Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(474,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.474");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.d (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: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 19) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 474.3 | ||
Root | \(-1.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.474 |
Dual form | 475.3.d.b.474.4 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.60555 | 1.80278 | 0.901388 | − | 0.433013i | \(-0.142549\pi\) | ||||
0.901388 | + | 0.433013i | \(0.142549\pi\) | |||||||
\(3\) | 3.60555 | 1.20185 | 0.600925 | − | 0.799305i | \(-0.294799\pi\) | ||||
0.600925 | + | 0.799305i | \(0.294799\pi\) | |||||||
\(4\) | 9.00000 | 2.25000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 13.0000 | 2.16667 | ||||||||
\(7\) | − | 5.00000i | − | 0.714286i | −0.934050 | − | 0.357143i | \(-0.883751\pi\) | ||
0.934050 | − | 0.357143i | \(-0.116249\pi\) | |||||||
\(8\) | 18.0278 | 2.25347 | ||||||||
\(9\) | 4.00000 | 0.444444 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.0000 | −0.909091 | −0.454545 | − | 0.890724i | \(-0.650198\pi\) | ||||
−0.454545 | + | 0.890724i | \(0.650198\pi\) | |||||||
\(12\) | 32.4500 | 2.70416 | ||||||||
\(13\) | −3.60555 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | − | 18.0278i | − | 1.28770i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 29.0000 | 1.81250 | ||||||||
\(17\) | 15.0000i | 0.882353i | 0.897420 | + | 0.441176i | \(0.145439\pi\) | ||||
−0.897420 | + | 0.441176i | \(0.854561\pi\) | |||||||
\(18\) | 14.4222 | 0.801234 | ||||||||
\(19\) | 6.00000 | + | 18.0278i | 0.315789 | + | 0.948829i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 18.0278i | − | 0.858465i | ||||||
\(22\) | −36.0555 | −1.63889 | ||||||||
\(23\) | − | 35.0000i | − | 1.52174i | −0.648905 | − | 0.760870i | \(-0.724773\pi\) | ||
0.648905 | − | 0.760870i | \(-0.275227\pi\) | |||||||
\(24\) | 65.0000 | 2.70833 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −13.0000 | −0.500000 | ||||||||
\(27\) | −18.0278 | −0.667695 | ||||||||
\(28\) | − | 45.0000i | − | 1.60714i | ||||||
\(29\) | 18.0278i | 0.621647i | 0.950468 | + | 0.310823i | \(0.100605\pi\) | ||||
−0.950468 | + | 0.310823i | \(0.899395\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.0555i | 1.16308i | 0.813517 | + | 0.581541i | \(0.197550\pi\) | ||||
−0.813517 | + | 0.581541i | \(0.802450\pi\) | |||||||
\(32\) | 32.4500 | 1.01406 | ||||||||
\(33\) | −36.0555 | −1.09259 | ||||||||
\(34\) | 54.0833i | 1.59068i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 1.00000 | ||||||||
\(37\) | −21.6333 | −0.584684 | −0.292342 | − | 0.956314i | \(-0.594435\pi\) | ||||
−0.292342 | + | 0.956314i | \(0.594435\pi\) | |||||||
\(38\) | 21.6333 | + | 65.0000i | 0.569298 | + | 1.71053i | ||||
\(39\) | −13.0000 | −0.333333 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 36.0555i | − | 0.879403i | −0.898144 | − | 0.439701i | \(-0.855084\pi\) | ||
0.898144 | − | 0.439701i | \(-0.144916\pi\) | |||||||
\(42\) | − | 65.0000i | − | 1.54762i | ||||||
\(43\) | 20.0000i | 0.465116i | 0.972582 | + | 0.232558i | \(0.0747096\pi\) | ||||
−0.972582 | + | 0.232558i | \(0.925290\pi\) | |||||||
\(44\) | −90.0000 | −2.04545 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 126.194i | − | 2.74335i | ||||||
\(47\) | 10.0000i | 0.212766i | 0.994325 | + | 0.106383i | \(0.0339270\pi\) | ||||
−0.994325 | + | 0.106383i | \(0.966073\pi\) | |||||||
\(48\) | 104.561 | 2.17835 | ||||||||
\(49\) | 24.0000 | 0.489796 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 54.0833i | 1.06046i | ||||||||
\(52\) | −32.4500 | −0.624038 | ||||||||
\(53\) | 75.7166 | 1.42861 | 0.714307 | − | 0.699832i | \(-0.246742\pi\) | ||||
0.714307 | + | 0.699832i | \(0.246742\pi\) | |||||||
\(54\) | −65.0000 | −1.20370 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 90.1388i | − | 1.60962i | ||||||
\(57\) | 21.6333 | + | 65.0000i | 0.379532 | + | 1.14035i | ||||
\(58\) | 65.0000i | 1.12069i | ||||||||
\(59\) | 18.0278i | 0.305555i | 0.988261 | + | 0.152778i | \(0.0488218\pi\) | ||||
−0.988261 | + | 0.152778i | \(0.951178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40.0000 | −0.655738 | −0.327869 | − | 0.944723i | \(-0.606330\pi\) | ||||
−0.327869 | + | 0.944723i | \(0.606330\pi\) | |||||||
\(62\) | 130.000i | 2.09677i | ||||||||
\(63\) | − | 20.0000i | − | 0.317460i | ||||||
\(64\) | 1.00000 | 0.0156250 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −130.000 | −1.96970 | ||||||||
\(67\) | 39.6611 | 0.591956 | 0.295978 | − | 0.955195i | \(-0.404354\pi\) | ||||
0.295978 | + | 0.955195i | \(0.404354\pi\) | |||||||
\(68\) | 135.000i | 1.98529i | ||||||||
\(69\) | − | 126.194i | − | 1.82890i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 108.167i | − | 1.52347i | −0.647887 | − | 0.761736i | \(-0.724347\pi\) | ||
0.647887 | − | 0.761736i | \(-0.275653\pi\) | |||||||
\(72\) | 72.1110 | 1.00154 | ||||||||
\(73\) | − | 105.000i | − | 1.43836i | −0.694826 | − | 0.719178i | \(-0.744519\pi\) | ||
0.694826 | − | 0.719178i | \(-0.255481\pi\) | |||||||
\(74\) | −78.0000 | −1.05405 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 54.0000 | + | 162.250i | 0.710526 | + | 2.13487i | ||||
\(77\) | 50.0000i | 0.649351i | ||||||||
\(78\) | −46.8722 | −0.600925 | ||||||||
\(79\) | − | 36.0555i | − | 0.456399i | −0.973614 | − | 0.228199i | \(-0.926716\pi\) | ||
0.973614 | − | 0.228199i | \(-0.0732838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −101.000 | −1.24691 | ||||||||
\(82\) | − | 130.000i | − | 1.58537i | ||||||
\(83\) | 40.0000i | 0.481928i | 0.970534 | + | 0.240964i | \(0.0774635\pi\) | ||||
−0.970534 | + | 0.240964i | \(0.922536\pi\) | |||||||
\(84\) | − | 162.250i | − | 1.93155i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 72.1110i | 0.838500i | ||||||||
\(87\) | 65.0000i | 0.747126i | ||||||||
\(88\) | −180.278 | −2.04861 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.0278i | 0.198107i | ||||||||
\(92\) | − | 315.000i | − | 3.42391i | ||||||
\(93\) | 130.000i | 1.39785i | ||||||||
\(94\) | 36.0555i | 0.383569i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 117.000 | 1.21875 | ||||||||
\(97\) | 122.589 | 1.26380 | 0.631901 | − | 0.775049i | \(-0.282275\pi\) | ||||
0.631901 | + | 0.775049i | \(0.282275\pi\) | |||||||
\(98\) | 86.5332 | 0.882992 | ||||||||
\(99\) | −40.0000 | −0.404040 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −50.0000 | −0.495050 | −0.247525 | − | 0.968882i | \(-0.579617\pi\) | ||||
−0.247525 | + | 0.968882i | \(0.579617\pi\) | |||||||
\(102\) | 195.000i | 1.91176i | ||||||||
\(103\) | −57.6888 | −0.560086 | −0.280043 | − | 0.959988i | \(-0.590349\pi\) | ||||
−0.280043 | + | 0.959988i | \(0.590349\pi\) | |||||||
\(104\) | −65.0000 | −0.625000 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 273.000 | 2.57547 | ||||||||
\(107\) | 75.7166 | 0.707632 | 0.353816 | − | 0.935315i | \(-0.384884\pi\) | ||||
0.353816 | + | 0.935315i | \(0.384884\pi\) | |||||||
\(108\) | −162.250 | −1.50231 | ||||||||
\(109\) | − | 198.305i | − | 1.81931i | −0.415359 | − | 0.909657i | \(-0.636344\pi\) | ||
0.415359 | − | 0.909657i | \(-0.363656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −78.0000 | −0.702703 | ||||||||
\(112\) | − | 145.000i | − | 1.29464i | ||||||
\(113\) | 122.589 | 1.08486 | 0.542428 | − | 0.840102i | \(-0.317505\pi\) | ||||
0.542428 | + | 0.840102i | \(0.317505\pi\) | |||||||
\(114\) | 78.0000 | + | 234.361i | 0.684211 | + | 2.05580i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 162.250i | 1.39871i | ||||||||
\(117\) | −14.4222 | −0.123267 | ||||||||
\(118\) | 65.0000i | 0.550847i | ||||||||
\(119\) | 75.0000 | 0.630252 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.0000 | −0.173554 | ||||||||
\(122\) | −144.222 | −1.18215 | ||||||||
\(123\) | − | 130.000i | − | 1.05691i | ||||||
\(124\) | 324.500i | 2.61693i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 72.1110i | − | 0.572310i | ||||||
\(127\) | −129.800 | −1.02205 | −0.511023 | − | 0.859567i | \(-0.670733\pi\) | ||||
−0.511023 | + | 0.859567i | \(0.670733\pi\) | |||||||
\(128\) | −126.194 | −0.985893 | ||||||||
\(129\) | 72.1110i | 0.559000i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 112.000 | 0.854962 | 0.427481 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427481 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(132\) | −324.500 | −2.45833 | ||||||||
\(133\) | 90.1388 | − | 30.0000i | 0.677735 | − | 0.225564i | ||||
\(134\) | 143.000 | 1.06716 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 270.416i | 1.98836i | ||||||||
\(137\) | 125.000i | 0.912409i | 0.889875 | + | 0.456204i | \(0.150791\pi\) | ||||
−0.889875 | + | 0.456204i | \(0.849209\pi\) | |||||||
\(138\) | − | 455.000i | − | 3.29710i | ||||||
\(139\) | −50.0000 | −0.359712 | −0.179856 | − | 0.983693i | \(-0.557563\pi\) | ||||
−0.179856 | + | 0.983693i | \(0.557563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 36.0555i | 0.255713i | ||||||||
\(142\) | − | 390.000i | − | 2.74648i | ||||||
\(143\) | 36.0555 | 0.252136 | ||||||||
\(144\) | 116.000 | 0.805556 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 378.583i | − | 2.59303i | ||||||
\(147\) | 86.5332 | 0.588661 | ||||||||
\(148\) | −194.700 | −1.31554 | ||||||||
\(149\) | −70.0000 | −0.469799 | −0.234899 | − | 0.972020i | \(-0.575476\pi\) | ||||
−0.234899 | + | 0.972020i | \(0.575476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 36.0555i | − | 0.238778i | −0.992848 | − | 0.119389i | \(-0.961906\pi\) | ||
0.992848 | − | 0.119389i | \(-0.0380936\pi\) | |||||||
\(152\) | 108.167 | + | 325.000i | 0.711622 | + | 2.13816i | ||||
\(153\) | 60.0000i | 0.392157i | ||||||||
\(154\) | 180.278i | 1.17063i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −117.000 | −0.750000 | ||||||||
\(157\) | 10.0000i | 0.0636943i | 0.999493 | + | 0.0318471i | \(0.0101390\pi\) | ||||
−0.999493 | + | 0.0318471i | \(0.989861\pi\) | |||||||
\(158\) | − | 130.000i | − | 0.822785i | ||||||
\(159\) | 273.000 | 1.71698 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −175.000 | −1.08696 | ||||||||
\(162\) | −364.161 | −2.24791 | ||||||||
\(163\) | 270.000i | 1.65644i | 0.560402 | + | 0.828221i | \(0.310647\pi\) | ||||
−0.560402 | + | 0.828221i | \(0.689353\pi\) | |||||||
\(164\) | − | 324.500i | − | 1.97866i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 144.222i | 0.868808i | ||||||||
\(167\) | 122.589 | 0.734064 | 0.367032 | − | 0.930208i | \(-0.380374\pi\) | ||||
0.367032 | + | 0.930208i | \(0.380374\pi\) | |||||||
\(168\) | − | 325.000i | − | 1.93452i | ||||||
\(169\) | −156.000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.0000 | + | 72.1110i | 0.140351 | + | 0.421702i | ||||
\(172\) | 180.000i | 1.04651i | ||||||||
\(173\) | 122.589 | 0.708605 | 0.354303 | − | 0.935131i | \(-0.384718\pi\) | ||||
0.354303 | + | 0.935131i | \(0.384718\pi\) | |||||||
\(174\) | 234.361i | 1.34690i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −290.000 | −1.64773 | ||||||||
\(177\) | 65.0000i | 0.367232i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 36.0555i | 0.201427i | 0.994915 | + | 0.100714i | \(0.0321126\pi\) | ||||
−0.994915 | + | 0.100714i | \(0.967887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 108.167i | − | 0.597605i | −0.954315 | − | 0.298803i | \(-0.903413\pi\) | ||
0.954315 | − | 0.298803i | \(-0.0965872\pi\) | |||||||
\(182\) | 65.0000i | 0.357143i | ||||||||
\(183\) | −144.222 | −0.788099 | ||||||||
\(184\) | − | 630.971i | − | 3.42919i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 468.722i | 2.52001i | ||||||||
\(187\) | − | 150.000i | − | 0.802139i | ||||||
\(188\) | 90.0000i | 0.478723i | ||||||||
\(189\) | 90.1388i | 0.476925i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 193.000 | 1.01047 | 0.505236 | − | 0.862981i | \(-0.331406\pi\) | ||||
0.505236 | + | 0.862981i | \(0.331406\pi\) | |||||||
\(192\) | 3.60555 | 0.0187789 | ||||||||
\(193\) | −266.811 | −1.38244 | −0.691220 | − | 0.722645i | \(-0.742926\pi\) | ||||
−0.691220 | + | 0.722645i | \(0.742926\pi\) | |||||||
\(194\) | 442.000 | 2.27835 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 216.000 | 1.10204 | ||||||||
\(197\) | 90.0000i | 0.456853i | 0.973561 | + | 0.228426i | \(0.0733580\pi\) | ||||
−0.973561 | + | 0.228426i | \(0.926642\pi\) | |||||||
\(198\) | −144.222 | −0.728394 | ||||||||
\(199\) | −123.000 | −0.618090 | −0.309045 | − | 0.951047i | \(-0.600009\pi\) | ||||
−0.309045 | + | 0.951047i | \(0.600009\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 143.000 | 0.711443 | ||||||||
\(202\) | −180.278 | −0.892463 | ||||||||
\(203\) | 90.1388 | 0.444033 | ||||||||
\(204\) | 486.749i | 2.38603i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −208.000 | −1.00971 | ||||||||
\(207\) | − | 140.000i | − | 0.676329i | ||||||
\(208\) | −104.561 | −0.502697 | ||||||||
\(209\) | −60.0000 | − | 180.278i | −0.287081 | − | 0.862572i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 234.361i | 1.11071i | 0.831612 | + | 0.555357i | \(0.187419\pi\) | ||||
−0.831612 | + | 0.555357i | \(0.812581\pi\) | |||||||
\(212\) | 681.449 | 3.21438 | ||||||||
\(213\) | − | 390.000i | − | 1.83099i | ||||||
\(214\) | 273.000 | 1.27570 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −325.000 | −1.50463 | ||||||||
\(217\) | 180.278 | 0.830772 | ||||||||
\(218\) | − | 715.000i | − | 3.27982i | ||||||
\(219\) | − | 378.583i | − | 1.72869i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 54.0833i | − | 0.244721i | ||||||
\(222\) | −281.233 | −1.26682 | ||||||||
\(223\) | 201.911 | 0.905430 | 0.452715 | − | 0.891655i | \(-0.350456\pi\) | ||||
0.452715 | + | 0.891655i | \(0.350456\pi\) | |||||||
\(224\) | − | 162.250i | − | 0.724329i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 442.000 | 1.95575 | ||||||||
\(227\) | 255.994 | 1.12773 | 0.563864 | − | 0.825868i | \(-0.309314\pi\) | ||||
0.563864 | + | 0.825868i | \(0.309314\pi\) | |||||||
\(228\) | 194.700 | + | 585.000i | 0.853946 | + | 2.56579i | ||||
\(229\) | 160.000 | 0.698690 | 0.349345 | − | 0.936994i | \(-0.386404\pi\) | ||||
0.349345 | + | 0.936994i | \(0.386404\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 180.278i | 0.780422i | ||||||||
\(232\) | 325.000i | 1.40086i | ||||||||
\(233\) | 270.000i | 1.15880i | 0.815044 | + | 0.579399i | \(0.196713\pi\) | ||||
−0.815044 | + | 0.579399i | \(0.803287\pi\) | |||||||
\(234\) | −52.0000 | −0.222222 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 162.250i | 0.687499i | ||||||||
\(237\) | − | 130.000i | − | 0.548523i | ||||||
\(238\) | 270.416 | 1.13620 | ||||||||
\(239\) | −197.000 | −0.824268 | −0.412134 | − | 0.911123i | \(-0.635216\pi\) | ||||
−0.412134 | + | 0.911123i | \(0.635216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 396.611i | − | 1.64569i | −0.568268 | − | 0.822844i | \(-0.692386\pi\) | ||
0.568268 | − | 0.822844i | \(-0.307614\pi\) | |||||||
\(242\) | −75.7166 | −0.312878 | ||||||||
\(243\) | −201.911 | −0.830909 | ||||||||
\(244\) | −360.000 | −1.47541 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 468.722i | − | 1.90537i | ||||||
\(247\) | −21.6333 | − | 65.0000i | −0.0875842 | − | 0.263158i | ||||
\(248\) | 650.000i | 2.62097i | ||||||||
\(249\) | 144.222i | 0.579205i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −402.000 | −1.60159 | −0.800797 | − | 0.598936i | \(-0.795590\pi\) | ||||
−0.800797 | + | 0.598936i | \(0.795590\pi\) | |||||||
\(252\) | − | 180.000i | − | 0.714286i | ||||||
\(253\) | 350.000i | 1.38340i | ||||||||
\(254\) | −468.000 | −1.84252 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −459.000 | −1.79297 | ||||||||
\(257\) | −418.244 | −1.62741 | −0.813704 | − | 0.581279i | \(-0.802552\pi\) | ||||
−0.813704 | + | 0.581279i | \(0.802552\pi\) | |||||||
\(258\) | 260.000i | 1.00775i | ||||||||
\(259\) | 108.167i | 0.417631i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 72.1110i | 0.276287i | ||||||||
\(262\) | 403.822 | 1.54130 | ||||||||
\(263\) | − | 310.000i | − | 1.17871i | −0.807875 | − | 0.589354i | \(-0.799382\pi\) | ||
0.807875 | − | 0.589354i | \(-0.200618\pi\) | |||||||
\(264\) | −650.000 | −2.46212 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 325.000 | − | 108.167i | 1.22180 | − | 0.406641i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 356.950 | 1.33190 | ||||||||
\(269\) | 108.167i | 0.402106i | 0.979580 | + | 0.201053i | \(0.0644364\pi\) | ||||
−0.979580 | + | 0.201053i | \(0.935564\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 105.000 | 0.387454 | 0.193727 | − | 0.981055i | \(-0.437942\pi\) | ||||
0.193727 | + | 0.981055i | \(0.437942\pi\) | |||||||
\(272\) | 435.000i | 1.59926i | ||||||||
\(273\) | 65.0000i | 0.238095i | ||||||||
\(274\) | 450.694i | 1.64487i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 1135.75i | − | 4.11503i | ||||||
\(277\) | − | 50.0000i | − | 0.180505i | −0.995919 | − | 0.0902527i | \(-0.971233\pi\) | ||
0.995919 | − | 0.0902527i | \(-0.0287675\pi\) | |||||||
\(278\) | −180.278 | −0.648480 | ||||||||
\(279\) | 144.222i | 0.516925i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 288.444i | 1.02649i | 0.858242 | + | 0.513246i | \(0.171557\pi\) | ||||
−0.858242 | + | 0.513246i | \(0.828443\pi\) | |||||||
\(282\) | 130.000i | 0.460993i | ||||||||
\(283\) | 320.000i | 1.13074i | 0.824837 | + | 0.565371i | \(0.191267\pi\) | ||||
−0.824837 | + | 0.565371i | \(0.808733\pi\) | |||||||
\(284\) | − | 973.499i | − | 3.42781i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 130.000 | 0.454545 | ||||||||
\(287\) | −180.278 | −0.628145 | ||||||||
\(288\) | 129.800 | 0.450694 | ||||||||
\(289\) | 64.0000 | 0.221453 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 442.000 | 1.51890 | ||||||||
\(292\) | − | 945.000i | − | 3.23630i | ||||||
\(293\) | 219.939 | 0.750644 | 0.375322 | − | 0.926895i | \(-0.377532\pi\) | ||||
0.375322 | + | 0.926895i | \(0.377532\pi\) | |||||||
\(294\) | 312.000 | 1.06122 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −390.000 | −1.31757 | ||||||||
\(297\) | 180.278 | 0.606995 | ||||||||
\(298\) | −252.389 | −0.846942 | ||||||||
\(299\) | 126.194i | 0.422054i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 100.000 | 0.332226 | ||||||||
\(302\) | − | 130.000i | − | 0.430464i | ||||||
\(303\) | −180.278 | −0.594975 | ||||||||
\(304\) | 174.000 | + | 522.805i | 0.572368 | + | 1.71975i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 216.333i | 0.706971i | ||||||||
\(307\) | 237.966 | 0.775135 | 0.387567 | − | 0.921841i | \(-0.373315\pi\) | ||||
0.387567 | + | 0.921841i | \(0.373315\pi\) | |||||||
\(308\) | 450.000i | 1.46104i | ||||||||
\(309\) | −208.000 | −0.673139 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 395.000 | 1.27010 | 0.635048 | − | 0.772472i | \(-0.280980\pi\) | ||||
0.635048 | + | 0.772472i | \(0.280980\pi\) | |||||||
\(312\) | −234.361 | −0.751157 | ||||||||
\(313\) | − | 125.000i | − | 0.399361i | −0.979861 | − | 0.199681i | \(-0.936010\pi\) | ||
0.979861 | − | 0.199681i | \(-0.0639904\pi\) | |||||||
\(314\) | 36.0555i | 0.114826i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 324.500i | − | 1.02690i | ||||||
\(317\) | 3.60555 | 0.0113740 | 0.00568699 | − | 0.999984i | \(-0.498190\pi\) | ||||
0.00568699 | + | 0.999984i | \(0.498190\pi\) | |||||||
\(318\) | 984.315 | 3.09533 | ||||||||
\(319\) | − | 180.278i | − | 0.565133i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 273.000 | 0.850467 | ||||||||
\(322\) | −630.971 | −1.95954 | ||||||||
\(323\) | −270.416 | + | 90.0000i | −0.837202 | + | 0.278638i | ||||
\(324\) | −909.000 | −2.80556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 973.499i | 2.98619i | ||||||||
\(327\) | − | 715.000i | − | 2.18654i | ||||||
\(328\) | − | 650.000i | − | 1.98171i | ||||||
\(329\) | 50.0000 | 0.151976 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 198.305i | 0.599110i | 0.954079 | + | 0.299555i | \(0.0968382\pi\) | ||||
−0.954079 | + | 0.299555i | \(0.903162\pi\) | |||||||
\(332\) | 360.000i | 1.08434i | ||||||||
\(333\) | −86.5332 | −0.259860 | ||||||||
\(334\) | 442.000 | 1.32335 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 522.805i | − | 1.55597i | ||||||
\(337\) | 57.6888 | 0.171183 | 0.0855917 | − | 0.996330i | \(-0.472722\pi\) | ||||
0.0855917 | + | 0.996330i | \(0.472722\pi\) | |||||||
\(338\) | −562.466 | −1.66410 | ||||||||
\(339\) | 442.000 | 1.30383 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 360.555i | − | 1.05735i | ||||||
\(342\) | 86.5332 | + | 260.000i | 0.253021 | + | 0.760234i | ||||
\(343\) | − | 365.000i | − | 1.06414i | ||||||
\(344\) | 360.555i | 1.04813i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 442.000 | 1.27746 | ||||||||
\(347\) | − | 40.0000i | − | 0.115274i | −0.998338 | − | 0.0576369i | \(-0.981643\pi\) | ||
0.998338 | − | 0.0576369i | \(-0.0183566\pi\) | |||||||
\(348\) | 585.000i | 1.68103i | ||||||||
\(349\) | −98.0000 | −0.280802 | −0.140401 | − | 0.990095i | \(-0.544839\pi\) | ||||
−0.140401 | + | 0.990095i | \(0.544839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 65.0000 | 0.185185 | ||||||||
\(352\) | −324.500 | −0.921874 | ||||||||
\(353\) | 185.000i | 0.524079i | 0.965057 | + | 0.262040i | \(0.0843951\pi\) | ||||
−0.965057 | + | 0.262040i | \(0.915605\pi\) | |||||||
\(354\) | 234.361i | 0.662036i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 270.416 | 0.757469 | ||||||||
\(358\) | 130.000i | 0.363128i | ||||||||
\(359\) | 225.000 | 0.626741 | 0.313370 | − | 0.949631i | \(-0.398542\pi\) | ||||
0.313370 | + | 0.949631i | \(0.398542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −289.000 | + | 216.333i | −0.800554 | + | 0.599261i | ||||
\(362\) | − | 390.000i | − | 1.07735i | ||||||
\(363\) | −75.7166 | −0.208586 | ||||||||
\(364\) | 162.250i | 0.445741i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −520.000 | −1.42077 | ||||||||
\(367\) | 50.0000i | 0.136240i | 0.997677 | + | 0.0681199i | \(0.0217000\pi\) | ||||
−0.997677 | + | 0.0681199i | \(0.978300\pi\) | |||||||
\(368\) | − | 1015.00i | − | 2.75815i | ||||||
\(369\) | − | 144.222i | − | 0.390846i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 378.583i | − | 1.02044i | ||||||
\(372\) | 1170.00i | 3.14516i | ||||||||
\(373\) | 436.272 | 1.16963 | 0.584815 | − | 0.811167i | \(-0.301167\pi\) | ||||
0.584815 | + | 0.811167i | \(0.301167\pi\) | |||||||
\(374\) | − | 540.833i | − | 1.44608i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 180.278i | 0.479462i | ||||||||
\(377\) | − | 65.0000i | − | 0.172414i | ||||||
\(378\) | 325.000i | 0.859788i | ||||||||
\(379\) | − | 486.749i | − | 1.28430i | −0.766579 | − | 0.642150i | \(-0.778043\pi\) | ||
0.766579 | − | 0.642150i | \(-0.221957\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −468.000 | −1.22835 | ||||||||
\(382\) | 695.871 | 1.82165 | ||||||||
\(383\) | −201.911 | −0.527182 | −0.263591 | − | 0.964634i | \(-0.584907\pi\) | ||||
−0.263591 | + | 0.964634i | \(0.584907\pi\) | |||||||
\(384\) | −455.000 | −1.18490 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −962.000 | −2.49223 | ||||||||
\(387\) | 80.0000i | 0.206718i | ||||||||
\(388\) | 1103.30 | 2.84355 | ||||||||
\(389\) | 478.000 | 1.22879 | 0.614396 | − | 0.788998i | \(-0.289400\pi\) | ||||
0.614396 | + | 0.788998i | \(0.289400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 525.000 | 1.34271 | ||||||||
\(392\) | 432.666 | 1.10374 | ||||||||
\(393\) | 403.822 | 1.02754 | ||||||||
\(394\) | 324.500i | 0.823603i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −360.000 | −0.909091 | ||||||||
\(397\) | 750.000i | 1.88917i | 0.328269 | + | 0.944584i | \(0.393535\pi\) | ||||
−0.328269 | + | 0.944584i | \(0.606465\pi\) | |||||||
\(398\) | −443.483 | −1.11428 | ||||||||
\(399\) | 325.000 | − | 108.167i | 0.814536 | − | 0.271094i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 288.444i | 0.719312i | 0.933085 | + | 0.359656i | \(0.117106\pi\) | ||||
−0.933085 | + | 0.359656i | \(0.882894\pi\) | |||||||
\(402\) | 515.594 | 1.28257 | ||||||||
\(403\) | − | 130.000i | − | 0.322581i | ||||||
\(404\) | −450.000 | −1.11386 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 325.000 | 0.800493 | ||||||||
\(407\) | 216.333 | 0.531531 | ||||||||
\(408\) | 975.000i | 2.38971i | ||||||||
\(409\) | − | 36.0555i | − | 0.0881553i | −0.999028 | − | 0.0440776i | \(-0.985965\pi\) | ||
0.999028 | − | 0.0440776i | \(-0.0140349\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 450.694i | 1.09658i | ||||||||
\(412\) | −519.199 | −1.26019 | ||||||||
\(413\) | 90.1388 | 0.218254 | ||||||||
\(414\) | − | 504.777i | − | 1.21927i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −117.000 | −0.281250 | ||||||||
\(417\) | −180.278 | −0.432320 | ||||||||
\(418\) | −216.333 | − | 650.000i | −0.517543 | − | 1.55502i | ||||
\(419\) | −112.000 | −0.267303 | −0.133652 | − | 0.991028i | \(-0.542670\pi\) | ||||
−0.133652 | + | 0.991028i | \(0.542670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 630.971i | − | 1.49874i | −0.662149 | − | 0.749372i | \(-0.730355\pi\) | ||
0.662149 | − | 0.749372i | \(-0.269645\pi\) | |||||||
\(422\) | 845.000i | 2.00237i | ||||||||
\(423\) | 40.0000i | 0.0945626i | ||||||||
\(424\) | 1365.00 | 3.21934 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 1406.16i | − | 3.30086i | ||||||
\(427\) | 200.000i | 0.468384i | ||||||||
\(428\) | 681.449 | 1.59217 | ||||||||
\(429\) | 130.000 | 0.303030 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 432.666i | 1.00387i | 0.864907 | + | 0.501933i | \(0.167378\pi\) | ||||
−0.864907 | + | 0.501933i | \(0.832622\pi\) | |||||||
\(432\) | −522.805 | −1.21020 | ||||||||
\(433\) | 735.532 | 1.69869 | 0.849345 | − | 0.527839i | \(-0.176997\pi\) | ||||
0.849345 | + | 0.527839i | \(0.176997\pi\) | |||||||
\(434\) | 650.000 | 1.49770 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 1784.75i | − | 4.09346i | ||||||
\(437\) | 630.971 | − | 210.000i | 1.44387 | − | 0.480549i | ||||
\(438\) | − | 1365.00i | − | 3.11644i | ||||||
\(439\) | 793.221i | 1.80688i | 0.428712 | + | 0.903441i | \(0.358967\pi\) | ||||
−0.428712 | + | 0.903441i | \(0.641033\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 96.0000 | 0.217687 | ||||||||
\(442\) | − | 195.000i | − | 0.441176i | ||||||
\(443\) | − | 670.000i | − | 1.51242i | −0.654332 | − | 0.756208i | \(-0.727050\pi\) | ||
0.654332 | − | 0.756208i | \(-0.272950\pi\) | |||||||
\(444\) | −702.000 | −1.58108 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 728.000 | 1.63229 | ||||||||
\(447\) | −252.389 | −0.564628 | ||||||||
\(448\) | − | 5.00000i | − | 0.0111607i | ||||||
\(449\) | − | 36.0555i | − | 0.0803018i | −0.999194 | − | 0.0401509i | \(-0.987216\pi\) | ||
0.999194 | − | 0.0401509i | \(-0.0127839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 360.555i | 0.799457i | ||||||||
\(452\) | 1103.30 | 2.44093 | ||||||||
\(453\) | − | 130.000i | − | 0.286976i | ||||||
\(454\) | 923.000 | 2.03304 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 390.000 | + | 1171.80i | 0.855263 | + | 2.56975i | ||||
\(457\) | − | 755.000i | − | 1.65208i | −0.563612 | − | 0.826039i | \(-0.690589\pi\) | ||
0.563612 | − | 0.826039i | \(-0.309411\pi\) | |||||||
\(458\) | 576.888 | 1.25958 | ||||||||
\(459\) | − | 270.416i | − | 0.589142i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 772.000 | 1.67462 | 0.837310 | − | 0.546728i | \(-0.184127\pi\) | ||||
0.837310 | + | 0.546728i | \(0.184127\pi\) | |||||||
\(462\) | 650.000i | 1.40693i | ||||||||
\(463\) | 350.000i | 0.755940i | 0.925818 | + | 0.377970i | \(0.123378\pi\) | ||||
−0.925818 | + | 0.377970i | \(0.876622\pi\) | |||||||
\(464\) | 522.805i | 1.12673i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 973.499i | 2.08905i | ||||||||
\(467\) | 70.0000i | 0.149893i | 0.997188 | + | 0.0749465i | \(0.0238786\pi\) | ||||
−0.997188 | + | 0.0749465i | \(0.976121\pi\) | |||||||
\(468\) | −129.800 | −0.277350 | ||||||||
\(469\) | − | 198.305i | − | 0.422826i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.0555i | 0.0765510i | ||||||||
\(472\) | 325.000i | 0.688559i | ||||||||
\(473\) | − | 200.000i | − | 0.422833i | ||||||
\(474\) | − | 468.722i | − | 0.988864i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 675.000 | 1.41807 | ||||||||
\(477\) | 302.866 | 0.634940 | ||||||||
\(478\) | −710.294 | −1.48597 | ||||||||
\(479\) | 370.000 | 0.772443 | 0.386221 | − | 0.922406i | \(-0.373780\pi\) | ||||
0.386221 | + | 0.922406i | \(0.373780\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 78.0000 | 0.162162 | ||||||||
\(482\) | − | 1430.00i | − | 2.96680i | ||||||
\(483\) | −630.971 | −1.30636 | ||||||||
\(484\) | −189.000 | −0.390496 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −728.000 | −1.49794 | ||||||||
\(487\) | −519.199 | −1.06612 | −0.533059 | − | 0.846078i | \(-0.678958\pi\) | ||||
−0.533059 | + | 0.846078i | \(0.678958\pi\) | |||||||
\(488\) | −721.110 | −1.47768 | ||||||||
\(489\) | 973.499i | 1.99080i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −632.000 | −1.28717 | −0.643585 | − | 0.765375i | \(-0.722554\pi\) | ||||
−0.643585 | + | 0.765375i | \(0.722554\pi\) | |||||||
\(492\) | − | 1170.00i | − | 2.37805i | ||||||
\(493\) | −270.416 | −0.548512 | ||||||||
\(494\) | −78.0000 | − | 234.361i | −0.157895 | − | 0.474415i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1045.61i | 2.10808i | ||||||||
\(497\) | −540.833 | −1.08819 | ||||||||
\(498\) | 520.000i | 1.04418i | ||||||||
\(499\) | −380.000 | −0.761523 | −0.380762 | − | 0.924673i | \(-0.624338\pi\) | ||||
−0.380762 | + | 0.924673i | \(0.624338\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 442.000 | 0.882236 | ||||||||
\(502\) | −1449.43 | −2.88731 | ||||||||
\(503\) | 45.0000i | 0.0894632i | 0.998999 | + | 0.0447316i | \(0.0142433\pi\) | ||||
−0.998999 | + | 0.0447316i | \(0.985757\pi\) | |||||||
\(504\) | − | 360.555i | − | 0.715387i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1261.94i | 2.49396i | ||||||||
\(507\) | −562.466 | −1.10940 | ||||||||
\(508\) | −1168.20 | −2.29960 | ||||||||
\(509\) | 829.277i | 1.62923i | 0.580004 | + | 0.814614i | \(0.303051\pi\) | ||||
−0.580004 | + | 0.814614i | \(0.696949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −525.000 | −1.02740 | ||||||||
\(512\) | −1150.17 | −2.24643 | ||||||||
\(513\) | −108.167 | − | 325.000i | −0.210851 | − | 0.633528i | ||||
\(514\) | −1508.00 | −2.93385 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 648.999i | 1.25775i | ||||||||
\(517\) | − | 100.000i | − | 0.193424i | ||||||
\(518\) | 390.000i | 0.752896i | ||||||||
\(519\) | 442.000 | 0.851638 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 612.944i | − | 1.17648i | −0.808688 | − | 0.588238i | \(-0.799822\pi\) | ||
0.808688 | − | 0.588238i | \(-0.200178\pi\) | |||||||
\(522\) | 260.000i | 0.498084i | ||||||||
\(523\) | −465.116 | −0.889323 | −0.444662 | − | 0.895699i | \(-0.646676\pi\) | ||||
−0.444662 | + | 0.895699i | \(0.646676\pi\) | |||||||
\(524\) | 1008.00 | 1.92366 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 1117.72i | − | 2.12494i | ||||||
\(527\) | −540.833 | −1.02625 | ||||||||
\(528\) | −1045.61 | −1.98032 | ||||||||
\(529\) | −696.000 | −1.31569 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 72.1110i | 0.135802i | ||||||||
\(532\) | 811.249 | − | 270.000i | 1.52490 | − | 0.507519i | ||||
\(533\) | 130.000i | 0.243902i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 715.000 | 1.33396 | ||||||||
\(537\) | 130.000i | 0.242086i | ||||||||
\(538\) | 390.000i | 0.724907i | ||||||||
\(539\) | −240.000 | −0.445269 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −600.000 | −1.10906 | −0.554529 | − | 0.832165i | \(-0.687101\pi\) | ||||
−0.554529 | + | 0.832165i | \(0.687101\pi\) | |||||||
\(542\) | 378.583 | 0.698492 | ||||||||
\(543\) | − | 390.000i | − | 0.718232i | ||||||
\(544\) | 486.749i | 0.894760i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 234.361i | 0.429232i | ||||||||
\(547\) | −598.522 | −1.09419 | −0.547095 | − | 0.837071i | \(-0.684266\pi\) | ||||
−0.547095 | + | 0.837071i | \(0.684266\pi\) | |||||||
\(548\) | 1125.00i | 2.05292i | ||||||||
\(549\) | −160.000 | −0.291439 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −325.000 | + | 108.167i | −0.589837 | + | 0.196310i | ||||
\(552\) | − | 2275.00i | − | 4.12138i | ||||||
\(553\) | −180.278 | −0.325999 | ||||||||
\(554\) | − | 180.278i | − | 0.325411i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −450.000 | −0.809353 | ||||||||
\(557\) | 380.000i | 0.682226i | 0.940022 | + | 0.341113i | \(0.110804\pi\) | ||||
−0.940022 | + | 0.341113i | \(0.889196\pi\) | |||||||
\(558\) | 520.000i | 0.931900i | ||||||||
\(559\) | − | 72.1110i | − | 0.129000i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 540.833i | − | 0.964051i | ||||||
\(562\) | 1040.00i | 1.85053i | ||||||||
\(563\) | −122.589 | −0.217742 | −0.108871 | − | 0.994056i | \(-0.534724\pi\) | ||||
−0.108871 | + | 0.994056i | \(0.534724\pi\) | |||||||
\(564\) | 324.500i | 0.575354i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1153.78i | 2.03847i | ||||||||
\(567\) | 505.000i | 0.890653i | ||||||||
\(568\) | − | 1950.00i | − | 3.43310i | ||||||
\(569\) | 36.0555i | 0.0633665i | 0.999498 | + | 0.0316832i | \(0.0100868\pi\) | ||||
−0.999498 | + | 0.0316832i | \(0.989913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −790.000 | −1.38354 | −0.691769 | − | 0.722119i | \(-0.743168\pi\) | ||||
−0.691769 | + | 0.722119i | \(0.743168\pi\) | |||||||
\(572\) | 324.500 | 0.567307 | ||||||||
\(573\) | 695.871 | 1.21444 | ||||||||
\(574\) | −650.000 | −1.13240 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.00000 | 0.00694444 | ||||||||
\(577\) | 675.000i | 1.16984i | 0.811090 | + | 0.584922i | \(0.198875\pi\) | ||||
−0.811090 | + | 0.584922i | \(0.801125\pi\) | |||||||
\(578\) | 230.755 | 0.399231 | ||||||||
\(579\) | −962.000 | −1.66149 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 200.000 | 0.344234 | ||||||||
\(582\) | 1593.65 | 2.73824 | ||||||||
\(583\) | −757.166 | −1.29874 | ||||||||
\(584\) | − | 1892.91i | − | 3.24129i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 793.000 | 1.35324 | ||||||||
\(587\) | − | 280.000i | − | 0.477002i | −0.971142 | − | 0.238501i | \(-0.923344\pi\) | ||
0.971142 | − | 0.238501i | \(-0.0766560\pi\) | |||||||
\(588\) | 778.799 | 1.32449 | ||||||||
\(589\) | −650.000 | + | 216.333i | −1.10357 | + | 0.367289i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 324.500i | 0.549069i | ||||||||
\(592\) | −627.366 | −1.05974 | ||||||||
\(593\) | − | 750.000i | − | 1.26476i | −0.774660 | − | 0.632378i | \(-0.782079\pi\) | ||
0.774660 | − | 0.632378i | \(-0.217921\pi\) | |||||||
\(594\) | 650.000 | 1.09428 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −630.000 | −1.05705 | ||||||||
\(597\) | −443.483 | −0.742852 | ||||||||
\(598\) | 455.000i | 0.760870i | ||||||||
\(599\) | 504.777i | 0.842700i | 0.906898 | + | 0.421350i | \(0.138444\pi\) | ||||
−0.906898 | + | 0.421350i | \(0.861556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 612.944i | − | 1.01987i | −0.860212 | − | 0.509937i | \(-0.829669\pi\) | ||
0.860212 | − | 0.509937i | \(-0.170331\pi\) | |||||||
\(602\) | 360.555 | 0.598929 | ||||||||
\(603\) | 158.644 | 0.263092 | ||||||||
\(604\) | − | 324.500i | − | 0.537251i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −650.000 | −1.07261 | ||||||||
\(607\) | −987.921 | −1.62755 | −0.813774 | − | 0.581182i | \(-0.802590\pi\) | ||||
−0.813774 | + | 0.581182i | \(0.802590\pi\) | |||||||
\(608\) | 194.700 | + | 585.000i | 0.320230 | + | 0.962171i | ||||
\(609\) | 325.000 | 0.533662 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 36.0555i | − | 0.0590107i | ||||||
\(612\) | 540.000i | 0.882353i | ||||||||
\(613\) | 1200.00i | 1.95759i | 0.204853 | + | 0.978793i | \(0.434328\pi\) | ||||
−0.204853 | + | 0.978793i | \(0.565672\pi\) | |||||||
\(614\) | 858.000 | 1.39739 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 901.388i | 1.46329i | ||||||||
\(617\) | − | 350.000i | − | 0.567261i | −0.958934 | − | 0.283630i | \(-0.908461\pi\) | ||
0.958934 | − | 0.283630i | \(-0.0915389\pi\) | |||||||
\(618\) | −749.955 | −1.21352 | ||||||||
\(619\) | −560.000 | −0.904685 | −0.452342 | − | 0.891844i | \(-0.649412\pi\) | ||||
−0.452342 | + | 0.891844i | \(0.649412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 630.971i | 1.01606i | ||||||||
\(622\) | 1424.19 | 2.28970 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −377.000 | −0.604167 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 450.694i | − | 0.719958i | ||||||
\(627\) | −216.333 | − | 650.000i | −0.345029 | − | 1.03668i | ||||
\(628\) | 90.0000i | 0.143312i | ||||||||
\(629\) | − | 324.500i | − | 0.515898i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1050.00 | −1.66403 | −0.832013 | − | 0.554757i | \(-0.812811\pi\) | ||||
−0.832013 | + | 0.554757i | \(0.812811\pi\) | |||||||
\(632\) | − | 650.000i | − | 1.02848i | ||||||
\(633\) | 845.000i | 1.33491i | ||||||||
\(634\) | 13.0000 | 0.0205047 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2457.00 | 3.86321 | ||||||||
\(637\) | −86.5332 | −0.135845 | ||||||||
\(638\) | − | 650.000i | − | 1.01881i | ||||||
\(639\) | − | 432.666i | − | 0.677099i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1225.89i | − | 1.91246i | −0.292615 | − | 0.956230i | \(-0.594525\pi\) | ||
0.292615 | − | 0.956230i | \(-0.405475\pi\) | |||||||
\(642\) | 984.315 | 1.53320 | ||||||||
\(643\) | 1030.00i | 1.60187i | 0.598754 | + | 0.800933i | \(0.295663\pi\) | ||||
−0.598754 | + | 0.800933i | \(0.704337\pi\) | |||||||
\(644\) | −1575.00 | −2.44565 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −975.000 | + | 324.500i | −1.50929 | + | 0.502321i | ||||
\(647\) | 555.000i | 0.857805i | 0.903351 | + | 0.428903i | \(0.141100\pi\) | ||||
−0.903351 | + | 0.428903i | \(0.858900\pi\) | |||||||
\(648\) | −1820.80 | −2.80988 | ||||||||
\(649\) | − | 180.278i | − | 0.277777i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 650.000 | 0.998464 | ||||||||
\(652\) | 2430.00i | 3.72699i | ||||||||
\(653\) | − | 50.0000i | − | 0.0765697i | −0.999267 | − | 0.0382848i | \(-0.987811\pi\) | ||
0.999267 | − | 0.0382848i | \(-0.0121894\pi\) | |||||||
\(654\) | − | 2577.97i | − | 3.94185i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1045.61i | − | 1.59392i | ||||||
\(657\) | − | 420.000i | − | 0.639269i | ||||||
\(658\) | 180.278 | 0.273978 | ||||||||
\(659\) | 198.305i | 0.300919i | 0.988616 | + | 0.150459i | \(0.0480752\pi\) | ||||
−0.988616 | + | 0.150459i | \(0.951925\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 198.305i | − | 0.300008i | −0.988685 | − | 0.150004i | \(-0.952071\pi\) | ||
0.988685 | − | 0.150004i | \(-0.0479287\pi\) | |||||||
\(662\) | 715.000i | 1.08006i | ||||||||
\(663\) | − | 195.000i | − | 0.294118i | ||||||
\(664\) | 721.110i | 1.08601i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −312.000 | −0.468468 | ||||||||
\(667\) | 630.971 | 0.945984 | ||||||||
\(668\) | 1103.30 | 1.65164 | ||||||||
\(669\) | 728.000 | 1.08819 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 400.000 | 0.596125 | ||||||||
\(672\) | − | 585.000i | − | 0.870536i | ||||||
\(673\) | −598.522 | −0.889334 | −0.444667 | − | 0.895696i | \(-0.646678\pi\) | ||||
−0.444667 | + | 0.895696i | \(0.646678\pi\) | |||||||
\(674\) | 208.000 | 0.308605 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1404.00 | −2.07692 | ||||||||
\(677\) | 68.5055 | 0.101190 | 0.0505949 | − | 0.998719i | \(-0.483888\pi\) | ||||
0.0505949 | + | 0.998719i | \(0.483888\pi\) | |||||||
\(678\) | 1593.65 | 2.35052 | ||||||||
\(679\) | − | 612.944i | − | 0.902715i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 923.000 | 1.35536 | ||||||||
\(682\) | − | 1300.00i | − | 1.90616i | ||||||
\(683\) | 237.966 | 0.348413 | 0.174207 | − | 0.984709i | \(-0.444264\pi\) | ||||
0.174207 | + | 0.984709i | \(0.444264\pi\) | |||||||
\(684\) | 216.000 | + | 648.999i | 0.315789 | + | 0.948829i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 1316.03i | − | 1.91841i | ||||||
\(687\) | 576.888 | 0.839721 | ||||||||
\(688\) | 580.000i | 0.843023i | ||||||||
\(689\) | −273.000 | −0.396226 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −820.000 | −1.18669 | −0.593343 | − | 0.804950i | \(-0.702192\pi\) | ||||
−0.593343 | + | 0.804950i | \(0.702192\pi\) | |||||||
\(692\) | 1103.30 | 1.59436 | ||||||||
\(693\) | 200.000i | 0.288600i | ||||||||
\(694\) | − | 144.222i | − | 0.207813i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1171.80i | 1.68363i | ||||||||
\(697\) | 540.833 | 0.775944 | ||||||||
\(698\) | −353.344 | −0.506224 | ||||||||
\(699\) | 973.499i | 1.39270i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −540.000 | −0.770328 | −0.385164 | − | 0.922848i | \(-0.625855\pi\) | ||||
−0.385164 | + | 0.922848i | \(0.625855\pi\) | |||||||
\(702\) | 234.361 | 0.333847 | ||||||||
\(703\) | −129.800 | − | 390.000i | −0.184637 | − | 0.554765i | ||||
\(704\) | −10.0000 | −0.0142045 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 667.027i | 0.944797i | ||||||||
\(707\) | 250.000i | 0.353607i | ||||||||
\(708\) | 585.000i | 0.826271i | ||||||||
\(709\) | −268.000 | −0.377997 | −0.188999 | − | 0.981977i | \(-0.560524\pi\) | ||||
−0.188999 | + | 0.981977i | \(0.560524\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 144.222i | − | 0.202844i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1261.94 | 1.76991 | ||||||||
\(714\) | 975.000 | 1.36555 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 324.500i | 0.453212i | ||||||||
\(717\) | −710.294 | −0.990647 | ||||||||
\(718\) | 811.249 | 1.12987 | ||||||||
\(719\) | −105.000 | −0.146036 | −0.0730181 | − | 0.997331i | \(-0.523263\pi\) | ||||
−0.0730181 | + | 0.997331i | \(0.523263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 288.444i | 0.400061i | ||||||||
\(722\) | −1042.00 | + | 780.000i | −1.44322 | + | 1.08033i | ||||
\(723\) | − | 1430.00i | − | 1.97787i | ||||||
\(724\) | − | 973.499i | − | 1.34461i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −273.000 | −0.376033 | ||||||||
\(727\) | 695.000i | 0.955983i | 0.878364 | + | 0.477992i | \(0.158635\pi\) | ||||
−0.878364 | + | 0.477992i | \(0.841365\pi\) | |||||||
\(728\) | 325.000i | 0.446429i | ||||||||
\(729\) | 181.000 | 0.248285 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −300.000 | −0.410397 | ||||||||
\(732\) | −1298.00 | −1.77322 | ||||||||
\(733\) | − | 160.000i | − | 0.218281i | −0.994026 | − | 0.109141i | \(-0.965190\pi\) | ||
0.994026 | − | 0.109141i | \(-0.0348098\pi\) | |||||||
\(734\) | 180.278i | 0.245610i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1135.75i | − | 1.54314i | ||||||
\(737\) | −396.611 | −0.538142 | ||||||||
\(738\) | − | 520.000i | − | 0.704607i | ||||||
\(739\) | −1028.00 | −1.39107 | −0.695535 | − | 0.718493i | \(-0.744832\pi\) | ||||
−0.695535 | + | 0.718493i | \(0.744832\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −78.0000 | − | 234.361i | −0.105263 | − | 0.316276i | ||||
\(742\) | − | 1365.00i | − | 1.83962i | ||||||
\(743\) | 526.410 | 0.708493 | 0.354247 | − | 0.935152i | \(-0.384737\pi\) | ||||
0.354247 | + | 0.935152i | \(0.384737\pi\) | |||||||
\(744\) | 2343.61i | 3.15001i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1573.00 | 2.10858 | ||||||||
\(747\) | 160.000i | 0.214190i | ||||||||
\(748\) | − | 1350.00i | − | 1.80481i | ||||||
\(749\) | − | 378.583i | − | 0.505451i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 36.0555i | − | 0.0480100i | −0.999712 | − | 0.0240050i | \(-0.992358\pi\) | ||
0.999712 | − | 0.0240050i | \(-0.00764176\pi\) | |||||||
\(752\) | 290.000i | 0.385638i | ||||||||
\(753\) | −1449.43 | −1.92488 | ||||||||
\(754\) | − | 234.361i | − | 0.310823i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 811.249i | 1.07308i | ||||||||
\(757\) | 60.0000i | 0.0792602i | 0.999214 | + | 0.0396301i | \(0.0126180\pi\) | ||||
−0.999214 | + | 0.0396301i | \(0.987382\pi\) | |||||||
\(758\) | − | 1755.00i | − | 2.31530i | ||||||
\(759\) | 1261.94i | 1.66264i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −655.000 | −0.860710 | −0.430355 | − | 0.902660i | \(-0.641612\pi\) | ||||
−0.430355 | + | 0.902660i | \(0.641612\pi\) | |||||||
\(762\) | −1687.40 | −2.21443 | ||||||||
\(763\) | −991.527 | −1.29951 | ||||||||
\(764\) | 1737.00 | 2.27356 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −728.000 | −0.950392 | ||||||||
\(767\) | − | 65.0000i | − | 0.0847458i | ||||||
\(768\) | −1654.95 | −2.15488 | ||||||||
\(769\) | 185.000 | 0.240572 | 0.120286 | − | 0.992739i | \(-0.461619\pi\) | ||||
0.120286 | + | 0.992739i | \(0.461619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1508.00 | −1.95590 | ||||||||
\(772\) | −2401.30 | −3.11049 | ||||||||
\(773\) | 320.894 | 0.415128 | 0.207564 | − | 0.978221i | \(-0.433446\pi\) | ||||
0.207564 | + | 0.978221i | \(0.433446\pi\) | |||||||
\(774\) | 288.444i | 0.372667i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2210.00 | 2.84794 | ||||||||
\(777\) | 390.000i | 0.501931i | ||||||||
\(778\) | 1723.45 | 2.21524 | ||||||||
\(779\) | 650.000 | − | 216.333i | 0.834403 | − | 0.277706i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1081.67i | 1.38497i | ||||||||
\(782\) | 1892.91 | 2.42061 | ||||||||
\(783\) | − | 325.000i | − | 0.415070i | ||||||
\(784\) | 696.000 | 0.887755 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1456.00 | 1.85242 | ||||||||
\(787\) | 68.5055 | 0.0870463 | 0.0435232 | − | 0.999052i | \(-0.486142\pi\) | ||||
0.0435232 | + | 0.999052i | \(0.486142\pi\) | |||||||
\(788\) | 810.000i | 1.02792i | ||||||||
\(789\) | − | 1117.72i | − | 1.41663i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 612.944i | − | 0.774897i | ||||||
\(792\) | −721.110 | −0.910493 | ||||||||
\(793\) | 144.222 | 0.181869 | ||||||||
\(794\) | 2704.16i | 3.40575i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1107.00 | −1.39070 | ||||||||
\(797\) | 1258.34 | 1.57884 | 0.789421 | − | 0.613852i | \(-0.210381\pi\) | ||||
0.789421 | + | 0.613852i | \(0.210381\pi\) | |||||||
\(798\) | 1171.80 | − | 390.000i | 1.46843 | − | 0.488722i | ||||
\(799\) | −150.000 | −0.187735 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1040.00i | 1.29676i | ||||||||
\(803\) | 1050.00i | 1.30760i | ||||||||
\(804\) | 1287.00 | 1.60075 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 468.722i | − | 0.581541i | ||||||
\(807\) | 390.000i | 0.483271i | ||||||||
\(808\) | −901.388 | −1.11558 | ||||||||
\(809\) | 7.00000 | 0.00865266 | 0.00432633 | − | 0.999991i | \(-0.498623\pi\) | ||||
0.00432633 | + | 0.999991i | \(0.498623\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1027.58i | − | 1.26706i | −0.773720 | − | 0.633528i | \(-0.781606\pi\) | ||
0.773720 | − | 0.633528i | \(-0.218394\pi\) | |||||||
\(812\) | 811.249 | 0.999075 | ||||||||
\(813\) | 378.583 | 0.465662 | ||||||||
\(814\) | 780.000 | 0.958231 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1568.41i | 1.92208i | ||||||||
\(817\) | −360.555 | + | 120.000i | −0.441316 | + | 0.146879i | ||||
\(818\) | − | 130.000i | − | 0.158924i | ||||||
\(819\) | 72.1110i | 0.0880477i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 842.000 | 1.02558 | 0.512789 | − | 0.858515i | \(-0.328612\pi\) | ||||
0.512789 | + | 0.858515i | \(0.328612\pi\) | |||||||
\(822\) | 1625.00i | 1.97689i | ||||||||
\(823\) | − | 775.000i | − | 0.941677i | −0.882219 | − | 0.470838i | \(-0.843951\pi\) | ||
0.882219 | − | 0.470838i | \(-0.156049\pi\) | |||||||
\(824\) | −1040.00 | −1.26214 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 325.000 | 0.393462 | ||||||||
\(827\) | −1265.55 | −1.53029 | −0.765144 | − | 0.643859i | \(-0.777332\pi\) | ||||
−0.765144 | + | 0.643859i | \(0.777332\pi\) | |||||||
\(828\) | − | 1260.00i | − | 1.52174i | ||||||
\(829\) | − | 1568.41i | − | 1.89194i | −0.324260 | − | 0.945968i | \(-0.605115\pi\) | ||
0.324260 | − | 0.945968i | \(-0.394885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 180.278i | − | 0.216941i | ||||||
\(832\) | −3.60555 | −0.00433360 | ||||||||
\(833\) | 360.000i | 0.432173i | ||||||||
\(834\) | −650.000 | −0.779376 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −540.000 | − | 1622.50i | −0.645933 | − | 1.94079i | ||||
\(837\) | − | 650.000i | − | 0.776583i | ||||||
\(838\) | −403.822 | −0.481888 | ||||||||
\(839\) | − | 1153.78i | − | 1.37518i | −0.726099 | − | 0.687590i | \(-0.758669\pi\) | ||
0.726099 | − | 0.687590i | \(-0.241331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 516.000 | 0.613555 | ||||||||
\(842\) | − | 2275.00i | − | 2.70190i | ||||||
\(843\) | 1040.00i | 1.23369i | ||||||||
\(844\) | 2109.25i | 2.49911i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 144.222i | 0.170475i | ||||||||
\(847\) | 105.000i | 0.123967i | ||||||||
\(848\) | 2195.78 | 2.58936 | ||||||||
\(849\) | 1153.78i | 1.35898i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 757.166i | 0.889737i | ||||||||
\(852\) | − | 3510.00i | − | 4.11972i | ||||||
\(853\) | − | 400.000i | − | 0.468933i | −0.972124 | − | 0.234467i | \(-0.924666\pi\) | ||
0.972124 | − | 0.234467i | \(-0.0753343\pi\) | |||||||
\(854\) | 721.110i | 0.844391i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1365.00 | 1.59463 | ||||||||
\(857\) | 158.644 | 0.185116 | 0.0925579 | − | 0.995707i | \(-0.470496\pi\) | ||||
0.0925579 | + | 0.995707i | \(0.470496\pi\) | |||||||
\(858\) | 468.722 | 0.546296 | ||||||||
\(859\) | −1432.00 | −1.66705 | −0.833527 | − | 0.552478i | \(-0.813682\pi\) | ||||
−0.833527 | + | 0.552478i | \(0.813682\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −650.000 | −0.754936 | ||||||||
\(862\) | 1560.00i | 1.80974i | ||||||||
\(863\) | 129.800 | 0.150405 | 0.0752027 | − | 0.997168i | \(-0.476040\pi\) | ||||
0.0752027 | + | 0.997168i | \(0.476040\pi\) | |||||||
\(864\) | −585.000 | −0.677083 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2652.00 | 3.06236 | ||||||||
\(867\) | 230.755 | 0.266154 | ||||||||
\(868\) | 1622.50 | 1.86924 | ||||||||
\(869\) | 360.555i | 0.414908i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −143.000 | −0.164179 | ||||||||
\(872\) | − | 3575.00i | − | 4.09977i | ||||||
\(873\) | 490.355 | 0.561690 | ||||||||
\(874\) | 2275.00 | − | 757.166i | 2.60297 | − | 0.866322i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 3407.25i | − | 3.88955i | ||||||
\(877\) | 393.005 | 0.448124 | 0.224062 | − | 0.974575i | \(-0.428068\pi\) | ||||
0.224062 | + | 0.974575i | \(0.428068\pi\) | |||||||
\(878\) | 2860.00i | 3.25740i | ||||||||
\(879\) | 793.000 | 0.902162 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 750.000 | 0.851305 | 0.425653 | − | 0.904887i | \(-0.360045\pi\) | ||||
0.425653 | + | 0.904887i | \(0.360045\pi\) | |||||||
\(882\) | 346.133 | 0.392441 | ||||||||
\(883\) | − | 120.000i | − | 0.135900i | −0.997689 | − | 0.0679502i | \(-0.978354\pi\) | ||
0.997689 | − | 0.0679502i | \(-0.0216459\pi\) | |||||||
\(884\) | − | 486.749i | − | 0.550622i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 2415.72i | − | 2.72655i | ||||||
\(887\) | 850.910 | 0.959312 | 0.479656 | − | 0.877457i | \(-0.340761\pi\) | ||||
0.479656 | + | 0.877457i | \(0.340761\pi\) | |||||||
\(888\) | −1406.16 | −1.58352 | ||||||||
\(889\) | 648.999i | 0.730033i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1010.00 | 1.13356 | ||||||||
\(892\) | 1817.20 | 2.03722 | ||||||||
\(893\) | −180.278 | + | 60.0000i | −0.201879 | + | 0.0671892i | ||||
\(894\) | −910.000 | −1.01790 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 630.971i | 0.704209i | ||||||||
\(897\) | 455.000i | 0.507246i | ||||||||
\(898\) | − | 130.000i | − | 0.144766i | ||||||
\(899\) | −650.000 | −0.723026 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1135.75i | 1.26054i | ||||||||
\(902\) | 1300.00i | 1.44124i | ||||||||
\(903\) | 360.555 | 0.399286 | ||||||||
\(904\) | 2210.00 | 2.44469 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 468.722i | − | 0.517353i | ||||||
\(907\) | −645.394 | −0.711570 | −0.355785 | − | 0.934568i | \(-0.615786\pi\) | ||||
−0.355785 | + | 0.934568i | \(0.615786\pi\) | |||||||
\(908\) | 2303.95 | 2.53739 | ||||||||
\(909\) | −200.000 | −0.220022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1225.89i | 1.34565i | 0.739802 | + | 0.672825i | \(0.234919\pi\) | ||||
−0.739802 | + | 0.672825i | \(0.765081\pi\) | |||||||
\(912\) | 627.366 | + | 1885.00i | 0.687901 | + | 2.06689i | ||||
\(913\) | − | 400.000i | − | 0.438116i | ||||||
\(914\) | − | 2722.19i | − | 2.97833i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1440.00 | 1.57205 | ||||||||
\(917\) | − | 560.000i | − | 0.610687i | ||||||
\(918\) | − | 975.000i | − | 1.06209i | ||||||
\(919\) | 513.000 | 0.558215 | 0.279108 | − | 0.960260i | \(-0.409961\pi\) | ||||
0.279108 | + | 0.960260i | \(0.409961\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 858.000 | 0.931596 | ||||||||
\(922\) | 2783.49 | 3.01896 | ||||||||
\(923\) | 390.000i | 0.422535i | ||||||||
\(924\) | 1622.50i | 1.75595i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1261.94i | 1.36279i | ||||||||
\(927\) | −230.755 | −0.248927 | ||||||||
\(928\) | 585.000i | 0.630388i | ||||||||
\(929\) | 1217.00 | 1.31001 | 0.655005 | − | 0.755624i | \(-0.272666\pi\) | ||||
0.655005 | + | 0.755624i | \(0.272666\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 144.000 | + | 432.666i | 0.154672 | + | 0.464733i | ||||
\(932\) | 2430.00i | 2.60730i | ||||||||
\(933\) | 1424.19 | 1.52647 | ||||||||
\(934\) | 252.389i | 0.270223i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −260.000 | −0.277778 | ||||||||
\(937\) | − | 1095.00i | − | 1.16862i | −0.811529 | − | 0.584312i | \(-0.801365\pi\) | ||
0.811529 | − | 0.584312i | \(-0.198635\pi\) | |||||||
\(938\) | − | 715.000i | − | 0.762260i | ||||||
\(939\) | − | 450.694i | − | 0.479972i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1099.69i | − | 1.16864i | −0.811522 | − | 0.584322i | \(-0.801361\pi\) | ||
0.811522 | − | 0.584322i | \(-0.198639\pi\) | |||||||
\(942\) | 130.000i | 0.138004i | ||||||||
\(943\) | −1261.94 | −1.33822 | ||||||||
\(944\) | 522.805i | 0.553819i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 721.110i | − | 0.762273i | ||||||
\(947\) | 640.000i | 0.675818i | 0.941179 | + | 0.337909i | \(0.109720\pi\) | ||||
−0.941179 | + | 0.337909i | \(0.890280\pi\) | |||||||
\(948\) | − | 1170.00i | − | 1.23418i | ||||||
\(949\) | 378.583i | 0.398928i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.0000 | 0.0136698 | ||||||||
\(952\) | 1352.08 | 1.42025 | ||||||||
\(953\) | −1168.20 | −1.22581 | −0.612906 | − | 0.790156i | \(-0.710000\pi\) | ||||
−0.612906 | + | 0.790156i | \(0.710000\pi\) | |||||||
\(954\) | 1092.00 | 1.14465 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1773.00 | −1.85460 | ||||||||
\(957\) | − | 650.000i | − | 0.679206i | ||||||
\(958\) | 1334.05 | 1.39254 | ||||||||
\(959\) | 625.000 | 0.651721 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −339.000 | −0.352758 | ||||||||
\(962\) | 281.233 | 0.292342 | ||||||||
\(963\) | 302.866 | 0.314503 | ||||||||
\(964\) | − | 3569.50i | − | 3.70280i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2275.00 | −2.35507 | ||||||||
\(967\) | − | 1010.00i | − | 1.04447i | −0.852802 | − | 0.522234i | \(-0.825099\pi\) | ||
0.852802 | − | 0.522234i | \(-0.174901\pi\) | |||||||
\(968\) | −378.583 | −0.391098 | ||||||||
\(969\) | −975.000 | + | 324.500i | −1.00619 | + | 0.334881i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 757.166i | 0.779779i | 0.920862 | + | 0.389890i | \(0.127487\pi\) | ||||
−0.920862 | + | 0.389890i | \(0.872513\pi\) | |||||||
\(972\) | −1817.20 | −1.86955 | ||||||||
\(973\) | 250.000i | 0.256937i | ||||||||
\(974\) | −1872.00 | −1.92197 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1160.00 | −1.18852 | ||||||||
\(977\) | 598.522 | 0.612612 | 0.306306 | − | 0.951933i | \(-0.400907\pi\) | ||||
0.306306 | + | 0.951933i | \(0.400907\pi\) | |||||||
\(978\) | 3510.00i | 3.58896i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 793.221i | − | 0.808584i | ||||||
\(982\) | −2278.71 | −2.32048 | ||||||||
\(983\) | −57.6888 | −0.0586865 | −0.0293432 | − | 0.999569i | \(-0.509342\pi\) | ||||
−0.0293432 | + | 0.999569i | \(0.509342\pi\) | |||||||
\(984\) | − | 2343.61i | − | 2.38172i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −975.000 | −0.988844 | ||||||||
\(987\) | 180.278 | 0.182652 | ||||||||
\(988\) | −194.700 | − | 585.000i | −0.197065 | − | 0.592105i | ||||
\(989\) | 700.000 | 0.707786 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 1170.00i | 1.17944i | ||||||||
\(993\) | 715.000i | 0.720040i | ||||||||
\(994\) | −1950.00 | −1.96177 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1298.00i | 1.30321i | ||||||||
\(997\) | − | 170.000i | − | 0.170512i | −0.996359 | − | 0.0852558i | \(-0.972829\pi\) | ||
0.996359 | − | 0.0852558i | \(-0.0271707\pi\) | |||||||
\(998\) | −1370.11 | −1.37286 | ||||||||
\(999\) | 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 \(a_p\))