Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(1,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, 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("1620.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.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: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.560145.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 90x + 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.19760\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 33.6841 | 1.81877 | 0.909385 | − | 0.415956i | \(-0.136553\pi\) | ||||
0.909385 | + | 0.415956i | \(0.136553\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.49850 | −0.260355 | −0.130178 | − | 0.991491i | \(-0.541555\pi\) | ||||
−0.130178 | + | 0.991491i | \(0.541555\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 39.6841 | 0.846645 | 0.423322 | − | 0.905979i | \(-0.360864\pi\) | ||||
0.423322 | + | 0.905979i | \(0.360864\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 106.365 | 1.51749 | 0.758745 | − | 0.651387i | \(-0.225813\pi\) | ||||
0.758745 | + | 0.651387i | \(0.225813\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −96.5507 | −1.16580 | −0.582902 | − | 0.812543i | \(-0.698083\pi\) | ||||
−0.582902 | + | 0.812543i | \(0.698083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 40.0552 | 0.363135 | 0.181567 | − | 0.983379i | \(-0.441883\pi\) | ||||
0.181567 | + | 0.983379i | \(0.441883\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 252.417 | 1.61630 | 0.808151 | − | 0.588976i | \(-0.200469\pi\) | ||||
0.808151 | + | 0.588976i | \(0.200469\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 48.8727 | 0.283154 | 0.141577 | − | 0.989927i | \(-0.454783\pi\) | ||||
0.141577 | + | 0.989927i | \(0.454783\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 168.420 | 0.813378 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −136.476 | −0.606391 | −0.303195 | − | 0.952928i | \(-0.598053\pi\) | ||||
−0.303195 | + | 0.952928i | \(0.598053\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 139.104 | 0.529865 | 0.264933 | − | 0.964267i | \(-0.414650\pi\) | ||||
0.264933 | + | 0.964267i | \(0.414650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −202.359 | −0.717662 | −0.358831 | − | 0.933402i | \(-0.616825\pi\) | ||||
−0.358831 | + | 0.933402i | \(0.616825\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 300.049 | 0.931206 | 0.465603 | − | 0.884994i | \(-0.345837\pi\) | ||||
0.465603 | + | 0.884994i | \(0.345837\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 791.617 | 2.30792 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −344.142 | −0.891915 | −0.445958 | − | 0.895054i | \(-0.647137\pi\) | ||||
−0.445958 | + | 0.895054i | \(0.647137\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −47.4925 | −0.116434 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −60.9339 | −0.134456 | −0.0672281 | − | 0.997738i | \(-0.521416\pi\) | ||||
−0.0672281 | + | 0.997738i | \(0.521416\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −122.122 | −0.256331 | −0.128165 | − | 0.991753i | \(-0.540909\pi\) | ||||
−0.128165 | + | 0.991753i | \(0.540909\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 198.420 | 0.378631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −744.667 | −1.35784 | −0.678922 | − | 0.734211i | \(-0.737552\pi\) | ||||
−0.678922 | + | 0.734211i | \(0.737552\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 436.971 | 0.730408 | 0.365204 | − | 0.930928i | \(-0.380999\pi\) | ||||
0.365204 | + | 0.930928i | \(0.380999\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 586.353 | 0.940102 | 0.470051 | − | 0.882639i | \(-0.344236\pi\) | ||||
0.470051 | + | 0.882639i | \(0.344236\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −319.948 | −0.473526 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 473.780 | 0.674740 | 0.337370 | − | 0.941372i | \(-0.390463\pi\) | ||||
0.337370 | + | 0.941372i | \(0.390463\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −998.864 | −1.32096 | −0.660479 | − | 0.750844i | \(-0.729647\pi\) | ||||
−0.660479 | + | 0.750844i | \(0.729647\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 531.826 | 0.678642 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 204.463 | 0.243517 | 0.121759 | − | 0.992560i | \(-0.461147\pi\) | ||||
0.121759 | + | 0.992560i | \(0.461147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1336.72 | 1.53985 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −482.754 | −0.521363 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1632.78 | −1.70911 | −0.854557 | − | 0.519358i | \(-0.826171\pi\) | ||||
−0.854557 | + | 0.519358i | \(0.826171\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1199.80 | −1.18203 | −0.591015 | − | 0.806661i | \(-0.701273\pi\) | ||||
−0.591015 | + | 0.806661i | \(0.701273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1609.66 | −1.53985 | −0.769924 | − | 0.638136i | \(-0.779706\pi\) | ||||
−0.769924 | + | 0.638136i | \(0.779706\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −206.586 | −0.186649 | −0.0933245 | − | 0.995636i | \(-0.529749\pi\) | ||||
−0.0933245 | + | 0.995636i | \(0.529749\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1604.44 | 1.40989 | 0.704944 | − | 0.709263i | \(-0.250972\pi\) | ||||
0.704944 | + | 0.709263i | \(0.250972\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1895.03 | 1.57760 | 0.788802 | − | 0.614647i | \(-0.210702\pi\) | ||||
0.788802 | + | 0.614647i | \(0.210702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 200.276 | 0.162399 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3582.81 | 2.75997 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1240.78 | −0.932215 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 946.537 | 0.661351 | 0.330675 | − | 0.943745i | \(-0.392723\pi\) | ||||
0.330675 | + | 0.943745i | \(0.392723\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1684.10 | 1.12321 | 0.561606 | − | 0.827405i | \(-0.310184\pi\) | ||||
0.561606 | + | 0.827405i | \(0.310184\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3252.22 | −2.12033 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −414.313 | −0.258374 | −0.129187 | − | 0.991620i | \(-0.541237\pi\) | ||||
−0.129187 | + | 0.991620i | \(0.541237\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −317.941 | −0.194010 | −0.0970049 | − | 0.995284i | \(-0.530926\pi\) | ||||
−0.0970049 | + | 0.995284i | \(0.530926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −376.939 | −0.220428 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1262.09 | 0.722832 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3037.54 | −1.67010 | −0.835050 | − | 0.550174i | \(-0.814561\pi\) | ||||
−0.835050 | + | 0.550174i | \(0.814561\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2120.80 | −1.14297 | −0.571485 | − | 0.820613i | \(-0.693632\pi\) | ||||
−0.571485 | + | 0.820613i | \(0.693632\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 244.363 | 0.126631 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2508.34 | 1.27508 | 0.637539 | − | 0.770418i | \(-0.279952\pi\) | ||||
0.637539 | + | 0.770418i | \(0.279952\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1349.22 | 0.660458 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1834.04 | −0.881308 | −0.440654 | − | 0.897677i | \(-0.645253\pi\) | ||||
−0.440654 | + | 0.897677i | \(0.645253\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3188.63 | 1.47751 | 0.738753 | − | 0.673976i | \(-0.235415\pi\) | ||||
0.738753 | + | 0.673976i | \(0.235415\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −622.174 | −0.283192 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −224.949 | −0.0988587 | −0.0494293 | − | 0.998778i | \(-0.515740\pi\) | ||||
−0.0494293 | + | 0.998778i | \(0.515740\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 842.102 | 0.363754 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3815.09 | 1.59303 | 0.796517 | − | 0.604616i | \(-0.206674\pi\) | ||||
0.796517 | + | 0.604616i | \(0.206674\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3356.82 | −1.37851 | −0.689256 | − | 0.724518i | \(-0.742062\pi\) | ||||
−0.689256 | + | 0.724518i | \(0.742062\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −682.378 | −0.271186 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1010.31 | −0.395086 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 831.167 | 0.314875 | 0.157438 | − | 0.987529i | \(-0.449677\pi\) | ||||
0.157438 | + | 0.987529i | \(0.449677\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3038.43 | 1.13322 | 0.566609 | − | 0.823987i | \(-0.308255\pi\) | ||||
0.566609 | + | 0.823987i | \(0.308255\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1288.06 | 0.465839 | 0.232919 | − | 0.972496i | \(-0.425172\pi\) | ||||
0.232919 | + | 0.972496i | \(0.425172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5069.77 | 1.80596 | 0.902981 | − | 0.429680i | \(-0.141374\pi\) | ||||
0.902981 | + | 0.429680i | \(0.141374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8502.45 | 2.93968 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 695.522 | 0.236963 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 917.087 | 0.303523 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2523.63 | 0.823384 | 0.411692 | − | 0.911323i | \(-0.364938\pi\) | ||||
0.411692 | + | 0.911323i | \(0.364938\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1011.80 | −0.320948 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1646.23 | 0.514993 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4221.00 | 1.28478 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2405.71 | −0.722412 | −0.361206 | − | 0.932486i | \(-0.617635\pi\) | ||||
−0.361206 | + | 0.932486i | \(0.617635\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5388.29 | 1.57548 | 0.787739 | − | 0.616009i | \(-0.211252\pi\) | ||||
0.787739 | + | 0.616009i | \(0.211252\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4714.12 | 1.36034 | 0.680171 | − | 0.733054i | \(-0.261906\pi\) | ||||
0.680171 | + | 0.733054i | \(0.261906\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5065.99 | 1.42439 | 0.712197 | − | 0.701979i | \(-0.247700\pi\) | ||||
0.712197 | + | 0.701979i | \(0.247700\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1500.25 | 0.416448 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6637.92 | −1.79653 | −0.898267 | − | 0.439451i | \(-0.855173\pi\) | ||||
−0.898267 | + | 0.439451i | \(0.855173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5058.82 | −1.35215 | −0.676073 | − | 0.736834i | \(-0.736320\pi\) | ||||
−0.676073 | + | 0.736834i | \(0.736320\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3958.09 | 1.03213 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3831.53 | −0.987021 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2428.65 | 0.610737 | 0.305368 | − | 0.952234i | \(-0.401220\pi\) | ||||
0.305368 | + | 0.952234i | \(0.401220\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −380.465 | −0.0945439 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3720.97 | 0.903142 | 0.451571 | − | 0.892235i | \(-0.350864\pi\) | ||||
0.451571 | + | 0.892235i | \(0.350864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4597.06 | −1.10289 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −217.013 | −0.0508807 | −0.0254403 | − | 0.999676i | \(-0.508099\pi\) | ||||
−0.0254403 | + | 0.999676i | \(0.508099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1720.71 | −0.398877 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −766.464 | −0.173725 | −0.0868627 | − | 0.996220i | \(-0.527684\pi\) | ||||
−0.0868627 | + | 0.996220i | \(0.527684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4030.90 | 0.903541 | 0.451770 | − | 0.892134i | \(-0.350793\pi\) | ||||
0.451770 | + | 0.892134i | \(0.350793\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −237.463 | −0.0520710 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1182.89 | −0.256582 | −0.128291 | − | 0.991737i | \(-0.540949\pi\) | ||||
−0.128291 | + | 0.991737i | \(0.540949\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8060.82 | 1.71127 | 0.855637 | − | 0.517576i | \(-0.173166\pi\) | ||||
0.855637 | + | 0.517576i | \(0.173166\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −820.131 | −0.172268 | −0.0861338 | − | 0.996284i | \(-0.527451\pi\) | ||||
−0.0861338 | + | 0.996284i | \(0.527451\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4685.61 | 0.963703 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6400.55 | 1.30278 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −409.740 | −0.0816972 | −0.0408486 | − | 0.999165i | \(-0.513006\pi\) | ||||
−0.0408486 | + | 0.999165i | \(0.513006\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −304.669 | −0.0601307 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1589.56 | 0.307446 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6816.28 | −1.30526 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −610.612 | −0.114635 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4200.96 | 0.780982 | 0.390491 | − | 0.920607i | \(-0.372305\pi\) | ||||
0.390491 | + | 0.920607i | \(0.372305\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8443.12 | −1.53944 | −0.769719 | − | 0.638382i | \(-0.779604\pi\) | ||||
−0.769719 | + | 0.638382i | \(0.779604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 134.035 | 0.0242048 | 0.0121024 | − | 0.999927i | \(-0.496148\pi\) | ||||
0.0121024 | + | 0.999927i | \(0.496148\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9580.61 | −1.69748 | −0.848740 | − | 0.528811i | \(-0.822638\pi\) | ||||
−0.848740 | + | 0.528811i | \(0.822638\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2397.59 | −0.420812 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10269.6 | −1.76910 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 992.102 | 0.169329 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10106.9 | 1.69365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8759.64 | −1.45460 | −0.727301 | − | 0.686318i | \(-0.759226\pi\) | ||||
−0.727301 | + | 0.686318i | \(0.759226\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3723.33 | −0.607246 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5558.66 | 0.898514 | 0.449257 | − | 0.893403i | \(-0.351689\pi\) | ||||
0.449257 | + | 0.893403i | \(0.351689\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −464.217 | −0.0737207 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15111.3 | 2.37881 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10687.1 | −1.65335 | −0.826675 | − | 0.562679i | \(-0.809771\pi\) | ||||
−0.826675 | + | 0.562679i | \(0.809771\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3939.46 | 0.604225 | 0.302113 | − | 0.953272i | \(-0.402308\pi\) | ||||
0.302113 | + | 0.953272i | \(0.402308\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5297.90 | 0.798806 | 0.399403 | − | 0.916775i | \(-0.369217\pi\) | ||||
0.399403 | + | 0.916775i | \(0.369217\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2184.86 | 0.326648 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1103.06 | −0.162165 | −0.0810827 | − | 0.996707i | \(-0.525838\pi\) | ||||
−0.0810827 | + | 0.996707i | \(0.525838\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2463.05 | 0.359097 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2931.77 | 0.420426 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7315.72 | −1.04054 | −0.520269 | − | 0.854002i | \(-0.674168\pi\) | ||||
−0.520269 | + | 0.854002i | \(0.674168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11592.1 | −1.62219 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1885.80 | −0.261778 | −0.130889 | − | 0.991397i | \(-0.541783\pi\) | ||||
−0.130889 | + | 0.991397i | \(0.541783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10017.0 | 1.36843 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5371.24 | −0.727973 | −0.363987 | − | 0.931404i | \(-0.618585\pi\) | ||||
−0.363987 | + | 0.931404i | \(0.618585\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 72.2612 | 0.00964067 | 0.00482033 | − | 0.999988i | \(-0.498466\pi\) | ||||
0.00482033 | + | 0.999988i | \(0.498466\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1599.74 | −0.211767 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1793.28 | 0.233735 | 0.116867 | − | 0.993148i | \(-0.462715\pi\) | ||||
0.116867 | + | 0.993148i | \(0.462715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4260.48 | 0.551053 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2368.90 | 0.301753 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 596.085 | 0.0753568 | 0.0376784 | − | 0.999290i | \(-0.488004\pi\) | ||||
0.0376784 | + | 0.999290i | \(0.488004\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 954.797 | 0.118903 | 0.0594517 | − | 0.998231i | \(-0.481065\pi\) | ||||
0.0594517 | + | 0.998231i | \(0.481065\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1939.47 | 0.239731 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1296.31 | 0.157877 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1167.04 | −0.141091 | −0.0705456 | − | 0.997509i | \(-0.522474\pi\) | ||||
−0.0705456 | + | 0.997509i | \(0.522474\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2052.50 | −0.244545 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4994.32 | −0.590750 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14857.0 | 1.73225 | 0.866124 | − | 0.499828i | \(-0.166604\pi\) | ||||
0.866124 | + | 0.499828i | \(0.166604\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2161.07 | 0.250176 | 0.125088 | − | 0.992146i | \(-0.460079\pi\) | ||||
0.125088 | + | 0.992146i | \(0.460079\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2659.13 | 0.303498 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4113.58 | −0.466207 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6031.12 | 0.674035 | 0.337017 | − | 0.941498i | \(-0.390582\pi\) | ||||
0.337017 | + | 0.941498i | \(0.390582\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7477.24 | 0.829869 | 0.414934 | − | 0.909851i | \(-0.363804\pi\) | ||||
0.414934 | + | 0.909851i | \(0.363804\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3867.36 | −0.423343 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6516.94 | −0.708511 | −0.354256 | − | 0.935149i | \(-0.615266\pi\) | ||||
−0.354256 | + | 0.935149i | \(0.615266\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7912.72 | 0.848633 | 0.424317 | − | 0.905514i | \(-0.360514\pi\) | ||||
0.424317 | + | 0.905514i | \(0.360514\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1022.32 | 0.108904 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8686.04 | 0.912961 | 0.456480 | − | 0.889733i | \(-0.349110\pi\) | ||||
0.456480 | + | 0.889733i | \(0.349110\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1321.28 | −0.137953 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6683.61 | 0.688643 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6787.39 | −0.694750 | −0.347375 | − | 0.937726i | \(-0.612927\pi\) | ||||
−0.347375 | + | 0.937726i | \(0.612927\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15130.9 | 1.52866 | 0.764332 | − | 0.644823i | \(-0.223069\pi\) | ||||
0.764332 | + | 0.644823i | \(0.223069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12316.7 | 1.23629 | 0.618147 | − | 0.786062i | \(-0.287883\pi\) | ||||
0.618147 | + | 0.786062i | \(0.287883\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16423.4 | −1.62737 | −0.813687 | − | 0.581303i | \(-0.802543\pi\) | ||||
−0.813687 | + | 0.581303i | \(0.802543\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25083.4 | −2.46960 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1922.11 | 0.186847 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2413.77 | −0.233161 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11761.8 | −1.12195 | −0.560973 | − | 0.827834i | \(-0.689573\pi\) | ||||
−0.560973 | + | 0.827834i | \(0.689573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5415.91 | −0.513398 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8163.92 | −0.764339 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18620.0 | −1.73255 | −0.866277 | − | 0.499564i | \(-0.833494\pi\) | ||||
−0.866277 | + | 0.499564i | \(0.833494\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10022.2 | −0.921171 | −0.460586 | − | 0.887615i | \(-0.652361\pi\) | ||||
−0.460586 | + | 0.887615i | \(0.652361\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26848.4 | 2.45272 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14719.0 | 1.32844 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3843.64 | −0.344820 | −0.172410 | − | 0.985025i | \(-0.555155\pi\) | ||||
−0.172410 | + | 0.985025i | \(0.555155\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6782.43 | −0.601220 | −0.300610 | − | 0.953747i | \(-0.597190\pi\) | ||||
−0.300610 | + | 0.953747i | \(0.597190\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5999.02 | −0.528620 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17019.1 | 1.48204 | 0.741018 | − | 0.671485i | \(-0.234343\pi\) | ||||
0.741018 | + | 0.671485i | \(0.234343\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19750.8 | 1.70983 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8048.29 | −0.688641 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2850.02 | −0.242444 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19278.7 | 1.62114 | 0.810572 | − | 0.585639i | \(-0.199156\pi\) | ||||
0.810572 | + | 0.585639i | \(0.199156\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8074.65 | 0.675105 | 0.337552 | − | 0.941307i | \(-0.390401\pi\) | ||||
0.337552 | + | 0.941307i | \(0.390401\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5198.35 | 0.429684 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10562.6 | −0.868133 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5520.23 | 0.448608 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1032.93 | −0.0834719 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7519.18 | −0.600879 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18260.8 | −1.45119 | −0.725594 | − | 0.688123i | \(-0.758435\pi\) | ||||
−0.725594 | + | 0.688123i | \(0.758435\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8022.21 | 0.630521 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10707.4 | 0.836958 | 0.418479 | − | 0.908226i | \(-0.362563\pi\) | ||||
0.418479 | + | 0.908226i | \(0.362563\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24371.1 | −1.88429 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15958.8 | 1.22720 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17348.5 | 1.31971 | 0.659857 | − | 0.751392i | \(-0.270617\pi\) | ||||
0.659857 | + | 0.751392i | \(0.270617\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8030.44 | −0.607605 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14947.1 | −1.11891 | −0.559455 | − | 0.828860i | \(-0.688990\pi\) | ||||
−0.559455 | + | 0.828860i | \(0.688990\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9475.14 | 0.705526 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26723.0 | −1.96887 | −0.984435 | − | 0.175750i | \(-0.943765\pi\) | ||||
−0.984435 | + | 0.175750i | \(0.943765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8419.93 | 0.617098 | 0.308549 | − | 0.951208i | \(-0.400157\pi\) | ||||
0.308549 | + | 0.951208i | \(0.400157\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1001.38 | 0.0726269 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2921.42 | 0.210780 | 0.105390 | − | 0.994431i | \(-0.466391\pi\) | ||||
0.105390 | + | 0.994431i | \(0.466391\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33645.8 | −2.40252 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3268.83 | 0.232215 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −64.7362 | −0.00455188 | −0.00227594 | − | 0.999997i | \(-0.500724\pi\) | ||||
−0.00227594 | + | 0.999997i | \(0.500724\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4718.69 | −0.330102 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20682.2 | −1.43223 | −0.716117 | − | 0.697980i | \(-0.754082\pi\) | ||||
−0.716117 | + | 0.697980i | \(0.754082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17914.1 | 1.23429 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20639.8 | −1.40788 | −0.703939 | − | 0.710260i | \(-0.748577\pi\) | ||||
−0.703939 | + | 0.710260i | \(0.748577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19749.2 | −1.34041 | −0.670205 | − | 0.742176i | \(-0.733794\pi\) | ||||
−0.670205 | + | 0.742176i | \(0.733794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6203.89 | −0.416899 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15180.4 | −1.01508 | −0.507539 | − | 0.861629i | \(-0.669445\pi\) | ||||
−0.507539 | + | 0.861629i | \(0.669445\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11907.2 | 0.788401 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15998.0 | −1.05408 | −0.527042 | − | 0.849839i | \(-0.676699\pi\) | ||||
−0.527042 | + | 0.849839i | \(0.676699\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1827.40 | 0.119235 | 0.0596176 | − | 0.998221i | \(-0.481012\pi\) | ||||
0.0596176 | + | 0.998221i | \(0.481012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12096.6 | −0.785464 | −0.392732 | − | 0.919653i | \(-0.628470\pi\) | ||||
−0.392732 | + | 0.919653i | \(0.628470\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6887.15 | 0.442902 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14516.3 | −0.920192 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20914.5 | 1.31948 | 0.659741 | − | 0.751493i | \(-0.270666\pi\) | ||||
0.659741 | + | 0.751493i | \(0.270666\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4732.68 | 0.295765 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31414.6 | 1.95399 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14490.4 | 0.892880 | 0.446440 | − | 0.894814i | \(-0.352692\pi\) | ||||
0.446440 | + | 0.894814i | \(0.352692\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11516.8 | 0.706345 | 0.353173 | − | 0.935558i | \(-0.385103\pi\) | ||||
0.353173 | + | 0.935558i | \(0.385103\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18928.4 | −1.15016 | −0.575078 | − | 0.818099i | \(-0.695028\pi\) | ||||
−0.575078 | + | 0.818099i | \(0.695028\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 578.781 | 0.0350064 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5144.16 | −0.308279 | −0.154140 | − | 0.988049i | \(-0.549261\pi\) | ||||
−0.154140 | + | 0.988049i | \(0.549261\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8420.52 | 0.502316 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2988.44 | −0.176651 | −0.0883257 | − | 0.996092i | \(-0.528152\pi\) | ||||
−0.0883257 | + | 0.996092i | \(0.528152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13451.0 | −0.791500 | −0.395750 | − | 0.918358i | \(-0.629515\pi\) | ||||
−0.395750 | + | 0.918358i | \(0.629515\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16261.1 | −0.948239 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10110.6 | 0.586935 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1159.98 | 0.0667370 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10085.7 | 0.577674 | 0.288837 | − | 0.957378i | \(-0.406731\pi\) | ||||
0.288837 | + | 0.957378i | \(0.406731\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20517.8 | −1.16479 | −0.582396 | − | 0.812905i | \(-0.697885\pi\) | ||||
−0.582396 | + | 0.812905i | \(0.697885\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −54998.8 | −3.10848 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15006.6 | −0.840719 | −0.420359 | − | 0.907358i | \(-0.638096\pi\) | ||||
−0.420359 | + | 0.907358i | \(0.638096\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2071.57 | −0.115548 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13657.0 | −0.755136 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25718.5 | 1.41589 | 0.707944 | − | 0.706269i | \(-0.249623\pi\) | ||||
0.707944 | + | 0.706269i | \(0.249623\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1589.70 | −0.0867639 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14795.9 | 0.804066 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14908.1 | −0.803239 | −0.401619 | − | 0.915807i | \(-0.631552\pi\) | ||||
−0.401619 | + | 0.915807i | \(0.631552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13176.8 | 0.706932 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40414.3 | −2.14984 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23392.0 | 1.23907 | 0.619537 | − | 0.784967i | \(-0.287320\pi\) | ||||
0.619537 | + | 0.784967i | \(0.287320\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1957.61 | 0.102823 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1884.70 | −0.0985785 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22561.1 | −1.17022 | −0.585110 | − | 0.810954i | \(-0.698949\pi\) | ||||
−0.585110 | + | 0.810954i | \(0.698949\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54219.8 | −2.80063 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6310.44 | 0.323260 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20864.7 | −1.06441 | −0.532206 | − | 0.846615i | \(-0.678637\pi\) | ||||
−0.532206 | + | 0.846615i | \(0.678637\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21524.0 | −1.08905 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24555.8 | 1.23737 | 0.618683 | − | 0.785641i | \(-0.287666\pi\) | ||||
0.618683 | + | 0.785641i | \(0.287666\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7073.22 | 0.353521 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14842.0 | 0.738801 | 0.369400 | − | 0.929270i | \(-0.379563\pi\) | ||||
0.369400 | + | 0.929270i | \(0.379563\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15518.1 | 0.766223 | 0.383111 | − | 0.923702i | \(-0.374853\pi\) | ||||
0.383111 | + | 0.923702i | \(0.374853\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15187.7 | −0.746891 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6958.66 | −0.339471 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39293.6 | −1.90925 | −0.954624 | − | 0.297814i | \(-0.903742\pi\) | ||||
−0.954624 | + | 0.297814i | \(0.903742\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10604.0 | −0.511152 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30307.7 | −1.45516 | −0.727578 | − | 0.686025i | \(-0.759354\pi\) | ||||
−0.727578 | + | 0.686025i | \(0.759354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27358.3 | −1.30320 | −0.651601 | − | 0.758562i | \(-0.725902\pi\) | ||||
−0.651601 | + | 0.758562i | \(0.725902\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 54044.2 | 2.56426 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2418.11 | −0.113837 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17282.2 | 0.810419 | 0.405209 | − | 0.914224i | \(-0.367199\pi\) | ||||
0.405209 | + | 0.914224i | \(0.367199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30621.8 | −1.42482 | −0.712411 | − | 0.701762i | \(-0.752397\pi\) | ||||
−0.712411 | + | 0.701762i | \(0.752397\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1221.82 | 0.0566309 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13430.6 | −0.617719 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4150.57 | −0.190165 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12541.7 | 0.570232 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32786.5 | −1.48502 | −0.742512 | − | 0.669833i | \(-0.766366\pi\) | ||||
−0.742512 | + | 0.669833i | \(0.766366\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63832.3 | 2.86930 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4846.32 | −0.217021 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13692.1 | −0.608529 | −0.304265 | − | 0.952588i | \(-0.598411\pi\) | ||||
−0.304265 | + | 0.952588i | \(0.598411\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31914.8 | 1.41310 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5569.48 | −0.244760 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6746.12 | 0.295366 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39429.7 | 1.71357 | 0.856783 | − | 0.515677i | \(-0.172459\pi\) | ||||
0.856783 | + | 0.515677i | \(0.172459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10397.9 | −0.450209 | −0.225105 | − | 0.974335i | \(-0.572272\pi\) | ||||
−0.225105 | + | 0.974335i | \(0.572272\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9170.20 | −0.394133 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19537.9 | 0.836653 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2913.08 | 0.123833 | 0.0619166 | − | 0.998081i | \(-0.480279\pi\) | ||||
0.0619166 | + | 0.998081i | \(0.480279\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16934.6 | −0.717257 | −0.358628 | − | 0.933480i | \(-0.616755\pi\) | ||||
−0.358628 | + | 0.933480i | \(0.616755\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1191.52 | −0.0501006 | −0.0250503 | − | 0.999686i | \(-0.507975\pi\) | ||||
−0.0250503 | + | 0.999686i | \(0.507975\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5792.37 | −0.242675 | −0.121337 | − | 0.992611i | \(-0.538718\pi\) | ||||
−0.121337 | + | 0.992611i | \(0.538718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 84200.5 | 3.50225 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15943.1 | 0.660761 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2620.21 | −0.107818 | −0.0539091 | − | 0.998546i | \(-0.517168\pi\) | ||||
−0.0539091 | + | 0.998546i | \(0.517168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39325.6 | 1.61243 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3110.87 | −0.126647 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −41794.5 | −1.69548 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5466.57 | −0.220201 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1485.11 | 0.0596121 | 0.0298060 | − | 0.999556i | \(-0.490511\pi\) | ||||
0.0298060 | + | 0.999556i | \(0.490511\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13999.8 | −0.558023 | −0.279011 | − | 0.960288i | \(-0.590007\pi\) | ||||
−0.279011 | + | 0.960288i | \(0.590007\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46006.2 | 1.82737 | 0.913686 | − | 0.406421i | \(-0.133223\pi\) | ||||
0.913686 | + | 0.406421i | \(0.133223\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37731.8 | −1.48830 | −0.744152 | − | 0.668010i | \(-0.767146\pi\) | ||||
−0.744152 | + | 0.668010i | \(0.767146\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1124.74 | −0.0442109 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4500.20 | −0.175672 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29551.4 | −1.14961 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4210.51 | 0.162676 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40443.7 | 1.55723 | 0.778614 | − | 0.627504i | \(-0.215923\pi\) | ||||
0.778614 | + | 0.627504i | \(0.215923\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35957.5 | −1.37507 | −0.687535 | − | 0.726151i | \(-0.741307\pi\) | ||||
−0.687535 | + | 0.726151i | \(0.741307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4208.35 | 0.160387 | 0.0801937 | − | 0.996779i | \(-0.474446\pi\) | ||||
0.0801937 | + | 0.996779i | \(0.474446\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6615.52 | 0.250426 | 0.125213 | − | 0.992130i | \(-0.460039\pi\) | ||||
0.125213 | + | 0.992130i | \(0.460039\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31883.2 | 1.20284 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28970.0 | −1.08560 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19075.4 | 0.712426 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12336.3 | 0.457663 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36604.7 | −1.35347 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16784.1 | −0.616489 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36352.8 | −1.33084 | −0.665421 | − | 0.746468i | \(-0.731748\pi\) | ||||
−0.665421 | + | 0.746468i | \(0.731748\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2245.96 | 0.0816817 | 0.0408409 | − | 0.999166i | \(-0.486996\pi\) | ||||
0.0408409 | + | 0.999166i | \(0.486996\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9487.71 | 0.343918 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 56727.5 | 2.04286 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13665.8 | −0.490527 | −0.245263 | − | 0.969456i | \(-0.578874\pi\) | ||||
−0.245263 | + | 0.969456i | \(0.578874\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17340.8 | 0.618396 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3411.89 | −0.121278 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43509.5 | 1.53660 | 0.768300 | − | 0.640091i | \(-0.221103\pi\) | ||||
0.768300 | + | 0.640091i | \(0.221103\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −76431.3 | −2.69058 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5051.55 | −0.176688 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6545.89 | −0.228223 | −0.114111 | − | 0.993468i | \(-0.536402\pi\) | ||||
−0.114111 | + | 0.993468i | \(0.536402\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −237.479 | −0.00822697 | −0.00411349 | − | 0.999992i | \(-0.501309\pi\) | ||||
−0.00411349 | + | 0.999992i | \(0.501309\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5571.86 | 0.192412 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34862.6 | −1.19629 | −0.598143 | − | 0.801390i | \(-0.704094\pi\) | ||||
−0.598143 | + | 0.801390i | \(0.704094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23268.9 | 0.795933 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30830.7 | −1.04796 | −0.523979 | − | 0.851731i | \(-0.675553\pi\) | ||||
−0.523979 | + | 0.851731i | \(0.675553\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4155.84 | 0.140816 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13955.8 | −0.469922 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27402.5 | −0.919824 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15192.1 | 0.506790 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16892.7 | −0.561772 | −0.280886 | − | 0.959741i | \(-0.590628\pi\) | ||||
−0.280886 | + | 0.959741i | \(0.590628\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3347.26 | 0.110627 | 0.0553135 | − | 0.998469i | \(-0.482384\pi\) | ||||
0.0553135 | + | 0.998469i | \(0.482384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10709.5 | −0.352859 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21331.5 | −0.698522 | −0.349261 | − | 0.937025i | \(-0.613567\pi\) | ||||
−0.349261 | + | 0.937025i | \(0.613567\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1942.09 | −0.0634010 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7531.13 | −0.244360 | −0.122180 | − | 0.992508i | \(-0.538988\pi\) | ||||
−0.122180 | + | 0.992508i | \(0.538988\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6440.28 | 0.208329 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8105.55 | −0.260608 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26751.6 | −0.857510 | −0.428755 | − | 0.903421i | \(-0.641048\pi\) | ||||
−0.428755 | + | 0.903421i | \(0.641048\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25348.9 | 0.807651 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2838.54 | 0.0901680 | 0.0450840 | − | 0.998983i | \(-0.485644\pi\) | ||||
0.0450840 | + | 0.998983i | \(0.485644\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1620.4.a.f.1.3 | yes | 3 | |
3.2 | odd | 2 | 1620.4.a.d.1.3 | ✓ | 3 | ||
9.2 | odd | 6 | 1620.4.i.u.1081.1 | 6 | |||
9.4 | even | 3 | 1620.4.i.s.541.1 | 6 | |||
9.5 | odd | 6 | 1620.4.i.u.541.1 | 6 | |||
9.7 | even | 3 | 1620.4.i.s.1081.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.4.a.d.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
1620.4.a.f.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
1620.4.i.s.541.1 | 6 | 9.4 | even | 3 | |||
1620.4.i.s.1081.1 | 6 | 9.7 | even | 3 | |||
1620.4.i.u.541.1 | 6 | 9.5 | odd | 6 | |||
1620.4.i.u.1081.1 | 6 | 9.2 | odd | 6 |