Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 2.47283 | 1.42769 | 0.713846 | − | 0.700303i | \(-0.246952\pi\) | ||||
0.713846 | + | 0.700303i | \(0.246952\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.114908 | −0.0513882 | −0.0256941 | − | 0.999670i | \(-0.508180\pi\) | ||||
−0.0256941 | + | 0.999670i | \(0.508180\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.11491 | 1.03830 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.284147 | −0.0733665 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.83076 | −1.41417 | −0.707084 | − | 0.707130i | \(-0.749990\pi\) | ||||
−0.707084 | + | 0.707130i | \(0.749990\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.75698 | 0.632495 | 0.316247 | − | 0.948677i | \(-0.397577\pi\) | ||||
0.316247 | + | 0.948677i | \(0.397577\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.47283 | −0.539617 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.81756 | 0.796016 | 0.398008 | − | 0.917382i | \(-0.369702\pi\) | ||||
0.398008 | + | 0.917382i | \(0.369702\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98680 | −0.997359 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.284147 | 0.0546842 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.17548 | −0.961063 | −0.480532 | − | 0.876977i | \(-0.659556\pi\) | ||||
−0.480532 | + | 0.876977i | \(0.659556\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.35793 | −0.962312 | −0.481156 | − | 0.876635i | \(-0.659783\pi\) | ||||
−0.481156 | + | 0.876635i | \(0.659783\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.47283 | −0.430465 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.114908 | 0.0194229 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.64207 | 0.434354 | 0.217177 | − | 0.976132i | \(-0.430315\pi\) | ||||
0.217177 | + | 0.976132i | \(0.430315\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.47283 | 0.395970 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.79811 | −1.37403 | −0.687017 | − | 0.726641i | \(-0.741080\pi\) | ||||
−0.687017 | + | 0.726641i | \(0.741080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.34472 | 1.42506 | 0.712528 | − | 0.701643i | \(-0.247550\pi\) | ||||
0.712528 | + | 0.701643i | \(0.247550\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.357926 | −0.0533565 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.51396 | −0.804294 | −0.402147 | − | 0.915575i | \(-0.631736\pi\) | ||||
−0.402147 | + | 0.915575i | \(0.631736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14.4185 | −2.01899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.0062 | −1.78654 | −0.893272 | − | 0.449516i | \(-0.851597\pi\) | ||||
−0.893272 | + | 0.449516i | \(0.851597\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.114908 | 0.0154941 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.81756 | 0.903007 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.92622 | 0.511150 | 0.255575 | − | 0.966789i | \(-0.417735\pi\) | ||||
0.255575 | + | 0.966789i | \(0.417735\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.11491 | 0.654897 | 0.327448 | − | 0.944869i | \(-0.393811\pi\) | ||||
0.327448 | + | 0.944869i | \(0.393811\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.11491 | −0.392441 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.114908 | −0.0142525 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.75698 | −0.703327 | −0.351664 | − | 0.936126i | \(-0.614384\pi\) | ||||
−0.351664 | + | 0.936126i | \(0.614384\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.44018 | 1.13646 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.83076 | −1.04802 | −0.524009 | − | 0.851713i | \(-0.675564\pi\) | ||||
−0.524009 | + | 0.851713i | \(0.675564\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.4596 | −1.69237 | −0.846186 | − | 0.532888i | \(-0.821107\pi\) | ||||
−0.846186 | + | 0.532888i | \(0.821107\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.3315 | −1.42392 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.64832 | 0.973012 | 0.486506 | − | 0.873677i | \(-0.338271\pi\) | ||||
0.486506 | + | 0.873677i | \(0.338271\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.64207 | −0.960230 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.93246 | 1.09023 | 0.545115 | − | 0.838361i | \(-0.316486\pi\) | ||||
0.545115 | + | 0.838361i | \(0.316486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.669998 | 0.0726715 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.7981 | −1.37210 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9868 | 1.27060 | 0.635299 | − | 0.772266i | \(-0.280877\pi\) | ||||
0.635299 | + | 0.772266i | \(0.280877\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.2493 | −1.37388 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.316798 | −0.0325028 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.73530 | −0.176193 | −0.0880965 | − | 0.996112i | \(-0.528078\pi\) | ||||
−0.0880965 | + | 0.996112i | \(0.528078\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.11491 | −0.313060 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.52717 | −0.450470 | −0.225235 | − | 0.974304i | \(-0.572315\pi\) | ||||
−0.225235 | + | 0.974304i | \(0.572315\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.56829 | −0.647193 | −0.323597 | − | 0.946195i | \(-0.604892\pi\) | ||||
−0.323597 | + | 0.946195i | \(0.604892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.284147 | 0.0277299 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.7500 | −1.42594 | −0.712969 | − | 0.701195i | \(-0.752650\pi\) | ||||
−0.712969 | + | 0.701195i | \(0.752650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9868 | 1.43547 | 0.717737 | − | 0.696314i | \(-0.245178\pi\) | ||||
0.717737 | + | 0.696314i | \(0.245178\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.53341 | 0.620124 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.1692 | −1.23886 | −0.619429 | − | 0.785053i | \(-0.712636\pi\) | ||||
−0.619429 | + | 0.785053i | \(0.712636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.438666 | −0.0409058 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.11491 | 0.287973 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.83076 | 0.534505 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21.7563 | −1.96170 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.14756 | 0.102641 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8238 | −1.04919 | −0.524596 | − | 0.851351i | \(-0.675784\pi\) | ||||
−0.524596 | + | 0.851351i | \(0.675784\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.1079 | 2.03454 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.60719 | 0.752014 | 0.376007 | − | 0.926617i | \(-0.377297\pi\) | ||||
0.376007 | + | 0.926617i | \(0.377297\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.75698 | −0.239061 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0326507 | −0.00281012 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.78963 | −0.409206 | −0.204603 | − | 0.978845i | \(-0.565590\pi\) | ||||
−0.204603 | + | 0.978845i | \(0.565590\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.71585 | 0.230356 | 0.115178 | − | 0.993345i | \(-0.463256\pi\) | ||||
0.115178 | + | 0.993345i | \(0.463256\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.6351 | −1.14828 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.594702 | 0.0493873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.47283 | 0.203956 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.9325 | 1.14139 | 0.570696 | − | 0.821161i | \(-0.306673\pi\) | ||||
0.570696 | + | 0.821161i | \(0.306673\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.338479 | −0.0275451 | −0.0137725 | − | 0.999905i | \(-0.504384\pi\) | ||||
−0.0137725 | + | 0.999905i | \(0.504384\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.1623 | −1.46833 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.615666 | 0.0494515 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4247 | 1.31084 | 0.655419 | − | 0.755266i | \(-0.272492\pi\) | ||||
0.655419 | + | 0.755266i | \(0.272492\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −32.1623 | −2.55063 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.81756 | −0.300866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.527166 | −0.0412908 | −0.0206454 | − | 0.999787i | \(-0.506572\pi\) | ||||
−0.0206454 | + | 0.999787i | \(0.506572\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.284147 | 0.0221208 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.65528 | −0.515001 | −0.257500 | − | 0.966278i | \(-0.582899\pi\) | ||||
−0.257500 | + | 0.966278i | \(0.582899\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.58774 | 0.656721 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.1623 | −1.53291 | −0.766455 | − | 0.642298i | \(-0.777981\pi\) | ||||
−0.766455 | + | 0.642298i | \(0.777981\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.98680 | 0.376966 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.70889 | 0.729765 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.7089 | −1.92157 | −0.960786 | − | 0.277290i | \(-0.910564\pi\) | ||||
−0.960786 | + | 0.277290i | \(0.910564\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3315 | 1.28824 | 0.644121 | − | 0.764924i | \(-0.277223\pi\) | ||||
0.644121 | + | 0.764924i | \(0.277223\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.6483 | 0.934990 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.303594 | −0.0223207 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.83076 | 0.426387 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.284147 | −0.0206687 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.10170 | 0.369146 | 0.184573 | − | 0.982819i | \(-0.440910\pi\) | ||||
0.184573 | + | 0.982819i | \(0.440910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.96735 | −0.645484 | −0.322742 | − | 0.946487i | \(-0.604605\pi\) | ||||
−0.322742 | + | 0.946487i | \(0.604605\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.284147 | −0.0203482 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3726 | 0.881515 | 0.440757 | − | 0.897626i | \(-0.354710\pi\) | ||||
0.440757 | + | 0.897626i | \(0.354710\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.2555 | −1.36499 | −0.682493 | − | 0.730892i | \(-0.739104\pi\) | ||||
−0.682493 | + | 0.730892i | \(0.739104\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.2361 | −1.00413 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.17548 | 0.363248 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.01097 | 0.0706091 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.8913 | 0.826505 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.75698 | −0.190704 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5745 | 1.07220 | 0.536098 | − | 0.844156i | \(-0.319898\pi\) | ||||
0.536098 | + | 0.844156i | \(0.319898\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.8370 | −1.49625 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.07378 | −0.0732311 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.35793 | 0.363720 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −35.7563 | −2.41618 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.83076 | −0.392219 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.680967 | −0.0456010 | −0.0228005 | − | 0.999740i | \(-0.507258\pi\) | ||||
−0.0228005 | + | 0.999740i | \(0.507258\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.5334 | −1.03556 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.6134 | 1.30179 | 0.650895 | − | 0.759168i | \(-0.274394\pi\) | ||||
0.650895 | + | 0.759168i | \(0.274394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.80435 | −0.317481 | −0.158740 | − | 0.987320i | \(-0.550743\pi\) | ||||
−0.158740 | + | 0.987320i | \(0.550743\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.47283 | 0.162701 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.0823 | −0.922559 | −0.461280 | − | 0.887255i | \(-0.652610\pi\) | ||||
−0.461280 | + | 0.887255i | \(0.652610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.633596 | 0.0413312 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.3859 | 1.38916 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.8370 | 1.34783 | 0.673917 | − | 0.738807i | \(-0.264611\pi\) | ||||
0.673917 | + | 0.738807i | \(0.264611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5140 | −0.741680 | −0.370840 | − | 0.928697i | \(-0.620930\pi\) | ||||
−0.370840 | + | 0.928697i | \(0.620930\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.2229 | −1.42560 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.114908 | −0.00734117 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.75698 | 0.175423 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 24.5613 | 1.55651 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.4270 | −1.16310 | −0.581550 | − | 0.813510i | \(-0.697554\pi\) | ||||
−0.581550 | + | 0.813510i | \(0.697554\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.81756 | −0.240008 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.65679 | 0.103753 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2966 | −0.704665 | −0.352332 | − | 0.935875i | \(-0.614611\pi\) | ||||
−0.352332 | + | 0.935875i | \(0.614611\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.64207 | −0.164170 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.1212 | −0.997874 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3921 | 0.887455 | 0.443727 | − | 0.896162i | \(-0.353656\pi\) | ||||
0.443727 | + | 0.896162i | \(0.353656\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.49452 | 0.0918074 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29.6414 | 1.81402 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.5683 | 1.25407 | 0.627036 | − | 0.778991i | \(-0.284268\pi\) | ||||
0.627036 | + | 0.778991i | \(0.284268\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.694171 | −0.0421679 | −0.0210839 | − | 0.999778i | \(-0.506712\pi\) | ||||
−0.0210839 | + | 0.999778i | \(0.506712\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.47283 | −0.149663 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.98680 | 0.300715 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.4053 | −1.40629 | −0.703144 | − | 0.711047i | \(-0.748221\pi\) | ||||
−0.703144 | + | 0.711047i | \(0.748221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.6894 | −0.999171 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.9255 | −1.42728 | −0.713638 | − | 0.700515i | \(-0.752954\pi\) | ||||
−0.713638 | + | 0.700515i | \(0.752954\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5264 | 0.804064 | 0.402032 | − | 0.915626i | \(-0.368304\pi\) | ||||
0.402032 | + | 0.915626i | \(0.368304\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.783389 | −0.0464039 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.79811 | 0.519336 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9978 | 0.999869 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.29111 | −0.251549 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.40530 | −0.198940 | −0.0994698 | − | 0.995041i | \(-0.531715\pi\) | ||||
−0.0994698 | + | 0.995041i | \(0.531715\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.451152 | −0.0262671 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.284147 | −0.0164879 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.81756 | 0.220775 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.34472 | −0.538621 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.1949 | −0.643132 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.587741 | −0.0336540 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.91302 | −0.337474 | −0.168737 | − | 0.985661i | \(-0.553969\pi\) | ||||
−0.168737 | + | 0.985661i | \(0.553969\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.2423 | −0.923992 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.0411 | −1.47666 | −0.738328 | − | 0.674441i | \(-0.764385\pi\) | ||||
−0.738328 | + | 0.674441i | \(0.764385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6810 | −0.716771 | −0.358385 | − | 0.933574i | \(-0.616673\pi\) | ||||
−0.358385 | + | 0.933574i | \(0.616673\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.357926 | 0.0201669 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.64207 | −0.373056 | −0.186528 | − | 0.982450i | \(-0.559724\pi\) | ||||
−0.186528 | + | 0.982450i | \(0.559724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.17548 | 0.289771 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −36.4744 | −2.03580 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0753 | −0.894453 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.98680 | −0.276618 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 37.0599 | 2.04941 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.51396 | 0.303995 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.88509 | −0.213544 | −0.106772 | − | 0.994284i | \(-0.534051\pi\) | ||||
−0.106772 | + | 0.994284i | \(0.534051\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.22982 | 0.450991 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.661521 | 0.0361427 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6506 | 0.580173 | 0.290086 | − | 0.957001i | \(-0.406316\pi\) | ||||
0.290086 | + | 0.957001i | \(0.406316\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −32.5653 | −1.76871 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.35793 | 0.290148 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.08475 | −0.0584009 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.01320 | 0.161757 | 0.0808786 | − | 0.996724i | \(-0.474227\pi\) | ||||
0.0808786 | + | 0.996724i | \(0.474227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.16300 | −0.383426 | −0.191713 | − | 0.981451i | \(-0.561404\pi\) | ||||
−0.191713 | + | 0.981451i | \(0.561404\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.284147 | 0.0151667 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.2229 | 1.55538 | 0.777688 | − | 0.628651i | \(-0.216392\pi\) | ||||
0.777688 | + | 0.628651i | \(0.216392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.01472 | 0.0538558 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.4185 | 0.763108 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.3246 | 1.38936 | 0.694679 | − | 0.719320i | \(-0.255547\pi\) | ||||
0.694679 | + | 0.719320i | \(0.255547\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3991 | −0.599950 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.47283 | 0.129790 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.66152 | 0.0869680 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.85021 | 0.148780 | 0.0743898 | − | 0.997229i | \(-0.476299\pi\) | ||||
0.0743898 | + | 0.997229i | \(0.476299\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.4053 | −1.42666 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0062 | 0.675251 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.1057 | 1.61059 | 0.805296 | − | 0.592872i | \(-0.202006\pi\) | ||||
0.805296 | + | 0.592872i | \(0.202006\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.83772 | 0.146539 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.17548 | −0.266551 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.9170 | −0.817603 | −0.408801 | − | 0.912623i | \(-0.634053\pi\) | ||||
−0.408801 | + | 0.912623i | \(0.634053\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.2383 | −1.49792 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.3983 | 0.837916 | 0.418958 | − | 0.908006i | \(-0.362395\pi\) | ||||
0.418958 | + | 0.908006i | \(0.362395\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.114908 | −0.00585623 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.1079 | 1.47964 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.4270 | −1.33990 | −0.669951 | − | 0.742406i | \(-0.733685\pi\) | ||||
−0.669951 | + | 0.742406i | \(0.733685\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.2593 | −1.12570 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.2841 | 1.07364 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.993757 | −0.0500013 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.5202 | 1.13026 | 0.565128 | − | 0.825003i | \(-0.308827\pi\) | ||||
0.565128 | + | 0.825003i | \(0.308827\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.81756 | −0.341305 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0404 | −0.751082 | −0.375541 | − | 0.926806i | \(-0.622543\pi\) | ||||
−0.375541 | + | 0.926806i | \(0.622543\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.35793 | −0.266897 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.993039 | 0.0493445 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.64207 | −0.130963 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.3664 | −1.05650 | −0.528250 | − | 0.849089i | \(-0.677152\pi\) | ||||
−0.528250 | + | 0.849089i | \(0.677152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.8440 | −0.584220 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.92622 | −0.193197 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.14132 | −0.0560250 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.71585 | 0.328877 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.69569 | −0.278253 | −0.139126 | − | 0.990275i | \(-0.544429\pi\) | ||||
−0.139126 | + | 0.990275i | \(0.544429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0558 | −0.977462 | −0.488731 | − | 0.872434i | \(-0.662540\pi\) | ||||
−0.488731 | + | 0.872434i | \(0.662540\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.1755 | −0.835101 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.0768 | 1.41043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.11491 | −0.247528 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.47283 | −0.119390 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.86341 | 0.426935 | 0.213468 | − | 0.976950i | \(-0.431524\pi\) | ||||
0.213468 | + | 0.976950i | \(0.431524\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.2897 | 1.35951 | 0.679757 | − | 0.733437i | \(-0.262085\pi\) | ||||
0.679757 | + | 0.733437i | \(0.262085\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.47060 | 0.0705098 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.5249 | 0.503476 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.33848 | −0.207064 | −0.103532 | − | 0.994626i | \(-0.533014\pi\) | ||||
−0.103532 | + | 0.994626i | \(0.533014\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.11491 | 0.148329 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.57677 | −0.407495 | −0.203747 | − | 0.979023i | \(-0.565312\pi\) | ||||
−0.203747 | + | 0.979023i | \(0.565312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.37737 | −0.0652938 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 34.4527 | 1.62956 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.3594 | −1.62152 | −0.810761 | − | 0.585377i | \(-0.800946\pi\) | ||||
−0.810761 | + | 0.585377i | \(0.800946\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.79811 | 0.414287 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.837003 | −0.0393259 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.114908 | 0.00538695 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.1234 | −0.473552 | −0.236776 | − | 0.971564i | \(-0.576091\pi\) | ||||
−0.236776 | + | 0.971564i | \(0.576091\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.65679 | −0.0773325 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.2577 | 1.54897 | 0.774484 | − | 0.632594i | \(-0.218010\pi\) | ||||
0.774484 | + | 0.632594i | \(0.218010\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.1281 | −1.44665 | −0.723323 | − | 0.690510i | \(-0.757386\pi\) | ||||
−0.723323 | + | 0.690510i | \(0.757386\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.52244 | 0.0706015 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.36417 | −0.387048 | −0.193524 | − | 0.981096i | \(-0.561992\pi\) | ||||
−0.193524 | + | 0.981096i | \(0.561992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.75698 | 0.265833 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 40.6157 | 1.87147 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.34472 | −0.429671 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.7485 | −0.630825 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −40.5132 | −1.85497 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.9045 | 0.589623 | 0.294812 | − | 0.955555i | \(-0.404743\pi\) | ||||
0.294812 | + | 0.955555i | \(0.404743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.64207 | 0.120468 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.44018 | −0.429543 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.199399 | 0.00905424 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.4402 | −0.699661 | −0.349831 | − | 0.936813i | \(-0.613761\pi\) | ||||
−0.349831 | + | 0.936813i | \(0.613761\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.30359 | −0.0589506 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.7159 | 1.02515 | 0.512576 | − | 0.858642i | \(-0.328691\pi\) | ||||
0.512576 | + | 0.858642i | \(0.328691\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.1770 | 1.35910 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.357926 | 0.0160876 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.83076 | 0.396114 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.7974 | 1.60251 | 0.801256 | − | 0.598322i | \(-0.204166\pi\) | ||||
0.801256 | + | 0.598322i | \(0.204166\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.4574 | −0.735262 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.5264 | −0.513939 | −0.256969 | − | 0.966420i | \(-0.582724\pi\) | ||||
−0.256969 | + | 0.966420i | \(0.582724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.520206 | 0.0231488 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.47283 | 0.109822 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.373365 | −0.0165491 | −0.00827455 | − | 0.999966i | \(-0.502634\pi\) | ||||
−0.00827455 | + | 0.999966i | \(0.502634\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.4596 | 0.639656 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.783389 | 0.0345875 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.754747 | 0.0332581 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.51396 | 0.242504 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −49.8580 | −2.18852 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.8734 | 1.22116 | 0.610578 | − | 0.791956i | \(-0.290937\pi\) | ||||
0.610578 | + | 0.791956i | \(0.290937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.6894 | −1.60432 | −0.802159 | − | 0.597111i | \(-0.796315\pi\) | ||||
−0.802159 | + | 0.597111i | \(0.796315\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.3315 | 0.538192 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.2408 | 1.36087 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.42626 | −0.366359 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.2298 | 0.530729 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.79811 | −0.381088 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.69489 | 0.0732764 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −63.5738 | −2.74341 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.7827 | 1.62440 | 0.812202 | − | 0.583376i | \(-0.198269\pi\) | ||||
0.812202 | + | 0.583376i | \(0.198269\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 42.8580 | 1.83921 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.72210 | −0.0737665 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.754747 | 0.0322706 | 0.0161353 | − | 0.999870i | \(-0.494864\pi\) | ||||
0.0161353 | + | 0.999870i | \(0.494864\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.9325 | 0.679981 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.2687 | −0.607867 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.64832 | −0.367764 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.750738 | −0.0318671 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.1079 | 0.555402 | 0.277701 | − | 0.960668i | \(-0.410428\pi\) | ||||
0.277701 | + | 0.960668i | \(0.410428\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.34472 | 0.395240 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.4185 | 0.608750 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.5918 | −1.33143 | −0.665717 | − | 0.746205i | \(-0.731874\pi\) | ||||
−0.665717 | + | 0.746205i | \(0.731874\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.51324 | 0.0636627 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.64207 | 0.362933 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.59470 | −0.276464 | −0.138232 | − | 0.990400i | \(-0.544142\pi\) | ||||
−0.138232 | + | 0.990400i | \(0.544142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.8781 | 1.29221 | 0.646105 | − | 0.763249i | \(-0.276397\pi\) | ||||
0.646105 | + | 0.763249i | \(0.276397\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.6157 | 0.527027 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.0374 | −0.793913 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.28343 | 0.136691 | 0.0683455 | − | 0.997662i | \(-0.478228\pi\) | ||||
0.0683455 | + | 0.997662i | \(0.478228\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.1748 | −0.921552 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.93246 | −0.412068 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.0062 | 0.538664 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.357926 | −0.0147984 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.12115 | 0.170098 | 0.0850490 | − | 0.996377i | \(-0.472895\pi\) | ||||
0.0850490 | + | 0.996377i | \(0.472895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.7717 | −0.608657 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.5955 | 1.25853 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −46.1600 | −1.89557 | −0.947783 | − | 0.318916i | \(-0.896681\pi\) | ||||
−0.947783 | + | 0.318916i | \(0.896681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.669998 | −0.0274673 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −47.6157 | −1.94878 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.3635 | 0.995464 | 0.497732 | − | 0.867331i | \(-0.334166\pi\) | ||||
0.497732 | + | 0.867331i | \(0.334166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.4115 | −0.751022 | −0.375511 | − | 0.926818i | \(-0.622533\pi\) | ||||
−0.375511 | + | 0.926818i | \(0.622533\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.9325 | −0.730266 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.114908 | −0.00467166 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.6630 | −0.919864 | −0.459932 | − | 0.887954i | \(-0.652126\pi\) | ||||
−0.459932 | + | 0.887954i | \(0.652126\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.7981 | 0.518606 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.51396 | −0.223071 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.4068 | 1.38968 | 0.694839 | − | 0.719165i | \(-0.255476\pi\) | ||||
0.694839 | + | 0.719165i | \(0.255476\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.49996 | 0.100808 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.6630 | −1.07341 | −0.536707 | − | 0.843769i | \(-0.680332\pi\) | ||||
−0.536707 | + | 0.843769i | \(0.680332\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.2772 | −1.37772 | −0.688858 | − | 0.724896i | \(-0.741888\pi\) | ||||
−0.688858 | + | 0.724896i | \(0.741888\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08475 | 0.0435294 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.9868 | −0.480241 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8021 | 0.992085 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.81756 | −0.272267 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.4053 | −0.614249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.9215 | −0.474587 | −0.237294 | − | 0.971438i | \(-0.576260\pi\) | ||||
−0.237294 | + | 0.971438i | \(0.576260\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 38.5132 | 1.53076 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.35864 | 0.0539161 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.5070 | −1.08816 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.9729 | 1.73682 | 0.868412 | − | 0.495843i | \(-0.165141\pi\) | ||||
0.868412 | + | 0.495843i | \(0.165141\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.3983 | 1.35654 | 0.678269 | − | 0.734814i | \(-0.262730\pi\) | ||||
0.678269 | + | 0.734814i | \(0.262730\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.65528 | −0.104551 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.6964 | −1.01023 | −0.505115 | − | 0.863052i | \(-0.668550\pi\) | ||||
−0.505115 | + | 0.863052i | \(0.668550\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.92622 | −0.154118 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.2493 | 0.519280 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.1857 | 1.72912 | 0.864561 | − | 0.502528i | \(-0.167597\pi\) | ||||
0.864561 | + | 0.502528i | \(0.167597\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.989031 | −0.0386446 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −45.0404 | −1.75719 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.7346 | −1.62575 | −0.812874 | − | 0.582439i | \(-0.802098\pi\) | ||||
−0.812874 | + | 0.582439i | \(0.802098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.1538 | 1.32843 | 0.664214 | − | 0.747542i | \(-0.268766\pi\) | ||||
0.664214 | + | 0.747542i | \(0.268766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.4185 | −0.559968 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.316798 | 0.0122849 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.7577 | −0.765021 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.68392 | −0.0651041 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.11491 | −0.197459 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.41627 | −0.247329 | −0.123664 | − | 0.992324i | \(-0.539465\pi\) | ||||
−0.123664 | + | 0.992324i | \(0.539465\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.41698 | −0.0545398 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.9798 | 1.80558 | 0.902791 | − | 0.430080i | \(-0.141515\pi\) | ||||
0.902791 | + | 0.430080i | \(0.141515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.73530 | 0.0665947 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.5008 | 1.85855 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.31832 | −0.356555 | −0.178278 | − | 0.983980i | \(-0.557053\pi\) | ||||
−0.178278 | + | 0.983980i | \(0.557053\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.550365 | 0.0210284 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.8804 | −0.453264 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.0062 | −0.495498 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.93871 | −0.149835 | −0.0749177 | − | 0.997190i | \(-0.523869\pi\) | ||||
−0.0749177 | + | 0.997190i | \(0.523869\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.11491 | 0.118326 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.312072 | −0.0118376 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 51.2997 | 1.94311 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −34.8231 | −1.31713 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.3928 | −0.505840 | −0.252920 | − | 0.967487i | \(-0.581391\pi\) | ||||
−0.252920 | + | 0.967487i | \(0.581391\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.28415 | 0.274727 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.56678 | 0.0590082 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.52717 | 0.170262 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.3176 | 1.40149 | 0.700746 | − | 0.713411i | \(-0.252851\pi\) | ||||
0.700746 | + | 0.713411i | \(0.252851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.9387 | 1.01028 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.4542 | −0.766015 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.114908 | 0.00429730 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 51.5264 | 1.92429 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.69168 | 0.286851 | 0.143426 | − | 0.989661i | \(-0.454188\pi\) | ||||
0.143426 | + | 0.989661i | \(0.454188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.56829 | 0.244616 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.4721 | −1.05889 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.8091 | 0.958525 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.3587 | 1.68226 | 0.841131 | − | 0.540831i | \(-0.181890\pi\) | ||||
0.841131 | + | 0.540831i | \(0.181890\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.0272 | −1.07508 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.4868 | −2.01527 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.75626 | −0.138741 | −0.0693704 | − | 0.997591i | \(-0.522099\pi\) | ||||
−0.0693704 | + | 0.997591i | \(0.522099\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.284147 | −0.0104809 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.75698 | 0.212061 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.3246 | 0.968365 | 0.484182 | − | 0.874967i | \(-0.339117\pi\) | ||||
0.484182 | + | 0.874967i | \(0.339117\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.81756 | 0.250449 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.9193 | 0.547335 | 0.273667 | − | 0.961824i | \(-0.411763\pi\) | ||||
0.273667 | + | 0.961824i | \(0.411763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.60095 | −0.0586541 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.9387 | 1.13199 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.7500 | 0.538954 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.3425 | −1.25318 | −0.626588 | − | 0.779351i | \(-0.715549\pi\) | ||||
−0.626588 | + | 0.779351i | \(0.715549\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −45.5669 | −1.66055 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.0388938 | 0.00141549 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.2320 | −0.371890 | −0.185945 | − | 0.982560i | \(-0.559535\pi\) | ||||
−0.185945 | + | 0.982560i | \(0.559535\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.44018 | −0.342657 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.9582 | 0.977232 | 0.488616 | − | 0.872499i | \(-0.337502\pi\) | ||||
0.488616 | + | 0.872499i | \(0.337502\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.9868 | −0.542558 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.08698 | 0.0754550 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.92622 | 0.141768 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.0265 | 1.76794 | 0.883970 | − | 0.467543i | \(-0.154861\pi\) | ||||
0.883970 | + | 0.467543i | \(0.154861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.9347 | −1.00604 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 52.3587 | 1.88321 | 0.941606 | − | 0.336716i | \(-0.109316\pi\) | ||||
0.941606 | + | 0.336716i | \(0.109316\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.7189 | 0.959771 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.53341 | −0.234385 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.2562 | −0.869069 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.83076 | 0.315989 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.47060 | −0.0525549 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.88733 | −0.0673616 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.6414 | −0.664493 | −0.332246 | − | 0.943193i | \(-0.607807\pi\) | ||||
−0.332246 | + | 0.943193i | \(0.607807\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 35.5893 | 1.26701 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.1692 | 0.468244 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.11491 | 0.181636 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.69569 | 0.131073 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.1421 | −0.571783 | −0.285892 | − | 0.958262i | \(-0.592290\pi\) | ||||
−0.285892 | + | 0.958262i | \(0.592290\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.1506 | 1.13741 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37.3378 | 1.31926 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.4596 | 0.510269 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.438666 | 0.0154609 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 50.8620 | 1.79043 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.8121 | 1.89193 | 0.945967 | − | 0.324264i | \(-0.105117\pi\) | ||||
0.945967 | + | 0.324264i | \(0.105117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.7306 | 1.00887 | 0.504433 | − | 0.863451i | \(-0.331701\pi\) | ||||
0.504433 | + | 0.863451i | \(0.331701\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.71657 | −0.0602027 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.0605754 | 0.00212186 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.7632 | 0.901341 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.11491 | −0.108844 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.87412 | −0.344609 | −0.172305 | − | 0.985044i | \(-0.555121\pi\) | ||||
−0.172305 | + | 0.985044i | \(0.555121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.5459 | 0.507038 | 0.253519 | − | 0.967330i | \(-0.418412\pi\) | ||||
0.253519 | + | 0.967330i | \(0.418412\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.3315 | 0.429328 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.6894 | 0.441255 | 0.220628 | − | 0.975358i | \(-0.429189\pi\) | ||||
0.220628 | + | 0.975358i | \(0.429189\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.2104 | 0.528278 | 0.264139 | − | 0.964485i | \(-0.414912\pi\) | ||||
0.264139 | + | 0.964485i | \(0.414912\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.8774 | −2.00775 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.83076 | −0.202024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.764742 | 0.0264650 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.52244 | −0.0526232 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.14060 | −0.315568 | −0.157784 | − | 0.987474i | \(-0.550435\pi\) | ||||
−0.157784 | + | 0.987474i | \(0.550435\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.21438 | −0.0763578 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −59.1638 | −2.03771 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.114908 | −0.00395294 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33.4487 | 1.14796 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.0863 | 0.345753 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.34000 | 0.251317 | 0.125658 | − | 0.992074i | \(-0.459896\pi\) | ||||
0.125658 | + | 0.992074i | \(0.459896\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.986796 | −0.0337477 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.7820 | 1.32477 | 0.662383 | − | 0.749165i | \(-0.269545\pi\) | ||||
0.662383 | + | 0.749165i | \(0.269545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.0474 | −1.36640 | −0.683199 | − | 0.730232i | \(-0.739412\pi\) | ||||
−0.683199 | + | 0.730232i | \(0.739412\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.7563 | 0.741451 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.7827 | −0.401087 | −0.200543 | − | 0.979685i | \(-0.564271\pi\) | ||||
−0.200543 | + | 0.979685i | \(0.564271\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.31680 | 0.0787735 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.0327 | 1.42750 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.64832 | −0.293374 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.75698 | −0.195068 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.40530 | −0.182942 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.14756 | −0.0387945 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.57302 | −0.154420 | −0.0772100 | − | 0.997015i | \(-0.524601\pi\) | ||||
−0.0772100 | + | 0.997015i | \(0.524601\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.42074 | −0.284024 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.31903 | −0.246584 | −0.123292 | − | 0.992370i | \(-0.539345\pi\) | ||||
−0.123292 | + | 0.992370i | \(0.539345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.0947 | 1.28199 | 0.640995 | − | 0.767545i | \(-0.278522\pi\) | ||||
0.640995 | + | 0.767545i | \(0.278522\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.11562 | −0.0375013 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.9721 | −0.435560 | −0.217780 | − | 0.975998i | \(-0.569881\pi\) | ||||
−0.217780 | + | 0.975998i | \(0.569881\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.8238 | 0.396558 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.64207 | 0.289520 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.2019 | −0.508712 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.95415 | 0.0987462 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.44018 | 0.315199 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.7299 | 0.924842 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 75.8363 | 2.52647 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.1079 | −0.768984 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.99152 | −0.0662004 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.3744 | −1.37382 | −0.686908 | − | 0.726745i | \(-0.741032\pi\) | ||||
−0.686908 | + | 0.726745i | \(0.741032\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.1017 | −0.467724 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.47212 | 0.0819049 | 0.0409524 | − | 0.999161i | \(-0.486961\pi\) | ||||
0.0409524 | + | 0.999161i | \(0.486961\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.93246 | −0.328717 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.45339 | −0.0480475 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.60719 | −0.284234 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.5885 | 0.514216 | 0.257108 | − | 0.966383i | \(-0.417230\pi\) | ||||
0.257108 | + | 0.966383i | \(0.417230\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.6219 | −0.481808 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.83076 | −0.290668 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.1755 | −0.433207 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.4596 | −0.671982 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.7391 | 1.04132 | 0.520662 | − | 0.853763i | \(-0.325685\pi\) | ||||
0.520662 | + | 0.853763i | \(0.325685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.75698 | 0.0903564 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −64.3954 | −2.10821 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.669998 | −0.0219113 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.9993 | −0.882028 | −0.441014 | − | 0.897500i | \(-0.645381\pi\) | ||||
−0.441014 | + | 0.897500i | \(0.645381\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.3579 | −1.02333 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.40530 | −0.241406 | −0.120703 | − | 0.992689i | \(-0.538515\pi\) | ||||
−0.120703 | + | 0.992689i | \(0.538515\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.5873 | −1.09375 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0326507 | 0.00106213 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.37514 | −0.174669 | −0.0873343 | − | 0.996179i | \(-0.527835\pi\) | ||||
−0.0873343 | + | 0.996179i | \(0.527835\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.4596 | −0.469379 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.4247 | −0.532609 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.2577 | −1.72519 | −0.862594 | − | 0.505897i | \(-0.831161\pi\) | ||||
−0.862594 | + | 0.505897i | \(0.831161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.586224 | −0.0189698 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.7981 | 0.413704 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.78963 | 0.154665 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.29263 | −0.0739556 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.9450 | −1.48056 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.03042 | 0.0331703 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.7019 | −0.344151 | −0.172075 | − | 0.985084i | \(-0.555047\pi\) | ||||
−0.172075 | + | 0.985084i | \(0.555047\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −39.7515 | −1.27700 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.5452 | −1.84671 | −0.923356 | − | 0.383944i | \(-0.874566\pi\) | ||||
−0.923356 | + | 0.383944i | \(0.874566\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.71585 | −0.0870662 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.3315 | −0.394925 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.7214 | 1.07884 | 0.539421 | − | 0.842036i | \(-0.318643\pi\) | ||||
0.539421 | + | 0.842036i | \(0.318643\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.9868 | −0.383100 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.6825 | 1.49046 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.3734 | −0.458439 | −0.229220 | − | 0.973375i | \(-0.573617\pi\) | ||||
−0.229220 | + | 0.973375i | \(0.573617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.42171 | −0.0452995 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.6351 | 0.434010 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.6740 | 1.13437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.60719 | −0.304875 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.21260 | 0.0701442 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6050 | 0.905928 | 0.452964 | − | 0.891529i | \(-0.350367\pi\) | ||||
0.452964 | + | 0.891529i | \(0.350367\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.750738 | 0.0237523 |
(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 | 8008.2.a.i.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.i.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial |