Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.23612.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 20x + 26 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.59056\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.59056 | −1.26945 | −0.634727 | − | 0.772736i | \(-0.718888\pi\) | ||||
−0.634727 | + | 0.772736i | \(0.718888\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.89212 | 0.611515 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −10.7717 | −0.732920 | ||||||||
\(7\) | 16.1465 | 0.871828 | 0.435914 | − | 0.899988i | \(-0.356425\pi\) | ||||
0.435914 | + | 0.899988i | \(0.356425\pi\) | |||||||
\(8\) | 11.1590 | 0.493164 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 14.6764 | 0.353058 | ||||||||
\(13\) | 54.1214 | 1.15466 | 0.577329 | − | 0.816511i | \(-0.304095\pi\) | ||||
0.577329 | + | 0.816511i | \(0.304095\pi\) | |||||||
\(14\) | −57.9749 | −1.10675 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.2041 | −1.23756 | ||||||||
\(17\) | 107.010 | 1.52668 | 0.763342 | − | 0.645995i | \(-0.223557\pi\) | ||||
0.763342 | + | 0.645995i | \(0.223557\pi\) | |||||||
\(18\) | −32.3150 | −0.423152 | ||||||||
\(19\) | 48.7496 | 0.588628 | 0.294314 | − | 0.955709i | \(-0.404909\pi\) | ||||
0.294314 | + | 0.955709i | \(0.404909\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 48.4394 | 0.503350 | ||||||||
\(22\) | −39.4962 | −0.382755 | ||||||||
\(23\) | −11.9498 | −0.108335 | −0.0541674 | − | 0.998532i | \(-0.517250\pi\) | ||||
−0.0541674 | + | 0.998532i | \(0.517250\pi\) | |||||||
\(24\) | 33.4771 | 0.284729 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −194.326 | −1.46579 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 78.9905 | 0.533136 | ||||||||
\(29\) | 239.733 | 1.53508 | 0.767538 | − | 0.641003i | \(-0.221481\pi\) | ||||
0.767538 | + | 0.641003i | \(0.221481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −82.0851 | −0.475578 | −0.237789 | − | 0.971317i | \(-0.576423\pi\) | ||||
−0.237789 | + | 0.971317i | \(0.576423\pi\) | |||||||
\(32\) | 195.115 | 1.07787 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | −384.224 | −1.93806 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 44.0291 | 0.203838 | ||||||||
\(37\) | 21.7573 | 0.0966723 | 0.0483361 | − | 0.998831i | \(-0.484608\pi\) | ||||
0.0483361 | + | 0.998831i | \(0.484608\pi\) | |||||||
\(38\) | −175.038 | −0.747236 | ||||||||
\(39\) | 162.364 | 0.666643 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −124.835 | −0.475510 | −0.237755 | − | 0.971325i | \(-0.576412\pi\) | ||||
−0.237755 | + | 0.971325i | \(0.576412\pi\) | |||||||
\(42\) | −173.925 | −0.638980 | ||||||||
\(43\) | −224.459 | −0.796039 | −0.398019 | − | 0.917377i | \(-0.630302\pi\) | ||||
−0.398019 | + | 0.917377i | \(0.630302\pi\) | |||||||
\(44\) | 53.8133 | 0.184379 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 42.9064 | 0.137526 | ||||||||
\(47\) | 186.832 | 0.579835 | 0.289917 | − | 0.957052i | \(-0.406372\pi\) | ||||
0.289917 | + | 0.957052i | \(0.406372\pi\) | |||||||
\(48\) | −237.612 | −0.714508 | ||||||||
\(49\) | −82.2913 | −0.239916 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 321.029 | 0.881431 | ||||||||
\(52\) | 264.768 | 0.706091 | ||||||||
\(53\) | −233.997 | −0.606453 | −0.303226 | − | 0.952919i | \(-0.598064\pi\) | ||||
−0.303226 | + | 0.952919i | \(0.598064\pi\) | |||||||
\(54\) | −96.9451 | −0.244307 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 180.179 | 0.429954 | ||||||||
\(57\) | 146.249 | 0.339844 | ||||||||
\(58\) | −860.774 | −1.94871 | ||||||||
\(59\) | 232.936 | 0.513996 | 0.256998 | − | 0.966412i | \(-0.417267\pi\) | ||||
0.256998 | + | 0.966412i | \(0.417267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 163.849 | 0.343913 | 0.171957 | − | 0.985105i | \(-0.444991\pi\) | ||||
0.171957 | + | 0.985105i | \(0.444991\pi\) | |||||||
\(62\) | 294.731 | 0.603725 | ||||||||
\(63\) | 145.318 | 0.290609 | ||||||||
\(64\) | −66.9386 | −0.130739 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −118.488 | −0.220984 | ||||||||
\(67\) | 876.918 | 1.59899 | 0.799497 | − | 0.600670i | \(-0.205100\pi\) | ||||
0.799497 | + | 0.600670i | \(0.205100\pi\) | |||||||
\(68\) | 523.503 | 0.933590 | ||||||||
\(69\) | −35.8493 | −0.0625471 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −733.141 | −1.22546 | −0.612731 | − | 0.790291i | \(-0.709929\pi\) | ||||
−0.612731 | + | 0.790291i | \(0.709929\pi\) | |||||||
\(72\) | 100.431 | 0.164388 | ||||||||
\(73\) | −1161.97 | −1.86299 | −0.931496 | − | 0.363750i | \(-0.881496\pi\) | ||||
−0.931496 | + | 0.363750i | \(0.881496\pi\) | |||||||
\(74\) | −78.1208 | −0.122721 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 238.489 | 0.359954 | ||||||||
\(77\) | 177.611 | 0.262866 | ||||||||
\(78\) | −582.978 | −0.846272 | ||||||||
\(79\) | −588.831 | −0.838591 | −0.419296 | − | 0.907850i | \(-0.637723\pi\) | ||||
−0.419296 | + | 0.907850i | \(0.637723\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 448.226 | 0.603638 | ||||||||
\(83\) | 1161.06 | 1.53546 | 0.767731 | − | 0.640772i | \(-0.221386\pi\) | ||||
0.767731 | + | 0.640772i | \(0.221386\pi\) | |||||||
\(84\) | 236.971 | 0.307806 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 805.933 | 1.01053 | ||||||||
\(87\) | 719.198 | 0.886277 | ||||||||
\(88\) | 122.749 | 0.148695 | ||||||||
\(89\) | −1042.16 | −1.24122 | −0.620610 | − | 0.784120i | \(-0.713115\pi\) | ||||
−0.620610 | + | 0.784120i | \(0.713115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 873.869 | 1.00666 | ||||||||
\(92\) | −58.4597 | −0.0662483 | ||||||||
\(93\) | −246.255 | −0.274575 | ||||||||
\(94\) | −670.831 | −0.736074 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 585.345 | 0.622307 | ||||||||
\(97\) | −1546.63 | −1.61893 | −0.809464 | − | 0.587169i | \(-0.800242\pi\) | ||||
−0.809464 | + | 0.587169i | \(0.800242\pi\) | |||||||
\(98\) | 295.472 | 0.304563 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −662.282 | −0.652470 | −0.326235 | − | 0.945289i | \(-0.605780\pi\) | ||||
−0.326235 | + | 0.945289i | \(0.605780\pi\) | |||||||
\(102\) | −1152.67 | −1.11894 | ||||||||
\(103\) | −399.592 | −0.382262 | −0.191131 | − | 0.981565i | \(-0.561216\pi\) | ||||
−0.191131 | + | 0.981565i | \(0.561216\pi\) | |||||||
\(104\) | 603.942 | 0.569436 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 840.181 | 0.769864 | ||||||||
\(107\) | 1591.22 | 1.43765 | 0.718827 | − | 0.695189i | \(-0.244679\pi\) | ||||
0.718827 | + | 0.695189i | \(0.244679\pi\) | |||||||
\(108\) | 132.087 | 0.117686 | ||||||||
\(109\) | 755.128 | 0.663561 | 0.331780 | − | 0.943357i | \(-0.392351\pi\) | ||||
0.331780 | + | 0.943357i | \(0.392351\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 65.2718 | 0.0558138 | ||||||||
\(112\) | −1278.87 | −1.07894 | ||||||||
\(113\) | 1145.65 | 0.953753 | 0.476876 | − | 0.878970i | \(-0.341769\pi\) | ||||
0.476876 | + | 0.878970i | \(0.341769\pi\) | |||||||
\(114\) | −525.115 | −0.431417 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1172.80 | 0.938722 | ||||||||
\(117\) | 487.092 | 0.384886 | ||||||||
\(118\) | −836.372 | −0.652494 | ||||||||
\(119\) | 1727.83 | 1.33101 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −588.309 | −0.436582 | ||||||||
\(123\) | −374.504 | −0.274536 | ||||||||
\(124\) | −401.570 | −0.290823 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −521.774 | −0.368915 | ||||||||
\(127\) | −1461.29 | −1.02101 | −0.510505 | − | 0.859875i | \(-0.670542\pi\) | ||||
−0.510505 | + | 0.859875i | \(0.670542\pi\) | |||||||
\(128\) | −1320.57 | −0.911900 | ||||||||
\(129\) | −673.377 | −0.459593 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1524.94 | −1.01706 | −0.508528 | − | 0.861045i | \(-0.669810\pi\) | ||||
−0.508528 | + | 0.861045i | \(0.669810\pi\) | |||||||
\(132\) | 161.440 | 0.106451 | ||||||||
\(133\) | 787.134 | 0.513182 | ||||||||
\(134\) | −3148.63 | −2.02985 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1194.12 | 0.752906 | ||||||||
\(137\) | 2125.68 | 1.32561 | 0.662805 | − | 0.748792i | \(-0.269366\pi\) | ||||
0.662805 | + | 0.748792i | \(0.269366\pi\) | |||||||
\(138\) | 128.719 | 0.0794007 | ||||||||
\(139\) | −1774.28 | −1.08268 | −0.541339 | − | 0.840805i | \(-0.682082\pi\) | ||||
−0.541339 | + | 0.840805i | \(0.682082\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 560.496 | 0.334768 | ||||||||
\(142\) | 2632.39 | 1.55567 | ||||||||
\(143\) | 595.335 | 0.348143 | ||||||||
\(144\) | −712.837 | −0.412521 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4172.13 | 2.36498 | ||||||||
\(147\) | −246.874 | −0.138516 | ||||||||
\(148\) | 106.439 | 0.0591165 | ||||||||
\(149\) | 1575.78 | 0.866393 | 0.433197 | − | 0.901299i | \(-0.357386\pi\) | ||||
0.433197 | + | 0.901299i | \(0.357386\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 420.978 | 0.226879 | 0.113439 | − | 0.993545i | \(-0.463813\pi\) | ||||
0.113439 | + | 0.993545i | \(0.463813\pi\) | |||||||
\(152\) | 543.998 | 0.290290 | ||||||||
\(153\) | 963.086 | 0.508895 | ||||||||
\(154\) | −637.724 | −0.333696 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 794.304 | 0.407662 | ||||||||
\(157\) | 2224.30 | 1.13069 | 0.565345 | − | 0.824854i | \(-0.308743\pi\) | ||||
0.565345 | + | 0.824854i | \(0.308743\pi\) | |||||||
\(158\) | 2114.23 | 1.06455 | ||||||||
\(159\) | −701.992 | −0.350136 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −192.947 | −0.0944492 | ||||||||
\(162\) | −290.835 | −0.141051 | ||||||||
\(163\) | 3093.37 | 1.48645 | 0.743226 | − | 0.669040i | \(-0.233295\pi\) | ||||
0.743226 | + | 0.669040i | \(0.233295\pi\) | |||||||
\(164\) | −610.706 | −0.290781 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4168.87 | −1.94920 | ||||||||
\(167\) | 2416.43 | 1.11970 | 0.559848 | − | 0.828595i | \(-0.310860\pi\) | ||||
0.559848 | + | 0.828595i | \(0.310860\pi\) | |||||||
\(168\) | 540.537 | 0.248234 | ||||||||
\(169\) | 732.122 | 0.333237 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 438.746 | 0.196209 | ||||||||
\(172\) | −1098.08 | −0.486789 | ||||||||
\(173\) | 3758.02 | 1.65154 | 0.825771 | − | 0.564005i | \(-0.190740\pi\) | ||||
0.825771 | + | 0.564005i | \(0.190740\pi\) | |||||||
\(174\) | −2582.32 | −1.12509 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −871.245 | −0.373140 | ||||||||
\(177\) | 698.809 | 0.296756 | ||||||||
\(178\) | 3741.93 | 1.57567 | ||||||||
\(179\) | 2533.99 | 1.05810 | 0.529049 | − | 0.848591i | \(-0.322549\pi\) | ||||
0.529049 | + | 0.848591i | \(0.322549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8995 | −0.00570798 | −0.00285399 | − | 0.999996i | \(-0.500908\pi\) | ||||
−0.00285399 | + | 0.999996i | \(0.500908\pi\) | |||||||
\(182\) | −3137.68 | −1.27791 | ||||||||
\(183\) | 491.547 | 0.198558 | ||||||||
\(184\) | −133.348 | −0.0534268 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 884.194 | 0.348561 | ||||||||
\(187\) | 1177.10 | 0.460312 | ||||||||
\(188\) | 914.004 | 0.354577 | ||||||||
\(189\) | 435.955 | 0.167783 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3495.39 | 1.32417 | 0.662087 | − | 0.749427i | \(-0.269671\pi\) | ||||
0.662087 | + | 0.749427i | \(0.269671\pi\) | |||||||
\(192\) | −200.816 | −0.0754824 | ||||||||
\(193\) | −3469.33 | −1.29393 | −0.646963 | − | 0.762522i | \(-0.723961\pi\) | ||||
−0.646963 | + | 0.762522i | \(0.723961\pi\) | |||||||
\(194\) | 5553.25 | 2.05516 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −402.579 | −0.146712 | ||||||||
\(197\) | −3638.39 | −1.31586 | −0.657930 | − | 0.753079i | \(-0.728568\pi\) | ||||
−0.657930 | + | 0.753079i | \(0.728568\pi\) | |||||||
\(198\) | −355.465 | −0.127585 | ||||||||
\(199\) | 51.6049 | 0.0183828 | 0.00919140 | − | 0.999958i | \(-0.497074\pi\) | ||||
0.00919140 | + | 0.999958i | \(0.497074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2630.75 | 0.923179 | ||||||||
\(202\) | 2377.96 | 0.828281 | ||||||||
\(203\) | 3870.84 | 1.33832 | ||||||||
\(204\) | 1570.51 | 0.539008 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1434.76 | 0.485265 | ||||||||
\(207\) | −107.548 | −0.0361116 | ||||||||
\(208\) | −4286.63 | −1.42896 | ||||||||
\(209\) | 536.246 | 0.177478 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2084.57 | 0.680131 | 0.340065 | − | 0.940402i | \(-0.389551\pi\) | ||||
0.340065 | + | 0.940402i | \(0.389551\pi\) | |||||||
\(212\) | −1144.74 | −0.370855 | ||||||||
\(213\) | −2199.42 | −0.707521 | ||||||||
\(214\) | −5713.37 | −1.82504 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 301.294 | 0.0949095 | ||||||||
\(217\) | −1325.38 | −0.414622 | ||||||||
\(218\) | −2711.33 | −0.842361 | ||||||||
\(219\) | −3485.91 | −1.07560 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5791.50 | 1.76280 | ||||||||
\(222\) | −234.362 | −0.0708531 | ||||||||
\(223\) | −1887.36 | −0.566757 | −0.283378 | − | 0.959008i | \(-0.591455\pi\) | ||||
−0.283378 | + | 0.959008i | \(0.591455\pi\) | |||||||
\(224\) | 3150.42 | 0.939715 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4113.54 | −1.21075 | ||||||||
\(227\) | 1150.73 | 0.336462 | 0.168231 | − | 0.985748i | \(-0.446194\pi\) | ||||
0.168231 | + | 0.985748i | \(0.446194\pi\) | |||||||
\(228\) | 715.466 | 0.207820 | ||||||||
\(229\) | 4106.79 | 1.18508 | 0.592542 | − | 0.805540i | \(-0.298125\pi\) | ||||
0.592542 | + | 0.805540i | \(0.298125\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 532.834 | 0.151766 | ||||||||
\(232\) | 2675.18 | 0.757045 | ||||||||
\(233\) | 5733.58 | 1.61210 | 0.806050 | − | 0.591848i | \(-0.201601\pi\) | ||||
0.806050 | + | 0.591848i | \(0.201601\pi\) | |||||||
\(234\) | −1748.93 | −0.488596 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1139.55 | 0.314316 | ||||||||
\(237\) | −1766.49 | −0.484161 | ||||||||
\(238\) | −6203.86 | −1.68965 | ||||||||
\(239\) | 6036.18 | 1.63367 | 0.816837 | − | 0.576868i | \(-0.195725\pi\) | ||||
0.816837 | + | 0.576868i | \(0.195725\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3720.90 | 0.994540 | 0.497270 | − | 0.867596i | \(-0.334336\pi\) | ||||
0.497270 | + | 0.867596i | \(0.334336\pi\) | |||||||
\(242\) | −434.458 | −0.115405 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 801.568 | 0.210308 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1344.68 | 0.348511 | ||||||||
\(247\) | 2638.39 | 0.679664 | ||||||||
\(248\) | −915.990 | −0.234538 | ||||||||
\(249\) | 3483.19 | 0.886500 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3809.88 | −0.958077 | −0.479038 | − | 0.877794i | \(-0.659015\pi\) | ||||
−0.479038 | + | 0.877794i | \(0.659015\pi\) | |||||||
\(252\) | 710.914 | 0.177712 | ||||||||
\(253\) | −131.447 | −0.0326641 | ||||||||
\(254\) | 5246.84 | 1.29613 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5277.10 | 1.28835 | ||||||||
\(257\) | −1225.95 | −0.297559 | −0.148780 | − | 0.988870i | \(-0.547535\pi\) | ||||
−0.148780 | + | 0.988870i | \(0.547535\pi\) | |||||||
\(258\) | 2417.80 | 0.583433 | ||||||||
\(259\) | 351.303 | 0.0842816 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2157.59 | 0.511692 | ||||||||
\(262\) | 5475.38 | 1.29111 | ||||||||
\(263\) | −7397.68 | −1.73445 | −0.867225 | − | 0.497916i | \(-0.834099\pi\) | ||||
−0.867225 | + | 0.497916i | \(0.834099\pi\) | |||||||
\(264\) | 368.248 | 0.0858489 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2826.25 | −0.651461 | ||||||||
\(267\) | −3126.47 | −0.716618 | ||||||||
\(268\) | 4289.99 | 0.977808 | ||||||||
\(269\) | −3214.48 | −0.728589 | −0.364295 | − | 0.931284i | \(-0.618690\pi\) | ||||
−0.364295 | + | 0.931284i | \(0.618690\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7377.37 | −1.65367 | −0.826833 | − | 0.562448i | \(-0.809860\pi\) | ||||
−0.826833 | + | 0.562448i | \(0.809860\pi\) | |||||||
\(272\) | −8475.60 | −1.88937 | ||||||||
\(273\) | 2621.61 | 0.581197 | ||||||||
\(274\) | −7632.36 | −1.68280 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −175.379 | −0.0382485 | ||||||||
\(277\) | 810.606 | 0.175829 | 0.0879144 | − | 0.996128i | \(-0.471980\pi\) | ||||
0.0879144 | + | 0.996128i | \(0.471980\pi\) | |||||||
\(278\) | 6370.65 | 1.37441 | ||||||||
\(279\) | −738.766 | −0.158526 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1114.72 | 0.236651 | 0.118325 | − | 0.992975i | \(-0.462247\pi\) | ||||
0.118325 | + | 0.992975i | \(0.462247\pi\) | |||||||
\(282\) | −2012.49 | −0.424972 | ||||||||
\(283\) | −2265.40 | −0.475844 | −0.237922 | − | 0.971284i | \(-0.576466\pi\) | ||||
−0.237922 | + | 0.971284i | \(0.576466\pi\) | |||||||
\(284\) | −3586.61 | −0.749388 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2137.59 | −0.441951 | ||||||||
\(287\) | −2015.64 | −0.414563 | ||||||||
\(288\) | 1756.03 | 0.359289 | ||||||||
\(289\) | 6538.04 | 1.33076 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4639.88 | −0.934689 | ||||||||
\(292\) | −5684.50 | −1.13925 | ||||||||
\(293\) | −3802.06 | −0.758084 | −0.379042 | − | 0.925380i | \(-0.623746\pi\) | ||||
−0.379042 | + | 0.925380i | \(0.623746\pi\) | |||||||
\(294\) | 886.416 | 0.175840 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 242.790 | 0.0476753 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | −5657.92 | −1.09985 | ||||||||
\(299\) | −646.738 | −0.125090 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3624.22 | −0.694009 | ||||||||
\(302\) | −1511.55 | −0.288013 | ||||||||
\(303\) | −1986.85 | −0.376704 | ||||||||
\(304\) | −3861.17 | −0.728465 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3458.02 | −0.646019 | ||||||||
\(307\) | 1356.35 | 0.252153 | 0.126077 | − | 0.992021i | \(-0.459761\pi\) | ||||
0.126077 | + | 0.992021i | \(0.459761\pi\) | |||||||
\(308\) | 868.895 | 0.160746 | ||||||||
\(309\) | −1198.78 | −0.220699 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8078.07 | −1.47288 | −0.736440 | − | 0.676503i | \(-0.763495\pi\) | ||||
−0.736440 | + | 0.676503i | \(0.763495\pi\) | |||||||
\(312\) | 1811.83 | 0.328764 | ||||||||
\(313\) | −5761.54 | −1.04045 | −0.520226 | − | 0.854029i | \(-0.674152\pi\) | ||||
−0.520226 | + | 0.854029i | \(0.674152\pi\) | |||||||
\(314\) | −7986.48 | −1.43536 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2880.63 | −0.512811 | ||||||||
\(317\) | −5107.00 | −0.904851 | −0.452426 | − | 0.891802i | \(-0.649441\pi\) | ||||
−0.452426 | + | 0.891802i | \(0.649441\pi\) | |||||||
\(318\) | 2520.54 | 0.444481 | ||||||||
\(319\) | 2637.06 | 0.462843 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4773.66 | 0.830030 | ||||||||
\(322\) | 692.786 | 0.119899 | ||||||||
\(323\) | 5216.67 | 0.898648 | ||||||||
\(324\) | 396.262 | 0.0679461 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11106.9 | −1.88698 | ||||||||
\(327\) | 2265.38 | 0.383107 | ||||||||
\(328\) | −1393.03 | −0.234504 | ||||||||
\(329\) | 3016.68 | 0.505516 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2780.94 | −0.461796 | −0.230898 | − | 0.972978i | \(-0.574166\pi\) | ||||
−0.230898 | + | 0.972978i | \(0.574166\pi\) | |||||||
\(332\) | 5680.06 | 0.938958 | ||||||||
\(333\) | 195.816 | 0.0322241 | ||||||||
\(334\) | −8676.35 | −1.42140 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3836.60 | −0.622928 | ||||||||
\(337\) | −4939.28 | −0.798397 | −0.399198 | − | 0.916865i | \(-0.630712\pi\) | ||||
−0.399198 | + | 0.916865i | \(0.630712\pi\) | |||||||
\(338\) | −2628.73 | −0.423029 | ||||||||
\(339\) | 3436.96 | 0.550649 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −902.936 | −0.143392 | ||||||||
\(342\) | −1575.34 | −0.249079 | ||||||||
\(343\) | −6866.96 | −1.08099 | ||||||||
\(344\) | −2504.74 | −0.392578 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13493.4 | −2.09656 | ||||||||
\(347\) | 2711.58 | 0.419496 | 0.209748 | − | 0.977755i | \(-0.432736\pi\) | ||||
0.209748 | + | 0.977755i | \(0.432736\pi\) | |||||||
\(348\) | 3518.40 | 0.541971 | ||||||||
\(349\) | 5496.03 | 0.842967 | 0.421484 | − | 0.906836i | \(-0.361510\pi\) | ||||
0.421484 | + | 0.906836i | \(0.361510\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1461.28 | 0.222214 | ||||||||
\(352\) | 2146.26 | 0.324989 | ||||||||
\(353\) | −6372.23 | −0.960792 | −0.480396 | − | 0.877052i | \(-0.659507\pi\) | ||||
−0.480396 | + | 0.877052i | \(0.659507\pi\) | |||||||
\(354\) | −2509.12 | −0.376718 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5098.36 | −0.759024 | ||||||||
\(357\) | 5183.48 | 0.768456 | ||||||||
\(358\) | −9098.46 | −1.34321 | ||||||||
\(359\) | 630.622 | 0.0927101 | 0.0463551 | − | 0.998925i | \(-0.485239\pi\) | ||||
0.0463551 | + | 0.998925i | \(0.485239\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4482.48 | −0.653518 | ||||||||
\(362\) | 49.9071 | 0.00724602 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | 4275.07 | 0.615590 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1764.93 | −0.252061 | ||||||||
\(367\) | 5374.49 | 0.764431 | 0.382216 | − | 0.924073i | \(-0.375161\pi\) | ||||
0.382216 | + | 0.924073i | \(0.375161\pi\) | |||||||
\(368\) | 946.471 | 0.134071 | ||||||||
\(369\) | −1123.51 | −0.158503 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3778.23 | −0.528722 | ||||||||
\(372\) | −1204.71 | −0.167907 | ||||||||
\(373\) | −7520.12 | −1.04391 | −0.521953 | − | 0.852974i | \(-0.674796\pi\) | ||||
−0.521953 | + | 0.852974i | \(0.674796\pi\) | |||||||
\(374\) | −4226.46 | −0.584346 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2084.86 | 0.285954 | ||||||||
\(377\) | 12974.7 | 1.77249 | ||||||||
\(378\) | −1565.32 | −0.212993 | ||||||||
\(379\) | −12509.1 | −1.69538 | −0.847690 | − | 0.530492i | \(-0.822007\pi\) | ||||
−0.847690 | + | 0.530492i | \(0.822007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4383.86 | −0.589481 | ||||||||
\(382\) | −12550.4 | −1.68098 | ||||||||
\(383\) | 11149.9 | 1.48755 | 0.743775 | − | 0.668430i | \(-0.233033\pi\) | ||||
0.743775 | + | 0.668430i | \(0.233033\pi\) | |||||||
\(384\) | −3961.72 | −0.526486 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12456.8 | 1.64258 | ||||||||
\(387\) | −2020.13 | −0.265346 | ||||||||
\(388\) | −7566.28 | −0.989999 | ||||||||
\(389\) | 3194.22 | 0.416333 | 0.208166 | − | 0.978093i | \(-0.433250\pi\) | ||||
0.208166 | + | 0.978093i | \(0.433250\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1278.74 | −0.165393 | ||||||||
\(392\) | −918.292 | −0.118318 | ||||||||
\(393\) | −4574.81 | −0.587198 | ||||||||
\(394\) | 13063.8 | 1.67042 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 484.320 | 0.0614596 | ||||||||
\(397\) | 584.410 | 0.0738809 | 0.0369404 | − | 0.999317i | \(-0.488239\pi\) | ||||
0.0369404 | + | 0.999317i | \(0.488239\pi\) | |||||||
\(398\) | −185.291 | −0.0233361 | ||||||||
\(399\) | 2361.40 | 0.296286 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6951.24 | −0.865657 | −0.432829 | − | 0.901476i | \(-0.642484\pi\) | ||||
−0.432829 | + | 0.901476i | \(0.642484\pi\) | |||||||
\(402\) | −9445.88 | −1.17193 | ||||||||
\(403\) | −4442.56 | −0.549130 | ||||||||
\(404\) | −3239.96 | −0.398995 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13898.5 | −1.69894 | ||||||||
\(407\) | 239.330 | 0.0291478 | ||||||||
\(408\) | 3582.37 | 0.434690 | ||||||||
\(409\) | 11754.1 | 1.42104 | 0.710519 | − | 0.703678i | \(-0.248460\pi\) | ||||
0.710519 | + | 0.703678i | \(0.248460\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6377.03 | 0.765342 | ||||||||
\(412\) | −1954.85 | −0.233759 | ||||||||
\(413\) | 3761.10 | 0.448116 | ||||||||
\(414\) | 386.157 | 0.0458420 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10559.9 | 1.24457 | ||||||||
\(417\) | −5322.83 | −0.625084 | ||||||||
\(418\) | −1925.42 | −0.225300 | ||||||||
\(419\) | 11829.8 | 1.37929 | 0.689646 | − | 0.724146i | \(-0.257766\pi\) | ||||
0.689646 | + | 0.724146i | \(0.257766\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2000.07 | −0.231538 | −0.115769 | − | 0.993276i | \(-0.536933\pi\) | ||||
−0.115769 | + | 0.993276i | \(0.536933\pi\) | |||||||
\(422\) | −7484.76 | −0.863395 | ||||||||
\(423\) | 1681.49 | 0.193278 | ||||||||
\(424\) | −2611.18 | −0.299081 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7897.16 | 0.898166 | ||||||||
\(427\) | 2645.58 | 0.299833 | ||||||||
\(428\) | 7784.43 | 0.879147 | ||||||||
\(429\) | 1786.00 | 0.201000 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8064.11 | −0.901240 | −0.450620 | − | 0.892716i | \(-0.648797\pi\) | ||||
−0.450620 | + | 0.892716i | \(0.648797\pi\) | |||||||
\(432\) | −2138.51 | −0.238169 | ||||||||
\(433\) | 10710.3 | 1.18869 | 0.594345 | − | 0.804210i | \(-0.297411\pi\) | ||||
0.594345 | + | 0.804210i | \(0.297411\pi\) | |||||||
\(434\) | 4758.87 | 0.526344 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3694.18 | 0.405777 | ||||||||
\(437\) | −582.546 | −0.0637688 | ||||||||
\(438\) | 12516.4 | 1.36542 | ||||||||
\(439\) | 4658.08 | 0.506419 | 0.253210 | − | 0.967411i | \(-0.418514\pi\) | ||||
0.253210 | + | 0.967411i | \(0.418514\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −740.622 | −0.0799721 | ||||||||
\(442\) | −20794.7 | −2.23779 | ||||||||
\(443\) | −2094.73 | −0.224658 | −0.112329 | − | 0.993671i | \(-0.535831\pi\) | ||||
−0.112329 | + | 0.993671i | \(0.535831\pi\) | |||||||
\(444\) | 319.318 | 0.0341310 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6776.67 | 0.719472 | ||||||||
\(447\) | 4727.33 | 0.500212 | ||||||||
\(448\) | −1080.82 | −0.113982 | ||||||||
\(449\) | −1402.21 | −0.147382 | −0.0736909 | − | 0.997281i | \(-0.523478\pi\) | ||||
−0.0736909 | + | 0.997281i | \(0.523478\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1373.18 | −0.143372 | ||||||||
\(452\) | 5604.67 | 0.583234 | ||||||||
\(453\) | 1262.93 | 0.130989 | ||||||||
\(454\) | −4131.78 | −0.427124 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1632.00 | 0.167599 | ||||||||
\(457\) | 4914.19 | 0.503011 | 0.251506 | − | 0.967856i | \(-0.419074\pi\) | ||||
0.251506 | + | 0.967856i | \(0.419074\pi\) | |||||||
\(458\) | −14745.7 | −1.50441 | ||||||||
\(459\) | 2889.26 | 0.293810 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2214.08 | −0.223688 | −0.111844 | − | 0.993726i | \(-0.535676\pi\) | ||||
−0.111844 | + | 0.993726i | \(0.535676\pi\) | |||||||
\(462\) | −1913.17 | −0.192660 | ||||||||
\(463\) | 5567.02 | 0.558793 | 0.279396 | − | 0.960176i | \(-0.409866\pi\) | ||||
0.279396 | + | 0.960176i | \(0.409866\pi\) | |||||||
\(464\) | −18987.8 | −1.89976 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20586.8 | −2.04649 | ||||||||
\(467\) | −497.054 | −0.0492525 | −0.0246263 | − | 0.999697i | \(-0.507840\pi\) | ||||
−0.0246263 | + | 0.999697i | \(0.507840\pi\) | |||||||
\(468\) | 2382.91 | 0.235364 | ||||||||
\(469\) | 14159.1 | 1.39405 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6672.90 | 0.652804 | ||||||||
\(472\) | 2599.35 | 0.253484 | ||||||||
\(473\) | −2469.05 | −0.240015 | ||||||||
\(474\) | 6342.70 | 0.614620 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8452.73 | 0.813929 | ||||||||
\(477\) | −2105.97 | −0.202151 | ||||||||
\(478\) | −21673.3 | −2.07388 | ||||||||
\(479\) | −9349.28 | −0.891815 | −0.445908 | − | 0.895079i | \(-0.647119\pi\) | ||||
−0.445908 | + | 0.895079i | \(0.647119\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1177.53 | 0.111624 | ||||||||
\(482\) | −13360.1 | −1.26252 | ||||||||
\(483\) | −578.840 | −0.0545303 | ||||||||
\(484\) | 591.946 | 0.0555923 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −872.506 | −0.0814355 | ||||||||
\(487\) | −197.750 | −0.0184003 | −0.00920013 | − | 0.999958i | \(-0.502929\pi\) | ||||
−0.00920013 | + | 0.999958i | \(0.502929\pi\) | |||||||
\(488\) | 1828.40 | 0.169606 | ||||||||
\(489\) | 9280.12 | 0.858204 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9997.05 | −0.918861 | −0.459430 | − | 0.888214i | \(-0.651946\pi\) | ||||
−0.459430 | + | 0.888214i | \(0.651946\pi\) | |||||||
\(492\) | −1832.12 | −0.167883 | ||||||||
\(493\) | 25653.7 | 2.34358 | ||||||||
\(494\) | −9473.31 | −0.862803 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6501.48 | 0.588558 | ||||||||
\(497\) | −11837.6 | −1.06839 | ||||||||
\(498\) | −12506.6 | −1.12537 | ||||||||
\(499\) | −8714.73 | −0.781813 | −0.390907 | − | 0.920430i | \(-0.627838\pi\) | ||||
−0.390907 | + | 0.920430i | \(0.627838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7249.30 | 0.646457 | ||||||||
\(502\) | 13679.6 | 1.21623 | ||||||||
\(503\) | −5978.53 | −0.529959 | −0.264979 | − | 0.964254i | \(-0.585365\pi\) | ||||
−0.264979 | + | 0.964254i | \(0.585365\pi\) | |||||||
\(504\) | 1621.61 | 0.143318 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 471.970 | 0.0414657 | ||||||||
\(507\) | 2196.36 | 0.192394 | ||||||||
\(508\) | −7148.79 | −0.624363 | ||||||||
\(509\) | −8205.79 | −0.714569 | −0.357284 | − | 0.933996i | \(-0.616297\pi\) | ||||
−0.357284 | + | 0.933996i | \(0.616297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18761.7 | −1.62421 | ||||||||
\(512\) | −8383.17 | −0.723608 | ||||||||
\(513\) | 1316.24 | 0.113281 | ||||||||
\(514\) | 4401.85 | 0.377738 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3294.24 | −0.281048 | ||||||||
\(517\) | 2055.15 | 0.174827 | ||||||||
\(518\) | −1261.38 | −0.106992 | ||||||||
\(519\) | 11274.1 | 0.953519 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5266.06 | −0.442822 | −0.221411 | − | 0.975181i | \(-0.571066\pi\) | ||||
−0.221411 | + | 0.975181i | \(0.571066\pi\) | |||||||
\(522\) | −7746.97 | −0.649570 | ||||||||
\(523\) | 22398.6 | 1.87270 | 0.936350 | − | 0.351068i | \(-0.114181\pi\) | ||||
0.936350 | + | 0.351068i | \(0.114181\pi\) | |||||||
\(524\) | −7460.18 | −0.621945 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26561.8 | 2.20181 | ||||||||
\(527\) | −8783.89 | −0.726057 | ||||||||
\(528\) | −2613.74 | −0.215432 | ||||||||
\(529\) | −12024.2 | −0.988264 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2096.43 | 0.171332 | ||||||||
\(532\) | 3850.75 | 0.313818 | ||||||||
\(533\) | −6756.22 | −0.549052 | ||||||||
\(534\) | 11225.8 | 0.909714 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9785.56 | 0.788566 | ||||||||
\(537\) | 7601.98 | 0.610893 | ||||||||
\(538\) | 11541.8 | 0.924911 | ||||||||
\(539\) | −905.205 | −0.0723375 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13030.2 | −1.03551 | −0.517757 | − | 0.855528i | \(-0.673233\pi\) | ||||
−0.517757 | + | 0.855528i | \(0.673233\pi\) | |||||||
\(542\) | 26488.9 | 2.09925 | ||||||||
\(543\) | −41.6986 | −0.00329550 | ||||||||
\(544\) | 20879.1 | 1.64556 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9413.04 | −0.737804 | ||||||||
\(547\) | −10448.9 | −0.816747 | −0.408374 | − | 0.912815i | \(-0.633904\pi\) | ||||
−0.408374 | + | 0.912815i | \(0.633904\pi\) | |||||||
\(548\) | 10399.1 | 0.810631 | ||||||||
\(549\) | 1474.64 | 0.114638 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11686.9 | 0.903588 | ||||||||
\(552\) | −400.044 | −0.0308460 | ||||||||
\(553\) | −9507.55 | −0.731107 | ||||||||
\(554\) | −2910.53 | −0.223207 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8679.97 | −0.662073 | ||||||||
\(557\) | 11448.7 | 0.870911 | 0.435456 | − | 0.900210i | \(-0.356587\pi\) | ||||
0.435456 | + | 0.900210i | \(0.356587\pi\) | |||||||
\(558\) | 2652.58 | 0.201242 | ||||||||
\(559\) | −12148.0 | −0.919153 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3531.31 | 0.265762 | ||||||||
\(562\) | −4002.49 | −0.300418 | ||||||||
\(563\) | 26035.8 | 1.94898 | 0.974492 | − | 0.224422i | \(-0.0720494\pi\) | ||||
0.974492 | + | 0.224422i | \(0.0720494\pi\) | |||||||
\(564\) | 2742.01 | 0.204715 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8134.05 | 0.604063 | ||||||||
\(567\) | 1307.86 | 0.0968697 | ||||||||
\(568\) | −8181.15 | −0.604354 | ||||||||
\(569\) | 25075.0 | 1.84745 | 0.923725 | − | 0.383057i | \(-0.125129\pi\) | ||||
0.923725 | + | 0.383057i | \(0.125129\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19056.6 | 1.39666 | 0.698330 | − | 0.715776i | \(-0.253927\pi\) | ||||
0.698330 | + | 0.715776i | \(0.253927\pi\) | |||||||
\(572\) | 2912.45 | 0.212894 | ||||||||
\(573\) | 10486.2 | 0.764512 | ||||||||
\(574\) | 7237.28 | 0.526268 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −602.447 | −0.0435798 | ||||||||
\(577\) | 6482.55 | 0.467716 | 0.233858 | − | 0.972271i | \(-0.424865\pi\) | ||||
0.233858 | + | 0.972271i | \(0.424865\pi\) | |||||||
\(578\) | −23475.2 | −1.68934 | ||||||||
\(579\) | −10408.0 | −0.747048 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18747.1 | 1.33866 | ||||||||
\(582\) | 16659.8 | 1.18654 | ||||||||
\(583\) | −2573.97 | −0.182852 | ||||||||
\(584\) | −12966.5 | −0.918762 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13651.5 | 0.962353 | ||||||||
\(587\) | −24650.3 | −1.73327 | −0.866633 | − | 0.498946i | \(-0.833720\pi\) | ||||
−0.866633 | + | 0.498946i | \(0.833720\pi\) | |||||||
\(588\) | −1207.74 | −0.0847045 | ||||||||
\(589\) | −4001.61 | −0.279938 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10915.2 | −0.759712 | ||||||||
\(592\) | −1723.27 | −0.119638 | ||||||||
\(593\) | −23163.2 | −1.60405 | −0.802024 | − | 0.597292i | \(-0.796243\pi\) | ||||
−0.802024 | + | 0.597292i | \(0.796243\pi\) | |||||||
\(594\) | −1066.40 | −0.0736612 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7708.88 | 0.529812 | ||||||||
\(597\) | 154.815 | 0.0106133 | ||||||||
\(598\) | 2322.15 | 0.158796 | ||||||||
\(599\) | 5355.44 | 0.365304 | 0.182652 | − | 0.983178i | \(-0.441532\pi\) | ||||
0.182652 | + | 0.983178i | \(0.441532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20417.6 | −1.38578 | −0.692889 | − | 0.721045i | \(-0.743662\pi\) | ||||
−0.692889 | + | 0.721045i | \(0.743662\pi\) | |||||||
\(602\) | 13013.0 | 0.881012 | ||||||||
\(603\) | 7892.26 | 0.532998 | ||||||||
\(604\) | 2059.48 | 0.138740 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7133.89 | 0.478208 | ||||||||
\(607\) | 6749.81 | 0.451345 | 0.225673 | − | 0.974203i | \(-0.427542\pi\) | ||||
0.225673 | + | 0.974203i | \(0.427542\pi\) | |||||||
\(608\) | 9511.77 | 0.634463 | ||||||||
\(609\) | 11612.5 | 0.772681 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10111.6 | 0.669511 | ||||||||
\(612\) | 4711.53 | 0.311197 | ||||||||
\(613\) | 30321.0 | 1.99780 | 0.998901 | − | 0.0468613i | \(-0.0149219\pi\) | ||||
0.998901 | + | 0.0468613i | \(0.0149219\pi\) | |||||||
\(614\) | −4870.06 | −0.320097 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1981.97 | 0.129636 | ||||||||
\(617\) | −15236.8 | −0.994182 | −0.497091 | − | 0.867699i | \(-0.665598\pi\) | ||||
−0.497091 | + | 0.867699i | \(0.665598\pi\) | |||||||
\(618\) | 4304.28 | 0.280168 | ||||||||
\(619\) | −20875.4 | −1.35550 | −0.677749 | − | 0.735293i | \(-0.737044\pi\) | ||||
−0.677749 | + | 0.735293i | \(0.737044\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −322.644 | −0.0208490 | ||||||||
\(622\) | 29004.8 | 1.86975 | ||||||||
\(623\) | −16827.2 | −1.08213 | ||||||||
\(624\) | −12859.9 | −0.825013 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 20687.2 | 1.32081 | ||||||||
\(627\) | 1608.74 | 0.102467 | ||||||||
\(628\) | 10881.5 | 0.691434 | ||||||||
\(629\) | 2328.24 | 0.147588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27966.1 | 1.76437 | 0.882183 | − | 0.470907i | \(-0.156073\pi\) | ||||
0.882183 | + | 0.470907i | \(0.156073\pi\) | |||||||
\(632\) | −6570.79 | −0.413563 | ||||||||
\(633\) | 6253.70 | 0.392674 | ||||||||
\(634\) | 18337.0 | 1.14867 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3434.23 | −0.214113 | ||||||||
\(637\) | −4453.72 | −0.277022 | ||||||||
\(638\) | −9468.52 | −0.587558 | ||||||||
\(639\) | −6598.27 | −0.408487 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17992.0 | −1.10865 | −0.554323 | − | 0.832301i | \(-0.687023\pi\) | ||||
−0.554323 | + | 0.832301i | \(0.687023\pi\) | |||||||
\(642\) | −17140.1 | −1.05369 | ||||||||
\(643\) | 9448.64 | 0.579499 | 0.289750 | − | 0.957102i | \(-0.406428\pi\) | ||||
0.289750 | + | 0.957102i | \(0.406428\pi\) | |||||||
\(644\) | −943.918 | −0.0577571 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18730.8 | −1.14079 | ||||||||
\(647\) | 7429.22 | 0.451426 | 0.225713 | − | 0.974194i | \(-0.427529\pi\) | ||||
0.225713 | + | 0.974194i | \(0.427529\pi\) | |||||||
\(648\) | 903.882 | 0.0547960 | ||||||||
\(649\) | 2562.30 | 0.154976 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3976.15 | −0.239382 | ||||||||
\(652\) | 15133.2 | 0.908988 | ||||||||
\(653\) | 4488.63 | 0.268995 | 0.134497 | − | 0.990914i | \(-0.457058\pi\) | ||||
0.134497 | + | 0.990914i | \(0.457058\pi\) | |||||||
\(654\) | −8134.00 | −0.486337 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9887.42 | 0.588474 | ||||||||
\(657\) | −10457.7 | −0.620998 | ||||||||
\(658\) | −10831.6 | −0.641730 | ||||||||
\(659\) | −25326.7 | −1.49710 | −0.748550 | − | 0.663078i | \(-0.769250\pi\) | ||||
−0.748550 | + | 0.663078i | \(0.769250\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15192.3 | 0.893969 | 0.446984 | − | 0.894542i | \(-0.352498\pi\) | ||||
0.446984 | + | 0.894542i | \(0.352498\pi\) | |||||||
\(662\) | 9985.15 | 0.586229 | ||||||||
\(663\) | 17374.5 | 1.01775 | ||||||||
\(664\) | 12956.4 | 0.757235 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −703.087 | −0.0409070 | ||||||||
\(667\) | −2864.75 | −0.166302 | ||||||||
\(668\) | 11821.5 | 0.684711 | ||||||||
\(669\) | −5662.07 | −0.327217 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1802.34 | 0.103694 | ||||||||
\(672\) | 9451.25 | 0.542545 | ||||||||
\(673\) | −11718.2 | −0.671180 | −0.335590 | − | 0.942008i | \(-0.608936\pi\) | ||||
−0.335590 | + | 0.942008i | \(0.608936\pi\) | |||||||
\(674\) | 17734.8 | 1.01353 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3581.63 | 0.203779 | ||||||||
\(677\) | 15649.1 | 0.888397 | 0.444198 | − | 0.895928i | \(-0.353489\pi\) | ||||
0.444198 | + | 0.895928i | \(0.353489\pi\) | |||||||
\(678\) | −12340.6 | −0.699024 | ||||||||
\(679\) | −24972.6 | −1.41143 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3452.20 | 0.194257 | ||||||||
\(682\) | 3242.05 | 0.182030 | ||||||||
\(683\) | 18162.8 | 1.01754 | 0.508770 | − | 0.860903i | \(-0.330101\pi\) | ||||
0.508770 | + | 0.860903i | \(0.330101\pi\) | |||||||
\(684\) | 2146.40 | 0.119985 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 24656.2 | 1.37227 | ||||||||
\(687\) | 12320.4 | 0.684208 | ||||||||
\(688\) | 17778.1 | 0.985149 | ||||||||
\(689\) | −12664.2 | −0.700246 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29606.7 | 1.62995 | 0.814973 | − | 0.579500i | \(-0.196752\pi\) | ||||
0.814973 | + | 0.579500i | \(0.196752\pi\) | |||||||
\(692\) | 18384.7 | 1.00994 | ||||||||
\(693\) | 1598.50 | 0.0876220 | ||||||||
\(694\) | −9736.08 | −0.532531 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8025.55 | 0.437080 | ||||||||
\(697\) | −13358.5 | −0.725953 | ||||||||
\(698\) | −19733.8 | −1.07011 | ||||||||
\(699\) | 17200.7 | 0.930746 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26164.7 | −1.40974 | −0.704870 | − | 0.709336i | \(-0.748995\pi\) | ||||
−0.704870 | + | 0.709336i | \(0.748995\pi\) | |||||||
\(702\) | −5246.80 | −0.282091 | ||||||||
\(703\) | 1060.66 | 0.0569040 | ||||||||
\(704\) | −736.324 | −0.0394194 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22879.9 | 1.21968 | ||||||||
\(707\) | −10693.5 | −0.568842 | ||||||||
\(708\) | 3418.66 | 0.181470 | ||||||||
\(709\) | −14508.9 | −0.768535 | −0.384268 | − | 0.923222i | \(-0.625546\pi\) | ||||
−0.384268 | + | 0.923222i | \(0.625546\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5299.48 | −0.279530 | ||||||||
\(712\) | −11629.5 | −0.612125 | ||||||||
\(713\) | 980.898 | 0.0515216 | ||||||||
\(714\) | −18611.6 | −0.975520 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12396.6 | 0.647043 | ||||||||
\(717\) | 18108.5 | 0.943202 | ||||||||
\(718\) | −2264.28 | −0.117691 | ||||||||
\(719\) | −2545.80 | −0.132048 | −0.0660239 | − | 0.997818i | \(-0.521031\pi\) | ||||
−0.0660239 | + | 0.997818i | \(0.521031\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6452.01 | −0.333267 | ||||||||
\(722\) | 16094.6 | 0.829611 | ||||||||
\(723\) | 11162.7 | 0.574198 | ||||||||
\(724\) | −67.9982 | −0.00349051 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1303.37 | −0.0666291 | ||||||||
\(727\) | 18984.8 | 0.968511 | 0.484255 | − | 0.874927i | \(-0.339091\pi\) | ||||
0.484255 | + | 0.874927i | \(0.339091\pi\) | |||||||
\(728\) | 9751.54 | 0.496451 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24019.2 | −1.21530 | ||||||||
\(732\) | 2404.70 | 0.121421 | ||||||||
\(733\) | −36740.4 | −1.85134 | −0.925672 | − | 0.378326i | \(-0.876500\pi\) | ||||
−0.925672 | + | 0.378326i | \(0.876500\pi\) | |||||||
\(734\) | −19297.4 | −0.970411 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2331.58 | −0.116770 | ||||||||
\(737\) | 9646.10 | 0.482115 | ||||||||
\(738\) | 4034.04 | 0.201213 | ||||||||
\(739\) | 1755.17 | 0.0873682 | 0.0436841 | − | 0.999045i | \(-0.486090\pi\) | ||||
0.0436841 | + | 0.999045i | \(0.486090\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7915.18 | 0.392404 | ||||||||
\(742\) | 13566.0 | 0.671189 | ||||||||
\(743\) | −17972.6 | −0.887419 | −0.443709 | − | 0.896171i | \(-0.646338\pi\) | ||||
−0.443709 | + | 0.896171i | \(0.646338\pi\) | |||||||
\(744\) | −2747.97 | −0.135411 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 27001.4 | 1.32519 | ||||||||
\(747\) | 10449.6 | 0.511821 | ||||||||
\(748\) | 5758.54 | 0.281488 | ||||||||
\(749\) | 25692.6 | 1.25339 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22704.9 | 1.10321 | 0.551606 | − | 0.834105i | \(-0.314015\pi\) | ||||
0.551606 | + | 0.834105i | \(0.314015\pi\) | |||||||
\(752\) | −14797.9 | −0.717583 | ||||||||
\(753\) | −11429.6 | −0.553146 | ||||||||
\(754\) | −46586.3 | −2.25010 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2132.74 | 0.102602 | ||||||||
\(757\) | −39860.3 | −1.91380 | −0.956901 | − | 0.290414i | \(-0.906207\pi\) | ||||
−0.956901 | + | 0.290414i | \(0.906207\pi\) | |||||||
\(758\) | 44914.6 | 2.15221 | ||||||||
\(759\) | −394.342 | −0.0188587 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19631.4 | 0.935135 | 0.467568 | − | 0.883957i | \(-0.345130\pi\) | ||||
0.467568 | + | 0.883957i | \(0.345130\pi\) | |||||||
\(762\) | 15740.5 | 0.748319 | ||||||||
\(763\) | 12192.7 | 0.578511 | ||||||||
\(764\) | 17099.8 | 0.809752 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40034.3 | −1.88838 | ||||||||
\(767\) | 12606.8 | 0.593490 | ||||||||
\(768\) | 15831.3 | 0.743832 | ||||||||
\(769\) | 35029.9 | 1.64267 | 0.821333 | − | 0.570449i | \(-0.193231\pi\) | ||||
0.821333 | + | 0.570449i | \(0.193231\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3677.86 | −0.171796 | ||||||||
\(772\) | −16972.4 | −0.791255 | ||||||||
\(773\) | 26736.9 | 1.24406 | 0.622032 | − | 0.782992i | \(-0.286307\pi\) | ||||
0.622032 | + | 0.782992i | \(0.286307\pi\) | |||||||
\(774\) | 7253.40 | 0.336845 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17258.8 | −0.798398 | ||||||||
\(777\) | 1053.91 | 0.0486600 | ||||||||
\(778\) | −11469.0 | −0.528515 | ||||||||
\(779\) | −6085.64 | −0.279898 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8064.55 | −0.369491 | ||||||||
\(782\) | 4591.39 | 0.209959 | ||||||||
\(783\) | 6472.78 | 0.295426 | ||||||||
\(784\) | 6517.81 | 0.296912 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 16426.1 | 0.745421 | ||||||||
\(787\) | −4799.45 | −0.217385 | −0.108693 | − | 0.994075i | \(-0.534666\pi\) | ||||
−0.108693 | + | 0.994075i | \(0.534666\pi\) | |||||||
\(788\) | −17799.4 | −0.804668 | ||||||||
\(789\) | −22193.0 | −1.00139 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18498.3 | 0.831508 | ||||||||
\(792\) | 1104.74 | 0.0495649 | ||||||||
\(793\) | 8867.72 | 0.397102 | ||||||||
\(794\) | −2098.36 | −0.0937884 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 252.457 | 0.0112413 | ||||||||
\(797\) | −38438.9 | −1.70838 | −0.854189 | − | 0.519963i | \(-0.825946\pi\) | ||||
−0.854189 | + | 0.519963i | \(0.825946\pi\) | |||||||
\(798\) | −8478.76 | −0.376121 | ||||||||
\(799\) | 19992.8 | 0.885224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9379.42 | −0.413740 | ||||||||
\(802\) | 24958.9 | 1.09891 | ||||||||
\(803\) | −12781.7 | −0.561713 | ||||||||
\(804\) | 12870.0 | 0.564538 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15951.3 | 0.697096 | ||||||||
\(807\) | −9643.45 | −0.420651 | ||||||||
\(808\) | −7390.42 | −0.321775 | ||||||||
\(809\) | 9960.91 | 0.432889 | 0.216444 | − | 0.976295i | \(-0.430554\pi\) | ||||
0.216444 | + | 0.976295i | \(0.430554\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34199.9 | −1.48079 | −0.740396 | − | 0.672171i | \(-0.765362\pi\) | ||||
−0.740396 | + | 0.672171i | \(0.765362\pi\) | |||||||
\(812\) | 18936.6 | 0.818404 | ||||||||
\(813\) | −22132.1 | −0.954744 | ||||||||
\(814\) | −859.329 | −0.0370018 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −25426.8 | −1.09083 | ||||||||
\(817\) | −10942.3 | −0.468570 | ||||||||
\(818\) | −42203.9 | −1.80394 | ||||||||
\(819\) | 7864.82 | 0.335555 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31796.4 | −1.35165 | −0.675823 | − | 0.737064i | \(-0.736212\pi\) | ||||
−0.675823 | + | 0.737064i | \(0.736212\pi\) | |||||||
\(822\) | −22897.1 | −0.971567 | ||||||||
\(823\) | 10783.6 | 0.456733 | 0.228366 | − | 0.973575i | \(-0.426662\pi\) | ||||
0.228366 | + | 0.973575i | \(0.426662\pi\) | |||||||
\(824\) | −4459.07 | −0.188518 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13504.5 | −0.568862 | ||||||||
\(827\) | −44197.5 | −1.85840 | −0.929201 | − | 0.369576i | \(-0.879503\pi\) | ||||
−0.929201 | + | 0.369576i | \(0.879503\pi\) | |||||||
\(828\) | −526.137 | −0.0220828 | ||||||||
\(829\) | 22487.7 | 0.942137 | 0.471069 | − | 0.882097i | \(-0.343868\pi\) | ||||
0.471069 | + | 0.882097i | \(0.343868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2431.82 | 0.101515 | ||||||||
\(832\) | −3622.81 | −0.150959 | ||||||||
\(833\) | −8805.96 | −0.366276 | ||||||||
\(834\) | 19111.9 | 0.793516 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2623.38 | 0.108530 | ||||||||
\(837\) | −2216.30 | −0.0915250 | ||||||||
\(838\) | −42475.6 | −1.75095 | ||||||||
\(839\) | 22491.0 | 0.925477 | 0.462738 | − | 0.886495i | \(-0.346867\pi\) | ||||
0.462738 | + | 0.886495i | \(0.346867\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33082.7 | 1.35646 | ||||||||
\(842\) | 7181.37 | 0.293927 | ||||||||
\(843\) | 3344.17 | 0.136630 | ||||||||
\(844\) | 10198.0 | 0.415910 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6037.48 | −0.245358 | ||||||||
\(847\) | 1953.72 | 0.0792571 | ||||||||
\(848\) | 18533.5 | 0.750524 | ||||||||
\(849\) | −6796.19 | −0.274729 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −259.994 | −0.0104730 | ||||||||
\(852\) | −10759.8 | −0.432660 | ||||||||
\(853\) | −22327.9 | −0.896241 | −0.448120 | − | 0.893973i | \(-0.647906\pi\) | ||||
−0.448120 | + | 0.893973i | \(0.647906\pi\) | |||||||
\(854\) | −9499.12 | −0.380624 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17756.5 | 0.708999 | ||||||||
\(857\) | 14505.9 | 0.578193 | 0.289096 | − | 0.957300i | \(-0.406645\pi\) | ||||
0.289096 | + | 0.957300i | \(0.406645\pi\) | |||||||
\(858\) | −6412.76 | −0.255161 | ||||||||
\(859\) | −8411.45 | −0.334104 | −0.167052 | − | 0.985948i | \(-0.553425\pi\) | ||||
−0.167052 | + | 0.985948i | \(0.553425\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6046.92 | −0.239348 | ||||||||
\(862\) | 28954.7 | 1.14408 | ||||||||
\(863\) | −32499.6 | −1.28192 | −0.640961 | − | 0.767573i | \(-0.721464\pi\) | ||||
−0.640961 | + | 0.767573i | \(0.721464\pi\) | |||||||
\(864\) | 5268.10 | 0.207436 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −38455.9 | −1.50899 | ||||||||
\(867\) | 19614.1 | 0.768316 | ||||||||
\(868\) | −6483.94 | −0.253548 | ||||||||
\(869\) | −6477.15 | −0.252845 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 47460.0 | 1.84629 | ||||||||
\(872\) | 8426.50 | 0.327245 | ||||||||
\(873\) | −13919.6 | −0.539643 | ||||||||
\(874\) | 2091.67 | 0.0809516 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17053.5 | −0.657745 | ||||||||
\(877\) | 32183.1 | 1.23916 | 0.619581 | − | 0.784933i | \(-0.287303\pi\) | ||||
0.619581 | + | 0.784933i | \(0.287303\pi\) | |||||||
\(878\) | −16725.1 | −0.642876 | ||||||||
\(879\) | −11406.2 | −0.437680 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6246.34 | −0.238870 | −0.119435 | − | 0.992842i | \(-0.538108\pi\) | ||||
−0.119435 | + | 0.992842i | \(0.538108\pi\) | |||||||
\(882\) | 2659.25 | 0.101521 | ||||||||
\(883\) | 11801.1 | 0.449762 | 0.224881 | − | 0.974386i | \(-0.427801\pi\) | ||||
0.224881 | + | 0.974386i | \(0.427801\pi\) | |||||||
\(884\) | 28332.7 | 1.07798 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7521.24 | 0.285193 | ||||||||
\(887\) | −32375.1 | −1.22553 | −0.612767 | − | 0.790264i | \(-0.709944\pi\) | ||||
−0.612767 | + | 0.790264i | \(0.709944\pi\) | |||||||
\(888\) | 728.371 | 0.0275254 | ||||||||
\(889\) | −23594.6 | −0.890145 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | −9233.17 | −0.346580 | ||||||||
\(893\) | 9107.98 | 0.341307 | ||||||||
\(894\) | −16973.8 | −0.634997 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −21322.6 | −0.795020 | ||||||||
\(897\) | −1940.21 | −0.0722205 | ||||||||
\(898\) | 5034.72 | 0.187095 | ||||||||
\(899\) | −19678.5 | −0.730049 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25039.9 | −0.925861 | ||||||||
\(902\) | 4930.49 | 0.182004 | ||||||||
\(903\) | −10872.7 | −0.400686 | ||||||||
\(904\) | 12784.4 | 0.470357 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4534.64 | −0.166284 | ||||||||
\(907\) | 19592.8 | 0.717277 | 0.358638 | − | 0.933477i | \(-0.383241\pi\) | ||||
0.358638 | + | 0.933477i | \(0.383241\pi\) | |||||||
\(908\) | 5629.53 | 0.205752 | ||||||||
\(909\) | −5960.54 | −0.217490 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18673.8 | 0.679133 | 0.339567 | − | 0.940582i | \(-0.389720\pi\) | ||||
0.339567 | + | 0.940582i | \(0.389720\pi\) | |||||||
\(912\) | −11583.5 | −0.420579 | ||||||||
\(913\) | 12771.7 | 0.462959 | ||||||||
\(914\) | −17644.7 | −0.638550 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20090.9 | 0.724696 | ||||||||
\(917\) | −24622.4 | −0.886698 | ||||||||
\(918\) | −10374.1 | −0.372979 | ||||||||
\(919\) | −4572.90 | −0.164142 | −0.0820708 | − | 0.996627i | \(-0.526153\pi\) | ||||
−0.0820708 | + | 0.996627i | \(0.526153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4069.05 | 0.145581 | ||||||||
\(922\) | 7949.78 | 0.283961 | ||||||||
\(923\) | −39678.6 | −1.41499 | ||||||||
\(924\) | 2606.69 | 0.0928070 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −19988.7 | −0.709362 | ||||||||
\(927\) | −3596.33 | −0.127421 | ||||||||
\(928\) | 46775.4 | 1.65461 | ||||||||
\(929\) | −44222.1 | −1.56176 | −0.780882 | − | 0.624679i | \(-0.785230\pi\) | ||||
−0.780882 | + | 0.624679i | \(0.785230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4011.67 | −0.141221 | ||||||||
\(932\) | 28049.3 | 0.985823 | ||||||||
\(933\) | −24234.2 | −0.850367 | ||||||||
\(934\) | 1784.70 | 0.0625238 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5435.48 | 0.189812 | ||||||||
\(937\) | −9218.62 | −0.321408 | −0.160704 | − | 0.987003i | \(-0.551376\pi\) | ||||
−0.160704 | + | 0.987003i | \(0.551376\pi\) | |||||||
\(938\) | −50839.2 | −1.76968 | ||||||||
\(939\) | −17284.6 | −0.600705 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26484.9 | −0.917516 | −0.458758 | − | 0.888561i | \(-0.651706\pi\) | ||||
−0.458758 | + | 0.888561i | \(0.651706\pi\) | |||||||
\(942\) | −23959.4 | −0.828705 | ||||||||
\(943\) | 1491.75 | 0.0515142 | ||||||||
\(944\) | −18449.5 | −0.636103 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8865.26 | 0.304688 | ||||||||
\(947\) | 44972.4 | 1.54320 | 0.771599 | − | 0.636110i | \(-0.219457\pi\) | ||||
0.771599 | + | 0.636110i | \(0.219457\pi\) | |||||||
\(948\) | −8641.90 | −0.296072 | ||||||||
\(949\) | −62887.5 | −2.15112 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15321.0 | −0.522416 | ||||||||
\(952\) | 19280.9 | 0.656404 | ||||||||
\(953\) | 2052.50 | 0.0697659 | 0.0348829 | − | 0.999391i | \(-0.488894\pi\) | ||||
0.0348829 | + | 0.999391i | \(0.488894\pi\) | |||||||
\(954\) | 7561.63 | 0.256621 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 29529.7 | 0.999016 | ||||||||
\(957\) | 7911.18 | 0.267223 | ||||||||
\(958\) | 33569.2 | 1.13212 | ||||||||
\(959\) | 34322.2 | 1.15570 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23053.0 | −0.773826 | ||||||||
\(962\) | −4228.00 | −0.141701 | ||||||||
\(963\) | 14321.0 | 0.479218 | ||||||||
\(964\) | 18203.1 | 0.608176 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2078.36 | 0.0692237 | ||||||||
\(967\) | −14950.9 | −0.497195 | −0.248598 | − | 0.968607i | \(-0.579970\pi\) | ||||
−0.248598 | + | 0.968607i | \(0.579970\pi\) | |||||||
\(968\) | 1350.24 | 0.0448331 | ||||||||
\(969\) | 15650.0 | 0.518835 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26751.9 | 0.884151 | 0.442076 | − | 0.896978i | \(-0.354242\pi\) | ||||
0.442076 | + | 0.896978i | \(0.354242\pi\) | |||||||
\(972\) | 1188.78 | 0.0392287 | ||||||||
\(973\) | −28648.3 | −0.943908 | ||||||||
\(974\) | 710.034 | 0.0233583 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12977.5 | −0.425615 | ||||||||
\(977\) | 56893.7 | 1.86304 | 0.931520 | − | 0.363690i | \(-0.118483\pi\) | ||||
0.931520 | + | 0.363690i | \(0.118483\pi\) | |||||||
\(978\) | −33320.8 | −1.08945 | ||||||||
\(979\) | −11463.7 | −0.374242 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6796.15 | 0.221187 | ||||||||
\(982\) | 35895.0 | 1.16645 | ||||||||
\(983\) | 34633.1 | 1.12373 | 0.561863 | − | 0.827230i | \(-0.310085\pi\) | ||||
0.561863 | + | 0.827230i | \(0.310085\pi\) | |||||||
\(984\) | −4179.10 | −0.135391 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −92111.0 | −2.97506 | ||||||||
\(987\) | 9050.03 | 0.291860 | ||||||||
\(988\) | 12907.3 | 0.415625 | ||||||||
\(989\) | 2682.23 | 0.0862386 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1961.79 | 0.0628843 | 0.0314422 | − | 0.999506i | \(-0.489990\pi\) | ||||
0.0314422 | + | 0.999506i | \(0.489990\pi\) | |||||||
\(992\) | −16016.0 | −0.512610 | ||||||||
\(993\) | −8342.83 | −0.266618 | ||||||||
\(994\) | 42503.8 | 1.35628 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17040.2 | 0.542108 | ||||||||
\(997\) | −13096.5 | −0.416017 | −0.208009 | − | 0.978127i | \(-0.566698\pi\) | ||||
−0.208009 | + | 0.978127i | \(0.566698\pi\) | |||||||
\(998\) | 31290.8 | 0.992476 | ||||||||
\(999\) | 587.447 | 0.0186046 |
(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 | 825.4.a.s.1.1 | 3 | ||
3.2 | odd | 2 | 2475.4.a.s.1.3 | 3 | |||
5.2 | odd | 4 | 825.4.c.l.199.2 | 6 | |||
5.3 | odd | 4 | 825.4.c.l.199.5 | 6 | |||
5.4 | even | 2 | 165.4.a.d.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 495.4.a.l.1.1 | 3 | |||
55.54 | odd | 2 | 1815.4.a.s.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.d.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
495.4.a.l.1.1 | 3 | 15.14 | odd | 2 | |||
825.4.a.s.1.1 | 3 | 1.1 | even | 1 | trivial | ||
825.4.c.l.199.2 | 6 | 5.2 | odd | 4 | |||
825.4.c.l.199.5 | 6 | 5.3 | odd | 4 | |||
1815.4.a.s.1.1 | 3 | 55.54 | odd | 2 | |||
2475.4.a.s.1.3 | 3 | 3.2 | odd | 2 |