Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [19,3,Mod(18,19)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("19.18");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.b (of order \(2\), degree \(1\), 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: | \(0.517712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 13 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 18.2 | ||
Root | \(3.60555i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 19.18 |
Dual form | 19.3.b.b.18.1 |
$q$-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 \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.60555i | 1.80278i | 0.433013 | + | 0.901388i | \(0.357451\pi\) | ||||
−0.433013 | + | 0.901388i | \(0.642549\pi\) | |||||||
\(3\) | − | 3.60555i | − | 1.20185i | −0.799305 | − | 0.600925i | \(-0.794799\pi\) | ||
0.799305 | − | 0.600925i | \(-0.205201\pi\) | |||||||
\(4\) | −9.00000 | −2.25000 | ||||||||
\(5\) | 4.00000 | 0.800000 | 0.400000 | − | 0.916515i | \(-0.369010\pi\) | ||||
0.400000 | + | 0.916515i | \(0.369010\pi\) | |||||||
\(6\) | 13.0000 | 2.16667 | ||||||||
\(7\) | −5.00000 | −0.714286 | −0.357143 | − | 0.934050i | \(-0.616249\pi\) | ||||
−0.357143 | + | 0.934050i | \(0.616249\pi\) | |||||||
\(8\) | − | 18.0278i | − | 2.25347i | ||||||
\(9\) | −4.00000 | −0.444444 | ||||||||
\(10\) | 14.4222i | 1.44222i | ||||||||
\(11\) | −10.0000 | −0.909091 | −0.454545 | − | 0.890724i | \(-0.650198\pi\) | ||||
−0.454545 | + | 0.890724i | \(0.650198\pi\) | |||||||
\(12\) | 32.4500i | 2.70416i | ||||||||
\(13\) | 3.60555i | 0.277350i | 0.990338 | + | 0.138675i | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | − | 18.0278i | − | 1.28770i | ||||||
\(15\) | − | 14.4222i | − | 0.961480i | ||||||
\(16\) | 29.0000 | 1.81250 | ||||||||
\(17\) | 15.0000 | 0.882353 | 0.441176 | − | 0.897420i | \(-0.354561\pi\) | ||||
0.441176 | + | 0.897420i | \(0.354561\pi\) | |||||||
\(18\) | − | 14.4222i | − | 0.801234i | ||||||
\(19\) | −6.00000 | + | 18.0278i | −0.315789 | + | 0.948829i | ||||
\(20\) | −36.0000 | −1.80000 | ||||||||
\(21\) | 18.0278i | 0.858465i | ||||||||
\(22\) | − | 36.0555i | − | 1.63889i | ||||||
\(23\) | 35.0000 | 1.52174 | 0.760870 | − | 0.648905i | \(-0.224773\pi\) | ||||
0.760870 | + | 0.648905i | \(0.224773\pi\) | |||||||
\(24\) | −65.0000 | −2.70833 | ||||||||
\(25\) | −9.00000 | −0.360000 | ||||||||
\(26\) | −13.0000 | −0.500000 | ||||||||
\(27\) | − | 18.0278i | − | 0.667695i | ||||||
\(28\) | 45.0000 | 1.60714 | ||||||||
\(29\) | 18.0278i | 0.621647i | 0.950468 | + | 0.310823i | \(0.100605\pi\) | ||||
−0.950468 | + | 0.310823i | \(0.899395\pi\) | |||||||
\(30\) | 52.0000 | 1.73333 | ||||||||
\(31\) | − | 36.0555i | − | 1.16308i | −0.813517 | − | 0.581541i | \(-0.802450\pi\) | ||
0.813517 | − | 0.581541i | \(-0.197550\pi\) | |||||||
\(32\) | 32.4500i | 1.01406i | ||||||||
\(33\) | 36.0555i | 1.09259i | ||||||||
\(34\) | 54.0833i | 1.59068i | ||||||||
\(35\) | −20.0000 | −0.571429 | ||||||||
\(36\) | 36.0000 | 1.00000 | ||||||||
\(37\) | − | 21.6333i | − | 0.584684i | −0.956314 | − | 0.292342i | \(-0.905565\pi\) | ||
0.956314 | − | 0.292342i | \(-0.0944346\pi\) | |||||||
\(38\) | −65.0000 | − | 21.6333i | −1.71053 | − | 0.569298i | ||||
\(39\) | 13.0000 | 0.333333 | ||||||||
\(40\) | − | 72.1110i | − | 1.80278i | ||||||
\(41\) | 36.0555i | 0.879403i | 0.898144 | + | 0.439701i | \(0.144916\pi\) | ||||
−0.898144 | + | 0.439701i | \(0.855084\pi\) | |||||||
\(42\) | −65.0000 | −1.54762 | ||||||||
\(43\) | −20.0000 | −0.465116 | −0.232558 | − | 0.972582i | \(-0.574710\pi\) | ||||
−0.232558 | + | 0.972582i | \(0.574710\pi\) | |||||||
\(44\) | 90.0000 | 2.04545 | ||||||||
\(45\) | −16.0000 | −0.355556 | ||||||||
\(46\) | 126.194i | 2.74335i | ||||||||
\(47\) | 10.0000 | 0.212766 | 0.106383 | − | 0.994325i | \(-0.466073\pi\) | ||||
0.106383 | + | 0.994325i | \(0.466073\pi\) | |||||||
\(48\) | − | 104.561i | − | 2.17835i | ||||||
\(49\) | −24.0000 | −0.489796 | ||||||||
\(50\) | − | 32.4500i | − | 0.648999i | ||||||
\(51\) | − | 54.0833i | − | 1.06046i | ||||||
\(52\) | − | 32.4500i | − | 0.624038i | ||||||
\(53\) | − | 75.7166i | − | 1.42861i | −0.699832 | − | 0.714307i | \(-0.746742\pi\) | ||
0.699832 | − | 0.714307i | \(-0.253258\pi\) | |||||||
\(54\) | 65.0000 | 1.20370 | ||||||||
\(55\) | −40.0000 | −0.727273 | ||||||||
\(56\) | 90.1388i | 1.60962i | ||||||||
\(57\) | 65.0000 | + | 21.6333i | 1.14035 | + | 0.379532i | ||||
\(58\) | −65.0000 | −1.12069 | ||||||||
\(59\) | 18.0278i | 0.305555i | 0.988261 | + | 0.152778i | \(0.0488218\pi\) | ||||
−0.988261 | + | 0.152778i | \(0.951178\pi\) | |||||||
\(60\) | 129.800i | 2.16333i | ||||||||
\(61\) | −40.0000 | −0.655738 | −0.327869 | − | 0.944723i | \(-0.606330\pi\) | ||||
−0.327869 | + | 0.944723i | \(0.606330\pi\) | |||||||
\(62\) | 130.000 | 2.09677 | ||||||||
\(63\) | 20.0000 | 0.317460 | ||||||||
\(64\) | −1.00000 | −0.0156250 | ||||||||
\(65\) | 14.4222i | 0.221880i | ||||||||
\(66\) | −130.000 | −1.96970 | ||||||||
\(67\) | 39.6611i | 0.591956i | 0.955195 | + | 0.295978i | \(0.0956455\pi\) | ||||
−0.955195 | + | 0.295978i | \(0.904354\pi\) | |||||||
\(68\) | −135.000 | −1.98529 | ||||||||
\(69\) | − | 126.194i | − | 1.82890i | ||||||
\(70\) | − | 72.1110i | − | 1.03016i | ||||||
\(71\) | 108.167i | 1.52347i | 0.647887 | + | 0.761736i | \(0.275653\pi\) | ||||
−0.647887 | + | 0.761736i | \(0.724347\pi\) | |||||||
\(72\) | 72.1110i | 1.00154i | ||||||||
\(73\) | 105.000 | 1.43836 | 0.719178 | − | 0.694826i | \(-0.244519\pi\) | ||||
0.719178 | + | 0.694826i | \(0.244519\pi\) | |||||||
\(74\) | 78.0000 | 1.05405 | ||||||||
\(75\) | 32.4500i | 0.432666i | ||||||||
\(76\) | 54.0000 | − | 162.250i | 0.710526 | − | 2.13487i | ||||
\(77\) | 50.0000 | 0.649351 | ||||||||
\(78\) | 46.8722i | 0.600925i | ||||||||
\(79\) | − | 36.0555i | − | 0.456399i | −0.973614 | − | 0.228199i | \(-0.926716\pi\) | ||
0.973614 | − | 0.228199i | \(-0.0732838\pi\) | |||||||
\(80\) | 116.000 | 1.45000 | ||||||||
\(81\) | −101.000 | −1.24691 | ||||||||
\(82\) | −130.000 | −1.58537 | ||||||||
\(83\) | −40.0000 | −0.481928 | −0.240964 | − | 0.970534i | \(-0.577464\pi\) | ||||
−0.240964 | + | 0.970534i | \(0.577464\pi\) | |||||||
\(84\) | − | 162.250i | − | 1.93155i | ||||||
\(85\) | 60.0000 | 0.705882 | ||||||||
\(86\) | − | 72.1110i | − | 0.838500i | ||||||
\(87\) | 65.0000 | 0.747126 | ||||||||
\(88\) | 180.278i | 2.04861i | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | − | 57.6888i | − | 0.640987i | ||||||
\(91\) | − | 18.0278i | − | 0.198107i | ||||||
\(92\) | −315.000 | −3.42391 | ||||||||
\(93\) | −130.000 | −1.39785 | ||||||||
\(94\) | 36.0555i | 0.383569i | ||||||||
\(95\) | −24.0000 | + | 72.1110i | −0.252632 | + | 0.759063i | ||||
\(96\) | 117.000 | 1.21875 | ||||||||
\(97\) | 122.589i | 1.26380i | 0.775049 | + | 0.631901i | \(0.217725\pi\) | ||||
−0.775049 | + | 0.631901i | \(0.782275\pi\) | |||||||
\(98\) | − | 86.5332i | − | 0.882992i | ||||||
\(99\) | 40.0000 | 0.404040 | ||||||||
\(100\) | 81.0000 | 0.810000 | ||||||||
\(101\) | −50.0000 | −0.495050 | −0.247525 | − | 0.968882i | \(-0.579617\pi\) | ||||
−0.247525 | + | 0.968882i | \(0.579617\pi\) | |||||||
\(102\) | 195.000 | 1.91176 | ||||||||
\(103\) | 57.6888i | 0.560086i | 0.959988 | + | 0.280043i | \(0.0903487\pi\) | ||||
−0.959988 | + | 0.280043i | \(0.909651\pi\) | |||||||
\(104\) | 65.0000 | 0.625000 | ||||||||
\(105\) | 72.1110i | 0.686772i | ||||||||
\(106\) | 273.000 | 2.57547 | ||||||||
\(107\) | 75.7166i | 0.707632i | 0.935315 | + | 0.353816i | \(0.115116\pi\) | ||||
−0.935315 | + | 0.353816i | \(0.884884\pi\) | |||||||
\(108\) | 162.250i | 1.50231i | ||||||||
\(109\) | − | 198.305i | − | 1.81931i | −0.415359 | − | 0.909657i | \(-0.636344\pi\) | ||
0.415359 | − | 0.909657i | \(-0.363656\pi\) | |||||||
\(110\) | − | 144.222i | − | 1.31111i | ||||||
\(111\) | −78.0000 | −0.702703 | ||||||||
\(112\) | −145.000 | −1.29464 | ||||||||
\(113\) | − | 122.589i | − | 1.08486i | −0.840102 | − | 0.542428i | \(-0.817505\pi\) | ||
0.840102 | − | 0.542428i | \(-0.182495\pi\) | |||||||
\(114\) | −78.0000 | + | 234.361i | −0.684211 | + | 2.05580i | ||||
\(115\) | 140.000 | 1.21739 | ||||||||
\(116\) | − | 162.250i | − | 1.39871i | ||||||
\(117\) | − | 14.4222i | − | 0.123267i | ||||||
\(118\) | −65.0000 | −0.550847 | ||||||||
\(119\) | −75.0000 | −0.630252 | ||||||||
\(120\) | −260.000 | −2.16667 | ||||||||
\(121\) | −21.0000 | −0.173554 | ||||||||
\(122\) | − | 144.222i | − | 1.18215i | ||||||
\(123\) | 130.000 | 1.05691 | ||||||||
\(124\) | 324.500i | 2.61693i | ||||||||
\(125\) | −136.000 | −1.08800 | ||||||||
\(126\) | 72.1110i | 0.572310i | ||||||||
\(127\) | − | 129.800i | − | 1.02205i | −0.859567 | − | 0.511023i | \(-0.829267\pi\) | ||
0.859567 | − | 0.511023i | \(-0.170733\pi\) | |||||||
\(128\) | 126.194i | 0.985893i | ||||||||
\(129\) | 72.1110i | 0.559000i | ||||||||
\(130\) | −52.0000 | −0.400000 | ||||||||
\(131\) | 112.000 | 0.854962 | 0.427481 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427481 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(132\) | − | 324.500i | − | 2.45833i | ||||||
\(133\) | 30.0000 | − | 90.1388i | 0.225564 | − | 0.677735i | ||||
\(134\) | −143.000 | −1.06716 | ||||||||
\(135\) | − | 72.1110i | − | 0.534156i | ||||||
\(136\) | − | 270.416i | − | 1.98836i | ||||||
\(137\) | 125.000 | 0.912409 | 0.456204 | − | 0.889875i | \(-0.349209\pi\) | ||||
0.456204 | + | 0.889875i | \(0.349209\pi\) | |||||||
\(138\) | 455.000 | 3.29710 | ||||||||
\(139\) | 50.0000 | 0.359712 | 0.179856 | − | 0.983693i | \(-0.442437\pi\) | ||||
0.179856 | + | 0.983693i | \(0.442437\pi\) | |||||||
\(140\) | 180.000 | 1.28571 | ||||||||
\(141\) | − | 36.0555i | − | 0.255713i | ||||||
\(142\) | −390.000 | −2.74648 | ||||||||
\(143\) | − | 36.0555i | − | 0.252136i | ||||||
\(144\) | −116.000 | −0.805556 | ||||||||
\(145\) | 72.1110i | 0.497317i | ||||||||
\(146\) | 378.583i | 2.59303i | ||||||||
\(147\) | 86.5332i | 0.588661i | ||||||||
\(148\) | 194.700i | 1.31554i | ||||||||
\(149\) | 70.0000 | 0.469799 | 0.234899 | − | 0.972020i | \(-0.424524\pi\) | ||||
0.234899 | + | 0.972020i | \(0.424524\pi\) | |||||||
\(150\) | −117.000 | −0.780000 | ||||||||
\(151\) | 36.0555i | 0.238778i | 0.992848 | + | 0.119389i | \(0.0380936\pi\) | ||||
−0.992848 | + | 0.119389i | \(0.961906\pi\) | |||||||
\(152\) | 325.000 | + | 108.167i | 2.13816 | + | 0.711622i | ||||
\(153\) | −60.0000 | −0.392157 | ||||||||
\(154\) | 180.278i | 1.17063i | ||||||||
\(155\) | − | 144.222i | − | 0.930465i | ||||||
\(156\) | −117.000 | −0.750000 | ||||||||
\(157\) | 10.0000 | 0.0636943 | 0.0318471 | − | 0.999493i | \(-0.489861\pi\) | ||||
0.0318471 | + | 0.999493i | \(0.489861\pi\) | |||||||
\(158\) | 130.000 | 0.822785 | ||||||||
\(159\) | −273.000 | −1.71698 | ||||||||
\(160\) | 129.800i | 0.811249i | ||||||||
\(161\) | −175.000 | −1.08696 | ||||||||
\(162\) | − | 364.161i | − | 2.24791i | ||||||
\(163\) | −270.000 | −1.65644 | −0.828221 | − | 0.560402i | \(-0.810647\pi\) | ||||
−0.828221 | + | 0.560402i | \(0.810647\pi\) | |||||||
\(164\) | − | 324.500i | − | 1.97866i | ||||||
\(165\) | 144.222i | 0.874073i | ||||||||
\(166\) | − | 144.222i | − | 0.868808i | ||||||
\(167\) | 122.589i | 0.734064i | 0.930208 | + | 0.367032i | \(0.119626\pi\) | ||||
−0.930208 | + | 0.367032i | \(0.880374\pi\) | |||||||
\(168\) | 325.000 | 1.93452 | ||||||||
\(169\) | 156.000 | 0.923077 | ||||||||
\(170\) | 216.333i | 1.27255i | ||||||||
\(171\) | 24.0000 | − | 72.1110i | 0.140351 | − | 0.421702i | ||||
\(172\) | 180.000 | 1.04651 | ||||||||
\(173\) | − | 122.589i | − | 0.708605i | −0.935131 | − | 0.354303i | \(-0.884718\pi\) | ||
0.935131 | − | 0.354303i | \(-0.115282\pi\) | |||||||
\(174\) | 234.361i | 1.34690i | ||||||||
\(175\) | 45.0000 | 0.257143 | ||||||||
\(176\) | −290.000 | −1.64773 | ||||||||
\(177\) | 65.0000 | 0.367232 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 36.0555i | 0.201427i | 0.994915 | + | 0.100714i | \(0.0321126\pi\) | ||||
−0.994915 | + | 0.100714i | \(0.967887\pi\) | |||||||
\(180\) | 144.000 | 0.800000 | ||||||||
\(181\) | 108.167i | 0.597605i | 0.954315 | + | 0.298803i | \(0.0965872\pi\) | ||||
−0.954315 | + | 0.298803i | \(0.903413\pi\) | |||||||
\(182\) | 65.0000 | 0.357143 | ||||||||
\(183\) | 144.222i | 0.788099i | ||||||||
\(184\) | − | 630.971i | − | 3.42919i | ||||||
\(185\) | − | 86.5332i | − | 0.467747i | ||||||
\(186\) | − | 468.722i | − | 2.52001i | ||||||
\(187\) | −150.000 | −0.802139 | ||||||||
\(188\) | −90.0000 | −0.478723 | ||||||||
\(189\) | 90.1388i | 0.476925i | ||||||||
\(190\) | −260.000 | − | 86.5332i | −1.36842 | − | 0.455438i | ||||
\(191\) | 193.000 | 1.01047 | 0.505236 | − | 0.862981i | \(-0.331406\pi\) | ||||
0.505236 | + | 0.862981i | \(0.331406\pi\) | |||||||
\(192\) | 3.60555i | 0.0187789i | ||||||||
\(193\) | 266.811i | 1.38244i | 0.722645 | + | 0.691220i | \(0.242926\pi\) | ||||
−0.722645 | + | 0.691220i | \(0.757074\pi\) | |||||||
\(194\) | −442.000 | −2.27835 | ||||||||
\(195\) | 52.0000 | 0.266667 | ||||||||
\(196\) | 216.000 | 1.10204 | ||||||||
\(197\) | 90.0000 | 0.456853 | 0.228426 | − | 0.973561i | \(-0.426642\pi\) | ||||
0.228426 | + | 0.973561i | \(0.426642\pi\) | |||||||
\(198\) | 144.222i | 0.728394i | ||||||||
\(199\) | 123.000 | 0.618090 | 0.309045 | − | 0.951047i | \(-0.399991\pi\) | ||||
0.309045 | + | 0.951047i | \(0.399991\pi\) | |||||||
\(200\) | 162.250i | 0.811249i | ||||||||
\(201\) | 143.000 | 0.711443 | ||||||||
\(202\) | − | 180.278i | − | 0.892463i | ||||||
\(203\) | − | 90.1388i | − | 0.444033i | ||||||
\(204\) | 486.749i | 2.38603i | ||||||||
\(205\) | 144.222i | 0.703522i | ||||||||
\(206\) | −208.000 | −1.00971 | ||||||||
\(207\) | −140.000 | −0.676329 | ||||||||
\(208\) | 104.561i | 0.502697i | ||||||||
\(209\) | 60.0000 | − | 180.278i | 0.287081 | − | 0.862572i | ||||
\(210\) | −260.000 | −1.23810 | ||||||||
\(211\) | − | 234.361i | − | 1.11071i | −0.831612 | − | 0.555357i | \(-0.812581\pi\) | ||
0.831612 | − | 0.555357i | \(-0.187419\pi\) | |||||||
\(212\) | 681.449i | 3.21438i | ||||||||
\(213\) | 390.000 | 1.83099 | ||||||||
\(214\) | −273.000 | −1.27570 | ||||||||
\(215\) | −80.0000 | −0.372093 | ||||||||
\(216\) | −325.000 | −1.50463 | ||||||||
\(217\) | 180.278i | 0.830772i | ||||||||
\(218\) | 715.000 | 3.27982 | ||||||||
\(219\) | − | 378.583i | − | 1.72869i | ||||||
\(220\) | 360.000 | 1.63636 | ||||||||
\(221\) | 54.0833i | 0.244721i | ||||||||
\(222\) | − | 281.233i | − | 1.26682i | ||||||
\(223\) | − | 201.911i | − | 0.905430i | −0.891655 | − | 0.452715i | \(-0.850456\pi\) | ||
0.891655 | − | 0.452715i | \(-0.149544\pi\) | |||||||
\(224\) | − | 162.250i | − | 0.724329i | ||||||
\(225\) | 36.0000 | 0.160000 | ||||||||
\(226\) | 442.000 | 1.95575 | ||||||||
\(227\) | 255.994i | 1.12773i | 0.825868 | + | 0.563864i | \(0.190686\pi\) | ||||
−0.825868 | + | 0.563864i | \(0.809314\pi\) | |||||||
\(228\) | −585.000 | − | 194.700i | −2.56579 | − | 0.853946i | ||||
\(229\) | −160.000 | −0.698690 | −0.349345 | − | 0.936994i | \(-0.613596\pi\) | ||||
−0.349345 | + | 0.936994i | \(0.613596\pi\) | |||||||
\(230\) | 504.777i | 2.19468i | ||||||||
\(231\) | − | 180.278i | − | 0.780422i | ||||||
\(232\) | 325.000 | 1.40086 | ||||||||
\(233\) | −270.000 | −1.15880 | −0.579399 | − | 0.815044i | \(-0.696713\pi\) | ||||
−0.579399 | + | 0.815044i | \(0.696713\pi\) | |||||||
\(234\) | 52.0000 | 0.222222 | ||||||||
\(235\) | 40.0000 | 0.170213 | ||||||||
\(236\) | − | 162.250i | − | 0.687499i | ||||||
\(237\) | −130.000 | −0.548523 | ||||||||
\(238\) | − | 270.416i | − | 1.13620i | ||||||
\(239\) | 197.000 | 0.824268 | 0.412134 | − | 0.911123i | \(-0.364784\pi\) | ||||
0.412134 | + | 0.911123i | \(0.364784\pi\) | |||||||
\(240\) | − | 418.244i | − | 1.74268i | ||||||
\(241\) | 396.611i | 1.64569i | 0.568268 | + | 0.822844i | \(0.307614\pi\) | ||||
−0.568268 | + | 0.822844i | \(0.692386\pi\) | |||||||
\(242\) | − | 75.7166i | − | 0.312878i | ||||||
\(243\) | 201.911i | 0.830909i | ||||||||
\(244\) | 360.000 | 1.47541 | ||||||||
\(245\) | −96.0000 | −0.391837 | ||||||||
\(246\) | 468.722i | 1.90537i | ||||||||
\(247\) | −65.0000 | − | 21.6333i | −0.263158 | − | 0.0875842i | ||||
\(248\) | −650.000 | −2.62097 | ||||||||
\(249\) | 144.222i | 0.579205i | ||||||||
\(250\) | − | 490.355i | − | 1.96142i | ||||||
\(251\) | −402.000 | −1.60159 | −0.800797 | − | 0.598936i | \(-0.795590\pi\) | ||||
−0.800797 | + | 0.598936i | \(0.795590\pi\) | |||||||
\(252\) | −180.000 | −0.714286 | ||||||||
\(253\) | −350.000 | −1.38340 | ||||||||
\(254\) | 468.000 | 1.84252 | ||||||||
\(255\) | − | 216.333i | − | 0.848365i | ||||||
\(256\) | −459.000 | −1.79297 | ||||||||
\(257\) | − | 418.244i | − | 1.62741i | −0.581279 | − | 0.813704i | \(-0.697448\pi\) | ||
0.581279 | − | 0.813704i | \(-0.302552\pi\) | |||||||
\(258\) | −260.000 | −1.00775 | ||||||||
\(259\) | 108.167i | 0.417631i | ||||||||
\(260\) | − | 129.800i | − | 0.499230i | ||||||
\(261\) | − | 72.1110i | − | 0.276287i | ||||||
\(262\) | 403.822i | 1.54130i | ||||||||
\(263\) | 310.000 | 1.17871 | 0.589354 | − | 0.807875i | \(-0.299382\pi\) | ||||
0.589354 | + | 0.807875i | \(0.299382\pi\) | |||||||
\(264\) | 650.000 | 2.46212 | ||||||||
\(265\) | − | 302.866i | − | 1.14289i | ||||||
\(266\) | 325.000 | + | 108.167i | 1.22180 | + | 0.406641i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 356.950i | − | 1.33190i | ||||||
\(269\) | 108.167i | 0.402106i | 0.979580 | + | 0.201053i | \(0.0644364\pi\) | ||||
−0.979580 | + | 0.201053i | \(0.935564\pi\) | |||||||
\(270\) | 260.000 | 0.962963 | ||||||||
\(271\) | 105.000 | 0.387454 | 0.193727 | − | 0.981055i | \(-0.437942\pi\) | ||||
0.193727 | + | 0.981055i | \(0.437942\pi\) | |||||||
\(272\) | 435.000 | 1.59926 | ||||||||
\(273\) | −65.0000 | −0.238095 | ||||||||
\(274\) | 450.694i | 1.64487i | ||||||||
\(275\) | 90.0000 | 0.327273 | ||||||||
\(276\) | 1135.75i | 4.11503i | ||||||||
\(277\) | −50.0000 | −0.180505 | −0.0902527 | − | 0.995919i | \(-0.528767\pi\) | ||||
−0.0902527 | + | 0.995919i | \(0.528767\pi\) | |||||||
\(278\) | 180.278i | 0.648480i | ||||||||
\(279\) | 144.222i | 0.516925i | ||||||||
\(280\) | 360.555i | 1.28770i | ||||||||
\(281\) | − | 288.444i | − | 1.02649i | −0.858242 | − | 0.513246i | \(-0.828443\pi\) | ||
0.858242 | − | 0.513246i | \(-0.171557\pi\) | |||||||
\(282\) | 130.000 | 0.460993 | ||||||||
\(283\) | −320.000 | −1.13074 | −0.565371 | − | 0.824837i | \(-0.691267\pi\) | ||||
−0.565371 | + | 0.824837i | \(0.691267\pi\) | |||||||
\(284\) | − | 973.499i | − | 3.42781i | ||||||
\(285\) | 260.000 | + | 86.5332i | 0.912281 | + | 0.303625i | ||||
\(286\) | 130.000 | 0.454545 | ||||||||
\(287\) | − | 180.278i | − | 0.628145i | ||||||
\(288\) | − | 129.800i | − | 0.450694i | ||||||
\(289\) | −64.0000 | −0.221453 | ||||||||
\(290\) | −260.000 | −0.896552 | ||||||||
\(291\) | 442.000 | 1.51890 | ||||||||
\(292\) | −945.000 | −3.23630 | ||||||||
\(293\) | − | 219.939i | − | 0.750644i | −0.926895 | − | 0.375322i | \(-0.877532\pi\) | ||
0.926895 | − | 0.375322i | \(-0.122468\pi\) | |||||||
\(294\) | −312.000 | −1.06122 | ||||||||
\(295\) | 72.1110i | 0.244444i | ||||||||
\(296\) | −390.000 | −1.31757 | ||||||||
\(297\) | 180.278i | 0.606995i | ||||||||
\(298\) | 252.389i | 0.846942i | ||||||||
\(299\) | 126.194i | 0.422054i | ||||||||
\(300\) | − | 292.050i | − | 0.973499i | ||||||
\(301\) | 100.000 | 0.332226 | ||||||||
\(302\) | −130.000 | −0.430464 | ||||||||
\(303\) | 180.278i | 0.594975i | ||||||||
\(304\) | −174.000 | + | 522.805i | −0.572368 | + | 1.71975i | ||||
\(305\) | −160.000 | −0.524590 | ||||||||
\(306\) | − | 216.333i | − | 0.706971i | ||||||
\(307\) | 237.966i | 0.775135i | 0.921841 | + | 0.387567i | \(0.126685\pi\) | ||||
−0.921841 | + | 0.387567i | \(0.873315\pi\) | |||||||
\(308\) | −450.000 | −1.46104 | ||||||||
\(309\) | 208.000 | 0.673139 | ||||||||
\(310\) | 520.000 | 1.67742 | ||||||||
\(311\) | 395.000 | 1.27010 | 0.635048 | − | 0.772472i | \(-0.280980\pi\) | ||||
0.635048 | + | 0.772472i | \(0.280980\pi\) | |||||||
\(312\) | − | 234.361i | − | 0.751157i | ||||||
\(313\) | 125.000 | 0.399361 | 0.199681 | − | 0.979861i | \(-0.436010\pi\) | ||||
0.199681 | + | 0.979861i | \(0.436010\pi\) | |||||||
\(314\) | 36.0555i | 0.114826i | ||||||||
\(315\) | 80.0000 | 0.253968 | ||||||||
\(316\) | 324.500i | 1.02690i | ||||||||
\(317\) | 3.60555i | 0.0113740i | 0.999984 | + | 0.00568699i | \(0.00181023\pi\) | ||||
−0.999984 | + | 0.00568699i | \(0.998190\pi\) | |||||||
\(318\) | − | 984.315i | − | 3.09533i | ||||||
\(319\) | − | 180.278i | − | 0.565133i | ||||||
\(320\) | −4.00000 | −0.0125000 | ||||||||
\(321\) | 273.000 | 0.850467 | ||||||||
\(322\) | − | 630.971i | − | 1.95954i | ||||||
\(323\) | −90.0000 | + | 270.416i | −0.278638 | + | 0.837202i | ||||
\(324\) | 909.000 | 2.80556 | ||||||||
\(325\) | − | 32.4500i | − | 0.0998460i | ||||||
\(326\) | − | 973.499i | − | 2.98619i | ||||||
\(327\) | −715.000 | −2.18654 | ||||||||
\(328\) | 650.000 | 1.98171 | ||||||||
\(329\) | −50.0000 | −0.151976 | ||||||||
\(330\) | −520.000 | −1.57576 | ||||||||
\(331\) | − | 198.305i | − | 0.599110i | −0.954079 | − | 0.299555i | \(-0.903162\pi\) | ||
0.954079 | − | 0.299555i | \(-0.0968382\pi\) | |||||||
\(332\) | 360.000 | 1.08434 | ||||||||
\(333\) | 86.5332i | 0.259860i | ||||||||
\(334\) | −442.000 | −1.32335 | ||||||||
\(335\) | 158.644i | 0.473565i | ||||||||
\(336\) | 522.805i | 1.55597i | ||||||||
\(337\) | 57.6888i | 0.171183i | 0.996330 | + | 0.0855917i | \(0.0272781\pi\) | ||||
−0.996330 | + | 0.0855917i | \(0.972722\pi\) | |||||||
\(338\) | 562.466i | 1.66410i | ||||||||
\(339\) | −442.000 | −1.30383 | ||||||||
\(340\) | −540.000 | −1.58824 | ||||||||
\(341\) | 360.555i | 1.05735i | ||||||||
\(342\) | 260.000 | + | 86.5332i | 0.760234 | + | 0.253021i | ||||
\(343\) | 365.000 | 1.06414 | ||||||||
\(344\) | 360.555i | 1.04813i | ||||||||
\(345\) | − | 504.777i | − | 1.46312i | ||||||
\(346\) | 442.000 | 1.27746 | ||||||||
\(347\) | −40.0000 | −0.115274 | −0.0576369 | − | 0.998338i | \(-0.518357\pi\) | ||||
−0.0576369 | + | 0.998338i | \(0.518357\pi\) | |||||||
\(348\) | −585.000 | −1.68103 | ||||||||
\(349\) | 98.0000 | 0.280802 | 0.140401 | − | 0.990095i | \(-0.455161\pi\) | ||||
0.140401 | + | 0.990095i | \(0.455161\pi\) | |||||||
\(350\) | 162.250i | 0.463571i | ||||||||
\(351\) | 65.0000 | 0.185185 | ||||||||
\(352\) | − | 324.500i | − | 0.921874i | ||||||
\(353\) | −185.000 | −0.524079 | −0.262040 | − | 0.965057i | \(-0.584395\pi\) | ||||
−0.262040 | + | 0.965057i | \(0.584395\pi\) | |||||||
\(354\) | 234.361i | 0.662036i | ||||||||
\(355\) | 432.666i | 1.21878i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 270.416i | 0.757469i | ||||||||
\(358\) | −130.000 | −0.363128 | ||||||||
\(359\) | −225.000 | −0.626741 | −0.313370 | − | 0.949631i | \(-0.601458\pi\) | ||||
−0.313370 | + | 0.949631i | \(0.601458\pi\) | |||||||
\(360\) | 288.444i | 0.801234i | ||||||||
\(361\) | −289.000 | − | 216.333i | −0.800554 | − | 0.599261i | ||||
\(362\) | −390.000 | −1.07735 | ||||||||
\(363\) | 75.7166i | 0.208586i | ||||||||
\(364\) | 162.250i | 0.445741i | ||||||||
\(365\) | 420.000 | 1.15068 | ||||||||
\(366\) | −520.000 | −1.42077 | ||||||||
\(367\) | 50.0000 | 0.136240 | 0.0681199 | − | 0.997677i | \(-0.478300\pi\) | ||||
0.0681199 | + | 0.997677i | \(0.478300\pi\) | |||||||
\(368\) | 1015.00 | 2.75815 | ||||||||
\(369\) | − | 144.222i | − | 0.390846i | ||||||
\(370\) | 312.000 | 0.843243 | ||||||||
\(371\) | 378.583i | 1.02044i | ||||||||
\(372\) | 1170.00 | 3.14516 | ||||||||
\(373\) | − | 436.272i | − | 1.16963i | −0.811167 | − | 0.584815i | \(-0.801167\pi\) | ||
0.811167 | − | 0.584815i | \(-0.198833\pi\) | |||||||
\(374\) | − | 540.833i | − | 1.44608i | ||||||
\(375\) | 490.355i | 1.30761i | ||||||||
\(376\) | − | 180.278i | − | 0.479462i | ||||||
\(377\) | −65.0000 | −0.172414 | ||||||||
\(378\) | −325.000 | −0.859788 | ||||||||
\(379\) | − | 486.749i | − | 1.28430i | −0.766579 | − | 0.642150i | \(-0.778043\pi\) | ||
0.766579 | − | 0.642150i | \(-0.221957\pi\) | |||||||
\(380\) | 216.000 | − | 648.999i | 0.568421 | − | 1.70789i | ||||
\(381\) | −468.000 | −1.22835 | ||||||||
\(382\) | 695.871i | 1.82165i | ||||||||
\(383\) | 201.911i | 0.527182i | 0.964634 | + | 0.263591i | \(0.0849070\pi\) | ||||
−0.964634 | + | 0.263591i | \(0.915093\pi\) | |||||||
\(384\) | 455.000 | 1.18490 | ||||||||
\(385\) | 200.000 | 0.519481 | ||||||||
\(386\) | −962.000 | −2.49223 | ||||||||
\(387\) | 80.0000 | 0.206718 | ||||||||
\(388\) | − | 1103.30i | − | 2.84355i | ||||||
\(389\) | −478.000 | −1.22879 | −0.614396 | − | 0.788998i | \(-0.710600\pi\) | ||||
−0.614396 | + | 0.788998i | \(0.710600\pi\) | |||||||
\(390\) | 187.489i | 0.480740i | ||||||||
\(391\) | 525.000 | 1.34271 | ||||||||
\(392\) | 432.666i | 1.10374i | ||||||||
\(393\) | − | 403.822i | − | 1.02754i | ||||||
\(394\) | 324.500i | 0.823603i | ||||||||
\(395\) | − | 144.222i | − | 0.365119i | ||||||
\(396\) | −360.000 | −0.909091 | ||||||||
\(397\) | 750.000 | 1.88917 | 0.944584 | − | 0.328269i | \(-0.106465\pi\) | ||||
0.944584 | + | 0.328269i | \(0.106465\pi\) | |||||||
\(398\) | 443.483i | 1.11428i | ||||||||
\(399\) | −325.000 | − | 108.167i | −0.814536 | − | 0.271094i | ||||
\(400\) | −261.000 | −0.652500 | ||||||||
\(401\) | − | 288.444i | − | 0.719312i | −0.933085 | − | 0.359656i | \(-0.882894\pi\) | ||
0.933085 | − | 0.359656i | \(-0.117106\pi\) | |||||||
\(402\) | 515.594i | 1.28257i | ||||||||
\(403\) | 130.000 | 0.322581 | ||||||||
\(404\) | 450.000 | 1.11386 | ||||||||
\(405\) | −404.000 | −0.997531 | ||||||||
\(406\) | 325.000 | 0.800493 | ||||||||
\(407\) | 216.333i | 0.531531i | ||||||||
\(408\) | −975.000 | −2.38971 | ||||||||
\(409\) | − | 36.0555i | − | 0.0881553i | −0.999028 | − | 0.0440776i | \(-0.985965\pi\) | ||
0.999028 | − | 0.0440776i | \(-0.0140349\pi\) | |||||||
\(410\) | −520.000 | −1.26829 | ||||||||
\(411\) | − | 450.694i | − | 1.09658i | ||||||
\(412\) | − | 519.199i | − | 1.26019i | ||||||
\(413\) | − | 90.1388i | − | 0.218254i | ||||||
\(414\) | − | 504.777i | − | 1.21927i | ||||||
\(415\) | −160.000 | −0.385542 | ||||||||
\(416\) | −117.000 | −0.281250 | ||||||||
\(417\) | − | 180.278i | − | 0.432320i | ||||||
\(418\) | 650.000 | + | 216.333i | 1.55502 | + | 0.517543i | ||||
\(419\) | 112.000 | 0.267303 | 0.133652 | − | 0.991028i | \(-0.457330\pi\) | ||||
0.133652 | + | 0.991028i | \(0.457330\pi\) | |||||||
\(420\) | − | 648.999i | − | 1.54524i | ||||||
\(421\) | 630.971i | 1.49874i | 0.662149 | + | 0.749372i | \(0.269645\pi\) | ||||
−0.662149 | + | 0.749372i | \(0.730355\pi\) | |||||||
\(422\) | 845.000 | 2.00237 | ||||||||
\(423\) | −40.0000 | −0.0945626 | ||||||||
\(424\) | −1365.00 | −3.21934 | ||||||||
\(425\) | −135.000 | −0.317647 | ||||||||
\(426\) | 1406.16i | 3.30086i | ||||||||
\(427\) | 200.000 | 0.468384 | ||||||||
\(428\) | − | 681.449i | − | 1.59217i | ||||||
\(429\) | −130.000 | −0.303030 | ||||||||
\(430\) | − | 288.444i | − | 0.670800i | ||||||
\(431\) | − | 432.666i | − | 1.00387i | −0.864907 | − | 0.501933i | \(-0.832622\pi\) | ||
0.864907 | − | 0.501933i | \(-0.167378\pi\) | |||||||
\(432\) | − | 522.805i | − | 1.21020i | ||||||
\(433\) | − | 735.532i | − | 1.69869i | −0.527839 | − | 0.849345i | \(-0.676997\pi\) | ||
0.527839 | − | 0.849345i | \(-0.323003\pi\) | |||||||
\(434\) | −650.000 | −1.49770 | ||||||||
\(435\) | 260.000 | 0.597701 | ||||||||
\(436\) | 1784.75i | 4.09346i | ||||||||
\(437\) | −210.000 | + | 630.971i | −0.480549 | + | 1.44387i | ||||
\(438\) | 1365.00 | 3.11644 | ||||||||
\(439\) | 793.221i | 1.80688i | 0.428712 | + | 0.903441i | \(0.358967\pi\) | ||||
−0.428712 | + | 0.903441i | \(0.641033\pi\) | |||||||
\(440\) | 721.110i | 1.63889i | ||||||||
\(441\) | 96.0000 | 0.217687 | ||||||||
\(442\) | −195.000 | −0.441176 | ||||||||
\(443\) | 670.000 | 1.51242 | 0.756208 | − | 0.654332i | \(-0.227050\pi\) | ||||
0.756208 | + | 0.654332i | \(0.227050\pi\) | |||||||
\(444\) | 702.000 | 1.58108 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 728.000 | 1.63229 | ||||||||
\(447\) | − | 252.389i | − | 0.564628i | ||||||
\(448\) | 5.00000 | 0.0111607 | ||||||||
\(449\) | − | 36.0555i | − | 0.0803018i | −0.999194 | − | 0.0401509i | \(-0.987216\pi\) | ||
0.999194 | − | 0.0401509i | \(-0.0127839\pi\) | |||||||
\(450\) | 129.800i | 0.288444i | ||||||||
\(451\) | − | 360.555i | − | 0.799457i | ||||||
\(452\) | 1103.30i | 2.44093i | ||||||||
\(453\) | 130.000 | 0.286976 | ||||||||
\(454\) | −923.000 | −2.03304 | ||||||||
\(455\) | − | 72.1110i | − | 0.158486i | ||||||
\(456\) | 390.000 | − | 1171.80i | 0.855263 | − | 2.56975i | ||||
\(457\) | −755.000 | −1.65208 | −0.826039 | − | 0.563612i | \(-0.809411\pi\) | ||||
−0.826039 | + | 0.563612i | \(0.809411\pi\) | |||||||
\(458\) | − | 576.888i | − | 1.25958i | ||||||
\(459\) | − | 270.416i | − | 0.589142i | ||||||
\(460\) | −1260.00 | −2.73913 | ||||||||
\(461\) | 772.000 | 1.67462 | 0.837310 | − | 0.546728i | \(-0.184127\pi\) | ||||
0.837310 | + | 0.546728i | \(0.184127\pi\) | |||||||
\(462\) | 650.000 | 1.40693 | ||||||||
\(463\) | −350.000 | −0.755940 | −0.377970 | − | 0.925818i | \(-0.623378\pi\) | ||||
−0.377970 | + | 0.925818i | \(0.623378\pi\) | |||||||
\(464\) | 522.805i | 1.12673i | ||||||||
\(465\) | −520.000 | −1.11828 | ||||||||
\(466\) | − | 973.499i | − | 2.08905i | ||||||
\(467\) | 70.0000 | 0.149893 | 0.0749465 | − | 0.997188i | \(-0.476121\pi\) | ||||
0.0749465 | + | 0.997188i | \(0.476121\pi\) | |||||||
\(468\) | 129.800i | 0.277350i | ||||||||
\(469\) | − | 198.305i | − | 0.422826i | ||||||
\(470\) | 144.222i | 0.306855i | ||||||||
\(471\) | − | 36.0555i | − | 0.0765510i | ||||||
\(472\) | 325.000 | 0.688559 | ||||||||
\(473\) | 200.000 | 0.422833 | ||||||||
\(474\) | − | 468.722i | − | 0.988864i | ||||||
\(475\) | 54.0000 | − | 162.250i | 0.113684 | − | 0.341579i | ||||
\(476\) | 675.000 | 1.41807 | ||||||||
\(477\) | 302.866i | 0.634940i | ||||||||
\(478\) | 710.294i | 1.48597i | ||||||||
\(479\) | −370.000 | −0.772443 | −0.386221 | − | 0.922406i | \(-0.626220\pi\) | ||||
−0.386221 | + | 0.922406i | \(0.626220\pi\) | |||||||
\(480\) | 468.000 | 0.975000 | ||||||||
\(481\) | 78.0000 | 0.162162 | ||||||||
\(482\) | −1430.00 | −2.96680 | ||||||||
\(483\) | 630.971i | 1.30636i | ||||||||
\(484\) | 189.000 | 0.390496 | ||||||||
\(485\) | 490.355i | 1.01104i | ||||||||
\(486\) | −728.000 | −1.49794 | ||||||||
\(487\) | − | 519.199i | − | 1.06612i | −0.846078 | − | 0.533059i | \(-0.821042\pi\) | ||
0.846078 | − | 0.533059i | \(-0.178958\pi\) | |||||||
\(488\) | 721.110i | 1.47768i | ||||||||
\(489\) | 973.499i | 1.99080i | ||||||||
\(490\) | − | 346.133i | − | 0.706394i | ||||||
\(491\) | −632.000 | −1.28717 | −0.643585 | − | 0.765375i | \(-0.722554\pi\) | ||||
−0.643585 | + | 0.765375i | \(0.722554\pi\) | |||||||
\(492\) | −1170.00 | −2.37805 | ||||||||
\(493\) | 270.416i | 0.548512i | ||||||||
\(494\) | 78.0000 | − | 234.361i | 0.157895 | − | 0.474415i | ||||
\(495\) | 160.000 | 0.323232 | ||||||||
\(496\) | − | 1045.61i | − | 2.10808i | ||||||
\(497\) | − | 540.833i | − | 1.08819i | ||||||
\(498\) | −520.000 | −1.04418 | ||||||||
\(499\) | 380.000 | 0.761523 | 0.380762 | − | 0.924673i | \(-0.375662\pi\) | ||||
0.380762 | + | 0.924673i | \(0.375662\pi\) | |||||||
\(500\) | 1224.00 | 2.44800 | ||||||||
\(501\) | 442.000 | 0.882236 | ||||||||
\(502\) | − | 1449.43i | − | 2.88731i | ||||||
\(503\) | −45.0000 | −0.0894632 | −0.0447316 | − | 0.998999i | \(-0.514243\pi\) | ||||
−0.0447316 | + | 0.998999i | \(0.514243\pi\) | |||||||
\(504\) | − | 360.555i | − | 0.715387i | ||||||
\(505\) | −200.000 | −0.396040 | ||||||||
\(506\) | − | 1261.94i | − | 2.49396i | ||||||
\(507\) | − | 562.466i | − | 1.10940i | ||||||
\(508\) | 1168.20i | 2.29960i | ||||||||
\(509\) | 829.277i | 1.62923i | 0.580004 | + | 0.814614i | \(0.303051\pi\) | ||||
−0.580004 | + | 0.814614i | \(0.696949\pi\) | |||||||
\(510\) | 780.000 | 1.52941 | ||||||||
\(511\) | −525.000 | −1.02740 | ||||||||
\(512\) | − | 1150.17i | − | 2.24643i | ||||||
\(513\) | 325.000 | + | 108.167i | 0.633528 | + | 0.210851i | ||||
\(514\) | 1508.00 | 2.93385 | ||||||||
\(515\) | 230.755i | 0.448069i | ||||||||
\(516\) | − | 648.999i | − | 1.25775i | ||||||
\(517\) | −100.000 | −0.193424 | ||||||||
\(518\) | −390.000 | −0.752896 | ||||||||
\(519\) | −442.000 | −0.851638 | ||||||||
\(520\) | 260.000 | 0.500000 | ||||||||
\(521\) | 612.944i | 1.17648i | 0.808688 | + | 0.588238i | \(0.200178\pi\) | ||||
−0.808688 | + | 0.588238i | \(0.799822\pi\) | |||||||
\(522\) | 260.000 | 0.498084 | ||||||||
\(523\) | 465.116i | 0.889323i | 0.895699 | + | 0.444662i | \(0.146676\pi\) | ||||
−0.895699 | + | 0.444662i | \(0.853324\pi\) | |||||||
\(524\) | −1008.00 | −1.92366 | ||||||||
\(525\) | − | 162.250i | − | 0.309047i | ||||||
\(526\) | 1117.72i | 2.12494i | ||||||||
\(527\) | − | 540.833i | − | 1.02625i | ||||||
\(528\) | 1045.61i | 1.98032i | ||||||||
\(529\) | 696.000 | 1.31569 | ||||||||
\(530\) | 1092.00 | 2.06038 | ||||||||
\(531\) | − | 72.1110i | − | 0.135802i | ||||||
\(532\) | −270.000 | + | 811.249i | −0.507519 | + | 1.52490i | ||||
\(533\) | −130.000 | −0.243902 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 302.866i | 0.566105i | ||||||||
\(536\) | 715.000 | 1.33396 | ||||||||
\(537\) | 130.000 | 0.242086 | ||||||||
\(538\) | −390.000 | −0.724907 | ||||||||
\(539\) | 240.000 | 0.445269 | ||||||||
\(540\) | 648.999i | 1.20185i | ||||||||
\(541\) | −600.000 | −1.10906 | −0.554529 | − | 0.832165i | \(-0.687101\pi\) | ||||
−0.554529 | + | 0.832165i | \(0.687101\pi\) | |||||||
\(542\) | 378.583i | 0.698492i | ||||||||
\(543\) | 390.000 | 0.718232 | ||||||||
\(544\) | 486.749i | 0.894760i | ||||||||
\(545\) | − | 793.221i | − | 1.45545i | ||||||
\(546\) | − | 234.361i | − | 0.429232i | ||||||
\(547\) | − | 598.522i | − | 1.09419i | −0.837071 | − | 0.547095i | \(-0.815734\pi\) | ||
0.837071 | − | 0.547095i | \(-0.184266\pi\) | |||||||
\(548\) | −1125.00 | −2.05292 | ||||||||
\(549\) | 160.000 | 0.291439 | ||||||||
\(550\) | 324.500i | 0.589999i | ||||||||
\(551\) | −325.000 | − | 108.167i | −0.589837 | − | 0.196310i | ||||
\(552\) | −2275.00 | −4.12138 | ||||||||
\(553\) | 180.278i | 0.325999i | ||||||||
\(554\) | − | 180.278i | − | 0.325411i | ||||||
\(555\) | −312.000 | −0.562162 | ||||||||
\(556\) | −450.000 | −0.809353 | ||||||||
\(557\) | 380.000 | 0.682226 | 0.341113 | − | 0.940022i | \(-0.389196\pi\) | ||||
0.341113 | + | 0.940022i | \(0.389196\pi\) | |||||||
\(558\) | −520.000 | −0.931900 | ||||||||
\(559\) | − | 72.1110i | − | 0.129000i | ||||||
\(560\) | −580.000 | −1.03571 | ||||||||
\(561\) | 540.833i | 0.964051i | ||||||||
\(562\) | 1040.00 | 1.85053 | ||||||||
\(563\) | 122.589i | 0.217742i | 0.994056 | + | 0.108871i | \(0.0347235\pi\) | ||||
−0.994056 | + | 0.108871i | \(0.965276\pi\) | |||||||
\(564\) | 324.500i | 0.575354i | ||||||||
\(565\) | − | 490.355i | − | 0.867885i | ||||||
\(566\) | − | 1153.78i | − | 2.03847i | ||||||
\(567\) | 505.000 | 0.890653 | ||||||||
\(568\) | 1950.00 | 3.43310 | ||||||||
\(569\) | 36.0555i | 0.0633665i | 0.999498 | + | 0.0316832i | \(0.0100868\pi\) | ||||
−0.999498 | + | 0.0316832i | \(0.989913\pi\) | |||||||
\(570\) | −312.000 | + | 937.443i | −0.547368 | + | 1.64464i | ||||
\(571\) | −790.000 | −1.38354 | −0.691769 | − | 0.722119i | \(-0.743168\pi\) | ||||
−0.691769 | + | 0.722119i | \(0.743168\pi\) | |||||||
\(572\) | 324.500i | 0.567307i | ||||||||
\(573\) | − | 695.871i | − | 1.21444i | ||||||
\(574\) | 650.000 | 1.13240 | ||||||||
\(575\) | −315.000 | −0.547826 | ||||||||
\(576\) | 4.00000 | 0.00694444 | ||||||||
\(577\) | 675.000 | 1.16984 | 0.584922 | − | 0.811090i | \(-0.301125\pi\) | ||||
0.584922 | + | 0.811090i | \(0.301125\pi\) | |||||||
\(578\) | − | 230.755i | − | 0.399231i | ||||||
\(579\) | 962.000 | 1.66149 | ||||||||
\(580\) | − | 648.999i | − | 1.11896i | ||||||
\(581\) | 200.000 | 0.344234 | ||||||||
\(582\) | 1593.65i | 2.73824i | ||||||||
\(583\) | 757.166i | 1.29874i | ||||||||
\(584\) | − | 1892.91i | − | 3.24129i | ||||||
\(585\) | − | 57.6888i | − | 0.0986134i | ||||||
\(586\) | 793.000 | 1.35324 | ||||||||
\(587\) | −280.000 | −0.477002 | −0.238501 | − | 0.971142i | \(-0.576656\pi\) | ||||
−0.238501 | + | 0.971142i | \(0.576656\pi\) | |||||||
\(588\) | − | 778.799i | − | 1.32449i | ||||||
\(589\) | 650.000 | + | 216.333i | 1.10357 | + | 0.367289i | ||||
\(590\) | −260.000 | −0.440678 | ||||||||
\(591\) | − | 324.500i | − | 0.549069i | ||||||
\(592\) | − | 627.366i | − | 1.05974i | ||||||
\(593\) | 750.000 | 1.26476 | 0.632378 | − | 0.774660i | \(-0.282079\pi\) | ||||
0.632378 | + | 0.774660i | \(0.282079\pi\) | |||||||
\(594\) | −650.000 | −1.09428 | ||||||||
\(595\) | −300.000 | −0.504202 | ||||||||
\(596\) | −630.000 | −1.05705 | ||||||||
\(597\) | − | 443.483i | − | 0.742852i | ||||||
\(598\) | −455.000 | −0.760870 | ||||||||
\(599\) | 504.777i | 0.842700i | 0.906898 | + | 0.421350i | \(0.138444\pi\) | ||||
−0.906898 | + | 0.421350i | \(0.861556\pi\) | |||||||
\(600\) | 585.000 | 0.975000 | ||||||||
\(601\) | 612.944i | 1.01987i | 0.860212 | + | 0.509937i | \(0.170331\pi\) | ||||
−0.860212 | + | 0.509937i | \(0.829669\pi\) | |||||||
\(602\) | 360.555i | 0.598929i | ||||||||
\(603\) | − | 158.644i | − | 0.263092i | ||||||
\(604\) | − | 324.500i | − | 0.537251i | ||||||
\(605\) | −84.0000 | −0.138843 | ||||||||
\(606\) | −650.000 | −1.07261 | ||||||||
\(607\) | − | 987.921i | − | 1.62755i | −0.581182 | − | 0.813774i | \(-0.697410\pi\) | ||
0.581182 | − | 0.813774i | \(-0.302590\pi\) | |||||||
\(608\) | −585.000 | − | 194.700i | −0.962171 | − | 0.320230i | ||||
\(609\) | −325.000 | −0.533662 | ||||||||
\(610\) | − | 576.888i | − | 0.945718i | ||||||
\(611\) | 36.0555i | 0.0590107i | ||||||||
\(612\) | 540.000 | 0.882353 | ||||||||
\(613\) | −1200.00 | −1.95759 | −0.978793 | − | 0.204853i | \(-0.934328\pi\) | ||||
−0.978793 | + | 0.204853i | \(0.934328\pi\) | |||||||
\(614\) | −858.000 | −1.39739 | ||||||||
\(615\) | 520.000 | 0.845528 | ||||||||
\(616\) | − | 901.388i | − | 1.46329i | ||||||
\(617\) | −350.000 | −0.567261 | −0.283630 | − | 0.958934i | \(-0.591539\pi\) | ||||
−0.283630 | + | 0.958934i | \(0.591539\pi\) | |||||||
\(618\) | 749.955i | 1.21352i | ||||||||
\(619\) | 560.000 | 0.904685 | 0.452342 | − | 0.891844i | \(-0.350588\pi\) | ||||
0.452342 | + | 0.891844i | \(0.350588\pi\) | |||||||
\(620\) | 1298.00i | 2.09355i | ||||||||
\(621\) | − | 630.971i | − | 1.01606i | ||||||
\(622\) | 1424.19i | 2.28970i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 377.000 | 0.604167 | ||||||||
\(625\) | −319.000 | −0.510400 | ||||||||
\(626\) | 450.694i | 0.719958i | ||||||||
\(627\) | −650.000 | − | 216.333i | −1.03668 | − | 0.345029i | ||||
\(628\) | −90.0000 | −0.143312 | ||||||||
\(629\) | − | 324.500i | − | 0.515898i | ||||||
\(630\) | 288.444i | 0.457848i | ||||||||
\(631\) | −1050.00 | −1.66403 | −0.832013 | − | 0.554757i | \(-0.812811\pi\) | ||||
−0.832013 | + | 0.554757i | \(0.812811\pi\) | |||||||
\(632\) | −650.000 | −1.02848 | ||||||||
\(633\) | −845.000 | −1.33491 | ||||||||
\(634\) | −13.0000 | −0.0205047 | ||||||||
\(635\) | − | 519.199i | − | 0.817637i | ||||||
\(636\) | 2457.00 | 3.86321 | ||||||||
\(637\) | − | 86.5332i | − | 0.135845i | ||||||
\(638\) | 650.000 | 1.01881 | ||||||||
\(639\) | − | 432.666i | − | 0.677099i | ||||||
\(640\) | 504.777i | 0.788714i | ||||||||
\(641\) | 1225.89i | 1.91246i | 0.292615 | + | 0.956230i | \(0.405475\pi\) | ||||
−0.292615 | + | 0.956230i | \(0.594525\pi\) | |||||||
\(642\) | 984.315i | 1.53320i | ||||||||
\(643\) | −1030.00 | −1.60187 | −0.800933 | − | 0.598754i | \(-0.795663\pi\) | ||||
−0.800933 | + | 0.598754i | \(0.795663\pi\) | |||||||
\(644\) | 1575.00 | 2.44565 | ||||||||
\(645\) | 288.444i | 0.447200i | ||||||||
\(646\) | −975.000 | − | 324.500i | −1.50929 | − | 0.502321i | ||||
\(647\) | 555.000 | 0.857805 | 0.428903 | − | 0.903351i | \(-0.358900\pi\) | ||||
0.428903 | + | 0.903351i | \(0.358900\pi\) | |||||||
\(648\) | 1820.80i | 2.80988i | ||||||||
\(649\) | − | 180.278i | − | 0.277777i | ||||||
\(650\) | 117.000 | 0.180000 | ||||||||
\(651\) | 650.000 | 0.998464 | ||||||||
\(652\) | 2430.00 | 3.72699 | ||||||||
\(653\) | 50.0000 | 0.0765697 | 0.0382848 | − | 0.999267i | \(-0.487811\pi\) | ||||
0.0382848 | + | 0.999267i | \(0.487811\pi\) | |||||||
\(654\) | − | 2577.97i | − | 3.94185i | ||||||
\(655\) | 448.000 | 0.683969 | ||||||||
\(656\) | 1045.61i | 1.59392i | ||||||||
\(657\) | −420.000 | −0.639269 | ||||||||
\(658\) | − | 180.278i | − | 0.273978i | ||||||
\(659\) | 198.305i | 0.300919i | 0.988616 | + | 0.150459i | \(0.0480752\pi\) | ||||
−0.988616 | + | 0.150459i | \(0.951925\pi\) | |||||||
\(660\) | − | 1298.00i | − | 1.96666i | ||||||
\(661\) | 198.305i | 0.300008i | 0.988685 | + | 0.150004i | \(0.0479287\pi\) | ||||
−0.988685 | + | 0.150004i | \(0.952071\pi\) | |||||||
\(662\) | 715.000 | 1.08006 | ||||||||
\(663\) | 195.000 | 0.294118 | ||||||||
\(664\) | 721.110i | 1.08601i | ||||||||
\(665\) | 120.000 | − | 360.555i | 0.180451 | − | 0.542188i | ||||
\(666\) | −312.000 | −0.468468 | ||||||||
\(667\) | 630.971i | 0.945984i | ||||||||
\(668\) | − | 1103.30i | − | 1.65164i | ||||||
\(669\) | −728.000 | −1.08819 | ||||||||
\(670\) | −572.000 | −0.853731 | ||||||||
\(671\) | 400.000 | 0.596125 | ||||||||
\(672\) | −585.000 | −0.870536 | ||||||||
\(673\) | 598.522i | 0.889334i | 0.895696 | + | 0.444667i | \(0.146678\pi\) | ||||
−0.895696 | + | 0.444667i | \(0.853322\pi\) | |||||||
\(674\) | −208.000 | −0.308605 | ||||||||
\(675\) | 162.250i | 0.240370i | ||||||||
\(676\) | −1404.00 | −2.07692 | ||||||||
\(677\) | 68.5055i | 0.101190i | 0.998719 | + | 0.0505949i | \(0.0161117\pi\) | ||||
−0.998719 | + | 0.0505949i | \(0.983888\pi\) | |||||||
\(678\) | − | 1593.65i | − | 2.35052i | ||||||
\(679\) | − | 612.944i | − | 0.902715i | ||||||
\(680\) | − | 1081.67i | − | 1.59068i | ||||||
\(681\) | 923.000 | 1.35536 | ||||||||
\(682\) | −1300.00 | −1.90616 | ||||||||
\(683\) | − | 237.966i | − | 0.348413i | −0.984709 | − | 0.174207i | \(-0.944264\pi\) | ||
0.984709 | − | 0.174207i | \(-0.0557361\pi\) | |||||||
\(684\) | −216.000 | + | 648.999i | −0.315789 | + | 0.948829i | ||||
\(685\) | 500.000 | 0.729927 | ||||||||
\(686\) | 1316.03i | 1.91841i | ||||||||
\(687\) | 576.888i | 0.839721i | ||||||||
\(688\) | −580.000 | −0.843023 | ||||||||
\(689\) | 273.000 | 0.396226 | ||||||||
\(690\) | 1820.00 | 2.63768 | ||||||||
\(691\) | −820.000 | −1.18669 | −0.593343 | − | 0.804950i | \(-0.702192\pi\) | ||||
−0.593343 | + | 0.804950i | \(0.702192\pi\) | |||||||
\(692\) | 1103.30i | 1.59436i | ||||||||
\(693\) | −200.000 | −0.288600 | ||||||||
\(694\) | − | 144.222i | − | 0.207813i | ||||||
\(695\) | 200.000 | 0.287770 | ||||||||
\(696\) | − | 1171.80i | − | 1.68363i | ||||||
\(697\) | 540.833i | 0.775944i | ||||||||
\(698\) | 353.344i | 0.506224i | ||||||||
\(699\) | 973.499i | 1.39270i | ||||||||
\(700\) | −405.000 | −0.578571 | ||||||||
\(701\) | −540.000 | −0.770328 | −0.385164 | − | 0.922848i | \(-0.625855\pi\) | ||||
−0.385164 | + | 0.922848i | \(0.625855\pi\) | |||||||
\(702\) | 234.361i | 0.333847i | ||||||||
\(703\) | 390.000 | + | 129.800i | 0.554765 | + | 0.184637i | ||||
\(704\) | 10.0000 | 0.0142045 | ||||||||
\(705\) | − | 144.222i | − | 0.204570i | ||||||
\(706\) | − | 667.027i | − | 0.944797i | ||||||
\(707\) | 250.000 | 0.353607 | ||||||||
\(708\) | −585.000 | −0.826271 | ||||||||
\(709\) | 268.000 | 0.377997 | 0.188999 | − | 0.981977i | \(-0.439476\pi\) | ||||
0.188999 | + | 0.981977i | \(0.439476\pi\) | |||||||
\(710\) | −1560.00 | −2.19718 | ||||||||
\(711\) | 144.222i | 0.202844i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1261.94i | − | 1.76991i | ||||||
\(714\) | −975.000 | −1.36555 | ||||||||
\(715\) | − | 144.222i | − | 0.201709i | ||||||
\(716\) | − | 324.500i | − | 0.453212i | ||||||
\(717\) | − | 710.294i | − | 0.990647i | ||||||
\(718\) | − | 811.249i | − | 1.12987i | ||||||
\(719\) | 105.000 | 0.146036 | 0.0730181 | − | 0.997331i | \(-0.476737\pi\) | ||||
0.0730181 | + | 0.997331i | \(0.476737\pi\) | |||||||
\(720\) | −464.000 | −0.644444 | ||||||||
\(721\) | − | 288.444i | − | 0.400061i | ||||||
\(722\) | 780.000 | − | 1042.00i | 1.08033 | − | 1.44322i | ||||
\(723\) | 1430.00 | 1.97787 | ||||||||
\(724\) | − | 973.499i | − | 1.34461i | ||||||
\(725\) | − | 162.250i | − | 0.223793i | ||||||
\(726\) | −273.000 | −0.376033 | ||||||||
\(727\) | 695.000 | 0.955983 | 0.477992 | − | 0.878364i | \(-0.341365\pi\) | ||||
0.477992 | + | 0.878364i | \(0.341365\pi\) | |||||||
\(728\) | −325.000 | −0.446429 | ||||||||
\(729\) | −181.000 | −0.248285 | ||||||||
\(730\) | 1514.33i | 2.07443i | ||||||||
\(731\) | −300.000 | −0.410397 | ||||||||
\(732\) | − | 1298.00i | − | 1.77322i | ||||||
\(733\) | 160.000 | 0.218281 | 0.109141 | − | 0.994026i | \(-0.465190\pi\) | ||||
0.109141 | + | 0.994026i | \(0.465190\pi\) | |||||||
\(734\) | 180.278i | 0.245610i | ||||||||
\(735\) | 346.133i | 0.470929i | ||||||||
\(736\) | 1135.75i | 1.54314i | ||||||||
\(737\) | − | 396.611i | − | 0.538142i | ||||||
\(738\) | 520.000 | 0.704607 | ||||||||
\(739\) | 1028.00 | 1.39107 | 0.695535 | − | 0.718493i | \(-0.255168\pi\) | ||||
0.695535 | + | 0.718493i | \(0.255168\pi\) | |||||||
\(740\) | 778.799i | 1.05243i | ||||||||
\(741\) | −78.0000 | + | 234.361i | −0.105263 | + | 0.316276i | ||||
\(742\) | −1365.00 | −1.83962 | ||||||||
\(743\) | − | 526.410i | − | 0.708493i | −0.935152 | − | 0.354247i | \(-0.884737\pi\) | ||
0.935152 | − | 0.354247i | \(-0.115263\pi\) | |||||||
\(744\) | 2343.61i | 3.15001i | ||||||||
\(745\) | 280.000 | 0.375839 | ||||||||
\(746\) | 1573.00 | 2.10858 | ||||||||
\(747\) | 160.000 | 0.214190 | ||||||||
\(748\) | 1350.00 | 1.80481 | ||||||||
\(749\) | − | 378.583i | − | 0.505451i | ||||||
\(750\) | −1768.00 | −2.35733 | ||||||||
\(751\) | 36.0555i | 0.0480100i | 0.999712 | + | 0.0240050i | \(0.00764176\pi\) | ||||
−0.999712 | + | 0.0240050i | \(0.992358\pi\) | |||||||
\(752\) | 290.000 | 0.385638 | ||||||||
\(753\) | 1449.43i | 1.92488i | ||||||||
\(754\) | − | 234.361i | − | 0.310823i | ||||||
\(755\) | 144.222i | 0.191023i | ||||||||
\(756\) | − | 811.249i | − | 1.07308i | ||||||
\(757\) | 60.0000 | 0.0792602 | 0.0396301 | − | 0.999214i | \(-0.487382\pi\) | ||||
0.0396301 | + | 0.999214i | \(0.487382\pi\) | |||||||
\(758\) | 1755.00 | 2.31530 | ||||||||
\(759\) | 1261.94i | 1.66264i | ||||||||
\(760\) | 1300.00 | + | 432.666i | 1.71053 | + | 0.569298i | ||||
\(761\) | −655.000 | −0.860710 | −0.430355 | − | 0.902660i | \(-0.641612\pi\) | ||||
−0.430355 | + | 0.902660i | \(0.641612\pi\) | |||||||
\(762\) | − | 1687.40i | − | 2.21443i | ||||||
\(763\) | 991.527i | 1.29951i | ||||||||
\(764\) | −1737.00 | −2.27356 | ||||||||
\(765\) | −240.000 | −0.313725 | ||||||||
\(766\) | −728.000 | −0.950392 | ||||||||
\(767\) | −65.0000 | −0.0847458 | ||||||||
\(768\) | 1654.95i | 2.15488i | ||||||||
\(769\) | −185.000 | −0.240572 | −0.120286 | − | 0.992739i | \(-0.538381\pi\) | ||||
−0.120286 | + | 0.992739i | \(0.538381\pi\) | |||||||
\(770\) | 721.110i | 0.936507i | ||||||||
\(771\) | −1508.00 | −1.95590 | ||||||||
\(772\) | − | 2401.30i | − | 3.11049i | ||||||
\(773\) | − | 320.894i | − | 0.415128i | −0.978221 | − | 0.207564i | \(-0.933446\pi\) | ||
0.978221 | − | 0.207564i | \(-0.0665536\pi\) | |||||||
\(774\) | 288.444i | 0.372667i | ||||||||
\(775\) | 324.500i | 0.418709i | ||||||||
\(776\) | 2210.00 | 2.84794 | ||||||||
\(777\) | 390.000 | 0.501931 | ||||||||
\(778\) | − | 1723.45i | − | 2.21524i | ||||||
\(779\) | −650.000 | − | 216.333i | −0.834403 | − | 0.277706i | ||||
\(780\) | −468.000 | −0.600000 | ||||||||
\(781\) | − | 1081.67i | − | 1.38497i | ||||||
\(782\) | 1892.91i | 2.42061i | ||||||||
\(783\) | 325.000 | 0.415070 | ||||||||
\(784\) | −696.000 | −0.887755 | ||||||||
\(785\) | 40.0000 | 0.0509554 | ||||||||
\(786\) | 1456.00 | 1.85242 | ||||||||
\(787\) | 68.5055i | 0.0870463i | 0.999052 | + | 0.0435232i | \(0.0138582\pi\) | ||||
−0.999052 | + | 0.0435232i | \(0.986142\pi\) | |||||||
\(788\) | −810.000 | −1.02792 | ||||||||
\(789\) | − | 1117.72i | − | 1.41663i | ||||||
\(790\) | 520.000 | 0.658228 | ||||||||
\(791\) | 612.944i | 0.774897i | ||||||||
\(792\) | − | 721.110i | − | 0.910493i | ||||||
\(793\) | − | 144.222i | − | 0.181869i | ||||||
\(794\) | 2704.16i | 3.40575i | ||||||||
\(795\) | −1092.00 | −1.37358 | ||||||||
\(796\) | −1107.00 | −1.39070 | ||||||||
\(797\) | 1258.34i | 1.57884i | 0.613852 | + | 0.789421i | \(0.289619\pi\) | ||||
−0.613852 | + | 0.789421i | \(0.710381\pi\) | |||||||
\(798\) | 390.000 | − | 1171.80i | 0.488722 | − | 1.46843i | ||||
\(799\) | 150.000 | 0.187735 | ||||||||
\(800\) | − | 292.050i | − | 0.365062i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1040.00 | 1.29676 | ||||||||
\(803\) | −1050.00 | −1.30760 | ||||||||
\(804\) | −1287.00 | −1.60075 | ||||||||
\(805\) | −700.000 | −0.869565 | ||||||||
\(806\) | 468.722i | 0.581541i | ||||||||
\(807\) | 390.000 | 0.483271 | ||||||||
\(808\) | 901.388i | 1.11558i | ||||||||
\(809\) | −7.00000 | −0.00865266 | −0.00432633 | − | 0.999991i | \(-0.501377\pi\) | ||||
−0.00432633 | + | 0.999991i | \(0.501377\pi\) | |||||||
\(810\) | − | 1456.64i | − | 1.79832i | ||||||
\(811\) | 1027.58i | 1.26706i | 0.773720 | + | 0.633528i | \(0.218394\pi\) | ||||
−0.773720 | + | 0.633528i | \(0.781606\pi\) | |||||||
\(812\) | 811.249i | 0.999075i | ||||||||
\(813\) | − | 378.583i | − | 0.465662i | ||||||
\(814\) | −780.000 | −0.958231 | ||||||||
\(815\) | −1080.00 | −1.32515 | ||||||||
\(816\) | − | 1568.41i | − | 1.92208i | ||||||
\(817\) | 120.000 | − | 360.555i | 0.146879 | − | 0.441316i | ||||
\(818\) | 130.000 | 0.158924 | ||||||||
\(819\) | 72.1110i | 0.0880477i | ||||||||
\(820\) | − | 1298.00i | − | 1.58292i | ||||||
\(821\) | 842.000 | 1.02558 | 0.512789 | − | 0.858515i | \(-0.328612\pi\) | ||||
0.512789 | + | 0.858515i | \(0.328612\pi\) | |||||||
\(822\) | 1625.00 | 1.97689 | ||||||||
\(823\) | 775.000 | 0.941677 | 0.470838 | − | 0.882219i | \(-0.343951\pi\) | ||||
0.470838 | + | 0.882219i | \(0.343951\pi\) | |||||||
\(824\) | 1040.00 | 1.26214 | ||||||||
\(825\) | − | 324.500i | − | 0.393333i | ||||||
\(826\) | 325.000 | 0.393462 | ||||||||
\(827\) | − | 1265.55i | − | 1.53029i | −0.643859 | − | 0.765144i | \(-0.722668\pi\) | ||
0.643859 | − | 0.765144i | \(-0.277332\pi\) | |||||||
\(828\) | 1260.00 | 1.52174 | ||||||||
\(829\) | − | 1568.41i | − | 1.89194i | −0.324260 | − | 0.945968i | \(-0.605115\pi\) | ||
0.324260 | − | 0.945968i | \(-0.394885\pi\) | |||||||
\(830\) | − | 576.888i | − | 0.695046i | ||||||
\(831\) | 180.278i | 0.216941i | ||||||||
\(832\) | − | 3.60555i | − | 0.00433360i | ||||||
\(833\) | −360.000 | −0.432173 | ||||||||
\(834\) | 650.000 | 0.779376 | ||||||||
\(835\) | 490.355i | 0.587251i | ||||||||
\(836\) | −540.000 | + | 1622.50i | −0.645933 | + | 1.94079i | ||||
\(837\) | −650.000 | −0.776583 | ||||||||
\(838\) | 403.822i | 0.481888i | ||||||||
\(839\) | − | 1153.78i | − | 1.37518i | −0.726099 | − | 0.687590i | \(-0.758669\pi\) | ||
0.726099 | − | 0.687590i | \(-0.241331\pi\) | |||||||
\(840\) | 1300.00 | 1.54762 | ||||||||
\(841\) | 516.000 | 0.613555 | ||||||||
\(842\) | −2275.00 | −2.70190 | ||||||||
\(843\) | −1040.00 | −1.23369 | ||||||||
\(844\) | 2109.25i | 2.49911i | ||||||||
\(845\) | 624.000 | 0.738462 | ||||||||
\(846\) | − | 144.222i | − | 0.170475i | ||||||
\(847\) | 105.000 | 0.123967 | ||||||||
\(848\) | − | 2195.78i | − | 2.58936i | ||||||
\(849\) | 1153.78i | 1.35898i | ||||||||
\(850\) | − | 486.749i | − | 0.572646i | ||||||
\(851\) | − | 757.166i | − | 0.889737i | ||||||
\(852\) | −3510.00 | −4.11972 | ||||||||
\(853\) | 400.000 | 0.468933 | 0.234467 | − | 0.972124i | \(-0.424666\pi\) | ||||
0.234467 | + | 0.972124i | \(0.424666\pi\) | |||||||
\(854\) | 721.110i | 0.844391i | ||||||||
\(855\) | 96.0000 | − | 288.444i | 0.112281 | − | 0.337362i | ||||
\(856\) | 1365.00 | 1.59463 | ||||||||
\(857\) | 158.644i | 0.185116i | 0.995707 | + | 0.0925579i | \(0.0295043\pi\) | ||||
−0.995707 | + | 0.0925579i | \(0.970496\pi\) | |||||||
\(858\) | − | 468.722i | − | 0.546296i | ||||||
\(859\) | 1432.00 | 1.66705 | 0.833527 | − | 0.552478i | \(-0.186318\pi\) | ||||
0.833527 | + | 0.552478i | \(0.186318\pi\) | |||||||
\(860\) | 720.000 | 0.837209 | ||||||||
\(861\) | −650.000 | −0.754936 | ||||||||
\(862\) | 1560.00 | 1.80974 | ||||||||
\(863\) | − | 129.800i | − | 0.150405i | −0.997168 | − | 0.0752027i | \(-0.976040\pi\) | ||
0.997168 | − | 0.0752027i | \(-0.0239604\pi\) | |||||||
\(864\) | 585.000 | 0.677083 | ||||||||
\(865\) | − | 490.355i | − | 0.566884i | ||||||
\(866\) | 2652.00 | 3.06236 | ||||||||
\(867\) | 230.755i | 0.266154i | ||||||||
\(868\) | − | 1622.50i | − | 1.86924i | ||||||
\(869\) | 360.555i | 0.414908i | ||||||||
\(870\) | 937.443i | 1.07752i | ||||||||
\(871\) | −143.000 | −0.164179 | ||||||||
\(872\) | −3575.00 | −4.09977 | ||||||||
\(873\) | − | 490.355i | − | 0.561690i | ||||||
\(874\) | −2275.00 | − | 757.166i | −2.60297 | − | 0.866322i | ||||
\(875\) | 680.000 | 0.777143 | ||||||||
\(876\) | 3407.25i | 3.88955i | ||||||||
\(877\) | 393.005i | 0.448124i | 0.974575 | + | 0.224062i | \(0.0719319\pi\) | ||||
−0.974575 | + | 0.224062i | \(0.928068\pi\) | |||||||
\(878\) | −2860.00 | −3.25740 | ||||||||
\(879\) | −793.000 | −0.902162 | ||||||||
\(880\) | −1160.00 | −1.31818 | ||||||||
\(881\) | 750.000 | 0.851305 | 0.425653 | − | 0.904887i | \(-0.360045\pi\) | ||||
0.425653 | + | 0.904887i | \(0.360045\pi\) | |||||||
\(882\) | 346.133i | 0.392441i | ||||||||
\(883\) | 120.000 | 0.135900 | 0.0679502 | − | 0.997689i | \(-0.478354\pi\) | ||||
0.0679502 | + | 0.997689i | \(0.478354\pi\) | |||||||
\(884\) | − | 486.749i | − | 0.550622i | ||||||
\(885\) | 260.000 | 0.293785 | ||||||||
\(886\) | 2415.72i | 2.72655i | ||||||||
\(887\) | 850.910i | 0.959312i | 0.877457 | + | 0.479656i | \(0.159239\pi\) | ||||
−0.877457 | + | 0.479656i | \(0.840761\pi\) | |||||||
\(888\) | 1406.16i | 1.58352i | ||||||||
\(889\) | 648.999i | 0.730033i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1010.00 | 1.13356 | ||||||||
\(892\) | 1817.20i | 2.03722i | ||||||||
\(893\) | −60.0000 | + | 180.278i | −0.0671892 | + | 0.201879i | ||||
\(894\) | 910.000 | 1.01790 | ||||||||
\(895\) | 144.222i | 0.161142i | ||||||||
\(896\) | − | 630.971i | − | 0.704209i | ||||||
\(897\) | 455.000 | 0.507246 | ||||||||
\(898\) | 130.000 | 0.144766 | ||||||||
\(899\) | 650.000 | 0.723026 | ||||||||
\(900\) | −324.000 | −0.360000 | ||||||||
\(901\) | − | 1135.75i | − | 1.26054i | ||||||
\(902\) | 1300.00 | 1.44124 | ||||||||
\(903\) | − | 360.555i | − | 0.399286i | ||||||
\(904\) | −2210.00 | −2.44469 | ||||||||
\(905\) | 432.666i | 0.478084i | ||||||||
\(906\) | 468.722i | 0.517353i | ||||||||
\(907\) | − | 645.394i | − | 0.711570i | −0.934568 | − | 0.355785i | \(-0.884214\pi\) | ||
0.934568 | − | 0.355785i | \(-0.115786\pi\) | |||||||
\(908\) | − | 2303.95i | − | 2.53739i | ||||||
\(909\) | 200.000 | 0.220022 | ||||||||
\(910\) | 260.000 | 0.285714 | ||||||||
\(911\) | − | 1225.89i | − | 1.34565i | −0.739802 | − | 0.672825i | \(-0.765081\pi\) | ||
0.739802 | − | 0.672825i | \(-0.234919\pi\) | |||||||
\(912\) | 1885.00 | + | 627.366i | 2.06689 | + | 0.687901i | ||||
\(913\) | 400.000 | 0.438116 | ||||||||
\(914\) | − | 2722.19i | − | 2.97833i | ||||||
\(915\) | 576.888i | 0.630479i | ||||||||
\(916\) | 1440.00 | 1.57205 | ||||||||
\(917\) | −560.000 | −0.610687 | ||||||||
\(918\) | 975.000 | 1.06209 | ||||||||
\(919\) | −513.000 | −0.558215 | −0.279108 | − | 0.960260i | \(-0.590039\pi\) | ||||
−0.279108 | + | 0.960260i | \(0.590039\pi\) | |||||||
\(920\) | − | 2523.89i | − | 2.74335i | ||||||
\(921\) | 858.000 | 0.931596 | ||||||||
\(922\) | 2783.49i | 3.01896i | ||||||||
\(923\) | −390.000 | −0.422535 | ||||||||
\(924\) | 1622.50i | 1.75595i | ||||||||
\(925\) | 194.700i | 0.210486i | ||||||||
\(926\) | − | 1261.94i | − | 1.36279i | ||||||
\(927\) | − | 230.755i | − | 0.248927i | ||||||
\(928\) | −585.000 | −0.630388 | ||||||||
\(929\) | −1217.00 | −1.31001 | −0.655005 | − | 0.755624i | \(-0.727334\pi\) | ||||
−0.655005 | + | 0.755624i | \(0.727334\pi\) | |||||||
\(930\) | − | 1874.89i | − | 2.01601i | ||||||
\(931\) | 144.000 | − | 432.666i | 0.154672 | − | 0.464733i | ||||
\(932\) | 2430.00 | 2.60730 | ||||||||
\(933\) | − | 1424.19i | − | 1.52647i | ||||||
\(934\) | 252.389i | 0.270223i | ||||||||
\(935\) | −600.000 | −0.641711 | ||||||||
\(936\) | −260.000 | −0.277778 | ||||||||
\(937\) | −1095.00 | −1.16862 | −0.584312 | − | 0.811529i | \(-0.698635\pi\) | ||||
−0.584312 | + | 0.811529i | \(0.698635\pi\) | |||||||
\(938\) | 715.000 | 0.762260 | ||||||||
\(939\) | − | 450.694i | − | 0.479972i | ||||||
\(940\) | −360.000 | −0.382979 | ||||||||
\(941\) | 1099.69i | 1.16864i | 0.811522 | + | 0.584322i | \(0.198639\pi\) | ||||
−0.811522 | + | 0.584322i | \(0.801361\pi\) | |||||||
\(942\) | 130.000 | 0.138004 | ||||||||
\(943\) | 1261.94i | 1.33822i | ||||||||
\(944\) | 522.805i | 0.553819i | ||||||||
\(945\) | 360.555i | 0.381540i | ||||||||
\(946\) | 721.110i | 0.762273i | ||||||||
\(947\) | 640.000 | 0.675818 | 0.337909 | − | 0.941179i | \(-0.390280\pi\) | ||||
0.337909 | + | 0.941179i | \(0.390280\pi\) | |||||||
\(948\) | 1170.00 | 1.23418 | ||||||||
\(949\) | 378.583i | 0.398928i | ||||||||
\(950\) | 585.000 | + | 194.700i | 0.615789 | + | 0.204947i | ||||
\(951\) | 13.0000 | 0.0136698 | ||||||||
\(952\) | 1352.08i | 1.42025i | ||||||||
\(953\) | 1168.20i | 1.22581i | 0.790156 | + | 0.612906i | \(0.210000\pi\) | ||||
−0.790156 | + | 0.612906i | \(0.790000\pi\) | |||||||
\(954\) | −1092.00 | −1.14465 | ||||||||
\(955\) | 772.000 | 0.808377 | ||||||||
\(956\) | −1773.00 | −1.85460 | ||||||||
\(957\) | −650.000 | −0.679206 | ||||||||
\(958\) | − | 1334.05i | − | 1.39254i | ||||||
\(959\) | −625.000 | −0.651721 | ||||||||
\(960\) | 14.4222i | 0.0150231i | ||||||||
\(961\) | −339.000 | −0.352758 | ||||||||
\(962\) | 281.233i | 0.292342i | ||||||||
\(963\) | − | 302.866i | − | 0.314503i | ||||||
\(964\) | − | 3569.50i | − | 3.70280i | ||||||
\(965\) | 1067.24i | 1.10595i | ||||||||
\(966\) | −2275.00 | −2.35507 | ||||||||
\(967\) | −1010.00 | −1.04447 | −0.522234 | − | 0.852802i | \(-0.674901\pi\) | ||||
−0.522234 | + | 0.852802i | \(0.674901\pi\) | |||||||
\(968\) | 378.583i | 0.391098i | ||||||||
\(969\) | 975.000 | + | 324.500i | 1.00619 | + | 0.334881i | ||||
\(970\) | −1768.00 | −1.82268 | ||||||||
\(971\) | − | 757.166i | − | 0.779779i | −0.920862 | − | 0.389890i | \(-0.872513\pi\) | ||
0.920862 | − | 0.389890i | \(-0.127487\pi\) | |||||||
\(972\) | − | 1817.20i | − | 1.86955i | ||||||
\(973\) | −250.000 | −0.256937 | ||||||||
\(974\) | 1872.00 | 1.92197 | ||||||||
\(975\) | −117.000 | −0.120000 | ||||||||
\(976\) | −1160.00 | −1.18852 | ||||||||
\(977\) | 598.522i | 0.612612i | 0.951933 | + | 0.306306i | \(0.0990930\pi\) | ||||
−0.951933 | + | 0.306306i | \(0.900907\pi\) | |||||||
\(978\) | −3510.00 | −3.58896 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 864.000 | 0.881633 | ||||||||
\(981\) | 793.221i | 0.808584i | ||||||||
\(982\) | − | 2278.71i | − | 2.32048i | ||||||
\(983\) | 57.6888i | 0.0586865i | 0.999569 | + | 0.0293432i | \(0.00934159\pi\) | ||||
−0.999569 | + | 0.0293432i | \(0.990658\pi\) | |||||||
\(984\) | − | 2343.61i | − | 2.38172i | ||||||
\(985\) | 360.000 | 0.365482 | ||||||||
\(986\) | −975.000 | −0.988844 | ||||||||
\(987\) | 180.278i | 0.182652i | ||||||||
\(988\) | 585.000 | + | 194.700i | 0.592105 | + | 0.197065i | ||||
\(989\) | −700.000 | −0.707786 | ||||||||
\(990\) | 576.888i | 0.582715i | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 1170.00 | 1.17944 | ||||||||
\(993\) | −715.000 | −0.720040 | ||||||||
\(994\) | 1950.00 | 1.96177 | ||||||||
\(995\) | 492.000 | 0.494472 | ||||||||
\(996\) | − | 1298.00i | − | 1.30321i | ||||||
\(997\) | −170.000 | −0.170512 | −0.0852558 | − | 0.996359i | \(-0.527171\pi\) | ||||
−0.0852558 | + | 0.996359i | \(0.527171\pi\) | |||||||
\(998\) | 1370.11i | 1.37286i | ||||||||
\(999\) | −390.000 | −0.390390 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))