Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [928,4,Mod(1,928)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(928, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("928.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 928 = 2^{5} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 928.a (trivial) |
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: | yes |
Analytic conductor: | \(54.7537724853\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 138x^{7} + 394x^{6} + 5872x^{5} - 10822x^{4} - 85158x^{3} + 30654x^{2} + 439999x + 396802 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.39022\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 928.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −3.39022 | −0.652448 | −0.326224 | − | 0.945292i | \(-0.605776\pi\) | ||||
−0.326224 | + | 0.945292i | \(0.605776\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −19.3767 | −1.73310 | −0.866550 | − | 0.499090i | \(-0.833668\pi\) | ||||
−0.866550 | + | 0.499090i | \(0.833668\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.92881 | 0.428115 | 0.214058 | − | 0.976821i | \(-0.431332\pi\) | ||||
0.214058 | + | 0.976821i | \(0.431332\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −15.5064 | −0.574311 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.4230 | 0.422745 | 0.211373 | − | 0.977406i | \(-0.432207\pi\) | ||||
0.211373 | + | 0.977406i | \(0.432207\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.5894 | 0.972633 | 0.486317 | − | 0.873783i | \(-0.338340\pi\) | ||||
0.486317 | + | 0.873783i | \(0.338340\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 65.6911 | 1.13076 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −60.6323 | −0.865028 | −0.432514 | − | 0.901627i | \(-0.642373\pi\) | ||||
−0.432514 | + | 0.901627i | \(0.642373\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 79.4211 | 0.958971 | 0.479485 | − | 0.877550i | \(-0.340823\pi\) | ||||
0.479485 | + | 0.877550i | \(0.340823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −26.8804 | −0.279323 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −94.7913 | −0.859363 | −0.429681 | − | 0.902981i | \(-0.641374\pi\) | ||||
−0.429681 | + | 0.902981i | \(0.641374\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 250.455 | 2.00364 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 144.106 | 1.02716 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 217.126 | 1.25797 | 0.628985 | − | 0.777417i | \(-0.283471\pi\) | ||||
0.628985 | + | 0.777417i | \(0.283471\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −52.2873 | −0.275820 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −153.634 | −0.741967 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 183.461 | 0.815157 | 0.407578 | − | 0.913170i | \(-0.366373\pi\) | ||||
0.407578 | + | 0.913170i | \(0.366373\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −154.558 | −0.634593 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −13.4451 | −0.0512141 | −0.0256070 | − | 0.999672i | \(-0.508152\pi\) | ||||
−0.0256070 | + | 0.999672i | \(0.508152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 322.822 | 1.14488 | 0.572440 | − | 0.819947i | \(-0.305997\pi\) | ||||
0.572440 | + | 0.819947i | \(0.305997\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 300.462 | 0.995339 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −245.009 | −0.760387 | −0.380194 | − | 0.924907i | \(-0.624143\pi\) | ||||
−0.380194 | + | 0.924907i | \(0.624143\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −280.134 | −0.816717 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 205.557 | 0.564386 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 321.562 | 0.833396 | 0.416698 | − | 0.909045i | \(-0.363187\pi\) | ||||
0.416698 | + | 0.909045i | \(0.363187\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −298.846 | −0.732660 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −269.255 | −0.625679 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −511.205 | −1.12802 | −0.564010 | − | 0.825768i | \(-0.690742\pi\) | ||||
−0.564010 | + | 0.825768i | \(0.690742\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 664.306 | 1.39435 | 0.697177 | − | 0.716899i | \(-0.254439\pi\) | ||||
0.697177 | + | 0.716899i | \(0.254439\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −122.947 | −0.245871 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −883.370 | −1.68567 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −477.855 | −0.871333 | −0.435667 | − | 0.900108i | \(-0.643487\pi\) | ||||
−0.435667 | + | 0.900108i | \(0.643487\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 321.363 | 0.560690 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −988.394 | −1.65212 | −0.826062 | − | 0.563580i | \(-0.809424\pi\) | ||||
−0.826062 | + | 0.563580i | \(0.809424\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −154.347 | −0.247466 | −0.123733 | − | 0.992316i | \(-0.539487\pi\) | ||||
−0.123733 | + | 0.992316i | \(0.539487\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −849.097 | −1.30727 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 122.286 | 0.180984 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −223.873 | −0.318831 | −0.159415 | − | 0.987212i | \(-0.550961\pi\) | ||||
−0.159415 | + | 0.987212i | \(0.550961\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −69.8789 | −0.0958559 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1174.40 | −1.55310 | −0.776552 | − | 0.630053i | \(-0.783033\pi\) | ||||
−0.776552 | + | 0.630053i | \(0.783033\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1174.85 | 1.49918 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 98.3164 | 0.121157 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 709.918 | 0.845519 | 0.422759 | − | 0.906242i | \(-0.361062\pi\) | ||||
0.422759 | + | 0.906242i | \(0.361062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 361.470 | 0.416399 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −736.107 | −0.820761 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1538.91 | −1.66199 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −802.826 | −0.840357 | −0.420178 | − | 0.907441i | \(-0.638033\pi\) | ||||
−0.420178 | + | 0.907441i | \(0.638033\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −239.155 | −0.242787 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 696.175 | 0.685861 | 0.342931 | − | 0.939361i | \(-0.388580\pi\) | ||||
0.342931 | + | 0.939361i | \(0.388580\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 225.517 | 0.215736 | 0.107868 | − | 0.994165i | \(-0.465598\pi\) | ||||
0.107868 | + | 0.994165i | \(0.465598\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 520.852 | 0.484095 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 754.805 | 0.681960 | 0.340980 | − | 0.940071i | \(-0.389241\pi\) | ||||
0.340980 | + | 0.940071i | \(0.389241\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1877.63 | −1.64995 | −0.824974 | − | 0.565170i | \(-0.808810\pi\) | ||||
−0.824974 | + | 0.565170i | \(0.808810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −621.973 | −0.531848 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 478.920 | 0.398699 | 0.199349 | − | 0.979928i | \(-0.436117\pi\) | ||||
0.199349 | + | 0.979928i | \(0.436117\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1836.74 | 1.48936 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −706.928 | −0.558594 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −480.741 | −0.370332 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1093.13 | −0.821286 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 45.5820 | 0.0334146 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2430.89 | −1.73940 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1178.05 | −0.823112 | −0.411556 | − | 0.911384i | \(-0.635015\pi\) | ||||
−0.411556 | + | 0.911384i | \(0.635015\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1094.44 | −0.746975 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1363.44 | −0.909347 | −0.454673 | − | 0.890658i | \(-0.650244\pi\) | ||||
−0.454673 | + | 0.890658i | \(0.650244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 629.714 | 0.410550 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2792.29 | −1.78017 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −709.000 | −0.442145 | −0.221073 | − | 0.975257i | \(-0.570956\pi\) | ||||
−0.221073 | + | 0.975257i | \(0.570956\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2088.68 | −1.27453 | −0.637264 | − | 0.770645i | \(-0.719934\pi\) | ||||
−0.637264 | + | 0.770645i | \(0.719934\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 830.634 | 0.496113 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 703.124 | 0.411176 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 561.923 | 0.321829 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 949.716 | 0.532866 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3552.78 | 1.95339 | 0.976696 | − | 0.214627i | \(-0.0688535\pi\) | ||||
0.976696 | + | 0.214627i | \(0.0688535\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1263.48 | 0.680931 | 0.340465 | − | 0.940257i | \(-0.389415\pi\) | ||||
0.340465 | + | 0.940257i | \(0.389415\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 940.188 | 0.496795 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4207.18 | −2.18019 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2205.44 | −1.12110 | −0.560551 | − | 0.828120i | \(-0.689411\pi\) | ||||
−0.560551 | + | 0.828120i | \(0.689411\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1090.17 | −0.543748 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −751.582 | −0.367906 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −322.051 | −0.154754 | −0.0773771 | − | 0.997002i | \(-0.524655\pi\) | ||||
−0.0773771 | + | 0.997002i | \(0.524655\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1013.15 | 0.478023 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4074.72 | 1.88809 | 0.944046 | − | 0.329815i | \(-0.106986\pi\) | ||||
0.944046 | + | 0.329815i | \(0.106986\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −118.605 | −0.0539848 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1231.53 | −0.550747 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −171.789 | −0.0754964 | −0.0377482 | − | 0.999287i | \(-0.512018\pi\) | ||||
−0.0377482 | + | 0.999287i | \(0.512018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1985.81 | 0.857788 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1733.10 | 0.735975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2612.73 | 1.09098 | 0.545489 | − | 0.838118i | \(-0.316344\pi\) | ||||
0.545489 | + | 0.838118i | \(0.316344\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1084.07 | −0.445184 | −0.222592 | − | 0.974912i | \(-0.571452\pi\) | ||||
−0.222592 | + | 0.974912i | \(0.571452\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2252.14 | −0.909745 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3554.86 | −1.41275 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −935.129 | −0.365687 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1142.59 | 0.439742 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2499.34 | 0.946839 | 0.473419 | − | 0.880837i | \(-0.343020\pi\) | ||||
0.473419 | + | 0.880837i | \(0.343020\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1189.90 | −0.443785 | −0.221893 | − | 0.975071i | \(-0.571223\pi\) | ||||
−0.221893 | + | 0.975071i | \(0.571223\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2994.82 | 1.09981 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3048.06 | −1.10236 | −0.551181 | − | 0.834386i | \(-0.685823\pi\) | ||||
−0.551181 | + | 0.834386i | \(0.685823\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1282.94 | −0.457009 | −0.228505 | − | 0.973543i | \(-0.573384\pi\) | ||||
−0.228505 | + | 0.973543i | \(0.573384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1620.04 | 0.568500 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −229.935 | −0.0794990 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 260.522 | 0.0887592 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1469.87 | 0.493542 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1224.91 | 0.405401 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 744.561 | 0.242927 | 0.121464 | − | 0.992596i | \(-0.461241\pi\) | ||||
0.121464 | + | 0.992596i | \(0.461241\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3350.87 | 1.07793 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6255.20 | −1.98419 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1721.55 | 0.538556 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 523.272 | 0.161459 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2764.19 | −0.841355 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 770.021 | 0.231231 | 0.115615 | − | 0.993294i | \(-0.463116\pi\) | ||||
0.115615 | + | 0.993294i | \(0.463116\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3883.65 | −1.15071 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5567.58 | −1.62790 | −0.813950 | − | 0.580935i | \(-0.802687\pi\) | ||||
−0.813950 | + | 0.580935i | \(0.802687\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4524.04 | 1.30549 | 0.652744 | − | 0.757578i | \(-0.273618\pi\) | ||||
0.652744 | + | 0.757578i | \(0.273618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −414.576 | −0.118083 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1448.90 | 0.407383 | 0.203692 | − | 0.979035i | \(-0.434706\pi\) | ||||
0.203692 | + | 0.979035i | \(0.434706\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4747.45 | 1.31783 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 758.978 | 0.208021 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3964.90 | −1.07309 | −0.536544 | − | 0.843873i | \(-0.680270\pi\) | ||||
−0.536544 | + | 0.843873i | \(0.680270\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2278.49 | 0.609006 | 0.304503 | − | 0.952511i | \(-0.401510\pi\) | ||||
0.304503 | + | 0.952511i | \(0.401510\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3653.96 | −0.964616 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5428.06 | 1.41545 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3620.76 | 0.932727 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3981.49 | 1.01332 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4850.92 | −1.21987 | −0.609935 | − | 0.792451i | \(-0.708805\pi\) | ||||
−0.609935 | + | 0.792451i | \(0.708805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1461.96 | −0.363292 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3983.00 | −0.978138 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7106.13 | −1.72478 | −0.862390 | − | 0.506244i | \(-0.831033\pi\) | ||||
−0.862390 | + | 0.506244i | \(0.831033\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1454.63 | 0.348981 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 449.686 | 0.106647 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2543.06 | −0.596242 | −0.298121 | − | 0.954528i | \(-0.596360\pi\) | ||||
−0.298121 | + | 0.954528i | \(0.596360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6230.80 | −1.44436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2406.78 | −0.551657 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7413.71 | 1.68038 | 0.840190 | − | 0.542293i | \(-0.182444\pi\) | ||||
0.840190 | + | 0.542293i | \(0.182444\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −618.554 | −0.138651 | −0.0693256 | − | 0.997594i | \(-0.522085\pi\) | ||||
−0.0693256 | + | 0.997594i | \(0.522085\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1225.46 | −0.271679 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3862.75 | 0.847029 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3471.99 | −0.753110 | −0.376555 | − | 0.926394i | \(-0.622891\pi\) | ||||
−0.376555 | + | 0.926394i | \(0.622891\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3366.85 | −0.722466 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4494.51 | −0.954163 | −0.477082 | − | 0.878859i | \(-0.658305\pi\) | ||||
−0.477082 | + | 0.878859i | \(0.658305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2869.00 | −0.602631 | −0.301316 | − | 0.953524i | \(-0.597426\pi\) | ||||
−0.301316 | + | 0.953524i | \(0.597426\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5217.26 | 1.08436 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −106.604 | −0.0219255 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1236.73 | −0.251726 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2721.76 | 0.548290 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5463.18 | 1.08929 | 0.544646 | − | 0.838666i | \(-0.316664\pi\) | ||||
0.544646 | + | 0.838666i | \(0.316664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9905.43 | 1.95497 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2222.54 | 0.434226 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4321.48 | −0.835845 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2559.59 | 0.490141 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2360.19 | −0.447489 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12872.0 | −2.41656 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6160.56 | −1.14528 | −0.572641 | − | 0.819806i | \(-0.694081\pi\) | ||||
−0.572641 | + | 0.819806i | \(0.694081\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −764.552 | −0.140757 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1676.59 | −0.305693 | −0.152846 | − | 0.988250i | \(-0.548844\pi\) | ||||
−0.152846 | + | 0.988250i | \(0.548844\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2401.33 | 0.433647 | 0.216823 | − | 0.976211i | \(-0.430430\pi\) | ||||
0.216823 | + | 0.976211i | \(0.430430\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2382.31 | 0.426120 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5693.87 | 1.00883 | 0.504415 | − | 0.863461i | \(-0.331708\pi\) | ||||
0.504415 | + | 0.863461i | \(0.331708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −447.266 | −0.0785019 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2558.95 | −0.444944 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4815.48 | −0.829537 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11418.1 | 1.94880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6365.58 | 1.07651 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1942.63 | −0.325533 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3478.46 | 0.577624 | 0.288812 | − | 0.957386i | \(-0.406740\pi\) | ||||
0.288812 | + | 0.957386i | \(0.406740\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2844.82 | −0.468153 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9259.24 | 1.51011 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7228.24 | 1.16839 | 0.584195 | − | 0.811614i | \(-0.301410\pi\) | ||||
0.584195 | + | 0.811614i | \(0.301410\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1623.64 | −0.260130 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3348.74 | 0.531801 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4940.71 | −0.777765 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6226.95 | −0.971732 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7713.95 | 1.19339 | 0.596695 | − | 0.802468i | \(-0.296480\pi\) | ||||
0.596695 | + | 0.802468i | \(0.296480\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9763.60 | −1.49752 | −0.748758 | − | 0.662843i | \(-0.769350\pi\) | ||||
−0.748758 | + | 0.662843i | \(0.769350\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6569.71 | 0.999047 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4230.58 | −0.637878 | −0.318939 | − | 0.947775i | \(-0.603326\pi\) | ||||
−0.318939 | + | 0.947775i | \(0.603326\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19151.8 | 2.86330 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1629.82 | 0.241622 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5847.37 | 0.859645 | 0.429823 | − | 0.902913i | \(-0.358576\pi\) | ||||
0.429823 | + | 0.902913i | \(0.358576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −551.292 | −0.0803750 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3705.96 | 0.535847 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2990.74 | 0.428883 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9915.51 | 1.41031 | 0.705157 | − | 0.709051i | \(-0.250876\pi\) | ||||
0.705157 | + | 0.709051i | \(0.250876\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 208.486 | 0.0294128 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2549.61 | 0.356790 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2758.32 | −0.382897 | −0.191448 | − | 0.981503i | \(-0.561318\pi\) | ||||
−0.191448 | + | 0.981503i | \(0.561318\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8241.26 | 1.13487 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1322.09 | −0.180613 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5044.05 | −0.683630 | −0.341815 | − | 0.939767i | \(-0.611042\pi\) | ||||
−0.341815 | + | 0.939767i | \(0.611042\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3993.86 | 0.537038 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3039.31 | 0.405487 | 0.202744 | − | 0.979232i | \(-0.435014\pi\) | ||||
0.202744 | + | 0.979232i | \(0.435014\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2369.49 | −0.313663 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5005.80 | −0.657517 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5131.66 | 0.668857 | 0.334428 | − | 0.942421i | \(-0.391457\pi\) | ||||
0.334428 | + | 0.942421i | \(0.391457\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5747.41 | 0.743373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4622.37 | 0.593302 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4337.90 | 0.552566 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3554.10 | 0.449308 | 0.224654 | − | 0.974439i | \(-0.427875\pi\) | ||||
0.224654 | + | 0.974439i | \(0.427875\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2134.87 | −0.267863 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4176.12 | −0.520063 | −0.260032 | − | 0.965600i | \(-0.583733\pi\) | ||||
−0.260032 | + | 0.965600i | \(0.583733\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9898.67 | 1.22354 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1354.02 | 0.166128 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2829.51 | 0.344604 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8769.07 | −1.06015 | −0.530077 | − | 0.847950i | \(-0.677837\pi\) | ||||
−0.530077 | + | 0.847950i | \(0.677837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2403.67 | 0.288477 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4053.24 | −0.482923 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22756.0 | 2.69168 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7081.09 | 0.831564 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12483.9 | −1.45556 | −0.727781 | − | 0.685810i | \(-0.759448\pi\) | ||||
−0.727781 | + | 0.685810i | \(0.759448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5644.50 | 0.653435 | 0.326717 | − | 0.945122i | \(-0.394058\pi\) | ||||
0.326717 | + | 0.945122i | \(0.394058\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3799.20 | 0.436699 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15185.6 | −1.73320 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5267.15 | 0.596945 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2383.75 | −0.268271 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3285.43 | −0.367178 | −0.183589 | − | 0.983003i | \(-0.558771\pi\) | ||||
−0.183589 | + | 0.983003i | \(0.558771\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2948.21 | −0.327210 | −0.163605 | − | 0.986526i | \(-0.552312\pi\) | ||||
−0.163605 | + | 0.986526i | \(0.552312\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1905.04 | −0.209977 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7528.42 | −0.824104 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17019.6 | −1.85034 | −0.925170 | − | 0.379553i | \(-0.876078\pi\) | ||||
−0.925170 | + | 0.379553i | \(0.876078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4343.87 | 0.469050 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13817.4 | 1.48191 | 0.740954 | − | 0.671556i | \(-0.234374\pi\) | ||||
0.740954 | + | 0.671556i | \(0.234374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13755.8 | −1.46537 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12044.7 | −1.27449 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5738.26 | −0.603129 | −0.301565 | − | 0.953446i | \(-0.597509\pi\) | ||||
−0.301565 | + | 0.953446i | \(0.597509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −207.364 | −0.0216505 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4283.48 | −0.444272 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7004.07 | −0.721662 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8452.49 | 0.865188 | 0.432594 | − | 0.901589i | \(-0.357598\pi\) | ||||
0.432594 | + | 0.901589i | \(0.357598\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8737.48 | −0.888520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7824.62 | 0.790518 | 0.395259 | − | 0.918570i | \(-0.370655\pi\) | ||||
0.395259 | + | 0.918570i | \(0.370655\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 370.241 | 0.0371632 | 0.0185816 | − | 0.999827i | \(-0.494085\pi\) | ||||
0.0185816 | + | 0.999827i | \(0.494085\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14263.3 | 1.42246 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17808.8 | 1.76466 | 0.882329 | − | 0.470634i | \(-0.155975\pi\) | ||||
0.882329 | + | 0.470634i | \(0.155975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3788.82 | −0.373031 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7476.92 | 0.731462 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4978.87 | 0.483993 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19891.4 | 1.92143 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4986.28 | −0.478629 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9586.99 | 0.914490 | 0.457245 | − | 0.889341i | \(-0.348836\pi\) | ||||
0.457245 | + | 0.889341i | \(0.348836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8363.88 | 0.792848 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2548.03 | 0.240040 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15556.1 | 1.45642 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17317.1 | −1.61132 | −0.805661 | − | 0.592377i | \(-0.798190\pi\) | ||||
−0.805661 | + | 0.592377i | \(0.798190\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1091.82 | 0.100969 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16160.0 | −1.48532 | −0.742658 | − | 0.669671i | \(-0.766435\pi\) | ||||
−0.742658 | + | 0.669671i | \(0.766435\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1758.34 | 0.160632 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4634.02 | 0.420775 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7836.78 | −0.707299 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11711.1 | 1.05063 | 0.525313 | − | 0.850909i | \(-0.323948\pi\) | ||||
0.525313 | + | 0.850909i | \(0.323948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13814.2 | −1.23188 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6140.30 | −0.544299 | −0.272150 | − | 0.962255i | \(-0.587735\pi\) | ||||
−0.272150 | + | 0.962255i | \(0.587735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13489.5 | −1.18867 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 402.096 | 0.0352223 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4198.30 | −0.365592 | −0.182796 | − | 0.983151i | \(-0.558515\pi\) | ||||
−0.182796 | + | 0.983151i | \(0.558515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1223.79 | −0.105944 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11445.1 | 0.985013 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4369.76 | −0.373893 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3778.76 | −0.321450 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 582.403 | 0.0492575 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4625.41 | −0.388950 | −0.194475 | − | 0.980908i | \(-0.562300\pi\) | ||||
−0.194475 | + | 0.980908i | \(0.562300\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6063.22 | 0.506933 | 0.253467 | − | 0.967344i | \(-0.418429\pi\) | ||||
0.253467 | + | 0.967344i | \(0.418429\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6732.33 | −0.559662 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13164.9 | −1.08818 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3181.62 | −0.261496 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7926.94 | 0.647834 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −612.956 | −0.0498125 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14625.6 | −1.18191 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8857.75 | −0.711806 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4320.50 | −0.345264 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6749.03 | −0.536347 | −0.268173 | − | 0.963371i | \(-0.586420\pi\) | ||||
−0.268173 | + | 0.963371i | \(0.586420\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3675.24 | 0.290460 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36382.2 | 2.85953 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2593.58 | −0.202730 | −0.101365 | − | 0.994849i | \(-0.532321\pi\) | ||||
−0.101365 | + | 0.994849i | \(0.532321\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10301.0 | −0.800793 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2303.21 | −0.178076 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1775.04 | −0.136496 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12051.8 | 0.921745 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17018.7 | −1.29463 | −0.647313 | − | 0.762224i | \(-0.724107\pi\) | ||||
−0.647313 | + | 0.762224i | \(0.724107\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14717.3 | 1.11355 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3170.30 | 0.238592 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17896.0 | −1.33966 | −0.669830 | − | 0.742515i | \(-0.733633\pi\) | ||||
−0.669830 | + | 0.742515i | \(0.733633\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9279.86 | −0.690985 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −554.057 | −0.0410374 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2825.90 | −0.208204 | −0.104102 | − | 0.994567i | \(-0.533197\pi\) | ||||
−0.104102 | + | 0.994567i | \(0.533197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23622.5 | −1.73130 | −0.865650 | − | 0.500650i | \(-0.833094\pi\) | ||||
−0.865650 | + | 0.500650i | \(0.833094\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8473.33 | −0.617764 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23740.9 | −1.72185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9005.48 | −0.649745 | −0.324873 | − | 0.945758i | \(-0.605321\pi\) | ||||
−0.324873 | + | 0.945758i | \(0.605321\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4034.01 | 0.289547 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9311.63 | −0.664908 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4959.45 | 0.352315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13697.9 | 0.968099 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13008.8 | −0.914705 | −0.457353 | − | 0.889285i | \(-0.651202\pi\) | ||||
−0.457353 | + | 0.889285i | \(0.651202\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17244.4 | 1.20636 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10333.6 | 0.719234 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9331.77 | 0.646222 | 0.323111 | − | 0.946361i | \(-0.395271\pi\) | ||||
0.323111 | + | 0.946361i | \(0.395271\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9315.16 | 0.641822 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4349.44 | 0.298175 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11051.3 | 0.753831 | 0.376916 | − | 0.926248i | \(-0.376985\pi\) | ||||
0.376916 | + | 0.926248i | \(0.376985\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1083.67 | −0.0735503 | −0.0367752 | − | 0.999324i | \(-0.511709\pi\) | ||||
−0.0367752 | + | 0.999324i | \(0.511709\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7409.81 | 0.500416 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21181.2 | 1.42337 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20189.0 | −1.34999 | −0.674997 | − | 0.737820i | \(-0.735855\pi\) | ||||
−0.674997 | + | 0.737820i | \(0.735855\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 779.532 | 0.0518690 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11169.8 | −0.739578 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25164.1 | 1.65802 | 0.829012 | − | 0.559231i | \(-0.188904\pi\) | ||||
0.829012 | + | 0.559231i | \(0.188904\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −883.226 | −0.0579108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8089.78 | 0.527848 | 0.263924 | − | 0.964543i | \(-0.414983\pi\) | ||||
0.263924 | + | 0.964543i | \(0.414983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26830.2 | −1.74216 | −0.871081 | − | 0.491139i | \(-0.836581\pi\) | ||||
−0.871081 | + | 0.491139i | \(0.836581\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13660.0 | −0.882700 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5628.80 | 0.361980 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15795.7 | 1.01093 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4152.71 | −0.264503 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11123.7 | −0.705134 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23534.6 | −1.48478 | −0.742392 | − | 0.669965i | \(-0.766309\pi\) | ||||
−0.742392 | + | 0.669965i | \(0.766309\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2524.23 | −0.158498 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22826.7 | 1.42654 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12771.1 | −0.794366 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15326.4 | 0.948833 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26058.4 | 1.60568 | 0.802842 | − | 0.596192i | \(-0.203320\pi\) | ||||
0.802842 | + | 0.596192i | \(0.203320\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6498.37 | −0.398555 | −0.199277 | − | 0.979943i | \(-0.563859\pi\) | ||||
−0.199277 | + | 0.979943i | \(0.563859\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21206.5 | 1.29458 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7402.89 | −0.449826 | −0.224913 | − | 0.974379i | \(-0.572210\pi\) | ||||
−0.224913 | + | 0.974379i | \(0.572210\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7884.29 | −0.476865 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5836.45 | −0.351380 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19401.4 | 1.16269 | 0.581344 | − | 0.813658i | \(-0.302527\pi\) | ||||
0.581344 | + | 0.813658i | \(0.302527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26418.9 | 1.57599 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2393.37 | 0.142122 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15564.9 | 0.920067 | 0.460033 | − | 0.887902i | \(-0.347837\pi\) | ||||
0.460033 | + | 0.887902i | \(0.347837\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −849.108 | −0.0499644 | −0.0249822 | − | 0.999688i | \(-0.507953\pi\) | ||||
−0.0249822 | + | 0.999688i | \(0.507953\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9371.21 | 0.548941 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12201.8 | −0.711525 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2748.95 | 0.159580 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2610.54 | −0.150866 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10245.6 | 0.589457 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1970.54 | 0.112866 | 0.0564328 | − | 0.998406i | \(-0.482027\pi\) | ||||
0.0564328 | + | 0.998406i | \(0.482027\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 36092.0 | 2.05805 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −226.339 | −0.0128492 | −0.00642460 | − | 0.999979i | \(-0.502045\pi\) | ||||
−0.00642460 | + | 0.999979i | \(0.502045\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6365.45 | −0.359770 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18875.3 | 1.06212 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2850.00 | 0.159667 | 0.0798333 | − | 0.996808i | \(-0.474561\pi\) | ||||
0.0798333 | + | 0.996808i | \(0.474561\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13738.0 | 0.766283 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15337.5 | −0.851764 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14659.8 | 0.810589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8042.88 | 0.442787 | 0.221393 | − | 0.975185i | \(-0.428940\pi\) | ||||
0.221393 | + | 0.975185i | \(0.428940\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1896.21 | −0.103941 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 40471.6 | 2.20889 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 815.209 | 0.0443016 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4912.08 | −0.265797 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6565.07 | −0.353722 | −0.176861 | − | 0.984236i | \(-0.556594\pi\) | ||||
−0.176861 | + | 0.984236i | \(0.556594\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14570.7 | 0.781711 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16094.9 | −0.859815 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5519.84 | 0.293628 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3420.82 | 0.181201 | 0.0906004 | − | 0.995887i | \(-0.471121\pi\) | ||||
0.0906004 | + | 0.995887i | \(0.471121\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3471.46 | 0.183108 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20581.7 | −1.08105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13624.2 | −0.712610 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13441.9 | 0.700134 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33111.5 | −1.71746 | −0.858729 | − | 0.512430i | \(-0.828745\pi\) | ||||
−0.858729 | + | 0.512430i | \(0.828745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1788.08 | 0.0923600 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7724.59 | −0.397345 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7263.19 | −0.372066 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15639.6 | −0.797857 | −0.398928 | − | 0.916982i | \(-0.630618\pi\) | ||||
−0.398928 | + | 0.916982i | \(0.630618\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14274.5 | 0.725218 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19573.4 | −0.990354 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15822.7 | −0.797303 | −0.398652 | − | 0.917102i | \(-0.630522\pi\) | ||||
−0.398652 | + | 0.917102i | \(0.630522\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18402.3 | −0.923510 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7369.95 | −0.368352 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12462.7 | −0.620360 | −0.310180 | − | 0.950678i | \(-0.600389\pi\) | ||||
−0.310180 | + | 0.950678i | \(0.600389\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12275.2 | −0.608556 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33179.8 | −1.63829 | −0.819144 | − | 0.573588i | \(-0.805551\pi\) | ||||
−0.819144 | + | 0.573588i | \(0.805551\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −68841.1 | −3.38543 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18210.8 | 0.891965 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5984.70 | 0.291958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26007.0 | −1.26366 | −0.631829 | − | 0.775108i | \(-0.717696\pi\) | ||||
−0.631829 | + | 0.775108i | \(0.717696\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16445.7 | 0.795903 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24482.0 | −1.18012 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35312.0 | −1.69543 | −0.847713 | − | 0.530455i | \(-0.822021\pi\) | ||||
−0.847713 | + | 0.530455i | \(0.822021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4956.38 | 0.237029 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28072.0 | −1.33720 | −0.668600 | − | 0.743622i | \(-0.733106\pi\) | ||||
−0.668600 | + | 0.743622i | \(0.733106\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14887.4 | −0.706368 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18217.7 | −0.860996 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23305.5 | −1.09715 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37676.6 | 1.76678 | 0.883388 | − | 0.468641i | \(-0.155256\pi\) | ||||
0.883388 | + | 0.468641i | \(0.155256\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24091.4 | 1.12533 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21924.0 | 1.02012 | 0.510058 | − | 0.860140i | \(-0.329624\pi\) | ||||
0.510058 | + | 0.860140i | \(0.329624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 54380.3 | 2.52052 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4931.51 | −0.227692 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1067.83 | −0.0491128 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15244.0 | −0.698428 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4179.08 | −0.190738 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42734.0 | 1.94298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31223.2 | −1.41421 | −0.707107 | − | 0.707106i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707106i | \(0.750000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8621.53 | 0.389017 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3797.26 | 0.170689 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30285.3 | 1.35620 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21123.8 | 0.942370 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41715.4 | −1.85400 | −0.926998 | − | 0.375067i | \(-0.877620\pi\) | ||||
−0.926998 | + | 0.375067i | \(0.877620\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14855.4 | 0.657757 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11008.3 | −0.485591 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2380.50 | −0.104615 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14563.1 | 0.637619 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25134.1 | −1.09636 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32949.3 | −1.43193 | −0.715967 | − | 0.698134i | \(-0.754014\pi\) | ||||
−0.715967 | + | 0.698134i | \(0.754014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30285.6 | 1.31131 | 0.655655 | − | 0.755061i | \(-0.272393\pi\) | ||||
0.655655 | + | 0.755061i | \(0.272393\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2097.03 | 0.0904627 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6240.26 | 0.268205 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25638.9 | 1.09791 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5605.09 | −0.239143 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1354.08 | −0.0575612 | −0.0287806 | − | 0.999586i | \(-0.509162\pi\) | ||||
−0.0287806 | + | 0.999586i | \(0.509162\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19487.5 | 0.825384 | 0.412692 | − | 0.910871i | \(-0.364589\pi\) | ||||
0.412692 | + | 0.910871i | \(0.364589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13095.6 | −0.552643 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34127.7 | −1.43499 | −0.717495 | − | 0.696563i | \(-0.754711\pi\) | ||||
−0.717495 | + | 0.696563i | \(0.754711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31388.5 | 1.31504 | 0.657520 | − | 0.753437i | \(-0.271605\pi\) | ||||
0.657520 | + | 0.753437i | \(0.271605\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11770.8 | 0.491366 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16985.2 | 0.706484 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −78954.4 | −3.27225 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31289.3 | 1.29213 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30992.9 | −1.27532 | −0.637661 | − | 0.770317i | \(-0.720098\pi\) | ||||
−0.637661 | + | 0.770317i | \(0.720098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15237.4 | 0.622542 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2298.16 | 0.0935610 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8667.23 | −0.351605 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9726.56 | 0.393186 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17390.5 | −0.700515 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11988.8 | −0.481228 | −0.240614 | − | 0.970621i | \(-0.577349\pi\) | ||||
−0.240614 | + | 0.970621i | \(0.577349\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 23863.0 | 0.954501 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46615.4 | −1.85805 | −0.929027 | − | 0.370012i | \(-0.879354\pi\) | ||||
−0.929027 | + | 0.370012i | \(0.879354\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21103.2 | −0.838221 | −0.419110 | − | 0.907935i | \(-0.637658\pi\) | ||||
−0.419110 | + | 0.907935i | \(0.637658\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 361.411 | 0.0143053 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26288.3 | −1.03692 | −0.518461 | − | 0.855101i | \(-0.673495\pi\) | ||||
−0.518461 | + | 0.855101i | \(0.673495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3328.70 | 0.130843 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4192.79 | 0.164238 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3452.78 | −0.134784 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21785.1 | −0.847487 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12448.9 | 0.482626 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19274.1 | −0.744666 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25801.8 | −0.993459 | −0.496729 | − | 0.867905i | \(-0.665466\pi\) | ||||
−0.496729 | + | 0.867905i | \(0.665466\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18521.4 | −0.710707 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14409.5 | 0.551042 | 0.275521 | − | 0.961295i | \(-0.411150\pi\) | ||||
0.275521 | + | 0.961295i | \(0.411150\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40391.4 | −1.53939 | −0.769694 | − | 0.638413i | \(-0.779591\pi\) | ||||
−0.769694 | + | 0.638413i | \(0.779591\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33581.6 | −1.27552 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18395.9 | 0.696362 | 0.348181 | − | 0.937427i | \(-0.386799\pi\) | ||||
0.348181 | + | 0.937427i | \(0.386799\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9340.55 | −0.352387 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1077.74 | −0.0405226 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19458.9 | −0.729189 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −50626.0 | −1.89077 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14650.8 | 0.545346 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6296.67 | −0.233599 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19497.1 | −0.720911 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8677.58 | −0.319792 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21005.7 | 0.771549 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15677.3 | 0.573930 | 0.286965 | − | 0.957941i | \(-0.407354\pi\) | ||||
0.286965 | + | 0.957941i | \(0.407354\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10795.2 | −0.393898 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22173.0 | 0.806392 | 0.403196 | − | 0.915114i | \(-0.367899\pi\) | ||||
0.403196 | + | 0.915114i | \(0.367899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18112.8 | −0.656568 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 43639.0 | 1.57668 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10810.5 | −0.389305 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24630.4 | 0.884093 | 0.442047 | − | 0.896992i | \(-0.354253\pi\) | ||||
0.442047 | + | 0.896992i | \(0.354253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20885.7 | 0.747237 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45060.3 | −1.60691 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45948.6 | 1.63328 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3496.96 | −0.123900 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12114.5 | 0.427840 | 0.213920 | − | 0.976851i | \(-0.431377\pi\) | ||||
0.213920 | + | 0.976851i | \(0.431377\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22248.5 | −0.783208 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5684.00 | 0.199449 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18119.7 | 0.633772 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44795.9 | −1.56181 | −0.780906 | − | 0.624649i | \(-0.785242\pi\) | ||||
−0.780906 | + | 0.624649i | \(0.785242\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8141.05 | −0.282932 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40211.6 | −1.39305 | −0.696525 | − | 0.717532i | \(-0.745272\pi\) | ||||
−0.696525 | + | 0.717532i | \(0.745272\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1274.48 | 0.0440115 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22139.6 | −0.762116 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9977.38 | −0.342367 | −0.171183 | − | 0.985239i | \(-0.554759\pi\) | ||||
−0.171183 | + | 0.985239i | \(0.554759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7036.61 | −0.240693 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19303.5 | −0.658210 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5358.75 | 0.182148 | 0.0910740 | − | 0.995844i | \(-0.470970\pi\) | ||||
0.0910740 | + | 0.995844i | \(0.470970\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48428.9 | −1.64097 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1516.33 | 0.0512184 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5621.52 | −0.189289 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17352.9 | 0.582488 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11704.3 | −0.391657 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23056.2 | 0.769125 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34177.6 | −1.13658 | −0.568292 | − | 0.822827i | \(-0.692395\pi\) | ||||
−0.568292 | + | 0.822827i | \(0.692395\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16325.5 | 0.541230 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34564.3 | 1.14235 | 0.571174 | − | 0.820829i | \(-0.306488\pi\) | ||||
0.571174 | + | 0.820829i | \(0.306488\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16560.7 | −0.545645 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −38709.8 | −1.27149 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26368.2 | 0.863451 | 0.431726 | − | 0.902005i | \(-0.357905\pi\) | ||||
0.431726 | + | 0.902005i | \(0.357905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10949.0 | 0.357439 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29115.3 | 0.947584 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34206.8 | −1.10989 | −0.554947 | − | 0.831885i | \(-0.687262\pi\) | ||||
−0.554947 | + | 0.831885i | \(0.687262\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59061.2 | 1.91050 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6585.94 | 0.212394 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30600.7 | −0.983868 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22991.7 | 0.736989 | 0.368494 | − | 0.929630i | \(-0.379873\pi\) | ||||
0.368494 | + | 0.929630i | \(0.379873\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11792.7 | −0.376870 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24859.0 | 0.792043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18342.9 | −0.582674 | −0.291337 | − | 0.956620i | \(-0.594100\pi\) | ||||
−0.291337 | + | 0.956620i | \(0.594100\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26437.8 | 0.837294 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 928.4.a.d.1.4 | ✓ | 9 | |
4.3 | odd | 2 | 928.4.a.e.1.6 | yes | 9 | ||
8.3 | odd | 2 | 1856.4.a.bf.1.4 | 9 | |||
8.5 | even | 2 | 1856.4.a.bg.1.6 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.d.1.4 | ✓ | 9 | 1.1 | even | 1 | trivial | |
928.4.a.e.1.6 | yes | 9 | 4.3 | odd | 2 | ||
1856.4.a.bf.1.4 | 9 | 8.3 | odd | 2 | |||
1856.4.a.bg.1.6 | 9 | 8.5 | even | 2 |