Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [46,4,Mod(1,46)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(46, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("46.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 46 = 2 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 46.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: | \(2.71408786026\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 46.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −10.1047 | −1.94465 | −0.972324 | − | 0.233637i | \(-0.924937\pi\) | ||||
−0.972324 | + | 0.233637i | \(0.924937\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 11.4031 | 1.01993 | 0.509963 | − | 0.860196i | \(-0.329659\pi\) | ||||
0.509963 | + | 0.860196i | \(0.329659\pi\) | |||||||
\(6\) | 20.2094 | 1.37507 | ||||||||
\(7\) | 9.40312 | 0.507721 | 0.253860 | − | 0.967241i | \(-0.418300\pi\) | ||||
0.253860 | + | 0.967241i | \(0.418300\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 75.1047 | 2.78166 | ||||||||
\(10\) | −22.8062 | −0.721197 | ||||||||
\(11\) | 10.3875 | 0.284723 | 0.142361 | − | 0.989815i | \(-0.454530\pi\) | ||||
0.142361 | + | 0.989815i | \(0.454530\pi\) | |||||||
\(12\) | −40.4187 | −0.972324 | ||||||||
\(13\) | −33.0891 | −0.705943 | −0.352971 | − | 0.935634i | \(-0.614829\pi\) | ||||
−0.352971 | + | 0.935634i | \(0.614829\pi\) | |||||||
\(14\) | −18.8062 | −0.359013 | ||||||||
\(15\) | −115.225 | −1.98340 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 138.837 | 1.98077 | 0.990383 | − | 0.138350i | \(-0.0441797\pi\) | ||||
0.990383 | + | 0.138350i | \(0.0441797\pi\) | |||||||
\(18\) | −150.209 | −1.96693 | ||||||||
\(19\) | 68.6281 | 0.828651 | 0.414326 | − | 0.910129i | \(-0.364018\pi\) | ||||
0.414326 | + | 0.910129i | \(0.364018\pi\) | |||||||
\(20\) | 45.6125 | 0.509963 | ||||||||
\(21\) | −95.0156 | −0.987338 | ||||||||
\(22\) | −20.7750 | −0.201329 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 80.8375 | 0.687537 | ||||||||
\(25\) | 5.03124 | 0.0402499 | ||||||||
\(26\) | 66.1781 | 0.499177 | ||||||||
\(27\) | −486.083 | −3.46469 | ||||||||
\(28\) | 37.6125 | 0.253860 | ||||||||
\(29\) | 215.602 | 1.38056 | 0.690279 | − | 0.723543i | \(-0.257488\pi\) | ||||
0.690279 | + | 0.723543i | \(0.257488\pi\) | |||||||
\(30\) | 230.450 | 1.40247 | ||||||||
\(31\) | 87.9266 | 0.509422 | 0.254711 | − | 0.967017i | \(-0.418020\pi\) | ||||
0.254711 | + | 0.967017i | \(0.418020\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −104.962 | −0.553685 | ||||||||
\(34\) | −277.675 | −1.40061 | ||||||||
\(35\) | 107.225 | 0.517838 | ||||||||
\(36\) | 300.419 | 1.39083 | ||||||||
\(37\) | −215.109 | −0.955777 | −0.477889 | − | 0.878420i | \(-0.658598\pi\) | ||||
−0.477889 | + | 0.878420i | \(0.658598\pi\) | |||||||
\(38\) | −137.256 | −0.585945 | ||||||||
\(39\) | 334.355 | 1.37281 | ||||||||
\(40\) | −91.2250 | −0.360598 | ||||||||
\(41\) | 175.267 | 0.667613 | 0.333807 | − | 0.942642i | \(-0.391667\pi\) | ||||
0.333807 | + | 0.942642i | \(0.391667\pi\) | |||||||
\(42\) | 190.031 | 0.698154 | ||||||||
\(43\) | −40.7125 | −0.144386 | −0.0721930 | − | 0.997391i | \(-0.523000\pi\) | ||||
−0.0721930 | + | 0.997391i | \(0.523000\pi\) | |||||||
\(44\) | 41.5500 | 0.142361 | ||||||||
\(45\) | 856.428 | 2.83708 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 405.245 | 1.25768 | 0.628841 | − | 0.777534i | \(-0.283529\pi\) | ||||
0.628841 | + | 0.777534i | \(0.283529\pi\) | |||||||
\(48\) | −161.675 | −0.486162 | ||||||||
\(49\) | −254.581 | −0.742219 | ||||||||
\(50\) | −10.0625 | −0.0284610 | ||||||||
\(51\) | −1402.91 | −3.85189 | ||||||||
\(52\) | −132.356 | −0.352971 | ||||||||
\(53\) | −276.994 | −0.717887 | −0.358944 | − | 0.933359i | \(-0.616863\pi\) | ||||
−0.358944 | + | 0.933359i | \(0.616863\pi\) | |||||||
\(54\) | 972.166 | 2.44991 | ||||||||
\(55\) | 118.450 | 0.290396 | ||||||||
\(56\) | −75.2250 | −0.179506 | ||||||||
\(57\) | −693.466 | −1.61143 | ||||||||
\(58\) | −431.203 | −0.976202 | ||||||||
\(59\) | 293.550 | 0.647745 | 0.323873 | − | 0.946101i | \(-0.395015\pi\) | ||||
0.323873 | + | 0.946101i | \(0.395015\pi\) | |||||||
\(60\) | −460.900 | −0.991699 | ||||||||
\(61\) | −450.731 | −0.946069 | −0.473035 | − | 0.881044i | \(-0.656841\pi\) | ||||
−0.473035 | + | 0.881044i | \(0.656841\pi\) | |||||||
\(62\) | −175.853 | −0.360216 | ||||||||
\(63\) | 706.219 | 1.41230 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −377.319 | −0.720010 | ||||||||
\(66\) | 209.925 | 0.391515 | ||||||||
\(67\) | 273.675 | 0.499026 | 0.249513 | − | 0.968371i | \(-0.419730\pi\) | ||||
0.249513 | + | 0.968371i | \(0.419730\pi\) | |||||||
\(68\) | 555.350 | 0.990383 | ||||||||
\(69\) | 232.408 | 0.405487 | ||||||||
\(70\) | −214.450 | −0.366167 | ||||||||
\(71\) | −643.842 | −1.07620 | −0.538099 | − | 0.842882i | \(-0.680857\pi\) | ||||
−0.538099 | + | 0.842882i | \(0.680857\pi\) | |||||||
\(72\) | −600.837 | −0.983464 | ||||||||
\(73\) | 106.345 | 0.170504 | 0.0852519 | − | 0.996359i | \(-0.472831\pi\) | ||||
0.0852519 | + | 0.996359i | \(0.472831\pi\) | |||||||
\(74\) | 430.219 | 0.675837 | ||||||||
\(75\) | −50.8391 | −0.0782720 | ||||||||
\(76\) | 274.512 | 0.414326 | ||||||||
\(77\) | 97.6750 | 0.144560 | ||||||||
\(78\) | −668.709 | −0.970723 | ||||||||
\(79\) | 60.0844 | 0.0855699 | 0.0427850 | − | 0.999084i | \(-0.486377\pi\) | ||||
0.0427850 | + | 0.999084i | \(0.486377\pi\) | |||||||
\(80\) | 182.450 | 0.254982 | ||||||||
\(81\) | 2883.89 | 3.95595 | ||||||||
\(82\) | −350.534 | −0.472074 | ||||||||
\(83\) | −372.878 | −0.493117 | −0.246558 | − | 0.969128i | \(-0.579300\pi\) | ||||
−0.246558 | + | 0.969128i | \(0.579300\pi\) | |||||||
\(84\) | −380.062 | −0.493669 | ||||||||
\(85\) | 1583.18 | 2.02024 | ||||||||
\(86\) | 81.4250 | 0.102096 | ||||||||
\(87\) | −2178.59 | −2.68470 | ||||||||
\(88\) | −83.1000 | −0.100665 | ||||||||
\(89\) | −543.947 | −0.647846 | −0.323923 | − | 0.946084i | \(-0.605002\pi\) | ||||
−0.323923 | + | 0.946084i | \(0.605002\pi\) | |||||||
\(90\) | −1712.86 | −2.00612 | ||||||||
\(91\) | −311.141 | −0.358422 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | −888.470 | −0.990646 | ||||||||
\(94\) | −810.491 | −0.889316 | ||||||||
\(95\) | 782.575 | 0.845163 | ||||||||
\(96\) | 323.350 | 0.343768 | ||||||||
\(97\) | 550.944 | 0.576700 | 0.288350 | − | 0.957525i | \(-0.406893\pi\) | ||||
0.288350 | + | 0.957525i | \(0.406893\pi\) | |||||||
\(98\) | 509.163 | 0.524828 | ||||||||
\(99\) | 780.150 | 0.792000 | ||||||||
\(100\) | 20.1250 | 0.0201250 | ||||||||
\(101\) | 1084.57 | 1.06851 | 0.534254 | − | 0.845324i | \(-0.320593\pi\) | ||||
0.534254 | + | 0.845324i | \(0.320593\pi\) | |||||||
\(102\) | 2805.82 | 2.72370 | ||||||||
\(103\) | 1369.19 | 1.30981 | 0.654905 | − | 0.755712i | \(-0.272709\pi\) | ||||
0.654905 | + | 0.755712i | \(0.272709\pi\) | |||||||
\(104\) | 264.713 | 0.249588 | ||||||||
\(105\) | −1083.47 | −1.00701 | ||||||||
\(106\) | 553.987 | 0.507623 | ||||||||
\(107\) | −1193.82 | −1.07861 | −0.539304 | − | 0.842111i | \(-0.681313\pi\) | ||||
−0.539304 | + | 0.842111i | \(0.681313\pi\) | |||||||
\(108\) | −1944.33 | −1.73235 | ||||||||
\(109\) | −893.309 | −0.784986 | −0.392493 | − | 0.919755i | \(-0.628387\pi\) | ||||
−0.392493 | + | 0.919755i | \(0.628387\pi\) | |||||||
\(110\) | −236.900 | −0.205341 | ||||||||
\(111\) | 2173.61 | 1.85865 | ||||||||
\(112\) | 150.450 | 0.126930 | ||||||||
\(113\) | 1842.16 | 1.53359 | 0.766797 | − | 0.641890i | \(-0.221849\pi\) | ||||
0.766797 | + | 0.641890i | \(0.221849\pi\) | |||||||
\(114\) | 1386.93 | 1.13946 | ||||||||
\(115\) | −262.272 | −0.212669 | ||||||||
\(116\) | 862.406 | 0.690279 | ||||||||
\(117\) | −2485.14 | −1.96369 | ||||||||
\(118\) | −587.100 | −0.458025 | ||||||||
\(119\) | 1305.51 | 1.00568 | ||||||||
\(120\) | 921.800 | 0.701237 | ||||||||
\(121\) | −1223.10 | −0.918933 | ||||||||
\(122\) | 901.462 | 0.668972 | ||||||||
\(123\) | −1771.02 | −1.29827 | ||||||||
\(124\) | 351.706 | 0.254711 | ||||||||
\(125\) | −1368.02 | −0.978874 | ||||||||
\(126\) | −1412.44 | −0.998650 | ||||||||
\(127\) | 599.361 | 0.418777 | 0.209389 | − | 0.977833i | \(-0.432853\pi\) | ||||
0.209389 | + | 0.977833i | \(0.432853\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 411.387 | 0.280780 | ||||||||
\(130\) | 754.637 | 0.509124 | ||||||||
\(131\) | −560.136 | −0.373582 | −0.186791 | − | 0.982400i | \(-0.559809\pi\) | ||||
−0.186791 | + | 0.982400i | \(0.559809\pi\) | |||||||
\(132\) | −419.850 | −0.276843 | ||||||||
\(133\) | 645.319 | 0.420724 | ||||||||
\(134\) | −547.350 | −0.352864 | ||||||||
\(135\) | −5542.86 | −3.53373 | ||||||||
\(136\) | −1110.70 | −0.700307 | ||||||||
\(137\) | −2111.69 | −1.31689 | −0.658445 | − | 0.752629i | \(-0.728785\pi\) | ||||
−0.658445 | + | 0.752629i | \(0.728785\pi\) | |||||||
\(138\) | −464.816 | −0.286723 | ||||||||
\(139\) | −944.952 | −0.576617 | −0.288308 | − | 0.957538i | \(-0.593093\pi\) | ||||
−0.288308 | + | 0.957538i | \(0.593093\pi\) | |||||||
\(140\) | 428.900 | 0.258919 | ||||||||
\(141\) | −4094.88 | −2.44575 | ||||||||
\(142\) | 1287.68 | 0.760986 | ||||||||
\(143\) | −343.713 | −0.200998 | ||||||||
\(144\) | 1201.67 | 0.695414 | ||||||||
\(145\) | 2458.53 | 1.40807 | ||||||||
\(146\) | −212.691 | −0.120564 | ||||||||
\(147\) | 2572.46 | 1.44336 | ||||||||
\(148\) | −860.437 | −0.477889 | ||||||||
\(149\) | −2480.47 | −1.36381 | −0.681906 | − | 0.731440i | \(-0.738849\pi\) | ||||
−0.681906 | + | 0.731440i | \(0.738849\pi\) | |||||||
\(150\) | 101.678 | 0.0553466 | ||||||||
\(151\) | 1164.53 | 0.627605 | 0.313802 | − | 0.949488i | \(-0.398397\pi\) | ||||
0.313802 | + | 0.949488i | \(0.398397\pi\) | |||||||
\(152\) | −549.025 | −0.292972 | ||||||||
\(153\) | 10427.3 | 5.50981 | ||||||||
\(154\) | −195.350 | −0.102219 | ||||||||
\(155\) | 1002.64 | 0.519573 | ||||||||
\(156\) | 1337.42 | 0.686405 | ||||||||
\(157\) | −1525.27 | −0.775347 | −0.387673 | − | 0.921797i | \(-0.626721\pi\) | ||||
−0.387673 | + | 0.921797i | \(0.626721\pi\) | |||||||
\(158\) | −120.169 | −0.0605071 | ||||||||
\(159\) | 2798.93 | 1.39604 | ||||||||
\(160\) | −364.900 | −0.180299 | ||||||||
\(161\) | −216.272 | −0.105867 | ||||||||
\(162\) | −5767.77 | −2.79728 | ||||||||
\(163\) | 1944.47 | 0.934371 | 0.467185 | − | 0.884159i | \(-0.345268\pi\) | ||||
0.467185 | + | 0.884159i | \(0.345268\pi\) | |||||||
\(164\) | 701.069 | 0.333807 | ||||||||
\(165\) | −1196.90 | −0.564718 | ||||||||
\(166\) | 745.756 | 0.348686 | ||||||||
\(167\) | −2632.58 | −1.21985 | −0.609926 | − | 0.792458i | \(-0.708801\pi\) | ||||
−0.609926 | + | 0.792458i | \(0.708801\pi\) | |||||||
\(168\) | 760.125 | 0.349077 | ||||||||
\(169\) | −1102.11 | −0.501645 | ||||||||
\(170\) | −3166.36 | −1.42852 | ||||||||
\(171\) | 5154.29 | 2.30502 | ||||||||
\(172\) | −162.850 | −0.0721930 | ||||||||
\(173\) | 1189.63 | 0.522806 | 0.261403 | − | 0.965230i | \(-0.415815\pi\) | ||||
0.261403 | + | 0.965230i | \(0.415815\pi\) | |||||||
\(174\) | 4357.17 | 1.89837 | ||||||||
\(175\) | 47.3094 | 0.0204357 | ||||||||
\(176\) | 166.200 | 0.0711807 | ||||||||
\(177\) | −2966.23 | −1.25964 | ||||||||
\(178\) | 1087.89 | 0.458096 | ||||||||
\(179\) | −1548.97 | −0.646790 | −0.323395 | − | 0.946264i | \(-0.604824\pi\) | ||||
−0.323395 | + | 0.946264i | \(0.604824\pi\) | |||||||
\(180\) | 3425.71 | 1.41854 | ||||||||
\(181\) | −1908.38 | −0.783697 | −0.391848 | − | 0.920030i | \(-0.628164\pi\) | ||||
−0.391848 | + | 0.920030i | \(0.628164\pi\) | |||||||
\(182\) | 622.281 | 0.253443 | ||||||||
\(183\) | 4554.50 | 1.83977 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −2452.92 | −0.974823 | ||||||||
\(186\) | 1776.94 | 0.700492 | ||||||||
\(187\) | 1442.17 | 0.563969 | ||||||||
\(188\) | 1620.98 | 0.628841 | ||||||||
\(189\) | −4570.70 | −1.75910 | ||||||||
\(190\) | −1565.15 | −0.597621 | ||||||||
\(191\) | 352.625 | 0.133587 | 0.0667933 | − | 0.997767i | \(-0.478723\pi\) | ||||
0.0667933 | + | 0.997767i | \(0.478723\pi\) | |||||||
\(192\) | −646.700 | −0.243081 | ||||||||
\(193\) | −1414.28 | −0.527472 | −0.263736 | − | 0.964595i | \(-0.584955\pi\) | ||||
−0.263736 | + | 0.964595i | \(0.584955\pi\) | |||||||
\(194\) | −1101.89 | −0.407788 | ||||||||
\(195\) | 3812.69 | 1.40017 | ||||||||
\(196\) | −1018.33 | −0.371110 | ||||||||
\(197\) | −432.530 | −0.156429 | −0.0782144 | − | 0.996937i | \(-0.524922\pi\) | ||||
−0.0782144 | + | 0.996937i | \(0.524922\pi\) | |||||||
\(198\) | −1560.30 | −0.560029 | ||||||||
\(199\) | −108.519 | −0.0386567 | −0.0193283 | − | 0.999813i | \(-0.506153\pi\) | ||||
−0.0193283 | + | 0.999813i | \(0.506153\pi\) | |||||||
\(200\) | −40.2499 | −0.0142305 | ||||||||
\(201\) | −2765.40 | −0.970429 | ||||||||
\(202\) | −2169.15 | −0.755549 | ||||||||
\(203\) | 2027.33 | 0.700939 | ||||||||
\(204\) | −5611.64 | −1.92595 | ||||||||
\(205\) | 1998.59 | 0.680916 | ||||||||
\(206\) | −2738.38 | −0.926175 | ||||||||
\(207\) | −1727.41 | −0.580015 | ||||||||
\(208\) | −529.425 | −0.176486 | ||||||||
\(209\) | 712.875 | 0.235936 | ||||||||
\(210\) | 2166.95 | 0.712065 | ||||||||
\(211\) | −1082.37 | −0.353144 | −0.176572 | − | 0.984288i | \(-0.556501\pi\) | ||||
−0.176572 | + | 0.984288i | \(0.556501\pi\) | |||||||
\(212\) | −1107.97 | −0.358944 | ||||||||
\(213\) | 6505.82 | 2.09282 | ||||||||
\(214\) | 2387.64 | 0.762691 | ||||||||
\(215\) | −464.250 | −0.147263 | ||||||||
\(216\) | 3888.66 | 1.22495 | ||||||||
\(217\) | 826.784 | 0.258644 | ||||||||
\(218\) | 1786.62 | 0.555069 | ||||||||
\(219\) | −1074.59 | −0.331570 | ||||||||
\(220\) | 473.800 | 0.145198 | ||||||||
\(221\) | −4594.00 | −1.39831 | ||||||||
\(222\) | −4347.22 | −1.31426 | ||||||||
\(223\) | −1619.44 | −0.486303 | −0.243151 | − | 0.969988i | \(-0.578181\pi\) | ||||
−0.243151 | + | 0.969988i | \(0.578181\pi\) | |||||||
\(224\) | −300.900 | −0.0897532 | ||||||||
\(225\) | 377.870 | 0.111961 | ||||||||
\(226\) | −3684.32 | −1.08441 | ||||||||
\(227\) | 6746.10 | 1.97249 | 0.986244 | − | 0.165299i | \(-0.0528589\pi\) | ||||
0.986244 | + | 0.165299i | \(0.0528589\pi\) | |||||||
\(228\) | −2773.86 | −0.805717 | ||||||||
\(229\) | 1192.63 | 0.344155 | 0.172077 | − | 0.985083i | \(-0.444952\pi\) | ||||
0.172077 | + | 0.985083i | \(0.444952\pi\) | |||||||
\(230\) | 524.544 | 0.150380 | ||||||||
\(231\) | −986.975 | −0.281118 | ||||||||
\(232\) | −1724.81 | −0.488101 | ||||||||
\(233\) | −2860.16 | −0.804187 | −0.402093 | − | 0.915599i | \(-0.631717\pi\) | ||||
−0.402093 | + | 0.915599i | \(0.631717\pi\) | |||||||
\(234\) | 4970.29 | 1.38854 | ||||||||
\(235\) | 4621.06 | 1.28274 | ||||||||
\(236\) | 1174.20 | 0.323873 | ||||||||
\(237\) | −607.134 | −0.166403 | ||||||||
\(238\) | −2611.01 | −0.711121 | ||||||||
\(239\) | −594.373 | −0.160865 | −0.0804327 | − | 0.996760i | \(-0.525630\pi\) | ||||
−0.0804327 | + | 0.996760i | \(0.525630\pi\) | |||||||
\(240\) | −1843.60 | −0.495849 | ||||||||
\(241\) | 3930.15 | 1.05047 | 0.525234 | − | 0.850958i | \(-0.323978\pi\) | ||||
0.525234 | + | 0.850958i | \(0.323978\pi\) | |||||||
\(242\) | 2446.20 | 0.649784 | ||||||||
\(243\) | −16016.5 | −4.22824 | ||||||||
\(244\) | −1802.92 | −0.473035 | ||||||||
\(245\) | −2903.02 | −0.757009 | ||||||||
\(246\) | 3542.04 | 0.918017 | ||||||||
\(247\) | −2270.84 | −0.584980 | ||||||||
\(248\) | −703.412 | −0.180108 | ||||||||
\(249\) | 3767.82 | 0.958938 | ||||||||
\(250\) | 2736.04 | 0.692169 | ||||||||
\(251\) | 2122.07 | 0.533641 | 0.266821 | − | 0.963746i | \(-0.414027\pi\) | ||||
0.266821 | + | 0.963746i | \(0.414027\pi\) | |||||||
\(252\) | 2824.87 | 0.706152 | ||||||||
\(253\) | −238.913 | −0.0593688 | ||||||||
\(254\) | −1198.72 | −0.296120 | ||||||||
\(255\) | −15997.5 | −3.92865 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1143.68 | 0.277591 | 0.138795 | − | 0.990321i | \(-0.455677\pi\) | ||||
0.138795 | + | 0.990321i | \(0.455677\pi\) | |||||||
\(258\) | −822.775 | −0.198541 | ||||||||
\(259\) | −2022.70 | −0.485268 | ||||||||
\(260\) | −1509.27 | −0.360005 | ||||||||
\(261\) | 16192.7 | 3.84024 | ||||||||
\(262\) | 1120.27 | 0.264163 | ||||||||
\(263\) | −947.534 | −0.222158 | −0.111079 | − | 0.993812i | \(-0.535431\pi\) | ||||
−0.111079 | + | 0.993812i | \(0.535431\pi\) | |||||||
\(264\) | 839.700 | 0.195757 | ||||||||
\(265\) | −3158.59 | −0.732192 | ||||||||
\(266\) | −1290.64 | −0.297496 | ||||||||
\(267\) | 5496.41 | 1.25983 | ||||||||
\(268\) | 1094.70 | 0.249513 | ||||||||
\(269\) | 3217.70 | 0.729317 | 0.364659 | − | 0.931141i | \(-0.381186\pi\) | ||||
0.364659 | + | 0.931141i | \(0.381186\pi\) | |||||||
\(270\) | 11085.7 | 2.49872 | ||||||||
\(271\) | −7284.05 | −1.63275 | −0.816374 | − | 0.577524i | \(-0.804019\pi\) | ||||
−0.816374 | + | 0.577524i | \(0.804019\pi\) | |||||||
\(272\) | 2221.40 | 0.495192 | ||||||||
\(273\) | 3143.98 | 0.697004 | ||||||||
\(274\) | 4223.38 | 0.931182 | ||||||||
\(275\) | 52.2620 | 0.0114601 | ||||||||
\(276\) | 929.631 | 0.202744 | ||||||||
\(277\) | 2524.08 | 0.547498 | 0.273749 | − | 0.961801i | \(-0.411736\pi\) | ||||
0.273749 | + | 0.961801i | \(0.411736\pi\) | |||||||
\(278\) | 1889.90 | 0.407730 | ||||||||
\(279\) | 6603.70 | 1.41704 | ||||||||
\(280\) | −857.800 | −0.183083 | ||||||||
\(281\) | −6277.44 | −1.33267 | −0.666336 | − | 0.745652i | \(-0.732138\pi\) | ||||
−0.666336 | + | 0.745652i | \(0.732138\pi\) | |||||||
\(282\) | 8189.75 | 1.72941 | ||||||||
\(283\) | −8.34415 | −0.00175268 | −0.000876340 | − | 1.00000i | \(-0.500279\pi\) | ||||
−0.000876340 | 1.00000i | \(0.500279\pi\) | ||||||||
\(284\) | −2575.37 | −0.538099 | ||||||||
\(285\) | −7907.67 | −1.64354 | ||||||||
\(286\) | 687.426 | 0.142127 | ||||||||
\(287\) | 1648.06 | 0.338961 | ||||||||
\(288\) | −2403.35 | −0.491732 | ||||||||
\(289\) | 14362.8 | 2.92344 | ||||||||
\(290\) | −4917.06 | −0.995655 | ||||||||
\(291\) | −5567.11 | −1.12148 | ||||||||
\(292\) | 425.381 | 0.0852519 | ||||||||
\(293\) | 3075.15 | 0.613147 | 0.306573 | − | 0.951847i | \(-0.400818\pi\) | ||||
0.306573 | + | 0.951847i | \(0.400818\pi\) | |||||||
\(294\) | −5144.93 | −1.02061 | ||||||||
\(295\) | 3347.39 | 0.660652 | ||||||||
\(296\) | 1720.87 | 0.337918 | ||||||||
\(297\) | −5049.19 | −0.986476 | ||||||||
\(298\) | 4960.94 | 0.964360 | ||||||||
\(299\) | 761.048 | 0.147199 | ||||||||
\(300\) | −203.357 | −0.0391360 | ||||||||
\(301\) | −382.825 | −0.0733078 | ||||||||
\(302\) | −2329.07 | −0.443784 | ||||||||
\(303\) | −10959.3 | −2.07787 | ||||||||
\(304\) | 1098.05 | 0.207163 | ||||||||
\(305\) | −5139.74 | −0.964921 | ||||||||
\(306\) | −20854.7 | −3.89602 | ||||||||
\(307\) | −1039.90 | −0.193323 | −0.0966616 | − | 0.995317i | \(-0.530816\pi\) | ||||
−0.0966616 | + | 0.995317i | \(0.530816\pi\) | |||||||
\(308\) | 390.700 | 0.0722799 | ||||||||
\(309\) | −13835.2 | −2.54712 | ||||||||
\(310\) | −2005.27 | −0.367393 | ||||||||
\(311\) | 5917.12 | 1.07887 | 0.539436 | − | 0.842027i | \(-0.318638\pi\) | ||||
0.539436 | + | 0.842027i | \(0.318638\pi\) | |||||||
\(312\) | −2674.84 | −0.485362 | ||||||||
\(313\) | 2581.67 | 0.466213 | 0.233107 | − | 0.972451i | \(-0.425111\pi\) | ||||
0.233107 | + | 0.972451i | \(0.425111\pi\) | |||||||
\(314\) | 3050.53 | 0.548253 | ||||||||
\(315\) | 8053.10 | 1.44045 | ||||||||
\(316\) | 240.338 | 0.0427850 | ||||||||
\(317\) | 7203.26 | 1.27626 | 0.638132 | − | 0.769927i | \(-0.279708\pi\) | ||||
0.638132 | + | 0.769927i | \(0.279708\pi\) | |||||||
\(318\) | −5597.87 | −0.987147 | ||||||||
\(319\) | 2239.56 | 0.393076 | ||||||||
\(320\) | 729.800 | 0.127491 | ||||||||
\(321\) | 12063.2 | 2.09751 | ||||||||
\(322\) | 432.544 | 0.0748594 | ||||||||
\(323\) | 9528.16 | 1.64136 | ||||||||
\(324\) | 11535.5 | 1.97797 | ||||||||
\(325\) | −166.479 | −0.0284142 | ||||||||
\(326\) | −3888.93 | −0.660700 | ||||||||
\(327\) | 9026.61 | 1.52652 | ||||||||
\(328\) | −1402.14 | −0.236037 | ||||||||
\(329\) | 3810.57 | 0.638552 | ||||||||
\(330\) | 2393.80 | 0.399316 | ||||||||
\(331\) | −11007.6 | −1.82789 | −0.913943 | − | 0.405843i | \(-0.866978\pi\) | ||||
−0.913943 | + | 0.405843i | \(0.866978\pi\) | |||||||
\(332\) | −1491.51 | −0.246558 | ||||||||
\(333\) | −16155.7 | −2.65864 | ||||||||
\(334\) | 5265.16 | 0.862565 | ||||||||
\(335\) | 3120.75 | 0.508969 | ||||||||
\(336\) | −1520.25 | −0.246835 | ||||||||
\(337\) | 1436.15 | 0.232143 | 0.116072 | − | 0.993241i | \(-0.462970\pi\) | ||||
0.116072 | + | 0.993241i | \(0.462970\pi\) | |||||||
\(338\) | 2204.23 | 0.354716 | ||||||||
\(339\) | −18614.5 | −2.98230 | ||||||||
\(340\) | 6332.72 | 1.01012 | ||||||||
\(341\) | 913.337 | 0.145044 | ||||||||
\(342\) | −10308.6 | −1.62990 | ||||||||
\(343\) | −5619.13 | −0.884561 | ||||||||
\(344\) | 325.700 | 0.0510482 | ||||||||
\(345\) | 2650.17 | 0.413567 | ||||||||
\(346\) | −2379.25 | −0.369680 | ||||||||
\(347\) | 4296.61 | 0.664710 | 0.332355 | − | 0.943154i | \(-0.392157\pi\) | ||||
0.332355 | + | 0.943154i | \(0.392157\pi\) | |||||||
\(348\) | −8714.34 | −1.34235 | ||||||||
\(349\) | 3496.28 | 0.536250 | 0.268125 | − | 0.963384i | \(-0.413596\pi\) | ||||
0.268125 | + | 0.963384i | \(0.413596\pi\) | |||||||
\(350\) | −94.6188 | −0.0144502 | ||||||||
\(351\) | 16084.0 | 2.44587 | ||||||||
\(352\) | −332.400 | −0.0503323 | ||||||||
\(353\) | 2884.90 | 0.434980 | 0.217490 | − | 0.976063i | \(-0.430213\pi\) | ||||
0.217490 | + | 0.976063i | \(0.430213\pi\) | |||||||
\(354\) | 5932.46 | 0.890697 | ||||||||
\(355\) | −7341.81 | −1.09764 | ||||||||
\(356\) | −2175.79 | −0.323923 | ||||||||
\(357\) | −13191.7 | −1.95569 | ||||||||
\(358\) | 3097.94 | 0.457350 | ||||||||
\(359\) | −9774.21 | −1.43694 | −0.718472 | − | 0.695556i | \(-0.755158\pi\) | ||||
−0.718472 | + | 0.695556i | \(0.755158\pi\) | |||||||
\(360\) | −6851.42 | −1.00306 | ||||||||
\(361\) | −2149.18 | −0.313337 | ||||||||
\(362\) | 3816.77 | 0.554157 | ||||||||
\(363\) | 12359.0 | 1.78700 | ||||||||
\(364\) | −1244.56 | −0.179211 | ||||||||
\(365\) | 1212.67 | 0.173901 | ||||||||
\(366\) | −9108.99 | −1.30091 | ||||||||
\(367\) | −5245.42 | −0.746073 | −0.373036 | − | 0.927817i | \(-0.621683\pi\) | ||||
−0.373036 | + | 0.927817i | \(0.621683\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | 13163.4 | 1.85707 | ||||||||
\(370\) | 4905.84 | 0.689304 | ||||||||
\(371\) | −2604.61 | −0.364486 | ||||||||
\(372\) | −3553.88 | −0.495323 | ||||||||
\(373\) | −12320.9 | −1.71032 | −0.855160 | − | 0.518364i | \(-0.826541\pi\) | ||||
−0.855160 | + | 0.518364i | \(0.826541\pi\) | |||||||
\(374\) | −2884.35 | −0.398787 | ||||||||
\(375\) | 13823.4 | 1.90357 | ||||||||
\(376\) | −3241.96 | −0.444658 | ||||||||
\(377\) | −7134.05 | −0.974595 | ||||||||
\(378\) | 9141.39 | 1.24387 | ||||||||
\(379\) | −1216.68 | −0.164899 | −0.0824495 | − | 0.996595i | \(-0.526274\pi\) | ||||
−0.0824495 | + | 0.996595i | \(0.526274\pi\) | |||||||
\(380\) | 3130.30 | 0.422582 | ||||||||
\(381\) | −6056.35 | −0.814374 | ||||||||
\(382\) | −705.250 | −0.0944600 | ||||||||
\(383\) | −3989.13 | −0.532206 | −0.266103 | − | 0.963945i | \(-0.585736\pi\) | ||||
−0.266103 | + | 0.963945i | \(0.585736\pi\) | |||||||
\(384\) | 1293.40 | 0.171884 | ||||||||
\(385\) | 1113.80 | 0.147440 | ||||||||
\(386\) | 2828.56 | 0.372979 | ||||||||
\(387\) | −3057.70 | −0.401632 | ||||||||
\(388\) | 2203.78 | 0.288350 | ||||||||
\(389\) | 15077.7 | 1.96522 | 0.982608 | − | 0.185693i | \(-0.0594530\pi\) | ||||
0.982608 | + | 0.185693i | \(0.0594530\pi\) | |||||||
\(390\) | −7625.37 | −0.990066 | ||||||||
\(391\) | −3193.26 | −0.413018 | ||||||||
\(392\) | 2036.65 | 0.262414 | ||||||||
\(393\) | 5660.00 | 0.726486 | ||||||||
\(394\) | 865.060 | 0.110612 | ||||||||
\(395\) | 685.150 | 0.0872750 | ||||||||
\(396\) | 3120.60 | 0.396000 | ||||||||
\(397\) | −12767.4 | −1.61405 | −0.807026 | − | 0.590515i | \(-0.798925\pi\) | ||||
−0.807026 | + | 0.590515i | \(0.798925\pi\) | |||||||
\(398\) | 217.037 | 0.0273344 | ||||||||
\(399\) | −6520.74 | −0.818159 | ||||||||
\(400\) | 80.4999 | 0.0100625 | ||||||||
\(401\) | −8846.67 | −1.10170 | −0.550850 | − | 0.834604i | \(-0.685696\pi\) | ||||
−0.550850 | + | 0.834604i | \(0.685696\pi\) | |||||||
\(402\) | 5530.80 | 0.686197 | ||||||||
\(403\) | −2909.41 | −0.359623 | ||||||||
\(404\) | 4338.30 | 0.534254 | ||||||||
\(405\) | 32885.3 | 4.03478 | ||||||||
\(406\) | −4054.66 | −0.495638 | ||||||||
\(407\) | −2234.45 | −0.272132 | ||||||||
\(408\) | 11223.3 | 1.36185 | ||||||||
\(409\) | −3945.27 | −0.476970 | −0.238485 | − | 0.971146i | \(-0.576651\pi\) | ||||
−0.238485 | + | 0.971146i | \(0.576651\pi\) | |||||||
\(410\) | −3997.19 | −0.481481 | ||||||||
\(411\) | 21338.0 | 2.56089 | ||||||||
\(412\) | 5476.76 | 0.654905 | ||||||||
\(413\) | 2760.29 | 0.328874 | ||||||||
\(414\) | 3454.82 | 0.410133 | ||||||||
\(415\) | −4251.97 | −0.502943 | ||||||||
\(416\) | 1058.85 | 0.124794 | ||||||||
\(417\) | 9548.44 | 1.12132 | ||||||||
\(418\) | −1425.75 | −0.166832 | ||||||||
\(419\) | 13937.2 | 1.62500 | 0.812502 | − | 0.582958i | \(-0.198105\pi\) | ||||
0.812502 | + | 0.582958i | \(0.198105\pi\) | |||||||
\(420\) | −4333.90 | −0.503506 | ||||||||
\(421\) | −2471.55 | −0.286119 | −0.143059 | − | 0.989714i | \(-0.545694\pi\) | ||||
−0.143059 | + | 0.989714i | \(0.545694\pi\) | |||||||
\(422\) | 2164.74 | 0.249710 | ||||||||
\(423\) | 30435.8 | 3.49844 | ||||||||
\(424\) | 2215.95 | 0.253811 | ||||||||
\(425\) | 698.525 | 0.0797257 | ||||||||
\(426\) | −13011.6 | −1.47985 | ||||||||
\(427\) | −4238.28 | −0.480339 | ||||||||
\(428\) | −4775.29 | −0.539304 | ||||||||
\(429\) | 3473.11 | 0.390870 | ||||||||
\(430\) | 928.500 | 0.104131 | ||||||||
\(431\) | 7340.81 | 0.820404 | 0.410202 | − | 0.911995i | \(-0.365458\pi\) | ||||
0.410202 | + | 0.911995i | \(0.365458\pi\) | |||||||
\(432\) | −7777.32 | −0.866173 | ||||||||
\(433\) | −8838.13 | −0.980909 | −0.490455 | − | 0.871467i | \(-0.663169\pi\) | ||||
−0.490455 | + | 0.871467i | \(0.663169\pi\) | |||||||
\(434\) | −1653.57 | −0.182889 | ||||||||
\(435\) | −24842.7 | −2.73820 | ||||||||
\(436\) | −3573.24 | −0.392493 | ||||||||
\(437\) | −1578.45 | −0.172786 | ||||||||
\(438\) | 2149.17 | 0.234455 | ||||||||
\(439\) | −10403.7 | −1.13107 | −0.565534 | − | 0.824725i | \(-0.691330\pi\) | ||||
−0.565534 | + | 0.824725i | \(0.691330\pi\) | |||||||
\(440\) | −947.600 | −0.102671 | ||||||||
\(441\) | −19120.2 | −2.06460 | ||||||||
\(442\) | 9188.01 | 0.988753 | ||||||||
\(443\) | −4415.27 | −0.473535 | −0.236767 | − | 0.971566i | \(-0.576088\pi\) | ||||
−0.236767 | + | 0.971566i | \(0.576088\pi\) | |||||||
\(444\) | 8694.45 | 0.929325 | ||||||||
\(445\) | −6202.69 | −0.660755 | ||||||||
\(446\) | 3238.88 | 0.343868 | ||||||||
\(447\) | 25064.4 | 2.65213 | ||||||||
\(448\) | 601.800 | 0.0634651 | ||||||||
\(449\) | 3711.34 | 0.390087 | 0.195044 | − | 0.980795i | \(-0.437515\pi\) | ||||
0.195044 | + | 0.980795i | \(0.437515\pi\) | |||||||
\(450\) | −755.740 | −0.0791687 | ||||||||
\(451\) | 1820.59 | 0.190085 | ||||||||
\(452\) | 7368.65 | 0.766797 | ||||||||
\(453\) | −11767.2 | −1.22047 | ||||||||
\(454\) | −13492.2 | −1.39476 | ||||||||
\(455\) | −3547.97 | −0.365564 | ||||||||
\(456\) | 5547.72 | 0.569728 | ||||||||
\(457\) | 15711.9 | 1.60825 | 0.804124 | − | 0.594461i | \(-0.202635\pi\) | ||||
0.804124 | + | 0.594461i | \(0.202635\pi\) | |||||||
\(458\) | −2385.27 | −0.243354 | ||||||||
\(459\) | −67486.5 | −6.86275 | ||||||||
\(460\) | −1049.09 | −0.106335 | ||||||||
\(461\) | 3177.04 | 0.320975 | 0.160488 | − | 0.987038i | \(-0.448693\pi\) | ||||
0.160488 | + | 0.987038i | \(0.448693\pi\) | |||||||
\(462\) | 1973.95 | 0.198780 | ||||||||
\(463\) | −14774.8 | −1.48303 | −0.741516 | − | 0.670935i | \(-0.765893\pi\) | ||||
−0.741516 | + | 0.670935i | \(0.765893\pi\) | |||||||
\(464\) | 3449.62 | 0.345140 | ||||||||
\(465\) | −10131.3 | −1.01039 | ||||||||
\(466\) | 5720.33 | 0.568646 | ||||||||
\(467\) | −2408.12 | −0.238618 | −0.119309 | − | 0.992857i | \(-0.538068\pi\) | ||||
−0.119309 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(468\) | −9940.58 | −0.981845 | ||||||||
\(469\) | 2573.40 | 0.253366 | ||||||||
\(470\) | −9242.12 | −0.907037 | ||||||||
\(471\) | 15412.3 | 1.50778 | ||||||||
\(472\) | −2348.40 | −0.229012 | ||||||||
\(473\) | −422.901 | −0.0411100 | ||||||||
\(474\) | 1214.27 | 0.117665 | ||||||||
\(475\) | 345.285 | 0.0333532 | ||||||||
\(476\) | 5222.02 | 0.502838 | ||||||||
\(477\) | −20803.5 | −1.99691 | ||||||||
\(478\) | 1188.75 | 0.113749 | ||||||||
\(479\) | −12528.3 | −1.19506 | −0.597528 | − | 0.801848i | \(-0.703850\pi\) | ||||
−0.597528 | + | 0.801848i | \(0.703850\pi\) | |||||||
\(480\) | 3687.20 | 0.350618 | ||||||||
\(481\) | 7117.77 | 0.674724 | ||||||||
\(482\) | −7860.29 | −0.742794 | ||||||||
\(483\) | 2185.36 | 0.205874 | ||||||||
\(484\) | −4892.40 | −0.459466 | ||||||||
\(485\) | 6282.48 | 0.588191 | ||||||||
\(486\) | 32033.1 | 2.98982 | ||||||||
\(487\) | 16798.6 | 1.56307 | 0.781537 | − | 0.623858i | \(-0.214436\pi\) | ||||
0.781537 | + | 0.623858i | \(0.214436\pi\) | |||||||
\(488\) | 3605.85 | 0.334486 | ||||||||
\(489\) | −19648.2 | −1.81702 | ||||||||
\(490\) | 5806.04 | 0.535286 | ||||||||
\(491\) | −18007.7 | −1.65514 | −0.827571 | − | 0.561361i | \(-0.810278\pi\) | ||||
−0.827571 | + | 0.561361i | \(0.810278\pi\) | |||||||
\(492\) | −7084.08 | −0.649136 | ||||||||
\(493\) | 29933.6 | 2.73456 | ||||||||
\(494\) | 4541.68 | 0.413643 | ||||||||
\(495\) | 8896.15 | 0.807782 | ||||||||
\(496\) | 1406.82 | 0.127355 | ||||||||
\(497\) | −6054.13 | −0.546408 | ||||||||
\(498\) | −7535.63 | −0.678072 | ||||||||
\(499\) | 696.627 | 0.0624956 | 0.0312478 | − | 0.999512i | \(-0.490052\pi\) | ||||
0.0312478 | + | 0.999512i | \(0.490052\pi\) | |||||||
\(500\) | −5472.07 | −0.489437 | ||||||||
\(501\) | 26601.4 | 2.37218 | ||||||||
\(502\) | −4244.14 | −0.377341 | ||||||||
\(503\) | −20469.0 | −1.81444 | −0.907222 | − | 0.420652i | \(-0.861801\pi\) | ||||
−0.907222 | + | 0.420652i | \(0.861801\pi\) | |||||||
\(504\) | −5649.75 | −0.499325 | ||||||||
\(505\) | 12367.5 | 1.08980 | ||||||||
\(506\) | 477.825 | 0.0419801 | ||||||||
\(507\) | 11136.5 | 0.975523 | ||||||||
\(508\) | 2397.44 | 0.209389 | ||||||||
\(509\) | 13437.5 | 1.17015 | 0.585073 | − | 0.810980i | \(-0.301066\pi\) | ||||
0.585073 | + | 0.810980i | \(0.301066\pi\) | |||||||
\(510\) | 31995.1 | 2.77797 | ||||||||
\(511\) | 999.978 | 0.0865683 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −33358.9 | −2.87102 | ||||||||
\(514\) | −2287.36 | −0.196286 | ||||||||
\(515\) | 15613.0 | 1.33591 | ||||||||
\(516\) | 1645.55 | 0.140390 | ||||||||
\(517\) | 4209.49 | 0.358091 | ||||||||
\(518\) | 4045.40 | 0.343136 | ||||||||
\(519\) | −12020.8 | −1.01667 | ||||||||
\(520\) | 3018.55 | 0.254562 | ||||||||
\(521\) | −4917.10 | −0.413478 | −0.206739 | − | 0.978396i | \(-0.566285\pi\) | ||||
−0.206739 | + | 0.978396i | \(0.566285\pi\) | |||||||
\(522\) | −32385.4 | −2.71546 | ||||||||
\(523\) | 15959.4 | 1.33434 | 0.667168 | − | 0.744908i | \(-0.267507\pi\) | ||||
0.667168 | + | 0.744908i | \(0.267507\pi\) | |||||||
\(524\) | −2240.54 | −0.186791 | ||||||||
\(525\) | −478.047 | −0.0397403 | ||||||||
\(526\) | 1895.07 | 0.157089 | ||||||||
\(527\) | 12207.5 | 1.00905 | ||||||||
\(528\) | −1679.40 | −0.138421 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 6317.19 | 0.517738 | ||||||||
\(531\) | 22047.0 | 1.80180 | ||||||||
\(532\) | 2581.27 | 0.210362 | ||||||||
\(533\) | −5799.43 | −0.471297 | ||||||||
\(534\) | −10992.8 | −0.890835 | ||||||||
\(535\) | −13613.3 | −1.10010 | ||||||||
\(536\) | −2189.40 | −0.176432 | ||||||||
\(537\) | 15651.9 | 1.25778 | ||||||||
\(538\) | −6435.39 | −0.515705 | ||||||||
\(539\) | −2644.46 | −0.211327 | ||||||||
\(540\) | −22171.4 | −1.76687 | ||||||||
\(541\) | −8018.32 | −0.637217 | −0.318608 | − | 0.947886i | \(-0.603216\pi\) | ||||
−0.318608 | + | 0.947886i | \(0.603216\pi\) | |||||||
\(542\) | 14568.1 | 1.15453 | ||||||||
\(543\) | 19283.6 | 1.52401 | ||||||||
\(544\) | −4442.80 | −0.350153 | ||||||||
\(545\) | −10186.5 | −0.800628 | ||||||||
\(546\) | −6287.96 | −0.492857 | ||||||||
\(547\) | 13255.0 | 1.03609 | 0.518047 | − | 0.855352i | \(-0.326659\pi\) | ||||
0.518047 | + | 0.855352i | \(0.326659\pi\) | |||||||
\(548\) | −8446.76 | −0.658445 | ||||||||
\(549\) | −33852.0 | −2.63164 | ||||||||
\(550\) | −104.524 | −0.00810349 | ||||||||
\(551\) | 14796.3 | 1.14400 | ||||||||
\(552\) | −1859.26 | −0.143361 | ||||||||
\(553\) | 564.981 | 0.0434456 | ||||||||
\(554\) | −5048.15 | −0.387140 | ||||||||
\(555\) | 24786.0 | 1.89569 | ||||||||
\(556\) | −3779.81 | −0.288308 | ||||||||
\(557\) | −10410.3 | −0.791918 | −0.395959 | − | 0.918268i | \(-0.629588\pi\) | ||||
−0.395959 | + | 0.918268i | \(0.629588\pi\) | |||||||
\(558\) | −13207.4 | −1.00200 | ||||||||
\(559\) | 1347.14 | 0.101928 | ||||||||
\(560\) | 1715.60 | 0.129460 | ||||||||
\(561\) | −14572.7 | −1.09672 | ||||||||
\(562\) | 12554.9 | 0.942341 | ||||||||
\(563\) | 19009.9 | 1.42304 | 0.711520 | − | 0.702666i | \(-0.248007\pi\) | ||||
0.711520 | + | 0.702666i | \(0.248007\pi\) | |||||||
\(564\) | −16379.5 | −1.22288 | ||||||||
\(565\) | 21006.4 | 1.56415 | ||||||||
\(566\) | 16.6883 | 0.00123933 | ||||||||
\(567\) | 27117.6 | 2.00852 | ||||||||
\(568\) | 5150.74 | 0.380493 | ||||||||
\(569\) | 11671.7 | 0.859934 | 0.429967 | − | 0.902845i | \(-0.358525\pi\) | ||||
0.429967 | + | 0.902845i | \(0.358525\pi\) | |||||||
\(570\) | 15815.3 | 1.16216 | ||||||||
\(571\) | −21359.8 | −1.56546 | −0.782732 | − | 0.622359i | \(-0.786174\pi\) | ||||
−0.782732 | + | 0.622359i | \(0.786174\pi\) | |||||||
\(572\) | −1374.85 | −0.100499 | ||||||||
\(573\) | −3563.16 | −0.259779 | ||||||||
\(574\) | −3296.12 | −0.239682 | ||||||||
\(575\) | −115.719 | −0.00839269 | ||||||||
\(576\) | 4806.70 | 0.347707 | ||||||||
\(577\) | 13416.4 | 0.967996 | 0.483998 | − | 0.875069i | \(-0.339184\pi\) | ||||
0.483998 | + | 0.875069i | \(0.339184\pi\) | |||||||
\(578\) | −28725.7 | −2.06718 | ||||||||
\(579\) | 14290.9 | 1.02575 | ||||||||
\(580\) | 9834.12 | 0.704034 | ||||||||
\(581\) | −3506.22 | −0.250366 | ||||||||
\(582\) | 11134.2 | 0.793005 | ||||||||
\(583\) | −2877.27 | −0.204399 | ||||||||
\(584\) | −850.762 | −0.0602822 | ||||||||
\(585\) | −28338.4 | −2.00282 | ||||||||
\(586\) | −6150.29 | −0.433560 | ||||||||
\(587\) | −11542.3 | −0.811586 | −0.405793 | − | 0.913965i | \(-0.633005\pi\) | ||||
−0.405793 | + | 0.913965i | \(0.633005\pi\) | |||||||
\(588\) | 10289.9 | 0.721678 | ||||||||
\(589\) | 6034.23 | 0.422133 | ||||||||
\(590\) | −6694.77 | −0.467152 | ||||||||
\(591\) | 4370.58 | 0.304199 | ||||||||
\(592\) | −3441.75 | −0.238944 | ||||||||
\(593\) | 3151.02 | 0.218207 | 0.109104 | − | 0.994030i | \(-0.465202\pi\) | ||||
0.109104 | + | 0.994030i | \(0.465202\pi\) | |||||||
\(594\) | 10098.4 | 0.697544 | ||||||||
\(595\) | 14886.8 | 1.02572 | ||||||||
\(596\) | −9921.87 | −0.681906 | ||||||||
\(597\) | 1096.55 | 0.0751736 | ||||||||
\(598\) | −1522.10 | −0.104086 | ||||||||
\(599\) | −293.676 | −0.0200322 | −0.0100161 | − | 0.999950i | \(-0.503188\pi\) | ||||
−0.0100161 | + | 0.999950i | \(0.503188\pi\) | |||||||
\(600\) | 406.713 | 0.0276733 | ||||||||
\(601\) | −19297.6 | −1.30976 | −0.654881 | − | 0.755732i | \(-0.727281\pi\) | ||||
−0.654881 | + | 0.755732i | \(0.727281\pi\) | |||||||
\(602\) | 765.650 | 0.0518365 | ||||||||
\(603\) | 20554.3 | 1.38812 | ||||||||
\(604\) | 4658.13 | 0.313802 | ||||||||
\(605\) | −13947.2 | −0.937244 | ||||||||
\(606\) | 21918.6 | 1.46928 | ||||||||
\(607\) | −24573.1 | −1.64315 | −0.821573 | − | 0.570103i | \(-0.806903\pi\) | ||||
−0.821573 | + | 0.570103i | \(0.806903\pi\) | |||||||
\(608\) | −2196.10 | −0.146486 | ||||||||
\(609\) | −20485.5 | −1.36308 | ||||||||
\(610\) | 10279.5 | 0.682302 | ||||||||
\(611\) | −13409.2 | −0.887852 | ||||||||
\(612\) | 41709.4 | 2.75491 | ||||||||
\(613\) | 14171.5 | 0.933738 | 0.466869 | − | 0.884326i | \(-0.345382\pi\) | ||||
0.466869 | + | 0.884326i | \(0.345382\pi\) | |||||||
\(614\) | 2079.80 | 0.136700 | ||||||||
\(615\) | −20195.2 | −1.32414 | ||||||||
\(616\) | −781.400 | −0.0511096 | ||||||||
\(617\) | −3693.48 | −0.240995 | −0.120498 | − | 0.992714i | \(-0.538449\pi\) | ||||
−0.120498 | + | 0.992714i | \(0.538449\pi\) | |||||||
\(618\) | 27670.5 | 1.80108 | ||||||||
\(619\) | 29215.7 | 1.89705 | 0.948527 | − | 0.316697i | \(-0.102574\pi\) | ||||
0.948527 | + | 0.316697i | \(0.102574\pi\) | |||||||
\(620\) | 4010.55 | 0.259786 | ||||||||
\(621\) | 11179.9 | 0.722438 | ||||||||
\(622\) | −11834.2 | −0.762878 | ||||||||
\(623\) | −5114.80 | −0.328925 | ||||||||
\(624\) | 5349.67 | 0.343202 | ||||||||
\(625\) | −16228.6 | −1.03863 | ||||||||
\(626\) | −5163.34 | −0.329663 | ||||||||
\(627\) | −7203.38 | −0.458812 | ||||||||
\(628\) | −6101.06 | −0.387673 | ||||||||
\(629\) | −29865.2 | −1.89317 | ||||||||
\(630\) | −16106.2 | −1.01855 | ||||||||
\(631\) | −10216.8 | −0.644571 | −0.322286 | − | 0.946643i | \(-0.604451\pi\) | ||||
−0.322286 | + | 0.946643i | \(0.604451\pi\) | |||||||
\(632\) | −480.675 | −0.0302535 | ||||||||
\(633\) | 10937.0 | 0.686740 | ||||||||
\(634\) | −14406.5 | −0.902454 | ||||||||
\(635\) | 6834.59 | 0.427122 | ||||||||
\(636\) | 11195.7 | 0.698019 | ||||||||
\(637\) | 8423.86 | 0.523964 | ||||||||
\(638\) | −4479.12 | −0.277947 | ||||||||
\(639\) | −48355.6 | −2.99361 | ||||||||
\(640\) | −1459.60 | −0.0901496 | ||||||||
\(641\) | 11330.1 | 0.698148 | 0.349074 | − | 0.937095i | \(-0.386496\pi\) | ||||
0.349074 | + | 0.937095i | \(0.386496\pi\) | |||||||
\(642\) | −24126.4 | −1.48317 | ||||||||
\(643\) | −18572.6 | −1.13908 | −0.569542 | − | 0.821962i | \(-0.692879\pi\) | ||||
−0.569542 | + | 0.821962i | \(0.692879\pi\) | |||||||
\(644\) | −865.087 | −0.0529336 | ||||||||
\(645\) | 4691.10 | 0.286375 | ||||||||
\(646\) | −19056.3 | −1.16062 | ||||||||
\(647\) | −13995.8 | −0.850436 | −0.425218 | − | 0.905091i | \(-0.639802\pi\) | ||||
−0.425218 | + | 0.905091i | \(0.639802\pi\) | |||||||
\(648\) | −23071.1 | −1.39864 | ||||||||
\(649\) | 3049.25 | 0.184428 | ||||||||
\(650\) | 332.958 | 0.0200918 | ||||||||
\(651\) | −8354.40 | −0.502972 | ||||||||
\(652\) | 7777.87 | 0.467185 | ||||||||
\(653\) | 20473.1 | 1.22691 | 0.613456 | − | 0.789729i | \(-0.289779\pi\) | ||||
0.613456 | + | 0.789729i | \(0.289779\pi\) | |||||||
\(654\) | −18053.2 | −1.07941 | ||||||||
\(655\) | −6387.30 | −0.381027 | ||||||||
\(656\) | 2804.28 | 0.166903 | ||||||||
\(657\) | 7987.03 | 0.474283 | ||||||||
\(658\) | −7621.14 | −0.451524 | ||||||||
\(659\) | −27951.8 | −1.65227 | −0.826135 | − | 0.563473i | \(-0.809465\pi\) | ||||
−0.826135 | + | 0.563473i | \(0.809465\pi\) | |||||||
\(660\) | −4787.60 | −0.282359 | ||||||||
\(661\) | 20698.3 | 1.21796 | 0.608980 | − | 0.793185i | \(-0.291579\pi\) | ||||
0.608980 | + | 0.793185i | \(0.291579\pi\) | |||||||
\(662\) | 22015.1 | 1.29251 | ||||||||
\(663\) | 46421.0 | 2.71922 | ||||||||
\(664\) | 2983.02 | 0.174343 | ||||||||
\(665\) | 7358.65 | 0.429107 | ||||||||
\(666\) | 32311.4 | 1.87994 | ||||||||
\(667\) | −4958.84 | −0.287866 | ||||||||
\(668\) | −10530.3 | −0.609926 | ||||||||
\(669\) | 16363.9 | 0.945688 | ||||||||
\(670\) | −6241.50 | −0.359896 | ||||||||
\(671\) | −4681.97 | −0.269367 | ||||||||
\(672\) | 3040.50 | 0.174538 | ||||||||
\(673\) | 28428.7 | 1.62830 | 0.814150 | − | 0.580654i | \(-0.197203\pi\) | ||||
0.814150 | + | 0.580654i | \(0.197203\pi\) | |||||||
\(674\) | −2872.31 | −0.164150 | ||||||||
\(675\) | −2445.60 | −0.139454 | ||||||||
\(676\) | −4408.46 | −0.250822 | ||||||||
\(677\) | −7179.44 | −0.407575 | −0.203787 | − | 0.979015i | \(-0.565325\pi\) | ||||
−0.203787 | + | 0.979015i | \(0.565325\pi\) | |||||||
\(678\) | 37228.9 | 2.10880 | ||||||||
\(679\) | 5180.59 | 0.292803 | ||||||||
\(680\) | −12665.4 | −0.714261 | ||||||||
\(681\) | −68167.3 | −3.83579 | ||||||||
\(682\) | −1826.67 | −0.102562 | ||||||||
\(683\) | 5146.87 | 0.288345 | 0.144172 | − | 0.989553i | \(-0.453948\pi\) | ||||
0.144172 | + | 0.989553i | \(0.453948\pi\) | |||||||
\(684\) | 20617.2 | 1.15251 | ||||||||
\(685\) | −24079.9 | −1.34313 | ||||||||
\(686\) | 11238.3 | 0.625479 | ||||||||
\(687\) | −12051.2 | −0.669260 | ||||||||
\(688\) | −651.400 | −0.0360965 | ||||||||
\(689\) | 9165.46 | 0.506787 | ||||||||
\(690\) | −5300.35 | −0.292436 | ||||||||
\(691\) | 29679.6 | 1.63396 | 0.816978 | − | 0.576669i | \(-0.195648\pi\) | ||||
0.816978 | + | 0.576669i | \(0.195648\pi\) | |||||||
\(692\) | 4758.50 | 0.261403 | ||||||||
\(693\) | 7335.85 | 0.402115 | ||||||||
\(694\) | −8593.23 | −0.470021 | ||||||||
\(695\) | −10775.4 | −0.588107 | ||||||||
\(696\) | 17428.7 | 0.949185 | ||||||||
\(697\) | 24333.7 | 1.32239 | ||||||||
\(698\) | −6992.55 | −0.379186 | ||||||||
\(699\) | 28901.1 | 1.56386 | ||||||||
\(700\) | 189.238 | 0.0102179 | ||||||||
\(701\) | 9627.78 | 0.518739 | 0.259370 | − | 0.965778i | \(-0.416485\pi\) | ||||
0.259370 | + | 0.965778i | \(0.416485\pi\) | |||||||
\(702\) | −32168.0 | −1.72949 | ||||||||
\(703\) | −14762.5 | −0.792006 | ||||||||
\(704\) | 664.800 | 0.0355903 | ||||||||
\(705\) | −46694.4 | −2.49449 | ||||||||
\(706\) | −5769.80 | −0.307577 | ||||||||
\(707\) | 10198.4 | 0.542504 | ||||||||
\(708\) | −11864.9 | −0.629818 | ||||||||
\(709\) | 11527.4 | 0.610606 | 0.305303 | − | 0.952255i | \(-0.401242\pi\) | ||||
0.305303 | + | 0.952255i | \(0.401242\pi\) | |||||||
\(710\) | 14683.6 | 0.776150 | ||||||||
\(711\) | 4512.62 | 0.238026 | ||||||||
\(712\) | 4351.57 | 0.229048 | ||||||||
\(713\) | −2022.31 | −0.106222 | ||||||||
\(714\) | 26383.5 | 1.38288 | ||||||||
\(715\) | −3919.40 | −0.205003 | ||||||||
\(716\) | −6195.88 | −0.323395 | ||||||||
\(717\) | 6005.96 | 0.312826 | ||||||||
\(718\) | 19548.4 | 1.01607 | ||||||||
\(719\) | −7837.87 | −0.406542 | −0.203271 | − | 0.979123i | \(-0.565157\pi\) | ||||
−0.203271 | + | 0.979123i | \(0.565157\pi\) | |||||||
\(720\) | 13702.8 | 0.709271 | ||||||||
\(721\) | 12874.7 | 0.665018 | ||||||||
\(722\) | 4298.36 | 0.221563 | ||||||||
\(723\) | −39712.9 | −2.04279 | ||||||||
\(724\) | −7633.54 | −0.391848 | ||||||||
\(725\) | 1084.74 | 0.0555674 | ||||||||
\(726\) | −24718.1 | −1.26360 | ||||||||
\(727\) | 726.845 | 0.0370800 | 0.0185400 | − | 0.999828i | \(-0.494098\pi\) | ||||
0.0185400 | + | 0.999828i | \(0.494098\pi\) | |||||||
\(728\) | 2489.12 | 0.126721 | ||||||||
\(729\) | 83977.2 | 4.26648 | ||||||||
\(730\) | −2425.34 | −0.122967 | ||||||||
\(731\) | −5652.42 | −0.285995 | ||||||||
\(732\) | 18218.0 | 0.919886 | ||||||||
\(733\) | −378.674 | −0.0190814 | −0.00954069 | − | 0.999954i | \(-0.503037\pi\) | ||||
−0.00954069 | + | 0.999954i | \(0.503037\pi\) | |||||||
\(734\) | 10490.8 | 0.527553 | ||||||||
\(735\) | 29334.1 | 1.47212 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 2842.80 | 0.142084 | ||||||||
\(738\) | −26326.8 | −1.31315 | ||||||||
\(739\) | 18952.9 | 0.943428 | 0.471714 | − | 0.881752i | \(-0.343636\pi\) | ||||
0.471714 | + | 0.881752i | \(0.343636\pi\) | |||||||
\(740\) | −9811.67 | −0.487411 | ||||||||
\(741\) | 22946.1 | 1.13758 | ||||||||
\(742\) | 5209.21 | 0.257731 | ||||||||
\(743\) | −19317.8 | −0.953838 | −0.476919 | − | 0.878947i | \(-0.658246\pi\) | ||||
−0.476919 | + | 0.878947i | \(0.658246\pi\) | |||||||
\(744\) | 7107.76 | 0.350246 | ||||||||
\(745\) | −28285.1 | −1.39099 | ||||||||
\(746\) | 24641.7 | 1.20938 | ||||||||
\(747\) | −28004.9 | −1.37168 | ||||||||
\(748\) | 5768.70 | 0.281985 | ||||||||
\(749\) | −11225.7 | −0.547632 | ||||||||
\(750\) | −27646.8 | −1.34602 | ||||||||
\(751\) | −25592.6 | −1.24353 | −0.621763 | − | 0.783206i | \(-0.713583\pi\) | ||||
−0.621763 | + | 0.783206i | \(0.713583\pi\) | |||||||
\(752\) | 6483.92 | 0.314421 | ||||||||
\(753\) | −21442.9 | −1.03774 | ||||||||
\(754\) | 14268.1 | 0.689143 | ||||||||
\(755\) | 13279.3 | 0.640111 | ||||||||
\(756\) | −18282.8 | −0.879548 | ||||||||
\(757\) | −36790.6 | −1.76642 | −0.883208 | − | 0.468981i | \(-0.844621\pi\) | ||||
−0.883208 | + | 0.468981i | \(0.844621\pi\) | |||||||
\(758\) | 2433.36 | 0.116601 | ||||||||
\(759\) | 2414.14 | 0.115451 | ||||||||
\(760\) | −6260.60 | −0.298810 | ||||||||
\(761\) | 2257.71 | 0.107545 | 0.0537726 | − | 0.998553i | \(-0.482875\pi\) | ||||
0.0537726 | + | 0.998553i | \(0.482875\pi\) | |||||||
\(762\) | 12112.7 | 0.575849 | ||||||||
\(763\) | −8399.90 | −0.398554 | ||||||||
\(764\) | 1410.50 | 0.0667933 | ||||||||
\(765\) | 118904. | 5.61960 | ||||||||
\(766\) | 7978.26 | 0.376327 | ||||||||
\(767\) | −9713.30 | −0.457271 | ||||||||
\(768\) | −2586.80 | −0.121540 | ||||||||
\(769\) | 6903.74 | 0.323739 | 0.161869 | − | 0.986812i | \(-0.448248\pi\) | ||||
0.161869 | + | 0.986812i | \(0.448248\pi\) | |||||||
\(770\) | −2227.60 | −0.104256 | ||||||||
\(771\) | −11556.5 | −0.539816 | ||||||||
\(772\) | −5657.12 | −0.263736 | ||||||||
\(773\) | −30096.1 | −1.40036 | −0.700182 | − | 0.713965i | \(-0.746898\pi\) | ||||
−0.700182 | + | 0.713965i | \(0.746898\pi\) | |||||||
\(774\) | 6115.40 | 0.283997 | ||||||||
\(775\) | 442.380 | 0.0205042 | ||||||||
\(776\) | −4407.55 | −0.203894 | ||||||||
\(777\) | 20438.7 | 0.943676 | ||||||||
\(778\) | −30155.4 | −1.38962 | ||||||||
\(779\) | 12028.3 | 0.553218 | ||||||||
\(780\) | 15250.7 | 0.700083 | ||||||||
\(781\) | −6687.91 | −0.306418 | ||||||||
\(782\) | 6386.52 | 0.292048 | ||||||||
\(783\) | −104800. | −4.78321 | ||||||||
\(784\) | −4073.30 | −0.185555 | ||||||||
\(785\) | −17392.8 | −0.790797 | ||||||||
\(786\) | −11320.0 | −0.513703 | ||||||||
\(787\) | −6753.37 | −0.305885 | −0.152943 | − | 0.988235i | \(-0.548875\pi\) | ||||
−0.152943 | + | 0.988235i | \(0.548875\pi\) | |||||||
\(788\) | −1730.12 | −0.0782144 | ||||||||
\(789\) | 9574.54 | 0.432018 | ||||||||
\(790\) | −1370.30 | −0.0617128 | ||||||||
\(791\) | 17322.1 | 0.778638 | ||||||||
\(792\) | −6241.20 | −0.280014 | ||||||||
\(793\) | 14914.3 | 0.667871 | ||||||||
\(794\) | 25534.9 | 1.14131 | ||||||||
\(795\) | 31916.6 | 1.42386 | ||||||||
\(796\) | −434.074 | −0.0193283 | ||||||||
\(797\) | 26666.0 | 1.18514 | 0.592570 | − | 0.805519i | \(-0.298113\pi\) | ||||
0.592570 | + | 0.805519i | \(0.298113\pi\) | |||||||
\(798\) | 13041.5 | 0.578526 | ||||||||
\(799\) | 56263.2 | 2.49118 | ||||||||
\(800\) | −161.000 | −0.00711525 | ||||||||
\(801\) | −40853.0 | −1.80208 | ||||||||
\(802\) | 17693.3 | 0.779019 | ||||||||
\(803\) | 1104.66 | 0.0485463 | ||||||||
\(804\) | −11061.6 | −0.485215 | ||||||||
\(805\) | −2466.17 | −0.107977 | ||||||||
\(806\) | 5818.82 | 0.254292 | ||||||||
\(807\) | −32513.8 | −1.41827 | ||||||||
\(808\) | −8676.60 | −0.377774 | ||||||||
\(809\) | −16430.2 | −0.714035 | −0.357018 | − | 0.934098i | \(-0.616206\pi\) | ||||
−0.357018 | + | 0.934098i | \(0.616206\pi\) | |||||||
\(810\) | −65770.7 | −2.85302 | ||||||||
\(811\) | −23394.6 | −1.01294 | −0.506470 | − | 0.862257i | \(-0.669050\pi\) | ||||
−0.506470 | + | 0.862257i | \(0.669050\pi\) | |||||||
\(812\) | 8109.31 | 0.350469 | ||||||||
\(813\) | 73603.0 | 3.17512 | ||||||||
\(814\) | 4468.90 | 0.192426 | ||||||||
\(815\) | 22173.0 | 0.952989 | ||||||||
\(816\) | −22446.5 | −0.962974 | ||||||||
\(817\) | −2794.02 | −0.119646 | ||||||||
\(818\) | 7890.54 | 0.337269 | ||||||||
\(819\) | −23368.1 | −0.997006 | ||||||||
\(820\) | 7994.37 | 0.340458 | ||||||||
\(821\) | 30615.7 | 1.30145 | 0.650727 | − | 0.759312i | \(-0.274464\pi\) | ||||
0.650727 | + | 0.759312i | \(0.274464\pi\) | |||||||
\(822\) | −42675.9 | −1.81082 | ||||||||
\(823\) | −959.744 | −0.0406496 | −0.0203248 | − | 0.999793i | \(-0.506470\pi\) | ||||
−0.0203248 | + | 0.999793i | \(0.506470\pi\) | |||||||
\(824\) | −10953.5 | −0.463087 | ||||||||
\(825\) | −528.092 | −0.0222858 | ||||||||
\(826\) | −5520.57 | −0.232549 | ||||||||
\(827\) | 37507.5 | 1.57710 | 0.788551 | − | 0.614970i | \(-0.210832\pi\) | ||||
0.788551 | + | 0.614970i | \(0.210832\pi\) | |||||||
\(828\) | −6909.63 | −0.290008 | ||||||||
\(829\) | −27029.9 | −1.13243 | −0.566217 | − | 0.824256i | \(-0.691594\pi\) | ||||
−0.566217 | + | 0.824256i | \(0.691594\pi\) | |||||||
\(830\) | 8503.95 | 0.355634 | ||||||||
\(831\) | −25505.0 | −1.06469 | ||||||||
\(832\) | −2117.70 | −0.0882428 | ||||||||
\(833\) | −35345.4 | −1.47016 | ||||||||
\(834\) | −19096.9 | −0.792891 | ||||||||
\(835\) | −30019.6 | −1.24416 | ||||||||
\(836\) | 2851.50 | 0.117968 | ||||||||
\(837\) | −42739.6 | −1.76499 | ||||||||
\(838\) | −27874.4 | −1.14905 | ||||||||
\(839\) | 38982.8 | 1.60409 | 0.802047 | − | 0.597261i | \(-0.203744\pi\) | ||||
0.802047 | + | 0.597261i | \(0.203744\pi\) | |||||||
\(840\) | 8667.80 | 0.356033 | ||||||||
\(841\) | 22095.0 | 0.905942 | ||||||||
\(842\) | 4943.10 | 0.202316 | ||||||||
\(843\) | 63431.6 | 2.59158 | ||||||||
\(844\) | −4329.48 | −0.176572 | ||||||||
\(845\) | −12567.5 | −0.511641 | ||||||||
\(846\) | −60871.6 | −2.47377 | ||||||||
\(847\) | −11501.0 | −0.466562 | ||||||||
\(848\) | −4431.90 | −0.179472 | ||||||||
\(849\) | 84.3151 | 0.00340835 | ||||||||
\(850\) | −1397.05 | −0.0563746 | ||||||||
\(851\) | 4947.52 | 0.199293 | ||||||||
\(852\) | 26023.3 | 1.04641 | ||||||||
\(853\) | −16634.7 | −0.667715 | −0.333858 | − | 0.942624i | \(-0.608350\pi\) | ||||
−0.333858 | + | 0.942624i | \(0.608350\pi\) | |||||||
\(854\) | 8476.56 | 0.339651 | ||||||||
\(855\) | 58775.0 | 2.35095 | ||||||||
\(856\) | 9550.57 | 0.381346 | ||||||||
\(857\) | −15234.4 | −0.607230 | −0.303615 | − | 0.952795i | \(-0.598194\pi\) | ||||
−0.303615 | + | 0.952795i | \(0.598194\pi\) | |||||||
\(858\) | −6946.22 | −0.276387 | ||||||||
\(859\) | 31925.2 | 1.26807 | 0.634036 | − | 0.773303i | \(-0.281397\pi\) | ||||
0.634036 | + | 0.773303i | \(0.281397\pi\) | |||||||
\(860\) | −1857.00 | −0.0736316 | ||||||||
\(861\) | −16653.1 | −0.659160 | ||||||||
\(862\) | −14681.6 | −0.580113 | ||||||||
\(863\) | −19518.9 | −0.769910 | −0.384955 | − | 0.922935i | \(-0.625783\pi\) | ||||
−0.384955 | + | 0.922935i | \(0.625783\pi\) | |||||||
\(864\) | 15554.6 | 0.612477 | ||||||||
\(865\) | 13565.4 | 0.533224 | ||||||||
\(866\) | 17676.3 | 0.693607 | ||||||||
\(867\) | −145132. | −5.68506 | ||||||||
\(868\) | 3307.14 | 0.129322 | ||||||||
\(869\) | 624.127 | 0.0243637 | ||||||||
\(870\) | 49685.4 | 1.93620 | ||||||||
\(871\) | −9055.65 | −0.352284 | ||||||||
\(872\) | 7146.48 | 0.277535 | ||||||||
\(873\) | 41378.5 | 1.60418 | ||||||||
\(874\) | 3156.89 | 0.122178 | ||||||||
\(875\) | −12863.6 | −0.496995 | ||||||||
\(876\) | −4298.34 | −0.165785 | ||||||||
\(877\) | 16853.3 | 0.648913 | 0.324456 | − | 0.945901i | \(-0.394819\pi\) | ||||
0.324456 | + | 0.945901i | \(0.394819\pi\) | |||||||
\(878\) | 20807.3 | 0.799786 | ||||||||
\(879\) | −31073.4 | −1.19235 | ||||||||
\(880\) | 1895.20 | 0.0725991 | ||||||||
\(881\) | 10834.3 | 0.414320 | 0.207160 | − | 0.978307i | \(-0.433578\pi\) | ||||
0.207160 | + | 0.978307i | \(0.433578\pi\) | |||||||
\(882\) | 38240.5 | 1.45989 | ||||||||
\(883\) | −23506.2 | −0.895863 | −0.447931 | − | 0.894068i | \(-0.647839\pi\) | ||||
−0.447931 | + | 0.894068i | \(0.647839\pi\) | |||||||
\(884\) | −18376.0 | −0.699154 | ||||||||
\(885\) | −33824.3 | −1.28474 | ||||||||
\(886\) | 8830.54 | 0.334840 | ||||||||
\(887\) | 34287.2 | 1.29792 | 0.648958 | − | 0.760824i | \(-0.275205\pi\) | ||||
0.648958 | + | 0.760824i | \(0.275205\pi\) | |||||||
\(888\) | −17388.9 | −0.657132 | ||||||||
\(889\) | 5635.87 | 0.212622 | ||||||||
\(890\) | 12405.4 | 0.467224 | ||||||||
\(891\) | 29956.4 | 1.12635 | ||||||||
\(892\) | −6477.75 | −0.243151 | ||||||||
\(893\) | 27811.2 | 1.04218 | ||||||||
\(894\) | −50128.7 | −1.87534 | ||||||||
\(895\) | −17663.1 | −0.659679 | ||||||||
\(896\) | −1203.60 | −0.0448766 | ||||||||
\(897\) | −7690.16 | −0.286251 | ||||||||
\(898\) | −7422.69 | −0.275833 | ||||||||
\(899\) | 18957.1 | 0.703287 | ||||||||
\(900\) | 1511.48 | 0.0559807 | ||||||||
\(901\) | −38457.1 | −1.42197 | ||||||||
\(902\) | −3641.18 | −0.134410 | ||||||||
\(903\) | 3868.33 | 0.142558 | ||||||||
\(904\) | −14737.3 | −0.542207 | ||||||||
\(905\) | −21761.5 | −0.799313 | ||||||||
\(906\) | 23534.5 | 0.863003 | ||||||||
\(907\) | 47930.9 | 1.75471 | 0.877354 | − | 0.479844i | \(-0.159307\pi\) | ||||
0.877354 | + | 0.479844i | \(0.159307\pi\) | |||||||
\(908\) | 26984.4 | 0.986244 | ||||||||
\(909\) | 81456.7 | 2.97222 | ||||||||
\(910\) | 7095.95 | 0.258493 | ||||||||
\(911\) | 9787.98 | 0.355972 | 0.177986 | − | 0.984033i | \(-0.443042\pi\) | ||||
0.177986 | + | 0.984033i | \(0.443042\pi\) | |||||||
\(912\) | −11095.4 | −0.402859 | ||||||||
\(913\) | −3873.27 | −0.140402 | ||||||||
\(914\) | −31423.7 | −1.13720 | ||||||||
\(915\) | 51935.5 | 1.87643 | ||||||||
\(916\) | 4770.54 | 0.172077 | ||||||||
\(917\) | −5267.03 | −0.189676 | ||||||||
\(918\) | 134973. | 4.85269 | ||||||||
\(919\) | 25226.6 | 0.905495 | 0.452748 | − | 0.891639i | \(-0.350444\pi\) | ||||
0.452748 | + | 0.891639i | \(0.350444\pi\) | |||||||
\(920\) | 2098.17 | 0.0751900 | ||||||||
\(921\) | 10507.9 | 0.375946 | ||||||||
\(922\) | −6354.08 | −0.226964 | ||||||||
\(923\) | 21304.1 | 0.759734 | ||||||||
\(924\) | −3947.90 | −0.140559 | ||||||||
\(925\) | −1082.27 | −0.0384700 | ||||||||
\(926\) | 29549.6 | 1.04866 | ||||||||
\(927\) | 102833. | 3.64344 | ||||||||
\(928\) | −6899.25 | −0.244051 | ||||||||
\(929\) | 38214.5 | 1.34960 | 0.674800 | − | 0.738001i | \(-0.264230\pi\) | ||||
0.674800 | + | 0.738001i | \(0.264230\pi\) | |||||||
\(930\) | 20262.7 | 0.714451 | ||||||||
\(931\) | −17471.4 | −0.615041 | ||||||||
\(932\) | −11440.7 | −0.402093 | ||||||||
\(933\) | −59790.6 | −2.09803 | ||||||||
\(934\) | 4816.25 | 0.168728 | ||||||||
\(935\) | 16445.3 | 0.575207 | ||||||||
\(936\) | 19881.2 | 0.694269 | ||||||||
\(937\) | −19742.9 | −0.688338 | −0.344169 | − | 0.938908i | \(-0.611839\pi\) | ||||
−0.344169 | + | 0.938908i | \(0.611839\pi\) | |||||||
\(938\) | −5146.80 | −0.179157 | ||||||||
\(939\) | −26087.0 | −0.906621 | ||||||||
\(940\) | 18484.2 | 0.641372 | ||||||||
\(941\) | −39767.5 | −1.37767 | −0.688833 | − | 0.724920i | \(-0.741877\pi\) | ||||
−0.688833 | + | 0.724920i | \(0.741877\pi\) | |||||||
\(942\) | −30824.7 | −1.06616 | ||||||||
\(943\) | −4031.15 | −0.139207 | ||||||||
\(944\) | 4696.80 | 0.161936 | ||||||||
\(945\) | −52120.2 | −1.79415 | ||||||||
\(946\) | 845.803 | 0.0290692 | ||||||||
\(947\) | 32884.3 | 1.12840 | 0.564200 | − | 0.825638i | \(-0.309185\pi\) | ||||
0.564200 | + | 0.825638i | \(0.309185\pi\) | |||||||
\(948\) | −2428.54 | −0.0832017 | ||||||||
\(949\) | −3518.87 | −0.120366 | ||||||||
\(950\) | −690.569 | −0.0235842 | ||||||||
\(951\) | −72786.7 | −2.48188 | ||||||||
\(952\) | −10444.0 | −0.355560 | ||||||||
\(953\) | 4674.79 | 0.158899 | 0.0794497 | − | 0.996839i | \(-0.474684\pi\) | ||||
0.0794497 | + | 0.996839i | \(0.474684\pi\) | |||||||
\(954\) | 41607.1 | 1.41203 | ||||||||
\(955\) | 4021.02 | 0.136248 | ||||||||
\(956\) | −2377.49 | −0.0804327 | ||||||||
\(957\) | −22630.1 | −0.764395 | ||||||||
\(958\) | 25056.6 | 0.845032 | ||||||||
\(959\) | −19856.5 | −0.668613 | ||||||||
\(960\) | −7374.40 | −0.247925 | ||||||||
\(961\) | −22059.9 | −0.740489 | ||||||||
\(962\) | −14235.5 | −0.477102 | ||||||||
\(963\) | −89661.6 | −3.00032 | ||||||||
\(964\) | 15720.6 | 0.525234 | ||||||||
\(965\) | −16127.2 | −0.537982 | ||||||||
\(966\) | −4370.72 | −0.145575 | ||||||||
\(967\) | −27165.3 | −0.903390 | −0.451695 | − | 0.892173i | \(-0.649180\pi\) | ||||
−0.451695 | + | 0.892173i | \(0.649180\pi\) | |||||||
\(968\) | 9784.80 | 0.324892 | ||||||||
\(969\) | −96279.0 | −3.19188 | ||||||||
\(970\) | −12565.0 | −0.415914 | ||||||||
\(971\) | 14597.4 | 0.482443 | 0.241221 | − | 0.970470i | \(-0.422452\pi\) | ||||
0.241221 | + | 0.970470i | \(0.422452\pi\) | |||||||
\(972\) | −64066.2 | −2.11412 | ||||||||
\(973\) | −8885.50 | −0.292760 | ||||||||
\(974\) | −33597.2 | −1.10526 | ||||||||
\(975\) | 1682.22 | 0.0552555 | ||||||||
\(976\) | −7211.70 | −0.236517 | ||||||||
\(977\) | 33327.5 | 1.09134 | 0.545670 | − | 0.838000i | \(-0.316275\pi\) | ||||
0.545670 | + | 0.838000i | \(0.316275\pi\) | |||||||
\(978\) | 39296.5 | 1.28483 | ||||||||
\(979\) | −5650.25 | −0.184456 | ||||||||
\(980\) | −11612.1 | −0.378505 | ||||||||
\(981\) | −67091.7 | −2.18356 | ||||||||
\(982\) | 36015.4 | 1.17036 | ||||||||
\(983\) | −21834.8 | −0.708465 | −0.354232 | − | 0.935157i | \(-0.615258\pi\) | ||||
−0.354232 | + | 0.935157i | \(0.615258\pi\) | |||||||
\(984\) | 14168.2 | 0.459009 | ||||||||
\(985\) | −4932.19 | −0.159546 | ||||||||
\(986\) | −59867.2 | −1.93363 | ||||||||
\(987\) | −38504.6 | −1.24176 | ||||||||
\(988\) | −9083.36 | −0.292490 | ||||||||
\(989\) | 936.388 | 0.0301066 | ||||||||
\(990\) | −17792.3 | −0.571188 | ||||||||
\(991\) | 45191.9 | 1.44861 | 0.724303 | − | 0.689482i | \(-0.242162\pi\) | ||||
0.724303 | + | 0.689482i | \(0.242162\pi\) | |||||||
\(992\) | −2813.65 | −0.0900539 | ||||||||
\(993\) | 111228. | 3.55459 | ||||||||
\(994\) | 12108.3 | 0.386369 | ||||||||
\(995\) | −1237.45 | −0.0394269 | ||||||||
\(996\) | 15071.3 | 0.479469 | ||||||||
\(997\) | 18760.0 | 0.595924 | 0.297962 | − | 0.954578i | \(-0.403693\pi\) | ||||
0.297962 | + | 0.954578i | \(0.403693\pi\) | |||||||
\(998\) | −1393.25 | −0.0441911 | ||||||||
\(999\) | 104561. | 3.31147 |
(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 | 46.4.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 414.4.a.j.1.1 | 2 | |||
4.3 | odd | 2 | 368.4.a.g.1.2 | 2 | |||
5.2 | odd | 4 | 1150.4.b.i.599.2 | 4 | |||
5.3 | odd | 4 | 1150.4.b.i.599.3 | 4 | |||
5.4 | even | 2 | 1150.4.a.k.1.2 | 2 | |||
7.6 | odd | 2 | 2254.4.a.d.1.2 | 2 | |||
8.3 | odd | 2 | 1472.4.a.l.1.1 | 2 | |||
8.5 | even | 2 | 1472.4.a.m.1.2 | 2 | |||
23.22 | odd | 2 | 1058.4.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
46.4.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
368.4.a.g.1.2 | 2 | 4.3 | odd | 2 | |||
414.4.a.j.1.1 | 2 | 3.2 | odd | 2 | |||
1058.4.a.f.1.1 | 2 | 23.22 | odd | 2 | |||
1150.4.a.k.1.2 | 2 | 5.4 | even | 2 | |||
1150.4.b.i.599.2 | 4 | 5.2 | odd | 4 | |||
1150.4.b.i.599.3 | 4 | 5.3 | odd | 4 | |||
1472.4.a.l.1.1 | 2 | 8.3 | odd | 2 | |||
1472.4.a.m.1.2 | 2 | 8.5 | even | 2 | |||
2254.4.a.d.1.2 | 2 | 7.6 | odd | 2 |