Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.53209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.53209 | 1.79046 | 0.895229 | − | 0.445607i | \(-0.147012\pi\) | ||||
0.895229 | + | 0.445607i | \(0.147012\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.41147 | 2.20574 | ||||||||
\(5\) | 0.879385 | 0.393273 | 0.196637 | − | 0.980476i | \(-0.436998\pi\) | ||||
0.196637 | + | 0.980476i | \(0.436998\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 6.10607 | 2.15882 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.22668 | 0.704139 | ||||||||
\(11\) | 3.87939 | 1.16968 | 0.584839 | − | 0.811149i | \(-0.301158\pi\) | ||||
0.584839 | + | 0.811149i | \(0.301158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.45336 | 1.51249 | 0.756245 | − | 0.654288i | \(-0.227032\pi\) | ||||
0.756245 | + | 0.654288i | \(0.227032\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.63816 | 1.65954 | ||||||||
\(17\) | −1.65270 | −0.400840 | −0.200420 | − | 0.979710i | \(-0.564231\pi\) | ||||
−0.200420 | + | 0.979710i | \(0.564231\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.41147 | −0.553230 | −0.276615 | − | 0.960981i | \(-0.589213\pi\) | ||||
−0.276615 | + | 0.960981i | \(0.589213\pi\) | |||||||
\(20\) | 3.87939 | 0.867457 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.82295 | 2.09426 | ||||||||
\(23\) | 3.16250 | 0.659428 | 0.329714 | − | 0.944081i | \(-0.393048\pi\) | ||||
0.329714 | + | 0.944081i | \(0.393048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.22668 | −0.845336 | ||||||||
\(26\) | 13.8084 | 2.70805 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.04963 | −1.12339 | −0.561694 | − | 0.827345i | \(-0.689850\pi\) | ||||
−0.561694 | + | 0.827345i | \(0.689850\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.55438 | 0.817990 | 0.408995 | − | 0.912537i | \(-0.365879\pi\) | ||||
0.408995 | + | 0.912537i | \(0.365879\pi\) | |||||||
\(32\) | 4.59627 | 0.812513 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.18479 | −0.717686 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.55438 | −0.748735 | −0.374368 | − | 0.927280i | \(-0.622140\pi\) | ||||
−0.374368 | + | 0.927280i | \(0.622140\pi\) | |||||||
\(38\) | −6.10607 | −0.990535 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.36959 | 0.849006 | ||||||||
\(41\) | 1.18479 | 0.185034 | 0.0925168 | − | 0.995711i | \(-0.470509\pi\) | ||||
0.0925168 | + | 0.995711i | \(0.470509\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.184793 | 0.0281806 | 0.0140903 | − | 0.999901i | \(-0.495515\pi\) | ||||
0.0140903 | + | 0.999901i | \(0.495515\pi\) | |||||||
\(44\) | 17.1138 | 2.58000 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.00774 | 1.18068 | ||||||||
\(47\) | 1.02229 | 0.149116 | 0.0745581 | − | 0.997217i | \(-0.476245\pi\) | ||||
0.0745581 | + | 0.997217i | \(0.476245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −10.7023 | −1.51354 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 24.0574 | 3.33616 | ||||||||
\(53\) | 7.29086 | 1.00148 | 0.500738 | − | 0.865599i | \(-0.333062\pi\) | ||||
0.500738 | + | 0.865599i | \(0.333062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.41147 | 0.460003 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15.3182 | −2.01138 | ||||||||
\(59\) | −6.66044 | −0.867116 | −0.433558 | − | 0.901126i | \(-0.642742\pi\) | ||||
−0.433558 | + | 0.901126i | \(0.642742\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.59627 | 0.332418 | 0.166209 | − | 0.986091i | \(-0.446847\pi\) | ||||
0.166209 | + | 0.986091i | \(0.446847\pi\) | |||||||
\(62\) | 11.5321 | 1.46458 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.63816 | −0.204769 | ||||||||
\(65\) | 4.79561 | 0.594822 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.95811 | −0.361391 | −0.180695 | − | 0.983539i | \(-0.557835\pi\) | ||||
−0.180695 | + | 0.983539i | \(0.557835\pi\) | |||||||
\(68\) | −7.29086 | −0.884147 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.68004 | −0.436741 | −0.218370 | − | 0.975866i | \(-0.570074\pi\) | ||||
−0.218370 | + | 0.975866i | \(0.570074\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7811 | 1.49591 | 0.747955 | − | 0.663750i | \(-0.231036\pi\) | ||||
0.747955 | + | 0.663750i | \(0.231036\pi\) | |||||||
\(74\) | −11.5321 | −1.34058 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.6382 | −1.22028 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.95811 | −0.670340 | −0.335170 | − | 0.942158i | \(-0.608794\pi\) | ||||
−0.335170 | + | 0.942158i | \(0.608794\pi\) | |||||||
\(80\) | 5.83750 | 0.652652 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | 0.331295 | ||||||||
\(83\) | 0.218941 | 0.0240319 | 0.0120159 | − | 0.999928i | \(-0.496175\pi\) | ||||
0.0120159 | + | 0.999928i | \(0.496175\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.45336 | −0.157639 | ||||||||
\(86\) | 0.467911 | 0.0504562 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 23.6878 | 2.52513 | ||||||||
\(89\) | −11.0273 | −1.16890 | −0.584448 | − | 0.811431i | \(-0.698689\pi\) | ||||
−0.584448 | + | 0.811431i | \(0.698689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 13.9513 | 1.45452 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.58853 | 0.266986 | ||||||||
\(95\) | −2.12061 | −0.217570 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.5030 | −1.26949 | −0.634743 | − | 0.772723i | \(-0.718894\pi\) | ||||
−0.634743 | + | 0.772723i | \(0.718894\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.6459 | −1.86459 | ||||||||
\(101\) | 9.71688 | 0.966866 | 0.483433 | − | 0.875381i | \(-0.339390\pi\) | ||||
0.483433 | + | 0.875381i | \(0.339390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.59627 | −0.649949 | −0.324975 | − | 0.945723i | \(-0.605356\pi\) | ||||
−0.324975 | + | 0.945723i | \(0.605356\pi\) | |||||||
\(104\) | 33.2986 | 3.26520 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.4611 | 1.79310 | ||||||||
\(107\) | 2.38919 | 0.230971 | 0.115486 | − | 0.993309i | \(-0.463158\pi\) | ||||
0.115486 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.95811 | 0.379118 | 0.189559 | − | 0.981869i | \(-0.439294\pi\) | ||||
0.189559 | + | 0.981869i | \(0.439294\pi\) | |||||||
\(110\) | 8.63816 | 0.823616 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.4534 | 1.54780 | 0.773901 | − | 0.633306i | \(-0.218303\pi\) | ||||
0.773901 | + | 0.633306i | \(0.218303\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.78106 | 0.259335 | ||||||||
\(116\) | −26.6878 | −2.47790 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.8648 | −1.55253 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.04963 | 0.368148 | ||||||||
\(122\) | 6.57398 | 0.595180 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 20.0915 | 1.80427 | ||||||||
\(125\) | −8.11381 | −0.725721 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6536 | 1.56651 | 0.783253 | − | 0.621702i | \(-0.213559\pi\) | ||||
0.783253 | + | 0.621702i | \(0.213559\pi\) | |||||||
\(128\) | −13.3405 | −1.17914 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.1429 | 1.06500 | ||||||||
\(131\) | 19.1976 | 1.67730 | 0.838650 | − | 0.544670i | \(-0.183345\pi\) | ||||
0.838650 | + | 0.544670i | \(0.183345\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.49020 | −0.647055 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.0915 | −0.865341 | ||||||||
\(137\) | 18.1557 | 1.55115 | 0.775573 | − | 0.631258i | \(-0.217461\pi\) | ||||
0.775573 | + | 0.631258i | \(0.217461\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.0574 | −1.87088 | −0.935441 | − | 0.353483i | \(-0.884997\pi\) | ||||
−0.935441 | + | 0.353483i | \(0.884997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.31820 | −0.781966 | ||||||||
\(143\) | 21.1557 | 1.76913 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.31996 | −0.441798 | ||||||||
\(146\) | 32.3628 | 2.67836 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −20.0915 | −1.65151 | ||||||||
\(149\) | −15.1557 | −1.24160 | −0.620802 | − | 0.783968i | \(-0.713193\pi\) | ||||
−0.620802 | + | 0.783968i | \(0.713193\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.9564 | −1.54265 | −0.771323 | − | 0.636444i | \(-0.780405\pi\) | ||||
−0.771323 | + | 0.636444i | \(0.780405\pi\) | |||||||
\(152\) | −14.7246 | −1.19432 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00505 | 0.321694 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.0574 | 1.44114 | 0.720568 | − | 0.693385i | \(-0.243881\pi\) | ||||
0.720568 | + | 0.693385i | \(0.243881\pi\) | |||||||
\(158\) | −15.0865 | −1.20021 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.04189 | 0.319539 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.958111 | 0.0750450 | 0.0375225 | − | 0.999296i | \(-0.488053\pi\) | ||||
0.0375225 | + | 0.999296i | \(0.488053\pi\) | |||||||
\(164\) | 5.22668 | 0.408135 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.554378 | 0.0430280 | ||||||||
\(167\) | −19.8384 | −1.53514 | −0.767572 | − | 0.640963i | \(-0.778535\pi\) | ||||
−0.767572 | + | 0.640963i | \(0.778535\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.7392 | 1.28763 | ||||||||
\(170\) | −3.68004 | −0.282247 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.815207 | 0.0621590 | ||||||||
\(173\) | −22.6827 | −1.72454 | −0.862268 | − | 0.506452i | \(-0.830957\pi\) | ||||
−0.862268 | + | 0.506452i | \(0.830957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.7520 | 1.94113 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −27.9222 | −2.09286 | ||||||||
\(179\) | −7.34730 | −0.549163 | −0.274581 | − | 0.961564i | \(-0.588539\pi\) | ||||
−0.274581 | + | 0.961564i | \(0.588539\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.44562 | 0.256111 | 0.128056 | − | 0.991767i | \(-0.459126\pi\) | ||||
0.128056 | + | 0.991767i | \(0.459126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 19.3105 | 1.42359 | ||||||||
\(185\) | −4.00505 | −0.294457 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.41147 | −0.468853 | ||||||||
\(188\) | 4.50980 | 0.328911 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.36959 | −0.389551 | ||||||||
\(191\) | 5.65776 | 0.409381 | 0.204690 | − | 0.978827i | \(-0.434381\pi\) | ||||
0.204690 | + | 0.978827i | \(0.434381\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.59627 | 0.690754 | 0.345377 | − | 0.938464i | \(-0.387751\pi\) | ||||
0.345377 | + | 0.938464i | \(0.387751\pi\) | |||||||
\(194\) | −31.6587 | −2.27296 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.31996 | 0.592772 | 0.296386 | − | 0.955068i | \(-0.404218\pi\) | ||||
0.296386 | + | 0.955068i | \(0.404218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.59627 | −0.467597 | −0.233798 | − | 0.972285i | \(-0.575116\pi\) | ||||
−0.233798 | + | 0.972285i | \(0.575116\pi\) | |||||||
\(200\) | −25.8084 | −1.82493 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.6040 | 1.73113 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.04189 | 0.0727687 | ||||||||
\(206\) | −16.7023 | −1.16371 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 36.2003 | 2.51004 | ||||||||
\(209\) | −9.35504 | −0.647101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.36959 | −0.231972 | −0.115986 | − | 0.993251i | \(-0.537003\pi\) | ||||
−0.115986 | + | 0.993251i | \(0.537003\pi\) | |||||||
\(212\) | 32.1634 | 2.20899 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.04963 | 0.413544 | ||||||||
\(215\) | 0.162504 | 0.0110827 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0223 | 0.678795 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15.0496 | 1.01465 | ||||||||
\(221\) | −9.01279 | −0.606266 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.27631 | 0.420293 | 0.210146 | − | 0.977670i | \(-0.432606\pi\) | ||||
0.210146 | + | 0.977670i | \(0.432606\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 41.6614 | 2.77127 | ||||||||
\(227\) | 6.16250 | 0.409020 | 0.204510 | − | 0.978865i | \(-0.434440\pi\) | ||||
0.204510 | + | 0.978865i | \(0.434440\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.3851 | −1.54533 | −0.772664 | − | 0.634815i | \(-0.781076\pi\) | ||||
−0.772664 | + | 0.634815i | \(0.781076\pi\) | |||||||
\(230\) | 7.04189 | 0.464328 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −36.9394 | −2.42519 | ||||||||
\(233\) | −8.52528 | −0.558510 | −0.279255 | − | 0.960217i | \(-0.590087\pi\) | ||||
−0.279255 | + | 0.960217i | \(0.590087\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.898986 | 0.0586434 | ||||||||
\(236\) | −29.3824 | −1.91263 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5621 | 0.941945 | 0.470973 | − | 0.882148i | \(-0.343903\pi\) | ||||
0.470973 | + | 0.882148i | \(0.343903\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.40373 | 0.348085 | 0.174043 | − | 0.984738i | \(-0.444317\pi\) | ||||
0.174043 | + | 0.984738i | \(0.444317\pi\) | |||||||
\(242\) | 10.2540 | 0.659154 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.4534 | 0.733226 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1506 | −0.836755 | ||||||||
\(248\) | 27.8093 | 1.76589 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −20.5449 | −1.29937 | ||||||||
\(251\) | 12.0669 | 0.761654 | 0.380827 | − | 0.924646i | \(-0.375639\pi\) | ||||
0.380827 | + | 0.924646i | \(0.375639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2686 | 0.771318 | ||||||||
\(254\) | 44.7006 | 2.80476 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30.5030 | −1.90644 | ||||||||
\(257\) | −10.5662 | −0.659104 | −0.329552 | − | 0.944137i | \(-0.606898\pi\) | ||||
−0.329552 | + | 0.944137i | \(0.606898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 21.1557 | 1.31202 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 48.6100 | 3.00314 | ||||||||
\(263\) | −28.3533 | −1.74834 | −0.874169 | − | 0.485622i | \(-0.838593\pi\) | ||||
−0.874169 | + | 0.485622i | \(0.838593\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.41147 | 0.393854 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.0496 | −0.797133 | ||||||||
\(269\) | −7.48339 | −0.456271 | −0.228135 | − | 0.973629i | \(-0.573263\pi\) | ||||
−0.228135 | + | 0.973629i | \(0.573263\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6382 | −0.828459 | −0.414229 | − | 0.910172i | \(-0.635949\pi\) | ||||
−0.414229 | + | 0.910172i | \(0.635949\pi\) | |||||||
\(272\) | −10.9709 | −0.665209 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 45.9718 | 2.77726 | ||||||||
\(275\) | −16.3969 | −0.988772 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.15064 | −0.369556 | −0.184778 | − | 0.982780i | \(-0.559157\pi\) | ||||
−0.184778 | + | 0.982780i | \(0.559157\pi\) | |||||||
\(278\) | −55.8512 | −3.34973 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.31221 | 0.197590 | 0.0987951 | − | 0.995108i | \(-0.468501\pi\) | ||||
0.0987951 | + | 0.995108i | \(0.468501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.0232 | −1.72525 | −0.862626 | − | 0.505843i | \(-0.831182\pi\) | ||||
−0.862626 | + | 0.505843i | \(0.831182\pi\) | |||||||
\(284\) | −16.2344 | −0.963336 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 53.5681 | 3.16755 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.2686 | −0.839328 | ||||||||
\(290\) | −13.4706 | −0.791021 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 56.3833 | 3.29958 | ||||||||
\(293\) | 8.41921 | 0.491856 | 0.245928 | − | 0.969288i | \(-0.420907\pi\) | ||||
0.245928 | + | 0.969288i | \(0.420907\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.85710 | −0.341013 | ||||||||
\(296\) | −27.8093 | −1.61638 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −38.3756 | −2.22304 | ||||||||
\(299\) | 17.2463 | 0.997378 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −47.9992 | −2.76204 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.0077 | −0.918107 | ||||||||
\(305\) | 2.28312 | 0.130731 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.6878 | 0.724130 | 0.362065 | − | 0.932153i | \(-0.382072\pi\) | ||||
0.362065 | + | 0.932153i | \(0.382072\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.1411 | 0.575979 | ||||||||
\(311\) | 16.4902 | 0.935073 | 0.467537 | − | 0.883974i | \(-0.345142\pi\) | ||||
0.467537 | + | 0.883974i | \(0.345142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.5185 | −1.61196 | −0.805980 | − | 0.591943i | \(-0.798361\pi\) | ||||
−0.805980 | + | 0.591943i | \(0.798361\pi\) | |||||||
\(314\) | 45.7229 | 2.58029 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.2841 | −1.47859 | ||||||||
\(317\) | −25.8949 | −1.45440 | −0.727200 | − | 0.686425i | \(-0.759179\pi\) | ||||
−0.727200 | + | 0.686425i | \(0.759179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.4688 | −1.31400 | ||||||||
\(320\) | −1.44057 | −0.0805303 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.98545 | 0.221756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.0496 | −1.27856 | ||||||||
\(326\) | 2.42602 | 0.134365 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.23442 | 0.399454 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.21894 | 0.451754 | 0.225877 | − | 0.974156i | \(-0.427475\pi\) | ||||
0.225877 | + | 0.974156i | \(0.427475\pi\) | |||||||
\(332\) | 0.965852 | 0.0530080 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −50.2327 | −2.74861 | ||||||||
\(335\) | −2.60132 | −0.142125 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.57129 | 0.249014 | 0.124507 | − | 0.992219i | \(-0.460265\pi\) | ||||
0.124507 | + | 0.992219i | \(0.460265\pi\) | |||||||
\(338\) | 42.3851 | 2.30544 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.41147 | −0.347711 | ||||||||
\(341\) | 17.6682 | 0.956786 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.12836 | 0.0608369 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −57.4347 | −3.08771 | ||||||||
\(347\) | 22.4662 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0993 | −1.39706 | −0.698531 | − | 0.715580i | \(-0.746162\pi\) | ||||
−0.698531 | + | 0.715580i | \(0.746162\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 17.8307 | 0.950379 | ||||||||
\(353\) | 0.355037 | 0.0188967 | 0.00944836 | − | 0.999955i | \(-0.496992\pi\) | ||||
0.00944836 | + | 0.999955i | \(0.496992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.23618 | −0.171758 | ||||||||
\(356\) | −48.6468 | −2.57828 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.6040 | −0.983252 | ||||||||
\(359\) | 5.45605 | 0.287959 | 0.143980 | − | 0.989581i | \(-0.454010\pi\) | ||||
0.143980 | + | 0.989581i | \(0.454010\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1848 | −0.693936 | ||||||||
\(362\) | 8.72462 | 0.458556 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.2395 | 0.588301 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.9240 | −0.570226 | −0.285113 | − | 0.958494i | \(-0.592031\pi\) | ||||
−0.285113 | + | 0.958494i | \(0.592031\pi\) | |||||||
\(368\) | 20.9932 | 1.09435 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.1411 | −0.527213 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.73143 | 0.0896500 | 0.0448250 | − | 0.998995i | \(-0.485727\pi\) | ||||
0.0448250 | + | 0.998995i | \(0.485727\pi\) | |||||||
\(374\) | −16.2344 | −0.839462 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.24216 | 0.321915 | ||||||||
\(377\) | −32.9908 | −1.69911 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.1334 | −0.623251 | −0.311626 | − | 0.950205i | \(-0.600873\pi\) | ||||
−0.311626 | + | 0.950205i | \(0.600873\pi\) | |||||||
\(380\) | −9.35504 | −0.479903 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.3259 | 0.732979 | ||||||||
\(383\) | 8.71183 | 0.445154 | 0.222577 | − | 0.974915i | \(-0.428553\pi\) | ||||
0.222577 | + | 0.974915i | \(0.428553\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.2986 | 1.23677 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −55.1566 | −2.80015 | ||||||||
\(389\) | 3.64321 | 0.184718 | 0.0923590 | − | 0.995726i | \(-0.470559\pi\) | ||||
0.0923590 | + | 0.995726i | \(0.470559\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.22668 | −0.264325 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 21.0669 | 1.06133 | ||||||||
\(395\) | −5.23947 | −0.263627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.4456 | 0.775194 | 0.387597 | − | 0.921829i | \(-0.373305\pi\) | ||||
0.387597 | + | 0.921829i | \(0.373305\pi\) | |||||||
\(398\) | −16.7023 | −0.837212 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −28.0574 | −1.40287 | ||||||||
\(401\) | 18.4219 | 0.919946 | 0.459973 | − | 0.887933i | \(-0.347859\pi\) | ||||
0.459973 | + | 0.887933i | \(0.347859\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.8367 | 1.23720 | ||||||||
\(404\) | 42.8658 | 2.13265 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.6682 | −0.875779 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.6364 | 1.41598 | 0.707989 | − | 0.706223i | \(-0.249602\pi\) | ||||
0.707989 | + | 0.706223i | \(0.249602\pi\) | |||||||
\(410\) | 2.63816 | 0.130289 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.0993 | −1.43362 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.192533 | 0.00945109 | ||||||||
\(416\) | 25.0651 | 1.22892 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.6878 | −1.15861 | ||||||||
\(419\) | 34.6955 | 1.69499 | 0.847494 | − | 0.530805i | \(-0.178111\pi\) | ||||
0.847494 | + | 0.530805i | \(0.178111\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.4020 | −1.33549 | −0.667745 | − | 0.744390i | \(-0.732740\pi\) | ||||
−0.667745 | + | 0.744390i | \(0.732740\pi\) | |||||||
\(422\) | −8.53209 | −0.415336 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 44.5185 | 2.16201 | ||||||||
\(425\) | 6.98545 | 0.338844 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.5398 | 0.509462 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.411474 | 0.0198430 | ||||||||
\(431\) | 26.5921 | 1.28090 | 0.640449 | − | 0.768000i | \(-0.278748\pi\) | ||||
0.640449 | + | 0.768000i | \(0.278748\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.1830 | −1.78690 | −0.893451 | − | 0.449160i | \(-0.851723\pi\) | ||||
−0.893451 | + | 0.449160i | \(0.851723\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.4611 | 0.836235 | ||||||||
\(437\) | −7.62630 | −0.364815 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.0746 | −1.19675 | −0.598373 | − | 0.801218i | \(-0.704186\pi\) | ||||
−0.598373 | + | 0.801218i | \(0.704186\pi\) | |||||||
\(440\) | 20.8307 | 0.993064 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.8212 | −1.08549 | ||||||||
\(443\) | 2.04458 | 0.0971408 | 0.0485704 | − | 0.998820i | \(-0.484533\pi\) | ||||
0.0485704 | + | 0.998820i | \(0.484533\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.69728 | −0.459695 | ||||||||
\(446\) | 15.8922 | 0.752516 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.2344 | −0.482992 | −0.241496 | − | 0.970402i | \(-0.577638\pi\) | ||||
−0.241496 | + | 0.970402i | \(0.577638\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.59627 | 0.216430 | ||||||||
\(452\) | 72.5836 | 3.41404 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.6040 | 0.732332 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −42.5945 | −1.99249 | −0.996244 | − | 0.0865948i | \(-0.972401\pi\) | ||||
−0.996244 | + | 0.0865948i | \(0.972401\pi\) | |||||||
\(458\) | −59.2131 | −2.76684 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.2686 | 0.572025 | ||||||||
\(461\) | −0.504748 | −0.0235084 | −0.0117542 | − | 0.999931i | \(-0.503742\pi\) | ||||
−0.0117542 | + | 0.999931i | \(0.503742\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.68004 | 0.124552 | 0.0622761 | − | 0.998059i | \(-0.480164\pi\) | ||||
0.0622761 | + | 0.998059i | \(0.480164\pi\) | |||||||
\(464\) | −40.1584 | −1.86431 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.5868 | −0.999988 | ||||||||
\(467\) | 31.4165 | 1.45378 | 0.726892 | − | 0.686752i | \(-0.240964\pi\) | ||||
0.726892 | + | 0.686752i | \(0.240964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.27631 | 0.104998 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −40.6691 | −1.87195 | ||||||||
\(473\) | 0.716881 | 0.0329622 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.1925 | 0.467666 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 36.8726 | 1.68651 | ||||||||
\(479\) | 16.4406 | 0.751189 | 0.375594 | − | 0.926784i | \(-0.377439\pi\) | ||||
0.375594 | + | 0.926784i | \(0.377439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.8367 | −1.13245 | ||||||||
\(482\) | 13.6827 | 0.623231 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.8648 | 0.812038 | ||||||||
\(485\) | −10.9949 | −0.499255 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.97535 | −0.134826 | −0.0674129 | − | 0.997725i | \(-0.521474\pi\) | ||||
−0.0674129 | + | 0.997725i | \(0.521474\pi\) | |||||||
\(488\) | 15.8530 | 0.717631 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.4861 | −1.19530 | −0.597650 | − | 0.801757i | \(-0.703899\pi\) | ||||
−0.597650 | + | 0.801757i | \(0.703899\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.99825 | 0.450298 | ||||||||
\(494\) | −33.2986 | −1.49817 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.2327 | 1.35749 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4439 | −0.601830 | −0.300915 | − | 0.953651i | \(-0.597292\pi\) | ||||
−0.300915 | + | 0.953651i | \(0.597292\pi\) | |||||||
\(500\) | −35.7939 | −1.60075 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 30.5544 | 1.36371 | ||||||||
\(503\) | 22.6631 | 1.01050 | 0.505250 | − | 0.862973i | \(-0.331400\pi\) | ||||
0.505250 | + | 0.862973i | \(0.331400\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.54488 | 0.380242 | ||||||||
\(506\) | 31.0651 | 1.38101 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 77.8786 | 3.45530 | ||||||||
\(509\) | −9.54757 | −0.423189 | −0.211594 | − | 0.977358i | \(-0.567866\pi\) | ||||
−0.211594 | + | 0.977358i | \(0.567866\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −50.5553 | −2.23425 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.7547 | −1.18010 | ||||||||
\(515\) | −5.80066 | −0.255608 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.96585 | 0.174418 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 29.2823 | 1.28411 | ||||||||
\(521\) | 3.11287 | 0.136377 | 0.0681887 | − | 0.997672i | \(-0.478278\pi\) | ||||
0.0681887 | + | 0.997672i | \(0.478278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.1489 | 0.706142 | 0.353071 | − | 0.935597i | \(-0.385137\pi\) | ||||
0.353071 | + | 0.935597i | \(0.385137\pi\) | |||||||
\(524\) | 84.6897 | 3.69968 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −71.7930 | −3.13032 | ||||||||
\(527\) | −7.52704 | −0.327883 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.9986 | −0.565155 | ||||||||
\(530\) | 16.2344 | 0.705178 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.46110 | 0.279861 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.10101 | 0.0908348 | ||||||||
\(536\) | −18.0624 | −0.780178 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.9486 | −0.816933 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.01548 | −0.215632 | −0.107816 | − | 0.994171i | \(-0.534386\pi\) | ||||
−0.107816 | + | 0.994171i | \(0.534386\pi\) | |||||||
\(542\) | −34.5330 | −1.48332 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.59627 | −0.325687 | ||||||||
\(545\) | 3.48070 | 0.149097 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4780 | 0.704549 | 0.352275 | − | 0.935897i | \(-0.385408\pi\) | ||||
0.352275 | + | 0.935897i | \(0.385408\pi\) | |||||||
\(548\) | 80.0934 | 3.42142 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −41.5185 | −1.77035 | ||||||||
\(551\) | 14.5885 | 0.621492 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15.5740 | −0.661675 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −97.3055 | −4.12667 | ||||||||
\(557\) | −34.5631 | −1.46448 | −0.732242 | − | 0.681045i | \(-0.761526\pi\) | ||||
−0.732242 | + | 0.681045i | \(0.761526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00774 | 0.0426229 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.38682 | 0.353777 | ||||||||
\(563\) | 37.2104 | 1.56823 | 0.784115 | − | 0.620615i | \(-0.213117\pi\) | ||||
0.784115 | + | 0.620615i | \(0.213117\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.4688 | 0.608709 | ||||||||
\(566\) | −73.4894 | −3.08899 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.4706 | −0.942845 | ||||||||
\(569\) | 0.404667 | 0.0169645 | 0.00848226 | − | 0.999964i | \(-0.497300\pi\) | ||||
0.00848226 | + | 0.999964i | \(0.497300\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.7793 | −1.58101 | −0.790507 | − | 0.612453i | \(-0.790183\pi\) | ||||
−0.790507 | + | 0.612453i | \(0.790183\pi\) | |||||||
\(572\) | 93.3278 | 3.90223 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.3669 | −0.557438 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.21120 | 0.0920535 | 0.0460267 | − | 0.998940i | \(-0.485344\pi\) | ||||
0.0460267 | + | 0.998940i | \(0.485344\pi\) | |||||||
\(578\) | −36.1293 | −1.50278 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −23.4688 | −0.974491 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.2841 | 1.17141 | ||||||||
\(584\) | 78.0420 | 3.22940 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.3182 | 0.880647 | ||||||||
\(587\) | −24.2098 | −0.999244 | −0.499622 | − | 0.866243i | \(-0.666528\pi\) | ||||
−0.499622 | + | 0.866243i | \(0.666528\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.9828 | −0.452537 | ||||||||
\(590\) | −14.8307 | −0.610570 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.2327 | −1.24255 | ||||||||
\(593\) | −12.2385 | −0.502577 | −0.251288 | − | 0.967912i | \(-0.580854\pi\) | ||||
−0.251288 | + | 0.967912i | \(0.580854\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −66.8590 | −2.73865 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 43.6691 | 1.78576 | ||||||||
\(599\) | 39.6168 | 1.61870 | 0.809349 | − | 0.587328i | \(-0.199820\pi\) | ||||
0.809349 | + | 0.587328i | \(0.199820\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.0077 | 1.22404 | 0.612021 | − | 0.790842i | \(-0.290357\pi\) | ||||
0.612021 | + | 0.790842i | \(0.290357\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −83.6255 | −3.40267 | ||||||||
\(605\) | 3.56118 | 0.144783 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.4843 | 0.790844 | 0.395422 | − | 0.918499i | \(-0.370598\pi\) | ||||
0.395422 | + | 0.918499i | \(0.370598\pi\) | |||||||
\(608\) | −11.0838 | −0.449507 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.78106 | 0.234068 | ||||||||
\(611\) | 5.57491 | 0.225537 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.5276 | −0.748325 | −0.374162 | − | 0.927363i | \(-0.622070\pi\) | ||||
−0.374162 | + | 0.927363i | \(0.622070\pi\) | |||||||
\(614\) | 32.1266 | 1.29652 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.8402 | 1.12080 | 0.560402 | − | 0.828221i | \(-0.310647\pi\) | ||||
0.560402 | + | 0.828221i | \(0.310647\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.9813 | 1.80795 | 0.903976 | − | 0.427583i | \(-0.140635\pi\) | ||||
0.903976 | + | 0.427583i | \(0.140635\pi\) | |||||||
\(620\) | 17.6682 | 0.709571 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 41.7547 | 1.67421 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.9982 | 0.559930 | ||||||||
\(626\) | −72.2113 | −2.88614 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 79.6596 | 3.17877 | ||||||||
\(629\) | 7.52704 | 0.300123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.43613 | 0.375646 | 0.187823 | − | 0.982203i | \(-0.439857\pi\) | ||||
0.187823 | + | 0.982203i | \(0.439857\pi\) | |||||||
\(632\) | −36.3806 | −1.44714 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −65.5681 | −2.60404 | ||||||||
\(635\) | 15.5243 | 0.616065 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −59.4252 | −2.35267 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.7314 | −0.463725 | ||||||||
\(641\) | 37.3901 | 1.47682 | 0.738410 | − | 0.674352i | \(-0.235577\pi\) | ||||
0.738410 | + | 0.674352i | \(0.235577\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.61175 | −0.0635611 | −0.0317806 | − | 0.999495i | \(-0.510118\pi\) | ||||
−0.0317806 | + | 0.999495i | \(0.510118\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.0915 | 0.397046 | ||||||||
\(647\) | 41.1762 | 1.61880 | 0.809402 | − | 0.587255i | \(-0.199791\pi\) | ||||
0.809402 | + | 0.587255i | \(0.199791\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.8384 | −1.01425 | ||||||||
\(650\) | −58.3637 | −2.28921 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.22668 | 0.165530 | ||||||||
\(653\) | 3.05199 | 0.119434 | 0.0597169 | − | 0.998215i | \(-0.480980\pi\) | ||||
0.0597169 | + | 0.998215i | \(0.480980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.8821 | 0.659637 | ||||||||
\(656\) | 7.86484 | 0.307070 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.6350 | 1.62187 | 0.810934 | − | 0.585138i | \(-0.198959\pi\) | ||||
0.810934 | + | 0.585138i | \(0.198959\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.3010 | −0.789616 | −0.394808 | − | 0.918764i | \(-0.629189\pi\) | ||||
−0.394808 | + | 0.918764i | \(0.629189\pi\) | |||||||
\(662\) | 20.8111 | 0.808846 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.33687 | 0.0518805 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.1320 | −0.740793 | ||||||||
\(668\) | −87.5167 | −3.38612 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.58677 | −0.254469 | ||||||||
\(671\) | 10.0719 | 0.388822 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.830689 | −0.0320207 | −0.0160104 | − | 0.999872i | \(-0.505096\pi\) | ||||
−0.0160104 | + | 0.999872i | \(0.505096\pi\) | |||||||
\(674\) | 11.5749 | 0.445849 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 73.8444 | 2.84017 | ||||||||
\(677\) | −10.8672 | −0.417660 | −0.208830 | − | 0.977952i | \(-0.566966\pi\) | ||||
−0.208830 | + | 0.977952i | \(0.566966\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.87433 | −0.340315 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 44.7374 | 1.71308 | ||||||||
\(683\) | 32.6946 | 1.25102 | 0.625512 | − | 0.780215i | \(-0.284890\pi\) | ||||
0.625512 | + | 0.780215i | \(0.284890\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.9659 | 0.610024 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.22668 | 0.0467668 | ||||||||
\(689\) | 39.7597 | 1.51472 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.9982 | −0.570560 | −0.285280 | − | 0.958444i | \(-0.592087\pi\) | ||||
−0.285280 | + | 0.958444i | \(0.592087\pi\) | |||||||
\(692\) | −100.064 | −3.80387 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 56.8863 | 2.15937 | ||||||||
\(695\) | −19.3969 | −0.735767 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.95811 | −0.0741687 | ||||||||
\(698\) | −66.0856 | −2.50138 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.4688 | 0.999714 | 0.499857 | − | 0.866108i | \(-0.333386\pi\) | ||||
0.499857 | + | 0.866108i | \(0.333386\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.9828 | 0.414223 | ||||||||
\(704\) | −6.35504 | −0.239514 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.898986 | 0.0338338 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.3601 | 0.576860 | 0.288430 | − | 0.957501i | \(-0.406867\pi\) | ||||
0.288430 | + | 0.957501i | \(0.406867\pi\) | |||||||
\(710\) | −8.19429 | −0.307526 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −67.3337 | −2.52344 | ||||||||
\(713\) | 14.4032 | 0.539405 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.6040 | 0.695750 | ||||||||
\(716\) | −32.4124 | −1.21131 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.8152 | 0.515579 | ||||||||
\(719\) | −26.7306 | −0.996883 | −0.498442 | − | 0.866923i | \(-0.666094\pi\) | ||||
−0.498442 | + | 0.866923i | \(0.666094\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −33.3851 | −1.24246 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.2003 | 0.564914 | ||||||||
\(725\) | 25.5699 | 0.949641 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.6441 | 1.69285 | 0.846424 | − | 0.532510i | \(-0.178751\pi\) | ||||
0.846424 | + | 0.532510i | \(0.178751\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 28.4593 | 1.05333 | ||||||||
\(731\) | −0.305407 | −0.0112959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.97502 | −0.220693 | −0.110346 | − | 0.993893i | \(-0.535196\pi\) | ||||
−0.110346 | + | 0.993893i | \(0.535196\pi\) | |||||||
\(734\) | −27.6604 | −1.02097 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.5357 | 0.535793 | ||||||||
\(737\) | −11.4757 | −0.422711 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.5963 | −1.30943 | −0.654715 | − | 0.755876i | \(-0.727211\pi\) | ||||
−0.654715 | + | 0.755876i | \(0.727211\pi\) | |||||||
\(740\) | −17.6682 | −0.649495 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.3087 | −1.07523 | −0.537616 | − | 0.843190i | \(-0.680675\pi\) | ||||
−0.537616 | + | 0.843190i | \(0.680675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.3277 | −0.488289 | ||||||||
\(746\) | 4.38413 | 0.160515 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −28.2841 | −1.03417 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3337 | −0.632515 | −0.316258 | − | 0.948673i | \(-0.602426\pi\) | ||||
−0.316258 | + | 0.948673i | \(0.602426\pi\) | |||||||
\(752\) | 6.78611 | 0.247464 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −83.5357 | −3.04219 | ||||||||
\(755\) | −16.6699 | −0.606681 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.77156 | −0.100734 | −0.0503671 | − | 0.998731i | \(-0.516039\pi\) | ||||
−0.0503671 | + | 0.998731i | \(0.516039\pi\) | |||||||
\(758\) | −30.7229 | −1.11590 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.9486 | −0.469696 | ||||||||
\(761\) | −7.50744 | −0.272144 | −0.136072 | − | 0.990699i | \(-0.543448\pi\) | ||||
−0.136072 | + | 0.990699i | \(0.543448\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 24.9590 | 0.902987 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.0591 | 0.797029 | ||||||||
\(767\) | −36.3218 | −1.31150 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.04364 | −0.0736957 | −0.0368478 | − | 0.999321i | \(-0.511732\pi\) | ||||
−0.0368478 | + | 0.999321i | \(0.511732\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 42.3337 | 1.52362 | ||||||||
\(773\) | 24.9418 | 0.897094 | 0.448547 | − | 0.893759i | \(-0.351942\pi\) | ||||
0.448547 | + | 0.893759i | \(0.351942\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.2499 | −0.691477 | ||||||||
\(776\) | −76.3441 | −2.74059 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.22493 | 0.330730 | ||||||||
\(779\) | −2.85710 | −0.102366 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.2763 | −0.510847 | ||||||||
\(782\) | −13.2344 | −0.473262 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.8794 | 0.566760 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.10700 | −0.253337 | −0.126669 | − | 0.991945i | \(-0.540428\pi\) | ||||
−0.126669 | + | 0.991945i | \(0.540428\pi\) | |||||||
\(788\) | 36.7033 | 1.30750 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.2668 | −0.472012 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.1584 | 0.502779 | ||||||||
\(794\) | 39.1097 | 1.38795 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29.0993 | −1.03140 | ||||||||
\(797\) | −33.6628 | −1.19240 | −0.596199 | − | 0.802837i | \(-0.703323\pi\) | ||||
−0.596199 | + | 0.802837i | \(0.703323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.68954 | −0.0597716 | ||||||||
\(800\) | −19.4270 | −0.686847 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 46.6459 | 1.64712 | ||||||||
\(803\) | 49.5827 | 1.74973 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 62.8887 | 2.21516 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 59.3319 | 2.08729 | ||||||||
\(809\) | −12.8161 | −0.450592 | −0.225296 | − | 0.974290i | \(-0.572335\pi\) | ||||
−0.225296 | + | 0.974290i | \(0.572335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.1239 | 0.917335 | 0.458667 | − | 0.888608i | \(-0.348327\pi\) | ||||
0.458667 | + | 0.888608i | \(0.348327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −44.7374 | −1.56805 | ||||||||
\(815\) | 0.842549 | 0.0295132 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.445622 | −0.0155904 | ||||||||
\(818\) | 72.5099 | 2.53525 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.59627 | 0.160509 | ||||||||
\(821\) | 27.6641 | 0.965483 | 0.482741 | − | 0.875763i | \(-0.339641\pi\) | ||||
0.482741 | + | 0.875763i | \(0.339641\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.8324 | 0.970178 | 0.485089 | − | 0.874465i | \(-0.338787\pi\) | ||||
0.485089 | + | 0.874465i | \(0.338787\pi\) | |||||||
\(824\) | −40.2772 | −1.40312 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.65507 | 0.161873 | 0.0809363 | − | 0.996719i | \(-0.474209\pi\) | ||||
0.0809363 | + | 0.996719i | \(0.474209\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.97359 | 0.346397 | 0.173199 | − | 0.984887i | \(-0.444590\pi\) | ||||
0.173199 | + | 0.984887i | \(0.444590\pi\) | |||||||
\(830\) | 0.487511 | 0.0169218 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.93346 | −0.309712 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.4456 | −0.603731 | ||||||||
\(836\) | −41.2695 | −1.42734 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 87.8522 | 3.03480 | ||||||||
\(839\) | 6.72967 | 0.232334 | 0.116167 | − | 0.993230i | \(-0.462939\pi\) | ||||
0.116167 | + | 0.993230i | \(0.462939\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.59802 | 0.262001 | ||||||||
\(842\) | −69.3842 | −2.39114 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.8648 | −0.511669 | ||||||||
\(845\) | 14.7202 | 0.506390 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 48.3979 | 1.66199 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.6878 | 0.606686 | ||||||||
\(851\) | −14.4032 | −0.493737 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.79055 | −0.198265 | −0.0991324 | − | 0.995074i | \(-0.531607\pi\) | ||||
−0.0991324 | + | 0.995074i | \(0.531607\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.5885 | 0.498626 | ||||||||
\(857\) | 34.9077 | 1.19242 | 0.596211 | − | 0.802827i | \(-0.296672\pi\) | ||||
0.596211 | + | 0.802827i | \(0.296672\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.6149 | 0.430416 | 0.215208 | − | 0.976568i | \(-0.430957\pi\) | ||||
0.215208 | + | 0.976568i | \(0.430957\pi\) | |||||||
\(860\) | 0.716881 | 0.0244455 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 67.3337 | 2.29339 | ||||||||
\(863\) | −24.2053 | −0.823959 | −0.411979 | − | 0.911193i | \(-0.635162\pi\) | ||||
−0.411979 | + | 0.911193i | \(0.635162\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.9469 | −0.678214 | ||||||||
\(866\) | −94.1508 | −3.19937 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.1138 | −0.784082 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.1317 | −0.546600 | ||||||||
\(872\) | 24.1685 | 0.818448 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −19.3105 | −0.653186 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.12567 | −0.0380111 | −0.0190055 | − | 0.999819i | \(-0.506050\pi\) | ||||
−0.0190055 | + | 0.999819i | \(0.506050\pi\) | |||||||
\(878\) | −63.4911 | −2.14272 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22.6459 | 0.763393 | ||||||||
\(881\) | 4.38331 | 0.147678 | 0.0738388 | − | 0.997270i | \(-0.476475\pi\) | ||||
0.0738388 | + | 0.997270i | \(0.476475\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.88949 | −0.231850 | −0.115925 | − | 0.993258i | \(-0.536983\pi\) | ||||
−0.115925 | + | 0.993258i | \(0.536983\pi\) | |||||||
\(884\) | −39.7597 | −1.33726 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.17705 | 0.173926 | ||||||||
\(887\) | −39.0752 | −1.31202 | −0.656009 | − | 0.754753i | \(-0.727757\pi\) | ||||
−0.656009 | + | 0.754753i | \(0.727757\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −24.5544 | −0.823065 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.6878 | 0.927056 | ||||||||
\(893\) | −2.46522 | −0.0824955 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.46110 | −0.215971 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.9145 | −0.864777 | ||||||||
\(899\) | −27.5523 | −0.918921 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0496 | −0.401431 | ||||||||
\(902\) | 11.6382 | 0.387508 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 100.465 | 3.34143 | ||||||||
\(905\) | 3.03003 | 0.100722 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.4938 | 1.41098 | 0.705492 | − | 0.708718i | \(-0.250726\pi\) | ||||
0.705492 | + | 0.708718i | \(0.250726\pi\) | |||||||
\(908\) | 27.1857 | 0.902190 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.4935 | −0.513322 | −0.256661 | − | 0.966501i | \(-0.582622\pi\) | ||||
−0.256661 | + | 0.966501i | \(0.582622\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.849356 | 0.0281096 | ||||||||
\(914\) | −107.853 | −3.56746 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −103.163 | −3.40859 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.52940 | 0.215385 | 0.107693 | − | 0.994184i | \(-0.465654\pi\) | ||||
0.107693 | + | 0.994184i | \(0.465654\pi\) | |||||||
\(920\) | 16.9813 | 0.559858 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.27807 | −0.0420909 | ||||||||
\(923\) | −20.0686 | −0.660567 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.2499 | 0.632933 | ||||||||
\(926\) | 6.78611 | 0.223005 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −27.8057 | −0.912767 | ||||||||
\(929\) | −58.2772 | −1.91201 | −0.956007 | − | 0.293343i | \(-0.905232\pi\) | ||||
−0.956007 | + | 0.293343i | \(0.905232\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −37.6091 | −1.23193 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 79.5494 | 2.60294 | ||||||||
\(935\) | −5.63816 | −0.184387 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.4175 | −1.05903 | −0.529516 | − | 0.848300i | \(-0.677626\pi\) | ||||
−0.529516 | + | 0.848300i | \(0.677626\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.96585 | 0.129352 | ||||||||
\(941\) | 27.3226 | 0.890693 | 0.445346 | − | 0.895358i | \(-0.353081\pi\) | ||||
0.445346 | + | 0.895358i | \(0.353081\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.74691 | 0.122016 | ||||||||
\(944\) | −44.2131 | −1.43901 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.81521 | 0.0590175 | ||||||||
\(947\) | −38.2131 | −1.24176 | −0.620879 | − | 0.783906i | \(-0.713224\pi\) | ||||
−0.620879 | + | 0.783906i | \(0.713224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 69.6998 | 2.26255 | ||||||||
\(950\) | 25.8084 | 0.837335 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.9377 | 1.90918 | 0.954590 | − | 0.297924i | \(-0.0962943\pi\) | ||||
0.954590 | + | 0.297924i | \(0.0962943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.97535 | 0.160998 | ||||||||
\(956\) | 64.2404 | 2.07768 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.6290 | 1.34497 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.2576 | −0.330892 | ||||||||
\(962\) | −62.8887 | −2.02761 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23.8384 | 0.767784 | ||||||||
\(965\) | 8.43882 | 0.271655 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.7187 | 0.794901 | 0.397451 | − | 0.917624i | \(-0.369895\pi\) | ||||
0.397451 | + | 0.917624i | \(0.369895\pi\) | |||||||
\(968\) | 24.7273 | 0.794766 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −27.8402 | −0.893894 | ||||||||
\(971\) | −8.17623 | −0.262388 | −0.131194 | − | 0.991357i | \(-0.541881\pi\) | ||||
−0.131194 | + | 0.991357i | \(0.541881\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.53384 | −0.241400 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.2344 | 0.551660 | ||||||||
\(977\) | −15.8485 | −0.507040 | −0.253520 | − | 0.967330i | \(-0.581588\pi\) | ||||
−0.253520 | + | 0.967330i | \(0.581588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.7793 | −1.36723 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −67.0651 | −2.14013 | ||||||||
\(983\) | −53.3063 | −1.70021 | −0.850104 | − | 0.526615i | \(-0.823461\pi\) | ||||
−0.850104 | + | 0.526615i | \(0.823461\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.31645 | 0.233121 | ||||||||
\(986\) | 25.3164 | 0.806240 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −58.0137 | −1.84566 | ||||||||
\(989\) | 0.584407 | 0.0185831 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.2094 | 1.27730 | 0.638648 | − | 0.769499i | \(-0.279494\pi\) | ||||
0.638648 | + | 0.769499i | \(0.279494\pi\) | |||||||
\(992\) | 20.9331 | 0.664628 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.80066 | −0.183893 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.7202 | −0.909577 | −0.454789 | − | 0.890599i | \(-0.650285\pi\) | ||||
−0.454789 | + | 0.890599i | \(0.650285\pi\) | |||||||
\(998\) | −34.0411 | −1.07755 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))