Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1058,4,Mod(1,1058)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1058, 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("1058.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1058 = 2 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1058.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: | \(62.4240207861\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{26}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 26 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(5.09902\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1058.1 |
$q$-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 | ||||||||
\(3\) | −4.00000 | −0.769800 | −0.384900 | − | 0.922958i | \(-0.625764\pi\) | ||||
−0.384900 | + | 0.922958i | \(0.625764\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 10.1980 | 0.912140 | 0.456070 | − | 0.889944i | \(-0.349257\pi\) | ||||
0.456070 | + | 0.889944i | \(0.349257\pi\) | |||||||
\(6\) | −8.00000 | −0.544331 | ||||||||
\(7\) | 20.3961 | 1.10128 | 0.550642 | − | 0.834741i | \(-0.314383\pi\) | ||||
0.550642 | + | 0.834741i | \(0.314383\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −11.0000 | −0.407407 | ||||||||
\(10\) | 20.3961 | 0.644981 | ||||||||
\(11\) | 71.3863 | 1.95671 | 0.978353 | − | 0.206942i | \(-0.0663511\pi\) | ||||
0.978353 | + | 0.206942i | \(0.0663511\pi\) | |||||||
\(12\) | −16.0000 | −0.384900 | ||||||||
\(13\) | −42.0000 | −0.896054 | −0.448027 | − | 0.894020i | \(-0.647873\pi\) | ||||
−0.448027 | + | 0.894020i | \(0.647873\pi\) | |||||||
\(14\) | 40.7922 | 0.778726 | ||||||||
\(15\) | −40.7922 | −0.702166 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 20.3961 | 0.290987 | 0.145493 | − | 0.989359i | \(-0.453523\pi\) | ||||
0.145493 | + | 0.989359i | \(0.453523\pi\) | |||||||
\(18\) | −22.0000 | −0.288081 | ||||||||
\(19\) | 91.7824 | 1.10823 | 0.554114 | − | 0.832441i | \(-0.313057\pi\) | ||||
0.554114 | + | 0.832441i | \(0.313057\pi\) | |||||||
\(20\) | 40.7922 | 0.456070 | ||||||||
\(21\) | −81.5843 | −0.847769 | ||||||||
\(22\) | 142.773 | 1.38360 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −32.0000 | −0.272166 | ||||||||
\(25\) | −21.0000 | −0.168000 | ||||||||
\(26\) | −84.0000 | −0.633606 | ||||||||
\(27\) | 152.000 | 1.08342 | ||||||||
\(28\) | 81.5843 | 0.550642 | ||||||||
\(29\) | −22.0000 | −0.140872 | −0.0704362 | − | 0.997516i | \(-0.522439\pi\) | ||||
−0.0704362 | + | 0.997516i | \(0.522439\pi\) | |||||||
\(30\) | −81.5843 | −0.496506 | ||||||||
\(31\) | 296.000 | 1.71494 | 0.857470 | − | 0.514533i | \(-0.172035\pi\) | ||||
0.857470 | + | 0.514533i | \(0.172035\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −285.545 | −1.50627 | ||||||||
\(34\) | 40.7922 | 0.205759 | ||||||||
\(35\) | 208.000 | 1.00453 | ||||||||
\(36\) | −44.0000 | −0.203704 | ||||||||
\(37\) | −275.347 | −1.22343 | −0.611713 | − | 0.791080i | \(-0.709519\pi\) | ||||
−0.611713 | + | 0.791080i | \(0.709519\pi\) | |||||||
\(38\) | 183.565 | 0.783635 | ||||||||
\(39\) | 168.000 | 0.689783 | ||||||||
\(40\) | 81.5843 | 0.322490 | ||||||||
\(41\) | −318.000 | −1.21130 | −0.605649 | − | 0.795732i | \(-0.707087\pi\) | ||||
−0.605649 | + | 0.795732i | \(0.707087\pi\) | |||||||
\(42\) | −163.169 | −0.599463 | ||||||||
\(43\) | 316.139 | 1.12118 | 0.560590 | − | 0.828093i | \(-0.310574\pi\) | ||||
0.560590 | + | 0.828093i | \(0.310574\pi\) | |||||||
\(44\) | 285.545 | 0.978353 | ||||||||
\(45\) | −112.178 | −0.371613 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −184.000 | −0.571046 | −0.285523 | − | 0.958372i | \(-0.592167\pi\) | ||||
−0.285523 | + | 0.958372i | \(0.592167\pi\) | |||||||
\(48\) | −64.0000 | −0.192450 | ||||||||
\(49\) | 73.0000 | 0.212828 | ||||||||
\(50\) | −42.0000 | −0.118794 | ||||||||
\(51\) | −81.5843 | −0.224002 | ||||||||
\(52\) | −168.000 | −0.448027 | ||||||||
\(53\) | 91.7824 | 0.237873 | 0.118937 | − | 0.992902i | \(-0.462051\pi\) | ||||
0.118937 | + | 0.992902i | \(0.462051\pi\) | |||||||
\(54\) | 304.000 | 0.766096 | ||||||||
\(55\) | 728.000 | 1.78479 | ||||||||
\(56\) | 163.169 | 0.389363 | ||||||||
\(57\) | −367.129 | −0.853114 | ||||||||
\(58\) | −44.0000 | −0.0996118 | ||||||||
\(59\) | −500.000 | −1.10330 | −0.551648 | − | 0.834077i | \(-0.686001\pi\) | ||||
−0.551648 | + | 0.834077i | \(0.686001\pi\) | |||||||
\(60\) | −163.169 | −0.351083 | ||||||||
\(61\) | 30.5941 | 0.0642160 | 0.0321080 | − | 0.999484i | \(-0.489778\pi\) | ||||
0.0321080 | + | 0.999484i | \(0.489778\pi\) | |||||||
\(62\) | 592.000 | 1.21265 | ||||||||
\(63\) | −224.357 | −0.448672 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −428.318 | −0.817327 | ||||||||
\(66\) | −571.090 | −1.06510 | ||||||||
\(67\) | −642.476 | −1.17151 | −0.585754 | − | 0.810489i | \(-0.699201\pi\) | ||||
−0.585754 | + | 0.810489i | \(0.699201\pi\) | |||||||
\(68\) | 81.5843 | 0.145493 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 416.000 | 0.710307 | ||||||||
\(71\) | 224.000 | 0.374421 | 0.187211 | − | 0.982320i | \(-0.440055\pi\) | ||||
0.187211 | + | 0.982320i | \(0.440055\pi\) | |||||||
\(72\) | −88.0000 | −0.144040 | ||||||||
\(73\) | −210.000 | −0.336694 | −0.168347 | − | 0.985728i | \(-0.553843\pi\) | ||||
−0.168347 | + | 0.985728i | \(0.553843\pi\) | |||||||
\(74\) | −550.694 | −0.865093 | ||||||||
\(75\) | 84.0000 | 0.129326 | ||||||||
\(76\) | 367.129 | 0.554114 | ||||||||
\(77\) | 1456.00 | 2.15489 | ||||||||
\(78\) | 336.000 | 0.487750 | ||||||||
\(79\) | 1080.99 | 1.53951 | 0.769754 | − | 0.638341i | \(-0.220379\pi\) | ||||
0.769754 | + | 0.638341i | \(0.220379\pi\) | |||||||
\(80\) | 163.169 | 0.228035 | ||||||||
\(81\) | −311.000 | −0.426612 | ||||||||
\(82\) | −636.000 | −0.856518 | ||||||||
\(83\) | 1152.38 | 1.52398 | 0.761988 | − | 0.647591i | \(-0.224224\pi\) | ||||
0.761988 | + | 0.647591i | \(0.224224\pi\) | |||||||
\(84\) | −326.337 | −0.423885 | ||||||||
\(85\) | 208.000 | 0.265421 | ||||||||
\(86\) | 632.278 | 0.792795 | ||||||||
\(87\) | 88.0000 | 0.108444 | ||||||||
\(88\) | 571.090 | 0.691800 | ||||||||
\(89\) | −815.843 | −0.971676 | −0.485838 | − | 0.874049i | \(-0.661486\pi\) | ||||
−0.485838 | + | 0.874049i | \(0.661486\pi\) | |||||||
\(90\) | −224.357 | −0.262770 | ||||||||
\(91\) | −856.635 | −0.986811 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1184.00 | −1.32016 | ||||||||
\(94\) | −368.000 | −0.403790 | ||||||||
\(95\) | 936.000 | 1.01086 | ||||||||
\(96\) | −128.000 | −0.136083 | ||||||||
\(97\) | 1244.16 | 1.30232 | 0.651162 | − | 0.758939i | \(-0.274282\pi\) | ||||
0.651162 | + | 0.758939i | \(0.274282\pi\) | |||||||
\(98\) | 146.000 | 0.150492 | ||||||||
\(99\) | −785.249 | −0.797177 | ||||||||
\(100\) | −84.0000 | −0.0840000 | ||||||||
\(101\) | 1934.00 | 1.90535 | 0.952674 | − | 0.303993i | \(-0.0983200\pi\) | ||||
0.952674 | + | 0.303993i | \(0.0983200\pi\) | |||||||
\(102\) | −163.169 | −0.158393 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | −336.000 | −0.316803 | ||||||||
\(105\) | −832.000 | −0.773285 | ||||||||
\(106\) | 183.565 | 0.168202 | ||||||||
\(107\) | 132.575 | 0.119780 | 0.0598900 | − | 0.998205i | \(-0.480925\pi\) | ||||
0.0598900 | + | 0.998205i | \(0.480925\pi\) | |||||||
\(108\) | 608.000 | 0.541711 | ||||||||
\(109\) | −1193.17 | −1.04849 | −0.524243 | − | 0.851569i | \(-0.675652\pi\) | ||||
−0.524243 | + | 0.851569i | \(0.675652\pi\) | |||||||
\(110\) | 1456.00 | 1.26204 | ||||||||
\(111\) | 1101.39 | 0.941794 | ||||||||
\(112\) | 326.337 | 0.275321 | ||||||||
\(113\) | 2080.40 | 1.73193 | 0.865963 | − | 0.500109i | \(-0.166707\pi\) | ||||
0.865963 | + | 0.500109i | \(0.166707\pi\) | |||||||
\(114\) | −734.259 | −0.603242 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −88.0000 | −0.0704362 | ||||||||
\(117\) | 462.000 | 0.365059 | ||||||||
\(118\) | −1000.00 | −0.780148 | ||||||||
\(119\) | 416.000 | 0.320459 | ||||||||
\(120\) | −326.337 | −0.248253 | ||||||||
\(121\) | 3765.00 | 2.82870 | ||||||||
\(122\) | 61.1882 | 0.0454076 | ||||||||
\(123\) | 1272.00 | 0.932458 | ||||||||
\(124\) | 1184.00 | 0.857470 | ||||||||
\(125\) | −1488.91 | −1.06538 | ||||||||
\(126\) | −448.714 | −0.317259 | ||||||||
\(127\) | −408.000 | −0.285072 | −0.142536 | − | 0.989790i | \(-0.545526\pi\) | ||||
−0.142536 | + | 0.989790i | \(0.545526\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −1264.56 | −0.863085 | ||||||||
\(130\) | −856.635 | −0.577938 | ||||||||
\(131\) | 196.000 | 0.130722 | 0.0653611 | − | 0.997862i | \(-0.479180\pi\) | ||||
0.0653611 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(132\) | −1142.18 | −0.753137 | ||||||||
\(133\) | 1872.00 | 1.22047 | ||||||||
\(134\) | −1284.95 | −0.828381 | ||||||||
\(135\) | 1550.10 | 0.988234 | ||||||||
\(136\) | 163.169 | 0.102879 | ||||||||
\(137\) | 2467.93 | 1.53904 | 0.769522 | − | 0.638620i | \(-0.220494\pi\) | ||||
0.769522 | + | 0.638620i | \(0.220494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2292.00 | −1.39860 | −0.699298 | − | 0.714830i | \(-0.746504\pi\) | ||||
−0.699298 | + | 0.714830i | \(0.746504\pi\) | |||||||
\(140\) | 832.000 | 0.502263 | ||||||||
\(141\) | 736.000 | 0.439591 | ||||||||
\(142\) | 448.000 | 0.264756 | ||||||||
\(143\) | −2998.22 | −1.75331 | ||||||||
\(144\) | −176.000 | −0.101852 | ||||||||
\(145\) | −224.357 | −0.128495 | ||||||||
\(146\) | −420.000 | −0.238078 | ||||||||
\(147\) | −292.000 | −0.163835 | ||||||||
\(148\) | −1101.39 | −0.611713 | ||||||||
\(149\) | 132.575 | 0.0728921 | 0.0364461 | − | 0.999336i | \(-0.488396\pi\) | ||||
0.0364461 | + | 0.999336i | \(0.488396\pi\) | |||||||
\(150\) | 168.000 | 0.0914476 | ||||||||
\(151\) | −3072.00 | −1.65560 | −0.827801 | − | 0.561022i | \(-0.810408\pi\) | ||||
−0.827801 | + | 0.561022i | \(0.810408\pi\) | |||||||
\(152\) | 734.259 | 0.391817 | ||||||||
\(153\) | −224.357 | −0.118550 | ||||||||
\(154\) | 2912.00 | 1.52374 | ||||||||
\(155\) | 3018.62 | 1.56427 | ||||||||
\(156\) | 672.000 | 0.344891 | ||||||||
\(157\) | −30.5941 | −0.0155521 | −0.00777604 | − | 0.999970i | \(-0.502475\pi\) | ||||
−0.00777604 | + | 0.999970i | \(0.502475\pi\) | |||||||
\(158\) | 2161.98 | 1.08860 | ||||||||
\(159\) | −367.129 | −0.183115 | ||||||||
\(160\) | 326.337 | 0.161245 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −622.000 | −0.301660 | ||||||||
\(163\) | 3116.00 | 1.49732 | 0.748662 | − | 0.662951i | \(-0.230696\pi\) | ||||
0.748662 | + | 0.662951i | \(0.230696\pi\) | |||||||
\(164\) | −1272.00 | −0.605649 | ||||||||
\(165\) | −2912.00 | −1.37393 | ||||||||
\(166\) | 2304.76 | 1.07761 | ||||||||
\(167\) | 2112.00 | 0.978632 | 0.489316 | − | 0.872107i | \(-0.337247\pi\) | ||||
0.489316 | + | 0.872107i | \(0.337247\pi\) | |||||||
\(168\) | −652.674 | −0.299732 | ||||||||
\(169\) | −433.000 | −0.197087 | ||||||||
\(170\) | 416.000 | 0.187681 | ||||||||
\(171\) | −1009.61 | −0.451500 | ||||||||
\(172\) | 1264.56 | 0.560590 | ||||||||
\(173\) | 442.000 | 0.194246 | 0.0971232 | − | 0.995272i | \(-0.469036\pi\) | ||||
0.0971232 | + | 0.995272i | \(0.469036\pi\) | |||||||
\(174\) | 176.000 | 0.0766812 | ||||||||
\(175\) | −428.318 | −0.185016 | ||||||||
\(176\) | 1142.18 | 0.489177 | ||||||||
\(177\) | 2000.00 | 0.849318 | ||||||||
\(178\) | −1631.69 | −0.687079 | ||||||||
\(179\) | 2764.00 | 1.15414 | 0.577070 | − | 0.816695i | \(-0.304196\pi\) | ||||
0.577070 | + | 0.816695i | \(0.304196\pi\) | |||||||
\(180\) | −448.714 | −0.185806 | ||||||||
\(181\) | −4456.54 | −1.83012 | −0.915061 | − | 0.403314i | \(-0.867858\pi\) | ||||
−0.915061 | + | 0.403314i | \(0.867858\pi\) | |||||||
\(182\) | −1713.27 | −0.697781 | ||||||||
\(183\) | −122.376 | −0.0494335 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2808.00 | −1.11594 | ||||||||
\(186\) | −2368.00 | −0.933496 | ||||||||
\(187\) | 1456.00 | 0.569376 | ||||||||
\(188\) | −736.000 | −0.285523 | ||||||||
\(189\) | 3100.20 | 1.19316 | ||||||||
\(190\) | 1872.00 | 0.714785 | ||||||||
\(191\) | 4018.03 | 1.52217 | 0.761084 | − | 0.648653i | \(-0.224667\pi\) | ||||
0.761084 | + | 0.648653i | \(0.224667\pi\) | |||||||
\(192\) | −256.000 | −0.0962250 | ||||||||
\(193\) | −1666.00 | −0.621354 | −0.310677 | − | 0.950516i | \(-0.600556\pi\) | ||||
−0.310677 | + | 0.950516i | \(0.600556\pi\) | |||||||
\(194\) | 2488.32 | 0.920882 | ||||||||
\(195\) | 1713.27 | 0.629179 | ||||||||
\(196\) | 292.000 | 0.106414 | ||||||||
\(197\) | −2190.00 | −0.792036 | −0.396018 | − | 0.918243i | \(-0.629608\pi\) | ||||
−0.396018 | + | 0.918243i | \(0.629608\pi\) | |||||||
\(198\) | −1570.50 | −0.563689 | ||||||||
\(199\) | 917.824 | 0.326949 | 0.163474 | − | 0.986548i | \(-0.447730\pi\) | ||||
0.163474 | + | 0.986548i | \(0.447730\pi\) | |||||||
\(200\) | −168.000 | −0.0593970 | ||||||||
\(201\) | 2569.91 | 0.901827 | ||||||||
\(202\) | 3868.00 | 1.34728 | ||||||||
\(203\) | −448.714 | −0.155141 | ||||||||
\(204\) | −326.337 | −0.112001 | ||||||||
\(205\) | −3242.98 | −1.10487 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −672.000 | −0.224014 | ||||||||
\(209\) | 6552.00 | 2.16848 | ||||||||
\(210\) | −1664.00 | −0.546795 | ||||||||
\(211\) | −1324.00 | −0.431981 | −0.215990 | − | 0.976396i | \(-0.569298\pi\) | ||||
−0.215990 | + | 0.976396i | \(0.569298\pi\) | |||||||
\(212\) | 367.129 | 0.118937 | ||||||||
\(213\) | −896.000 | −0.288230 | ||||||||
\(214\) | 265.149 | 0.0846973 | ||||||||
\(215\) | 3224.00 | 1.02267 | ||||||||
\(216\) | 1216.00 | 0.383048 | ||||||||
\(217\) | 6037.24 | 1.88864 | ||||||||
\(218\) | −2386.34 | −0.741392 | ||||||||
\(219\) | 840.000 | 0.259187 | ||||||||
\(220\) | 2912.00 | 0.892395 | ||||||||
\(221\) | −856.635 | −0.260740 | ||||||||
\(222\) | 2202.78 | 0.665949 | ||||||||
\(223\) | −1928.00 | −0.578962 | −0.289481 | − | 0.957184i | \(-0.593483\pi\) | ||||
−0.289481 | + | 0.957184i | \(0.593483\pi\) | |||||||
\(224\) | 652.674 | 0.194681 | ||||||||
\(225\) | 231.000 | 0.0684444 | ||||||||
\(226\) | 4160.80 | 1.22466 | ||||||||
\(227\) | 3905.85 | 1.14203 | 0.571014 | − | 0.820940i | \(-0.306550\pi\) | ||||
0.571014 | + | 0.820940i | \(0.306550\pi\) | |||||||
\(228\) | −1468.52 | −0.426557 | ||||||||
\(229\) | −1070.79 | −0.308996 | −0.154498 | − | 0.987993i | \(-0.549376\pi\) | ||||
−0.154498 | + | 0.987993i | \(0.549376\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5824.00 | −1.65884 | ||||||||
\(232\) | −176.000 | −0.0498059 | ||||||||
\(233\) | 762.000 | 0.214250 | 0.107125 | − | 0.994246i | \(-0.465835\pi\) | ||||
0.107125 | + | 0.994246i | \(0.465835\pi\) | |||||||
\(234\) | 924.000 | 0.258136 | ||||||||
\(235\) | −1876.44 | −0.520874 | ||||||||
\(236\) | −2000.00 | −0.551648 | ||||||||
\(237\) | −4323.97 | −1.18511 | ||||||||
\(238\) | 832.000 | 0.226599 | ||||||||
\(239\) | −136.000 | −0.0368080 | −0.0184040 | − | 0.999831i | \(-0.505859\pi\) | ||||
−0.0184040 | + | 0.999831i | \(0.505859\pi\) | |||||||
\(240\) | −652.674 | −0.175541 | ||||||||
\(241\) | 1448.12 | 0.387061 | 0.193531 | − | 0.981094i | \(-0.438006\pi\) | ||||
0.193531 | + | 0.981094i | \(0.438006\pi\) | |||||||
\(242\) | 7530.00 | 2.00019 | ||||||||
\(243\) | −2860.00 | −0.755017 | ||||||||
\(244\) | 122.376 | 0.0321080 | ||||||||
\(245\) | 744.457 | 0.194129 | ||||||||
\(246\) | 2544.00 | 0.659348 | ||||||||
\(247\) | −3854.86 | −0.993032 | ||||||||
\(248\) | 2368.00 | 0.606323 | ||||||||
\(249\) | −4609.51 | −1.17316 | ||||||||
\(250\) | −2977.83 | −0.753337 | ||||||||
\(251\) | 10.1980 | 0.00256452 | 0.00128226 | − | 0.999999i | \(-0.499592\pi\) | ||||
0.00128226 | + | 0.999999i | \(0.499592\pi\) | |||||||
\(252\) | −897.427 | −0.224336 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −816.000 | −0.201576 | ||||||||
\(255\) | −832.000 | −0.204321 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2918.00 | −0.708248 | −0.354124 | − | 0.935198i | \(-0.615221\pi\) | ||||
−0.354124 | + | 0.935198i | \(0.615221\pi\) | |||||||
\(258\) | −2529.11 | −0.610294 | ||||||||
\(259\) | −5616.00 | −1.34734 | ||||||||
\(260\) | −1713.27 | −0.408664 | ||||||||
\(261\) | 242.000 | 0.0573924 | ||||||||
\(262\) | 392.000 | 0.0924345 | ||||||||
\(263\) | −5262.19 | −1.23377 | −0.616883 | − | 0.787055i | \(-0.711605\pi\) | ||||
−0.616883 | + | 0.787055i | \(0.711605\pi\) | |||||||
\(264\) | −2284.36 | −0.532548 | ||||||||
\(265\) | 936.000 | 0.216974 | ||||||||
\(266\) | 3744.00 | 0.863005 | ||||||||
\(267\) | 3263.37 | 0.747997 | ||||||||
\(268\) | −2569.91 | −0.585754 | ||||||||
\(269\) | −5238.00 | −1.18724 | −0.593618 | − | 0.804747i | \(-0.702301\pi\) | ||||
−0.593618 | + | 0.804747i | \(0.702301\pi\) | |||||||
\(270\) | 3100.20 | 0.698787 | ||||||||
\(271\) | 3048.00 | 0.683221 | 0.341610 | − | 0.939842i | \(-0.389028\pi\) | ||||
0.341610 | + | 0.939842i | \(0.389028\pi\) | |||||||
\(272\) | 326.337 | 0.0727467 | ||||||||
\(273\) | 3426.54 | 0.759647 | ||||||||
\(274\) | 4935.85 | 1.08827 | ||||||||
\(275\) | −1499.11 | −0.328727 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5650.00 | 1.22554 | 0.612772 | − | 0.790260i | \(-0.290054\pi\) | ||||
0.612772 | + | 0.790260i | \(0.290054\pi\) | |||||||
\(278\) | −4584.00 | −0.988957 | ||||||||
\(279\) | −3256.00 | −0.698680 | ||||||||
\(280\) | 1664.00 | 0.355154 | ||||||||
\(281\) | −4283.18 | −0.909299 | −0.454649 | − | 0.890671i | \(-0.650235\pi\) | ||||
−0.454649 | + | 0.890671i | \(0.650235\pi\) | |||||||
\(282\) | 1472.00 | 0.310838 | ||||||||
\(283\) | 3253.17 | 0.683326 | 0.341663 | − | 0.939823i | \(-0.389010\pi\) | ||||
0.341663 | + | 0.939823i | \(0.389010\pi\) | |||||||
\(284\) | 896.000 | 0.187211 | ||||||||
\(285\) | −3744.00 | −0.778159 | ||||||||
\(286\) | −5996.45 | −1.23978 | ||||||||
\(287\) | −6485.95 | −1.33398 | ||||||||
\(288\) | −352.000 | −0.0720201 | ||||||||
\(289\) | −4497.00 | −0.915327 | ||||||||
\(290\) | −448.714 | −0.0908599 | ||||||||
\(291\) | −4976.64 | −1.00253 | ||||||||
\(292\) | −840.000 | −0.168347 | ||||||||
\(293\) | −4069.02 | −0.811312 | −0.405656 | − | 0.914026i | \(-0.632957\pi\) | ||||
−0.405656 | + | 0.914026i | \(0.632957\pi\) | |||||||
\(294\) | −584.000 | −0.115849 | ||||||||
\(295\) | −5099.02 | −1.00636 | ||||||||
\(296\) | −2202.78 | −0.432547 | ||||||||
\(297\) | 10850.7 | 2.11994 | ||||||||
\(298\) | 265.149 | 0.0515425 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 336.000 | 0.0646632 | ||||||||
\(301\) | 6448.00 | 1.23474 | ||||||||
\(302\) | −6144.00 | −1.17069 | ||||||||
\(303\) | −7736.00 | −1.46674 | ||||||||
\(304\) | 1468.52 | 0.277057 | ||||||||
\(305\) | 312.000 | 0.0585740 | ||||||||
\(306\) | −448.714 | −0.0838276 | ||||||||
\(307\) | 4492.00 | 0.835088 | 0.417544 | − | 0.908657i | \(-0.362891\pi\) | ||||
0.417544 | + | 0.908657i | \(0.362891\pi\) | |||||||
\(308\) | 5824.00 | 1.07745 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6037.24 | 1.10610 | ||||||||
\(311\) | −2880.00 | −0.525112 | −0.262556 | − | 0.964917i | \(-0.584565\pi\) | ||||
−0.262556 | + | 0.964917i | \(0.584565\pi\) | |||||||
\(312\) | 1344.00 | 0.243875 | ||||||||
\(313\) | 2263.96 | 0.408840 | 0.204420 | − | 0.978883i | \(-0.434469\pi\) | ||||
0.204420 | + | 0.978883i | \(0.434469\pi\) | |||||||
\(314\) | −61.1882 | −0.0109970 | ||||||||
\(315\) | −2288.00 | −0.409251 | ||||||||
\(316\) | 4323.97 | 0.769754 | ||||||||
\(317\) | −8454.00 | −1.49787 | −0.748934 | − | 0.662645i | \(-0.769434\pi\) | ||||
−0.748934 | + | 0.662645i | \(0.769434\pi\) | |||||||
\(318\) | −734.259 | −0.129482 | ||||||||
\(319\) | −1570.50 | −0.275646 | ||||||||
\(320\) | 652.674 | 0.114018 | ||||||||
\(321\) | −530.298 | −0.0922067 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1872.00 | 0.322479 | ||||||||
\(324\) | −1244.00 | −0.213306 | ||||||||
\(325\) | 882.000 | 0.150537 | ||||||||
\(326\) | 6232.00 | 1.05877 | ||||||||
\(327\) | 4772.68 | 0.807125 | ||||||||
\(328\) | −2544.00 | −0.428259 | ||||||||
\(329\) | −3752.88 | −0.628884 | ||||||||
\(330\) | −5824.00 | −0.971517 | ||||||||
\(331\) | −10052.0 | −1.66921 | −0.834604 | − | 0.550850i | \(-0.814304\pi\) | ||||
−0.834604 | + | 0.550850i | \(0.814304\pi\) | |||||||
\(332\) | 4609.51 | 0.761988 | ||||||||
\(333\) | 3028.82 | 0.498433 | ||||||||
\(334\) | 4224.00 | 0.691997 | ||||||||
\(335\) | −6552.00 | −1.06858 | ||||||||
\(336\) | −1305.35 | −0.211942 | ||||||||
\(337\) | −489.506 | −0.0791249 | −0.0395624 | − | 0.999217i | \(-0.512596\pi\) | ||||
−0.0395624 | + | 0.999217i | \(0.512596\pi\) | |||||||
\(338\) | −866.000 | −0.139362 | ||||||||
\(339\) | −8321.60 | −1.33324 | ||||||||
\(340\) | 832.000 | 0.132710 | ||||||||
\(341\) | 21130.3 | 3.35564 | ||||||||
\(342\) | −2019.21 | −0.319259 | ||||||||
\(343\) | −5506.94 | −0.866900 | ||||||||
\(344\) | 2529.11 | 0.396397 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 884.000 | 0.137353 | ||||||||
\(347\) | −8604.00 | −1.33109 | −0.665543 | − | 0.746359i | \(-0.731800\pi\) | ||||
−0.665543 | + | 0.746359i | \(0.731800\pi\) | |||||||
\(348\) | 352.000 | 0.0542218 | ||||||||
\(349\) | −1174.00 | −0.180065 | −0.0900326 | − | 0.995939i | \(-0.528697\pi\) | ||||
−0.0900326 | + | 0.995939i | \(0.528697\pi\) | |||||||
\(350\) | −856.635 | −0.130826 | ||||||||
\(351\) | −6384.00 | −0.970805 | ||||||||
\(352\) | 2284.36 | 0.345900 | ||||||||
\(353\) | −2818.00 | −0.424892 | −0.212446 | − | 0.977173i | \(-0.568143\pi\) | ||||
−0.212446 | + | 0.977173i | \(0.568143\pi\) | |||||||
\(354\) | 4000.00 | 0.600558 | ||||||||
\(355\) | 2284.36 | 0.341525 | ||||||||
\(356\) | −3263.37 | −0.485838 | ||||||||
\(357\) | −1664.00 | −0.246690 | ||||||||
\(358\) | 5528.00 | 0.816100 | ||||||||
\(359\) | 1366.54 | 0.200900 | 0.100450 | − | 0.994942i | \(-0.467972\pi\) | ||||
0.100450 | + | 0.994942i | \(0.467972\pi\) | |||||||
\(360\) | −897.427 | −0.131385 | ||||||||
\(361\) | 1565.00 | 0.228167 | ||||||||
\(362\) | −8913.09 | −1.29409 | ||||||||
\(363\) | −15060.0 | −2.17753 | ||||||||
\(364\) | −3426.54 | −0.493405 | ||||||||
\(365\) | −2141.59 | −0.307112 | ||||||||
\(366\) | −244.753 | −0.0349548 | ||||||||
\(367\) | 3079.81 | 0.438051 | 0.219025 | − | 0.975719i | \(-0.429712\pi\) | ||||
0.219025 | + | 0.975719i | \(0.429712\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3498.00 | 0.493492 | ||||||||
\(370\) | −5616.00 | −0.789086 | ||||||||
\(371\) | 1872.00 | 0.261966 | ||||||||
\(372\) | −4736.00 | −0.660081 | ||||||||
\(373\) | 4415.75 | 0.612973 | 0.306486 | − | 0.951875i | \(-0.400847\pi\) | ||||
0.306486 | + | 0.951875i | \(0.400847\pi\) | |||||||
\(374\) | 2912.00 | 0.402609 | ||||||||
\(375\) | 5955.65 | 0.820130 | ||||||||
\(376\) | −1472.00 | −0.201895 | ||||||||
\(377\) | 924.000 | 0.126229 | ||||||||
\(378\) | 6200.41 | 0.843689 | ||||||||
\(379\) | 10.1980 | 0.00138216 | 0.000691079 | − | 1.00000i | \(-0.499780\pi\) | ||||
0.000691079 | 1.00000i | \(0.499780\pi\) | ||||||||
\(380\) | 3744.00 | 0.505429 | ||||||||
\(381\) | 1632.00 | 0.219449 | ||||||||
\(382\) | 8036.05 | 1.07634 | ||||||||
\(383\) | −40.7922 | −0.00544225 | −0.00272113 | − | 0.999996i | \(-0.500866\pi\) | ||||
−0.00272113 | + | 0.999996i | \(0.500866\pi\) | |||||||
\(384\) | −512.000 | −0.0680414 | ||||||||
\(385\) | 14848.3 | 1.96556 | ||||||||
\(386\) | −3332.00 | −0.439364 | ||||||||
\(387\) | −3477.53 | −0.456777 | ||||||||
\(388\) | 4976.64 | 0.651162 | ||||||||
\(389\) | −14328.2 | −1.86753 | −0.933767 | − | 0.357881i | \(-0.883499\pi\) | ||||
−0.933767 | + | 0.357881i | \(0.883499\pi\) | |||||||
\(390\) | 3426.54 | 0.444897 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 584.000 | 0.0752461 | ||||||||
\(393\) | −784.000 | −0.100630 | ||||||||
\(394\) | −4380.00 | −0.560054 | ||||||||
\(395\) | 11024.0 | 1.40425 | ||||||||
\(396\) | −3141.00 | −0.398588 | ||||||||
\(397\) | 11046.0 | 1.39643 | 0.698215 | − | 0.715888i | \(-0.253978\pi\) | ||||
0.698215 | + | 0.715888i | \(0.253978\pi\) | |||||||
\(398\) | 1835.65 | 0.231188 | ||||||||
\(399\) | −7488.00 | −0.939521 | ||||||||
\(400\) | −336.000 | −0.0420000 | ||||||||
\(401\) | −4425.95 | −0.551175 | −0.275588 | − | 0.961276i | \(-0.588872\pi\) | ||||
−0.275588 | + | 0.961276i | \(0.588872\pi\) | |||||||
\(402\) | 5139.81 | 0.637688 | ||||||||
\(403\) | −12432.0 | −1.53668 | ||||||||
\(404\) | 7736.00 | 0.952674 | ||||||||
\(405\) | −3171.59 | −0.389130 | ||||||||
\(406\) | −897.427 | −0.109701 | ||||||||
\(407\) | −19656.0 | −2.39389 | ||||||||
\(408\) | −652.674 | −0.0791966 | ||||||||
\(409\) | −5194.00 | −0.627938 | −0.313969 | − | 0.949433i | \(-0.601659\pi\) | ||||
−0.313969 | + | 0.949433i | \(0.601659\pi\) | |||||||
\(410\) | −6485.95 | −0.781264 | ||||||||
\(411\) | −9871.70 | −1.18476 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10198.0 | −1.21504 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11752.0 | 1.39008 | ||||||||
\(416\) | −1344.00 | −0.158401 | ||||||||
\(417\) | 9168.00 | 1.07664 | ||||||||
\(418\) | 13104.0 | 1.53334 | ||||||||
\(419\) | 5272.39 | 0.614733 | 0.307366 | − | 0.951591i | \(-0.400552\pi\) | ||||
0.307366 | + | 0.951591i | \(0.400552\pi\) | |||||||
\(420\) | −3328.00 | −0.386642 | ||||||||
\(421\) | −9616.75 | −1.11328 | −0.556641 | − | 0.830753i | \(-0.687910\pi\) | ||||
−0.556641 | + | 0.830753i | \(0.687910\pi\) | |||||||
\(422\) | −2648.00 | −0.305456 | ||||||||
\(423\) | 2024.00 | 0.232648 | ||||||||
\(424\) | 734.259 | 0.0841008 | ||||||||
\(425\) | −428.318 | −0.0488858 | ||||||||
\(426\) | −1792.00 | −0.203809 | ||||||||
\(427\) | 624.000 | 0.0707201 | ||||||||
\(428\) | 530.298 | 0.0598900 | ||||||||
\(429\) | 11992.9 | 1.34970 | ||||||||
\(430\) | 6448.00 | 0.723140 | ||||||||
\(431\) | 7607.74 | 0.850236 | 0.425118 | − | 0.905138i | \(-0.360233\pi\) | ||||
0.425118 | + | 0.905138i | \(0.360233\pi\) | |||||||
\(432\) | 2432.00 | 0.270856 | ||||||||
\(433\) | −9932.89 | −1.10241 | −0.551206 | − | 0.834369i | \(-0.685832\pi\) | ||||
−0.551206 | + | 0.834369i | \(0.685832\pi\) | |||||||
\(434\) | 12074.5 | 1.33547 | ||||||||
\(435\) | 897.427 | 0.0989158 | ||||||||
\(436\) | −4772.68 | −0.524243 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1680.00 | 0.183273 | ||||||||
\(439\) | −6768.00 | −0.735806 | −0.367903 | − | 0.929864i | \(-0.619924\pi\) | ||||
−0.367903 | + | 0.929864i | \(0.619924\pi\) | |||||||
\(440\) | 5824.00 | 0.631019 | ||||||||
\(441\) | −803.000 | −0.0867077 | ||||||||
\(442\) | −1713.27 | −0.184371 | ||||||||
\(443\) | −7292.00 | −0.782062 | −0.391031 | − | 0.920378i | \(-0.627881\pi\) | ||||
−0.391031 | + | 0.920378i | \(0.627881\pi\) | |||||||
\(444\) | 4405.55 | 0.470897 | ||||||||
\(445\) | −8320.00 | −0.886305 | ||||||||
\(446\) | −3856.00 | −0.409388 | ||||||||
\(447\) | −530.298 | −0.0561124 | ||||||||
\(448\) | 1305.35 | 0.137661 | ||||||||
\(449\) | −10198.0 | −1.07188 | −0.535939 | − | 0.844257i | \(-0.680042\pi\) | ||||
−0.535939 | + | 0.844257i | \(0.680042\pi\) | |||||||
\(450\) | 462.000 | 0.0483975 | ||||||||
\(451\) | −22700.8 | −2.37016 | ||||||||
\(452\) | 8321.60 | 0.865963 | ||||||||
\(453\) | 12288.0 | 1.27448 | ||||||||
\(454\) | 7811.70 | 0.807536 | ||||||||
\(455\) | −8736.00 | −0.900110 | ||||||||
\(456\) | −2937.04 | −0.301621 | ||||||||
\(457\) | 10707.9 | 1.09605 | 0.548027 | − | 0.836461i | \(-0.315379\pi\) | ||||
0.548027 | + | 0.836461i | \(0.315379\pi\) | |||||||
\(458\) | −2141.59 | −0.218493 | ||||||||
\(459\) | 3100.20 | 0.315262 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4794.00 | 0.484336 | 0.242168 | − | 0.970234i | \(-0.422142\pi\) | ||||
0.242168 | + | 0.970234i | \(0.422142\pi\) | |||||||
\(462\) | −11648.0 | −1.17297 | ||||||||
\(463\) | 9848.00 | 0.988500 | 0.494250 | − | 0.869320i | \(-0.335443\pi\) | ||||
0.494250 | + | 0.869320i | \(0.335443\pi\) | |||||||
\(464\) | −352.000 | −0.0352181 | ||||||||
\(465\) | −12074.5 | −1.20417 | ||||||||
\(466\) | 1524.00 | 0.151498 | ||||||||
\(467\) | −5986.25 | −0.593170 | −0.296585 | − | 0.955006i | \(-0.595848\pi\) | ||||
−0.296585 | + | 0.955006i | \(0.595848\pi\) | |||||||
\(468\) | 1848.00 | 0.182530 | ||||||||
\(469\) | −13104.0 | −1.29016 | ||||||||
\(470\) | −3752.88 | −0.368314 | ||||||||
\(471\) | 122.376 | 0.0119720 | ||||||||
\(472\) | −4000.00 | −0.390074 | ||||||||
\(473\) | 22568.0 | 2.19382 | ||||||||
\(474\) | −8647.94 | −0.838002 | ||||||||
\(475\) | −1927.43 | −0.186182 | ||||||||
\(476\) | 1664.00 | 0.160230 | ||||||||
\(477\) | −1009.61 | −0.0969113 | ||||||||
\(478\) | −272.000 | −0.0260272 | ||||||||
\(479\) | 2651.49 | 0.252922 | 0.126461 | − | 0.991972i | \(-0.459638\pi\) | ||||
0.126461 | + | 0.991972i | \(0.459638\pi\) | |||||||
\(480\) | −1305.35 | −0.124127 | ||||||||
\(481\) | 11564.6 | 1.09626 | ||||||||
\(482\) | 2896.24 | 0.273693 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15060.0 | 1.41435 | ||||||||
\(485\) | 12688.0 | 1.18790 | ||||||||
\(486\) | −5720.00 | −0.533878 | ||||||||
\(487\) | 9328.00 | 0.867951 | 0.433975 | − | 0.900925i | \(-0.357110\pi\) | ||||
0.433975 | + | 0.900925i | \(0.357110\pi\) | |||||||
\(488\) | 244.753 | 0.0227038 | ||||||||
\(489\) | −12464.0 | −1.15264 | ||||||||
\(490\) | 1488.91 | 0.137270 | ||||||||
\(491\) | 1332.00 | 0.122428 | 0.0612142 | − | 0.998125i | \(-0.480503\pi\) | ||||
0.0612142 | + | 0.998125i | \(0.480503\pi\) | |||||||
\(492\) | 5088.00 | 0.466229 | ||||||||
\(493\) | −448.714 | −0.0409920 | ||||||||
\(494\) | −7709.72 | −0.702179 | ||||||||
\(495\) | −8008.00 | −0.727137 | ||||||||
\(496\) | 4736.00 | 0.428735 | ||||||||
\(497\) | 4568.72 | 0.412344 | ||||||||
\(498\) | −9219.03 | −0.829547 | ||||||||
\(499\) | −6308.00 | −0.565902 | −0.282951 | − | 0.959134i | \(-0.591313\pi\) | ||||
−0.282951 | + | 0.959134i | \(0.591313\pi\) | |||||||
\(500\) | −5955.65 | −0.532690 | ||||||||
\(501\) | −8448.00 | −0.753351 | ||||||||
\(502\) | 20.3961 | 0.00181339 | ||||||||
\(503\) | 1325.75 | 0.117519 | 0.0587595 | − | 0.998272i | \(-0.481285\pi\) | ||||
0.0587595 | + | 0.998272i | \(0.481285\pi\) | |||||||
\(504\) | −1794.85 | −0.158629 | ||||||||
\(505\) | 19723.0 | 1.73795 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1732.00 | 0.151718 | ||||||||
\(508\) | −1632.00 | −0.142536 | ||||||||
\(509\) | 5034.00 | 0.438366 | 0.219183 | − | 0.975684i | \(-0.429661\pi\) | ||||
0.219183 | + | 0.975684i | \(0.429661\pi\) | |||||||
\(510\) | −1664.00 | −0.144477 | ||||||||
\(511\) | −4283.18 | −0.370796 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 13950.9 | 1.20068 | ||||||||
\(514\) | −5836.00 | −0.500807 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5058.23 | −0.431543 | ||||||||
\(517\) | −13135.1 | −1.11737 | ||||||||
\(518\) | −11232.0 | −0.952714 | ||||||||
\(519\) | −1768.00 | −0.149531 | ||||||||
\(520\) | −3426.54 | −0.288969 | ||||||||
\(521\) | 7077.44 | 0.595141 | 0.297570 | − | 0.954700i | \(-0.403824\pi\) | ||||
0.297570 | + | 0.954700i | \(0.403824\pi\) | |||||||
\(522\) | 484.000 | 0.0405826 | ||||||||
\(523\) | −13573.6 | −1.13486 | −0.567430 | − | 0.823422i | \(-0.692062\pi\) | ||||
−0.567430 | + | 0.823422i | \(0.692062\pi\) | |||||||
\(524\) | 784.000 | 0.0653611 | ||||||||
\(525\) | 1713.27 | 0.142425 | ||||||||
\(526\) | −10524.4 | −0.872404 | ||||||||
\(527\) | 6037.24 | 0.499025 | ||||||||
\(528\) | −4568.72 | −0.376568 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 1872.00 | 0.153424 | ||||||||
\(531\) | 5500.00 | 0.449491 | ||||||||
\(532\) | 7488.00 | 0.610237 | ||||||||
\(533\) | 13356.0 | 1.08539 | ||||||||
\(534\) | 6526.74 | 0.528914 | ||||||||
\(535\) | 1352.00 | 0.109256 | ||||||||
\(536\) | −5139.81 | −0.414190 | ||||||||
\(537\) | −11056.0 | −0.888457 | ||||||||
\(538\) | −10476.0 | −0.839503 | ||||||||
\(539\) | 5211.20 | 0.416442 | ||||||||
\(540\) | 6200.41 | 0.494117 | ||||||||
\(541\) | −13334.0 | −1.05966 | −0.529828 | − | 0.848105i | \(-0.677743\pi\) | ||||
−0.529828 | + | 0.848105i | \(0.677743\pi\) | |||||||
\(542\) | 6096.00 | 0.483110 | ||||||||
\(543\) | 17826.2 | 1.40883 | ||||||||
\(544\) | 652.674 | 0.0514397 | ||||||||
\(545\) | −12168.0 | −0.956367 | ||||||||
\(546\) | 6853.08 | 0.537152 | ||||||||
\(547\) | −1468.00 | −0.114748 | −0.0573740 | − | 0.998353i | \(-0.518273\pi\) | ||||
−0.0573740 | + | 0.998353i | \(0.518273\pi\) | |||||||
\(548\) | 9871.70 | 0.769522 | ||||||||
\(549\) | −336.535 | −0.0261621 | ||||||||
\(550\) | −2998.22 | −0.232445 | ||||||||
\(551\) | −2019.21 | −0.156119 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22048.0 | 1.69544 | ||||||||
\(554\) | 11300.0 | 0.866590 | ||||||||
\(555\) | 11232.0 | 0.859048 | ||||||||
\(556\) | −9168.00 | −0.699298 | ||||||||
\(557\) | 18427.9 | 1.40182 | 0.700910 | − | 0.713250i | \(-0.252778\pi\) | ||||
0.700910 | + | 0.713250i | \(0.252778\pi\) | |||||||
\(558\) | −6512.00 | −0.494041 | ||||||||
\(559\) | −13277.8 | −1.00464 | ||||||||
\(560\) | 3328.00 | 0.251132 | ||||||||
\(561\) | −5824.00 | −0.438306 | ||||||||
\(562\) | −8566.35 | −0.642971 | ||||||||
\(563\) | 22507.1 | 1.68483 | 0.842416 | − | 0.538828i | \(-0.181133\pi\) | ||||
0.842416 | + | 0.538828i | \(0.181133\pi\) | |||||||
\(564\) | 2944.00 | 0.219796 | ||||||||
\(565\) | 21216.0 | 1.57976 | ||||||||
\(566\) | 6506.35 | 0.483184 | ||||||||
\(567\) | −6343.18 | −0.469821 | ||||||||
\(568\) | 1792.00 | 0.132378 | ||||||||
\(569\) | −8382.79 | −0.617618 | −0.308809 | − | 0.951124i | \(-0.599930\pi\) | ||||
−0.308809 | + | 0.951124i | \(0.599930\pi\) | |||||||
\(570\) | −7488.00 | −0.550242 | ||||||||
\(571\) | 4089.41 | 0.299714 | 0.149857 | − | 0.988708i | \(-0.452119\pi\) | ||||
0.149857 | + | 0.988708i | \(0.452119\pi\) | |||||||
\(572\) | −11992.9 | −0.876657 | ||||||||
\(573\) | −16072.1 | −1.17177 | ||||||||
\(574\) | −12971.9 | −0.943270 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −704.000 | −0.0509259 | ||||||||
\(577\) | −8378.00 | −0.604473 | −0.302236 | − | 0.953233i | \(-0.597733\pi\) | ||||
−0.302236 | + | 0.953233i | \(0.597733\pi\) | |||||||
\(578\) | −8994.00 | −0.647234 | ||||||||
\(579\) | 6664.00 | 0.478318 | ||||||||
\(580\) | −897.427 | −0.0642477 | ||||||||
\(581\) | 23504.0 | 1.67833 | ||||||||
\(582\) | −9953.29 | −0.708895 | ||||||||
\(583\) | 6552.00 | 0.465448 | ||||||||
\(584\) | −1680.00 | −0.119039 | ||||||||
\(585\) | 4711.49 | 0.332985 | ||||||||
\(586\) | −8138.04 | −0.573685 | ||||||||
\(587\) | 27228.0 | 1.91451 | 0.957257 | − | 0.289238i | \(-0.0934020\pi\) | ||||
0.957257 | + | 0.289238i | \(0.0934020\pi\) | |||||||
\(588\) | −1168.00 | −0.0819175 | ||||||||
\(589\) | 27167.6 | 1.90054 | ||||||||
\(590\) | −10198.0 | −0.711604 | ||||||||
\(591\) | 8760.00 | 0.609709 | ||||||||
\(592\) | −4405.55 | −0.305857 | ||||||||
\(593\) | −13462.0 | −0.932240 | −0.466120 | − | 0.884722i | \(-0.654348\pi\) | ||||
−0.466120 | + | 0.884722i | \(0.654348\pi\) | |||||||
\(594\) | 21701.4 | 1.49902 | ||||||||
\(595\) | 4242.38 | 0.292304 | ||||||||
\(596\) | 530.298 | 0.0364461 | ||||||||
\(597\) | −3671.29 | −0.251685 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16224.0 | −1.10667 | −0.553334 | − | 0.832959i | \(-0.686645\pi\) | ||||
−0.553334 | + | 0.832959i | \(0.686645\pi\) | |||||||
\(600\) | 672.000 | 0.0457238 | ||||||||
\(601\) | 13118.0 | 0.890340 | 0.445170 | − | 0.895446i | \(-0.353143\pi\) | ||||
0.445170 | + | 0.895446i | \(0.353143\pi\) | |||||||
\(602\) | 12896.0 | 0.873093 | ||||||||
\(603\) | 7067.24 | 0.477281 | ||||||||
\(604\) | −12288.0 | −0.827801 | ||||||||
\(605\) | 38395.6 | 2.58017 | ||||||||
\(606\) | −15472.0 | −1.03714 | ||||||||
\(607\) | 1144.00 | 0.0764968 | 0.0382484 | − | 0.999268i | \(-0.487822\pi\) | ||||
0.0382484 | + | 0.999268i | \(0.487822\pi\) | |||||||
\(608\) | 2937.04 | 0.195909 | ||||||||
\(609\) | 1794.85 | 0.119427 | ||||||||
\(610\) | 624.000 | 0.0414181 | ||||||||
\(611\) | 7728.00 | 0.511688 | ||||||||
\(612\) | −897.427 | −0.0592751 | ||||||||
\(613\) | −27259.4 | −1.79608 | −0.898038 | − | 0.439917i | \(-0.855008\pi\) | ||||
−0.898038 | + | 0.439917i | \(0.855008\pi\) | |||||||
\(614\) | 8984.00 | 0.590496 | ||||||||
\(615\) | 12971.9 | 0.850533 | ||||||||
\(616\) | 11648.0 | 0.761869 | ||||||||
\(617\) | −21334.3 | −1.39204 | −0.696018 | − | 0.718024i | \(-0.745047\pi\) | ||||
−0.696018 | + | 0.718024i | \(0.745047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19692.4 | 1.27868 | 0.639342 | − | 0.768923i | \(-0.279207\pi\) | ||||
0.639342 | + | 0.768923i | \(0.279207\pi\) | |||||||
\(620\) | 12074.5 | 0.782133 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5760.00 | −0.371310 | ||||||||
\(623\) | −16640.0 | −1.07009 | ||||||||
\(624\) | 2688.00 | 0.172446 | ||||||||
\(625\) | −12559.0 | −0.803776 | ||||||||
\(626\) | 4527.93 | 0.289093 | ||||||||
\(627\) | −26208.0 | −1.66929 | ||||||||
\(628\) | −122.376 | −0.00777604 | ||||||||
\(629\) | −5616.00 | −0.356001 | ||||||||
\(630\) | −4576.00 | −0.289384 | ||||||||
\(631\) | 5384.56 | 0.339709 | 0.169854 | − | 0.985469i | \(-0.445670\pi\) | ||||
0.169854 | + | 0.985469i | \(0.445670\pi\) | |||||||
\(632\) | 8647.94 | 0.544298 | ||||||||
\(633\) | 5296.00 | 0.332539 | ||||||||
\(634\) | −16908.0 | −1.05915 | ||||||||
\(635\) | −4160.80 | −0.260026 | ||||||||
\(636\) | −1468.52 | −0.0915574 | ||||||||
\(637\) | −3066.00 | −0.190705 | ||||||||
\(638\) | −3141.00 | −0.194911 | ||||||||
\(639\) | −2464.00 | −0.152542 | ||||||||
\(640\) | 1305.35 | 0.0806226 | ||||||||
\(641\) | −10422.4 | −0.642215 | −0.321108 | − | 0.947043i | \(-0.604055\pi\) | ||||
−0.321108 | + | 0.947043i | \(0.604055\pi\) | |||||||
\(642\) | −1060.60 | −0.0652000 | ||||||||
\(643\) | −18162.7 | −1.11395 | −0.556973 | − | 0.830531i | \(-0.688037\pi\) | ||||
−0.556973 | + | 0.830531i | \(0.688037\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12896.0 | −0.787255 | ||||||||
\(646\) | 3744.00 | 0.228027 | ||||||||
\(647\) | −23824.0 | −1.44763 | −0.723816 | − | 0.689993i | \(-0.757614\pi\) | ||||
−0.723816 | + | 0.689993i | \(0.757614\pi\) | |||||||
\(648\) | −2488.00 | −0.150830 | ||||||||
\(649\) | −35693.1 | −2.15883 | ||||||||
\(650\) | 1764.00 | 0.106446 | ||||||||
\(651\) | −24149.0 | −1.45387 | ||||||||
\(652\) | 12464.0 | 0.748662 | ||||||||
\(653\) | −5690.00 | −0.340991 | −0.170495 | − | 0.985358i | \(-0.554537\pi\) | ||||
−0.170495 | + | 0.985358i | \(0.554537\pi\) | |||||||
\(654\) | 9545.36 | 0.570724 | ||||||||
\(655\) | 1998.82 | 0.119237 | ||||||||
\(656\) | −5088.00 | −0.302825 | ||||||||
\(657\) | 2310.00 | 0.137172 | ||||||||
\(658\) | −7505.76 | −0.444688 | ||||||||
\(659\) | −4109.81 | −0.242937 | −0.121468 | − | 0.992595i | \(-0.538760\pi\) | ||||
−0.121468 | + | 0.992595i | \(0.538760\pi\) | |||||||
\(660\) | −11648.0 | −0.686966 | ||||||||
\(661\) | −20936.6 | −1.23198 | −0.615990 | − | 0.787754i | \(-0.711244\pi\) | ||||
−0.615990 | + | 0.787754i | \(0.711244\pi\) | |||||||
\(662\) | −20104.0 | −1.18031 | ||||||||
\(663\) | 3426.54 | 0.200718 | ||||||||
\(664\) | 9219.03 | 0.538807 | ||||||||
\(665\) | 19090.7 | 1.11324 | ||||||||
\(666\) | 6057.64 | 0.352445 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 8448.00 | 0.489316 | ||||||||
\(669\) | 7712.00 | 0.445685 | ||||||||
\(670\) | −13104.0 | −0.755600 | ||||||||
\(671\) | 2184.00 | 0.125652 | ||||||||
\(672\) | −2610.70 | −0.149866 | ||||||||
\(673\) | 18986.0 | 1.08745 | 0.543727 | − | 0.839262i | \(-0.317013\pi\) | ||||
0.543727 | + | 0.839262i | \(0.317013\pi\) | |||||||
\(674\) | −979.012 | −0.0559497 | ||||||||
\(675\) | −3192.00 | −0.182015 | ||||||||
\(676\) | −1732.00 | −0.0985435 | ||||||||
\(677\) | −1091.19 | −0.0619466 | −0.0309733 | − | 0.999520i | \(-0.509861\pi\) | ||||
−0.0309733 | + | 0.999520i | \(0.509861\pi\) | |||||||
\(678\) | −16643.2 | −0.942741 | ||||||||
\(679\) | 25376.0 | 1.43423 | ||||||||
\(680\) | 1664.00 | 0.0938404 | ||||||||
\(681\) | −15623.4 | −0.879133 | ||||||||
\(682\) | 42260.7 | 2.37279 | ||||||||
\(683\) | −21396.0 | −1.19868 | −0.599338 | − | 0.800496i | \(-0.704569\pi\) | ||||
−0.599338 | + | 0.800496i | \(0.704569\pi\) | |||||||
\(684\) | −4038.42 | −0.225750 | ||||||||
\(685\) | 25168.0 | 1.40382 | ||||||||
\(686\) | −11013.9 | −0.612991 | ||||||||
\(687\) | 4283.18 | 0.237865 | ||||||||
\(688\) | 5058.23 | 0.280295 | ||||||||
\(689\) | −3854.86 | −0.213147 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15700.0 | 0.864336 | 0.432168 | − | 0.901793i | \(-0.357749\pi\) | ||||
0.432168 | + | 0.901793i | \(0.357749\pi\) | |||||||
\(692\) | 1768.00 | 0.0971232 | ||||||||
\(693\) | −16016.0 | −0.877919 | ||||||||
\(694\) | −17208.0 | −0.941220 | ||||||||
\(695\) | −23373.9 | −1.27572 | ||||||||
\(696\) | 704.000 | 0.0383406 | ||||||||
\(697\) | −6485.95 | −0.352472 | ||||||||
\(698\) | −2348.00 | −0.127325 | ||||||||
\(699\) | −3048.00 | −0.164930 | ||||||||
\(700\) | −1713.27 | −0.0925079 | ||||||||
\(701\) | −10657.0 | −0.574190 | −0.287095 | − | 0.957902i | \(-0.592690\pi\) | ||||
−0.287095 | + | 0.957902i | \(0.592690\pi\) | |||||||
\(702\) | −12768.0 | −0.686463 | ||||||||
\(703\) | −25272.0 | −1.35583 | ||||||||
\(704\) | 4568.72 | 0.244588 | ||||||||
\(705\) | 7505.76 | 0.400969 | ||||||||
\(706\) | −5636.00 | −0.300444 | ||||||||
\(707\) | 39446.0 | 2.09833 | ||||||||
\(708\) | 8000.00 | 0.424659 | ||||||||
\(709\) | 9188.43 | 0.486712 | 0.243356 | − | 0.969937i | \(-0.421752\pi\) | ||||
0.243356 | + | 0.969937i | \(0.421752\pi\) | |||||||
\(710\) | 4568.72 | 0.241494 | ||||||||
\(711\) | −11890.9 | −0.627207 | ||||||||
\(712\) | −6526.74 | −0.343539 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −3328.00 | −0.174436 | ||||||||
\(715\) | −30576.0 | −1.59927 | ||||||||
\(716\) | 11056.0 | 0.577070 | ||||||||
\(717\) | 544.000 | 0.0283348 | ||||||||
\(718\) | 2733.07 | 0.142058 | ||||||||
\(719\) | −18600.0 | −0.964761 | −0.482380 | − | 0.875962i | \(-0.660228\pi\) | ||||
−0.482380 | + | 0.875962i | \(0.660228\pi\) | |||||||
\(720\) | −1794.85 | −0.0929032 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3130.00 | 0.161339 | ||||||||
\(723\) | −5792.49 | −0.297960 | ||||||||
\(724\) | −17826.2 | −0.915061 | ||||||||
\(725\) | 462.000 | 0.0236666 | ||||||||
\(726\) | −30120.0 | −1.53975 | ||||||||
\(727\) | −16786.0 | −0.856337 | −0.428169 | − | 0.903699i | \(-0.640841\pi\) | ||||
−0.428169 | + | 0.903699i | \(0.640841\pi\) | |||||||
\(728\) | −6853.08 | −0.348890 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | −4283.18 | −0.217161 | ||||||||
\(731\) | 6448.00 | 0.326249 | ||||||||
\(732\) | −489.506 | −0.0247167 | ||||||||
\(733\) | 7108.03 | 0.358174 | 0.179087 | − | 0.983833i | \(-0.442686\pi\) | ||||
0.179087 | + | 0.983833i | \(0.442686\pi\) | |||||||
\(734\) | 6159.62 | 0.309749 | ||||||||
\(735\) | −2977.83 | −0.149441 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −45864.0 | −2.29230 | ||||||||
\(738\) | 6996.00 | 0.348952 | ||||||||
\(739\) | −35364.0 | −1.76033 | −0.880166 | − | 0.474665i | \(-0.842569\pi\) | ||||
−0.880166 | + | 0.474665i | \(0.842569\pi\) | |||||||
\(740\) | −11232.0 | −0.557968 | ||||||||
\(741\) | 15419.4 | 0.764436 | ||||||||
\(742\) | 3744.00 | 0.185238 | ||||||||
\(743\) | −7505.76 | −0.370605 | −0.185302 | − | 0.982682i | \(-0.559326\pi\) | ||||
−0.185302 | + | 0.982682i | \(0.559326\pi\) | |||||||
\(744\) | −9472.00 | −0.466748 | ||||||||
\(745\) | 1352.00 | 0.0664878 | ||||||||
\(746\) | 8831.50 | 0.433437 | ||||||||
\(747\) | −12676.2 | −0.620879 | ||||||||
\(748\) | 5824.00 | 0.284688 | ||||||||
\(749\) | 2704.00 | 0.131912 | ||||||||
\(750\) | 11911.3 | 0.579919 | ||||||||
\(751\) | 37936.7 | 1.84332 | 0.921658 | − | 0.388004i | \(-0.126835\pi\) | ||||
0.921658 | + | 0.388004i | \(0.126835\pi\) | |||||||
\(752\) | −2944.00 | −0.142761 | ||||||||
\(753\) | −40.7922 | −0.00197417 | ||||||||
\(754\) | 1848.00 | 0.0892575 | ||||||||
\(755\) | −31328.4 | −1.51014 | ||||||||
\(756\) | 12400.8 | 0.596578 | ||||||||
\(757\) | −32440.0 | −1.55753 | −0.778765 | − | 0.627316i | \(-0.784154\pi\) | ||||
−0.778765 | + | 0.627316i | \(0.784154\pi\) | |||||||
\(758\) | 20.3961 | 0.000977334 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7488.00 | 0.357393 | ||||||||
\(761\) | 9046.00 | 0.430903 | 0.215452 | − | 0.976515i | \(-0.430878\pi\) | ||||
0.215452 | + | 0.976515i | \(0.430878\pi\) | |||||||
\(762\) | 3264.00 | 0.155174 | ||||||||
\(763\) | −24336.0 | −1.15468 | ||||||||
\(764\) | 16072.1 | 0.761084 | ||||||||
\(765\) | −2288.00 | −0.108134 | ||||||||
\(766\) | −81.5843 | −0.00384825 | ||||||||
\(767\) | 21000.0 | 0.988613 | ||||||||
\(768\) | −1024.00 | −0.0481125 | ||||||||
\(769\) | −40690.2 | −1.90810 | −0.954048 | − | 0.299655i | \(-0.903128\pi\) | ||||
−0.954048 | + | 0.299655i | \(0.903128\pi\) | |||||||
\(770\) | 29696.7 | 1.38986 | ||||||||
\(771\) | 11672.0 | 0.545210 | ||||||||
\(772\) | −6664.00 | −0.310677 | ||||||||
\(773\) | −26076.4 | −1.21333 | −0.606664 | − | 0.794958i | \(-0.707493\pi\) | ||||
−0.606664 | + | 0.794958i | \(0.707493\pi\) | |||||||
\(774\) | −6955.06 | −0.322990 | ||||||||
\(775\) | −6216.00 | −0.288110 | ||||||||
\(776\) | 9953.29 | 0.460441 | ||||||||
\(777\) | 22464.0 | 1.03718 | ||||||||
\(778\) | −28656.5 | −1.32055 | ||||||||
\(779\) | −29186.8 | −1.34239 | ||||||||
\(780\) | 6853.08 | 0.314589 | ||||||||
\(781\) | 15990.5 | 0.732632 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3344.00 | −0.152624 | ||||||||
\(784\) | 1168.00 | 0.0532070 | ||||||||
\(785\) | −312.000 | −0.0141857 | ||||||||
\(786\) | −1568.00 | −0.0711561 | ||||||||
\(787\) | 28870.6 | 1.30766 | 0.653829 | − | 0.756642i | \(-0.273161\pi\) | ||||
0.653829 | + | 0.756642i | \(0.273161\pi\) | |||||||
\(788\) | −8760.00 | −0.396018 | ||||||||
\(789\) | 21048.8 | 0.949753 | ||||||||
\(790\) | 22048.0 | 0.992953 | ||||||||
\(791\) | 42432.0 | 1.90734 | ||||||||
\(792\) | −6281.99 | −0.281845 | ||||||||
\(793\) | −1284.95 | −0.0575410 | ||||||||
\(794\) | 22092.0 | 0.987425 | ||||||||
\(795\) | −3744.00 | −0.167026 | ||||||||
\(796\) | 3671.29 | 0.163474 | ||||||||
\(797\) | −24607.9 | −1.09367 | −0.546835 | − | 0.837240i | \(-0.684168\pi\) | ||||
−0.546835 | + | 0.837240i | \(0.684168\pi\) | |||||||
\(798\) | −14976.0 | −0.664342 | ||||||||
\(799\) | −3752.88 | −0.166167 | ||||||||
\(800\) | −672.000 | −0.0296985 | ||||||||
\(801\) | 8974.27 | 0.395868 | ||||||||
\(802\) | −8851.90 | −0.389740 | ||||||||
\(803\) | −14991.1 | −0.658811 | ||||||||
\(804\) | 10279.6 | 0.450913 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24864.0 | −1.08660 | ||||||||
\(807\) | 20952.0 | 0.913935 | ||||||||
\(808\) | 15472.0 | 0.673642 | ||||||||
\(809\) | −9594.00 | −0.416943 | −0.208472 | − | 0.978028i | \(-0.566849\pi\) | ||||
−0.208472 | + | 0.978028i | \(0.566849\pi\) | |||||||
\(810\) | −6343.18 | −0.275156 | ||||||||
\(811\) | 14060.0 | 0.608771 | 0.304386 | − | 0.952549i | \(-0.401549\pi\) | ||||
0.304386 | + | 0.952549i | \(0.401549\pi\) | |||||||
\(812\) | −1794.85 | −0.0775703 | ||||||||
\(813\) | −12192.0 | −0.525944 | ||||||||
\(814\) | −39312.0 | −1.69273 | ||||||||
\(815\) | 31777.1 | 1.36577 | ||||||||
\(816\) | −1305.35 | −0.0560004 | ||||||||
\(817\) | 29016.0 | 1.24252 | ||||||||
\(818\) | −10388.0 | −0.444019 | ||||||||
\(819\) | 9422.99 | 0.402034 | ||||||||
\(820\) | −12971.9 | −0.552437 | ||||||||
\(821\) | −14850.0 | −0.631265 | −0.315633 | − | 0.948882i | \(-0.602217\pi\) | ||||
−0.315633 | + | 0.948882i | \(0.602217\pi\) | |||||||
\(822\) | −19743.4 | −0.837750 | ||||||||
\(823\) | 944.000 | 0.0399827 | 0.0199914 | − | 0.999800i | \(-0.493636\pi\) | ||||
0.0199914 | + | 0.999800i | \(0.493636\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5996.45 | 0.253054 | ||||||||
\(826\) | −20396.1 | −0.859165 | ||||||||
\(827\) | 15959.9 | 0.671078 | 0.335539 | − | 0.942026i | \(-0.391082\pi\) | ||||
0.335539 | + | 0.942026i | \(0.391082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27482.0 | 1.15137 | 0.575687 | − | 0.817670i | \(-0.304735\pi\) | ||||
0.575687 | + | 0.817670i | \(0.304735\pi\) | |||||||
\(830\) | 23504.0 | 0.982935 | ||||||||
\(831\) | −22600.0 | −0.943424 | ||||||||
\(832\) | −2688.00 | −0.112007 | ||||||||
\(833\) | 1488.91 | 0.0619301 | ||||||||
\(834\) | 18336.0 | 0.761299 | ||||||||
\(835\) | 21538.3 | 0.892649 | ||||||||
\(836\) | 26208.0 | 1.08424 | ||||||||
\(837\) | 44992.0 | 1.85801 | ||||||||
\(838\) | 10544.8 | 0.434682 | ||||||||
\(839\) | 11748.1 | 0.483422 | 0.241711 | − | 0.970348i | \(-0.422291\pi\) | ||||
0.241711 | + | 0.970348i | \(0.422291\pi\) | |||||||
\(840\) | −6656.00 | −0.273397 | ||||||||
\(841\) | −23905.0 | −0.980155 | ||||||||
\(842\) | −19233.5 | −0.787209 | ||||||||
\(843\) | 17132.7 | 0.699978 | ||||||||
\(844\) | −5296.00 | −0.215990 | ||||||||
\(845\) | −4415.75 | −0.179771 | ||||||||
\(846\) | 4048.00 | 0.164507 | ||||||||
\(847\) | 76791.2 | 3.11520 | ||||||||
\(848\) | 1468.52 | 0.0594683 | ||||||||
\(849\) | −13012.7 | −0.526024 | ||||||||
\(850\) | −856.635 | −0.0345675 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −3584.00 | −0.144115 | ||||||||
\(853\) | −12850.0 | −0.515798 | −0.257899 | − | 0.966172i | \(-0.583030\pi\) | ||||
−0.257899 | + | 0.966172i | \(0.583030\pi\) | |||||||
\(854\) | 1248.00 | 0.0500067 | ||||||||
\(855\) | −10296.0 | −0.411831 | ||||||||
\(856\) | 1060.60 | 0.0423486 | ||||||||
\(857\) | 25098.0 | 1.00039 | 0.500193 | − | 0.865914i | \(-0.333262\pi\) | ||||
0.500193 | + | 0.865914i | \(0.333262\pi\) | |||||||
\(858\) | 23985.8 | 0.954384 | ||||||||
\(859\) | 40052.0 | 1.59087 | 0.795435 | − | 0.606039i | \(-0.207243\pi\) | ||||
0.795435 | + | 0.606039i | \(0.207243\pi\) | |||||||
\(860\) | 12896.0 | 0.511337 | ||||||||
\(861\) | 25943.8 | 1.02690 | ||||||||
\(862\) | 15215.5 | 0.601208 | ||||||||
\(863\) | 11928.0 | 0.470491 | 0.235246 | − | 0.971936i | \(-0.424411\pi\) | ||||
0.235246 | + | 0.971936i | \(0.424411\pi\) | |||||||
\(864\) | 4864.00 | 0.191524 | ||||||||
\(865\) | 4507.53 | 0.177180 | ||||||||
\(866\) | −19865.8 | −0.779523 | ||||||||
\(867\) | 17988.0 | 0.704619 | ||||||||
\(868\) | 24149.0 | 0.944319 | ||||||||
\(869\) | 77168.0 | 3.01236 | ||||||||
\(870\) | 1794.85 | 0.0699440 | ||||||||
\(871\) | 26984.0 | 1.04973 | ||||||||
\(872\) | −9545.36 | −0.370696 | ||||||||
\(873\) | −13685.8 | −0.530576 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30368.0 | −1.17329 | ||||||||
\(876\) | 3360.00 | 0.129593 | ||||||||
\(877\) | 3306.00 | 0.127293 | 0.0636463 | − | 0.997973i | \(-0.479727\pi\) | ||||
0.0636463 | + | 0.997973i | \(0.479727\pi\) | |||||||
\(878\) | −13536.0 | −0.520294 | ||||||||
\(879\) | 16276.1 | 0.624549 | ||||||||
\(880\) | 11648.0 | 0.446198 | ||||||||
\(881\) | −28065.0 | −1.07325 | −0.536625 | − | 0.843821i | \(-0.680301\pi\) | ||||
−0.536625 | + | 0.843821i | \(0.680301\pi\) | |||||||
\(882\) | −1606.00 | −0.0613116 | ||||||||
\(883\) | −6812.00 | −0.259617 | −0.129809 | − | 0.991539i | \(-0.541436\pi\) | ||||
−0.129809 | + | 0.991539i | \(0.541436\pi\) | |||||||
\(884\) | −3426.54 | −0.130370 | ||||||||
\(885\) | 20396.1 | 0.774697 | ||||||||
\(886\) | −14584.0 | −0.553001 | ||||||||
\(887\) | 25440.0 | 0.963012 | 0.481506 | − | 0.876443i | \(-0.340090\pi\) | ||||
0.481506 | + | 0.876443i | \(0.340090\pi\) | |||||||
\(888\) | 8811.11 | 0.332974 | ||||||||
\(889\) | −8321.60 | −0.313945 | ||||||||
\(890\) | −16640.0 | −0.626712 | ||||||||
\(891\) | −22201.1 | −0.834754 | ||||||||
\(892\) | −7712.00 | −0.289481 | ||||||||
\(893\) | −16888.0 | −0.632849 | ||||||||
\(894\) | −1060.60 | −0.0396774 | ||||||||
\(895\) | 28187.4 | 1.05274 | ||||||||
\(896\) | 2610.70 | 0.0973407 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20396.0 | −0.757932 | ||||||||
\(899\) | −6512.00 | −0.241588 | ||||||||
\(900\) | 924.000 | 0.0342222 | ||||||||
\(901\) | 1872.00 | 0.0692179 | ||||||||
\(902\) | −45401.7 | −1.67595 | ||||||||
\(903\) | −25792.0 | −0.950503 | ||||||||
\(904\) | 16643.2 | 0.612328 | ||||||||
\(905\) | −45448.0 | −1.66933 | ||||||||
\(906\) | 24576.0 | 0.901195 | ||||||||
\(907\) | −9514.77 | −0.348327 | −0.174164 | − | 0.984717i | \(-0.555722\pi\) | ||||
−0.174164 | + | 0.984717i | \(0.555722\pi\) | |||||||
\(908\) | 15623.4 | 0.571014 | ||||||||
\(909\) | −21274.0 | −0.776253 | ||||||||
\(910\) | −17472.0 | −0.636474 | ||||||||
\(911\) | 41628.4 | 1.51395 | 0.756976 | − | 0.653443i | \(-0.226676\pi\) | ||||
0.756976 | + | 0.653443i | \(0.226676\pi\) | |||||||
\(912\) | −5874.07 | −0.213278 | ||||||||
\(913\) | 82264.0 | 2.98197 | ||||||||
\(914\) | 21415.9 | 0.775027 | ||||||||
\(915\) | −1248.00 | −0.0450903 | ||||||||
\(916\) | −4283.18 | −0.154498 | ||||||||
\(917\) | 3997.63 | 0.143962 | ||||||||
\(918\) | 6200.41 | 0.222924 | ||||||||
\(919\) | 30043.4 | 1.07839 | 0.539195 | − | 0.842181i | \(-0.318728\pi\) | ||||
0.539195 | + | 0.842181i | \(0.318728\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17968.0 | −0.642851 | ||||||||
\(922\) | 9588.00 | 0.342477 | ||||||||
\(923\) | −9408.00 | −0.335502 | ||||||||
\(924\) | −23296.0 | −0.829418 | ||||||||
\(925\) | 5782.29 | 0.205536 | ||||||||
\(926\) | 19696.0 | 0.698975 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −704.000 | −0.0249029 | ||||||||
\(929\) | 16266.0 | 0.574457 | 0.287228 | − | 0.957862i | \(-0.407266\pi\) | ||||
0.287228 | + | 0.957862i | \(0.407266\pi\) | |||||||
\(930\) | −24149.0 | −0.851479 | ||||||||
\(931\) | 6700.11 | 0.235862 | ||||||||
\(932\) | 3048.00 | 0.107125 | ||||||||
\(933\) | 11520.0 | 0.404231 | ||||||||
\(934\) | −11972.5 | −0.419435 | ||||||||
\(935\) | 14848.3 | 0.519351 | ||||||||
\(936\) | 3696.00 | 0.129068 | ||||||||
\(937\) | 11013.9 | 0.384000 | 0.192000 | − | 0.981395i | \(-0.438503\pi\) | ||||
0.192000 | + | 0.981395i | \(0.438503\pi\) | |||||||
\(938\) | −26208.0 | −0.912283 | ||||||||
\(939\) | −9055.86 | −0.314725 | ||||||||
\(940\) | −7505.76 | −0.260437 | ||||||||
\(941\) | 42393.2 | 1.46863 | 0.734315 | − | 0.678809i | \(-0.237504\pi\) | ||||
0.734315 | + | 0.678809i | \(0.237504\pi\) | |||||||
\(942\) | 244.753 | 0.00846548 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −8000.00 | −0.275824 | ||||||||
\(945\) | 31616.0 | 1.08833 | ||||||||
\(946\) | 45136.0 | 1.55127 | ||||||||
\(947\) | −3428.00 | −0.117629 | −0.0588147 | − | 0.998269i | \(-0.518732\pi\) | ||||
−0.0588147 | + | 0.998269i | \(0.518732\pi\) | |||||||
\(948\) | −17295.9 | −0.592557 | ||||||||
\(949\) | 8820.00 | 0.301696 | ||||||||
\(950\) | −3854.86 | −0.131651 | ||||||||
\(951\) | 33816.0 | 1.15306 | ||||||||
\(952\) | 3328.00 | 0.113299 | ||||||||
\(953\) | −21191.5 | −0.720316 | −0.360158 | − | 0.932891i | \(-0.617277\pi\) | ||||
−0.360158 | + | 0.932891i | \(0.617277\pi\) | |||||||
\(954\) | −2019.21 | −0.0685266 | ||||||||
\(955\) | 40976.0 | 1.38843 | ||||||||
\(956\) | −544.000 | −0.0184040 | ||||||||
\(957\) | 6281.99 | 0.212192 | ||||||||
\(958\) | 5302.98 | 0.178843 | ||||||||
\(959\) | 50336.0 | 1.69493 | ||||||||
\(960\) | −2610.70 | −0.0877707 | ||||||||
\(961\) | 57825.0 | 1.94102 | ||||||||
\(962\) | 23129.2 | 0.775170 | ||||||||
\(963\) | −1458.32 | −0.0487993 | ||||||||
\(964\) | 5792.49 | 0.193531 | ||||||||
\(965\) | −16989.9 | −0.566762 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3568.00 | −0.118655 | −0.0593274 | − | 0.998239i | \(-0.518896\pi\) | ||||
−0.0593274 | + | 0.998239i | \(0.518896\pi\) | |||||||
\(968\) | 30120.0 | 1.00010 | ||||||||
\(969\) | −7488.00 | −0.248245 | ||||||||
\(970\) | 25376.0 | 0.839973 | ||||||||
\(971\) | 31195.8 | 1.03102 | 0.515510 | − | 0.856883i | \(-0.327602\pi\) | ||||
0.515510 | + | 0.856883i | \(0.327602\pi\) | |||||||
\(972\) | −11440.0 | −0.377508 | ||||||||
\(973\) | −46747.8 | −1.54025 | ||||||||
\(974\) | 18656.0 | 0.613734 | ||||||||
\(975\) | −3528.00 | −0.115884 | ||||||||
\(976\) | 489.506 | 0.0160540 | ||||||||
\(977\) | −11401.4 | −0.373350 | −0.186675 | − | 0.982422i | \(-0.559771\pi\) | ||||
−0.186675 | + | 0.982422i | \(0.559771\pi\) | |||||||
\(978\) | −24928.0 | −0.815040 | ||||||||
\(979\) | −58240.0 | −1.90129 | ||||||||
\(980\) | 2977.83 | 0.0970645 | ||||||||
\(981\) | 13124.9 | 0.427161 | ||||||||
\(982\) | 2664.00 | 0.0865699 | ||||||||
\(983\) | −34326.6 | −1.11378 | −0.556891 | − | 0.830585i | \(-0.688006\pi\) | ||||
−0.556891 | + | 0.830585i | \(0.688006\pi\) | |||||||
\(984\) | 10176.0 | 0.329674 | ||||||||
\(985\) | −22333.7 | −0.722448 | ||||||||
\(986\) | −897.427 | −0.0289857 | ||||||||
\(987\) | 15011.5 | 0.484115 | ||||||||
\(988\) | −15419.4 | −0.496516 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −16016.0 | −0.514164 | ||||||||
\(991\) | −10376.0 | −0.332598 | −0.166299 | − | 0.986075i | \(-0.553182\pi\) | ||||
−0.166299 | + | 0.986075i | \(0.553182\pi\) | |||||||
\(992\) | 9472.00 | 0.303162 | ||||||||
\(993\) | 40208.0 | 1.28496 | ||||||||
\(994\) | 9137.44 | 0.291572 | ||||||||
\(995\) | 9360.00 | 0.298223 | ||||||||
\(996\) | −18438.1 | −0.586578 | ||||||||
\(997\) | 25922.0 | 0.823428 | 0.411714 | − | 0.911313i | \(-0.364930\pi\) | ||||
0.411714 | + | 0.911313i | \(0.364930\pi\) | |||||||
\(998\) | −12616.0 | −0.400153 | ||||||||
\(999\) | −41852.8 | −1.32549 |
(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 | 1058.4.a.i.1.2 | yes | 2 | |
23.22 | odd | 2 | inner | 1058.4.a.i.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1058.4.a.i.1.1 | ✓ | 2 | 23.22 | odd | 2 | inner | |
1058.4.a.i.1.2 | yes | 2 | 1.1 | even | 1 | trivial |