Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 46x^{7} + 145x^{6} + 680x^{5} - 1501x^{4} - 3203x^{3} + 4784x^{2} + 3584x - 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | no (minimal twist has level 169) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(4.83438\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.83438 | 1.35566 | 0.677829 | − | 0.735219i | \(-0.262921\pi\) | ||||
0.677829 | + | 0.735219i | \(0.262921\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.70249 | 0.837811 | ||||||||
\(5\) | −11.3710 | −1.01705 | −0.508527 | − | 0.861046i | \(-0.669810\pi\) | ||||
−0.508527 | + | 0.861046i | \(0.669810\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 31.0623 | 1.67721 | 0.838603 | − | 0.544744i | \(-0.183373\pi\) | ||||
0.838603 | + | 0.544744i | \(0.183373\pi\) | |||||||
\(8\) | −4.97517 | −0.219873 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −43.6008 | −1.37878 | ||||||||
\(11\) | 20.9478 | 0.574182 | 0.287091 | − | 0.957903i | \(-0.407312\pi\) | ||||
0.287091 | + | 0.957903i | \(0.407312\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 119.105 | 2.27372 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −72.6966 | −1.13588 | ||||||||
\(17\) | −114.389 | −1.63196 | −0.815980 | − | 0.578080i | \(-0.803802\pi\) | ||||
−0.815980 | + | 0.578080i | \(0.803802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −45.1768 | −0.545488 | −0.272744 | − | 0.962087i | \(-0.587931\pi\) | ||||
−0.272744 | + | 0.962087i | \(0.587931\pi\) | |||||||
\(20\) | −76.2140 | −0.852098 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 80.3219 | 0.778395 | ||||||||
\(23\) | −73.9590 | −0.670501 | −0.335250 | − | 0.942129i | \(-0.608821\pi\) | ||||
−0.335250 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.29980 | 0.0343984 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 208.194 | 1.40518 | ||||||||
\(29\) | 27.2113 | 0.174242 | 0.0871208 | − | 0.996198i | \(-0.472233\pi\) | ||||
0.0871208 | + | 0.996198i | \(0.472233\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 179.587 | 1.04048 | 0.520239 | − | 0.854021i | \(-0.325843\pi\) | ||||
0.520239 | + | 0.854021i | \(0.325843\pi\) | |||||||
\(32\) | −238.945 | −1.32000 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −438.610 | −2.21238 | ||||||||
\(35\) | −353.209 | −1.70581 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 354.736 | 1.57617 | 0.788085 | − | 0.615567i | \(-0.211073\pi\) | ||||
0.788085 | + | 0.615567i | \(0.211073\pi\) | |||||||
\(38\) | −173.225 | −0.739496 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 56.5727 | 0.223623 | ||||||||
\(41\) | −81.4187 | −0.310133 | −0.155067 | − | 0.987904i | \(-0.549559\pi\) | ||||
−0.155067 | + | 0.987904i | \(0.549559\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −256.018 | −0.907962 | −0.453981 | − | 0.891011i | \(-0.649997\pi\) | ||||
−0.453981 | + | 0.891011i | \(0.649997\pi\) | |||||||
\(44\) | 140.402 | 0.481056 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −283.587 | −0.908970 | ||||||||
\(47\) | −463.501 | −1.43848 | −0.719240 | − | 0.694762i | \(-0.755510\pi\) | ||||
−0.719240 | + | 0.694762i | \(0.755510\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 621.865 | 1.81302 | ||||||||
\(50\) | 16.4871 | 0.0466325 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −76.6055 | −0.198539 | −0.0992695 | − | 0.995061i | \(-0.531651\pi\) | ||||
−0.0992695 | + | 0.995061i | \(0.531651\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −238.198 | −0.583974 | ||||||||
\(56\) | −154.540 | −0.368773 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 104.338 | 0.236212 | ||||||||
\(59\) | −54.4676 | −0.120188 | −0.0600939 | − | 0.998193i | \(-0.519140\pi\) | ||||
−0.0600939 | + | 0.998193i | \(0.519140\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −494.496 | −1.03793 | −0.518965 | − | 0.854795i | \(-0.673683\pi\) | ||||
−0.518965 | + | 0.854795i | \(0.673683\pi\) | |||||||
\(62\) | 688.606 | 1.41053 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −334.634 | −0.653582 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −611.991 | −1.11592 | −0.557960 | − | 0.829868i | \(-0.688416\pi\) | ||||
−0.557960 | + | 0.829868i | \(0.688416\pi\) | |||||||
\(68\) | −766.688 | −1.36727 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1354.34 | −2.31249 | ||||||||
\(71\) | −16.3056 | −0.0272551 | −0.0136276 | − | 0.999907i | \(-0.504338\pi\) | ||||
−0.0136276 | + | 0.999907i | \(0.504338\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 321.825 | 0.515983 | 0.257992 | − | 0.966147i | \(-0.416939\pi\) | ||||
0.257992 | + | 0.966147i | \(0.416939\pi\) | |||||||
\(74\) | 1360.19 | 2.13675 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −302.797 | −0.457016 | ||||||||
\(77\) | 650.686 | 0.963021 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 385.324 | 0.548764 | 0.274382 | − | 0.961621i | \(-0.411527\pi\) | ||||
0.274382 | + | 0.961621i | \(0.411527\pi\) | |||||||
\(80\) | 826.633 | 1.15526 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −312.190 | −0.420435 | ||||||||
\(83\) | −663.760 | −0.877797 | −0.438899 | − | 0.898537i | \(-0.644631\pi\) | ||||
−0.438899 | + | 0.898537i | \(0.644631\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1300.71 | 1.65979 | ||||||||
\(86\) | −981.671 | −1.23089 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −104.219 | −0.126247 | ||||||||
\(89\) | −545.723 | −0.649961 | −0.324980 | − | 0.945721i | \(-0.605358\pi\) | ||||
−0.324980 | + | 0.945721i | \(0.605358\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −495.709 | −0.561753 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1777.24 | −1.95009 | ||||||||
\(95\) | 513.706 | 0.554791 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −689.189 | −0.721408 | −0.360704 | − | 0.932680i | \(-0.617464\pi\) | ||||
−0.360704 | + | 0.932680i | \(0.617464\pi\) | |||||||
\(98\) | 2384.47 | 2.45783 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 28.8194 | 0.0288194 | ||||||||
\(101\) | −471.398 | −0.464414 | −0.232207 | − | 0.972666i | \(-0.574595\pi\) | ||||
−0.232207 | + | 0.972666i | \(0.574595\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −335.521 | −0.320970 | −0.160485 | − | 0.987038i | \(-0.551306\pi\) | ||||
−0.160485 | + | 0.987038i | \(0.551306\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −293.735 | −0.269151 | ||||||||
\(107\) | −1629.26 | −1.47203 | −0.736014 | − | 0.676967i | \(-0.763294\pi\) | ||||
−0.736014 | + | 0.676967i | \(0.763294\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1518.95 | −1.33476 | −0.667381 | − | 0.744717i | \(-0.732585\pi\) | ||||
−0.667381 | + | 0.744717i | \(0.732585\pi\) | |||||||
\(110\) | −913.341 | −0.791669 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2258.12 | −1.90511 | ||||||||
\(113\) | −1195.41 | −0.995173 | −0.497586 | − | 0.867414i | \(-0.665780\pi\) | ||||
−0.497586 | + | 0.867414i | \(0.665780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 840.988 | 0.681935 | ||||||||
\(116\) | 182.383 | 0.145982 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −208.850 | −0.162934 | ||||||||
\(119\) | −3553.17 | −2.73713 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −892.190 | −0.670315 | ||||||||
\(122\) | −1896.09 | −1.40708 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1203.68 | 0.871723 | ||||||||
\(125\) | 1372.48 | 0.982069 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 526.425 | 0.367816 | 0.183908 | − | 0.982943i | \(-0.441125\pi\) | ||||
0.183908 | + | 0.982943i | \(0.441125\pi\) | |||||||
\(128\) | 628.446 | 0.433963 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 834.024 | 0.556252 | 0.278126 | − | 0.960545i | \(-0.410287\pi\) | ||||
0.278126 | + | 0.960545i | \(0.410287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1403.30 | −0.914896 | ||||||||
\(134\) | −2346.61 | −1.51281 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 569.103 | 0.358825 | ||||||||
\(137\) | 466.762 | 0.291082 | 0.145541 | − | 0.989352i | \(-0.453508\pi\) | ||||
0.145541 | + | 0.989352i | \(0.453508\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −713.080 | −0.435127 | −0.217563 | − | 0.976046i | \(-0.569811\pi\) | ||||
−0.217563 | + | 0.976046i | \(0.569811\pi\) | |||||||
\(140\) | −2367.38 | −1.42914 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −62.5218 | −0.0369487 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −309.420 | −0.177213 | ||||||||
\(146\) | 1234.00 | 0.699497 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2377.61 | 1.32053 | ||||||||
\(149\) | −662.814 | −0.364428 | −0.182214 | − | 0.983259i | \(-0.558326\pi\) | ||||
−0.182214 | + | 0.983259i | \(0.558326\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 190.862 | 0.102862 | 0.0514310 | − | 0.998677i | \(-0.483622\pi\) | ||||
0.0514310 | + | 0.998677i | \(0.483622\pi\) | |||||||
\(152\) | 224.762 | 0.119938 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2494.98 | 1.30553 | ||||||||
\(155\) | −2042.09 | −1.05822 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2833.96 | −1.44060 | −0.720302 | − | 0.693661i | \(-0.755997\pi\) | ||||
−0.720302 | + | 0.693661i | \(0.755997\pi\) | |||||||
\(158\) | 1477.48 | 0.743937 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2717.05 | 1.34251 | ||||||||
\(161\) | −2297.34 | −1.12457 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3565.55 | 1.71334 | 0.856672 | − | 0.515861i | \(-0.172528\pi\) | ||||
0.856672 | + | 0.515861i | \(0.172528\pi\) | |||||||
\(164\) | −545.708 | −0.259833 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2545.11 | −1.18999 | ||||||||
\(167\) | 120.630 | 0.0558959 | 0.0279480 | − | 0.999609i | \(-0.491103\pi\) | ||||
0.0279480 | + | 0.999609i | \(0.491103\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4987.44 | 2.25011 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1715.96 | −0.760700 | ||||||||
\(173\) | 2080.28 | 0.914223 | 0.457112 | − | 0.889409i | \(-0.348884\pi\) | ||||
0.457112 | + | 0.889409i | \(0.348884\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 133.562 | 0.0576932 | ||||||||
\(176\) | −1522.83 | −0.652204 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2092.51 | −0.881125 | ||||||||
\(179\) | 553.140 | 0.230970 | 0.115485 | − | 0.993309i | \(-0.463158\pi\) | ||||
0.115485 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3305.19 | −1.35731 | −0.678655 | − | 0.734457i | \(-0.737437\pi\) | ||||
−0.678655 | + | 0.734457i | \(0.737437\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 367.958 | 0.147425 | ||||||||
\(185\) | −4033.71 | −1.60305 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2396.19 | −0.937042 | ||||||||
\(188\) | −3106.61 | −1.20517 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1969.75 | 0.752107 | ||||||||
\(191\) | 3318.14 | 1.25703 | 0.628514 | − | 0.777798i | \(-0.283664\pi\) | ||||
0.628514 | + | 0.777798i | \(0.283664\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3902.18 | −1.45536 | −0.727681 | − | 0.685916i | \(-0.759402\pi\) | ||||
−0.727681 | + | 0.685916i | \(0.759402\pi\) | |||||||
\(194\) | −2642.61 | −0.977983 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4168.04 | 1.51897 | ||||||||
\(197\) | 3632.99 | 1.31391 | 0.656953 | − | 0.753932i | \(-0.271845\pi\) | ||||
0.656953 | + | 0.753932i | \(0.271845\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2957.23 | 1.05343 | 0.526715 | − | 0.850042i | \(-0.323424\pi\) | ||||
0.526715 | + | 0.850042i | \(0.323424\pi\) | |||||||
\(200\) | −21.3922 | −0.00756330 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1807.52 | −0.629587 | ||||||||
\(203\) | 845.245 | 0.292239 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 925.813 | 0.315422 | ||||||||
\(206\) | −1286.52 | −0.435125 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −946.355 | −0.313209 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3194.05 | −1.04212 | −0.521061 | − | 0.853520i | \(-0.674464\pi\) | ||||
−0.521061 | + | 0.853520i | \(0.674464\pi\) | |||||||
\(212\) | −513.447 | −0.166338 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6247.22 | −1.99557 | ||||||||
\(215\) | 2911.18 | 0.923446 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5578.39 | 1.74509 | ||||||||
\(218\) | −5824.23 | −1.80948 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1596.52 | −0.489259 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 75.1092 | 0.0225546 | 0.0112773 | − | 0.999936i | \(-0.496410\pi\) | ||||
0.0112773 | + | 0.999936i | \(0.496410\pi\) | |||||||
\(224\) | −7422.18 | −2.21391 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4583.65 | −1.34911 | ||||||||
\(227\) | −4322.79 | −1.26394 | −0.631968 | − | 0.774995i | \(-0.717752\pi\) | ||||
−0.631968 | + | 0.774995i | \(0.717752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −677.923 | −0.195626 | −0.0978132 | − | 0.995205i | \(-0.531185\pi\) | ||||
−0.0978132 | + | 0.995205i | \(0.531185\pi\) | |||||||
\(230\) | 3224.67 | 0.924472 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −135.381 | −0.0383111 | ||||||||
\(233\) | −92.9061 | −0.0261222 | −0.0130611 | − | 0.999915i | \(-0.504158\pi\) | ||||
−0.0130611 | + | 0.999915i | \(0.504158\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5270.47 | 1.46301 | ||||||||
\(236\) | −365.068 | −0.100695 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −13624.2 | −3.71062 | ||||||||
\(239\) | 2082.56 | 0.563638 | 0.281819 | − | 0.959468i | \(-0.409062\pi\) | ||||
0.281819 | + | 0.959468i | \(0.409062\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6541.25 | −1.74838 | −0.874189 | − | 0.485586i | \(-0.838606\pi\) | ||||
−0.874189 | + | 0.485586i | \(0.838606\pi\) | |||||||
\(242\) | −3421.00 | −0.908719 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3314.35 | −0.869589 | ||||||||
\(245\) | −7071.23 | −1.84394 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −893.476 | −0.228773 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5262.62 | 1.33135 | ||||||||
\(251\) | 2409.29 | 0.605868 | 0.302934 | − | 0.953012i | \(-0.402034\pi\) | ||||
0.302934 | + | 0.953012i | \(0.402034\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1549.28 | −0.384989 | ||||||||
\(254\) | 2018.51 | 0.498633 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5086.77 | 1.24189 | ||||||||
\(257\) | 263.587 | 0.0639770 | 0.0319885 | − | 0.999488i | \(-0.489816\pi\) | ||||
0.0319885 | + | 0.999488i | \(0.489816\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11018.9 | 2.64356 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3197.97 | 0.754088 | ||||||||
\(263\) | 7324.62 | 1.71732 | 0.858660 | − | 0.512545i | \(-0.171297\pi\) | ||||
0.858660 | + | 0.512545i | \(0.171297\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 871.081 | 0.201925 | ||||||||
\(266\) | −5380.77 | −1.24029 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4101.86 | −0.934930 | ||||||||
\(269\) | 4683.37 | 1.06152 | 0.530762 | − | 0.847521i | \(-0.321906\pi\) | ||||
0.530762 | + | 0.847521i | \(0.321906\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1629.37 | −0.365231 | −0.182615 | − | 0.983184i | \(-0.558456\pi\) | ||||
−0.182615 | + | 0.983184i | \(0.558456\pi\) | |||||||
\(272\) | 8315.66 | 1.85372 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1789.75 | 0.394608 | ||||||||
\(275\) | 90.0714 | 0.0197510 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6200.66 | 1.34499 | 0.672494 | − | 0.740103i | \(-0.265223\pi\) | ||||
0.672494 | + | 0.740103i | \(0.265223\pi\) | |||||||
\(278\) | −2734.22 | −0.589883 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1757.28 | 0.375062 | ||||||||
\(281\) | −2951.26 | −0.626538 | −0.313269 | − | 0.949664i | \(-0.601424\pi\) | ||||
−0.313269 | + | 0.949664i | \(0.601424\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5249.17 | 1.10258 | 0.551291 | − | 0.834313i | \(-0.314135\pi\) | ||||
0.551291 | + | 0.834313i | \(0.314135\pi\) | |||||||
\(284\) | −109.288 | −0.0228346 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2529.05 | −0.520157 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8171.77 | 1.66330 | ||||||||
\(290\) | −1186.43 | −0.240241 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2157.03 | 0.432296 | ||||||||
\(293\) | 2912.33 | 0.580684 | 0.290342 | − | 0.956923i | \(-0.406231\pi\) | ||||
0.290342 | + | 0.956923i | \(0.406231\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 619.352 | 0.122237 | ||||||||
\(296\) | −1764.87 | −0.346558 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2541.48 | −0.494040 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7952.50 | −1.52284 | ||||||||
\(302\) | 731.840 | 0.139446 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3284.20 | 0.619611 | ||||||||
\(305\) | 5622.92 | 1.05563 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5000.10 | 0.929546 | 0.464773 | − | 0.885430i | \(-0.346136\pi\) | ||||
0.464773 | + | 0.885430i | \(0.346136\pi\) | |||||||
\(308\) | 4361.22 | 0.806829 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7830.14 | −1.43459 | ||||||||
\(311\) | 7840.94 | 1.42964 | 0.714822 | − | 0.699307i | \(-0.246508\pi\) | ||||
0.714822 | + | 0.699307i | \(0.246508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7518.43 | −1.35772 | −0.678860 | − | 0.734267i | \(-0.737526\pi\) | ||||
−0.678860 | + | 0.734267i | \(0.737526\pi\) | |||||||
\(314\) | −10866.5 | −1.95297 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2582.63 | 0.459761 | ||||||||
\(317\) | −485.238 | −0.0859738 | −0.0429869 | − | 0.999076i | \(-0.513687\pi\) | ||||
−0.0429869 | + | 0.999076i | \(0.513687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 570.017 | 0.100046 | ||||||||
\(320\) | 3805.13 | 0.664728 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8808.86 | −1.52453 | ||||||||
\(323\) | 5167.72 | 0.890215 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13671.7 | 2.32271 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 405.072 | 0.0681901 | ||||||||
\(329\) | −14397.4 | −2.41263 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8222.88 | 1.36547 | 0.682735 | − | 0.730666i | \(-0.260790\pi\) | ||||
0.682735 | + | 0.730666i | \(0.260790\pi\) | |||||||
\(332\) | −4448.84 | −0.735428 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 462.541 | 0.0757758 | ||||||||
\(335\) | 6958.96 | 1.13495 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7744.78 | 1.25188 | 0.625942 | − | 0.779870i | \(-0.284715\pi\) | ||||
0.625942 | + | 0.779870i | \(0.284715\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8718.02 | 1.39059 | ||||||||
\(341\) | 3761.96 | 0.597423 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8662.19 | 1.36360 | ||||||||
\(344\) | 1273.73 | 0.199637 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7976.58 | 1.23937 | ||||||||
\(347\) | 3532.61 | 0.546514 | 0.273257 | − | 0.961941i | \(-0.411899\pi\) | ||||
0.273257 | + | 0.961941i | \(0.411899\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3366.19 | 0.516298 | 0.258149 | − | 0.966105i | \(-0.416888\pi\) | ||||
0.258149 | + | 0.966105i | \(0.416888\pi\) | |||||||
\(350\) | 512.127 | 0.0782123 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5005.37 | −0.757919 | ||||||||
\(353\) | 9967.98 | 1.50295 | 0.751476 | − | 0.659761i | \(-0.229342\pi\) | ||||
0.751476 | + | 0.659761i | \(0.229342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 185.411 | 0.0277199 | ||||||||
\(356\) | −3657.70 | −0.544544 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2120.95 | 0.313117 | ||||||||
\(359\) | −2742.72 | −0.403219 | −0.201609 | − | 0.979466i | \(-0.564617\pi\) | ||||
−0.201609 | + | 0.979466i | \(0.564617\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4818.05 | −0.702443 | ||||||||
\(362\) | −12673.4 | −1.84005 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3659.47 | −0.524783 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1641.86 | −0.233527 | −0.116763 | − | 0.993160i | \(-0.537252\pi\) | ||||
−0.116763 | + | 0.993160i | \(0.537252\pi\) | |||||||
\(368\) | 5376.57 | 0.761611 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15466.8 | −2.17319 | ||||||||
\(371\) | −2379.54 | −0.332991 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11207.5 | 1.55577 | 0.777887 | − | 0.628404i | \(-0.216291\pi\) | ||||
0.777887 | + | 0.628404i | \(0.216291\pi\) | |||||||
\(374\) | −9187.91 | −1.27031 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2306.00 | 0.316284 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3844.47 | 0.521048 | 0.260524 | − | 0.965467i | \(-0.416105\pi\) | ||||
0.260524 | + | 0.965467i | \(0.416105\pi\) | |||||||
\(380\) | 3443.11 | 0.464810 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12723.0 | 1.70410 | ||||||||
\(383\) | −12154.3 | −1.62156 | −0.810778 | − | 0.585354i | \(-0.800955\pi\) | ||||
−0.810778 | + | 0.585354i | \(0.800955\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7398.96 | −0.979444 | ||||||||
\(386\) | −14962.4 | −1.97297 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4619.28 | −0.604403 | ||||||||
\(389\) | 5269.41 | 0.686812 | 0.343406 | − | 0.939187i | \(-0.388419\pi\) | ||||
0.343406 | + | 0.939187i | \(0.388419\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8460.07 | 1.09423 | ||||||||
\(392\) | −3093.88 | −0.398634 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13930.3 | 1.78121 | ||||||||
\(395\) | −4381.53 | −0.558123 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 655.483 | 0.0828659 | 0.0414329 | − | 0.999141i | \(-0.486808\pi\) | ||||
0.0414329 | + | 0.999141i | \(0.486808\pi\) | |||||||
\(398\) | 11339.2 | 1.42809 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −312.581 | −0.0390726 | ||||||||
\(401\) | −7699.97 | −0.958898 | −0.479449 | − | 0.877570i | \(-0.659163\pi\) | ||||
−0.479449 | + | 0.877570i | \(0.659163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3159.53 | −0.389091 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3240.99 | 0.396177 | ||||||||
\(407\) | 7430.94 | 0.905008 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −555.201 | −0.0671220 | −0.0335610 | − | 0.999437i | \(-0.510685\pi\) | ||||
−0.0335610 | + | 0.999437i | \(0.510685\pi\) | |||||||
\(410\) | 3549.92 | 0.427605 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2248.83 | −0.268912 | ||||||||
\(413\) | −1691.89 | −0.201580 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7547.62 | 0.892767 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3628.69 | −0.424605 | ||||||||
\(419\) | −3316.99 | −0.386744 | −0.193372 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193372 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13270.3 | −1.53623 | −0.768117 | − | 0.640310i | \(-0.778806\pi\) | ||||
−0.768117 | + | 0.640310i | \(0.778806\pi\) | |||||||
\(422\) | −12247.2 | −1.41276 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 381.125 | 0.0436535 | ||||||||
\(425\) | −491.849 | −0.0561369 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15360.2 | −1.74082 | ||||||||
\(428\) | −10920.1 | −1.23328 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11162.6 | 1.25188 | ||||||||
\(431\) | −13692.2 | −1.53023 | −0.765117 | − | 0.643892i | \(-0.777319\pi\) | ||||
−0.765117 | + | 0.643892i | \(0.777319\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15189.1 | −1.68578 | −0.842888 | − | 0.538089i | \(-0.819146\pi\) | ||||
−0.842888 | + | 0.538089i | \(0.819146\pi\) | |||||||
\(434\) | 21389.7 | 2.36575 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10180.7 | −1.11828 | ||||||||
\(437\) | 3341.23 | 0.365750 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2802.04 | −0.304634 | −0.152317 | − | 0.988332i | \(-0.548673\pi\) | ||||
−0.152317 | + | 0.988332i | \(0.548673\pi\) | |||||||
\(440\) | 1185.07 | 0.128400 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7539.78 | 0.808636 | 0.404318 | − | 0.914618i | \(-0.367509\pi\) | ||||
0.404318 | + | 0.914618i | \(0.367509\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6205.42 | 0.661045 | ||||||||
\(446\) | 287.997 | 0.0305764 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10394.5 | −1.09619 | ||||||||
\(449\) | −5558.82 | −0.584269 | −0.292135 | − | 0.956377i | \(-0.594366\pi\) | ||||
−0.292135 | + | 0.956377i | \(0.594366\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1705.54 | −0.178073 | ||||||||
\(452\) | −8012.20 | −0.833766 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16575.2 | −1.71347 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4327.71 | −0.442980 | −0.221490 | − | 0.975163i | \(-0.571092\pi\) | ||||
−0.221490 | + | 0.975163i | \(0.571092\pi\) | |||||||
\(458\) | −2599.42 | −0.265203 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5636.71 | 0.571333 | ||||||||
\(461\) | 11292.7 | 1.14090 | 0.570450 | − | 0.821333i | \(-0.306769\pi\) | ||||
0.570450 | + | 0.821333i | \(0.306769\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8582.54 | 0.861478 | 0.430739 | − | 0.902477i | \(-0.358253\pi\) | ||||
0.430739 | + | 0.902477i | \(0.358253\pi\) | |||||||
\(464\) | −1978.17 | −0.197918 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −356.238 | −0.0354128 | ||||||||
\(467\) | −17543.0 | −1.73831 | −0.869157 | − | 0.494536i | \(-0.835338\pi\) | ||||
−0.869157 | + | 0.494536i | \(0.835338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19009.8 | −1.87163 | ||||||||
\(470\) | 20209.0 | 1.98334 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 270.986 | 0.0264261 | ||||||||
\(473\) | −5363.01 | −0.521335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −194.252 | −0.0187639 | ||||||||
\(476\) | −23815.1 | −2.29320 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7985.32 | 0.764101 | ||||||||
\(479\) | −6299.15 | −0.600867 | −0.300434 | − | 0.953803i | \(-0.597131\pi\) | ||||
−0.300434 | + | 0.953803i | \(0.597131\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −25081.7 | −2.37020 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5979.89 | −0.561597 | ||||||||
\(485\) | 7836.78 | 0.733711 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3571.73 | 0.332342 | 0.166171 | − | 0.986097i | \(-0.446860\pi\) | ||||
0.166171 | + | 0.986097i | \(0.446860\pi\) | |||||||
\(488\) | 2460.20 | 0.228213 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −27113.8 | −2.49975 | ||||||||
\(491\) | 13385.2 | 1.23028 | 0.615139 | − | 0.788419i | \(-0.289100\pi\) | ||||
0.615139 | + | 0.788419i | \(0.289100\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3112.66 | −0.284356 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13055.4 | −1.18186 | ||||||||
\(497\) | −506.488 | −0.0457125 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19227.7 | −1.72495 | −0.862476 | − | 0.506098i | \(-0.831087\pi\) | ||||
−0.862476 | + | 0.506098i | \(0.831087\pi\) | |||||||
\(500\) | 9199.05 | 0.822788 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9238.13 | 0.821350 | ||||||||
\(503\) | 18651.2 | 1.65332 | 0.826658 | − | 0.562705i | \(-0.190239\pi\) | ||||
0.826658 | + | 0.562705i | \(0.190239\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5360.26 | 0.472334 | ||||||||
\(506\) | −5940.53 | −0.521914 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3528.35 | 0.308160 | ||||||||
\(509\) | 15886.1 | 1.38338 | 0.691688 | − | 0.722196i | \(-0.256867\pi\) | ||||
0.691688 | + | 0.722196i | \(0.256867\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9996.62 | 0.865410 | ||||||||
\(512\) | 14477.1 | 1.24961 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1010.69 | 0.0867310 | ||||||||
\(515\) | 3815.21 | 0.326443 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9709.33 | −0.825949 | ||||||||
\(518\) | 42250.7 | 3.58377 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1824.67 | −0.153436 | −0.0767179 | − | 0.997053i | \(-0.524444\pi\) | ||||
−0.0767179 | + | 0.997053i | \(0.524444\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16206.3 | 1.35498 | 0.677488 | − | 0.735534i | \(-0.263069\pi\) | ||||
0.677488 | + | 0.735534i | \(0.263069\pi\) | |||||||
\(524\) | 5590.04 | 0.466034 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28085.4 | 2.32810 | ||||||||
\(527\) | −20542.7 | −1.69802 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6697.07 | −0.550429 | ||||||||
\(530\) | 3340.06 | 0.273741 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9405.57 | −0.766510 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18526.4 | 1.49713 | ||||||||
\(536\) | 3044.76 | 0.245361 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17957.8 | 1.43906 | ||||||||
\(539\) | 13026.7 | 1.04100 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2429.83 | 0.193099 | 0.0965496 | − | 0.995328i | \(-0.469219\pi\) | ||||
0.0965496 | + | 0.995328i | \(0.469219\pi\) | |||||||
\(542\) | −6247.65 | −0.495128 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 27332.6 | 2.15418 | ||||||||
\(545\) | 17272.0 | 1.35752 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2409.16 | −0.188315 | −0.0941573 | − | 0.995557i | \(-0.530016\pi\) | ||||
−0.0941573 | + | 0.995557i | \(0.530016\pi\) | |||||||
\(548\) | 3128.47 | 0.243871 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 345.368 | 0.0267756 | ||||||||
\(551\) | −1229.32 | −0.0950468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11969.1 | 0.920390 | ||||||||
\(554\) | 23775.7 | 1.82334 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4779.41 | −0.364554 | ||||||||
\(557\) | 8668.70 | 0.659434 | 0.329717 | − | 0.944080i | \(-0.393047\pi\) | ||||
0.329717 | + | 0.944080i | \(0.393047\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 25677.1 | 1.93760 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11316.2 | −0.849371 | ||||||||
\(563\) | 7818.35 | 0.585265 | 0.292632 | − | 0.956225i | \(-0.405469\pi\) | ||||
0.292632 | + | 0.956225i | \(0.405469\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13593.0 | 1.01214 | ||||||||
\(566\) | 20127.3 | 1.49473 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 81.1229 | 0.00599268 | ||||||||
\(569\) | −9117.24 | −0.671730 | −0.335865 | − | 0.941910i | \(-0.609029\pi\) | ||||
−0.335865 | + | 0.941910i | \(0.609029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11842.4 | −0.867932 | −0.433966 | − | 0.900929i | \(-0.642886\pi\) | ||||
−0.433966 | + | 0.900929i | \(0.642886\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9697.35 | −0.705156 | ||||||||
\(575\) | −318.009 | −0.0230642 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10958.1 | −0.790623 | −0.395312 | − | 0.918547i | \(-0.629363\pi\) | ||||
−0.395312 | + | 0.918547i | \(0.629363\pi\) | |||||||
\(578\) | 31333.7 | 2.25486 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2073.88 | −0.148471 | ||||||||
\(581\) | −20617.9 | −1.47225 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1604.72 | −0.113997 | ||||||||
\(584\) | −1601.13 | −0.113451 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11167.0 | 0.787209 | ||||||||
\(587\) | −23057.8 | −1.62129 | −0.810644 | − | 0.585539i | \(-0.800883\pi\) | ||||
−0.810644 | + | 0.585539i | \(0.800883\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8113.18 | −0.567568 | ||||||||
\(590\) | 2374.83 | 0.165712 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −25788.1 | −1.79035 | ||||||||
\(593\) | 9904.56 | 0.685888 | 0.342944 | − | 0.939356i | \(-0.388576\pi\) | ||||
0.342944 | + | 0.939356i | \(0.388576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40403.2 | 2.78381 | ||||||||
\(596\) | −4442.50 | −0.305322 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21334.5 | −1.45527 | −0.727633 | − | 0.685967i | \(-0.759380\pi\) | ||||
−0.727633 | + | 0.685967i | \(0.759380\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19484.4 | −1.32244 | −0.661219 | − | 0.750193i | \(-0.729960\pi\) | ||||
−0.661219 | + | 0.750193i | \(0.729960\pi\) | |||||||
\(602\) | −30492.9 | −2.06445 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1279.25 | 0.0861789 | ||||||||
\(605\) | 10145.1 | 0.681747 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19855.7 | 1.32770 | 0.663852 | − | 0.747864i | \(-0.268921\pi\) | ||||
0.663852 | + | 0.747864i | \(0.268921\pi\) | |||||||
\(608\) | 10794.8 | 0.720043 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21560.4 | 1.43108 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5153.57 | 0.339561 | 0.169781 | − | 0.985482i | \(-0.445694\pi\) | ||||
0.169781 | + | 0.985482i | \(0.445694\pi\) | |||||||
\(614\) | 19172.3 | 1.26015 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3237.27 | −0.211743 | ||||||||
\(617\) | 924.218 | 0.0603040 | 0.0301520 | − | 0.999545i | \(-0.490401\pi\) | ||||
0.0301520 | + | 0.999545i | \(0.490401\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15690.6 | −1.01883 | −0.509417 | − | 0.860520i | \(-0.670139\pi\) | ||||
−0.509417 | + | 0.860520i | \(0.670139\pi\) | |||||||
\(620\) | −13687.1 | −0.886589 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30065.2 | 1.93811 | ||||||||
\(623\) | −16951.4 | −1.09012 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16144.0 | −1.03322 | ||||||||
\(626\) | −28828.5 | −1.84061 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18994.6 | −1.20695 | ||||||||
\(629\) | −40577.8 | −2.57225 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21103.6 | 1.33141 | 0.665705 | − | 0.746215i | \(-0.268131\pi\) | ||||
0.665705 | + | 0.746215i | \(0.268131\pi\) | |||||||
\(632\) | −1917.05 | −0.120659 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1860.59 | −0.116551 | ||||||||
\(635\) | −5985.98 | −0.374089 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2185.66 | 0.135629 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7146.06 | −0.441364 | ||||||||
\(641\) | 6695.38 | 0.412561 | 0.206280 | − | 0.978493i | \(-0.433864\pi\) | ||||
0.206280 | + | 0.978493i | \(0.433864\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9647.69 | −0.591707 | −0.295854 | − | 0.955233i | \(-0.595604\pi\) | ||||
−0.295854 | + | 0.955233i | \(0.595604\pi\) | |||||||
\(644\) | −15397.9 | −0.942175 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19815.0 | 1.20683 | ||||||||
\(647\) | 23747.5 | 1.44299 | 0.721493 | − | 0.692422i | \(-0.243456\pi\) | ||||
0.721493 | + | 0.692422i | \(0.243456\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1140.98 | −0.0690096 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23898.0 | 1.43546 | ||||||||
\(653\) | −19833.5 | −1.18858 | −0.594292 | − | 0.804249i | \(-0.702568\pi\) | ||||
−0.594292 | + | 0.804249i | \(0.702568\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9483.70 | −0.565738 | ||||||||
\(656\) | 5918.86 | 0.352275 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −55205.1 | −3.27070 | ||||||||
\(659\) | −10807.4 | −0.638841 | −0.319421 | − | 0.947613i | \(-0.603488\pi\) | ||||
−0.319421 | + | 0.947613i | \(0.603488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13431.5 | 0.790356 | 0.395178 | − | 0.918605i | \(-0.370683\pi\) | ||||
0.395178 | + | 0.918605i | \(0.370683\pi\) | |||||||
\(662\) | 31529.7 | 1.85111 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3302.32 | 0.193004 | ||||||||
\(665\) | 15956.9 | 0.930498 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2012.52 | −0.116829 | ||||||||
\(668\) | 808.520 | 0.0468302 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 26683.3 | 1.53861 | ||||||||
\(671\) | −10358.6 | −0.595961 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21581.4 | 1.23611 | 0.618054 | − | 0.786136i | \(-0.287921\pi\) | ||||
0.618054 | + | 0.786136i | \(0.287921\pi\) | |||||||
\(674\) | 29696.4 | 1.69713 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17482.4 | −0.992474 | −0.496237 | − | 0.868187i | \(-0.665285\pi\) | ||||
−0.496237 | + | 0.868187i | \(0.665285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21407.8 | −1.20995 | ||||||||
\(680\) | −6471.27 | −0.364944 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14424.8 | 0.809902 | ||||||||
\(683\) | 2842.23 | 0.159231 | 0.0796155 | − | 0.996826i | \(-0.474631\pi\) | ||||
0.0796155 | + | 0.996826i | \(0.474631\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5307.56 | −0.296046 | ||||||||
\(686\) | 33214.1 | 1.84857 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18611.6 | 1.03134 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22875.5 | −1.25937 | −0.629686 | − | 0.776850i | \(-0.716816\pi\) | ||||
−0.629686 | + | 0.776850i | \(0.716816\pi\) | |||||||
\(692\) | 13943.0 | 0.765946 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13545.4 | 0.740886 | ||||||||
\(695\) | 8108.43 | 0.442547 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9313.38 | 0.506125 | ||||||||
\(698\) | 12907.2 | 0.699923 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 895.195 | 0.0483360 | ||||||||
\(701\) | −11980.3 | −0.645492 | −0.322746 | − | 0.946486i | \(-0.604606\pi\) | ||||
−0.322746 | + | 0.946486i | \(0.604606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16025.9 | −0.859782 | ||||||||
\(704\) | −7009.85 | −0.375275 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 38221.0 | 2.03749 | ||||||||
\(707\) | −14642.7 | −0.778918 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4204.77 | −0.222727 | −0.111363 | − | 0.993780i | \(-0.535522\pi\) | ||||
−0.111363 | + | 0.993780i | \(0.535522\pi\) | |||||||
\(710\) | 710.936 | 0.0375788 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2715.06 | 0.142909 | ||||||||
\(713\) | −13282.1 | −0.697641 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3707.41 | 0.193509 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10516.7 | −0.546627 | ||||||||
\(719\) | 11537.0 | 0.598411 | 0.299205 | − | 0.954189i | \(-0.403278\pi\) | ||||
0.299205 | + | 0.954189i | \(0.403278\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10422.0 | −0.538332 | ||||||||
\(722\) | −18474.3 | −0.952272 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22153.0 | −1.13717 | ||||||||
\(725\) | 117.003 | 0.00599364 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33899.7 | −1.72940 | −0.864698 | − | 0.502293i | \(-0.832490\pi\) | ||||
−0.864698 | + | 0.502293i | \(0.832490\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14031.8 | −0.711426 | ||||||||
\(731\) | 29285.6 | 1.48176 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 378.221 | 0.0190585 | 0.00952927 | − | 0.999955i | \(-0.496967\pi\) | ||||
0.00952927 | + | 0.999955i | \(0.496967\pi\) | |||||||
\(734\) | −6295.51 | −0.316582 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17672.1 | 0.885059 | ||||||||
\(737\) | −12819.9 | −0.640741 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22663.6 | −1.12814 | −0.564069 | − | 0.825728i | \(-0.690765\pi\) | ||||
−0.564069 | + | 0.825728i | \(0.690765\pi\) | |||||||
\(740\) | −27035.9 | −1.34305 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9124.06 | −0.451422 | ||||||||
\(743\) | 16407.3 | 0.810130 | 0.405065 | − | 0.914288i | \(-0.367249\pi\) | ||||
0.405065 | + | 0.914288i | \(0.367249\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7536.86 | 0.370643 | ||||||||
\(746\) | 42974.0 | 2.10910 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16060.4 | −0.785064 | ||||||||
\(749\) | −50608.7 | −2.46889 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21957.9 | 1.06692 | 0.533458 | − | 0.845827i | \(-0.320892\pi\) | ||||
0.533458 | + | 0.845827i | \(0.320892\pi\) | |||||||
\(752\) | 33694.9 | 1.63395 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2170.30 | −0.104616 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20823.5 | 0.999792 | 0.499896 | − | 0.866085i | \(-0.333371\pi\) | ||||
0.499896 | + | 0.866085i | \(0.333371\pi\) | |||||||
\(758\) | 14741.2 | 0.706364 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2555.77 | −0.121984 | ||||||||
\(761\) | −28456.1 | −1.35550 | −0.677749 | − | 0.735294i | \(-0.737044\pi\) | ||||
−0.677749 | + | 0.735294i | \(0.737044\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47182.0 | −2.23867 | ||||||||
\(764\) | 22239.8 | 1.05315 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −46604.2 | −2.19828 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13450.0 | 0.630713 | 0.315356 | − | 0.948973i | \(-0.397876\pi\) | ||||
0.315356 | + | 0.948973i | \(0.397876\pi\) | |||||||
\(770\) | −28370.4 | −1.32779 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26154.3 | −1.21932 | ||||||||
\(773\) | 26577.8 | 1.23666 | 0.618329 | − | 0.785919i | \(-0.287810\pi\) | ||||
0.618329 | + | 0.785919i | \(0.287810\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 772.190 | 0.0357908 | ||||||||
\(776\) | 3428.83 | 0.158618 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20204.9 | 0.931083 | ||||||||
\(779\) | 3678.24 | 0.169174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −341.566 | −0.0156494 | ||||||||
\(782\) | 32439.1 | 1.48340 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −45207.5 | −2.05938 | ||||||||
\(785\) | 32225.0 | 1.46517 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8281.40 | −0.375095 | −0.187548 | − | 0.982256i | \(-0.560054\pi\) | ||||
−0.187548 | + | 0.982256i | \(0.560054\pi\) | |||||||
\(788\) | 24350.0 | 1.10080 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16800.4 | −0.756624 | ||||||||
\(791\) | −37132.1 | −1.66911 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 2513.37 | 0.112338 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19820.8 | 0.882575 | ||||||||
\(797\) | −20668.8 | −0.918605 | −0.459302 | − | 0.888280i | \(-0.651901\pi\) | ||||
−0.459302 | + | 0.888280i | \(0.651901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53019.3 | 2.34754 | ||||||||
\(800\) | −1027.42 | −0.0454059 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −29524.6 | −1.29994 | ||||||||
\(803\) | 6741.52 | 0.296268 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26123.0 | 1.14375 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2345.28 | 0.102112 | ||||||||
\(809\) | −7238.85 | −0.314591 | −0.157296 | − | 0.987552i | \(-0.550278\pi\) | ||||
−0.157296 | + | 0.987552i | \(0.550278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13101.3 | 0.567260 | 0.283630 | − | 0.958934i | \(-0.408461\pi\) | ||||
0.283630 | + | 0.958934i | \(0.408461\pi\) | |||||||
\(812\) | 5665.24 | 0.244841 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 28493.1 | 1.22688 | ||||||||
\(815\) | −40543.9 | −1.74256 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11566.1 | 0.495283 | ||||||||
\(818\) | −2128.85 | −0.0909946 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6205.25 | 0.264264 | ||||||||
\(821\) | −12092.9 | −0.514062 | −0.257031 | − | 0.966403i | \(-0.582744\pi\) | ||||
−0.257031 | + | 0.966403i | \(0.582744\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27041.2 | 1.14532 | 0.572659 | − | 0.819794i | \(-0.305912\pi\) | ||||
0.572659 | + | 0.819794i | \(0.305912\pi\) | |||||||
\(824\) | 1669.27 | 0.0705727 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6487.35 | −0.273273 | ||||||||
\(827\) | 25572.3 | 1.07526 | 0.537628 | − | 0.843182i | \(-0.319320\pi\) | ||||
0.537628 | + | 0.843182i | \(0.319320\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17505.8 | −0.733415 | −0.366707 | − | 0.930336i | \(-0.619515\pi\) | ||||
−0.366707 | + | 0.930336i | \(0.619515\pi\) | |||||||
\(830\) | 28940.5 | 1.21029 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −71134.3 | −2.95877 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1371.68 | −0.0568491 | ||||||||
\(836\) | −6342.93 | −0.262410 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12718.6 | −0.524293 | ||||||||
\(839\) | 28293.4 | 1.16424 | 0.582119 | − | 0.813103i | \(-0.302224\pi\) | ||||
0.582119 | + | 0.813103i | \(0.302224\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23648.5 | −0.969640 | ||||||||
\(842\) | −50883.3 | −2.08261 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21408.1 | −0.873100 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27713.4 | −1.12426 | ||||||||
\(848\) | 5568.95 | 0.225517 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1885.94 | −0.0761025 | ||||||||
\(851\) | −26235.9 | −1.05682 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15866.0 | −0.636861 | −0.318430 | − | 0.947946i | \(-0.603156\pi\) | ||||
−0.318430 | + | 0.947946i | \(0.603156\pi\) | |||||||
\(854\) | −58896.8 | −2.35996 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8105.86 | 0.323660 | ||||||||
\(857\) | −23623.3 | −0.941607 | −0.470804 | − | 0.882238i | \(-0.656036\pi\) | ||||
−0.470804 | + | 0.882238i | \(0.656036\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33403.1 | 1.32677 | 0.663387 | − | 0.748277i | \(-0.269118\pi\) | ||||
0.663387 | + | 0.748277i | \(0.269118\pi\) | |||||||
\(860\) | 19512.2 | 0.773673 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −52501.2 | −2.07447 | ||||||||
\(863\) | 45490.5 | 1.79434 | 0.897169 | − | 0.441687i | \(-0.145620\pi\) | ||||
0.897169 | + | 0.441687i | \(0.145620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23654.9 | −0.929814 | ||||||||
\(866\) | −58240.8 | −2.28534 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 37389.0 | 1.46206 | ||||||||
\(869\) | 8071.70 | 0.315090 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 7557.03 | 0.293479 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12811.6 | 0.495833 | ||||||||
\(875\) | 42632.4 | 1.64713 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19570.1 | −0.753518 | −0.376759 | − | 0.926311i | \(-0.622961\pi\) | ||||
−0.376759 | + | 0.926311i | \(0.622961\pi\) | |||||||
\(878\) | −10744.1 | −0.412979 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 17316.1 | 0.663326 | ||||||||
\(881\) | 3016.95 | 0.115373 | 0.0576864 | − | 0.998335i | \(-0.481628\pi\) | ||||
0.0576864 | + | 0.998335i | \(0.481628\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17163.8 | 0.654141 | 0.327071 | − | 0.945000i | \(-0.393939\pi\) | ||||
0.327071 | + | 0.945000i | \(0.393939\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28910.4 | 1.09623 | ||||||||
\(887\) | −28464.7 | −1.07751 | −0.538754 | − | 0.842463i | \(-0.681105\pi\) | ||||
−0.538754 | + | 0.842463i | \(0.681105\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16352.0 | 0.616903 | ||||||||
\(890\) | 23793.9 | 0.896151 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 503.418 | 0.0188965 | ||||||||
\(893\) | 20939.5 | 0.784674 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6289.76 | −0.234909 | ||||||||
\(896\) | 19520.9 | 0.727845 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21314.6 | −0.792070 | ||||||||
\(899\) | 4886.80 | 0.181295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8762.80 | 0.324008 | ||||||||
\(902\) | −6539.70 | −0.241406 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5947.36 | 0.218812 | ||||||||
\(905\) | 37583.4 | 1.38046 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26610.1 | −0.974171 | −0.487085 | − | 0.873354i | \(-0.661940\pi\) | ||||
−0.487085 | + | 0.873354i | \(0.661940\pi\) | |||||||
\(908\) | −28973.4 | −1.05894 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52648.2 | 1.91472 | 0.957362 | − | 0.288890i | \(-0.0932863\pi\) | ||||
0.957362 | + | 0.288890i | \(0.0932863\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13904.3 | −0.504015 | ||||||||
\(914\) | −16594.1 | −0.600529 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4543.77 | −0.163898 | ||||||||
\(917\) | 25906.7 | 0.932949 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46923.5 | 1.68429 | 0.842146 | − | 0.539250i | \(-0.181292\pi\) | ||||
0.842146 | + | 0.539250i | \(0.181292\pi\) | |||||||
\(920\) | −4184.06 | −0.149939 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 43300.6 | 1.54667 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1525.30 | 0.0542178 | ||||||||
\(926\) | 32908.7 | 1.16787 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6502.00 | −0.229999 | ||||||||
\(929\) | −41163.7 | −1.45376 | −0.726878 | − | 0.686767i | \(-0.759029\pi\) | ||||
−0.726878 | + | 0.686767i | \(0.759029\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28093.9 | −0.988980 | ||||||||
\(932\) | −622.702 | −0.0218855 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −67266.5 | −2.35656 | ||||||||
\(935\) | 27247.1 | 0.953022 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23380.3 | −0.815156 | −0.407578 | − | 0.913170i | \(-0.633627\pi\) | ||||
−0.407578 | + | 0.913170i | \(0.633627\pi\) | |||||||
\(938\) | −72891.0 | −2.53729 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 35325.3 | 1.22573 | ||||||||
\(941\) | 34506.2 | 1.19540 | 0.597700 | − | 0.801720i | \(-0.296082\pi\) | ||||
0.597700 | + | 0.801720i | \(0.296082\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6021.65 | 0.207945 | ||||||||
\(944\) | 3959.61 | 0.136519 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20563.8 | −0.706753 | ||||||||
\(947\) | 483.439 | 0.0165889 | 0.00829443 | − | 0.999966i | \(-0.497360\pi\) | ||||
0.00829443 | + | 0.999966i | \(0.497360\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −744.835 | −0.0254375 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17677.6 | 0.601823 | ||||||||
\(953\) | 11962.7 | 0.406619 | 0.203310 | − | 0.979114i | \(-0.434830\pi\) | ||||
0.203310 | + | 0.979114i | \(0.434830\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37730.6 | −1.27846 | ||||||||
\(956\) | 13958.3 | 0.472222 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24153.3 | −0.814571 | ||||||||
\(959\) | 14498.7 | 0.488204 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2460.54 | 0.0825934 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −43842.6 | −1.46481 | ||||||||
\(965\) | 44371.7 | 1.48018 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7695.43 | 0.255913 | 0.127957 | − | 0.991780i | \(-0.459158\pi\) | ||||
0.127957 | + | 0.991780i | \(0.459158\pi\) | |||||||
\(968\) | 4438.79 | 0.147385 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 30049.2 | 0.994661 | ||||||||
\(971\) | 44177.9 | 1.46008 | 0.730039 | − | 0.683406i | \(-0.239502\pi\) | ||||
0.730039 | + | 0.683406i | \(0.239502\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22149.9 | −0.729797 | ||||||||
\(974\) | 13695.4 | 0.450542 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35948.2 | 1.17897 | ||||||||
\(977\) | −3412.61 | −0.111749 | −0.0558746 | − | 0.998438i | \(-0.517795\pi\) | ||||
−0.0558746 | + | 0.998438i | \(0.517795\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11431.7 | −0.373196 | ||||||||
\(980\) | −47394.8 | −1.54487 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 51324.0 | 1.66784 | ||||||||
\(983\) | −6313.78 | −0.204861 | −0.102431 | − | 0.994740i | \(-0.532662\pi\) | ||||
−0.102431 | + | 0.994740i | \(0.532662\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41310.7 | −1.33631 | ||||||||
\(986\) | −11935.1 | −0.385489 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18934.8 | 0.608789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12177.5 | 0.390344 | 0.195172 | − | 0.980769i | \(-0.437474\pi\) | ||||
0.195172 | + | 0.980769i | \(0.437474\pi\) | |||||||
\(992\) | −42911.5 | −1.37343 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1942.07 | −0.0619705 | ||||||||
\(995\) | −33626.7 | −1.07139 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17506.2 | 0.556096 | 0.278048 | − | 0.960567i | \(-0.410313\pi\) | ||||
0.278048 | + | 0.960567i | \(0.410313\pi\) | |||||||
\(998\) | −73726.4 | −2.33845 | ||||||||
\(999\) | 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 | 1521.4.a.bg.1.8 | 9 | ||
3.2 | odd | 2 | 169.4.a.l.1.2 | yes | 9 | ||
13.12 | even | 2 | 1521.4.a.bh.1.2 | 9 | |||
39.2 | even | 12 | 169.4.e.h.147.4 | 36 | |||
39.5 | even | 4 | 169.4.b.g.168.15 | 18 | |||
39.8 | even | 4 | 169.4.b.g.168.4 | 18 | |||
39.11 | even | 12 | 169.4.e.h.147.15 | 36 | |||
39.17 | odd | 6 | 169.4.c.l.146.2 | 18 | |||
39.20 | even | 12 | 169.4.e.h.23.4 | 36 | |||
39.23 | odd | 6 | 169.4.c.l.22.2 | 18 | |||
39.29 | odd | 6 | 169.4.c.k.22.8 | 18 | |||
39.32 | even | 12 | 169.4.e.h.23.15 | 36 | |||
39.35 | odd | 6 | 169.4.c.k.146.8 | 18 | |||
39.38 | odd | 2 | 169.4.a.k.1.8 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.4.a.k.1.8 | ✓ | 9 | 39.38 | odd | 2 | ||
169.4.a.l.1.2 | yes | 9 | 3.2 | odd | 2 | ||
169.4.b.g.168.4 | 18 | 39.8 | even | 4 | |||
169.4.b.g.168.15 | 18 | 39.5 | even | 4 | |||
169.4.c.k.22.8 | 18 | 39.29 | odd | 6 | |||
169.4.c.k.146.8 | 18 | 39.35 | odd | 6 | |||
169.4.c.l.22.2 | 18 | 39.23 | odd | 6 | |||
169.4.c.l.146.2 | 18 | 39.17 | odd | 6 | |||
169.4.e.h.23.4 | 36 | 39.20 | even | 12 | |||
169.4.e.h.23.15 | 36 | 39.32 | even | 12 | |||
169.4.e.h.147.4 | 36 | 39.2 | even | 12 | |||
169.4.e.h.147.15 | 36 | 39.11 | even | 12 | |||
1521.4.a.bg.1.8 | 9 | 1.1 | even | 1 | trivial | ||
1521.4.a.bh.1.2 | 9 | 13.12 | even | 2 |