Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 7x^{5} + 11x^{4} + 12x^{3} - 14x^{2} - 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.80982\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(5\) | −3.20729 | −1.43434 | −0.717172 | − | 0.696896i | \(-0.754564\pi\) | ||||
−0.717172 | + | 0.696896i | \(0.754564\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.68779 | 1.39385 | 0.696927 | − | 0.717142i | \(-0.254550\pi\) | ||||
0.696927 | + | 0.717142i | \(0.254550\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41235 | 0.727350 | 0.363675 | − | 0.931526i | \(-0.381522\pi\) | ||||
0.363675 | + | 0.931526i | \(0.381522\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.292389 | −0.0810942 | −0.0405471 | − | 0.999178i | \(-0.512910\pi\) | ||||
−0.0405471 | + | 0.999178i | \(0.512910\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.20729 | 0.828119 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.19061 | 1.74398 | 0.871989 | − | 0.489525i | \(-0.162830\pi\) | ||||
0.871989 | + | 0.489525i | \(0.162830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.96484 | −0.680180 | −0.340090 | − | 0.940393i | \(-0.610458\pi\) | ||||
−0.340090 | + | 0.940393i | \(0.610458\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.68779 | −0.804743 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.50281 | 1.14742 | 0.573708 | − | 0.819060i | \(-0.305504\pi\) | ||||
0.573708 | + | 0.819060i | \(0.305504\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.28672 | 1.05734 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.32252 | 0.616976 | 0.308488 | − | 0.951228i | \(-0.400177\pi\) | ||||
0.308488 | + | 0.951228i | \(0.400177\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.32412 | −0.597029 | −0.298514 | − | 0.954405i | \(-0.596491\pi\) | ||||
−0.298514 | + | 0.954405i | \(0.596491\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.41235 | −0.419936 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.8278 | −1.99927 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.357486 | −0.0587703 | −0.0293852 | − | 0.999568i | \(-0.509355\pi\) | ||||
−0.0293852 | + | 0.999568i | \(0.509355\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.292389 | 0.0468197 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.49808 | 0.546309 | 0.273154 | − | 0.961970i | \(-0.411933\pi\) | ||||
0.273154 | + | 0.961970i | \(0.411933\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.1409 | −1.69898 | −0.849488 | − | 0.527608i | \(-0.823089\pi\) | ||||
−0.849488 | + | 0.527608i | \(0.823089\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.20729 | −0.478115 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.406706 | −0.0593241 | −0.0296621 | − | 0.999560i | \(-0.509443\pi\) | ||||
−0.0296621 | + | 0.999560i | \(0.509443\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.59982 | 0.942832 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.19061 | −1.00689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.6914 | −1.46858 | −0.734291 | − | 0.678834i | \(-0.762485\pi\) | ||||
−0.734291 | + | 0.678834i | \(0.762485\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.73710 | −1.04327 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.96484 | 0.392702 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.65193 | −0.475441 | −0.237720 | − | 0.971334i | \(-0.576400\pi\) | ||||
−0.237720 | + | 0.971334i | \(0.576400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.48361 | 1.21425 | 0.607126 | − | 0.794606i | \(-0.292322\pi\) | ||||
0.607126 | + | 0.794606i | \(0.292322\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.68779 | 0.464618 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.937777 | 0.116317 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.18677 | 0.511496 | 0.255748 | − | 0.966744i | \(-0.417678\pi\) | ||||
0.255748 | + | 0.966744i | \(0.417678\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.50281 | −0.662461 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.68125 | 0.318206 | 0.159103 | − | 0.987262i | \(-0.449140\pi\) | ||||
0.159103 | + | 0.987262i | \(0.449140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.27452 | −0.734377 | −0.367189 | − | 0.930147i | \(-0.619680\pi\) | ||||
−0.367189 | + | 0.930147i | \(0.619680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.28672 | −0.610457 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.89624 | 1.01382 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.66323 | 0.749672 | 0.374836 | − | 0.927091i | \(-0.377699\pi\) | ||||
0.374836 | + | 0.927091i | \(0.377699\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2090 | 1.12059 | 0.560293 | − | 0.828295i | \(-0.310689\pi\) | ||||
0.560293 | + | 0.828295i | \(0.310689\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.0624 | −2.50147 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.32252 | −0.356211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.51995 | −0.479114 | −0.239557 | − | 0.970882i | \(-0.577002\pi\) | ||||
−0.239557 | + | 0.970882i | \(0.577002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.07827 | −0.113034 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.32412 | 0.344695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.50909 | 0.975613 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.77054 | 0.179771 | 0.0898853 | − | 0.995952i | \(-0.471350\pi\) | ||||
0.0898853 | + | 0.995952i | \(0.471350\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.41235 | 0.242450 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.8099 | 1.87165 | 0.935826 | − | 0.352463i | \(-0.114656\pi\) | ||||
0.935826 | + | 0.352463i | \(0.114656\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.82075 | 0.573536 | 0.286768 | − | 0.958000i | \(-0.407419\pi\) | ||||
0.286768 | + | 0.958000i | \(0.407419\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.8278 | 1.15428 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.11502 | 0.881182 | 0.440591 | − | 0.897708i | \(-0.354769\pi\) | ||||
0.440591 | + | 0.897708i | \(0.354769\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.8744 | −1.80784 | −0.903922 | − | 0.427697i | \(-0.859325\pi\) | ||||
−0.903922 | + | 0.427697i | \(0.859325\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.357486 | 0.0339311 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.5304 | 1.17876 | 0.589381 | − | 0.807855i | \(-0.299372\pi\) | ||||
0.589381 | + | 0.807855i | \(0.299372\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.6491 | −1.64579 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.292389 | −0.0270314 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26.5175 | 2.43085 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.18058 | −0.470962 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.49808 | −0.315412 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.919585 | −0.0822502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.13671 | −0.100867 | −0.0504333 | − | 0.998727i | \(-0.516060\pi\) | ||||
−0.0504333 | + | 0.998727i | \(0.516060\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.1409 | 0.980904 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1630 | 1.06269 | 0.531343 | − | 0.847157i | \(-0.321688\pi\) | ||||
0.531343 | + | 0.847157i | \(0.321688\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.9337 | −0.948072 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.20729 | 0.276040 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.4346 | −1.23323 | −0.616616 | − | 0.787264i | \(-0.711497\pi\) | ||||
−0.616616 | + | 0.787264i | \(0.711497\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.433633 | −0.0367803 | −0.0183902 | − | 0.999831i | \(-0.505854\pi\) | ||||
−0.0183902 | + | 0.999831i | \(0.505854\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.406706 | 0.0342508 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.705344 | −0.0589839 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.6563 | −0.884956 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.59982 | −0.544344 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.0992 | −1.56466 | −0.782332 | − | 0.622862i | \(-0.785970\pi\) | ||||
−0.782332 | + | 0.622862i | \(0.785970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.70546 | 0.708440 | 0.354220 | − | 0.935162i | \(-0.384746\pi\) | ||||
0.354220 | + | 0.935162i | \(0.384746\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.19061 | 0.581326 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.6614 | 0.856345 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.6106 | 1.80452 | 0.902261 | − | 0.431191i | \(-0.141907\pi\) | ||||
0.902261 | + | 0.431191i | \(0.141907\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.6914 | 0.847887 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.2932 | 1.59933 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.50323 | −0.744350 | −0.372175 | − | 0.928162i | \(-0.621388\pi\) | ||||
−0.372175 | + | 0.928162i | \(0.621388\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.73710 | 0.602332 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9145 | −0.993424 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.96484 | −0.226727 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.88163 | 0.295115 | 0.147557 | − | 0.989053i | \(-0.452859\pi\) | ||||
0.147557 | + | 0.989053i | \(0.452859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.4963 | 1.47378 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.65193 | 0.274496 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.65909 | −0.572467 | −0.286234 | − | 0.958160i | \(-0.592403\pi\) | ||||
−0.286234 | + | 0.958160i | \(0.592403\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.78926 | 0.727630 | 0.363815 | − | 0.931471i | \(-0.381474\pi\) | ||||
0.363815 | + | 0.931471i | \(0.381474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.48361 | −0.701048 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.14656 | 0.0842969 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.3462 | 1.26848 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.68779 | −0.268248 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.9580 | 1.08232 | 0.541162 | − | 0.840918i | \(-0.317985\pi\) | ||||
0.541162 | + | 0.840918i | \(0.317985\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.569004 | −0.0409578 | −0.0204789 | − | 0.999790i | \(-0.506519\pi\) | ||||
−0.0204789 | + | 0.999790i | \(0.506519\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.937777 | −0.0671556 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.1326 | 1.71938 | 0.859688 | − | 0.510820i | \(-0.170658\pi\) | ||||
0.859688 | + | 0.510820i | \(0.170658\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.6151 | 0.752482 | 0.376241 | − | 0.926522i | \(-0.377216\pi\) | ||||
0.376241 | + | 0.926522i | \(0.377216\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.18677 | −0.295312 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.2528 | 0.859975 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.2194 | −0.783595 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.50281 | 0.382472 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.15222 | −0.494729 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9203 | 1.02716 | 0.513579 | − | 0.858042i | \(-0.328319\pi\) | ||||
0.513579 | + | 0.858042i | \(0.328319\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.68125 | −0.183716 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 35.7322 | 2.43692 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.2587 | −0.832171 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.27452 | 0.423993 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.10246 | −0.141427 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.5962 | −0.977431 | −0.488715 | − | 0.872443i | \(-0.662534\pi\) | ||||
−0.488715 | + | 0.872443i | \(0.662534\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.28672 | 0.352448 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.67692 | 0.509535 | 0.254767 | − | 0.967002i | \(-0.418001\pi\) | ||||
0.254767 | + | 0.967002i | \(0.418001\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.74042 | −0.511501 | −0.255751 | − | 0.966743i | \(-0.582323\pi\) | ||||
−0.255751 | + | 0.966743i | \(0.582323\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.89624 | −0.585330 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.6688 | −1.02650 | −0.513250 | − | 0.858239i | \(-0.671558\pi\) | ||||
−0.513250 | + | 0.858239i | \(0.671558\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.30442 | 0.0850912 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.66323 | −0.432823 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.3027 | 1.31327 | 0.656636 | − | 0.754208i | \(-0.271979\pi\) | ||||
0.656636 | + | 0.754208i | \(0.271979\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.43764 | 0.479100 | 0.239550 | − | 0.970884i | \(-0.423000\pi\) | ||||
0.239550 | + | 0.970884i | \(0.423000\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.1675 | −1.35235 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.866886 | 0.0551586 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.2090 | −0.646970 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.3028 | 1.78646 | 0.893228 | − | 0.449604i | \(-0.148435\pi\) | ||||
0.893228 | + | 0.449604i | \(0.148435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.2747 | 0.834573 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 23.0624 | 1.44422 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.82120 | −0.487873 | −0.243936 | − | 0.969791i | \(-0.578439\pi\) | ||||
−0.243936 | + | 0.969791i | \(0.578439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.31833 | −0.0819173 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.32252 | 0.205659 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.44120 | −0.397182 | −0.198591 | − | 0.980082i | \(-0.563636\pi\) | ||||
−0.198591 | + | 0.980082i | \(0.563636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.2906 | 2.10645 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.51995 | 0.276617 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.7914 | 1.32865 | 0.664323 | − | 0.747446i | \(-0.268720\pi\) | ||||
0.664323 | + | 0.747446i | \(0.268720\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1627 | −0.617340 | −0.308670 | − | 0.951169i | \(-0.599884\pi\) | ||||
−0.308670 | + | 0.951169i | \(0.599884\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.07827 | 0.0652599 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.7534 | 0.769059 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.38295 | 0.323430 | 0.161715 | − | 0.986838i | \(-0.448297\pi\) | ||||
0.161715 | + | 0.986838i | \(0.448297\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.32412 | −0.199010 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.2566 | −1.02945 | −0.514723 | − | 0.857357i | \(-0.672105\pi\) | ||||
−0.514723 | + | 0.857357i | \(0.672105\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.13015 | −0.364399 | −0.182200 | − | 0.983262i | \(-0.558322\pi\) | ||||
−0.182200 | + | 0.983262i | \(0.558322\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.50909 | −0.563270 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.9002 | 0.761475 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.7048 | 2.04146 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.77054 | −0.103791 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.6848 | 1.03316 | 0.516578 | − | 0.856240i | \(-0.327206\pi\) | ||||
0.516578 | + | 0.856240i | \(0.327206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.7128 | 0.681945 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.41235 | −0.139979 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.60896 | −0.0930488 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −41.0854 | −2.36813 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.8099 | −1.08060 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.4167 | −1.74165 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.1101 | 0.634085 | 0.317042 | − | 0.948411i | \(-0.397310\pi\) | ||||
0.317042 | + | 0.948411i | \(0.397310\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.82075 | −0.331131 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.3481 | 1.60747 | 0.803737 | − | 0.594985i | \(-0.202842\pi\) | ||||
0.803737 | + | 0.594985i | \(0.202842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.4209 | 1.77601 | 0.888006 | − | 0.459831i | \(-0.152090\pi\) | ||||
0.888006 | + | 0.459831i | \(0.152090\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.8278 | −0.666423 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.57882 | −0.425669 | −0.212834 | − | 0.977088i | \(-0.568269\pi\) | ||||
−0.212834 | + | 0.977088i | \(0.568269\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.01507 | 0.448758 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.11502 | −0.508751 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.3190 | −1.18622 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.54578 | −0.0857444 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.8744 | 1.04376 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.49985 | −0.0826892 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.3509 | 1.61327 | 0.806636 | − | 0.591049i | \(-0.201286\pi\) | ||||
0.806636 | + | 0.591049i | \(0.201286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.357486 | −0.0195901 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.4282 | −0.733661 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.2626 | −1.32167 | −0.660833 | − | 0.750533i | \(-0.729797\pi\) | ||||
−0.660833 | + | 0.750533i | \(0.729797\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.5304 | −0.680559 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.01892 | −0.434249 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.47578 | −0.0796844 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.6491 | 0.950197 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.9314 | 0.908924 | 0.454462 | − | 0.890766i | \(-0.349831\pi\) | ||||
0.454462 | + | 0.890766i | \(0.349831\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.41024 | 0.129017 | 0.0645087 | − | 0.997917i | \(-0.479452\pi\) | ||||
0.0645087 | + | 0.997917i | \(0.479452\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.292389 | 0.0156066 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.2607 | −0.652570 | −0.326285 | − | 0.945271i | \(-0.605797\pi\) | ||||
−0.326285 | + | 0.945271i | \(0.605797\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.59956 | −0.456417 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −26.5175 | −1.40345 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.1673 | 0.642166 | 0.321083 | − | 0.947051i | \(-0.395953\pi\) | ||||
0.321083 | + | 0.947051i | \(0.395953\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.2097 | −0.537355 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.18058 | 0.271910 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.1242 | 1.05335 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.82364 | 0.408391 | 0.204195 | − | 0.978930i | \(-0.434542\pi\) | ||||
0.204195 | + | 0.978930i | \(0.434542\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.49808 | 0.182103 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −39.4278 | −2.04699 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.1180 | −0.938114 | −0.469057 | − | 0.883168i | \(-0.655406\pi\) | ||||
−0.469057 | + | 0.883168i | \(0.655406\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.919585 | 0.0474872 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.971469 | −0.0500332 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.116915 | 0.00600553 | 0.00300276 | − | 0.999995i | \(-0.499044\pi\) | ||||
0.00300276 | + | 0.999995i | \(0.499044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.13671 | 0.0582354 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.723537 | −0.0369710 | −0.0184855 | − | 0.999829i | \(-0.505884\pi\) | ||||
−0.0184855 | + | 0.999829i | \(0.505884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28.5328 | −1.45417 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.1409 | −0.566325 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.8520 | −1.26004 | −0.630022 | − | 0.776577i | \(-0.716954\pi\) | ||||
−0.630022 | + | 0.776577i | \(0.716954\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.5686 | 2.00107 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.1630 | −0.613542 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.3709 | −1.07529 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.6468 | 0.735102 | 0.367551 | − | 0.930003i | \(-0.380196\pi\) | ||||
0.367551 | + | 0.930003i | \(0.380196\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.9337 | 0.547370 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.34823 | −0.267078 | −0.133539 | − | 0.991044i | \(-0.542634\pi\) | ||||
−0.133539 | + | 0.991044i | \(0.542634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.971935 | 0.0484156 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.20729 | −0.159372 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.862380 | −0.0427466 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.7435 | 0.827913 | 0.413957 | − | 0.910297i | \(-0.364146\pi\) | ||||
0.413957 | + | 0.910297i | \(0.364146\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.4346 | 0.712007 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.4676 | −0.662695 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.7433 | −1.60731 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.433633 | 0.0212351 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.99429 | 0.292840 | 0.146420 | − | 0.989222i | \(-0.453225\pi\) | ||||
0.146420 | + | 0.989222i | \(0.453225\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.60581 | 0.126999 | 0.0634996 | − | 0.997982i | \(-0.479774\pi\) | ||||
0.0634996 | + | 0.997982i | \(0.479774\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.406706 | −0.0197747 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.0147 | 1.84398 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.9736 | 1.69249 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.705344 | 0.0340543 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.60689 | 0.173738 | 0.0868690 | − | 0.996220i | \(-0.472314\pi\) | ||||
0.0868690 | + | 0.996220i | \(0.472314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.1030 | 0.533576 | 0.266788 | − | 0.963755i | \(-0.414038\pi\) | ||||
0.266788 | + | 0.963755i | \(0.414038\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.6563 | 0.510930 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.3149 | −0.780450 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.7654 | −1.80245 | −0.901223 | − | 0.433356i | \(-0.857329\pi\) | ||||
−0.901223 | + | 0.433356i | \(0.857329\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.59982 | 0.314277 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.3294 | −1.01339 | −0.506695 | − | 0.862125i | \(-0.669133\pi\) | ||||
−0.506695 | + | 0.862125i | \(0.669133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.4968 | 0.687215 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.0992 | 0.903359 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.7910 | 1.35873 | 0.679365 | − | 0.733800i | \(-0.262255\pi\) | ||||
0.679365 | + | 0.733800i | \(0.262255\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.43859 | 0.397358 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.70546 | −0.409018 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.45833 | 0.162129 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.7766 | 0.878332 | 0.439166 | − | 0.898406i | \(-0.355274\pi\) | ||||
0.439166 | + | 0.898406i | \(0.355274\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.19061 | −0.335629 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0426 | −0.560878 | −0.280439 | − | 0.959872i | \(-0.590480\pi\) | ||||
−0.280439 | + | 0.959872i | \(0.590480\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0030 | 0.976094 | 0.488047 | − | 0.872817i | \(-0.337709\pi\) | ||||
0.488047 | + | 0.872817i | \(0.337709\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.6614 | −0.494411 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.3609 | −1.68258 | −0.841291 | − | 0.540582i | \(-0.818204\pi\) | ||||
−0.841291 | + | 0.540582i | \(0.818204\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.4400 | 0.712951 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.6106 | −1.04184 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.8758 | −1.23575 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.6743 | −0.719184 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.6914 | −0.489528 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.2203 | 0.466976 | 0.233488 | − | 0.972360i | \(-0.424986\pi\) | ||||
0.233488 | + | 0.972360i | \(0.424986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.104525 | 0.00476593 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.2932 | −0.923375 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.67862 | −0.257853 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.8144 | −1.26039 | −0.630195 | − | 0.776437i | \(-0.717025\pi\) | ||||
−0.630195 | + | 0.776437i | \(0.717025\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.50323 | 0.429751 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.01324 | 0.271374 | 0.135687 | − | 0.990752i | \(-0.456676\pi\) | ||||
0.135687 | + | 0.990752i | \(0.456676\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.8909 | 1.07599 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.73710 | −0.347757 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.88791 | 0.443533 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.63868 | 0.297188 | 0.148594 | − | 0.988898i | \(-0.452525\pi\) | ||||
0.148594 | + | 0.988898i | \(0.452525\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.5316 | 1.89639 | 0.948195 | − | 0.317689i | \(-0.102907\pi\) | ||||
0.948195 | + | 0.317689i | \(0.102907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −60.3287 | −2.68459 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9145 | 0.573553 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.1257 | −1.55692 | −0.778461 | − | 0.627693i | \(-0.783999\pi\) | ||||
−0.778461 | + | 0.627693i | \(0.783999\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.1391 | −1.02362 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.96484 | 0.130901 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.6689 | −0.822648 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.981115 | −0.0431494 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.88163 | −0.170385 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.8196 | −1.65691 | −0.828454 | − | 0.560057i | \(-0.810779\pi\) | ||||
−0.828454 | + | 0.560057i | \(0.810779\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.84372 | −0.124347 | −0.0621737 | − | 0.998065i | \(-0.519803\pi\) | ||||
−0.0621737 | + | 0.998065i | \(0.519803\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19.4963 | −0.850889 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.9024 | −1.04121 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.28097 | 0.316564 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.65193 | −0.158480 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.02280 | −0.0443025 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.2345 | −1.26392 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.65909 | 0.330514 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.9211 | 0.685769 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.0033 | 1.59090 | 0.795448 | − | 0.606022i | \(-0.207236\pi\) | ||||
0.795448 | + | 0.606022i | \(0.207236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.78926 | −0.420097 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 60.5358 | 2.59307 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.2638 | −1.42226 | −0.711128 | − | 0.703063i | \(-0.751815\pi\) | ||||
−0.711128 | + | 0.703063i | \(0.751815\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.48361 | 0.404750 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.85072 | −0.419655 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.5726 | 1.04493 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.14656 | −0.0486688 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.8570 | −1.64642 | −0.823212 | − | 0.567734i | \(-0.807820\pi\) | ||||
−0.823212 | + | 0.567734i | \(0.807820\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.25749 | 0.137777 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.3462 | −0.732359 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.4700 | 0.651984 | 0.325992 | − | 0.945373i | \(-0.394302\pi\) | ||||
0.325992 | + | 0.945373i | \(0.394302\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.1887 | −1.69075 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.68779 | 0.154873 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.7094 | −0.910107 | −0.455053 | − | 0.890464i | \(-0.650380\pi\) | ||||
−0.455053 | + | 0.890464i | \(0.650380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.9576 | 0.960745 | 0.480372 | − | 0.877065i | \(-0.340502\pi\) | ||||
0.480372 | + | 0.877065i | \(0.340502\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.9580 | −0.624880 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.0918 | 1.21321 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.8858 | −0.994381 | −0.497190 | − | 0.867641i | \(-0.665635\pi\) | ||||
−0.497190 | + | 0.867641i | \(0.665635\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.569004 | 0.0236470 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.6488 | 1.56193 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.7915 | −1.06817 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.937777 | 0.0387723 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.2904 | −0.754926 | −0.377463 | − | 0.926025i | \(-0.623203\pi\) | ||||
−0.377463 | + | 0.926025i | \(0.623203\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.85546 | 0.406087 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.1326 | −0.992682 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.7008 | −1.38393 | −0.691964 | − | 0.721932i | \(-0.743254\pi\) | ||||
−0.691964 | + | 0.721932i | \(0.743254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −85.0493 | −3.48668 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.6151 | −0.434446 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.1340 | −0.904372 | −0.452186 | − | 0.891924i | \(-0.649356\pi\) | ||||
−0.452186 | + | 0.891924i | \(0.649356\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.70740 | 0.273601 | 0.136800 | − | 0.990599i | \(-0.456318\pi\) | ||||
0.136800 | + | 0.990599i | \(0.456318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.18677 | 0.170499 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.6156 | 0.675521 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.2730 | 1.22874 | 0.614371 | − | 0.789017i | \(-0.289410\pi\) | ||||
0.614371 | + | 0.789017i | \(0.289410\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.2528 | −0.496507 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.118916 | 0.00481084 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.52415 | 0.101949 | 0.0509747 | − | 0.998700i | \(-0.483767\pi\) | ||||
0.0509747 | + | 0.998700i | \(0.483767\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.2194 | 0.452409 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.6084 | 0.507593 | 0.253797 | − | 0.967258i | \(-0.418321\pi\) | ||||
0.253797 | + | 0.967258i | \(0.418321\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.97122 | −0.159617 | −0.0798085 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798085 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.50281 | −0.220820 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.6687 | −0.667816 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.4842 | −0.939368 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.15222 | 0.285632 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.57054 | −0.102494 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −48.8417 | −1.94436 | −0.972179 | − | 0.234238i | \(-0.924741\pi\) | ||||
−0.972179 | + | 0.234238i | \(0.924741\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.9203 | −0.593030 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.64576 | 0.144677 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.92972 | −0.0764582 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.68125 | 0.106069 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.7538 | −0.464246 | −0.232123 | − | 0.972686i | \(-0.574567\pi\) | ||||
−0.232123 | + | 0.972686i | \(0.574567\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.9663 | −0.747958 | −0.373979 | − | 0.927437i | \(-0.622007\pi\) | ||||
−0.373979 | + | 0.927437i | \(0.622007\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −35.7322 | −1.40695 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.2745 | 1.46541 | 0.732705 | − | 0.680546i | \(-0.238257\pi\) | ||||
0.732705 | + | 0.680546i | \(0.238257\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.80972 | −0.345812 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.2587 | 0.480454 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.70587 | −0.379820 | −0.189910 | − | 0.981802i | \(-0.560820\pi\) | ||||
−0.189910 | + | 0.981802i | \(0.560820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.0103 | −1.52426 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.27452 | −0.244792 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.9798 | 0.856211 | 0.428105 | − | 0.903729i | \(-0.359181\pi\) | ||||
0.428105 | + | 0.903729i | \(0.359181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.2779 | −0.944300 | −0.472150 | − | 0.881518i | \(-0.656522\pi\) | ||||
−0.472150 | + | 0.881518i | \(0.656522\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.10246 | 0.0816526 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 35.0676 | 1.35986 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.2832 | 0.707928 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.5962 | 0.564320 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.8778 | 0.883186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.1769 | 1.04759 | 0.523795 | − | 0.851844i | \(-0.324516\pi\) | ||||
0.523795 | + | 0.851844i | \(0.324516\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.28672 | −0.203486 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.2103 | 1.19951 | 0.599755 | − | 0.800184i | \(-0.295265\pi\) | ||||
0.599755 | + | 0.800184i | \(0.295265\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.52937 | 0.250574 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.67692 | −0.294180 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.68394 | 0.332282 | 0.166141 | − | 0.986102i | \(-0.446869\pi\) | ||||
0.166141 | + | 0.986102i | \(0.446869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 46.2960 | 1.76888 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.74042 | 0.295316 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.12606 | 0.119094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.3984 | −0.395573 | −0.197787 | − | 0.980245i | \(-0.563375\pi\) | ||||
−0.197787 | + | 0.980245i | \(0.563375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.89624 | 0.337940 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.39079 | 0.0527556 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.1533 | 0.952751 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.6688 | 0.592650 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.3918 | 1.26119 | 0.630596 | − | 0.776111i | \(-0.282811\pi\) | ||||
0.630596 | + | 0.776111i | \(0.282811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.05989 | 0.0399744 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.30442 | −0.0491274 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 69.3669 | 2.60881 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.92848 | −0.222649 | −0.111324 | − | 0.993784i | \(-0.535509\pi\) | ||||
−0.111324 | + | 0.993784i | \(0.535509\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.66323 | 0.249891 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.2920 | −0.685040 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.26224 | 0.0846032 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.3027 | −0.758218 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.67728 | −0.174433 | −0.0872166 | − | 0.996189i | \(-0.527797\pi\) | ||||
−0.0872166 | + | 0.996189i | \(0.527797\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.4657 | 0.799426 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.43764 | −0.276609 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.5652 | 0.652356 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.8553 | 1.03310 | 0.516548 | − | 0.856258i | \(-0.327217\pi\) | ||||
0.516548 | + | 0.856258i | \(0.327217\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −80.1101 | −2.96298 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.6613 | −0.873949 | −0.436974 | − | 0.899474i | \(-0.643950\pi\) | ||||
−0.436974 | + | 0.899474i | \(0.643950\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.1675 | 0.780777 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.0999 | 0.372036 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.47093 | 0.0908945 | 0.0454473 | − | 0.998967i | \(-0.485529\pi\) | ||||
0.0454473 | + | 0.998967i | \(0.485529\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.866886 | −0.0318459 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.8973 | 0.693276 | 0.346638 | − | 0.937999i | \(-0.387323\pi\) | ||||
0.346638 | + | 0.937999i | \(0.387323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 61.2565 | 2.24427 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.2090 | 0.373529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.6143 | 1.22824 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.2273 | 1.43142 | 0.715712 | − | 0.698396i | \(-0.246102\pi\) | ||||
0.715712 | + | 0.698396i | \(0.246102\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.3028 | −1.03141 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.9210 | −1.01615 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.1963 | 1.24288 | 0.621442 | − | 0.783460i | \(-0.286547\pi\) | ||||
0.621442 | + | 0.783460i | \(0.286547\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.2747 | −0.481841 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0455 | −0.400398 | −0.200199 | − | 0.979755i | \(-0.564159\pi\) | ||||
−0.200199 | + | 0.979755i | \(0.564159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −69.6051 | −2.51987 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −23.0624 | −0.833822 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.06778 | 0.0385555 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.17138 | 0.294668 | 0.147334 | − | 0.989087i | \(-0.452931\pi\) | ||||
0.147334 | + | 0.989087i | \(0.452931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.82120 | 0.281673 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −47.9579 | −1.72493 | −0.862463 | − | 0.506120i | \(-0.831079\pi\) | ||||
−0.862463 | + | 0.506120i | \(0.831079\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.5737 | −0.631264 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.31833 | 0.0472950 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.3712 | −0.371588 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.46812 | 0.231447 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.32252 | −0.118737 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −72.5187 | −2.58830 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.9997 | 1.92488 | 0.962440 | − | 0.271495i | \(-0.0875180\pi\) | ||||
0.962440 | + | 0.271495i | \(0.0875180\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.44120 | 0.229313 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 46.2096 | 1.64302 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.77290 | −0.0984687 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −34.2906 | −1.21616 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.87813 | 0.208214 | 0.104107 | − | 0.994566i | \(-0.466802\pi\) | ||||
0.104107 | + | 0.994566i | \(0.466802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.92446 | −0.103460 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.51995 | −0.159705 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.1363 | −0.534149 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −65.0863 | −2.29399 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.7914 | −0.767094 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.91670 | −0.137704 | −0.0688519 | − | 0.997627i | \(-0.521934\pi\) | ||||
−0.0688519 | + | 0.997627i | \(0.521934\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.4761 | 0.473211 | 0.236605 | − | 0.971606i | \(-0.423965\pi\) | ||||
0.236605 | + | 0.971606i | \(0.423965\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.1627 | 0.356421 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.4796 | 1.06765 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.0310 | 1.15561 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.07827 | −0.0376778 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.0639 | 0.770035 | 0.385018 | − | 0.922909i | \(-0.374195\pi\) | ||||
0.385018 | + | 0.922909i | \(0.374195\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.8677 | −0.448540 | −0.224270 | − | 0.974527i | \(-0.572000\pi\) | ||||
−0.224270 | + | 0.974527i | \(0.572000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.7534 | −0.444016 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.6784 | −0.823380 | −0.411690 | − | 0.911324i | \(-0.635061\pi\) | ||||
−0.411690 | + | 0.911324i | \(0.635061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.1173 | 1.11548 | 0.557741 | − | 0.830015i | \(-0.311668\pi\) | ||||
0.557741 | + | 0.830015i | \(0.311668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.38295 | −0.186732 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 47.4567 | 1.64428 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.20729 | 0.110993 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.32412 | 0.114898 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.63931 | 0.160167 | 0.0800835 | − | 0.996788i | \(-0.474481\pi\) | ||||
0.0800835 | + | 0.996788i | \(0.474481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9609 | −0.619340 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.2566 | 0.594351 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 41.4206 | 1.42491 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.1049 | −0.656452 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.13015 | 0.210386 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.96718 | −0.0674340 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.45984 | −0.152702 | −0.0763510 | − | 0.997081i | \(-0.524327\pi\) | ||||
−0.0763510 | + | 0.997081i | \(0.524327\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.50909 | 0.325204 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.4705 | 1.65572 | 0.827860 | − | 0.560935i | \(-0.189558\pi\) | ||||
0.827860 | + | 0.560935i | \(0.189558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.3642 | −0.387741 | −0.193871 | − | 0.981027i | \(-0.562104\pi\) | ||||
−0.193871 | + | 0.981027i | \(0.562104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.9002 | −0.439638 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.2403 | 1.06343 | 0.531717 | − | 0.846922i | \(-0.321547\pi\) | ||||
0.531717 | + | 0.846922i | \(0.321547\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.4495 | −0.423296 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34.7048 | −1.17864 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.0740 | 0.545274 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.22417 | −0.0414793 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.77054 | 0.0599236 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.39124 | −0.114645 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.45334 | −0.116611 | −0.0583055 | − | 0.998299i | \(-0.518570\pi\) | ||||
−0.0583055 | + | 0.998299i | \(0.518570\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.6848 | −0.596493 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0397 | −0.607772 | −0.303886 | − | 0.952708i | \(-0.598284\pi\) | ||||
−0.303886 | + | 0.952708i | \(0.598284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.7645 | −0.665129 | −0.332565 | − | 0.943081i | \(-0.607914\pi\) | ||||
−0.332565 | + | 0.943081i | \(0.607914\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.7128 | −0.393721 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.0636 | 0.472209 | 0.236105 | − | 0.971728i | \(-0.424129\pi\) | ||||
0.236105 | + | 0.971728i | \(0.424129\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.19195 | −0.140593 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.41235 | 0.0808167 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.20582 | 0.0403511 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.5649 | 0.821115 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.60896 | 0.0537217 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.0444 | −0.368353 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −76.8780 | −2.56118 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 41.0854 | 1.36724 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.3970 | −1.04367 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.8587 | −0.460170 | −0.230085 | − | 0.973171i | \(-0.573900\pi\) | ||||
−0.230085 | + | 0.973171i | \(0.573900\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.8099 | 0.623884 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.7036 | −1.24918 | −0.624588 | − | 0.780954i | \(-0.714733\pi\) | ||||
−0.624588 | + | 0.780954i | \(0.714733\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.6277 | 0.815058 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.4167 | 1.00554 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.8546 | 1.48123 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.6184 | −0.812086 | −0.406043 | − | 0.913854i | \(-0.633092\pi\) | ||||
−0.406043 | + | 0.913854i | \(0.633092\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.1101 | −0.366089 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.783970 | −0.0258047 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.88993 | −0.0621404 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.82075 | 0.191179 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.1432 | 0.923349 | 0.461675 | − | 0.887049i | \(-0.347249\pi\) | ||||
0.461675 | + | 0.887049i | \(0.347249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.5674 | −0.641295 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.3481 | −0.928076 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −55.6345 | −1.81944 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.4087 | 0.470713 | 0.235357 | − | 0.971909i | \(-0.424374\pi\) | ||||
0.235357 | + | 0.971909i | \(0.424374\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.4209 | −1.02538 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.8231 | 1.03740 | 0.518702 | − | 0.854955i | \(-0.326415\pi\) | ||||
0.518702 | + | 0.854955i | \(0.326415\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.2493 | 0.626844 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.8278 | 0.384759 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.53847 | 0.244967 | 0.122484 | − | 0.992471i | \(-0.460914\pi\) | ||||
0.122484 | + | 0.992471i | \(0.460914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.83460 | 0.0595537 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.57882 | 0.245760 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.31282 | 0.301672 | 0.150836 | − | 0.988559i | \(-0.451803\pi\) | ||||
0.150836 | + | 0.988559i | \(0.451803\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47.9747 | −1.55242 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.01507 | −0.259090 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −53.2319 | −1.71895 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.9503 | −0.643557 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.11502 | 0.293727 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.82496 | 0.0587476 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.56361 | 0.275387 | 0.137693 | − | 0.990475i | \(-0.456031\pi\) | ||||
0.137693 | + | 0.990475i | \(0.456031\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.3190 | 0.684864 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.1699 | −0.551010 | −0.275505 | − | 0.961300i | \(-0.588845\pi\) | ||||
−0.275505 | + | 0.961300i | \(0.588845\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.59915 | −0.0512664 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.54578 | 0.0495045 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.8510 | 0.539112 | 0.269556 | − | 0.962985i | \(-0.413123\pi\) | ||||
0.269556 | + | 0.962985i | \(0.413123\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.9037 | −0.348484 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.8744 | −0.602615 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.9668 | 0.764424 | 0.382212 | − | 0.924075i | \(-0.375162\pi\) | ||||
0.382212 | + | 0.924075i | \(0.375162\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −77.4002 | −2.46618 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.49985 | 0.0477406 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −61.3065 | −1.94943 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7821 | −0.564867 | −0.282434 | − | 0.959287i | \(-0.591142\pi\) | ||||
−0.282434 | + | 0.959287i | \(0.591142\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29.3509 | −0.931423 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.0456 | −1.07932 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.0948 | −1.07979 | −0.539896 | − | 0.841732i | \(-0.681536\pi\) | ||||
−0.539896 | + | 0.841732i | \(0.681536\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.357486 | 0.0113104 |
(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 | 4008.2.a.g.1.1 | ✓ | 7 | |
4.3 | odd | 2 | 8016.2.a.w.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.g.1.1 | ✓ | 7 | 1.1 | even | 1 | trivial | |
8016.2.a.w.1.1 | 7 | 4.3 | odd | 2 |