Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,3,Mod(511,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, 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("960.511");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.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: | \(26.1581053786\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 511.5 | ||
Root | \(1.40906 - 0.120653i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.511 |
Dual form | 960.3.e.c.511.2 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 6.33166i | − 0.904523i | −0.891885 | − | 0.452262i | \(-0.850617\pi\) | ||||
0.891885 | − | 0.452262i | \(-0.149383\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 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 | ||||||||
\(15\) | − 3.87298i | − 0.258199i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 13.9110 | 0.818296 | 0.409148 | − | 0.912468i | \(-0.365826\pi\) | ||||
0.409148 | + | 0.912468i | \(0.365826\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.2468i | 0.907727i | 0.891071 | + | 0.453864i | \(0.149955\pi\) | ||||
−0.891071 | + | 0.453864i | \(0.850045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.9668 | 0.522227 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 28.6177 | 0.986817 | 0.493409 | − | 0.869798i | \(-0.335751\pi\) | ||||
0.493409 | + | 0.869798i | \(0.335751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 23.4939i | 0.757866i | 0.925424 | + | 0.378933i | \(0.123709\pi\) | ||||
−0.925424 | + | 0.378933i | \(0.876291\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.0728 | 0.487054 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | − 32.1597i | − 0.824608i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −44.0791 | −1.07510 | −0.537550 | − | 0.843232i | \(-0.680650\pi\) | ||||
−0.537550 | + | 0.843232i | \(0.680650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50.2937i | 1.16962i | 0.811170 | + | 0.584811i | \(0.198831\pi\) | ||||
−0.811170 | + | 0.584811i | \(0.801169\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.70820 | 0.149071 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 24.0946i | 0.472444i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −81.6070 | −1.53975 | −0.769877 | − | 0.638192i | \(-0.779682\pi\) | ||||
−0.769877 | + | 0.638192i | \(0.779682\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.7499i | 0.377270i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −29.8724 | −0.524077 | ||||||||
\(58\) | 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 | ||||||||
\(63\) | 18.9950i | 0.301508i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 41.5180 | 0.638738 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.49911i | − 0.0671509i | −0.999436 | − | 0.0335754i | \(-0.989311\pi\) | ||||
0.999436 | − | 0.0335754i | \(-0.0106894\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −58.3958 | −0.846316 | ||||||||
\(70\) | 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 | ||||||||
\(75\) | 8.66025i | 0.115470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −58.7555 | −0.763058 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 141.309i | 1.78872i | 0.447352 | + | 0.894358i | \(0.352367\pi\) | ||||
−0.447352 | + | 0.894358i | \(0.647633\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 49.5673i | 0.569739i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −46.3079 | −0.520313 | −0.260157 | − | 0.965566i | \(-0.583774\pi\) | ||||
−0.260157 | + | 0.965566i | \(0.583774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 117.563i | 1.29190i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −40.6926 | −0.437554 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 27.8389i | 0.281201i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 43.3949 | 0.429653 | 0.214826 | − | 0.976652i | \(-0.431081\pi\) | ||||
0.214826 | + | 0.976652i | \(0.431081\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 85.7919i | − 0.832931i | −0.909152 | − | 0.416465i | \(-0.863269\pi\) | ||||
0.909152 | − | 0.416465i | \(-0.136731\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −24.5224 | −0.233547 | ||||||||
\(106\) | 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 | ||||||||
\(111\) | 116.625i | 1.05068i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −172.814 | −1.52933 | −0.764664 | − | 0.644429i | \(-0.777095\pi\) | ||||
−0.764664 | + | 0.644429i | \(0.777095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 75.3886i | − 0.655553i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 55.7022 | 0.476087 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 88.0800i | − 0.740168i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 34.8885 | 0.288335 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 76.3472i | − 0.620709i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.3785i | 0.176208i | 0.996111 | + | 0.0881041i | \(0.0280808\pi\) | ||||
−0.996111 | + | 0.0881041i | \(0.971919\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −87.1113 | −0.675282 | ||||||||
\(130\) | 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 | ||||||||
\(135\) | 11.6190i | 0.0860663i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.5084 | −0.142397 | −0.0711987 | − | 0.997462i | \(-0.522682\pi\) | ||||
−0.0711987 | + | 0.997462i | \(0.522682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 257.370i | − 1.85158i | −0.378038 | − | 0.925790i | \(-0.623401\pi\) | ||||
0.378038 | − | 0.925790i | \(-0.376599\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −53.9697 | −0.382764 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 172.299i | 1.20489i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −63.9911 | −0.441318 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.4326i | 0.104984i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 111.673 | 0.749486 | 0.374743 | − | 0.927129i | \(-0.377731\pi\) | ||||
0.374743 | + | 0.927129i | \(0.377731\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.45275i | 0.0427335i | 0.999772 | + | 0.0213667i | \(0.00680176\pi\) | ||||
−0.999772 | + | 0.0213667i | \(0.993198\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −41.7331 | −0.272765 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | − 141.347i | − 0.888977i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 213.471 | 1.32591 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 249.298i | 1.52944i | 0.644364 | + | 0.764719i | \(0.277122\pi\) | ||||
−0.644364 | + | 0.764719i | \(0.722878\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −35.9398 | −0.217817 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | − 51.7404i | − 0.302576i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 27.7204 | 0.160234 | 0.0801168 | − | 0.996785i | \(-0.474471\pi\) | ||||
0.0801168 | + | 0.996785i | \(0.474471\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 31.6583i | − 0.180905i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 33.3855 | 0.188619 | ||||||||
\(178\) | 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 | ||||||||
\(183\) | 92.0694i | 0.503112i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −150.563 | −0.813853 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 129.089i | − 0.690317i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −32.9003 | −0.174076 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 71.9113i | 0.368776i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −134.496 | −0.682719 | −0.341359 | − | 0.939933i | \(-0.610887\pi\) | ||||
−0.341359 | + | 0.939933i | \(0.610887\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 176.014i | − 0.884491i | −0.896894 | − | 0.442245i | \(-0.854182\pi\) | ||||
0.896894 | − | 0.442245i | \(-0.145818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.79269 | 0.0387696 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 181.198i | − 0.892599i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 98.5638 | 0.480799 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 101.144i | − 0.488621i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 160.044 | 0.765761 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 218.087i | 1.03359i | 0.856110 | + | 0.516793i | \(0.172874\pi\) | ||||
−0.856110 | + | 0.516793i | \(0.827126\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.0987 | −0.108445 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 112.460i | − 0.523071i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 148.755 | 0.685508 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 70.8243i | 0.323399i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −258.292 | −1.16874 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 328.579i | 1.47345i | 0.676193 | + | 0.736724i | \(0.263628\pi\) | ||||
−0.676193 | + | 0.736724i | \(0.736372\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | 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 | ||||||||
\(231\) | − 101.767i | − 0.440552i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 108.746 | 0.466720 | 0.233360 | − | 0.972390i | \(-0.425028\pi\) | ||||
0.233360 | + | 0.972390i | \(0.425028\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 69.6746i | − 0.296488i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −244.754 | −1.03272 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.9234 | −0.0813202 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 320.229i | − 1.29647i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −120.984 | −0.485881 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | − 53.8772i | − 0.211283i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −251.062 | −0.976895 | −0.488447 | − | 0.872593i | \(-0.662437\pi\) | ||||
−0.488447 | + | 0.872593i | \(0.662437\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 426.335i | − 1.64608i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −85.8531 | −0.328939 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | − 80.2076i | − 0.300403i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −148.696 | −0.552772 | −0.276386 | − | 0.961047i | \(-0.589137\pi\) | ||||
−0.276386 | + | 0.961047i | \(0.589137\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 83.3415i | − 0.307533i | −0.988107 | − | 0.153767i | \(-0.950860\pi\) | ||||
0.988107 | − | 0.153767i | \(-0.0491404\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −203.624 | −0.745877 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | − 70.4816i | − 0.252622i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −343.671 | −1.22303 | −0.611514 | − | 0.791233i | \(-0.709439\pi\) | ||||
−0.611514 | + | 0.791233i | \(0.709439\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 314.955i | 1.11292i | 0.830876 | + | 0.556458i | \(0.187840\pi\) | ||||
−0.830876 | + | 0.556458i | \(0.812160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 66.7966 | 0.234374 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 279.094i | 0.972453i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −95.4831 | −0.330391 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 118.740i | 0.408040i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.55421 | 0.0223693 | 0.0111847 | − | 0.999937i | \(-0.496440\pi\) | ||||
0.0111847 | + | 0.999937i | \(0.496440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 43.1005i | 0.146104i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −48.2184 | −0.162351 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 625.997i | − 2.09364i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 318.443 | 1.05795 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 75.1622i | 0.248060i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −118.861 | −0.389709 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 354.559i | 1.15492i | 0.816420 | + | 0.577458i | \(0.195955\pi\) | ||||
−0.816420 | + | 0.577458i | \(0.804045\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 148.596 | 0.480893 | ||||||||
\(310\) | 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 | ||||||||
\(315\) | − 42.4741i | − 0.134838i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 214.004 | 0.675092 | 0.337546 | − | 0.941309i | \(-0.390403\pi\) | ||||
0.337546 | + | 0.941309i | \(0.390403\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 265.562i | − 0.832481i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −317.095 | −0.987836 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 239.921i | 0.742790i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −92.8371 | −0.285652 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 141.127i | − 0.431582i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 197.291 | 0.599669 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 412.454i | − 1.24609i | −0.782188 | − | 0.623043i | \(-0.785896\pi\) | ||||
0.782188 | − | 0.623043i | \(-0.214104\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −202.001 | −0.606610 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 299.323i | − 0.882958i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 218.014 | 0.639338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 366.667i | − 1.06900i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 130.577 | 0.378484 | ||||||||
\(346\) | 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 | ||||||||
\(351\) | 96.4791i | 0.274869i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 256.065 | 0.725396 | 0.362698 | − | 0.931907i | \(-0.381856\pi\) | ||||
0.362698 | + | 0.931907i | \(0.381856\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 29.8203i | − 0.0840009i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 152.559 | 0.427336 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 60.4287i | 0.166470i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −91.4338 | −0.250503 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 245.301i | 0.668396i | 0.942503 | + | 0.334198i | \(0.108465\pi\) | ||||
−0.942503 | + | 0.334198i | \(0.891535\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 132.237 | 0.358367 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | − 19.3649i | − 0.0516398i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −531.357 | −1.40943 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 208.691i | − 0.550636i | −0.961353 | − | 0.275318i | \(-0.911217\pi\) | ||||
0.961353 | − | 0.275318i | \(-0.0887831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −38.7606 | −0.101734 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | − 150.881i | − 0.389874i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −386.588 | −0.993801 | −0.496900 | − | 0.867808i | \(-0.665529\pi\) | ||||
−0.496900 | + | 0.867808i | \(0.665529\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 469.008i | 1.19951i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.03655 | −0.00772658 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 189.142i | 0.474039i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.9333 | 0.0422276 | 0.0211138 | − | 0.999777i | \(-0.493279\pi\) | ||||
0.0211138 | + | 0.999777i | \(0.493279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 436.220i | − 1.08243i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.1246 | −0.0496904 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | − 33.7896i | − 0.0822132i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −122.044 | −0.295505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 156.190i | − 0.376362i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 445.777 | 1.06901 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | − 93.4783i | − 0.220989i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 69.5552 | 0.163659 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 336.568i | − 0.788215i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −298.430 | −0.695641 | ||||||||
\(430\) | 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 | ||||||||
\(435\) | − 110.836i | − 0.254795i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −581.473 | −1.33060 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 446.143i | − 1.01627i | −0.861277 | − | 0.508136i | \(-0.830335\pi\) | ||||
0.861277 | − | 0.508136i | \(-0.169665\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −26.7301 | −0.0606125 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 193.424i | 0.432716i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −750.226 | −1.67088 | −0.835441 | − | 0.549581i | \(-0.814788\pi\) | ||||
−0.835441 | + | 0.549581i | \(0.814788\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 409.037i | 0.906957i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.1765 | −0.0246722 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | − 72.2839i | − 0.157481i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.48690 | 0.00973297 | 0.00486648 | − | 0.999988i | \(-0.498451\pi\) | ||||
0.00486648 | + | 0.999988i | \(0.498451\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 515.108i | 1.11254i | 0.831000 | + | 0.556272i | \(0.187769\pi\) | ||||
−0.831000 | + | 0.556272i | \(0.812231\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 90.9913 | 0.195680 | ||||||||
\(466\) | 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 | ||||||||
\(471\) | 131.476i | 0.279142i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 466.707 | 0.986696 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 86.2341i | 0.181545i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 244.821 | 0.513251 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 369.743i | 0.765512i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −153.292 | −0.316066 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 357.751i | 0.734601i | 0.930102 | + | 0.367301i | \(0.119718\pi\) | ||||
−0.930102 | + | 0.367301i | \(0.880282\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −431.797 | −0.883021 | ||||||||
\(490\) | 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 | ||||||||
\(495\) | − 62.2496i | − 0.125757i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 84.4394 | 0.169898 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 207.096i | 0.415021i | 0.978233 | + | 0.207511i | \(0.0665362\pi\) | ||||
−0.978233 | + | 0.207511i | \(0.933464\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −137.158 | −0.273769 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 304.406i | 0.600406i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 389.029 | 0.764300 | 0.382150 | − | 0.924100i | \(-0.375184\pi\) | ||||
0.382150 | + | 0.924100i | \(0.375184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 258.904i | − 0.506662i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 89.6171 | 0.174692 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 191.836i | 0.372498i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 289.148 | 0.559280 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 48.0132i | 0.0925109i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −151.753 | −0.291273 | −0.145637 | − | 0.989338i | \(-0.546523\pi\) | ||||
−0.145637 | + | 0.989338i | \(0.546523\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 557.762i | − 1.06647i | −0.845968 | − | 0.533234i | \(-0.820977\pi\) | ||||
0.845968 | − | 0.533234i | \(-0.179023\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 54.8338 | 0.104445 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 326.824i | 0.620159i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −607.689 | −1.14875 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 57.8254i | 0.108899i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 818.435 | 1.53552 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 409.368i | − 0.765174i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −353.899 | −0.659030 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 86.3015i | 0.158935i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 182.194 | 0.334302 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 113.651i | 0.207771i | 0.994589 | + | 0.103885i | \(0.0331275\pi\) | ||||
−0.994589 | + | 0.103885i | \(0.966872\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −159.469 | −0.290472 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 493.564i | 0.895761i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 894.718 | 1.61794 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 260.783i | − 0.469878i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −233.232 | −0.418728 | −0.209364 | − | 0.977838i | \(-0.567139\pi\) | ||||
−0.209364 | + | 0.977838i | \(0.567139\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 933.825i | − 1.67053i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 223.589 | 0.398554 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | − 56.9850i | − 0.100503i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 381.089 | 0.669752 | 0.334876 | − | 0.942262i | \(-0.391306\pi\) | ||||
0.334876 | + | 0.942262i | \(0.391306\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 453.871i | − 0.794870i | −0.917630 | − | 0.397435i | \(-0.869900\pi\) | ||||
0.917630 | − | 0.397435i | \(-0.130100\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.96939 | −0.00343697 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | − 132.753i | − 0.229281i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 442.269 | 0.761220 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 757.282i | 1.29894i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −124.554 | −0.212913 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | − 232.953i | − 0.394168i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −163.937 | −0.276454 | −0.138227 | − | 0.990401i | \(-0.544140\pi\) | ||||
−0.138227 | + | 0.990401i | \(0.544140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 196.953i | 0.331013i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 304.865 | 0.510661 | ||||||||
\(598\) | 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 | ||||||||
\(603\) | 13.4973i | 0.0223836i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −78.0132 | −0.128947 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 660.957i | 1.08889i | 0.838796 | + | 0.544445i | \(0.183260\pi\) | ||||
−0.838796 | + | 0.544445i | \(0.816740\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 313.844 | 0.515342 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 170.718i | 0.277590i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −63.6752 | −0.103201 | −0.0516007 | − | 0.998668i | \(-0.516432\pi\) | ||||
−0.0516007 | + | 0.998668i | \(0.516432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 872.350i | 1.40929i | 0.709561 | + | 0.704644i | \(0.248893\pi\) | ||||
−0.709561 | + | 0.704644i | \(0.751107\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 175.187 | 0.282105 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 293.206i | 0.470636i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 277.204i | 0.442112i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 936.682 | 1.48916 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 340.783i | 0.540068i | 0.962851 | + | 0.270034i | \(0.0870349\pi\) | ||||
−0.962851 | + | 0.270034i | \(0.912965\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −377.737 | −0.596742 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 50.0397i | − 0.0788027i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −165.436 | −0.259712 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 40.0081i | − 0.0626105i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 766.210 | 1.19534 | 0.597668 | − | 0.801744i | \(-0.296094\pi\) | ||||
0.597668 | + | 0.801744i | \(0.296094\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1163.47i | 1.80943i | 0.426014 | + | 0.904717i | \(0.359917\pi\) | ||||
−0.426014 | + | 0.904717i | \(0.640083\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 194.787 | 0.301995 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 257.652i | 0.395778i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −109.569 | −0.167793 | −0.0838967 | − | 0.996474i | \(-0.526737\pi\) | ||||
−0.0838967 | + | 0.996474i | \(0.526737\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 3.92016i | − 0.00598498i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −122.671 | −0.186714 | ||||||||
\(658\) | 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 | ||||||||
\(663\) | − 447.375i | − 0.674773i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −244.181 | −0.367189 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 964.841i | 1.44654i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −569.116 | −0.850696 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | − 25.9808i | − 0.0384900i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −989.373 | −1.46141 | −0.730704 | − | 0.682695i | \(-0.760808\pi\) | ||||
−0.730704 | + | 0.682695i | \(0.760808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 434.063i | − 0.639268i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 273.057 | 0.400965 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 473.107i | 0.688656i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1515.23 | 2.19917 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 893.378i | 1.29288i | 0.762966 | + | 0.646438i | \(0.223742\pi\) | ||||
−0.762966 | + | 0.646438i | \(0.776258\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 176.266 | 0.254353 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 575.496i | 0.828052i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −613.186 | −0.879750 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 188.353i | 0.269461i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1127.42 | −1.60830 | −0.804149 | − | 0.594428i | \(-0.797378\pi\) | ||||
−0.804149 | + | 0.594428i | \(0.797378\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1161.29i | 1.65191i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 120.680 | 0.171177 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | − 423.926i | − 0.596239i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −792.091 | −1.11093 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 385.271i | − 0.538841i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 310.026 | 0.432393 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 621.154i | 0.859134i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 143.089 | 0.197363 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 295.050i | − 0.405846i | −0.979195 | − | 0.202923i | \(-0.934956\pi\) | ||||
0.979195 | − | 0.202923i | \(-0.0650441\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | − 34.5084i | − 0.0469502i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41.7501 | −0.0566487 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 482.679i | − 0.653151i | −0.945171 | − | 0.326576i | \(-0.894105\pi\) | ||||
0.945171 | − | 0.326576i | \(-0.105895\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 554.652 | 0.748519 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | − 209.551i | − 0.280523i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1159.17 | 1.54762 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 395.508i | 0.526642i | 0.964708 | + | 0.263321i | \(0.0848179\pi\) | ||||
−0.964708 | + | 0.263321i | \(0.915182\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 530.389 | 0.704368 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 541.891i | 0.713954i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −369.354 | −0.485354 | −0.242677 | − | 0.970107i | \(-0.578025\pi\) | ||||
−0.242677 | + | 0.970107i | \(0.578025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 515.903i | 0.676150i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 93.3181 | 0.121984 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | − 434.852i | − 0.564010i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1176.93 | 1.52254 | 0.761272 | − | 0.648432i | \(-0.224575\pi\) | ||||
0.761272 | + | 0.648432i | \(0.224575\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 117.469i | 0.151573i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 738.433 | 0.950365 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 760.224i | − 0.975897i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 123.754 | 0.158455 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 148.702i | − 0.189913i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −169.734 | −0.216222 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 603.482i | − 0.766814i | −0.923580 | − | 0.383407i | \(-0.874751\pi\) | ||||
0.923580 | − | 0.383407i | \(-0.125249\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −84.4626 | −0.107050 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1094.20i | 1.38331i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −986.975 | −1.24461 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 316.062i | 0.397563i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −860.121 | −1.07920 | −0.539599 | − | 0.841922i | \(-0.681424\pi\) | ||||
−0.539599 | + | 0.841922i | \(0.681424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 433.460i | 0.542503i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 138.924 | 0.173438 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 379.448i | − 0.472538i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −477.336 | −0.592963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 257.548i | − 0.319143i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 941.012 | 1.16318 | 0.581589 | − | 0.813483i | \(-0.302431\pi\) | ||||
0.581589 | + | 0.813483i | \(0.302431\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1105.29i | − 1.36287i | −0.731878 | − | 0.681436i | \(-0.761356\pi\) | ||||
0.731878 | − | 0.681436i | \(-0.238644\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 144.352 | 0.177554 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 557.448i | − 0.683985i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −867.407 | −1.06170 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 352.688i | − 0.430632i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 193.170 | 0.235286 | 0.117643 | − | 0.993056i | \(-0.462466\pi\) | ||||
0.117643 | + | 0.993056i | \(0.462466\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 178.778i | 0.217227i | 0.994084 | + | 0.108614i | \(0.0346411\pi\) | ||||
−0.994084 | + | 0.108614i | \(0.965359\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 80.3639 | 0.0974108 | ||||||||
\(826\) | 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 | ||||||||
\(831\) | − 249.554i | − 0.300306i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 123.948 | 0.148797 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 177.071i | − 0.212061i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 122.078 | 0.145851 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | − 595.256i | − 0.706116i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −392.986 | −0.465072 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 220.903i | − 0.260806i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −545.518 | −0.642542 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 115.695i | 0.135316i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −717.784 | −0.837554 | −0.418777 | − | 0.908089i | \(-0.637541\pi\) | ||||
−0.418777 | + | 0.908089i | \(0.637541\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 252.894i | 0.294405i | 0.989106 | + | 0.147203i | \(0.0470269\pi\) | ||||
−0.989106 | + | 0.147203i | \(0.952973\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −483.405 | −0.561446 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | − 165.382i | − 0.190752i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1311.29 | 1.50897 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 83.5368i | 0.0959091i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −205.663 | −0.235582 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 11.3522i | 0.0129149i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −458.454 | −0.520379 | −0.260189 | − | 0.965558i | \(-0.583785\pi\) | ||||
−0.260189 | + | 0.965558i | \(0.583785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 771.505i | − 0.873732i | −0.899527 | − | 0.436866i | \(-0.856088\pi\) | ||||
0.899527 | − | 0.436866i | \(-0.143912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −74.6523 | −0.0843529 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | − 83.5166i | − 0.0937336i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −537.401 | −0.601793 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 456.882i | − 0.510482i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1084.26 | 1.20876 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 672.340i | 0.747876i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1135.24 | −1.25997 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 551.560i | 0.610808i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −111.415 | −0.123110 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 392.544i | 0.432793i | 0.976306 | + | 0.216397i | \(0.0694304\pi\) | ||||
−0.976306 | + | 0.216397i | \(0.930570\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −130.185 | −0.143218 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | − 205.874i | − 0.224998i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.1004 | 0.0121051 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 970.018i | 1.05551i | 0.849395 | + | 0.527757i | \(0.176967\pi\) | ||||
−0.849395 | + | 0.527757i | \(0.823033\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −614.115 | −0.666791 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 247.616i | − 0.268273i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 336.669 | 0.363966 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 257.376i | 0.277644i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 980.857 | 1.05582 | 0.527910 | − | 0.849300i | \(-0.322976\pi\) | ||||
0.527910 | + | 0.849300i | \(0.322976\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 153.670i | 0.165059i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 334.956 | 0.359010 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | − 40.7420i | − 0.0433887i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1581.10 | 1.68023 | 0.840117 | − | 0.542405i | \(-0.182486\pi\) | ||||
0.840117 | + | 0.542405i | \(0.182486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1486.12i | − 1.57595i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 73.5673 | 0.0778490 | ||||||||
\(946\) | 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 | ||||||||
\(951\) | 370.666i | 0.389765i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1106.52 | 1.16109 | 0.580546 | − | 0.814228i | \(-0.302839\pi\) | ||||
0.580546 | + | 0.814228i | \(0.302839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2.54247i | − 0.00266227i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 459.966 | 0.480633 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 123.521i | 0.128802i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 409.039 | 0.425638 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 549.225i | − 0.570327i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 171.384 | 0.177600 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 406.453i | − 0.420324i | −0.977667 | − | 0.210162i | \(-0.932601\pi\) | ||||
0.977667 | − | 0.210162i | \(-0.0673992\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −415.555 | −0.428850 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | − 160.798i | − 0.164922i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1457.74 | −1.49205 | −0.746027 | − | 0.665916i | \(-0.768041\pi\) | ||||
−0.746027 | + | 0.665916i | \(0.768041\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 429.720i | 0.438938i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 244.439 | 0.249174 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 341.718i | 0.346219i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1695.65 | −1.71450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 605.720i | − 0.611221i | −0.952157 | − | 0.305611i | \(-0.901139\pi\) | ||||
0.952157 | − | 0.305611i | \(-0.0988605\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 714.392 | 0.719428 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | − 349.876i | − 0.350227i |
(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 | 960.3.e.c.511.5 | 8 | ||
3.2 | odd | 2 | 2880.3.e.j.2431.5 | 8 | |||
4.3 | odd | 2 | inner | 960.3.e.c.511.2 | 8 | ||
8.3 | odd | 2 | 60.3.c.a.31.4 | yes | 8 | ||
8.5 | even | 2 | 60.3.c.a.31.3 | ✓ | 8 | ||
12.11 | even | 2 | 2880.3.e.j.2431.8 | 8 | |||
24.5 | odd | 2 | 180.3.c.b.91.6 | 8 | |||
24.11 | even | 2 | 180.3.c.b.91.5 | 8 | |||
40.3 | even | 4 | 300.3.f.b.199.15 | 16 | |||
40.13 | odd | 4 | 300.3.f.b.199.1 | 16 | |||
40.19 | odd | 2 | 300.3.c.d.151.5 | 8 | |||
40.27 | even | 4 | 300.3.f.b.199.2 | 16 | |||
40.29 | even | 2 | 300.3.c.d.151.6 | 8 | |||
40.37 | odd | 4 | 300.3.f.b.199.16 | 16 | |||
120.29 | odd | 2 | 900.3.c.u.451.3 | 8 | |||
120.53 | even | 4 | 900.3.f.f.199.16 | 16 | |||
120.59 | even | 2 | 900.3.c.u.451.4 | 8 | |||
120.77 | even | 4 | 900.3.f.f.199.1 | 16 | |||
120.83 | odd | 4 | 900.3.f.f.199.2 | 16 | |||
120.107 | odd | 4 | 900.3.f.f.199.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.3 | ✓ | 8 | 8.5 | even | 2 | ||
60.3.c.a.31.4 | yes | 8 | 8.3 | odd | 2 | ||
180.3.c.b.91.5 | 8 | 24.11 | even | 2 | |||
180.3.c.b.91.6 | 8 | 24.5 | odd | 2 | |||
300.3.c.d.151.5 | 8 | 40.19 | odd | 2 | |||
300.3.c.d.151.6 | 8 | 40.29 | even | 2 | |||
300.3.f.b.199.1 | 16 | 40.13 | odd | 4 | |||
300.3.f.b.199.2 | 16 | 40.27 | even | 4 | |||
300.3.f.b.199.15 | 16 | 40.3 | even | 4 | |||
300.3.f.b.199.16 | 16 | 40.37 | odd | 4 | |||
900.3.c.u.451.3 | 8 | 120.29 | odd | 2 | |||
900.3.c.u.451.4 | 8 | 120.59 | even | 2 | |||
900.3.f.f.199.1 | 16 | 120.77 | even | 4 | |||
900.3.f.f.199.2 | 16 | 120.83 | odd | 4 | |||
900.3.f.f.199.15 | 16 | 120.107 | odd | 4 | |||
900.3.f.f.199.16 | 16 | 120.53 | even | 4 | |||
960.3.e.c.511.2 | 8 | 4.3 | odd | 2 | inner | ||
960.3.e.c.511.5 | 8 | 1.1 | even | 1 | trivial | ||
2880.3.e.j.2431.5 | 8 | 3.2 | odd | 2 | |||
2880.3.e.j.2431.8 | 8 | 12.11 | even | 2 |