Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} - 105 x^{18} + 103 x^{17} + 4500 x^{16} - 4345 x^{15} - 101844 x^{14} + 95592 x^{13} + \cdots + 150528 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-3.55600\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.55600 | 1.25723 | 0.628617 | − | 0.777715i | \(-0.283621\pi\) | ||||
0.628617 | + | 0.777715i | \(0.283621\pi\) | |||||||
\(3\) | 6.62353 | 1.27470 | 0.637349 | − | 0.770575i | \(-0.280031\pi\) | ||||
0.637349 | + | 0.770575i | \(0.280031\pi\) | |||||||
\(4\) | 4.64511 | 0.580639 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 23.5532 | 1.60259 | ||||||||
\(7\) | −2.03165 | −0.109699 | −0.0548493 | − | 0.998495i | \(-0.517468\pi\) | ||||
−0.0548493 | + | 0.998495i | \(0.517468\pi\) | |||||||
\(8\) | −11.9300 | −0.527236 | ||||||||
\(9\) | 16.8711 | 0.624855 | ||||||||
\(10\) | −17.7800 | −0.562252 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 30.7670 | 0.740139 | ||||||||
\(13\) | −18.7788 | −0.400638 | −0.200319 | − | 0.979731i | \(-0.564198\pi\) | ||||
−0.200319 | + | 0.979731i | \(0.564198\pi\) | |||||||
\(14\) | −7.22452 | −0.137917 | ||||||||
\(15\) | −33.1176 | −0.570062 | ||||||||
\(16\) | −79.5838 | −1.24350 | ||||||||
\(17\) | −128.340 | −1.83100 | −0.915499 | − | 0.402320i | \(-0.868204\pi\) | ||||
−0.915499 | + | 0.402320i | \(0.868204\pi\) | |||||||
\(18\) | 59.9936 | 0.785590 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | −23.2255 | −0.259670 | ||||||||
\(21\) | −13.4567 | −0.139833 | ||||||||
\(22\) | −39.1160 | −0.379070 | ||||||||
\(23\) | 68.3956 | 0.620064 | 0.310032 | − | 0.950726i | \(-0.399660\pi\) | ||||
0.310032 | + | 0.950726i | \(0.399660\pi\) | |||||||
\(24\) | −79.0185 | −0.672066 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −66.7772 | −0.503696 | ||||||||
\(27\) | −67.0891 | −0.478196 | ||||||||
\(28\) | −9.43722 | −0.0636952 | ||||||||
\(29\) | −89.8328 | −0.575225 | −0.287613 | − | 0.957747i | \(-0.592862\pi\) | ||||
−0.287613 | + | 0.957747i | \(0.592862\pi\) | |||||||
\(30\) | −117.766 | −0.716702 | ||||||||
\(31\) | −43.4357 | −0.251654 | −0.125827 | − | 0.992052i | \(-0.540158\pi\) | ||||
−0.125827 | + | 0.992052i | \(0.540158\pi\) | |||||||
\(32\) | −187.560 | −1.03613 | ||||||||
\(33\) | −72.8588 | −0.384336 | ||||||||
\(34\) | −456.376 | −2.30199 | ||||||||
\(35\) | 10.1582 | 0.0490587 | ||||||||
\(36\) | 78.3681 | 0.362815 | ||||||||
\(37\) | −142.330 | −0.632405 | −0.316202 | − | 0.948692i | \(-0.602408\pi\) | ||||
−0.316202 | + | 0.948692i | \(0.602408\pi\) | |||||||
\(38\) | 67.5639 | 0.288429 | ||||||||
\(39\) | −124.382 | −0.510692 | ||||||||
\(40\) | 59.6499 | 0.235787 | ||||||||
\(41\) | 367.030 | 1.39806 | 0.699029 | − | 0.715093i | \(-0.253616\pi\) | ||||
0.699029 | + | 0.715093i | \(0.253616\pi\) | |||||||
\(42\) | −47.8518 | −0.175802 | ||||||||
\(43\) | −298.680 | −1.05926 | −0.529631 | − | 0.848228i | \(-0.677670\pi\) | ||||
−0.529631 | + | 0.848228i | \(0.677670\pi\) | |||||||
\(44\) | −51.0962 | −0.175069 | ||||||||
\(45\) | −84.3555 | −0.279444 | ||||||||
\(46\) | 243.215 | 0.779566 | ||||||||
\(47\) | −51.7860 | −0.160718 | −0.0803592 | − | 0.996766i | \(-0.525607\pi\) | ||||
−0.0803592 | + | 0.996766i | \(0.525607\pi\) | |||||||
\(48\) | −527.126 | −1.58508 | ||||||||
\(49\) | −338.872 | −0.987966 | ||||||||
\(50\) | 88.8999 | 0.251447 | ||||||||
\(51\) | −850.062 | −2.33397 | ||||||||
\(52\) | −87.2294 | −0.232626 | ||||||||
\(53\) | 35.2083 | 0.0912497 | 0.0456249 | − | 0.998959i | \(-0.485472\pi\) | ||||
0.0456249 | + | 0.998959i | \(0.485472\pi\) | |||||||
\(54\) | −238.568 | −0.601205 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | 24.2375 | 0.0578370 | ||||||||
\(57\) | 125.847 | 0.292436 | ||||||||
\(58\) | −319.445 | −0.723193 | ||||||||
\(59\) | 374.758 | 0.826938 | 0.413469 | − | 0.910518i | \(-0.364317\pi\) | ||||
0.413469 | + | 0.910518i | \(0.364317\pi\) | |||||||
\(60\) | −153.835 | −0.331000 | ||||||||
\(61\) | 470.097 | 0.986717 | 0.493358 | − | 0.869826i | \(-0.335769\pi\) | ||||
0.493358 | + | 0.869826i | \(0.335769\pi\) | |||||||
\(62\) | −154.457 | −0.316388 | ||||||||
\(63\) | −34.2761 | −0.0685457 | ||||||||
\(64\) | −30.2919 | −0.0591639 | ||||||||
\(65\) | 93.8938 | 0.179171 | ||||||||
\(66\) | −259.086 | −0.483200 | ||||||||
\(67\) | 682.651 | 1.24476 | 0.622381 | − | 0.782714i | \(-0.286165\pi\) | ||||
0.622381 | + | 0.782714i | \(0.286165\pi\) | |||||||
\(68\) | −596.152 | −1.06315 | ||||||||
\(69\) | 453.020 | 0.790394 | ||||||||
\(70\) | 36.1226 | 0.0616783 | ||||||||
\(71\) | −636.206 | −1.06343 | −0.531717 | − | 0.846922i | \(-0.678453\pi\) | ||||
−0.531717 | + | 0.846922i | \(0.678453\pi\) | |||||||
\(72\) | −201.272 | −0.329446 | ||||||||
\(73\) | −400.595 | −0.642275 | −0.321138 | − | 0.947033i | \(-0.604065\pi\) | ||||
−0.321138 | + | 0.947033i | \(0.604065\pi\) | |||||||
\(74\) | −506.126 | −0.795081 | ||||||||
\(75\) | 165.588 | 0.254940 | ||||||||
\(76\) | 88.2571 | 0.133208 | ||||||||
\(77\) | 22.3481 | 0.0330754 | ||||||||
\(78\) | −442.300 | −0.642060 | ||||||||
\(79\) | −830.373 | −1.18259 | −0.591293 | − | 0.806457i | \(-0.701382\pi\) | ||||
−0.591293 | + | 0.806457i | \(0.701382\pi\) | |||||||
\(80\) | 397.919 | 0.556109 | ||||||||
\(81\) | −899.886 | −1.23441 | ||||||||
\(82\) | 1305.16 | 1.75769 | ||||||||
\(83\) | 1257.69 | 1.66324 | 0.831622 | − | 0.555342i | \(-0.187413\pi\) | ||||
0.831622 | + | 0.555342i | \(0.187413\pi\) | |||||||
\(84\) | −62.5076 | −0.0811922 | ||||||||
\(85\) | 641.699 | 0.818847 | ||||||||
\(86\) | −1062.11 | −1.33174 | ||||||||
\(87\) | −595.010 | −0.733239 | ||||||||
\(88\) | 131.230 | 0.158968 | ||||||||
\(89\) | −512.429 | −0.610307 | −0.305154 | − | 0.952303i | \(-0.598708\pi\) | ||||
−0.305154 | + | 0.952303i | \(0.598708\pi\) | |||||||
\(90\) | −299.968 | −0.351326 | ||||||||
\(91\) | 38.1518 | 0.0439494 | ||||||||
\(92\) | 317.705 | 0.360033 | ||||||||
\(93\) | −287.697 | −0.320783 | ||||||||
\(94\) | −184.151 | −0.202061 | ||||||||
\(95\) | −95.0000 | −0.102598 | ||||||||
\(96\) | −1242.31 | −1.32076 | ||||||||
\(97\) | −575.971 | −0.602897 | −0.301448 | − | 0.953483i | \(-0.597470\pi\) | ||||
−0.301448 | + | 0.953483i | \(0.597470\pi\) | |||||||
\(98\) | −1205.03 | −1.24211 | ||||||||
\(99\) | −185.582 | −0.188401 | ||||||||
\(100\) | 116.128 | 0.116128 | ||||||||
\(101\) | −972.694 | −0.958284 | −0.479142 | − | 0.877737i | \(-0.659052\pi\) | ||||
−0.479142 | + | 0.877737i | \(0.659052\pi\) | |||||||
\(102\) | −3022.82 | −2.93435 | ||||||||
\(103\) | 113.627 | 0.108699 | 0.0543493 | − | 0.998522i | \(-0.482692\pi\) | ||||
0.0543493 | + | 0.998522i | \(0.482692\pi\) | |||||||
\(104\) | 224.030 | 0.211230 | ||||||||
\(105\) | 67.2833 | 0.0625350 | ||||||||
\(106\) | 125.201 | 0.114722 | ||||||||
\(107\) | 388.179 | 0.350717 | 0.175359 | − | 0.984505i | \(-0.443892\pi\) | ||||
0.175359 | + | 0.984505i | \(0.443892\pi\) | |||||||
\(108\) | −311.636 | −0.277659 | ||||||||
\(109\) | 683.095 | 0.600263 | 0.300132 | − | 0.953898i | \(-0.402969\pi\) | ||||
0.300132 | + | 0.953898i | \(0.402969\pi\) | |||||||
\(110\) | 195.580 | 0.169525 | ||||||||
\(111\) | −942.729 | −0.806125 | ||||||||
\(112\) | 161.686 | 0.136410 | ||||||||
\(113\) | −413.578 | −0.344302 | −0.172151 | − | 0.985071i | \(-0.555072\pi\) | ||||
−0.172151 | + | 0.985071i | \(0.555072\pi\) | |||||||
\(114\) | 447.511 | 0.367660 | ||||||||
\(115\) | −341.978 | −0.277301 | ||||||||
\(116\) | −417.283 | −0.333998 | ||||||||
\(117\) | −316.818 | −0.250341 | ||||||||
\(118\) | 1332.64 | 1.03966 | ||||||||
\(119\) | 260.741 | 0.200858 | ||||||||
\(120\) | 395.093 | 0.300557 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1671.66 | 1.24053 | ||||||||
\(123\) | 2431.03 | 1.78210 | ||||||||
\(124\) | −201.763 | −0.146120 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −121.886 | −0.0861781 | ||||||||
\(127\) | 1361.99 | 0.951629 | 0.475814 | − | 0.879546i | \(-0.342153\pi\) | ||||
0.475814 | + | 0.879546i | \(0.342153\pi\) | |||||||
\(128\) | 1392.76 | 0.961749 | ||||||||
\(129\) | −1978.32 | −1.35024 | ||||||||
\(130\) | 333.886 | 0.225260 | ||||||||
\(131\) | −796.587 | −0.531283 | −0.265642 | − | 0.964072i | \(-0.585584\pi\) | ||||
−0.265642 | + | 0.964072i | \(0.585584\pi\) | |||||||
\(132\) | −338.437 | −0.223160 | ||||||||
\(133\) | −38.6013 | −0.0251666 | ||||||||
\(134\) | 2427.50 | 1.56496 | ||||||||
\(135\) | 335.445 | 0.213856 | ||||||||
\(136\) | 1531.09 | 0.965368 | ||||||||
\(137\) | −1610.58 | −1.00439 | −0.502193 | − | 0.864755i | \(-0.667473\pi\) | ||||
−0.502193 | + | 0.864755i | \(0.667473\pi\) | |||||||
\(138\) | 1610.94 | 0.993711 | ||||||||
\(139\) | 1431.53 | 0.873528 | 0.436764 | − | 0.899576i | \(-0.356124\pi\) | ||||
0.436764 | + | 0.899576i | \(0.356124\pi\) | |||||||
\(140\) | 47.1861 | 0.0284854 | ||||||||
\(141\) | −343.006 | −0.204867 | ||||||||
\(142\) | −2262.35 | −1.33699 | ||||||||
\(143\) | 206.566 | 0.120797 | ||||||||
\(144\) | −1342.67 | −0.777006 | ||||||||
\(145\) | 449.164 | 0.257249 | ||||||||
\(146\) | −1424.51 | −0.807490 | ||||||||
\(147\) | −2244.53 | −1.25936 | ||||||||
\(148\) | −661.140 | −0.367199 | ||||||||
\(149\) | 180.642 | 0.0993205 | 0.0496602 | − | 0.998766i | \(-0.484186\pi\) | ||||
0.0496602 | + | 0.998766i | \(0.484186\pi\) | |||||||
\(150\) | 588.831 | 0.320519 | ||||||||
\(151\) | −1550.01 | −0.835349 | −0.417675 | − | 0.908597i | \(-0.637155\pi\) | ||||
−0.417675 | + | 0.908597i | \(0.637155\pi\) | |||||||
\(152\) | −226.670 | −0.120956 | ||||||||
\(153\) | −2165.23 | −1.14411 | ||||||||
\(154\) | 79.4698 | 0.0415835 | ||||||||
\(155\) | 217.178 | 0.112543 | ||||||||
\(156\) | −577.766 | −0.296528 | ||||||||
\(157\) | 454.288 | 0.230931 | 0.115465 | − | 0.993312i | \(-0.463164\pi\) | ||||
0.115465 | + | 0.993312i | \(0.463164\pi\) | |||||||
\(158\) | −2952.80 | −1.48679 | ||||||||
\(159\) | 233.203 | 0.116316 | ||||||||
\(160\) | 937.800 | 0.463372 | ||||||||
\(161\) | −138.956 | −0.0680201 | ||||||||
\(162\) | −3199.99 | −1.55194 | ||||||||
\(163\) | 611.534 | 0.293859 | 0.146930 | − | 0.989147i | \(-0.453061\pi\) | ||||
0.146930 | + | 0.989147i | \(0.453061\pi\) | |||||||
\(164\) | 1704.89 | 0.811767 | ||||||||
\(165\) | 364.294 | 0.171880 | ||||||||
\(166\) | 4472.34 | 2.09109 | ||||||||
\(167\) | −376.046 | −0.174248 | −0.0871238 | − | 0.996197i | \(-0.527768\pi\) | ||||
−0.0871238 | + | 0.996197i | \(0.527768\pi\) | |||||||
\(168\) | 160.538 | 0.0737247 | ||||||||
\(169\) | −1844.36 | −0.839489 | ||||||||
\(170\) | 2281.88 | 1.02948 | ||||||||
\(171\) | 320.551 | 0.143352 | ||||||||
\(172\) | −1387.40 | −0.615049 | ||||||||
\(173\) | 1418.39 | 0.623342 | 0.311671 | − | 0.950190i | \(-0.399111\pi\) | ||||
0.311671 | + | 0.950190i | \(0.399111\pi\) | |||||||
\(174\) | −2115.85 | −0.921853 | ||||||||
\(175\) | −50.7911 | −0.0219397 | ||||||||
\(176\) | 875.422 | 0.374929 | ||||||||
\(177\) | 2482.22 | 1.05410 | ||||||||
\(178\) | −1822.19 | −0.767299 | ||||||||
\(179\) | 1469.38 | 0.613555 | 0.306777 | − | 0.951781i | \(-0.400749\pi\) | ||||
0.306777 | + | 0.951781i | \(0.400749\pi\) | |||||||
\(180\) | −391.840 | −0.162256 | ||||||||
\(181\) | −3885.53 | −1.59563 | −0.797815 | − | 0.602902i | \(-0.794011\pi\) | ||||
−0.797815 | + | 0.602902i | \(0.794011\pi\) | |||||||
\(182\) | 135.668 | 0.0552547 | ||||||||
\(183\) | 3113.70 | 1.25777 | ||||||||
\(184\) | −815.958 | −0.326920 | ||||||||
\(185\) | 711.652 | 0.282820 | ||||||||
\(186\) | −1023.05 | −0.403300 | ||||||||
\(187\) | 1411.74 | 0.552067 | ||||||||
\(188\) | −240.552 | −0.0933193 | ||||||||
\(189\) | 136.301 | 0.0524574 | ||||||||
\(190\) | −337.820 | −0.128990 | ||||||||
\(191\) | −1138.46 | −0.431290 | −0.215645 | − | 0.976472i | \(-0.569185\pi\) | ||||
−0.215645 | + | 0.976472i | \(0.569185\pi\) | |||||||
\(192\) | −200.639 | −0.0754161 | ||||||||
\(193\) | −313.065 | −0.116761 | −0.0583806 | − | 0.998294i | \(-0.518594\pi\) | ||||
−0.0583806 | + | 0.998294i | \(0.518594\pi\) | |||||||
\(194\) | −2048.15 | −0.757982 | ||||||||
\(195\) | 621.908 | 0.228388 | ||||||||
\(196\) | −1574.10 | −0.573651 | ||||||||
\(197\) | 4160.28 | 1.50461 | 0.752303 | − | 0.658817i | \(-0.228943\pi\) | ||||
0.752303 | + | 0.658817i | \(0.228943\pi\) | |||||||
\(198\) | −659.929 | −0.236864 | ||||||||
\(199\) | −449.741 | −0.160207 | −0.0801037 | − | 0.996787i | \(-0.525525\pi\) | ||||
−0.0801037 | + | 0.996787i | \(0.525525\pi\) | |||||||
\(200\) | −298.249 | −0.105447 | ||||||||
\(201\) | 4521.56 | 1.58670 | ||||||||
\(202\) | −3458.90 | −1.20479 | ||||||||
\(203\) | 182.508 | 0.0631014 | ||||||||
\(204\) | −3948.63 | −1.35519 | ||||||||
\(205\) | −1835.15 | −0.625231 | ||||||||
\(206\) | 404.056 | 0.136660 | ||||||||
\(207\) | 1153.91 | 0.387450 | ||||||||
\(208\) | 1494.49 | 0.498192 | ||||||||
\(209\) | −209.000 | −0.0691714 | ||||||||
\(210\) | 239.259 | 0.0786212 | ||||||||
\(211\) | 2981.68 | 0.972831 | 0.486415 | − | 0.873728i | \(-0.338304\pi\) | ||||
0.486415 | + | 0.873728i | \(0.338304\pi\) | |||||||
\(212\) | 163.547 | 0.0529831 | ||||||||
\(213\) | −4213.93 | −1.35556 | ||||||||
\(214\) | 1380.36 | 0.440934 | ||||||||
\(215\) | 1493.40 | 0.473717 | ||||||||
\(216\) | 800.371 | 0.252122 | ||||||||
\(217\) | 88.2459 | 0.0276061 | ||||||||
\(218\) | 2429.08 | 0.754671 | ||||||||
\(219\) | −2653.35 | −0.818707 | ||||||||
\(220\) | 255.481 | 0.0782933 | ||||||||
\(221\) | 2410.06 | 0.733567 | ||||||||
\(222\) | −3352.34 | −1.01349 | ||||||||
\(223\) | 2932.71 | 0.880667 | 0.440333 | − | 0.897834i | \(-0.354860\pi\) | ||||
0.440333 | + | 0.897834i | \(0.354860\pi\) | |||||||
\(224\) | 381.055 | 0.113662 | ||||||||
\(225\) | 421.777 | 0.124971 | ||||||||
\(226\) | −1470.68 | −0.432868 | ||||||||
\(227\) | −1015.09 | −0.296800 | −0.148400 | − | 0.988927i | \(-0.547412\pi\) | ||||
−0.148400 | + | 0.988927i | \(0.547412\pi\) | |||||||
\(228\) | 584.573 | 0.169800 | ||||||||
\(229\) | 3284.66 | 0.947845 | 0.473922 | − | 0.880567i | \(-0.342838\pi\) | ||||
0.473922 | + | 0.880567i | \(0.342838\pi\) | |||||||
\(230\) | −1216.07 | −0.348632 | ||||||||
\(231\) | 148.023 | 0.0421611 | ||||||||
\(232\) | 1071.70 | 0.303279 | ||||||||
\(233\) | −2449.22 | −0.688644 | −0.344322 | − | 0.938852i | \(-0.611891\pi\) | ||||
−0.344322 | + | 0.938852i | \(0.611891\pi\) | |||||||
\(234\) | −1126.60 | −0.314737 | ||||||||
\(235\) | 258.930 | 0.0718754 | ||||||||
\(236\) | 1740.79 | 0.480152 | ||||||||
\(237\) | −5500.00 | −1.50744 | ||||||||
\(238\) | 927.194 | 0.252525 | ||||||||
\(239\) | −1926.68 | −0.521450 | −0.260725 | − | 0.965413i | \(-0.583962\pi\) | ||||
−0.260725 | + | 0.965413i | \(0.583962\pi\) | |||||||
\(240\) | 2635.63 | 0.708871 | ||||||||
\(241\) | 2237.67 | 0.598095 | 0.299048 | − | 0.954238i | \(-0.403331\pi\) | ||||
0.299048 | + | 0.954238i | \(0.403331\pi\) | |||||||
\(242\) | 430.276 | 0.114294 | ||||||||
\(243\) | −4149.01 | −1.09531 | ||||||||
\(244\) | 2183.65 | 0.572926 | ||||||||
\(245\) | 1694.36 | 0.441832 | ||||||||
\(246\) | 8644.74 | 2.24052 | ||||||||
\(247\) | −356.796 | −0.0919126 | ||||||||
\(248\) | 518.187 | 0.132681 | ||||||||
\(249\) | 8330.33 | 2.12013 | ||||||||
\(250\) | −444.500 | −0.112450 | ||||||||
\(251\) | −6247.82 | −1.57115 | −0.785575 | − | 0.618766i | \(-0.787633\pi\) | ||||
−0.785575 | + | 0.618766i | \(0.787633\pi\) | |||||||
\(252\) | −159.216 | −0.0398003 | ||||||||
\(253\) | −752.352 | −0.186956 | ||||||||
\(254\) | 4843.22 | 1.19642 | ||||||||
\(255\) | 4250.31 | 1.04378 | ||||||||
\(256\) | 5194.99 | 1.26831 | ||||||||
\(257\) | −2215.15 | −0.537655 | −0.268827 | − | 0.963188i | \(-0.586636\pi\) | ||||
−0.268827 | + | 0.963188i | \(0.586636\pi\) | |||||||
\(258\) | −7034.89 | −1.69757 | ||||||||
\(259\) | 289.165 | 0.0693739 | ||||||||
\(260\) | 436.147 | 0.104033 | ||||||||
\(261\) | −1515.58 | −0.359433 | ||||||||
\(262\) | −2832.66 | −0.667948 | ||||||||
\(263\) | 3788.00 | 0.888130 | 0.444065 | − | 0.895995i | \(-0.353536\pi\) | ||||
0.444065 | + | 0.895995i | \(0.353536\pi\) | |||||||
\(264\) | 869.204 | 0.202636 | ||||||||
\(265\) | −176.042 | −0.0408081 | ||||||||
\(266\) | −137.266 | −0.0316403 | ||||||||
\(267\) | −3394.08 | −0.777957 | ||||||||
\(268\) | 3170.99 | 0.722757 | ||||||||
\(269\) | −3992.71 | −0.904981 | −0.452490 | − | 0.891769i | \(-0.649464\pi\) | ||||
−0.452490 | + | 0.891769i | \(0.649464\pi\) | |||||||
\(270\) | 1192.84 | 0.268867 | ||||||||
\(271\) | 1481.05 | 0.331983 | 0.165992 | − | 0.986127i | \(-0.446918\pi\) | ||||
0.165992 | + | 0.986127i | \(0.446918\pi\) | |||||||
\(272\) | 10213.8 | 2.27684 | ||||||||
\(273\) | 252.699 | 0.0560222 | ||||||||
\(274\) | −5727.21 | −1.26275 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | 2104.33 | 0.458934 | ||||||||
\(277\) | 64.3176 | 0.0139512 | 0.00697558 | − | 0.999976i | \(-0.497780\pi\) | ||||
0.00697558 | + | 0.999976i | \(0.497780\pi\) | |||||||
\(278\) | 5090.50 | 1.09823 | ||||||||
\(279\) | −732.807 | −0.157247 | ||||||||
\(280\) | −121.187 | −0.0258655 | ||||||||
\(281\) | −4851.92 | −1.03004 | −0.515020 | − | 0.857178i | \(-0.672216\pi\) | ||||
−0.515020 | + | 0.857178i | \(0.672216\pi\) | |||||||
\(282\) | −1219.73 | −0.257566 | ||||||||
\(283\) | 3689.34 | 0.774943 | 0.387471 | − | 0.921882i | \(-0.373349\pi\) | ||||
0.387471 | + | 0.921882i | \(0.373349\pi\) | |||||||
\(284\) | −2955.25 | −0.617471 | ||||||||
\(285\) | −629.235 | −0.130781 | ||||||||
\(286\) | 734.549 | 0.151870 | ||||||||
\(287\) | −745.674 | −0.153365 | ||||||||
\(288\) | −3164.34 | −0.647433 | ||||||||
\(289\) | 11558.1 | 2.35256 | ||||||||
\(290\) | 1597.23 | 0.323422 | ||||||||
\(291\) | −3814.96 | −0.768511 | ||||||||
\(292\) | −1860.81 | −0.372930 | ||||||||
\(293\) | 622.035 | 0.124026 | 0.0620131 | − | 0.998075i | \(-0.480248\pi\) | ||||
0.0620131 | + | 0.998075i | \(0.480248\pi\) | |||||||
\(294\) | −7981.54 | −1.58331 | ||||||||
\(295\) | −1873.79 | −0.369818 | ||||||||
\(296\) | 1698.00 | 0.333426 | ||||||||
\(297\) | 737.980 | 0.144182 | ||||||||
\(298\) | 642.362 | 0.124869 | ||||||||
\(299\) | −1284.38 | −0.248421 | ||||||||
\(300\) | 769.175 | 0.148028 | ||||||||
\(301\) | 606.812 | 0.116200 | ||||||||
\(302\) | −5511.82 | −1.05023 | ||||||||
\(303\) | −6442.66 | −1.22152 | ||||||||
\(304\) | −1512.09 | −0.285278 | ||||||||
\(305\) | −2350.48 | −0.441273 | ||||||||
\(306\) | −7699.56 | −1.43841 | ||||||||
\(307\) | −1729.87 | −0.321593 | −0.160796 | − | 0.986988i | \(-0.551406\pi\) | ||||
−0.160796 | + | 0.986988i | \(0.551406\pi\) | |||||||
\(308\) | 103.809 | 0.0192048 | ||||||||
\(309\) | 752.609 | 0.138558 | ||||||||
\(310\) | 772.286 | 0.141493 | ||||||||
\(311\) | 1861.95 | 0.339490 | 0.169745 | − | 0.985488i | \(-0.445706\pi\) | ||||
0.169745 | + | 0.985488i | \(0.445706\pi\) | |||||||
\(312\) | 1483.87 | 0.269255 | ||||||||
\(313\) | −1044.72 | −0.188662 | −0.0943309 | − | 0.995541i | \(-0.530071\pi\) | ||||
−0.0943309 | + | 0.995541i | \(0.530071\pi\) | |||||||
\(314\) | 1615.45 | 0.290334 | ||||||||
\(315\) | 171.380 | 0.0306546 | ||||||||
\(316\) | −3857.17 | −0.686655 | ||||||||
\(317\) | −6228.94 | −1.10363 | −0.551817 | − | 0.833965i | \(-0.686065\pi\) | ||||
−0.551817 | + | 0.833965i | \(0.686065\pi\) | |||||||
\(318\) | 829.270 | 0.146236 | ||||||||
\(319\) | 988.161 | 0.173437 | ||||||||
\(320\) | 151.460 | 0.0264589 | ||||||||
\(321\) | 2571.12 | 0.447058 | ||||||||
\(322\) | −494.126 | −0.0855173 | ||||||||
\(323\) | −2438.46 | −0.420060 | ||||||||
\(324\) | −4180.07 | −0.716747 | ||||||||
\(325\) | −469.469 | −0.0801275 | ||||||||
\(326\) | 2174.61 | 0.369450 | ||||||||
\(327\) | 4524.50 | 0.765154 | ||||||||
\(328\) | −4378.66 | −0.737106 | ||||||||
\(329\) | 105.211 | 0.0176306 | ||||||||
\(330\) | 1295.43 | 0.216094 | ||||||||
\(331\) | −755.428 | −0.125444 | −0.0627221 | − | 0.998031i | \(-0.519978\pi\) | ||||
−0.0627221 | + | 0.998031i | \(0.519978\pi\) | |||||||
\(332\) | 5842.10 | 0.965744 | ||||||||
\(333\) | −2401.27 | −0.395161 | ||||||||
\(334\) | −1337.22 | −0.219070 | ||||||||
\(335\) | −3413.25 | −0.556675 | ||||||||
\(336\) | 1070.93 | 0.173881 | ||||||||
\(337\) | 721.457 | 0.116618 | 0.0583090 | − | 0.998299i | \(-0.481429\pi\) | ||||
0.0583090 | + | 0.998299i | \(0.481429\pi\) | |||||||
\(338\) | −6558.53 | −1.05544 | ||||||||
\(339\) | −2739.34 | −0.438881 | ||||||||
\(340\) | 2980.76 | 0.475454 | ||||||||
\(341\) | 477.792 | 0.0758766 | ||||||||
\(342\) | 1139.88 | 0.180227 | ||||||||
\(343\) | 1385.32 | 0.218077 | ||||||||
\(344\) | 3563.25 | 0.558481 | ||||||||
\(345\) | −2265.10 | −0.353475 | ||||||||
\(346\) | 5043.79 | 0.783687 | ||||||||
\(347\) | −10349.7 | −1.60115 | −0.800575 | − | 0.599233i | \(-0.795472\pi\) | ||||
−0.800575 | + | 0.599233i | \(0.795472\pi\) | |||||||
\(348\) | −2763.89 | −0.425747 | ||||||||
\(349\) | −6974.56 | −1.06974 | −0.534870 | − | 0.844934i | \(-0.679640\pi\) | ||||
−0.534870 | + | 0.844934i | \(0.679640\pi\) | |||||||
\(350\) | −180.613 | −0.0275834 | ||||||||
\(351\) | 1259.85 | 0.191583 | ||||||||
\(352\) | 2063.16 | 0.312406 | ||||||||
\(353\) | −4958.12 | −0.747575 | −0.373788 | − | 0.927514i | \(-0.621941\pi\) | ||||
−0.373788 | + | 0.927514i | \(0.621941\pi\) | |||||||
\(354\) | 8826.76 | 1.32525 | ||||||||
\(355\) | 3181.03 | 0.475582 | ||||||||
\(356\) | −2380.29 | −0.354368 | ||||||||
\(357\) | 1727.02 | 0.256033 | ||||||||
\(358\) | 5225.10 | 0.771382 | ||||||||
\(359\) | 2029.28 | 0.298332 | 0.149166 | − | 0.988812i | \(-0.452341\pi\) | ||||
0.149166 | + | 0.988812i | \(0.452341\pi\) | |||||||
\(360\) | 1006.36 | 0.147333 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −13816.9 | −2.00608 | ||||||||
\(363\) | 801.447 | 0.115882 | ||||||||
\(364\) | 177.219 | 0.0255187 | ||||||||
\(365\) | 2002.97 | 0.287234 | ||||||||
\(366\) | 11072.3 | 1.58131 | ||||||||
\(367\) | −11859.7 | −1.68684 | −0.843422 | − | 0.537251i | \(-0.819463\pi\) | ||||
−0.843422 | + | 0.537251i | \(0.819463\pi\) | |||||||
\(368\) | −5443.19 | −0.771048 | ||||||||
\(369\) | 6192.19 | 0.873585 | ||||||||
\(370\) | 2530.63 | 0.355571 | ||||||||
\(371\) | −71.5309 | −0.0100100 | ||||||||
\(372\) | −1336.39 | −0.186259 | ||||||||
\(373\) | −9368.52 | −1.30049 | −0.650246 | − | 0.759724i | \(-0.725334\pi\) | ||||
−0.650246 | + | 0.759724i | \(0.725334\pi\) | |||||||
\(374\) | 5020.13 | 0.694077 | ||||||||
\(375\) | −827.941 | −0.114012 | ||||||||
\(376\) | 617.806 | 0.0847364 | ||||||||
\(377\) | 1686.95 | 0.230457 | ||||||||
\(378\) | 484.687 | 0.0659513 | ||||||||
\(379\) | 13120.7 | 1.77828 | 0.889139 | − | 0.457637i | \(-0.151304\pi\) | ||||
0.889139 | + | 0.457637i | \(0.151304\pi\) | |||||||
\(380\) | −441.285 | −0.0595723 | ||||||||
\(381\) | 9021.16 | 1.21304 | ||||||||
\(382\) | −4048.38 | −0.542233 | ||||||||
\(383\) | −10579.2 | −1.41142 | −0.705709 | − | 0.708502i | \(-0.749371\pi\) | ||||
−0.705709 | + | 0.708502i | \(0.749371\pi\) | |||||||
\(384\) | 9224.99 | 1.22594 | ||||||||
\(385\) | −111.741 | −0.0147918 | ||||||||
\(386\) | −1113.26 | −0.146796 | ||||||||
\(387\) | −5039.06 | −0.661886 | ||||||||
\(388\) | −2675.45 | −0.350065 | ||||||||
\(389\) | 4479.17 | 0.583812 | 0.291906 | − | 0.956447i | \(-0.405711\pi\) | ||||
0.291906 | + | 0.956447i | \(0.405711\pi\) | |||||||
\(390\) | 2211.50 | 0.287138 | ||||||||
\(391\) | −8777.88 | −1.13534 | ||||||||
\(392\) | 4042.74 | 0.520891 | ||||||||
\(393\) | −5276.21 | −0.677226 | ||||||||
\(394\) | 14793.9 | 1.89164 | ||||||||
\(395\) | 4151.86 | 0.528868 | ||||||||
\(396\) | −862.049 | −0.109393 | ||||||||
\(397\) | −1849.10 | −0.233763 | −0.116881 | − | 0.993146i | \(-0.537290\pi\) | ||||
−0.116881 | + | 0.993146i | \(0.537290\pi\) | |||||||
\(398\) | −1599.28 | −0.201418 | ||||||||
\(399\) | −255.677 | −0.0320798 | ||||||||
\(400\) | −1989.60 | −0.248699 | ||||||||
\(401\) | 1261.89 | 0.157147 | 0.0785733 | − | 0.996908i | \(-0.474964\pi\) | ||||
0.0785733 | + | 0.996908i | \(0.474964\pi\) | |||||||
\(402\) | 16078.6 | 1.99485 | ||||||||
\(403\) | 815.668 | 0.100822 | ||||||||
\(404\) | −4518.27 | −0.556417 | ||||||||
\(405\) | 4499.43 | 0.552045 | ||||||||
\(406\) | 648.999 | 0.0793332 | ||||||||
\(407\) | 1565.63 | 0.190677 | ||||||||
\(408\) | 10141.2 | 1.23055 | ||||||||
\(409\) | −3119.09 | −0.377089 | −0.188544 | − | 0.982065i | \(-0.560377\pi\) | ||||
−0.188544 | + | 0.982065i | \(0.560377\pi\) | |||||||
\(410\) | −6525.78 | −0.786062 | ||||||||
\(411\) | −10667.7 | −1.28029 | ||||||||
\(412\) | 527.808 | 0.0631146 | ||||||||
\(413\) | −761.376 | −0.0907139 | ||||||||
\(414\) | 4103.30 | 0.487116 | ||||||||
\(415\) | −6288.44 | −0.743826 | ||||||||
\(416\) | 3522.14 | 0.415114 | ||||||||
\(417\) | 9481.75 | 1.11348 | ||||||||
\(418\) | −743.203 | −0.0869647 | ||||||||
\(419\) | 1487.06 | 0.173383 | 0.0866916 | − | 0.996235i | \(-0.472371\pi\) | ||||
0.0866916 | + | 0.996235i | \(0.472371\pi\) | |||||||
\(420\) | 312.538 | 0.0363102 | ||||||||
\(421\) | −4548.51 | −0.526557 | −0.263279 | − | 0.964720i | \(-0.584804\pi\) | ||||
−0.263279 | + | 0.964720i | \(0.584804\pi\) | |||||||
\(422\) | 10602.8 | 1.22308 | ||||||||
\(423\) | −873.686 | −0.100426 | ||||||||
\(424\) | −420.035 | −0.0481101 | ||||||||
\(425\) | −3208.50 | −0.366200 | ||||||||
\(426\) | −14984.7 | −1.70425 | ||||||||
\(427\) | −955.070 | −0.108241 | ||||||||
\(428\) | 1803.14 | 0.203640 | ||||||||
\(429\) | 1368.20 | 0.153979 | ||||||||
\(430\) | 5310.53 | 0.595573 | ||||||||
\(431\) | 11111.9 | 1.24186 | 0.620930 | − | 0.783866i | \(-0.286755\pi\) | ||||
0.620930 | + | 0.783866i | \(0.286755\pi\) | |||||||
\(432\) | 5339.20 | 0.594636 | ||||||||
\(433\) | −4335.51 | −0.481181 | −0.240591 | − | 0.970627i | \(-0.577341\pi\) | ||||
−0.240591 | + | 0.970627i | \(0.577341\pi\) | |||||||
\(434\) | 313.802 | 0.0347073 | ||||||||
\(435\) | 2975.05 | 0.327914 | ||||||||
\(436\) | 3173.05 | 0.348536 | ||||||||
\(437\) | 1299.52 | 0.142252 | ||||||||
\(438\) | −9435.30 | −1.02931 | ||||||||
\(439\) | 9210.53 | 1.00135 | 0.500677 | − | 0.865634i | \(-0.333084\pi\) | ||||
0.500677 | + | 0.865634i | \(0.333084\pi\) | |||||||
\(440\) | −656.149 | −0.0710924 | ||||||||
\(441\) | −5717.15 | −0.617336 | ||||||||
\(442\) | 8570.17 | 0.922266 | ||||||||
\(443\) | −86.1483 | −0.00923935 | −0.00461967 | − | 0.999989i | \(-0.501470\pi\) | ||||
−0.00461967 | + | 0.999989i | \(0.501470\pi\) | |||||||
\(444\) | −4379.08 | −0.468067 | ||||||||
\(445\) | 2562.14 | 0.272938 | ||||||||
\(446\) | 10428.7 | 1.10720 | ||||||||
\(447\) | 1196.49 | 0.126604 | ||||||||
\(448\) | 61.5425 | 0.00649020 | ||||||||
\(449\) | 3806.18 | 0.400055 | 0.200027 | − | 0.979790i | \(-0.435897\pi\) | ||||
0.200027 | + | 0.979790i | \(0.435897\pi\) | |||||||
\(450\) | 1499.84 | 0.157118 | ||||||||
\(451\) | −4037.33 | −0.421531 | ||||||||
\(452\) | −1921.11 | −0.199915 | ||||||||
\(453\) | −10266.5 | −1.06482 | ||||||||
\(454\) | −3609.64 | −0.373147 | ||||||||
\(455\) | −190.759 | −0.0196548 | ||||||||
\(456\) | −1501.35 | −0.154183 | ||||||||
\(457\) | −14610.5 | −1.49551 | −0.747756 | − | 0.663974i | \(-0.768869\pi\) | ||||
−0.747756 | + | 0.663974i | \(0.768869\pi\) | |||||||
\(458\) | 11680.2 | 1.19166 | ||||||||
\(459\) | 8610.20 | 0.875576 | ||||||||
\(460\) | −1588.53 | −0.161012 | ||||||||
\(461\) | −10506.5 | −1.06147 | −0.530735 | − | 0.847538i | \(-0.678084\pi\) | ||||
−0.530735 | + | 0.847538i | \(0.678084\pi\) | |||||||
\(462\) | 526.370 | 0.0530064 | ||||||||
\(463\) | 12658.3 | 1.27058 | 0.635292 | − | 0.772272i | \(-0.280880\pi\) | ||||
0.635292 | + | 0.772272i | \(0.280880\pi\) | |||||||
\(464\) | 7149.24 | 0.715291 | ||||||||
\(465\) | 1438.49 | 0.143459 | ||||||||
\(466\) | −8709.43 | −0.865787 | ||||||||
\(467\) | −9572.46 | −0.948523 | −0.474262 | − | 0.880384i | \(-0.657285\pi\) | ||||
−0.474262 | + | 0.880384i | \(0.657285\pi\) | |||||||
\(468\) | −1471.66 | −0.145357 | ||||||||
\(469\) | −1386.90 | −0.136549 | ||||||||
\(470\) | 920.754 | 0.0903643 | ||||||||
\(471\) | 3008.99 | 0.294367 | ||||||||
\(472\) | −4470.86 | −0.435991 | ||||||||
\(473\) | 3285.48 | 0.319380 | ||||||||
\(474\) | −19558.0 | −1.89520 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | 1211.17 | 0.116626 | ||||||||
\(477\) | 594.003 | 0.0570179 | ||||||||
\(478\) | −6851.26 | −0.655585 | ||||||||
\(479\) | 9171.36 | 0.874843 | 0.437422 | − | 0.899256i | \(-0.355892\pi\) | ||||
0.437422 | + | 0.899256i | \(0.355892\pi\) | |||||||
\(480\) | 6211.54 | 0.590660 | ||||||||
\(481\) | 2672.79 | 0.253365 | ||||||||
\(482\) | 7957.15 | 0.751946 | ||||||||
\(483\) | −920.377 | −0.0867051 | ||||||||
\(484\) | 562.058 | 0.0527853 | ||||||||
\(485\) | 2879.85 | 0.269624 | ||||||||
\(486\) | −14753.9 | −1.37706 | ||||||||
\(487\) | 14170.5 | 1.31854 | 0.659269 | − | 0.751907i | \(-0.270866\pi\) | ||||
0.659269 | + | 0.751907i | \(0.270866\pi\) | |||||||
\(488\) | −5608.24 | −0.520232 | ||||||||
\(489\) | 4050.51 | 0.374582 | ||||||||
\(490\) | 6025.15 | 0.555486 | ||||||||
\(491\) | −12909.8 | −1.18658 | −0.593292 | − | 0.804987i | \(-0.702172\pi\) | ||||
−0.593292 | + | 0.804987i | \(0.702172\pi\) | |||||||
\(492\) | 11292.4 | 1.03476 | ||||||||
\(493\) | 11529.1 | 1.05324 | ||||||||
\(494\) | −1268.77 | −0.115556 | ||||||||
\(495\) | 927.910 | 0.0842555 | ||||||||
\(496\) | 3456.78 | 0.312931 | ||||||||
\(497\) | 1292.55 | 0.116657 | ||||||||
\(498\) | 29622.6 | 2.66551 | ||||||||
\(499\) | 6754.72 | 0.605977 | 0.302989 | − | 0.952994i | \(-0.402016\pi\) | ||||
0.302989 | + | 0.952994i | \(0.402016\pi\) | |||||||
\(500\) | −580.639 | −0.0519339 | ||||||||
\(501\) | −2490.75 | −0.222113 | ||||||||
\(502\) | −22217.2 | −1.97530 | ||||||||
\(503\) | −4202.12 | −0.372492 | −0.186246 | − | 0.982503i | \(-0.559632\pi\) | ||||
−0.186246 | + | 0.982503i | \(0.559632\pi\) | |||||||
\(504\) | 408.913 | 0.0361398 | ||||||||
\(505\) | 4863.47 | 0.428558 | ||||||||
\(506\) | −2675.36 | −0.235048 | ||||||||
\(507\) | −12216.2 | −1.07010 | ||||||||
\(508\) | 6326.58 | 0.552552 | ||||||||
\(509\) | 15491.8 | 1.34905 | 0.674523 | − | 0.738254i | \(-0.264350\pi\) | ||||
0.674523 | + | 0.738254i | \(0.264350\pi\) | |||||||
\(510\) | 15114.1 | 1.31228 | ||||||||
\(511\) | 813.867 | 0.0704566 | ||||||||
\(512\) | 7331.28 | 0.632812 | ||||||||
\(513\) | −1274.69 | −0.109706 | ||||||||
\(514\) | −7877.07 | −0.675958 | ||||||||
\(515\) | −568.133 | −0.0486115 | ||||||||
\(516\) | −9189.50 | −0.784002 | ||||||||
\(517\) | 569.646 | 0.0484584 | ||||||||
\(518\) | 1028.27 | 0.0872192 | ||||||||
\(519\) | 9394.74 | 0.794573 | ||||||||
\(520\) | −1120.15 | −0.0944651 | ||||||||
\(521\) | 5852.76 | 0.492157 | 0.246079 | − | 0.969250i | \(-0.420858\pi\) | ||||
0.246079 | + | 0.969250i | \(0.420858\pi\) | |||||||
\(522\) | −5389.39 | −0.451891 | ||||||||
\(523\) | 22907.7 | 1.91527 | 0.957633 | − | 0.287990i | \(-0.0929870\pi\) | ||||
0.957633 | + | 0.287990i | \(0.0929870\pi\) | |||||||
\(524\) | −3700.23 | −0.308484 | ||||||||
\(525\) | −336.416 | −0.0279665 | ||||||||
\(526\) | 13470.1 | 1.11659 | ||||||||
\(527\) | 5574.53 | 0.460778 | ||||||||
\(528\) | 5798.38 | 0.477921 | ||||||||
\(529\) | −7489.04 | −0.615521 | ||||||||
\(530\) | −626.004 | −0.0513054 | ||||||||
\(531\) | 6322.58 | 0.516717 | ||||||||
\(532\) | −179.307 | −0.0146127 | ||||||||
\(533\) | −6892.36 | −0.560115 | ||||||||
\(534\) | −12069.4 | −0.978075 | ||||||||
\(535\) | −1940.90 | −0.156845 | ||||||||
\(536\) | −8144.01 | −0.656283 | ||||||||
\(537\) | 9732.45 | 0.782097 | ||||||||
\(538\) | −14198.1 | −1.13777 | ||||||||
\(539\) | 3727.60 | 0.297883 | ||||||||
\(540\) | 1558.18 | 0.124173 | ||||||||
\(541\) | −18829.9 | −1.49642 | −0.748208 | − | 0.663464i | \(-0.769086\pi\) | ||||
−0.748208 | + | 0.663464i | \(0.769086\pi\) | |||||||
\(542\) | 5266.61 | 0.417381 | ||||||||
\(543\) | −25735.9 | −2.03395 | ||||||||
\(544\) | 24071.4 | 1.89716 | ||||||||
\(545\) | −3415.48 | −0.268446 | ||||||||
\(546\) | 898.598 | 0.0704330 | ||||||||
\(547\) | −7921.96 | −0.619230 | −0.309615 | − | 0.950862i | \(-0.600200\pi\) | ||||
−0.309615 | + | 0.950862i | \(0.600200\pi\) | |||||||
\(548\) | −7481.31 | −0.583186 | ||||||||
\(549\) | 7931.05 | 0.616555 | ||||||||
\(550\) | −977.899 | −0.0758141 | ||||||||
\(551\) | −1706.82 | −0.131966 | ||||||||
\(552\) | −5404.52 | −0.416724 | ||||||||
\(553\) | 1687.02 | 0.129728 | ||||||||
\(554\) | 228.713 | 0.0175399 | ||||||||
\(555\) | 4713.64 | 0.360510 | ||||||||
\(556\) | 6649.59 | 0.507204 | ||||||||
\(557\) | −17173.0 | −1.30636 | −0.653181 | − | 0.757201i | \(-0.726566\pi\) | ||||
−0.653181 | + | 0.757201i | \(0.726566\pi\) | |||||||
\(558\) | −2605.86 | −0.197697 | ||||||||
\(559\) | 5608.84 | 0.424381 | ||||||||
\(560\) | −808.431 | −0.0610044 | ||||||||
\(561\) | 9350.68 | 0.703719 | ||||||||
\(562\) | −17253.4 | −1.29500 | ||||||||
\(563\) | 25463.5 | 1.90614 | 0.953072 | − | 0.302743i | \(-0.0979025\pi\) | ||||
0.953072 | + | 0.302743i | \(0.0979025\pi\) | |||||||
\(564\) | −1593.30 | −0.118954 | ||||||||
\(565\) | 2067.89 | 0.153976 | ||||||||
\(566\) | 13119.3 | 0.974285 | ||||||||
\(567\) | 1828.25 | 0.135413 | ||||||||
\(568\) | 7589.93 | 0.560680 | ||||||||
\(569\) | −12332.0 | −0.908585 | −0.454293 | − | 0.890853i | \(-0.650108\pi\) | ||||
−0.454293 | + | 0.890853i | \(0.650108\pi\) | |||||||
\(570\) | −2237.56 | −0.164423 | ||||||||
\(571\) | 5342.66 | 0.391565 | 0.195782 | − | 0.980647i | \(-0.437275\pi\) | ||||
0.195782 | + | 0.980647i | \(0.437275\pi\) | |||||||
\(572\) | 959.523 | 0.0701393 | ||||||||
\(573\) | −7540.65 | −0.549765 | ||||||||
\(574\) | −2651.62 | −0.192816 | ||||||||
\(575\) | 1709.89 | 0.124013 | ||||||||
\(576\) | −511.058 | −0.0369689 | ||||||||
\(577\) | 18443.8 | 1.33072 | 0.665358 | − | 0.746524i | \(-0.268279\pi\) | ||||
0.665358 | + | 0.746524i | \(0.268279\pi\) | |||||||
\(578\) | 41100.6 | 2.95771 | ||||||||
\(579\) | −2073.59 | −0.148835 | ||||||||
\(580\) | 2086.42 | 0.149368 | ||||||||
\(581\) | −2555.18 | −0.182456 | ||||||||
\(582\) | −13566.0 | −0.966199 | ||||||||
\(583\) | −387.292 | −0.0275128 | ||||||||
\(584\) | 4779.09 | 0.338630 | ||||||||
\(585\) | 1584.09 | 0.111956 | ||||||||
\(586\) | 2211.95 | 0.155930 | ||||||||
\(587\) | 27202.4 | 1.91271 | 0.956356 | − | 0.292203i | \(-0.0943883\pi\) | ||||
0.956356 | + | 0.292203i | \(0.0943883\pi\) | |||||||
\(588\) | −10426.1 | −0.731232 | ||||||||
\(589\) | −825.278 | −0.0577334 | ||||||||
\(590\) | −6663.19 | −0.464948 | ||||||||
\(591\) | 27555.7 | 1.91792 | ||||||||
\(592\) | 11327.2 | 0.786393 | ||||||||
\(593\) | 12203.9 | 0.845115 | 0.422557 | − | 0.906336i | \(-0.361133\pi\) | ||||
0.422557 | + | 0.906336i | \(0.361133\pi\) | |||||||
\(594\) | 2624.25 | 0.181270 | ||||||||
\(595\) | −1303.71 | −0.0898264 | ||||||||
\(596\) | 839.101 | 0.0576693 | ||||||||
\(597\) | −2978.87 | −0.204216 | ||||||||
\(598\) | −4567.27 | −0.312324 | ||||||||
\(599\) | −9661.42 | −0.659023 | −0.329512 | − | 0.944152i | \(-0.606884\pi\) | ||||
−0.329512 | + | 0.944152i | \(0.606884\pi\) | |||||||
\(600\) | −1975.46 | −0.134413 | ||||||||
\(601\) | −12317.1 | −0.835981 | −0.417990 | − | 0.908451i | \(-0.637265\pi\) | ||||
−0.417990 | + | 0.908451i | \(0.637265\pi\) | |||||||
\(602\) | 2157.82 | 0.146090 | ||||||||
\(603\) | 11517.1 | 0.777797 | ||||||||
\(604\) | −7199.95 | −0.485036 | ||||||||
\(605\) | −605.000 | −0.0406558 | ||||||||
\(606\) | −22910.1 | −1.53574 | ||||||||
\(607\) | −1513.16 | −0.101181 | −0.0505907 | − | 0.998719i | \(-0.516110\pi\) | ||||
−0.0505907 | + | 0.998719i | \(0.516110\pi\) | |||||||
\(608\) | −3563.64 | −0.237705 | ||||||||
\(609\) | 1208.85 | 0.0804352 | ||||||||
\(610\) | −8358.31 | −0.554784 | ||||||||
\(611\) | 972.476 | 0.0643898 | ||||||||
\(612\) | −10057.7 | −0.664314 | ||||||||
\(613\) | 18887.0 | 1.24444 | 0.622218 | − | 0.782844i | \(-0.286232\pi\) | ||||
0.622218 | + | 0.782844i | \(0.286232\pi\) | |||||||
\(614\) | −6151.42 | −0.404318 | ||||||||
\(615\) | −12155.2 | −0.796981 | ||||||||
\(616\) | −266.612 | −0.0174385 | ||||||||
\(617\) | −27905.7 | −1.82081 | −0.910405 | − | 0.413718i | \(-0.864230\pi\) | ||||
−0.910405 | + | 0.413718i | \(0.864230\pi\) | |||||||
\(618\) | 2676.27 | 0.174200 | ||||||||
\(619\) | −9303.29 | −0.604089 | −0.302044 | − | 0.953294i | \(-0.597669\pi\) | ||||
−0.302044 | + | 0.953294i | \(0.597669\pi\) | |||||||
\(620\) | 1008.82 | 0.0653469 | ||||||||
\(621\) | −4588.60 | −0.296512 | ||||||||
\(622\) | 6621.08 | 0.426819 | ||||||||
\(623\) | 1041.07 | 0.0669498 | ||||||||
\(624\) | 9898.76 | 0.635044 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −3715.03 | −0.237192 | ||||||||
\(627\) | −1384.32 | −0.0881727 | ||||||||
\(628\) | 2110.22 | 0.134087 | ||||||||
\(629\) | 18266.7 | 1.15793 | ||||||||
\(630\) | 609.428 | 0.0385400 | ||||||||
\(631\) | −15151.5 | −0.955895 | −0.477948 | − | 0.878388i | \(-0.658619\pi\) | ||||
−0.477948 | + | 0.878388i | \(0.658619\pi\) | |||||||
\(632\) | 9906.33 | 0.623501 | ||||||||
\(633\) | 19749.2 | 1.24007 | ||||||||
\(634\) | −22150.1 | −1.38753 | ||||||||
\(635\) | −6809.94 | −0.425581 | ||||||||
\(636\) | 1083.25 | 0.0675375 | ||||||||
\(637\) | 6363.60 | 0.395817 | ||||||||
\(638\) | 3513.90 | 0.218051 | ||||||||
\(639\) | −10733.5 | −0.664492 | ||||||||
\(640\) | −6963.81 | −0.430107 | ||||||||
\(641\) | −19587.3 | −1.20694 | −0.603471 | − | 0.797385i | \(-0.706216\pi\) | ||||
−0.603471 | + | 0.797385i | \(0.706216\pi\) | |||||||
\(642\) | 9142.88 | 0.562057 | ||||||||
\(643\) | −3234.59 | −0.198382 | −0.0991912 | − | 0.995068i | \(-0.531626\pi\) | ||||
−0.0991912 | + | 0.995068i | \(0.531626\pi\) | |||||||
\(644\) | −645.464 | −0.0394951 | ||||||||
\(645\) | 9891.58 | 0.603846 | ||||||||
\(646\) | −8671.14 | −0.528114 | ||||||||
\(647\) | −192.466 | −0.0116949 | −0.00584746 | − | 0.999983i | \(-0.501861\pi\) | ||||
−0.00584746 | + | 0.999983i | \(0.501861\pi\) | |||||||
\(648\) | 10735.6 | 0.650825 | ||||||||
\(649\) | −4122.34 | −0.249331 | ||||||||
\(650\) | −1669.43 | −0.100739 | ||||||||
\(651\) | 584.499 | 0.0351894 | ||||||||
\(652\) | 2840.64 | 0.170626 | ||||||||
\(653\) | −3595.41 | −0.215466 | −0.107733 | − | 0.994180i | \(-0.534359\pi\) | ||||
−0.107733 | + | 0.994180i | \(0.534359\pi\) | |||||||
\(654\) | 16089.1 | 0.961978 | ||||||||
\(655\) | 3982.93 | 0.237597 | ||||||||
\(656\) | −29209.6 | −1.73848 | ||||||||
\(657\) | −6758.47 | −0.401329 | ||||||||
\(658\) | 374.129 | 0.0221658 | ||||||||
\(659\) | 10575.7 | 0.625146 | 0.312573 | − | 0.949894i | \(-0.398809\pi\) | ||||
0.312573 | + | 0.949894i | \(0.398809\pi\) | |||||||
\(660\) | 1692.19 | 0.0998003 | ||||||||
\(661\) | 15026.1 | 0.884189 | 0.442095 | − | 0.896968i | \(-0.354236\pi\) | ||||
0.442095 | + | 0.896968i | \(0.354236\pi\) | |||||||
\(662\) | −2686.30 | −0.157713 | ||||||||
\(663\) | 15963.1 | 0.935077 | ||||||||
\(664\) | −15004.2 | −0.876922 | ||||||||
\(665\) | 193.006 | 0.0112548 | ||||||||
\(666\) | −8538.90 | −0.496811 | ||||||||
\(667\) | −6144.17 | −0.356677 | ||||||||
\(668\) | −1746.78 | −0.101175 | ||||||||
\(669\) | 19424.9 | 1.12258 | ||||||||
\(670\) | −12137.5 | −0.699871 | ||||||||
\(671\) | −5171.06 | −0.297506 | ||||||||
\(672\) | 2523.93 | 0.144885 | ||||||||
\(673\) | −32280.0 | −1.84889 | −0.924444 | − | 0.381318i | \(-0.875470\pi\) | ||||
−0.924444 | + | 0.381318i | \(0.875470\pi\) | |||||||
\(674\) | 2565.50 | 0.146616 | ||||||||
\(675\) | −1677.23 | −0.0956392 | ||||||||
\(676\) | −8567.25 | −0.487440 | ||||||||
\(677\) | −7504.25 | −0.426015 | −0.213007 | − | 0.977051i | \(-0.568326\pi\) | ||||
−0.213007 | + | 0.977051i | \(0.568326\pi\) | |||||||
\(678\) | −9741.09 | −0.551776 | ||||||||
\(679\) | 1170.17 | 0.0661369 | ||||||||
\(680\) | −7655.46 | −0.431725 | ||||||||
\(681\) | −6723.45 | −0.378330 | ||||||||
\(682\) | 1699.03 | 0.0953947 | ||||||||
\(683\) | −16560.3 | −0.927761 | −0.463880 | − | 0.885898i | \(-0.653543\pi\) | ||||
−0.463880 | + | 0.885898i | \(0.653543\pi\) | |||||||
\(684\) | 1488.99 | 0.0832355 | ||||||||
\(685\) | 8052.89 | 0.449175 | ||||||||
\(686\) | 4926.20 | 0.274174 | ||||||||
\(687\) | 21756.0 | 1.20822 | ||||||||
\(688\) | 23770.1 | 1.31719 | ||||||||
\(689\) | −661.169 | −0.0365581 | ||||||||
\(690\) | −8054.69 | −0.444401 | ||||||||
\(691\) | −30146.7 | −1.65968 | −0.829838 | − | 0.558004i | \(-0.811567\pi\) | ||||
−0.829838 | + | 0.558004i | \(0.811567\pi\) | |||||||
\(692\) | 6588.58 | 0.361937 | ||||||||
\(693\) | 377.037 | 0.0206673 | ||||||||
\(694\) | −36803.3 | −2.01302 | ||||||||
\(695\) | −7157.63 | −0.390654 | ||||||||
\(696\) | 7098.46 | 0.386589 | ||||||||
\(697\) | −47104.5 | −2.55984 | ||||||||
\(698\) | −24801.5 | −1.34491 | ||||||||
\(699\) | −16222.5 | −0.877813 | ||||||||
\(700\) | −235.930 | −0.0127390 | ||||||||
\(701\) | −16632.4 | −0.896143 | −0.448071 | − | 0.893998i | \(-0.647889\pi\) | ||||
−0.448071 | + | 0.893998i | \(0.647889\pi\) | |||||||
\(702\) | 4480.02 | 0.240865 | ||||||||
\(703\) | −2704.28 | −0.145084 | ||||||||
\(704\) | 333.211 | 0.0178386 | ||||||||
\(705\) | 1715.03 | 0.0916195 | ||||||||
\(706\) | −17631.1 | −0.939878 | ||||||||
\(707\) | 1976.17 | 0.105122 | ||||||||
\(708\) | 11530.2 | 0.612049 | ||||||||
\(709\) | 23519.2 | 1.24582 | 0.622908 | − | 0.782295i | \(-0.285951\pi\) | ||||
0.622908 | + | 0.782295i | \(0.285951\pi\) | |||||||
\(710\) | 11311.7 | 0.597918 | ||||||||
\(711\) | −14009.3 | −0.738945 | ||||||||
\(712\) | 6113.26 | 0.321776 | ||||||||
\(713\) | −2970.81 | −0.156042 | ||||||||
\(714\) | 6141.29 | 0.321894 | ||||||||
\(715\) | −1032.83 | −0.0540220 | ||||||||
\(716\) | 6825.41 | 0.356254 | ||||||||
\(717\) | −12761.4 | −0.664691 | ||||||||
\(718\) | 7216.11 | 0.375074 | ||||||||
\(719\) | 17047.8 | 0.884249 | 0.442124 | − | 0.896954i | \(-0.354225\pi\) | ||||
0.442124 | + | 0.896954i | \(0.354225\pi\) | |||||||
\(720\) | 6713.33 | 0.347488 | ||||||||
\(721\) | −230.849 | −0.0119241 | ||||||||
\(722\) | 1283.71 | 0.0661702 | ||||||||
\(723\) | 14821.3 | 0.762391 | ||||||||
\(724\) | −18048.7 | −0.926484 | ||||||||
\(725\) | −2245.82 | −0.115045 | ||||||||
\(726\) | 2849.94 | 0.145690 | ||||||||
\(727\) | 9340.76 | 0.476520 | 0.238260 | − | 0.971201i | \(-0.423423\pi\) | ||||
0.238260 | + | 0.971201i | \(0.423423\pi\) | |||||||
\(728\) | −455.150 | −0.0231717 | ||||||||
\(729\) | −3184.17 | −0.161773 | ||||||||
\(730\) | 7122.57 | 0.361121 | ||||||||
\(731\) | 38332.6 | 1.93951 | ||||||||
\(732\) | 14463.5 | 0.730308 | ||||||||
\(733\) | 31801.8 | 1.60249 | 0.801246 | − | 0.598335i | \(-0.204171\pi\) | ||||
0.801246 | + | 0.598335i | \(0.204171\pi\) | |||||||
\(734\) | −42173.1 | −2.12076 | ||||||||
\(735\) | 11222.7 | 0.563202 | ||||||||
\(736\) | −12828.3 | −0.642468 | ||||||||
\(737\) | −7509.16 | −0.375310 | ||||||||
\(738\) | 22019.4 | 1.09830 | ||||||||
\(739\) | 14361.5 | 0.714880 | 0.357440 | − | 0.933936i | \(-0.383650\pi\) | ||||
0.357440 | + | 0.933936i | \(0.383650\pi\) | |||||||
\(740\) | 3305.70 | 0.164216 | ||||||||
\(741\) | −2363.25 | −0.117161 | ||||||||
\(742\) | −254.363 | −0.0125849 | ||||||||
\(743\) | 22926.6 | 1.13203 | 0.566014 | − | 0.824396i | \(-0.308485\pi\) | ||||
0.566014 | + | 0.824396i | \(0.308485\pi\) | |||||||
\(744\) | 3432.22 | 0.169128 | ||||||||
\(745\) | −903.209 | −0.0444175 | ||||||||
\(746\) | −33314.4 | −1.63502 | ||||||||
\(747\) | 21218.6 | 1.03929 | ||||||||
\(748\) | 6557.68 | 0.320551 | ||||||||
\(749\) | −788.643 | −0.0384732 | ||||||||
\(750\) | −2944.15 | −0.143340 | ||||||||
\(751\) | −16355.6 | −0.794704 | −0.397352 | − | 0.917666i | \(-0.630071\pi\) | ||||
−0.397352 | + | 0.917666i | \(0.630071\pi\) | |||||||
\(752\) | 4121.33 | 0.199853 | ||||||||
\(753\) | −41382.6 | −2.00274 | ||||||||
\(754\) | 5998.78 | 0.289738 | ||||||||
\(755\) | 7750.03 | 0.373580 | ||||||||
\(756\) | 633.134 | 0.0304588 | ||||||||
\(757\) | −14584.0 | −0.700215 | −0.350108 | − | 0.936709i | \(-0.613855\pi\) | ||||
−0.350108 | + | 0.936709i | \(0.613855\pi\) | |||||||
\(758\) | 46657.3 | 2.23571 | ||||||||
\(759\) | −4983.22 | −0.238313 | ||||||||
\(760\) | 1133.35 | 0.0540932 | ||||||||
\(761\) | −26442.2 | −1.25956 | −0.629782 | − | 0.776772i | \(-0.716856\pi\) | ||||
−0.629782 | + | 0.776772i | \(0.716856\pi\) | |||||||
\(762\) | 32079.2 | 1.52507 | ||||||||
\(763\) | −1387.81 | −0.0658480 | ||||||||
\(764\) | −5288.29 | −0.250424 | ||||||||
\(765\) | 10826.2 | 0.511661 | ||||||||
\(766\) | −37619.7 | −1.77448 | ||||||||
\(767\) | −7037.49 | −0.331303 | ||||||||
\(768\) | 34409.2 | 1.61671 | ||||||||
\(769\) | 2313.64 | 0.108494 | 0.0542470 | − | 0.998528i | \(-0.482724\pi\) | ||||
0.0542470 | + | 0.998528i | \(0.482724\pi\) | |||||||
\(770\) | −397.349 | −0.0185967 | ||||||||
\(771\) | −14672.1 | −0.685348 | ||||||||
\(772\) | −1454.22 | −0.0677960 | ||||||||
\(773\) | 19113.5 | 0.889346 | 0.444673 | − | 0.895693i | \(-0.353320\pi\) | ||||
0.444673 | + | 0.895693i | \(0.353320\pi\) | |||||||
\(774\) | −17918.9 | −0.832146 | ||||||||
\(775\) | −1085.89 | −0.0503308 | ||||||||
\(776\) | 6871.32 | 0.317868 | ||||||||
\(777\) | 1915.29 | 0.0884307 | ||||||||
\(778\) | 15927.9 | 0.733988 | ||||||||
\(779\) | 6973.56 | 0.320737 | ||||||||
\(780\) | 2888.83 | 0.132611 | ||||||||
\(781\) | 6998.27 | 0.320637 | ||||||||
\(782\) | −31214.1 | −1.42738 | ||||||||
\(783\) | 6026.80 | 0.275071 | ||||||||
\(784\) | 26968.8 | 1.22853 | ||||||||
\(785\) | −2271.44 | −0.103275 | ||||||||
\(786\) | −18762.2 | −0.851432 | ||||||||
\(787\) | 19512.0 | 0.883771 | 0.441886 | − | 0.897071i | \(-0.354310\pi\) | ||||
0.441886 | + | 0.897071i | \(0.354310\pi\) | |||||||
\(788\) | 19324.9 | 0.873633 | ||||||||
\(789\) | 25089.9 | 1.13210 | ||||||||
\(790\) | 14764.0 | 0.664911 | ||||||||
\(791\) | 840.243 | 0.0377694 | ||||||||
\(792\) | 2213.99 | 0.0993317 | ||||||||
\(793\) | −8827.83 | −0.395316 | ||||||||
\(794\) | −6575.40 | −0.293895 | ||||||||
\(795\) | −1166.02 | −0.0520180 | ||||||||
\(796\) | −2089.09 | −0.0930226 | ||||||||
\(797\) | −34672.5 | −1.54098 | −0.770492 | − | 0.637450i | \(-0.779989\pi\) | ||||
−0.770492 | + | 0.637450i | \(0.779989\pi\) | |||||||
\(798\) | −909.185 | −0.0403318 | ||||||||
\(799\) | 6646.20 | 0.294275 | ||||||||
\(800\) | −4689.00 | −0.207226 | ||||||||
\(801\) | −8645.23 | −0.381354 | ||||||||
\(802\) | 4487.28 | 0.197570 | ||||||||
\(803\) | 4406.54 | 0.193653 | ||||||||
\(804\) | 21003.1 | 0.921297 | ||||||||
\(805\) | 694.778 | 0.0304195 | ||||||||
\(806\) | 2900.51 | 0.126757 | ||||||||
\(807\) | −26445.8 | −1.15358 | ||||||||
\(808\) | 11604.2 | 0.505241 | ||||||||
\(809\) | −13939.7 | −0.605802 | −0.302901 | − | 0.953022i | \(-0.597955\pi\) | ||||
−0.302901 | + | 0.953022i | \(0.597955\pi\) | |||||||
\(810\) | 16000.0 | 0.694051 | ||||||||
\(811\) | −18909.7 | −0.818755 | −0.409377 | − | 0.912365i | \(-0.634254\pi\) | ||||
−0.409377 | + | 0.912365i | \(0.634254\pi\) | |||||||
\(812\) | 847.772 | 0.0366391 | ||||||||
\(813\) | 9809.78 | 0.423178 | ||||||||
\(814\) | 5567.39 | 0.239726 | ||||||||
\(815\) | −3057.67 | −0.131418 | ||||||||
\(816\) | 67651.2 | 2.90229 | ||||||||
\(817\) | −5674.92 | −0.243012 | ||||||||
\(818\) | −11091.5 | −0.474089 | ||||||||
\(819\) | 643.662 | 0.0274620 | ||||||||
\(820\) | −8524.47 | −0.363033 | ||||||||
\(821\) | 3660.58 | 0.155609 | 0.0778045 | − | 0.996969i | \(-0.475209\pi\) | ||||
0.0778045 | + | 0.996969i | \(0.475209\pi\) | |||||||
\(822\) | −37934.3 | −1.60962 | ||||||||
\(823\) | 190.131 | 0.00805292 | 0.00402646 | − | 0.999992i | \(-0.498718\pi\) | ||||
0.00402646 | + | 0.999992i | \(0.498718\pi\) | |||||||
\(824\) | −1355.56 | −0.0573098 | ||||||||
\(825\) | −1821.47 | −0.0768672 | ||||||||
\(826\) | −2707.45 | −0.114049 | ||||||||
\(827\) | 42596.9 | 1.79110 | 0.895550 | − | 0.444960i | \(-0.146782\pi\) | ||||
0.895550 | + | 0.444960i | \(0.146782\pi\) | |||||||
\(828\) | 5360.03 | 0.224969 | ||||||||
\(829\) | −31088.8 | −1.30248 | −0.651242 | − | 0.758870i | \(-0.725752\pi\) | ||||
−0.651242 | + | 0.758870i | \(0.725752\pi\) | |||||||
\(830\) | −22361.7 | −0.935163 | ||||||||
\(831\) | 426.009 | 0.0177835 | ||||||||
\(832\) | 568.845 | 0.0237033 | ||||||||
\(833\) | 43490.8 | 1.80896 | ||||||||
\(834\) | 33717.0 | 1.39991 | ||||||||
\(835\) | 1880.23 | 0.0779259 | ||||||||
\(836\) | −970.828 | −0.0401636 | ||||||||
\(837\) | 2914.06 | 0.120340 | ||||||||
\(838\) | 5287.98 | 0.217983 | ||||||||
\(839\) | −12089.2 | −0.497456 | −0.248728 | − | 0.968573i | \(-0.580013\pi\) | ||||
−0.248728 | + | 0.968573i | \(0.580013\pi\) | |||||||
\(840\) | −802.688 | −0.0329707 | ||||||||
\(841\) | −16319.1 | −0.669116 | ||||||||
\(842\) | −16174.5 | −0.662006 | ||||||||
\(843\) | −32136.8 | −1.31299 | ||||||||
\(844\) | 13850.2 | 0.564863 | ||||||||
\(845\) | 9221.79 | 0.375431 | ||||||||
\(846\) | −3106.82 | −0.126259 | ||||||||
\(847\) | −245.829 | −0.00997260 | ||||||||
\(848\) | −2802.01 | −0.113469 | ||||||||
\(849\) | 24436.5 | 0.987818 | ||||||||
\(850\) | −11409.4 | −0.460399 | ||||||||
\(851\) | −9734.77 | −0.392131 | ||||||||
\(852\) | −19574.2 | −0.787089 | ||||||||
\(853\) | −7367.29 | −0.295722 | −0.147861 | − | 0.989008i | \(-0.547239\pi\) | ||||
−0.147861 | + | 0.989008i | \(0.547239\pi\) | |||||||
\(854\) | −3396.23 | −0.136085 | ||||||||
\(855\) | −1602.75 | −0.0641088 | ||||||||
\(856\) | −4630.97 | −0.184911 | ||||||||
\(857\) | 35901.9 | 1.43102 | 0.715510 | − | 0.698602i | \(-0.246194\pi\) | ||||
0.715510 | + | 0.698602i | \(0.246194\pi\) | |||||||
\(858\) | 4865.31 | 0.193588 | ||||||||
\(859\) | 11900.5 | 0.472691 | 0.236345 | − | 0.971669i | \(-0.424050\pi\) | ||||
0.236345 | + | 0.971669i | \(0.424050\pi\) | |||||||
\(860\) | 6937.01 | 0.275058 | ||||||||
\(861\) | −4938.99 | −0.195494 | ||||||||
\(862\) | 39513.9 | 1.56131 | ||||||||
\(863\) | −19339.6 | −0.762836 | −0.381418 | − | 0.924403i | \(-0.624564\pi\) | ||||
−0.381418 | + | 0.924403i | \(0.624564\pi\) | |||||||
\(864\) | 12583.2 | 0.495474 | ||||||||
\(865\) | −7091.95 | −0.278767 | ||||||||
\(866\) | −15417.1 | −0.604958 | ||||||||
\(867\) | 76555.4 | 2.99880 | ||||||||
\(868\) | 409.912 | 0.0160292 | ||||||||
\(869\) | 9134.10 | 0.356563 | ||||||||
\(870\) | 10579.3 | 0.412265 | ||||||||
\(871\) | −12819.3 | −0.498699 | ||||||||
\(872\) | −8149.31 | −0.316480 | ||||||||
\(873\) | −9717.26 | −0.376723 | ||||||||
\(874\) | 4621.08 | 0.178845 | ||||||||
\(875\) | 253.956 | 0.00981174 | ||||||||
\(876\) | −12325.1 | −0.475373 | ||||||||
\(877\) | −50436.3 | −1.94198 | −0.970988 | − | 0.239130i | \(-0.923138\pi\) | ||||
−0.970988 | + | 0.239130i | \(0.923138\pi\) | |||||||
\(878\) | 32752.6 | 1.25894 | ||||||||
\(879\) | 4120.06 | 0.158096 | ||||||||
\(880\) | −4377.11 | −0.167673 | ||||||||
\(881\) | −13741.6 | −0.525500 | −0.262750 | − | 0.964864i | \(-0.584629\pi\) | ||||
−0.262750 | + | 0.964864i | \(0.584629\pi\) | |||||||
\(882\) | −20330.2 | −0.776136 | ||||||||
\(883\) | −27411.6 | −1.04470 | −0.522352 | − | 0.852730i | \(-0.674945\pi\) | ||||
−0.522352 | + | 0.852730i | \(0.674945\pi\) | |||||||
\(884\) | 11195.0 | 0.425937 | ||||||||
\(885\) | −12411.1 | −0.471406 | ||||||||
\(886\) | −306.343 | −0.0116160 | ||||||||
\(887\) | −31762.6 | −1.20235 | −0.601174 | − | 0.799118i | \(-0.705300\pi\) | ||||
−0.601174 | + | 0.799118i | \(0.705300\pi\) | |||||||
\(888\) | 11246.7 | 0.425018 | ||||||||
\(889\) | −2767.08 | −0.104392 | ||||||||
\(890\) | 9110.97 | 0.343147 | ||||||||
\(891\) | 9898.74 | 0.372189 | ||||||||
\(892\) | 13622.7 | 0.511349 | ||||||||
\(893\) | −983.933 | −0.0368713 | ||||||||
\(894\) | 4254.70 | 0.159170 | ||||||||
\(895\) | −7346.88 | −0.274390 | ||||||||
\(896\) | −2829.60 | −0.105503 | ||||||||
\(897\) | −8507.16 | −0.316662 | ||||||||
\(898\) | 13534.8 | 0.502963 | ||||||||
\(899\) | 3901.95 | 0.144758 | ||||||||
\(900\) | 1959.20 | 0.0725630 | ||||||||
\(901\) | −4518.63 | −0.167078 | ||||||||
\(902\) | −14356.7 | −0.529963 | ||||||||
\(903\) | 4019.24 | 0.148119 | ||||||||
\(904\) | 4933.97 | 0.181528 | ||||||||
\(905\) | 19427.6 | 0.713587 | ||||||||
\(906\) | −36507.7 | −1.33873 | ||||||||
\(907\) | −31664.4 | −1.15920 | −0.579602 | − | 0.814900i | \(-0.696792\pi\) | ||||
−0.579602 | + | 0.814900i | \(0.696792\pi\) | |||||||
\(908\) | −4715.18 | −0.172334 | ||||||||
\(909\) | −16410.4 | −0.598789 | ||||||||
\(910\) | −678.338 | −0.0247106 | ||||||||
\(911\) | 10601.3 | 0.385551 | 0.192775 | − | 0.981243i | \(-0.438251\pi\) | ||||
0.192775 | + | 0.981243i | \(0.438251\pi\) | |||||||
\(912\) | −10015.4 | −0.363643 | ||||||||
\(913\) | −13834.6 | −0.501487 | ||||||||
\(914\) | −51954.8 | −1.88021 | ||||||||
\(915\) | −15568.5 | −0.562490 | ||||||||
\(916\) | 15257.6 | 0.550355 | ||||||||
\(917\) | 1618.38 | 0.0582810 | ||||||||
\(918\) | 30617.8 | 1.10080 | ||||||||
\(919\) | 30143.7 | 1.08199 | 0.540995 | − | 0.841026i | \(-0.318048\pi\) | ||||
0.540995 | + | 0.841026i | \(0.318048\pi\) | |||||||
\(920\) | 4079.79 | 0.146203 | ||||||||
\(921\) | −11457.8 | −0.409934 | ||||||||
\(922\) | −37361.1 | −1.33452 | ||||||||
\(923\) | 11947.2 | 0.426052 | ||||||||
\(924\) | 687.584 | 0.0244804 | ||||||||
\(925\) | −3558.26 | −0.126481 | ||||||||
\(926\) | 45012.8 | 1.59742 | ||||||||
\(927\) | 1917.01 | 0.0679209 | ||||||||
\(928\) | 16849.0 | 0.596009 | ||||||||
\(929\) | 11299.3 | 0.399051 | 0.199525 | − | 0.979893i | \(-0.436060\pi\) | ||||
0.199525 | + | 0.979893i | \(0.436060\pi\) | |||||||
\(930\) | 5115.25 | 0.180361 | ||||||||
\(931\) | −6438.58 | −0.226655 | ||||||||
\(932\) | −11376.9 | −0.399853 | ||||||||
\(933\) | 12332.7 | 0.432748 | ||||||||
\(934\) | −34039.6 | −1.19252 | ||||||||
\(935\) | −7058.69 | −0.246892 | ||||||||
\(936\) | 3779.63 | 0.131988 | ||||||||
\(937\) | 17889.6 | 0.623722 | 0.311861 | − | 0.950128i | \(-0.399048\pi\) | ||||
0.311861 | + | 0.950128i | \(0.399048\pi\) | |||||||
\(938\) | −4931.83 | −0.171674 | ||||||||
\(939\) | −6919.74 | −0.240487 | ||||||||
\(940\) | 1202.76 | 0.0417336 | ||||||||
\(941\) | −8311.62 | −0.287940 | −0.143970 | − | 0.989582i | \(-0.545987\pi\) | ||||
−0.143970 | + | 0.989582i | \(0.545987\pi\) | |||||||
\(942\) | 10700.0 | 0.370088 | ||||||||
\(943\) | 25103.2 | 0.866886 | ||||||||
\(944\) | −29824.7 | −1.02830 | ||||||||
\(945\) | −681.506 | −0.0234597 | ||||||||
\(946\) | 11683.2 | 0.401535 | ||||||||
\(947\) | 6398.75 | 0.219569 | 0.109784 | − | 0.993955i | \(-0.464984\pi\) | ||||
0.109784 | + | 0.993955i | \(0.464984\pi\) | |||||||
\(948\) | −25548.1 | −0.875278 | ||||||||
\(949\) | 7522.67 | 0.257320 | ||||||||
\(950\) | 1689.10 | 0.0576859 | ||||||||
\(951\) | −41257.6 | −1.40680 | ||||||||
\(952\) | −3110.63 | −0.105899 | ||||||||
\(953\) | −36676.8 | −1.24667 | −0.623335 | − | 0.781955i | \(-0.714223\pi\) | ||||
−0.623335 | + | 0.781955i | \(0.714223\pi\) | |||||||
\(954\) | 2112.27 | 0.0716849 | ||||||||
\(955\) | 5692.32 | 0.192879 | ||||||||
\(956\) | −8949.63 | −0.302774 | ||||||||
\(957\) | 6545.11 | 0.221080 | ||||||||
\(958\) | 32613.3 | 1.09988 | ||||||||
\(959\) | 3272.12 | 0.110180 | ||||||||
\(960\) | 1003.20 | 0.0337271 | ||||||||
\(961\) | −27904.3 | −0.936670 | ||||||||
\(962\) | 9504.42 | 0.318539 | ||||||||
\(963\) | 6549.01 | 0.219147 | ||||||||
\(964\) | 10394.2 | 0.347277 | ||||||||
\(965\) | 1565.32 | 0.0522172 | ||||||||
\(966\) | −3272.86 | −0.109009 | ||||||||
\(967\) | 54104.1 | 1.79925 | 0.899623 | − | 0.436668i | \(-0.143842\pi\) | ||||
0.899623 | + | 0.436668i | \(0.143842\pi\) | |||||||
\(968\) | −1443.53 | −0.0479305 | ||||||||
\(969\) | −16151.2 | −0.535450 | ||||||||
\(970\) | 10240.7 | 0.338980 | ||||||||
\(971\) | −37068.9 | −1.22513 | −0.612564 | − | 0.790421i | \(-0.709862\pi\) | ||||
−0.612564 | + | 0.790421i | \(0.709862\pi\) | |||||||
\(972\) | −19272.6 | −0.635977 | ||||||||
\(973\) | −2908.35 | −0.0958248 | ||||||||
\(974\) | 50390.4 | 1.65771 | ||||||||
\(975\) | −3109.54 | −0.102138 | ||||||||
\(976\) | −37412.1 | −1.22698 | ||||||||
\(977\) | 18502.7 | 0.605890 | 0.302945 | − | 0.953008i | \(-0.402030\pi\) | ||||
0.302945 | + | 0.953008i | \(0.402030\pi\) | |||||||
\(978\) | 14403.6 | 0.470937 | ||||||||
\(979\) | 5636.72 | 0.184015 | ||||||||
\(980\) | 7870.50 | 0.256545 | ||||||||
\(981\) | 11524.6 | 0.375078 | ||||||||
\(982\) | −45907.3 | −1.49181 | ||||||||
\(983\) | −58984.3 | −1.91384 | −0.956922 | − | 0.290347i | \(-0.906229\pi\) | ||||
−0.956922 | + | 0.290347i | \(0.906229\pi\) | |||||||
\(984\) | −29002.1 | −0.939588 | ||||||||
\(985\) | −20801.4 | −0.672880 | ||||||||
\(986\) | 40997.5 | 1.32417 | ||||||||
\(987\) | 696.866 | 0.0224737 | ||||||||
\(988\) | −1657.36 | −0.0533680 | ||||||||
\(989\) | −20428.4 | −0.656811 | ||||||||
\(990\) | 3299.65 | 0.105929 | ||||||||
\(991\) | −33096.5 | −1.06089 | −0.530447 | − | 0.847718i | \(-0.677976\pi\) | ||||
−0.530447 | + | 0.847718i | \(0.677976\pi\) | |||||||
\(992\) | 8146.80 | 0.260747 | ||||||||
\(993\) | −5003.59 | −0.159904 | ||||||||
\(994\) | 4596.29 | 0.146665 | ||||||||
\(995\) | 2248.70 | 0.0716469 | ||||||||
\(996\) | 38695.3 | 1.23103 | ||||||||
\(997\) | 6392.68 | 0.203067 | 0.101534 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101534 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(998\) | 24019.8 | 0.761856 | ||||||||
\(999\) | 9548.81 | 0.302413 |
(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 | 1045.4.a.c.1.16 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.c.1.16 | ✓ | 20 | 1.1 | even | 1 | trivial |