Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,4,Mod(361,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, 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("980.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.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: | \(57.8218718056\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.961 |
Dual form | 980.4.i.n.361.1 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.00000 | + | 3.46410i | 0.384900 | + | 0.666667i | 0.991755 | − | 0.128146i | \(-0.0409025\pi\) |
−0.606855 | + | 0.794812i | \(0.707569\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.50000 | − | 9.52628i | 0.203704 | − | 0.352825i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 30.0000 | + | 51.9615i | 0.822304 | + | 1.42427i | 0.903963 | + | 0.427611i | \(0.140645\pi\) |
−0.0816590 | + | 0.996660i | \(0.526022\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −86.0000 | −1.83478 | −0.917389 | − | 0.397992i | \(-0.869707\pi\) | ||||
−0.917389 | + | 0.397992i | \(0.869707\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.0000 | 0.344265 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.00000 | + | 15.5885i | 0.128401 | + | 0.222397i | 0.923057 | − | 0.384662i | \(-0.125682\pi\) |
−0.794656 | + | 0.607060i | \(0.792349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.0000 | − | 38.1051i | 0.265639 | − | 0.460101i | −0.702092 | − | 0.712087i | \(-0.747750\pi\) |
0.967731 | + | 0.251986i | \(0.0810837\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.0000 | + | 41.5692i | −0.217580 | + | 0.376860i | −0.954068 | − | 0.299591i | \(-0.903150\pi\) |
0.736487 | + | 0.676451i | \(0.236483\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 152.000 | 1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −186.000 | −1.19101 | −0.595506 | − | 0.803351i | \(-0.703048\pi\) | ||||
−0.595506 | + | 0.803351i | \(0.703048\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 88.0000 | + | 152.420i | 0.509847 | + | 0.883081i | 0.999935 | + | 0.0114083i | \(0.00363144\pi\) |
−0.490088 | + | 0.871673i | \(0.663035\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −120.000 | + | 207.846i | −0.633010 | + | 1.09640i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −127.000 | + | 219.970i | −0.564288 | + | 0.977376i | 0.432827 | + | 0.901477i | \(0.357516\pi\) |
−0.997115 | + | 0.0758992i | \(0.975817\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −172.000 | − | 297.913i | −0.706206 | − | 1.22319i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −186.000 | −0.708496 | −0.354248 | − | 0.935152i | \(-0.615263\pi\) | ||||
−0.354248 | + | 0.935152i | \(0.615263\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −100.000 | −0.354648 | −0.177324 | − | 0.984153i | \(-0.556744\pi\) | ||||
−0.177324 | + | 0.984153i | \(0.556744\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −27.5000 | − | 47.6314i | −0.0910991 | − | 0.157788i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 84.0000 | − | 145.492i | 0.260695 | − | 0.451537i | −0.705732 | − | 0.708479i | \(-0.749382\pi\) |
0.966427 | + | 0.256942i | \(0.0827150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −36.0000 | + | 62.3538i | −0.0988433 | + | 0.171202i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 249.000 | + | 431.281i | 0.645335 | + | 1.11775i | 0.984224 | + | 0.176927i | \(0.0566157\pi\) |
−0.338888 | + | 0.940827i | \(0.610051\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 300.000 | 0.735491 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 176.000 | 0.408978 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −126.000 | − | 218.238i | −0.278031 | − | 0.481563i | 0.692865 | − | 0.721068i | \(-0.256348\pi\) |
−0.970895 | + | 0.239505i | \(0.923015\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −29.0000 | + | 50.2295i | −0.0608700 | + | 0.105430i | −0.894855 | − | 0.446358i | \(-0.852721\pi\) |
0.833985 | + | 0.551788i | \(0.186054\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −215.000 | + | 372.391i | −0.410269 | + | 0.710606i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 518.000 | + | 897.202i | 0.944534 | + | 1.63598i | 0.756682 | + | 0.653783i | \(0.226819\pi\) |
0.187852 | + | 0.982197i | \(0.439847\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −192.000 | −0.334987 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 168.000 | 0.280816 | 0.140408 | − | 0.990094i | \(-0.455159\pi\) | ||||
0.140408 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 253.000 | + | 438.209i | 0.405636 | + | 0.702582i | 0.994395 | − | 0.105727i | \(-0.0337168\pi\) |
−0.588759 | + | 0.808308i | \(0.700383\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 50.0000 | − | 86.6025i | 0.0769800 | − | 0.133333i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −136.000 | + | 235.559i | −0.193686 | + | 0.335474i | −0.946469 | − | 0.322795i | \(-0.895378\pi\) |
0.752783 | + | 0.658269i | \(0.228711\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 155.500 | + | 269.334i | 0.213306 | + | 0.369457i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −948.000 | −1.25369 | −0.626846 | − | 0.779143i | \(-0.715655\pi\) | ||||
−0.626846 | + | 0.779143i | \(0.715655\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 90.0000 | 0.114846 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −372.000 | − | 644.323i | −0.458421 | − | 0.794008i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −507.000 | + | 878.150i | −0.603841 | + | 1.04588i | 0.388392 | + | 0.921494i | \(0.373031\pi\) |
−0.992233 | + | 0.124390i | \(0.960303\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −352.000 | + | 609.682i | −0.392481 | + | 0.679796i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −110.000 | − | 190.526i | −0.118797 | − | 0.205763i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 766.000 | 0.801809 | 0.400905 | − | 0.916120i | \(-0.368696\pi\) | ||||
0.400905 | + | 0.916120i | \(0.368696\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 660.000 | 0.670025 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −657.000 | − | 1137.96i | −0.647267 | − | 1.12110i | −0.983773 | − | 0.179418i | \(-0.942579\pi\) |
0.336506 | − | 0.941681i | \(-0.390755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −224.000 | + | 387.979i | −0.214285 | + | 0.371153i | −0.953051 | − | 0.302809i | \(-0.902076\pi\) |
0.738766 | + | 0.673962i | \(0.235409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −774.000 | + | 1340.61i | −0.699303 | + | 1.21123i | 0.269406 | + | 0.963027i | \(0.413173\pi\) |
−0.968708 | + | 0.248201i | \(0.920161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −139.000 | − | 240.755i | −0.122145 | − | 0.211561i | 0.798468 | − | 0.602037i | \(-0.205644\pi\) |
−0.920613 | + | 0.390476i | \(0.872311\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1016.00 | −0.868779 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −558.000 | −0.464533 | −0.232266 | − | 0.972652i | \(-0.574614\pi\) | ||||
−0.232266 | + | 0.972652i | \(0.574614\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 120.000 | + | 207.846i | 0.0973048 | + | 0.168537i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −473.000 | + | 819.260i | −0.373751 | + | 0.647356i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1134.50 | + | 1965.01i | −0.852367 | + | 1.47634i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −372.000 | − | 644.323i | −0.272700 | − | 0.472330i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 344.000 | 0.240355 | 0.120177 | − | 0.992752i | \(-0.461654\pi\) | ||||
0.120177 | + | 0.992752i | \(0.461654\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −200.000 | − | 346.410i | −0.136504 | − | 0.236432i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 390.000 | − | 675.500i | 0.260110 | − | 0.450524i | −0.706161 | − | 0.708052i | \(-0.749574\pi\) |
0.966271 | + | 0.257527i | \(0.0829077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 380.000 | − | 658.179i | 0.242261 | − | 0.419608i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −333.000 | − | 576.773i | −0.207665 | − | 0.359686i | 0.743314 | − | 0.668943i | \(-0.233253\pi\) |
−0.950979 | + | 0.309257i | \(0.899920\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −884.000 | −0.539424 | −0.269712 | − | 0.962941i | \(-0.586928\pi\) | ||||
−0.269712 | + | 0.962941i | \(0.586928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 672.000 | 0.401366 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2580.00 | − | 4468.69i | −1.50874 | − | 2.61322i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −465.000 | + | 805.404i | −0.266318 | + | 0.461277i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 57.0000 | − | 98.7269i | 0.0313397 | − | 0.0542820i | −0.849930 | − | 0.526895i | \(-0.823356\pi\) |
0.881270 | + | 0.472613i | \(0.156689\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000 | + | 34.6410i | 0.0107787 | + | 0.0186692i | 0.871364 | − | 0.490636i | \(-0.163236\pi\) |
−0.860586 | + | 0.509306i | \(0.829902\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 198.000 | 0.104623 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 880.000 | 0.456021 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −77.0000 | − | 133.368i | −0.0391418 | − | 0.0677957i | 0.845791 | − | 0.533515i | \(-0.179129\pi\) |
−0.884933 | + | 0.465719i | \(0.845796\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −996.000 | + | 1725.12i | −0.496779 | + | 0.860447i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1090.00 | + | 1887.94i | −0.523775 | + | 0.907206i | 0.475842 | + | 0.879531i | \(0.342144\pi\) |
−0.999617 | + | 0.0276746i | \(0.991190\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 600.000 | + | 1039.23i | 0.283091 | + | 0.490327i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3696.00 | −1.71261 | −0.856303 | − | 0.516474i | \(-0.827244\pi\) | ||||
−0.856303 | + | 0.516474i | \(0.827244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5199.00 | 2.36641 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −242.000 | − | 419.156i | −0.108223 | − | 0.187448i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 651.000 | − | 1127.57i | 0.286096 | − | 0.495533i | −0.686778 | − | 0.726867i | \(-0.740976\pi\) |
0.972874 | + | 0.231334i | \(0.0743090\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 504.000 | − | 872.954i | 0.214028 | − | 0.370707i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2154.00 | + | 3730.84i | 0.899427 | + | 1.55785i | 0.828227 | + | 0.560392i | \(0.189350\pi\) |
0.0712000 | + | 0.997462i | \(0.477317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1550.00 | −0.636523 | −0.318261 | − | 0.948003i | \(-0.603099\pi\) | ||||
−0.318261 | + | 0.948003i | \(0.603099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −232.000 | −0.0937155 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 635.000 | + | 1099.85i | 0.252357 | + | 0.437096i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −540.000 | + | 935.307i | −0.211170 | + | 0.365756i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.0000 | + | 41.5692i | −0.00909204 | + | 0.0157479i | −0.870536 | − | 0.492105i | \(-0.836227\pi\) |
0.861444 | + | 0.507853i | \(0.169561\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −529.000 | − | 916.255i | −0.197297 | − | 0.341728i | 0.750354 | − | 0.661036i | \(-0.229883\pi\) |
−0.947651 | + | 0.319308i | \(0.896550\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1720.00 | −0.631650 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3714.00 | −1.34321 | −0.671603 | − | 0.740911i | \(-0.734394\pi\) | ||||
−0.671603 | + | 0.740911i | \(0.734394\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −884.000 | − | 1531.13i | −0.314900 | − | 0.545423i | 0.664516 | − | 0.747274i | \(-0.268638\pi\) |
−0.979416 | + | 0.201851i | \(0.935304\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2072.00 | + | 3588.81i | −0.727103 | + | 1.25938i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −465.000 | + | 805.404i | −0.158424 | + | 0.274399i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 264.000 | + | 457.261i | 0.0886438 | + | 0.153536i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2640.00 | 0.873745 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4036.00 | −1.31682 | −0.658412 | − | 0.752658i | \(-0.728771\pi\) | ||||
−0.658412 | + | 0.752658i | \(0.728771\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 336.000 | + | 581.969i | 0.108086 | + | 0.187211i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −250.000 | + | 433.013i | −0.0793017 | + | 0.137355i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1012.00 | + | 1752.84i | −0.312259 | + | 0.540848i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −774.000 | − | 1340.61i | −0.235588 | − | 0.408050i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −680.000 | −0.204198 | −0.102099 | − | 0.994774i | \(-0.532556\pi\) | ||||
−0.102099 | + | 0.994774i | \(0.532556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −275.000 | −0.0814815 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1194.00 | + | 2068.07i | 0.349113 | + | 0.604681i | 0.986092 | − | 0.166200i | \(-0.0531497\pi\) |
−0.636979 | + | 0.770881i | \(0.719816\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1937.00 | + | 3354.98i | −0.558954 | + | 0.968137i | 0.438630 | + | 0.898668i | \(0.355464\pi\) |
−0.997584 | + | 0.0694695i | \(0.977869\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1581.00 | + | 2738.37i | −0.444527 | + | 0.769943i | −0.998019 | − | 0.0629112i | \(-0.979962\pi\) |
0.553492 | + | 0.832854i | \(0.313295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −420.000 | − | 727.461i | −0.116586 | − | 0.201933i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1088.00 | −0.298199 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5424.00 | 1.46799 | 0.733995 | − | 0.679155i | \(-0.237654\pi\) | ||||
0.733995 | + | 0.679155i | \(0.237654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1943.00 | − | 3365.37i | −0.519335 | − | 0.899514i | −0.999747 | − | 0.0224714i | \(-0.992847\pi\) |
0.480413 | − | 0.877042i | \(-0.340487\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1430.00 | − | 2476.83i | 0.377508 | − | 0.653864i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1892.00 | + | 3277.04i | −0.487389 | + | 0.844182i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1896.00 | − | 3283.97i | −0.482547 | − | 0.835795i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5100.00 | 1.28251 | 0.641253 | − | 0.767329i | \(-0.278415\pi\) | ||||
0.641253 | + | 0.767329i | \(0.278415\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2880.00 | −0.715668 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 180.000 | + | 311.769i | 0.0442041 | + | 0.0765637i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1089.00 | − | 1886.20i | 0.264319 | − | 0.457814i | −0.703066 | − | 0.711125i | \(-0.748186\pi\) |
0.967385 | + | 0.253311i | \(0.0815195\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1023.00 | + | 1771.89i | −0.242613 | + | 0.420219i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3072.00 | + | 5320.86i | 0.720257 | + | 1.24752i | 0.960897 | + | 0.276907i | \(0.0893095\pi\) |
−0.240639 | + | 0.970615i | \(0.577357\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2490.00 | 0.577206 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4056.00 | −0.929675 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 411.000 | + | 711.873i | 0.0931566 | + | 0.161352i | 0.908838 | − | 0.417150i | \(-0.136971\pi\) |
−0.815681 | + | 0.578502i | \(0.803638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4240.00 | − | 7343.90i | 0.950412 | − | 1.64616i | 0.205878 | − | 0.978578i | \(-0.433995\pi\) |
0.744534 | − | 0.667584i | \(-0.232672\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 750.000 | − | 1299.04i | 0.164461 | − | 0.284854i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 569.000 | + | 985.537i | 0.123422 | + | 0.213773i | 0.921115 | − | 0.389291i | \(-0.127280\pi\) |
−0.797693 | + | 0.603064i | \(0.793946\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1936.00 | 0.415431 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5706.00 | 1.21136 | 0.605679 | − | 0.795709i | \(-0.292902\pi\) | ||||
0.605679 | + | 0.795709i | \(0.292902\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1514.00 | − | 2622.32i | −0.318014 | − | 0.550816i | 0.662060 | − | 0.749451i | \(-0.269683\pi\) |
−0.980074 | + | 0.198635i | \(0.936349\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 440.000 | − | 762.102i | 0.0914504 | − | 0.158397i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2294.50 | − | 3974.19i | 0.467026 | − | 0.808913i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1532.00 | + | 2653.50i | 0.308617 | + | 0.534540i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3390.00 | −0.675925 | −0.337962 | − | 0.941160i | \(-0.609738\pi\) | ||||
−0.337962 | + | 0.941160i | \(0.609738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1260.00 | −0.248678 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4560.00 | + | 7898.15i | 0.890902 | + | 1.54309i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2064.00 | − | 3574.95i | 0.399211 | − | 0.691454i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2628.00 | − | 4551.83i | 0.498266 | − | 0.863022i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 145.000 | + | 251.147i | 0.0272219 | + | 0.0471497i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4156.00 | 0.772624 | 0.386312 | − | 0.922368i | \(-0.373749\pi\) | ||||
0.386312 | + | 0.922368i | \(0.373749\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1792.00 | −0.329914 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3276.00 | + | 5674.20i | 0.597315 | + | 1.03458i | 0.993216 | + | 0.116286i | \(0.0370990\pi\) |
−0.395901 | + | 0.918293i | \(0.629568\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −683.000 | + | 1182.99i | −0.123340 | + | 0.213631i | −0.921083 | − | 0.389367i | \(-0.872694\pi\) |
0.797743 | + | 0.602998i | \(0.206027\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1299.00 | + | 2249.93i | −0.230155 | + | 0.398640i | −0.957854 | − | 0.287257i | \(-0.907257\pi\) |
0.727699 | + | 0.685897i | \(0.240590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5580.00 | − | 9664.84i | −0.979373 | − | 1.69632i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6192.00 | −1.07665 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 792.000 | 0.136434 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1075.00 | + | 1861.95i | 0.183478 | + | 0.317793i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 556.000 | − | 963.020i | 0.0940271 | − | 0.162860i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1646.00 | − | 2850.96i | 0.273330 | − | 0.473422i | −0.696382 | − | 0.717671i | \(-0.745208\pi\) |
0.969713 | + | 0.244249i | \(0.0785415\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1397.00 | + | 2419.67i | 0.229895 | + | 0.398190i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5180.00 | 0.844817 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6194.00 | 1.00121 | 0.500606 | − | 0.865675i | \(-0.333110\pi\) | ||||
0.500606 | + | 0.865675i | \(0.333110\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1116.00 | − | 1932.97i | −0.178799 | − | 0.309689i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5280.00 | + | 9145.23i | −0.838499 | + | 1.45232i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −480.000 | + | 831.384i | −0.0749053 | + | 0.129740i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5010.00 | + | 8677.57i | 0.775075 | + | 1.34247i | 0.934753 | + | 0.355299i | \(0.115621\pi\) |
−0.159678 | + | 0.987169i | \(0.551046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3130.00 | 0.480072 | 0.240036 | − | 0.970764i | \(-0.422841\pi\) | ||||
0.240036 | + | 0.970764i | \(0.422841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13072.0 | −1.98784 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2097.00 | + | 3632.11i | 0.316181 | + | 0.547642i | 0.979688 | − | 0.200528i | \(-0.0642658\pi\) |
−0.663506 | + | 0.748171i | \(0.730932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 420.000 | − | 727.461i | 0.0627924 | − | 0.108760i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2052.00 | − | 3554.17i | 0.301672 | − | 0.522512i | −0.674842 | − | 0.737962i | \(-0.735788\pi\) |
0.976515 | + | 0.215450i | \(0.0691218\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2461.50 | + | 4263.44i | 0.358872 | + | 0.621584i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9076.00 | −1.31230 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2530.00 | 0.362812 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3748.00 | + | 6491.73i | 0.533090 | + | 0.923339i | 0.999253 | + | 0.0386401i | \(0.0123026\pi\) |
−0.466163 | + | 0.884699i | \(0.654364\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1023.00 | + | 1771.89i | −0.144323 | + | 0.249975i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2921.00 | − | 5059.32i | 0.405479 | − | 0.702310i | −0.588898 | − | 0.808207i | \(-0.700438\pi\) |
0.994377 | + | 0.105897i | \(0.0337714\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −250.000 | − | 433.013i | −0.0344265 | − | 0.0596285i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15996.0 | 2.18524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −412.000 | −0.0558391 | −0.0279195 | − | 0.999610i | \(-0.508888\pi\) | ||||
−0.0279195 | + | 0.999610i | \(0.508888\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 688.000 | + | 1191.65i | 0.0925126 | + | 0.160237i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1284.00 | − | 2223.95i | 0.171304 | − | 0.296707i | −0.767572 | − | 0.640963i | \(-0.778535\pi\) |
0.938876 | + | 0.344256i | \(0.111869\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −550.000 | + | 952.628i | −0.0722431 | + | 0.125129i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6543.00 | − | 11332.8i | −0.852810 | − | 1.47711i | −0.878662 | − | 0.477445i | \(-0.841563\pi\) |
0.0258510 | − | 0.999666i | \(-0.491770\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −864.000 | −0.111750 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3120.00 | 0.400466 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 680.000 | + | 1177.79i | 0.0866190 | + | 0.150029i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5227.00 | − | 9053.43i | 0.660795 | − | 1.14453i | −0.319612 | − | 0.947548i | \(-0.603553\pi\) |
0.980407 | − | 0.196982i | \(-0.0631141\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5415.00 | − | 9379.06i | 0.674345 | − | 1.16800i | −0.302315 | − | 0.953208i | \(-0.597760\pi\) |
0.976660 | − | 0.214791i | \(-0.0689071\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7568.00 | − | 13108.2i | −0.935456 | − | 1.62026i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1555.00 | 0.190787 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15240.0 | −1.85607 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4283.00 | − | 7418.37i | −0.517801 | − | 0.896858i | −0.999786 | − | 0.0206786i | \(-0.993417\pi\) |
0.481985 | − | 0.876180i | \(-0.339916\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1332.00 | − | 2307.09i | 0.159861 | − | 0.276887i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2370.00 | + | 4104.96i | −0.280334 | + | 0.485553i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1768.00 | − | 3062.27i | −0.207624 | − | 0.359616i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13884.0 | −1.61880 | −0.809401 | − | 0.587257i | \(-0.800208\pi\) | ||||
−0.809401 | + | 0.587257i | \(0.800208\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4286.00 | 0.496168 | 0.248084 | − | 0.968738i | \(-0.420199\pi\) | ||||
0.248084 | + | 0.968738i | \(0.420199\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −924.000 | − | 1600.41i | −0.106209 | − | 0.183959i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 225.000 | − | 389.711i | 0.0256802 | − | 0.0444795i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10320.0 | − | 17874.8i | 1.16143 | − | 2.01166i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3168.00 | − | 5487.14i | −0.354054 | − | 0.613239i | 0.632902 | − | 0.774232i | \(-0.281864\pi\) |
−0.986956 | + | 0.160993i | \(0.948530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8974.00 | 0.995988 | 0.497994 | − | 0.867180i | \(-0.334070\pi\) | ||||
0.497994 | + | 0.867180i | \(0.334070\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3720.00 | −0.410024 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1056.00 | + | 1829.05i | 0.115596 | + | 0.200218i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1484.00 | + | 2570.36i | −0.161338 | + | 0.279446i | −0.935349 | − | 0.353727i | \(-0.884914\pi\) |
0.774011 | + | 0.633173i | \(0.218248\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6186.00 | − | 10714.5i | 0.663444 | − | 1.14912i | −0.316261 | − | 0.948672i | \(-0.602427\pi\) |
0.979705 | − | 0.200446i | \(-0.0642393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2535.00 | + | 4390.75i | 0.270046 | + | 0.467734i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 456.000 | 0.0482507 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11394.0 | 1.19759 | 0.598793 | − | 0.800904i | \(-0.295647\pi\) | ||||
0.598793 | + | 0.800904i | \(0.295647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5580.00 | − | 9664.84i | −0.582599 | − | 1.00909i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −80.0000 | + | 138.564i | −0.00829741 | + | 0.0143715i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 179.000 | − | 310.037i | 0.0183222 | − | 0.0317351i | −0.856719 | − | 0.515784i | \(-0.827501\pi\) |
0.875041 | + | 0.484049i | \(0.160834\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1368.00 | + | 2369.45i | 0.139113 | + | 0.240950i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7530.00 | 0.760753 | 0.380376 | − | 0.924832i | \(-0.375794\pi\) | ||||
0.380376 | + | 0.924832i | \(0.375794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13768.0 | −1.38197 | −0.690986 | − | 0.722868i | \(-0.742823\pi\) | ||||
−0.690986 | + | 0.722868i | \(0.742823\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1760.00 | + | 3048.41i | 0.175523 | + | 0.304014i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6690.00 | − | 11587.4i | 0.662904 | − | 1.14818i | −0.316945 | − | 0.948444i | \(-0.602657\pi\) |
0.979849 | − | 0.199740i | \(-0.0640097\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 308.000 | − | 533.472i | 0.0301314 | − | 0.0521891i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3000.00 | − | 5196.15i | −0.291628 | − | 0.505115i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1100.00 | −0.106256 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5478.00 | 0.525829 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3168.00 | − | 5487.14i | −0.302191 | − | 0.523411i | 0.674441 | − | 0.738329i | \(-0.264385\pi\) |
−0.976632 | + | 0.214918i | \(0.931051\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10922.0 | − | 18917.5i | 1.03534 | − | 1.79327i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1915.00 | − | 3316.88i | 0.179290 | − | 0.310539i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2504.00 | + | 4337.06i | 0.232992 | + | 0.403554i | 0.958687 | − | 0.284462i | \(-0.0918151\pi\) |
−0.725695 | + | 0.688016i | \(0.758482\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8720.00 | −0.806405 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12900.0 | 1.18568 | 0.592840 | − | 0.805320i | \(-0.298007\pi\) | ||||
0.592840 | + | 0.805320i | \(0.298007\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1674.00 | − | 2899.45i | −0.152927 | − | 0.264878i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1650.00 | − | 2857.88i | 0.149822 | − | 0.259500i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4058.00 | − | 7028.66i | 0.364050 | − | 0.630553i | −0.624573 | − | 0.780966i | \(-0.714727\pi\) |
0.988623 | + | 0.150413i | \(0.0480603\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7392.00 | − | 12803.3i | −0.659182 | − | 1.14174i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4944.00 | 0.438255 | 0.219127 | − | 0.975696i | \(-0.429679\pi\) | ||||
0.219127 | + | 0.975696i | \(0.429679\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6570.00 | −0.578933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10398.0 | + | 18009.9i | 0.910831 | + | 1.57761i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2733.00 | + | 4733.69i | −0.237992 | + | 0.412215i | −0.960138 | − | 0.279526i | \(-0.909823\pi\) |
0.722146 | + | 0.691741i | \(0.243156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3344.00 | − | 5791.98i | 0.287800 | − | 0.498484i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1120.00 | + | 1939.90i | 0.0958313 | + | 0.165985i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10080.0 | 0.857481 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5208.00 | 0.440474 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5037.00 | + | 8724.34i | 0.423560 | + | 0.733628i | 0.996285 | − | 0.0861198i | \(-0.0274468\pi\) |
−0.572724 | + | 0.819748i | \(0.694113\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6914.00 | + | 11975.4i | −0.578065 | + | 1.00124i | 0.417636 | + | 0.908614i | \(0.362859\pi\) |
−0.995701 | + | 0.0926239i | \(0.970475\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1584.00 | + | 2743.57i | −0.130930 | + | 0.226777i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4931.50 | + | 8541.61i | 0.405318 | + | 0.702031i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2772.00 | −0.226543 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15996.0 | 1.29993 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3870.00 | + | 6703.04i | 0.312738 | + | 0.541678i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8616.00 | + | 14923.3i | −0.692380 | + | 1.19924i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7613.00 | − | 13186.1i | 0.605006 | − | 1.04790i | −0.387044 | − | 0.922061i | \(-0.626504\pi\) |
0.992050 | − | 0.125841i | \(-0.0401628\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3100.00 | − | 5369.36i | −0.244998 | − | 0.424348i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1390.00 | −0.109250 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13228.0 | −1.03398 | −0.516991 | − | 0.855991i | \(-0.672948\pi\) | ||||
−0.516991 | + | 0.855991i | \(0.672948\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 319.000 | + | 552.524i | 0.0247989 | + | 0.0429529i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4092.00 | + | 7087.55i | −0.316379 | + | 0.547985i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2540.00 | + | 4399.41i | −0.194265 | + | 0.336477i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4245.00 | + | 7352.56i | 0.322920 | + | 0.559314i | 0.981089 | − | 0.193556i | \(-0.0620022\pi\) |
−0.658169 | + | 0.752870i | \(0.728669\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8600.00 | 0.650700 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4320.00 | −0.325117 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5142.00 | − | 8906.21i | −0.384919 | − | 0.666699i | 0.606839 | − | 0.794825i | \(-0.292437\pi\) |
−0.991758 | + | 0.128125i | \(0.959104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1395.00 | + | 2416.21i | −0.103873 | + | 0.179913i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −885.000 | + | 1532.86i | −0.0652041 | + | 0.112937i | −0.896785 | − | 0.442468i | \(-0.854103\pi\) |
0.831580 | + | 0.555404i | \(0.187437\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3034.00 | − | 5255.04i | −0.222362 | − | 0.385143i | 0.733162 | − | 0.680054i | \(-0.238043\pi\) |
−0.955525 | + | 0.294911i | \(0.904710\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −192.000 | −0.0139981 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1200.00 | 0.0870321 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10753.0 | + | 18624.7i | 0.775829 | + | 1.34377i | 0.934327 | + | 0.356416i | \(0.116001\pi\) |
−0.158499 | + | 0.987359i | \(0.550665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2116.00 | − | 3665.02i | 0.151879 | − | 0.263062i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14940.0 | + | 25876.8i | −1.06132 | + | 1.83827i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2365.00 | + | 4096.30i | 0.167147 | + | 0.289506i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12108.0 | −0.851364 | −0.425682 | − | 0.904873i | \(-0.639966\pi\) | ||||
−0.425682 | + | 0.904873i | \(0.639966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7744.00 | 0.541742 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7428.00 | − | 12865.7i | −0.517000 | − | 0.895471i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7737.00 | − | 13400.9i | 0.535785 | − | 0.928007i | −0.463340 | − | 0.886181i | \(-0.653349\pi\) |
0.999125 | − | 0.0418262i | \(-0.0133176\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3536.00 | − | 6124.53i | 0.242410 | − | 0.419867i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1260.00 | + | 2182.38i | 0.0859469 | + | 0.148864i | 0.905794 | − | 0.423718i | \(-0.139275\pi\) |
−0.819847 | + | 0.572582i | \(0.805942\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12790.0 | 0.868078 | 0.434039 | − | 0.900894i | \(-0.357088\pi\) | ||||
0.434039 | + | 0.900894i | \(0.357088\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11396.0 | 0.769620 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5672.50 | + | 9825.06i | 0.381190 | + | 0.660240i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5788.00 | − | 10025.1i | 0.387031 | − | 0.670357i | −0.605018 | − | 0.796212i | \(-0.706834\pi\) |
0.992049 | + | 0.125855i | \(0.0401674\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7224.00 | + | 12512.3i | −0.478317 | + | 0.828470i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10063.0 | − | 17429.6i | −0.663035 | − | 1.14841i | −0.979814 | − | 0.199912i | \(-0.935935\pi\) |
0.316778 | − | 0.948500i | \(-0.397399\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3720.00 | −0.243910 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27942.0 | −1.82318 | −0.911590 | − | 0.411100i | \(-0.865145\pi\) | ||||
−0.911590 | + | 0.411100i | \(0.865145\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11270.0 | − | 19520.2i | −0.731792 | − | 1.26750i | −0.956116 | − | 0.292987i | \(-0.905351\pi\) |
0.224324 | − | 0.974515i | \(-0.427983\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3648.00 | + | 6318.52i | −0.235731 | + | 0.408299i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5280.00 | + | 9145.23i | 0.336304 | + | 0.582496i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4572.00 | −0.289821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5128.00 | −0.323522 | −0.161761 | − | 0.986830i | \(-0.551717\pi\) | ||||
−0.161761 | + | 0.986830i | \(0.551717\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8072.00 | − | 13981.1i | −0.506845 | − | 0.877882i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 860.000 | − | 1489.56i | 0.0537450 | − | 0.0930890i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 924.000 | − | 1600.41i | 0.0572032 | − | 0.0990789i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6399.00 | + | 11083.4i | 0.394298 | + | 0.682945i | 0.993011 | − | 0.118019i | \(-0.0376543\pi\) |
−0.598713 | + | 0.800964i | \(0.704321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21148.0 | 1.29704 | 0.648519 | − | 0.761198i | \(-0.275389\pi\) | ||||
0.648519 | + | 0.761198i | \(0.275389\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2000.00 | −0.122093 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8232.00 | + | 14258.2i | 0.500206 | + | 0.866382i | 1.00000 | 0.000237943i | \(7.57396e-5\pi\) | |
−0.499794 | + | 0.866144i | \(0.666591\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7560.00 | − | 13094.3i | 0.457251 | − | 0.791982i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12117.0 | − | 20987.3i | 0.726148 | − | 1.25773i | −0.232351 | − | 0.972632i | \(-0.574642\pi\) |
0.958500 | − | 0.285094i | \(-0.0920248\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1950.00 | − | 3377.50i | −0.116325 | − | 0.201481i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5566.00 | 0.330518 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22836.0 | −1.34987 | −0.674935 | − | 0.737877i | \(-0.735828\pi\) | ||||
−0.674935 | + | 0.737877i | \(0.735828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13159.0 | + | 22792.1i | 0.774320 | + | 1.34116i | 0.935176 | + | 0.354184i | \(0.115241\pi\) |
−0.160855 | + | 0.986978i | \(0.551425\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3096.00 | − | 5362.43i | 0.181355 | − | 0.314117i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4464.00 | − | 7731.87i | 0.259141 | − | 0.448845i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1360.00 | − | 2355.59i | −0.0785959 | − | 0.136132i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3480.00 | −0.200214 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28802.0 | 1.64968 | 0.824841 | − | 0.565365i | \(-0.191265\pi\) | ||||
0.824841 | + | 0.565365i | \(0.191265\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1900.00 | − | 3290.90i | −0.108342 | − | 0.187654i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1263.00 | − | 2187.58i | 0.0717002 | − | 0.124188i | −0.827946 | − | 0.560807i | \(-0.810491\pi\) |
0.899647 | + | 0.436619i | \(0.143824\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4776.00 | + | 8272.27i | −0.268747 | + | 0.465483i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11538.0 | + | 19984.4i | 0.646397 | + | 1.11959i | 0.983977 | + | 0.178296i | \(0.0570584\pi\) |
−0.337580 | + | 0.941297i | \(0.609608\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3330.00 | −0.185741 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15496.0 | −0.860567 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21414.0 | − | 37090.1i | −1.18405 | − | 2.05083i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3934.00 | − | 6813.89i | 0.216579 | − | 0.375127i | −0.737181 | − | 0.675696i | \(-0.763843\pi\) |
0.953760 | + | 0.300569i | \(0.0971766\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2210.00 | + | 3827.83i | −0.120619 | + | 0.208918i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1674.00 | − | 2899.45i | −0.0909717 | − | 0.157568i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12648.0 | −0.684394 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21510.0 | 1.15895 | 0.579473 | − | 0.814991i | \(-0.303258\pi\) | ||||
0.579473 | + | 0.814991i | \(0.303258\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5588.00 | + | 9678.70i | 0.299794 | + | 0.519259i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1680.00 | − | 2909.85i | 0.0897482 | − | 0.155448i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15007.0 | + | 25992.9i | −0.794922 | + | 1.37685i | 0.127967 | + | 0.991778i | \(0.459155\pi\) |
−0.922889 | + | 0.385067i | \(0.874178\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1496.00 | + | 2591.15i | 0.0789091 | + | 0.136675i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8448.00 | −0.443731 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25800.0 | −1.34946 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10848.0 | + | 18789.3i | 0.565029 | + | 0.978659i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −408.000 | + | 706.677i | −0.0211625 | + | 0.0366545i | −0.876413 | − | 0.481561i | \(-0.840070\pi\) |
0.855250 | + | 0.518215i | \(0.173403\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7772.00 | − | 13461.5i | 0.399784 | − | 0.692446i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2325.00 | + | 4027.02i | 0.119101 | + | 0.206289i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9952.00 | 0.507702 | 0.253851 | − | 0.967243i | \(-0.418303\pi\) | ||||
0.253851 | + | 0.967243i | \(0.418303\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −900.000 | − | 1558.85i | −0.0455372 | − | 0.0788728i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16973.0 | + | 29398.1i | −0.855269 | + | 1.48137i | 0.0211266 | + | 0.999777i | \(0.493275\pi\) |
−0.876395 | + | 0.481592i | \(0.840059\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31080.0 | + | 53832.1i | −1.55339 | + | 2.69055i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11710.0 | − | 20282.3i | −0.582895 | − | 1.00960i | −0.995134 | − | 0.0985280i | \(-0.968587\pi\) |
0.412239 | − | 0.911076i | \(-0.364747\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15136.0 | −0.750384 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14592.0 | −0.720496 | −0.360248 | − | 0.932857i | \(-0.617308\pi\) | ||||
−0.360248 | + | 0.932857i | \(0.617308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −285.000 | − | 493.634i | −0.0140156 | − | 0.0242757i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5214.00 | + | 9030.91i | −0.255382 | + | 0.442334i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4528.00 | + | 7842.73i | −0.220012 | + | 0.381072i | −0.954811 | − | 0.297213i | \(-0.903943\pi\) |
0.734799 | + | 0.678285i | \(0.237276\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10200.0 | + | 17666.9i | 0.493637 | + | 0.855004i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 200.000 | 0.00964072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17554.0 | −0.842815 | −0.421408 | − | 0.906871i | \(-0.638464\pi\) | ||||
−0.421408 | + | 0.906871i | \(0.638464\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5760.00 | − | 9976.61i | −0.275461 | − | 0.477112i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18219.0 | + | 31556.2i | −0.867856 | + | 1.50317i | −0.00367239 | + | 0.999993i | \(0.501169\pi\) |
−0.864183 | + | 0.503177i | \(0.832164\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 495.000 | − | 857.365i | 0.0233945 | − | 0.0405204i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10836.0 | + | 18768.5i | 0.510124 | + | 0.883561i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9022.00 | 0.423071 | 0.211536 | − | 0.977370i | \(-0.432154\pi\) | ||||
0.211536 | + | 0.977370i | \(0.432154\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8712.00 | 0.406946 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 735.000 | + | 1273.06i | 0.0341994 | + | 0.0592350i | 0.882618 | − | 0.470090i | \(-0.155779\pi\) |
−0.848419 | + | 0.529325i | \(0.822445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2200.00 | − | 3810.51i | 0.101969 | − | 0.176616i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4092.00 | + | 7087.55i | −0.188204 | + | 0.325979i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5040.00 | + | 8729.54i | 0.230916 | + | 0.399958i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28272.0 | −1.29037 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −770.000 | −0.0350095 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2626.00 | + | 4548.37i | 0.118941 | + | 0.206012i | 0.919348 | − | 0.393444i | \(-0.128717\pi\) |
−0.800407 | + | 0.599457i | \(0.795383\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12288.0 | + | 21283.4i | −0.554454 | + | 0.960343i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2494.00 | − | 4319.73i | 0.111683 | − | 0.193440i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4980.00 | + | 8625.61i | 0.222167 | + | 0.384804i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12294.0 | −0.546394 | −0.273197 | − | 0.961958i | \(-0.588081\pi\) | ||||
−0.273197 | + | 0.961958i | \(0.588081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3024.00 | 0.133894 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5577.00 | + | 9659.65i | 0.246009 | + | 0.426101i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15180.0 | + | 26292.5i | −0.667112 | + | 1.15547i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1644.00 | + | 2847.49i | −0.0717119 | + | 0.124209i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7773.00 | − | 13463.2i | −0.337805 | − | 0.585095i | 0.646215 | − | 0.763156i | \(-0.276351\pi\) |
−0.984020 | + | 0.178061i | \(0.943018\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19364.0 | −0.838424 | −0.419212 | − | 0.907888i | \(-0.637694\pi\) | ||||
−0.419212 | + | 0.907888i | \(0.637694\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33920.0 | 1.46326 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5450.00 | + | 9439.68i | 0.234239 | + | 0.405715i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2200.00 | + | 3810.51i | −0.0942084 | + | 0.163174i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3657.00 | − | 6334.11i | 0.155457 | − | 0.269259i | −0.777768 | − | 0.628551i | \(-0.783648\pi\) |
0.933225 | + | 0.359292i | \(0.116982\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5992.00 | − | 10378.4i | −0.253789 | − | 0.439575i | 0.710777 | − | 0.703417i | \(-0.248343\pi\) |
−0.964566 | + | 0.263843i | \(0.915010\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6000.00 | 0.253204 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13500.0 | 0.567643 | 0.283822 | − | 0.958877i | \(-0.408398\pi\) | ||||
0.283822 | + | 0.958877i | \(0.408398\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22301.0 | − | 38626.5i | −0.934313 | − | 1.61828i | −0.775854 | − | 0.630913i | \(-0.782681\pi\) |
−0.158459 | − | 0.987365i | \(-0.550653\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2276.00 | + | 3942.15i | −0.0950103 | + | 0.164563i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9240.00 | + | 16004.1i | −0.382950 | + | 0.663289i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13376.0 | + | 23167.9i | 0.552380 | + | 0.956751i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35448.0 | −1.45864 | −0.729321 | − | 0.684172i | \(-0.760164\pi\) | ||||
−0.729321 | + | 0.684172i | \(0.760164\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10207.0 | 0.418508 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11412.0 | + | 19766.2i | 0.466252 | + | 0.807572i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12997.5 | − | 22512.3i | 0.529145 | − | 0.916506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6056.00 | − | 10489.3i | 0.244807 | − | 0.424019i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6096.00 | − | 10558.6i | −0.245556 | − | 0.425316i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12590.0 | −0.505362 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2420.00 | −0.0967980 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12453.0 | + | 21569.2i | 0.496367 | + | 0.859733i | 0.999991 | − | 0.00419015i | \(-0.00133377\pi\) |
−0.503624 | + | 0.863923i | \(0.668000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11602.0 | − | 20095.3i | 0.460833 | − | 0.798185i | −0.538170 | − | 0.842836i | \(-0.680884\pi\) |
0.999003 | + | 0.0446509i | \(0.0142175\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9924.00 | + | 17188.9i | −0.391445 | + | 0.678002i | −0.992640 | − | 0.121100i | \(-0.961358\pi\) |
0.601196 | + | 0.799102i | \(0.294691\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3255.00 | − | 5637.83i | −0.127946 | − | 0.221609i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18356.0 | 0.719034 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16320.0 | −0.637075 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44548.0 | − | 77159.4i | −1.73301 | − | 3.00166i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4213.00 | − | 7297.13i | 0.163332 | − | 0.282899i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13771.0 | + | 23852.1i | −0.530232 | + | 0.918389i | 0.469146 | + | 0.883121i | \(0.344562\pi\) |
−0.999378 | + | 0.0352683i | \(0.988771\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6780.00 | − | 11743.3i | −0.260164 | − | 0.450616i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20718.0 | 0.792290 | 0.396145 | − | 0.918188i | \(-0.370348\pi\) | ||||
0.396145 | + | 0.918188i | \(0.370348\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25172.0 | 0.959349 | 0.479675 | − | 0.877446i | \(-0.340755\pi\) | ||||
0.479675 | + | 0.877446i | \(0.340755\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2520.00 | − | 4364.77i | −0.0957162 | − | 0.165785i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6432.00 | + | 11140.6i | −0.243478 | + | 0.421717i | −0.961703 | − | 0.274095i | \(-0.911622\pi\) |
0.718224 | + | 0.695812i | \(0.244955\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9330.00 | + | 16160.0i | −0.350804 | + | 0.607611i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3696.00 | − | 6401.66i | −0.138502 | − | 0.239892i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21540.0 | 0.804472 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16512.0 | 0.614626 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16368.0 | − | 28350.2i | −0.607234 | − | 1.05176i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4482.00 | + | 7763.05i | −0.165724 | + | 0.287042i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3875.00 | + | 6711.70i | −0.142331 | + | 0.246524i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11546.0 | + | 19998.3i | 0.422689 | + | 0.732118i | 0.996201 | − | 0.0870783i | \(-0.0277530\pi\) |
−0.573513 | + | 0.819197i | \(0.694420\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14454.0 | −0.527403 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14208.0 | −0.516720 | −0.258360 | − | 0.966049i | \(-0.583182\pi\) | ||||
−0.258360 | + | 0.966049i | \(0.583182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28440.0 | − | 49259.5i | −1.03092 | − | 1.78560i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −580.000 | + | 1004.59i | −0.0209554 | + | 0.0362959i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13292.0 | − | 23022.4i | 0.477108 | − | 0.826376i | −0.522547 | − | 0.852610i | \(-0.675018\pi\) |
0.999656 | + | 0.0262342i | \(0.00835157\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8312.00 | + | 14396.8i | 0.297383 | + | 0.515082i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14448.0 | −0.515235 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6350.00 | 0.225715 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2464.00 | + | 4267.77i | 0.0873014 | + | 0.151210i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 81.0000 | − | 140.296i | 0.00286063 | − | 0.00495475i | −0.864592 | − | 0.502475i | \(-0.832423\pi\) |
0.867452 | + | 0.497521i | \(0.165756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13104.0 | + | 22696.8i | −0.459813 | + | 0.796420i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2700.00 | + | 4676.54i | 0.0944379 | + | 0.163571i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29734.0 | 1.03668 | 0.518339 | − | 0.855175i | \(-0.326551\pi\) | ||||
0.518339 | + | 0.855175i | \(0.326551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5464.00 | −0.189894 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8571.00 | + | 14845.4i | 0.296925 | + | 0.514290i | 0.975431 | − | 0.220306i | \(-0.0707055\pi\) |
−0.678506 | + | 0.734595i | \(0.737372\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4464.00 | − | 7731.87i | 0.154155 | − | 0.267004i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13218.0 | + | 22894.2i | −0.453566 | + | 0.785600i | −0.998605 | − | 0.0528113i | \(-0.983182\pi\) |
0.545038 | + | 0.838411i | \(0.316515\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21758.0 | − | 37686.0i | −0.744251 | − | 1.28908i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10392.0 | −0.354347 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27882.0 | 0.947730 | 0.473865 | − | 0.880598i | \(-0.342858\pi\) | ||||
0.473865 | + | 0.880598i | \(0.342858\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 120.000 | + | 207.846i | 0.00406608 | + | 0.00704266i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22320.0 | − | 38659.4i | 0.753922 | − | 1.30583i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −592.500 | + | 1026.24i | −0.0198886 | + | 0.0344480i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8514.00 | + | 14746.7i | 0.284901 | + | 0.493463i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5290.00 | −0.176467 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12656.0 | 0.420879 | 0.210439 | − | 0.977607i | \(-0.432511\pi\) | ||||
0.210439 | + | 0.977607i | \(0.432511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1584.00 | + | 2743.57i | 0.0525133 | + | 0.0909557i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1458.00 | − | 2525.33i | 0.0481869 | − | 0.0834621i | −0.840926 | − | 0.541150i | \(-0.817989\pi\) |
0.889113 | + | 0.457688i | \(0.151322\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4300.00 | + | 7447.82i | −0.141241 | + | 0.244637i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3447.00 | + | 5970.38i | 0.112875 | + | 0.195506i | 0.916928 | − | 0.399052i | \(-0.130661\pi\) |
−0.804053 | + | 0.594558i | \(0.797327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −60840.0 | −1.98616 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3058.00 | −0.0995254 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22632.0 | − | 39199.8i | −0.734332 | − | 1.27190i | −0.955016 | − | 0.296555i | \(-0.904162\pi\) |
0.220683 | − | 0.975346i | \(-0.429171\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9285.00 | + | 16082.1i | −0.300350 | + | 0.520221i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2400.00 | − | 4156.92i | 0.0771644 | − | 0.133653i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26008.0 | − | 45047.2i | −0.833674 | − | 1.44397i | −0.895105 | − | 0.445855i | \(-0.852900\pi\) |
0.0614307 | − | 0.998111i | \(-0.480434\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13168.0 | 0.420820 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8840.00 | −0.281655 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6929.00 | − | 12001.4i | −0.220104 | − | 0.381231i | 0.734735 | − | 0.678354i | \(-0.237306\pi\) |
−0.954839 | + | 0.297123i | \(0.903973\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19304.0 | + | 33435.5i | −0.611363 | + | 1.05891i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))