Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1584,4,Mod(1,1584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1584, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1584.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1584.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: | \(93.4590254491\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 11) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1584.1 |
$q$-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 | ||||||||
\(5\) | 12.8564 | 1.14991 | 0.574956 | − | 0.818184i | \(-0.305019\pi\) | ||||
0.574956 | + | 0.818184i | \(0.305019\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.9282 | −0.914037 | −0.457019 | − | 0.889457i | \(-0.651083\pi\) | ||||
−0.457019 | + | 0.889457i | \(0.651083\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 74.6410 | 1.59244 | 0.796219 | − | 0.605009i | \(-0.206830\pi\) | ||||
0.796219 | + | 0.605009i | \(0.206830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 82.7846 | 1.18107 | 0.590536 | − | 0.807011i | \(-0.298916\pi\) | ||||
0.590536 | + | 0.807011i | \(0.298916\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 67.9230 | 0.820138 | 0.410069 | − | 0.912055i | \(-0.365505\pi\) | ||||
0.410069 | + | 0.912055i | \(0.365505\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.3538 | 0.121064 | 0.0605319 | − | 0.998166i | \(-0.480720\pi\) | ||||
0.0605319 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 40.2872 | 0.322297 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −168.995 | −1.08212 | −0.541061 | − | 0.840983i | \(-0.681977\pi\) | ||||
−0.541061 | + | 0.840983i | \(0.681977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 65.4974 | 0.379474 | 0.189737 | − | 0.981835i | \(-0.439237\pi\) | ||||
0.189737 | + | 0.981835i | \(0.439237\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −217.636 | −1.05106 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.8564 | 0.181534 | 0.0907669 | − | 0.995872i | \(-0.471068\pi\) | ||||
0.0907669 | + | 0.995872i | \(0.471068\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −274.928 | −1.04723 | −0.523617 | − | 0.851954i | \(-0.675418\pi\) | ||||
−0.523617 | + | 0.851954i | \(0.675418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.28719 | 0.00811146 | 0.00405573 | − | 0.999992i | \(-0.498709\pi\) | ||||
0.00405573 | + | 0.999992i | \(0.498709\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 71.8461 | 0.222975 | 0.111488 | − | 0.993766i | \(-0.464438\pi\) | ||||
0.111488 | + | 0.993766i | \(0.464438\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −56.4359 | −0.164536 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 149.005 | 0.386178 | 0.193089 | − | 0.981181i | \(-0.438149\pi\) | ||||
0.193089 | + | 0.981181i | \(0.438149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −141.420 | −0.346711 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 545.631 | 1.20398 | 0.601992 | − | 0.798502i | \(-0.294374\pi\) | ||||
0.601992 | + | 0.798502i | \(0.294374\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 101.303 | 0.212631 | 0.106315 | − | 0.994332i | \(-0.466095\pi\) | ||||
0.106315 | + | 0.994332i | \(0.466095\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 959.615 | 1.83116 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −411.641 | −0.750596 | −0.375298 | − | 0.926904i | \(-0.622460\pi\) | ||||
−0.375298 | + | 0.926904i | \(0.622460\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −470.636 | −0.786679 | −0.393339 | − | 0.919393i | \(-0.628680\pi\) | ||||
−0.393339 | + | 0.919393i | \(0.628680\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 610.600 | 0.978977 | 0.489488 | − | 0.872010i | \(-0.337184\pi\) | ||||
0.489488 | + | 0.872010i | \(0.337184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 186.210 | 0.275593 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 978.225 | 1.39315 | 0.696576 | − | 0.717483i | \(-0.254706\pi\) | ||||
0.696576 | + | 0.717483i | \(0.254706\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 26.1539 | 0.0345875 | 0.0172938 | − | 0.999850i | \(-0.494495\pi\) | ||||
0.0172938 | + | 0.999850i | \(0.494495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1064.31 | 1.35813 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 352.887 | 0.420292 | 0.210146 | − | 0.977670i | \(-0.432606\pi\) | ||||
0.210146 | + | 0.977670i | \(0.432606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1263.54 | −1.45555 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 873.246 | 0.943086 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 847.585 | 0.887208 | 0.443604 | − | 0.896223i | \(-0.353700\pi\) | ||||
0.443604 | + | 0.896223i | \(0.353700\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1293.46 | −1.27430 | −0.637150 | − | 0.770740i | \(-0.719887\pi\) | ||||
−0.637150 | + | 0.770740i | \(0.719887\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1725.24 | 1.65042 | 0.825209 | − | 0.564828i | \(-0.191057\pi\) | ||||
0.825209 | + | 0.564828i | \(0.191057\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −484.179 | −0.437452 | −0.218726 | − | 0.975786i | \(-0.570190\pi\) | ||||
−0.218726 | + | 0.975786i | \(0.570190\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −64.2563 | −0.0564645 | −0.0282323 | − | 0.999601i | \(-0.508988\pi\) | ||||
−0.0282323 | + | 0.999601i | \(0.508988\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2005.08 | 1.66922 | 0.834612 | − | 0.550839i | \(-0.185692\pi\) | ||||
0.834612 | + | 0.550839i | \(0.185692\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 171.682 | 0.139213 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1401.39 | −1.07954 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1089.10 | −0.779298 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −109.605 | −0.0765816 | −0.0382908 | − | 0.999267i | \(-0.512191\pi\) | ||||
−0.0382908 | + | 0.999267i | \(0.512191\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1156.71 | 0.771469 | 0.385734 | − | 0.922610i | \(-0.373948\pi\) | ||||
0.385734 | + | 0.922610i | \(0.373948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1149.82 | −0.749636 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −198.323 | −0.123678 | −0.0618391 | − | 0.998086i | \(-0.519697\pi\) | ||||
−0.0618391 | + | 0.998086i | \(0.519697\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2900.14 | 1.76969 | 0.884844 | − | 0.465888i | \(-0.154265\pi\) | ||||
0.884844 | + | 0.465888i | \(0.154265\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −821.051 | −0.480138 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2172.67 | −1.24435 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3488.34 | −1.91796 | −0.958980 | − | 0.283472i | \(-0.908514\pi\) | ||||
−0.958980 | + | 0.283472i | \(0.908514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1163.32 | 0.626953 | 0.313477 | − | 0.949596i | \(-0.398506\pi\) | ||||
0.313477 | + | 0.949596i | \(0.398506\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 842.061 | 0.436361 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 342.057 | 0.173880 | 0.0869398 | − | 0.996214i | \(-0.472291\pi\) | ||||
0.0869398 | + | 0.996214i | \(0.472291\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −226.056 | −0.110657 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1394.89 | 0.670285 | 0.335142 | − | 0.942167i | \(-0.391216\pi\) | ||||
0.335142 | + | 0.942167i | \(0.391216\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 478.703 | 0.221815 | 0.110908 | − | 0.993831i | \(-0.464624\pi\) | ||||
0.110908 | + | 0.993831i | \(0.464624\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3374.28 | 1.53586 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1808.58 | −0.794822 | −0.397411 | − | 0.917641i | \(-0.630091\pi\) | ||||
−0.397411 | + | 0.917641i | \(0.630091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −681.990 | −0.294592 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4429.85 | −1.84973 | −0.924867 | − | 0.380292i | \(-0.875824\pi\) | ||||
−0.924867 | + | 0.380292i | \(0.875824\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3409.17 | 1.40001 | 0.700005 | − | 0.714138i | \(-0.253181\pi\) | ||||
0.700005 | + | 0.714138i | \(0.253181\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 525.267 | 0.208748 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −910.631 | −0.356106 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2923.75 | 1.10762 | 0.553810 | − | 0.832643i | \(-0.313173\pi\) | ||||
0.553810 | + | 0.832643i | \(0.313173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2484.18 | −0.926505 | −0.463253 | − | 0.886226i | \(-0.653318\pi\) | ||||
−0.463253 | + | 0.886226i | \(0.653318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5125.67 | 1.85375 | 0.926876 | − | 0.375369i | \(-0.122484\pi\) | ||||
0.926876 | + | 0.375369i | \(0.122484\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.69219 | 0.00274013 | 0.00137006 | − | 0.999999i | \(-0.499564\pi\) | ||||
0.00137006 | + | 0.999999i | \(0.499564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2860.78 | 0.989100 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3534.59 | −1.20423 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −747.154 | −0.247281 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3107.34 | −1.01383 | −0.506915 | − | 0.861996i | \(-0.669214\pi\) | ||||
−0.506915 | + | 0.861996i | \(0.669214\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.4050 | 0.00932746 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1108.75 | −0.346853 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6179.13 | 1.88078 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3185 | 0.00369913 | 0.00184957 | − | 0.999998i | \(-0.499411\pi\) | ||||
0.00184957 | + | 0.999998i | \(0.499411\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4615.90 | 1.34964 | 0.674820 | − | 0.737983i | \(-0.264221\pi\) | ||||
0.674820 | + | 0.737983i | \(0.264221\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5074.63 | 1.46437 | 0.732186 | − | 0.681105i | \(-0.238500\pi\) | ||||
0.732186 | + | 0.681105i | \(0.238500\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −211.683 | −0.0595184 | −0.0297592 | − | 0.999557i | \(-0.509474\pi\) | ||||
−0.0297592 | + | 0.999557i | \(0.509474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 923.683 | 0.256402 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4312.49 | 1.16716 | 0.583581 | − | 0.812055i | \(-0.301651\pi\) | ||||
0.583581 | + | 0.812055i | \(0.301651\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −996.584 | −0.266372 | −0.133186 | − | 0.991091i | \(-0.542521\pi\) | ||||
−0.133186 | + | 0.991091i | \(0.542521\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −725.563 | −0.189202 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5069.85 | 1.30602 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −276.892 | −0.0696306 | −0.0348153 | − | 0.999394i | \(-0.511084\pi\) | ||||
−0.0348153 | + | 0.999394i | \(0.511084\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −146.892 | −0.0365021 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3235.18 | 0.785233 | 0.392617 | − | 0.919702i | \(-0.371570\pi\) | ||||
0.392617 | + | 0.919702i | \(0.371570\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −691.626 | −0.165929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 207.944 | 0.0487544 | 0.0243772 | − | 0.999703i | \(-0.492240\pi\) | ||||
0.0243772 | + | 0.999703i | \(0.492240\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1915.67 | 0.444071 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5033.04 | −1.14078 | −0.570390 | − | 0.821374i | \(-0.693208\pi\) | ||||
−0.570390 | + | 0.821374i | \(0.693208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1487.01 | −0.333319 | −0.166660 | − | 0.986015i | \(-0.553298\pi\) | ||||
−0.166660 | + | 0.986015i | \(0.553298\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −443.159 | −0.0971764 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −235.836 | −0.0511552 | −0.0255776 | − | 0.999673i | \(-0.508142\pi\) | ||||
−0.0255776 | + | 0.999673i | \(0.508142\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4915.01 | 1.04343 | 0.521717 | − | 0.853118i | \(-0.325292\pi\) | ||||
0.521717 | + | 0.853118i | \(0.325292\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5199.56 | 1.09216 | 0.546081 | − | 0.837733i | \(-0.316119\pi\) | ||||
0.546081 | + | 0.837733i | \(0.316119\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4654.04 | 0.957210 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1940.29 | 0.394930 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8880.92 | 1.77075 | 0.885373 | − | 0.464881i | \(-0.153903\pi\) | ||||
0.885373 | + | 0.464881i | \(0.153903\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7014.85 | 1.38448 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 996.743 | 0.192786 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −38.7180 | −0.00741417 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1302.39 | 0.244507 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1497.93 | 0.278474 | 0.139237 | − | 0.990259i | \(-0.455535\pi\) | ||||
0.139237 | + | 0.990259i | \(0.455535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7484.71 | −1.36469 | −0.682345 | − | 0.731030i | \(-0.739040\pi\) | ||||
−0.682345 | + | 0.731030i | \(0.739040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −658.363 | −0.118891 | −0.0594455 | − | 0.998232i | \(-0.518933\pi\) | ||||
−0.0594455 | + | 0.998232i | \(0.518933\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −233.708 | −0.0414080 | −0.0207040 | − | 0.999786i | \(-0.506591\pi\) | ||||
−0.0207040 | + | 0.999786i | \(0.506591\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1858.94 | 0.326272 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5622.98 | 0.968641 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3007.08 | 0.513239 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1216.23 | −0.203808 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8532.95 | −1.41696 | −0.708480 | − | 0.705731i | \(-0.750619\pi\) | ||||
−0.708480 | + | 0.705731i | \(0.750619\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5292.22 | −0.863120 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11691.2 | 1.88979 | 0.944895 | − | 0.327373i | \(-0.106163\pi\) | ||||
0.944895 | + | 0.327373i | \(0.106163\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −720.472 | −0.114416 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6761.73 | 1.06443 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4598.79 | 0.711459 | 0.355729 | − | 0.934589i | \(-0.384232\pi\) | ||||
0.355729 | + | 0.934589i | \(0.384232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6720.27 | 1.03074 | 0.515369 | − | 0.856968i | \(-0.327655\pi\) | ||||
0.515369 | + | 0.856968i | \(0.327655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5738.70 | −0.865270 | −0.432635 | − | 0.901569i | \(-0.642416\pi\) | ||||
−0.432635 | + | 0.901569i | \(0.642416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6050.69 | −0.904611 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4115.27 | −0.605001 | −0.302501 | − | 0.953149i | \(-0.597821\pi\) | ||||
−0.302501 | + | 0.953149i | \(0.597821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2245.46 | −0.327374 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7850.12 | 1.12574 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9662.99 | −1.37440 | −0.687199 | − | 0.726469i | \(-0.741160\pi\) | ||||
−0.687199 | + | 0.726469i | \(0.741160\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2522.39 | −0.352981 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −141.780 | −0.0196812 | −0.00984062 | − | 0.999952i | \(-0.503132\pi\) | ||||
−0.00984062 | + | 0.999952i | \(0.503132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12613.9 | −1.72321 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2819.73 | 0.382163 | 0.191082 | − | 0.981574i | \(-0.438800\pi\) | ||||
0.191082 | + | 0.981574i | \(0.438800\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6337.84 | −0.845557 | −0.422778 | − | 0.906233i | \(-0.638945\pi\) | ||||
−0.422778 | + | 0.906233i | \(0.638945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2393.99 | 0.316907 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8805.25 | 1.14767 | 0.573836 | − | 0.818970i | \(-0.305455\pi\) | ||||
0.573836 | + | 0.818970i | \(0.305455\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1105.49 | 0.142985 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12576.5 | 1.60200 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4315.26 | 0.545534 | 0.272767 | − | 0.962080i | \(-0.412061\pi\) | ||||
0.272767 | + | 0.962080i | \(0.412061\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −361.681 | −0.0450411 | −0.0225206 | − | 0.999746i | \(-0.507169\pi\) | ||||
−0.0225206 | + | 0.999746i | \(0.507169\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4888.79 | 0.604288 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −449.420 | −0.0547345 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9220.50 | 1.11473 | 0.557365 | − | 0.830268i | \(-0.311812\pi\) | ||||
0.557365 | + | 0.830268i | \(0.311812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9236.55 | −1.10049 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 336.245 | 0.0397726 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14912.9 | −1.73876 | −0.869380 | − | 0.494144i | \(-0.835481\pi\) | ||||
−0.869380 | + | 0.494144i | \(0.835481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13486.0 | −1.56121 | −0.780603 | − | 0.625027i | \(-0.785088\pi\) | ||||
−0.780603 | + | 0.625027i | \(0.785088\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3335.16 | 0.380656 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1714.87 | −0.194352 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 406.334 | 0.0454116 | 0.0227058 | − | 0.999742i | \(-0.492772\pi\) | ||||
0.0227058 | + | 0.999742i | \(0.492772\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1766.69 | −0.196078 | −0.0980391 | − | 0.995183i | \(-0.531257\pi\) | ||||
−0.0980391 | + | 0.995183i | \(0.531257\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 907.033 | 0.0992889 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7824.19 | −0.850634 | −0.425317 | − | 0.905044i | \(-0.639837\pi\) | ||||
−0.425317 | + | 0.905044i | \(0.639837\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11667.9 | 1.25137 | 0.625686 | − | 0.780075i | \(-0.284819\pi\) | ||||
0.625686 | + | 0.780075i | \(0.284819\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4536.86 | 0.483299 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16975.3 | −1.78421 | −0.892107 | − | 0.451825i | \(-0.850773\pi\) | ||||
−0.892107 | + | 0.451825i | \(0.850773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3024.21 | 0.315753 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16244.6 | −1.67375 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16192.9 | −1.65748 | −0.828741 | − | 0.559632i | \(-0.810943\pi\) | ||||
−0.828741 | + | 0.559632i | \(0.810943\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8586.04 | −0.867444 | −0.433722 | − | 0.901047i | \(-0.642800\pi\) | ||||
−0.433722 | + | 0.901047i | \(0.642800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7917.20 | 0.794694 | 0.397347 | − | 0.917668i | \(-0.369931\pi\) | ||||
0.397347 | + | 0.917668i | \(0.369931\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15155.0 | −1.50169 | −0.750844 | − | 0.660480i | \(-0.770353\pi\) | ||||
−0.750844 | + | 0.660480i | \(0.770353\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6968.34 | 0.686073 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.1591 | −0.00244570 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2736.43 | 0.264328 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10001.1 | 0.953993 | 0.476996 | − | 0.878905i | \(-0.341725\pi\) | ||||
0.476996 | + | 0.878905i | \(0.341725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3049.56 | 0.289081 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10896.9 | 1.02021 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7044.54 | −0.655480 | −0.327740 | − | 0.944768i | \(-0.606287\pi\) | ||||
−0.327740 | + | 0.944768i | \(0.606287\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13326.4 | −1.22487 | −0.612437 | − | 0.790520i | \(-0.709811\pi\) | ||||
−0.612437 | + | 0.790520i | \(0.709811\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13990.2 | −1.27806 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7967.02 | 0.719054 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20069.1 | 1.80044 | 0.900218 | − | 0.435440i | \(-0.143407\pi\) | ||||
0.900218 | + | 0.435440i | \(0.143407\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7782.35 | 0.689856 | 0.344928 | − | 0.938629i | \(-0.387903\pi\) | ||||
0.344928 | + | 0.938629i | \(0.387903\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16629.3 | −1.46533 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1475.93 | 0.128526 | 0.0642628 | − | 0.997933i | \(-0.479530\pi\) | ||||
0.0642628 | + | 0.997933i | \(0.479530\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10336.4 | −0.894821 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22180.4 | 1.89784 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −790.307 | −0.0672295 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7609.43 | −0.639875 | −0.319938 | − | 0.947439i | \(-0.603662\pi\) | ||||
−0.319938 | + | 0.947439i | \(0.603662\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12452.9 | −1.04116 | −0.520581 | − | 0.853812i | \(-0.674285\pi\) | ||||
−0.520581 | + | 0.853812i | \(0.674285\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5422.18 | 0.448186 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11988.7 | −0.985344 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20520.9 | −1.66765 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6224.81 | −0.503031 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 620.795 | 0.0496095 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9312.17 | 0.740039 | 0.370020 | − | 0.929024i | \(-0.379351\pi\) | ||||
0.370020 | + | 0.929024i | \(0.379351\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −826.105 | −0.0649292 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11018.6 | 0.861278 | 0.430639 | − | 0.902524i | \(-0.358288\pi\) | ||||
0.430639 | + | 0.902524i | \(0.358288\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11478.6 | −0.887490 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16559.6 | −1.27339 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12018.4 | 0.914250 | 0.457125 | − | 0.889403i | \(-0.348879\pi\) | ||||
0.457125 | + | 0.889403i | \(0.348879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 170.718 | 0.0129170 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8763.89 | −0.656046 | −0.328023 | − | 0.944670i | \(-0.606382\pi\) | ||||
−0.328023 | + | 0.944670i | \(0.606382\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25778.1 | 1.91946 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10273.2 | 0.756895 | 0.378447 | − | 0.925623i | \(-0.376458\pi\) | ||||
0.378447 | + | 0.925623i | \(0.376458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2602.62 | −0.190747 | −0.0953734 | − | 0.995442i | \(-0.530404\pi\) | ||||
−0.0953734 | + | 0.995442i | \(0.530404\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 537.988 | 0.0390185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19727.0 | −1.42331 | −0.711653 | − | 0.702532i | \(-0.752053\pi\) | ||||
−0.711653 | + | 0.702532i | \(0.752053\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −442.739 | −0.0316143 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1639.06 | −0.116437 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10116.2 | −0.711309 | −0.355654 | − | 0.934618i | \(-0.615742\pi\) | ||||
−0.355654 | + | 0.934618i | \(0.615742\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4448.78 | 0.311221 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3130.32 | −0.216774 | −0.108387 | − | 0.994109i | \(-0.534569\pi\) | ||||
−0.108387 | + | 0.994109i | \(0.534569\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18016.9 | −1.24138 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10080.1 | 0.687581 | 0.343790 | − | 0.939046i | \(-0.388289\pi\) | ||||
0.343790 | + | 0.939046i | \(0.388289\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4777.02 | 0.324224 | 0.162112 | − | 0.986772i | \(-0.448169\pi\) | ||||
0.162112 | + | 0.986772i | \(0.448169\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1555.63 | 0.104537 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2571.35 | 0.171941 | 0.0859703 | − | 0.996298i | \(-0.472601\pi\) | ||||
0.0859703 | + | 0.996298i | \(0.472601\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5362.67 | 0.355074 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12711.9 | 0.837564 | 0.418782 | − | 0.908087i | \(-0.362457\pi\) | ||||
0.418782 | + | 0.908087i | \(0.362457\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16236.1 | −1.05939 | −0.529693 | − | 0.848189i | \(-0.677693\pi\) | ||||
−0.529693 | + | 0.848189i | \(0.677693\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12657.3 | −0.821874 | −0.410937 | − | 0.911664i | \(-0.634798\pi\) | ||||
−0.410937 | + | 0.911664i | \(0.634798\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5973.75 | −0.384162 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19037.8 | −1.21842 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3382.28 | 0.214404 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3949.97 | 0.249201 | 0.124600 | − | 0.992207i | \(-0.460235\pi\) | ||||
0.124600 | + | 0.992207i | \(0.460235\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1409.13 | −0.0880621 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4212.44 | −0.262014 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7398.27 | 0.455872 | 0.227936 | − | 0.973676i | \(-0.426802\pi\) | ||||
0.227936 | + | 0.973676i | \(0.426802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12491.7 | 0.766134 | 0.383067 | − | 0.923721i | \(-0.374868\pi\) | ||||
0.383067 | + | 0.923721i | \(0.374868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10472.0 | −0.636315 | −0.318158 | − | 0.948038i | \(-0.603064\pi\) | ||||
−0.318158 | + | 0.948038i | \(0.603064\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6001.94 | −0.363015 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6337.94 | −0.379820 | −0.189910 | − | 0.981801i | \(-0.560820\pi\) | ||||
−0.189910 | + | 0.981801i | \(0.560820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14871.2 | 0.887121 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15196.7 | 0.898302 | 0.449151 | − | 0.893456i | \(-0.351726\pi\) | ||||
0.449151 | + | 0.893456i | \(0.351726\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2298.17 | 0.135232 | 0.0676161 | − | 0.997711i | \(-0.478461\pi\) | ||||
0.0676161 | + | 0.997711i | \(0.478461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14782.5 | −0.862016 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2256.73 | −0.131006 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1114.33 | −0.0641106 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23199.6 | 1.32880 | 0.664398 | − | 0.747379i | \(-0.268688\pi\) | ||||
0.664398 | + | 0.747379i | \(0.268688\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2145.38 | 0.121793 | 0.0608963 | − | 0.998144i | \(-0.480604\pi\) | ||||
0.0608963 | + | 0.998144i | \(0.480604\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14348.1 | −0.810941 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29544.6 | −1.65519 | −0.827593 | − | 0.561329i | \(-0.810290\pi\) | ||||
−0.827593 | + | 0.561329i | \(0.810290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2549.72 | −0.142219 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11121.9 | 0.614964 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27803.1 | −1.53065 | −0.765325 | − | 0.643644i | \(-0.777422\pi\) | ||||
−0.765325 | + | 0.643644i | \(0.777422\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37285.4 | 2.03498 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22759.8 | −1.23686 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19697.8 | 1.06130 | 0.530652 | − | 0.847590i | \(-0.321947\pi\) | ||||
0.530652 | + | 0.847590i | \(0.321947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2775.09 | 0.148883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21896.0 | 1.16476 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19122.5 | 1.01292 | 0.506460 | − | 0.862263i | \(-0.330954\pi\) | ||||
0.506460 | + | 0.862263i | \(0.330954\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 874.641 | 0.0459405 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10555.8 | −0.552117 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1837.44 | 0.0953060 | 0.0476530 | − | 0.998864i | \(-0.484826\pi\) | ||||
0.0476530 | + | 0.998864i | \(0.484826\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29205.2 | −1.50854 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6808.33 | −0.348765 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7555.46 | 0.385442 | 0.192721 | − | 0.981254i | \(-0.438269\pi\) | ||||
0.192721 | + | 0.981254i | \(0.438269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 189.344 | 0.00958021 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11984.6 | 0.603905 | 0.301952 | − | 0.953323i | \(-0.402362\pi\) | ||||
0.301952 | + | 0.953323i | \(0.402362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4528.05 | 0.226313 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27142.5 | 1.35109 | 0.675543 | − | 0.737321i | \(-0.263909\pi\) | ||||
0.675543 | + | 0.737321i | \(0.263909\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29222.6 | −1.44290 | −0.721450 | − | 0.692467i | \(-0.756524\pi\) | ||||
−0.721450 | + | 0.692467i | \(0.756524\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44847.6 | −2.20549 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8196.29 | 0.399847 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8859.39 | 0.430471 | 0.215236 | − | 0.976562i | \(-0.430948\pi\) | ||||
0.215236 | + | 0.976562i | \(0.430948\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14956.2 | 0.720941 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35734.4 | 1.71571 | 0.857853 | − | 0.513896i | \(-0.171798\pi\) | ||||
0.857853 | + | 0.513896i | \(0.171798\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34394.7 | −1.63838 | −0.819189 | − | 0.573524i | \(-0.805576\pi\) | ||||
−0.819189 | + | 0.573524i | \(0.805576\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1087.74 | 0.0516107 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40726.4 | 1.91727 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11602.7 | −0.544091 | −0.272045 | − | 0.962284i | \(-0.587700\pi\) | ||||
−0.272045 | + | 0.962284i | \(0.587700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12680.6 | 0.590026 | 0.295013 | − | 0.955493i | \(-0.404676\pi\) | ||||
0.295013 | + | 0.955493i | \(0.404676\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2638.71 | 0.122303 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18674.0 | −0.858876 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5176.99 | 0.237193 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4397.62 | 0.199946 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4417.61 | 0.200090 | 0.100045 | − | 0.994983i | \(-0.468101\pi\) | ||||
0.100045 | + | 0.994983i | \(0.468101\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33942.4 | −1.52573 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7561.33 | 0.338601 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27030.1 | 1.20132 | 0.600661 | − | 0.799504i | \(-0.294904\pi\) | ||||
0.600661 | + | 0.799504i | \(0.294904\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5947.75 | 0.263350 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6716.60 | −0.295173 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2906.27 | −0.127246 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23647.0 | −1.02767 | −0.513835 | − | 0.857889i | \(-0.671776\pi\) | ||||
−0.513835 | + | 0.857889i | \(0.671776\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33486.1 | −1.44988 | −0.724941 | − | 0.688811i | \(-0.758133\pi\) | ||||
−0.724941 | + | 0.688811i | \(0.758133\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17933.3 | 0.770768 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 155.353 | 0.00665251 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2605.69 | −0.110766 | −0.0553832 | − | 0.998465i | \(-0.517638\pi\) | ||||
−0.0553832 | + | 0.998465i | \(0.517638\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31976.2 | −1.35434 | −0.677169 | − | 0.735828i | \(-0.736793\pi\) | ||||
−0.677169 | + | 0.735828i | \(0.736793\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37759.0 | −1.58768 | −0.793839 | − | 0.608128i | \(-0.791921\pi\) | ||||
−0.793839 | + | 0.608128i | \(0.791921\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1137.55 | −0.0476584 | −0.0238292 | − | 0.999716i | \(-0.507586\pi\) | ||||
−0.0238292 | + | 0.999716i | \(0.507586\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4672.03 | −0.194329 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6154.40 | 0.255068 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37372.2 | −1.53782 | −0.768911 | − | 0.639356i | \(-0.779201\pi\) | ||||
−0.768911 | + | 0.639356i | \(0.779201\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4170.26 | 0.170989 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 43381.1 | 1.76610 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2048.31 | −0.0830943 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 545.589 | 0.0219772 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22490.8 | −0.902780 | −0.451390 | − | 0.892327i | \(-0.649072\pi\) | ||||
−0.451390 | + | 0.892327i | \(0.649072\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43409.5 | −1.73027 | −0.865135 | − | 0.501539i | \(-0.832767\pi\) | ||||
−0.865135 | + | 0.501539i | \(0.832767\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29533.2 | −1.17306 | −0.586532 | − | 0.809926i | \(-0.699507\pi\) | ||||
−0.586532 | + | 0.809926i | \(0.699507\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14351.6 | 0.566090 | 0.283045 | − | 0.959107i | \(-0.408655\pi\) | ||||
0.283045 | + | 0.959107i | \(0.408655\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23251.9 | −0.913975 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10760.5 | −0.420051 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30725.3 | −1.19528 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18436.5 | 0.712307 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43248.7 | −1.66523 | −0.832614 | − | 0.553854i | \(-0.813156\pi\) | ||||
−0.832614 | + | 0.553854i | \(0.813156\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3816.13 | −0.145935 | −0.0729675 | − | 0.997334i | \(-0.523247\pi\) | ||||
−0.0729675 | + | 0.997334i | \(0.523247\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48787.6 | −1.85938 | −0.929690 | − | 0.368343i | \(-0.879925\pi\) | ||||
−0.929690 | + | 0.368343i | \(0.879925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41495.1 | 1.57077 | 0.785384 | − | 0.619009i | \(-0.212466\pi\) | ||||
0.785384 | + | 0.619009i | \(0.212466\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1855.41 | 0.0699984 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4880.01 | 0.182870 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56951.9 | −2.12703 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11068.7 | −0.410637 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12335.3 | 0.456104 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 43829.7 | 1.60989 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21615.3 | −0.791316 | −0.395658 | − | 0.918398i | \(-0.629483\pi\) | ||||
−0.395658 | + | 0.918398i | \(0.629483\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3646.35 | 0.132611 | 0.0663057 | − | 0.997799i | \(-0.478879\pi\) | ||||
0.0663057 | + | 0.997799i | \(0.478879\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −287.693 | −0.0104285 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19581.1 | −0.705151 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31280.0 | −1.12278 | −0.561388 | − | 0.827553i | \(-0.689733\pi\) | ||||
−0.561388 | + | 0.827553i | \(0.689733\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35128.7 | −1.25274 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1645.99 | 0.0585079 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6557.92 | −0.231602 | −0.115801 | − | 0.993272i | \(-0.536944\pi\) | ||||
−0.115801 | + | 0.993272i | \(0.536944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3833.30 | −0.134942 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11707.4 | −0.409491 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24473.3 | −0.853265 | −0.426632 | − | 0.904425i | \(-0.640300\pi\) | ||||
−0.426632 | + | 0.904425i | \(0.640300\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15420.8 | −0.534224 | −0.267112 | − | 0.963665i | \(-0.586069\pi\) | ||||
−0.267112 | + | 0.963665i | \(0.586069\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3671.34 | −0.126782 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33141.2 | −1.13722 | −0.568608 | − | 0.822609i | \(-0.692518\pi\) | ||||
−0.568608 | + | 0.822609i | \(0.692518\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45575.8 | 1.55896 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20735.4 | 0.704813 | 0.352406 | − | 0.935847i | \(-0.385363\pi\) | ||||
0.352406 | + | 0.935847i | \(0.385363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37589.0 | 1.27367 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3357.26 | 0.113046 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25501.1 | −0.856000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31937.7 | −1.06540 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8178.87 | 0.271990 | 0.135995 | − | 0.990710i | \(-0.456577\pi\) | ||||
0.135995 | + | 0.990710i | \(0.456577\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20576.1 | −0.680039 | −0.340020 | − | 0.940418i | \(-0.610434\pi\) | ||||
−0.340020 | + | 0.940418i | \(0.610434\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −49094.1 | −1.61756 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14541.9 | −0.476188 | −0.238094 | − | 0.971242i | \(-0.576523\pi\) | ||||
−0.238094 | + | 0.971242i | \(0.576523\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3881.76 | −0.126723 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29285.7 | −0.950223 | −0.475111 | − | 0.879926i | \(-0.657592\pi\) | ||||
−0.475111 | + | 0.879926i | \(0.657592\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 65897.7 | 2.13165 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.5427 | 0.000982004 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38085.9 | 1.22083 | 0.610413 | − | 0.792083i | \(-0.291003\pi\) | ||||
0.610413 | + | 0.792083i | \(0.291003\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 98.8940 | 0.00315090 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26803.6 | −0.851434 | −0.425717 | − | 0.904856i | \(-0.639978\pi\) | ||||
−0.425717 | + | 0.904856i | \(0.639978\pi\) | |||||||
\(998\) | 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 | 1584.4.a.bc.1.2 | 2 | ||
3.2 | odd | 2 | 176.4.a.i.1.1 | 2 | |||
4.3 | odd | 2 | 99.4.a.c.1.2 | 2 | |||
12.11 | even | 2 | 11.4.a.a.1.1 | ✓ | 2 | ||
20.19 | odd | 2 | 2475.4.a.q.1.1 | 2 | |||
24.5 | odd | 2 | 704.4.a.n.1.2 | 2 | |||
24.11 | even | 2 | 704.4.a.p.1.1 | 2 | |||
33.32 | even | 2 | 1936.4.a.w.1.1 | 2 | |||
44.43 | even | 2 | 1089.4.a.v.1.1 | 2 | |||
60.23 | odd | 4 | 275.4.b.c.199.3 | 4 | |||
60.47 | odd | 4 | 275.4.b.c.199.2 | 4 | |||
60.59 | even | 2 | 275.4.a.b.1.2 | 2 | |||
84.83 | odd | 2 | 539.4.a.e.1.1 | 2 | |||
132.35 | odd | 10 | 121.4.c.f.81.1 | 8 | |||
132.47 | even | 10 | 121.4.c.c.9.1 | 8 | |||
132.59 | even | 10 | 121.4.c.c.27.1 | 8 | |||
132.71 | even | 10 | 121.4.c.c.3.2 | 8 | |||
132.83 | odd | 10 | 121.4.c.f.3.1 | 8 | |||
132.95 | odd | 10 | 121.4.c.f.27.2 | 8 | |||
132.107 | odd | 10 | 121.4.c.f.9.2 | 8 | |||
132.119 | even | 10 | 121.4.c.c.81.2 | 8 | |||
132.131 | odd | 2 | 121.4.a.c.1.2 | 2 | |||
156.155 | even | 2 | 1859.4.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.4.a.a.1.1 | ✓ | 2 | 12.11 | even | 2 | ||
99.4.a.c.1.2 | 2 | 4.3 | odd | 2 | |||
121.4.a.c.1.2 | 2 | 132.131 | odd | 2 | |||
121.4.c.c.3.2 | 8 | 132.71 | even | 10 | |||
121.4.c.c.9.1 | 8 | 132.47 | even | 10 | |||
121.4.c.c.27.1 | 8 | 132.59 | even | 10 | |||
121.4.c.c.81.2 | 8 | 132.119 | even | 10 | |||
121.4.c.f.3.1 | 8 | 132.83 | odd | 10 | |||
121.4.c.f.9.2 | 8 | 132.107 | odd | 10 | |||
121.4.c.f.27.2 | 8 | 132.95 | odd | 10 | |||
121.4.c.f.81.1 | 8 | 132.35 | odd | 10 | |||
176.4.a.i.1.1 | 2 | 3.2 | odd | 2 | |||
275.4.a.b.1.2 | 2 | 60.59 | even | 2 | |||
275.4.b.c.199.2 | 4 | 60.47 | odd | 4 | |||
275.4.b.c.199.3 | 4 | 60.23 | odd | 4 | |||
539.4.a.e.1.1 | 2 | 84.83 | odd | 2 | |||
704.4.a.n.1.2 | 2 | 24.5 | odd | 2 | |||
704.4.a.p.1.1 | 2 | 24.11 | even | 2 | |||
1089.4.a.v.1.1 | 2 | 44.43 | even | 2 | |||
1584.4.a.bc.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1859.4.a.a.1.2 | 2 | 156.155 | even | 2 | |||
1936.4.a.w.1.1 | 2 | 33.32 | even | 2 | |||
2475.4.a.q.1.1 | 2 | 20.19 | odd | 2 |