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: | \(1\) |
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 | \(-0.458445\pi\) | ||||
0.130178 | + | 0.991491i | \(0.458445\pi\) | |||||||
\(12\) | 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 | \(-0.774187\pi\) | ||||
−0.758745 | + | 0.651387i | \(0.774187\pi\) | |||||||
\(18\) | 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 | \(-0.558117\pi\) | ||||
−0.181567 | + | 0.983379i | \(0.558117\pi\) | |||||||
\(24\) | 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 | \(-0.799531\pi\) | ||||
−0.808151 | + | 0.588976i | \(0.799531\pi\) | |||||||
\(30\) | 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 | \(-0.585350\pi\) | ||||
−0.264933 | + | 0.964267i | \(0.585350\pi\) | |||||||
\(42\) | 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 | \(-0.654163\pi\) | ||||
−0.465603 | + | 0.884994i | \(0.654163\pi\) | |||||||
\(48\) | 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 | \(-0.352863\pi\) | ||||
0.445958 | + | 0.895054i | \(0.352863\pi\) | |||||||
\(54\) | 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 | \(-0.478584\pi\) | ||||
0.0672281 | + | 0.997738i | \(0.478584\pi\) | |||||||
\(60\) | 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 | \(-0.619001\pi\) | ||||
−0.365204 | + | 0.930928i | \(0.619001\pi\) | |||||||
\(72\) | 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 | \(-0.270353\pi\) | ||||
0.660479 | + | 0.750844i | \(0.270353\pi\) | |||||||
\(84\) | 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 | \(-0.538853\pi\) | ||||
−0.121759 | + | 0.992560i | \(0.538853\pi\) | |||||||
\(90\) | 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 | \(-0.298727\pi\) | ||||
0.591015 | + | 0.806661i | \(0.298727\pi\) | |||||||
\(102\) | 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 | \(-0.470251\pi\) | ||||
0.0933245 | + | 0.995636i | \(0.470251\pi\) | |||||||
\(108\) | 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 | \(-0.789298\pi\) | ||||
−0.788802 | + | 0.614647i | \(0.789298\pi\) | |||||||
\(114\) | 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 | \(-0.689816\pi\) | ||||
−0.561606 | + | 0.827405i | \(0.689816\pi\) | |||||||
\(132\) | 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 | \(-0.458763\pi\) | ||||
0.129187 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(138\) | 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 | \(-0.185439\pi\) | ||||
0.835050 | + | 0.550174i | \(0.185439\pi\) | |||||||
\(150\) | 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 | \(-0.764585\pi\) | ||||
−0.738753 | + | 0.673976i | \(0.764585\pi\) | |||||||
\(168\) | 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 | \(-0.484260\pi\) | ||||
0.0494293 | + | 0.998778i | \(0.484260\pi\) | |||||||
\(174\) | 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 | \(-0.793326\pi\) | ||||
−0.796517 | + | 0.604616i | \(0.793326\pi\) | |||||||
\(180\) | 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 | \(-0.550323\pi\) | ||||
−0.157438 | + | 0.987529i | \(0.550323\pi\) | |||||||
\(192\) | 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 | \(-0.574828\pi\) | ||||
−0.232919 | + | 0.972496i | \(0.574828\pi\) | |||||||
\(198\) | 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 | \(-0.788748\pi\) | ||||
−0.787739 | + | 0.616009i | \(0.788748\pi\) | |||||||
\(228\) | 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 | \(-0.752300\pi\) | ||||
−0.712197 | + | 0.701979i | \(0.752300\pi\) | |||||||
\(234\) | 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 | \(-0.144827\pi\) | ||||
0.898267 | + | 0.439451i | \(0.144827\pi\) | |||||||
\(240\) | 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 | \(-0.598780\pi\) | ||||
−0.305368 | + | 0.952234i | \(0.598780\pi\) | |||||||
\(252\) | 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 | \(-0.649136\pi\) | ||||
−0.451571 | + | 0.892235i | \(0.649136\pi\) | |||||||
\(258\) | 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 | \(-0.491901\pi\) | ||||
0.0254403 | + | 0.999676i | \(0.491901\pi\) | |||||||
\(264\) | 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 | \(-0.472316\pi\) | ||||
0.0868627 | + | 0.996220i | \(0.472316\pi\) | |||||||
\(270\) | 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 | \(-0.826834\pi\) | ||||
−0.855637 | + | 0.517576i | \(0.826834\pi\) | |||||||
\(282\) | 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 | \(-0.486994\pi\) | ||||
0.0408486 | + | 0.999165i | \(0.486994\pi\) | |||||||
\(294\) | 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 | \(-0.220396\pi\) | ||||
0.769719 | + | 0.638382i | \(0.220396\pi\) | |||||||
\(312\) | 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 | \(-0.177362\pi\) | ||||
0.848740 | + | 0.528811i | \(0.177362\pi\) | |||||||
\(318\) | 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 | \(-0.190229\pi\) | ||||
0.826675 | + | 0.562679i | \(0.190229\pi\) | |||||||
\(348\) | 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 | \(-0.630783\pi\) | ||||
−0.399403 | + | 0.916775i | \(0.630783\pi\) | |||||||
\(354\) | 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 | \(-0.474162\pi\) | ||||
0.0810827 | + | 0.996707i | \(0.474162\pi\) | |||||||
\(360\) | 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 | \(-0.501534\pi\) | ||||
−0.00482033 | + | 0.999988i | \(0.501534\pi\) | |||||||
\(384\) | 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 | \(-0.537285\pi\) | ||||
−0.116867 | + | 0.993148i | \(0.537285\pi\) | |||||||
\(390\) | 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 | \(-0.518935\pi\) | ||||
−0.0594517 | + | 0.998231i | \(0.518935\pi\) | |||||||
\(402\) | 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 | \(-0.833396\pi\) | ||||
−0.866124 | + | 0.499828i | \(0.833396\pi\) | |||||||
\(420\) | 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 | \(-0.609418\pi\) | ||||
−0.337017 | + | 0.941498i | \(0.609418\pi\) | |||||||
\(432\) | 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 | \(-0.639486\pi\) | ||||
−0.424317 | + | 0.905514i | \(0.639486\pi\) | |||||||
\(444\) | 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 | \(-0.650890\pi\) | ||||
−0.456480 | + | 0.889733i | \(0.650890\pi\) | |||||||
\(450\) | 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 | \(-0.776931\pi\) | ||||
−0.764332 | + | 0.644823i | \(0.776931\pi\) | |||||||
\(462\) | 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 | \(-0.197457\pi\) | ||||
0.813687 | + | 0.581303i | \(0.197457\pi\) | |||||||
\(468\) | 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 | \(-0.310427\pi\) | ||||
0.560973 | + | 0.827834i | \(0.310427\pi\) | |||||||
\(480\) | 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 | \(-0.347639\pi\) | ||||
0.460586 | + | 0.887615i | \(0.347639\pi\) | |||||||
\(492\) | 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 | \(-0.402810\pi\) | ||||
0.300610 | + | 0.953747i | \(0.402810\pi\) | |||||||
\(504\) | 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 | \(-0.765657\pi\) | ||||
−0.741018 | + | 0.671485i | \(0.765657\pi\) | |||||||
\(510\) | 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 | \(-0.800844\pi\) | ||||
−0.810572 | + | 0.585639i | \(0.800844\pi\) | |||||||
\(522\) | 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 | \(-0.729383\pi\) | ||||
−0.659857 | + | 0.751392i | \(0.729383\pi\) | |||||||
\(558\) | 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 | \(-0.311010\pi\) | ||||
0.559455 | + | 0.828860i | \(0.311010\pi\) | |||||||
\(564\) | 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 | \(-0.0562351\pi\) | ||||
0.984435 | + | 0.175750i | \(0.0562351\pi\) | |||||||
\(570\) | 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 | \(-0.499276\pi\) | ||||
0.00227594 | + | 0.999997i | \(0.499276\pi\) | |||||||
\(588\) | 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 | \(-0.245918\pi\) | ||||
0.716117 | + | 0.697980i | \(0.245918\pi\) | |||||||
\(594\) | 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 | \(-0.251423\pi\) | ||||
0.703939 | + | 0.710260i | \(0.251423\pi\) | |||||||
\(600\) | 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 | \(-0.518988\pi\) | ||||
−0.0596176 | + | 0.998221i | \(0.518988\pi\) | |||||||
\(618\) | 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 | \(-0.647308\pi\) | ||||
−0.446440 | + | 0.894814i | \(0.647308\pi\) | |||||||
\(642\) | 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 | \(-0.304972\pi\) | ||||
0.575078 | + | 0.818099i | \(0.304972\pi\) | |||||||
\(648\) | 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 | \(-0.450739\pi\) | ||||
0.154140 | + | 0.988049i | \(0.450739\pi\) | |||||||
\(654\) | 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 | \(-0.471848\pi\) | ||||
0.0883257 | + | 0.996092i | \(0.471848\pi\) | |||||||
\(660\) | 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 | \(-0.302115\pi\) | ||||
0.582396 | + | 0.812905i | \(0.302115\pi\) | |||||||
\(678\) | 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 | \(-0.361904\pi\) | ||||
0.420359 | + | 0.907358i | \(0.361904\pi\) | |||||||
\(684\) | 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 | \(-0.368448\pi\) | ||||
0.401619 | + | 0.915807i | \(0.368448\pi\) | |||||||
\(702\) | 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 | \(-0.301051\pi\) | ||||
0.585110 | + | 0.810954i | \(0.301051\pi\) | |||||||
\(720\) | 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 | \(-0.625147\pi\) | ||||
−0.383111 | + | 0.923702i | \(0.625147\pi\) | |||||||
\(744\) | 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 | \(-0.274098\pi\) | ||||
0.651601 | + | 0.758562i | \(0.274098\pi\) | |||||||
\(762\) | 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 | \(-0.247603\pi\) | ||||
0.712411 | + | 0.701762i | \(0.247603\pi\) | |||||||
\(774\) | 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 | \(-0.401589\pi\) | ||||
0.304265 | + | 0.952588i | \(0.401589\pi\) | |||||||
\(798\) | 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 | \(-0.827541\pi\) | ||||
−0.856783 | + | 0.515677i | \(0.827541\pi\) | |||||||
\(810\) | 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 | \(-0.519721\pi\) | ||||
−0.0619166 | + | 0.998081i | \(0.519721\pi\) | |||||||
\(822\) | 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 | \(-0.492025\pi\) | ||||
0.0250503 | + | 0.999686i | \(0.492025\pi\) | |||||||
\(828\) | 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 | \(-0.482832\pi\) | ||||
0.0539091 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(840\) | 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 | \(-0.409993\pi\) | ||||
0.279011 | + | 0.960288i | \(0.409993\pi\) | |||||||
\(858\) | 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 | \(-0.232854\pi\) | ||||
0.744152 | + | 0.668010i | \(0.232854\pi\) | |||||||
\(864\) | 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 | \(-0.258693\pi\) | ||||
0.687535 | + | 0.726151i | \(0.258693\pi\) | |||||||
\(882\) | 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 | \(-0.539961\pi\) | ||||
−0.125213 | + | 0.992130i | \(0.539961\pi\) | |||||||
\(888\) | 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 | \(-0.513004\pi\) | ||||
−0.0408409 | + | 0.999166i | \(0.513004\pi\) | |||||||
\(912\) | 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 | \(-0.778897\pi\) | ||||
−0.768300 | + | 0.640091i | \(0.778897\pi\) | |||||||
\(930\) | 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 | \(-0.498691\pi\) | ||||
0.00411349 | + | 0.999992i | \(0.498691\pi\) | |||||||
\(942\) | 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 | \(-0.295906\pi\) | ||||
0.598143 | + | 0.801390i | \(0.295906\pi\) | |||||||
\(948\) | 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 | \(-0.324447\pi\) | ||||
0.523979 | + | 0.851731i | \(0.324447\pi\) | |||||||
\(954\) | 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 | \(-0.517616\pi\) | ||||
−0.0553135 | + | 0.998469i | \(0.517616\pi\) | |||||||
\(972\) | 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 | \(-0.386433\pi\) | ||||
0.349261 | + | 0.937025i | \(0.386433\pi\) | |||||||
\(978\) | 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 | \(-0.461012\pi\) | ||||
0.122180 | + | 0.992508i | \(0.461012\pi\) | |||||||
\(984\) | 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.d.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 1620.4.a.f.1.3 | yes | 3 | ||
9.2 | odd | 6 | 1620.4.i.s.1081.1 | 6 | |||
9.4 | even | 3 | 1620.4.i.u.541.1 | 6 | |||
9.5 | odd | 6 | 1620.4.i.s.541.1 | 6 | |||
9.7 | even | 3 | 1620.4.i.u.1081.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.4.a.d.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1620.4.a.f.1.3 | yes | 3 | 3.2 | odd | 2 | ||
1620.4.i.s.541.1 | 6 | 9.5 | odd | 6 | |||
1620.4.i.s.1081.1 | 6 | 9.2 | odd | 6 | |||
1620.4.i.u.541.1 | 6 | 9.4 | even | 3 | |||
1620.4.i.u.1081.1 | 6 | 9.7 | even | 3 |