Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(783,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.783");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.f (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: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 783.6 | ||
Character | \(\chi\) | \(=\) | 784.783 |
Dual form | 784.4.f.j.783.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −5.68961 | −1.09497 | −0.547483 | − | 0.836817i | \(-0.684414\pi\) | ||||
−0.547483 | + | 0.836817i | \(0.684414\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 20.4139i | − 1.82587i | −0.408103 | − | 0.912936i | \(-0.633810\pi\) | ||||
0.408103 | − | 0.912936i | \(-0.366190\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.37166 | 0.198951 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27.4118i | 0.751362i | 0.926749 | + | 0.375681i | \(0.122591\pi\) | ||||
−0.926749 | + | 0.375681i | \(0.877409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 33.2667i | − 0.709732i | −0.934917 | − | 0.354866i | \(-0.884527\pi\) | ||||
0.934917 | − | 0.354866i | \(-0.115473\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 116.147i | 1.99927i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 51.6329i | − 0.736637i | −0.929700 | − | 0.368318i | \(-0.879934\pi\) | ||||
0.929700 | − | 0.368318i | \(-0.120066\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −123.055 | −1.48583 | −0.742914 | − | 0.669387i | \(-0.766557\pi\) | ||||
−0.742914 | + | 0.669387i | \(0.766557\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 203.652i | − 1.84628i | −0.384469 | − | 0.923138i | \(-0.625615\pi\) | ||||
0.384469 | − | 0.923138i | \(-0.374385\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −291.726 | −2.33381 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 123.057 | 0.877122 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −27.1005 | −0.173532 | −0.0867662 | − | 0.996229i | \(-0.527653\pi\) | ||||
−0.0867662 | + | 0.996229i | \(0.527653\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −132.591 | −0.768196 | −0.384098 | − | 0.923292i | \(-0.625488\pi\) | ||||
−0.384098 | + | 0.923292i | \(0.625488\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 155.963i | − 0.822715i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −98.1248 | −0.435990 | −0.217995 | − | 0.975950i | \(-0.569952\pi\) | ||||
−0.217995 | + | 0.975950i | \(0.569952\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 189.274i | 0.777132i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 475.182i | − 1.81002i | −0.425388 | − | 0.905011i | \(-0.639862\pi\) | ||||
0.425388 | − | 0.905011i | \(-0.360138\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 288.305i | 1.02247i | 0.859442 | + | 0.511233i | \(0.170811\pi\) | ||||
−0.859442 | + | 0.511233i | \(0.829189\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 109.656i | − 0.363258i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 568.917 | 1.76564 | 0.882821 | − | 0.469710i | \(-0.155642\pi\) | ||||
0.882821 | + | 0.469710i | \(0.155642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 293.771i | 0.806592i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −133.525 | −0.346059 | −0.173029 | − | 0.984917i | \(-0.555356\pi\) | ||||
−0.173029 | + | 0.984917i | \(0.555356\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 559.581 | 1.37189 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 700.134 | 1.62693 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −307.068 | −0.677573 | −0.338786 | − | 0.940863i | \(-0.610016\pi\) | ||||
−0.338786 | + | 0.940863i | \(0.610016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 735.787i | 1.54439i | 0.635385 | + | 0.772195i | \(0.280841\pi\) | ||||
−0.635385 | + | 0.772195i | \(0.719159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −679.101 | −1.29588 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 130.251i | − 0.237504i | −0.992924 | − | 0.118752i | \(-0.962111\pi\) | ||||
0.992924 | − | 0.118752i | \(-0.0378893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1158.70i | 2.02161i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 708.596i | − 1.18443i | −0.805778 | − | 0.592217i | \(-0.798253\pi\) | ||||
0.805778 | − | 0.592217i | \(-0.201747\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 562.738i | − 0.902240i | −0.892463 | − | 0.451120i | \(-0.851025\pi\) | ||||
0.892463 | − | 0.451120i | \(-0.148975\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1659.81 | 2.55544 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 787.673i | 1.12177i | 0.827893 | + | 0.560887i | \(0.189540\pi\) | ||||
−0.827893 | + | 0.560887i | \(0.810460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −845.180 | −1.15937 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 300.047 | 0.396801 | 0.198400 | − | 0.980121i | \(-0.436425\pi\) | ||||
0.198400 | + | 0.980121i | \(0.436425\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1054.03 | −1.34500 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 154.191 | 0.190012 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1134.02i | 1.35062i | 0.737532 | + | 0.675312i | \(0.235991\pi\) | ||||
−0.737532 | + | 0.675312i | \(0.764009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 754.392 | 0.841149 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2512.03i | 2.71293i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 234.071i | − 0.245013i | −0.992468 | − | 0.122507i | \(-0.960907\pi\) | ||||
0.992468 | − | 0.122507i | \(-0.0390933\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 147.247i | 0.149484i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 548.705i | 0.540576i | 0.962780 | + | 0.270288i | \(0.0871189\pi\) | ||||
−0.962780 | + | 0.270288i | \(0.912881\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 407.887 | 0.390197 | 0.195099 | − | 0.980784i | \(-0.437497\pi\) | ||||
0.195099 | + | 0.980784i | \(0.437497\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 431.721i | 0.390056i | 0.980798 | + | 0.195028i | \(0.0624798\pi\) | ||||
−0.980798 | + | 0.195028i | \(0.937520\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1417.95 | 1.24601 | 0.623004 | − | 0.782219i | \(-0.285912\pi\) | ||||
0.623004 | + | 0.782219i | \(0.285912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 558.292 | 0.477394 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −705.689 | −0.587483 | −0.293742 | − | 0.955885i | \(-0.594901\pi\) | ||||
−0.293742 | + | 0.955885i | \(0.594901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4157.32 | −3.37106 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 178.697i | − 0.141202i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 579.591 | 0.435456 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2703.60i | 1.98191i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3403.52i | 2.43536i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1941.75i | 1.35671i | 0.734735 | + | 0.678355i | \(0.237307\pi\) | ||||
−0.734735 | + | 0.678355i | \(0.762693\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 1640.34i | − 1.11957i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1042.75 | −0.695463 | −0.347731 | − | 0.937594i | \(-0.613048\pi\) | ||||
−0.347731 | + | 0.937594i | \(0.613048\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 2512.06i | − 1.60151i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2026.12 | −1.26353 | −0.631763 | − | 0.775162i | \(-0.717668\pi\) | ||||
−0.631763 | + | 0.775162i | \(0.717668\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −995.762 | −0.607622 | −0.303811 | − | 0.952732i | \(-0.598259\pi\) | ||||
−0.303811 | + | 0.952732i | \(0.598259\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3236.92 | −1.93332 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 911.900 | 0.533265 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 553.226i | 0.316848i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 925.945 | 0.509103 | 0.254551 | − | 0.967059i | \(-0.418072\pi\) | ||||
0.254551 | + | 0.967059i | \(0.418072\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2101.38i | 1.13250i | 0.824233 | + | 0.566251i | \(0.191607\pi\) | ||||
−0.824233 | + | 0.566251i | \(0.808393\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 277.355i | − 0.146554i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2706.70i | 1.40263i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2459.33i | − 1.25016i | −0.780560 | − | 0.625081i | \(-0.785066\pi\) | ||||
0.780560 | − | 0.625081i | \(-0.214934\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 759.707 | 0.378922 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2902.94i | 1.39494i | 0.716612 | + | 0.697472i | \(0.245692\pi\) | ||||
−0.716612 | + | 0.697472i | \(0.754308\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3183.80 | −1.50217 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1040.40 | 0.482089 | 0.241044 | − | 0.970514i | \(-0.422510\pi\) | ||||
0.241044 | + | 0.970514i | \(0.422510\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1090.33 | 0.496281 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −661.010 | −0.295606 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 144.134i | 0.0633428i | 0.999498 | + | 0.0316714i | \(0.0100830\pi\) | ||||
−0.999498 | + | 0.0316714i | \(0.989917\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1747.10 | 0.741919 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 717.436i | 0.299574i | 0.988718 | + | 0.149787i | \(0.0478587\pi\) | ||||
−0.988718 | + | 0.149787i | \(0.952141\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 473.409i | − 0.194410i | −0.995264 | − | 0.0972050i | \(-0.969010\pi\) | ||||
0.995264 | − | 0.0972050i | \(-0.0309903\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 4186.34i | − 1.69106i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2003.11i | 0.796061i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1415.35 | 0.553481 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 2529.99i | − 0.958450i | −0.877692 | − | 0.479225i | \(-0.840918\pi\) | ||||
0.877692 | − | 0.479225i | \(-0.159082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3252.98 | 1.21324 | 0.606619 | − | 0.794993i | \(-0.292525\pi\) | ||||
0.606619 | + | 0.794993i | \(0.292525\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3863.82 | 1.41894 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5178.04 | 1.87269 | 0.936346 | − | 0.351078i | \(-0.114185\pi\) | ||||
0.936346 | + | 0.351078i | \(0.114185\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2039.63 | −0.726561 | −0.363280 | − | 0.931680i | \(-0.618343\pi\) | ||||
−0.363280 | + | 0.931680i | \(0.618343\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 741.080i | 0.260058i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9700.30 | −3.30487 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1093.95i | − 0.367318i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 3373.16i | − 1.11639i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1313.78i | 0.428647i | 0.976763 | + | 0.214323i | \(0.0687546\pi\) | ||||
−0.976763 | + | 0.214323i | \(0.931245\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4031.63i | 1.29692i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5885.41 | 1.86689 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3201.76i | 0.987922i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1717.66 | −0.522815 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 769.389 | 0.231041 | 0.115520 | − | 0.993305i | \(-0.463146\pi\) | ||||
0.115520 | + | 0.993305i | \(0.463146\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1567.05 | −0.464312 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3693.41 | 1.07991 | 0.539956 | − | 0.841693i | \(-0.318441\pi\) | ||||
0.539956 | + | 0.841693i | \(0.318441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 224.251i | − 0.0647115i | −0.999476 | − | 0.0323557i | \(-0.989699\pi\) | ||||
0.999476 | − | 0.0323557i | \(-0.0103009\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2826.69 | 0.794775 | 0.397387 | − | 0.917651i | \(-0.369917\pi\) | ||||
0.397387 | + | 0.917651i | \(0.369917\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 11613.8i | − 3.22383i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 4481.55i | − 1.22830i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 635.796i | − 0.172076i | −0.996292 | − | 0.0860381i | \(-0.972579\pi\) | ||||
0.996292 | − | 0.0860381i | \(-0.0274207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 6316.97i | − 1.68843i | −0.536004 | − | 0.844216i | \(-0.680067\pi\) | ||||
0.536004 | − | 0.844216i | \(-0.319933\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1486.21 | 0.392348 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4093.63i | 1.05454i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1707.15 | −0.434483 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2027.17 | −0.509775 | −0.254888 | − | 0.966971i | \(-0.582039\pi\) | ||||
−0.254888 | + | 0.966971i | \(0.582039\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5582.47 | 1.38722 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5997.01 | 1.47273 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5246.80i | 1.27349i | 0.771075 | + | 0.636744i | \(0.219719\pi\) | ||||
−0.771075 | + | 0.636744i | \(0.780281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −145.575 | −0.0345244 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 631.404i | − 0.148038i | −0.997257 | − | 0.0740191i | \(-0.976417\pi\) | ||||
0.997257 | − | 0.0740191i | \(-0.0235826\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2725.77i | 0.631859i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6452.11i | − 1.47889i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1164.99i | 0.264056i | 0.991246 | + | 0.132028i | \(0.0421488\pi\) | ||||
−0.991246 | + | 0.132028i | \(0.957851\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7955.89 | −1.78334 | −0.891672 | − | 0.452683i | \(-0.850467\pi\) | ||||
−0.891672 | + | 0.452683i | \(0.850467\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 7996.74i | − 1.75353i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3600.97 | −0.781087 | −0.390544 | − | 0.920584i | \(-0.627713\pi\) | ||||
−0.390544 | + | 0.920584i | \(0.627713\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −712.235 | −0.152833 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1629.95 | 0.346031 | 0.173016 | − | 0.984919i | \(-0.444649\pi\) | ||||
0.173016 | + | 0.984919i | \(0.444649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3562.61 | −0.748323 | −0.374162 | − | 0.927364i | \(-0.622069\pi\) | ||||
−0.374162 | + | 0.927364i | \(0.622069\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 14292.4i | − 2.97057i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2247.04 | 0.457366 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1331.77i | 0.268281i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2256.82i | − 0.449982i | −0.974361 | − | 0.224991i | \(-0.927765\pi\) | ||||
0.974361 | − | 0.224991i | \(-0.0722352\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6268.44i | 1.23716i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3373.21i | 0.659036i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6774.82 | −1.31036 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 3121.92i | − 0.591912i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15020.2 | 2.81986 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7898.99 | −1.46847 | −0.734234 | − | 0.678897i | \(-0.762458\pi\) | ||||
−0.734234 | + | 0.678897i | \(0.762458\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2320.72 | −0.427253 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6032.25 | 1.09986 | 0.549932 | − | 0.835209i | \(-0.314654\pi\) | ||||
0.549932 | + | 0.835209i | \(0.314654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 648.749i | − 0.117155i | −0.998283 | − | 0.0585774i | \(-0.981344\pi\) | ||||
0.998283 | − | 0.0585774i | \(-0.0186564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5400.21 | −0.956801 | −0.478401 | − | 0.878142i | \(-0.658783\pi\) | ||||
−0.478401 | + | 0.878142i | \(0.658783\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 742.875i | − 0.130386i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 2456.32i | − 0.427098i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6353.68i | 1.09452i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9704.75i | 1.65638i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8067.57 | −1.36434 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4604.90i | − 0.764678i | −0.924022 | − | 0.382339i | \(-0.875119\pi\) | ||||
0.924022 | − | 0.382339i | \(-0.124881\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −527.093 | −0.0867403 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2658.94 | −0.433651 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8621.08 | −1.39353 | −0.696766 | − | 0.717299i | \(-0.745378\pi\) | ||||
−0.696766 | + | 0.717299i | \(0.745378\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4015.09 | 0.643274 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3634.57i | − 0.577193i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 23653.5 | 3.69120 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2071.61i | 0.320489i | 0.987077 | + | 0.160244i | \(0.0512283\pi\) | ||||
−0.987077 | + | 0.160244i | \(0.948772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2795.68i | 0.428794i | 0.976747 | + | 0.214397i | \(0.0687787\pi\) | ||||
−0.976747 | + | 0.214397i | \(0.931221\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 4093.69i | − 0.622521i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 348.273i | 0.0525118i | 0.999655 | + | 0.0262559i | \(0.00835848\pi\) | ||||
−0.999655 | + | 0.0262559i | \(0.991642\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14465.2 | −2.16263 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4852.06i | 0.713321i | 0.934234 | + | 0.356660i | \(0.116085\pi\) | ||||
−0.934234 | + | 0.356660i | \(0.883915\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8283.51 | 1.20768 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3297.65 | −0.476809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11487.7 | −1.64737 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9356.53 | −1.33081 | −0.665404 | − | 0.746483i | \(-0.731741\pi\) | ||||
−0.665404 | + | 0.746483i | \(0.731741\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 2552.52i | − 0.360105i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4573.24 | −0.634835 | −0.317418 | − | 0.948286i | \(-0.602816\pi\) | ||||
−0.317418 | + | 0.948286i | \(0.602816\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 19364.7i | − 2.66664i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 901.544i | 0.123161i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 11843.8i | − 1.60521i | −0.596514 | − | 0.802603i | \(-0.703448\pi\) | ||||
0.596514 | − | 0.802603i | \(-0.296552\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 11047.8i | − 1.48555i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10479.3 | −1.39808 | −0.699041 | − | 0.715082i | \(-0.746389\pi\) | ||||
−0.699041 | + | 0.715082i | \(0.746389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1548.68i | 0.203420i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1599.54 | −0.208483 | −0.104242 | − | 0.994552i | \(-0.533242\pi\) | ||||
−0.104242 | + | 0.994552i | \(0.533242\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10515.1 | −1.36003 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5932.85 | 0.761508 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16079.4 | 2.04821 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 11.6116i | − 0.00146793i | −1.00000 | 0.000733966i | \(-0.999766\pi\) | |||||
1.00000 | 0.000733966i | \(-0.000233629\pi\) | ||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7462.34 | −0.929306 | −0.464653 | − | 0.885493i | \(-0.653821\pi\) | ||||
−0.464653 | + | 0.885493i | \(0.653821\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4410.87i | 0.545213i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17253.4i | 2.11686i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2689.78i | − 0.327586i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5640.51i | 0.681920i | 0.940078 | + | 0.340960i | \(0.110752\pi\) | ||||
−0.940078 | + | 0.340960i | \(0.889248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11527.8 | 1.38352 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 6125.12i | − 0.724507i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5665.50 | 0.665325 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8037.03 | −0.937076 | −0.468538 | − | 0.883443i | \(-0.655219\pi\) | ||||
−0.468538 | + | 0.883443i | \(0.655219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9815.24 | 1.13626 | 0.568130 | − | 0.822939i | \(-0.307667\pi\) | ||||
0.568130 | + | 0.822939i | \(0.307667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3056.03 | 0.351275 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15062.7i | 1.71917i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5188.36 | −0.583907 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 4053.33i | − 0.452998i | −0.974011 | − | 0.226499i | \(-0.927272\pi\) | ||||
0.974011 | − | 0.226499i | \(-0.0727280\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 13331.5i | − 1.47961i | −0.672822 | − | 0.739805i | \(-0.734918\pi\) | ||||
0.672822 | − | 0.739805i | \(-0.265082\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 3147.64i | − 0.346938i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25060.4i | 2.74325i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11361.5 | 1.23521 | 0.617604 | − | 0.786489i | \(-0.288104\pi\) | ||||
0.617604 | + | 0.786489i | \(0.288104\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12669.9i | 1.35884i | 0.733750 | + | 0.679419i | \(0.237768\pi\) | ||||
−0.733750 | + | 0.679419i | \(0.762232\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23149.7 | 2.46607 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5268.26 | −0.557450 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8911.65 | 0.936674 | 0.468337 | − | 0.883550i | \(-0.344853\pi\) | ||||
0.468337 | + | 0.883550i | \(0.344853\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13025.6 | 1.35998 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 11956.0i | − 1.24005i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13833.7 | 1.41600 | 0.707999 | − | 0.706213i | \(-0.249598\pi\) | ||||
0.707999 | + | 0.706213i | \(0.249598\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 6353.78i | − 0.646120i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 852.971i | 0.0861753i | 0.999071 | + | 0.0430877i | \(0.0137195\pi\) | ||||
−0.999071 | + | 0.0430877i | \(0.986281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 6647.58i | − 0.667255i | −0.942705 | − | 0.333628i | \(-0.891727\pi\) | ||||
0.942705 | − | 0.333628i | \(-0.108273\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 15400.1i | − 1.53583i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7396.09 | 0.732870 | 0.366435 | − | 0.930444i | \(-0.380578\pi\) | ||||
0.366435 | + | 0.930444i | \(0.380578\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13992.6i | 1.36889i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7902.96 | −0.768242 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35898.3 | 3.46764 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −717.253 | −0.0688485 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10779.1 | −1.02820 | −0.514102 | − | 0.857729i | \(-0.671875\pi\) | ||||
−0.514102 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3264.28i | 0.309436i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4778.29 | −0.447363 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5643.59i | − 0.525124i | −0.964915 | − | 0.262562i | \(-0.915433\pi\) | ||||
0.964915 | − | 0.262562i | \(-0.0845675\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 16516.6i | − 1.52742i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2800.93i | − 0.257442i | −0.991681 | − | 0.128721i | \(-0.958913\pi\) | ||||
0.991681 | − | 0.128721i | \(-0.0410872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1399.28i | 0.127830i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3005.88 | 0.272938 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 17704.6i | − 1.58831i | −0.607712 | − | 0.794157i | \(-0.707913\pi\) | ||||
0.607712 | − | 0.794157i | \(-0.292087\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5919.49 | −0.527871 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8247.73 | −0.731110 | −0.365555 | − | 0.930790i | \(-0.619121\pi\) | ||||
−0.365555 | + | 0.930790i | \(0.619121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11201.2 | 0.987022 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6203.55 | −0.543410 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 409.106i | 0.0356253i | 0.999841 | + | 0.0178127i | \(0.00567025\pi\) | ||||
−0.999841 | + | 0.0178127i | \(0.994330\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15142.7 | −1.30325 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 8326.55i | − 0.712450i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15595.1i | 1.32664i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 820.066i | − 0.0693582i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 10656.7i | − 0.896123i | −0.894003 | − | 0.448062i | \(-0.852114\pi\) | ||||
0.894003 | − | 0.448062i | \(-0.147886\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3241.19 | −0.270989 | −0.135494 | − | 0.990778i | \(-0.543262\pi\) | ||||
−0.135494 | + | 0.990778i | \(0.543262\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6846.07i | 0.565882i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29307.1 | −2.40874 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1649.46 | −0.134803 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15807.7 | −1.28463 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8813.09 | 0.712193 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 4081.93i | − 0.328023i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15351.8 | −1.22001 | −0.610004 | − | 0.792399i | \(-0.708832\pi\) | ||||
−0.610004 | + | 0.792399i | \(0.708832\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2693.51i | 0.212872i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 28945.8i | − 2.27505i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3418.07i | 0.267178i | 0.991037 | + | 0.133589i | \(0.0426502\pi\) | ||||
−0.991037 | + | 0.133589i | \(0.957350\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3952.40i | 0.307257i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3334.85 | 0.257839 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 11396.9i | − 0.871660i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13943.5 | −1.06069 | −0.530345 | − | 0.847782i | \(-0.677938\pi\) | ||||
−0.530345 | + | 0.847782i | \(0.677938\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9590.94 | 0.725677 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8052.81 | −0.606042 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10616.9 | −0.794761 | −0.397380 | − | 0.917654i | \(-0.630081\pi\) | ||||
−0.397380 | + | 0.917654i | \(0.630081\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14405.8i | 1.07267i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 421.063 | 0.0310227 | 0.0155113 | − | 0.999880i | \(-0.495062\pi\) | ||||
0.0155113 | + | 0.999880i | \(0.495062\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25824.9i | 1.89271i | 0.323126 | + | 0.946356i | \(0.395266\pi\) | ||||
−0.323126 | + | 0.946356i | \(0.604734\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14394.7i | 1.04947i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 59410.5i | 4.30885i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 8500.59i | − 0.613318i | −0.951820 | − | 0.306659i | \(-0.900789\pi\) | ||||
0.951820 | − | 0.306659i | \(-0.0992110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18508.2 | −1.32845 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 3660.17i | − 0.260015i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3647.90 | −0.257816 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20752.1 | −1.45916 | −0.729582 | − | 0.683893i | \(-0.760285\pi\) | ||||
−0.729582 | + | 0.683893i | \(0.760285\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16316.0 | 1.14141 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29461.1 | −2.05053 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 4423.58i | − 0.306332i | −0.988201 | − | 0.153166i | \(-0.951053\pi\) | ||||
0.988201 | − | 0.153166i | \(-0.0489469\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11604.7 | 0.795559 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19047.4i | 1.29926i | 0.760250 | + | 0.649630i | \(0.225076\pi\) | ||||
−0.760250 | + | 0.649630i | \(0.774924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 13205.5i | − 0.896282i | −0.893963 | − | 0.448141i | \(-0.852086\pi\) | ||||
0.893963 | − | 0.448141i | \(-0.147914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 699.667i | − 0.0472515i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 11831.7i | − 0.795086i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8202.94 | −0.548512 | −0.274256 | − | 0.961657i | \(-0.588432\pi\) | ||||
−0.274256 | + | 0.961657i | \(0.588432\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 18926.0i | − 1.25313i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13977.1 | −0.920932 | −0.460466 | − | 0.887677i | \(-0.652318\pi\) | ||||
−0.460466 | + | 0.887677i | \(0.652318\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 55190.9 | 3.61872 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17469.6 | 1.13987 | 0.569935 | − | 0.821690i | \(-0.306968\pi\) | ||||
0.569935 | + | 0.821690i | \(0.306968\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11475.8 | 0.745156 | 0.372578 | − | 0.928001i | \(-0.378474\pi\) | ||||
0.372578 | + | 0.928001i | \(0.378474\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 25060.7i | − 1.61941i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 33013.2 | 2.11285 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19192.0i | 1.22241i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5066.47i | 0.321166i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 25620.4i | − 1.61638i | −0.588924 | − | 0.808188i | \(-0.700448\pi\) | ||||
0.588924 | − | 0.808188i | \(-0.299552\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 7474.90i | − 0.469353i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39638.5 | 2.47718 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 3806.34i | − 0.235644i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13393.0 | 0.825258 | 0.412629 | − | 0.910899i | \(-0.364611\pi\) | ||||
0.412629 | + | 0.910899i | \(0.364611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6636.01 | 0.406997 | 0.203498 | − | 0.979075i | \(-0.434769\pi\) | ||||
0.203498 | + | 0.979075i | \(0.434769\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33485.7 | −2.04418 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10046.4 | −0.610458 | −0.305229 | − | 0.952279i | \(-0.598733\pi\) | ||||
−0.305229 | + | 0.952279i | \(0.598733\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 8417.29i | − 0.509102i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8981.76 | −0.538260 | −0.269130 | − | 0.963104i | \(-0.586736\pi\) | ||||
−0.269130 | + | 0.963104i | \(0.586736\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21286.6i | 1.26983i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 3022.84i | − 0.179501i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30917.7i | 1.82759i | 0.406177 | + | 0.913794i | \(0.366862\pi\) | ||||
−0.406177 | + | 0.913794i | \(0.633138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 3506.27i | − 0.206321i | −0.994665 | − | 0.103160i | \(-0.967105\pi\) | ||||
0.994665 | − | 0.103160i | \(-0.0328955\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9772.79 | 0.572464 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5519.07i | 0.320389i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4377.52 | −0.252982 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20169.3 | −1.16040 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3063.54 | −0.175469 | −0.0877345 | − | 0.996144i | \(-0.527963\pi\) | ||||
−0.0877345 | + | 0.996144i | \(0.527963\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −35898.8 | −2.04703 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6003.94i | 0.340842i | 0.985371 | + | 0.170421i | \(0.0545128\pi\) | ||||
−0.985371 | + | 0.170421i | \(0.945487\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21014.0 | −1.18247 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1856.95i | − 0.104033i | −0.998646 | − | 0.0520164i | \(-0.983435\pi\) | ||||
0.998646 | − | 0.0520164i | \(-0.0165648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41360.9i | 2.30703i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1275.90i | 0.0708569i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4441.94i | 0.245609i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9303.94 | 0.512212 | 0.256106 | − | 0.966649i | \(-0.417560\pi\) | ||||
0.256106 | + | 0.966649i | \(0.417560\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20327.4i | 1.10944i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24535.0 | −1.33333 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16082.8 | −0.870251 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28304.2 | −1.52502 | −0.762508 | − | 0.646979i | \(-0.776032\pi\) | ||||
−0.762508 | + | 0.646979i | \(0.776032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12074.7 | 0.647806 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 66078.0i | 3.52999i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5950.28 | −0.315187 | −0.157593 | − | 0.987504i | \(-0.550374\pi\) | ||||
−0.157593 | + | 0.987504i | \(0.550374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4231.11i | 0.223177i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27002.4i | 1.41830i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 18615.4i | − 0.973674i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3617.43i | 0.188418i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11142.8 | 0.577966 | 0.288983 | − | 0.957334i | \(-0.406683\pi\) | ||||
0.288983 | + | 0.957334i | \(0.406683\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 35941.1i | 1.84877i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7905.92 | 0.404991 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5517.58 | −0.281480 | −0.140740 | − | 0.990047i | \(-0.544948\pi\) | ||||
−0.140740 | + | 0.990047i | \(0.544948\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14363.9 | 0.729762 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14886.0 | 0.753186 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20181.2i | 1.01693i | 0.861083 | + | 0.508464i | \(0.169787\pi\) | ||||
−0.861083 | + | 0.508464i | \(0.830213\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3570.43 | 0.178451 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16392.3i | 0.815968i | 0.912989 | + | 0.407984i | \(0.133768\pi\) | ||||
−0.912989 | + | 0.407984i | \(0.866232\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 23291.1i | − 1.15468i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 20914.6i | − 1.03268i | −0.856383 | − | 0.516341i | \(-0.827294\pi\) | ||||
0.856383 | − | 0.516341i | \(-0.172706\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 18902.1i | − 0.929556i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1611.75 | 0.0789437 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 18466.3i | − 0.897266i | −0.893716 | − | 0.448633i | \(-0.851911\pi\) | ||||
0.893716 | − | 0.448633i | \(-0.148089\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11533.8 | 0.558187 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 42897.3 | 2.06780 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21663.1 | 1.04010 | 0.520051 | − | 0.854135i | \(-0.325913\pi\) | ||||
0.520051 | + | 0.854135i | \(0.325913\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31762.1 | −1.51896 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26900.4i | 1.28139i | 0.767795 | + | 0.640696i | \(0.221354\pi\) | ||||
−0.767795 | + | 0.640696i | \(0.778646\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5661.88 | −0.267589 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10215.1i | 0.480895i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30388.7i | 1.42502i | 0.701660 | + | 0.712512i | \(0.252442\pi\) | ||||
−0.701660 | + | 0.712512i | \(0.747558\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 29852.3i | − 1.39443i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 801.174i | − 0.0372784i | −0.999826 | − | 0.0186392i | \(-0.994067\pi\) | ||||
0.999826 | − | 0.0186392i | \(-0.00593339\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38680.3 | 1.79282 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58473.5i | 2.68938i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19423.9 | 0.889939 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3334.90 | −0.152209 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50204.3 | −2.28264 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33591.9 | −1.52150 | −0.760752 | − | 0.649043i | \(-0.775169\pi\) | ||||
−0.760752 | + | 0.649043i | \(0.775169\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3592.44i | 0.162097i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24477.2 | 1.09610 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 15508.5i | − 0.691864i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2563.22i | − 0.113919i | −0.998376 | − | 0.0569597i | \(-0.981859\pi\) | ||||
0.998376 | − | 0.0569597i | \(-0.0181406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 29374.9i | − 1.30064i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6091.56i | 0.268707i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15425.7 | 0.677908 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 6628.37i | − 0.289132i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34904.7 | 1.51692 | 0.758458 | − | 0.651722i | \(-0.225953\pi\) | ||||
0.758458 | + | 0.651722i | \(0.225953\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21556.7 | 0.933363 | 0.466682 | − | 0.884425i | \(-0.345449\pi\) | ||||
0.466682 | + | 0.884425i | \(0.345449\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 45265.9 | 1.95270 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 59260.2 | 2.54699 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 35477.3i | − 1.51921i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25349.0 | −1.07757 | −0.538785 | − | 0.842443i | \(-0.681117\pi\) | ||||
−0.538785 | + | 0.842443i | \(0.681117\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16954.9i | 0.718116i | 0.933315 | + | 0.359058i | \(0.116902\pi\) | ||||
−0.933315 | + | 0.359058i | \(0.883098\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 45498.3i | 1.92006i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38797.2i | 1.63133i | 0.578523 | + | 0.815666i | \(0.303629\pi\) | ||||
−0.578523 | + | 0.815666i | \(0.696371\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29945.2i | 1.25457i | 0.778789 | + | 0.627285i | \(0.215834\pi\) | ||||
−0.778789 | + | 0.627285i | \(0.784166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20488.1 | 0.855264 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 21238.7i | − 0.880232i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16316.3 | −0.673802 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36918.6 | −1.51916 | −0.759578 | − | 0.650416i | \(-0.774595\pi\) | ||||
−0.759578 | + | 0.650416i | \(0.774595\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23654.6 | −0.969887 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9273.79 | −0.378893 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 22257.8i | − 0.906145i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20269.9 | 0.819388 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19983.3i | 0.804957i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 21921.6i | − 0.879930i | −0.898015 | − | 0.439965i | \(-0.854991\pi\) | ||||
0.898015 | − | 0.439965i | \(-0.145009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13493.8i | 0.539739i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7836.91i | 0.312373i | 0.987728 | + | 0.156187i | \(0.0499201\pi\) | ||||
−0.987728 | + | 0.156187i | \(0.950080\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5866.31 | 0.233010 | 0.116505 | − | 0.993190i | \(-0.462831\pi\) | ||||
0.116505 | + | 0.993190i | \(0.462831\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 472.119i | 0.0186224i | 0.999957 | + | 0.00931120i | \(0.00296389\pi\) | ||||
−0.999957 | + | 0.00931120i | \(0.997036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2942.33 | 0.115656 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12784.8 | −0.500801 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21591.6 | −0.842858 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4333.03 | −0.168564 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 1257.35i | − 0.0487455i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23962.5 | 0.922640 | 0.461320 | − | 0.887234i | \(-0.347376\pi\) | ||||
0.461320 | + | 0.887234i | \(0.347376\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12840.4i | 0.492715i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 24460.0i | − 0.935390i | −0.883890 | − | 0.467695i | \(-0.845085\pi\) | ||||
0.883890 | − | 0.467695i | \(-0.154915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17519.7i | 0.667708i | 0.942625 | + | 0.333854i | \(0.108349\pi\) | ||||
−0.942625 | + | 0.333854i | \(0.891651\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 35665.0i | − 1.35465i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7452.05 | −0.282092 | −0.141046 | − | 0.990003i | \(-0.545046\pi\) | ||||
−0.141046 | + | 0.990003i | \(0.545046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 23167.9i | − 0.871106i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −70008.1 | −2.62344 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14645.6 | 0.546983 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 38546.1 | 1.43480 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3593.29 | 0.133307 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6894.30i | 0.254919i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9664.11 | −0.354968 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 37014.8i | − 1.35508i | −0.735486 | − | 0.677540i | \(-0.763046\pi\) | ||||
0.735486 | − | 0.677540i | \(-0.236954\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2947.46i | 0.107548i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12342.5i | 0.448876i | 0.974488 | + | 0.224438i | \(0.0720546\pi\) | ||||
−0.974488 | + | 0.224438i | \(0.927945\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8224.84i | 0.298141i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −85459.3 | −3.08765 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 16482.6i | − 0.591633i | −0.955245 | − | 0.295817i | \(-0.904408\pi\) | ||||
0.955245 | − | 0.295817i | \(-0.0955918\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44942.2 | 1.60792 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23572.6 | −0.840631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28625.5 | 1.01752 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2191.03 | 0.0776299 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21750.4i | 0.768145i | 0.923303 | + | 0.384073i | \(0.125479\pi\) | ||||
−0.923303 | + | 0.384073i | \(0.874521\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34321.2 | −1.20431 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 28892.8i | − 1.01058i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 20698.0i | − 0.721638i | −0.932636 | − | 0.360819i | \(-0.882497\pi\) | ||||
0.932636 | − | 0.360819i | \(-0.117503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3691.13i | 0.128281i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 40305.4i | − 1.39630i | −0.715951 | − | 0.698151i | \(-0.754006\pi\) | ||||
0.715951 | − | 0.698151i | \(-0.245994\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −96771.7 | −3.34180 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 7361.90i | − 0.252618i | −0.991991 | − | 0.126309i | \(-0.959687\pi\) | ||||
0.991991 | − | 0.126309i | \(-0.0403131\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18720.4 | −0.640348 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30725.1 | 1.04767 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38052.9 | −1.29345 | −0.646723 | − | 0.762725i | \(-0.723861\pi\) | ||||
−0.646723 | + | 0.762725i | \(0.723861\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −51647.0 | −1.75001 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4226.67i | 0.142768i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12210.6 | −0.409874 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2319.06i | 0.0776019i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 66405.9i | − 2.21522i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 6095.61i | − 0.202711i | −0.994850 | − | 0.101356i | \(-0.967682\pi\) | ||||
0.994850 | − | 0.101356i | \(-0.0323180\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 36150.0i | − 1.19846i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22135.7 | 0.731585 | 0.365792 | − | 0.930697i | \(-0.380798\pi\) | ||||
0.365792 | + | 0.930697i | \(0.380798\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 55216.2i | − 1.81368i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49659.8 | −1.62616 | −0.813080 | − | 0.582153i | \(-0.802211\pi\) | ||||
−0.813080 | + | 0.582153i | \(0.802211\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31085.5 | −1.01481 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7616.74 | 0.247894 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50074.5 | 1.62475 | 0.812375 | − | 0.583135i | \(-0.198174\pi\) | ||||
0.812375 | + | 0.583135i | \(0.198174\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 105704.i | − 3.41930i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58713.8 | 1.88776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 6833.25i | − 0.219037i | −0.993985 | − | 0.109518i | \(-0.965069\pi\) | ||||
0.993985 | − | 0.109518i | \(-0.0349308\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26200.1i | 0.837297i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41636.7i | 1.32661i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29362.7i | 0.932724i | 0.884594 | + | 0.466362i | \(0.154436\pi\) | ||||
−0.884594 | + | 0.466362i | \(0.845564\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12074.9 | −0.382416 |
(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 | 784.4.f.j.783.6 | yes | 24 | |
4.3 | odd | 2 | inner | 784.4.f.j.783.20 | yes | 24 | |
7.6 | odd | 2 | inner | 784.4.f.j.783.19 | yes | 24 | |
28.27 | even | 2 | inner | 784.4.f.j.783.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.4.f.j.783.5 | ✓ | 24 | 28.27 | even | 2 | inner | |
784.4.f.j.783.6 | yes | 24 | 1.1 | even | 1 | trivial | |
784.4.f.j.783.19 | yes | 24 | 7.6 | odd | 2 | inner | |
784.4.f.j.783.20 | yes | 24 | 4.3 | odd | 2 | inner |