Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.4481.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 17x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.476971\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | −1.95394 | −0.376036 | −0.188018 | − | 0.982166i | \(-0.560206\pi\) | ||||
−0.188018 | + | 0.982166i | \(0.560206\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.5450 | 1.65871 | 0.829357 | − | 0.558718i | \(-0.188707\pi\) | ||||
0.829357 | + | 0.558718i | \(0.188707\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.63711 | 0.412365 | 0.206183 | − | 0.978514i | \(-0.433896\pi\) | ||||
0.206183 | + | 0.978514i | \(0.433896\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −23.1821 | −0.858597 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −67.0439 | −1.83768 | −0.918841 | − | 0.394627i | \(-0.870874\pi\) | ||||
−0.918841 | + | 0.394627i | \(0.870874\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.82134 | 0.145531 | 0.0727654 | − | 0.997349i | \(-0.476818\pi\) | ||||
0.0727654 | + | 0.997349i | \(0.476818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −36.2359 | −0.623737 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 105.453 | 1.50448 | 0.752238 | − | 0.658892i | \(-0.228975\pi\) | ||||
0.752238 | + | 0.658892i | \(0.228975\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −109.724 | −1.32486 | −0.662430 | − | 0.749124i | \(-0.730475\pi\) | ||||
−0.662430 | + | 0.749124i | \(0.730475\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −14.9225 | −0.155064 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 51.0034 | 0.462389 | 0.231195 | − | 0.972908i | \(-0.425737\pi\) | ||||
0.231195 | + | 0.972908i | \(0.425737\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 218.917 | 1.75134 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 98.0530 | 0.698900 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.96376 | 0.0229649 | 0.0114824 | − | 0.999934i | \(-0.496345\pi\) | ||||
0.0114824 | + | 0.999934i | \(0.496345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 131.000 | 0.691036 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 141.630 | 0.683996 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.2588 | 0.183322 | 0.0916610 | − | 0.995790i | \(-0.470782\pi\) | ||||
0.0916610 | + | 0.995790i | \(0.470782\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.3285 | −0.0547249 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.3560 | −0.0699201 | −0.0349600 | − | 0.999389i | \(-0.511130\pi\) | ||||
−0.0349600 | + | 0.999389i | \(0.511130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −61.0816 | −0.216625 | −0.108312 | − | 0.994117i | \(-0.534545\pi\) | ||||
−0.108312 | + | 0.994117i | \(0.534545\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −429.912 | −1.42417 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 77.6986 | 0.241138 | 0.120569 | − | 0.992705i | \(-0.461528\pi\) | ||||
0.120569 | + | 0.992705i | \(0.461528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −284.675 | −0.829955 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −206.049 | −0.565738 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −524.666 | −1.35978 | −0.679891 | − | 0.733313i | \(-0.737973\pi\) | ||||
−0.679891 | + | 0.733313i | \(0.737973\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1243.33 | −3.04819 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 214.394 | 0.498195 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −606.470 | −1.33823 | −0.669116 | − | 0.743158i | \(-0.733327\pi\) | ||||
−0.669116 | + | 0.743158i | \(0.733327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −390.164 | −0.818941 | −0.409471 | − | 0.912323i | \(-0.634287\pi\) | ||||
−0.409471 | + | 0.912323i | \(0.634287\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −177.044 | −0.354055 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 126.502 | 0.241394 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 746.727 | 1.36160 | 0.680800 | − | 0.732469i | \(-0.261632\pi\) | ||||
0.680800 | + | 0.732469i | \(0.261632\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −99.6578 | −0.173875 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 150.049 | 0.250810 | 0.125405 | − | 0.992106i | \(-0.459977\pi\) | ||||
0.125405 | + | 0.992106i | \(0.459977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 707.612 | 1.13452 | 0.567258 | − | 0.823540i | \(-0.308004\pi\) | ||||
0.567258 | + | 0.823540i | \(0.308004\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −427.751 | −0.658566 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −512.022 | −0.757796 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −76.5205 | −0.108978 | −0.0544888 | − | 0.998514i | \(-0.517353\pi\) | ||||
−0.0544888 | + | 0.998514i | \(0.517353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 434.327 | 0.595785 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1173.70 | −1.55217 | −0.776086 | − | 0.630627i | \(-0.782798\pi\) | ||||
−0.776086 | + | 0.630627i | \(0.782798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1955.62 | 2.49550 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −56.6643 | −0.0698282 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1242.33 | −1.47963 | −0.739813 | − | 0.672812i | \(-0.765086\pi\) | ||||
−0.739813 | + | 0.672812i | \(0.765086\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 52.0953 | 0.0600118 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.74495 | −0.00863564 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2034.82 | −2.19756 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1574.55 | −1.64816 | −0.824079 | − | 0.566475i | \(-0.808307\pi\) | ||||
−0.824079 | + | 0.566475i | \(0.808307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1554.22 | 1.57783 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 849.035 | 0.836457 | 0.418228 | − | 0.908342i | \(-0.362651\pi\) | ||||
0.418228 | + | 0.908342i | \(0.362651\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1707.56 | −1.63350 | −0.816752 | − | 0.576988i | \(-0.804228\pi\) | ||||
−0.816752 | + | 0.576988i | \(0.804228\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −276.737 | −0.257208 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −478.551 | −0.432367 | −0.216184 | − | 0.976353i | \(-0.569361\pi\) | ||||
−0.216184 | + | 0.976353i | \(0.569361\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −532.818 | −0.468209 | −0.234104 | − | 0.972211i | \(-0.575216\pi\) | ||||
−0.234104 | + | 0.972211i | \(0.575216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −80.6174 | −0.0689357 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1412.19 | 1.17565 | 0.587823 | − | 0.808990i | \(-0.299985\pi\) | ||||
0.587823 | + | 0.808990i | \(0.299985\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 945.859 | 0.766972 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −158.133 | −0.124952 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 805.355 | 0.620393 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3163.89 | 2.37708 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 35.8665 | 0.0262925 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1741.69 | 1.24625 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1632.35 | −1.14053 | −0.570266 | − | 0.821460i | \(-0.693160\pi\) | ||||
−0.570266 | + | 0.821460i | \(0.693160\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 119.350 | 0.0814587 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1143.85 | −0.762890 | −0.381445 | − | 0.924391i | \(-0.624574\pi\) | ||||
−0.381445 | + | 0.924391i | \(0.624574\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −837.972 | −0.546326 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1818.39 | 1.15928 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −414.515 | −0.258499 | −0.129250 | − | 0.991612i | \(-0.541257\pi\) | ||||
−0.129250 | + | 0.991612i | \(0.541257\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −710.102 | −0.433310 | −0.216655 | − | 0.976248i | \(-0.569515\pi\) | ||||
−0.216655 | + | 0.976248i | \(0.569515\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −151.819 | −0.0906768 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −457.330 | −0.267439 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 537.805 | 0.308016 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 556.238 | 0.312093 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2997.89 | 1.64830 | 0.824149 | − | 0.566373i | \(-0.191654\pi\) | ||||
0.824149 | + | 0.566373i | \(0.191654\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2508.50 | 1.35191 | 0.675955 | − | 0.736943i | \(-0.263731\pi\) | ||||
0.675955 | + | 0.736943i | \(0.263731\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2444.62 | −1.29174 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 73.5078 | 0.0380922 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3686.80 | −1.87413 | −0.937066 | − | 0.349152i | \(-0.886470\pi\) | ||||
−0.937066 | + | 0.349152i | \(0.886470\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1025.17 | 0.511328 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 389.519 | 0.190673 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1949.12 | 0.936605 | 0.468302 | − | 0.883568i | \(-0.344866\pi\) | ||||
0.468302 | + | 0.883568i | \(0.344866\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2429.39 | 1.14623 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −855.533 | −0.396426 | −0.198213 | − | 0.980159i | \(-0.563514\pi\) | ||||
−0.198213 | + | 0.980159i | \(0.563514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2150.47 | −0.978821 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2543.63 | 1.13752 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2725.49 | −1.19777 | −0.598887 | − | 0.800834i | \(-0.704390\pi\) | ||||
−0.598887 | + | 0.800834i | \(0.704390\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1671.89 | 0.722190 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1185.01 | 0.503224 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2447.11 | −1.02182 | −0.510910 | − | 0.859634i | \(-0.670691\pi\) | ||||
−0.510910 | + | 0.859634i | \(0.670691\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2433.45 | 0.999320 | 0.499660 | − | 0.866222i | \(-0.333458\pi\) | ||||
0.499660 | + | 0.866222i | \(0.333458\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 762.359 | 0.307952 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 765.145 | 0.304079 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7069.98 | −2.76475 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 748.841 | 0.288202 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4530.41 | 1.71628 | 0.858138 | − | 0.513419i | \(-0.171621\pi\) | ||||
0.858138 | + | 0.513419i | \(0.171621\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1819.70 | −0.678678 | −0.339339 | − | 0.940664i | \(-0.610203\pi\) | ||||
−0.339339 | + | 0.940664i | \(0.610203\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −247.177 | −0.0907729 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1325.30 | 0.479307 | 0.239653 | − | 0.970859i | \(-0.422966\pi\) | ||||
0.239653 | + | 0.970859i | \(0.422966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −921.014 | −0.328085 | −0.164043 | − | 0.986453i | \(-0.552453\pi\) | ||||
−0.164043 | + | 0.986453i | \(0.552453\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1459.06 | −0.512011 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 221.476 | 0.0765743 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −340.412 | −0.115978 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1182.37 | −0.397006 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7356.31 | 2.43467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −342.370 | −0.111705 | −0.0558525 | − | 0.998439i | \(-0.517788\pi\) | ||||
−0.0558525 | + | 0.998439i | \(0.517788\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −293.186 | −0.0943136 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1132.76 | −0.359318 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.2717 | 0.00946992 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1382.63 | −0.426620 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 719.330 | 0.218947 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4038.47 | 1.21272 | 0.606358 | − | 0.795192i | \(-0.292630\pi\) | ||||
0.606358 | + | 0.795192i | \(0.292630\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5074.96 | −1.50369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2948.69 | −0.862165 | −0.431083 | − | 0.902312i | \(-0.641868\pi\) | ||||
−0.431083 | + | 0.902312i | \(0.641868\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4405.85 | −1.27138 | −0.635692 | − | 0.771943i | \(-0.719285\pi\) | ||||
−0.635692 | + | 0.771943i | \(0.719285\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1000.46 | 0.284959 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4942.11 | −1.38956 | −0.694781 | − | 0.719221i | \(-0.744499\pi\) | ||||
−0.694781 | + | 0.719221i | \(0.744499\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1440.92 | 0.399980 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 149.517 | 0.0409795 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3855.85 | −1.04357 | −0.521787 | − | 0.853076i | \(-0.674734\pi\) | ||||
−0.521787 | + | 0.853076i | \(0.674734\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2496.50 | −0.667275 | −0.333638 | − | 0.942701i | \(-0.608276\pi\) | ||||
−0.333638 | + | 0.942701i | \(0.608276\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3496.08 | −0.922937 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5279.29 | −1.37666 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −748.463 | −0.192808 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2293.34 | 0.583673 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5442.61 | −1.36866 | −0.684332 | − | 0.729170i | \(-0.739906\pi\) | ||||
−0.684332 | + | 0.729170i | \(0.739906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3419.47 | −0.849725 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3821.18 | −0.938397 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3794.51 | 0.920992 | 0.460496 | − | 0.887662i | \(-0.347672\pi\) | ||||
0.460496 | + | 0.887662i | \(0.347672\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 315.098 | 0.0755956 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −672.281 | −0.159437 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5771.07 | −1.35308 | −0.676539 | − | 0.736407i | \(-0.736521\pi\) | ||||
−0.676539 | + | 0.736407i | \(0.736521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9729.93 | −2.25549 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2427.44 | 0.556394 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −433.094 | −0.0981643 | −0.0490822 | − | 0.998795i | \(-0.515630\pi\) | ||||
−0.0490822 | + | 0.998795i | \(0.515630\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4929.23 | −1.10491 | −0.552453 | − | 0.833544i | \(-0.686308\pi\) | ||||
−0.552453 | + | 0.833544i | \(0.686308\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −101.791 | −0.0225666 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14677.1 | −3.21840 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2954.50 | 0.640862 | 0.320431 | − | 0.947272i | \(-0.396172\pi\) | ||||
0.320431 | + | 0.947272i | \(0.396172\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −91.8882 | −0.0197176 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3383.21 | 0.718241 | 0.359120 | − | 0.933291i | \(-0.383077\pi\) | ||||
0.359120 | + | 0.933291i | \(0.383077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5168.89 | 1.08572 | 0.542859 | − | 0.839824i | \(-0.317342\pi\) | ||||
0.542859 | + | 0.839824i | \(0.317342\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3975.93 | 0.826364 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −140.187 | −0.0288326 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6207.31 | 1.26345 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3076.58 | 0.619768 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3081.13 | 0.614340 | 0.307170 | − | 0.951655i | \(-0.400618\pi\) | ||||
0.307170 | + | 0.951655i | \(0.400618\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11247.0 | −2.21974 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6573.86 | −1.28436 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 347.912 | 0.0672919 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −466.487 | −0.0893285 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1658.97 | −0.314538 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7235.60 | −1.35839 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2412.26 | −0.448453 | −0.224227 | − | 0.974537i | \(-0.571986\pi\) | ||||
−0.224227 | + | 0.974537i | \(0.571986\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3336.48 | 0.614257 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9542.56 | −1.73990 | −0.869950 | − | 0.493140i | \(-0.835849\pi\) | ||||
−0.869950 | + | 0.493140i | \(0.835849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2692.28 | 0.486188 | 0.243094 | − | 0.970003i | \(-0.421838\pi\) | ||||
0.243094 | + | 0.970003i | \(0.421838\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3283.29 | −0.587277 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7174.82 | −1.27122 | −0.635612 | − | 0.772009i | \(-0.719252\pi\) | ||||
−0.635612 | + | 0.772009i | \(0.719252\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1944.27 | −0.341249 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 935.062 | 0.162586 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11570.7 | −1.99322 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1493.31 | 0.254873 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1041.10 | 0.176064 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 593.393 | 0.0994371 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9152.83 | 1.51989 | 0.759947 | − | 0.649985i | \(-0.225225\pi\) | ||||
0.759947 | + | 0.649985i | \(0.225225\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −956.467 | −0.157400 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13848.0 | 2.25851 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1319.39 | −0.213269 | −0.106635 | − | 0.994298i | \(-0.534008\pi\) | ||||
−0.106635 | + | 0.994298i | \(0.534008\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2759.35 | −0.442086 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −265.746 | −0.0422022 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4793.62 | −0.754610 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1848.15 | −0.288409 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 274.593 | 0.0424810 | 0.0212405 | − | 0.999774i | \(-0.493238\pi\) | ||||
0.0212405 | + | 0.999774i | \(0.493238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1680.66 | −0.257775 | −0.128887 | − | 0.991659i | \(-0.541141\pi\) | ||||
−0.128887 | + | 0.991659i | \(0.541141\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 668.853 | 0.101711 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8331.96 | 1.25628 | 0.628138 | − | 0.778102i | \(-0.283817\pi\) | ||||
0.628138 | + | 0.778102i | \(0.283817\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2782.65 | 0.416022 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1573.62 | −0.233291 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13073.6 | −1.92200 | −0.960998 | − | 0.276554i | \(-0.910807\pi\) | ||||
−0.960998 | + | 0.276554i | \(0.910807\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5180.28 | 0.755253 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6182.06 | −0.893867 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13122.7 | 1.88184 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5042.03 | −0.717145 | −0.358572 | − | 0.933502i | \(-0.616736\pi\) | ||||
−0.358572 | + | 0.933502i | \(0.616736\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 425.531 | 0.0600332 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4006.94 | −0.560727 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12889.1 | 1.78921 | 0.894603 | − | 0.446861i | \(-0.147458\pi\) | ||||
0.894603 | + | 0.446861i | \(0.147458\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3403.16 | −0.468636 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 197.819 | 0.0270244 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6489.95 | 0.879595 | 0.439798 | − | 0.898097i | \(-0.355050\pi\) | ||||
0.439798 | + | 0.898097i | \(0.355050\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3189.52 | 0.428882 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2537.38 | 0.338522 | 0.169261 | − | 0.985571i | \(-0.445862\pi\) | ||||
0.169261 | + | 0.985571i | \(0.445862\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9495.45 | −1.25697 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1416.00 | 0.185993 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10725.7 | 1.39798 | 0.698989 | − | 0.715132i | \(-0.253634\pi\) | ||||
0.698989 | + | 0.715132i | \(0.253634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5378.46 | 0.695653 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2235.02 | 0.286875 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1419.07 | −0.180763 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14172.8 | −1.79172 | −0.895859 | − | 0.444339i | \(-0.853439\pi\) | ||||
−0.895859 | + | 0.444339i | \(0.853439\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1637.35 | 0.205439 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7984.76 | 0.994363 | 0.497182 | − | 0.867647i | \(-0.334368\pi\) | ||||
0.497182 | + | 0.867647i | \(0.334368\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.0381 | 0.00334210 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8054.59 | 0.988237 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2766.15 | −0.336887 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −227.055 | −0.0274503 | −0.0137251 | − | 0.999906i | \(-0.504369\pi\) | ||||
−0.0137251 | + | 0.999906i | \(0.504369\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 809.938 | 0.0972051 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4631.68 | −0.551840 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21766.3 | −2.57461 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1387.50 | 0.162940 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11876.4 | 1.38472 | 0.692361 | − | 0.721551i | \(-0.256571\pi\) | ||||
0.692361 | + | 0.721551i | \(0.256571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10927.3 | −1.26500 | −0.632499 | − | 0.774561i | \(-0.717971\pi\) | ||||
−0.632499 | + | 0.774561i | \(0.717971\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1801.22 | −0.207041 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23085.4 | 2.63484 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2979.73 | −0.337703 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 893.596 | 0.100567 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1085.02 | 0.121262 | 0.0606308 | − | 0.998160i | \(-0.480689\pi\) | ||||
0.0606308 | + | 0.998160i | \(0.480689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3697.66 | −0.410389 | −0.205194 | − | 0.978721i | \(-0.565783\pi\) | ||||
−0.205194 | + | 0.978721i | \(0.565783\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1050.84 | −0.115825 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5596.28 | −0.612601 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 338.575 | 0.0368093 | 0.0184047 | − | 0.999831i | \(-0.494141\pi\) | ||||
0.0184047 | + | 0.999831i | \(0.494141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6599.36 | 0.712596 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11170.8 | −1.19806 | −0.599028 | − | 0.800728i | \(-0.704446\pi\) | ||||
−0.599028 | + | 0.800728i | \(0.704446\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23039.0 | −2.45428 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5857.70 | −0.619820 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11355.0 | −1.19348 | −0.596741 | − | 0.802434i | \(-0.703538\pi\) | ||||
−0.596741 | + | 0.802434i | \(0.703538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1230.66 | 0.128491 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4901.46 | −0.508368 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 966.108 | 0.0995425 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2057.24 | −0.210577 | −0.105288 | − | 0.994442i | \(-0.533577\pi\) | ||||
−0.105288 | + | 0.994442i | \(0.533577\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10340.0 | 1.05148 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19378.0 | −1.95775 | −0.978876 | − | 0.204456i | \(-0.934457\pi\) | ||||
−0.978876 | + | 0.204456i | \(0.934457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 184.925 | 0.0185620 | 0.00928101 | − | 0.999957i | \(-0.497046\pi\) | ||||
0.00928101 | + | 0.999957i | \(0.497046\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −143.630 | −0.0143241 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14640.0 | 1.45066 | 0.725332 | − | 0.688400i | \(-0.241686\pi\) | ||||
0.725332 | + | 0.688400i | \(0.241686\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5702.84 | 0.561477 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7203.80 | 0.704742 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4095.15 | 0.398087 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24020.4 | −2.32027 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12162.9 | 1.16750 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9831.22 | −0.937786 | −0.468893 | − | 0.883255i | \(-0.655347\pi\) | ||||
−0.468893 | + | 0.883255i | \(0.655347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 281.441 | 0.0266790 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −761.098 | −0.0717001 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29200.0 | −2.73382 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20368.4 | 1.89523 | 0.947617 | − | 0.319408i | \(-0.103484\pi\) | ||||
0.947617 | + | 0.319408i | \(0.103484\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3808.46 | −0.352198 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17333.5 | 1.59318 | 0.796589 | − | 0.604521i | \(-0.206635\pi\) | ||||
0.796589 | + | 0.604521i | \(0.206635\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3058.13 | 0.279374 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28823.0 | 2.61717 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1145.94 | 0.103425 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6797.87 | 0.609849 | 0.304924 | − | 0.952377i | \(-0.401369\pi\) | ||||
0.304924 | + | 0.952377i | \(0.401369\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1671.66 | 0.149071 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12318.5 | 1.09196 | 0.545978 | − | 0.837799i | \(-0.316158\pi\) | ||||
0.545978 | + | 0.837799i | \(0.316158\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15745.3 | 1.38744 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4201.89 | 0.368072 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11321.6 | 0.985896 | 0.492948 | − | 0.870059i | \(-0.335919\pi\) | ||||
0.492948 | + | 0.870059i | \(0.335919\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5404.11 | 0.467835 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10758.7 | −0.925944 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −31666.7 | −2.70952 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5209.22 | −0.443136 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5325.44 | 0.450407 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9789.88 | 0.823229 | 0.411614 | − | 0.911358i | \(-0.364965\pi\) | ||||
0.411614 | + | 0.911358i | \(0.364965\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3258.08 | 0.272401 | 0.136200 | − | 0.990681i | \(-0.456511\pi\) | ||||
0.136200 | + | 0.990681i | \(0.456511\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3266.78 | −0.271570 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 417.990 | 0.0345501 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9565.65 | −0.786196 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14059.3 | 1.14900 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −125.212 | −0.0101755 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8874.73 | −0.717174 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4781.52 | 0.384242 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19085.7 | 1.52519 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13740.7 | 1.09198 | 0.545989 | − | 0.837792i | \(-0.316154\pi\) | ||||
0.545989 | + | 0.837792i | \(0.316154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4754.82 | −0.375781 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9881.11 | −0.776625 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1021.13 | 0.0798178 | 0.0399089 | − | 0.999203i | \(-0.487293\pi\) | ||||
0.0399089 | + | 0.999203i | \(0.487293\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9044.83 | 0.703140 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3181.99 | −0.246020 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −584.396 | −0.0449386 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1495.05 | −0.114345 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4146.36 | −0.315417 | −0.157708 | − | 0.987486i | \(-0.550411\pi\) | ||||
−0.157708 | + | 0.987486i | \(0.550411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −416.658 | −0.0315255 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13814.3 | 1.03965 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 466.827 | 0.0349457 | 0.0174728 | − | 0.999847i | \(-0.494438\pi\) | ||||
0.0174728 | + | 0.999847i | \(0.494438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26189.1 | 1.95006 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3317.00 | 0.245681 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23329.9 | −1.71888 | −0.859438 | − | 0.511239i | \(-0.829187\pi\) | ||||
−0.859438 | + | 0.511239i | \(0.829187\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10730.4 | 0.786431 | 0.393216 | − | 0.919446i | \(-0.371363\pi\) | ||||
0.393216 | + | 0.919446i | \(0.371363\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8852.16 | −0.645382 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11165.5 | 0.809799 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8469.82 | −0.611097 | −0.305549 | − | 0.952176i | \(-0.598840\pi\) | ||||
−0.305549 | + | 0.952176i | \(0.598840\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3555.59 | 0.255208 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8963.67 | −0.640062 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35175.7 | 2.49885 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2932.58 | −0.207260 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 299.884 | 0.0210861 | 0.0105431 | − | 0.999944i | \(-0.496644\pi\) | ||||
0.0105431 | + | 0.999944i | \(0.496644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −434.918 | −0.0304253 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2589.55 | −0.180237 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10265.4 | −0.710873 | −0.355437 | − | 0.934700i | \(-0.615668\pi\) | ||||
−0.355437 | + | 0.934700i | \(0.615668\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14935.3 | 1.02906 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1799.61 | 0.123372 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15166.9 | 1.03456 | 0.517281 | − | 0.855816i | \(-0.326944\pi\) | ||||
0.517281 | + | 0.855816i | \(0.326944\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12237.0 | 0.830546 | 0.415273 | − | 0.909697i | \(-0.363686\pi\) | ||||
0.415273 | + | 0.909697i | \(0.363686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17310.7 | −1.16907 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 58674.3 | 3.94289 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4989.45 | −0.333633 | −0.166817 | − | 0.985988i | \(-0.553349\pi\) | ||||
−0.166817 | + | 0.985988i | \(0.553349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −432.752 | −0.0287947 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 530.008 | 0.0350930 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13819.8 | −0.910566 | −0.455283 | − | 0.890347i | \(-0.650462\pi\) | ||||
−0.455283 | + | 0.890347i | \(0.650462\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 665.145 | 0.0436118 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18400.5 | −1.20061 | −0.600304 | − | 0.799772i | \(-0.704954\pi\) | ||||
−0.600304 | + | 0.799772i | \(0.704954\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10113.9 | −0.656723 | −0.328362 | − | 0.944552i | \(-0.606496\pi\) | ||||
−0.328362 | + | 0.944552i | \(0.606496\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5001.04 | 0.323164 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9487.82 | −0.610147 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4935.00 | 0.315840 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14373.8 | −0.915525 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4350.86 | 0.275803 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2969.78 | −0.187361 | −0.0936806 | − | 0.995602i | \(-0.529863\pi\) | ||||
−0.0936806 | + | 0.995602i | \(0.529863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 668.972 | 0.0420051 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30271.9 | −1.89182 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1941.86 | −0.120784 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3478.44 | −0.215344 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −150.409 | −0.00926804 | −0.00463402 | − | 0.999989i | \(-0.501475\pi\) | ||||
−0.00463402 | + | 0.999989i | \(0.501475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17894.8 | 1.09751 | 0.548756 | − | 0.835983i | \(-0.315102\pi\) | ||||
0.548756 | + | 0.835983i | \(0.315102\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2213.34 | 0.135117 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17611.1 | −1.07012 | −0.535058 | − | 0.844815i | \(-0.679710\pi\) | ||||
−0.535058 | + | 0.844815i | \(0.679710\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40660.1 | 2.45924 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −59.1491 | −0.00356104 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7388.11 | 0.442755 | 0.221378 | − | 0.975188i | \(-0.428945\pi\) | ||||
0.221378 | + | 0.975188i | \(0.428945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21212.7 | −1.26542 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16403.9 | −0.974092 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26209.7 | −1.54929 | −0.774647 | − | 0.632394i | \(-0.782072\pi\) | ||||
−0.774647 | + | 0.632394i | \(0.782072\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2052.04 | −0.120749 | −0.0603745 | − | 0.998176i | \(-0.519230\pi\) | ||||
−0.0603745 | + | 0.998176i | \(0.519230\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1405.53 | −0.0823322 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15540.2 | −0.906199 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1479.10 | 0.0858635 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7890.93 | −0.456026 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26158.2 | 1.50495 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13523.9 | 0.774605 | 0.387303 | − | 0.921953i | \(-0.373407\pi\) | ||||
0.387303 | + | 0.921953i | \(0.373407\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21465.5 | 1.22401 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17142.3 | −0.973161 | −0.486581 | − | 0.873636i | \(-0.661756\pi\) | ||||
−0.486581 | + | 0.873636i | \(0.661756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12025.0 | −0.679643 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5761.57 | 0.324206 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1380.52 | 0.0773412 | 0.0386706 | − | 0.999252i | \(-0.487688\pi\) | ||||
0.0386706 | + | 0.999252i | \(0.487688\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7687.18 | −0.428777 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8608.78 | 0.478087 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3578.93 | −0.197890 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20983.5 | 1.15521 | 0.577605 | − | 0.816316i | \(-0.303987\pi\) | ||||
0.577605 | + | 0.816316i | \(0.303987\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11869.8 | 0.650641 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13168.8 | −0.718737 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1935.69 | −0.105193 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9656.59 | 0.522526 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21041.5 | 1.13370 | 0.566852 | − | 0.823820i | \(-0.308161\pi\) | ||||
0.566852 | + | 0.823820i | \(0.308161\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4527.07 | −0.242876 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2815.47 | −0.150407 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6484.17 | 0.344926 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31968.5 | 1.69338 | 0.846688 | − | 0.532090i | \(-0.178593\pi\) | ||||
0.846688 | + | 0.532090i | \(0.178593\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1773.91 | 0.0935678 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 202.165 | 0.0106187 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8481.18 | −0.443606 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7534.10 | 0.392422 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19937.6 | −1.03414 | −0.517070 | − | 0.855943i | \(-0.672977\pi\) | ||||
−0.517070 | + | 0.855943i | \(0.672977\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13040.8 | −0.673601 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4878.01 | 0.250920 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6348.59 | 0.325215 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3277.64 | 0.167209 | 0.0836046 | − | 0.996499i | \(-0.473357\pi\) | ||||
0.0836046 | + | 0.996499i | \(0.473357\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4895.69 | −0.248727 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6441.23 | −0.325906 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13185.3 | −0.664405 | −0.332203 | − | 0.943208i | \(-0.607792\pi\) | ||||
−0.332203 | + | 0.943208i | \(0.607792\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10315.4 | 0.517674 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50063.5 | −2.50219 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 877.219 | 0.0436658 | 0.0218329 | − | 0.999762i | \(-0.493050\pi\) | ||||
0.0218329 | + | 0.999762i | \(0.493050\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1462.45 | 0.0725028 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22616.9 | 1.11674 | 0.558368 | − | 0.829593i | \(-0.311428\pi\) | ||||
0.558368 | + | 0.829593i | \(0.311428\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55595.8 | 2.73406 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27208.8 | 1.33269 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3654.75 | −0.178293 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4283.99 | 0.208156 | 0.104078 | − | 0.994569i | \(-0.466811\pi\) | ||||
0.104078 | + | 0.994569i | \(0.466811\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10634.6 | 0.514668 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46520.1 | 2.24243 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2313.30 | −0.111068 | −0.0555339 | − | 0.998457i | \(-0.517686\pi\) | ||||
−0.0555339 | + | 0.998457i | \(0.517686\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6681.45 | 0.319527 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11861.2 | −0.565006 | −0.282503 | − | 0.959266i | \(-0.591165\pi\) | ||||
−0.282503 | + | 0.959266i | \(0.591165\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4069.19 | −0.193073 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −45335.5 | −2.14262 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4136.94 | −0.194754 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5533.00 | −0.259460 | −0.129730 | − | 0.991549i | \(-0.541411\pi\) | ||||
−0.129730 | + | 0.991549i | \(0.541411\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7414.25 | −0.346326 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4550.04 | 0.211712 | 0.105856 | − | 0.994381i | \(-0.466242\pi\) | ||||
0.105856 | + | 0.994381i | \(0.466242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 867.733 | 0.0402192 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −615.684 | −0.0284267 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2014.09 | 0.0926343 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10059.8 | −0.460909 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2843.54 | 0.129782 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −68371.7 | −3.10865 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30380.6 | −1.37605 | −0.688025 | − | 0.725687i | \(-0.741522\pi\) | ||||
−0.688025 | + | 0.725687i | \(0.741522\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11276.3 | 0.508806 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10785.1 | 0.484796 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2661.44 | −0.119181 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19011.7 | 0.848147 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10663.5 | −0.473926 | −0.236963 | − | 0.971519i | \(-0.576152\pi\) | ||||
−0.236963 | + | 0.971519i | \(0.576152\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8193.54 | 0.362787 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28799.8 | 1.27040 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −47441.1 | −2.08488 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7223.63 | 0.316273 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 846.241 | 0.0369134 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17366.0 | 0.754706 | 0.377353 | − | 0.926069i | \(-0.376834\pi\) | ||||
0.377353 | + | 0.926069i | \(0.376834\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36870.4 | 1.59642 | 0.798209 | − | 0.602381i | \(-0.205781\pi\) | ||||
0.798209 | + | 0.602381i | \(0.205781\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9631.44 | 0.415485 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36146.4 | 1.55356 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6702.10 | 0.286997 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1207.68 | −0.0515260 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18414.0 | 0.782769 | 0.391385 | − | 0.920227i | \(-0.371996\pi\) | ||||
0.391385 | + | 0.920227i | \(0.371996\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10266.0 | −0.434813 | −0.217406 | − | 0.976081i | \(-0.569760\pi\) | ||||
−0.217406 | + | 0.976081i | \(0.569760\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28678.1 | 1.21023 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9632.80 | 0.405036 | 0.202518 | − | 0.979278i | \(-0.435087\pi\) | ||||
0.202518 | + | 0.979278i | \(0.435087\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1547.06 | 0.0648150 | 0.0324075 | − | 0.999475i | \(-0.489683\pi\) | ||||
0.0324075 | + | 0.999475i | \(0.489683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5772.93 | −0.240988 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30019.7 | −1.24865 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15865.9 | −0.657558 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 388.658 | 0.0160502 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30042.2 | 1.23620 | 0.618100 | − | 0.786100i | \(-0.287903\pi\) | ||||
0.618100 | + | 0.786100i | \(0.287903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6610.61 | −0.270085 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −39880.4 | −1.62358 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24163.0 | 0.980224 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10099.7 | −0.408270 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2104.34 | 0.0847661 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20127.2 | −0.807903 | −0.403951 | − | 0.914780i | \(-0.632363\pi\) | ||||
−0.403951 | + | 0.914780i | \(0.632363\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 47171.5 | 1.88682 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27981.2 | 1.11531 | 0.557655 | − | 0.830073i | \(-0.311701\pi\) | ||||
0.557655 | + | 0.830073i | \(0.311701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21727.5 | −0.863018 | −0.431509 | − | 0.902109i | \(-0.642019\pi\) | ||||
−0.431509 | + | 0.902109i | \(0.642019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 273.917 | 0.0108421 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22813.4 | 0.899858 | 0.449929 | − | 0.893064i | \(-0.351449\pi\) | ||||
0.449929 | + | 0.893064i | \(0.351449\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50544.1 | −1.98677 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12128.7 | −0.475102 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5130.24 | 0.200266 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5093.68 | 0.198155 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36501.4 | 1.41510 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13301.5 | 0.513911 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13995.8 | −0.538886 | −0.269443 | − | 0.963016i | \(-0.586840\pi\) | ||||
−0.269443 | + | 0.963016i | \(0.586840\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6020.35 | −0.231014 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31340.0 | −1.19849 | −0.599247 | − | 0.800564i | \(-0.704533\pi\) | ||||
−0.599247 | + | 0.800564i | \(0.704533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3532.88 | −0.134644 | −0.0673221 | − | 0.997731i | \(-0.521446\pi\) | ||||
−0.0673221 | + | 0.997731i | \(0.521446\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21976.0 | 0.834705 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19969.1 | −0.755916 | −0.377958 | − | 0.925823i | \(-0.623374\pi\) | ||||
−0.377958 | + | 0.925823i | \(0.623374\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12466.4 | −0.470316 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29119.0 | −1.09486 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8525.37 | −0.319474 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −45381.7 | −1.69491 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −679.800 | −0.0253042 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 114.949 | 0.00426447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −55327.6 | −2.04576 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 911.489 | 0.0335908 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45128.3 | 1.65759 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28674.1 | 1.04973 | 0.524867 | − | 0.851184i | \(-0.324115\pi\) | ||||
0.524867 | + | 0.851184i | \(0.324115\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19682.4 | −0.718179 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10404.6 | −0.378397 | −0.189199 | − | 0.981939i | \(-0.560589\pi\) | ||||
−0.189199 | + | 0.981939i | \(0.560589\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 78689.4 | 2.85240 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14137.9 | 0.510804 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8735.71 | −0.314590 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51963.1 | −1.86519 | −0.932593 | − | 0.360930i | \(-0.882459\pi\) | ||||
−0.932593 | + | 0.360930i | \(0.882459\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4713.42 | 0.168635 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1023.53 | 0.0365005 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9032.26 | 0.321058 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 39584.9 | 1.40252 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19454.4 | −0.687059 | −0.343530 | − | 0.939142i | \(-0.611623\pi\) | ||||
−0.343530 | + | 0.939142i | \(0.611623\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31235.5 | 1.09957 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18645.6 | 0.654266 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −131113. | −4.58593 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40950.3 | −1.42773 | −0.713867 | − | 0.700281i | \(-0.753058\pi\) | ||||
−0.713867 | + | 0.700281i | \(0.753058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5260.56 | −0.182824 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31672.6 | −1.09723 | −0.548617 | − | 0.836074i | \(-0.684845\pi\) | ||||
−0.548617 | + | 0.836074i | \(0.684845\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −936.219 | −0.0323303 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13887.3 | 0.478045 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15659.5 | −0.537343 | −0.268671 | − | 0.963232i | \(-0.586585\pi\) | ||||
−0.268671 | + | 0.963232i | \(0.586585\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4826.86 | 0.165107 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14019.2 | 0.478027 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32414.0 | 1.10178 | 0.550888 | − | 0.834579i | \(-0.314289\pi\) | ||||
0.550888 | + | 0.834579i | \(0.314289\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 84016.4 | 2.84681 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3799.00 | 0.128322 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3165.70 | −0.106596 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29775.3 | −0.999473 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11093.8 | 0.371229 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33746.3 | −1.12573 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53609.9 | 1.78281 | 0.891406 | − | 0.453207i | \(-0.149720\pi\) | ||||
0.891406 | + | 0.453207i | \(0.149720\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22608.4 | 0.749523 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50535.9 | −1.67021 | −0.835106 | − | 0.550090i | \(-0.814593\pi\) | ||||
−0.835106 | + | 0.550090i | \(0.814593\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5423.13 | −0.178682 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2917.84 | −0.0958416 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46165.9 | 1.51175 | 0.755874 | − | 0.654718i | \(-0.227212\pi\) | ||||
0.755874 | + | 0.654718i | \(0.227212\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 83290.7 | 2.71908 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12351.9 | 0.402002 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11758.6 | −0.381526 | −0.190763 | − | 0.981636i | \(-0.561096\pi\) | ||||
−0.190763 | + | 0.981636i | \(0.561096\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24577.6 | 0.795033 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1159.45 | −0.0373920 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3115.37 | −0.100165 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49542.4 | 1.58806 | 0.794030 | − | 0.607879i | \(-0.207979\pi\) | ||||
0.794030 | + | 0.607879i | \(0.207979\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17884.1 | −0.571536 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17080.2 | −0.544200 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23095.8 | −0.733651 | −0.366826 | − | 0.930290i | \(-0.619555\pi\) | ||||
−0.366826 | + | 0.930290i | \(0.619555\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4045.55 | 0.128124 |
(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 | 1856.4.a.q.1.2 | 3 | ||
4.3 | odd | 2 | 1856.4.a.t.1.2 | 3 | |||
8.3 | odd | 2 | 464.4.a.h.1.2 | 3 | |||
8.5 | even | 2 | 232.4.a.a.1.2 | ✓ | 3 | ||
24.5 | odd | 2 | 2088.4.a.a.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.a.1.2 | ✓ | 3 | 8.5 | even | 2 | ||
464.4.a.h.1.2 | 3 | 8.3 | odd | 2 | |||
1856.4.a.q.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1856.4.a.t.1.2 | 3 | 4.3 | odd | 2 | |||
2088.4.a.a.1.3 | 3 | 24.5 | odd | 2 |