Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(3583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.3583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3583.8 | ||
Root | \(0.382683 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.3583 |
Dual form | 4032.2.b.p.3583.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.61313i | 1.16863i | 0.811529 | + | 0.584313i | \(0.198636\pi\) | ||||
−0.811529 | + | 0.584313i | \(0.801364\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.61313 | + | 0.414214i | 0.987669 | + | 0.156558i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.77791i | − | 1.32515i | −0.748994 | − | 0.662577i | \(-0.769463\pi\) | ||
0.748994 | − | 0.662577i | \(-0.230537\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.06147i | 0.742515i | 0.928530 | + | 0.371257i | \(0.121073\pi\) | ||||
−0.928530 | + | 0.371257i | \(0.878927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.14386 | −0.950667 | −0.475333 | − | 0.879806i | \(-0.657673\pi\) | ||||
−0.475333 | + | 0.879806i | \(0.657673\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.65685i | 1.59656i | 0.602284 | + | 0.798282i | \(0.294258\pi\) | ||||
−0.602284 | + | 0.798282i | \(0.705742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.82843 | −0.365685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.65685 | 0.679061 | 0.339530 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339530 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.06147 | −0.549856 | −0.274928 | − | 0.961465i | \(-0.588654\pi\) | ||||
−0.274928 | + | 0.961465i | \(0.588654\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.08239 | + | 6.82843i | −0.182958 | + | 1.15421i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.65685 | 1.25878 | 0.629390 | − | 0.777090i | \(-0.283305\pi\) | ||||
0.629390 | + | 0.777090i | \(0.283305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.55582i | 1.49237i | 0.665740 | + | 0.746184i | \(0.268116\pi\) | ||||
−0.665740 | + | 0.746184i | \(0.731884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.65685i | − | 0.557665i | −0.960340 | − | 0.278833i | \(-0.910053\pi\) | ||
0.960340 | − | 0.278833i | \(-0.0899474\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.39104 | 1.07809 | 0.539047 | − | 0.842276i | \(-0.318785\pi\) | ||||
0.539047 | + | 0.842276i | \(0.318785\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.65685 | + | 2.16478i | 0.950979 | + | 0.309255i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.22625 | 0.704708 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.47343 | −1.10315 | −0.551573 | − | 0.834126i | \(-0.685972\pi\) | ||||
−0.551573 | + | 0.834126i | \(0.685972\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.61313i | 0.334576i | 0.985908 | + | 0.167288i | \(0.0535011\pi\) | ||||
−0.985908 | + | 0.167288i | \(0.946499\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.4853 | 1.54861 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.6569i | 1.91279i | 0.292078 | + | 0.956395i | \(0.405653\pi\) | ||||
−0.292078 | + | 0.956395i | \(0.594347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.82843i | − | 1.04774i | −0.851798 | − | 0.523871i | \(-0.824487\pi\) | ||
0.851798 | − | 0.523871i | \(-0.175513\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6173i | 1.47674i | 0.674395 | + | 0.738371i | \(0.264405\pi\) | ||||
−0.674395 | + | 0.738371i | \(0.735595\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.828427 | − | 5.22625i | 0.0944080 | − | 0.595587i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.8284i | − | 1.44331i | −0.692252 | − | 0.721655i | \(-0.743382\pi\) | ||
0.692252 | − | 0.721655i | \(-0.256618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.5349 | 1.26612 | 0.633060 | − | 0.774103i | \(-0.281799\pi\) | ||||
0.633060 | + | 0.774103i | \(0.281799\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.16478i | − | 0.229467i | −0.993396 | − | 0.114733i | \(-0.963399\pi\) | ||
0.993396 | − | 0.114733i | \(-0.0366014\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.97908 | − | 12.4853i | 0.207463 | − | 1.30881i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 10.8284i | − | 1.11097i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5140i | 1.37214i | 0.727537 | + | 0.686068i | \(0.240665\pi\) | ||||
−0.727537 | + | 0.686068i | \(0.759335\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.67459i | 0.564643i | 0.959320 | + | 0.282322i | \(0.0911045\pi\) | ||||
−0.959320 | + | 0.282322i | \(0.908895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9469 | 1.66982 | 0.834912 | − | 0.550384i | \(-0.185519\pi\) | ||||
0.834912 | + | 0.550384i | \(0.185519\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.343146i | 0.0331732i | 0.999862 | + | 0.0165866i | \(0.00527991\pi\) | ||||
−0.999862 | + | 0.0165866i | \(0.994720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.31371 | 0.508961 | 0.254480 | − | 0.967078i | \(-0.418096\pi\) | ||||
0.254480 | + | 0.967078i | \(0.418096\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.82843 | −0.830509 | −0.415254 | − | 0.909705i | \(-0.636307\pi\) | ||||
−0.415254 | + | 0.909705i | \(0.636307\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.0083 | −1.86579 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.26810 | + | 8.00000i | −0.116247 | + | 0.733359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.28772i | 0.741276i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.65685i | 0.324493i | 0.986750 | + | 0.162247i | \(0.0518740\pi\) | ||||
−0.986750 | + | 0.162247i | \(0.948126\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.6997 | −1.19695 | −0.598473 | − | 0.801143i | \(-0.704226\pi\) | ||||
−0.598473 | + | 0.801143i | \(0.704226\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.8284 | − | 1.71644i | −0.938944 | − | 0.148834i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.97908 | −0.167863 | −0.0839315 | − | 0.996472i | \(-0.526748\pi\) | ||||
−0.0839315 | + | 0.996472i | \(0.526748\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.55582 | −0.799098 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.55582i | 0.793568i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.34315i | 0.678956i | 0.940614 | + | 0.339478i | \(0.110250\pi\) | ||||
−0.940614 | + | 0.339478i | \(0.889750\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.00000i | − | 0.642575i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.67459i | 0.452882i | 0.974025 | + | 0.226441i | \(0.0727090\pi\) | ||||
−0.974025 | + | 0.226441i | \(0.927291\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.17157 | + | 20.0083i | −0.249955 | + | 1.57688i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.3137i | − | 1.35611i | −0.735009 | − | 0.678057i | \(-0.762822\pi\) | ||
0.735009 | − | 0.678057i | \(-0.237178\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.49435 | 0.502548 | 0.251274 | − | 0.967916i | \(-0.419150\pi\) | ||||
0.251274 | + | 0.967916i | \(0.419150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.82843 | −0.756033 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9008i | 0.828776i | 0.910100 | + | 0.414388i | \(0.136004\pi\) | ||||
−0.910100 | + | 0.414388i | \(0.863996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.77791 | − | 0.757359i | −0.361176 | − | 0.0572510i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2.00000i | − | 0.149487i | −0.997203 | − | 0.0747435i | \(-0.976186\pi\) | ||
0.997203 | − | 0.0747435i | \(-0.0238138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.71644i | 0.127582i | 0.997963 | + | 0.0637911i | \(0.0203191\pi\) | ||||
−0.997963 | + | 0.0637911i | \(0.979681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.0083i | 1.47104i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.12293 | 0.447753 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.82843i | 0.349373i | 0.984624 | + | 0.174686i | \(0.0558911\pi\) | ||||
−0.984624 | + | 0.174686i | \(0.944109\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.4853 | −0.754747 | −0.377374 | − | 0.926061i | \(-0.623173\pi\) | ||||
−0.377374 | + | 0.926061i | \(0.623173\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.65685 | 0.260540 | 0.130270 | − | 0.991479i | \(-0.458416\pi\) | ||||
0.130270 | + | 0.991479i | \(0.458416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.6173 | −0.894416 | −0.447208 | − | 0.894430i | \(-0.647582\pi\) | ||||
−0.447208 | + | 0.894430i | \(0.647582\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.55582 | + | 1.51472i | 0.670687 | + | 0.106312i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.9706 | −1.74402 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.28772i | 0.573274i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.9706i | 0.755245i | 0.925960 | + | 0.377622i | \(0.123258\pi\) | ||||
−0.925960 | + | 0.377622i | \(0.876742\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.55582 | 0.651702 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | − | 1.26810i | −0.543075 | − | 0.0860843i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.6274 | 0.983947 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.5545 | −1.23151 | −0.615753 | − | 0.787939i | \(-0.711148\pi\) | ||||
−0.615753 | + | 0.787939i | \(0.711148\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.98454i | 0.197224i | 0.995126 | + | 0.0986121i | \(0.0314403\pi\) | ||||
−0.995126 | + | 0.0986121i | \(0.968560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.3137i | 1.25989i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.34315i | − | 0.539673i | −0.962906 | − | 0.269837i | \(-0.913030\pi\) | ||
0.962906 | − | 0.269837i | \(-0.0869697\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.9665i | − | 1.54382i | −0.635734 | − | 0.771908i | \(-0.719302\pi\) | ||
0.635734 | − | 0.771908i | \(-0.280698\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.65685 | + | 17.3952i | −0.361403 | + | 1.11134i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.7990i | 1.25978i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.08239 | −0.0683200 | −0.0341600 | − | 0.999416i | \(-0.510876\pi\) | ||||
−0.0341600 | + | 0.999416i | \(0.510876\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.3137 | 0.962765 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.12293i | 0.381938i | 0.981596 | + | 0.190969i | \(0.0611630\pi\) | ||||
−0.981596 | + | 0.190969i | \(0.938837\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0083 | + | 3.17157i | 1.24326 | + | 0.197072i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.14214i | − | 0.255415i | −0.991812 | − | 0.127708i | \(-0.959238\pi\) | ||
0.991812 | − | 0.127708i | \(-0.0407619\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.22625i | − | 0.321046i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4370i | 0.819271i | 0.912249 | + | 0.409636i | \(0.134344\pi\) | ||||
−0.912249 | + | 0.409636i | \(0.865656\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.79337 | 0.108939 | 0.0544696 | − | 0.998515i | \(-0.482653\pi\) | ||||
0.0544696 | + | 0.998515i | \(0.482653\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.65685i | 0.220517i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.9706 | 1.62050 | 0.810252 | − | 0.586082i | \(-0.199330\pi\) | ||||
0.810252 | + | 0.586082i | \(0.199330\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.6274 | 1.70777 | 0.853884 | − | 0.520463i | \(-0.174241\pi\) | ||||
0.853884 | + | 0.520463i | \(0.174241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.08239 | 0.0643415 | 0.0321708 | − | 0.999482i | \(-0.489758\pi\) | ||||
0.0321708 | + | 0.999482i | \(0.489758\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.95815 | + | 24.9706i | −0.233642 | + | 1.47397i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.62742 | 0.448672 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.67459i | 0.331513i | 0.986167 | + | 0.165757i | \(0.0530066\pi\) | ||||
−0.986167 | + | 0.165757i | \(0.946993\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 22.1421i | − | 1.28916i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.5838 | 2.11569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.51472 | − | 9.55582i | 0.0873069 | − | 0.550788i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.82843 | −0.390995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5349 | −0.658331 | −0.329166 | − | 0.944272i | \(-0.606767\pi\) | ||||
−0.329166 | + | 0.944272i | \(0.606767\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0083 | 1.13457 | 0.567284 | − | 0.823522i | \(-0.307994\pi\) | ||||
0.567284 | + | 0.823522i | \(0.307994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.6788i | 0.886216i | 0.896468 | + | 0.443108i | \(0.146124\pi\) | ||||
−0.896468 | + | 0.443108i | \(0.853876\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.6569 | 1.55336 | 0.776682 | − | 0.629893i | \(-0.216901\pi\) | ||||
0.776682 | + | 0.629893i | \(0.216901\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 7.31371i | − | 0.409489i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 12.6863i | − | 0.705884i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.73606i | 0.484589i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.3137 | + | 3.06147i | 1.06480 | + | 0.168784i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.3137i | − | 0.951647i | −0.879541 | − | 0.475824i | \(-0.842150\pi\) | ||
0.879541 | − | 0.475824i | \(-0.157850\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −40.9133 | −2.23533 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.82843 | 0.480915 | 0.240458 | − | 0.970660i | \(-0.422703\pi\) | ||||
0.240458 | + | 0.970660i | \(0.422703\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.12293i | 0.331576i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4985 | + | 8.41421i | 0.890836 | + | 0.454325i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.6569i | 1.05524i | 0.849482 | + | 0.527618i | \(0.176915\pi\) | ||||
−0.849482 | + | 0.527618i | \(0.823085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.73606i | 0.467631i | 0.972281 | + | 0.233815i | \(0.0751211\pi\) | ||||
−0.972281 | + | 0.233815i | \(0.924879\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 29.5641i | − | 1.57354i | −0.617246 | − | 0.786770i | \(-0.711752\pi\) | ||
0.617246 | − | 0.786770i | \(-0.288248\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.0698 | 1.22442 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 14.9706i | − | 0.790116i | −0.918656 | − | 0.395058i | \(-0.870724\pi\) | ||
0.918656 | − | 0.395058i | \(-0.129276\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.82843 | −0.0962330 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.9706 | −1.72576 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4525 | −0.545616 | −0.272808 | − | 0.962068i | \(-0.587952\pi\) | ||||
−0.272808 | + | 0.962068i | \(0.587952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.22625 | − | 0.828427i | −0.271333 | − | 0.0430098i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.97056 | −0.360922 | −0.180461 | − | 0.983582i | \(-0.557759\pi\) | ||||
−0.180461 | + | 0.983582i | \(0.557759\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 17.4721i | − | 0.899860i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.31371i | 0.272947i | 0.990644 | + | 0.136473i | \(0.0435768\pi\) | ||||
−0.990644 | + | 0.136473i | \(0.956423\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.7206 | −0.598895 | −0.299447 | − | 0.954113i | \(-0.596802\pi\) | ||||
−0.299447 | + | 0.954113i | \(0.596802\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.6569 | + | 2.16478i | 0.696018 | + | 0.110328i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.6569 | 0.996642 | 0.498321 | − | 0.866993i | \(-0.333950\pi\) | ||||
0.498321 | + | 0.866993i | \(0.333950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.4412 | −1.18547 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.5223 | 1.68669 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.9706i | 1.70494i | 0.522778 | + | 0.852469i | \(0.324896\pi\) | ||||
−0.522778 | + | 0.852469i | \(0.675104\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.1716 | 0.757632 | 0.378816 | − | 0.925472i | \(-0.376331\pi\) | ||||
0.378816 | + | 0.925472i | \(0.376331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.6274i | 0.728644i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15.3137i | − | 0.759072i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.896683i | 0.0443381i | 0.999754 | + | 0.0221691i | \(0.00705721\pi\) | ||||
−0.999754 | + | 0.0221691i | \(0.992943\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.1421 | − | 3.50981i | −1.08954 | − | 0.172706i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.1421i | 1.47962i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.6047 | −1.69055 | −0.845275 | − | 0.534332i | \(-0.820563\pi\) | ||||
−0.845275 | + | 0.534332i | \(0.820563\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.3137 | 1.03877 | 0.519383 | − | 0.854541i | \(-0.326162\pi\) | ||||
0.519383 | + | 0.854541i | \(0.326162\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5.59767i | − | 0.271527i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.08239 | + | 6.82843i | −0.0523806 | + | 0.330451i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.3431i | 0.594548i | 0.954792 | + | 0.297274i | \(0.0960775\pi\) | ||||
−0.954792 | + | 0.297274i | \(0.903922\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.59767i | − | 0.269007i | −0.990913 | − | 0.134503i | \(-0.957056\pi\) | ||
0.990913 | − | 0.134503i | \(-0.0429439\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 31.7289i | − | 1.51780i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.5445 | −1.07599 | −0.537996 | − | 0.842948i | \(-0.680818\pi\) | ||||
−0.537996 | + | 0.842948i | \(0.680818\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 10.0000i | − | 0.475114i | −0.971374 | − | 0.237557i | \(-0.923653\pi\) | ||
0.971374 | − | 0.237557i | \(-0.0763467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.65685 | 0.268161 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.3137 | −1.00586 | −0.502928 | − | 0.864328i | \(-0.667744\pi\) | ||||
−0.502928 | + | 0.864328i | \(0.667744\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.1116 | 0.899932 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32.6256 | + | 5.17157i | 1.52951 | + | 0.242447i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.1127 | 1.73606 | 0.868029 | − | 0.496513i | \(-0.165386\pi\) | ||||
0.868029 | + | 0.496513i | \(0.165386\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3756i | 0.483239i | 0.970371 | + | 0.241619i | \(0.0776786\pi\) | ||||
−0.970371 | + | 0.241619i | \(0.922321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.1421i | − | 0.750189i | −0.926987 | − | 0.375094i | \(-0.877610\pi\) | ||
0.926987 | − | 0.375094i | \(-0.122390\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.10201 | −0.374916 | −0.187458 | − | 0.982273i | \(-0.560025\pi\) | ||||
−0.187458 | + | 0.982273i | \(0.560025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.48528 | + | 40.9133i | −0.299462 | + | 1.88920i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.31371 | −0.336285 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.57675 | 0.347645 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.0894 | −1.37482 | −0.687410 | − | 0.726269i | \(-0.741252\pi\) | ||||
−0.687410 | + | 0.726269i | \(0.741252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 36.5838i | − | 1.66808i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.3137 | −1.60351 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 30.2843i | − | 1.37231i | −0.727455 | − | 0.686156i | \(-0.759297\pi\) | ||
0.727455 | − | 0.686156i | \(-0.240703\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 30.2843i | − | 1.36671i | −0.730086 | − | 0.683355i | \(-0.760520\pi\) | ||
0.730086 | − | 0.683355i | \(-0.239480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.1953i | 0.504213i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.65685 | − | 23.0698i | 0.164032 | − | 1.03482i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.3137i | − | 0.775068i | −0.921855 | − | 0.387534i | \(-0.873327\pi\) | ||
0.921855 | − | 0.387534i | \(-0.126673\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.4721 | 0.779043 | 0.389522 | − | 0.921017i | \(-0.372640\pi\) | ||||
0.389522 | + | 0.921017i | \(0.372640\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.8284 | −0.659856 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 26.0543i | − | 1.15484i | −0.816448 | − | 0.577419i | \(-0.804060\pi\) | ||
0.816448 | − | 0.577419i | \(-0.195940\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.22625 | + | 32.9706i | −0.231196 | + | 1.45853i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 44.2843i | 1.95140i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 14.7821i | − | 0.650115i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.896683i | 0.0392844i | 0.999807 | + | 0.0196422i | \(0.00625271\pi\) | ||||
−0.999807 | + | 0.0196422i | \(0.993747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.9259 | 0.827573 | 0.413787 | − | 0.910374i | \(-0.364206\pi\) | ||||
0.413787 | + | 0.910374i | \(0.364206\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 9.37258i | − | 0.408276i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −35.6274 | −1.54902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45.6569 | 1.97762 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.896683 | −0.0387670 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.32957 | − | 13.3137i | 0.186488 | − | 0.573462i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.3137 | −1.08832 | −0.544161 | − | 0.838981i | \(-0.683152\pi\) | ||||
−0.544161 | + | 0.838981i | \(0.683152\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.8854i | 0.594785i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 33.3137i | − | 1.42439i | −0.701981 | − | 0.712196i | \(-0.747701\pi\) | ||
0.701981 | − | 0.712196i | \(-0.252299\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.1535 | −0.645560 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.31371 | − | 33.5223i | 0.225962 | − | 1.42551i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.31371 | −0.225149 | −0.112575 | − | 0.993643i | \(-0.535910\pi\) | ||||
−0.112575 | + | 0.993643i | \(0.535910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.4721 | −0.738992 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.51528 | −0.190296 | −0.0951481 | − | 0.995463i | \(-0.530332\pi\) | ||||
−0.0951481 | + | 0.995463i | \(0.530332\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 23.0698i | − | 0.970553i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.85786 | −0.329419 | −0.164709 | − | 0.986342i | \(-0.552669\pi\) | ||||
−0.164709 | + | 0.986342i | \(0.552669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 8.34315i | − | 0.349150i | −0.984644 | − | 0.174575i | \(-0.944145\pi\) | ||
0.984644 | − | 0.174575i | \(-0.0558551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 14.0000i | − | 0.583840i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.6871i | 1.48567i | 0.669473 | + | 0.742836i | \(0.266520\pi\) | ||||
−0.669473 | + | 0.742836i | \(0.733480\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.1421 | + | 4.77791i | 1.25051 | + | 0.198221i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.0070 | 1.19725 | 0.598624 | − | 0.801030i | \(-0.295714\pi\) | ||||
0.598624 | + | 0.801030i | \(0.295714\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.6863 | 0.522730 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.79337i | − | 0.0736447i | −0.999322 | − | 0.0368224i | \(-0.988276\pi\) | ||
0.999322 | − | 0.0368224i | \(-0.0117236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.9050 | − | 3.31371i | −0.857022 | − | 0.135849i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.1716i | 1.27364i | 0.771014 | + | 0.636818i | \(0.219750\pi\) | ||||
−0.771014 | + | 0.636818i | \(0.780250\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 42.1814i | − | 1.72062i | −0.509774 | − | 0.860308i | \(-0.670271\pi\) | ||
0.509774 | − | 0.860308i | \(-0.329729\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.2919i | 0.743671i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3183 | 0.702927 | 0.351464 | − | 0.936202i | \(-0.385684\pi\) | ||||
0.351464 | + | 0.936202i | \(0.385684\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 35.3137i | − | 1.42864i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.31371 | 0.214619 | 0.107309 | − | 0.994226i | \(-0.465776\pi\) | ||||
0.107309 | + | 0.994226i | \(0.465776\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.1127 | −0.527897 | −0.263949 | − | 0.964537i | \(-0.585025\pi\) | ||||
−0.263949 | + | 0.964537i | \(0.585025\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.87576 | 0.115586 | 0.0577932 | − | 0.998329i | \(-0.481594\pi\) | ||||
0.0577932 | + | 0.998329i | \(0.481594\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.896683 | − | 5.65685i | 0.0359248 | − | 0.226637i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7990 | −1.23196 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.4412i | 0.934662i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 26.4853i | − | 1.05436i | −0.849753 | − | 0.527181i | \(-0.823249\pi\) | ||
0.849753 | − | 0.527181i | \(-0.176751\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.55582 | −0.379211 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.3431 | − | 31.8059i | 0.409810 | − | 1.26019i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.1421 | −1.11155 | −0.555774 | − | 0.831334i | \(-0.687578\pi\) | ||||
−0.555774 | + | 0.831334i | \(0.687578\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.1326 | −0.675642 | −0.337821 | − | 0.941210i | \(-0.609690\pi\) | ||||
−0.337821 | + | 0.941210i | \(0.609690\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.70099 | −0.184815 | −0.0924074 | − | 0.995721i | \(-0.529456\pi\) | ||||
−0.0924074 | + | 0.995721i | \(0.529456\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.9469i | 0.665222i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.68629 | 0.105123 | 0.0525614 | − | 0.998618i | \(-0.483261\pi\) | ||||
0.0525614 | + | 0.998618i | \(0.483261\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 35.7990i | − | 1.39878i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 17.0294i | − | 0.663373i | −0.943390 | − | 0.331686i | \(-0.892382\pi\) | ||
0.943390 | − | 0.331686i | \(-0.107618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 30.9092i | − | 1.20223i | −0.799164 | − | 0.601114i | \(-0.794724\pi\) | ||
0.799164 | − | 0.601114i | \(-0.205276\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.48528 | − | 28.2960i | 0.173932 | − | 1.09727i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.0000i | 1.08416i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.22625 | 0.201757 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.68629 | 0.257738 | 0.128869 | − | 0.991662i | \(-0.458865\pi\) | ||||
0.128869 | + | 0.991662i | \(0.458865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 24.4148i | − | 0.938338i | −0.883109 | − | 0.469169i | \(-0.844554\pi\) | ||
0.883109 | − | 0.469169i | \(-0.155446\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.59767 | + | 35.3137i | −0.214819 | + | 1.35522i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.6569i | 1.67048i | 0.549883 | + | 0.835242i | \(0.314672\pi\) | ||||
−0.549883 | + | 0.835242i | \(0.685328\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 5.22625i | − | 0.199685i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.55582i | 0.364048i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.4399 | −1.23407 | −0.617036 | − | 0.786935i | \(-0.711667\pi\) | ||||
−0.617036 | + | 0.786935i | \(0.711667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 5.17157i | − | 0.196169i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29.2548 | −1.10811 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.31371 | 0.351774 | 0.175887 | − | 0.984410i | \(-0.443721\pi\) | ||||
0.175887 | + | 0.984410i | \(0.443721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.7289 | −1.19668 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.35049 | + | 14.8284i | −0.0883994 | + | 0.557680i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0000 | 0.676004 | 0.338002 | − | 0.941145i | \(-0.390249\pi\) | ||||
0.338002 | + | 0.941145i | \(0.390249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 23.4412i | − | 0.877880i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 24.9706i | − | 0.933846i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.4190 | −1.28361 | −0.641806 | − | 0.766867i | \(-0.721814\pi\) | ||||
−0.641806 | + | 0.766867i | \(0.721814\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.2843 | + | 7.01962i | 1.64923 | + | 0.261424i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.68629 | −0.248323 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.1814 | 1.56442 | 0.782211 | − | 0.623013i | \(-0.214092\pi\) | ||||
0.782211 | + | 0.623013i | \(0.214092\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.1953 | 0.414075 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 24.4148i | − | 0.901782i | −0.892579 | − | 0.450891i | \(-0.851106\pi\) | ||
0.892579 | − | 0.450891i | \(-0.148894\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.3137 | 1.15346 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.6274i | 0.611649i | 0.952088 | + | 0.305825i | \(0.0989322\pi\) | ||||
−0.952088 | + | 0.305825i | \(0.901068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.3431i | − | 0.893063i | −0.894768 | − | 0.446532i | \(-0.852659\pi\) | ||
0.894768 | − | 0.446532i | \(-0.147341\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 26.1313i | − | 0.957375i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.142136 | + | 0.896683i | −0.00519352 | + | 0.0327641i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.9706i | 0.546284i | 0.961974 | + | 0.273142i | \(0.0880628\pi\) | ||||
−0.961974 | + | 0.273142i | \(0.911937\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.8017 | −0.793445 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.3137 | −1.79234 | −0.896169 | − | 0.443714i | \(-0.853661\pi\) | ||||
−0.896169 | + | 0.443714i | \(0.853661\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.76245i | 0.281389i | 0.990053 | + | 0.140694i | \(0.0449335\pi\) | ||||
−0.990053 | + | 0.140694i | \(0.955067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.8854 | + | 2.20101i | 0.502685 | + | 0.0796819i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.4853i | 1.46184i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.5140i | − | 0.487326i | −0.969860 | − | 0.243663i | \(-0.921651\pi\) | ||
0.969860 | − | 0.243663i | \(-0.0783491\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 26.9510i | − | 0.969361i | −0.874691 | − | 0.484680i | \(-0.838936\pi\) | ||
0.874691 | − | 0.484680i | \(-0.161064\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.59767 | 0.201074 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 39.5980i | − | 1.41874i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.6569 | −0.631812 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.8284 | −0.529249 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.51528 | 0.160952 | 0.0804761 | − | 0.996757i | \(-0.474356\pi\) | ||||
0.0804761 | + | 0.996757i | \(0.474356\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.0698 | − | 3.65685i | −0.820267 | − | 0.130023i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.4853 | 0.443365 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 41.3617i | − | 1.46511i | −0.680710 | − | 0.732553i | \(-0.738329\pi\) | ||
0.680710 | − | 0.732553i | \(-0.261671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.6274i | 0.800500i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.2346 | 0.890509 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −52.2843 | − | 8.28772i | −1.84278 | − | 0.292104i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.5147 | 0.615785 | 0.307892 | − | 0.951421i | \(-0.400376\pi\) | ||||
0.307892 | + | 0.951421i | \(0.400376\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.5628 | 1.35412 | 0.677062 | − | 0.735926i | \(-0.263253\pi\) | ||||
0.677062 | + | 0.735926i | \(0.263253\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 45.2429 | 1.58479 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.1535i | 0.530154i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.5980 | −1.73098 | −0.865491 | − | 0.500925i | \(-0.832993\pi\) | ||||
−0.865491 | + | 0.500925i | \(0.832993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25.1127i | − | 0.875374i | −0.899127 | − | 0.437687i | \(-0.855798\pi\) | ||
0.899127 | − | 0.437687i | \(-0.144202\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.2548i | 1.50412i | 0.659096 | + | 0.752059i | \(0.270939\pi\) | ||||
−0.659096 | + | 0.752059i | \(0.729061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.19986i | 0.215330i | 0.994187 | + | 0.107665i | \(0.0343374\pi\) | ||||
−0.994187 | + | 0.107665i | \(0.965663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.62742 | + | 20.3797i | −0.229626 | + | 0.706116i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.9706i | 0.587291i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.1814 | 1.45626 | 0.728132 | − | 0.685437i | \(-0.240389\pi\) | ||||
0.728132 | + | 0.685437i | \(0.240389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 25.6829i | − | 0.883519i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.2919 | + | 2.89949i | 0.628516 | + | 0.0996278i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58.6274i | 2.00972i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.8059i | 1.08901i | 0.838757 | + | 0.544506i | \(0.183283\pi\) | ||||
−0.838757 | + | 0.544506i | \(0.816717\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7.01962i | − | 0.239786i | −0.992787 | − | 0.119893i | \(-0.961745\pi\) | ||
0.992787 | − | 0.119893i | \(-0.0382551\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.50434 | −0.0854470 | −0.0427235 | − | 0.999087i | \(-0.513603\pi\) | ||||
−0.0427235 | + | 0.999087i | \(0.513603\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.4558i | 0.934608i | 0.884097 | + | 0.467304i | \(0.154775\pi\) | ||||
−0.884097 | + | 0.467304i | \(0.845225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.4853 | −0.968529 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.6569 | −0.870349 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 74.8070 | 2.53474 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.43289 | + | 21.6569i | −0.116053 | + | 0.732135i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.343146 | −0.0115872 | −0.00579360 | − | 0.999983i | \(-0.501844\pi\) | ||||
−0.00579360 | + | 0.999983i | \(0.501844\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 27.7708i | − | 0.935621i | −0.883829 | − | 0.467811i | \(-0.845043\pi\) | ||
0.883829 | − | 0.467811i | \(-0.154957\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 24.3431i | − | 0.819212i | −0.912263 | − | 0.409606i | \(-0.865666\pi\) | ||
0.912263 | − | 0.409606i | \(-0.134334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.1701 | 1.85243 | 0.926216 | − | 0.376993i | \(-0.123042\pi\) | ||||
0.926216 | + | 0.376993i | \(0.123042\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.51472 | + | 9.55582i | −0.0508020 | + | 0.320492i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.6274 | −1.02491 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.22625 | 0.174694 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.1953 | −0.373386 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.12293i | − | 0.203985i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.48528 | −0.149096 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.0000i | 0.863316i | 0.902037 | + | 0.431658i | \(0.142071\pi\) | ||||
−0.902037 | + | 0.431658i | \(0.857929\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24.3431i | − | 0.806524i | −0.915084 | − | 0.403262i | \(-0.867876\pi\) | ||
0.915084 | − | 0.403262i | \(-0.132124\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.0698i | − | 0.763499i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35.7990 | − | 5.67459i | −1.18219 | − | 0.187392i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 29.7990i | − | 0.982978i | −0.870884 | − | 0.491489i | \(-0.836453\pi\) | ||
0.870884 | − | 0.491489i | \(-0.163547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.1814 | −1.38842 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.0000 | −0.460317 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 57.8602i | − | 1.89833i | −0.314777 | − | 0.949166i | \(-0.601930\pi\) | ||
0.314777 | − | 0.949166i | \(-0.398070\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.5851 | − | 8.97056i | −0.904064 | − | 0.293998i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.0000i | 0.523256i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.7176i | 1.46086i | 0.682987 | + | 0.730431i | \(0.260681\pi\) | ||||
−0.682987 | + | 0.730431i | \(0.739319\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 24.7862i | − | 0.808008i | −0.914757 | − | 0.404004i | \(-0.867618\pi\) | ||
0.914757 | − | 0.404004i | \(-0.132382\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −73.1675 | −2.38266 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 28.3431i | − | 0.921028i | −0.887652 | − | 0.460514i | \(-0.847665\pi\) | ||
0.887652 | − | 0.460514i | \(-0.152335\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.2843 | 1.95691 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.627417 | −0.0203240 | −0.0101620 | − | 0.999948i | \(-0.503235\pi\) | ||||
−0.0101620 | + | 0.999948i | \(0.503235\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.6173 | −0.408286 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.22625 | − | 0.828427i | −0.168764 | − | 0.0267513i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6274 | −0.697659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 27.3994i | − | 0.882017i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.0294i | − | 0.547630i | −0.961782 | − | 0.273815i | \(-0.911714\pi\) | ||
0.961782 | − | 0.273815i | \(-0.0882856\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.14386 | −0.132983 | −0.0664914 | − | 0.997787i | \(-0.521180\pi\) | ||||
−0.0664914 | + | 0.997787i | \(0.521180\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.17157 | − | 0.819760i | −0.165793 | − | 0.0262803i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.6274 | −0.531958 | −0.265979 | − | 0.963979i | \(-0.585695\pi\) | ||||
−0.265979 | + | 0.963979i | \(0.585695\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.32957 | −0.138374 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.5223 | −1.06920 | −0.534598 | − | 0.845107i | \(-0.679537\pi\) | ||||
−0.534598 | + | 0.845107i | \(0.679537\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.55582i | 0.304474i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.0000 | 0.890348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.4853i | 0.460140i | 0.973174 | + | 0.230070i | \(0.0738955\pi\) | ||||
−0.973174 | + | 0.230070i | \(0.926104\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 32.9706i | − | 1.04524i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 17.3952i | − | 0.550911i | −0.961314 | − | 0.275456i | \(-0.911171\pi\) | ||
0.961314 | − | 0.275456i | \(-0.0888287\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))