Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(361,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.i (of order \(3\), degree \(2\), 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: | \(34.6931230834\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.361 |
Dual form | 588.4.i.e.373.1 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.00000 | − | 15.5885i | −0.804984 | − | 1.39427i | −0.916302 | − | 0.400489i | \(-0.868840\pi\) |
0.111317 | − | 0.993785i | \(-0.464493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.0000 | + | 31.1769i | −0.493382 | + | 0.854563i | −0.999971 | − | 0.00762479i | \(-0.997573\pi\) |
0.506589 | + | 0.862188i | \(0.330906\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.0000 | 0.213346 | 0.106673 | − | 0.994294i | \(-0.465980\pi\) | ||||
0.106673 | + | 0.994294i | \(0.465980\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −54.0000 | −0.929516 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.00000 | − | 15.5885i | 0.128401 | − | 0.222397i | −0.794656 | − | 0.607060i | \(-0.792349\pi\) |
0.923057 | + | 0.384662i | \(0.125682\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −50.0000 | − | 86.6025i | −0.603726 | − | 1.04568i | −0.992251 | − | 0.124246i | \(-0.960349\pi\) |
0.388526 | − | 0.921438i | \(-0.372984\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −36.0000 | − | 62.3538i | −0.326370 | − | 0.565290i | 0.655418 | − | 0.755266i | \(-0.272492\pi\) |
−0.981789 | + | 0.189976i | \(0.939159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −99.5000 | + | 172.339i | −0.796000 | + | 1.37871i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −234.000 | −1.49837 | −0.749185 | − | 0.662361i | \(-0.769554\pi\) | ||||
−0.749185 | + | 0.662361i | \(0.769554\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | + | 13.8564i | −0.0463498 | + | 0.0802801i | −0.888270 | − | 0.459323i | \(-0.848092\pi\) |
0.841920 | + | 0.539603i | \(0.181426\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 54.0000 | + | 93.5307i | 0.284854 | + | 0.493382i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 113.000 | + | 195.722i | 0.502083 | + | 0.869634i | 0.999997 | + | 0.00240737i | \(0.000766290\pi\) |
−0.497914 | + | 0.867227i | \(0.665900\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.0000 | − | 25.9808i | 0.0615878 | − | 0.106673i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −90.0000 | −0.342820 | −0.171410 | − | 0.985200i | \(-0.554832\pi\) | ||||
−0.171410 | + | 0.985200i | \(0.554832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 452.000 | 1.60301 | 0.801504 | − | 0.597989i | \(-0.204033\pi\) | ||||
0.801504 | + | 0.597989i | \(0.204033\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −81.0000 | + | 140.296i | −0.268328 | + | 0.464758i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 216.000 | + | 374.123i | 0.670358 | + | 1.16109i | 0.977803 | + | 0.209528i | \(0.0671929\pi\) |
−0.307444 | + | 0.951566i | \(0.599474\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −27.0000 | − | 46.7654i | −0.0741325 | − | 0.128401i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −207.000 | + | 358.535i | −0.536484 | + | 0.929217i | 0.462606 | + | 0.886564i | \(0.346914\pi\) |
−0.999090 | + | 0.0426532i | \(0.986419\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 648.000 | 1.58866 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −300.000 | −0.697122 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −342.000 | + | 592.361i | −0.754654 | + | 1.30710i | 0.190892 | + | 0.981611i | \(0.438862\pi\) |
−0.945546 | + | 0.325489i | \(0.894471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 211.000 | + | 365.463i | 0.442882 | + | 0.767094i | 0.997902 | − | 0.0647433i | \(-0.0206228\pi\) |
−0.555020 | + | 0.831837i | \(0.687290\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −90.0000 | − | 155.885i | −0.171740 | − | 0.297463i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −166.000 | + | 287.520i | −0.302688 | + | 0.524272i | −0.976744 | − | 0.214409i | \(-0.931218\pi\) |
0.674056 | + | 0.738681i | \(0.264551\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −360.000 | −0.601748 | −0.300874 | − | 0.953664i | \(-0.597278\pi\) | ||||
−0.300874 | + | 0.953664i | \(0.597278\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.0000 | − | 22.5167i | 0.0208429 | − | 0.0361010i | −0.855416 | − | 0.517942i | \(-0.826698\pi\) |
0.876259 | + | 0.481841i | \(0.160032\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 298.500 | + | 517.017i | 0.459571 | + | 0.796000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −256.000 | − | 443.405i | −0.364585 | − | 0.631481i | 0.624124 | − | 0.781325i | \(-0.285456\pi\) |
−0.988710 | + | 0.149845i | \(0.952123\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1188.00 | 1.57108 | 0.785542 | − | 0.618809i | \(-0.212384\pi\) | ||||
0.785542 | + | 0.618809i | \(0.212384\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −324.000 | −0.413444 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −351.000 | + | 607.950i | −0.432542 | + | 0.749185i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −315.000 | − | 545.596i | −0.375168 | − | 0.649810i | 0.615184 | − | 0.788383i | \(-0.289082\pi\) |
−0.990352 | + | 0.138574i | \(0.955748\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 24.0000 | + | 41.5692i | 0.0267600 | + | 0.0463498i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −900.000 | + | 1558.85i | −0.971979 | + | 1.68352i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1054.00 | 1.10327 | 0.551637 | − | 0.834085i | \(-0.314004\pi\) | ||||
0.551637 | + | 0.834085i | \(0.314004\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 324.000 | 0.328921 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 279.000 | − | 483.242i | 0.274867 | − | 0.476083i | −0.695235 | − | 0.718783i | \(-0.744700\pi\) |
0.970101 | + | 0.242700i | \(0.0780329\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | + | 6.92820i | 0.00382652 | + | 0.00662773i | 0.867932 | − | 0.496682i | \(-0.165449\pi\) |
−0.864106 | + | 0.503310i | \(0.832115\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −882.000 | − | 1527.67i | −0.796880 | − | 1.38024i | −0.921639 | − | 0.388049i | \(-0.873149\pi\) |
0.124759 | − | 0.992187i | \(-0.460184\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −811.000 | + | 1404.69i | −0.712658 | + | 1.23436i | 0.251198 | + | 0.967936i | \(0.419175\pi\) |
−0.963856 | + | 0.266424i | \(0.914158\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 678.000 | 0.579756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1134.00 | −0.944051 | −0.472025 | − | 0.881585i | \(-0.656477\pi\) | ||||
−0.472025 | + | 0.881585i | \(0.656477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −648.000 | + | 1122.37i | −0.525446 | + | 0.910099i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −45.0000 | − | 77.9423i | −0.0355577 | − | 0.0615878i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.5000 | + | 30.3109i | 0.0131480 | + | 0.0227730i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −135.000 | + | 233.827i | −0.0989637 | + | 0.171410i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1332.00 | 0.953102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −592.000 | −0.413634 | −0.206817 | − | 0.978380i | \(-0.566310\pi\) | ||||
−0.206817 | + | 0.978380i | \(0.566310\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 678.000 | − | 1174.33i | 0.462749 | − | 0.801504i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −954.000 | − | 1652.38i | −0.636270 | − | 1.10205i | −0.986245 | − | 0.165293i | \(-0.947143\pi\) |
0.349975 | − | 0.936759i | \(-0.386190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 243.000 | + | 420.888i | 0.154919 | + | 0.268328i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −477.000 | + | 826.188i | −0.297466 | + | 0.515226i | −0.975556 | − | 0.219753i | \(-0.929475\pi\) |
0.678089 | + | 0.734979i | \(0.262808\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2564.00 | −1.56457 | −0.782286 | − | 0.622919i | \(-0.785947\pi\) | ||||
−0.782286 | + | 0.622919i | \(0.785947\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1296.00 | 0.774063 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −180.000 | + | 311.769i | −0.105261 | + | 0.182318i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2106.00 | + | 3647.70i | 1.20616 | + | 2.08914i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 369.000 | + | 639.127i | 0.202884 | + | 0.351405i | 0.949456 | − | 0.313899i | \(-0.101635\pi\) |
−0.746573 | + | 0.665304i | \(0.768302\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1220.00 | − | 2113.10i | 0.657498 | − | 1.13882i | −0.323763 | − | 0.946138i | \(-0.604948\pi\) |
0.981261 | − | 0.192682i | \(-0.0617185\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −162.000 | −0.0856008 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 288.000 | 0.149243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1277.00 | + | 2211.83i | −0.649145 | + | 1.12435i | 0.334183 | + | 0.942508i | \(0.391540\pi\) |
−0.983328 | + | 0.181843i | \(0.941794\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 621.000 | + | 1075.60i | 0.309739 | + | 0.536484i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 410.000 | + | 710.141i | 0.197016 | + | 0.341242i | 0.947560 | − | 0.319579i | \(-0.103541\pi\) |
−0.750543 | + | 0.660821i | \(0.770208\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 972.000 | − | 1683.55i | 0.458607 | − | 0.794330i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1944.00 | −0.900786 | −0.450393 | − | 0.892830i | \(-0.648716\pi\) | ||||
−0.450393 | + | 0.892830i | \(0.648716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2097.00 | −0.954483 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −450.000 | + | 779.423i | −0.201242 | + | 0.348561i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −621.000 | − | 1075.60i | −0.272912 | − | 0.472697i | 0.696694 | − | 0.717368i | \(-0.254653\pi\) |
−0.969606 | + | 0.244671i | \(0.921320\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1026.00 | + | 1777.08i | 0.435700 | + | 0.754654i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −558.000 | + | 966.484i | −0.232999 | + | 0.403567i | −0.958689 | − | 0.284455i | \(-0.908187\pi\) |
0.725690 | + | 0.688022i | \(0.241521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1070.00 | −0.439406 | −0.219703 | − | 0.975567i | \(-0.570509\pi\) | ||||
−0.219703 | + | 0.975567i | \(0.570509\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1266.00 | 0.511396 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2034.00 | − | 3522.99i | 0.808339 | − | 1.40008i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 324.000 | + | 561.184i | 0.126702 | + | 0.219454i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 288.000 | + | 498.831i | 0.109104 | + | 0.188974i | 0.915408 | − | 0.402528i | \(-0.131868\pi\) |
−0.806303 | + | 0.591502i | \(0.798535\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 671.000 | − | 1162.21i | 0.250257 | − | 0.433458i | −0.713339 | − | 0.700819i | \(-0.752818\pi\) |
0.963597 | + | 0.267361i | \(0.0861515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −540.000 | −0.198309 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1422.00 | 0.514281 | 0.257140 | − | 0.966374i | \(-0.417220\pi\) | ||||
0.257140 | + | 0.966374i | \(0.417220\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 436.000 | − | 755.174i | 0.155313 | − | 0.269009i | −0.777860 | − | 0.628437i | \(-0.783695\pi\) |
0.933173 | + | 0.359428i | \(0.117028\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 498.000 | + | 862.561i | 0.174757 | + | 0.302688i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 810.000 | + | 1402.96i | 0.275965 | + | 0.477986i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −324.000 | + | 561.184i | −0.108790 | + | 0.188430i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3600.00 | 1.19147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1340.00 | 0.437201 | 0.218600 | − | 0.975814i | \(-0.429851\pi\) | ||||
0.218600 | + | 0.975814i | \(0.429851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −540.000 | + | 935.307i | −0.173710 | + | 0.300874i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4068.00 | − | 7045.98i | −1.29040 | − | 2.23503i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −39.0000 | − | 67.5500i | −0.0120337 | − | 0.0208429i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 90.0000 | − | 155.885i | 0.0273939 | − | 0.0474477i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4880.00 | −1.46542 | −0.732711 | − | 0.680540i | \(-0.761745\pi\) | ||||
−0.732711 | + | 0.680540i | \(0.761745\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1791.00 | 0.530667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1350.00 | − | 2338.27i | 0.394725 | − | 0.683684i | −0.598341 | − | 0.801242i | \(-0.704173\pi\) |
0.993066 | + | 0.117557i | \(0.0375064\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 127.000 | + | 219.970i | 0.0366480 | + | 0.0634762i | 0.883768 | − | 0.467926i | \(-0.154999\pi\) |
−0.847120 | + | 0.531402i | \(0.821665\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2205.00 | − | 3819.17i | −0.619976 | − | 1.07383i | −0.989490 | − | 0.144604i | \(-0.953809\pi\) |
0.369514 | − | 0.929225i | \(-0.379524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3888.00 | − | 6734.21i | 1.07926 | − | 1.86933i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1536.00 | −0.420987 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3888.00 | −1.05228 | −0.526138 | − | 0.850399i | \(-0.676360\pi\) | ||||
−0.526138 | + | 0.850399i | \(0.676360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2569.00 | − | 4449.64i | 0.686655 | − | 1.18932i | −0.286259 | − | 0.958152i | \(-0.592412\pi\) |
0.972914 | − | 0.231169i | \(-0.0742550\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −500.000 | − | 866.025i | −0.128803 | − | 0.223093i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1782.00 | − | 3086.51i | 0.453533 | − | 0.785542i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4788.00 | −1.20405 | −0.602024 | − | 0.798478i | \(-0.705639\pi\) | ||||
−0.602024 | + | 0.798478i | \(0.705639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2592.00 | 0.644101 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −486.000 | + | 841.777i | −0.119351 | + | 0.206722i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2943.00 | − | 5097.43i | −0.714316 | − | 1.23723i | −0.963223 | − | 0.268705i | \(-0.913404\pi\) |
0.248906 | − | 0.968528i | \(-0.419929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1053.00 | + | 1823.85i | 0.249728 | + | 0.432542i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1116.00 | + | 1932.97i | −0.261656 | + | 0.453201i | −0.966682 | − | 0.255980i | \(-0.917602\pi\) |
0.705026 | + | 0.709181i | \(0.250935\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7452.00 | 1.72744 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1890.00 | −0.433206 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −333.000 | + | 576.773i | −0.0754772 | + | 0.130730i | −0.901294 | − | 0.433209i | \(-0.857381\pi\) |
0.825816 | + | 0.563939i | \(0.190715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2768.00 | − | 4794.32i | −0.620458 | − | 1.07466i | −0.989401 | − | 0.145212i | \(-0.953614\pi\) |
0.368943 | − | 0.929452i | \(-0.379720\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3582.00 | − | 6204.21i | −0.785464 | − | 1.36046i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1063.00 | + | 1841.17i | −0.230576 | + | 0.399369i | −0.957978 | − | 0.286843i | \(-0.907394\pi\) |
0.727402 | + | 0.686212i | \(0.240728\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 144.000 | 0.0308998 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2934.00 | −0.622875 | −0.311437 | − | 0.950267i | \(-0.600810\pi\) | ||||
−0.311437 | + | 0.950267i | \(0.600810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1018.00 | − | 1763.23i | 0.213830 | − | 0.370364i | −0.739080 | − | 0.673617i | \(-0.764740\pi\) |
0.952910 | + | 0.303253i | \(0.0980729\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2700.00 | + | 4676.54i | 0.561173 | + | 0.971979i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2294.50 | + | 3974.19i | 0.467026 | + | 0.808913i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1581.00 | − | 2738.37i | 0.318487 | − | 0.551637i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2286.00 | −0.455800 | −0.227900 | − | 0.973684i | \(-0.573186\pi\) | ||||
−0.227900 | + | 0.973684i | \(0.573186\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12312.0 | 2.42994 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 486.000 | − | 841.777i | 0.0949514 | − | 0.164461i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −360.000 | − | 623.538i | −0.0696299 | − | 0.120603i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −837.000 | − | 1449.73i | −0.158694 | − | 0.274867i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3798.00 | − | 6578.33i | 0.713026 | − | 1.23500i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1244.00 | −0.231267 | −0.115633 | − | 0.993292i | \(-0.536890\pi\) | ||||
−0.115633 | + | 0.993292i | \(0.536890\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.0000 | 0.00441849 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 612.000 | − | 1060.02i | 0.111586 | − | 0.193273i | −0.804824 | − | 0.593514i | \(-0.797740\pi\) |
0.916410 | + | 0.400241i | \(0.131074\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 949.000 | + | 1643.72i | 0.171376 | + | 0.296832i | 0.938901 | − | 0.344187i | \(-0.111845\pi\) |
−0.767525 | + | 0.641019i | \(0.778512\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4581.00 | + | 7934.52i | 0.811655 | + | 1.40583i | 0.911705 | + | 0.410845i | \(0.134766\pi\) |
−0.100050 | + | 0.994982i | \(0.531900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4212.00 | − | 7295.40i | 0.739269 | − | 1.28045i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5292.00 | −0.920158 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1800.00 | −0.310076 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −995.000 | + | 1723.39i | −0.169824 | + | 0.294143i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2433.00 | + | 4214.08i | 0.411453 | + | 0.712658i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2174.00 | + | 3765.48i | 0.361009 | + | 0.625285i | 0.988127 | − | 0.153639i | \(-0.0490992\pi\) |
−0.627119 | + | 0.778924i | \(0.715766\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1017.00 | − | 1761.50i | 0.167361 | − | 0.289878i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5976.00 | 0.974638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7154.00 | 1.15639 | 0.578195 | − | 0.815899i | \(-0.303757\pi\) | ||||
0.578195 | + | 0.815899i | \(0.303757\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1701.00 | + | 2946.22i | −0.272524 | + | 0.472025i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −288.000 | − | 498.831i | −0.0457363 | − | 0.0792176i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1944.00 | + | 3367.11i | 0.303366 | + | 0.525446i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 918.000 | − | 1590.02i | 0.142020 | − | 0.245985i | −0.786237 | − | 0.617925i | \(-0.787974\pi\) |
0.928257 | + | 0.371939i | \(0.121307\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5894.00 | −0.904007 | −0.452004 | − | 0.892016i | \(-0.649291\pi\) | ||||
−0.452004 | + | 0.892016i | \(0.649291\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −270.000 | −0.0410585 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5553.00 | − | 9618.08i | 0.837270 | − | 1.45019i | −0.0548984 | − | 0.998492i | \(-0.517484\pi\) |
0.892169 | − | 0.451703i | \(-0.149183\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3240.00 | + | 5611.84i | 0.484398 | + | 0.839002i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6588.00 | − | 11410.8i | −0.968527 | − | 1.67754i | −0.699823 | − | 0.714316i | \(-0.746738\pi\) |
−0.268704 | − | 0.963223i | \(-0.586595\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1570.50 | + | 2720.19i | −0.228969 | + | 0.396586i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 105.000 | 0.0151820 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −468.000 | −0.0671130 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3056.00 | + | 5293.15i | −0.434665 | + | 0.752861i | −0.997268 | − | 0.0738656i | \(-0.976466\pi\) |
0.562604 | + | 0.826727i | \(0.309800\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 405.000 | + | 701.481i | 0.0571367 | + | 0.0989637i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6809.00 | + | 11793.5i | 0.945192 | + | 1.63712i | 0.755366 | + | 0.655303i | \(0.227459\pi\) |
0.189826 | + | 0.981818i | \(0.439208\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1998.00 | − | 3460.64i | 0.275137 | − | 0.476551i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2340.00 | −0.319671 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 692.000 | 0.0937880 | 0.0468940 | − | 0.998900i | \(-0.485068\pi\) | ||||
0.0468940 | + | 0.998900i | \(0.485068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −888.000 | + | 1538.06i | −0.119406 | + | 0.206817i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4032.00 | − | 6983.63i | −0.537926 | − | 0.931715i | −0.999016 | − | 0.0443613i | \(-0.985875\pi\) |
0.461090 | − | 0.887353i | \(-0.347459\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2034.00 | − | 3522.99i | −0.267168 | − | 0.462749i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6327.00 | + | 10958.7i | −0.824657 | + | 1.42835i | 0.0775239 | + | 0.996990i | \(0.475299\pi\) |
−0.902181 | + | 0.431358i | \(0.858035\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1296.00 | −0.167625 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5724.00 | −0.734701 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4608.00 | + | 7981.29i | −0.586971 | + | 1.01666i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −53.0000 | − | 91.7987i | −0.00670024 | − | 0.0116051i | 0.862656 | − | 0.505791i | \(-0.168799\pi\) |
−0.869356 | + | 0.494186i | \(0.835466\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2007.00 | + | 3476.23i | 0.249937 | + | 0.432904i | 0.963508 | − | 0.267679i | \(-0.0862567\pi\) |
−0.713571 | + | 0.700583i | \(0.752923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −80.0000 | + | 138.564i | −0.00988855 | + | 0.0171275i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1458.00 | 0.178885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8136.00 | −0.990876 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1957.00 | − | 3389.62i | 0.236595 | − | 0.409795i | −0.723140 | − | 0.690702i | \(-0.757302\pi\) |
0.959735 | + | 0.280907i | \(0.0906352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1431.00 | + | 2478.56i | 0.171742 | + | 0.297466i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10692.0 | − | 18519.1i | −1.26470 | − | 2.19052i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3846.00 | + | 6661.47i | −0.451653 | + | 0.782286i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4428.00 | −0.516282 | −0.258141 | − | 0.966107i | \(-0.583110\pi\) | ||||
−0.258141 | + | 0.966107i | \(0.583110\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15490.0 | −1.79320 | −0.896599 | − | 0.442843i | \(-0.853970\pi\) | ||||
−0.896599 | + | 0.442843i | \(0.853970\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1944.00 | − | 3367.11i | 0.223453 | − | 0.387032i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1791.00 | + | 3102.10i | 0.204415 | + | 0.354057i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 540.000 | + | 935.307i | 0.0607726 | + | 0.105261i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3384.00 | + | 5861.26i | −0.378194 | + | 0.655051i | −0.990800 | − | 0.135338i | \(-0.956788\pi\) |
0.612606 | + | 0.790389i | \(0.290121\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1298.00 | −0.144060 | −0.0720299 | − | 0.997402i | \(-0.522948\pi\) | ||||
−0.0720299 | + | 0.997402i | \(0.522948\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12636.0 | 1.39276 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3600.00 | + | 6235.38i | −0.394076 | + | 0.682560i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1124.00 | − | 1946.83i | −0.122200 | − | 0.211656i | 0.798435 | − | 0.602081i | \(-0.205661\pi\) |
−0.920635 | + | 0.390425i | \(0.872328\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4806.00 | + | 8324.24i | 0.515440 | + | 0.892768i | 0.999839 | + | 0.0179214i | \(0.00570486\pi\) |
−0.484399 | + | 0.874847i | \(0.660962\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5670.00 | + | 9820.73i | −0.604008 | + | 1.04617i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2214.00 | 0.234270 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 162.000 | 0.0170273 | 0.00851364 | − | 0.999964i | \(-0.497290\pi\) | ||||
0.00851364 | + | 0.999964i | \(0.497290\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1620.00 | − | 2805.92i | 0.169142 | − | 0.292962i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3660.00 | − | 6339.31i | −0.379607 | − | 0.657498i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −685.000 | − | 1186.45i | −0.0701159 | − | 0.121444i | 0.828836 | − | 0.559492i | \(-0.189004\pi\) |
−0.898952 | + | 0.438047i | \(0.855670\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −243.000 | + | 420.888i | −0.0247108 | + | 0.0428004i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15354.0 | 1.55121 | 0.775604 | − | 0.631220i | \(-0.217445\pi\) | ||||
0.775604 | + | 0.631220i | \(0.217445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13024.0 | −1.30729 | −0.653646 | − | 0.756800i | \(-0.726762\pi\) | ||||
−0.653646 | + | 0.756800i | \(0.726762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 432.000 | − | 748.246i | 0.0430828 | − | 0.0746217i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7218.00 | − | 12501.9i | −0.715223 | − | 1.23880i | −0.962873 | − | 0.269953i | \(-0.912992\pi\) |
0.247650 | − | 0.968849i | \(-0.420342\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3831.00 | + | 6635.49i | 0.374784 | + | 0.649145i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8136.00 | + | 14092.0i | −0.790896 | + | 1.36987i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19900.0 | 1.92226 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3726.00 | 0.357656 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6048.00 | − | 10475.4i | 0.576911 | − | 0.999238i | −0.418921 | − | 0.908023i | \(-0.637591\pi\) |
0.995831 | − | 0.0912156i | \(-0.0290752\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1130.00 | + | 1957.22i | 0.107118 | + | 0.185533i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9486.00 | − | 16430.2i | −0.888118 | − | 1.53826i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3028.00 | + | 5244.65i | −0.281749 | + | 0.488004i | −0.971816 | − | 0.235742i | \(-0.924248\pi\) |
0.690067 | + | 0.723746i | \(0.257581\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2460.00 | 0.227495 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7524.00 | 0.691555 | 0.345777 | − | 0.938317i | \(-0.387615\pi\) | ||||
0.345777 | + | 0.938317i | \(0.387615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2106.00 | + | 3647.70i | −0.192392 | + | 0.333233i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2916.00 | − | 5050.66i | −0.264777 | − | 0.458607i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2638.00 | − | 4569.15i | −0.236660 | − | 0.409906i | 0.723094 | − | 0.690749i | \(-0.242719\pi\) |
−0.959754 | + | 0.280843i | \(0.909386\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2916.00 | + | 5050.66i | −0.260034 | + | 0.450393i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4968.00 | −0.440382 | −0.220191 | − | 0.975457i | \(-0.570668\pi\) | ||||
−0.220191 | + | 0.975457i | \(0.570668\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10044.0 | −0.885054 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3145.50 | + | 5448.17i | −0.275536 | + | 0.477242i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5499.00 | + | 9524.55i | 0.478858 | + | 0.829407i | 0.999706 | − | 0.0242426i | \(-0.00771742\pi\) |
−0.520848 | + | 0.853650i | \(0.674384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1350.00 | + | 2338.27i | 0.116187 | + | 0.201242i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 72.0000 | − | 124.708i | 0.00616058 | − | 0.0106704i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15552.0 | −1.32297 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3726.00 | −0.315131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4419.00 | + | 7653.93i | −0.371593 | + | 0.643618i | −0.989811 | − | 0.142389i | \(-0.954522\pi\) |
0.618218 | + | 0.786007i | \(0.287855\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11218.0 | + | 19430.1i | 0.937914 | + | 1.62451i | 0.769354 | + | 0.638823i | \(0.220578\pi\) |
0.168560 | + | 0.985691i | \(0.446088\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 144.000 | + | 249.415i | 0.0119027 | + | 0.0206161i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3491.50 | − | 6047.46i | 0.286965 | − | 0.497038i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6156.00 | 0.503103 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −900.000 | −0.0731395 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15876.0 | + | 27498.0i | −1.28295 | + | 2.22214i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1674.00 | + | 2899.45i | 0.134522 | + | 0.232999i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2381.00 | + | 4124.01i | 0.189218 | + | 0.327736i | 0.944990 | − | 0.327100i | \(-0.106071\pi\) |
−0.755771 | + | 0.654835i | \(0.772738\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1605.00 | + | 2779.94i | −0.126846 | + | 0.219703i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29196.0 | 2.29471 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6004.00 | −0.469310 | −0.234655 | − | 0.972079i | \(-0.575396\pi\) | ||||
−0.234655 | + | 0.972079i | \(0.575396\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1899.00 | − | 3289.16i | 0.147627 | − | 0.255698i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11700.0 | + | 20265.0i | 0.904604 | + | 1.56682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6102.00 | − | 10569.0i | −0.466695 | − | 0.808339i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2637.00 | − | 4567.42i | 0.200598 | − | 0.347447i | −0.748123 | − | 0.663560i | \(-0.769045\pi\) |
0.948721 | + | 0.316114i | \(0.102378\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4520.00 | 0.341996 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1944.00 | 0.146303 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6210.00 | + | 10756.0i | −0.464867 | + | 0.805174i | −0.999196 | − | 0.0401033i | \(-0.987231\pi\) |
0.534328 | + | 0.845277i | \(0.320565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10206.0 | + | 17677.3i | 0.759946 | + | 1.31627i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10683.0 | + | 18503.5i | 0.787091 | + | 1.36328i | 0.927742 | + | 0.373222i | \(0.121747\pi\) |
−0.140651 | + | 0.990059i | \(0.544920\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10570.0 | + | 18307.8i | −0.774677 | + | 1.34178i | 0.160298 | + | 0.987069i | \(0.448754\pi\) |
−0.934976 | + | 0.354712i | \(0.884579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1728.00 | 0.125983 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14328.0 | 1.03916 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1633.00 | − | 2828.44i | 0.117821 | − | 0.204072i | −0.801083 | − | 0.598553i | \(-0.795742\pi\) |
0.918904 | + | 0.394482i | \(0.129076\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2013.00 | − | 3486.62i | −0.144486 | − | 0.250257i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7452.00 | − | 12907.2i | −0.529383 | − | 0.916918i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −810.000 | + | 1402.96i | −0.0572468 | + | 0.0991544i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17028.0 | −1.19731 | −0.598655 | − | 0.801007i | \(-0.704298\pi\) | ||||
−0.598655 | + | 0.801007i | \(0.704298\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1600.00 | 0.111930 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2133.00 | − | 3694.46i | 0.148460 | − | 0.257140i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4761.00 | + | 8246.29i | 0.329698 | + | 0.571053i | 0.982452 | − | 0.186517i | \(-0.0597198\pi\) |
−0.652754 | + | 0.757570i | \(0.726386\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1308.00 | − | 2265.52i | −0.0896698 | − | 0.155313i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5148.00 | − | 8916.60i | 0.351155 | − | 0.608218i | −0.635297 | − | 0.772268i | \(-0.719123\pi\) |
0.986452 | + | 0.164050i | \(0.0524558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3382.00 | 0.229542 | 0.114771 | − | 0.993392i | \(-0.463387\pi\) | ||||
0.114771 | + | 0.993392i | \(0.463387\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2988.00 | 0.201792 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 315.000 | − | 545.596i | 0.0211679 | − | 0.0366639i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10328.0 | − | 17888.6i | −0.690611 | − | 1.19617i | −0.971638 | − | 0.236473i | \(-0.924009\pi\) |
0.281028 | − | 0.959700i | \(-0.409325\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2160.00 | + | 3741.23i | 0.143018 | + | 0.247715i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11057.0 | − | 19151.3i | 0.728529 | − | 1.26185i | −0.228976 | − | 0.973432i | \(-0.573538\pi\) |
0.957505 | − | 0.288417i | \(-0.0931288\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4860.00 | 0.318657 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19962.0 | 1.30250 | 0.651248 | − | 0.758865i | \(-0.274246\pi\) | ||||
0.651248 | + | 0.758865i | \(0.274246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −302.000 | + | 523.079i | −0.0196097 | + | 0.0339650i | −0.875664 | − | 0.482921i | \(-0.839576\pi\) |
0.856054 | + | 0.516886i | \(0.172909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 972.000 | + | 1683.55i | 0.0628100 | + | 0.108790i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 449.500 | + | 778.557i | 0.0287680 | + | 0.0498276i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5400.00 | − | 9353.07i | 0.343948 | − | 0.595735i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4068.00 | 0.257872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 152.000 | 0.00958958 | 0.00479479 | − | 0.999989i | \(-0.498474\pi\) | ||||
0.00479479 | + | 0.999989i | \(0.498474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2010.00 | − | 3481.42i | 0.126209 | − | 0.218600i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5328.00 | + | 9228.37i | 0.332969 | + | 0.576719i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1620.00 | + | 2805.92i | 0.100291 | + | 0.173710i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2097.00 | + | 3632.11i | −0.129215 | + | 0.223806i | −0.923372 | − | 0.383905i | \(-0.874579\pi\) |
0.794158 | + | 0.607711i | \(0.207912\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7252.00 | 0.444776 | 0.222388 | − | 0.974958i | \(-0.428615\pi\) | ||||
0.222388 | + | 0.974958i | \(0.428615\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24408.0 | −1.49002 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3348.00 | + | 5798.91i | −0.203437 | + | 0.352362i | −0.949633 | − | 0.313363i | \(-0.898544\pi\) |
0.746197 | + | 0.665725i | \(0.231878\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12312.0 | − | 21325.0i | −0.744666 | − | 1.28980i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14211.0 | − | 24614.2i | −0.851638 | − | 1.47508i | −0.879730 | − | 0.475474i | \(-0.842276\pi\) |
0.0280919 | − | 0.999605i | \(-0.491057\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17172.0 | + | 29742.8i | −1.02437 | + | 1.77427i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −234.000 | −0.0138953 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19908.0 | −1.17679 | −0.588396 | − | 0.808573i | \(-0.700240\pi\) | ||||
−0.588396 | + | 0.808573i | \(0.700240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7159.00 | − | 12399.8i | 0.421260 | − | 0.729644i | −0.574803 | − | 0.818292i | \(-0.694921\pi\) |
0.996063 | + | 0.0886482i | \(0.0282547\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −270.000 | − | 467.654i | −0.0158159 | − | 0.0273939i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8424.00 | + | 14590.8i | 0.489023 | + | 0.847013i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7320.00 | + | 12678.6i | −0.423031 | + | 0.732711i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15192.0 | −0.874040 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30050.0 | 1.72116 | 0.860581 | − | 0.509313i | \(-0.170101\pi\) | ||||
0.860581 | + | 0.509313i | \(0.170101\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2686.50 | − | 4653.15i | 0.153190 | − | 0.265333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11079.0 | + | 19189.4i | 0.628952 | + | 1.08938i | 0.987762 | + | 0.155966i | \(0.0498492\pi\) |
−0.358810 | + | 0.933411i | \(0.616817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4050.00 | − | 7014.81i | −0.227895 | − | 0.394725i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1566.00 | − | 2712.39i | 0.0877325 | − | 0.151957i | −0.818820 | − | 0.574051i | \(-0.805371\pi\) |
0.906552 | + | 0.422093i | \(0.138705\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17172.0 | 0.957822 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 762.000 | 0.0423175 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2070.00 | + | 3585.35i | −0.114457 | + | 0.198245i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10466.0 | − | 18127.6i | −0.576187 | − | 0.997986i | −0.995912 | − | 0.0903340i | \(-0.971207\pi\) |
0.419724 | − | 0.907652i | \(-0.362127\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23076.0 | + | 39968.8i | 1.25946 | + | 2.18144i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −810.000 | + | 1402.96i | −0.0440186 | + | 0.0762424i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13230.0 | −0.715886 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21834.0 | −1.17640 | −0.588202 | − | 0.808714i | \(-0.700164\pi\) | ||||
−0.588202 | + | 0.808714i | \(0.700164\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11300.0 | − | 19572.2i | 0.606241 | − | 1.05004i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11664.0 | − | 20202.6i | −0.623109 | − | 1.07926i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6223.00 | − | 10778.6i | −0.329633 | − | 0.570941i | 0.652806 | − | 0.757525i | \(-0.273592\pi\) |
−0.982439 | + | 0.186584i | \(0.940258\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2304.00 | + | 3990.65i | −0.121528 | + | 0.210494i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1152.00 | 0.0605088 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6480.00 | 0.338935 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5832.00 | + | 10101.3i | −0.303766 | + | 0.526138i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6264.00 | − | 10849.6i | −0.324907 | − | 0.562755i | 0.656587 | − | 0.754250i | \(-0.272000\pi\) |
−0.981493 | + | 0.191496i | \(0.938666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7707.00 | − | 13348.9i | −0.396440 | − | 0.686655i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23283.0 | − | 40327.3i | 1.19270 | − | 2.06582i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11576.0 | −0.590550 | −0.295275 | − | 0.955412i | \(-0.595411\pi\) | ||||
−0.295275 | + | 0.955412i | \(0.595411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4068.00 | − | 7045.98i | 0.205828 | − | 0.356505i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14669.0 | − | 25407.5i | −0.739170 | − | 1.28028i | −0.952869 | − | 0.303381i | \(-0.901884\pi\) |
0.213699 | − | 0.976900i | \(-0.431449\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5976.00 | − | 10350.7i | −0.298682 | − | 0.517333i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1270.00 | + | 2199.70i | −0.0632175 | + | 0.109496i | −0.895902 | − | 0.444252i | \(-0.853470\pi\) |
0.832684 | + | 0.553748i | \(0.186803\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3000.00 | −0.148728 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18792.0 | −0.927876 | −0.463938 | − | 0.885868i | \(-0.653564\pi\) | ||||
−0.463938 | + | 0.885868i | \(0.653564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6642.00 | − | 11504.3i | 0.326636 | − | 0.565751i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5346.00 | − | 9259.54i | −0.261847 | − | 0.453533i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2416.00 | − | 4184.63i | −0.117392 | − | 0.203328i | 0.801342 | − | 0.598207i | \(-0.204120\pi\) |
−0.918733 | + | 0.394879i | \(0.870787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7182.00 | + | 12439.6i | −0.347579 | + | 0.602024i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43920.0 | −2.11710 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20818.0 | −0.999529 | −0.499764 | − | 0.866161i | \(-0.666580\pi\) | ||||
−0.499764 | + | 0.866161i | \(0.666580\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3888.00 | − | 6734.21i | 0.185936 | − | 0.322051i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6021.00 | + | 10428.7i | 0.286808 | + | 0.496766i | 0.973046 | − | 0.230611i | \(-0.0740724\pi\) |
−0.686238 | + | 0.727377i | \(0.740739\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1458.00 | + | 2525.33i | 0.0689073 | + | 0.119351i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3420.00 | + | 5923.61i | −0.161003 | + | 0.278865i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13058.0 | −0.612332 | −0.306166 | − | 0.951978i | \(-0.599046\pi\) | ||||
−0.306166 | + | 0.951978i | \(0.599046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17658.0 | −0.824821 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5913.00 | + | 10241.6i | −0.275130 | + | 0.476540i | −0.970168 | − | 0.242434i | \(-0.922054\pi\) |
0.695038 | + | 0.718973i | \(0.255388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1592.00 | − | 2757.42i | −0.0737888 | − | 0.127806i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4500.00 | + | 7794.23i | 0.206969 | + | 0.358482i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6480.00 | − | 11223.7i | 0.296892 | − | 0.514232i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6318.00 | 0.288361 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 45972.0 | 2.09021 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5998.00 | − | 10388.8i | 0.271672 | − | 0.470549i | −0.697618 | − | 0.716470i | \(-0.745757\pi\) |
0.969290 | + | 0.245920i | \(0.0790902\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3348.00 | + | 5798.91i | 0.151067 | + | 0.261656i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2110.00 | + | 3654.63i | 0.0944871 | + | 0.163657i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11178.0 | − | 19360.9i | 0.498670 | − | 0.863722i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6966.00 | −0.309596 | −0.154798 | − | 0.987946i | \(-0.549473\pi\) | ||||
−0.154798 | + | 0.987946i | \(0.549473\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7776.00 | 0.344299 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2835.00 | + | 4910.36i | −0.125056 | + | 0.216603i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 468.000 | + | 810.600i | 0.0205671 | + | 0.0356232i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 999.000 | + | 1730.32i | 0.0435768 | + | 0.0754772i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20403.0 | − | 35339.0i | 0.886689 | − | 1.53579i | 0.0429232 | − | 0.999078i | \(-0.486333\pi\) |
0.843766 | − | 0.536712i | \(-0.180334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17980.0 | 0.778500 | 0.389250 | − | 0.921132i | \(-0.372734\pi\) | ||||
0.389250 | + | 0.921132i | \(0.372734\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16608.0 | −0.716443 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7380.00 | − | 12782.5i | 0.317190 | − | 0.549390i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22600.0 | − | 39144.3i | −0.967777 | − | 1.67624i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6417.00 | + | 11114.6i | 0.272783 | + | 0.472474i | 0.969573 | − | 0.244801i | \(-0.0787226\pi\) |
−0.696790 | + | 0.717275i | \(0.745389\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18932.0 | − | 32791.2i | 0.801857 | − | 1.38886i | −0.116536 | − | 0.993186i | \(-0.537179\pi\) |
0.918393 | − | 0.395670i | \(-0.129488\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21492.0 | −0.906976 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42516.0 | 1.78770 | 0.893849 | − | 0.448368i | \(-0.147995\pi\) | ||||
0.893849 | + | 0.448368i | \(0.147995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22819.0 | − | 39523.7i | 0.956015 | − | 1.65587i | 0.223988 | − | 0.974592i | \(-0.428092\pi\) |
0.732028 | − | 0.681275i | \(-0.238574\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3189.00 | + | 5523.51i | 0.133123 | + | 0.230576i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17496.0 | + | 30304.0i | 0.725119 | + | 1.25594i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 216.000 | − | 374.123i | 0.00892001 | − | 0.0154499i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17496.0 | −0.719939 | −0.359970 | − | 0.932964i | \(-0.617213\pi\) | ||||
−0.359970 | + | 0.932964i | \(0.617213\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30367.0 | 1.24511 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4401.00 | + | 7622.76i | −0.179808 | + | 0.311437i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18873.0 | + | 32689.0i | 0.768344 | + | 1.33081i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3054.00 | − | 5289.68i | −0.123455 | − | 0.213830i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8136.00 | − | 14092.0i | 0.327730 | − | 0.567646i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32174.0 | −1.29146 | −0.645731 | − | 0.763565i | \(-0.723447\pi\) | ||||
−0.645731 | + | 0.763565i | \(0.723447\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16200.0 | 0.647986 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19467.0 | + | 33717.8i | −0.775939 | + | 1.34397i | 0.158326 | + | 0.987387i | \(0.449390\pi\) |
−0.934265 | + | 0.356579i | \(0.883943\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14890.0 | + | 25790.2i | 0.591432 | + | 1.02439i | 0.994040 | + | 0.109018i | \(0.0347706\pi\) |
−0.402608 | + | 0.915373i | \(0.631896\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24048.0 | + | 41652.4i | 0.948556 | + | 1.64295i | 0.748471 | + | 0.663168i | \(0.230788\pi\) |
0.200085 | + | 0.979779i | \(0.435878\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11178.0 | + | 19360.9i | −0.439380 | + | 0.761028i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13767.0 | 0.539275 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18432.0 | 0.719520 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1660.00 | + | 2875.20i | −0.0645774 | + | 0.111851i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4743.00 | − | 8215.12i | −0.183879 | − | 0.318487i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10651.0 | − | 18448.1i | −0.410101 | − | 0.710316i | 0.584799 | − | 0.811178i | \(-0.301173\pi\) |
−0.994900 | + | 0.100862i | \(0.967840\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3429.00 | + | 5939.20i | −0.131578 | + | 0.227900i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7470.00 | 0.285665 | 0.142832 | − | 0.989747i | \(-0.454379\pi\) | ||||
0.142832 | + | 0.989747i | \(0.454379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 764.000 | 0.0291174 | 0.0145587 | − | 0.999894i | \(-0.495366\pi\) | ||||
0.0145587 | + | 0.999894i | \(0.495366\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18468.0 | − | 31987.5i | 0.701463 | − | 1.21497i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16164.0 | + | 27996.9i | 0.611876 | + | 1.05980i | 0.990924 | + | 0.134423i | \(0.0429182\pi\) |
−0.379048 | + | 0.925377i | \(0.623748\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1458.00 | − | 2525.33i | −0.0548202 | − | 0.0949514i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21600.0 | − | 37412.3i | 0.809425 | − | 1.40197i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20088.0 | 0.750243 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2160.00 | −0.0804017 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1872.00 | − | 3242.40i | 0.0694490 | − | 0.120289i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3726.00 | + | 6453.62i | 0.137770 | + | 0.238625i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9630.00 | + | 16679.6i | 0.353715 | + | 0.612652i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18158.0 | − | 31450.6i | 0.664748 | − | 1.15138i | −0.314605 | − | 0.949223i | \(-0.601872\pi\) |
0.979354 | − | 0.202155i | \(-0.0647944\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5022.00 | −0.183244 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13392.0 | −0.487044 | −0.243522 | − | 0.969895i | \(-0.578303\pi\) | ||||
−0.243522 | + | 0.969895i | \(0.578303\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21384.0 | + | 37038.2i | −0.775145 | + | 1.34259i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11394.0 | − | 19735.0i | −0.411666 | − | 0.713026i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19036.0 | − | 32971.3i | −0.683286 | − | 1.18349i | −0.973972 | − | 0.226667i | \(-0.927217\pi\) |
0.290686 | − | 0.956818i | \(-0.406116\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1866.00 | + | 3232.01i | −0.0667609 | + | 0.115633i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3600.00 | −0.128381 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44974.0 | −1.59863 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.0000 | − | 62.3538i | 0.00127551 | − | 0.00220924i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6399.00 | − | 11083.4i | −0.225990 | − | 0.391426i | 0.730626 | − | 0.682778i | \(-0.239228\pi\) |
−0.956616 | + | 0.291352i | \(0.905895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1836.00 | − | 3180.05i | −0.0644244 | − | 0.111586i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5832.00 | − | 10101.3i | 0.203986 | − | 0.353314i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34874.0 | −1.21588 | −0.607942 | − | 0.793981i | \(-0.708005\pi\) | ||||
−0.607942 | + | 0.793981i | \(0.708005\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5694.00 | 0.197888 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8595.00 | − | 14887.0i | 0.297757 | − | 0.515730i | −0.677866 | − | 0.735186i | \(-0.737095\pi\) |
0.975622 | + | 0.219456i | \(0.0704283\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3240.00 | + | 5611.84i | 0.111886 | + | 0.193793i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20142.0 | − | 34887.0i | −0.691158 | − | 1.19712i | −0.971459 | − | 0.237209i | \(-0.923767\pi\) |
0.280300 | − | 0.959912i | \(-0.409566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 130.000 | − | 225.167i | 0.00444676 | − | 0.00770202i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27486.0 | 0.937218 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15498.0 | 0.526789 | 0.263394 | − | 0.964688i | \(-0.415158\pi\) | ||||
0.263394 | + | 0.964688i | \(0.415158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5184.00 | − | 8978.95i | 0.175655 | − | 0.304243i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12636.0 | − | 21886.2i | −0.426817 | − | 0.739269i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14767.5 | + | 25578.1i | 0.495703 | + | 0.858583i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7938.00 | + | 13749.0i | −0.265627 | + | 0.460079i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24156.0 | −0.805813 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37160.0 | 1.23577 | 0.617883 | − | 0.786270i | \(-0.287991\pi\) | ||||
0.617883 | + | 0.786270i | \(0.287991\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2700.00 | + | 4676.54i | −0.0895113 | + | 0.155038i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9234.00 | + | 15993.8i | 0.305183 | + | 0.528593i | 0.977302 | − | 0.211850i | \(-0.0679489\pi\) |
−0.672119 | + | 0.740443i | \(0.734616\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2985.00 | + | 5170.17i | 0.0980477 | + | 0.169824i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5193.00 | + | 8994.54i | −0.170050 | + | 0.294535i | −0.938437 | − | 0.345450i | \(-0.887726\pi\) |
0.768387 | + | 0.639985i | \(0.221060\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22680.0 | 0.740404 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14598.0 | 0.475105 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22068.0 | − | 38222.9i | 0.716032 | − | 1.24020i | −0.246528 | − | 0.969136i | \(-0.579290\pi\) |
0.962560 | − | 0.271069i | \(-0.0873771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12798.0 | − | 22166.8i | −0.413988 | − | 0.717048i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16272.0 | − | 28183.9i | −0.523174 | − | 0.906165i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14216.0 | − | 24622.8i | 0.455687 | − | 0.789274i | −0.543040 | − | 0.839707i | \(-0.682727\pi\) |
0.998727 | + | 0.0504332i | \(0.0160602\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13044.0 | 0.416857 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15696.0 | −0.500097 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19889.0 | + | 34448.8i | −0.631786 | + | 1.09429i | 0.355400 | + | 0.934714i | \(0.384345\pi\) |
−0.987186 | + | 0.159572i | \(0.948989\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3051.00 | − | 5284.49i | −0.0966260 | − | 0.167361i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))