Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(1,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, 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("1620.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.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: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 167x^{5} + 940x^{4} + 1153x^{3} - 13196x^{2} + 16629x + 714 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{7} \) |
Twist minimal: | no (minimal twist has level 180) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.0415615\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.7344 | −0.741588 | −0.370794 | − | 0.928715i | \(-0.620914\pi\) | ||||
−0.370794 | + | 0.928715i | \(0.620914\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −21.6430 | −0.593237 | −0.296619 | − | 0.954996i | \(-0.595859\pi\) | ||||
−0.296619 | + | 0.954996i | \(0.595859\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −79.6266 | −1.69880 | −0.849401 | − | 0.527747i | \(-0.823037\pi\) | ||||
−0.849401 | + | 0.527747i | \(0.823037\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 64.3628 | 0.918251 | 0.459125 | − | 0.888371i | \(-0.348163\pi\) | ||||
0.459125 | + | 0.888371i | \(0.348163\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −144.503 | −1.74480 | −0.872399 | − | 0.488795i | \(-0.837437\pi\) | ||||
−0.872399 | + | 0.488795i | \(0.837437\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 26.9451 | 0.244280 | 0.122140 | − | 0.992513i | \(-0.461024\pi\) | ||||
0.122140 | + | 0.992513i | \(0.461024\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −297.006 | −1.90182 | −0.950908 | − | 0.309472i | \(-0.899848\pi\) | ||||
−0.950908 | + | 0.309472i | \(0.899848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −96.6507 | −0.559967 | −0.279984 | − | 0.960005i | \(-0.590329\pi\) | ||||
−0.279984 | + | 0.960005i | \(0.590329\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 68.6720 | 0.331648 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 401.580 | 1.78431 | 0.892153 | − | 0.451734i | \(-0.149194\pi\) | ||||
0.892153 | + | 0.451734i | \(0.149194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.6890 | 0.0445246 | 0.0222623 | − | 0.999752i | \(-0.492913\pi\) | ||||
0.0222623 | + | 0.999752i | \(0.492913\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 292.271 | 1.03653 | 0.518267 | − | 0.855219i | \(-0.326577\pi\) | ||||
0.518267 | + | 0.855219i | \(0.326577\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −175.362 | −0.544239 | −0.272119 | − | 0.962263i | \(-0.587725\pi\) | ||||
−0.272119 | + | 0.962263i | \(0.587725\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −154.366 | −0.450048 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −155.406 | −0.402767 | −0.201383 | − | 0.979513i | \(-0.564544\pi\) | ||||
−0.201383 | + | 0.979513i | \(0.564544\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 108.215 | 0.265304 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −595.163 | −1.31328 | −0.656641 | − | 0.754203i | \(-0.728023\pi\) | ||||
−0.656641 | + | 0.754203i | \(0.728023\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −62.1070 | −0.130360 | −0.0651802 | − | 0.997874i | \(-0.520762\pi\) | ||||
−0.0651802 | + | 0.997874i | \(0.520762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 398.133 | 0.759728 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −160.664 | −0.292958 | −0.146479 | − | 0.989214i | \(-0.546794\pi\) | ||||
−0.146479 | + | 0.989214i | \(0.546794\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 959.723 | 1.60420 | 0.802100 | − | 0.597190i | \(-0.203716\pi\) | ||||
0.802100 | + | 0.597190i | \(0.203716\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 763.424 | 1.22400 | 0.612000 | − | 0.790858i | \(-0.290365\pi\) | ||||
0.612000 | + | 0.790858i | \(0.290365\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 297.254 | 0.439938 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 63.9649 | 0.0910964 | 0.0455482 | − | 0.998962i | \(-0.485497\pi\) | ||||
0.0455482 | + | 0.998962i | \(0.485497\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −917.326 | −1.21313 | −0.606564 | − | 0.795035i | \(-0.707452\pi\) | ||||
−0.606564 | + | 0.795035i | \(0.707452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −321.814 | −0.410654 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1318.88 | 1.57080 | 0.785399 | − | 0.618990i | \(-0.212458\pi\) | ||||
0.785399 | + | 0.618990i | \(0.212458\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1093.62 | 1.25981 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 722.513 | 0.780297 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −128.169 | −0.134161 | −0.0670804 | − | 0.997748i | \(-0.521368\pi\) | ||||
−0.0670804 | + | 0.997748i | \(0.521368\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 460.408 | 0.453587 | 0.226793 | − | 0.973943i | \(-0.427176\pi\) | ||||
0.226793 | + | 0.973943i | \(0.427176\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 717.461 | 0.686345 | 0.343173 | − | 0.939272i | \(-0.388498\pi\) | ||||
0.343173 | + | 0.939272i | \(0.388498\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1361.76 | −1.23034 | −0.615171 | − | 0.788393i | \(-0.710913\pi\) | ||||
−0.615171 | + | 0.788393i | \(0.710913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 225.862 | 0.198474 | 0.0992369 | − | 0.995064i | \(-0.468360\pi\) | ||||
0.0992369 | + | 0.995064i | \(0.468360\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1968.47 | −1.63874 | −0.819371 | − | 0.573263i | \(-0.805677\pi\) | ||||
−0.819371 | + | 0.573263i | \(0.805677\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −134.725 | −0.109245 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −883.984 | −0.680964 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −862.580 | −0.648069 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 751.204 | 0.524871 | 0.262435 | − | 0.964950i | \(-0.415474\pi\) | ||||
0.262435 | + | 0.964950i | \(0.415474\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 79.5797 | 0.0530757 | 0.0265378 | − | 0.999648i | \(-0.491552\pi\) | ||||
0.0265378 | + | 0.999648i | \(0.491552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1984.66 | 1.29392 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −803.584 | −0.501130 | −0.250565 | − | 0.968100i | \(-0.580616\pi\) | ||||
−0.250565 | + | 0.968100i | \(0.580616\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1761.67 | 1.07498 | 0.537491 | − | 0.843270i | \(-0.319372\pi\) | ||||
0.537491 | + | 0.843270i | \(0.319372\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1723.36 | 1.00779 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1485.03 | 0.850518 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2409.91 | 1.32502 | 0.662509 | − | 0.749054i | \(-0.269492\pi\) | ||||
0.662509 | + | 0.749054i | \(0.269492\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1847.68 | 0.995774 | 0.497887 | − | 0.867242i | \(-0.334109\pi\) | ||||
0.497887 | + | 0.867242i | \(0.334109\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 483.254 | 0.250425 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −86.1401 | −0.0437881 | −0.0218940 | − | 0.999760i | \(-0.506970\pi\) | ||||
−0.0218940 | + | 0.999760i | \(0.506970\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −370.074 | −0.181155 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1127.15 | −0.541625 | −0.270812 | − | 0.962632i | \(-0.587292\pi\) | ||||
−0.270812 | + | 0.962632i | \(0.587292\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 968.645 | 0.448838 | 0.224419 | − | 0.974493i | \(-0.427952\pi\) | ||||
0.224419 | + | 0.974493i | \(0.427952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4143.39 | 1.88593 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1752.07 | −0.769987 | −0.384993 | − | 0.922919i | \(-0.625796\pi\) | ||||
−0.384993 | + | 0.922919i | \(0.625796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −343.360 | −0.148318 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 880.297 | 0.367578 | 0.183789 | − | 0.982966i | \(-0.441164\pi\) | ||||
0.183789 | + | 0.982966i | \(0.441164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 335.846 | 0.137919 | 0.0689593 | − | 0.997619i | \(-0.478032\pi\) | ||||
0.0689593 | + | 0.997619i | \(0.478032\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2007.90 | −0.797966 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1393.00 | −0.544741 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3977.29 | 1.50674 | 0.753368 | − | 0.657599i | \(-0.228428\pi\) | ||||
0.753368 | + | 0.657599i | \(0.228428\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4159.11 | 1.55119 | 0.775593 | − | 0.631233i | \(-0.217451\pi\) | ||||
0.775593 | + | 0.631233i | \(0.217451\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1581.17 | −0.571846 | −0.285923 | − | 0.958253i | \(-0.592300\pi\) | ||||
−0.285923 | + | 0.958253i | \(0.592300\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2139.37 | −0.762090 | −0.381045 | − | 0.924557i | \(-0.624436\pi\) | ||||
−0.381045 | + | 0.924557i | \(0.624436\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4079.20 | 1.41036 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −58.4448 | −0.0199120 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3127.47 | 1.03508 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −176.284 | −0.0575162 | −0.0287581 | − | 0.999586i | \(-0.509155\pi\) | ||||
−0.0287581 | + | 0.999586i | \(0.509155\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1461.36 | −0.463552 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1327.44 | 0.415265 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5124.99 | −1.55993 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3622.37 | −1.08777 | −0.543883 | − | 0.839161i | \(-0.683046\pi\) | ||||
−0.543883 | + | 0.839161i | \(0.683046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −776.343 | −0.226994 | −0.113497 | − | 0.993538i | \(-0.536205\pi\) | ||||
−0.113497 | + | 0.993538i | \(0.536205\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5086.09 | 1.46768 | 0.733838 | − | 0.679324i | \(-0.237727\pi\) | ||||
0.733838 | + | 0.679324i | \(0.237727\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3896.93 | −1.09569 | −0.547846 | − | 0.836579i | \(-0.684552\pi\) | ||||
−0.547846 | + | 0.836579i | \(0.684552\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 876.812 | 0.243391 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1234.73 | 0.334176 | 0.167088 | − | 0.985942i | \(-0.446564\pi\) | ||||
0.167088 | + | 0.985942i | \(0.446564\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1918.45 | 0.512772 | 0.256386 | − | 0.966574i | \(-0.417468\pi\) | ||||
0.256386 | + | 0.966574i | \(0.417468\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 771.832 | 0.201267 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11506.2 | 2.96407 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7109.99 | −1.78796 | −0.893981 | − | 0.448105i | \(-0.852099\pi\) | ||||
−0.893981 | + | 0.448105i | \(0.852099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −583.172 | −0.144916 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4182.28 | 1.01511 | 0.507555 | − | 0.861619i | \(-0.330549\pi\) | ||||
0.507555 | + | 0.861619i | \(0.330549\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5515.46 | −1.32322 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4216.61 | 0.988620 | 0.494310 | − | 0.869286i | \(-0.335421\pi\) | ||||
0.494310 | + | 0.869286i | \(0.335421\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 777.029 | 0.180123 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3271.14 | 0.741431 | 0.370715 | − | 0.928747i | \(-0.379113\pi\) | ||||
0.370715 | + | 0.928747i | \(0.379113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6407.18 | 1.43619 | 0.718096 | − | 0.695944i | \(-0.245014\pi\) | ||||
0.718096 | + | 0.695944i | \(0.245014\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −541.075 | −0.118647 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6326.26 | 1.37223 | 0.686116 | − | 0.727492i | \(-0.259314\pi\) | ||||
0.686116 | + | 0.727492i | \(0.259314\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3982.57 | 0.845481 | 0.422741 | − | 0.906251i | \(-0.361068\pi\) | ||||
0.422741 | + | 0.906251i | \(0.361068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3679.68 | −0.772913 | −0.386456 | − | 0.922308i | \(-0.626301\pi\) | ||||
−0.386456 | + | 0.922308i | \(0.626301\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −160.541 | −0.0330189 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −770.434 | −0.156815 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8946.28 | −1.78378 | −0.891890 | − | 0.452253i | \(-0.850620\pi\) | ||||
−0.891890 | + | 0.452253i | \(0.850620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2975.82 | 0.587318 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2145.54 | −0.414983 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4014.17 | −0.768681 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 310.535 | 0.0582989 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9746.88 | −1.81200 | −0.906000 | − | 0.423278i | \(-0.860879\pi\) | ||||
−0.906000 | + | 0.423278i | \(0.860879\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5279.02 | −0.962527 | −0.481264 | − | 0.876576i | \(-0.659822\pi\) | ||||
−0.481264 | + | 0.876576i | \(0.659822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4534.39 | 0.818847 | 0.409424 | − | 0.912344i | \(-0.365730\pi\) | ||||
0.409424 | + | 0.912344i | \(0.365730\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2234.77 | −0.395953 | −0.197977 | − | 0.980207i | \(-0.563437\pi\) | ||||
−0.197977 | + | 0.980207i | \(0.563437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6428.11 | 1.12823 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9300.58 | −1.60216 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1990.66 | −0.339761 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2408.50 | 0.403601 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1841.53 | −0.305799 | −0.152899 | − | 0.988242i | \(-0.548861\pi\) | ||||
−0.152899 | + | 0.988242i | \(0.548861\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 803.318 | 0.131015 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7034.18 | 1.13702 | 0.568511 | − | 0.822676i | \(-0.307520\pi\) | ||||
0.568511 | + | 0.822676i | \(0.307520\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2091.81 | 0.332193 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6831.03 | 1.07534 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11775.1 | 1.82168 | 0.910839 | − | 0.412761i | \(-0.135436\pi\) | ||||
0.910839 | + | 0.412761i | \(0.135436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7898.58 | 1.21147 | 0.605733 | − | 0.795668i | \(-0.292880\pi\) | ||||
0.605733 | + | 0.795668i | \(0.292880\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8967.91 | −1.35216 | −0.676082 | − | 0.736826i | \(-0.736323\pi\) | ||||
−0.676082 | + | 0.736826i | \(0.736323\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4798.62 | −0.717420 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8351.48 | −1.22778 | −0.613892 | − | 0.789390i | \(-0.710397\pi\) | ||||
−0.613892 | + | 0.789390i | \(0.710397\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14022.0 | 2.04432 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3817.12 | −0.547390 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 110.518 | 0.0157193 | 0.00785964 | − | 0.999969i | \(-0.497498\pi\) | ||||
0.00785964 | + | 0.999969i | \(0.497498\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2134.41 | 0.298687 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4895.94 | 0.679631 | 0.339816 | − | 0.940492i | \(-0.389635\pi\) | ||||
0.339816 | + | 0.940492i | \(0.389635\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23649.6 | 3.23081 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10326.8 | 1.39962 | 0.699808 | − | 0.714331i | \(-0.253269\pi\) | ||||
0.699808 | + | 0.714331i | \(0.253269\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8332.52 | 1.11168 | 0.555838 | − | 0.831291i | \(-0.312398\pi\) | ||||
0.555838 | + | 0.831291i | \(0.312398\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1486.27 | −0.196746 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2071.50 | −0.269998 | −0.134999 | − | 0.990846i | \(-0.543103\pi\) | ||||
−0.134999 | + | 0.990846i | \(0.543103\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1734.26 | 0.224310 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −319.825 | −0.0407396 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7891.46 | −0.997635 | −0.498818 | − | 0.866707i | \(-0.666232\pi\) | ||||
−0.498818 | + | 0.866707i | \(0.666232\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1733.64 | −0.215894 | −0.107947 | − | 0.994157i | \(-0.534428\pi\) | ||||
−0.107947 | + | 0.994157i | \(0.534428\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7695.97 | 0.951274 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8691.39 | −1.05852 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9412.60 | −1.13795 | −0.568977 | − | 0.822353i | \(-0.692661\pi\) | ||||
−0.568977 | + | 0.822353i | \(0.692661\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8174.21 | 0.973914 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4586.63 | 0.542527 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3868.71 | 0.451071 | 0.225535 | − | 0.974235i | \(-0.427587\pi\) | ||||
0.225535 | + | 0.974235i | \(0.427587\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12925.0 | 1.49626 | 0.748129 | − | 0.663554i | \(-0.230953\pi\) | ||||
0.748129 | + | 0.663554i | \(0.230953\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1609.07 | 0.183650 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 853.002 | 0.0966737 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13183.6 | 1.47339 | 0.736697 | − | 0.676223i | \(-0.236384\pi\) | ||||
0.736697 | + | 0.676223i | \(0.236384\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7584.46 | −0.841769 | −0.420884 | − | 0.907114i | \(-0.638280\pi\) | ||||
−0.420884 | + | 0.907114i | \(0.638280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3893.63 | −0.426219 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7546.46 | −0.820439 | −0.410220 | − | 0.911987i | \(-0.634548\pi\) | ||||
−0.410220 | + | 0.911987i | \(0.634548\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2045.04 | −0.219330 | −0.109665 | − | 0.993969i | \(-0.534978\pi\) | ||||
−0.109665 | + | 0.993969i | \(0.534978\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6594.40 | −0.702482 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10723.2 | −1.12708 | −0.563541 | − | 0.826088i | \(-0.690561\pi\) | ||||
−0.563541 | + | 0.826088i | \(0.690561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −252.984 | −0.0264137 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5468.11 | −0.563405 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4660.58 | −0.477052 | −0.238526 | − | 0.971136i | \(-0.576664\pi\) | ||||
−0.238526 | + | 0.971136i | \(0.576664\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16640.4 | 1.68117 | 0.840584 | − | 0.541681i | \(-0.182212\pi\) | ||||
0.840584 | + | 0.541681i | \(0.182212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3468.69 | −0.348172 | −0.174086 | − | 0.984730i | \(-0.555697\pi\) | ||||
−0.174086 | + | 0.984730i | \(0.555697\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9920.55 | 0.983016 | 0.491508 | − | 0.870873i | \(-0.336446\pi\) | ||||
0.491508 | + | 0.870873i | \(0.336446\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2206.62 | 0.217254 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6325.63 | −0.614911 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3612.56 | −0.348959 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18264.7 | −1.74224 | −0.871120 | − | 0.491070i | \(-0.836606\pi\) | ||||
−0.871120 | + | 0.491070i | \(0.836606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31976.4 | −3.03118 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 640.845 | 0.0599985 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3244.55 | −0.301899 | −0.150949 | − | 0.988542i | \(-0.548233\pi\) | ||||
−0.150949 | + | 0.988542i | \(0.548233\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 591.093 | 0.0543293 | 0.0271646 | − | 0.999631i | \(-0.491352\pi\) | ||||
0.0271646 | + | 0.999631i | \(0.491352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19116.2 | −1.74635 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13181.2 | −1.18965 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9644.97 | −0.865267 | −0.432634 | − | 0.901570i | \(-0.642416\pi\) | ||||
−0.432634 | + | 0.901570i | \(0.642416\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −723.099 | −0.0640982 | −0.0320491 | − | 0.999486i | \(-0.510203\pi\) | ||||
−0.0320491 | + | 0.999486i | \(0.510203\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2302.04 | −0.202850 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2684.55 | 0.233773 | 0.116886 | − | 0.993145i | \(-0.462709\pi\) | ||||
0.116886 | + | 0.993145i | \(0.462709\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10485.2 | −0.907704 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3587.31 | −0.306943 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3795.37 | 0.322863 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4203.80 | 0.353497 | 0.176748 | − | 0.984256i | \(-0.443442\pi\) | ||||
0.176748 | + | 0.984256i | \(0.443442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10571.8 | 0.883883 | 0.441942 | − | 0.897044i | \(-0.354290\pi\) | ||||
0.441942 | + | 0.897044i | \(0.354290\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6220.71 | −0.514190 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11441.0 | −0.940327 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −930.752 | −0.0756386 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6808.82 | 0.550226 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3340.95 | 0.266985 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15310.3 | 1.21671 | 0.608356 | − | 0.793664i | \(-0.291829\pi\) | ||||
0.608356 | + | 0.793664i | \(0.291829\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1129.31 | −0.0887601 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −894.345 | −0.0699075 | −0.0349538 | − | 0.999389i | \(-0.511128\pi\) | ||||
−0.0349538 | + | 0.999389i | \(0.511128\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42918.2 | 3.31829 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −878.520 | −0.0675560 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25371.2 | −1.93000 | −0.965001 | − | 0.262245i | \(-0.915537\pi\) | ||||
−0.965001 | + | 0.262245i | \(0.915537\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23272.6 | −1.76087 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −848.897 | −0.0635466 | −0.0317733 | − | 0.999495i | \(-0.510115\pi\) | ||||
−0.0317733 | + | 0.999495i | \(0.510115\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9842.34 | 0.732868 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8636.66 | 0.636323 | 0.318161 | − | 0.948037i | \(-0.396935\pi\) | ||||
0.318161 | + | 0.948037i | \(0.396935\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7231.98 | −0.530033 | −0.265017 | − | 0.964244i | \(-0.585377\pi\) | ||||
−0.265017 | + | 0.964244i | \(0.585377\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 673.627 | 0.0488559 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5882.23 | −0.424403 | −0.212201 | − | 0.977226i | \(-0.568063\pi\) | ||||
−0.212201 | + | 0.977226i | \(0.568063\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12598.9 | 0.899640 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3363.45 | 0.238936 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19332.8 | −1.35937 | −0.679684 | − | 0.733505i | \(-0.737883\pi\) | ||||
−0.679684 | + | 0.733505i | \(0.737883\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13966.3 | 0.977029 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4318.26 | 0.299039 | 0.149519 | − | 0.988759i | \(-0.452227\pi\) | ||||
0.149519 | + | 0.988759i | \(0.452227\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4419.92 | 0.304536 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15381.6 | −1.04921 | −0.524605 | − | 0.851346i | \(-0.675787\pi\) | ||||
−0.524605 | + | 0.851346i | \(0.675787\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4172.55 | 0.283198 | 0.141599 | − | 0.989924i | \(-0.454776\pi\) | ||||
0.141599 | + | 0.989924i | \(0.454776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4312.90 | 0.289825 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 692.820 | 0.0463274 | 0.0231637 | − | 0.999732i | \(-0.492626\pi\) | ||||
0.0231637 | + | 0.999732i | \(0.492626\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13963.5 | 0.924555 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11649.8 | 0.767584 | 0.383792 | − | 0.923419i | \(-0.374618\pi\) | ||||
0.383792 | + | 0.923419i | \(0.374618\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21787.2 | 1.42159 | 0.710793 | − | 0.703402i | \(-0.248336\pi\) | ||||
0.710793 | + | 0.703402i | \(0.248336\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4970.00 | −0.322716 | −0.161358 | − | 0.986896i | \(-0.551587\pi\) | ||||
−0.161358 | + | 0.986896i | \(0.551587\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18114.0 | −1.16488 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25846.8 | 1.63844 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16907.2 | −1.06666 | −0.533331 | − | 0.845906i | \(-0.679060\pi\) | ||||
−0.533331 | + | 0.845906i | \(0.679060\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3756.02 | −0.234729 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12291.7 | 0.764542 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21469.9 | −1.32295 | −0.661474 | − | 0.749968i | \(-0.730069\pi\) | ||||
−0.661474 | + | 0.749968i | \(0.730069\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17712.4 | −1.08633 | −0.543165 | − | 0.839626i | \(-0.682774\pi\) | ||||
−0.543165 | + | 0.839626i | \(0.682774\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12632.9 | −0.767619 | −0.383809 | − | 0.923412i | \(-0.625388\pi\) | ||||
−0.383809 | + | 0.923412i | \(0.625388\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12881.1 | 0.779088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16170.2 | −0.969047 | −0.484523 | − | 0.874778i | \(-0.661007\pi\) | ||||
−0.484523 | + | 0.874778i | \(0.661007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −397.899 | −0.0237362 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7752.76 | −0.458277 | −0.229139 | − | 0.973394i | \(-0.573591\pi\) | ||||
−0.229139 | + | 0.973394i | \(0.573591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11693.5 | 0.688087 | 0.344044 | − | 0.938954i | \(-0.388203\pi\) | ||||
0.344044 | + | 0.938954i | \(0.388203\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9923.28 | −0.578659 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8002.85 | −0.464575 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1344.18 | 0.0773347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4118.91 | −0.235917 | −0.117959 | − | 0.993019i | \(-0.537635\pi\) | ||||
−0.117959 | + | 0.993019i | \(0.537635\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13603.9 | 0.772293 | 0.386146 | − | 0.922438i | \(-0.373806\pi\) | ||||
0.386146 | + | 0.922438i | \(0.373806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1760.32 | 0.0994920 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28073.3 | −1.57276 | −0.786381 | − | 0.617742i | \(-0.788048\pi\) | ||||
−0.786381 | + | 0.617742i | \(0.788048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4017.92 | 0.224112 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12374.4 | 0.684221 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15917.5 | −0.876311 | −0.438155 | − | 0.898899i | \(-0.644368\pi\) | ||||
−0.438155 | + | 0.898899i | \(0.644368\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8808.33 | −0.480746 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 752.334 | 0.0408848 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17451.6 | −0.940280 | −0.470140 | − | 0.882592i | \(-0.655797\pi\) | ||||
−0.470140 | + | 0.882592i | \(0.655797\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −58029.3 | −3.11325 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6323.42 | −0.336375 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30178.3 | 1.59855 | 0.799273 | − | 0.600968i | \(-0.205218\pi\) | ||||
0.799273 | + | 0.600968i | \(0.205218\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2604.26 | −0.136789 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8616.79 | −0.450699 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7009.26 | 0.363562 | 0.181781 | − | 0.983339i | \(-0.441814\pi\) | ||||
0.181781 | + | 0.983339i | \(0.441814\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9853.90 | −0.508985 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7425.16 | −0.380363 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31166.0 | −1.58994 | −0.794968 | − | 0.606651i | \(-0.792513\pi\) | ||||
−0.794968 | + | 0.606651i | \(0.792513\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18811.4 | 0.951798 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32076.1 | 1.61632 | 0.808158 | − | 0.588966i | \(-0.200465\pi\) | ||||
0.808158 | + | 0.588966i | \(0.200465\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3477.24 | 0.173794 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35798.6 | −1.78197 | −0.890984 | − | 0.454035i | \(-0.849984\pi\) | ||||
−0.890984 | + | 0.454035i | \(0.849984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1043.92 | 0.0515449 | 0.0257724 | − | 0.999668i | \(-0.491795\pi\) | ||||
0.0257724 | + | 0.999668i | \(0.491795\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12049.6 | −0.592566 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18703.0 | 0.912407 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40244.7 | −1.95546 | −0.977731 | − | 0.209864i | \(-0.932698\pi\) | ||||
−0.977731 | + | 0.209864i | \(0.932698\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9238.39 | −0.445324 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1971.31 | 0.0946480 | 0.0473240 | − | 0.998880i | \(-0.484931\pi\) | ||||
0.0473240 | + | 0.998880i | \(0.484931\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14876.5 | 0.708635 | 0.354317 | − | 0.935125i | \(-0.384713\pi\) | ||||
0.354317 | + | 0.935125i | \(0.384713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3102.08 | −0.147186 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47390.8 | 2.23101 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2284.74 | 0.107139 | 0.0535695 | − | 0.998564i | \(-0.482940\pi\) | ||||
0.0535695 | + | 0.998564i | \(0.482940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15649.7 | −0.728177 | −0.364089 | − | 0.931364i | \(-0.618620\pi\) | ||||
−0.364089 | + | 0.931364i | \(0.618620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2416.27 | −0.111993 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1689.09 | −0.0776865 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20771.3 | −0.951671 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 430.700 | 0.0195826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30420.7 | −1.37786 | −0.688932 | − | 0.724826i | \(-0.741920\pi\) | ||||
−0.688932 | + | 0.724826i | \(0.741920\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27035.7 | 1.21527 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4945.37 | 0.221457 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18616.0 | 0.827367 | 0.413683 | − | 0.910421i | \(-0.364242\pi\) | ||||
0.413683 | + | 0.910421i | \(0.364242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11286.8 | −0.499748 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16522.8 | −0.726123 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1850.37 | 0.0810149 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42989.2 | −1.86826 | −0.934129 | − | 0.356935i | \(-0.883822\pi\) | ||||
−0.934129 | + | 0.356935i | \(0.883822\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28303.4 | −1.22548 | −0.612741 | − | 0.790284i | \(-0.709933\pi\) | ||||
−0.612741 | + | 0.790284i | \(0.709933\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5635.73 | 0.242222 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42234.0 | −1.80854 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10594.2 | −0.450353 | −0.225176 | − | 0.974318i | \(-0.572296\pi\) | ||||
−0.225176 | + | 0.974318i | \(0.572296\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24598.3 | −1.04185 | −0.520925 | − | 0.853602i | \(-0.674413\pi\) | ||||
−0.520925 | + | 0.853602i | \(0.674413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15104.9 | 0.635126 | 0.317563 | − | 0.948237i | \(-0.397135\pi\) | ||||
0.317563 | + | 0.948237i | \(0.397135\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33824.6 | −1.41710 | −0.708551 | − | 0.705660i | \(-0.750651\pi\) | ||||
−0.708551 | + | 0.705660i | \(0.750651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9935.45 | −0.413257 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4843.22 | −0.200727 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5366.62 | −0.220830 | −0.110415 | − | 0.993886i | \(-0.535218\pi\) | ||||
−0.110415 | + | 0.993886i | \(0.535218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63823.8 | 2.61691 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20717.0 | −0.843414 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11847.0 | 0.480600 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10820.6 | 0.435870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16383.3 | 0.657623 | 0.328812 | − | 0.944396i | \(-0.393352\pi\) | ||||
0.328812 | + | 0.944396i | \(0.393352\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28118.4 | 1.12078 | 0.560389 | − | 0.828230i | \(-0.310652\pi\) | ||||
0.560389 | + | 0.828230i | \(0.310652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32222.9 | 1.27990 | 0.639949 | − | 0.768417i | \(-0.278955\pi\) | ||||
0.639949 | + | 0.768417i | \(0.278955\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37447.4 | −1.47709 | −0.738543 | − | 0.674206i | \(-0.764486\pi\) | ||||
−0.738543 | + | 0.674206i | \(0.764486\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8760.37 | 0.344349 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1384.39 | −0.0540418 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12793.1 | 0.497678 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1716.80 | 0.0663296 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7833.73 | −0.301626 | −0.150813 | − | 0.988562i | \(-0.548189\pi\) | ||||
−0.150813 | + | 0.988562i | \(0.548189\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3195.87 | 0.122215 | 0.0611076 | − | 0.998131i | \(-0.480537\pi\) | ||||
0.0611076 | + | 0.998131i | \(0.480537\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6033.49 | 0.229947 | 0.114973 | − | 0.993369i | \(-0.463322\pi\) | ||||
0.114973 | + | 0.993369i | \(0.463322\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3479.21 | 0.131703 | 0.0658515 | − | 0.997829i | \(-0.479024\pi\) | ||||
0.0658515 | + | 0.997829i | \(0.479024\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10317.3 | −0.389238 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25340.3 | 0.949587 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4401.49 | −0.164386 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28705.9 | 1.06496 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10002.3 | −0.369841 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1679.23 | −0.0616791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4383.31 | 0.160469 | 0.0802345 | − | 0.996776i | \(-0.474433\pi\) | ||||
0.0802345 | + | 0.996776i | \(0.474433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4685.36 | 0.170398 | 0.0851992 | − | 0.996364i | \(-0.472847\pi\) | ||||
0.0851992 | + | 0.996364i | \(0.472847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19853.7 | 0.719672 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1092.98 | −0.0393603 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36353.0 | 1.30487 | 0.652434 | − | 0.757846i | \(-0.273748\pi\) | ||||
0.652434 | + | 0.757846i | \(0.273748\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −76419.5 | −2.72522 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10039.5 | 0.356861 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8542.11 | −0.301677 | −0.150838 | − | 0.988558i | \(-0.548197\pi\) | ||||
−0.150838 | + | 0.988558i | \(0.548197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22306.3 | 0.785242 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6965.02 | 0.243615 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33521.5 | 1.16873 | 0.584364 | − | 0.811491i | \(-0.301344\pi\) | ||||
0.584364 | + | 0.811491i | \(0.301344\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24074.0 | −0.833994 | −0.416997 | − | 0.908908i | \(-0.636917\pi\) | ||||
−0.416997 | + | 0.908908i | \(0.636917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 314.960 | 0.0108765 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41080.3 | 1.40964 | 0.704820 | − | 0.709386i | \(-0.251028\pi\) | ||||
0.704820 | + | 0.709386i | \(0.251028\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60788.8 | −2.07934 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28047.0 | 0.953337 | 0.476668 | − | 0.879083i | \(-0.341844\pi\) | ||||
0.476668 | + | 0.879083i | \(0.341844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19886.5 | −0.673833 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11036.7 | 0.371632 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20449.6 | −0.686437 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20795.5 | −0.693712 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5313.03 | −0.176686 | −0.0883432 | − | 0.996090i | \(-0.528157\pi\) | ||||
−0.0883432 | + | 0.996090i | \(0.528157\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17611.7 | −0.582065 | −0.291032 | − | 0.956713i | \(-0.593999\pi\) | ||||
−0.291032 | + | 0.956713i | \(0.593999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24195.4 | −0.797193 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43273.1 | 1.41702 | 0.708511 | − | 0.705700i | \(-0.249367\pi\) | ||||
0.708511 | + | 0.705700i | \(0.249367\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28544.5 | −0.931856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46719.7 | −1.51590 | −0.757948 | − | 0.652315i | \(-0.773798\pi\) | ||||
−0.757948 | + | 0.652315i | \(0.773798\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7905.85 | 0.255737 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7875.27 | 0.253204 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4961.78 | −0.159047 | −0.0795237 | − | 0.996833i | \(-0.525340\pi\) | ||||
−0.0795237 | + | 0.996833i | \(0.525340\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10696.8 | 0.340817 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29340.1 | 0.932007 | 0.466004 | − | 0.884783i | \(-0.345693\pi\) | ||||
0.466004 | + | 0.884783i | \(0.345693\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1620.4.a.k.1.3 | 7 | ||
3.2 | odd | 2 | 1620.4.a.l.1.3 | 7 | |||
9.2 | odd | 6 | 180.4.i.c.121.1 | yes | 14 | ||
9.4 | even | 3 | 540.4.i.c.181.5 | 14 | |||
9.5 | odd | 6 | 180.4.i.c.61.1 | ✓ | 14 | ||
9.7 | even | 3 | 540.4.i.c.361.5 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.4.i.c.61.1 | ✓ | 14 | 9.5 | odd | 6 | ||
180.4.i.c.121.1 | yes | 14 | 9.2 | odd | 6 | ||
540.4.i.c.181.5 | 14 | 9.4 | even | 3 | |||
540.4.i.c.361.5 | 14 | 9.7 | even | 3 | |||
1620.4.a.k.1.3 | 7 | 1.1 | even | 1 | trivial | ||
1620.4.a.l.1.3 | 7 | 3.2 | odd | 2 |