Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (of order \(2\), degree \(1\), 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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 48x^{14} + 921x^{12} + 8986x^{10} + 46812x^{8} + 125072x^{6} + 152129x^{4} + 65614x^{2} + 5041 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.5 | ||
Root | \(-1.96467i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.j.485.12 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.96467i | − 0.982333i | −0.871066 | − | 0.491167i | \(-0.836571\pi\) | ||||
0.871066 | − | 0.491167i | \(-0.163429\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.140085 | 0.0350211 | ||||||||
\(5\) | − 9.62261i | − 1.92452i | −0.272127 | − | 0.962261i | \(-0.587727\pi\) | ||||
0.272127 | − | 0.962261i | \(-0.412273\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.23056 | 0.747223 | 0.373612 | − | 0.927585i | \(-0.378119\pi\) | ||||
0.373612 | + | 0.927585i | \(0.378119\pi\) | |||||||
\(8\) | − 8.13389i | − 1.01674i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −18.9052 | −1.89052 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.2247 | −1.32497 | −0.662487 | − | 0.749073i | \(-0.730499\pi\) | ||||
−0.662487 | + | 0.749073i | \(0.730499\pi\) | |||||||
\(14\) | − 10.2763i | − 0.734022i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.4200 | −0.963752 | ||||||||
\(17\) | 7.71825i | 0.454015i | 0.973893 | + | 0.227007i | \(0.0728941\pi\) | ||||
−0.973893 | + | 0.227007i | \(0.927106\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.0290 | −0.738370 | −0.369185 | − | 0.929356i | \(-0.620363\pi\) | ||||
−0.369185 | + | 0.929356i | \(0.620363\pi\) | |||||||
\(20\) | − 1.34798i | − 0.0673989i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 5.68512i | − 0.247179i | −0.992333 | − | 0.123590i | \(-0.960559\pi\) | ||||
0.992333 | − | 0.123590i | \(-0.0394407\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −67.5947 | −2.70379 | ||||||||
\(26\) | 33.8407i | 1.30157i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.732721 | 0.0261686 | ||||||||
\(29\) | 24.0845i | 0.830501i | 0.909707 | + | 0.415250i | \(0.136306\pi\) | ||||
−0.909707 | + | 0.415250i | \(0.863694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 15.0159 | 0.484383 | 0.242192 | − | 0.970228i | \(-0.422134\pi\) | ||||
0.242192 | + | 0.970228i | \(0.422134\pi\) | |||||||
\(32\) | − 2.24031i | − 0.0700097i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.1638 | 0.445994 | ||||||||
\(35\) | − 50.3317i | − 1.43805i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.65533 | −0.206901 | −0.103450 | − | 0.994635i | \(-0.532988\pi\) | ||||
−0.103450 | + | 0.994635i | \(0.532988\pi\) | |||||||
\(38\) | 27.5624i | 0.725325i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −78.2692 | −1.95673 | ||||||||
\(41\) | 18.1953i | 0.443789i | 0.975071 | + | 0.221894i | \(0.0712240\pi\) | ||||
−0.975071 | + | 0.221894i | \(0.928776\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 53.6955 | 1.24873 | 0.624366 | − | 0.781132i | \(-0.285358\pi\) | ||||
0.624366 | + | 0.781132i | \(0.285358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −11.1694 | −0.242812 | ||||||||
\(47\) | − 38.8113i | − 0.825772i | −0.910783 | − | 0.412886i | \(-0.864521\pi\) | ||||
0.910783 | − | 0.412886i | \(-0.135479\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −21.6412 | −0.441658 | ||||||||
\(50\) | 132.801i | 2.65602i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.41291 | −0.0464021 | ||||||||
\(53\) | − 81.6140i | − 1.53989i | −0.638112 | − | 0.769944i | \(-0.720284\pi\) | ||||
0.638112 | − | 0.769944i | \(-0.279716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 42.5448i | − 0.759728i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 47.3181 | 0.815829 | ||||||||
\(59\) | 0 0.000434171i | 0 7.35883e-6i | −1.00000 | 3.67942e-6i | \(-0.999999\pi\) | |||||
1.00000 | 3.67942e-6i | \(-1.17119e-6\pi\) | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.77983 | −0.0783579 | −0.0391789 | − | 0.999232i | \(-0.512474\pi\) | ||||
−0.0391789 | + | 0.999232i | \(0.512474\pi\) | |||||||
\(62\) | − 29.5012i | − 0.475826i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −66.0816 | −1.03253 | ||||||||
\(65\) | 165.746i | 2.54994i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 111.796 | 1.66860 | 0.834298 | − | 0.551313i | \(-0.185873\pi\) | ||||
0.834298 | + | 0.551313i | \(0.185873\pi\) | |||||||
\(68\) | 1.08121i | 0.0159001i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −98.8850 | −1.41264 | ||||||||
\(71\) | − 99.6336i | − 1.40329i | −0.712526 | − | 0.701645i | \(-0.752449\pi\) | ||||
0.712526 | − | 0.701645i | \(-0.247551\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 34.2957 | 0.469804 | 0.234902 | − | 0.972019i | \(-0.424523\pi\) | ||||
0.234902 | + | 0.972019i | \(0.424523\pi\) | |||||||
\(74\) | 15.0402i | 0.203246i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.96525 | −0.0258585 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 61.7290 | 0.781380 | 0.390690 | − | 0.920522i | \(-0.372236\pi\) | ||||
0.390690 | + | 0.920522i | \(0.372236\pi\) | |||||||
\(80\) | 148.381i | 1.85476i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 35.7478 | 0.435948 | ||||||||
\(83\) | 65.2314i | 0.785921i | 0.919555 | + | 0.392961i | \(0.128549\pi\) | ||||
−0.919555 | + | 0.392961i | \(0.871451\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 74.2697 | 0.873761 | ||||||||
\(86\) | − 105.494i | − 1.22667i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 92.5976i | − 1.04042i | −0.854038 | − | 0.520211i | \(-0.825853\pi\) | ||||
0.854038 | − | 0.520211i | \(-0.174147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −90.0947 | −0.990051 | ||||||||
\(92\) | − 0.796398i | − 0.00865650i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −76.2513 | −0.811184 | ||||||||
\(95\) | 134.996i | 1.42101i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52.4236 | −0.540450 | −0.270225 | − | 0.962797i | \(-0.587098\pi\) | ||||
−0.270225 | + | 0.962797i | \(0.587098\pi\) | |||||||
\(98\) | 42.5178i | 0.433855i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.46897 | −0.0946897 | ||||||||
\(101\) | 58.9222i | 0.583389i | 0.956512 | + | 0.291694i | \(0.0942190\pi\) | ||||
−0.956512 | + | 0.291694i | \(0.905781\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −96.7152 | −0.938982 | −0.469491 | − | 0.882937i | \(-0.655563\pi\) | ||||
−0.469491 | + | 0.882937i | \(0.655563\pi\) | |||||||
\(104\) | 140.103i | 1.34715i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −160.344 | −1.51268 | ||||||||
\(107\) | 18.3916i | 0.171884i | 0.996300 | + | 0.0859422i | \(0.0273900\pi\) | ||||
−0.996300 | + | 0.0859422i | \(0.972610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −50.6495 | −0.464674 | −0.232337 | − | 0.972635i | \(-0.574637\pi\) | ||||
−0.232337 | + | 0.972635i | \(0.574637\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −80.6555 | −0.720138 | ||||||||
\(113\) | − 9.83566i | − 0.0870412i | −0.999053 | − | 0.0435206i | \(-0.986143\pi\) | ||||
0.999053 | − | 0.0435206i | \(-0.0138574\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −54.7058 | −0.475702 | ||||||||
\(116\) | 3.37387i | 0.0290851i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.000853002 0 | −7.22883e−6 0 | ||||||||
\(119\) | 40.3708i | 0.339250i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.39077i | 0.0769736i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.10349 | 0.0169637 | ||||||||
\(125\) | 409.872i | 3.27898i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −215.481 | −1.69670 | −0.848349 | − | 0.529437i | \(-0.822403\pi\) | ||||
−0.848349 | + | 0.529437i | \(0.822403\pi\) | |||||||
\(128\) | 120.867i | 0.944274i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 325.636 | 2.50489 | ||||||||
\(131\) | − 166.588i | − 1.27166i | −0.771827 | − | 0.635832i | \(-0.780657\pi\) | ||||
0.771827 | − | 0.635832i | \(-0.219343\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −73.3797 | −0.551727 | ||||||||
\(134\) | − 219.642i | − 1.63912i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 62.7794 | 0.461613 | ||||||||
\(137\) | 43.7479i | 0.319328i | 0.987171 | + | 0.159664i | \(0.0510411\pi\) | ||||
−0.987171 | + | 0.159664i | \(0.948959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 103.074 | 0.741539 | 0.370769 | − | 0.928725i | \(-0.379094\pi\) | ||||
0.370769 | + | 0.928725i | \(0.379094\pi\) | |||||||
\(140\) | − 7.05069i | − 0.0503620i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −195.747 | −1.37850 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 231.756 | 1.59832 | ||||||||
\(146\) | − 67.3796i | − 0.461504i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.07239 | −0.00724590 | ||||||||
\(149\) | 90.4963i | 0.607358i | 0.952774 | + | 0.303679i | \(0.0982150\pi\) | ||||
−0.952774 | + | 0.303679i | \(0.901785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −240.354 | −1.59175 | −0.795873 | − | 0.605464i | \(-0.792988\pi\) | ||||
−0.795873 | + | 0.605464i | \(0.792988\pi\) | |||||||
\(152\) | 114.110i | 0.750727i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 144.492i | − 0.932207i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −29.6036 | −0.188558 | −0.0942789 | − | 0.995546i | \(-0.530055\pi\) | ||||
−0.0942789 | + | 0.995546i | \(0.530055\pi\) | |||||||
\(158\) | − 121.277i | − 0.767576i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −21.5576 | −0.134735 | ||||||||
\(161\) | − 29.7364i | − 0.184698i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 210.084 | 1.28886 | 0.644430 | − | 0.764663i | \(-0.277095\pi\) | ||||
0.644430 | + | 0.764663i | \(0.277095\pi\) | |||||||
\(164\) | 2.54888i | 0.0155420i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 128.158 | 0.772036 | ||||||||
\(167\) | 15.2464i | 0.0912955i | 0.998958 | + | 0.0456478i | \(0.0145352\pi\) | ||||
−0.998958 | + | 0.0456478i | \(0.985465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 127.689 | 0.755557 | ||||||||
\(170\) | − 145.915i | − 0.858325i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.52190 | 0.0437320 | ||||||||
\(173\) | − 214.396i | − 1.23928i | −0.784885 | − | 0.619642i | \(-0.787278\pi\) | ||||
0.784885 | − | 0.619642i | \(-0.212722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −353.558 | −2.02033 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −181.923 | −1.02204 | ||||||||
\(179\) | 204.595i | 1.14299i | 0.820605 | + | 0.571495i | \(0.193636\pi\) | ||||
−0.820605 | + | 0.571495i | \(0.806364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 136.759 | 0.755572 | 0.377786 | − | 0.925893i | \(-0.376685\pi\) | ||||
0.377786 | + | 0.925893i | \(0.376685\pi\) | |||||||
\(182\) | 177.006i | 0.972561i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −46.2422 | −0.251316 | ||||||||
\(185\) | 73.6643i | 0.398185i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 5.43686i | − 0.0289195i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 265.222 | 1.39590 | ||||||||
\(191\) | − 244.731i | − 1.28132i | −0.767827 | − | 0.640658i | \(-0.778662\pi\) | ||||
0.767827 | − | 0.640658i | \(-0.221338\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.7364 | 0.0815358 | 0.0407679 | − | 0.999169i | \(-0.487020\pi\) | ||||
0.0407679 | + | 0.999169i | \(0.487020\pi\) | |||||||
\(194\) | 102.995i | 0.530902i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.03160 | −0.0154674 | ||||||||
\(197\) | − 95.4172i | − 0.484351i | −0.970232 | − | 0.242176i | \(-0.922139\pi\) | ||||
0.970232 | − | 0.242176i | \(-0.0778610\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −65.2214 | −0.327746 | −0.163873 | − | 0.986481i | \(-0.552399\pi\) | ||||
−0.163873 | + | 0.986481i | \(0.552399\pi\) | |||||||
\(200\) | 549.807i | 2.74904i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 115.763 | 0.573082 | ||||||||
\(203\) | 125.976i | 0.620569i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 175.087 | 0.854081 | ||||||||
\(206\) | 190.013i | 0.922394i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 265.605 | 1.27695 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 275.123 | 1.30390 | 0.651951 | − | 0.758261i | \(-0.273951\pi\) | ||||
0.651951 | + | 0.758261i | \(0.273951\pi\) | |||||||
\(212\) | − 11.4329i | − 0.0539286i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 36.1334 | 0.168848 | ||||||||
\(215\) | − 516.691i | − 2.40321i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 78.5415 | 0.361942 | ||||||||
\(218\) | 99.5094i | 0.456465i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 132.944i | − 0.601558i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 182.909 | 0.820218 | 0.410109 | − | 0.912037i | \(-0.365491\pi\) | ||||
0.410109 | + | 0.912037i | \(0.365491\pi\) | |||||||
\(224\) | − 11.7181i | − 0.0523128i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.3238 | −0.0855035 | ||||||||
\(227\) | − 250.411i | − 1.10313i | −0.834132 | − | 0.551565i | \(-0.814031\pi\) | ||||
0.834132 | − | 0.551565i | \(-0.185969\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −350.485 | −1.53050 | −0.765252 | − | 0.643731i | \(-0.777386\pi\) | ||||
−0.765252 | + | 0.643731i | \(0.777386\pi\) | |||||||
\(230\) | 107.479i | 0.467298i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 195.901 | 0.844400 | ||||||||
\(233\) | − 364.712i | − 1.56529i | −0.622471 | − | 0.782643i | \(-0.713871\pi\) | ||||
0.622471 | − | 0.782643i | \(-0.286129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −373.466 | −1.58922 | ||||||||
\(236\) | 0 6.08206e-5i | 0 2.57715e-7i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 79.3151 | 0.333257 | ||||||||
\(239\) | 242.816i | 1.01597i | 0.861367 | + | 0.507983i | \(0.169609\pi\) | ||||
−0.861367 | + | 0.507983i | \(0.830391\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 418.345 | 1.73587 | 0.867935 | − | 0.496677i | \(-0.165447\pi\) | ||||
0.867935 | + | 0.496677i | \(0.165447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.669580 | −0.00274418 | ||||||||
\(245\) | 208.245i | 0.849980i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 241.645 | 0.978321 | ||||||||
\(248\) | − 122.138i | − 0.492490i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 805.262 | 3.22105 | ||||||||
\(251\) | − 276.186i | − 1.10034i | −0.835051 | − | 0.550172i | \(-0.814562\pi\) | ||||
0.835051 | − | 0.550172i | \(-0.185438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 423.348i | 1.66672i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −26.8629 | −0.104933 | ||||||||
\(257\) | 161.198i | 0.627231i | 0.949550 | + | 0.313615i | \(0.101540\pi\) | ||||
−0.949550 | + | 0.313615i | \(0.898460\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −40.0417 | −0.154601 | ||||||||
\(260\) | 23.2185i | 0.0893019i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −327.290 | −1.24920 | ||||||||
\(263\) | 55.4784i | 0.210944i | 0.994422 | + | 0.105472i | \(0.0336354\pi\) | ||||
−0.994422 | + | 0.105472i | \(0.966365\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −785.340 | −2.96355 | ||||||||
\(266\) | 144.167i | 0.541980i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.6609 | 0.0584361 | ||||||||
\(269\) | 58.2016i | 0.216363i | 0.994131 | + | 0.108181i | \(0.0345027\pi\) | ||||
−0.994131 | + | 0.108181i | \(0.965497\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −425.905 | −1.57161 | −0.785803 | − | 0.618477i | \(-0.787750\pi\) | ||||
−0.785803 | + | 0.618477i | \(0.787750\pi\) | |||||||
\(272\) | − 119.016i | − 0.437558i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 85.9501 | 0.313686 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 127.884 | 0.461677 | 0.230838 | − | 0.972992i | \(-0.425853\pi\) | ||||
0.230838 | + | 0.972992i | \(0.425853\pi\) | |||||||
\(278\) | − 202.506i | − 0.728438i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −409.392 | −1.46211 | ||||||||
\(281\) | − 74.3983i | − 0.264763i | −0.991199 | − | 0.132381i | \(-0.957738\pi\) | ||||
0.991199 | − | 0.132381i | \(-0.0422624\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −494.336 | −1.74677 | −0.873386 | − | 0.487029i | \(-0.838081\pi\) | ||||
−0.873386 | + | 0.487029i | \(0.838081\pi\) | |||||||
\(284\) | − 13.9571i | − 0.0491448i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 95.1718i | 0.331609i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 229.429 | 0.793871 | ||||||||
\(290\) | − 455.323i | − 1.57008i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.80429 | 0.0164531 | ||||||||
\(293\) | − 13.6119i | − 0.0464568i | −0.999730 | − | 0.0232284i | \(-0.992606\pi\) | ||||
0.999730 | − | 0.0232284i | \(-0.00739450\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.00417786 | −1.41622e−5 0 | ||||||||
\(296\) | 62.2676i | 0.210363i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 177.795 | 0.596628 | ||||||||
\(299\) | 97.9244i | 0.327506i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 280.857 | 0.933081 | ||||||||
\(302\) | 472.215i | 1.56362i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 216.328 | 0.711605 | ||||||||
\(305\) | 45.9945i | 0.150801i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 215.268 | 0.701198 | 0.350599 | − | 0.936526i | \(-0.385978\pi\) | ||||
0.350599 | + | 0.936526i | \(0.385978\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −283.879 | −0.915738 | ||||||||
\(311\) | − 90.0470i | − 0.289540i | −0.989465 | − | 0.144770i | \(-0.953756\pi\) | ||||
0.989465 | − | 0.144770i | \(-0.0462442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 258.266 | 0.825130 | 0.412565 | − | 0.910928i | \(-0.364633\pi\) | ||||
0.412565 | + | 0.910928i | \(0.364633\pi\) | |||||||
\(314\) | 58.1611i | 0.185227i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.64728 | 0.0273648 | ||||||||
\(317\) | − 105.042i | − 0.331363i | −0.986179 | − | 0.165681i | \(-0.947018\pi\) | ||||
0.986179 | − | 0.165681i | \(-0.0529824\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 635.878i | 1.98712i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −58.4221 | −0.181435 | ||||||||
\(323\) | − 108.279i | − 0.335231i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1164.30 | 3.58245 | ||||||||
\(326\) | − 412.746i | − 1.26609i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 147.999 | 0.451216 | ||||||||
\(329\) | − 203.005i | − 0.617036i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 258.731 | 0.781664 | 0.390832 | − | 0.920462i | \(-0.372187\pi\) | ||||
0.390832 | + | 0.920462i | \(0.372187\pi\) | |||||||
\(332\) | 9.13791i | 0.0275238i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 29.9540 | 0.0896826 | ||||||||
\(335\) | − 1075.77i | − 3.21125i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 367.989 | 1.09196 | 0.545978 | − | 0.837799i | \(-0.316158\pi\) | ||||
0.545978 | + | 0.837799i | \(0.316158\pi\) | |||||||
\(338\) | − 250.867i | − 0.742209i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.4040 | 0.0306001 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −369.493 | −1.07724 | ||||||||
\(344\) | − 436.753i | − 1.26963i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −421.217 | −1.21739 | ||||||||
\(347\) | − 417.073i | − 1.20194i | −0.799272 | − | 0.600969i | \(-0.794781\pi\) | ||||
0.799272 | − | 0.600969i | \(-0.205219\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −279.831 | −0.801807 | −0.400903 | − | 0.916120i | \(-0.631304\pi\) | ||||
−0.400903 | + | 0.916120i | \(0.631304\pi\) | |||||||
\(350\) | 694.624i | 1.98464i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 333.271i | − 0.944111i | −0.881569 | − | 0.472056i | \(-0.843512\pi\) | ||||
0.881569 | − | 0.472056i | \(-0.156488\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −958.736 | −2.70066 | ||||||||
\(356\) | − 12.9715i | − 0.0364368i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 401.962 | 1.12280 | ||||||||
\(359\) | − 496.763i | − 1.38374i | −0.722022 | − | 0.691871i | \(-0.756787\pi\) | ||||
0.722022 | − | 0.691871i | \(-0.243213\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −164.187 | −0.454810 | ||||||||
\(362\) | − 268.685i | − 0.742224i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.6209 | −0.0346727 | ||||||||
\(365\) | − 330.014i | − 0.904148i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 165.189 | 0.450106 | 0.225053 | − | 0.974346i | \(-0.427744\pi\) | ||||
0.225053 | + | 0.974346i | \(0.427744\pi\) | |||||||
\(368\) | 87.6648i | 0.238220i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 144.726 | 0.391151 | ||||||||
\(371\) | − 426.887i | − 1.15064i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −393.501 | −1.05496 | −0.527481 | − | 0.849567i | \(-0.676864\pi\) | ||||
−0.527481 | + | 0.849567i | \(0.676864\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −315.687 | −0.839592 | ||||||||
\(377\) | − 414.848i | − 1.10039i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 189.140 | 0.499049 | 0.249525 | − | 0.968368i | \(-0.419726\pi\) | ||||
0.249525 | + | 0.968368i | \(0.419726\pi\) | |||||||
\(380\) | 18.9108i | 0.0497653i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −480.815 | −1.25868 | ||||||||
\(383\) | 468.923i | 1.22434i | 0.790725 | + | 0.612171i | \(0.209704\pi\) | ||||
−0.790725 | + | 0.612171i | \(0.790296\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 30.9168i | − 0.0800954i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.34374 | −0.0189272 | ||||||||
\(389\) | − 454.980i | − 1.16961i | −0.811173 | − | 0.584807i | \(-0.801170\pi\) | ||||
0.811173 | − | 0.584807i | \(-0.198830\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.8792 | 0.112223 | ||||||||
\(392\) | 176.027i | 0.449049i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −187.463 | −0.475794 | ||||||||
\(395\) | − 593.994i | − 1.50378i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 168.638 | 0.424782 | 0.212391 | − | 0.977185i | \(-0.431875\pi\) | ||||
0.212391 | + | 0.977185i | \(0.431875\pi\) | |||||||
\(398\) | 128.138i | 0.321956i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1042.31 | 2.60578 | ||||||||
\(401\) | − 69.7963i | − 0.174056i | −0.996206 | − | 0.0870278i | \(-0.972263\pi\) | ||||
0.996206 | − | 0.0870278i | \(-0.0277369\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −258.644 | −0.641796 | ||||||||
\(404\) | 8.25409i | 0.0204309i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 247.500 | 0.609606 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −553.915 | −1.35431 | −0.677157 | − | 0.735838i | \(-0.736788\pi\) | ||||
−0.677157 | + | 0.735838i | \(0.736788\pi\) | |||||||
\(410\) | − 343.987i | − 0.838992i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.5483 | −0.0328842 | ||||||||
\(413\) | − 0.00227096i | 0 5.49869e-6i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 627.697 | 1.51252 | ||||||||
\(416\) | 38.5886i | 0.0927610i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 307.485i | 0.733855i | 0.930250 | + | 0.366927i | \(0.119590\pi\) | ||||
−0.930250 | + | 0.366927i | \(0.880410\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.54659 | −0.00842420 | −0.00421210 | − | 0.999991i | \(-0.501341\pi\) | ||||
−0.00421210 | + | 0.999991i | \(0.501341\pi\) | |||||||
\(422\) | − 540.526i | − 1.28087i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −663.839 | −1.56566 | ||||||||
\(425\) | − 521.713i | − 1.22756i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.0012 | −0.0585508 | ||||||||
\(428\) | 2.57638i | 0.00601959i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1015.12 | −2.36076 | ||||||||
\(431\) | − 118.926i | − 0.275930i | −0.990437 | − | 0.137965i | \(-0.955944\pi\) | ||||
0.990437 | − | 0.137965i | \(-0.0440562\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 199.452 | 0.460628 | 0.230314 | − | 0.973116i | \(-0.426025\pi\) | ||||
0.230314 | + | 0.973116i | \(0.426025\pi\) | |||||||
\(434\) | − 154.308i | − 0.355548i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.09521 | −0.0162734 | ||||||||
\(437\) | 79.7567i | 0.182510i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.94474 | 0.0180973 | 0.00904867 | − | 0.999959i | \(-0.497120\pi\) | ||||
0.00904867 | + | 0.999959i | \(0.497120\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −261.191 | −0.590930 | ||||||||
\(443\) | − 469.310i | − 1.05939i | −0.848188 | − | 0.529696i | \(-0.822306\pi\) | ||||
0.848188 | − | 0.529696i | \(-0.177694\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −891.031 | −2.00232 | ||||||||
\(446\) | − 359.354i | − 0.805728i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −345.644 | −0.771527 | ||||||||
\(449\) | − 738.513i | − 1.64479i | −0.568913 | − | 0.822397i | \(-0.692636\pi\) | ||||
0.568913 | − | 0.822397i | \(-0.307364\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 1.37782i | − 0.00304828i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −491.974 | −1.08364 | ||||||||
\(455\) | 866.946i | 1.90538i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 181.188 | 0.396473 | 0.198236 | − | 0.980154i | \(-0.436479\pi\) | ||||
0.198236 | + | 0.980154i | \(0.436479\pi\) | |||||||
\(458\) | 688.587i | 1.50347i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.66343 | −0.0166596 | ||||||||
\(461\) | 561.409i | 1.21781i | 0.793244 | + | 0.608903i | \(0.208390\pi\) | ||||
−0.793244 | + | 0.608903i | \(0.791610\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 379.155 | 0.818909 | 0.409454 | − | 0.912331i | \(-0.365719\pi\) | ||||
0.409454 | + | 0.912331i | \(0.365719\pi\) | |||||||
\(464\) | − 371.384i | − 0.800397i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −716.537 | −1.53763 | ||||||||
\(467\) | 456.305i | 0.977098i | 0.872536 | + | 0.488549i | \(0.162474\pi\) | ||||
−0.872536 | + | 0.488549i | \(0.837526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 584.756 | 1.24681 | ||||||||
\(470\) | 733.737i | 1.56114i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.00353150 | −7.48199e−6 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 948.287 | 1.99639 | ||||||||
\(476\) | 5.65532i | 0.0118809i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 477.052 | 0.998017 | ||||||||
\(479\) | − 538.316i | − 1.12383i | −0.827194 | − | 0.561917i | \(-0.810064\pi\) | ||||
0.827194 | − | 0.561917i | \(-0.189936\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 131.861 | 0.274138 | ||||||||
\(482\) | − 821.908i | − 1.70520i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 504.452i | 1.04011i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 194.690 | 0.399775 | 0.199887 | − | 0.979819i | \(-0.435942\pi\) | ||||
0.199887 | + | 0.979819i | \(0.435942\pi\) | |||||||
\(488\) | 38.8786i | 0.0796693i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 409.132 | 0.834964 | ||||||||
\(491\) | − 203.856i | − 0.415185i | −0.978215 | − | 0.207593i | \(-0.933437\pi\) | ||||
0.978215 | − | 0.207593i | \(-0.0665628\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −185.890 | −0.377060 | ||||||||
\(494\) | − 474.752i | − 0.961037i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −231.546 | −0.466826 | ||||||||
\(497\) | − 521.140i | − 1.04857i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −855.119 | −1.71367 | −0.856833 | − | 0.515595i | \(-0.827571\pi\) | ||||
−0.856833 | + | 0.515595i | \(0.827571\pi\) | |||||||
\(500\) | 57.4167i | 0.114833i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −542.614 | −1.08090 | ||||||||
\(503\) | 272.283i | 0.541319i | 0.962675 | + | 0.270659i | \(0.0872417\pi\) | ||||
−0.962675 | + | 0.270659i | \(0.912758\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 566.986 | 1.12274 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −30.1855 | −0.0594203 | ||||||||
\(509\) | 943.531i | 1.85370i | 0.375437 | + | 0.926848i | \(0.377493\pi\) | ||||
−0.375437 | + | 0.926848i | \(0.622507\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 179.386 | 0.351048 | ||||||||
\(512\) | 536.245i | 1.04735i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 316.701 | 0.616150 | ||||||||
\(515\) | 930.653i | 1.80709i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 78.6685i | 0.151870i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1348.16 | 2.59262 | ||||||||
\(521\) | − 324.370i | − 0.622591i | −0.950313 | − | 0.311295i | \(-0.899237\pi\) | ||||
0.950313 | − | 0.311295i | \(-0.100763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −121.137 | −0.231620 | −0.115810 | − | 0.993271i | \(-0.536946\pi\) | ||||
−0.115810 | + | 0.993271i | \(0.536946\pi\) | |||||||
\(524\) | − 23.3364i | − 0.0445351i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 108.997 | 0.207218 | ||||||||
\(527\) | 115.896i | 0.219917i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 496.679 | 0.938902 | ||||||||
\(530\) | 1542.93i | 2.91119i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.2794 | −0.0193221 | ||||||||
\(533\) | − 313.408i | − 0.588008i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 176.976 | 0.330795 | ||||||||
\(536\) | − 909.336i | − 1.69652i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 114.347 | 0.212540 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 596.978 | 1.10347 | 0.551736 | − | 0.834019i | \(-0.313966\pi\) | ||||
0.551736 | + | 0.834019i | \(0.313966\pi\) | |||||||
\(542\) | 836.762i | 1.54384i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.2913 | 0.0317854 | ||||||||
\(545\) | 487.381i | 0.894277i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 338.385 | 0.618620 | 0.309310 | − | 0.950961i | \(-0.399902\pi\) | ||||
0.309310 | + | 0.950961i | \(0.399902\pi\) | |||||||
\(548\) | 6.12841i | 0.0111832i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 337.882i | − 0.613217i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 322.877 | 0.583865 | ||||||||
\(554\) | − 251.250i | − 0.453520i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.4391 | 0.0259695 | ||||||||
\(557\) | 477.662i | 0.857562i | 0.903408 | + | 0.428781i | \(0.141057\pi\) | ||||
−0.903408 | + | 0.428781i | \(0.858943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −924.886 | −1.65454 | ||||||||
\(560\) | 776.116i | 1.38592i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −146.168 | −0.260085 | ||||||||
\(563\) | 471.956i | 0.838288i | 0.907920 | + | 0.419144i | \(0.137670\pi\) | ||||
−0.907920 | + | 0.419144i | \(0.862330\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −94.6447 | −0.167513 | ||||||||
\(566\) | 971.206i | 1.71591i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −810.409 | −1.42678 | ||||||||
\(569\) | − 128.554i | − 0.225929i | −0.993599 | − | 0.112965i | \(-0.963965\pi\) | ||||
0.993599 | − | 0.112965i | \(-0.0360346\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −266.234 | −0.466259 | −0.233130 | − | 0.972446i | \(-0.574897\pi\) | ||||
−0.233130 | + | 0.972446i | \(0.574897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 186.981 | 0.325751 | ||||||||
\(575\) | 384.284i | 0.668320i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 720.993 | 1.24955 | 0.624777 | − | 0.780803i | \(-0.285190\pi\) | ||||
0.624777 | + | 0.780803i | \(0.285190\pi\) | |||||||
\(578\) | − 450.751i | − 0.779846i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 32.4654 | 0.0559749 | ||||||||
\(581\) | 341.197i | 0.587258i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − 278.957i | − 0.477667i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.7428 | −0.0456361 | ||||||||
\(587\) | 411.867i | 0.701648i | 0.936441 | + | 0.350824i | \(0.114098\pi\) | ||||
−0.936441 | + | 0.350824i | \(0.885902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −210.658 | −0.357654 | ||||||||
\(590\) | 0.00820810i | 0 1.39120e-5i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 118.045 | 0.199401 | ||||||||
\(593\) | 750.336i | 1.26532i | 0.774429 | + | 0.632661i | \(0.218037\pi\) | ||||
−0.774429 | + | 0.632661i | \(0.781963\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 388.472 | 0.652895 | ||||||||
\(596\) | 12.6771i | 0.0212704i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 192.389 | 0.321720 | ||||||||
\(599\) | − 543.614i | − 0.907535i | −0.891120 | − | 0.453768i | \(-0.850080\pi\) | ||||
0.891120 | − | 0.453768i | \(-0.149920\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 736.195 | 1.22495 | 0.612475 | − | 0.790490i | \(-0.290174\pi\) | ||||
0.612475 | + | 0.790490i | \(0.290174\pi\) | |||||||
\(602\) | − 551.791i | − 0.916596i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −33.6698 | −0.0557447 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −559.641 | −0.921979 | −0.460989 | − | 0.887406i | \(-0.652505\pi\) | ||||
−0.460989 | + | 0.887406i | \(0.652505\pi\) | |||||||
\(608\) | 31.4293i | 0.0516930i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 90.3638 | 0.148137 | ||||||||
\(611\) | 668.512i | 1.09413i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 109.915 | 0.179306 | 0.0896530 | − | 0.995973i | \(-0.471424\pi\) | ||||
0.0896530 | + | 0.995973i | \(0.471424\pi\) | |||||||
\(614\) | − 422.929i | − 0.688810i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 61.1594i | − 0.0991238i | −0.998771 | − | 0.0495619i | \(-0.984217\pi\) | ||||
0.998771 | − | 0.0495619i | \(-0.0157825\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 81.8184 | 0.132178 | 0.0660892 | − | 0.997814i | \(-0.478948\pi\) | ||||
0.0660892 | + | 0.997814i | \(0.478948\pi\) | |||||||
\(620\) | − 20.2411i | − 0.0326469i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −176.912 | −0.284425 | ||||||||
\(623\) | − 484.337i | − 0.777427i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2254.17 | 3.60668 | ||||||||
\(626\) | − 507.406i | − 0.810553i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.14700 | −0.00660351 | ||||||||
\(629\) | − 59.0857i | − 0.0939360i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.29210 | 0.0147260 | 0.00736300 | − | 0.999973i | \(-0.497656\pi\) | ||||
0.00736300 | + | 0.999973i | \(0.497656\pi\) | |||||||
\(632\) | − 502.097i | − 0.794457i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −206.373 | −0.325509 | ||||||||
\(635\) | 2073.49i | 3.26533i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 372.763 | 0.585185 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1163.06 | 1.81728 | ||||||||
\(641\) | 349.041i | 0.544525i | 0.962223 | + | 0.272263i | \(0.0877719\pi\) | ||||
−0.962223 | + | 0.272263i | \(0.912228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 906.166 | 1.40928 | 0.704639 | − | 0.709566i | \(-0.251109\pi\) | ||||
0.704639 | + | 0.709566i | \(0.251109\pi\) | |||||||
\(644\) | − 4.16561i | − 0.00646833i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −212.733 | −0.329308 | ||||||||
\(647\) | 56.5419i | 0.0873909i | 0.999045 | + | 0.0436954i | \(0.0139131\pi\) | ||||
−0.999045 | + | 0.0436954i | \(0.986087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − 2287.45i | − 3.51916i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 29.4296 | 0.0451373 | ||||||||
\(653\) | 568.547i | 0.870669i | 0.900269 | + | 0.435334i | \(0.143370\pi\) | ||||
−0.900269 | + | 0.435334i | \(0.856630\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1603.01 | −2.44735 | ||||||||
\(656\) | − 280.573i | − 0.427702i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −398.837 | −0.606135 | ||||||||
\(659\) | 380.801i | 0.577847i | 0.957352 | + | 0.288923i | \(0.0932973\pi\) | ||||
−0.957352 | + | 0.288923i | \(0.906703\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 350.773 | 0.530671 | 0.265335 | − | 0.964156i | \(-0.414517\pi\) | ||||
0.265335 | + | 0.964156i | \(0.414517\pi\) | |||||||
\(662\) | − 508.319i | − 0.767854i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 530.585 | 0.799074 | ||||||||
\(665\) | 706.104i | 1.06181i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 136.924 | 0.205283 | ||||||||
\(668\) | 2.13578i | 0.00319727i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2113.53 | −3.15452 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 482.896 | 0.717527 | 0.358763 | − | 0.933429i | \(-0.383198\pi\) | ||||
0.358763 | + | 0.933429i | \(0.383198\pi\) | |||||||
\(674\) | − 722.976i | − 1.07267i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.8873 | 0.0264605 | ||||||||
\(677\) | − 849.679i | − 1.25507i | −0.778590 | − | 0.627533i | \(-0.784065\pi\) | ||||
0.778590 | − | 0.627533i | \(-0.215935\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −274.205 | −0.403836 | ||||||||
\(680\) | − 604.101i | − 0.888384i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 831.602i | 1.21757i | 0.793334 | + | 0.608786i | \(0.208343\pi\) | ||||
−0.793334 | + | 0.608786i | \(0.791657\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 420.969 | 0.614554 | ||||||||
\(686\) | 725.931i | 1.05821i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −827.986 | −1.20347 | ||||||||
\(689\) | 1405.77i | 2.04031i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 910.760 | 1.31803 | 0.659016 | − | 0.752129i | \(-0.270973\pi\) | ||||
0.659016 | + | 0.752129i | \(0.270973\pi\) | |||||||
\(692\) | − 30.0336i | − 0.0434011i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −819.409 | −1.18070 | ||||||||
\(695\) | − 991.840i | − 1.42711i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −140.436 | −0.201486 | ||||||||
\(698\) | 549.774i | 0.787642i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −49.5280 | −0.0707543 | ||||||||
\(701\) | − 900.411i | − 1.28447i | −0.766509 | − | 0.642234i | \(-0.778008\pi\) | ||||
0.766509 | − | 0.642234i | \(-0.221992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 107.397 | 0.152769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −654.767 | −0.927432 | ||||||||
\(707\) | 308.196i | 0.435921i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −922.297 | −1.30084 | −0.650421 | − | 0.759574i | \(-0.725408\pi\) | ||||
−0.650421 | + | 0.759574i | \(0.725408\pi\) | |||||||
\(710\) | 1883.60i | 2.65295i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −753.178 | −1.05783 | ||||||||
\(713\) | − 85.3672i | − 0.119730i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 28.6606i | 0.0400288i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −975.974 | −1.35930 | ||||||||
\(719\) | 10.3358i | 0.0143753i | 0.999974 | + | 0.00718763i | \(0.00228791\pi\) | ||||
−0.999974 | + | 0.00718763i | \(0.997712\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −505.875 | −0.701629 | ||||||||
\(722\) | 322.572i | 0.446775i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.1578 | 0.0264610 | ||||||||
\(725\) | − 1627.99i | − 2.24550i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 119.809 | 0.164799 | 0.0823995 | − | 0.996599i | \(-0.473742\pi\) | ||||
0.0823995 | + | 0.996599i | \(0.473742\pi\) | |||||||
\(728\) | 732.820i | 1.00662i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −648.368 | −0.888175 | ||||||||
\(731\) | 414.435i | 0.566942i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1272.26 | −1.73570 | −0.867848 | − | 0.496830i | \(-0.834497\pi\) | ||||
−0.867848 | + | 0.496830i | \(0.834497\pi\) | |||||||
\(734\) | − 324.541i | − 0.442154i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.7364 | −0.0173049 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 168.978 | 0.228658 | 0.114329 | − | 0.993443i | \(-0.463528\pi\) | ||||
0.114329 | + | 0.993443i | \(0.463528\pi\) | |||||||
\(740\) | 10.3192i | 0.0139449i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −838.691 | −1.13031 | ||||||||
\(743\) | 963.291i | 1.29649i | 0.761432 | + | 0.648245i | \(0.224497\pi\) | ||||
−0.761432 | + | 0.648245i | \(0.775503\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 870.811 | 1.16887 | ||||||||
\(746\) | 773.098i | 1.03632i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 96.1986i | 0.128436i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −412.835 | −0.549713 | −0.274857 | − | 0.961485i | \(-0.588630\pi\) | ||||
−0.274857 | + | 0.961485i | \(0.588630\pi\) | |||||||
\(752\) | 598.472i | 0.795840i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −815.038 | −1.08095 | ||||||||
\(755\) | 2312.83i | 3.06335i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 902.073 | 1.19164 | 0.595821 | − | 0.803117i | \(-0.296827\pi\) | ||||
0.595821 | + | 0.803117i | \(0.296827\pi\) | |||||||
\(758\) | − 371.596i | − 0.490233i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1098.04 | 1.44479 | ||||||||
\(761\) | − 972.116i | − 1.27742i | −0.769448 | − | 0.638709i | \(-0.779469\pi\) | ||||
0.769448 | − | 0.638709i | \(-0.220531\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −264.925 | −0.347215 | ||||||||
\(764\) | − 34.2830i | − 0.0448731i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 921.278 | 1.20271 | ||||||||
\(767\) | 0.00747845i | 0 9.75027e-6i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1404.29 | −1.82613 | −0.913064 | − | 0.407817i | \(-0.866290\pi\) | ||||
−0.913064 | + | 0.407817i | \(0.866290\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.20443 | 0.00285548 | ||||||||
\(773\) | − 145.730i | − 0.188525i | −0.995547 | − | 0.0942627i | \(-0.969951\pi\) | ||||
0.995547 | − | 0.0942627i | \(-0.0300494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1014.99 | −1.30967 | ||||||||
\(776\) | 426.408i | 0.549494i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −893.883 | −1.14895 | ||||||||
\(779\) | − 255.263i | − 0.327680i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 86.2080i | − 0.110240i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 333.709 | 0.425649 | ||||||||
\(785\) | 284.864i | 0.362884i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 914.791 | 1.16238 | 0.581189 | − | 0.813769i | \(-0.302588\pi\) | ||||
0.581189 | + | 0.813769i | \(0.302588\pi\) | |||||||
\(788\) | − 13.3665i | − 0.0169625i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1167.00 | −1.47722 | ||||||||
\(791\) | − 51.4460i | − 0.0650392i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 82.3310 | 0.103822 | ||||||||
\(794\) | − 331.318i | − 0.417277i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.13651 | −0.0114780 | ||||||||
\(797\) | − 373.062i | − 0.468082i | −0.972227 | − | 0.234041i | \(-0.924805\pi\) | ||||
0.972227 | − | 0.234041i | \(-0.0751951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 299.555 | 0.374913 | ||||||||
\(800\) | 151.433i | 0.189291i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −137.126 | −0.170981 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −286.142 | −0.355456 | ||||||||
\(806\) | 508.149i | 0.630457i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 479.267 | 0.593152 | ||||||||
\(809\) | − 1578.26i | − 1.95088i | −0.220263 | − | 0.975440i | \(-0.570692\pi\) | ||||
0.220263 | − | 0.975440i | \(-0.429308\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −720.185 | −0.888021 | −0.444010 | − | 0.896022i | \(-0.646445\pi\) | ||||
−0.444010 | + | 0.896022i | \(0.646445\pi\) | |||||||
\(812\) | 17.6472i | 0.0217330i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 2021.56i | − 2.48044i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −753.295 | −0.922025 | ||||||||
\(818\) | 1088.26i | 1.33039i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.5269 | 0.0299109 | ||||||||
\(821\) | − 932.683i | − 1.13603i | −0.823017 | − | 0.568017i | \(-0.807711\pi\) | ||||
0.823017 | − | 0.568017i | \(-0.192289\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 499.235 | 0.606604 | 0.303302 | − | 0.952895i | \(-0.401911\pi\) | ||||
0.303302 | + | 0.952895i | \(0.401911\pi\) | |||||||
\(824\) | 786.670i | 0.954697i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.00446168 | −5.40155e−6 0 | ||||||||
\(827\) | 729.473i | 0.882072i | 0.897490 | + | 0.441036i | \(0.145389\pi\) | ||||
−0.897490 | + | 0.441036i | \(0.854611\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1480.29 | −1.78564 | −0.892818 | − | 0.450418i | \(-0.851275\pi\) | ||||
−0.892818 | + | 0.450418i | \(0.851275\pi\) | |||||||
\(830\) | − 1233.22i | − 1.48580i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1138.23 | 1.36807 | ||||||||
\(833\) | − 167.032i | − 0.200519i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 146.710 | 0.175700 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 604.106 | 0.720890 | ||||||||
\(839\) | 980.006i | 1.16806i | 0.811730 | + | 0.584032i | \(0.198526\pi\) | ||||
−0.811730 | + | 0.584032i | \(0.801474\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 260.936 | 0.310268 | ||||||||
\(842\) | 6.96787i | 0.00827538i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 38.5405 | 0.0456641 | ||||||||
\(845\) | − 1228.70i | − 1.45409i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1258.49i | 1.48407i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1024.99 | −1.20587 | ||||||||
\(851\) | 43.5215i | 0.0511416i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1390.45 | 1.63007 | 0.815037 | − | 0.579408i | \(-0.196716\pi\) | ||||
0.815037 | + | 0.579408i | \(0.196716\pi\) | |||||||
\(854\) | 49.1190i | 0.0575164i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 149.595 | 0.174761 | ||||||||
\(857\) | 1044.64i | 1.21895i | 0.792804 | + | 0.609477i | \(0.208621\pi\) | ||||
−0.792804 | + | 0.609477i | \(0.791379\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 480.571 | 0.559454 | 0.279727 | − | 0.960080i | \(-0.409756\pi\) | ||||
0.279727 | + | 0.960080i | \(0.409756\pi\) | |||||||
\(860\) | − 72.3803i | − 0.0841632i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −233.650 | −0.271056 | ||||||||
\(863\) | − 652.084i | − 0.755602i | −0.925887 | − | 0.377801i | \(-0.876680\pi\) | ||||
0.925887 | − | 0.377801i | \(-0.123320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2063.05 | −2.38503 | ||||||||
\(866\) | − 391.856i | − 0.452490i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.0024 | 0.0126756 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1925.65 | −2.21085 | ||||||||
\(872\) | 411.977i | 0.472451i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 156.695 | 0.179285 | ||||||||
\(875\) | 2143.86i | 2.45013i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 348.132 | 0.396958 | 0.198479 | − | 0.980105i | \(-0.436400\pi\) | ||||
0.198479 | + | 0.980105i | \(0.436400\pi\) | |||||||
\(878\) | − 15.6088i | − 0.0177776i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 81.0204i | 0.0919641i | 0.998942 | + | 0.0459821i | \(0.0146417\pi\) | ||||
−0.998942 | + | 0.0459821i | \(0.985358\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 975.621 | 1.10489 | 0.552447 | − | 0.833548i | \(-0.313694\pi\) | ||||
0.552447 | + | 0.833548i | \(0.313694\pi\) | |||||||
\(884\) | − 18.6234i | − 0.0210672i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −922.039 | −1.04068 | ||||||||
\(887\) | − 1534.16i | − 1.72960i | −0.502113 | − | 0.864802i | \(-0.667444\pi\) | ||||
0.502113 | − | 0.864802i | \(-0.332556\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1127.08 | −1.26781 | ||||||||
\(890\) | 1750.58i | 1.96694i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.6227 | 0.0287250 | ||||||||
\(893\) | 544.485i | 0.609725i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1968.74 | 2.19971 | ||||||||
\(896\) | 632.203i | 0.705584i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1450.93 | −1.61574 | ||||||||
\(899\) | 361.650i | 0.402281i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 629.917 | 0.699131 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −80.0021 | −0.0884979 | ||||||||
\(905\) | − 1315.97i | − 1.45412i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1040.31 | 1.14698 | 0.573490 | − | 0.819213i | \(-0.305589\pi\) | ||||
0.573490 | + | 0.819213i | \(0.305589\pi\) | |||||||
\(908\) | − 35.0787i | − 0.0386329i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1703.26 | 1.87171 | ||||||||
\(911\) | − 373.647i | − 0.410150i | −0.978746 | − | 0.205075i | \(-0.934256\pi\) | ||||
0.978746 | − | 0.205075i | \(-0.0657439\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − 355.974i | − 0.389468i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −49.0976 | −0.0536000 | ||||||||
\(917\) | − 871.349i | − 0.950217i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.74930 | −0.00516790 | −0.00258395 | − | 0.999997i | \(-0.500822\pi\) | ||||
−0.00258395 | + | 0.999997i | \(0.500822\pi\) | |||||||
\(920\) | 444.970i | 0.483663i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1102.98 | 1.19629 | ||||||||
\(923\) | 1716.16i | 1.85932i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 517.460 | 0.559416 | ||||||||
\(926\) | − 744.913i | − 0.804442i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 53.9568 | 0.0581431 | ||||||||
\(929\) | 493.733i | 0.531467i | 0.964047 | + | 0.265733i | \(0.0856141\pi\) | ||||
−0.964047 | + | 0.265733i | \(0.914386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 303.605 | 0.326107 | ||||||||
\(932\) | − 51.0904i | − 0.0548181i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 896.487 | 0.959836 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 587.140 | 0.626617 | 0.313308 | − | 0.949651i | \(-0.398563\pi\) | ||||
0.313308 | + | 0.949651i | \(0.398563\pi\) | |||||||
\(938\) | − 1148.85i | − 1.22479i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −52.3168 | −0.0556562 | ||||||||
\(941\) | 1066.36i | 1.13322i | 0.823986 | + | 0.566610i | \(0.191745\pi\) | ||||
−0.823986 | + | 0.566610i | \(0.808255\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 103.443 | 0.109695 | ||||||||
\(944\) | 0.00669494i | 0 7.09209e-6i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 198.618i | − 0.209734i | −0.994486 | − | 0.104867i | \(-0.966558\pi\) | ||||
0.994486 | − | 0.104867i | \(-0.0334416\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −590.732 | −0.622478 | ||||||||
\(950\) | − 1863.07i | − 1.96112i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 328.371 | 0.344928 | ||||||||
\(953\) | − 1114.25i | − 1.16920i | −0.811321 | − | 0.584601i | \(-0.801251\pi\) | ||||
0.811321 | − | 0.584601i | \(-0.198749\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2354.95 | −2.46592 | ||||||||
\(956\) | 34.0147i | 0.0355802i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1057.61 | −1.10398 | ||||||||
\(959\) | 228.826i | 0.238609i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −735.523 | −0.765373 | ||||||||
\(962\) | − 259.062i | − 0.269295i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 58.6036 | 0.0607921 | ||||||||
\(965\) | − 151.425i | − 0.156918i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 983.820 | 1.01739 | 0.508697 | − | 0.860945i | \(-0.330127\pi\) | ||||
0.508697 | + | 0.860945i | \(0.330127\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 991.080 | 1.02173 | ||||||||
\(971\) | 115.916i | 0.119378i | 0.998217 | + | 0.0596890i | \(0.0190109\pi\) | ||||
−0.998217 | + | 0.0596890i | \(0.980989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 539.134 | 0.554095 | ||||||||
\(974\) | − 382.502i | − 0.392712i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 73.7052 | 0.0755176 | ||||||||
\(977\) | − 114.282i | − 0.116973i | −0.998288 | − | 0.0584863i | \(-0.981373\pi\) | ||||
0.998288 | − | 0.0584863i | \(-0.0186274\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 29.1719i | 0.0297673i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −400.509 | −0.407850 | ||||||||
\(983\) | 1020.67i | 1.03832i | 0.854677 | + | 0.519160i | \(0.173755\pi\) | ||||
−0.854677 | + | 0.519160i | \(0.826245\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −918.163 | −0.932145 | ||||||||
\(986\) | 365.213i | 0.370398i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.8508 | 0.0342619 | ||||||||
\(989\) | − 305.265i | − 0.308661i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 544.638 | 0.549584 | 0.274792 | − | 0.961504i | \(-0.411391\pi\) | ||||
0.274792 | + | 0.961504i | \(0.411391\pi\) | |||||||
\(992\) | − 33.6402i | − 0.0339115i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1023.87 | −1.03005 | ||||||||
\(995\) | 627.600i | 0.630754i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1249.59 | −1.25335 | −0.626677 | − | 0.779279i | \(-0.715585\pi\) | ||||
−0.626677 | + | 0.779279i | \(0.715585\pi\) | |||||||
\(998\) | 1680.02i | 1.68339i | ||||||||
\(999\) | 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 | 1089.3.b.j.485.5 | 16 | ||
3.2 | odd | 2 | inner | 1089.3.b.j.485.12 | 16 | ||
11.2 | odd | 10 | 99.3.l.a.26.6 | yes | 32 | ||
11.6 | odd | 10 | 99.3.l.a.80.3 | yes | 32 | ||
11.10 | odd | 2 | 1089.3.b.i.485.12 | 16 | |||
33.2 | even | 10 | 99.3.l.a.26.3 | ✓ | 32 | ||
33.17 | even | 10 | 99.3.l.a.80.6 | yes | 32 | ||
33.32 | even | 2 | 1089.3.b.i.485.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.l.a.26.3 | ✓ | 32 | 33.2 | even | 10 | ||
99.3.l.a.26.6 | yes | 32 | 11.2 | odd | 10 | ||
99.3.l.a.80.3 | yes | 32 | 11.6 | odd | 10 | ||
99.3.l.a.80.6 | yes | 32 | 33.17 | even | 10 | ||
1089.3.b.i.485.5 | 16 | 33.32 | even | 2 | |||
1089.3.b.i.485.12 | 16 | 11.10 | odd | 2 | |||
1089.3.b.j.485.5 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.b.j.485.12 | 16 | 3.2 | odd | 2 | inner |