340942\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.506710 | 0.0446133 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.1541 | −1.41139 | −0.705696 | − | 0.708515i | \(-0.749366\pi\) | ||||
−0.705696 | + | 0.708515i | \(0.749366\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.8341 | 1.02615 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.63635 | 0.571166 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.16222 | 0.270167 | 0.135084 | − | 0.990834i | \(-0.456870\pi\) | ||||
0.135084 | + | 0.990834i | \(0.456870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.31329 | −0.365848 | −0.182924 | − | 0.983127i | \(-0.558556\pi\) | ||||
−0.182924 | + | 0.983127i | \(0.558556\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0459748 | −0.00387177 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.45667 | 0.456309 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.9847 | 1.74268 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.727207 | −0.0599790 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.8440 | 1.29799 | 0.648994 | − | 0.760793i | \(-0.275190\pi\) | ||||
0.648994 | + | 0.760793i | \(0.275190\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.42965 | 0.360479 | 0.180240 | − | 0.983623i | \(-0.442313\pi\) | ||||
0.180240 | + | 0.983623i | \(0.442313\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.22264 | 0.341380 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.7440 | 1.34491 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.02597 | 0.321308 | 0.160654 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160654 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.06719 | −0.163939 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.5952 | 1.30788 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.62470 | 0.127256 | 0.0636281 | − | 0.997974i | \(-0.479733\pi\) | ||||
0.0636281 | + | 0.997974i | \(0.479733\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.31806 | 0.102611 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.7196 | 1.37118 | 0.685591 | − | 0.727987i | \(-0.259544\pi\) | ||||
0.685591 | + | 0.727987i | \(0.259544\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.61668 | 0.662822 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.2214 | −0.858120 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.23597 | −0.398083 | −0.199042 | − | 0.979991i | \(-0.563783\pi\) | ||||
−0.199042 | + | 0.979991i | \(0.563783\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27.2553 | 2.06031 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.26133 | −0.245136 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0376 | −1.19871 | −0.599355 | − | 0.800484i | \(-0.704576\pi\) | ||||
−0.599355 | + | 0.800484i | \(0.704576\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.62033 | 0.343426 | 0.171713 | − | 0.985147i | \(-0.445070\pi\) | ||||
0.171713 | + | 0.985147i | \(0.445070\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.981873 | −0.0725822 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −27.3413 | −2.01018 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.70353 | 0.124575 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.46430 | 0.397469 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.9325 | 1.51462 | 0.757310 | − | 0.653056i | \(-0.226513\pi\) | ||||
0.757310 | + | 0.653056i | \(0.226513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0646429 | −0.00465310 | −0.00232655 | − | 0.999997i | \(-0.500741\pi\) | ||||
−0.00232655 | + | 0.999997i | \(0.500741\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.22154 | 0.373922 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.466359 | 0.0332267 | 0.0166134 | − | 0.999862i | \(-0.494712\pi\) | ||||
0.0166134 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1551 | −0.719879 | −0.359940 | − | 0.932976i | \(-0.617203\pi\) | ||||
−0.359940 | + | 0.932976i | \(0.617203\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.51511 | 0.177402 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.2786 | 1.21272 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −42.4037 | −2.96161 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.7359 | −1.09372 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.52702 | −0.313140 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2361 | 1.18658 | 0.593292 | − | 0.804987i | \(-0.297828\pi\) | ||||
0.593292 | + | 0.804987i | \(0.297828\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.68657 | −0.321118 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.26412 | −0.427210 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.7868 | 0.935910 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.92067 | −0.332508 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.74857 | 0.453958 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.1432 | 1.54979 | 0.774893 | − | 0.632093i | \(-0.217804\pi\) | ||||
0.774893 | + | 0.632093i | \(0.217804\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.8440 | −1.72293 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.1287 | 1.00413 | 0.502064 | − | 0.864830i | \(-0.332574\pi\) | ||||
0.502064 | + | 0.864830i | \(0.332574\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.7020 | 1.56628 | 0.783138 | − | 0.621848i | \(-0.213618\pi\) | ||||
0.783138 | + | 0.621848i | \(0.213618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.08528 | 0.0714062 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.7419 | −1.22782 | −0.613911 | − | 0.789375i | \(-0.710405\pi\) | ||||
−0.613911 | + | 0.789375i | \(0.710405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.568356 | 0.0370754 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.57273 | 0.232074 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.7737 | −0.826264 | −0.413132 | − | 0.910671i | \(-0.635565\pi\) | ||||
−0.413132 | + | 0.910671i | \(0.635565\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.74355 | −0.176728 | −0.0883639 | − | 0.996088i | \(-0.528164\pi\) | ||||
−0.0883639 | + | 0.996088i | \(0.528164\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.81187 | −0.501131 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.98999 | 0.574349 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.9339 | −1.14110 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.401952 | 0.0254727 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.43708 | −0.153827 | −0.0769136 | − | 0.997038i | \(-0.524507\pi\) | ||||
−0.0769136 | + | 0.997038i | \(0.524507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.34829 | −0.399114 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.63013 | 0.102082 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.3908 | −1.27194 | −0.635971 | − | 0.771713i | \(-0.719400\pi\) | ||||
−0.635971 | + | 0.771713i | \(0.719400\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.5126 | −1.39886 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.3839 | −1.01414 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.2691 | 1.31151 | 0.655754 | − | 0.754974i | \(-0.272351\pi\) | ||||
0.655754 | + | 0.754974i | \(0.272351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.5553 | 1.56985 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.10524 | −0.128839 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.1856 | −1.35268 | −0.676341 | − | 0.736588i | \(-0.736436\pi\) | ||||
−0.676341 | + | 0.736588i | \(0.736436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.1494 | −0.798769 | −0.399384 | − | 0.916784i | \(-0.630776\pi\) | ||||
−0.399384 | + | 0.916784i | \(0.630776\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.29936 | 0.260209 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.4262 | −0.628723 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.33426 | 0.200336 | 0.100168 | − | 0.994971i | \(-0.468062\pi\) | ||||
0.100168 | + | 0.994971i | \(0.468062\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.0729 | −0.782656 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0793 | −0.899553 | −0.449777 | − | 0.893141i | \(-0.648496\pi\) | ||||
−0.449777 | + | 0.893141i | \(0.648496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.52764 | 0.269140 | 0.134570 | − | 0.990904i | \(-0.457035\pi\) | ||||
0.134570 | + | 0.990904i | \(0.457035\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.33194 | −0.256602 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −34.9148 | −2.06096 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8931 | −0.876067 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.16447 | −0.126884 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.2843 | 0.776077 | 0.388038 | − | 0.921643i | \(-0.373153\pi\) | ||||
0.388038 | + | 0.921643i | \(0.373153\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 40.3177 | 2.34739 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.09031 | −0.121292 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.1489 | −1.45440 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.15781 | −0.297291 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.51899 | −0.259609 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.1383 | 0.695035 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.6964 | −1.52365 | −0.761823 | − | 0.647786i | \(-0.775695\pi\) | ||||
−0.761823 | + | 0.647786i | \(0.775695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.24369 | −0.298303 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.85153 | −0.331810 | −0.165905 | − | 0.986142i | \(-0.553054\pi\) | ||||
−0.165905 | + | 0.986142i | \(0.553054\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.8900 | −0.728587 | −0.364293 | − | 0.931284i | \(-0.618689\pi\) | ||||
−0.364293 | + | 0.931284i | \(0.618689\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −33.2565 | −1.87379 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.0687 | 1.18334 | 0.591669 | − | 0.806181i | \(-0.298469\pi\) | ||||
0.591669 | + | 0.806181i | \(0.298469\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.60972 | −0.370073 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.12857 | −0.118805 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.59882 | −0.311527 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −41.3036 | −2.29111 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.48015 | 0.0818523 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.467978 | 0.0258005 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.2904 | −1.17023 | −0.585113 | − | 0.810951i | \(-0.698950\pi\) | ||||
−0.585113 | + | 0.810951i | \(0.698950\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.3469 | 1.16980 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −31.0926 | −1.69877 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.6961 | −1.18186 | −0.590930 | − | 0.806723i | \(-0.701239\pi\) | ||||
−0.590930 | + | 0.806723i | \(0.701239\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.72445 | 0.310909 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.27399 | −0.285603 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.0738 | −0.759916 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.07474 | −0.327053 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.7539 | −0.738347 | −0.369173 | − | 0.929361i | \(-0.620359\pi\) | ||||
−0.369173 | + | 0.929361i | \(0.620359\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.39400 | 0.128148 | 0.0640741 | − | 0.997945i | \(-0.479591\pi\) | ||||
0.0640741 | + | 0.997945i | \(0.479591\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.28078 | −0.441995 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.8324 | 1.00235 | 0.501173 | − | 0.865347i | \(-0.332902\pi\) | ||||
0.501173 | + | 0.865347i | \(0.332902\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 57.9370 | 3.07498 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.34223 | 0.0710382 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.4127 | −0.760673 | −0.380336 | − | 0.924848i | \(-0.624192\pi\) | ||||
−0.380336 | + | 0.924848i | \(0.624192\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.12153 | −0.216923 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.90030 | 0.152226 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 60.8311 | 3.18404 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2947 | 0.589579 | 0.294790 | − | 0.955562i | \(-0.404750\pi\) | ||||
0.294790 | + | 0.955562i | \(0.404750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 33.1069 | 1.72348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.0420 | 1.09245 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.25807 | 0.116918 | 0.0584592 | − | 0.998290i | \(-0.481381\pi\) | ||||
0.0584592 | + | 0.998290i | \(0.481381\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.36162 | −0.225233 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.1845 | −1.34857 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.2568 | 0.732320 | 0.366160 | − | 0.930552i | \(-0.380672\pi\) | ||||
0.366160 | + | 0.930552i | \(0.380672\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.25508 | −0.166763 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.62065 | 0.287202 | 0.143601 | − | 0.989636i | \(-0.454132\pi\) | ||||
0.143601 | + | 0.989636i | \(0.454132\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.4166 | −0.683774 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.89074 | 0.248610 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.6700 | 1.20012 | 0.600058 | − | 0.799956i | \(-0.295144\pi\) | ||||
0.600058 | + | 0.799956i | \(0.295144\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.85130 | −0.397057 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.86894 | 0.245606 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −44.1673 | −2.22230 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.156130 | 0.00783594 | 0.00391797 | − | 0.999992i | \(-0.498753\pi\) | ||||
0.00391797 | + | 0.999992i | \(0.498753\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.56688 | −0.178567 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.82148 | −0.240773 | −0.120387 | − | 0.992727i | \(-0.538413\pi\) | ||||
−0.120387 | + | 0.992727i | \(0.538413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.8930 | −1.04075 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 30.5190 | 1.51650 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.61193 | 0.426878 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1441 | 0.996059 | 0.498030 | − | 0.867160i | \(-0.334057\pi\) | ||||
0.498030 | + | 0.867160i | \(0.334057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.953112 | −0.0470136 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.1971 | 1.63352 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.96907 | −0.243922 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.30005 | 0.0636637 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.8326 | 0.920035 | 0.460017 | − | 0.887910i | \(-0.347843\pi\) | ||||
0.460017 | + | 0.887910i | \(0.347843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.7069 | 0.911716 | 0.455858 | − | 0.890052i | \(-0.349332\pi\) | ||||
0.455858 | + | 0.890052i | \(0.349332\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.443746 | −0.0215757 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.8947 | −0.625483 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.99451 | 0.483668 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.64467 | −0.0794054 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.1512 | 1.93402 | 0.967008 | − | 0.254747i | \(-0.0819923\pi\) | ||||
0.967008 | + | 0.254747i | \(0.0819923\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.92321 | −0.236594 | −0.118297 | − | 0.992978i | \(-0.537744\pi\) | ||||
−0.118297 | + | 0.992978i | \(0.537744\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.32491 | −0.303256 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.8643 | 0.998073 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.33871 | −0.397985 | −0.198992 | − | 0.980001i | \(-0.563767\pi\) | ||||
−0.198992 | + | 0.980001i | \(0.563767\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.01897 | −0.334237 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.3769 | −1.72832 | −0.864158 | − | 0.503220i | \(-0.832149\pi\) | ||||
−0.864158 | + | 0.503220i | \(0.832149\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.0258 | 1.23374 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.77546 | −0.225872 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.8393 | 1.26663 | 0.633313 | − | 0.773895i | \(-0.281694\pi\) | ||||
0.633313 | + | 0.773895i | \(0.281694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.3563 | 0.628922 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.33512 | −0.0627294 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −53.1501 | −2.49172 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4784 | 0.490159 | 0.245080 | − | 0.969503i | \(-0.421186\pi\) | ||||
0.245080 | + | 0.969503i | \(0.421186\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.58520 | −0.120667 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.6985 | −0.964024 | −0.482012 | − | 0.876165i | \(-0.660094\pi\) | ||||
−0.482012 | + | 0.876165i | \(0.660094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.9521 | −0.973726 | −0.486863 | − | 0.873478i | \(-0.661859\pi\) | ||||
−0.486863 | + | 0.873478i | \(0.661859\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.04673 | −0.234037 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0636 | 0.558235 | 0.279118 | − | 0.960257i | \(-0.409958\pi\) | ||||
0.279118 | + | 0.960257i | \(0.409958\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.6013 | −1.18216 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.21345 | −0.0559129 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.97306 | 0.0907215 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 34.2667 | 1.57226 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.9525 | −0.913560 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.2636 | −1.10863 | −0.554316 | − | 0.832306i | \(-0.687020\pi\) | ||||
−0.554316 | + | 0.832306i | \(0.687020\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.1163 | 1.55557 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.00188 | −0.227593 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.7580 | 1.21502 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.2435 | 1.00795 | 0.503974 | − | 0.863719i | \(-0.331871\pi\) | ||||
0.503974 | + | 0.863719i | \(0.331871\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.489693 | −0.0221447 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1889 | −0.459819 | −0.229909 | − | 0.973212i | \(-0.573843\pi\) | ||||
−0.229909 | + | 0.973212i | \(0.573843\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.17462 | −0.368166 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.7219 | 0.571807 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 47.7047 | 2.13985 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.72453 | 0.166733 | 0.0833665 | − | 0.996519i | \(-0.473433\pi\) | ||||
0.0833665 | + | 0.996519i | \(0.473433\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.34078 | −0.238608 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 55.8653 | 2.48597 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.59712 | −0.115342 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.5337 | −1.30906 | −0.654528 | − | 0.756038i | \(-0.727133\pi\) | ||||
−0.654528 | + | 0.756038i | \(0.727133\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50.0876 | 2.21575 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.86999 | 0.303317 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 64.8243 | 2.85650 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.179020 | −0.00787328 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.57815 | 0.0692731 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.4590 | −1.55349 | −0.776744 | − | 0.629816i | \(-0.783130\pi\) | ||||
−0.776744 | + | 0.629816i | \(0.783130\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.2287 | −1.49672 | −0.748358 | − | 0.663295i | \(-0.769158\pi\) | ||||
−0.748358 | + | 0.663295i | \(0.769158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.21489 | −0.358527 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.52264 | −0.284131 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.25824 | 0.272098 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.4782 | −1.36604 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 52.9111 | 2.29183 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.3142 | 1.13766 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.83384 | 0.208595 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.83165 | −0.121968 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.8437 | −1.54104 | −0.770520 | − | 0.637416i | \(-0.780003\pi\) | ||||
−0.770520 | + | 0.637416i | \(0.780003\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.39259 | −0.0597619 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.2981 | −0.783803 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.53567 | 0.151174 | 0.0755871 | − | 0.997139i | \(-0.475917\pi\) | ||||
0.0755871 | + | 0.997139i | \(0.475917\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.47700 | −0.404469 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.7235 | 0.925451 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.3669 | −1.54648 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.24084 | 0.349804 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.87431 | 0.121788 | 0.0608942 | − | 0.998144i | \(-0.480605\pi\) | ||||
0.0608942 | + | 0.998144i | \(0.480605\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.81632 | 0.330595 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.513454 | −0.0216780 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.6026 | −0.488990 | −0.244495 | − | 0.969651i | \(-0.578622\pi\) | ||||
−0.244495 | + | 0.969651i | \(0.578622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −70.7676 | −2.97721 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.1290 | 1.05532 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.9509 | 1.33945 | 0.669725 | − | 0.742609i | \(-0.266412\pi\) | ||||
0.669725 | + | 0.742609i | \(0.266412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.1988 | −1.64042 | −0.820209 | − | 0.572063i | \(-0.806143\pi\) | ||||
−0.820209 | + | 0.572063i | \(0.806143\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.30916 | −0.263569 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 48.0526 | 2.00393 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.3956 | −0.932341 | −0.466171 | − | 0.884695i | \(-0.654367\pi\) | ||||
−0.466171 | + | 0.884695i | \(0.654367\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0194837 | 0.000809716 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.09148 | −0.169743 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.04938 | −0.333371 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 50.3980 | 2.08370 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.4270 | −0.512916 | −0.256458 | − | 0.966555i | \(-0.582555\pi\) | ||||
−0.256458 | + | 0.966555i | \(0.582555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.3335 | 0.714213 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.140563 | −0.00578200 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.80507 | 0.402646 | 0.201323 | − | 0.979525i | \(-0.435476\pi\) | ||||
0.201323 | + | 0.979525i | \(0.435476\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.5931 | −0.680250 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.06082 | 0.125271 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.90435 | 0.404681 | 0.202340 | − | 0.979315i | \(-0.435145\pi\) | ||||
0.202340 | + | 0.979315i | \(0.435145\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.6079 | 1.69722 | 0.848610 | − | 0.529018i | \(-0.177440\pi\) | ||||
0.848610 | + | 0.529018i | \(0.177440\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.2757 | 0.988583 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.8545 | −1.45769 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.4240 | 1.51899 | 0.759497 | − | 0.650511i | \(-0.225445\pi\) | ||||
0.759497 | + | 0.650511i | \(0.225445\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.20786 | −0.211033 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.709190 | −0.0286907 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.4155 | −1.34964 | −0.674819 | − | 0.737983i | \(-0.735778\pi\) | ||||
−0.674819 | + | 0.737983i | \(0.735778\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.7807 | 0.515369 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.1297 | 0.890909 | 0.445454 | − | 0.895305i | \(-0.353042\pi\) | ||||
0.445454 | + | 0.895305i | \(0.353042\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.0337 | 1.04638 | 0.523191 | − | 0.852215i | \(-0.324741\pi\) | ||||
0.523191 | + | 0.852215i | \(0.324741\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.63387 | 0.386594 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.4293 | 0.858548 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50140 | 0.380056 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.36447 | 0.0544916 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.6509 | 0.424678 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5675 | 0.619732 | 0.309866 | − | 0.950780i | \(-0.399716\pi\) | ||||
0.309866 | + | 0.950780i | \(0.399716\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.19507 | −0.206485 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 40.2404 | 1.59689 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.2176 | −0.444459 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −45.2345 | −1.78945 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.0898 | 1.26747 | 0.633736 | − | 0.773550i | \(-0.281521\pi\) | ||||
0.633736 | + | 0.773550i | \(0.281521\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.78556 | 0.188724 | 0.0943620 | − | 0.995538i | \(-0.469919\pi\) | ||||
0.0943620 | + | 0.995538i | \(0.469919\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.88804 | 0.0743416 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.8439 | −0.622887 | −0.311444 | − | 0.950265i | \(-0.600812\pi\) | ||||
−0.311444 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.6992 | −0.498487 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.15542 | −0.162864 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.6996 | −1.86663 | −0.933315 | − | 0.359058i | \(-0.883098\pi\) | ||||
−0.933315 | + | 0.359058i | \(0.883098\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −60.1916 | −2.35188 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −47.4941 | −1.85292 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.6129 | −0.647146 | −0.323573 | − | 0.946203i | \(-0.604884\pi\) | ||||
−0.323573 | + | 0.946203i | \(0.604884\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.9128 | 1.51353 | 0.756766 | − | 0.653685i | \(-0.226778\pi\) | ||||
0.756766 | + | 0.653685i | \(0.226778\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.03406 | −0.0789962 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 44.0950 | 1.70993 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.4631 | 1.17954 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.97550 | −0.269689 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.82329 | −0.147596 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.3230 | −1.47724 | −0.738622 | − | 0.674119i | \(-0.764523\pi\) | ||||
−0.738622 | + | 0.674119i | \(0.764523\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.8223 | 0.609001 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.7614 | 0.951659 | 0.475829 | − | 0.879538i | \(-0.342148\pi\) | ||||
0.475829 | + | 0.879538i | \(0.342148\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.0322 | 0.845520 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.55988 | −0.174735 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.6227 | −0.750843 | −0.375422 | − | 0.926854i | \(-0.622502\pi\) | ||||
−0.375422 | + | 0.926854i | \(0.622502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.7827 | 0.450194 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.14393 | −0.272558 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −31.8878 | −1.21483 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.1053 | 1.33547 | 0.667734 | − | 0.744400i | \(-0.267264\pi\) | ||||
0.667734 | + | 0.744400i | \(0.267264\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.4751 | 0.397915 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0717 | −0.609633 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.5184 | 0.625681 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.64891 | 0.213662 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.6272 | −0.476923 | −0.238461 | − | 0.971152i | \(-0.576643\pi\) | ||||
−0.238461 | + | 0.971152i | \(0.576643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.3039 | −1.06750 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.171306 | −0.00645175 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.9989 | 1.72997 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.3950 | −1.06640 | −0.533198 | − | 0.845990i | \(-0.679010\pi\) | ||||
−0.533198 | + | 0.845990i | \(0.679010\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.4838 | 1.29324 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.3069 | 0.910302 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.3320 | 0.760373 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.85007 | 0.143784 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.2026 | −1.12637 | −0.563183 | − | 0.826332i | \(-0.690423\pi\) | ||||
−0.563183 | + | 0.826332i | \(0.690423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 53.3756 | 1.98781 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.826922 | 0.0307536 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 50.0315 | 1.85812 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8672 | 0.477219 | 0.238609 | − | 0.971116i | \(-0.423308\pi\) | ||||
0.238609 | + | 0.971116i | \(0.423308\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.2174 | −0.822866 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.44020 | 0.0902540 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.8470 | −0.400644 | −0.200322 | − | 0.979730i | \(-0.564199\pi\) | ||||
−0.200322 | + | 0.979730i | \(0.564199\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.70963 | −0.0999463 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.79350 | 0.360748 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.61885 | 0.317049 | 0.158525 | − | 0.987355i | \(-0.449326\pi\) | ||||
0.158525 | + | 0.987355i | \(0.449326\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.40537 | 0.198571 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.10452 | 0.150580 | 0.0752902 | − | 0.997162i | \(-0.476012\pi\) | ||||
0.0752902 | + | 0.997162i | \(0.476012\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 59.0359 | 2.16291 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.87962 | 0.141948 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.6668 | 0.791687 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.9781 | 1.60478 | 0.802391 | − | 0.596799i | \(-0.203561\pi\) | ||||
0.802391 | + | 0.596799i | \(0.203561\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.734550 | 0.0267685 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.5052 | 0.600686 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.83983 | −0.175907 | −0.0879533 | − | 0.996125i | \(-0.528033\pi\) | ||||
−0.0879533 | + | 0.996125i | \(0.528033\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.91341 | 0.0694525 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.3984 | 0.739443 | 0.369721 | − | 0.929143i | \(-0.379453\pi\) | ||||
0.369721 | + | 0.929143i | \(0.379453\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.0664 | −0.545442 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.7339 | 0.568860 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.3081 | −1.81652 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.8238 | 0.967292 | 0.483646 | − | 0.875264i | \(-0.339312\pi\) | ||||
0.483646 | + | 0.875264i | \(0.339312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.14590 | 0.221339 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.0637 | −0.865510 | −0.432755 | − | 0.901511i | \(-0.642459\pi\) | ||||
−0.432755 | + | 0.901511i | \(0.642459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.9208 | 1.43400 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.78542 | 0.243425 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43.8966 | −1.57276 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.2489 | −0.652997 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.0306 | 0.358465 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.0011 | 0.535412 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.9260 | 0.710285 | 0.355143 | − | 0.934812i | \(-0.384432\pi\) | ||||
0.355143 | + | 0.934812i | \(0.384432\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.41063 | −0.228224 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −58.2693 | −2.07182 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.1460 | −0.537851 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.70253 | −0.273181 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.3504 | 0.543738 | 0.271869 | − | 0.962334i | \(-0.412358\pi\) | ||||
0.271869 | + | 0.962334i | \(0.412358\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.221404 | −0.00783271 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.3197 | −0.717962 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.1605 | −0.676158 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 61.8349 | 2.17940 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.68688 | 0.235389 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.7103 | −0.692976 | −0.346488 | − | 0.938054i | \(-0.612626\pi\) | ||||
−0.346488 | + | 0.938054i | \(0.612626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.7177 | −1.60537 | −0.802683 | − | 0.596406i | \(-0.796595\pi\) | ||||
−0.802683 | + | 0.596406i | \(0.796595\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.96330 | 0.138999 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.05376 | 0.212054 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.48466 | −0.226869 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.4972 | 1.45003 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.1844 | 0.355440 | 0.177720 | − | 0.984081i | \(-0.443128\pi\) | ||||
0.177720 | + | 0.984081i | \(0.443128\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.0653 | 0.804006 | 0.402003 | − | 0.915638i | \(-0.368314\pi\) | ||||
0.402003 | + | 0.915638i | \(0.368314\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.14252 | 0.109408 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.4008 | 1.26578 | 0.632889 | − | 0.774242i | \(-0.281869\pi\) | ||||
0.632889 | + | 0.774242i | \(0.281869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.9621 | 1.76999 | 0.884993 | − | 0.465604i | \(-0.154163\pi\) | ||||
0.884993 | + | 0.465604i | \(0.154163\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.00496 | −0.0348618 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.50206 | −0.121339 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 66.0246 | 2.28487 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00356 | 0.276643 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.2271 | 1.11260 | 0.556302 | − | 0.830980i | \(-0.312220\pi\) | ||||
0.556302 | + | 0.830980i | \(0.312220\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.71762 | 0.0937112 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.54498 | 0.156537 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.1065 | 1.10450 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.5222 | −1.01440 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.36466 | −0.0468349 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.6910 | −1.36059 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.0180 | −1.54139 | −0.770694 | − | 0.637206i | \(-0.780090\pi\) | ||||
−0.770694 | + | 0.637206i | \(0.780090\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −41.8117 | −1.42993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.2873 | −0.932115 | −0.466057 | − | 0.884754i | \(-0.654326\pi\) | ||||
−0.466057 | + | 0.884754i | \(0.654326\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.4292 | −1.55003 | −0.775013 | − | 0.631946i | \(-0.782257\pi\) | ||||
−0.775013 | + | 0.631946i | \(0.782257\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.5235 | 0.358641 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.2979 | 1.57600 | 0.788000 | − | 0.615675i | \(-0.211117\pi\) | ||||
0.788000 | + | 0.615675i | \(0.211117\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.5096 | −0.663348 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.48888 | 0.152450 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.9117 | 0.471923 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.7971 | 1.31459 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.8914 | −0.707067 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 44.3970 | 1.50089 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.2644 | −0.684279 | −0.342140 | − | 0.939649i | \(-0.611152\pi\) | ||||
−0.342140 | + | 0.939649i | \(0.611152\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.00396 | −0.135050 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.4246 | −1.19348 | −0.596742 | − | 0.802433i | \(-0.703539\pi\) | ||||
−0.596742 | + | 0.802433i | \(0.703539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.30116 | 0.279356 | 0.139678 | − | 0.990197i | \(-0.455393\pi\) | ||||
0.139678 | + | 0.990197i | \(0.455393\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.1520 | −0.408484 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.4612 | 0.922055 | 0.461028 | − | 0.887386i | \(-0.347481\pi\) | ||||
0.461028 | + | 0.887386i | \(0.347481\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.1335 | 1.11126 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.61282 | −0.322042 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.588365 | 0.0196889 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −59.7576 | −1.99747 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.58002 | 0.253089 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.3079 | 0.844067 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.95512 | −0.331653 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.55459 | 0.0517336 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.2157 | 0.572270 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.2682 | 0.606585 | 0.303292 | − | 0.952898i | \(-0.401914\pi\) | ||||
0.303292 | + | 0.952898i | \(0.401914\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −43.6171 | −1.44669 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.5548 | −1.01233 | −0.506163 | − | 0.862438i | \(-0.668936\pi\) | ||||
−0.506163 | + | 0.862438i | \(0.668936\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.56515 | 0.0517989 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.65854 | −0.120948 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.5611 | −1.63665 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.50873 | −0.148729 | −0.0743646 | − | 0.997231i | \(-0.523693\pi\) | ||||
−0.0743646 | + | 0.997231i | \(0.523693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.04645 | 0.265140 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −72.2933 | −2.37956 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −65.1869 | −2.14333 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −50.6118 | −1.66231 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 57.1290 | 1.87434 | 0.937171 | − | 0.348869i | \(-0.113434\pi\) | ||||
0.937171 | + | 0.348869i | \(0.113434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.30649 | 0.305008 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.76368 | 0.0577404 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.34750 | 0.207585 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.3179 | −0.729095 | −0.364548 | − | 0.931185i | \(-0.618776\pi\) | ||||
−0.364548 | + | 0.931185i | \(0.618776\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.88513 | 0.126786 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.0794 | −0.915361 | −0.457680 | − | 0.889117i | \(-0.651320\pi\) | ||||
−0.457680 | + | 0.889117i | \(0.651320\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.5568 | −2.00457 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.3604 | 0.662324 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.45613 | 0.0473177 | 0.0236589 | − | 0.999720i | \(-0.492468\pi\) | ||||
0.0236589 | + | 0.999720i | \(0.492468\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −75.9045 | −2.46396 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.35024 | −0.205921 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.8519 | 1.09657 | 0.548285 | − | 0.836292i | \(-0.315281\pi\) | ||||
0.548285 | + | 0.836292i | \(0.315281\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 77.9961 | 2.52389 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.99221 | 0.0643989 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.70175 | 0.313286 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.8065 | −0.348595 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.5449 | −0.662050 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.240865 | −0.00775371 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.0534134 | 0.00171766 | 0.000858830 | − | 1.00000i | \(-0.499727\pi\) | ||||
0.000858830 | 1.00000i | \(0.499727\pi\) | ||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.68752 | 0.0542108 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.3689 | 0.621577 | 0.310788 | − | 0.950479i | \(-0.399407\pi\) | ||||
0.310788 | + | 0.950479i | \(0.399407\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.2332 | −0.424238 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.4491 | 0.398691 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.5302 | −1.26468 | −0.632341 | − | 0.774690i | \(-0.717906\pi\) | ||||
−0.632341 | + | 0.774690i | \(0.717906\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.19755 | −0.261995 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.2863 | 0.456127 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.8057 | −1.46098 | −0.730488 | − | 0.682926i | \(-0.760707\pi\) | ||||
−0.730488 | + | 0.682926i | \(0.760707\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.73769 | 0.0553675 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.141051 | −0.00448971 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.09352 | −0.289157 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.4464 | 0.871865 | 0.435932 | − | 0.899979i | \(-0.356419\pi\) | ||||
0.435932 | + | 0.899979i | \(0.356419\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.41705 | 0.203639 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −37.8389 | −1.19957 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.2907 | −1.37103 | −0.685515 | − | 0.728058i | \(-0.740423\pi\) | ||||
−0.685515 | + | 0.728058i | \(0.740423\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.0691 | −0.413487 |
(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 | 8048.2.a.t.1.8 | 21 | ||
4.3 | odd | 2 | 2012.2.a.a.1.14 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2012.2.a.a.1.14 | ✓ | 21 | 4.3 | odd | 2 | ||
8048.2.a.t.1.8 | 21 | 1.1 | even | 1 | trivial |