Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(1,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.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: | \(45.3134668844\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.9792.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 2x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 384) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.06909\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.1 |
$q$-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 | ||||||||
\(5\) | −17.4288 | −1.55888 | −0.779441 | − | 0.626475i | \(-0.784497\pi\) | ||||
−0.779441 | + | 0.626475i | \(0.784497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.99032 | −0.161462 | −0.0807310 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807310 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.6274 | −0.291299 | −0.145649 | − | 0.989336i | \(-0.546527\pi\) | ||||
−0.145649 | + | 0.989336i | \(0.546527\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 43.3156 | 0.924121 | 0.462061 | − | 0.886848i | \(-0.347110\pi\) | ||||
0.462061 | + | 0.886848i | \(0.347110\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −52.2865 | −0.900021 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −37.8823 | −0.540459 | −0.270229 | − | 0.962796i | \(-0.587100\pi\) | ||||
−0.270229 | + | 0.962796i | \(0.587100\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 79.8823 | 0.964539 | 0.482270 | − | 0.876023i | \(-0.339813\pi\) | ||||
0.482270 | + | 0.876023i | \(0.339813\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.97095 | −0.0932201 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −191.204 | −1.73343 | −0.866714 | − | 0.498806i | \(-0.833772\pi\) | ||||
−0.866714 | + | 0.498806i | \(0.833772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 178.765 | 1.43012 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −138.918 | −0.889530 | −0.444765 | − | 0.895647i | \(-0.646713\pi\) | ||||
−0.444765 | + | 0.895647i | \(0.646713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −212.136 | −1.22906 | −0.614529 | − | 0.788894i | \(-0.710654\pi\) | ||||
−0.614529 | + | 0.788894i | \(0.710654\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −31.8823 | −0.168181 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 52.1177 | 0.251700 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 270.404 | 1.20146 | 0.600731 | − | 0.799451i | \(-0.294876\pi\) | ||||
0.600731 | + | 0.799451i | \(0.294876\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 129.947 | 0.533542 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 441.411 | 1.68139 | 0.840693 | − | 0.541511i | \(-0.182148\pi\) | ||||
0.840693 | + | 0.541511i | \(0.182148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64.1177 | 0.227392 | 0.113696 | − | 0.993516i | \(-0.463731\pi\) | ||||
0.113696 | + | 0.993516i | \(0.463731\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −156.860 | −0.519628 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 436.234 | 1.35386 | 0.676929 | − | 0.736049i | \(-0.263311\pi\) | ||||
0.676929 | + | 0.736049i | \(0.263311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −334.058 | −0.973930 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −113.647 | −0.312034 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −278.348 | −0.721398 | −0.360699 | − | 0.932682i | \(-0.617462\pi\) | ||||
−0.360699 | + | 0.932682i | \(0.617462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 185.224 | 0.454101 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 239.647 | 0.556877 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 830.039 | 1.83156 | 0.915778 | − | 0.401684i | \(-0.131575\pi\) | ||||
0.915778 | + | 0.401684i | \(0.131575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 724.580 | 1.52087 | 0.760434 | − | 0.649416i | \(-0.224986\pi\) | ||||
0.760434 | + | 0.649416i | \(0.224986\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −26.9128 | −0.0538206 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −754.940 | −1.44060 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 859.529 | 1.56729 | 0.783643 | − | 0.621211i | \(-0.213359\pi\) | ||||
0.783643 | + | 0.621211i | \(0.213359\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −573.613 | −1.00079 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 681.264 | 1.13875 | 0.569374 | − | 0.822078i | \(-0.307186\pi\) | ||||
0.569374 | + | 0.822078i | \(0.307186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 785.058 | 1.25869 | 0.629343 | − | 0.777128i | \(-0.283324\pi\) | ||||
0.629343 | + | 0.777128i | \(0.283324\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 536.294 | 0.825678 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31.7793 | 0.0470337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1018.82 | 1.45096 | 0.725481 | − | 0.688243i | \(-0.241618\pi\) | ||||
0.725481 | + | 0.688243i | \(0.241618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 467.334 | 0.618031 | 0.309015 | − | 0.951057i | \(-0.400001\pi\) | ||||
0.309015 | + | 0.951057i | \(0.400001\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 660.244 | 0.842512 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −416.753 | −0.513570 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −510.706 | −0.608256 | −0.304128 | − | 0.952631i | \(-0.598365\pi\) | ||||
−0.304128 | + | 0.952631i | \(0.598365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −129.527 | −0.149210 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −636.409 | −0.709597 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1392.26 | −1.50360 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −234.235 | −0.245186 | −0.122593 | − | 0.992457i | \(-0.539121\pi\) | ||||
−0.122593 | + | 0.992457i | \(0.539121\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −95.6468 | −0.0970996 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 205.555 | 0.202509 | 0.101255 | − | 0.994861i | \(-0.467714\pi\) | ||||
0.101255 | + | 0.994861i | \(0.467714\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −391.379 | −0.374405 | −0.187203 | − | 0.982321i | \(-0.559942\pi\) | ||||
−0.187203 | + | 0.982321i | \(0.559942\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 156.353 | 0.145319 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 934.274 | 0.844109 | 0.422055 | − | 0.906570i | \(-0.361309\pi\) | ||||
0.422055 | + | 0.906570i | \(0.361309\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −584.123 | −0.513292 | −0.256646 | − | 0.966505i | \(-0.582617\pi\) | ||||
−0.256646 | + | 0.966505i | \(0.582617\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 811.211 | 0.693664 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −582.706 | −0.485101 | −0.242551 | − | 0.970139i | \(-0.577984\pi\) | ||||
−0.242551 | + | 0.970139i | \(0.577984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3332.47 | 2.70221 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 389.840 | 0.308040 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 113.280 | 0.0872635 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1218.06 | −0.915145 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1324.23 | 0.970749 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −937.053 | −0.670501 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1461.03 | −1.02083 | −0.510416 | − | 0.859928i | \(-0.670509\pi\) | ||||
−0.510416 | + | 0.859928i | \(0.670509\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 192.353 | 0.131285 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 98.4323 | 0.0656494 | 0.0328247 | − | 0.999461i | \(-0.489550\pi\) | ||||
0.0328247 | + | 0.999461i | \(0.489550\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −238.873 | −0.155736 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −470.579 | −0.300007 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2171.06 | −1.35391 | −0.676956 | − | 0.736024i | \(-0.736701\pi\) | ||||
−0.676956 | + | 0.736024i | \(0.736701\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1624.70 | −0.991407 | −0.495703 | − | 0.868492i | \(-0.665090\pi\) | ||||
−0.495703 | + | 0.868492i | \(0.665090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1308.70 | 0.781650 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −460.333 | −0.269195 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2421.17 | 1.38667 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1002.17 | −0.562299 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −636.658 | −0.350047 | −0.175024 | − | 0.984564i | \(-0.556000\pi\) | ||||
−0.175024 | + | 0.984564i | \(0.556000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1819.34 | −0.980503 | −0.490252 | − | 0.871581i | \(-0.663095\pi\) | ||||
−0.490252 | + | 0.871581i | \(0.663095\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −340.940 | −0.180153 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3697.29 | 1.91596 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1656.50 | 0.842059 | 0.421029 | − | 0.907047i | \(-0.361669\pi\) | ||||
0.421029 | + | 0.907047i | \(0.361669\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −835.045 | −0.416499 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 571.761 | 0.279882 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2228.82 | 1.07101 | 0.535505 | − | 0.844532i | \(-0.320121\pi\) | ||||
0.535505 | + | 0.844532i | \(0.320121\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 555.671 | 0.262175 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1667.01 | −0.772439 | −0.386219 | − | 0.922407i | \(-0.626219\pi\) | ||||
−0.386219 | + | 0.922407i | \(0.626219\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −320.761 | −0.146000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 718.940 | 0.321513 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2500.53 | 1.09891 | 0.549457 | − | 0.835522i | \(-0.314835\pi\) | ||||
0.549457 | + | 0.835522i | \(0.314835\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −534.562 | −0.230909 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2490.12 | 1.05745 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −378.742 | −0.158148 | −0.0790740 | − | 0.996869i | \(-0.525196\pi\) | ||||
−0.0790740 | + | 0.996869i | \(0.525196\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3093.88 | −1.27053 | −0.635265 | − | 0.772294i | \(-0.719109\pi\) | ||||
−0.635265 | + | 0.772294i | \(0.719109\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2173.74 | 0.878073 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4712.82 | −1.87294 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 402.590 | 0.157435 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −80.7385 | −0.0310734 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3656.98 | 1.38539 | 0.692695 | − | 0.721230i | \(-0.256423\pi\) | ||||
0.692695 | + | 0.721230i | \(0.256423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2788.12 | 1.03986 | 0.519930 | − | 0.854209i | \(-0.325958\pi\) | ||||
0.519930 | + | 0.854209i | \(0.325958\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2264.82 | −0.831729 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1147.74 | 0.415091 | 0.207546 | − | 0.978225i | \(-0.433452\pi\) | ||||
0.207546 | + | 0.978225i | \(0.433452\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4842.73 | 1.72508 | 0.862542 | − | 0.505986i | \(-0.168871\pi\) | ||||
0.862542 | + | 0.505986i | \(0.168871\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2578.59 | 0.904873 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 415.408 | 0.143625 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7693.29 | −2.62109 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1720.84 | −0.577809 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −848.942 | −0.280969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3222.35 | 1.05135 | 0.525677 | − | 0.850684i | \(-0.323812\pi\) | ||||
0.525677 | + | 0.850684i | \(0.323812\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2043.79 | 0.657457 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1117.50 | −0.354478 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 634.355 | 0.198446 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2355.17 | 0.726703 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1640.89 | −0.499449 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4932.61 | 1.48122 | 0.740610 | − | 0.671935i | \(-0.234537\pi\) | ||||
0.740610 | + | 0.671935i | \(0.234537\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1608.88 | 0.476705 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3619.49 | −1.05830 | −0.529150 | − | 0.848529i | \(-0.677489\pi\) | ||||
−0.529150 | + | 0.848529i | \(0.677489\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 305.759 | 0.0882320 | 0.0441160 | − | 0.999026i | \(-0.485953\pi\) | ||||
0.0441160 | + | 0.999026i | \(0.485953\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 95.3380 | 0.0271549 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −639.648 | −0.179849 | −0.0899244 | − | 0.995949i | \(-0.528663\pi\) | ||||
−0.0899244 | + | 0.995949i | \(0.528663\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7603.05 | −2.11050 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3056.45 | 0.837713 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1744.94 | 0.472262 | 0.236131 | − | 0.971721i | \(-0.424121\pi\) | ||||
0.236131 | + | 0.971721i | \(0.424121\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3357.29 | 0.897354 | 0.448677 | − | 0.893694i | \(-0.351895\pi\) | ||||
0.448677 | + | 0.893694i | \(0.351895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5822.24 | 1.51824 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3460.15 | 0.891351 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1402.00 | 0.356820 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1317.45 | −0.331301 | −0.165650 | − | 0.986185i | \(-0.552972\pi\) | ||||
−0.165650 | + | 0.986185i | \(0.552972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2032.01 | 0.504945 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1980.73 | 0.486424 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3036.12 | −0.736917 | −0.368459 | − | 0.929644i | \(-0.620114\pi\) | ||||
−0.368459 | + | 0.929644i | \(0.620114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −808.592 | −0.193990 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1250.26 | −0.296510 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1655.76 | 0.388206 | 0.194103 | − | 0.980981i | \(-0.437820\pi\) | ||||
0.194103 | + | 0.980981i | \(0.437820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4851.29 | 1.12458 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1532.12 | −0.351177 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5292.72 | 1.19964 | 0.599820 | − | 0.800135i | \(-0.295239\pi\) | ||||
0.599820 | + | 0.800135i | \(0.295239\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8010.52 | −1.79559 | −0.897795 | − | 0.440414i | \(-0.854832\pi\) | ||||
−0.897795 | + | 0.440414i | \(0.854832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −388.582 | −0.0861467 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1899.80 | −0.416591 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5692.81 | −1.23483 | −0.617415 | − | 0.786638i | \(-0.711820\pi\) | ||||
−0.617415 | + | 0.786638i | \(0.711820\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1909.23 | −0.409686 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2024.83 | −0.429861 | −0.214931 | − | 0.976629i | \(-0.568953\pi\) | ||||
−0.214931 | + | 0.976629i | \(0.568953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −247.761 | −0.0520419 | −0.0260210 | − | 0.999661i | \(-0.508284\pi\) | ||||
−0.0260210 | + | 0.999661i | \(0.508284\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4176.77 | −0.868106 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1319.96 | −0.271480 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3477.94 | −0.707905 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −702.706 | −0.141558 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8133.61 | −1.62174 | −0.810871 | − | 0.585225i | \(-0.801006\pi\) | ||||
−0.810871 | + | 0.585225i | \(0.801006\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14466.6 | −2.85518 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −286.940 | −0.0560605 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8282.12 | −1.60190 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −191.732 | −0.0367152 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 616.664 | 0.116919 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12628.6 | −2.37085 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2974.82 | −0.553035 | −0.276518 | − | 0.961009i | \(-0.589180\pi\) | ||||
−0.276518 | + | 0.961009i | \(0.589180\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1174.14 | −0.216163 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4451.52 | 0.811648 | 0.405824 | − | 0.913951i | \(-0.366985\pi\) | ||||
0.405824 | + | 0.913951i | \(0.366985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8273.75 | 1.49412 | 0.747061 | − | 0.664755i | \(-0.231464\pi\) | ||||
0.747061 | + | 0.664755i | \(0.231464\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 469.060 | 0.0839001 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −429.036 | −0.0760160 | −0.0380080 | − | 0.999277i | \(-0.512101\pi\) | ||||
−0.0380080 | + | 0.999277i | \(0.512101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1476.34 | 0.259119 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2802.82 | 0.487347 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3026.12 | −0.521293 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7743.29 | 1.32160 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1752.37 | −0.296349 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1304.48 | −0.218596 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8196.71 | −1.36112 | −0.680562 | − | 0.732691i | \(-0.738264\pi\) | ||||
−0.680562 | + | 0.732691i | \(0.738264\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2433.63 | 0.400487 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14980.6 | −2.44322 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2000.35 | −0.323341 | −0.161670 | − | 0.986845i | \(-0.551688\pi\) | ||||
−0.161670 | + | 0.986845i | \(0.551688\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1748.12 | −0.280073 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2254.46 | 0.358023 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2024.62 | 0.318715 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9997.40 | 1.56012 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7707.48 | 1.19239 | 0.596195 | − | 0.802840i | \(-0.296679\pi\) | ||||
0.596195 | + | 0.802840i | \(0.296679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9681.98 | 1.48500 | 0.742499 | − | 0.669847i | \(-0.233640\pi\) | ||||
0.742499 | + | 0.669847i | \(0.233640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1169.52 | 0.177847 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10540.3 | −1.58925 | −0.794626 | − | 0.607099i | \(-0.792333\pi\) | ||||
−0.794626 | + | 0.607099i | \(0.792333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11873.6 | −1.77518 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 339.840 | 0.0503816 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −514.158 | −0.0755884 | −0.0377942 | − | 0.999286i | \(-0.512033\pi\) | ||||
−0.0377942 | + | 0.999286i | \(0.512033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −477.826 | −0.0696641 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3654.17 | −0.528359 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13682.7 | −1.96214 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11272.4 | 1.60331 | 0.801657 | − | 0.597785i | \(-0.203952\pi\) | ||||
0.801657 | + | 0.597785i | \(0.203952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3972.70 | 0.560462 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 832.350 | 0.116478 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6956.92 | 0.965726 | 0.482863 | − | 0.875696i | \(-0.339597\pi\) | ||||
0.482863 | + | 0.875696i | \(0.339597\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2811.16 | −0.387114 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6017.30 | −0.822034 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10201.3 | 1.38260 | 0.691299 | − | 0.722569i | \(-0.257039\pi\) | ||||
0.691299 | + | 0.722569i | \(0.257039\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4383.10 | −0.589378 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2461.56 | 0.328406 | 0.164203 | − | 0.986427i | \(-0.447495\pi\) | ||||
0.164203 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −553.877 | −0.0733200 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 577.060 | 0.0757974 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 546.451 | 0.0712240 | 0.0356120 | − | 0.999366i | \(-0.488662\pi\) | ||||
0.0356120 | + | 0.999366i | \(0.488662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7243.25 | 0.936846 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 295.297 | 0.0379027 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17756.8 | −2.26188 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2084.56 | −0.263529 | −0.131764 | − | 0.991281i | \(-0.542064\pi\) | ||||
−0.131764 | + | 0.991281i | \(0.542064\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −716.620 | −0.0899144 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9710.59 | −1.20929 | −0.604643 | − | 0.796497i | \(-0.706684\pi\) | ||||
−0.604643 | + | 0.796497i | \(0.706684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9188.81 | −1.13580 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1411.74 | −0.173209 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2873.69 | −0.349984 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6659.89 | 0.805160 | 0.402580 | − | 0.915385i | \(-0.368114\pi\) | ||||
0.402580 | + | 0.915385i | \(0.368114\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6513.17 | −0.781681 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2482.08 | −0.295727 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8145.09 | −0.963438 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4874.11 | −0.572389 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10576.7 | −1.23318 | −0.616592 | − | 0.787283i | \(-0.711487\pi\) | ||||
−0.616592 | + | 0.787283i | \(0.711487\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4871.09 | 0.563901 | 0.281951 | − | 0.959429i | \(-0.409019\pi\) | ||||
0.281951 | + | 0.959429i | \(0.409019\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3926.11 | 0.451286 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6772.00 | −0.772918 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2166.72 | −0.245562 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1381.00 | −0.155420 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16916.7 | 1.89060 | 0.945302 | − | 0.326196i | \(-0.105767\pi\) | ||||
0.945302 | + | 0.326196i | \(0.105767\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1163.88 | −0.129174 | −0.0645870 | − | 0.997912i | \(-0.520573\pi\) | ||||
−0.0645870 | + | 0.997912i | \(0.520573\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7263.52 | 0.800596 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15273.8 | −1.67196 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1856.28 | 0.201812 | 0.100906 | − | 0.994896i | \(-0.467826\pi\) | ||||
0.100906 | + | 0.994896i | \(0.467826\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3006.52 | −0.324643 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1472.21 | 0.157893 | 0.0789465 | − | 0.996879i | \(-0.474844\pi\) | ||||
0.0789465 | + | 0.996879i | \(0.474844\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8901.02 | 0.948200 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1909.97 | −0.202100 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9620.94 | 1.01123 | 0.505613 | − | 0.862761i | \(-0.331267\pi\) | ||||
0.505613 | + | 0.862761i | \(0.331267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4691.06 | −0.489786 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5458.03 | −0.566094 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2257.51 | 0.232602 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3613.53 | −0.369877 | −0.184938 | − | 0.982750i | \(-0.559209\pi\) | ||||
−0.184938 | + | 0.982750i | \(0.559209\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1022.82 | −0.104011 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17710.7 | 1.78931 | 0.894654 | − | 0.446759i | \(-0.147422\pi\) | ||||
0.894654 | + | 0.446759i | \(0.147422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1674.57 | −0.168087 | −0.0840433 | − | 0.996462i | \(-0.526783\pi\) | ||||
−0.0840433 | + | 0.996462i | \(0.526783\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11091.9 | 1.10618 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15208.3 | 1.50697 | 0.753484 | − | 0.657466i | \(-0.228372\pi\) | ||||
0.753484 | + | 0.657466i | \(0.228372\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2570.26 | −0.253057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4969.51 | 0.486163 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −681.406 | −0.0662391 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14280.1 | 1.37940 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2505.14 | −0.240466 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6458.37 | 0.616056 | 0.308028 | − | 0.951377i | \(-0.400331\pi\) | ||||
0.308028 | + | 0.951377i | \(0.400331\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11712.7 | 1.11030 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1715.28 | 0.161590 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4082.45 | 0.382216 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11337.7 | 1.05495 | 0.527474 | − | 0.849571i | \(-0.323139\pi\) | ||||
0.527474 | + | 0.849571i | \(0.323139\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6686.46 | 0.618348 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14946.7 | −1.37380 | −0.686898 | − | 0.726754i | \(-0.741028\pi\) | ||||
−0.686898 | + | 0.726754i | \(0.741028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5262.51 | 0.480754 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1667.01 | 0.151367 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2037.19 | −0.183865 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2631.77 | 0.236101 | 0.118051 | − | 0.993008i | \(-0.462336\pi\) | ||||
0.118051 | + | 0.993008i | \(0.462336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5001.04 | −0.445968 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6907.45 | −0.612302 | −0.306151 | − | 0.951983i | \(-0.599041\pi\) | ||||
−0.306151 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3582.58 | −0.315689 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −962.283 | −0.0842929 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12020.3 | −1.04674 | −0.523368 | − | 0.852107i | \(-0.675325\pi\) | ||||
−0.523368 | + | 0.852107i | \(0.675325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2347.57 | −0.203230 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2156.82 | 0.185626 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6821.29 | 0.583654 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4636.04 | −0.394377 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7501.60 | 0.634458 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15846.1 | −1.33249 | −0.666247 | − | 0.745731i | \(-0.732101\pi\) | ||||
−0.666247 | + | 0.745731i | \(0.732101\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8891.64 | 0.743411 | 0.371706 | − | 0.928351i | \(-0.378773\pi\) | ||||
0.371706 | + | 0.928351i | \(0.378773\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1603.69 | −0.133316 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8036.20 | 0.664255 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24392.0 | 2.00477 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7470.35 | 0.610519 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19120.0 | 1.55381 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16283.3 | −1.31587 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1136.23 | −0.0913068 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3550.17 | 0.283705 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12833.5 | −1.01988 | −0.509940 | − | 0.860210i | \(-0.670333\pi\) | ||||
−0.509940 | + | 0.860210i | \(0.670333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9281.63 | −0.733541 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10180.6 | 0.800162 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16257.0 | −1.27075 | −0.635375 | − | 0.772204i | \(-0.719155\pi\) | ||||
−0.635375 | + | 0.772204i | \(0.719155\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6521.22 | 0.506956 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11097.1 | −0.857986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3046.59 | −0.234275 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14138.5 | −1.08134 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1558.32 | −0.118542 | −0.0592712 | − | 0.998242i | \(-0.518878\pi\) | ||||
−0.0592712 | + | 0.998242i | \(0.518878\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2777.30 | 0.210138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1207.77 | 0.0908951 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9782.16 | 0.732272 | 0.366136 | − | 0.930561i | \(-0.380681\pi\) | ||||
0.366136 | + | 0.930561i | \(0.380681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10155.9 | 0.756216 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −242.216 | −0.0179402 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7887.05 | −0.581094 | −0.290547 | − | 0.956861i | \(-0.593837\pi\) | ||||
−0.290547 | + | 0.956861i | \(0.593837\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21819.3 | 1.59914 | 0.799570 | − | 0.600573i | \(-0.205061\pi\) | ||||
0.799570 | + | 0.600573i | \(0.205061\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10970.9 | 0.799856 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34180.5 | −2.47900 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7190.22 | 0.518774 | 0.259387 | − | 0.965773i | \(-0.416479\pi\) | ||||
0.259387 | + | 0.965773i | \(0.416479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8364.35 | 0.600363 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1397.48 | −0.0997884 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2958.12 | 0.210142 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6794.46 | −0.480199 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13305.6 | 0.935569 | 0.467785 | − | 0.883843i | \(-0.345052\pi\) | ||||
0.467785 | + | 0.883843i | \(0.345052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16945.9 | −1.18548 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3443.21 | 0.239653 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8062.23 | −0.558307 | −0.279153 | − | 0.960246i | \(-0.590054\pi\) | ||||
−0.279153 | + | 0.960246i | \(0.590054\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1974.34 | −0.136034 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14528.2 | 0.995978 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2185.21 | −0.149058 | −0.0745288 | − | 0.997219i | \(-0.523745\pi\) | ||||
−0.0745288 | + | 0.997219i | \(0.523745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3542.25 | 0.240418 | 0.120209 | − | 0.992749i | \(-0.461643\pi\) | ||||
0.120209 | + | 0.992749i | \(0.461643\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7735.76 | 0.522429 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21229.3 | 1.42660 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6050.64 | −0.404593 | −0.202296 | − | 0.979324i | \(-0.564840\pi\) | ||||
−0.202296 | + | 0.979324i | \(0.564840\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1246.22 | 0.0829220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18895.7 | 1.25113 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22514.2 | −1.48343 | −0.741713 | − | 0.670717i | \(-0.765986\pi\) | ||||
−0.741713 | + | 0.670717i | \(0.765986\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −23079.9 | −1.51328 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4255.88 | −0.277691 | −0.138845 | − | 0.990314i | \(-0.544339\pi\) | ||||
−0.138845 | + | 0.990314i | \(0.544339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −228.949 | −0.0148663 | −0.00743315 | − | 0.999972i | \(-0.502366\pi\) | ||||
−0.00743315 | + | 0.999972i | \(0.502366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5162.51 | −0.333598 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1527.17 | 0.0982102 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6013.82 | −0.384884 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2546.83 | −0.162218 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10243.5 | −0.649340 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11429.2 | −0.721058 | −0.360529 | − | 0.932748i | \(-0.617404\pi\) | ||||
−0.360529 | + | 0.932748i | \(0.617404\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9667.04 | 0.606999 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25464.1 | 1.59136 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14469.9 | −0.900030 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6131.38 | 0.379583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29381.4 | 1.81045 | 0.905223 | − | 0.424938i | \(-0.139704\pi\) | ||||
0.905223 | + | 0.424938i | \(0.139704\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 249.316 | 0.0152909 | 0.00764546 | − | 0.999971i | \(-0.497566\pi\) | ||||
0.00764546 | + | 0.999971i | \(0.497566\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3352.49 | −0.204658 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16025.8 | 0.973785 | 0.486893 | − | 0.873462i | \(-0.338130\pi\) | ||||
0.486893 | + | 0.873462i | \(0.338130\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8821.17 | −0.533530 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1903.06 | 0.114573 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14008.6 | −0.839511 | −0.419755 | − | 0.907637i | \(-0.637884\pi\) | ||||
−0.419755 | + | 0.907637i | \(0.637884\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1715.56 | −0.102340 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7065.52 | 0.419562 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1011.91 | −0.0598152 | −0.0299076 | − | 0.999553i | \(-0.509521\pi\) | ||||
−0.0299076 | + | 0.999553i | \(0.509521\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23619.4 | −1.38985 | −0.694923 | − | 0.719084i | \(-0.744561\pi\) | ||||
−0.694923 | + | 0.719084i | \(0.744561\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4922.67 | −0.288357 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4163.28 | 0.242775 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26561.6 | 1.54194 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14797.8 | 0.855183 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7700.41 | −0.443027 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25811.9 | −1.47842 | −0.739208 | − | 0.673477i | \(-0.764800\pi\) | ||||
−0.739208 | + | 0.673477i | \(0.764800\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4826.64 | 0.275226 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18255.2 | 1.03634 | 0.518172 | − | 0.855277i | \(-0.326613\pi\) | ||||
0.518172 | + | 0.855277i | \(0.326613\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 700.438 | 0.0395881 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10858.5 | −0.611009 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20090.4 | −1.12553 | −0.562765 | − | 0.826617i | \(-0.690262\pi\) | ||||
−0.562765 | + | 0.826617i | \(0.690262\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37839.0 | 2.11059 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 917.278 | 0.0509408 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12056.8 | −0.666659 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16521.5 | 0.909563 | 0.454782 | − | 0.890603i | \(-0.349717\pi\) | ||||
0.454782 | + | 0.890603i | \(0.349717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 286.014 | 0.0156779 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28316.7 | 1.54549 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16721.7 | −0.908720 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1918.95 | −0.103836 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12431.4 | 0.669795 | 0.334897 | − | 0.942255i | \(-0.391298\pi\) | ||||
0.334897 | + | 0.942255i | \(0.391298\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21600.4 | 1.15886 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22809.2 | −1.21850 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −614.674 | −0.0326976 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −980.957 | −0.0519614 | −0.0259807 | − | 0.999662i | \(-0.508271\pi\) | ||||
−0.0259807 | + | 0.999662i | \(0.508271\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9169.36 | 0.483654 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40561.4 | 2.13048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8023.06 | 0.419644 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5234.81 | 0.272660 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4115.73 | 0.213478 | 0.106739 | − | 0.994287i | \(-0.465959\pi\) | ||||
0.106739 | + | 0.994287i | \(0.465959\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1170.35 | 0.0604522 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10071.9 | 0.518088 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24833.5 | −1.27213 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20850.1 | 1.06367 | 0.531833 | − | 0.846849i | \(-0.321503\pi\) | ||||
0.531833 | + | 0.846849i | \(0.321503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2428.92 | −0.122896 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31517.2 | −1.58815 | −0.794074 | − | 0.607821i | \(-0.792044\pi\) | ||||
−0.794074 | + | 0.607821i | \(0.792044\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17466.7 | 0.876558 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9134.57 | −0.456549 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11415.0 | 0.568213 | 0.284106 | − | 0.958793i | \(-0.408303\pi\) | ||||
0.284106 | + | 0.958793i | \(0.408303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10380.4 | 0.514622 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5732.08 | 0.283028 | 0.141514 | − | 0.989936i | \(-0.454803\pi\) | ||||
0.141514 | + | 0.989936i | \(0.454803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11096.2 | 0.545683 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4206.01 | 0.206010 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2793.78 | −0.136291 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7843.07 | 0.381089 | 0.190544 | − | 0.981679i | \(-0.438975\pi\) | ||||
0.190544 | + | 0.981679i | \(0.438975\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3952.34 | −0.191277 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31709.0 | 1.52849 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29125.9 | 1.39841 | 0.699206 | − | 0.714920i | \(-0.253537\pi\) | ||||
0.699206 | + | 0.714920i | \(0.253537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6096.02 | 0.291530 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14228.5 | −0.677768 | −0.338884 | − | 0.940828i | \(-0.610049\pi\) | ||||
−0.338884 | + | 0.940828i | \(0.610049\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1746.71 | 0.0828771 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5942.19 | 0.280837 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35953.6 | 1.69258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28133.7 | −1.31928 | −0.659641 | − | 0.751581i | \(-0.729292\pi\) | ||||
−0.659641 | + | 0.751581i | \(0.729292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9108.35 | −0.425459 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14686.9 | 0.683377 | 0.341689 | − | 0.939813i | \(-0.389001\pi\) | ||||
0.341689 | + | 0.939813i | \(0.389001\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37922.5 | −1.75770 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2425.78 | −0.112000 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35260.9 | 1.62176 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7240.08 | −0.331716 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3750.78 | −0.171190 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28870.9 | −1.31267 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21001.0 | 0.951214 | 0.475607 | − | 0.879658i | \(-0.342228\pi\) | ||||
0.475607 | + | 0.879658i | \(0.342228\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4967.27 | 0.224131 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1742.48 | 0.0783253 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31385.6 | 1.40547 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14553.9 | 0.649274 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13362.7 | −0.593892 | −0.296946 | − | 0.954894i | \(-0.595968\pi\) | ||||
−0.296946 | + | 0.954894i | \(0.595968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16525.5 | −0.731704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4596.36 | −0.202752 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8343.14 | −0.366654 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9965.13 | −0.436304 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15878.2 | 0.692612 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39481.6 | 1.71582 | 0.857911 | − | 0.513798i | \(-0.171762\pi\) | ||||
0.857911 | + | 0.513798i | \(0.171762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31157.5 | −1.34906 | −0.674531 | − | 0.738247i | \(-0.735654\pi\) | ||||
−0.674531 | + | 0.738247i | \(0.735654\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24031.6 | −1.03668 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38845.8 | −1.66958 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5121.87 | 0.219329 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1165.75 | −0.0497368 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21229.9 | 0.902470 | 0.451235 | − | 0.892405i | \(-0.350984\pi\) | ||||
0.451235 | + | 0.892405i | \(0.350984\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24603.8 | 1.04208 | 0.521041 | − | 0.853532i | \(-0.325544\pi\) | ||||
0.521041 | + | 0.853532i | \(0.325544\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5699.41 | −0.240519 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13668.1 | −0.574710 | −0.287355 | − | 0.957824i | \(-0.592776\pi\) | ||||
−0.287355 | + | 0.957824i | \(0.592776\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27518.8 | −1.15291 | −0.576457 | − | 0.817127i | \(-0.695565\pi\) | ||||
−0.576457 | + | 0.817127i | \(0.695565\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17078.4 | −0.712929 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12654.9 | 0.526369 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29054.1 | 1.20414 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5727.68 | −0.236532 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29951.5 | −1.23247 | −0.616234 | − | 0.787563i | \(-0.711343\pi\) | ||||
−0.616234 | + | 0.787563i | \(0.711343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5090.88 | −0.208737 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6074.48 | −0.248180 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5590.49 | 0.227596 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3642.38 | 0.147761 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −743.283 | −0.0300464 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −51702.3 | −2.08265 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5174.61 | −0.207708 | −0.103854 | − | 0.994593i | \(-0.533118\pi\) | ||||
−0.103854 | + | 0.994593i | \(0.533118\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12530.3 | −0.501201 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9258.34 | −0.369030 | −0.184515 | − | 0.982830i | \(-0.559071\pi\) | ||||
−0.184515 | + | 0.982830i | \(0.559071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24353.0 | −0.967304 | −0.483652 | − | 0.875260i | \(-0.660690\pi\) | ||||
−0.483652 | + | 0.875260i | \(0.660690\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3959.88 | −0.156739 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42283.4 | 1.66784 | 0.833919 | − | 0.551887i | \(-0.186092\pi\) | ||||
0.833919 | + | 0.551887i | \(0.186092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43581.4 | −1.71308 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10433.8 | −0.408709 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10827.4 | −0.422663 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37231.0 | 1.44836 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2108.12 | −0.0817286 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2802.08 | 0.108260 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49843.1 | 1.91914 | 0.959568 | − | 0.281476i | \(-0.0908239\pi\) | ||||
0.959568 | + | 0.281476i | \(0.0908239\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24400.8 | −0.936314 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8986.94 | 0.343675 | 0.171837 | − | 0.985125i | \(-0.445030\pi\) | ||||
0.171837 | + | 0.985125i | \(0.445030\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3693.99 | −0.140784 | −0.0703922 | − | 0.997519i | \(-0.522425\pi\) | ||||
−0.0703922 | + | 0.997519i | \(0.522425\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −43399.8 | −1.64844 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51613.0 | −1.95377 | −0.976886 | − | 0.213763i | \(-0.931428\pi\) | ||||
−0.976886 | + | 0.213763i | \(0.931428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4368.95 | 0.164825 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −860.821 | −0.0323665 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34847.4 | 1.30585 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6601.03 | 0.246534 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24846.4 | −0.924856 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29469.5 | 1.09328 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10544.5 | 0.389886 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −575.197 | −0.0211975 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 53922.7 | 1.98061 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17016.8 | 0.622971 | 0.311486 | − | 0.950251i | \(-0.399173\pi\) | ||||
0.311486 | + | 0.950251i | \(0.399173\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1849.99 | 0.0675032 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2991.72 | −0.108804 | −0.0544019 | − | 0.998519i | \(-0.517325\pi\) | ||||
−0.0544019 | + | 0.998519i | \(0.517325\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4966.55 | −0.180032 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −37885.7 | −1.36881 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −294.344 | −0.0105999 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5174.82 | −0.185747 | −0.0928736 | − | 0.995678i | \(-0.529605\pi\) | ||||
−0.0928736 | + | 0.995678i | \(0.529605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8924.46 | −0.319295 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29509.3 | 1.05234 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48338.6 | 1.71823 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3522.41 | −0.124802 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49256.5 | 1.73956 | 0.869780 | − | 0.493439i | \(-0.164260\pi\) | ||||
0.869780 | + | 0.493439i | \(0.164260\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26685.3 | −0.939394 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13354.6 | 0.468605 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7016.69 | −0.245423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31566.5 | −1.10057 | −0.550283 | − | 0.834978i | \(-0.685480\pi\) | ||||
−0.550283 | + | 0.834978i | \(0.685480\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24821.3 | 0.862632 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37575.6 | −1.30173 | −0.650866 | − | 0.759193i | \(-0.725594\pi\) | ||||
−0.650866 | + | 0.759193i | \(0.725594\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −84399.7 | −2.91456 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1407.18 | 0.0484397 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10289.3 | −0.353070 | −0.176535 | − | 0.984294i | \(-0.556489\pi\) | ||||
−0.176535 | + | 0.984294i | \(0.556489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34005.2 | 1.16318 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1287.11 | −0.0438879 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36779.7 | 1.25017 | 0.625085 | − | 0.780557i | \(-0.285064\pi\) | ||||
0.625085 | + | 0.780557i | \(0.285064\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63736.9 | −2.15966 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4429.01 | 0.149602 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6492.15 | 0.218605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15210.9 | 0.510586 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8408.47 | 0.281370 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −48593.6 | −1.62102 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35228.9 | −1.17155 | −0.585773 | − | 0.810475i | \(-0.699209\pi\) | ||||
−0.585773 | + | 0.810475i | \(0.699209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9078.36 | −0.300969 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15314.8 | −0.506155 | −0.253077 | − | 0.967446i | \(-0.581443\pi\) | ||||
−0.253077 | + | 0.967446i | \(0.581443\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4858.38 | 0.160074 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23229.9 | 0.763027 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24074.3 | 0.788337 | 0.394168 | − | 0.919038i | \(-0.371033\pi\) | ||||
0.394168 | + | 0.919038i | \(0.371033\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5427.49 | 0.177184 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5257.10 | −0.171097 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15244.1 | 0.494620 | 0.247310 | − | 0.968936i | \(-0.420453\pi\) | ||||
0.247310 | + | 0.968936i | \(0.420453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20003.7 | −0.647079 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3913.43 | −0.126207 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12259.6 | −0.394168 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37518.6 | 1.20264 | 0.601321 | − | 0.799008i | \(-0.294641\pi\) | ||||
0.601321 | + | 0.799008i | \(0.294641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24590.1 | −0.785845 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −84403.1 | −2.68920 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1717.01 | 0.0545420 | 0.0272710 | − | 0.999628i | \(-0.491318\pi\) | ||||
0.0272710 | + | 0.999628i | \(0.491318\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7300.90 | 0.231221 |
(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 | 768.4.a.v.1.1 | 4 | ||
3.2 | odd | 2 | 2304.4.a.by.1.4 | 4 | |||
4.3 | odd | 2 | 768.4.a.u.1.1 | 4 | |||
8.3 | odd | 2 | inner | 768.4.a.v.1.4 | 4 | ||
8.5 | even | 2 | 768.4.a.u.1.4 | 4 | |||
12.11 | even | 2 | 2304.4.a.cb.1.4 | 4 | |||
16.3 | odd | 4 | 384.4.d.f.193.4 | yes | 8 | ||
16.5 | even | 4 | 384.4.d.f.193.1 | ✓ | 8 | ||
16.11 | odd | 4 | 384.4.d.f.193.5 | yes | 8 | ||
16.13 | even | 4 | 384.4.d.f.193.8 | yes | 8 | ||
24.5 | odd | 2 | 2304.4.a.cb.1.1 | 4 | |||
24.11 | even | 2 | 2304.4.a.by.1.1 | 4 | |||
48.5 | odd | 4 | 1152.4.d.p.577.8 | 8 | |||
48.11 | even | 4 | 1152.4.d.p.577.7 | 8 | |||
48.29 | odd | 4 | 1152.4.d.p.577.2 | 8 | |||
48.35 | even | 4 | 1152.4.d.p.577.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.d.f.193.1 | ✓ | 8 | 16.5 | even | 4 | ||
384.4.d.f.193.4 | yes | 8 | 16.3 | odd | 4 | ||
384.4.d.f.193.5 | yes | 8 | 16.11 | odd | 4 | ||
384.4.d.f.193.8 | yes | 8 | 16.13 | even | 4 | ||
768.4.a.u.1.1 | 4 | 4.3 | odd | 2 | |||
768.4.a.u.1.4 | 4 | 8.5 | even | 2 | |||
768.4.a.v.1.1 | 4 | 1.1 | even | 1 | trivial | ||
768.4.a.v.1.4 | 4 | 8.3 | odd | 2 | inner | ||
1152.4.d.p.577.1 | 8 | 48.35 | even | 4 | |||
1152.4.d.p.577.2 | 8 | 48.29 | odd | 4 | |||
1152.4.d.p.577.7 | 8 | 48.11 | even | 4 | |||
1152.4.d.p.577.8 | 8 | 48.5 | odd | 4 | |||
2304.4.a.by.1.1 | 4 | 24.11 | even | 2 | |||
2304.4.a.by.1.4 | 4 | 3.2 | odd | 2 | |||
2304.4.a.cb.1.1 | 4 | 24.5 | odd | 2 | |||
2304.4.a.cb.1.4 | 4 | 12.11 | even | 2 |