Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,3,Mod(2431,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.2431");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(78.4743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2431 |
Dual form | 2880.3.e.e.2431.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 5.25731i | − 0.751044i | −0.926813 | − | 0.375522i | \(-0.877463\pi\) | ||||
0.926813 | − | 0.375522i | \(-0.122537\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.9192i | 1.81084i | 0.424522 | + | 0.905418i | \(0.360442\pi\) | ||||
−0.424522 | + | 0.905418i | \(0.639558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.47214 | 0.651703 | 0.325851 | − | 0.945421i | \(-0.394349\pi\) | ||||
0.325851 | + | 0.945421i | \(0.394349\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.8885 | −0.699326 | −0.349663 | − | 0.936876i | \(-0.613704\pi\) | ||||
−0.349663 | + | 0.936876i | \(0.613704\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.2169i | 0.800890i | 0.916321 | + | 0.400445i | \(0.131144\pi\) | ||||
−0.916321 | + | 0.400445i | \(0.868856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.555029i | 0.0241317i | 0.999927 | + | 0.0120659i | \(0.00384077\pi\) | ||||
−0.999927 | + | 0.0120659i | \(0.996159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.9443 | −0.377389 | −0.188694 | − | 0.982036i | \(-0.560426\pi\) | ||||
−0.188694 | + | 0.982036i | \(0.560426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.29451i | − 0.267565i | −0.991011 | − | 0.133782i | \(-0.957288\pi\) | ||||
0.991011 | − | 0.133782i | \(-0.0427123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.7557i | 0.335877i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.3607 | 0.496235 | 0.248117 | − | 0.968730i | \(-0.420188\pi\) | ||||
0.248117 | + | 0.968730i | \(0.420188\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14.5836 | 0.355697 | 0.177849 | − | 0.984058i | \(-0.443086\pi\) | ||||
0.177849 | + | 0.984058i | \(0.443086\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 22.2703i | − 0.517915i | −0.965889 | − | 0.258957i | \(-0.916621\pi\) | ||||
0.965889 | − | 0.258957i | \(-0.0833789\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 53.3902i | − 1.13596i | −0.823042 | − | 0.567981i | \(-0.807725\pi\) | ||||
0.823042 | − | 0.567981i | \(-0.192275\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 21.3607 | 0.435932 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −66.3607 | −1.25209 | −0.626044 | − | 0.779788i | \(-0.715327\pi\) | ||||
−0.626044 | + | 0.779788i | \(0.715327\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 44.5407i | − 0.809830i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 17.4370i | 0.295543i | 0.989022 | + | 0.147771i | \(0.0472100\pi\) | ||||
−0.989022 | + | 0.147771i | \(0.952790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −90.1378 | −1.47767 | −0.738834 | − | 0.673887i | \(-0.764623\pi\) | ||||
−0.738834 | + | 0.673887i | \(0.764623\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18.9443 | −0.291450 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 50.2220i | − 0.749582i | −0.927109 | − | 0.374791i | \(-0.877715\pi\) | ||||
0.927109 | − | 0.374791i | \(-0.122285\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 80.7868i | 1.13784i | 0.822392 | + | 0.568921i | \(0.192639\pi\) | ||||
−0.822392 | + | 0.568921i | \(0.807361\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.55418 | −0.0760846 | −0.0380423 | − | 0.999276i | \(-0.512112\pi\) | ||||
−0.0380423 | + | 0.999276i | \(0.512112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 104.721 | 1.36002 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 13.8448i | − 0.175251i | −0.996154 | − | 0.0876253i | \(-0.972072\pi\) | ||||
0.996154 | − | 0.0876253i | \(-0.0279278\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 76.2155i | − 0.918260i | −0.888369 | − | 0.459130i | \(-0.848161\pi\) | ||||
0.888369 | − | 0.459130i | \(-0.151839\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.5836 | 0.312748 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 111.443 | 1.25217 | 0.626083 | − | 0.779757i | \(-0.284657\pi\) | ||||
0.626083 | + | 0.779757i | \(0.284657\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 44.5407i | − 0.489458i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 34.0260i | − 0.358169i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −92.8328 | −0.957039 | −0.478520 | − | 0.878077i | \(-0.658826\pi\) | ||||
−0.478520 | + | 0.878077i | \(0.658826\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 64.1115 | 0.634767 | 0.317383 | − | 0.948297i | \(-0.397196\pi\) | ||||
0.317383 | + | 0.948297i | \(0.397196\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 137.769i | 1.33757i | 0.743458 | + | 0.668783i | \(0.233184\pi\) | ||||
−0.743458 | + | 0.668783i | \(0.766816\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 51.3320i | − 0.479739i | −0.970805 | − | 0.239869i | \(-0.922895\pi\) | ||||
0.970805 | − | 0.239869i | \(-0.0771046\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −133.469 | −1.22449 | −0.612243 | − | 0.790669i | \(-0.709733\pi\) | ||||
−0.612243 | + | 0.790669i | \(0.709733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −170.721 | −1.51081 | −0.755404 | − | 0.655259i | \(-0.772559\pi\) | ||||
−0.755404 | + | 0.655259i | \(0.772559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.24108i | − 0.0107920i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 62.5018i | 0.525225i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −275.774 | −2.27912 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 198.637i | − 1.56407i | −0.623235 | − | 0.782035i | \(-0.714182\pi\) | ||||
0.623235 | − | 0.782035i | \(-0.285818\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.77041i | 0.0593161i | 0.999560 | + | 0.0296580i | \(0.00944183\pi\) | ||||
−0.999560 | + | 0.0296580i | \(0.990558\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 80.0000 | 0.601504 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.832816 | −0.00607895 | −0.00303947 | − | 0.999995i | \(-0.500967\pi\) | ||||
−0.00303947 | + | 0.999995i | \(0.500967\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 237.658i | 1.70977i | 0.518817 | + | 0.854885i | \(0.326373\pi\) | ||||
−0.518817 | + | 0.854885i | \(0.673627\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 168.758i | 1.18013i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.4721 | 0.168773 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −36.9706 | −0.248125 | −0.124062 | − | 0.992274i | \(-0.539592\pi\) | ||||
−0.124062 | + | 0.992274i | \(0.539592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 282.723i | 1.87234i | 0.351552 | + | 0.936168i | \(0.385654\pi\) | ||||
−0.351552 | + | 0.936168i | \(0.614346\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.5471i | 0.119659i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −204.748 | −1.30413 | −0.652063 | − | 0.758165i | \(-0.726096\pi\) | ||||
−0.652063 | + | 0.758165i | \(0.726096\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.91796 | 0.0181240 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 107.235i | − 0.657885i | −0.944350 | − | 0.328943i | \(-0.893308\pi\) | ||||
0.944350 | − | 0.328943i | \(-0.106692\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 33.2090i | − 0.198856i | −0.995045 | − | 0.0994280i | \(-0.968299\pi\) | ||||
0.995045 | − | 0.0994280i | \(-0.0317013\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −97.2229 | −0.575284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −226.361 | −1.30844 | −0.654222 | − | 0.756303i | \(-0.727004\pi\) | ||||
−0.654222 | + | 0.756303i | \(0.727004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 26.2866i | − 0.150209i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 224.337i | 1.25328i | 0.779308 | + | 0.626641i | \(0.215571\pi\) | ||||
−0.779308 | + | 0.626641i | \(0.784429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −86.2229 | −0.476370 | −0.238185 | − | 0.971220i | \(-0.576552\pi\) | ||||
−0.238185 | + | 0.971220i | \(0.576552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −41.0557 | −0.221923 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 236.810i | − 1.26636i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 31.0198i | 0.162407i | 0.996698 | + | 0.0812036i | \(0.0258764\pi\) | ||||
−0.996698 | + | 0.0812036i | \(0.974124\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 110.223 | 0.571103 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −172.525 | −0.875760 | −0.437880 | − | 0.899033i | \(-0.644271\pi\) | ||||
−0.437880 | + | 0.899033i | \(0.644271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 272.208i | − 1.36788i | −0.729538 | − | 0.683940i | \(-0.760265\pi\) | ||||
0.729538 | − | 0.683940i | \(-0.239735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 57.5374i | 0.283436i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.6099 | −0.159073 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −303.108 | −1.45028 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 205.266i | 0.972826i | 0.873729 | + | 0.486413i | \(0.161695\pi\) | ||||
−0.873729 | + | 0.486413i | \(0.838305\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 49.7980i | 0.231618i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −43.6068 | −0.200953 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −100.721 | −0.455753 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 235.731i | 1.05709i | 0.848905 | + | 0.528545i | \(0.177262\pi\) | ||||
−0.848905 | + | 0.528545i | \(0.822738\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 58.5165i | − 0.257782i | −0.991659 | − | 0.128891i | \(-0.958858\pi\) | ||||
0.991659 | − | 0.128891i | \(-0.0411417\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −162.721 | −0.710574 | −0.355287 | − | 0.934757i | \(-0.615617\pi\) | ||||
−0.355287 | + | 0.934757i | \(0.615617\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −319.050 | −1.36931 | −0.684656 | − | 0.728867i | \(-0.740047\pi\) | ||||
−0.684656 | + | 0.728867i | \(0.740047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 119.384i | 0.508017i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 236.810i | − 0.990837i | −0.868654 | − | 0.495419i | \(-0.835015\pi\) | ||||
0.868654 | − | 0.495419i | \(-0.164985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.917961 | −0.00380897 | −0.00190448 | − | 0.999998i | \(-0.500606\pi\) | ||||
−0.00190448 | + | 0.999998i | \(0.500606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −47.7639 | −0.194955 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 128.920i | 0.521942i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 136.690i | − 0.544582i | −0.962215 | − | 0.272291i | \(-0.912219\pi\) | ||||
0.962215 | − | 0.272291i | \(-0.0877813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.0557 | −0.0436985 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 274.944 | 1.06982 | 0.534911 | − | 0.844908i | \(-0.320345\pi\) | ||||
0.534911 | + | 0.844908i | \(0.320345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 96.5278i | − 0.372694i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 406.385i | − 1.54519i | −0.634899 | − | 0.772596i | \(-0.718958\pi\) | ||||
0.634899 | − | 0.772596i | \(-0.281042\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 148.387 | 0.559951 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −348.525 | −1.29563 | −0.647816 | − | 0.761797i | \(-0.724317\pi\) | ||||
−0.647816 | + | 0.761797i | \(0.724317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 247.849i | − 0.914571i | −0.889320 | − | 0.457286i | \(-0.848822\pi\) | ||||
0.889320 | − | 0.457286i | \(-0.151178\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 99.5959i | 0.362167i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 54.7539 | 0.197667 | 0.0988337 | − | 0.995104i | \(-0.468489\pi\) | ||||
0.0988337 | + | 0.995104i | \(0.468489\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 50.3607 | 0.179220 | 0.0896098 | − | 0.995977i | \(-0.471438\pi\) | ||||
0.0896098 | + | 0.995977i | \(0.471438\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 147.336i | 0.520621i | 0.965525 | + | 0.260310i | \(0.0838249\pi\) | ||||
−0.965525 | + | 0.260310i | \(0.916175\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 76.6705i | − 0.267145i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −147.663 | −0.510943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 178.859 | 0.610441 | 0.305220 | − | 0.952282i | \(-0.401270\pi\) | ||||
0.305220 | + | 0.952282i | \(0.401270\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 38.9904i | − 0.132171i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.70228i | 0.0157267i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −117.082 | −0.388977 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 201.554 | 0.660833 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 284.550i | 0.926873i | 0.886130 | + | 0.463436i | \(0.153384\pi\) | ||||
−0.886130 | + | 0.463436i | \(0.846616\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 282.199i | − 0.907392i | −0.891157 | − | 0.453696i | \(-0.850105\pi\) | ||||
0.891157 | − | 0.453696i | \(-0.149895\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −567.548 | −1.81325 | −0.906626 | − | 0.421935i | \(-0.861351\pi\) | ||||
−0.906626 | + | 0.421935i | \(0.861351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 161.141 | 0.508331 | 0.254165 | − | 0.967161i | \(-0.418199\pi\) | ||||
0.254165 | + | 0.967161i | \(0.418199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 218.001i | − 0.683389i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 180.907i | − 0.560083i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42.3607 | 0.130341 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −280.689 | −0.853158 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 331.966i | − 1.00292i | −0.865181 | − | 0.501459i | \(-0.832797\pi\) | ||||
0.865181 | − | 0.501459i | \(-0.167203\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 112.300i | 0.335223i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −269.108 | −0.798541 | −0.399271 | − | 0.916833i | \(-0.630737\pi\) | ||||
−0.399271 | + | 0.916833i | \(0.630737\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 165.220 | 0.484516 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 369.908i | − 1.07845i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 503.075i | − 1.44978i | −0.688863 | − | 0.724892i | \(-0.741890\pi\) | ||||
0.688863 | − | 0.724892i | \(-0.258110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.504658 | 0.00144601 | 0.000723006 | − | 1.00000i | \(-0.499770\pi\) | ||||
0.000723006 | 1.00000i | \(0.499770\pi\) | ||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 335.994 | 0.951824 | 0.475912 | − | 0.879493i | \(-0.342118\pi\) | ||||
0.475912 | + | 0.879493i | \(0.342118\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 180.645i | − 0.508859i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 98.4859i | − 0.274334i | −0.990548 | − | 0.137167i | \(-0.956200\pi\) | ||||
0.990548 | − | 0.137167i | \(-0.0437997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 129.446 | 0.358576 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.4195 | 0.0340261 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 498.473i | 1.35824i | 0.734029 | + | 0.679118i | \(0.237638\pi\) | ||||
−0.734029 | + | 0.679118i | \(0.762362\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 348.879i | 0.940374i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −600.354 | −1.60953 | −0.804765 | − | 0.593594i | \(-0.797709\pi\) | ||||
−0.804765 | + | 0.593594i | \(0.797709\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −92.7214 | −0.245945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 303.490i | − 0.800765i | −0.916348 | − | 0.400383i | \(-0.868877\pi\) | ||||
0.916348 | − | 0.400383i | \(-0.131123\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 332.583i | 0.868362i | 0.900826 | + | 0.434181i | \(0.142962\pi\) | ||||
−0.900826 | + | 0.434181i | \(0.857038\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −234.164 | −0.608218 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 392.354 | 1.00862 | 0.504312 | − | 0.863522i | \(-0.331746\pi\) | ||||
0.504312 | + | 0.863522i | \(0.331746\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 6.59849i | − 0.0168759i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.9579i | 0.0783744i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −334.190 | −0.841789 | −0.420895 | − | 0.907110i | \(-0.638284\pi\) | ||||
−0.420895 | + | 0.907110i | \(0.638284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −121.003 | −0.301753 | −0.150877 | − | 0.988553i | \(-0.548210\pi\) | ||||
−0.150877 | + | 0.988553i | \(0.548210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 70.2722i | − 0.174373i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 365.730i | 0.898599i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −607.410 | −1.48511 | −0.742555 | − | 0.669785i | \(-0.766386\pi\) | ||||
−0.742555 | + | 0.669785i | \(0.766386\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 91.6718 | 0.221966 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 170.423i | 0.410658i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 466.760i | − 1.11398i | −0.830518 | − | 0.556992i | \(-0.811955\pi\) | ||||
0.830518 | − | 0.556992i | \(-0.188045\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 73.0883 | 0.173606 | 0.0868031 | − | 0.996225i | \(-0.472335\pi\) | ||||
0.0868031 | + | 0.996225i | \(0.472335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −59.4427 | −0.139865 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 473.882i | 1.10979i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 463.630i | 1.07571i | 0.843038 | + | 0.537853i | \(0.180765\pi\) | ||||
−0.843038 | + | 0.537853i | \(0.819235\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −99.8359 | −0.230568 | −0.115284 | − | 0.993333i | \(-0.536778\pi\) | ||||
−0.115284 | + | 0.993333i | \(0.536778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.44582 | −0.0193268 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 374.086i | 0.852133i | 0.904692 | + | 0.426066i | \(0.140101\pi\) | ||||
−0.904692 | + | 0.426066i | \(0.859899\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 290.100i | − 0.654854i | −0.944877 | − | 0.327427i | \(-0.893818\pi\) | ||||
0.944877 | − | 0.327427i | \(-0.106182\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −249.193 | −0.559985 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −299.921 | −0.667976 | −0.333988 | − | 0.942577i | \(-0.608394\pi\) | ||||
−0.333988 | + | 0.942577i | \(0.608394\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 290.493i | 0.644109i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 99.5959i | 0.218892i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 822.328 | 1.79941 | 0.899703 | − | 0.436503i | \(-0.143783\pi\) | ||||
0.899703 | + | 0.436503i | \(0.143783\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −456.885 | −0.991075 | −0.495537 | − | 0.868587i | \(-0.665029\pi\) | ||||
−0.495537 | + | 0.868587i | \(0.665029\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 400.249i | 0.864469i | 0.901761 | + | 0.432234i | \(0.142275\pi\) | ||||
−0.901761 | + | 0.432234i | \(0.857725\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 913.145i | 1.95534i | 0.210139 | + | 0.977672i | \(0.432608\pi\) | ||||
−0.210139 | + | 0.977672i | \(0.567392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −264.033 | −0.562969 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 443.607 | 0.937858 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 76.0845i | 0.160178i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 526.131i | 1.09840i | 0.835692 | + | 0.549198i | \(0.185067\pi\) | ||||
−0.835692 | + | 0.549198i | \(0.814933\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 155.554 | 0.323397 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 207.580 | 0.428001 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 443.541i | 0.910762i | 0.890297 | + | 0.455381i | \(0.150497\pi\) | ||||
−0.890297 | + | 0.455381i | \(0.849503\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 287.163i | − 0.584854i | −0.956288 | − | 0.292427i | \(-0.905537\pi\) | ||||
0.956288 | − | 0.292427i | \(-0.0944628\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 130.111 | 0.263918 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 424.721 | 0.854570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 810.936i | − 1.62512i | −0.582876 | − | 0.812561i | \(-0.698073\pi\) | ||||
0.582876 | − | 0.812561i | \(-0.301927\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 642.471i | − 1.27728i | −0.769506 | − | 0.638639i | \(-0.779498\pi\) | ||||
0.769506 | − | 0.638639i | \(-0.220502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −143.358 | −0.283876 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −915.050 | −1.79774 | −0.898870 | − | 0.438216i | \(-0.855611\pi\) | ||||
−0.898870 | + | 0.438216i | \(0.855611\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.2000i | 0.0571429i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 308.061i | − 0.598177i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1063.49 | 2.05704 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1006.98 | −1.93279 | −0.966396 | − | 0.257058i | \(-0.917247\pi\) | ||||
−0.966396 | + | 0.257058i | \(0.917247\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 774.173i | 1.48025i | 0.672467 | + | 0.740127i | \(0.265235\pi\) | ||||
−0.672467 | + | 0.740127i | \(0.734765\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 98.6096i | 0.187115i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.692 | 0.999418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 123.554 | 0.231809 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 114.782i | 0.214546i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 425.487i | 0.789401i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 259.115 | 0.478955 | 0.239477 | − | 0.970902i | \(-0.423024\pi\) | ||||
0.239477 | + | 0.970902i | \(0.423024\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 298.446 | 0.547607 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 149.818i | 0.273890i | 0.990579 | + | 0.136945i | \(0.0437284\pi\) | ||||
−0.990579 | + | 0.136945i | \(0.956272\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 166.538i | − 0.302247i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −72.7864 | −0.131621 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 511.698 | 0.918668 | 0.459334 | − | 0.888264i | \(-0.348088\pi\) | ||||
0.459334 | + | 0.888264i | \(0.348088\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 188.677i | − 0.337526i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 490.726i | 0.871627i | 0.900037 | + | 0.435814i | \(0.143539\pi\) | ||||
−0.900037 | + | 0.435814i | \(0.856461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 381.745 | 0.675654 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 232.748 | 0.409047 | 0.204523 | − | 0.978862i | \(-0.434436\pi\) | ||||
0.204523 | + | 0.978862i | \(0.434436\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 210.755i | 0.369098i | 0.982823 | + | 0.184549i | \(0.0590824\pi\) | ||||
−0.982823 | + | 0.184549i | \(0.940918\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.77515i | 0.00482634i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 341.712 | 0.592222 | 0.296111 | − | 0.955154i | \(-0.404310\pi\) | ||||
0.296111 | + | 0.955154i | \(0.404310\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −400.689 | −0.689654 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1321.85i | − 2.26733i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 618.412i | 1.05351i | 0.850016 | + | 0.526756i | \(0.176592\pi\) | ||||
−0.850016 | + | 0.526756i | \(0.823408\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 126.217 | 0.214290 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −120.663 | −0.203478 | −0.101739 | − | 0.994811i | \(-0.532441\pi\) | ||||
−0.101739 | + | 0.994811i | \(0.532441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 139.758i | − 0.234888i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 849.927i | 1.41891i | 0.704751 | + | 0.709455i | \(0.251059\pi\) | ||||
−0.704751 | + | 0.709455i | \(0.748941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3576 | −0.0188978 | −0.00944890 | − | 0.999955i | \(-0.503008\pi\) | ||||
−0.00944890 | + | 0.999955i | \(0.503008\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 616.649 | 1.01926 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1115.12i | − 1.83710i | −0.395305 | − | 0.918550i | \(-0.629361\pi\) | ||||
0.395305 | − | 0.918550i | \(-0.370639\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 452.329i | − 0.740309i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −499.475 | −0.814805 | −0.407402 | − | 0.913249i | \(-0.633565\pi\) | ||||
−0.407402 | + | 0.913249i | \(0.633565\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −545.935 | −0.884822 | −0.442411 | − | 0.896813i | \(-0.645877\pi\) | ||||
−0.442411 | + | 0.896813i | \(0.645877\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 455.011i | − 0.735075i | −0.930009 | − | 0.367537i | \(-0.880201\pi\) | ||||
0.930009 | − | 0.367537i | \(-0.119799\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 585.889i | − 0.940432i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −218.282 | −0.347030 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 267.706i | 0.424257i | 0.977242 | + | 0.212128i | \(0.0680395\pi\) | ||||
−0.977242 | + | 0.212128i | \(0.931960\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 444.165i | 0.699473i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 180.971 | 0.284098 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 418.571 | 0.652997 | 0.326499 | − | 0.945198i | \(-0.394131\pi\) | ||||
0.326499 | + | 0.945198i | \(0.394131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 439.339i | − 0.683265i | −0.939834 | − | 0.341633i | \(-0.889020\pi\) | ||||
0.939834 | − | 0.341633i | \(-0.110980\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 419.644i | − 0.648600i | −0.945954 | − | 0.324300i | \(-0.894871\pi\) | ||||
0.945954 | − | 0.324300i | \(-0.105129\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −347.331 | −0.535179 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −370.085 | −0.566746 | −0.283373 | − | 0.959010i | \(-0.591453\pi\) | ||||
−0.283373 | + | 0.959010i | \(0.591453\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 17.3752i | − 0.0265270i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 322.823i | − 0.489868i | −0.969540 | − | 0.244934i | \(-0.921234\pi\) | ||||
0.969540 | − | 0.244934i | \(-0.0787664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 812.735 | 1.22955 | 0.614777 | − | 0.788701i | \(-0.289246\pi\) | ||||
0.614777 | + | 0.788701i | \(0.289246\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −178.885 | −0.269001 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6.07439i | − 0.00910703i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1795.47i | − 2.67581i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 467.378 | 0.694469 | 0.347235 | − | 0.937778i | \(-0.387121\pi\) | ||||
0.347235 | + | 0.937778i | \(0.387121\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 548.237 | 0.809803 | 0.404902 | − | 0.914360i | \(-0.367306\pi\) | ||||
0.404902 | + | 0.914360i | \(0.367306\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 488.051i | 0.718779i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.9663i | 0.0350898i | 0.999846 | + | 0.0175449i | \(0.00558500\pi\) | ||||
−0.999846 | + | 0.0175449i | \(0.994415\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.86223 | 0.00271859 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −562.217 | −0.815989 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 186.981i | 0.270595i | 0.990805 | + | 0.135298i | \(0.0431990\pi\) | ||||
−0.990805 | + | 0.135298i | \(0.956801\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 531.420i | − 0.764633i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −173.378 | −0.248748 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −706.636 | −1.00804 | −0.504020 | − | 0.863692i | \(-0.668146\pi\) | ||||
−0.504020 | + | 0.863692i | \(0.668146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 279.393i | 0.397429i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 337.054i | − 0.476738i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 188.597 | 0.266005 | 0.133002 | − | 0.991116i | \(-0.457538\pi\) | ||||
0.133002 | + | 0.991116i | \(0.457538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.60369 | 0.00645679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 377.354i | − 0.527769i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 156.085i | − 0.217086i | −0.994092 | − | 0.108543i | \(-0.965381\pi\) | ||||
0.994092 | − | 0.108543i | \(-0.0346186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 724.296 | 1.00457 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −54.7214 | −0.0754777 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 715.164i | − 0.983719i | −0.870675 | − | 0.491859i | \(-0.836317\pi\) | ||||
0.870675 | − | 0.491859i | \(-0.163683\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 264.762i | 0.362191i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1233.29 | −1.68252 | −0.841259 | − | 0.540632i | \(-0.818185\pi\) | ||||
−0.841259 | + | 0.540632i | \(0.818185\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1000.38 | 1.35737 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 8.55656i | − 0.0115786i | −0.999983 | − | 0.00578928i | \(-0.998157\pi\) | ||||
0.999983 | − | 0.00578928i | \(-0.00184280\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1010.56i | 1.36011i | 0.733163 | + | 0.680053i | \(0.238043\pi\) | ||||
−0.733163 | + | 0.680053i | \(0.761957\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 82.6687 | 0.110965 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −269.868 | −0.360305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1104.31i | − 1.47046i | −0.677820 | − | 0.735228i | \(-0.737075\pi\) | ||||
0.677820 | − | 0.735228i | \(-0.262925\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 632.188i | − 0.837335i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 875.633 | 1.15671 | 0.578357 | − | 0.815783i | \(-0.303694\pi\) | ||||
0.578357 | + | 0.815783i | \(0.303694\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 647.207 | 0.850470 | 0.425235 | − | 0.905083i | \(-0.360192\pi\) | ||||
0.425235 | + | 0.905083i | \(0.360192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 701.688i | 0.919644i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 147.729i | 0.192606i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 631.430 | 0.821106 | 0.410553 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410553 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −421.522 | −0.545306 | −0.272653 | − | 0.962112i | \(-0.587901\pi\) | ||||
−0.272653 | + | 0.962112i | \(0.587901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 41.4725i | − 0.0535129i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 221.917i | 0.284874i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1609.21 | −2.06044 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 457.830 | 0.583223 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 838.633i | − 1.06561i | −0.846239 | − | 0.532804i | \(-0.821138\pi\) | ||||
0.846239 | − | 0.532804i | \(-0.178862\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 897.535i | 1.13468i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −763.659 | −0.963001 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1213.57 | 1.52268 | 0.761339 | − | 0.648354i | \(-0.224542\pi\) | ||||
0.761339 | + | 0.648354i | \(0.224542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 634.732i | 0.794408i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 110.635i | − 0.137777i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.52476 | −0.00810529 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 229.214 | 0.283330 | 0.141665 | − | 0.989915i | \(-0.454754\pi\) | ||||
0.141665 | + | 0.989915i | \(0.454754\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 454.225i | − 0.560080i | −0.959988 | − | 0.280040i | \(-0.909652\pi\) | ||||
0.959988 | − | 0.280040i | \(-0.0903478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 239.785i | 0.294215i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 338.885 | 0.414792 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1130.90 | 1.37747 | 0.688733 | − | 0.725015i | \(-0.258167\pi\) | ||||
0.688733 | + | 0.725015i | \(0.258167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 780.148i | 0.947931i | 0.880543 | + | 0.473966i | \(0.157178\pi\) | ||||
−0.880543 | + | 0.473966i | \(0.842822\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 209.175i | 0.252932i | 0.991971 | + | 0.126466i | \(0.0403635\pi\) | ||||
−0.991971 | + | 0.126466i | \(0.959636\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 508.525 | 0.613419 | 0.306710 | − | 0.951803i | \(-0.400772\pi\) | ||||
0.306710 | + | 0.951803i | \(0.400772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −253.947 | −0.304859 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 74.2575i | 0.0889311i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 274.028i | 0.326613i | 0.986575 | + | 0.163306i | \(0.0522159\pi\) | ||||
−0.986575 | + | 0.163306i | \(0.947784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −721.223 | −0.857578 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 217.397 | 0.257275 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1449.83i | 1.71172i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1907i | 0.0119750i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1583.28 | 1.85613 | 0.928066 | − | 0.372416i | \(-0.121471\pi\) | ||||
0.928066 | + | 0.372416i | \(0.121471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1007.38 | 1.17547 | 0.587735 | − | 0.809054i | \(-0.300020\pi\) | ||||
0.587735 | + | 0.809054i | \(0.300020\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 76.6086i | 0.0891835i | 0.999005 | + | 0.0445917i | \(0.0141987\pi\) | ||||
−0.999005 | + | 0.0445917i | \(0.985801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 255.450i | 0.296002i | 0.988987 | + | 0.148001i | \(0.0472839\pi\) | ||||
−0.988987 | + | 0.148001i | \(0.952716\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 506.158 | 0.585154 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 275.777 | 0.317350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 425.487i | − 0.488504i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 58.7785i | 0.0671755i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −601.522 | −0.685886 | −0.342943 | − | 0.939356i | \(-0.611424\pi\) | ||||
−0.342943 | + | 0.939356i | \(0.611424\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −237.850 | −0.269977 | −0.134989 | − | 0.990847i | \(-0.543100\pi\) | ||||
−0.134989 | + | 0.990847i | \(0.543100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.30294i | 0.00147559i | 1.00000 | 0.000737794i | \(0.000234847\pi\) | |||||
−1.00000 | 0.000737794i | \(0.999765\pi\) | ||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 536.353i | 0.604682i | 0.953200 | + | 0.302341i | \(0.0977682\pi\) | ||||
−0.953200 | + | 0.302341i | \(0.902232\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1044.30 | −1.17469 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 812.433 | 0.909780 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 501.634i | − 0.560485i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 90.7773i | 0.100976i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 788.932 | 0.875618 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 192.800 | 0.213039 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 332.159i | − 0.366217i | −0.983093 | − | 0.183108i | \(-0.941384\pi\) | ||||
0.983093 | − | 0.183108i | \(-0.0586159\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1450.06i | 1.59172i | 0.605478 | + | 0.795862i | \(0.292982\pi\) | ||||
−0.605478 | + | 0.795862i | \(0.707018\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1518.15 | 1.66282 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40.8514 | 0.0445490 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 814.405i | 0.886186i | 0.896476 | + | 0.443093i | \(0.146119\pi\) | ||||
−0.896476 | + | 0.443093i | \(0.853881\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 684.437i | 0.741535i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 91.8034 | 0.0992469 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −400.039 | −0.430612 | −0.215306 | − | 0.976547i | \(-0.569075\pi\) | ||||
−0.215306 | + | 0.976547i | \(0.569075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 325.043i | 0.349134i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 529.524i | 0.566335i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 249.279 | 0.266039 | 0.133020 | − | 0.991113i | \(-0.457533\pi\) | ||||
0.133020 | + | 0.991113i | \(0.457533\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 724.229 | 0.769638 | 0.384819 | − | 0.922992i | \(-0.374264\pi\) | ||||
0.384819 | + | 0.922992i | \(0.374264\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.09432i | 0.00858358i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1141.54i | − 1.20542i | −0.797959 | − | 0.602712i | \(-0.794087\pi\) | ||||
0.797959 | − | 0.602712i | \(-0.205913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.0557 | −0.0495845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1295.33 | −1.35921 | −0.679604 | − | 0.733579i | \(-0.737848\pi\) | ||||
−0.679604 | + | 0.733579i | \(0.737848\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 69.3623i | − 0.0726307i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.37837i | 0.00456556i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 892.201 | 0.928409 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −246.466 | −0.255405 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 398.477i | − 0.412075i | −0.978544 | − | 0.206037i | \(-0.933943\pi\) | ||||
0.978544 | − | 0.206037i | \(-0.0660569\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 928.093i | − 0.955811i | −0.878411 | − | 0.477906i | \(-0.841396\pi\) | ||||
0.878411 | − | 0.477906i | \(-0.158604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1249.44 | 1.28411 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1378.05 | 1.41049 | 0.705247 | − | 0.708962i | \(-0.250836\pi\) | ||||
0.705247 | + | 0.708962i | \(0.250836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2219.85i | 2.26747i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 311.291i | − 0.316675i | −0.987385 | − | 0.158337i | \(-0.949387\pi\) | ||||
0.987385 | − | 0.158337i | \(-0.0506134\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 385.777 | 0.391652 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.3607 | 0.0124982 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 961.147i | 0.969876i | 0.874549 | + | 0.484938i | \(0.161158\pi\) | ||||
−0.874549 | + | 0.484938i | \(0.838842\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 608.676i | 0.611735i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1089.68 | 1.09296 | 0.546479 | − | 0.837473i | \(-0.315968\pi\) | ||||
0.546479 | + | 0.837473i | \(0.315968\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.3.b.a.11.3 | ✓ | 4 | 24.11 | even | 2 | ||
20.3.b.a.11.4 | yes | 4 | 24.5 | odd | 2 | ||
100.3.b.f.51.1 | 4 | 120.29 | odd | 2 | |||
100.3.b.f.51.2 | 4 | 120.59 | even | 2 | |||
100.3.d.b.99.1 | 8 | 120.83 | odd | 4 | |||
100.3.d.b.99.2 | 8 | 120.77 | even | 4 | |||
100.3.d.b.99.7 | 8 | 120.53 | even | 4 | |||
100.3.d.b.99.8 | 8 | 120.107 | odd | 4 | |||
180.3.c.a.91.1 | 4 | 8.5 | even | 2 | |||
180.3.c.a.91.2 | 4 | 8.3 | odd | 2 | |||
320.3.b.c.191.2 | 4 | 12.11 | even | 2 | |||
320.3.b.c.191.3 | 4 | 3.2 | odd | 2 | |||
900.3.c.k.451.3 | 4 | 40.19 | odd | 2 | |||
900.3.c.k.451.4 | 4 | 40.29 | even | 2 | |||
900.3.f.e.199.1 | 8 | 40.27 | even | 4 | |||
900.3.f.e.199.2 | 8 | 40.13 | odd | 4 | |||
900.3.f.e.199.7 | 8 | 40.37 | odd | 4 | |||
900.3.f.e.199.8 | 8 | 40.3 | even | 4 | |||
1280.3.g.e.1151.3 | 8 | 48.29 | odd | 4 | |||
1280.3.g.e.1151.4 | 8 | 48.11 | even | 4 | |||
1280.3.g.e.1151.5 | 8 | 48.35 | even | 4 | |||
1280.3.g.e.1151.6 | 8 | 48.5 | odd | 4 | |||
1600.3.b.s.1151.2 | 4 | 15.14 | odd | 2 | |||
1600.3.b.s.1151.3 | 4 | 60.59 | even | 2 | |||
1600.3.h.n.1599.3 | 8 | 15.8 | even | 4 | |||
1600.3.h.n.1599.4 | 8 | 60.47 | odd | 4 | |||
1600.3.h.n.1599.5 | 8 | 15.2 | even | 4 | |||
1600.3.h.n.1599.6 | 8 | 60.23 | odd | 4 | |||
2880.3.e.e.2431.1 | 4 | 1.1 | even | 1 | trivial | ||
2880.3.e.e.2431.2 | 4 | 4.3 | odd | 2 | inner |