Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,4,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(110.628581261\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 81 x^{12} - 7 x^{11} + 2512 x^{10} + 517 x^{9} - 36970 x^{8} - 12987 x^{7} + 257291 x^{6} + \cdots + 42064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{3} \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.955230\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.955230 | −0.337725 | −0.168862 | − | 0.985640i | \(-0.554009\pi\) | ||||
−0.168862 | + | 0.985640i | \(0.554009\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −7.08754 | −0.885942 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.86569 | −0.194986 | ||||||||
\(7\) | 12.4836 | 0.674049 | 0.337024 | − | 0.941496i | \(-0.390580\pi\) | ||||
0.337024 | + | 0.941496i | \(0.390580\pi\) | |||||||
\(8\) | 14.4121 | 0.636929 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −44.7266 | −1.22596 | −0.612980 | − | 0.790098i | \(-0.710029\pi\) | ||||
−0.612980 | + | 0.790098i | \(0.710029\pi\) | |||||||
\(12\) | −21.2626 | −0.511499 | ||||||||
\(13\) | −7.13628 | −0.152250 | −0.0761250 | − | 0.997098i | \(-0.524255\pi\) | ||||
−0.0761250 | + | 0.997098i | \(0.524255\pi\) | |||||||
\(14\) | −11.9247 | −0.227643 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 42.9334 | 0.670835 | ||||||||
\(17\) | 26.5116 | 0.378236 | 0.189118 | − | 0.981954i | \(-0.439437\pi\) | ||||
0.189118 | + | 0.981954i | \(0.439437\pi\) | |||||||
\(18\) | −8.59707 | −0.112575 | ||||||||
\(19\) | −46.3901 | −0.560138 | −0.280069 | − | 0.959980i | \(-0.590357\pi\) | ||||
−0.280069 | + | 0.959980i | \(0.590357\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 37.4507 | 0.389162 | ||||||||
\(22\) | 42.7241 | 0.414037 | ||||||||
\(23\) | 145.454 | 1.31866 | 0.659330 | − | 0.751854i | \(-0.270840\pi\) | ||||
0.659330 | + | 0.751854i | \(0.270840\pi\) | |||||||
\(24\) | 43.2362 | 0.367731 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.81679 | 0.0514186 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −88.4777 | −0.597168 | ||||||||
\(29\) | −213.354 | −1.36616 | −0.683082 | − | 0.730341i | \(-0.739361\pi\) | ||||
−0.683082 | + | 0.730341i | \(0.739361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −148.082 | −0.857945 | −0.428972 | − | 0.903318i | \(-0.641124\pi\) | ||||
−0.428972 | + | 0.903318i | \(0.641124\pi\) | |||||||
\(32\) | −156.308 | −0.863487 | ||||||||
\(33\) | −134.180 | −0.707809 | ||||||||
\(34\) | −25.3247 | −0.127740 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −63.7878 | −0.295314 | ||||||||
\(37\) | 402.312 | 1.78756 | 0.893781 | − | 0.448505i | \(-0.148043\pi\) | ||||
0.893781 | + | 0.448505i | \(0.148043\pi\) | |||||||
\(38\) | 44.3132 | 0.189173 | ||||||||
\(39\) | −21.4089 | −0.0879015 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 233.656 | 0.890022 | 0.445011 | − | 0.895525i | \(-0.353200\pi\) | ||||
0.445011 | + | 0.895525i | \(0.353200\pi\) | |||||||
\(42\) | −35.7740 | −0.131430 | ||||||||
\(43\) | 87.5080 | 0.310345 | 0.155173 | − | 0.987887i | \(-0.450407\pi\) | ||||
0.155173 | + | 0.987887i | \(0.450407\pi\) | |||||||
\(44\) | 317.001 | 1.08613 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −138.942 | −0.445344 | ||||||||
\(47\) | −75.9842 | −0.235818 | −0.117909 | − | 0.993024i | \(-0.537619\pi\) | ||||
−0.117909 | + | 0.993024i | \(0.537619\pi\) | |||||||
\(48\) | 128.800 | 0.387307 | ||||||||
\(49\) | −187.161 | −0.545658 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 79.5348 | 0.218375 | ||||||||
\(52\) | 50.5787 | 0.134885 | ||||||||
\(53\) | 167.029 | 0.432891 | 0.216446 | − | 0.976295i | \(-0.430554\pi\) | ||||
0.216446 | + | 0.976295i | \(0.430554\pi\) | |||||||
\(54\) | −25.7912 | −0.0649952 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 179.914 | 0.429321 | ||||||||
\(57\) | −139.170 | −0.323396 | ||||||||
\(58\) | 203.802 | 0.461388 | ||||||||
\(59\) | −595.082 | −1.31310 | −0.656551 | − | 0.754282i | \(-0.727985\pi\) | ||||
−0.656551 | + | 0.754282i | \(0.727985\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −865.794 | −1.81727 | −0.908636 | − | 0.417589i | \(-0.862875\pi\) | ||||
−0.908636 | + | 0.417589i | \(0.862875\pi\) | |||||||
\(62\) | 141.452 | 0.289749 | ||||||||
\(63\) | 112.352 | 0.224683 | ||||||||
\(64\) | −194.158 | −0.379214 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 128.172 | 0.239044 | ||||||||
\(67\) | −406.302 | −0.740862 | −0.370431 | − | 0.928860i | \(-0.620790\pi\) | ||||
−0.370431 | + | 0.928860i | \(0.620790\pi\) | |||||||
\(68\) | −187.902 | −0.335095 | ||||||||
\(69\) | 436.361 | 0.761329 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 526.158 | 0.879486 | 0.439743 | − | 0.898124i | \(-0.355070\pi\) | ||||
0.439743 | + | 0.898124i | \(0.355070\pi\) | |||||||
\(72\) | 129.709 | 0.212310 | ||||||||
\(73\) | 1001.69 | 1.60602 | 0.803009 | − | 0.595967i | \(-0.203231\pi\) | ||||
0.803009 | + | 0.595967i | \(0.203231\pi\) | |||||||
\(74\) | −384.301 | −0.603704 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 328.792 | 0.496250 | ||||||||
\(77\) | −558.347 | −0.826357 | ||||||||
\(78\) | 20.4504 | 0.0296865 | ||||||||
\(79\) | −133.956 | −0.190774 | −0.0953872 | − | 0.995440i | \(-0.530409\pi\) | ||||
−0.0953872 | + | 0.995440i | \(0.530409\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −223.195 | −0.300582 | ||||||||
\(83\) | 516.642 | 0.683238 | 0.341619 | − | 0.939838i | \(-0.389025\pi\) | ||||
0.341619 | + | 0.939838i | \(0.389025\pi\) | |||||||
\(84\) | −265.433 | −0.344775 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −83.5903 | −0.104811 | ||||||||
\(87\) | −640.061 | −0.788756 | ||||||||
\(88\) | −644.602 | −0.780850 | ||||||||
\(89\) | −610.698 | −0.727347 | −0.363673 | − | 0.931527i | \(-0.618478\pi\) | ||||
−0.363673 | + | 0.931527i | \(0.618478\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −89.0862 | −0.102624 | ||||||||
\(92\) | −1030.91 | −1.16826 | ||||||||
\(93\) | −444.246 | −0.495335 | ||||||||
\(94\) | 72.5824 | 0.0796415 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −468.924 | −0.498534 | ||||||||
\(97\) | −1639.57 | −1.71621 | −0.858107 | − | 0.513471i | \(-0.828359\pi\) | ||||
−0.858107 | + | 0.513471i | \(0.828359\pi\) | |||||||
\(98\) | 178.782 | 0.184282 | ||||||||
\(99\) | −402.539 | −0.408653 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −433.248 | −0.426830 | −0.213415 | − | 0.976962i | \(-0.568459\pi\) | ||||
−0.213415 | + | 0.976962i | \(0.568459\pi\) | |||||||
\(102\) | −75.9741 | −0.0737505 | ||||||||
\(103\) | 81.3244 | 0.0777974 | 0.0388987 | − | 0.999243i | \(-0.487615\pi\) | ||||
0.0388987 | + | 0.999243i | \(0.487615\pi\) | |||||||
\(104\) | −102.849 | −0.0969725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −159.551 | −0.146198 | ||||||||
\(107\) | 391.773 | 0.353964 | 0.176982 | − | 0.984214i | \(-0.443367\pi\) | ||||
0.176982 | + | 0.984214i | \(0.443367\pi\) | |||||||
\(108\) | −191.363 | −0.170500 | ||||||||
\(109\) | 1815.92 | 1.59572 | 0.797862 | − | 0.602840i | \(-0.205964\pi\) | ||||
0.797862 | + | 0.602840i | \(0.205964\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1206.94 | 1.03205 | ||||||||
\(112\) | 535.962 | 0.452176 | ||||||||
\(113\) | 1087.20 | 0.905094 | 0.452547 | − | 0.891741i | \(-0.350515\pi\) | ||||
0.452547 | + | 0.891741i | \(0.350515\pi\) | |||||||
\(114\) | 132.940 | 0.109219 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1512.15 | 1.21034 | ||||||||
\(117\) | −64.2266 | −0.0507500 | ||||||||
\(118\) | 568.440 | 0.443467 | ||||||||
\(119\) | 330.959 | 0.254949 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 669.465 | 0.502979 | ||||||||
\(122\) | 827.033 | 0.613738 | ||||||||
\(123\) | 700.967 | 0.513854 | ||||||||
\(124\) | 1049.54 | 0.760089 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −107.322 | −0.0758810 | ||||||||
\(127\) | 871.466 | 0.608898 | 0.304449 | − | 0.952529i | \(-0.401528\pi\) | ||||
0.304449 | + | 0.952529i | \(0.401528\pi\) | |||||||
\(128\) | 1435.93 | 0.991557 | ||||||||
\(129\) | 262.524 | 0.179178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1708.16 | 1.13925 | 0.569627 | − | 0.821904i | \(-0.307088\pi\) | ||||
0.569627 | + | 0.821904i | \(0.307088\pi\) | |||||||
\(132\) | 951.003 | 0.627077 | ||||||||
\(133\) | −579.114 | −0.377560 | ||||||||
\(134\) | 388.112 | 0.250207 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 382.087 | 0.240910 | ||||||||
\(137\) | −2401.86 | −1.49784 | −0.748921 | − | 0.662659i | \(-0.769428\pi\) | ||||
−0.748921 | + | 0.662659i | \(0.769428\pi\) | |||||||
\(138\) | −416.825 | −0.257120 | ||||||||
\(139\) | −2161.94 | −1.31923 | −0.659617 | − | 0.751602i | \(-0.729282\pi\) | ||||
−0.659617 | + | 0.751602i | \(0.729282\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −227.953 | −0.136150 | ||||||||
\(142\) | −502.602 | −0.297024 | ||||||||
\(143\) | 319.181 | 0.186652 | ||||||||
\(144\) | 386.401 | 0.223612 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −956.847 | −0.542392 | ||||||||
\(147\) | −561.482 | −0.315036 | ||||||||
\(148\) | −2851.40 | −1.58368 | ||||||||
\(149\) | −1527.70 | −0.839959 | −0.419980 | − | 0.907534i | \(-0.637963\pi\) | ||||
−0.419980 | + | 0.907534i | \(0.637963\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2584.71 | 1.39299 | 0.696493 | − | 0.717564i | \(-0.254743\pi\) | ||||
0.696493 | + | 0.717564i | \(0.254743\pi\) | |||||||
\(152\) | −668.578 | −0.356768 | ||||||||
\(153\) | 238.605 | 0.126079 | ||||||||
\(154\) | 533.349 | 0.279081 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 151.736 | 0.0778757 | ||||||||
\(157\) | −692.965 | −0.352259 | −0.176129 | − | 0.984367i | \(-0.556358\pi\) | ||||
−0.176129 | + | 0.984367i | \(0.556358\pi\) | |||||||
\(158\) | 127.958 | 0.0644293 | ||||||||
\(159\) | 501.088 | 0.249930 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1815.78 | 0.888841 | ||||||||
\(162\) | −77.3736 | −0.0375250 | ||||||||
\(163\) | −3620.52 | −1.73976 | −0.869881 | − | 0.493262i | \(-0.835805\pi\) | ||||
−0.869881 | + | 0.493262i | \(0.835805\pi\) | |||||||
\(164\) | −1656.04 | −0.788508 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −493.511 | −0.230746 | ||||||||
\(167\) | 1555.61 | 0.720817 | 0.360409 | − | 0.932794i | \(-0.382637\pi\) | ||||
0.360409 | + | 0.932794i | \(0.382637\pi\) | |||||||
\(168\) | 539.742 | 0.247869 | ||||||||
\(169\) | −2146.07 | −0.976820 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −417.511 | −0.186713 | ||||||||
\(172\) | −620.216 | −0.274948 | ||||||||
\(173\) | −2175.91 | −0.956250 | −0.478125 | − | 0.878292i | \(-0.658683\pi\) | ||||
−0.478125 | + | 0.878292i | \(0.658683\pi\) | |||||||
\(174\) | 611.405 | 0.266382 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1920.27 | −0.822417 | ||||||||
\(177\) | −1785.24 | −0.758120 | ||||||||
\(178\) | 583.357 | 0.245643 | ||||||||
\(179\) | −1865.44 | −0.778937 | −0.389468 | − | 0.921040i | \(-0.627341\pi\) | ||||
−0.389468 | + | 0.921040i | \(0.627341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −257.830 | −0.105881 | −0.0529403 | − | 0.998598i | \(-0.516859\pi\) | ||||
−0.0529403 | + | 0.998598i | \(0.516859\pi\) | |||||||
\(182\) | 85.0978 | 0.0346586 | ||||||||
\(183\) | −2597.38 | −1.04920 | ||||||||
\(184\) | 2096.29 | 0.839893 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 424.357 | 0.167287 | ||||||||
\(187\) | −1185.77 | −0.463702 | ||||||||
\(188\) | 538.541 | 0.208921 | ||||||||
\(189\) | 337.056 | 0.129721 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3960.87 | −1.50052 | −0.750258 | − | 0.661145i | \(-0.770071\pi\) | ||||
−0.750258 | + | 0.661145i | \(0.770071\pi\) | |||||||
\(192\) | −582.473 | −0.218939 | ||||||||
\(193\) | 1253.72 | 0.467590 | 0.233795 | − | 0.972286i | \(-0.424886\pi\) | ||||
0.233795 | + | 0.972286i | \(0.424886\pi\) | |||||||
\(194\) | 1566.16 | 0.579608 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1326.51 | 0.483422 | ||||||||
\(197\) | −5059.84 | −1.82994 | −0.914971 | − | 0.403519i | \(-0.867787\pi\) | ||||
−0.914971 | + | 0.403519i | \(0.867787\pi\) | |||||||
\(198\) | 384.517 | 0.138012 | ||||||||
\(199\) | −5323.91 | −1.89649 | −0.948246 | − | 0.317536i | \(-0.897145\pi\) | ||||
−0.948246 | + | 0.317536i | \(0.897145\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1218.91 | −0.427737 | ||||||||
\(202\) | 413.852 | 0.144151 | ||||||||
\(203\) | −2663.41 | −0.920862 | ||||||||
\(204\) | −563.706 | −0.193467 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −77.6835 | −0.0262741 | ||||||||
\(207\) | 1309.08 | 0.439553 | ||||||||
\(208\) | −306.385 | −0.102135 | ||||||||
\(209\) | 2074.87 | 0.686707 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1029.61 | −0.335931 | −0.167965 | − | 0.985793i | \(-0.553720\pi\) | ||||
−0.167965 | + | 0.985793i | \(0.553720\pi\) | |||||||
\(212\) | −1183.83 | −0.383517 | ||||||||
\(213\) | 1578.47 | 0.507771 | ||||||||
\(214\) | −374.233 | −0.119542 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 389.126 | 0.122577 | ||||||||
\(217\) | −1848.59 | −0.578297 | ||||||||
\(218\) | −1734.62 | −0.538915 | ||||||||
\(219\) | 3005.08 | 0.927235 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −189.194 | −0.0575864 | ||||||||
\(222\) | −1152.90 | −0.348548 | ||||||||
\(223\) | 1245.08 | 0.373886 | 0.186943 | − | 0.982371i | \(-0.440142\pi\) | ||||
0.186943 | + | 0.982371i | \(0.440142\pi\) | |||||||
\(224\) | −1951.28 | −0.582032 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1038.53 | −0.305673 | ||||||||
\(227\) | −4598.29 | −1.34449 | −0.672245 | − | 0.740329i | \(-0.734670\pi\) | ||||
−0.672245 | + | 0.740329i | \(0.734670\pi\) | |||||||
\(228\) | 986.375 | 0.286510 | ||||||||
\(229\) | 6354.76 | 1.83378 | 0.916888 | − | 0.399145i | \(-0.130693\pi\) | ||||
0.916888 | + | 0.399145i | \(0.130693\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1675.04 | −0.477097 | ||||||||
\(232\) | −3074.87 | −0.870150 | ||||||||
\(233\) | 635.967 | 0.178814 | 0.0894068 | − | 0.995995i | \(-0.471503\pi\) | ||||
0.0894068 | + | 0.995995i | \(0.471503\pi\) | |||||||
\(234\) | 61.3511 | 0.0171395 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4217.66 | 1.16333 | ||||||||
\(237\) | −401.867 | −0.110144 | ||||||||
\(238\) | −316.142 | −0.0861028 | ||||||||
\(239\) | −6458.06 | −1.74786 | −0.873928 | − | 0.486056i | \(-0.838435\pi\) | ||||
−0.873928 | + | 0.486056i | \(0.838435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 509.747 | 0.136248 | 0.0681239 | − | 0.997677i | \(-0.478299\pi\) | ||||
0.0681239 | + | 0.997677i | \(0.478299\pi\) | |||||||
\(242\) | −639.493 | −0.169868 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 6136.35 | 1.61000 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −669.585 | −0.173541 | ||||||||
\(247\) | 331.053 | 0.0852810 | ||||||||
\(248\) | −2134.17 | −0.546450 | ||||||||
\(249\) | 1549.92 | 0.394468 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2645.82 | 0.665349 | 0.332674 | − | 0.943042i | \(-0.392049\pi\) | ||||
0.332674 | + | 0.943042i | \(0.392049\pi\) | |||||||
\(252\) | −796.299 | −0.199056 | ||||||||
\(253\) | −6505.64 | −1.61662 | ||||||||
\(254\) | −832.450 | −0.205640 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 181.620 | 0.0443408 | ||||||||
\(257\) | −3975.12 | −0.964829 | −0.482415 | − | 0.875943i | \(-0.660240\pi\) | ||||
−0.482415 | + | 0.875943i | \(0.660240\pi\) | |||||||
\(258\) | −250.771 | −0.0605128 | ||||||||
\(259\) | 5022.29 | 1.20490 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1920.18 | −0.455388 | ||||||||
\(262\) | −1631.68 | −0.384754 | ||||||||
\(263\) | 4820.25 | 1.13015 | 0.565075 | − | 0.825040i | \(-0.308847\pi\) | ||||
0.565075 | + | 0.825040i | \(0.308847\pi\) | |||||||
\(264\) | −1933.81 | −0.450824 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 553.187 | 0.127512 | ||||||||
\(267\) | −1832.09 | −0.419934 | ||||||||
\(268\) | 2879.68 | 0.656360 | ||||||||
\(269\) | 4196.29 | 0.951123 | 0.475562 | − | 0.879682i | \(-0.342245\pi\) | ||||
0.475562 | + | 0.879682i | \(0.342245\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2039.98 | −0.457269 | −0.228634 | − | 0.973512i | \(-0.573426\pi\) | ||||
−0.228634 | + | 0.973512i | \(0.573426\pi\) | |||||||
\(272\) | 1138.24 | 0.253734 | ||||||||
\(273\) | −267.259 | −0.0592499 | ||||||||
\(274\) | 2294.32 | 0.505858 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3092.72 | −0.674493 | ||||||||
\(277\) | −4613.40 | −1.00069 | −0.500347 | − | 0.865825i | \(-0.666794\pi\) | ||||
−0.500347 | + | 0.865825i | \(0.666794\pi\) | |||||||
\(278\) | 2065.15 | 0.445538 | ||||||||
\(279\) | −1332.74 | −0.285982 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2512.14 | −0.533317 | −0.266658 | − | 0.963791i | \(-0.585919\pi\) | ||||
−0.266658 | + | 0.963791i | \(0.585919\pi\) | |||||||
\(282\) | 217.747 | 0.0459811 | ||||||||
\(283\) | 1061.91 | 0.223054 | 0.111527 | − | 0.993761i | \(-0.464426\pi\) | ||||
0.111527 | + | 0.993761i | \(0.464426\pi\) | |||||||
\(284\) | −3729.17 | −0.779174 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −304.892 | −0.0630371 | ||||||||
\(287\) | 2916.85 | 0.599918 | ||||||||
\(288\) | −1406.77 | −0.287829 | ||||||||
\(289\) | −4210.13 | −0.856938 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4918.70 | −0.990856 | ||||||||
\(292\) | −7099.54 | −1.42284 | ||||||||
\(293\) | −7941.52 | −1.58344 | −0.791721 | − | 0.610883i | \(-0.790814\pi\) | ||||
−0.791721 | + | 0.610883i | \(0.790814\pi\) | |||||||
\(294\) | 536.345 | 0.106395 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5798.15 | 1.13855 | ||||||||
\(297\) | −1207.62 | −0.235936 | ||||||||
\(298\) | 1459.30 | 0.283675 | ||||||||
\(299\) | −1038.00 | −0.200766 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1092.41 | 0.209188 | ||||||||
\(302\) | −2468.99 | −0.470446 | ||||||||
\(303\) | −1299.75 | −0.246430 | ||||||||
\(304\) | −1991.69 | −0.375760 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −227.922 | −0.0425799 | ||||||||
\(307\) | −5405.88 | −1.00498 | −0.502492 | − | 0.864582i | \(-0.667583\pi\) | ||||
−0.502492 | + | 0.864582i | \(0.667583\pi\) | |||||||
\(308\) | 3957.30 | 0.732104 | ||||||||
\(309\) | 243.973 | 0.0449164 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4625.83 | −0.843431 | −0.421715 | − | 0.906728i | \(-0.638572\pi\) | ||||
−0.421715 | + | 0.906728i | \(0.638572\pi\) | |||||||
\(312\) | −308.546 | −0.0559871 | ||||||||
\(313\) | −1053.32 | −0.190214 | −0.0951069 | − | 0.995467i | \(-0.530319\pi\) | ||||
−0.0951069 | + | 0.995467i | \(0.530319\pi\) | |||||||
\(314\) | 661.941 | 0.118967 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 949.415 | 0.169015 | ||||||||
\(317\) | 2710.00 | 0.480154 | 0.240077 | − | 0.970754i | \(-0.422827\pi\) | ||||
0.240077 | + | 0.970754i | \(0.422827\pi\) | |||||||
\(318\) | −478.654 | −0.0844075 | ||||||||
\(319\) | 9542.57 | 1.67486 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1175.32 | 0.204361 | ||||||||
\(322\) | −1734.49 | −0.300184 | ||||||||
\(323\) | −1229.88 | −0.211864 | ||||||||
\(324\) | −574.090 | −0.0984380 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3458.43 | 0.587561 | ||||||||
\(327\) | 5447.77 | 0.921292 | ||||||||
\(328\) | 3367.46 | 0.566881 | ||||||||
\(329\) | −948.554 | −0.158953 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4387.70 | −0.728609 | −0.364304 | − | 0.931280i | \(-0.618693\pi\) | ||||
−0.364304 | + | 0.931280i | \(0.618693\pi\) | |||||||
\(332\) | −3661.72 | −0.605309 | ||||||||
\(333\) | 3620.81 | 0.595854 | ||||||||
\(334\) | −1485.96 | −0.243438 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1607.89 | 0.261064 | ||||||||
\(337\) | −3872.64 | −0.625983 | −0.312992 | − | 0.949756i | \(-0.601331\pi\) | ||||
−0.312992 | + | 0.949756i | \(0.601331\pi\) | |||||||
\(338\) | 2049.99 | 0.329896 | ||||||||
\(339\) | 3261.61 | 0.522556 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6623.19 | 1.05181 | ||||||||
\(342\) | 398.819 | 0.0630575 | ||||||||
\(343\) | −6618.29 | −1.04185 | ||||||||
\(344\) | 1261.17 | 0.197668 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2078.49 | 0.322949 | ||||||||
\(347\) | 5782.93 | 0.894651 | 0.447326 | − | 0.894371i | \(-0.352377\pi\) | ||||
0.447326 | + | 0.894371i | \(0.352377\pi\) | |||||||
\(348\) | 4536.45 | 0.698792 | ||||||||
\(349\) | −2916.63 | −0.447345 | −0.223673 | − | 0.974664i | \(-0.571805\pi\) | ||||
−0.223673 | + | 0.974664i | \(0.571805\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −192.680 | −0.0293005 | ||||||||
\(352\) | 6991.11 | 1.05860 | ||||||||
\(353\) | −3487.56 | −0.525847 | −0.262924 | − | 0.964817i | \(-0.584687\pi\) | ||||
−0.262924 | + | 0.964817i | \(0.584687\pi\) | |||||||
\(354\) | 1705.32 | 0.256036 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4328.34 | 0.644387 | ||||||||
\(357\) | 992.878 | 0.147195 | ||||||||
\(358\) | 1781.93 | 0.263066 | ||||||||
\(359\) | 10606.5 | 1.55931 | 0.779653 | − | 0.626212i | \(-0.215396\pi\) | ||||
0.779653 | + | 0.626212i | \(0.215396\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4706.96 | −0.686245 | ||||||||
\(362\) | 246.287 | 0.0357585 | ||||||||
\(363\) | 2008.39 | 0.290395 | ||||||||
\(364\) | 631.402 | 0.0909188 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2481.10 | 0.354342 | ||||||||
\(367\) | −2685.12 | −0.381913 | −0.190957 | − | 0.981598i | \(-0.561159\pi\) | ||||
−0.190957 | + | 0.981598i | \(0.561159\pi\) | |||||||
\(368\) | 6244.83 | 0.884604 | ||||||||
\(369\) | 2102.90 | 0.296674 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2085.12 | 0.291790 | ||||||||
\(372\) | 3148.61 | 0.438838 | ||||||||
\(373\) | −688.479 | −0.0955712 | −0.0477856 | − | 0.998858i | \(-0.515216\pi\) | ||||
−0.0477856 | + | 0.998858i | \(0.515216\pi\) | |||||||
\(374\) | 1132.69 | 0.156604 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1095.09 | −0.150199 | ||||||||
\(377\) | 1522.55 | 0.207999 | ||||||||
\(378\) | −321.966 | −0.0438099 | ||||||||
\(379\) | −12235.4 | −1.65829 | −0.829146 | − | 0.559033i | \(-0.811173\pi\) | ||||
−0.829146 | + | 0.559033i | \(0.811173\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2614.40 | 0.351548 | ||||||||
\(382\) | 3783.54 | 0.506762 | ||||||||
\(383\) | 1902.17 | 0.253777 | 0.126888 | − | 0.991917i | \(-0.459501\pi\) | ||||
0.126888 | + | 0.991917i | \(0.459501\pi\) | |||||||
\(384\) | 4307.78 | 0.572476 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1197.59 | −0.157917 | ||||||||
\(387\) | 787.572 | 0.103448 | ||||||||
\(388\) | 11620.5 | 1.52047 | ||||||||
\(389\) | 187.985 | 0.0245019 | 0.0122509 | − | 0.999925i | \(-0.496100\pi\) | ||||
0.0122509 | + | 0.999925i | \(0.496100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3856.21 | 0.498765 | ||||||||
\(392\) | −2697.37 | −0.347546 | ||||||||
\(393\) | 5124.47 | 0.657748 | ||||||||
\(394\) | 4833.31 | 0.618017 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2853.01 | 0.362043 | ||||||||
\(397\) | −7547.41 | −0.954140 | −0.477070 | − | 0.878865i | \(-0.658301\pi\) | ||||
−0.477070 | + | 0.878865i | \(0.658301\pi\) | |||||||
\(398\) | 5085.56 | 0.640493 | ||||||||
\(399\) | −1737.34 | −0.217985 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5396.95 | 0.672097 | 0.336049 | − | 0.941845i | \(-0.390909\pi\) | ||||
0.336049 | + | 0.941845i | \(0.390909\pi\) | |||||||
\(402\) | 1164.34 | 0.144457 | ||||||||
\(403\) | 1056.75 | 0.130622 | ||||||||
\(404\) | 3070.66 | 0.378147 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2544.17 | 0.310998 | ||||||||
\(407\) | −17994.1 | −2.19148 | ||||||||
\(408\) | 1146.26 | 0.139089 | ||||||||
\(409\) | −4090.41 | −0.494518 | −0.247259 | − | 0.968949i | \(-0.579530\pi\) | ||||
−0.247259 | + | 0.968949i | \(0.579530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7205.57 | −0.864780 | ||||||||
\(412\) | −576.390 | −0.0689240 | ||||||||
\(413\) | −7428.73 | −0.885095 | ||||||||
\(414\) | −1250.48 | −0.148448 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1115.46 | 0.131466 | ||||||||
\(417\) | −6485.83 | −0.761661 | ||||||||
\(418\) | −1981.98 | −0.231918 | ||||||||
\(419\) | 2841.80 | 0.331339 | 0.165670 | − | 0.986181i | \(-0.447021\pi\) | ||||
0.165670 | + | 0.986181i | \(0.447021\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16539.8 | −1.91473 | −0.957363 | − | 0.288889i | \(-0.906714\pi\) | ||||
−0.957363 | + | 0.288889i | \(0.906714\pi\) | |||||||
\(422\) | 983.516 | 0.113452 | ||||||||
\(423\) | −683.858 | −0.0786060 | ||||||||
\(424\) | 2407.24 | 0.275721 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1507.81 | −0.171487 | ||||||||
\(427\) | −10808.2 | −1.22493 | ||||||||
\(428\) | −2776.71 | −0.313592 | ||||||||
\(429\) | 957.544 | 0.107764 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2301.49 | −0.257214 | −0.128607 | − | 0.991696i | \(-0.541050\pi\) | ||||
−0.128607 | + | 0.991696i | \(0.541050\pi\) | |||||||
\(432\) | 1159.20 | 0.129102 | ||||||||
\(433\) | −7556.52 | −0.838668 | −0.419334 | − | 0.907832i | \(-0.637736\pi\) | ||||
−0.419334 | + | 0.907832i | \(0.637736\pi\) | |||||||
\(434\) | 1765.83 | 0.195305 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12870.4 | −1.41372 | ||||||||
\(437\) | −6747.61 | −0.738632 | ||||||||
\(438\) | −2870.54 | −0.313150 | ||||||||
\(439\) | −8328.02 | −0.905409 | −0.452705 | − | 0.891660i | \(-0.649541\pi\) | ||||
−0.452705 | + | 0.891660i | \(0.649541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1684.45 | −0.181886 | ||||||||
\(442\) | 180.724 | 0.0194484 | ||||||||
\(443\) | 11675.9 | 1.25223 | 0.626114 | − | 0.779731i | \(-0.284644\pi\) | ||||
0.626114 | + | 0.779731i | \(0.284644\pi\) | |||||||
\(444\) | −8554.21 | −0.914335 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1189.34 | −0.126271 | ||||||||
\(447\) | −4583.10 | −0.484951 | ||||||||
\(448\) | −2423.78 | −0.255609 | ||||||||
\(449\) | −1034.94 | −0.108779 | −0.0543893 | − | 0.998520i | \(-0.517321\pi\) | ||||
−0.0543893 | + | 0.998520i | \(0.517321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10450.6 | −1.09113 | ||||||||
\(452\) | −7705.60 | −0.801861 | ||||||||
\(453\) | 7754.13 | 0.804241 | ||||||||
\(454\) | 4392.43 | 0.454068 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2005.73 | −0.205980 | ||||||||
\(457\) | 15279.9 | 1.56403 | 0.782016 | − | 0.623259i | \(-0.214192\pi\) | ||||
0.782016 | + | 0.623259i | \(0.214192\pi\) | |||||||
\(458\) | −6070.26 | −0.619311 | ||||||||
\(459\) | 715.814 | 0.0727915 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15795.3 | 1.59580 | 0.797898 | − | 0.602793i | \(-0.205946\pi\) | ||||
0.797898 | + | 0.602793i | \(0.205946\pi\) | |||||||
\(462\) | 1600.05 | 0.161128 | ||||||||
\(463\) | 1773.18 | 0.177985 | 0.0889923 | − | 0.996032i | \(-0.471635\pi\) | ||||
0.0889923 | + | 0.996032i | \(0.471635\pi\) | |||||||
\(464\) | −9160.01 | −0.916471 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −607.494 | −0.0603898 | ||||||||
\(467\) | 13051.2 | 1.29323 | 0.646615 | − | 0.762817i | \(-0.276184\pi\) | ||||
0.646615 | + | 0.762817i | \(0.276184\pi\) | |||||||
\(468\) | 455.208 | 0.0449615 | ||||||||
\(469\) | −5072.10 | −0.499377 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2078.90 | −0.203377 | ||||||||
\(472\) | −8576.35 | −0.836353 | ||||||||
\(473\) | −3913.93 | −0.380471 | ||||||||
\(474\) | 383.875 | 0.0371982 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2345.69 | −0.225870 | ||||||||
\(477\) | 1503.26 | 0.144297 | ||||||||
\(478\) | 6168.94 | 0.590294 | ||||||||
\(479\) | −633.119 | −0.0603924 | −0.0301962 | − | 0.999544i | \(-0.509613\pi\) | ||||
−0.0301962 | + | 0.999544i | \(0.509613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2871.02 | −0.272156 | ||||||||
\(482\) | −486.926 | −0.0460142 | ||||||||
\(483\) | 5447.34 | 0.513173 | ||||||||
\(484\) | −4744.85 | −0.445610 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −232.121 | −0.0216651 | ||||||||
\(487\) | −6437.29 | −0.598976 | −0.299488 | − | 0.954100i | \(-0.596816\pi\) | ||||
−0.299488 | + | 0.954100i | \(0.596816\pi\) | |||||||
\(488\) | −12477.9 | −1.15747 | ||||||||
\(489\) | −10861.6 | −1.00445 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3114.41 | 0.286256 | 0.143128 | − | 0.989704i | \(-0.454284\pi\) | ||||
0.143128 | + | 0.989704i | \(0.454284\pi\) | |||||||
\(492\) | −4968.13 | −0.455245 | ||||||||
\(493\) | −5656.35 | −0.516733 | ||||||||
\(494\) | −316.232 | −0.0288015 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6357.67 | −0.575540 | ||||||||
\(497\) | 6568.33 | 0.592816 | ||||||||
\(498\) | −1480.53 | −0.133222 | ||||||||
\(499\) | −7664.80 | −0.687623 | −0.343811 | − | 0.939039i | \(-0.611718\pi\) | ||||
−0.343811 | + | 0.939039i | \(0.611718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4666.82 | 0.416164 | ||||||||
\(502\) | −2527.37 | −0.224705 | ||||||||
\(503\) | 8278.58 | 0.733844 | 0.366922 | − | 0.930252i | \(-0.380412\pi\) | ||||
0.366922 | + | 0.930252i | \(0.380412\pi\) | |||||||
\(504\) | 1619.22 | 0.143107 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6214.38 | 0.545974 | ||||||||
\(507\) | −6438.22 | −0.563967 | ||||||||
\(508\) | −6176.55 | −0.539449 | ||||||||
\(509\) | −7111.22 | −0.619252 | −0.309626 | − | 0.950858i | \(-0.600204\pi\) | ||||
−0.309626 | + | 0.950858i | \(0.600204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12504.7 | 1.08253 | ||||||||
\(512\) | −11660.9 | −1.00653 | ||||||||
\(513\) | −1252.53 | −0.107799 | ||||||||
\(514\) | 3797.15 | 0.325847 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1860.65 | −0.158741 | ||||||||
\(517\) | 3398.51 | 0.289103 | ||||||||
\(518\) | −4797.44 | −0.406926 | ||||||||
\(519\) | −6527.72 | −0.552091 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −812.539 | −0.0683262 | −0.0341631 | − | 0.999416i | \(-0.510877\pi\) | ||||
−0.0341631 | + | 0.999416i | \(0.510877\pi\) | |||||||
\(522\) | 1834.22 | 0.153796 | ||||||||
\(523\) | 6446.12 | 0.538946 | 0.269473 | − | 0.963008i | \(-0.413150\pi\) | ||||
0.269473 | + | 0.963008i | \(0.413150\pi\) | |||||||
\(524\) | −12106.6 | −1.00931 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4604.45 | −0.381680 | ||||||||
\(527\) | −3925.89 | −0.324506 | ||||||||
\(528\) | −5760.80 | −0.474823 | ||||||||
\(529\) | 8989.76 | 0.738865 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5355.73 | −0.437701 | ||||||||
\(532\) | 4104.49 | 0.334497 | ||||||||
\(533\) | −1667.43 | −0.135506 | ||||||||
\(534\) | 1750.07 | 0.141822 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5855.66 | −0.471877 | ||||||||
\(537\) | −5596.33 | −0.449719 | ||||||||
\(538\) | −4008.42 | −0.321218 | ||||||||
\(539\) | 8371.06 | 0.668955 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4552.44 | −0.361783 | −0.180892 | − | 0.983503i | \(-0.557898\pi\) | ||||
−0.180892 | + | 0.983503i | \(0.557898\pi\) | |||||||
\(542\) | 1948.65 | 0.154431 | ||||||||
\(543\) | −773.491 | −0.0611302 | ||||||||
\(544\) | −4143.97 | −0.326602 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 255.293 | 0.0200102 | ||||||||
\(547\) | 14318.6 | 1.11923 | 0.559615 | − | 0.828753i | \(-0.310949\pi\) | ||||
0.559615 | + | 0.828753i | \(0.310949\pi\) | |||||||
\(548\) | 17023.2 | 1.32700 | ||||||||
\(549\) | −7792.15 | −0.605757 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9897.50 | 0.765241 | ||||||||
\(552\) | 6288.86 | 0.484913 | ||||||||
\(553\) | −1672.24 | −0.128591 | ||||||||
\(554\) | 4406.86 | 0.337959 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15322.8 | 1.16877 | ||||||||
\(557\) | −14882.2 | −1.13210 | −0.566050 | − | 0.824371i | \(-0.691529\pi\) | ||||
−0.566050 | + | 0.824371i | \(0.691529\pi\) | |||||||
\(558\) | 1273.07 | 0.0965831 | ||||||||
\(559\) | −624.482 | −0.0472500 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3557.32 | −0.267719 | ||||||||
\(562\) | 2399.68 | 0.180114 | ||||||||
\(563\) | 5655.46 | 0.423356 | 0.211678 | − | 0.977339i | \(-0.432107\pi\) | ||||
0.211678 | + | 0.977339i | \(0.432107\pi\) | |||||||
\(564\) | 1615.62 | 0.120621 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1014.37 | −0.0753308 | ||||||||
\(567\) | 1011.17 | 0.0748943 | ||||||||
\(568\) | 7583.03 | 0.560170 | ||||||||
\(569\) | −10016.7 | −0.738001 | −0.369001 | − | 0.929429i | \(-0.620300\pi\) | ||||
−0.369001 | + | 0.929429i | \(0.620300\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17386.3 | −1.27424 | −0.637121 | − | 0.770764i | \(-0.719875\pi\) | ||||
−0.637121 | + | 0.770764i | \(0.719875\pi\) | |||||||
\(572\) | −2262.21 | −0.165363 | ||||||||
\(573\) | −11882.6 | −0.866324 | ||||||||
\(574\) | −2786.27 | −0.202607 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1747.42 | −0.126405 | ||||||||
\(577\) | −8886.10 | −0.641132 | −0.320566 | − | 0.947226i | \(-0.603873\pi\) | ||||
−0.320566 | + | 0.947226i | \(0.603873\pi\) | |||||||
\(578\) | 4021.65 | 0.289409 | ||||||||
\(579\) | 3761.16 | 0.269963 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6449.52 | 0.460536 | ||||||||
\(582\) | 4698.49 | 0.334637 | ||||||||
\(583\) | −7470.65 | −0.530708 | ||||||||
\(584\) | 14436.5 | 1.02292 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7585.97 | 0.534767 | ||||||||
\(587\) | 20817.3 | 1.46375 | 0.731876 | − | 0.681438i | \(-0.238645\pi\) | ||||
0.731876 | + | 0.681438i | \(0.238645\pi\) | |||||||
\(588\) | 3979.53 | 0.279104 | ||||||||
\(589\) | 6869.54 | 0.480568 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15179.5 | −1.05652 | ||||||||
\(592\) | 17272.7 | 1.19916 | ||||||||
\(593\) | 24320.9 | 1.68422 | 0.842108 | − | 0.539309i | \(-0.181314\pi\) | ||||
0.842108 | + | 0.539309i | \(0.181314\pi\) | |||||||
\(594\) | 1153.55 | 0.0796815 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10827.6 | 0.744155 | ||||||||
\(597\) | −15971.7 | −1.09494 | ||||||||
\(598\) | 991.527 | 0.0678036 | ||||||||
\(599\) | 18650.6 | 1.27219 | 0.636096 | − | 0.771610i | \(-0.280548\pi\) | ||||
0.636096 | + | 0.771610i | \(0.280548\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15558.8 | −1.05600 | −0.528000 | − | 0.849245i | \(-0.677058\pi\) | ||||
−0.528000 | + | 0.849245i | \(0.677058\pi\) | |||||||
\(602\) | −1043.50 | −0.0706479 | ||||||||
\(603\) | −3656.72 | −0.246954 | ||||||||
\(604\) | −18319.2 | −1.23410 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1241.56 | 0.0832257 | ||||||||
\(607\) | 27620.1 | 1.84690 | 0.923448 | − | 0.383722i | \(-0.125358\pi\) | ||||
0.923448 | + | 0.383722i | \(0.125358\pi\) | |||||||
\(608\) | 7251.14 | 0.483672 | ||||||||
\(609\) | −7990.24 | −0.531660 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 542.245 | 0.0359033 | ||||||||
\(612\) | −1691.12 | −0.111698 | ||||||||
\(613\) | −10581.1 | −0.697173 | −0.348587 | − | 0.937277i | \(-0.613338\pi\) | ||||
−0.348587 | + | 0.937277i | \(0.613338\pi\) | |||||||
\(614\) | 5163.86 | 0.339408 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8046.93 | −0.526331 | ||||||||
\(617\) | 26415.2 | 1.72356 | 0.861780 | − | 0.507283i | \(-0.169350\pi\) | ||||
0.861780 | + | 0.507283i | \(0.169350\pi\) | |||||||
\(618\) | −233.051 | −0.0151694 | ||||||||
\(619\) | −4747.92 | −0.308296 | −0.154148 | − | 0.988048i | \(-0.549263\pi\) | ||||
−0.154148 | + | 0.988048i | \(0.549263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3927.25 | 0.253776 | ||||||||
\(622\) | 4418.73 | 0.284847 | ||||||||
\(623\) | −7623.68 | −0.490267 | ||||||||
\(624\) | −919.156 | −0.0589674 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1006.16 | 0.0642399 | ||||||||
\(627\) | 6224.61 | 0.396471 | ||||||||
\(628\) | 4911.42 | 0.312081 | ||||||||
\(629\) | 10666.0 | 0.676120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24505.3 | −1.54602 | −0.773012 | − | 0.634391i | \(-0.781251\pi\) | ||||
−0.773012 | + | 0.634391i | \(0.781251\pi\) | |||||||
\(632\) | −1930.58 | −0.121510 | ||||||||
\(633\) | −3088.84 | −0.193950 | ||||||||
\(634\) | −2588.68 | −0.162160 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3551.48 | −0.221423 | ||||||||
\(637\) | 1335.63 | 0.0830764 | ||||||||
\(638\) | −9115.35 | −0.565643 | ||||||||
\(639\) | 4735.42 | 0.293162 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6380.17 | −0.393138 | −0.196569 | − | 0.980490i | \(-0.562980\pi\) | ||||
−0.196569 | + | 0.980490i | \(0.562980\pi\) | |||||||
\(642\) | −1122.70 | −0.0690178 | ||||||||
\(643\) | −21527.0 | −1.32029 | −0.660143 | − | 0.751140i | \(-0.729504\pi\) | ||||
−0.660143 | + | 0.751140i | \(0.729504\pi\) | |||||||
\(644\) | −12869.4 | −0.787462 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1174.82 | 0.0715519 | ||||||||
\(647\) | 23849.2 | 1.44916 | 0.724581 | − | 0.689189i | \(-0.242033\pi\) | ||||
0.724581 | + | 0.689189i | \(0.242033\pi\) | |||||||
\(648\) | 1167.38 | 0.0707699 | ||||||||
\(649\) | 26615.9 | 1.60981 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5545.77 | −0.333880 | ||||||||
\(652\) | 25660.6 | 1.54133 | ||||||||
\(653\) | 11845.8 | 0.709898 | 0.354949 | − | 0.934886i | \(-0.384498\pi\) | ||||
0.354949 | + | 0.934886i | \(0.384498\pi\) | |||||||
\(654\) | −5203.87 | −0.311143 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10031.6 | 0.597058 | ||||||||
\(657\) | 9015.24 | 0.535339 | ||||||||
\(658\) | 906.087 | 0.0536823 | ||||||||
\(659\) | −13126.8 | −0.775944 | −0.387972 | − | 0.921671i | \(-0.626824\pi\) | ||||
−0.387972 | + | 0.921671i | \(0.626824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24494.4 | 1.44133 | 0.720667 | − | 0.693281i | \(-0.243836\pi\) | ||||
0.720667 | + | 0.693281i | \(0.243836\pi\) | |||||||
\(662\) | 4191.26 | 0.246069 | ||||||||
\(663\) | −567.583 | −0.0332475 | ||||||||
\(664\) | 7445.87 | 0.435174 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3458.71 | −0.201235 | ||||||||
\(667\) | −31033.1 | −1.80151 | ||||||||
\(668\) | −11025.4 | −0.638602 | ||||||||
\(669\) | 3735.24 | 0.215863 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38724.0 | 2.22790 | ||||||||
\(672\) | −5853.83 | −0.336037 | ||||||||
\(673\) | −28081.1 | −1.60839 | −0.804196 | − | 0.594364i | \(-0.797404\pi\) | ||||
−0.804196 | + | 0.594364i | \(0.797404\pi\) | |||||||
\(674\) | 3699.27 | 0.211410 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15210.4 | 0.865406 | ||||||||
\(677\) | −6825.24 | −0.387467 | −0.193733 | − | 0.981054i | \(-0.562060\pi\) | ||||
−0.193733 | + | 0.981054i | \(0.562060\pi\) | |||||||
\(678\) | −3115.59 | −0.176480 | ||||||||
\(679\) | −20467.6 | −1.15681 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13794.9 | −0.776242 | ||||||||
\(682\) | −6326.67 | −0.355221 | ||||||||
\(683\) | −31450.7 | −1.76197 | −0.880987 | − | 0.473140i | \(-0.843121\pi\) | ||||
−0.880987 | + | 0.473140i | \(0.843121\pi\) | |||||||
\(684\) | 2959.12 | 0.165417 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6321.99 | 0.351858 | ||||||||
\(687\) | 19064.3 | 1.05873 | ||||||||
\(688\) | 3757.02 | 0.208190 | ||||||||
\(689\) | −1191.97 | −0.0659077 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6136.45 | 0.337832 | 0.168916 | − | 0.985630i | \(-0.445973\pi\) | ||||
0.168916 | + | 0.985630i | \(0.445973\pi\) | |||||||
\(692\) | 15421.8 | 0.847182 | ||||||||
\(693\) | −5025.12 | −0.275452 | ||||||||
\(694\) | −5524.03 | −0.302146 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9224.60 | −0.502382 | ||||||||
\(697\) | 6194.59 | 0.336638 | ||||||||
\(698\) | 2786.05 | 0.151080 | ||||||||
\(699\) | 1907.90 | 0.103238 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5291.43 | 0.285099 | 0.142550 | − | 0.989788i | \(-0.454470\pi\) | ||||
0.142550 | + | 0.989788i | \(0.454470\pi\) | |||||||
\(702\) | 184.053 | 0.00989551 | ||||||||
\(703\) | −18663.3 | −1.00128 | ||||||||
\(704\) | 8684.00 | 0.464902 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3331.42 | 0.177592 | ||||||||
\(707\) | −5408.48 | −0.287704 | ||||||||
\(708\) | 12653.0 | 0.671650 | ||||||||
\(709\) | −4385.62 | −0.232307 | −0.116153 | − | 0.993231i | \(-0.537056\pi\) | ||||
−0.116153 | + | 0.993231i | \(0.537056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1205.60 | −0.0635915 | ||||||||
\(712\) | −8801.42 | −0.463268 | ||||||||
\(713\) | −21539.1 | −1.13134 | ||||||||
\(714\) | −948.427 | −0.0497115 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13221.4 | 0.690093 | ||||||||
\(717\) | −19374.2 | −1.00912 | ||||||||
\(718\) | −10131.7 | −0.526616 | ||||||||
\(719\) | 6410.26 | 0.332493 | 0.166246 | − | 0.986084i | \(-0.446835\pi\) | ||||
0.166246 | + | 0.986084i | \(0.446835\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1015.22 | 0.0524393 | ||||||||
\(722\) | 4496.23 | 0.231762 | ||||||||
\(723\) | 1529.24 | 0.0786627 | ||||||||
\(724\) | 1827.38 | 0.0938040 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1918.48 | −0.0980736 | ||||||||
\(727\) | 31663.6 | 1.61532 | 0.807661 | − | 0.589647i | \(-0.200733\pi\) | ||||
0.807661 | + | 0.589647i | \(0.200733\pi\) | |||||||
\(728\) | −1283.92 | −0.0653642 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2319.98 | 0.117384 | ||||||||
\(732\) | 18409.0 | 0.929532 | ||||||||
\(733\) | 25767.7 | 1.29843 | 0.649215 | − | 0.760605i | \(-0.275097\pi\) | ||||
0.649215 | + | 0.760605i | \(0.275097\pi\) | |||||||
\(734\) | 2564.91 | 0.128982 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22735.5 | −1.13865 | ||||||||
\(737\) | 18172.5 | 0.908267 | ||||||||
\(738\) | −2008.75 | −0.100194 | ||||||||
\(739\) | 3389.01 | 0.168697 | 0.0843484 | − | 0.996436i | \(-0.473119\pi\) | ||||
0.0843484 | + | 0.996436i | \(0.473119\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 993.159 | 0.0492370 | ||||||||
\(742\) | −1991.77 | −0.0985447 | ||||||||
\(743\) | −17203.7 | −0.849453 | −0.424727 | − | 0.905322i | \(-0.639630\pi\) | ||||
−0.424727 | + | 0.905322i | \(0.639630\pi\) | |||||||
\(744\) | −6402.50 | −0.315493 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 657.655 | 0.0322768 | ||||||||
\(747\) | 4649.77 | 0.227746 | ||||||||
\(748\) | 8404.21 | 0.410813 | ||||||||
\(749\) | 4890.72 | 0.238589 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17081.3 | 0.829970 | 0.414985 | − | 0.909828i | \(-0.363787\pi\) | ||||
0.414985 | + | 0.909828i | \(0.363787\pi\) | |||||||
\(752\) | −3262.27 | −0.158195 | ||||||||
\(753\) | 7937.46 | 0.384139 | ||||||||
\(754\) | −1454.39 | −0.0702463 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2388.90 | −0.114925 | ||||||||
\(757\) | 4684.65 | 0.224923 | 0.112461 | − | 0.993656i | \(-0.464127\pi\) | ||||
0.112461 | + | 0.993656i | \(0.464127\pi\) | |||||||
\(758\) | 11687.7 | 0.560046 | ||||||||
\(759\) | −19516.9 | −0.933359 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25366.8 | 1.20834 | 0.604169 | − | 0.796856i | \(-0.293505\pi\) | ||||
0.604169 | + | 0.796856i | \(0.293505\pi\) | |||||||
\(762\) | −2497.35 | −0.118726 | ||||||||
\(763\) | 22669.2 | 1.07560 | ||||||||
\(764\) | 28072.8 | 1.32937 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1817.01 | −0.0857068 | ||||||||
\(767\) | 4246.67 | 0.199920 | ||||||||
\(768\) | 544.859 | 0.0256001 | ||||||||
\(769\) | −21287.7 | −0.998250 | −0.499125 | − | 0.866530i | \(-0.666345\pi\) | ||||
−0.499125 | + | 0.866530i | \(0.666345\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11925.4 | −0.557044 | ||||||||
\(772\) | −8885.79 | −0.414257 | ||||||||
\(773\) | 23748.4 | 1.10501 | 0.552504 | − | 0.833511i | \(-0.313673\pi\) | ||||
0.552504 | + | 0.833511i | \(0.313673\pi\) | |||||||
\(774\) | −752.312 | −0.0349371 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −23629.5 | −1.09311 | ||||||||
\(777\) | 15066.9 | 0.695651 | ||||||||
\(778\) | −179.569 | −0.00827490 | ||||||||
\(779\) | −10839.3 | −0.498535 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23533.2 | −1.07821 | ||||||||
\(782\) | −3683.57 | −0.168445 | ||||||||
\(783\) | −5760.55 | −0.262919 | ||||||||
\(784\) | −8035.46 | −0.366047 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4895.04 | −0.222138 | ||||||||
\(787\) | 19191.0 | 0.869231 | 0.434615 | − | 0.900616i | \(-0.356884\pi\) | ||||
0.434615 | + | 0.900616i | \(0.356884\pi\) | |||||||
\(788\) | 35861.8 | 1.62122 | ||||||||
\(789\) | 14460.8 | 0.652492 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13572.2 | 0.610077 | ||||||||
\(792\) | −5801.42 | −0.260283 | ||||||||
\(793\) | 6178.55 | 0.276680 | ||||||||
\(794\) | 7209.51 | 0.322237 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 37733.4 | 1.68018 | ||||||||
\(797\) | −20205.5 | −0.898012 | −0.449006 | − | 0.893529i | \(-0.648222\pi\) | ||||
−0.449006 | + | 0.893529i | \(0.648222\pi\) | |||||||
\(798\) | 1659.56 | 0.0736188 | ||||||||
\(799\) | −2014.46 | −0.0891948 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5496.28 | −0.242449 | ||||||||
\(802\) | −5155.33 | −0.226984 | ||||||||
\(803\) | −44802.3 | −1.96891 | ||||||||
\(804\) | 8639.05 | 0.378950 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1009.44 | −0.0441143 | ||||||||
\(807\) | 12588.9 | 0.549131 | ||||||||
\(808\) | −6244.00 | −0.271861 | ||||||||
\(809\) | −18217.3 | −0.791700 | −0.395850 | − | 0.918315i | \(-0.629550\pi\) | ||||
−0.395850 | + | 0.918315i | \(0.629550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25637.1 | −1.11004 | −0.555019 | − | 0.831837i | \(-0.687289\pi\) | ||||
−0.555019 | + | 0.831837i | \(0.687289\pi\) | |||||||
\(812\) | 18877.0 | 0.815830 | ||||||||
\(813\) | −6119.93 | −0.264004 | ||||||||
\(814\) | 17188.5 | 0.740117 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3414.71 | 0.146493 | ||||||||
\(817\) | −4059.51 | −0.173836 | ||||||||
\(818\) | 3907.29 | 0.167011 | ||||||||
\(819\) | −801.776 | −0.0342080 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3325.18 | −0.141352 | −0.0706758 | − | 0.997499i | \(-0.522516\pi\) | ||||
−0.0706758 | + | 0.997499i | \(0.522516\pi\) | |||||||
\(822\) | 6882.97 | 0.292057 | ||||||||
\(823\) | 4282.17 | 0.181370 | 0.0906848 | − | 0.995880i | \(-0.471094\pi\) | ||||
0.0906848 | + | 0.995880i | \(0.471094\pi\) | |||||||
\(824\) | 1172.05 | 0.0495515 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7096.15 | 0.298918 | ||||||||
\(827\) | −15503.1 | −0.651869 | −0.325935 | − | 0.945392i | \(-0.605679\pi\) | ||||
−0.325935 | + | 0.945392i | \(0.605679\pi\) | |||||||
\(828\) | −9278.17 | −0.389419 | ||||||||
\(829\) | 26065.5 | 1.09203 | 0.546015 | − | 0.837775i | \(-0.316144\pi\) | ||||
0.546015 | + | 0.837775i | \(0.316144\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13840.2 | −0.577751 | ||||||||
\(832\) | 1385.56 | 0.0577353 | ||||||||
\(833\) | −4961.93 | −0.206388 | ||||||||
\(834\) | 6195.46 | 0.257232 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −14705.7 | −0.608383 | ||||||||
\(837\) | −3998.21 | −0.165112 | ||||||||
\(838\) | −2714.57 | −0.111901 | ||||||||
\(839\) | 44675.9 | 1.83836 | 0.919180 | − | 0.393838i | \(-0.128853\pi\) | ||||
0.919180 | + | 0.393838i | \(0.128853\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21130.8 | 0.866406 | ||||||||
\(842\) | 15799.3 | 0.646650 | ||||||||
\(843\) | −7536.43 | −0.307910 | ||||||||
\(844\) | 7297.41 | 0.297615 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 653.242 | 0.0265472 | ||||||||
\(847\) | 8357.30 | 0.339032 | ||||||||
\(848\) | 7171.14 | 0.290399 | ||||||||
\(849\) | 3185.74 | 0.128780 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58517.8 | 2.35719 | ||||||||
\(852\) | −11187.5 | −0.449856 | ||||||||
\(853\) | −16623.4 | −0.667261 | −0.333631 | − | 0.942704i | \(-0.608274\pi\) | ||||
−0.333631 | + | 0.942704i | \(0.608274\pi\) | |||||||
\(854\) | 10324.3 | 0.413689 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5646.26 | 0.225450 | ||||||||
\(857\) | −5804.93 | −0.231380 | −0.115690 | − | 0.993285i | \(-0.536908\pi\) | ||||
−0.115690 | + | 0.993285i | \(0.536908\pi\) | |||||||
\(858\) | −914.675 | −0.0363945 | ||||||||
\(859\) | −30984.8 | −1.23072 | −0.615360 | − | 0.788246i | \(-0.710989\pi\) | ||||
−0.615360 | + | 0.788246i | \(0.710989\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8750.56 | 0.346363 | ||||||||
\(862\) | 2198.46 | 0.0868674 | ||||||||
\(863\) | 3511.89 | 0.138524 | 0.0692620 | − | 0.997599i | \(-0.477936\pi\) | ||||
0.0692620 | + | 0.997599i | \(0.477936\pi\) | |||||||
\(864\) | −4220.31 | −0.166178 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7218.22 | 0.283239 | ||||||||
\(867\) | −12630.4 | −0.494753 | ||||||||
\(868\) | 13101.9 | 0.512337 | ||||||||
\(869\) | 5991.37 | 0.233882 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2899.49 | 0.112796 | ||||||||
\(872\) | 26171.2 | 1.01636 | ||||||||
\(873\) | −14756.1 | −0.572071 | ||||||||
\(874\) | 6445.52 | 0.249454 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21298.6 | −0.821476 | ||||||||
\(877\) | 36724.0 | 1.41401 | 0.707003 | − | 0.707211i | \(-0.250047\pi\) | ||||
0.707003 | + | 0.707211i | \(0.250047\pi\) | |||||||
\(878\) | 7955.18 | 0.305779 | ||||||||
\(879\) | −23824.5 | −0.914200 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41245.8 | 1.57731 | 0.788654 | − | 0.614838i | \(-0.210779\pi\) | ||||
0.788654 | + | 0.614838i | \(0.210779\pi\) | |||||||
\(882\) | 1609.03 | 0.0614274 | ||||||||
\(883\) | 2065.87 | 0.0787340 | 0.0393670 | − | 0.999225i | \(-0.487466\pi\) | ||||
0.0393670 | + | 0.999225i | \(0.487466\pi\) | |||||||
\(884\) | 1340.92 | 0.0510182 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11153.1 | −0.422909 | ||||||||
\(887\) | −10866.5 | −0.411342 | −0.205671 | − | 0.978621i | \(-0.565938\pi\) | ||||
−0.205671 | + | 0.978621i | \(0.565938\pi\) | |||||||
\(888\) | 17394.5 | 0.657342 | ||||||||
\(889\) | 10879.0 | 0.410427 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3622.85 | −0.136218 | ||||||||
\(892\) | −8824.54 | −0.331242 | ||||||||
\(893\) | 3524.92 | 0.132091 | ||||||||
\(894\) | 4377.91 | 0.163780 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 17925.5 | 0.668358 | ||||||||
\(897\) | −3114.00 | −0.115912 | ||||||||
\(898\) | 988.601 | 0.0367372 | ||||||||
\(899\) | 31593.8 | 1.17209 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4428.22 | 0.163735 | ||||||||
\(902\) | 9982.74 | 0.368502 | ||||||||
\(903\) | 3277.23 | 0.120775 | ||||||||
\(904\) | 15668.9 | 0.576481 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7406.98 | −0.271612 | ||||||||
\(907\) | 12436.5 | 0.455290 | 0.227645 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227645 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(908\) | 32590.6 | 1.19114 | ||||||||
\(909\) | −3899.24 | −0.142277 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19230.5 | 0.699380 | 0.349690 | − | 0.936866i | \(-0.386287\pi\) | ||||
0.349690 | + | 0.936866i | \(0.386287\pi\) | |||||||
\(912\) | −5975.06 | −0.216945 | ||||||||
\(913\) | −23107.6 | −0.837623 | ||||||||
\(914\) | −14595.8 | −0.528212 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −45039.6 | −1.62462 | ||||||||
\(917\) | 21323.9 | 0.767912 | ||||||||
\(918\) | −683.767 | −0.0245835 | ||||||||
\(919\) | −24215.5 | −0.869201 | −0.434600 | − | 0.900623i | \(-0.643110\pi\) | ||||
−0.434600 | + | 0.900623i | \(0.643110\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16217.7 | −0.580228 | ||||||||
\(922\) | −15088.2 | −0.538940 | ||||||||
\(923\) | −3754.82 | −0.133902 | ||||||||
\(924\) | 11871.9 | 0.422681 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1693.80 | −0.0601098 | ||||||||
\(927\) | 731.920 | 0.0259325 | ||||||||
\(928\) | 33348.8 | 1.17967 | ||||||||
\(929\) | −19194.4 | −0.677878 | −0.338939 | − | 0.940808i | \(-0.610068\pi\) | ||||
−0.338939 | + | 0.940808i | \(0.610068\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8682.41 | 0.305644 | ||||||||
\(932\) | −4507.44 | −0.158418 | ||||||||
\(933\) | −13877.5 | −0.486955 | ||||||||
\(934\) | −12466.9 | −0.436756 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −925.637 | −0.0323242 | ||||||||
\(937\) | 37196.1 | 1.29685 | 0.648423 | − | 0.761281i | \(-0.275429\pi\) | ||||
0.648423 | + | 0.761281i | \(0.275429\pi\) | |||||||
\(938\) | 4845.02 | 0.168652 | ||||||||
\(939\) | −3159.95 | −0.109820 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33682.5 | 1.16686 | 0.583431 | − | 0.812163i | \(-0.301710\pi\) | ||||
0.583431 | + | 0.812163i | \(0.301710\pi\) | |||||||
\(942\) | 1985.82 | 0.0686854 | ||||||||
\(943\) | 33986.1 | 1.17364 | ||||||||
\(944\) | −25548.9 | −0.880875 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3738.70 | 0.128494 | ||||||||
\(947\) | 44386.5 | 1.52309 | 0.761546 | − | 0.648110i | \(-0.224440\pi\) | ||||
0.761546 | + | 0.648110i | \(0.224440\pi\) | |||||||
\(948\) | 2848.24 | 0.0975809 | ||||||||
\(949\) | −7148.37 | −0.244516 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8130.01 | 0.277217 | ||||||||
\(952\) | 4769.81 | 0.162385 | ||||||||
\(953\) | 7655.67 | 0.260222 | 0.130111 | − | 0.991499i | \(-0.458467\pi\) | ||||
0.130111 | + | 0.991499i | \(0.458467\pi\) | |||||||
\(954\) | −1435.96 | −0.0487327 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 45771.8 | 1.54850 | ||||||||
\(957\) | 28627.7 | 0.966983 | ||||||||
\(958\) | 604.774 | 0.0203960 | ||||||||
\(959\) | −29983.7 | −1.00962 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7862.76 | −0.263931 | ||||||||
\(962\) | 2742.48 | 0.0919139 | ||||||||
\(963\) | 3525.96 | 0.117988 | ||||||||
\(964\) | −3612.85 | −0.120708 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5203.46 | −0.173311 | ||||||||
\(967\) | −14646.4 | −0.487070 | −0.243535 | − | 0.969892i | \(-0.578307\pi\) | ||||
−0.243535 | + | 0.969892i | \(0.578307\pi\) | |||||||
\(968\) | 9648.37 | 0.320362 | ||||||||
\(969\) | −3689.63 | −0.122320 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44429.7 | −1.46840 | −0.734200 | − | 0.678933i | \(-0.762443\pi\) | ||||
−0.734200 | + | 0.678933i | \(0.762443\pi\) | |||||||
\(972\) | −1722.27 | −0.0568332 | ||||||||
\(973\) | −26988.7 | −0.889229 | ||||||||
\(974\) | 6149.09 | 0.202289 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37171.5 | −1.21909 | ||||||||
\(977\) | 4615.83 | 0.151150 | 0.0755749 | − | 0.997140i | \(-0.475921\pi\) | ||||
0.0755749 | + | 0.997140i | \(0.475921\pi\) | |||||||
\(978\) | 10375.3 | 0.339228 | ||||||||
\(979\) | 27314.4 | 0.891698 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16343.3 | 0.531908 | ||||||||
\(982\) | −2974.98 | −0.0966756 | ||||||||
\(983\) | −20086.5 | −0.651738 | −0.325869 | − | 0.945415i | \(-0.605657\pi\) | ||||
−0.325869 | + | 0.945415i | \(0.605657\pi\) | |||||||
\(984\) | 10102.4 | 0.327289 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5403.12 | 0.174513 | ||||||||
\(987\) | −2845.66 | −0.0917714 | ||||||||
\(988\) | −2346.35 | −0.0755540 | ||||||||
\(989\) | 12728.4 | 0.409240 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 983.787 | 0.0315348 | 0.0157674 | − | 0.999876i | \(-0.494981\pi\) | ||||
0.0157674 | + | 0.999876i | \(0.494981\pi\) | |||||||
\(992\) | 23146.4 | 0.740824 | ||||||||
\(993\) | −13163.1 | −0.420663 | ||||||||
\(994\) | −6274.26 | −0.200209 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10985.1 | −0.349476 | ||||||||
\(997\) | 884.133 | 0.0280850 | 0.0140425 | − | 0.999901i | \(-0.495530\pi\) | ||||
0.0140425 | + | 0.999901i | \(0.495530\pi\) | |||||||
\(998\) | 7321.65 | 0.232227 | ||||||||
\(999\) | 10862.4 | 0.344016 |
(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 | 1875.4.a.g.1.6 | 14 | ||
5.4 | even | 2 | 1875.4.a.f.1.9 | 14 | |||
25.6 | even | 5 | 75.4.g.b.61.5 | yes | 28 | ||
25.21 | even | 5 | 75.4.g.b.16.5 | ✓ | 28 | ||
75.56 | odd | 10 | 225.4.h.a.136.3 | 28 | |||
75.71 | odd | 10 | 225.4.h.a.91.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.b.16.5 | ✓ | 28 | 25.21 | even | 5 | ||
75.4.g.b.61.5 | yes | 28 | 25.6 | even | 5 | ||
225.4.h.a.91.3 | 28 | 75.71 | odd | 10 | |||
225.4.h.a.136.3 | 28 | 75.56 | odd | 10 | |||
1875.4.a.f.1.9 | 14 | 5.4 | even | 2 | |||
1875.4.a.g.1.6 | 14 | 1.1 | even | 1 | trivial |