Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,3,Mod(2431,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.2431");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.e (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(78.4743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.85100625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{19} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.8 | ||
Root | \(1.40906 + 0.120653i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2431 |
Dual form | 2880.3.e.j.2431.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.33166i | 0.904523i | 0.891885 | + | 0.452262i | \(0.149383\pi\) | ||||
−0.891885 | + | 0.452262i | \(0.850617\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 9.27963i | − 0.843602i | −0.906688 | − | 0.421801i | \(-0.861398\pi\) | ||||
0.906688 | − | 0.421801i | \(-0.138602\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.5674 | −1.42826 | −0.714131 | − | 0.700012i | \(-0.753178\pi\) | ||||
−0.714131 | + | 0.700012i | \(0.753178\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.9110 | −0.818296 | −0.409148 | − | 0.912468i | \(-0.634174\pi\) | ||||
−0.409148 | + | 0.912468i | \(0.634174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 17.2468i | − 0.907727i | −0.891071 | − | 0.453864i | \(-0.850045\pi\) | ||||
0.891071 | − | 0.453864i | \(-0.149955\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 33.7148i | 1.46586i | 0.680303 | + | 0.732931i | \(0.261848\pi\) | ||||
−0.680303 | + | 0.732931i | \(0.738152\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −28.6177 | −0.986817 | −0.493409 | − | 0.869798i | \(-0.664249\pi\) | ||||
−0.493409 | + | 0.869798i | \(0.664249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 23.4939i | − 0.757866i | −0.925424 | − | 0.378933i | \(-0.876291\pi\) | ||||
0.925424 | − | 0.378933i | \(-0.123709\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.1580i | 0.404515i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 67.3338 | 1.81983 | 0.909916 | − | 0.414793i | \(-0.136146\pi\) | ||||
0.909916 | + | 0.414793i | \(0.136146\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 44.0791 | 1.07510 | 0.537550 | − | 0.843232i | \(-0.319350\pi\) | ||||
0.537550 | + | 0.843232i | \(0.319350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 50.2937i | − 1.16962i | −0.811170 | − | 0.584811i | \(-0.801169\pi\) | ||||
0.811170 | − | 0.584811i | \(-0.198831\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 31.1594i | 0.662967i | 0.943461 | + | 0.331483i | \(0.107549\pi\) | ||||
−0.943461 | + | 0.331483i | \(0.892451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.91003 | 0.181837 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 81.6070 | 1.53975 | 0.769877 | − | 0.638192i | \(-0.220318\pi\) | ||||
0.769877 | + | 0.638192i | \(0.220318\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 20.7499i | − 0.377270i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 19.2751i | − 0.326697i | −0.986568 | − | 0.163349i | \(-0.947770\pi\) | ||||
0.986568 | − | 0.163349i | \(-0.0522296\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 53.1563 | 0.871415 | 0.435707 | − | 0.900088i | \(-0.356498\pi\) | ||||
0.435707 | + | 0.900088i | \(0.356498\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −41.5180 | −0.638738 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.49911i | 0.0671509i | 0.999436 | + | 0.0335754i | \(0.0106894\pi\) | ||||
−0.999436 | + | 0.0335754i | \(0.989311\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3360i | 0.187832i | 0.995580 | + | 0.0939158i | \(0.0299385\pi\) | ||||
−0.995580 | + | 0.0939158i | \(0.970062\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.8904 | 0.560143 | 0.280071 | − | 0.959979i | \(-0.409642\pi\) | ||||
0.280071 | + | 0.959979i | \(0.409642\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 58.7555 | 0.763058 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 141.309i | − 1.78872i | −0.447352 | − | 0.894358i | \(-0.647633\pi\) | ||||
0.447352 | − | 0.894358i | \(-0.352367\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 69.8503i | 0.841570i | 0.907160 | + | 0.420785i | \(0.138245\pi\) | ||||
−0.907160 | + | 0.420785i | \(0.861755\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −31.1060 | −0.365953 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 46.3079 | 0.520313 | 0.260157 | − | 0.965566i | \(-0.416226\pi\) | ||||
0.260157 | + | 0.965566i | \(0.416226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 117.563i | − 1.29190i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 38.5651i | − 0.405948i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 68.5543 | 0.706745 | 0.353373 | − | 0.935483i | \(-0.385035\pi\) | ||||
0.353373 | + | 0.935483i | \(0.385035\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −43.3949 | −0.429653 | −0.214826 | − | 0.976652i | \(-0.568919\pi\) | ||||
−0.214826 | + | 0.976652i | \(0.568919\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 85.7919i | 0.832931i | 0.909152 | + | 0.416465i | \(0.136731\pi\) | ||||
−0.909152 | + | 0.416465i | \(0.863269\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 183.075i | 1.71098i | 0.517818 | + | 0.855491i | \(0.326745\pi\) | ||||
−0.517818 | + | 0.855491i | \(0.673255\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −81.4798 | −0.747521 | −0.373761 | − | 0.927525i | \(-0.621932\pi\) | ||||
−0.373761 | + | 0.927525i | \(0.621932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 172.814 | 1.52933 | 0.764664 | − | 0.644429i | \(-0.222905\pi\) | ||||
0.764664 | + | 0.644429i | \(0.222905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 75.3886i | 0.655553i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 88.0800i | − 0.740168i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 34.8885 | 0.288335 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 22.3785i | − 0.176208i | −0.996111 | − | 0.0881041i | \(-0.971919\pi\) | ||||
0.996111 | − | 0.0881041i | \(-0.0280808\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.75315i | 0.0133828i | 0.999978 | + | 0.00669141i | \(0.00212996\pi\) | ||||
−0.999978 | + | 0.00669141i | \(0.997870\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 109.201 | 0.821060 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.5084 | 0.142397 | 0.0711987 | − | 0.997462i | \(-0.477318\pi\) | ||||
0.0711987 | + | 0.997462i | \(0.477318\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 257.370i | 1.85158i | 0.378038 | + | 0.925790i | \(0.376599\pi\) | ||||
−0.378038 | + | 0.925790i | \(0.623401\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 172.299i | 1.20489i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −63.9911 | −0.441318 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −111.673 | −0.749486 | −0.374743 | − | 0.927129i | \(-0.622269\pi\) | ||||
−0.374743 | + | 0.927129i | \(0.622269\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 6.45275i | − 0.0427335i | −0.999772 | − | 0.0213667i | \(-0.993198\pi\) | ||||
0.999772 | − | 0.0213667i | \(-0.00680176\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 52.5339i | − 0.338928i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 75.9075 | 0.483488 | 0.241744 | − | 0.970340i | \(-0.422281\pi\) | ||||
0.241744 | + | 0.970340i | \(0.422281\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −213.471 | −1.32591 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 249.298i | − 1.52944i | −0.644364 | − | 0.764719i | \(-0.722878\pi\) | ||||
0.644364 | − | 0.764719i | \(-0.277122\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 79.1883i | 0.474182i | 0.971487 | + | 0.237091i | \(0.0761939\pi\) | ||||
−0.971487 | + | 0.237091i | \(0.923806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 175.749 | 1.03993 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −27.7204 | −0.160234 | −0.0801168 | − | 0.996785i | \(-0.525529\pi\) | ||||
−0.0801168 | + | 0.996785i | \(0.525529\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 31.6583i | 0.180905i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 204.324i | 1.14147i | 0.821133 | + | 0.570737i | \(0.193342\pi\) | ||||
−0.821133 | + | 0.570737i | \(0.806658\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 49.8262 | 0.275283 | 0.137641 | − | 0.990482i | \(-0.456048\pi\) | ||||
0.137641 | + | 0.990482i | \(0.456048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 150.563 | 0.813853 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 129.089i | 0.690317i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.13703i | 0.00595301i | 0.999996 | + | 0.00297651i | \(0.000947453\pi\) | ||||
−0.999996 | + | 0.00297651i | \(0.999053\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −76.6452 | −0.397126 | −0.198563 | − | 0.980088i | \(-0.563627\pi\) | ||||
−0.198563 | + | 0.980088i | \(0.563627\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 134.496 | 0.682719 | 0.341359 | − | 0.939933i | \(-0.389113\pi\) | ||||
0.341359 | + | 0.939933i | \(0.389113\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 176.014i | 0.884491i | 0.896894 | + | 0.442245i | \(0.145818\pi\) | ||||
−0.896894 | + | 0.442245i | \(0.854182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 181.198i | − 0.892599i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 98.5638 | 0.480799 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −160.044 | −0.765761 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 218.087i | − 1.03359i | −0.856110 | − | 0.516793i | \(-0.827126\pi\) | ||||
0.856110 | − | 0.516793i | \(-0.172874\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 112.460i | − 0.523071i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 148.755 | 0.685508 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 258.292 | 1.16874 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 328.579i | − 1.47345i | −0.676193 | − | 0.736724i | \(-0.736372\pi\) | ||||
0.676193 | − | 0.736724i | \(-0.263628\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 157.649i | − 0.694491i | −0.937774 | − | 0.347245i | \(-0.887117\pi\) | ||||
0.937774 | − | 0.347245i | \(-0.112883\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 273.148 | 1.19279 | 0.596393 | − | 0.802692i | \(-0.296600\pi\) | ||||
0.596393 | + | 0.802692i | \(0.296600\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −108.746 | −0.466720 | −0.233360 | − | 0.972390i | \(-0.574972\pi\) | ||||
−0.233360 | + | 0.972390i | \(0.574972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 69.6746i | 0.296488i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 178.994i | − 0.748927i | −0.927242 | − | 0.374464i | \(-0.877827\pi\) | ||||
0.927242 | − | 0.374464i | \(-0.122173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 358.623 | 1.48806 | 0.744032 | − | 0.668144i | \(-0.232911\pi\) | ||||
0.744032 | + | 0.668144i | \(0.232911\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.9234 | 0.0813202 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 320.229i | 1.29647i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 306.220i | − 1.22000i | −0.792401 | − | 0.610000i | \(-0.791169\pi\) | ||||
0.792401 | − | 0.610000i | \(-0.208831\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 312.861 | 1.23660 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 251.062 | 0.976895 | 0.488447 | − | 0.872593i | \(-0.337563\pi\) | ||||
0.488447 | + | 0.872593i | \(0.337563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 426.335i | 1.64608i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 48.7645i | 0.185416i | 0.995693 | + | 0.0927082i | \(0.0295524\pi\) | ||||
−0.995693 | + | 0.0927082i | \(0.970448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 182.479 | 0.688599 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 148.696 | 0.552772 | 0.276386 | − | 0.961047i | \(-0.410863\pi\) | ||||
0.276386 | + | 0.961047i | \(0.410863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 83.3415i | 0.307533i | 0.988107 | + | 0.153767i | \(0.0491404\pi\) | ||||
−0.988107 | + | 0.153767i | \(0.950860\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 46.3981i | − 0.168720i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −144.080 | −0.520146 | −0.260073 | − | 0.965589i | \(-0.583747\pi\) | ||||
−0.260073 | + | 0.965589i | \(0.583747\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 343.671 | 1.22303 | 0.611514 | − | 0.791233i | \(-0.290561\pi\) | ||||
0.611514 | + | 0.791233i | \(0.290561\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 314.955i | − 1.11292i | −0.830876 | − | 0.556458i | \(-0.812160\pi\) | ||||
0.830876 | − | 0.556458i | \(-0.187840\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 279.094i | 0.972453i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −95.4831 | −0.330391 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.55421 | −0.0223693 | −0.0111847 | − | 0.999937i | \(-0.503560\pi\) | ||||
−0.0111847 | + | 0.999937i | \(0.503560\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 43.1005i | − 0.146104i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 625.997i | − 2.09364i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 318.443 | 1.05795 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 118.861 | 0.389709 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 354.559i | − 1.15492i | −0.816420 | − | 0.577458i | \(-0.804045\pi\) | ||||
0.816420 | − | 0.577458i | \(-0.195955\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 193.387i | − 0.621823i | −0.950439 | − | 0.310912i | \(-0.899366\pi\) | ||||
0.950439 | − | 0.310912i | \(-0.100634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.5224 | −0.0751514 | −0.0375757 | − | 0.999294i | \(-0.511964\pi\) | ||||
−0.0375757 | + | 0.999294i | \(0.511964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −214.004 | −0.675092 | −0.337546 | − | 0.941309i | \(-0.609597\pi\) | ||||
−0.337546 | + | 0.941309i | \(0.609597\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 265.562i | 0.832481i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 239.921i | 0.742790i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −92.8371 | −0.285652 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −197.291 | −0.599669 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 412.454i | 1.24609i | 0.782188 | + | 0.623043i | \(0.214104\pi\) | ||||
−0.782188 | + | 0.623043i | \(0.785896\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.0603i | 0.0300308i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 103.268 | 0.306433 | 0.153216 | − | 0.988193i | \(-0.451037\pi\) | ||||
0.153216 | + | 0.988193i | \(0.451037\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −218.014 | −0.639338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 366.667i | 1.06900i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 153.211i | − 0.441531i | −0.975327 | − | 0.220766i | \(-0.929144\pi\) | ||||
0.975327 | − | 0.220766i | \(-0.0708556\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 84.7317 | 0.242784 | 0.121392 | − | 0.992605i | \(-0.461264\pi\) | ||||
0.121392 | + | 0.992605i | \(0.461264\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −256.065 | −0.725396 | −0.362698 | − | 0.931907i | \(-0.618144\pi\) | ||||
−0.362698 | + | 0.931907i | \(0.618144\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.8203i | 0.0840009i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 667.258i | − 1.85866i | −0.369253 | − | 0.929329i | \(-0.620386\pi\) | ||||
0.369253 | − | 0.929329i | \(-0.379614\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 63.5473 | 0.176031 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 91.4338 | 0.250503 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 245.301i | − 0.668396i | −0.942503 | − | 0.334198i | \(-0.891535\pi\) | ||||
0.942503 | − | 0.334198i | \(-0.108465\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 516.708i | 1.39274i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −698.787 | −1.87342 | −0.936712 | − | 0.350101i | \(-0.886147\pi\) | ||||
−0.936712 | + | 0.350101i | \(0.886147\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 531.357 | 1.40943 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 208.691i | 0.550636i | 0.961353 | + | 0.275318i | \(0.0887831\pi\) | ||||
−0.961353 | + | 0.275318i | \(0.911217\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 156.524i | − 0.408680i | −0.978900 | − | 0.204340i | \(-0.934495\pi\) | ||||
0.978900 | − | 0.204340i | \(-0.0655048\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 131.381 | 0.341250 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 386.588 | 0.993801 | 0.496900 | − | 0.867808i | \(-0.334471\pi\) | ||||
0.496900 | + | 0.867808i | \(0.334471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 469.008i | − 1.19951i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 315.976i | − 0.799938i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 561.155 | 1.41349 | 0.706744 | − | 0.707470i | \(-0.250163\pi\) | ||||
0.706744 | + | 0.707470i | \(0.250163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.9333 | −0.0422276 | −0.0211138 | − | 0.999777i | \(-0.506721\pi\) | ||||
−0.0211138 | + | 0.999777i | \(0.506721\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 436.220i | 1.08243i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 624.832i | − 1.53521i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 258.490 | 0.632006 | 0.316003 | − | 0.948758i | \(-0.397659\pi\) | ||||
0.316003 | + | 0.948758i | \(0.397659\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 122.044 | 0.295505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 156.190i | 0.376362i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 258.917i | − 0.617941i | −0.951072 | − | 0.308970i | \(-0.900016\pi\) | ||||
0.951072 | − | 0.308970i | \(-0.0999844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −97.4654 | −0.231509 | −0.115755 | − | 0.993278i | \(-0.536929\pi\) | ||||
−0.115755 | + | 0.993278i | \(0.536929\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −69.5552 | −0.163659 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 336.568i | 0.788215i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 389.968i | 0.904799i | 0.891815 | + | 0.452399i | \(0.149432\pi\) | ||||
−0.891815 | + | 0.452399i | \(0.850568\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 275.893 | 0.637166 | 0.318583 | − | 0.947895i | \(-0.396793\pi\) | ||||
0.318583 | + | 0.947895i | \(0.396793\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 581.473 | 1.33060 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 446.143i | 1.01627i | 0.861277 | + | 0.508136i | \(0.169665\pi\) | ||||
−0.861277 | + | 0.508136i | \(0.830335\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 794.679i | 1.79386i | 0.442174 | + | 0.896929i | \(0.354207\pi\) | ||||
−0.442174 | + | 0.896929i | \(0.645793\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 103.548 | 0.232691 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 750.226 | 1.67088 | 0.835441 | − | 0.549581i | \(-0.185212\pi\) | ||||
0.835441 | + | 0.549581i | \(0.185212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 409.037i | − 0.906957i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 262.878i | − 0.577754i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 101.092 | 0.221209 | 0.110604 | − | 0.993865i | \(-0.464721\pi\) | ||||
0.110604 | + | 0.993865i | \(0.464721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.48690 | −0.00973297 | −0.00486648 | − | 0.999988i | \(-0.501549\pi\) | ||||
−0.00486648 | + | 0.999988i | \(0.501549\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 515.108i | − 1.11254i | −0.831000 | − | 0.556272i | \(-0.812231\pi\) | ||||
0.831000 | − | 0.556272i | \(-0.187769\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 295.498i | 0.632758i | 0.948633 | + | 0.316379i | \(0.102467\pi\) | ||||
−0.948633 | + | 0.316379i | \(0.897533\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.4869 | −0.0607396 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −466.707 | −0.986696 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 86.2341i | − 0.181545i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 273.155i | 0.570260i | 0.958489 | + | 0.285130i | \(0.0920368\pi\) | ||||
−0.958489 | + | 0.285130i | \(0.907963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1250.21 | −2.59920 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 153.292 | 0.316066 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 357.751i | − 0.734601i | −0.930102 | − | 0.367301i | \(-0.880282\pi\) | ||||
0.930102 | − | 0.367301i | \(-0.119718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 422.379i | 0.860242i | 0.902771 | + | 0.430121i | \(0.141529\pi\) | ||||
−0.902771 | + | 0.430121i | \(0.858471\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 398.102 | 0.807509 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −84.4394 | −0.169898 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 207.096i | − 0.415021i | −0.978233 | − | 0.207511i | \(-0.933464\pi\) | ||||
0.978233 | − | 0.207511i | \(-0.0665362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 702.853i | 1.39732i | 0.715452 | + | 0.698661i | \(0.246221\pi\) | ||||
−0.715452 | + | 0.698661i | \(0.753779\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −97.0340 | −0.192147 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −389.029 | −0.764300 | −0.382150 | − | 0.924100i | \(-0.624816\pi\) | ||||
−0.382150 | + | 0.924100i | \(0.624816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 258.904i | 0.506662i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 191.836i | 0.372498i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 289.148 | 0.559280 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 151.753 | 0.291273 | 0.145637 | − | 0.989338i | \(-0.453477\pi\) | ||||
0.145637 | + | 0.989338i | \(0.453477\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 557.762i | 1.06647i | 0.845968 | + | 0.533234i | \(0.179023\pi\) | ||||
−0.845968 | + | 0.533234i | \(0.820977\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 326.824i | 0.620159i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −607.689 | −1.14875 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −818.435 | −1.53552 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 409.368i | 0.765174i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 82.6818i | − 0.153398i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −340.979 | −0.630275 | −0.315137 | − | 0.949046i | \(-0.602051\pi\) | ||||
−0.315137 | + | 0.949046i | \(0.602051\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −182.194 | −0.334302 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 113.651i | − 0.207771i | −0.994589 | − | 0.103885i | \(-0.966872\pi\) | ||||
0.994589 | − | 0.103885i | \(-0.0331275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 493.564i | 0.895761i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 894.718 | 1.61794 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 233.232 | 0.418728 | 0.209364 | − | 0.977838i | \(-0.432861\pi\) | ||||
0.209364 | + | 0.977838i | \(0.432861\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 933.825i | 1.67053i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 167.786i | 0.298021i | 0.988836 | + | 0.149011i | \(0.0476088\pi\) | ||||
−0.988836 | + | 0.149011i | \(0.952391\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 386.424 | 0.683936 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −381.089 | −0.669752 | −0.334876 | − | 0.942262i | \(-0.608694\pi\) | ||||
−0.334876 | + | 0.942262i | \(0.608694\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 453.871i | 0.794870i | 0.917630 | + | 0.397435i | \(0.130100\pi\) | ||||
−0.917630 | + | 0.397435i | \(0.869900\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 168.574i | 0.293172i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 688.294 | 1.19288 | 0.596442 | − | 0.802656i | \(-0.296581\pi\) | ||||
0.596442 | + | 0.802656i | \(0.296581\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −442.269 | −0.761220 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 757.282i | − 1.29894i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 249.163i | − 0.424468i | −0.977219 | − | 0.212234i | \(-0.931926\pi\) | ||||
0.977219 | − | 0.212234i | \(-0.0680739\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −405.194 | −0.687936 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 163.937 | 0.276454 | 0.138227 | − | 0.990401i | \(-0.455860\pi\) | ||||
0.138227 | + | 0.990401i | \(0.455860\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 196.953i | − 0.331013i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 170.412i | 0.284494i | 0.989831 | + | 0.142247i | \(0.0454327\pi\) | ||||
−0.989831 | + | 0.142247i | \(0.954567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1119.87 | 1.86335 | 0.931674 | − | 0.363295i | \(-0.118348\pi\) | ||||
0.931674 | + | 0.363295i | \(0.118348\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 78.0132 | 0.128947 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 660.957i | − 1.08889i | −0.838796 | − | 0.544445i | \(-0.816740\pi\) | ||||
0.838796 | − | 0.544445i | \(-0.183260\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 578.550i | − 0.946890i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 179.315 | 0.292520 | 0.146260 | − | 0.989246i | \(-0.453276\pi\) | ||||
0.146260 | + | 0.989246i | \(0.453276\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 63.6752 | 0.103201 | 0.0516007 | − | 0.998668i | \(-0.483568\pi\) | ||||
0.0516007 | + | 0.998668i | \(0.483568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 872.350i | − 1.40929i | −0.709561 | − | 0.704644i | \(-0.751107\pi\) | ||||
0.709561 | − | 0.704644i | \(-0.248893\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 293.206i | 0.470636i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −936.682 | −1.48916 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 340.783i | − 0.540068i | −0.962851 | − | 0.270034i | \(-0.912965\pi\) | ||||
0.962851 | − | 0.270034i | \(-0.0870349\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 50.0397i | − 0.0788027i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −165.436 | −0.259712 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −766.210 | −1.19534 | −0.597668 | − | 0.801744i | \(-0.703906\pi\) | ||||
−0.597668 | + | 0.801744i | \(0.703906\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1163.47i | − 1.80943i | −0.426014 | − | 0.904717i | \(-0.640083\pi\) | ||||
0.426014 | − | 0.904717i | \(-0.359917\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 740.530i | − 1.14456i | −0.820059 | − | 0.572279i | \(-0.806059\pi\) | ||||
0.820059 | − | 0.572279i | \(-0.193941\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −178.866 | −0.275603 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 109.569 | 0.167793 | 0.0838967 | − | 0.996474i | \(-0.473263\pi\) | ||||
0.0838967 | + | 0.996474i | \(0.473263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.92016i | 0.00598498i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 723.214i | − 1.09744i | −0.836006 | − | 0.548721i | \(-0.815115\pi\) | ||||
0.836006 | − | 0.548721i | \(-0.184885\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −700.333 | −1.05951 | −0.529753 | − | 0.848152i | \(-0.677715\pi\) | ||||
−0.529753 | + | 0.848152i | \(0.677715\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 244.181 | 0.367189 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 964.841i | − 1.44654i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 493.271i | − 0.735128i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1221.18 | −1.81454 | −0.907269 | − | 0.420552i | \(-0.861837\pi\) | ||||
−0.907269 | + | 0.420552i | \(0.861837\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 989.373 | 1.46141 | 0.730704 | − | 0.682695i | \(-0.239192\pi\) | ||||
0.730704 | + | 0.682695i | \(0.239192\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 434.063i | 0.639268i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 307.312i | 0.449945i | 0.974365 | + | 0.224972i | \(0.0722292\pi\) | ||||
−0.974365 | + | 0.224972i | \(0.927771\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.6222 | 0.0636821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1515.23 | −2.19917 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 893.378i | − 1.29288i | −0.762966 | − | 0.646438i | \(-0.776258\pi\) | ||||
0.762966 | − | 0.646438i | \(-0.223742\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 575.496i | 0.828052i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −613.186 | −0.879750 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1127.42 | 1.60830 | 0.804149 | − | 0.594428i | \(-0.202622\pi\) | ||||
0.804149 | + | 0.594428i | \(0.202622\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1161.29i | − 1.65191i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 274.762i | − 0.388631i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1093.27 | −1.54199 | −0.770997 | − | 0.636839i | \(-0.780242\pi\) | ||||
−0.770997 | + | 0.636839i | \(0.780242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 792.091 | 1.11093 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 385.271i | 0.538841i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 769.690i | 1.07050i | 0.844693 | + | 0.535251i | \(0.179783\pi\) | ||||
−0.844693 | + | 0.535251i | \(0.820217\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −543.205 | −0.753405 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −143.089 | −0.197363 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 295.050i | 0.405846i | 0.979195 | + | 0.202923i | \(0.0650441\pi\) | ||||
−0.979195 | + | 0.202923i | \(0.934956\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 699.638i | 0.957097i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −261.200 | −0.356344 | −0.178172 | − | 0.983999i | \(-0.557018\pi\) | ||||
−0.178172 | + | 0.983999i | \(0.557018\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.7501 | 0.0566487 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 482.679i | 0.653151i | 0.945171 | + | 0.326576i | \(0.105895\pi\) | ||||
−0.945171 | + | 0.326576i | \(0.894105\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.7067i | 0.0319067i | 0.999873 | + | 0.0159534i | \(0.00507833\pi\) | ||||
−0.999873 | + | 0.0159534i | \(0.994922\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −249.709 | −0.335180 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1159.17 | −1.54762 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 395.508i | − 0.526642i | −0.964708 | − | 0.263321i | \(-0.915182\pi\) | ||||
0.964708 | − | 0.263321i | \(-0.0848179\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 14.4288i | − 0.0191110i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −393.940 | −0.520396 | −0.260198 | − | 0.965555i | \(-0.583788\pi\) | ||||
−0.260198 | + | 0.965555i | \(0.583788\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 369.354 | 0.485354 | 0.242677 | − | 0.970107i | \(-0.421975\pi\) | ||||
0.242677 | + | 0.970107i | \(0.421975\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 515.903i | − 0.676150i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 357.890i | 0.466610i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −873.491 | −1.13588 | −0.567940 | − | 0.823070i | \(-0.692259\pi\) | ||||
−0.567940 | + | 0.823070i | \(0.692259\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1176.93 | −1.52254 | −0.761272 | − | 0.648432i | \(-0.775425\pi\) | ||||
−0.761272 | + | 0.648432i | \(0.775425\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 117.469i | − 0.151573i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 760.224i | − 0.975897i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 123.754 | 0.158455 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 169.734 | 0.216222 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 603.482i | 0.766814i | 0.923580 | + | 0.383407i | \(0.125249\pi\) | ||||
−0.923580 | + | 0.383407i | \(0.874751\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1094.20i | 1.38331i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −986.975 | −1.24461 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 860.121 | 1.07920 | 0.539599 | − | 0.841922i | \(-0.318576\pi\) | ||||
0.539599 | + | 0.841922i | \(0.318576\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 433.460i | − 0.542503i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 379.448i | − 0.472538i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −477.336 | −0.592963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −941.012 | −1.16318 | −0.581589 | − | 0.813483i | \(-0.697569\pi\) | ||||
−0.581589 | + | 0.813483i | \(0.697569\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1105.29i | 1.36287i | 0.731878 | + | 0.681436i | \(0.238644\pi\) | ||||
−0.731878 | + | 0.681436i | \(0.761356\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 557.448i | − 0.683985i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −867.407 | −1.06170 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −193.170 | −0.235286 | −0.117643 | − | 0.993056i | \(-0.537534\pi\) | ||||
−0.117643 | + | 0.993056i | \(0.537534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 178.778i | − 0.217227i | −0.994084 | − | 0.108614i | \(-0.965359\pi\) | ||||
0.994084 | − | 0.108614i | \(-0.0346411\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1558.61i | 1.88465i | 0.334697 | + | 0.942326i | \(0.391366\pi\) | ||||
−0.334697 | + | 0.942326i | \(0.608634\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 565.477 | 0.682119 | 0.341059 | − | 0.940042i | \(-0.389214\pi\) | ||||
0.341059 | + | 0.940042i | \(0.389214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −123.948 | −0.148797 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 177.071i | 0.212061i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1280.25i | − 1.52592i | −0.646443 | − | 0.762962i | \(-0.723744\pi\) | ||||
0.646443 | − | 0.762962i | \(-0.276256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.0271 | −0.0261915 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 392.986 | 0.465072 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 220.903i | 0.260806i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2270.15i | 2.66762i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −120.366 | −0.141109 | −0.0705546 | − | 0.997508i | \(-0.522477\pi\) | ||||
−0.0705546 | + | 0.997508i | \(0.522477\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 717.784 | 0.837554 | 0.418777 | − | 0.908089i | \(-0.362459\pi\) | ||||
0.418777 | + | 0.908089i | \(0.362459\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 252.894i | − 0.294405i | −0.989106 | − | 0.147203i | \(-0.952973\pi\) | ||||
0.989106 | − | 0.147203i | \(-0.0470269\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1234.73i | − 1.43075i | −0.698743 | − | 0.715373i | \(-0.746257\pi\) | ||||
0.698743 | − | 0.715373i | \(-0.253743\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −61.9847 | −0.0716586 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1311.29 | −1.50897 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 83.5368i | − 0.0959091i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 70.7902i | 0.0809030i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 685.723 | 0.781896 | 0.390948 | − | 0.920413i | \(-0.372147\pi\) | ||||
0.390948 | + | 0.920413i | \(0.372147\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 458.454 | 0.520379 | 0.260189 | − | 0.965558i | \(-0.416215\pi\) | ||||
0.260189 | + | 0.965558i | \(0.416215\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 771.505i | 0.873732i | 0.899527 | + | 0.436866i | \(0.143912\pi\) | ||||
−0.899527 | + | 0.436866i | \(0.856088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1161.05i | 1.30896i | 0.756080 | + | 0.654480i | \(0.227112\pi\) | ||||
−0.756080 | + | 0.654480i | \(0.772888\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 141.693 | 0.159385 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 537.401 | 0.601793 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 456.882i | 0.510482i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 672.340i | 0.747876i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1135.24 | −1.25997 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 111.415 | 0.123110 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 392.544i | − 0.432793i | −0.976306 | − | 0.216397i | \(-0.930570\pi\) | ||||
0.976306 | − | 0.216397i | \(-0.0694304\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1013.40i | − 1.11240i | −0.831048 | − | 0.556201i | \(-0.812259\pi\) | ||||
0.831048 | − | 0.556201i | \(-0.187741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 648.185 | 0.709950 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.1004 | −0.0121051 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 970.018i | − 1.05551i | −0.849395 | − | 0.527757i | \(-0.823033\pi\) | ||||
0.849395 | − | 0.527757i | \(-0.176967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 247.616i | − 0.268273i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 336.669 | 0.363966 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −980.857 | −1.05582 | −0.527910 | − | 0.849300i | \(-0.677024\pi\) | ||||
−0.527910 | + | 0.849300i | \(0.677024\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 153.670i | − 0.165059i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 288.652i | 0.308719i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 964.666 | 1.02953 | 0.514763 | − | 0.857333i | \(-0.327880\pi\) | ||||
0.514763 | + | 0.857333i | \(0.327880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1581.10 | −1.68023 | −0.840117 | − | 0.542405i | \(-0.817514\pi\) | ||||
−0.840117 | + | 0.542405i | \(0.817514\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1486.12i | 1.57595i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1245.27i | − 1.31497i | −0.753469 | − | 0.657483i | \(-0.771621\pi\) | ||||
0.753469 | − | 0.657483i | \(-0.228379\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −759.229 | −0.800031 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1106.52 | −1.16109 | −0.580546 | − | 0.814228i | \(-0.697161\pi\) | ||||
−0.580546 | + | 0.814228i | \(0.697161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.54247i | 0.00266227i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 123.521i | 0.128802i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 409.039 | 0.425638 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −171.384 | −0.177600 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 406.453i | 0.420324i | 0.977667 | + | 0.210162i | \(0.0673992\pi\) | ||||
−0.977667 | + | 0.210162i | \(0.932601\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1815.22i | − 1.86943i | −0.355393 | − | 0.934717i | \(-0.615653\pi\) | ||||
0.355393 | − | 0.934717i | \(-0.384347\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1629.58 | −1.67480 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1457.74 | 1.49205 | 0.746027 | − | 0.665916i | \(-0.231959\pi\) | ||||
0.746027 | + | 0.665916i | \(0.231959\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 429.720i | − 0.438938i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 19.9496i | − 0.0202946i | −0.999949 | − | 0.0101473i | \(-0.996770\pi\) | ||||
0.999949 | − | 0.0101473i | \(-0.00323004\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 300.741 | 0.305321 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1695.65 | 1.71450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 605.720i | 0.611221i | 0.952157 | + | 0.305611i | \(0.0988605\pi\) | ||||
−0.952157 | + | 0.305611i | \(0.901139\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 393.578i | 0.395556i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1238.47 | −1.24220 | −0.621099 | − | 0.783732i | \(-0.713314\pi\) | ||||
−0.621099 | + | 0.783732i | \(0.713314\pi\) | |||||||
\(998\) | 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 | 2880.3.e.j.2431.8 | 8 | ||
3.2 | odd | 2 | 960.3.e.c.511.2 | 8 | |||
4.3 | odd | 2 | inner | 2880.3.e.j.2431.5 | 8 | ||
8.3 | odd | 2 | 180.3.c.b.91.6 | 8 | |||
8.5 | even | 2 | 180.3.c.b.91.5 | 8 | |||
12.11 | even | 2 | 960.3.e.c.511.5 | 8 | |||
24.5 | odd | 2 | 60.3.c.a.31.4 | yes | 8 | ||
24.11 | even | 2 | 60.3.c.a.31.3 | ✓ | 8 | ||
40.3 | even | 4 | 900.3.f.f.199.16 | 16 | |||
40.13 | odd | 4 | 900.3.f.f.199.2 | 16 | |||
40.19 | odd | 2 | 900.3.c.u.451.3 | 8 | |||
40.27 | even | 4 | 900.3.f.f.199.1 | 16 | |||
40.29 | even | 2 | 900.3.c.u.451.4 | 8 | |||
40.37 | odd | 4 | 900.3.f.f.199.15 | 16 | |||
120.29 | odd | 2 | 300.3.c.d.151.5 | 8 | |||
120.53 | even | 4 | 300.3.f.b.199.15 | 16 | |||
120.59 | even | 2 | 300.3.c.d.151.6 | 8 | |||
120.77 | even | 4 | 300.3.f.b.199.2 | 16 | |||
120.83 | odd | 4 | 300.3.f.b.199.1 | 16 | |||
120.107 | odd | 4 | 300.3.f.b.199.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.3 | ✓ | 8 | 24.11 | even | 2 | ||
60.3.c.a.31.4 | yes | 8 | 24.5 | odd | 2 | ||
180.3.c.b.91.5 | 8 | 8.5 | even | 2 | |||
180.3.c.b.91.6 | 8 | 8.3 | odd | 2 | |||
300.3.c.d.151.5 | 8 | 120.29 | odd | 2 | |||
300.3.c.d.151.6 | 8 | 120.59 | even | 2 | |||
300.3.f.b.199.1 | 16 | 120.83 | odd | 4 | |||
300.3.f.b.199.2 | 16 | 120.77 | even | 4 | |||
300.3.f.b.199.15 | 16 | 120.53 | even | 4 | |||
300.3.f.b.199.16 | 16 | 120.107 | odd | 4 | |||
900.3.c.u.451.3 | 8 | 40.19 | odd | 2 | |||
900.3.c.u.451.4 | 8 | 40.29 | even | 2 | |||
900.3.f.f.199.1 | 16 | 40.27 | even | 4 | |||
900.3.f.f.199.2 | 16 | 40.13 | odd | 4 | |||
900.3.f.f.199.15 | 16 | 40.37 | odd | 4 | |||
900.3.f.f.199.16 | 16 | 40.3 | even | 4 | |||
960.3.e.c.511.2 | 8 | 3.2 | odd | 2 | |||
960.3.e.c.511.5 | 8 | 12.11 | even | 2 | |||
2880.3.e.j.2431.5 | 8 | 4.3 | odd | 2 | inner | ||
2880.3.e.j.2431.8 | 8 | 1.1 | even | 1 | trivial |