Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1540841.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 27x^{2} - 18x + 92 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.60719\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.607192 | 0.214675 | 0.107337 | − | 0.994223i | \(-0.465768\pi\) | ||||
0.107337 | + | 0.994223i | \(0.465768\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −7.63132 | −0.953915 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.82158 | −0.123943 | ||||||||
\(7\) | −8.95080 | −0.483298 | −0.241649 | − | 0.970364i | \(-0.577688\pi\) | ||||
−0.241649 | + | 0.970364i | \(0.577688\pi\) | |||||||
\(8\) | −9.49121 | −0.419456 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 22.8940 | 0.550743 | ||||||||
\(13\) | 0.460387 | 0.00982218 | 0.00491109 | − | 0.999988i | \(-0.498437\pi\) | ||||
0.00491109 | + | 0.999988i | \(0.498437\pi\) | |||||||
\(14\) | −5.43485 | −0.103752 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 55.2876 | 0.863868 | ||||||||
\(17\) | −128.395 | −1.83179 | −0.915893 | − | 0.401423i | \(-0.868516\pi\) | ||||
−0.915893 | + | 0.401423i | \(0.868516\pi\) | |||||||
\(18\) | 5.46473 | 0.0715582 | ||||||||
\(19\) | −0.0245858 | −0.000296862 0 | −0.000148431 | − | 1.00000i | \(-0.500047\pi\) | ||||
−0.000148431 | 1.00000i | \(0.500047\pi\) | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 26.8524 | 0.279032 | ||||||||
\(22\) | −6.67911 | −0.0647269 | ||||||||
\(23\) | −171.528 | −1.55505 | −0.777525 | − | 0.628852i | \(-0.783525\pi\) | ||||
−0.777525 | + | 0.628852i | \(0.783525\pi\) | |||||||
\(24\) | 28.4736 | 0.242173 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.279543 | 0.00210857 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 68.3064 | 0.461025 | ||||||||
\(29\) | −226.938 | −1.45315 | −0.726574 | − | 0.687088i | \(-0.758889\pi\) | ||||
−0.726574 | + | 0.687088i | \(0.758889\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 195.637 | 1.13347 | 0.566734 | − | 0.823901i | \(-0.308207\pi\) | ||||
0.566734 | + | 0.823901i | \(0.308207\pi\) | |||||||
\(32\) | 109.500 | 0.604907 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | −77.9604 | −0.393238 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −68.6819 | −0.317972 | ||||||||
\(37\) | −338.584 | −1.50440 | −0.752200 | − | 0.658935i | \(-0.771007\pi\) | ||||
−0.752200 | + | 0.658935i | \(0.771007\pi\) | |||||||
\(38\) | −0.0149283 | −6.37287e−5 0 | ||||||||
\(39\) | −1.38116 | −0.00567084 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 136.972 | 0.521744 | 0.260872 | − | 0.965373i | \(-0.415990\pi\) | ||||
0.260872 | + | 0.965373i | \(0.415990\pi\) | |||||||
\(42\) | 16.3046 | 0.0599011 | ||||||||
\(43\) | −336.083 | −1.19191 | −0.595956 | − | 0.803017i | \(-0.703227\pi\) | ||||
−0.595956 | + | 0.803017i | \(0.703227\pi\) | |||||||
\(44\) | 83.9445 | 0.287616 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −104.151 | −0.333830 | ||||||||
\(47\) | 540.292 | 1.67680 | 0.838400 | − | 0.545055i | \(-0.183491\pi\) | ||||
0.838400 | + | 0.545055i | \(0.183491\pi\) | |||||||
\(48\) | −165.863 | −0.498754 | ||||||||
\(49\) | −262.883 | −0.766423 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 385.185 | 1.05758 | ||||||||
\(52\) | −3.51336 | −0.00936952 | ||||||||
\(53\) | 622.387 | 1.61305 | 0.806523 | − | 0.591203i | \(-0.201347\pi\) | ||||
0.806523 | + | 0.591203i | \(0.201347\pi\) | |||||||
\(54\) | −16.3942 | −0.0413142 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 84.9539 | 0.202722 | ||||||||
\(57\) | 0.0737574 | 0.000171393 0 | ||||||||
\(58\) | −137.795 | −0.311954 | ||||||||
\(59\) | −9.86955 | −0.0217781 | −0.0108890 | − | 0.999941i | \(-0.503466\pi\) | ||||
−0.0108890 | + | 0.999941i | \(0.503466\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 902.712 | 1.89476 | 0.947380 | − | 0.320110i | \(-0.103720\pi\) | ||||
0.947380 | + | 0.320110i | \(0.103720\pi\) | |||||||
\(62\) | 118.789 | 0.243327 | ||||||||
\(63\) | −80.5572 | −0.161099 | ||||||||
\(64\) | −375.813 | −0.734010 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 20.0373 | 0.0373701 | ||||||||
\(67\) | −146.979 | −0.268005 | −0.134003 | − | 0.990981i | \(-0.542783\pi\) | ||||
−0.134003 | + | 0.990981i | \(0.542783\pi\) | |||||||
\(68\) | 979.823 | 1.74737 | ||||||||
\(69\) | 514.585 | 0.897809 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −893.798 | −1.49400 | −0.747002 | − | 0.664821i | \(-0.768508\pi\) | ||||
−0.747002 | + | 0.664821i | \(0.768508\pi\) | |||||||
\(72\) | −85.4209 | −0.139819 | ||||||||
\(73\) | 1149.71 | 1.84333 | 0.921664 | − | 0.387988i | \(-0.126830\pi\) | ||||
0.921664 | + | 0.387988i | \(0.126830\pi\) | |||||||
\(74\) | −205.585 | −0.322957 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.187622 | 0.000283181 0 | ||||||||
\(77\) | 98.4588 | 0.145720 | ||||||||
\(78\) | −0.838629 | −0.00121739 | ||||||||
\(79\) | −459.528 | −0.654443 | −0.327221 | − | 0.944948i | \(-0.606112\pi\) | ||||
−0.327221 | + | 0.944948i | \(0.606112\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 83.1686 | 0.112005 | ||||||||
\(83\) | 125.876 | 0.166466 | 0.0832331 | − | 0.996530i | \(-0.473475\pi\) | ||||
0.0832331 | + | 0.996530i | \(0.473475\pi\) | |||||||
\(84\) | −204.919 | −0.266173 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −204.067 | −0.255873 | ||||||||
\(87\) | 680.813 | 0.838975 | ||||||||
\(88\) | 104.403 | 0.126471 | ||||||||
\(89\) | 150.461 | 0.179201 | 0.0896003 | − | 0.995978i | \(-0.471441\pi\) | ||||
0.0896003 | + | 0.995978i | \(0.471441\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.12083 | −0.00474704 | ||||||||
\(92\) | 1308.99 | 1.48339 | ||||||||
\(93\) | −586.912 | −0.654408 | ||||||||
\(94\) | 328.061 | 0.359967 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −328.499 | −0.349243 | ||||||||
\(97\) | 1264.58 | 1.32370 | 0.661851 | − | 0.749635i | \(-0.269771\pi\) | ||||
0.661851 | + | 0.749635i | \(0.269771\pi\) | |||||||
\(98\) | −159.621 | −0.164532 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 690.792 | 0.680558 | 0.340279 | − | 0.940324i | \(-0.389478\pi\) | ||||
0.340279 | + | 0.940324i | \(0.389478\pi\) | |||||||
\(102\) | 233.881 | 0.227036 | ||||||||
\(103\) | 11.7823 | 0.0112713 | 0.00563563 | − | 0.999984i | \(-0.498206\pi\) | ||||
0.00563563 | + | 0.999984i | \(0.498206\pi\) | |||||||
\(104\) | −4.36963 | −0.00411997 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 377.908 | 0.346280 | ||||||||
\(107\) | 462.884 | 0.418212 | 0.209106 | − | 0.977893i | \(-0.432945\pi\) | ||||
0.209106 | + | 0.977893i | \(0.432945\pi\) | |||||||
\(108\) | 206.046 | 0.183581 | ||||||||
\(109\) | 330.525 | 0.290446 | 0.145223 | − | 0.989399i | \(-0.453610\pi\) | ||||
0.145223 | + | 0.989399i | \(0.453610\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1015.75 | 0.868566 | ||||||||
\(112\) | −494.868 | −0.417506 | ||||||||
\(113\) | −1142.31 | −0.950965 | −0.475483 | − | 0.879725i | \(-0.657727\pi\) | ||||
−0.475483 | + | 0.879725i | \(0.657727\pi\) | |||||||
\(114\) | 0.0447849 | 3.67938e−5 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1731.83 | 1.38618 | ||||||||
\(117\) | 4.14348 | 0.00327406 | ||||||||
\(118\) | −5.99271 | −0.00467520 | ||||||||
\(119\) | 1149.24 | 0.885298 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 548.119 | 0.406757 | ||||||||
\(123\) | −410.917 | −0.301229 | ||||||||
\(124\) | −1492.97 | −1.08123 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −48.9137 | −0.0345839 | ||||||||
\(127\) | −629.589 | −0.439898 | −0.219949 | − | 0.975511i | \(-0.570589\pi\) | ||||
−0.219949 | + | 0.975511i | \(0.570589\pi\) | |||||||
\(128\) | −1104.19 | −0.762480 | ||||||||
\(129\) | 1008.25 | 0.688151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 572.566 | 0.381873 | 0.190937 | − | 0.981602i | \(-0.438848\pi\) | ||||
0.190937 | + | 0.981602i | \(0.438848\pi\) | |||||||
\(132\) | −251.833 | −0.166055 | ||||||||
\(133\) | 0.220063 | 0.000143473 0 | ||||||||
\(134\) | −89.2446 | −0.0575340 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1218.62 | 0.768354 | ||||||||
\(137\) | 948.680 | 0.591615 | 0.295807 | − | 0.955248i | \(-0.404411\pi\) | ||||
0.295807 | + | 0.955248i | \(0.404411\pi\) | |||||||
\(138\) | 312.452 | 0.192737 | ||||||||
\(139\) | 2488.86 | 1.51872 | 0.759362 | − | 0.650668i | \(-0.225511\pi\) | ||||
0.759362 | + | 0.650668i | \(0.225511\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1620.87 | −0.968101 | ||||||||
\(142\) | −542.707 | −0.320725 | ||||||||
\(143\) | −5.06425 | −0.00296150 | ||||||||
\(144\) | 497.588 | 0.287956 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 698.093 | 0.395716 | ||||||||
\(147\) | 788.650 | 0.442495 | ||||||||
\(148\) | 2583.84 | 1.43507 | ||||||||
\(149\) | −2186.43 | −1.20214 | −0.601072 | − | 0.799195i | \(-0.705259\pi\) | ||||
−0.601072 | + | 0.799195i | \(0.705259\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3668.21 | 1.97692 | 0.988459 | − | 0.151488i | \(-0.0484064\pi\) | ||||
0.988459 | + | 0.151488i | \(0.0484064\pi\) | |||||||
\(152\) | 0.233349 | 0.000124520 0 | ||||||||
\(153\) | −1155.55 | −0.610595 | ||||||||
\(154\) | 59.7834 | 0.0312824 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.5401 | 0.00540950 | ||||||||
\(157\) | −1418.28 | −0.720960 | −0.360480 | − | 0.932767i | \(-0.617387\pi\) | ||||
−0.360480 | + | 0.932767i | \(0.617387\pi\) | |||||||
\(158\) | −279.022 | −0.140492 | ||||||||
\(159\) | −1867.16 | −0.931293 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1535.32 | 0.751552 | ||||||||
\(162\) | 49.1825 | 0.0238527 | ||||||||
\(163\) | 601.009 | 0.288802 | 0.144401 | − | 0.989519i | \(-0.453875\pi\) | ||||
0.144401 | + | 0.989519i | \(0.453875\pi\) | |||||||
\(164\) | −1045.28 | −0.497699 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 76.4309 | 0.0357361 | ||||||||
\(167\) | 2221.19 | 1.02923 | 0.514614 | − | 0.857422i | \(-0.327935\pi\) | ||||
0.514614 | + | 0.857422i | \(0.327935\pi\) | |||||||
\(168\) | −254.862 | −0.117042 | ||||||||
\(169\) | −2196.79 | −0.999904 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.221272 | −9.89539e−5 0 | ||||||||
\(172\) | 2564.76 | 1.13698 | ||||||||
\(173\) | 237.280 | 0.104278 | 0.0521390 | − | 0.998640i | \(-0.483396\pi\) | ||||
0.0521390 | + | 0.998640i | \(0.483396\pi\) | |||||||
\(174\) | 413.384 | 0.180107 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −608.163 | −0.260466 | ||||||||
\(177\) | 29.6086 | 0.0125736 | ||||||||
\(178\) | 91.3588 | 0.0384698 | ||||||||
\(179\) | 1065.77 | 0.445023 | 0.222512 | − | 0.974930i | \(-0.428574\pi\) | ||||
0.222512 | + | 0.974930i | \(0.428574\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1241.00 | −0.509627 | −0.254813 | − | 0.966990i | \(-0.582014\pi\) | ||||
−0.254813 | + | 0.966990i | \(0.582014\pi\) | |||||||
\(182\) | −2.50213 | −0.00101907 | ||||||||
\(183\) | −2708.14 | −1.09394 | ||||||||
\(184\) | 1628.01 | 0.652275 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −356.368 | −0.140485 | ||||||||
\(187\) | 1412.34 | 0.552304 | ||||||||
\(188\) | −4123.14 | −1.59952 | ||||||||
\(189\) | 241.672 | 0.0930107 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1956.80 | −0.741305 | −0.370653 | − | 0.928772i | \(-0.620866\pi\) | ||||
−0.370653 | + | 0.928772i | \(0.620866\pi\) | |||||||
\(192\) | 1127.44 | 0.423781 | ||||||||
\(193\) | −2778.02 | −1.03610 | −0.518048 | − | 0.855352i | \(-0.673341\pi\) | ||||
−0.518048 | + | 0.855352i | \(0.673341\pi\) | |||||||
\(194\) | 767.846 | 0.284165 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2006.15 | 0.731102 | ||||||||
\(197\) | −800.242 | −0.289416 | −0.144708 | − | 0.989474i | \(-0.546224\pi\) | ||||
−0.144708 | + | 0.989474i | \(0.546224\pi\) | |||||||
\(198\) | −60.1120 | −0.0215756 | ||||||||
\(199\) | −2536.78 | −0.903657 | −0.451829 | − | 0.892105i | \(-0.649228\pi\) | ||||
−0.451829 | + | 0.892105i | \(0.649228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 440.938 | 0.154733 | ||||||||
\(202\) | 419.443 | 0.146099 | ||||||||
\(203\) | 2031.27 | 0.702303 | ||||||||
\(204\) | −2939.47 | −1.00884 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.15409 | 0.00241966 | ||||||||
\(207\) | −1543.76 | −0.518350 | ||||||||
\(208\) | 25.4537 | 0.00848507 | ||||||||
\(209\) | 0.270444 | 8.95071e−5 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1598.95 | 0.521688 | 0.260844 | − | 0.965381i | \(-0.415999\pi\) | ||||
0.260844 | + | 0.965381i | \(0.415999\pi\) | |||||||
\(212\) | −4749.63 | −1.53871 | ||||||||
\(213\) | 2681.40 | 0.862564 | ||||||||
\(214\) | 281.060 | 0.0897797 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 256.263 | 0.0807244 | ||||||||
\(217\) | −1751.11 | −0.547802 | ||||||||
\(218\) | 200.692 | 0.0623513 | ||||||||
\(219\) | −3449.12 | −1.06425 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −59.1113 | −0.0179921 | ||||||||
\(222\) | 616.756 | 0.186459 | ||||||||
\(223\) | 5074.55 | 1.52384 | 0.761922 | − | 0.647669i | \(-0.224256\pi\) | ||||
0.761922 | + | 0.647669i | \(0.224256\pi\) | |||||||
\(224\) | −980.111 | −0.292350 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −693.599 | −0.204148 | ||||||||
\(227\) | −1048.19 | −0.306480 | −0.153240 | − | 0.988189i | \(-0.548971\pi\) | ||||
−0.153240 | + | 0.988189i | \(0.548971\pi\) | |||||||
\(228\) | −0.562866 | −0.000163494 0 | ||||||||
\(229\) | −734.662 | −0.211999 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −295.376 | −0.0841313 | ||||||||
\(232\) | 2153.91 | 0.609532 | ||||||||
\(233\) | 2012.78 | 0.565929 | 0.282965 | − | 0.959130i | \(-0.408682\pi\) | ||||
0.282965 | + | 0.959130i | \(0.408682\pi\) | |||||||
\(234\) | 2.51589 | 0.000702858 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 75.3176 | 0.0207744 | ||||||||
\(237\) | 1378.59 | 0.377843 | ||||||||
\(238\) | 697.808 | 0.190051 | ||||||||
\(239\) | 5566.41 | 1.50653 | 0.753267 | − | 0.657715i | \(-0.228477\pi\) | ||||
0.753267 | + | 0.657715i | \(0.228477\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3361.25 | −0.898412 | −0.449206 | − | 0.893428i | \(-0.648293\pi\) | ||||
−0.449206 | + | 0.893428i | \(0.648293\pi\) | |||||||
\(242\) | 73.4702 | 0.0195159 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −6888.88 | −1.80744 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −249.506 | −0.0646663 | ||||||||
\(247\) | −0.0113190 | −2.91583e−6 0 | ||||||||
\(248\) | −1856.83 | −0.475440 | ||||||||
\(249\) | −377.628 | −0.0961093 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2930.46 | −0.736929 | −0.368464 | − | 0.929642i | \(-0.620116\pi\) | ||||
−0.368464 | + | 0.929642i | \(0.620116\pi\) | |||||||
\(252\) | 614.758 | 0.153675 | ||||||||
\(253\) | 1886.81 | 0.468865 | ||||||||
\(254\) | −382.281 | −0.0944349 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2336.05 | 0.570325 | ||||||||
\(257\) | 3412.89 | 0.828367 | 0.414184 | − | 0.910193i | \(-0.364067\pi\) | ||||
0.414184 | + | 0.910193i | \(0.364067\pi\) | |||||||
\(258\) | 612.201 | 0.147729 | ||||||||
\(259\) | 3030.59 | 0.727073 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2042.44 | −0.484383 | ||||||||
\(262\) | 347.658 | 0.0819785 | ||||||||
\(263\) | −3709.06 | −0.869622 | −0.434811 | − | 0.900522i | \(-0.643185\pi\) | ||||
−0.434811 | + | 0.900522i | \(0.643185\pi\) | |||||||
\(264\) | −313.210 | −0.0730179 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.133620 | 3.07999e−5 0 | ||||||||
\(267\) | −451.384 | −0.103462 | ||||||||
\(268\) | 1121.64 | 0.255654 | ||||||||
\(269\) | −5764.39 | −1.30655 | −0.653273 | − | 0.757122i | \(-0.726605\pi\) | ||||
−0.653273 | + | 0.757122i | \(0.726605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1886.33 | −0.422827 | −0.211414 | − | 0.977397i | \(-0.567807\pi\) | ||||
−0.211414 | + | 0.977397i | \(0.567807\pi\) | |||||||
\(272\) | −7098.64 | −1.58242 | ||||||||
\(273\) | 12.3625 | 0.00274070 | ||||||||
\(274\) | 576.031 | 0.127005 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3926.97 | −0.856433 | ||||||||
\(277\) | 4095.99 | 0.888462 | 0.444231 | − | 0.895912i | \(-0.353477\pi\) | ||||
0.444231 | + | 0.895912i | \(0.353477\pi\) | |||||||
\(278\) | 1511.22 | 0.326032 | ||||||||
\(279\) | 1760.73 | 0.377822 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8788.69 | −1.86580 | −0.932899 | − | 0.360138i | \(-0.882729\pi\) | ||||
−0.932899 | + | 0.360138i | \(0.882729\pi\) | |||||||
\(282\) | −984.182 | −0.207827 | ||||||||
\(283\) | 1767.75 | 0.371314 | 0.185657 | − | 0.982615i | \(-0.440559\pi\) | ||||
0.185657 | + | 0.982615i | \(0.440559\pi\) | |||||||
\(284\) | 6820.86 | 1.42515 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.07497 | −0.000635759 0 | ||||||||
\(287\) | −1226.01 | −0.252158 | ||||||||
\(288\) | 985.498 | 0.201636 | ||||||||
\(289\) | 11572.3 | 2.35544 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3793.75 | −0.764240 | ||||||||
\(292\) | −8773.78 | −1.75838 | ||||||||
\(293\) | −3079.85 | −0.614085 | −0.307043 | − | 0.951696i | \(-0.599339\pi\) | ||||
−0.307043 | + | 0.951696i | \(0.599339\pi\) | |||||||
\(294\) | 478.862 | 0.0949924 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3213.57 | 0.631030 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | −1327.58 | −0.258070 | ||||||||
\(299\) | −78.9695 | −0.0152740 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3008.21 | 0.576048 | ||||||||
\(302\) | 2227.31 | 0.424394 | ||||||||
\(303\) | −2072.38 | −0.392921 | ||||||||
\(304\) | −1.35929 | −0.000256449 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −701.643 | −0.131079 | ||||||||
\(307\) | −2872.16 | −0.533950 | −0.266975 | − | 0.963703i | \(-0.586024\pi\) | ||||
−0.266975 | + | 0.963703i | \(0.586024\pi\) | |||||||
\(308\) | −751.370 | −0.139004 | ||||||||
\(309\) | −35.3468 | −0.00650747 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −317.978 | −0.0579771 | −0.0289885 | − | 0.999580i | \(-0.509229\pi\) | ||||
−0.0289885 | + | 0.999580i | \(0.509229\pi\) | |||||||
\(312\) | 13.1089 | 0.00237867 | ||||||||
\(313\) | 8274.81 | 1.49431 | 0.747156 | − | 0.664648i | \(-0.231419\pi\) | ||||
0.747156 | + | 0.664648i | \(0.231419\pi\) | |||||||
\(314\) | −861.166 | −0.154772 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3506.81 | 0.624283 | ||||||||
\(317\) | −1024.34 | −0.181492 | −0.0907459 | − | 0.995874i | \(-0.528925\pi\) | ||||
−0.0907459 | + | 0.995874i | \(0.528925\pi\) | |||||||
\(318\) | −1133.73 | −0.199925 | ||||||||
\(319\) | 2496.32 | 0.438141 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1388.65 | −0.241455 | ||||||||
\(322\) | 932.232 | 0.161339 | ||||||||
\(323\) | 3.15669 | 0.000543787 0 | ||||||||
\(324\) | −618.137 | −0.105991 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 364.928 | 0.0619984 | ||||||||
\(327\) | −991.575 | −0.167689 | ||||||||
\(328\) | −1300.03 | −0.218849 | ||||||||
\(329\) | −4836.04 | −0.810394 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4575.83 | 0.759850 | 0.379925 | − | 0.925017i | \(-0.375950\pi\) | ||||
0.379925 | + | 0.925017i | \(0.375950\pi\) | |||||||
\(332\) | −960.600 | −0.158795 | ||||||||
\(333\) | −3047.25 | −0.501467 | ||||||||
\(334\) | 1348.69 | 0.220949 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1484.60 | 0.241047 | ||||||||
\(337\) | 917.888 | 0.148370 | 0.0741848 | − | 0.997245i | \(-0.476365\pi\) | ||||
0.0741848 | + | 0.997245i | \(0.476365\pi\) | |||||||
\(338\) | −1333.87 | −0.214654 | ||||||||
\(339\) | 3426.92 | 0.549040 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2152.01 | −0.341753 | ||||||||
\(342\) | −0.134355 | −2.12429e−5 0 | ||||||||
\(343\) | 5423.14 | 0.853708 | ||||||||
\(344\) | 3189.84 | 0.499955 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 144.075 | 0.0223859 | ||||||||
\(347\) | −5402.26 | −0.835760 | −0.417880 | − | 0.908502i | \(-0.637227\pi\) | ||||
−0.417880 | + | 0.908502i | \(0.637227\pi\) | |||||||
\(348\) | −5195.50 | −0.800311 | ||||||||
\(349\) | 5115.85 | 0.784656 | 0.392328 | − | 0.919825i | \(-0.371670\pi\) | ||||
0.392328 | + | 0.919825i | \(0.371670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.4304 | −0.00189028 | ||||||||
\(352\) | −1204.50 | −0.182386 | ||||||||
\(353\) | 3102.03 | 0.467718 | 0.233859 | − | 0.972270i | \(-0.424865\pi\) | ||||
0.233859 | + | 0.972270i | \(0.424865\pi\) | |||||||
\(354\) | 17.9781 | 0.00269923 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1148.22 | −0.170942 | ||||||||
\(357\) | −3447.71 | −0.511127 | ||||||||
\(358\) | 647.125 | 0.0955352 | ||||||||
\(359\) | 3496.32 | 0.514008 | 0.257004 | − | 0.966410i | \(-0.417265\pi\) | ||||
0.257004 | + | 0.966410i | \(0.417265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6859.00 | −1.00000 | ||||||||
\(362\) | −753.522 | −0.109404 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | 31.4474 | 0.00452827 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1644.36 | −0.234841 | ||||||||
\(367\) | −7644.54 | −1.08731 | −0.543654 | − | 0.839309i | \(-0.682960\pi\) | ||||
−0.543654 | + | 0.839309i | \(0.682960\pi\) | |||||||
\(368\) | −9483.39 | −1.34336 | ||||||||
\(369\) | 1232.75 | 0.173915 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5570.86 | −0.779582 | ||||||||
\(372\) | 4478.91 | 0.624249 | ||||||||
\(373\) | 5189.90 | 0.720437 | 0.360218 | − | 0.932868i | \(-0.382702\pi\) | ||||
0.360218 | + | 0.932868i | \(0.382702\pi\) | |||||||
\(374\) | 857.564 | 0.118566 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5128.02 | −0.703344 | ||||||||
\(377\) | −104.479 | −0.0142731 | ||||||||
\(378\) | 146.741 | 0.0199670 | ||||||||
\(379\) | 8573.91 | 1.16204 | 0.581019 | − | 0.813890i | \(-0.302654\pi\) | ||||
0.581019 | + | 0.813890i | \(0.302654\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1888.77 | 0.253975 | ||||||||
\(382\) | −1188.15 | −0.159140 | ||||||||
\(383\) | 11740.2 | 1.56631 | 0.783157 | − | 0.621824i | \(-0.213608\pi\) | ||||
0.783157 | + | 0.621824i | \(0.213608\pi\) | |||||||
\(384\) | 3312.57 | 0.440218 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1686.79 | −0.222424 | ||||||||
\(387\) | −3024.75 | −0.397304 | ||||||||
\(388\) | −9650.45 | −1.26270 | ||||||||
\(389\) | −3763.68 | −0.490556 | −0.245278 | − | 0.969453i | \(-0.578879\pi\) | ||||
−0.245278 | + | 0.969453i | \(0.578879\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22023.4 | 2.84852 | ||||||||
\(392\) | 2495.08 | 0.321481 | ||||||||
\(393\) | −1717.70 | −0.220474 | ||||||||
\(394\) | −485.900 | −0.0621302 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 755.500 | 0.0958720 | ||||||||
\(397\) | −1151.35 | −0.145554 | −0.0727768 | − | 0.997348i | \(-0.523186\pi\) | ||||
−0.0727768 | + | 0.997348i | \(0.523186\pi\) | |||||||
\(398\) | −1540.31 | −0.193992 | ||||||||
\(399\) | −0.660188 | −8.28339e−5 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10051.0 | −1.25168 | −0.625842 | − | 0.779950i | \(-0.715245\pi\) | ||||
−0.625842 | + | 0.779950i | \(0.715245\pi\) | |||||||
\(402\) | 267.734 | 0.0332173 | ||||||||
\(403\) | 90.0688 | 0.0111331 | ||||||||
\(404\) | −5271.66 | −0.649195 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1233.37 | 0.150767 | ||||||||
\(407\) | 3724.42 | 0.453594 | ||||||||
\(408\) | −3655.87 | −0.443609 | ||||||||
\(409\) | −6263.39 | −0.757225 | −0.378612 | − | 0.925555i | \(-0.623599\pi\) | ||||
−0.378612 | + | 0.925555i | \(0.623599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2846.04 | −0.341569 | ||||||||
\(412\) | −89.9142 | −0.0107518 | ||||||||
\(413\) | 88.3403 | 0.0105253 | ||||||||
\(414\) | −937.356 | −0.111277 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 50.4123 | 0.00594150 | ||||||||
\(417\) | −7466.59 | −0.876836 | ||||||||
\(418\) | 0.164211 | 1.92149e−5 0 | ||||||||
\(419\) | 8625.67 | 1.00571 | 0.502854 | − | 0.864372i | \(-0.332283\pi\) | ||||
0.502854 | + | 0.864372i | \(0.332283\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9095.24 | −1.05291 | −0.526455 | − | 0.850203i | \(-0.676479\pi\) | ||||
−0.526455 | + | 0.850203i | \(0.676479\pi\) | |||||||
\(422\) | 970.868 | 0.111993 | ||||||||
\(423\) | 4862.62 | 0.558934 | ||||||||
\(424\) | −5907.21 | −0.676602 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1628.12 | 0.185171 | ||||||||
\(427\) | −8079.99 | −0.915733 | ||||||||
\(428\) | −3532.42 | −0.398939 | ||||||||
\(429\) | 15.1928 | 0.00170982 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4008.72 | −0.448013 | −0.224006 | − | 0.974588i | \(-0.571914\pi\) | ||||
−0.224006 | + | 0.974588i | \(0.571914\pi\) | |||||||
\(432\) | −1492.76 | −0.166251 | ||||||||
\(433\) | −2715.38 | −0.301369 | −0.150684 | − | 0.988582i | \(-0.548148\pi\) | ||||
−0.150684 | + | 0.988582i | \(0.548148\pi\) | |||||||
\(434\) | −1063.26 | −0.117599 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2522.34 | −0.277060 | ||||||||
\(437\) | 4.21717 | 0.000461635 0 | ||||||||
\(438\) | −2094.28 | −0.228467 | ||||||||
\(439\) | −11087.5 | −1.20541 | −0.602707 | − | 0.797962i | \(-0.705911\pi\) | ||||
−0.602707 | + | 0.797962i | \(0.705911\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2365.95 | −0.255474 | ||||||||
\(442\) | −35.8919 | −0.00386245 | ||||||||
\(443\) | −7132.98 | −0.765007 | −0.382503 | − | 0.923954i | \(-0.624938\pi\) | ||||
−0.382503 | + | 0.923954i | \(0.624938\pi\) | |||||||
\(444\) | −7751.52 | −0.828538 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3081.23 | 0.327131 | ||||||||
\(447\) | 6559.29 | 0.694058 | ||||||||
\(448\) | 3363.83 | 0.354745 | ||||||||
\(449\) | 6291.28 | 0.661255 | 0.330628 | − | 0.943761i | \(-0.392740\pi\) | ||||
0.330628 | + | 0.943761i | \(0.392740\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1506.70 | −0.157312 | ||||||||
\(452\) | 8717.30 | 0.907140 | ||||||||
\(453\) | −11004.6 | −1.14137 | ||||||||
\(454\) | −636.455 | −0.0657936 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.700047 | −7.18919e−5 0 | ||||||||
\(457\) | −7291.98 | −0.746400 | −0.373200 | − | 0.927751i | \(-0.621739\pi\) | ||||
−0.373200 | + | 0.927751i | \(0.621739\pi\) | |||||||
\(458\) | −446.081 | −0.0455109 | ||||||||
\(459\) | 3466.66 | 0.352527 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16805.4 | −1.69784 | −0.848922 | − | 0.528519i | \(-0.822748\pi\) | ||||
−0.848922 | + | 0.528519i | \(0.822748\pi\) | |||||||
\(462\) | −179.350 | −0.0180609 | ||||||||
\(463\) | −7478.48 | −0.750658 | −0.375329 | − | 0.926892i | \(-0.622470\pi\) | ||||
−0.375329 | + | 0.926892i | \(0.622470\pi\) | |||||||
\(464\) | −12546.8 | −1.25533 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1222.14 | 0.121491 | ||||||||
\(467\) | 7526.83 | 0.745824 | 0.372912 | − | 0.927867i | \(-0.378359\pi\) | ||||
0.372912 | + | 0.927867i | \(0.378359\pi\) | |||||||
\(468\) | −31.6202 | −0.00312317 | ||||||||
\(469\) | 1315.58 | 0.129526 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4254.83 | 0.416247 | ||||||||
\(472\) | 93.6739 | 0.00913494 | ||||||||
\(473\) | 3696.92 | 0.359375 | ||||||||
\(474\) | 837.066 | 0.0811133 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8770.20 | −0.844499 | ||||||||
\(477\) | 5601.48 | 0.537682 | ||||||||
\(478\) | 3379.88 | 0.323415 | ||||||||
\(479\) | 1258.80 | 0.120075 | 0.0600376 | − | 0.998196i | \(-0.480878\pi\) | ||||
0.0600376 | + | 0.998196i | \(0.480878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −155.879 | −0.0147765 | ||||||||
\(482\) | −2040.93 | −0.192866 | ||||||||
\(483\) | −4605.95 | −0.433909 | ||||||||
\(484\) | −923.389 | −0.0867195 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −147.548 | −0.0137714 | ||||||||
\(487\) | −5127.97 | −0.477147 | −0.238574 | − | 0.971124i | \(-0.576680\pi\) | ||||
−0.238574 | + | 0.971124i | \(0.576680\pi\) | |||||||
\(488\) | −8567.83 | −0.794769 | ||||||||
\(489\) | −1803.03 | −0.166740 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11932.3 | 1.09673 | 0.548366 | − | 0.836238i | \(-0.315250\pi\) | ||||
0.548366 | + | 0.836238i | \(0.315250\pi\) | |||||||
\(492\) | 3135.84 | 0.287347 | ||||||||
\(493\) | 29137.7 | 2.66185 | ||||||||
\(494\) | −0.00687279 | −6.25955e−7 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10816.3 | 0.979166 | ||||||||
\(497\) | 8000.21 | 0.722049 | ||||||||
\(498\) | −229.293 | −0.0206322 | ||||||||
\(499\) | 14716.3 | 1.32022 | 0.660111 | − | 0.751168i | \(-0.270509\pi\) | ||||
0.660111 | + | 0.751168i | \(0.270509\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6663.57 | −0.594225 | ||||||||
\(502\) | −1779.35 | −0.158200 | ||||||||
\(503\) | 5598.95 | 0.496312 | 0.248156 | − | 0.968720i | \(-0.420175\pi\) | ||||
0.248156 | + | 0.968720i | \(0.420175\pi\) | |||||||
\(504\) | 764.585 | 0.0675741 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1145.66 | 0.100654 | ||||||||
\(507\) | 6590.36 | 0.577295 | ||||||||
\(508\) | 4804.60 | 0.419625 | ||||||||
\(509\) | −16720.0 | −1.45600 | −0.727998 | − | 0.685579i | \(-0.759549\pi\) | ||||
−0.727998 | + | 0.685579i | \(0.759549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10290.8 | −0.890877 | ||||||||
\(512\) | 10251.9 | 0.884915 | ||||||||
\(513\) | 0.663817 | 5.71310e−5 0 | ||||||||
\(514\) | 2072.28 | 0.177830 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7694.27 | −0.656437 | ||||||||
\(517\) | −5943.21 | −0.505574 | ||||||||
\(518\) | 1840.15 | 0.156084 | ||||||||
\(519\) | −711.841 | −0.0602050 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3498.81 | 0.294214 | 0.147107 | − | 0.989121i | \(-0.453004\pi\) | ||||
0.147107 | + | 0.989121i | \(0.453004\pi\) | |||||||
\(522\) | −1240.15 | −0.103985 | ||||||||
\(523\) | 5681.71 | 0.475036 | 0.237518 | − | 0.971383i | \(-0.423666\pi\) | ||||
0.237518 | + | 0.971383i | \(0.423666\pi\) | |||||||
\(524\) | −4369.44 | −0.364274 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2252.11 | −0.186686 | ||||||||
\(527\) | −25118.8 | −2.07627 | ||||||||
\(528\) | 1824.49 | 0.150380 | ||||||||
\(529\) | 17255.0 | 1.41818 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −88.8259 | −0.00725935 | ||||||||
\(532\) | −1.67937 | −0.000136861 0 | ||||||||
\(533\) | 63.0603 | 0.00512466 | ||||||||
\(534\) | −274.076 | −0.0222106 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1395.01 | 0.112417 | ||||||||
\(537\) | −3197.30 | −0.256934 | ||||||||
\(538\) | −3500.09 | −0.280482 | ||||||||
\(539\) | 2891.72 | 0.231085 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11641.7 | 0.925169 | 0.462585 | − | 0.886575i | \(-0.346922\pi\) | ||||
0.462585 | + | 0.886575i | \(0.346922\pi\) | |||||||
\(542\) | −1145.36 | −0.0907704 | ||||||||
\(543\) | 3722.99 | 0.294233 | ||||||||
\(544\) | −14059.2 | −1.10806 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.50640 | 0.000588360 0 | ||||||||
\(547\) | 16460.2 | 1.28663 | 0.643315 | − | 0.765602i | \(-0.277559\pi\) | ||||
0.643315 | + | 0.765602i | \(0.277559\pi\) | |||||||
\(548\) | −7239.68 | −0.564350 | ||||||||
\(549\) | 8124.41 | 0.631587 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.57945 | 0.000431384 0 | ||||||||
\(552\) | −4884.04 | −0.376591 | ||||||||
\(553\) | 4113.15 | 0.316291 | ||||||||
\(554\) | 2487.05 | 0.190730 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18993.3 | −1.44873 | ||||||||
\(557\) | 11769.7 | 0.895331 | 0.447666 | − | 0.894201i | \(-0.352255\pi\) | ||||
0.447666 | + | 0.894201i | \(0.352255\pi\) | |||||||
\(558\) | 1069.10 | 0.0811089 | ||||||||
\(559\) | −154.728 | −0.0117072 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4237.03 | −0.318873 | ||||||||
\(562\) | −5336.42 | −0.400540 | ||||||||
\(563\) | −21123.9 | −1.58129 | −0.790644 | − | 0.612276i | \(-0.790254\pi\) | ||||
−0.790644 | + | 0.612276i | \(0.790254\pi\) | |||||||
\(564\) | 12369.4 | 0.923486 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1073.36 | 0.0797118 | ||||||||
\(567\) | −725.015 | −0.0536997 | ||||||||
\(568\) | 8483.23 | 0.626670 | ||||||||
\(569\) | −21890.4 | −1.61282 | −0.806410 | − | 0.591357i | \(-0.798592\pi\) | ||||
−0.806410 | + | 0.591357i | \(0.798592\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6630.99 | 0.485986 | 0.242993 | − | 0.970028i | \(-0.421871\pi\) | ||||
0.242993 | + | 0.970028i | \(0.421871\pi\) | |||||||
\(572\) | 38.6469 | 0.00282502 | ||||||||
\(573\) | 5870.41 | 0.427993 | ||||||||
\(574\) | −744.425 | −0.0541319 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3382.32 | −0.244670 | ||||||||
\(577\) | −13361.3 | −0.964015 | −0.482007 | − | 0.876167i | \(-0.660092\pi\) | ||||
−0.482007 | + | 0.876167i | \(0.660092\pi\) | |||||||
\(578\) | 7026.58 | 0.505653 | ||||||||
\(579\) | 8334.07 | 0.598190 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1126.69 | −0.0804527 | ||||||||
\(582\) | −2303.54 | −0.164063 | ||||||||
\(583\) | −6846.26 | −0.486352 | ||||||||
\(584\) | −10912.1 | −0.773196 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1870.06 | −0.131829 | ||||||||
\(587\) | 9451.34 | 0.664563 | 0.332282 | − | 0.943180i | \(-0.392182\pi\) | ||||
0.332282 | + | 0.943180i | \(0.392182\pi\) | |||||||
\(588\) | −6018.44 | −0.422102 | ||||||||
\(589\) | −4.80990 | −0.000336483 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2400.73 | 0.167094 | ||||||||
\(592\) | −18719.5 | −1.29960 | ||||||||
\(593\) | −712.344 | −0.0493296 | −0.0246648 | − | 0.999696i | \(-0.507852\pi\) | ||||
−0.0246648 | + | 0.999696i | \(0.507852\pi\) | |||||||
\(594\) | 180.336 | 0.0124567 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16685.3 | 1.14674 | ||||||||
\(597\) | 7610.35 | 0.521727 | ||||||||
\(598\) | −47.9496 | −0.00327894 | ||||||||
\(599\) | 23951.9 | 1.63380 | 0.816901 | − | 0.576777i | \(-0.195690\pi\) | ||||
0.816901 | + | 0.576777i | \(0.195690\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18577.3 | 1.26087 | 0.630434 | − | 0.776243i | \(-0.282877\pi\) | ||||
0.630434 | + | 0.776243i | \(0.282877\pi\) | |||||||
\(602\) | 1826.56 | 0.123663 | ||||||||
\(603\) | −1322.81 | −0.0893351 | ||||||||
\(604\) | −27993.3 | −1.88581 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1258.33 | −0.0843501 | ||||||||
\(607\) | 6230.72 | 0.416634 | 0.208317 | − | 0.978061i | \(-0.433201\pi\) | ||||
0.208317 | + | 0.978061i | \(0.433201\pi\) | |||||||
\(608\) | −2.69214 | −0.000179574 0 | ||||||||
\(609\) | −6093.82 | −0.405475 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 248.743 | 0.0164698 | ||||||||
\(612\) | 8818.40 | 0.582456 | ||||||||
\(613\) | 17744.8 | 1.16918 | 0.584588 | − | 0.811330i | \(-0.301256\pi\) | ||||
0.584588 | + | 0.811330i | \(0.301256\pi\) | |||||||
\(614\) | −1743.95 | −0.114626 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −934.493 | −0.0611230 | ||||||||
\(617\) | −15305.4 | −0.998656 | −0.499328 | − | 0.866413i | \(-0.666420\pi\) | ||||
−0.499328 | + | 0.866413i | \(0.666420\pi\) | |||||||
\(618\) | −21.4623 | −0.00139699 | ||||||||
\(619\) | 17372.3 | 1.12803 | 0.564015 | − | 0.825764i | \(-0.309256\pi\) | ||||
0.564015 | + | 0.825764i | \(0.309256\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4631.27 | 0.299270 | ||||||||
\(622\) | −193.074 | −0.0124462 | ||||||||
\(623\) | −1346.75 | −0.0866073 | ||||||||
\(624\) | −76.3610 | −0.00489886 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5024.40 | 0.320791 | ||||||||
\(627\) | −0.811331 | −5.16770e−5 0 | ||||||||
\(628\) | 10823.3 | 0.687735 | ||||||||
\(629\) | 43472.4 | 2.75574 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23699.3 | 1.49517 | 0.747586 | − | 0.664165i | \(-0.231213\pi\) | ||||
0.747586 | + | 0.664165i | \(0.231213\pi\) | |||||||
\(632\) | 4361.48 | 0.274510 | ||||||||
\(633\) | −4796.85 | −0.301197 | ||||||||
\(634\) | −621.973 | −0.0389617 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14248.9 | 0.888374 | ||||||||
\(637\) | −121.028 | −0.00752795 | ||||||||
\(638\) | 1515.74 | 0.0940577 | ||||||||
\(639\) | −8044.19 | −0.498002 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15423.9 | −0.950400 | −0.475200 | − | 0.879878i | \(-0.657624\pi\) | ||||
−0.475200 | + | 0.879878i | \(0.657624\pi\) | |||||||
\(642\) | −843.179 | −0.0518343 | ||||||||
\(643\) | −13152.3 | −0.806652 | −0.403326 | − | 0.915056i | \(-0.632146\pi\) | ||||
−0.403326 | + | 0.915056i | \(0.632146\pi\) | |||||||
\(644\) | −11716.5 | −0.716917 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.91672 | 0.000116737 0 | ||||||||
\(647\) | 5601.87 | 0.340390 | 0.170195 | − | 0.985410i | \(-0.445560\pi\) | ||||
0.170195 | + | 0.985410i | \(0.445560\pi\) | |||||||
\(648\) | −768.788 | −0.0466062 | ||||||||
\(649\) | 108.565 | 0.00656633 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5253.33 | 0.316274 | ||||||||
\(652\) | −4586.49 | −0.275492 | ||||||||
\(653\) | 27505.9 | 1.64837 | 0.824186 | − | 0.566319i | \(-0.191633\pi\) | ||||
0.824186 | + | 0.566319i | \(0.191633\pi\) | |||||||
\(654\) | −602.076 | −0.0359986 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7572.87 | 0.450718 | ||||||||
\(657\) | 10347.4 | 0.614443 | ||||||||
\(658\) | −2936.41 | −0.173971 | ||||||||
\(659\) | 16490.6 | 0.974785 | 0.487392 | − | 0.873183i | \(-0.337948\pi\) | ||||
0.487392 | + | 0.873183i | \(0.337948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12184.4 | 0.716973 | 0.358487 | − | 0.933535i | \(-0.383293\pi\) | ||||
0.358487 | + | 0.933535i | \(0.383293\pi\) | |||||||
\(662\) | 2778.41 | 0.163121 | ||||||||
\(663\) | 177.334 | 0.0103878 | ||||||||
\(664\) | −1194.72 | −0.0698253 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1850.27 | −0.107652 | ||||||||
\(667\) | 38926.3 | 2.25972 | ||||||||
\(668\) | −16950.6 | −0.981795 | ||||||||
\(669\) | −15223.7 | −0.879791 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9929.83 | −0.571292 | ||||||||
\(672\) | 2940.33 | 0.168788 | ||||||||
\(673\) | 13598.5 | 0.778876 | 0.389438 | − | 0.921053i | \(-0.372669\pi\) | ||||
0.389438 | + | 0.921053i | \(0.372669\pi\) | |||||||
\(674\) | 557.334 | 0.0318512 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16764.4 | 0.953823 | ||||||||
\(677\) | −23318.1 | −1.32377 | −0.661883 | − | 0.749607i | \(-0.730242\pi\) | ||||
−0.661883 | + | 0.749607i | \(0.730242\pi\) | |||||||
\(678\) | 2080.80 | 0.117865 | ||||||||
\(679\) | −11319.0 | −0.639742 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3144.58 | 0.176947 | ||||||||
\(682\) | −1306.68 | −0.0733658 | ||||||||
\(683\) | −11493.5 | −0.643906 | −0.321953 | − | 0.946756i | \(-0.604339\pi\) | ||||
−0.321953 | + | 0.946756i | \(0.604339\pi\) | |||||||
\(684\) | 1.68860 | 9.43935e−5 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3292.89 | 0.183270 | ||||||||
\(687\) | 2203.99 | 0.122398 | ||||||||
\(688\) | −18581.2 | −1.02965 | ||||||||
\(689\) | 286.539 | 0.0158436 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20253.1 | −1.11500 | −0.557501 | − | 0.830176i | \(-0.688240\pi\) | ||||
−0.557501 | + | 0.830176i | \(0.688240\pi\) | |||||||
\(692\) | −1810.76 | −0.0994724 | ||||||||
\(693\) | 886.129 | 0.0485733 | ||||||||
\(694\) | −3280.21 | −0.179416 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6461.74 | −0.351913 | ||||||||
\(697\) | −17586.6 | −0.955723 | ||||||||
\(698\) | 3106.30 | 0.168446 | ||||||||
\(699\) | −6038.34 | −0.326739 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26895.3 | 1.44910 | 0.724551 | − | 0.689221i | \(-0.242047\pi\) | ||||
0.724551 | + | 0.689221i | \(0.242047\pi\) | |||||||
\(702\) | −7.54766 | −0.000405795 0 | ||||||||
\(703\) | 8.32435 | 0.000446599 0 | ||||||||
\(704\) | 4133.94 | 0.221312 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1883.53 | 0.100407 | ||||||||
\(707\) | −6183.14 | −0.328912 | ||||||||
\(708\) | −225.953 | −0.0119941 | ||||||||
\(709\) | −18567.3 | −0.983512 | −0.491756 | − | 0.870733i | \(-0.663645\pi\) | ||||
−0.491756 | + | 0.870733i | \(0.663645\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4135.76 | −0.218148 | ||||||||
\(712\) | −1428.06 | −0.0751668 | ||||||||
\(713\) | −33557.4 | −1.76260 | ||||||||
\(714\) | −2093.42 | −0.109726 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8133.21 | −0.424514 | ||||||||
\(717\) | −16699.2 | −0.869797 | ||||||||
\(718\) | 2122.94 | 0.110344 | ||||||||
\(719\) | −19223.5 | −0.997104 | −0.498552 | − | 0.866860i | \(-0.666135\pi\) | ||||
−0.498552 | + | 0.866860i | \(0.666135\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −105.461 | −0.00544738 | ||||||||
\(722\) | −4164.73 | −0.214675 | ||||||||
\(723\) | 10083.8 | 0.518698 | ||||||||
\(724\) | 9470.43 | 0.486140 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −220.411 | −0.0112675 | ||||||||
\(727\) | 33855.9 | 1.72716 | 0.863581 | − | 0.504210i | \(-0.168216\pi\) | ||||
0.863581 | + | 0.504210i | \(0.168216\pi\) | |||||||
\(728\) | 39.1117 | 0.00199117 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43151.4 | 2.18333 | ||||||||
\(732\) | 20666.6 | 1.04353 | ||||||||
\(733\) | −26532.1 | −1.33695 | −0.668477 | − | 0.743733i | \(-0.733053\pi\) | ||||
−0.668477 | + | 0.743733i | \(0.733053\pi\) | |||||||
\(734\) | −4641.71 | −0.233418 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18782.3 | −0.940661 | ||||||||
\(737\) | 1616.77 | 0.0808067 | ||||||||
\(738\) | 748.517 | 0.0373351 | ||||||||
\(739\) | −15358.9 | −0.764528 | −0.382264 | − | 0.924053i | \(-0.624856\pi\) | ||||
−0.382264 | + | 0.924053i | \(0.624856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0339569 | 1.68345e−6 0 | ||||||||
\(742\) | −3382.58 | −0.167356 | ||||||||
\(743\) | 30995.4 | 1.53043 | 0.765216 | − | 0.643774i | \(-0.222632\pi\) | ||||
0.765216 | + | 0.643774i | \(0.222632\pi\) | |||||||
\(744\) | 5570.50 | 0.274495 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3151.27 | 0.154660 | ||||||||
\(747\) | 1132.88 | 0.0554887 | ||||||||
\(748\) | −10778.0 | −0.526851 | ||||||||
\(749\) | −4143.19 | −0.202121 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32222.4 | −1.56566 | −0.782831 | − | 0.622234i | \(-0.786225\pi\) | ||||
−0.782831 | + | 0.622234i | \(0.786225\pi\) | |||||||
\(752\) | 29871.4 | 1.44853 | ||||||||
\(753\) | 8791.38 | 0.425466 | ||||||||
\(754\) | −63.4389 | −0.00306407 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1844.27 | −0.0887243 | ||||||||
\(757\) | 36596.5 | 1.75710 | 0.878549 | − | 0.477651i | \(-0.158512\pi\) | ||||
0.878549 | + | 0.477651i | \(0.158512\pi\) | |||||||
\(758\) | 5206.01 | 0.249460 | ||||||||
\(759\) | −5660.44 | −0.270700 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24718.0 | 1.17743 | 0.588716 | − | 0.808340i | \(-0.299634\pi\) | ||||
0.588716 | + | 0.808340i | \(0.299634\pi\) | |||||||
\(762\) | 1146.84 | 0.0545220 | ||||||||
\(763\) | −2958.46 | −0.140372 | ||||||||
\(764\) | 14933.0 | 0.707142 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7128.58 | 0.336248 | ||||||||
\(767\) | −4.54381 | −0.000213908 0 | ||||||||
\(768\) | −7008.15 | −0.329277 | ||||||||
\(769\) | 36376.7 | 1.70582 | 0.852910 | − | 0.522058i | \(-0.174836\pi\) | ||||
0.852910 | + | 0.522058i | \(0.174836\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10238.7 | −0.478258 | ||||||||
\(772\) | 21200.0 | 0.988347 | ||||||||
\(773\) | −7525.40 | −0.350155 | −0.175078 | − | 0.984555i | \(-0.556018\pi\) | ||||
−0.175078 | + | 0.984555i | \(0.556018\pi\) | |||||||
\(774\) | −1836.60 | −0.0852911 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12002.4 | −0.555235 | ||||||||
\(777\) | −9091.78 | −0.419776 | ||||||||
\(778\) | −2285.28 | −0.105310 | ||||||||
\(779\) | −3.36758 | −0.000154886 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9831.78 | 0.450459 | ||||||||
\(782\) | 13372.4 | 0.611505 | ||||||||
\(783\) | 6127.32 | 0.279658 | ||||||||
\(784\) | −14534.2 | −0.662089 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1042.97 | −0.0473303 | ||||||||
\(787\) | 41044.5 | 1.85906 | 0.929530 | − | 0.368747i | \(-0.120213\pi\) | ||||
0.929530 | + | 0.368747i | \(0.120213\pi\) | |||||||
\(788\) | 6106.90 | 0.276078 | ||||||||
\(789\) | 11127.2 | 0.502077 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10224.5 | 0.459599 | ||||||||
\(792\) | 939.630 | 0.0421569 | ||||||||
\(793\) | 415.597 | 0.0186107 | ||||||||
\(794\) | −699.093 | −0.0312467 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19359.0 | 0.862012 | ||||||||
\(797\) | 10836.9 | 0.481635 | 0.240817 | − | 0.970570i | \(-0.422584\pi\) | ||||
0.240817 | + | 0.970570i | \(0.422584\pi\) | |||||||
\(798\) | −0.400861 | −1.77823e−5 0 | ||||||||
\(799\) | −69370.7 | −3.07154 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1354.15 | 0.0597335 | ||||||||
\(802\) | −6102.91 | −0.268705 | ||||||||
\(803\) | −12646.8 | −0.555785 | ||||||||
\(804\) | −3364.93 | −0.147602 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 54.6890 | 0.00239000 | ||||||||
\(807\) | 17293.2 | 0.754335 | ||||||||
\(808\) | −6556.45 | −0.285464 | ||||||||
\(809\) | −16093.5 | −0.699402 | −0.349701 | − | 0.936861i | \(-0.613717\pi\) | ||||
−0.349701 | + | 0.936861i | \(0.613717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7289.26 | 0.315611 | 0.157805 | − | 0.987470i | \(-0.449558\pi\) | ||||
0.157805 | + | 0.987470i | \(0.449558\pi\) | |||||||
\(812\) | −15501.3 | −0.669937 | ||||||||
\(813\) | 5658.98 | 0.244120 | ||||||||
\(814\) | 2261.44 | 0.0973751 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 21295.9 | 0.913611 | ||||||||
\(817\) | 8.26288 | 0.000353833 0 | ||||||||
\(818\) | −3803.08 | −0.162557 | ||||||||
\(819\) | −37.0875 | −0.00158235 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33153.4 | −1.40933 | −0.704666 | − | 0.709539i | \(-0.748903\pi\) | ||||
−0.704666 | + | 0.709539i | \(0.748903\pi\) | |||||||
\(822\) | −1728.09 | −0.0733262 | ||||||||
\(823\) | 2781.57 | 0.117812 | 0.0589060 | − | 0.998264i | \(-0.481239\pi\) | ||||
0.0589060 | + | 0.998264i | \(0.481239\pi\) | |||||||
\(824\) | −111.828 | −0.00472780 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 53.6395 | 0.00225951 | ||||||||
\(827\) | 4498.61 | 0.189156 | 0.0945780 | − | 0.995517i | \(-0.469850\pi\) | ||||
0.0945780 | + | 0.995517i | \(0.469850\pi\) | |||||||
\(828\) | 11780.9 | 0.494462 | ||||||||
\(829\) | 15630.3 | 0.654843 | 0.327421 | − | 0.944878i | \(-0.393820\pi\) | ||||
0.327421 | + | 0.944878i | \(0.393820\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12288.0 | −0.512954 | ||||||||
\(832\) | −173.019 | −0.00720958 | ||||||||
\(833\) | 33752.9 | 1.40392 | ||||||||
\(834\) | −4533.66 | −0.188235 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.06384 | −8.53822e−5 0 | ||||||||
\(837\) | −5282.20 | −0.218136 | ||||||||
\(838\) | 5237.43 | 0.215900 | ||||||||
\(839\) | −6182.34 | −0.254396 | −0.127198 | − | 0.991877i | \(-0.540598\pi\) | ||||
−0.127198 | + | 0.991877i | \(0.540598\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27111.8 | 1.11164 | ||||||||
\(842\) | −5522.56 | −0.226033 | ||||||||
\(843\) | 26366.1 | 1.07722 | ||||||||
\(844\) | −12202.1 | −0.497646 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2952.55 | 0.119989 | ||||||||
\(847\) | −1083.05 | −0.0439362 | ||||||||
\(848\) | 34410.3 | 1.39346 | ||||||||
\(849\) | −5303.26 | −0.214378 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58076.7 | 2.33942 | ||||||||
\(852\) | −20462.6 | −0.822813 | ||||||||
\(853\) | −31979.3 | −1.28365 | −0.641824 | − | 0.766852i | \(-0.721822\pi\) | ||||
−0.641824 | + | 0.766852i | \(0.721822\pi\) | |||||||
\(854\) | −4906.11 | −0.196585 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4393.33 | −0.175422 | ||||||||
\(857\) | 8439.63 | 0.336397 | 0.168199 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168199 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(858\) | 9.22492 | 0.000367056 0 | ||||||||
\(859\) | 47640.1 | 1.89227 | 0.946134 | − | 0.323774i | \(-0.104952\pi\) | ||||
0.946134 | + | 0.323774i | \(0.104952\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3678.04 | 0.145583 | ||||||||
\(862\) | −2434.06 | −0.0961770 | ||||||||
\(863\) | −27963.3 | −1.10299 | −0.551496 | − | 0.834177i | \(-0.685943\pi\) | ||||
−0.551496 | + | 0.834177i | \(0.685943\pi\) | |||||||
\(864\) | −2956.50 | −0.116414 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1648.75 | −0.0646962 | ||||||||
\(867\) | −34716.8 | −1.35991 | ||||||||
\(868\) | 13363.3 | 0.522557 | ||||||||
\(869\) | 5054.81 | 0.197322 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −67.6673 | −0.00263240 | ||||||||
\(872\) | −3137.08 | −0.121829 | ||||||||
\(873\) | 11381.3 | 0.441234 | ||||||||
\(874\) | 2.56063 | 9.91013e−5 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 26321.3 | 1.01520 | ||||||||
\(877\) | 30584.0 | 1.17759 | 0.588796 | − | 0.808282i | \(-0.299602\pi\) | ||||
0.588796 | + | 0.808282i | \(0.299602\pi\) | |||||||
\(878\) | −6732.23 | −0.258772 | ||||||||
\(879\) | 9239.56 | 0.354542 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14444.3 | 0.552372 | 0.276186 | − | 0.961104i | \(-0.410929\pi\) | ||||
0.276186 | + | 0.961104i | \(0.410929\pi\) | |||||||
\(882\) | −1436.58 | −0.0548439 | ||||||||
\(883\) | 19921.4 | 0.759241 | 0.379620 | − | 0.925142i | \(-0.376055\pi\) | ||||
0.379620 | + | 0.925142i | \(0.376055\pi\) | |||||||
\(884\) | 451.097 | 0.0171630 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4331.09 | −0.164228 | ||||||||
\(887\) | 13172.5 | 0.498635 | 0.249317 | − | 0.968422i | \(-0.419794\pi\) | ||||
0.249317 | + | 0.968422i | \(0.419794\pi\) | |||||||
\(888\) | −9640.71 | −0.364325 | ||||||||
\(889\) | 5635.33 | 0.212602 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | −38725.5 | −1.45362 | ||||||||
\(893\) | −13.2835 | −0.000497778 0 | ||||||||
\(894\) | 3982.75 | 0.148997 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 9883.38 | 0.368505 | ||||||||
\(897\) | 236.908 | 0.00881844 | ||||||||
\(898\) | 3820.01 | 0.141955 | ||||||||
\(899\) | −44397.5 | −1.64710 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −79911.4 | −2.95475 | ||||||||
\(902\) | −914.854 | −0.0337709 | ||||||||
\(903\) | −9024.64 | −0.332582 | ||||||||
\(904\) | 10841.9 | 0.398888 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6681.92 | −0.245024 | ||||||||
\(907\) | −16309.7 | −0.597084 | −0.298542 | − | 0.954396i | \(-0.596500\pi\) | ||||
−0.298542 | + | 0.954396i | \(0.596500\pi\) | |||||||
\(908\) | 7999.10 | 0.292356 | ||||||||
\(909\) | 6217.13 | 0.226853 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14994.4 | −0.545320 | −0.272660 | − | 0.962110i | \(-0.587903\pi\) | ||||
−0.272660 | + | 0.962110i | \(0.587903\pi\) | |||||||
\(912\) | 4.07787 | 0.000148061 0 | ||||||||
\(913\) | −1384.64 | −0.0501914 | ||||||||
\(914\) | −4427.63 | −0.160233 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5606.44 | 0.202229 | ||||||||
\(917\) | −5124.93 | −0.184558 | ||||||||
\(918\) | 2104.93 | 0.0756787 | ||||||||
\(919\) | 40263.5 | 1.44524 | 0.722618 | − | 0.691248i | \(-0.242939\pi\) | ||||
0.722618 | + | 0.691248i | \(0.242939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8616.48 | 0.308276 | ||||||||
\(922\) | −10204.1 | −0.364484 | ||||||||
\(923\) | −411.493 | −0.0146744 | ||||||||
\(924\) | 2254.11 | 0.0802541 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4540.87 | −0.161147 | ||||||||
\(927\) | 106.040 | 0.00375709 | ||||||||
\(928\) | −24849.6 | −0.879019 | ||||||||
\(929\) | −9469.52 | −0.334429 | −0.167215 | − | 0.985921i | \(-0.553477\pi\) | ||||
−0.167215 | + | 0.985921i | \(0.553477\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.46319 | 0.000227522 0 | ||||||||
\(932\) | −15360.2 | −0.539848 | ||||||||
\(933\) | 953.933 | 0.0334731 | ||||||||
\(934\) | 4570.23 | 0.160110 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −39.3266 | −0.00137332 | ||||||||
\(937\) | −6356.51 | −0.221620 | −0.110810 | − | 0.993842i | \(-0.535345\pi\) | ||||
−0.110810 | + | 0.993842i | \(0.535345\pi\) | |||||||
\(938\) | 798.810 | 0.0278061 | ||||||||
\(939\) | −24824.4 | −0.862742 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5764.45 | −0.199698 | −0.0998489 | − | 0.995003i | \(-0.531836\pi\) | ||||
−0.0998489 | + | 0.995003i | \(0.531836\pi\) | |||||||
\(942\) | 2583.50 | 0.0893577 | ||||||||
\(943\) | −23494.7 | −0.811338 | ||||||||
\(944\) | −545.663 | −0.0188134 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2244.74 | 0.0771487 | ||||||||
\(947\) | 2284.74 | 0.0783993 | 0.0391997 | − | 0.999231i | \(-0.487519\pi\) | ||||
0.0391997 | + | 0.999231i | \(0.487519\pi\) | |||||||
\(948\) | −10520.4 | −0.360430 | ||||||||
\(949\) | 529.310 | 0.0181055 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3073.03 | 0.104784 | ||||||||
\(952\) | −10907.7 | −0.371344 | ||||||||
\(953\) | 17209.0 | 0.584947 | 0.292474 | − | 0.956274i | \(-0.405522\pi\) | ||||
0.292474 | + | 0.956274i | \(0.405522\pi\) | |||||||
\(954\) | 3401.18 | 0.115427 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −42479.1 | −1.43710 | ||||||||
\(957\) | −7488.95 | −0.252961 | ||||||||
\(958\) | 764.333 | 0.0257771 | ||||||||
\(959\) | −8491.45 | −0.285926 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8482.92 | 0.284748 | ||||||||
\(962\) | −94.6487 | −0.00317214 | ||||||||
\(963\) | 4165.96 | 0.139404 | ||||||||
\(964\) | 25650.8 | 0.857008 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2796.70 | −0.0931493 | ||||||||
\(967\) | 7966.25 | 0.264920 | 0.132460 | − | 0.991188i | \(-0.457712\pi\) | ||||
0.132460 | + | 0.991188i | \(0.457712\pi\) | |||||||
\(968\) | −1148.44 | −0.0381324 | ||||||||
\(969\) | −9.47008 | −0.000313955 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25547.5 | −0.844343 | −0.422172 | − | 0.906516i | \(-0.638732\pi\) | ||||
−0.422172 | + | 0.906516i | \(0.638732\pi\) | |||||||
\(972\) | 1854.41 | 0.0611937 | ||||||||
\(973\) | −22277.3 | −0.733996 | ||||||||
\(974\) | −3113.66 | −0.102431 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 49908.7 | 1.63682 | ||||||||
\(977\) | −12899.8 | −0.422417 | −0.211209 | − | 0.977441i | \(-0.567740\pi\) | ||||
−0.211209 | + | 0.977441i | \(0.567740\pi\) | |||||||
\(978\) | −1094.78 | −0.0357948 | ||||||||
\(979\) | −1655.07 | −0.0540310 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2974.73 | 0.0968152 | ||||||||
\(982\) | 7245.18 | 0.235441 | ||||||||
\(983\) | 7399.28 | 0.240082 | 0.120041 | − | 0.992769i | \(-0.461697\pi\) | ||||
0.120041 | + | 0.992769i | \(0.461697\pi\) | |||||||
\(984\) | 3900.10 | 0.126352 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17692.2 | 0.571433 | ||||||||
\(987\) | 14508.1 | 0.467881 | ||||||||
\(988\) | 0.0863787 | 2.78145e−6 0 | ||||||||
\(989\) | 57647.8 | 1.85348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38466.4 | −1.23302 | −0.616511 | − | 0.787346i | \(-0.711454\pi\) | ||||
−0.616511 | + | 0.787346i | \(0.711454\pi\) | |||||||
\(992\) | 21422.2 | 0.685642 | ||||||||
\(993\) | −13727.5 | −0.438700 | ||||||||
\(994\) | 4857.66 | 0.155006 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2881.80 | 0.0916801 | ||||||||
\(997\) | 62092.5 | 1.97241 | 0.986203 | − | 0.165538i | \(-0.0529361\pi\) | ||||
0.986203 | + | 0.165538i | \(0.0529361\pi\) | |||||||
\(998\) | 8935.60 | 0.283418 | ||||||||
\(999\) | 9141.76 | 0.289522 |
(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 | 825.4.a.t.1.3 | 4 | ||
3.2 | odd | 2 | 2475.4.a.be.1.2 | 4 | |||
5.2 | odd | 4 | 825.4.c.p.199.5 | 8 | |||
5.3 | odd | 4 | 825.4.c.p.199.4 | 8 | |||
5.4 | even | 2 | 165.4.a.h.1.2 | ✓ | 4 | ||
15.14 | odd | 2 | 495.4.a.m.1.3 | 4 | |||
55.54 | odd | 2 | 1815.4.a.t.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.h.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
495.4.a.m.1.3 | 4 | 15.14 | odd | 2 | |||
825.4.a.t.1.3 | 4 | 1.1 | even | 1 | trivial | ||
825.4.c.p.199.4 | 8 | 5.3 | odd | 4 | |||
825.4.c.p.199.5 | 8 | 5.2 | odd | 4 | |||
1815.4.a.t.1.3 | 4 | 55.54 | odd | 2 | |||
2475.4.a.be.1.2 | 4 | 3.2 | odd | 2 |