Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.11256624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 16x^{3} + 20x^{2} + 31x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1002) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.50259\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.368511 | −0.164803 | −0.0824016 | − | 0.996599i | \(-0.526259\pi\) | ||||
−0.0824016 | + | 0.996599i | \(0.526259\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.85901 | −1.83653 | −0.918267 | − | 0.395962i | \(-0.870411\pi\) | ||||
−0.918267 | + | 0.395962i | \(0.870411\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.29593 | 1.29527 | 0.647636 | − | 0.761950i | \(-0.275758\pi\) | ||||
0.647636 | + | 0.761950i | \(0.275758\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.50259 | 0.971445 | 0.485722 | − | 0.874113i | \(-0.338557\pi\) | ||||
0.485722 | + | 0.874113i | \(0.338557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.368511 | 0.0951492 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50259 | −0.364433 | −0.182216 | − | 0.983258i | \(-0.558327\pi\) | ||||
−0.182216 | + | 0.983258i | \(0.558327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.29593 | −1.44439 | −0.722193 | − | 0.691691i | \(-0.756866\pi\) | ||||
−0.722193 | + | 0.691691i | \(0.756866\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.85901 | 1.06032 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.29593 | −0.895764 | −0.447882 | − | 0.894093i | \(-0.647822\pi\) | ||||
−0.447882 | + | 0.894093i | \(0.647822\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.86420 | −0.972840 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.30112 | 1.35578 | 0.677892 | − | 0.735161i | \(-0.262894\pi\) | ||||
0.677892 | + | 0.735161i | \(0.262894\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.15494 | 0.925855 | 0.462928 | − | 0.886396i | \(-0.346799\pi\) | ||||
0.462928 | + | 0.886396i | \(0.346799\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.29593 | −0.747826 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.79060 | 0.302667 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.424828 | −0.0698413 | −0.0349207 | − | 0.999390i | \(-0.511118\pi\) | ||||
−0.0349207 | + | 0.999390i | \(0.511118\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.50259 | −0.560864 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.06151 | −0.790474 | −0.395237 | − | 0.918579i | \(-0.629338\pi\) | ||||
−0.395237 | + | 0.918579i | \(0.629338\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0191 | 1.68040 | 0.840202 | − | 0.542274i | \(-0.182436\pi\) | ||||
0.840202 | + | 0.542274i | \(0.182436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.368511 | −0.0549344 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.146177 | −0.0213221 | −0.0106611 | − | 0.999943i | \(-0.503394\pi\) | ||||
−0.0106611 | + | 0.999943i | \(0.503394\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.6100 | 2.37286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.50259 | 0.210405 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.1195 | 1.52738 | 0.763690 | − | 0.645584i | \(-0.223386\pi\) | ||||
0.763690 | + | 0.645584i | \(0.223386\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.58310 | −0.213465 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.29593 | 0.833917 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.87468 | −0.764819 | −0.382409 | − | 0.923993i | \(-0.624906\pi\) | ||||
−0.382409 | + | 0.923993i | \(0.624906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.71283 | 0.603417 | 0.301708 | − | 0.953400i | \(-0.402443\pi\) | ||||
0.301708 | + | 0.953400i | \(0.402443\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.85901 | −0.612178 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.29075 | −0.160097 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9414 | 1.45887 | 0.729436 | − | 0.684049i | \(-0.239783\pi\) | ||||
0.729436 | + | 0.684049i | \(0.239783\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.29593 | 0.517170 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2821 | −1.45762 | −0.728810 | − | 0.684716i | \(-0.759926\pi\) | ||||
−0.728810 | + | 0.684716i | \(0.759926\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.75098 | −1.02422 | −0.512112 | − | 0.858919i | \(-0.671137\pi\) | ||||
−0.512112 | + | 0.858919i | \(0.671137\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.86420 | 0.561669 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −20.8740 | −2.37881 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.06151 | −0.794481 | −0.397241 | − | 0.917714i | \(-0.630032\pi\) | ||||
−0.397241 | + | 0.917714i | \(0.630032\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.3020 | −1.13079 | −0.565394 | − | 0.824821i | \(-0.691276\pi\) | ||||
−0.565394 | + | 0.824821i | \(0.691276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.553723 | 0.0600597 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.30112 | −0.782762 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.57185 | −0.590614 | −0.295307 | − | 0.955402i | \(-0.595422\pi\) | ||||
−0.295307 | + | 0.955402i | \(0.595422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.0191 | −1.78409 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.15494 | −0.534543 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.32012 | 0.238039 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.41434 | 0.448209 | 0.224104 | − | 0.974565i | \(-0.428054\pi\) | ||||
0.224104 | + | 0.974565i | \(0.428054\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.29593 | 0.431758 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.5193 | −1.24572 | −0.622858 | − | 0.782335i | \(-0.714029\pi\) | ||||
−0.622858 | + | 0.782335i | \(0.714029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8037 | −1.06452 | −0.532261 | − | 0.846580i | \(-0.678657\pi\) | ||||
−0.532261 | + | 0.846580i | \(0.678657\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.79060 | −0.174745 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.1731 | 1.17681 | 0.588407 | − | 0.808565i | \(-0.299755\pi\) | ||||
0.588407 | + | 0.808565i | \(0.299755\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.08927 | 0.870594 | 0.435297 | − | 0.900287i | \(-0.356643\pi\) | ||||
0.435297 | + | 0.900287i | \(0.356643\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.424828 | 0.0403229 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.24838 | 0.870015 | 0.435007 | − | 0.900427i | \(-0.356746\pi\) | ||||
0.435007 | + | 0.900427i | \(0.356746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.58310 | 0.147625 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.50259 | 0.323815 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.30112 | 0.669293 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.45504 | 0.677731 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.06151 | 0.456381 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.63507 | 0.325130 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6152 | 1.29689 | 0.648444 | − | 0.761263i | \(-0.275420\pi\) | ||||
0.648444 | + | 0.761263i | \(0.275420\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.0191 | −0.970182 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.11346 | −0.446765 | −0.223383 | − | 0.974731i | \(-0.571710\pi\) | ||||
−0.223383 | + | 0.974731i | \(0.571710\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.5920 | 2.65266 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.368511 | 0.0317164 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.46988 | 0.552759 | 0.276380 | − | 0.961049i | \(-0.410865\pi\) | ||||
0.276380 | + | 0.961049i | \(0.410865\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.79937 | 0.576715 | 0.288357 | − | 0.957523i | \(-0.406891\pi\) | ||||
0.288357 | + | 0.957523i | \(0.406891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.146177 | 0.0123103 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.0469 | 1.25829 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.69055 | −0.223438 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.6100 | −1.36997 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.51410 | −0.779426 | −0.389713 | − | 0.920936i | \(-0.627426\pi\) | ||||
−0.389713 | + | 0.920936i | \(0.627426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.92468 | −0.400765 | −0.200383 | − | 0.979718i | \(-0.564218\pi\) | ||||
−0.200383 | + | 0.979718i | \(0.564218\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.50259 | −0.121478 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.89965 | −0.152584 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0365 | 0.880811 | 0.440406 | − | 0.897799i | \(-0.354835\pi\) | ||||
0.440406 | + | 0.897799i | \(0.354835\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.1195 | −0.881833 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.8740 | 1.64510 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.67482 | 0.679464 | 0.339732 | − | 0.940522i | \(-0.389664\pi\) | ||||
0.339732 | + | 0.940522i | \(0.389664\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.58310 | 0.123244 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.731834 | −0.0562949 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.29593 | −0.481462 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.68149 | −0.203870 | −0.101935 | − | 0.994791i | \(-0.532503\pi\) | ||||
−0.101935 | + | 0.994791i | \(0.532503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.6352 | 1.78665 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.87468 | 0.441568 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.82708 | 0.435536 | 0.217768 | − | 0.976001i | \(-0.430122\pi\) | ||||
0.217768 | + | 0.976001i | \(0.430122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.1695 | −1.35053 | −0.675264 | − | 0.737576i | \(-0.735970\pi\) | ||||
−0.675264 | + | 0.737576i | \(0.735970\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.71283 | −0.348383 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.156554 | 0.0115101 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.45504 | −0.472040 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.85901 | 0.353441 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.7468 | 1.57354 | 0.786772 | − | 0.617244i | \(-0.211751\pi\) | ||||
0.786772 | + | 0.617244i | \(0.211751\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.9950 | −1.79918 | −0.899588 | − | 0.436739i | \(-0.856133\pi\) | ||||
−0.899588 | + | 0.436739i | \(0.856133\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.29075 | 0.0924322 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.56410 | 0.467673 | 0.233836 | − | 0.972276i | \(-0.424872\pi\) | ||||
0.233836 | + | 0.972276i | \(0.424872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.19755 | −0.368444 | −0.184222 | − | 0.982885i | \(-0.558977\pi\) | ||||
−0.184222 | + | 0.982885i | \(0.558977\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.9414 | −0.842280 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −35.4762 | −2.48994 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.86522 | 0.130273 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.29593 | −0.298588 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.0469 | −1.87087 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0331 | −1.72335 | −0.861675 | − | 0.507461i | \(-0.830584\pi\) | ||||
−0.861675 | + | 0.507461i | \(0.830584\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.2821 | 0.841557 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.06068 | −0.276936 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.0479 | −1.70036 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.75098 | 0.591336 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.26298 | −0.354026 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.03208 | −0.336973 | −0.168486 | − | 0.985704i | \(-0.553888\pi\) | ||||
−0.168486 | + | 0.985704i | \(0.553888\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.86420 | −0.324280 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.3349 | 1.01781 | 0.508907 | − | 0.860821i | \(-0.330050\pi\) | ||||
0.508907 | + | 0.860821i | \(0.330050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.3099 | −1.60644 | −0.803221 | − | 0.595681i | \(-0.796882\pi\) | ||||
−0.803221 | + | 0.595681i | \(0.796882\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.8740 | 1.37341 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.89197 | −0.517020 | −0.258510 | − | 0.966009i | \(-0.583231\pi\) | ||||
−0.258510 | + | 0.966009i | \(0.583231\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0538679 | 0.00351396 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.06151 | 0.458694 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.17307 | −0.399303 | −0.199651 | − | 0.979867i | \(-0.563981\pi\) | ||||
−0.199651 | + | 0.979867i | \(0.563981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.9013 | −1.02429 | −0.512147 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512147 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.12097 | −0.391054 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.0521 | −1.40314 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.3020 | 0.652860 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.977421 | 0.0616943 | 0.0308471 | − | 0.999524i | \(-0.490179\pi\) | ||||
0.0308471 | + | 0.999524i | \(0.490179\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.4550 | −1.16026 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.553723 | −0.0346755 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.3626 | −0.771159 | −0.385580 | − | 0.922675i | \(-0.625999\pi\) | ||||
−0.385580 | + | 0.922675i | \(0.625999\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.06424 | 0.128266 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.30112 | 0.451928 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.0183 | 1.78934 | 0.894671 | − | 0.446725i | \(-0.147410\pi\) | ||||
0.894671 | + | 0.446725i | \(0.147410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.09766 | −0.251717 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.57185 | 0.340991 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.03619 | 0.307062 | 0.153531 | − | 0.988144i | \(-0.450936\pi\) | ||||
0.153531 | + | 0.988144i | \(0.450936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.4646 | 1.30388 | 0.651941 | − | 0.758270i | \(-0.273955\pi\) | ||||
0.651941 | + | 0.758270i | \(0.273955\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.0191 | 1.03005 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.8963 | −1.26009 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.4250 | 1.34739 | 0.673693 | − | 0.739011i | \(-0.264707\pi\) | ||||
0.673693 | + | 0.739011i | \(0.264707\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.15494 | 0.308618 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.7465 | −1.71487 | −0.857437 | − | 0.514589i | \(-0.827944\pi\) | ||||
−0.857437 | + | 0.514589i | \(0.827944\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.84966 | 0.169394 | 0.0846972 | − | 0.996407i | \(-0.473008\pi\) | ||||
0.0846972 | + | 0.996407i | \(0.473008\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.32012 | −0.137432 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.5939 | 1.45173 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7422 | −0.867189 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.41434 | −0.258773 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.8546 | −1.21834 | −0.609168 | − | 0.793041i | \(-0.708497\pi\) | ||||
−0.609168 | + | 0.793041i | \(0.708497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.16489 | 0.126045 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.29593 | −0.249275 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.0469 | −0.870185 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −53.5421 | −3.08612 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.5193 | 0.719214 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.73673 | −0.0994450 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.2508 | −0.756265 | −0.378132 | − | 0.925751i | \(-0.623434\pi\) | ||||
−0.378132 | + | 0.925751i | \(0.623434\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8037 | 0.614602 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.17394 | 0.123273 | 0.0616365 | − | 0.998099i | \(-0.480368\pi\) | ||||
0.0616365 | + | 0.998099i | \(0.480368\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.2769 | −1.08960 | −0.544798 | − | 0.838567i | \(-0.683394\pi\) | ||||
−0.544798 | + | 0.838567i | \(0.683394\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.79060 | 0.100889 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.64901 | 0.317280 | 0.158640 | − | 0.987336i | \(-0.449289\pi\) | ||||
0.158640 | + | 0.987336i | \(0.449289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.3651 | 1.75611 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.1731 | −0.679434 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.46023 | 0.526381 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.0373 | −0.945060 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.08927 | −0.502638 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.710277 | 0.0391588 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6490 | −0.750218 | −0.375109 | − | 0.926981i | \(-0.622395\pi\) | ||||
−0.375109 | + | 0.926981i | \(0.622395\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.424828 | −0.0232804 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.40053 | −0.240427 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.27072 | 0.341588 | 0.170794 | − | 0.985307i | \(-0.445367\pi\) | ||||
0.170794 | + | 0.985307i | \(0.445367\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.24838 | −0.502303 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.1453 | 1.19924 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −46.6950 | −2.52130 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.58310 | −0.0852312 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.0357 | −0.968207 | −0.484103 | − | 0.875011i | \(-0.660854\pi\) | ||||
−0.484103 | + | 0.875011i | \(0.660854\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.1722 | −1.66861 | −0.834306 | − | 0.551302i | \(-0.814131\pi\) | ||||
−0.834306 | + | 0.551302i | \(0.814131\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.50259 | −0.186955 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.6969 | −1.84673 | −0.923366 | − | 0.383921i | \(-0.874574\pi\) | ||||
−0.923366 | + | 0.383921i | \(0.874574\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.52610 | 0.240220 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.30112 | −0.386416 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.4571 | −1.50191 | −0.750954 | − | 0.660355i | \(-0.770406\pi\) | ||||
−0.750954 | + | 0.660355i | \(0.770406\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.6388 | 1.08625 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.45504 | −0.391288 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.22483 | 0.168795 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.4726 | 1.27746 | 0.638729 | − | 0.769432i | \(-0.279460\pi\) | ||||
0.638729 | + | 0.769432i | \(0.279460\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.06151 | −0.263491 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −54.0297 | −2.80508 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.1966 | 1.40818 | 0.704092 | − | 0.710109i | \(-0.251354\pi\) | ||||
0.704092 | + | 0.710109i | \(0.251354\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.63507 | −0.187714 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.5729 | 1.31707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5055 | −1.15603 | −0.578014 | − | 0.816027i | \(-0.696172\pi\) | ||||
−0.578014 | + | 0.816027i | \(0.696172\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.6152 | −0.748758 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.0294 | −0.665770 | −0.332885 | − | 0.942967i | \(-0.608022\pi\) | ||||
−0.332885 | + | 0.942967i | \(0.608022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.69230 | 0.392036 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.0191 | 0.560135 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.04833 | −0.255961 | −0.127980 | − | 0.991777i | \(-0.540849\pi\) | ||||
−0.127980 | + | 0.991777i | \(0.540849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.45504 | 0.326446 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.11346 | 0.257940 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.60224 | 0.130933 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.8268 | 1.04527 | 0.522633 | − | 0.852558i | \(-0.324950\pi\) | ||||
0.522633 | + | 0.852558i | \(0.324950\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.5920 | −1.53152 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.4008 | −1.01877 | −0.509383 | − | 0.860540i | \(-0.670126\pi\) | ||||
−0.509383 | + | 0.860540i | \(0.670126\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0557 | 0.899417 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.368511 | −0.0183115 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.82503 | −0.0904635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.47404 | 0.171780 | 0.0858902 | − | 0.996305i | \(-0.472627\pi\) | ||||
0.0858902 | + | 0.996305i | \(0.472627\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.46988 | −0.319136 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.5452 | 1.40462 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.79639 | 0.186357 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.79937 | −0.332966 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.1457 | 1.32616 | 0.663078 | − | 0.748550i | \(-0.269250\pi\) | ||||
0.663078 | + | 0.748550i | \(0.269250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.9446 | −1.16699 | −0.583494 | − | 0.812117i | \(-0.698315\pi\) | ||||
−0.583494 | + | 0.812117i | \(0.698315\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.146177 | −0.00710738 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.30892 | 0.354535 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.8997 | −1.10819 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.0469 | −0.726472 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.3330 | −0.642229 | −0.321114 | − | 0.947040i | \(-0.604057\pi\) | ||||
−0.321114 | + | 0.947040i | \(0.604057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.4335 | −1.79894 | −0.899469 | − | 0.436984i | \(-0.856047\pi\) | ||||
−0.899469 | + | 0.436984i | \(0.856047\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.69055 | 0.129002 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.0469 | 1.29383 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.0185 | −1.67134 | −0.835671 | − | 0.549230i | \(-0.814921\pi\) | ||||
−0.835671 | + | 0.549230i | \(0.814921\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.6100 | 0.790952 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −41.8058 | −1.98625 | −0.993127 | − | 0.117040i | \(-0.962659\pi\) | ||||
−0.993127 | + | 0.117040i | \(0.962659\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.05329 | 0.0973352 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.51410 | 0.450002 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.4981 | −1.20333 | −0.601664 | − | 0.798749i | \(-0.705496\pi\) | ||||
−0.601664 | + | 0.798749i | \(0.705496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.7439 | −1.02388 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.92468 | 0.231382 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.27175 | 0.294024 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.6022 | 0.776620 | 0.388310 | − | 0.921529i | \(-0.373059\pi\) | ||||
0.388310 | + | 0.921529i | \(0.373059\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.50259 | 0.0701351 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.0557 | 0.747788 | 0.373894 | − | 0.927472i | \(-0.378022\pi\) | ||||
0.373894 | + | 0.927472i | \(0.378022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.3662 | −0.853550 | −0.426775 | − | 0.904358i | \(-0.640350\pi\) | ||||
−0.426775 | + | 0.904358i | \(0.640350\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.89965 | 0.0880944 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.4102 | −1.45349 | −0.726745 | − | 0.686908i | \(-0.758968\pi\) | ||||
−0.726745 | + | 0.686908i | \(0.758968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −58.0233 | −2.67927 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.0365 | −0.508537 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 47.3375 | 2.17658 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.6247 | 1.40516 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.1195 | 0.509126 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.0521 | 1.37312 | 0.686558 | − | 0.727075i | \(-0.259121\pi\) | ||||
0.686558 | + | 0.727075i | \(0.259121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.48800 | −0.0678470 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.8740 | −0.949799 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.62673 | −0.0738662 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.34706 | −0.242299 | −0.121149 | − | 0.992634i | \(-0.538658\pi\) | ||||
−0.121149 | + | 0.992634i | \(0.538658\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.67482 | −0.392289 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.10548 | −0.365795 | −0.182897 | − | 0.983132i | \(-0.558548\pi\) | ||||
−0.182897 | + | 0.983132i | \(0.558548\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.9706 | −0.494092 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.58310 | −0.0711550 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 59.6790 | 2.67697 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.2824 | −0.594602 | −0.297301 | − | 0.954784i | \(-0.596087\pi\) | ||||
−0.297301 | + | 0.954784i | \(0.596087\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.68031 | 0.119509 | 0.0597546 | − | 0.998213i | \(-0.480968\pi\) | ||||
0.0597546 | + | 0.998213i | \(0.480968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.61350 | 0.205298 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.731834 | 0.0325019 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.1627 | −0.539102 | −0.269551 | − | 0.962986i | \(-0.586875\pi\) | ||||
−0.269551 | + | 0.962986i | \(0.586875\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.5211 | 1.88102 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.29593 | 0.277972 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.98129 | 0.175437 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.627968 | −0.0276180 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.68149 | 0.117704 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.19124 | −0.271243 | −0.135622 | − | 0.990761i | \(-0.543303\pi\) | ||||
−0.135622 | + | 0.990761i | \(0.543303\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.6144 | −0.945134 | −0.472567 | − | 0.881295i | \(-0.656672\pi\) | ||||
−0.472567 | + | 0.881295i | \(0.656672\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.6352 | −1.03152 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.74579 | −0.337412 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.54496 | −0.197607 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.87468 | −0.254940 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.7284 | −0.767902 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.48591 | −0.193943 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.82708 | −0.251457 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 71.3554 | 3.07350 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.8438 | 0.810157 | 0.405079 | − | 0.914282i | \(-0.367244\pi\) | ||||
0.405079 | + | 0.914282i | \(0.367244\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.1695 | 0.779727 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.34950 | −0.143477 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.8050 | 1.27437 | 0.637186 | − | 0.770710i | \(-0.280098\pi\) | ||||
0.637186 | + | 0.770710i | \(0.280098\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.71283 | 0.201139 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −45.9674 | −1.95828 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.3119 | 1.45909 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.156554 | −0.00664534 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.0194 | 0.509280 | 0.254640 | − | 0.967036i | \(-0.418043\pi\) | ||||
0.254640 | + | 0.967036i | \(0.418043\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.5956 | 1.63242 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.45504 | 0.272532 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.2081 | −1.39955 | −0.699777 | − | 0.714362i | \(-0.746717\pi\) | ||||
−0.699777 | + | 0.714362i | \(0.746717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.40813 | −0.143381 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.85901 | −0.204059 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.8156 | −0.621103 | −0.310552 | − | 0.950556i | \(-0.600514\pi\) | ||||
−0.310552 | + | 0.950556i | \(0.600514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.7454 | −0.742624 | −0.371312 | − | 0.928508i | \(-0.621092\pi\) | ||||
−0.371312 | + | 0.928508i | \(0.621092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.7468 | −0.908486 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.8963 | 0.871435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.51631 | 0.396169 | 0.198085 | − | 0.980185i | \(-0.436528\pi\) | ||||
0.198085 | + | 0.980185i | \(0.436528\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.9950 | 1.03875 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.0573 | 2.07673 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 47.7686 | 1.97837 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.29075 | −0.0533657 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.6116 | 1.55240 | 0.776198 | − | 0.630490i | \(-0.217146\pi\) | ||||
0.776198 | + | 0.630490i | \(0.217146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.4552 | −1.33729 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.56410 | −0.270011 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.3295 | 0.547378 | 0.273689 | − | 0.961818i | \(-0.411756\pi\) | ||||
0.273689 | + | 0.961818i | \(0.411756\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.69055 | −0.110302 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.19755 | 0.212721 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.5217 | 1.77825 | 0.889124 | − | 0.457666i | \(-0.151315\pi\) | ||||
0.889124 | + | 0.457666i | \(0.151315\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.6773 | −0.965818 | −0.482909 | − | 0.875671i | \(-0.660420\pi\) | ||||
−0.482909 | + | 0.875671i | \(0.660420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.9414 | 0.486291 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.74727 | −0.111692 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.173561 | −0.00704461 | −0.00352231 | − | 0.999994i | \(-0.501121\pi\) | ||||
−0.00352231 | + | 0.999994i | \(0.501121\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 35.4762 | 1.43757 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.511999 | −0.0207133 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.9055 | −1.85411 | −0.927053 | − | 0.374929i | \(-0.877667\pi\) | ||||
−0.927053 | + | 0.374929i | \(0.877667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.86522 | −0.0752130 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.2940 | 0.494939 | 0.247470 | − | 0.968896i | \(-0.420401\pi\) | ||||
0.247470 | + | 0.968896i | \(0.420401\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.4206 | −0.901161 | −0.450580 | − | 0.892736i | \(-0.648783\pi\) | ||||
−0.450580 | + | 0.892736i | \(0.648783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.29593 | 0.172390 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.0737 | 1.08468 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.9814 | 0.919257 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.0469 | 1.08015 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.638344 | 0.0254525 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.7953 | −1.14632 | −0.573161 | − | 0.819443i | \(-0.694283\pi\) | ||||
−0.573161 | + | 0.819443i | \(0.694283\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.0331 | 0.994976 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.38586 | −0.213731 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 58.1781 | 2.30510 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.2821 | −0.485873 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.3314 | −0.526557 | −0.263278 | − | 0.964720i | \(-0.584804\pi\) | ||||
−0.263278 | + | 0.964720i | \(0.584804\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.3737 | −0.764025 | −0.382012 | − | 0.924157i | \(-0.624769\pi\) | ||||
−0.382012 | + | 0.924157i | \(0.624769\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.06068 | 0.159889 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.9846 | −0.471164 | −0.235582 | − | 0.971854i | \(-0.575700\pi\) | ||||
−0.235582 | + | 0.971854i | \(0.575700\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.2373 | −0.990649 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.0479 | 0.981706 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −49.8602 | −1.95118 | −0.975591 | − | 0.219597i | \(-0.929526\pi\) | ||||
−0.975591 | + | 0.219597i | \(0.929526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.88437 | 0.0736283 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.75098 | −0.341408 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.6776 | 0.532803 | 0.266401 | − | 0.963862i | \(-0.414165\pi\) | ||||
0.266401 | + | 0.963862i | \(0.414165\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7673 | −0.652170 | −0.326085 | − | 0.945340i | \(-0.605730\pi\) | ||||
−0.326085 | + | 0.945340i | \(0.605730\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.26298 | 0.204397 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.2735 | −0.437168 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.3651 | −1.21446 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.03208 | 0.194551 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.2460 | 0.781589 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.06233 | −0.156591 | −0.0782957 | − | 0.996930i | \(-0.524948\pi\) | ||||
−0.0782957 | + | 0.996930i | \(0.524948\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.86420 | 0.187223 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.7458 | 1.22009 | 0.610045 | − | 0.792367i | \(-0.291151\pi\) | ||||
0.610045 | + | 0.792367i | \(0.291151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.4493 | −0.823150 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.3349 | −0.587635 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.63079 | −0.100665 | −0.0503323 | − | 0.998733i | \(-0.516028\pi\) | ||||
−0.0503323 | + | 0.998733i | \(0.516028\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.38422 | −0.0910965 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.3099 | 0.927480 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.9471 | 1.48376 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.6234 | 1.16497 | 0.582484 | − | 0.812842i | \(-0.302081\pi\) | ||||
0.582484 | + | 0.812842i | \(0.302081\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20.8740 | −0.792937 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.50564 | −0.0950445 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.60539 | 0.288075 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.89197 | 0.298502 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.4102 | 0.506495 | 0.253248 | − | 0.967401i | \(-0.418501\pi\) | ||||
0.253248 | + | 0.967401i | \(0.418501\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.67469 | 0.100878 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0538679 | −0.00202878 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 60.8314 | 2.28780 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.2761 | −0.611262 | −0.305631 | − | 0.952150i | \(-0.598867\pi\) | ||||
−0.305631 | + | 0.952150i | \(0.598867\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.06151 | −0.264827 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.1453 | −0.829348 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.54496 | −0.207370 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.17307 | 0.230537 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.8035 | −1.26066 | −0.630329 | − | 0.776328i | \(-0.717080\pi\) | ||||
−0.630329 | + | 0.776328i | \(0.717080\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 52.4954 | 1.95503 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.9013 | 0.591377 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −35.5141 | −1.31896 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.96312 | 0.295336 | 0.147668 | − | 0.989037i | \(-0.452823\pi\) | ||||
0.147668 | + | 0.989037i | \(0.452823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.5573 | −0.612394 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.5816 | 1.27730 | 0.638651 | − | 0.769497i | \(-0.279493\pi\) | ||||
0.638651 | + | 0.769497i | \(0.279493\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.12097 | 0.225775 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 51.2994 | 1.88964 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.91361 | 0.364678 | 0.182339 | − | 0.983236i | \(-0.441633\pi\) | ||||
0.182339 | + | 0.983236i | \(0.441633\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.0521 | 0.810104 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.1326 | −1.28889 | −0.644444 | − | 0.764651i | \(-0.722911\pi\) | ||||
−0.644444 | + | 0.764651i | \(0.722911\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.50605 | 0.128452 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.3020 | −0.376929 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −59.1491 | −2.16126 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.810730 | −0.0295840 | −0.0147920 | − | 0.999891i | \(-0.504709\pi\) | ||||
−0.0147920 | + | 0.999891i | \(0.504709\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.977421 | −0.0356192 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.81480 | 0.0660474 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.08330 | 0.293793 | 0.146896 | − | 0.989152i | \(-0.453072\pi\) | ||||
0.146896 | + | 0.989152i | \(0.453072\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.4550 | 0.669876 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.6549 | 1.72749 | 0.863745 | − | 0.503929i | \(-0.168113\pi\) | ||||
0.863745 | + | 0.503929i | \(0.168113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.1649 | −1.59888 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.553723 | 0.0200199 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.5766 | −0.742979 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.1365 | −0.798262 | −0.399131 | − | 0.916894i | \(-0.630688\pi\) | ||||
−0.399131 | + | 0.916894i | \(0.630688\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.3626 | 0.445229 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.7111 | 1.17654 | 0.588268 | − | 0.808666i | \(-0.299810\pi\) | ||||
0.588268 | + | 0.808666i | \(0.299810\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.0747 | −0.900709 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.06424 | −0.0740544 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.8669 | 1.14175 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.7632 | −1.88801 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.30112 | −0.260921 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.06709 | −0.145161 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.1925 | −1.36142 | −0.680708 | − | 0.732555i | \(-0.738328\pi\) | ||||
−0.680708 | + | 0.732555i | \(0.738328\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.0183 | −1.03308 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −44.9380 | −1.59781 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.5071 | 0.586186 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.09766 | 0.145329 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.496624 | −0.0175913 | −0.00879566 | − | 0.999961i | \(-0.502800\pi\) | ||||
−0.00879566 | + | 0.999961i | \(0.502800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.219645 | 0.00777048 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.57185 | −0.196871 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.5936 | −1.32665 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.69230 | −0.271118 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.03619 | −0.177282 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.1686 | 1.06067 | 0.530336 | − | 0.847788i | \(-0.322066\pi\) | ||||
0.530336 | + | 0.847788i | \(0.322066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.34079 | −0.117311 | −0.0586555 | − | 0.998278i | \(-0.518681\pi\) | ||||
−0.0586555 | + | 0.998278i | \(0.518681\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.4646 | −0.752796 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.19677 | −0.111978 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −69.3758 | −2.42715 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.0191 | −0.594697 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.6959 | −0.931694 | −0.465847 | − | 0.884865i | \(-0.654250\pi\) | ||||
−0.465847 | + | 0.884865i | \(0.654250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.7998 | −0.690179 | −0.345090 | − | 0.938570i | \(-0.612151\pi\) | ||||
−0.345090 | + | 0.938570i | \(0.612151\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.8963 | 0.727515 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.9527 | 1.84135 | 0.920674 | − | 0.390333i | \(-0.127640\pi\) | ||||
0.920674 | + | 0.390333i | \(0.127640\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.4115 | 0.604725 | 0.302362 | − | 0.953193i | \(-0.402225\pi\) | ||||
0.302362 | + | 0.953193i | \(0.402225\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.4250 | −0.777914 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.9581 | −0.864746 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.368511 | −0.0127529 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.15494 | −0.178181 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.5735 | 1.19361 | 0.596804 | − | 0.802387i | \(-0.296437\pi\) | ||||
0.596804 | + | 0.802387i | \(0.296437\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.3064 | 0.838151 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.7465 | 0.990083 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.269689 | 0.00927758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.2241 | −1.24468 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.84966 | −0.0978000 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.82503 | 0.0625613 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.8981 | −1.29761 | −0.648804 | − | 0.760956i | \(-0.724730\pi\) | ||||
−0.648804 | + | 0.760956i | \(0.724730\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.32012 | 0.0793465 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.7888 | −0.505177 | −0.252588 | − | 0.967574i | \(-0.581282\pi\) | ||||
−0.252588 | + | 0.967574i | \(0.581282\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.6848 | −0.535158 | −0.267579 | − | 0.963536i | \(-0.586224\pi\) | ||||
−0.267579 | + | 0.963536i | \(0.586224\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24.5939 | −0.838158 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.4309 | 0.865679 | 0.432839 | − | 0.901471i | \(-0.357512\pi\) | ||||
0.432839 | + | 0.901471i | \(0.357512\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.988158 | 0.0335984 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.7422 | 0.500672 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.3358 | −1.02907 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.8258 | 1.41721 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.41434 | 0.149403 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.6628 | −0.597113 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.8789 | −0.367354 | −0.183677 | − | 0.982987i | \(-0.558800\pi\) | ||||
−0.183677 | + | 0.982987i | \(0.558800\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.8546 | 0.703407 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.0839 | 1.18201 | 0.591004 | − | 0.806669i | \(-0.298732\pi\) | ||||
0.591004 | + | 0.806669i | \(0.298732\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.8391 | −1.07147 | −0.535736 | − | 0.844385i | \(-0.679966\pi\) | ||||
−0.535736 | + | 0.844385i | \(0.679966\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.16489 | −0.0727719 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.8743 | 1.60746 | 0.803731 | − | 0.594993i | \(-0.202845\pi\) | ||||
0.803731 | + | 0.594993i | \(0.202845\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −71.0153 | −2.38178 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.29593 | 0.143919 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.920322 | 0.0307974 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.14734 | −0.0717778 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.0469 | 0.502402 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.6369 | 1.25526 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.7081 | −0.556627 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 53.5421 | 1.78177 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.69566 | 0.222571 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.1837 | −0.537371 | −0.268685 | − | 0.963228i | \(-0.586589\pi\) | ||||
−0.268685 | + | 0.963228i | \(0.586589\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.5193 | −0.415239 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.65866 | 0.286874 | 0.143437 | − | 0.989659i | \(-0.454185\pi\) | ||||
0.143437 | + | 0.989659i | \(0.454185\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.2565 | −1.46468 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.73673 | 0.0574146 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.8464 | 0.820499 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.7780 | 1.27917 | 0.639584 | − | 0.768721i | \(-0.279107\pi\) | ||||
0.639584 | + | 0.768721i | \(0.279107\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.2508 | 0.436630 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −43.0193 | −1.41600 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.06645 | 0.0679444 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.8037 | −0.354841 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.8787 | 1.27557 | 0.637785 | − | 0.770214i | \(-0.279851\pi\) | ||||
0.637785 | + | 0.770214i | \(0.279851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −104.575 | −3.42732 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.17394 | −0.0711718 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.37876 | 0.0777936 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.5796 | 0.606969 | 0.303484 | − | 0.952836i | \(-0.401850\pi\) | ||||
0.303484 | + | 0.952836i | \(0.401850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.2769 | 0.629079 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.2550 | 1.57307 | 0.786534 | − | 0.617547i | \(-0.211874\pi\) | ||||
0.786534 | + | 0.617547i | \(0.211874\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.7439 | 0.708078 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.79060 | −0.0582482 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −54.1601 | −1.75997 | −0.879984 | − | 0.475004i | \(-0.842447\pi\) | ||||
−0.879984 | + | 0.475004i | \(0.842447\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.6511 | −0.994978 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.64901 | −0.183182 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.2537 | 1.36873 | 0.684366 | − | 0.729139i | \(-0.260079\pi\) | ||||
0.684366 | + | 0.729139i | \(0.260079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.01394 | −0.259325 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −31.3651 | −1.01389 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31.4372 | −1.01516 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.42655 | −0.142792 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.1731 | 0.392272 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.21092 | 0.296510 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.54868 | 0.242749 | 0.121375 | − | 0.992607i | \(-0.461270\pi\) | ||||
0.121375 | + | 0.992607i | \(0.461270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.46023 | −0.303906 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.8294 | −0.828904 | −0.414452 | − | 0.910071i | \(-0.636027\pi\) | ||||
−0.414452 | + | 0.910071i | \(0.636027\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.0382 | −1.05916 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.0373 | 0.545631 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.80544 | −0.185733 | −0.0928663 | − | 0.995679i | \(-0.529603\pi\) | ||||
−0.0928663 | + | 0.995679i | \(0.529603\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.9363 | −0.765007 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.08927 | 0.290198 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.5608 | 1.61264 | 0.806320 | − | 0.591480i | \(-0.201456\pi\) | ||||
0.806320 | + | 0.591480i | \(0.201456\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.41894 | −0.0770740 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.710277 | −0.0226084 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.3375 | −1.50525 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.6618 | 0.624579 | 0.312290 | − | 0.949987i | \(-0.398904\pi\) | ||||
0.312290 | + | 0.949987i | \(0.398904\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.6490 | 0.433138 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.91535 | 0.0607208 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.2060 | 0.608261 | 0.304130 | − | 0.952630i | \(-0.401634\pi\) | ||||
0.304130 | + | 0.952630i | \(0.401634\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.424828 | 0.0134410 |
(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 | 8016.2.a.r.1.3 | 5 | ||
4.3 | odd | 2 | 1002.2.a.j.1.3 | ✓ | 5 | ||
12.11 | even | 2 | 3006.2.a.t.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1002.2.a.j.1.3 | ✓ | 5 | 4.3 | odd | 2 | ||
3006.2.a.t.1.3 | 5 | 12.11 | even | 2 | |||
8016.2.a.r.1.3 | 5 | 1.1 | even | 1 | trivial |