Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [464,4,Mod(1,464)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(464, 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("464.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 464 = 2^{4} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 464.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: | \(27.3768862427\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 116) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 464.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.60555 | −0.693889 | −0.346944 | − | 0.937886i | \(-0.612781\pi\) | ||||
−0.346944 | + | 0.937886i | \(0.612781\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.2111 | −1.09219 | −0.546097 | − | 0.837722i | \(-0.683887\pi\) | ||||
−0.546097 | + | 0.837722i | \(0.683887\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 24.4222 | 1.31868 | 0.659338 | − | 0.751847i | \(-0.270837\pi\) | ||||
0.659338 | + | 0.751847i | \(0.270837\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −14.0000 | −0.518519 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.6056 | 0.537391 | 0.268695 | − | 0.963225i | \(-0.413408\pi\) | ||||
0.268695 | + | 0.963225i | \(0.413408\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.36669 | −0.114496 | −0.0572482 | − | 0.998360i | \(-0.518233\pi\) | ||||
−0.0572482 | + | 0.998360i | \(0.518233\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 44.0278 | 0.757861 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 57.3221 | 0.817803 | 0.408902 | − | 0.912578i | \(-0.365912\pi\) | ||||
0.408902 | + | 0.912578i | \(0.365912\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −27.2666 | −0.329231 | −0.164616 | − | 0.986358i | \(-0.552638\pi\) | ||||
−0.164616 | + | 0.986358i | \(0.552638\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −88.0555 | −0.915014 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 54.0555 | 0.490059 | 0.245029 | − | 0.969516i | \(-0.421202\pi\) | ||||
0.245029 | + | 0.969516i | \(0.421202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.1110 | 0.192888 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 147.828 | 1.05368 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.816654 | 0.00473146 | 0.00236573 | − | 0.999997i | \(-0.499247\pi\) | ||||
0.00236573 | + | 0.999997i | \(0.499247\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −70.6888 | −0.372889 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −298.222 | −1.44025 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −245.066 | −1.08888 | −0.544442 | − | 0.838799i | \(-0.683258\pi\) | ||||
−0.544442 | + | 0.838799i | \(0.683258\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19.3499 | 0.0794477 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 55.2111 | 0.210306 | 0.105153 | − | 0.994456i | \(-0.466467\pi\) | ||||
0.105153 | + | 0.994456i | \(0.466467\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −87.5500 | −0.310494 | −0.155247 | − | 0.987876i | \(-0.549617\pi\) | ||||
−0.155247 | + | 0.987876i | \(0.549617\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 170.955 | 0.566323 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −474.672 | −1.47315 | −0.736575 | − | 0.676356i | \(-0.763558\pi\) | ||||
−0.736575 | + | 0.676356i | \(0.763558\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 253.444 | 0.738904 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −206.678 | −0.567465 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −211.700 | −0.548664 | −0.274332 | − | 0.961635i | \(-0.588457\pi\) | ||||
−0.274332 | + | 0.961635i | \(0.588457\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −239.405 | −0.586935 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 98.3112 | 0.228450 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −614.389 | −1.35570 | −0.677852 | − | 0.735198i | \(-0.737089\pi\) | ||||
−0.677852 | + | 0.735198i | \(0.737089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −673.766 | −1.41421 | −0.707106 | − | 0.707108i | \(-0.750000\pi\) | ||||
−0.707106 | + | 0.707108i | \(0.750000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −341.911 | −0.683757 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 65.5332 | 0.125052 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −999.532 | −1.82257 | −0.911286 | − | 0.411774i | \(-0.864909\pi\) | ||||
−0.911286 | + | 0.411774i | \(0.864909\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −194.900 | −0.340046 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 650.522 | 1.08736 | 0.543681 | − | 0.839292i | \(-0.317030\pi\) | ||||
0.543681 | + | 0.839292i | \(0.317030\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1041.73 | −1.67021 | −0.835107 | − | 0.550088i | \(-0.814594\pi\) | ||||
−0.835107 | + | 0.550088i | \(0.814594\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −86.9335 | −0.133843 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 478.811 | 0.708644 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1004.92 | 1.43116 | 0.715582 | − | 0.698529i | \(-0.246162\pi\) | ||||
0.715582 | + | 0.698529i | \(0.246162\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −155.000 | −0.212620 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 438.500 | 0.579899 | 0.289949 | − | 0.957042i | \(-0.406362\pi\) | ||||
0.289949 | + | 0.957042i | \(0.406362\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −699.966 | −0.893200 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 104.561 | 0.128852 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1361.32 | 1.62134 | 0.810672 | − | 0.585500i | \(-0.199102\pi\) | ||||
0.810672 | + | 0.585500i | \(0.199102\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −131.066 | −0.150983 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.94449 | −0.00328311 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 332.955 | 0.359584 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −796.567 | −0.833805 | −0.416903 | − | 0.908951i | \(-0.636884\pi\) | ||||
−0.416903 | + | 0.908951i | \(0.636884\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −274.478 | −0.278647 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1234.80 | −1.21651 | −0.608253 | − | 0.793743i | \(-0.708129\pi\) | ||||
−0.608253 | + | 0.793743i | \(0.708129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −349.610 | −0.334447 | −0.167224 | − | 0.985919i | \(-0.553480\pi\) | ||||
−0.167224 | + | 0.985919i | \(0.553480\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1075.25 | 0.999373 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 276.244 | 0.249584 | 0.124792 | − | 0.992183i | \(-0.460174\pi\) | ||||
0.124792 | + | 0.992183i | \(0.460174\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −598.300 | −0.525750 | −0.262875 | − | 0.964830i | \(-0.584671\pi\) | ||||
−0.262875 | + | 0.964830i | \(0.584671\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 883.600 | 0.755564 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −977.532 | −0.813792 | −0.406896 | − | 0.913474i | \(-0.633389\pi\) | ||||
−0.406896 | + | 0.913474i | \(0.633389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −660.077 | −0.535239 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 75.1337 | 0.0593685 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1399.93 | 1.07842 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −946.622 | −0.711211 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −199.066 | −0.145929 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1231.97 | 0.881523 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −143.822 | −0.100489 | −0.0502446 | − | 0.998737i | \(-0.516000\pi\) | ||||
−0.0502446 | + | 0.998737i | \(0.516000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 315.666 | 0.215448 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −591.334 | −0.394390 | −0.197195 | − | 0.980364i | \(-0.563183\pi\) | ||||
−0.197195 | + | 0.980364i | \(0.563183\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −665.911 | −0.434149 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1805.14 | −1.15083 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1166.15 | −0.727235 | −0.363618 | − | 0.931548i | \(-0.618458\pi\) | ||||
−0.363618 | + | 0.931548i | \(0.618458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1738.48 | 1.06083 | 0.530416 | − | 0.847738i | \(-0.322036\pi\) | ||||
0.530416 | + | 0.847738i | \(0.322036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1711.45 | 1.02220 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −105.217 | −0.0615293 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 354.122 | 0.202815 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −913.806 | −0.512717 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2783.57 | 1.53046 | 0.765230 | − | 0.643757i | \(-0.222625\pi\) | ||||
0.765230 | + | 0.643757i | \(0.222625\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2731.24 | −1.47196 | −0.735978 | − | 0.677006i | \(-0.763277\pi\) | ||||
−0.735978 | + | 0.677006i | \(0.763277\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −802.510 | −0.424046 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.97224 | −0.00516768 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −606.676 | −0.308395 | −0.154198 | − | 0.988040i | \(-0.549279\pi\) | ||||
−0.154198 | + | 0.988040i | \(0.549279\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 763.294 | 0.380712 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1320.15 | 0.646228 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1132.29 | 0.544098 | 0.272049 | − | 0.962283i | \(-0.412299\pi\) | ||||
0.272049 | + | 0.962283i | \(0.412299\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 863.188 | 0.407267 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 922.787 | 0.427589 | 0.213795 | − | 0.976879i | \(-0.431418\pi\) | ||||
0.213795 | + | 0.976879i | \(0.431418\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2168.20 | −0.986891 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 381.733 | 0.170712 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1454.47 | 0.639197 | 0.319599 | − | 0.947553i | \(-0.396452\pi\) | ||||
0.319599 | + | 0.947553i | \(0.396452\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 588.844 | 0.254357 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2215.21 | 0.940708 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2862.23 | −1.19516 | −0.597578 | − | 0.801811i | \(-0.703870\pi\) | ||||
−0.597578 | + | 0.801811i | \(0.703870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3740.03 | −1.53588 | −0.767940 | − | 0.640522i | \(-0.778718\pi\) | ||||
−0.767940 | + | 0.640522i | \(0.778718\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2429.30 | 0.981306 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2992.53 | 1.18927 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1123.83 | 0.439480 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3610.28 | 1.38947 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −210.466 | −0.0797319 | −0.0398659 | − | 0.999205i | \(-0.512693\pi\) | ||||
−0.0398659 | + | 0.999205i | \(0.512693\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4151.21 | 1.54824 | 0.774120 | − | 0.633038i | \(-0.218192\pi\) | ||||
0.774120 | + | 0.633038i | \(0.218192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −236.283 | −0.0867723 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3838.13 | 1.38810 | 0.694050 | − | 0.719927i | \(-0.255825\pi\) | ||||
0.694050 | + | 0.719927i | \(0.255825\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3706.40 | 1.32030 | 0.660150 | − | 0.751134i | \(-0.270493\pi\) | ||||
0.660150 | + | 0.751134i | \(0.270493\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3603.87 | 1.26466 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −708.244 | −0.244872 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −674.188 | −0.229694 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −756.777 | −0.254105 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −534.577 | −0.176926 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 267.272 | 0.0872028 | 0.0436014 | − | 0.999049i | \(-0.486117\pi\) | ||||
0.0436014 | + | 0.999049i | \(0.486117\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2345.49 | −0.754508 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1069.08 | 0.339120 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.9445 | 0.00623926 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3756.02 | 1.15894 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −307.630 | −0.0936355 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5263.48 | 1.58058 | 0.790288 | − | 0.612735i | \(-0.209931\pi\) | ||||
0.790288 | + | 0.612735i | \(0.209931\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −337.554 | −0.100016 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2314.81 | −0.676825 | −0.338412 | − | 0.940998i | \(-0.609890\pi\) | ||||
−0.338412 | + | 0.940998i | \(0.609890\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3344.50 | −0.965112 | −0.482556 | − | 0.875865i | \(-0.660292\pi\) | ||||
−0.482556 | + | 0.875865i | \(0.660292\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1726.38 | −0.491720 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5063.82 | −1.42378 | −0.711892 | − | 0.702289i | \(-0.752161\pi\) | ||||
−0.711892 | + | 0.702289i | \(0.752161\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5796.27 | 1.60897 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3623.28 | −0.993068 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1854.88 | 0.502018 | 0.251009 | − | 0.967985i | \(-0.419238\pi\) | ||||
0.251009 | + | 0.967985i | \(0.419238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2981.31 | −0.796859 | −0.398430 | − | 0.917199i | \(-0.630445\pi\) | ||||
−0.398430 | + | 0.917199i | \(0.630445\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3432.48 | −0.906148 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3094.83 | −0.807027 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 146.332 | 0.0376958 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1581.03 | −0.402385 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1639.16 | −0.412203 | −0.206102 | − | 0.978531i | \(-0.566078\pi\) | ||||
−0.206102 | + | 0.978531i | \(0.566078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1059.79 | 0.263353 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2523.76 | 0.619781 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −972.955 | −0.236153 | −0.118076 | − | 0.993005i | \(-0.537673\pi\) | ||||
−0.118076 | + | 0.993005i | \(0.537673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5985.06 | −1.43588 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 406.000 | 0.0962865 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3991.31 | 0.935796 | 0.467898 | − | 0.883782i | \(-0.345011\pi\) | ||||
0.467898 | + | 0.883782i | \(0.345011\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2585.09 | 0.599248 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4908.31 | −1.12503 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1932.74 | 0.438072 | 0.219036 | − | 0.975717i | \(-0.429709\pi\) | ||||
0.219036 | + | 0.975717i | \(0.429709\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2679.57 | −0.600635 | −0.300317 | − | 0.953839i | \(-0.597093\pi\) | ||||
−0.300317 | + | 0.953839i | \(0.597093\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 472.567 | 0.104766 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 472.710 | 0.103656 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4898.39 | 1.06251 | 0.531256 | − | 0.847211i | \(-0.321720\pi\) | ||||
0.531256 | + | 0.847211i | \(0.321720\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.4332 | −0.00245335 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4851.20 | −1.02989 | −0.514943 | − | 0.857224i | \(-0.672187\pi\) | ||||
−0.514943 | + | 0.857224i | \(0.672187\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6486.83 | −1.36255 | −0.681276 | − | 0.732027i | \(-0.738574\pi\) | ||||
−0.681276 | + | 0.732027i | \(0.738574\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1200.49 | −0.249511 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1348.38 | 0.277325 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1627.17 | −0.331198 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2872.06 | 0.578568 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1673.60 | −0.333696 | −0.166848 | − | 0.985983i | \(-0.553359\pi\) | ||||
−0.166848 | + | 0.985983i | \(0.553359\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7502.36 | 1.48069 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2898.24 | 0.566239 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −290.099 | −0.0561100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2138.16 | −0.409441 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4452.13 | 0.844120 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8227.43 | 1.54459 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4619.62 | −0.858813 | −0.429406 | − | 0.903111i | \(-0.641277\pi\) | ||||
−0.429406 | + | 0.903111i | \(0.641277\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1260.54 | 0.232069 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3307.00 | −0.602967 | −0.301483 | − | 0.953471i | \(-0.597482\pi\) | ||||
−0.301483 | + | 0.953471i | \(0.597482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6739.95 | 1.21714 | 0.608570 | − | 0.793501i | \(-0.291744\pi\) | ||||
0.608570 | + | 0.793501i | \(0.291744\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4175.11 | 0.746796 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9278.23 | 1.64390 | 0.821952 | − | 0.569557i | \(-0.192885\pi\) | ||||
0.821952 | + | 0.569557i | \(0.192885\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −568.561 | −0.0997909 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −996.012 | −0.173184 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1562.98 | −0.269246 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −129.396 | −0.0220850 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2157.20 | 0.364812 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11592.5 | −1.94261 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8424.51 | −1.39895 | −0.699475 | − | 0.714657i | \(-0.746583\pi\) | ||||
−0.699475 | + | 0.714657i | \(0.746583\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3430.93 | 0.564606 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12205.4 | 1.99060 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7069.41 | 1.14272 | 0.571358 | − | 0.820701i | \(-0.306417\pi\) | ||||
0.571358 | + | 0.820701i | \(0.306417\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3524.54 | 0.564681 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0109 | 0.00254264 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2187.15 | −0.344301 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2379.94 | 0.371397 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10677.5 | −1.65186 | −0.825931 | − | 0.563772i | \(-0.809350\pi\) | ||||
−0.825931 | + | 0.563772i | \(0.809350\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8612.96 | 1.32103 | 0.660517 | − | 0.750811i | \(-0.270337\pi\) | ||||
0.660517 | + | 0.750811i | \(0.270337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −793.345 | −0.120643 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9586.96 | −1.44550 | −0.722751 | − | 0.691109i | \(-0.757123\pi\) | ||||
−0.722751 | + | 0.691109i | \(0.757123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7943.58 | −1.18761 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5047.53 | −0.748301 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10525.2 | 1.54736 | 0.773678 | − | 0.633579i | \(-0.218415\pi\) | ||||
0.773678 | + | 0.633579i | \(0.218415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6115.53 | −0.891607 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3413.10 | 0.493502 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12720.7 | 1.82420 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8807.65 | −1.25274 | −0.626370 | − | 0.779526i | \(-0.715460\pi\) | ||||
−0.626370 | + | 0.779526i | \(0.715460\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −772.955 | −0.109047 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5170.18 | −0.723510 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3134.23 | −0.435079 | −0.217540 | − | 0.976052i | \(-0.569803\pi\) | ||||
−0.217540 | + | 0.976052i | \(0.569803\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4441.92 | −0.611679 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 155.634 | 0.0212614 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7830.92 | 1.06134 | 0.530670 | − | 0.847579i | \(-0.321941\pi\) | ||||
0.530670 | + | 0.847579i | \(0.321941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 518.557 | 0.0697282 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13034.5 | −1.73899 | −0.869496 | − | 0.493939i | \(-0.835556\pi\) | ||||
−0.869496 | + | 0.493939i | \(0.835556\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5846.81 | −0.773976 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1225.70 | 0.160997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5012.18 | −0.653284 | −0.326642 | − | 0.945148i | \(-0.605917\pi\) | ||||
−0.326642 | + | 0.945148i | \(0.605917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3098.58 | 0.400772 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2132.08 | 0.273663 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12271.1 | −1.56311 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2200.61 | 0.278200 | 0.139100 | − | 0.990278i | \(-0.455579\pi\) | ||||
0.139100 | + | 0.990278i | \(0.455579\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2400.98 | 0.301251 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9028.68 | −1.12437 | −0.562183 | − | 0.827013i | \(-0.690038\pi\) | ||||
−0.562183 | + | 0.827013i | \(0.690038\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.38273 | −0.000541735 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1892.72 | 0.232222 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4804.66 | −0.585156 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5274.47 | −0.637667 | −0.318833 | − | 0.947811i | \(-0.603291\pi\) | ||||
−0.318833 | + | 0.947811i | \(0.603291\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4204.63 | 0.504620 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15004.7 | −1.78773 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5354.56 | −0.633362 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6268.16 | −0.736099 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2450.27 | −0.285688 | −0.142844 | − | 0.989745i | \(-0.545625\pi\) | ||||
−0.142844 | + | 0.989745i | \(0.545625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2060.09 | −0.238487 | −0.119243 | − | 0.992865i | \(-0.538047\pi\) | ||||
−0.119243 | + | 0.992865i | \(0.538047\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6645.41 | 0.763855 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1382.10 | 0.157745 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16454.9 | −1.86489 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 379.365 | 0.0426945 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10108.0 | 1.12966 | 0.564830 | − | 0.825207i | \(-0.308942\pi\) | ||||
0.564830 | + | 0.825207i | \(0.308942\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11457.1 | −1.27158 | −0.635791 | − | 0.771861i | \(-0.719326\pi\) | ||||
−0.635791 | + | 0.771861i | \(0.719326\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1276.80 | −0.140731 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1473.91 | −0.161343 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14239.8 | 1.54813 | 0.774064 | − | 0.633107i | \(-0.218221\pi\) | ||||
0.774064 | + | 0.633107i | \(0.218221\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3548.22 | −0.383135 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3220.82 | 0.345431 | 0.172716 | − | 0.984972i | \(-0.444746\pi\) | ||||
0.172716 | + | 0.984972i | \(0.444746\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16623.2 | −1.77082 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10036.3 | −1.06197 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3189.72 | 0.335262 | 0.167631 | − | 0.985850i | \(-0.446388\pi\) | ||||
0.167631 | + | 0.985850i | \(0.446388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1082.44 | 0.113016 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9847.63 | 1.02137 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1600.47 | 0.164903 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11209.7 | 1.14741 | 0.573704 | − | 0.819062i | \(-0.305506\pi\) | ||||
0.573704 | + | 0.819062i | \(0.305506\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8473.79 | 0.861705 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8038.44 | −0.812121 | −0.406060 | − | 0.913846i | \(-0.633098\pi\) | ||||
−0.406060 | + | 0.913846i | \(0.633098\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16556.0 | −1.66182 | −0.830909 | − | 0.556408i | \(-0.812179\pi\) | ||||
−0.830909 | + | 0.556408i | \(0.812179\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 35.9554 | 0.00358579 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17211.9 | 1.70550 | 0.852752 | − | 0.522317i | \(-0.174932\pi\) | ||||
0.852752 | + | 0.522317i | \(0.174932\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24410.8 | −2.40338 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2187.40 | 0.213992 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1716.47 | −0.166857 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −657.426 | −0.0635048 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2963.80 | 0.284493 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6601.25 | −0.629685 | −0.314842 | − | 0.949144i | \(-0.601952\pi\) | ||||
−0.314842 | + | 0.949144i | \(0.601952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1315.20 | 0.124673 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4759.89 | −0.448411 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9726.96 | 0.910677 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −669.609 | −0.0623057 | −0.0311529 | − | 0.999515i | \(-0.509918\pi\) | ||||
−0.0311529 | + | 0.999515i | \(0.509918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4082.54 | −0.377543 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2822.98 | 0.259469 | 0.129735 | − | 0.991549i | \(-0.458587\pi\) | ||||
0.129735 | + | 0.991549i | \(0.458587\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1662.34 | −0.151862 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3351.68 | 0.304337 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15887.2 | 1.43388 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1879.69 | −0.168630 | −0.0843151 | − | 0.996439i | \(-0.526870\pi\) | ||||
−0.0843151 | + | 0.996439i | \(0.526870\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3327.16 | −0.296699 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5616.84 | 0.497897 | 0.248949 | − | 0.968517i | \(-0.419915\pi\) | ||||
0.248949 | + | 0.968517i | \(0.419915\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15078.3 | 1.32866 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7817.55 | 0.684792 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15417.9 | −1.34261 | −0.671304 | − | 0.741182i | \(-0.734266\pi\) | ||||
−0.671304 | + | 0.741182i | \(0.734266\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25441.4 | −2.20247 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4030.76 | −0.346905 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4269.12 | 0.365282 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9306.21 | −0.791657 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5244.16 | −0.443532 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8475.84 | 0.712732 | 0.356366 | − | 0.934346i | \(-0.384016\pi\) | ||||
0.356366 | + | 0.934346i | \(0.384016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15153.8 | −1.26698 | −0.633490 | − | 0.773750i | \(-0.718378\pi\) | ||||
−0.633490 | + | 0.773750i | \(0.718378\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2123.11 | −0.176495 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 46.8123 | 0.00386941 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9245.00 | −0.759842 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8601.44 | 0.702958 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −296.301 | −0.0240792 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3373.24 | −0.272594 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10319.9 | 0.829306 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4968.91 | 0.397080 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21278.1 | 1.69098 | 0.845488 | − | 0.533994i | \(-0.179310\pi\) | ||||
0.845488 | + | 0.533994i | \(0.179310\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13484.9 | 1.06573 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7305.91 | 0.574221 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13816.0 | 1.07994 | 0.539972 | − | 0.841683i | \(-0.318435\pi\) | ||||
0.539972 | + | 0.841683i | \(0.318435\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9432.73 | 0.733295 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 790.732 | 0.0611367 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24542.3 | 1.88724 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10789.7 | −0.825222 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7735.09 | −0.588414 | −0.294207 | − | 0.955742i | \(-0.595055\pi\) | ||||
−0.294207 | + | 0.955742i | \(0.595055\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 469.854 | 0.0355505 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4052.03 | −0.304950 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7911.82 | 0.592262 | 0.296131 | − | 0.955147i | \(-0.404304\pi\) | ||||
0.296131 | + | 0.955147i | \(0.404304\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11936.7 | 0.888819 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3785.44 | −0.280377 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16436.7 | 1.21101 | 0.605503 | − | 0.795843i | \(-0.292972\pi\) | ||||
0.605503 | + | 0.795843i | \(0.292972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10244.9 | −0.750854 | −0.375427 | − | 0.926852i | \(-0.622504\pi\) | ||||
−0.375427 | + | 0.926852i | \(0.622504\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 758.846 | 0.0553250 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1303.33 | 0.0945266 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7544.04 | 0.544303 | 0.272151 | − | 0.962254i | \(-0.412265\pi\) | ||||
0.272151 | + | 0.962254i | \(0.412265\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14967.4 | −1.07431 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10709.1 | 0.764698 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4150.49 | −0.294847 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −917.465 | −0.0648419 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19532.4 | 1.37341 | 0.686703 | − | 0.726938i | \(-0.259057\pi\) | ||||
0.686703 | + | 0.726938i | \(0.259057\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.2674 | −0.00155774 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13838.6 | −0.963186 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6854.78 | −0.474691 | −0.237346 | − | 0.971425i | \(-0.576277\pi\) | ||||
−0.237346 | + | 0.971425i | \(0.576277\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17094.7 | −1.17784 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13363.6 | −0.916141 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15947.1 | 1.08778 | 0.543890 | − | 0.839156i | \(-0.316951\pi\) | ||||
0.543890 | + | 0.839156i | \(0.316951\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10663.2 | −0.723729 | −0.361864 | − | 0.932231i | \(-0.617860\pi\) | ||||
−0.361864 | + | 0.932231i | \(0.617860\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13993.5 | 0.945037 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11559.3 | 0.776781 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16197.4 | −1.08309 | −0.541543 | − | 0.840673i | \(-0.682160\pi\) | ||||
−0.541543 | + | 0.840673i | \(0.682160\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2553.61 | 0.169914 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2547.42 | 0.168670 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12176.2 | 0.802268 | 0.401134 | − | 0.916019i | \(-0.368616\pi\) | ||||
0.401134 | + | 0.916019i | \(0.368616\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2430.82 | 0.159382 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27706.3 | 1.80780 | 0.903900 | − | 0.427744i | \(-0.140692\pi\) | ||||
0.903900 | + | 0.427744i | \(0.140692\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23136.1 | 1.50229 | 0.751147 | − | 0.660136i | \(-0.229501\pi\) | ||||
0.751147 | + | 0.660136i | \(0.229501\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7990.90 | 0.516367 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33246.5 | 2.13803 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18057.5 | −1.15568 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1927.44 | 0.122767 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14047.7 | −0.890492 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 425.446 | 0.0268411 | 0.0134205 | − | 0.999910i | \(-0.495728\pi\) | ||||
0.0134205 | + | 0.999910i | \(0.495728\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −963.665 | −0.0605091 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1756.22 | 0.109754 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1360.16 | −0.0846018 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9107.30 | −0.563817 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20327.6 | −1.25256 | −0.626280 | − | 0.779598i | \(-0.715423\pi\) | ||||
−0.626280 | + | 0.779598i | \(0.715423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13733.7 | 0.842307 | 0.421153 | − | 0.906989i | \(-0.361625\pi\) | ||||
0.421153 | + | 0.906989i | \(0.361625\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3854.63 | −0.235312 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9986.00 | 0.606786 | 0.303393 | − | 0.952866i | \(-0.401881\pi\) | ||||
0.303393 | + | 0.952866i | \(0.401881\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12045.4 | −0.728543 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −71.9109 | −0.00432935 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21134.3 | 1.26654 | 0.633268 | − | 0.773933i | \(-0.281713\pi\) | ||||
0.633268 | + | 0.773933i | \(0.281713\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7220.84 | 0.430750 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14584.3 | 0.866037 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1452.86 | −0.0858806 | −0.0429403 | − | 0.999078i | \(-0.513673\pi\) | ||||
−0.0429403 | + | 0.999078i | \(0.513673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19476.0 | −1.14604 | −0.573018 | − | 0.819543i | \(-0.694228\pi\) | ||||
−0.573018 | + | 0.819543i | \(0.694228\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1109.18 | 0.0649726 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8131.51 | 0.474175 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1567.61 | −0.0910016 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18977.7 | −1.09674 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13209.6 | −0.759984 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13453.9 | 0.770592 | 0.385296 | − | 0.922793i | \(-0.374099\pi\) | ||||
0.385296 | + | 0.922793i | \(0.374099\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3564.28 | 0.203243 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7227.43 | 0.410299 | 0.205150 | − | 0.978731i | \(-0.434232\pi\) | ||||
0.205150 | + | 0.978731i | \(0.434232\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19453.9 | −1.09952 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8346.16 | 0.469641 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27923.5 | 1.56437 | 0.782185 | − | 0.623047i | \(-0.214105\pi\) | ||||
0.782185 | + | 0.623047i | \(0.214105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14240.0 | 0.794282 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12058.8 | 0.669681 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1136.13 | 0.0628200 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8332.36 | 0.458724 | 0.229362 | − | 0.973341i | \(-0.426336\pi\) | ||||
0.229362 | + | 0.973341i | \(0.426336\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6703.35 | −0.367445 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21228.7 | −1.15863 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3164.82 | 0.171989 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18257.8 | 0.987947 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14927.5 | 0.804288 | 0.402144 | − | 0.915576i | \(-0.368265\pi\) | ||||
0.402144 | + | 0.915576i | \(0.368265\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6682.13 | 0.358494 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20898.7 | −1.11644 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30156.5 | −1.60418 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15555.3 | 0.823966 | 0.411983 | − | 0.911191i | \(-0.364836\pi\) | ||||
0.411983 | + | 0.911191i | \(0.364836\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14068.8 | −0.742085 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 44.1446 | 0.00231870 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1284.82 | 0.0672019 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6687.86 | −0.348344 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7336.33 | 0.380527 | 0.190264 | − | 0.981733i | \(-0.439066\pi\) | ||||
0.190264 | + | 0.981733i | \(0.439066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8538.24 | −0.441027 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10749.3 | 0.552932 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −699.220 | −0.0358184 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3280.35 | 0.167347 | 0.0836735 | − | 0.996493i | \(-0.473335\pi\) | ||||
0.0836735 | + | 0.996493i | \(0.473335\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16561.0 | 0.841386 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5018.55 | −0.253923 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37704.0 | −1.89990 | −0.949952 | − | 0.312395i | \(-0.898869\pi\) | ||||
−0.949952 | + | 0.312395i | \(0.898869\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11158.6 | 0.559987 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19596.4 | −0.979433 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5442.77 | −0.270928 | −0.135464 | − | 0.990782i | \(-0.543252\pi\) | ||||
−0.135464 | + | 0.990782i | \(0.543252\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −527.606 | −0.0261567 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15637.1 | 0.772097 | 0.386049 | − | 0.922478i | \(-0.373840\pi\) | ||||
0.386049 | + | 0.922478i | \(0.373840\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33990.4 | −1.67156 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6138.99 | −0.300688 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6746.49 | 0.329120 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29072.1 | 1.41259 | 0.706296 | − | 0.707917i | \(-0.250365\pi\) | ||||
0.706296 | + | 0.707917i | \(0.250365\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5910.08 | 0.286023 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33351.5 | 1.60766 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7801.68 | −0.374580 | −0.187290 | − | 0.982305i | \(-0.559970\pi\) | ||||
−0.187290 | + | 0.982305i | \(0.559970\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3821.12 | −0.182738 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13233.8 | −0.630386 | −0.315193 | − | 0.949028i | \(-0.602069\pi\) | ||||
−0.315193 | + | 0.949028i | \(0.602069\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14611.8 | −0.693294 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9799.53 | 0.463141 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3297.23 | 0.155223 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35703.3 | −1.67424 | −0.837122 | − | 0.547017i | \(-0.815763\pi\) | ||||
−0.837122 | + | 0.547017i | \(0.815763\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3508.04 | 0.163864 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36775.8 | 1.71117 | 0.855585 | − | 0.517663i | \(-0.173198\pi\) | ||||
0.855585 | + | 0.517663i | \(0.173198\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.6904 | 0.000912643 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21579.5 | 0.996343 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1505.42 | −0.0692391 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12753.8 | 0.584338 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4287.00 | −0.195664 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7408.19 | 0.336827 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24987.9 | 1.13179 | 0.565897 | − | 0.824476i | \(-0.308530\pi\) | ||||
0.565897 | + | 0.824476i | \(0.308530\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14390.9 | −0.649339 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23873.5 | −1.07313 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3615.90 | 0.161922 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9320.67 | −0.415811 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12969.3 | 0.576409 | 0.288204 | − | 0.957569i | \(-0.406942\pi\) | ||||
0.288204 | + | 0.957569i | \(0.406942\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27209.2 | −1.20475 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19058.5 | −0.840697 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20423.7 | −0.897557 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16120.5 | −0.705807 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6968.59 | −0.303973 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23818.8 | 1.03514 | 0.517568 | − | 0.855642i | \(-0.326837\pi\) | ||||
0.517568 | + | 0.855642i | \(0.326837\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11646.6 | 0.504276 | 0.252138 | − | 0.967691i | \(-0.418866\pi\) | ||||
0.252138 | + | 0.967691i | \(0.418866\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9661.31 | 0.416774 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13826.5 | −0.594261 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2387.19 | 0.102224 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1834.93 | 0.0782877 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4592.82 | −0.195238 | −0.0976190 | − | 0.995224i | \(-0.531123\pi\) | ||||
−0.0976190 | + | 0.995224i | \(0.531123\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4271.24 | 0.180907 | 0.0904533 | − | 0.995901i | \(-0.471168\pi\) | ||||
0.0904533 | + | 0.995901i | \(0.471168\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1704.38 | −0.0719259 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20409.8 | −0.858185 | −0.429093 | − | 0.903260i | \(-0.641167\pi\) | ||||
−0.429093 | + | 0.903260i | \(0.641167\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28910.2 | 1.21121 | 0.605606 | − | 0.795765i | \(-0.292931\pi\) | ||||
0.605606 | + | 0.795765i | \(0.292931\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17661.4 | −0.737265 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14528.0 | 0.604278 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11268.3 | −0.467011 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 120.724 | 0.00498546 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15702.7 | −0.646148 | −0.323074 | − | 0.946374i | \(-0.604716\pi\) | ||||
−0.323074 | + | 0.946374i | \(0.604716\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17491.2 | 0.714627 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26476.1 | 1.07788 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23118.6 | −0.937857 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23388.6 | 0.945459 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13247.2 | −0.533617 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22605.4 | −0.907379 | −0.453690 | − | 0.891160i | \(-0.649893\pi\) | ||||
−0.453690 | + | 0.891160i | \(0.649893\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4661.38 | −0.186451 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16881.0 | −0.672864 | −0.336432 | − | 0.941708i | \(-0.609220\pi\) | ||||
−0.336432 | + | 0.941708i | \(0.609220\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16871.7 | −0.670147 | −0.335074 | − | 0.942192i | \(-0.608761\pi\) | ||||
−0.335074 | + | 0.942192i | \(0.608761\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4861.64 | −0.192432 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17711.7 | −0.698624 | −0.349312 | − | 0.937006i | \(-0.613585\pi\) | ||||
−0.349312 | + | 0.937006i | \(0.613585\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17760.7 | −0.698128 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5866.86 | 0.229814 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19701.9 | 0.769093 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5364.18 | 0.208678 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11151.9 | 0.432343 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30087.3 | 1.16244 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42056.4 | 1.61932 | 0.809660 | − | 0.586899i | \(-0.199652\pi\) | ||||
0.809660 | + | 0.586899i | \(0.199652\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6034.26 | 0.231548 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44296.3 | −1.69396 | −0.846981 | − | 0.531622i | \(-0.821583\pi\) | ||||
−0.846981 | + | 0.531622i | \(0.821583\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32695.6 | 1.24609 | 0.623044 | − | 0.782187i | \(-0.285896\pi\) | ||||
0.623044 | + | 0.782187i | \(0.285896\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27050.2 | −1.02744 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26911.3 | −1.01871 | −0.509353 | − | 0.860558i | \(-0.670115\pi\) | ||||
−0.509353 | + | 0.860558i | \(0.670115\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3512.44 | −0.132512 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3038.86 | −0.114260 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12942.7 | 0.485007 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34951.0 | 1.30534 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1045.97 | 0.0389341 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.6830 | −0.000878611 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12135.1 | −0.448699 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7709.26 | 0.284107 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45669.9 | 1.67748 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23856.5 | 0.873366 | 0.436683 | − | 0.899615i | \(-0.356153\pi\) | ||||
0.436683 | + | 0.899615i | \(0.356153\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17287.2 | 0.630781 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15194.9 | 0.552613 | 0.276306 | − | 0.961070i | \(-0.410890\pi\) | ||||
0.276306 | + | 0.961070i | \(0.410890\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8597.03 | 0.311632 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29664.4 | −1.07178 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14441.7 | −0.520072 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42629.9 | −1.53018 | −0.765088 | − | 0.643926i | \(-0.777305\pi\) | ||||
−0.765088 | + | 0.643926i | \(0.777305\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16656.3 | 0.595920 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3491.15 | −0.124499 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5908.80 | −0.210033 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4894.54 | 0.173417 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24680.5 | −0.871627 | −0.435814 | − | 0.900037i | \(-0.643539\pi\) | ||||
−0.435814 | + | 0.900037i | \(0.643539\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6910.56 | −0.243270 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11923.5 | 0.418392 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13723.2 | −0.479997 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15589.4 | 0.543525 | 0.271763 | − | 0.962364i | \(-0.412393\pi\) | ||||
0.271763 | + | 0.962364i | \(0.412393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24301.2 | −0.844559 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −56872.4 | −1.97023 | −0.985116 | − | 0.171892i | \(-0.945012\pi\) | ||||
−0.985116 | + | 0.171892i | \(0.945012\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2984.46 | 0.103062 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −44085.5 | −1.51757 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6452.91 | 0.221427 | 0.110714 | − | 0.993852i | \(-0.464686\pi\) | ||||
0.110714 | + | 0.993852i | \(0.464686\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5590.66 | 0.191233 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33453.1 | −1.14069 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7140.93 | 0.242725 | 0.121363 | − | 0.992608i | \(-0.461274\pi\) | ||||
0.121363 | + | 0.992608i | \(0.461274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2570.02 | 0.0870827 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2049.98 | 0.0692438 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28480.0 | −0.958987 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29790.3 | −0.999978 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3867.42 | −0.129414 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −50690.8 | −1.69098 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5957.77 | 0.198127 | 0.0990635 | − | 0.995081i | \(-0.468415\pi\) | ||||
0.0990635 | + | 0.995081i | \(0.468415\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5635.41 | 0.186827 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43221.7 | 1.42848 | 0.714238 | − | 0.699903i | \(-0.246774\pi\) | ||||
0.714238 | + | 0.699903i | \(0.246774\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42457.4 | 1.39889 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 466.546 | 0.0153245 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28243.3 | −0.924854 | −0.462427 | − | 0.886657i | \(-0.653021\pi\) | ||||
−0.462427 | + | 0.886657i | \(0.653021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26689.4 | 0.871295 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8376.20 | 0.272611 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37893.9 | 1.22953 | 0.614765 | − | 0.788710i | \(-0.289251\pi\) | ||||
0.614765 | + | 0.788710i | \(0.289251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −46867.8 | −1.51607 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 41797.5 | 1.34795 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4732.56 | −0.152160 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29795.8 | 0.955091 | 0.477545 | − | 0.878607i | \(-0.341527\pi\) | ||||
0.477545 | + | 0.878607i | \(0.341527\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30375.0 | 0.970716 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45259.2 | −1.44202 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43164.3 | −1.37114 | −0.685571 | − | 0.728006i | \(-0.740447\pi\) | ||||
−0.685571 | + | 0.728006i | \(0.740447\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36227.6 | −1.14734 |
(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 | 464.4.a.d.1.1 | 2 | ||
4.3 | odd | 2 | 116.4.a.a.1.2 | ✓ | 2 | ||
8.3 | odd | 2 | 1856.4.a.j.1.1 | 2 | |||
8.5 | even | 2 | 1856.4.a.k.1.2 | 2 | |||
12.11 | even | 2 | 1044.4.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
116.4.a.a.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
464.4.a.d.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1044.4.a.d.1.2 | 2 | 12.11 | even | 2 | |||
1856.4.a.j.1.1 | 2 | 8.3 | odd | 2 | |||
1856.4.a.k.1.2 | 2 | 8.5 | even | 2 |