Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,4,Mod(1,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.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: | \(56.6418336055\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{89}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 22 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 480) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(5.21699\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 24.8680 | 1.34274 | 0.671372 | − | 0.741121i | \(-0.265705\pi\) | ||||
0.671372 | + | 0.741121i | \(0.265705\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25.7359 | 0.705425 | 0.352712 | − | 0.935732i | \(-0.385259\pi\) | ||||
0.352712 | + | 0.935732i | \(0.385259\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −60.6039 | −1.29296 | −0.646481 | − | 0.762930i | \(-0.723760\pi\) | ||||
−0.646481 | + | 0.762930i | \(0.723760\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −28.6039 | −0.408086 | −0.204043 | − | 0.978962i | \(-0.565408\pi\) | ||||
−0.204043 | + | 0.978962i | \(0.565408\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −86.6039 | −1.04570 | −0.522850 | − | 0.852425i | \(-0.675131\pi\) | ||||
−0.522850 | + | 0.852425i | \(0.675131\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −74.6039 | −0.775233 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −52.3398 | −0.474505 | −0.237252 | − | 0.971448i | \(-0.576247\pi\) | ||||
−0.237252 | + | 0.971448i | \(0.576247\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −0.0384197 | −0.0192099 | − | 0.999815i | \(-0.506115\pi\) | ||||
−0.0192099 | + | 0.999815i | \(0.506115\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 84.8680 | 0.491701 | 0.245851 | − | 0.969308i | \(-0.420933\pi\) | ||||
0.245851 | + | 0.969308i | \(0.420933\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −77.2078 | −0.407277 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −124.340 | −0.600493 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 448.227 | 1.99157 | 0.995785 | − | 0.0917169i | \(-0.0292355\pi\) | ||||
0.995785 | + | 0.0917169i | \(0.0292355\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 181.812 | 0.746491 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 183.208 | 0.697860 | 0.348930 | − | 0.937149i | \(-0.386545\pi\) | ||||
0.348930 | + | 0.937149i | \(0.386545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −252.000 | −0.893713 | −0.446856 | − | 0.894606i | \(-0.647456\pi\) | ||||
−0.446856 | + | 0.894606i | \(0.647456\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 41.9243 | 0.130112 | 0.0650562 | − | 0.997882i | \(-0.479277\pi\) | ||||
0.0650562 | + | 0.997882i | \(0.479277\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 275.416 | 0.802961 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 85.8117 | 0.235609 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 228.792 | 0.592963 | 0.296481 | − | 0.955039i | \(-0.404187\pi\) | ||||
0.296481 | + | 0.955039i | \(0.404187\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −128.680 | −0.315476 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 259.812 | 0.603735 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −179.849 | −0.396852 | −0.198426 | − | 0.980116i | \(-0.563583\pi\) | ||||
−0.198426 | + | 0.980116i | \(0.563583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −480.039 | −1.00758 | −0.503792 | − | 0.863825i | \(-0.668062\pi\) | ||||
−0.503792 | + | 0.863825i | \(0.668062\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 223.812 | 0.447581 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 303.019 | 0.578230 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −855.472 | −1.55989 | −0.779944 | − | 0.625849i | \(-0.784753\pi\) | ||||
−0.779944 | + | 0.625849i | \(0.784753\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 157.019 | 0.273955 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 675.775 | 1.12957 | 0.564787 | − | 0.825237i | \(-0.308958\pi\) | ||||
0.564787 | + | 0.825237i | \(0.308958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −621.623 | −0.996651 | −0.498325 | − | 0.866990i | \(-0.666052\pi\) | ||||
−0.498325 | + | 0.866990i | \(0.666052\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 640.000 | 0.947205 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −513.699 | −0.731591 | −0.365795 | − | 0.930695i | \(-0.619203\pi\) | ||||
−0.365795 | + | 0.930695i | \(0.619203\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1284.30 | −1.69844 | −0.849220 | − | 0.528039i | \(-0.822928\pi\) | ||||
−0.849220 | + | 0.528039i | \(0.822928\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 143.019 | 0.182502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.0000 | 0.0221816 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1004.87 | −1.19681 | −0.598405 | − | 0.801194i | \(-0.704198\pi\) | ||||
−0.598405 | + | 0.801194i | \(0.704198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1507.10 | −1.73612 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −254.604 | −0.283884 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 433.019 | 0.467651 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 300.416 | 0.314460 | 0.157230 | − | 0.987562i | \(-0.449744\pi\) | ||||
0.157230 | + | 0.987562i | \(0.449744\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 231.623 | 0.235142 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1649.25 | 1.62481 | 0.812407 | − | 0.583091i | \(-0.198157\pi\) | ||||
0.812407 | + | 0.583091i | \(0.198157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1326.38 | −1.26885 | −0.634427 | − | 0.772983i | \(-0.718764\pi\) | ||||
−0.634427 | + | 0.772983i | \(0.718764\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 373.019 | 0.346695 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1189.43 | −1.07464 | −0.537322 | − | 0.843377i | \(-0.680564\pi\) | ||||
−0.537322 | + | 0.843377i | \(0.680564\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1864.42 | −1.63834 | −0.819168 | − | 0.573554i | \(-0.805564\pi\) | ||||
−0.819168 | + | 0.573554i | \(0.805564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1344.68 | −1.14983 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1218.19 | −1.01414 | −0.507069 | − | 0.861906i | \(-0.669271\pi\) | ||||
−0.507069 | + | 0.861906i | \(0.669271\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 261.699 | 0.212205 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −545.435 | −0.430987 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −711.320 | −0.547955 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −668.662 | −0.502376 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −549.623 | −0.402909 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1740.19 | 1.21588 | 0.607941 | − | 0.793982i | \(-0.291996\pi\) | ||||
0.607941 | + | 0.793982i | \(0.291996\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 756.000 | 0.515985 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 456.303 | 0.304331 | 0.152166 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152166 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2153.66 | −1.40411 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1329.51 | 0.829109 | 0.414555 | − | 0.910024i | \(-0.363937\pi\) | ||||
0.414555 | + | 0.910024i | \(0.363937\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1097.25 | −0.669550 | −0.334775 | − | 0.942298i | \(-0.608660\pi\) | ||||
−0.334775 | + | 0.942298i | \(0.608660\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −125.773 | −0.0751204 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1559.70 | −0.912087 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.0000 | 0.0171818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −826.247 | −0.463590 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1590.16 | −0.874299 | −0.437150 | − | 0.899389i | \(-0.644012\pi\) | ||||
−0.437150 | + | 0.899389i | \(0.644012\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1166.60 | −0.628721 | −0.314361 | − | 0.949304i | \(-0.601790\pi\) | ||||
−0.314361 | + | 0.949304i | \(0.601790\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −257.435 | −0.136029 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −424.340 | −0.219895 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1770.57 | −0.900041 | −0.450021 | − | 0.893018i | \(-0.648583\pi\) | ||||
−0.450021 | + | 0.893018i | \(0.648583\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −686.377 | −0.342347 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1301.58 | −0.637138 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4018.35 | 1.93093 | 0.965464 | − | 0.260538i | \(-0.0838999\pi\) | ||||
0.965464 | + | 0.260538i | \(0.0838999\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 386.039 | 0.182140 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2899.74 | −1.34365 | −0.671823 | − | 0.740712i | \(-0.734488\pi\) | ||||
−0.671823 | + | 0.740712i | \(0.734488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1475.83 | 0.671748 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −779.435 | −0.348567 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3127.74 | 1.37455 | 0.687276 | − | 0.726396i | \(-0.258806\pi\) | ||||
0.687276 | + | 0.726396i | \(0.258806\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 621.699 | 0.268549 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 539.546 | 0.229123 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2852.53 | 1.19111 | 0.595553 | − | 0.803316i | \(-0.296933\pi\) | ||||
0.595553 | + | 0.803316i | \(0.296933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1666.91 | 0.684532 | 0.342266 | − | 0.939603i | \(-0.388806\pi\) | ||||
0.342266 | + | 0.939603i | \(0.388806\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1440.12 | 0.581729 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2241.14 | −0.890657 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −736.147 | −0.287874 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −671.435 | −0.258411 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3144.00 | −1.19106 | −0.595528 | − | 0.803334i | \(-0.703057\pi\) | ||||
−0.595528 | + | 0.803334i | \(0.703057\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1063.13 | −0.396507 | −0.198253 | − | 0.980151i | \(-0.563527\pi\) | ||||
−0.198253 | + | 0.980151i | \(0.563527\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −909.058 | −0.333841 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4600.87 | 1.66395 | 0.831976 | − | 0.554812i | \(-0.187210\pi\) | ||||
0.831976 | + | 0.554812i | \(0.187210\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1834.83 | −0.653606 | −0.326803 | − | 0.945092i | \(-0.605971\pi\) | ||||
−0.326803 | + | 0.945092i | \(0.605971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2566.42 | 0.900602 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −149.208 | −0.0515878 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −916.039 | −0.312092 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −471.058 | −0.158168 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2228.83 | −0.737663 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1896.80 | −0.618867 | −0.309434 | − | 0.950921i | \(-0.600139\pi\) | ||||
−0.309434 | + | 0.950921i | \(0.600139\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2027.32 | −0.652160 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1260.00 | 0.399680 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2110.49 | 0.660229 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1864.87 | 0.575417 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1733.51 | 0.527639 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5967.06 | −1.79186 | −0.895928 | − | 0.444200i | \(-0.853488\pi\) | ||||
−0.895928 | + | 0.444200i | \(0.853488\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6375.03 | −1.86399 | −0.931995 | − | 0.362472i | \(-0.881933\pi\) | ||||
−0.931995 | + | 0.362472i | \(0.881933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1360.12 | 0.392485 | 0.196242 | − | 0.980555i | \(-0.437126\pi\) | ||||
0.196242 | + | 0.980555i | \(0.437126\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1920.00 | −0.546869 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 96.7594 | 0.0272056 | 0.0136028 | − | 0.999907i | \(-0.495670\pi\) | ||||
0.0136028 | + | 0.999907i | \(0.495670\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −209.621 | −0.0581880 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1541.10 | 0.422384 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6068.00 | −1.64229 | −0.821143 | − | 0.570722i | \(-0.806663\pi\) | ||||
−0.821143 | + | 0.570722i | \(0.806663\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −542.753 | −0.145070 | −0.0725349 | − | 0.997366i | \(-0.523109\pi\) | ||||
−0.0725349 | + | 0.997366i | \(0.523109\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1377.08 | −0.359095 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5248.53 | 1.35205 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3852.91 | 0.980595 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4658.42 | 1.17146 | 0.585731 | − | 0.810505i | \(-0.300807\pi\) | ||||
0.585731 | + | 0.810505i | \(0.300807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1347.01 | −0.334727 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −429.058 | −0.105367 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6519.33 | −1.58235 | −0.791176 | − | 0.611588i | \(-0.790531\pi\) | ||||
−0.791176 | + | 0.611588i | \(0.790531\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11146.5 | 2.67417 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −54.0000 | −0.0128066 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1205.17 | −0.282562 | −0.141281 | − | 0.989970i | \(-0.545122\pi\) | ||||
−0.141281 | + | 0.989970i | \(0.545122\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1143.96 | −0.265181 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3014.61 | 0.690978 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6083.66 | 1.37891 | 0.689456 | − | 0.724327i | \(-0.257850\pi\) | ||||
0.689456 | + | 0.724327i | \(0.257850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3151.36 | −0.706389 | −0.353194 | − | 0.935550i | \(-0.614905\pi\) | ||||
−0.353194 | + | 0.935550i | \(0.614905\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4521.29 | 1.00235 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 643.398 | 0.141085 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6780.54 | −1.47077 | −0.735385 | − | 0.677650i | \(-0.762998\pi\) | ||||
−0.735385 | + | 0.677650i | \(0.762998\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 763.812 | 0.163900 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5163.29 | 1.09614 | 0.548071 | − | 0.836432i | \(-0.315362\pi\) | ||||
0.548071 | + | 0.836432i | \(0.315362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6543.64 | −1.37448 | −0.687242 | − | 0.726429i | \(-0.741179\pi\) | ||||
−0.687242 | + | 0.726429i | \(0.741179\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1299.06 | −0.269999 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4556.00 | 0.937047 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4094.82 | −0.833466 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −901.247 | −0.181553 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −267.208 | −0.0532780 | −0.0266390 | − | 0.999645i | \(-0.508480\pi\) | ||||
−0.0266390 | + | 0.999645i | \(0.508480\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 899.243 | 0.177478 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −694.870 | −0.135759 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3172.00 | 0.613516 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6266.73 | −1.20003 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4947.74 | −0.938087 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2400.19 | 0.450606 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 646.800 | 0.120244 | 0.0601219 | − | 0.998191i | \(-0.480851\pi\) | ||||
0.0601219 | + | 0.998191i | \(0.480851\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3979.14 | 0.732573 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5855.48 | 1.06763 | 0.533816 | − | 0.845601i | \(-0.320757\pi\) | ||||
0.533816 | + | 0.845601i | \(0.320757\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3939.52 | −0.711421 | −0.355710 | − | 0.934596i | \(-0.615761\pi\) | ||||
−0.355710 | + | 0.934596i | \(0.615761\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1119.06 | −0.200164 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.1943 | −0.00286929 | −0.00143464 | − | 0.999999i | \(-0.500457\pi\) | ||||
−0.00143464 | + | 0.999999i | \(0.500457\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −154.416 | −0.0271022 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3568.30 | 0.620446 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2477.21 | 0.426735 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1515.10 | −0.258592 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5593.25 | 0.945894 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1042.57 | 0.174708 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1946.45 | −0.323223 | −0.161611 | − | 0.986854i | \(-0.551669\pi\) | ||||
−0.161611 | + | 0.986854i | \(0.551669\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4034.04 | 0.663857 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4277.36 | 0.697603 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3713.10 | −0.600195 | −0.300097 | − | 0.953909i | \(-0.597019\pi\) | ||||
−0.300097 | + | 0.953909i | \(0.597019\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3654.57 | 0.585512 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2184.16 | 0.346858 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1680.69 | −0.264573 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −785.097 | −0.122517 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12200.6 | −1.88750 | −0.943751 | − | 0.330658i | \(-0.892729\pi\) | ||||
−0.943751 | + | 0.330658i | \(0.892729\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1455.52 | 0.223244 | 0.111622 | − | 0.993751i | \(-0.464395\pi\) | ||||
0.111622 | + | 0.993751i | \(0.464395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1636.30 | 0.248830 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 364.526 | 0.0549625 | 0.0274813 | − | 0.999622i | \(-0.491251\pi\) | ||||
0.0274813 | + | 0.999622i | \(0.491251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3378.87 | −0.505161 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2133.96 | 0.316362 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11180.1 | 1.64363 | 0.821814 | − | 0.569756i | \(-0.192962\pi\) | ||||
0.821814 | + | 0.569756i | \(0.192962\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 641.233 | 0.0934879 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2005.99 | 0.290047 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3108.12 | 0.445716 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5558.37 | 0.790585 | 0.395292 | − | 0.918555i | \(-0.370643\pi\) | ||||
0.395292 | + | 0.918555i | \(0.370643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1648.87 | 0.232620 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5689.60 | 0.796197 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9598.80 | −1.33246 | −0.666229 | − | 0.745747i | \(-0.732093\pi\) | ||||
−0.666229 | + | 0.745747i | \(0.732093\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 363.623 | 0.0496752 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5518.37 | 0.747915 | 0.373958 | − | 0.927446i | \(-0.378001\pi\) | ||||
0.373958 | + | 0.927446i | \(0.378001\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5220.58 | −0.701990 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7208.20 | −0.961675 | −0.480838 | − | 0.876810i | \(-0.659667\pi\) | ||||
−0.480838 | + | 0.876810i | \(0.659667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3200.00 | −0.423603 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2268.00 | −0.297904 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8580.13 | 1.11833 | 0.559164 | − | 0.829057i | \(-0.311122\pi\) | ||||
0.559164 | + | 0.829057i | \(0.311122\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1497.12 | 0.193639 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1368.91 | −0.175706 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2568.50 | 0.327177 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10323.7 | −1.30512 | −0.652558 | − | 0.757738i | \(-0.726304\pi\) | ||||
−0.652558 | + | 0.757738i | \(0.726304\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6460.99 | 0.810661 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6130.00 | 0.763386 | 0.381693 | − | 0.924289i | \(-0.375341\pi\) | ||||
0.381693 | + | 0.924289i | \(0.375341\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5143.33 | −0.635750 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11535.5 | 1.40490 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4015.45 | 0.485456 | 0.242728 | − | 0.970094i | \(-0.421958\pi\) | ||||
0.242728 | + | 0.970094i | \(0.421958\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3988.54 | −0.478686 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4472.47 | −0.532871 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6421.51 | 0.759566 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3291.75 | 0.386565 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11923.3 | 1.39020 | 0.695098 | − | 0.718915i | \(-0.255361\pi\) | ||||
0.695098 | + | 0.718915i | \(0.255361\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12939.9 | 1.49799 | 0.748993 | − | 0.662577i | \(-0.230537\pi\) | ||||
0.748993 | + | 0.662577i | \(0.230537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 377.318 | 0.0433708 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −715.097 | −0.0816172 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11937.6 | −1.35293 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4679.09 | 0.526594 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5958.20 | 0.665885 | 0.332942 | − | 0.942947i | \(-0.391959\pi\) | ||||
0.332942 | + | 0.942947i | \(0.391959\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8063.83 | 0.894972 | 0.447486 | − | 0.894291i | \(-0.352319\pi\) | ||||
0.447486 | + | 0.894291i | \(0.352319\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −90.0000 | −0.00991993 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4532.83 | 0.496189 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6065.39 | 0.659420 | 0.329710 | − | 0.944082i | \(-0.393049\pi\) | ||||
0.329710 | + | 0.944082i | \(0.393049\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2478.74 | 0.267654 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5019.57 | 0.538345 | 0.269172 | − | 0.963092i | \(-0.413250\pi\) | ||||
0.269172 | + | 0.963092i | \(0.413250\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5024.35 | 0.535229 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4770.47 | 0.504777 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1830.39 | 0.192386 | 0.0961931 | − | 0.995363i | \(-0.469333\pi\) | ||||
0.0961931 | + | 0.995363i | \(0.469333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4715.02 | 0.492288 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3499.81 | 0.362992 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7535.48 | 0.776414 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7111.06 | −0.727881 | −0.363940 | − | 0.931422i | \(-0.618569\pi\) | ||||
−0.363940 | + | 0.931422i | \(0.618569\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 772.305 | 0.0785362 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2347.58 | −0.237176 | −0.118588 | − | 0.992944i | \(-0.537837\pi\) | ||||
−0.118588 | + | 0.992944i | \(0.537837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8669.58 | 0.870215 | 0.435107 | − | 0.900379i | \(-0.356710\pi\) | ||||
0.435107 | + | 0.900379i | \(0.356710\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1273.02 | 0.126957 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6448.02 | 0.638927 | 0.319463 | − | 0.947599i | \(-0.396497\pi\) | ||||
0.319463 | + | 0.947599i | \(0.396497\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21273.8 | −2.09453 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5311.70 | 0.519639 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6485.45 | −0.630447 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2165.10 | −0.209140 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2059.13 | 0.197654 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7603.95 | −0.725330 | −0.362665 | − | 0.931920i | \(-0.618133\pi\) | ||||
−0.362665 | + | 0.931920i | \(0.618133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27164.3 | −2.57502 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3904.75 | 0.367852 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1502.08 | −0.140631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14109.5 | 1.31286 | 0.656429 | − | 0.754388i | \(-0.272066\pi\) | ||||
0.656429 | + | 0.754388i | \(0.272066\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12055.0 | −1.11482 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15808.3 | −1.45299 | −0.726493 | − | 0.687173i | \(-0.758851\pi\) | ||||
−0.726493 | + | 0.687173i | \(0.758851\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 171.623 | 0.0156786 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1158.12 | −0.105159 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16805.1 | 1.51673 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14653.7 | 1.31461 | 0.657304 | − | 0.753625i | \(-0.271697\pi\) | ||||
0.657304 | + | 0.753625i | \(0.271697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8699.23 | 0.775754 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 323.889 | 0.0287108 | 0.0143554 | − | 0.999897i | \(-0.495430\pi\) | ||||
0.0143554 | + | 0.999897i | \(0.495430\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8246.23 | −0.726639 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4427.49 | −0.387834 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2178.99 | −0.189748 | −0.0948741 | − | 0.995489i | \(-0.530245\pi\) | ||||
−0.0948741 | + | 0.995489i | \(0.530245\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15458.5 | −1.33825 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2338.30 | 0.201245 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6631.89 | 0.567449 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1078.96 | 0.0917845 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9383.22 | −0.793599 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12371.2 | −1.04029 | −0.520145 | − | 0.854078i | \(-0.674122\pi\) | ||||
−0.520145 | + | 0.854078i | \(0.674122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3963.16 | −0.331351 | −0.165676 | − | 0.986180i | \(-0.552980\pi\) | ||||
−0.165676 | + | 0.986180i | \(0.552980\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1865.10 | −0.155047 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2427.55 | −0.200656 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9427.54 | −0.774845 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1618.64 | −0.132284 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11103.1 | −0.902305 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5947.16 | 0.480595 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8557.58 | −0.687685 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7088.07 | 0.566428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2426.23 | −0.192813 | −0.0964066 | − | 0.995342i | \(-0.530735\pi\) | ||||
−0.0964066 | + | 0.995342i | \(0.530735\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5000.73 | −0.395215 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9322.08 | 0.732686 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1636.29 | 0.127902 | 0.0639512 | − | 0.997953i | \(-0.479630\pi\) | ||||
0.0639512 | + | 0.997953i | \(0.479630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4320.35 | −0.335862 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 519.623 | 0.0401755 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12774.6 | −0.982339 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6723.41 | 0.514221 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4160.34 | 0.316480 | 0.158240 | − | 0.987401i | \(-0.449418\pi\) | ||||
0.158240 | + | 0.987401i | \(0.449418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15272.2 | 1.15554 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2208.44 | 0.166204 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16665.2 | −1.24752 | −0.623762 | − | 0.781614i | \(-0.714397\pi\) | ||||
−0.623762 | + | 0.781614i | \(0.714397\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6090.94 | 0.453536 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2014.30 | 0.149194 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12324.4 | 0.908025 | 0.454013 | − | 0.890995i | \(-0.349992\pi\) | ||||
0.454013 | + | 0.890995i | \(0.349992\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14208.0 | 1.04131 | 0.520653 | − | 0.853768i | \(-0.325688\pi\) | ||||
0.520653 | + | 0.853768i | \(0.325688\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9432.00 | 0.687657 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1308.50 | −0.0949009 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13281.1 | 0.958232 | 0.479116 | − | 0.877752i | \(-0.340957\pi\) | ||||
0.479116 | + | 0.877752i | \(0.340957\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3189.39 | 0.228923 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31938.0 | −2.28057 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5888.18 | 0.418291 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2727.17 | 0.192743 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24241.4 | −1.70451 | −0.852256 | − | 0.523124i | \(-0.824766\pi\) | ||||
−0.852256 | + | 0.523124i | \(0.824766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7349.90 | −0.514172 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13802.6 | −0.960683 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18184.5 | 1.25927 | 0.629637 | − | 0.776889i | \(-0.283204\pi\) | ||||
0.629637 | + | 0.776889i | \(0.283204\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3556.60 | 0.245053 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5504.49 | 0.377360 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10505.1 | 0.716569 | 0.358285 | − | 0.933612i | \(-0.383362\pi\) | ||||
0.358285 | + | 0.933612i | \(0.383362\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4822.88 | −0.327337 | −0.163669 | − | 0.986515i | \(-0.552333\pi\) | ||||
−0.163669 | + | 0.986515i | \(0.552333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7699.25 | −0.519963 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3343.31 | 0.224669 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27083.2 | −1.81099 | −0.905496 | − | 0.424355i | \(-0.860501\pi\) | ||||
−0.905496 | + | 0.424355i | \(0.860501\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 447.623 | 0.0297843 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2540.77 | −0.168230 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10078.3 | 0.664042 | 0.332021 | − | 0.943272i | \(-0.392269\pi\) | ||||
0.332021 | + | 0.943272i | \(0.392269\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2748.12 | 0.180187 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24141.2 | 1.57518 | 0.787591 | − | 0.616199i | \(-0.211328\pi\) | ||||
0.787591 | + | 0.616199i | \(0.211328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22858.7 | 1.48428 | 0.742140 | − | 0.670245i | \(-0.233811\pi\) | ||||
0.742140 | + | 0.670245i | \(0.233811\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1413.17 | 0.0913184 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24989.1 | −1.60701 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6686.49 | 0.425890 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12821.0 | −0.812732 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 569.330 | 0.0359187 | 0.0179593 | − | 0.999839i | \(-0.494283\pi\) | ||||
0.0179593 | + | 0.999839i | \(0.494283\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5690.39 | 0.357303 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8700.96 | −0.543759 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16691.3 | −1.03820 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6081.97 | 0.376524 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25927.2 | 1.59760 | 0.798802 | − | 0.601594i | \(-0.205468\pi\) | ||||
0.798802 | + | 0.601594i | \(0.205468\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19555.1 | 1.19935 | 0.599673 | − | 0.800245i | \(-0.295297\pi\) | ||||
0.599673 | + | 0.800245i | \(0.295297\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3780.00 | −0.230756 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8653.85 | −0.525839 | −0.262919 | − | 0.964818i | \(-0.584685\pi\) | ||||
−0.262919 | + | 0.964818i | \(0.584685\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4628.57 | −0.279949 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6331.48 | −0.381183 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27732.5 | 1.66195 | 0.830976 | − | 0.556308i | \(-0.187782\pi\) | ||||
0.830976 | + | 0.556308i | \(0.187782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2281.51 | −0.136101 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5594.61 | −0.332217 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30254.7 | 1.78840 | 0.894201 | − | 0.447665i | \(-0.147744\pi\) | ||||
0.894201 | + | 0.447665i | \(0.147744\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20714.2 | 1.21890 | 0.609448 | − | 0.792826i | \(-0.291391\pi\) | ||||
0.609448 | + | 0.792826i | \(0.291391\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5200.52 | −0.304633 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10768.3 | 0.627936 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 314.039 | 0.0182303 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17901.2 | 1.03453 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12354.2 | −0.710775 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5092.56 | −0.291685 | −0.145842 | − | 0.989308i | \(-0.546589\pi\) | ||||
−0.145842 | + | 0.989308i | \(0.546589\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27189.5 | 1.54354 | 0.771771 | − | 0.635901i | \(-0.219371\pi\) | ||||
0.771771 | + | 0.635901i | \(0.219371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7470.72 | 0.422239 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19125.1 | 1.07617 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7705.95 | −0.431713 | −0.215856 | − | 0.976425i | \(-0.569254\pi\) | ||||
−0.215856 | + | 0.976425i | \(0.569254\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6647.56 | −0.370789 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4080.35 | −0.226601 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13865.7 | −0.766678 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15821.6 | −0.871033 | −0.435516 | − | 0.900181i | \(-0.643434\pi\) | ||||
−0.435516 | + | 0.900181i | \(0.643434\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5760.00 | 0.315735 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5486.24 | 0.299432 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5240.45 | −0.284787 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −290.278 | −0.0157072 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2108.00 | 0.113578 | 0.0567888 | − | 0.998386i | \(-0.481914\pi\) | ||||
0.0567888 | + | 0.998386i | \(0.481914\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38818.2 | −2.08258 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 628.864 | 0.0335949 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 41013.4 | 2.18171 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −301.312 | −0.0159605 | −0.00798027 | − | 0.999968i | \(-0.502540\pi\) | ||||
−0.00798027 | + | 0.999968i | \(0.502540\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4623.29 | −0.243864 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4441.97 | −0.233314 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7798.49 | 0.407898 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18204.0 | 0.948175 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12744.9 | 0.661061 | 0.330530 | − | 0.943795i | \(-0.392772\pi\) | ||||
0.330530 | + | 0.943795i | \(0.392772\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32984.3 | −1.70375 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1628.26 | 0.0837561 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −150.000 | −0.00768395 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3416.70 | −0.174303 | −0.0871515 | − | 0.996195i | \(-0.527776\pi\) | ||||
−0.0871515 | + | 0.996195i | \(0.527776\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7208.18 | 0.364712 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5965.41 | 0.300597 | 0.150298 | − | 0.988641i | \(-0.451977\pi\) | ||||
0.150298 | + | 0.988641i | \(0.451977\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4131.23 | 0.207324 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22016.4 | −1.10038 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8546.50 | −0.425424 | −0.212712 | − | 0.977115i | \(-0.568230\pi\) | ||||
−0.212712 | + | 0.977115i | \(0.568230\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15745.6 | −0.780606 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33899.8 | −1.67384 | −0.836919 | − | 0.547326i | \(-0.815646\pi\) | ||||
−0.836919 | + | 0.547326i | \(0.815646\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7950.78 | 0.390999 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11558.7 | −0.566147 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29578.8 | −1.44297 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18256.9 | −0.887087 | −0.443544 | − | 0.896253i | \(-0.646279\pi\) | ||||
−0.443544 | + | 0.896253i | \(0.646279\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13975.3 | −0.676344 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5833.02 | 0.281173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1117.87 | −0.0536717 | −0.0268359 | − | 0.999640i | \(-0.508543\pi\) | ||||
−0.0268359 | + | 0.999640i | \(0.508543\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4041.04 | 0.193255 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28438.3 | 1.35465 | 0.677324 | − | 0.735685i | \(-0.263140\pi\) | ||||
0.677324 | + | 0.735685i | \(0.263140\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46364.2 | −2.19987 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1287.17 | 0.0608339 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10899.5 | 0.513115 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4566.26 | 0.214127 | 0.107063 | − | 0.994252i | \(-0.465855\pi\) | ||||
0.107063 | + | 0.994252i | \(0.465855\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19558.0 | 0.913572 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29259.6 | −1.36144 | −0.680720 | − | 0.732543i | \(-0.738333\pi\) | ||||
−0.680720 | + | 0.732543i | \(0.738333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2121.70 | 0.0983402 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −33439.5 | −1.54393 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15866.5 | −0.729752 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17391.7 | 0.796829 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 162.000 | 0.00739388 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8852.83 | 0.402511 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7865.23 | −0.356246 | −0.178123 | − | 0.984008i | \(-0.557002\pi\) | ||||
−0.178123 | + | 0.984008i | \(0.557002\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3615.50 | 0.163137 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30293.9 | −1.36173 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29092.2 | 1.30277 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3431.88 | 0.153102 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11603.9 | −0.515724 | −0.257862 | − | 0.966182i | \(-0.583018\pi\) | ||||
−0.257862 | + | 0.966182i | \(0.583018\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1199.20 | −0.0530970 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9043.83 | −0.398936 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15998.1 | −0.703062 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6507.92 | 0.284937 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18251.0 | −0.796115 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6069.60 | −0.263777 | −0.131889 | − | 0.991265i | \(-0.542104\pi\) | ||||
−0.131889 | + | 0.991265i | \(0.542104\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26995.1 | −1.16883 | −0.584417 | − | 0.811453i | \(-0.698677\pi\) | ||||
−0.584417 | + | 0.811453i | \(0.698677\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9454.07 | 0.407834 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20091.7 | −0.863537 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21824.2 | 0.934555 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13563.9 | −0.578705 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23158.9 | −0.984472 | −0.492236 | − | 0.870462i | \(-0.663820\pi\) | ||||
−0.492236 | + | 0.870462i | \(0.663820\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30150.7 | −1.27702 | −0.638511 | − | 0.769613i | \(-0.720449\pi\) | ||||
−0.638511 | + | 0.769613i | \(0.720449\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1930.19 | −0.0814554 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33988.7 | 1.42914 | 0.714572 | − | 0.699562i | \(-0.246622\pi\) | ||||
0.714572 | + | 0.699562i | \(0.246622\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11198.3 | 0.469158 | 0.234579 | − | 0.972097i | \(-0.424629\pi\) | ||||
0.234579 | + | 0.972097i | \(0.424629\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20341.6 | 0.849149 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7877.96 | −0.327677 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14498.7 | 0.600896 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2291.43 | −0.0946279 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20126.3 | 0.828174 | 0.414087 | − | 0.910237i | \(-0.364101\pi\) | ||||
0.414087 | + | 0.910237i | \(0.364101\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24353.0 | −0.998524 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15489.9 | −0.632858 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7379.16 | −0.300415 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16628.3 | −0.674562 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19630.9 | 0.793558 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23460.1 | −0.945009 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24676.2 | 0.990500 | 0.495250 | − | 0.868751i | \(-0.335077\pi\) | ||||
0.495250 | + | 0.868751i | \(0.335077\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3897.17 | 0.155884 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44115.5 | −1.75841 | −0.879204 | − | 0.476446i | \(-0.841925\pi\) | ||||
−0.879204 | + | 0.476446i | \(0.841925\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 408.822 | 0.0162385 | 0.00811923 | − | 0.999967i | \(-0.497416\pi\) | ||||
0.00811923 | + | 0.999967i | \(0.497416\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13668.0 | −0.541004 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34369.3 | 1.35567 | 0.677836 | − | 0.735213i | \(-0.262918\pi\) | ||||
0.677836 | + | 0.735213i | \(0.262918\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15638.7 | −0.614719 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12284.5 | 0.481202 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13220.5 | −0.516082 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51844.9 | 2.01687 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2703.74 | 0.104820 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3108.50 | −0.120099 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41868.4 | −1.61208 | −0.806040 | − | 0.591861i | \(-0.798394\pi\) | ||||
−0.806040 | + | 0.591861i | \(0.798394\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 801.623 | 0.0307600 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2174.40 | −0.0831526 | −0.0415763 | − | 0.999135i | \(-0.513238\pi\) | ||||
−0.0415763 | + | 0.999135i | \(0.513238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19480.7 | −0.742442 | −0.371221 | − | 0.928545i | \(-0.621061\pi\) | ||||
−0.371221 | + | 0.928545i | \(0.621061\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2697.73 | −0.102467 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14546.7 | −0.550653 | −0.275326 | − | 0.961351i | \(-0.588786\pi\) | ||||
−0.275326 | + | 0.961351i | \(0.588786\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43275.0 | 1.63262 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2084.61 | 0.0783805 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3630.80 | −0.136058 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14262.6 | −0.532679 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9515.99 | −0.354214 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −509.208 | −0.0188910 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6544.35 | −0.241980 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18800.2 | 0.692836 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8334.54 | −0.306132 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22357.6 | −0.818492 | −0.409246 | − | 0.912424i | \(-0.634208\pi\) | ||||
−0.409246 | + | 0.912424i | \(0.634208\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14843.2 | 0.541605 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32284.2 | −1.17412 | −0.587060 | − | 0.809544i | \(-0.699715\pi\) | ||||
−0.587060 | + | 0.809544i | \(0.699715\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33052.7 | −1.19812 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7200.58 | −0.260157 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11347.3 | 0.408639 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12767.9 | 0.458295 | 0.229147 | − | 0.973392i | \(-0.426406\pi\) | ||||
0.229147 | + | 0.973392i | \(0.426406\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1940.40 | −0.0694228 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40954.6 | −1.46049 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11205.7 | 0.398314 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11937.4 | −0.422951 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17645.4 | −0.623171 | −0.311586 | − | 0.950218i | \(-0.600860\pi\) | ||||
−0.311586 | + | 0.950218i | \(0.600860\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23852.1 | −0.839656 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17566.4 | −0.616398 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3680.74 | 0.128741 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45735.0 | 1.59455 | 0.797277 | − | 0.603614i | \(-0.206273\pi\) | ||||
0.797277 | + | 0.603614i | \(0.206273\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11818.6 | 0.410739 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14982.6 | 0.519042 | 0.259521 | − | 0.965737i | \(-0.416435\pi\) | ||||
0.259521 | + | 0.965737i | \(0.416435\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9589.06 | −0.331138 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3357.17 | 0.115565 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31821.4 | −1.09193 | −0.545964 | − | 0.837809i | \(-0.683836\pi\) | ||||
−0.545964 | + | 0.837809i | \(0.683836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37672.8 | 1.28863 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.5830 | 0.00165658 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19627.5 | 0.667154 | 0.333577 | − | 0.942723i | \(-0.391744\pi\) | ||||
0.333577 | + | 0.942723i | \(0.391744\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15720.0 | 0.532657 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 463.247 | 0.0156475 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33062.3 | 1.11328 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22588.4 | −0.758230 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10704.9 | −0.358214 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5315.65 | 0.177323 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34374.9 | −1.14315 | −0.571573 | − | 0.820551i | \(-0.693667\pi\) | ||||
−0.571573 | + | 0.820551i | \(0.693667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7431.62 | −0.246376 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33737.5 | −1.11503 | −0.557513 | − | 0.830169i | \(-0.688244\pi\) | ||||
−0.557513 | + | 0.830169i | \(0.688244\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27286.3 | −0.899034 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4545.29 | 0.149298 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38438.8 | 1.25872 | 0.629358 | − | 0.777116i | \(-0.283318\pi\) | ||||
0.629358 | + | 0.777116i | \(0.283318\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25861.3 | −0.844259 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16779.7 | −0.546112 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18714.3 | 0.607217 | 0.303609 | − | 0.952797i | \(-0.401808\pi\) | ||||
0.303609 | + | 0.952797i | \(0.401808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23004.3 | −0.744142 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3127.71 | −0.100867 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13189.6 | 0.424071 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23659.4 | −0.758392 | −0.379196 | − | 0.925316i | \(-0.623799\pi\) | ||||
−0.379196 | + | 0.925316i | \(0.623799\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5839.36 | 0.186613 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9174.15 | 0.292301 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52118.0 | −1.65556 | −0.827780 | − | 0.561053i | \(-0.810396\pi\) | ||||
−0.827780 | + | 0.561053i | \(0.810396\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12102.1 | −0.383278 |
(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 | 960.4.a.bk.1.2 | 2 | ||
4.3 | odd | 2 | 960.4.a.bn.1.1 | 2 | |||
8.3 | odd | 2 | 480.4.a.o.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 480.4.a.r.1.2 | yes | 2 | ||
24.5 | odd | 2 | 1440.4.a.y.1.2 | 2 | |||
24.11 | even | 2 | 1440.4.a.s.1.1 | 2 | |||
40.19 | odd | 2 | 2400.4.a.bb.1.2 | 2 | |||
40.29 | even | 2 | 2400.4.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.4.a.o.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
480.4.a.r.1.2 | yes | 2 | 8.5 | even | 2 | ||
960.4.a.bk.1.2 | 2 | 1.1 | even | 1 | trivial | ||
960.4.a.bn.1.1 | 2 | 4.3 | odd | 2 | |||
1440.4.a.s.1.1 | 2 | 24.11 | even | 2 | |||
1440.4.a.y.1.2 | 2 | 24.5 | odd | 2 | |||
2400.4.a.y.1.1 | 2 | 40.29 | even | 2 | |||
2400.4.a.bb.1.2 | 2 | 40.19 | odd | 2 |