Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.14 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.33 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.34274 | + | 1.78803i | 0.600492 | + | 0.799631i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.521655i | 0.197167i | 0.995129 | + | 0.0985835i | \(0.0314311\pi\) | ||||
−0.995129 | + | 0.0985835i | \(0.968569\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.11151 | −0.938154 | −0.469077 | − | 0.883157i | \(-0.655413\pi\) | ||||
−0.469077 | + | 0.883157i | \(0.655413\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.31690i | − | 1.47464i | −0.675543 | − | 0.737321i | \(-0.736091\pi\) | ||
0.675543 | − | 0.737321i | \(-0.263909\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.78803 | − | 1.34274i | 0.461667 | − | 0.346694i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.37821i | 1.30441i | 0.758044 | + | 0.652203i | \(0.226155\pi\) | ||||
−0.758044 | + | 0.652203i | \(0.773845\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.478140 | 0.109693 | 0.0548464 | − | 0.998495i | \(-0.482533\pi\) | ||||
0.0548464 | + | 0.998495i | \(0.482533\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.521655 | 0.113834 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 9.04648i | − | 1.88632i | −0.332336 | − | 0.943161i | \(-0.607837\pi\) | ||
0.332336 | − | 0.943161i | \(-0.392163\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.39410 | + | 4.80172i | −0.278820 | + | 0.960343i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.80917 | 0.707345 | 0.353672 | − | 0.935369i | \(-0.384933\pi\) | ||||
0.353672 | + | 0.935369i | \(0.384933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.77664 | 0.678305 | 0.339153 | − | 0.940731i | \(-0.389860\pi\) | ||||
0.339153 | + | 0.940731i | \(0.389860\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.11151i | 0.541644i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.932734 | + | 0.700447i | −0.157661 | + | 0.118397i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.87811i | 0.966356i | 0.875522 | + | 0.483178i | \(0.160518\pi\) | ||||
−0.875522 | + | 0.483178i | \(0.839482\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.31690 | −0.851385 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.50011 | 0.858973 | 0.429486 | − | 0.903073i | \(-0.358695\pi\) | ||||
0.429486 | + | 0.903073i | \(0.358695\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.92028i | 0.445339i | 0.974894 | + | 0.222670i | \(0.0714771\pi\) | ||||
−0.974894 | + | 0.222670i | \(0.928523\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.34274 | − | 1.78803i | −0.200164 | − | 0.266544i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.7573i | − | 1.71497i | −0.514505 | − | 0.857487i | \(-0.672024\pi\) | ||
0.514505 | − | 0.857487i | \(-0.327976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.72788 | 0.961125 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.37821 | 0.753099 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 13.8500i | − | 1.90244i | −0.308508 | − | 0.951222i | \(-0.599830\pi\) | ||
0.308508 | − | 0.951222i | \(-0.400170\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.17794 | − | 5.56346i | −0.563354 | − | 0.750177i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.478140i | − | 0.0633312i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.17583 | −0.283269 | −0.141635 | − | 0.989919i | \(-0.545236\pi\) | ||||
−0.141635 | + | 0.989919i | \(0.545236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.47318 | −0.956842 | −0.478421 | − | 0.878131i | \(-0.658791\pi\) | ||||
−0.478421 | + | 0.878131i | \(0.658791\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.521655i | − | 0.0657223i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.50677 | − | 7.13921i | 1.17917 | − | 0.885510i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.04648 | −1.08907 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.15816 | −0.493482 | −0.246741 | − | 0.969081i | \(-0.579360\pi\) | ||||
−0.246741 | + | 0.969081i | \(0.579360\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.31980i | − | 0.973759i | −0.873469 | − | 0.486879i | \(-0.838135\pi\) | ||
0.873469 | − | 0.486879i | \(-0.161865\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.80172 | + | 1.39410i | 0.554455 | + | 0.160977i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.62313i | − | 0.184973i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.27946 | 0.706494 | 0.353247 | − | 0.935530i | \(-0.385077\pi\) | ||||
0.353247 | + | 0.935530i | \(0.385077\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.47106i | − | 0.600527i | −0.953856 | − | 0.300264i | \(-0.902925\pi\) | ||
0.953856 | − | 0.300264i | \(-0.0970746\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.61639 | + | 7.22153i | −1.04304 | + | 0.783285i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.80917i | − | 0.408386i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.7914 | 1.56789 | 0.783944 | − | 0.620832i | \(-0.213205\pi\) | ||||
0.783944 | + | 0.620832i | \(0.213205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.77358 | 0.290751 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 3.77664i | − | 0.391620i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.642017 | + | 0.854928i | 0.0658696 | + | 0.0877138i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.8652i | 1.91547i | 0.287653 | + | 0.957735i | \(0.407125\pi\) | ||||
−0.287653 | + | 0.957735i | \(0.592875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.11151 | 0.312718 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.9616 | 1.09072 | 0.545361 | − | 0.838201i | \(-0.316393\pi\) | ||||
0.545361 | + | 0.838201i | \(0.316393\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.1101i | − | 1.29178i | −0.763431 | − | 0.645890i | \(-0.776487\pi\) | ||
0.763431 | − | 0.645890i | \(-0.223513\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.700447 | + | 0.932734i | 0.0683566 | + | 0.0910255i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.9550i | 1.34908i | 0.738239 | + | 0.674539i | \(0.235658\pi\) | ||||
−0.738239 | + | 0.674539i | \(0.764342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.26791 | 0.887705 | 0.443853 | − | 0.896100i | \(-0.353611\pi\) | ||||
0.443853 | + | 0.896100i | \(0.353611\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.87811 | 0.557926 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.92649i | − | 0.933805i | −0.884309 | − | 0.466903i | \(-0.845370\pi\) | ||
0.884309 | − | 0.466903i | \(-0.154630\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.1754 | − | 12.1471i | 1.50836 | − | 1.13272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.31690i | 0.491547i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.80557 | −0.257186 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.31853 | −0.119867 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.50011i | − | 0.495928i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4575 | + | 3.95477i | −0.935349 | + | 0.353725i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.53959i | 0.580295i | 0.956982 | + | 0.290147i | \(0.0937044\pi\) | ||||
−0.956982 | + | 0.290147i | \(0.906296\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.92028 | 0.257117 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.36980 | 0.818643 | 0.409322 | − | 0.912390i | \(-0.365765\pi\) | ||||
0.409322 | + | 0.912390i | \(0.365765\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.249424i | 0.0216278i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.78803 | + | 1.34274i | −0.153889 | + | 0.115565i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 19.3515i | − | 1.65331i | −0.562711 | − | 0.826654i | \(-0.690241\pi\) | ||
0.562711 | − | 0.826654i | \(-0.309759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0859 | 1.70367 | 0.851834 | − | 0.523812i | \(-0.175491\pi\) | ||||
0.851834 | + | 0.523812i | \(0.175491\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.7573 | −0.990141 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.5436i | 1.38344i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.11472 | + | 6.81090i | 0.424754 | + | 0.565615i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 6.72788i | − | 0.554906i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.78079 | −0.719350 | −0.359675 | − | 0.933078i | \(-0.617113\pi\) | ||||
−0.359675 | + | 0.933078i | \(0.617113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.86906 | 0.396238 | 0.198119 | − | 0.980178i | \(-0.436517\pi\) | ||||
0.198119 | + | 0.980178i | \(0.436517\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 5.37821i | − | 0.434802i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.07105 | + | 6.75275i | 0.407316 | + | 0.542394i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.22949i | − | 0.656785i | −0.944541 | − | 0.328393i | \(-0.893493\pi\) | ||
0.944541 | − | 0.328393i | \(-0.106507\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.8500 | −1.09838 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.71914 | 0.371920 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.02693i | 0.158761i | 0.996844 | + | 0.0793806i | \(0.0252942\pi\) | ||||
−0.996844 | + | 0.0793806i | \(0.974706\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.56346 | + | 4.17794i | −0.433115 | + | 0.325252i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 15.5470i | − | 1.20307i | −0.798848 | − | 0.601533i | \(-0.794557\pi\) | ||
0.798848 | − | 0.601533i | \(-0.205443\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.2694 | −1.17457 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.478140 | −0.0365643 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.3736i | 1.39692i | 0.715650 | + | 0.698459i | \(0.246131\pi\) | ||||
−0.715650 | + | 0.698459i | \(0.753869\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50484 | − | 0.727238i | −0.189348 | − | 0.0549741i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.17583i | 0.163546i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.2319 | 1.28797 | 0.643986 | − | 0.765037i | \(-0.277279\pi\) | ||||
0.643986 | + | 0.765037i | \(0.277279\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.1646 | 1.42449 | 0.712246 | − | 0.701930i | \(-0.247678\pi\) | ||||
0.712246 | + | 0.701930i | \(0.247678\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.47318i | 0.552433i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.5102 | + | 7.89278i | −0.772728 | + | 0.580289i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 16.7343i | − | 1.22373i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.521655 | −0.0379448 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8740 | −0.786814 | −0.393407 | − | 0.919365i | \(-0.628704\pi\) | ||||
−0.393407 | + | 0.919365i | \(0.628704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 0.422686i | − | 0.0304256i | −0.999884 | − | 0.0152128i | \(-0.995157\pi\) | ||
0.999884 | − | 0.0152128i | \(-0.00484257\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.13921 | − | 9.50677i | −0.511249 | − | 0.680794i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.02213i | − | 0.642800i | −0.946944 | − | 0.321400i | \(-0.895847\pi\) | ||
0.946944 | − | 0.321400i | \(-0.104153\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.32112 | 0.164540 | 0.0822698 | − | 0.996610i | \(-0.473783\pi\) | ||||
0.0822698 | + | 0.996610i | \(0.473783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.98707i | 0.139465i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.38521 | + | 9.83436i | 0.515806 | + | 0.686861i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.04648i | 0.628774i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.48773 | −0.102909 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.63198 | 0.663093 | 0.331546 | − | 0.943439i | \(-0.392430\pi\) | ||||
0.331546 | + | 0.943439i | \(0.392430\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.15816i | 0.284912i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.22155 | + | 3.92118i | −0.356107 | + | 0.267422i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.97010i | 0.133739i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.31980 | −0.562200 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.5954 | 1.92353 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.1438i | − | 0.947141i | −0.880756 | − | 0.473570i | \(-0.842965\pi\) | ||
0.880756 | − | 0.473570i | \(-0.157035\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.39410 | − | 4.80172i | 0.0929400 | − | 0.320114i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 9.52142i | − | 0.631959i | −0.948766 | − | 0.315979i | \(-0.897667\pi\) | ||
0.948766 | − | 0.315979i | \(-0.102333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5476 | −0.961334 | −0.480667 | − | 0.876903i | \(-0.659605\pi\) | ||||
−0.480667 | + | 0.876903i | \(0.659605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.62313 | −0.106794 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.7819i | 1.55800i | 0.627021 | + | 0.779002i | \(0.284274\pi\) | ||||
−0.627021 | + | 0.779002i | \(0.715726\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.0224 | − | 15.7870i | 1.37135 | − | 1.02983i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.27946i | − | 0.407895i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.68266 | 0.367581 | 0.183790 | − | 0.982965i | \(-0.441163\pi\) | ||||
0.183790 | + | 0.982965i | \(0.441163\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.38321 | 0.346763 | 0.173382 | − | 0.984855i | \(-0.444531\pi\) | ||||
0.173382 | + | 0.984855i | \(0.444531\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.03379 | + | 12.0296i | 0.577148 | + | 0.768546i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.54222i | − | 0.161758i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.47106 | −0.346715 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.4504 | −0.975220 | −0.487610 | − | 0.873061i | \(-0.662131\pi\) | ||||
−0.487610 | + | 0.873061i | \(0.662131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.1482i | 1.76966i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.22153 | + | 9.61639i | 0.452230 | + | 0.602202i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4600i | 0.714853i | 0.933941 | + | 0.357426i | \(0.116346\pi\) | ||||
−0.933941 | + | 0.357426i | \(0.883654\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.06635 | −0.190533 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.80917 | −0.235782 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 30.5405i | − | 1.88321i | −0.336719 | − | 0.941605i | \(-0.609317\pi\) | ||
0.336719 | − | 0.941605i | \(-0.390683\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.7642 | − | 18.5969i | 1.52125 | − | 1.14240i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 14.7914i | − | 0.905220i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.29684 | −0.444896 | −0.222448 | − | 0.974945i | \(-0.571405\pi\) | ||||
−0.222448 | + | 0.974945i | \(0.571405\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.6066 | −0.765798 | −0.382899 | − | 0.923790i | \(-0.625074\pi\) | ||||
−0.382899 | + | 0.923790i | \(0.625074\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.77358i | − | 0.167865i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.33775 | − | 14.9406i | 0.261576 | − | 0.900950i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.6688i | 1.06162i | 0.847492 | + | 0.530809i | \(0.178112\pi\) | ||||
−0.847492 | + | 0.530809i | \(0.821888\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.77664 | −0.226102 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.79446 | 0.166704 | 0.0833518 | − | 0.996520i | \(-0.473437\pi\) | ||||
0.0833518 | + | 0.996520i | \(0.473437\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.406056i | − | 0.0241375i | −0.999927 | − | 0.0120687i | \(-0.996158\pi\) | ||
0.999927 | − | 0.0120687i | \(-0.00384170\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.854928 | − | 0.642017i | 0.0506416 | − | 0.0380298i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.86916i | 0.169361i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9251 | −0.701476 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.8652 | 1.10590 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 10.9198i | − | 0.637944i | −0.947764 | − | 0.318972i | \(-0.896662\pi\) | ||
0.947764 | − | 0.318972i | \(-0.103338\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.92158 | − | 3.89045i | −0.170101 | − | 0.226511i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.11151i | − | 0.180548i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −48.0992 | −2.78165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.52338 | −0.0878062 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 10.9616i | − | 0.629728i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.0345 | − | 13.3623i | −0.574576 | − | 0.765121i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.14641i | 0.122502i | 0.998122 | + | 0.0612512i | \(0.0195091\pi\) | ||||
−0.998122 | + | 0.0612512i | \(0.980491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.1101 | −0.745809 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.7310 | −1.40237 | −0.701184 | − | 0.712981i | \(-0.747345\pi\) | ||||
−0.701184 | + | 0.712981i | \(0.747345\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.4415i | − | 1.15542i | −0.816242 | − | 0.577711i | \(-0.803946\pi\) | ||
0.816242 | − | 0.577711i | \(-0.196054\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.932734 | − | 0.700447i | 0.0525536 | − | 0.0394657i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.1454i | − | 0.962984i | −0.876451 | − | 0.481492i | \(-0.840095\pi\) | ||
0.876451 | − | 0.481492i | \(-0.159905\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.8522 | −0.663598 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.9550 | 0.778891 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.57153i | 0.143084i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.5302 | + | 7.41228i | 1.41616 | + | 0.411159i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 9.26791i | − | 0.512517i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.13324 | 0.338136 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.2384 | −0.892544 | −0.446272 | − | 0.894897i | \(-0.647249\pi\) | ||||
−0.446272 | + | 0.894897i | \(0.647249\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.87811i | − | 0.322119i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.78803 | − | 1.34274i | 0.0976905 | − | 0.0733617i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 12.1370i | − | 0.661142i | −0.943781 | − | 0.330571i | \(-0.892759\pi\) | ||
0.943781 | − | 0.330571i | \(-0.107241\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.92649 | −0.539133 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.7510 | −0.636355 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.16121i | 0.386669i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.1471 | − | 16.1754i | −0.653976 | − | 0.870853i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 9.65658i | − | 0.518392i | −0.965825 | − | 0.259196i | \(-0.916542\pi\) | ||
0.965825 | − | 0.259196i | \(-0.0834576\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.00457 | −0.428475 | −0.214237 | − | 0.976782i | \(-0.568727\pi\) | ||||
−0.214237 | + | 0.976782i | \(0.568727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.31690 | 0.283795 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5108i | 0.825556i | 0.910832 | + | 0.412778i | \(0.135442\pi\) | ||||
−0.910832 | + | 0.412778i | \(0.864558\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.58332 | − | 7.43491i | −0.296332 | − | 0.394604i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.80557i | 0.148486i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.7425 | 0.672523 | 0.336261 | − | 0.941769i | \(-0.390837\pi\) | ||||
0.336261 | + | 0.941769i | \(0.390837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7714 | −0.987967 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.31853i | 0.0692051i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.8760 | − | 11.1713i | 0.778648 | − | 0.584734i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.40243i | − | 0.125406i | −0.998032 | − | 0.0627029i | \(-0.980028\pi\) | ||
0.998032 | − | 0.0627029i | \(-0.0199720\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.50011 | −0.286324 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.22492 | 0.375099 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.44244i | − | 0.230021i | −0.993364 | − | 0.115010i | \(-0.963310\pi\) | ||
0.993364 | − | 0.115010i | \(-0.0366901\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.95477 | + | 10.4575i | 0.204223 | + | 0.540024i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 20.2530i | − | 1.04308i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.3897 | 0.585047 | 0.292524 | − | 0.956258i | \(-0.405505\pi\) | ||||
0.292524 | + | 0.956258i | \(0.405505\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.53959 | 0.335033 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 37.1019i | − | 1.89582i | −0.318537 | − | 0.947910i | \(-0.603192\pi\) | ||
0.318537 | − | 0.947910i | \(-0.396808\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.90221 | − | 2.17944i | 0.147910 | − | 0.111075i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2.92028i | − | 0.148446i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.3456 | −0.625946 | −0.312973 | − | 0.949762i | \(-0.601325\pi\) | ||||
−0.312973 | + | 0.949762i | \(0.601325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 48.6538 | 2.46053 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 9.36980i | − | 0.472644i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.43168 | + | 11.2279i | 0.424244 | + | 0.564935i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5577i | 0.630255i | 0.949049 | + | 0.315128i | \(0.102047\pi\) | ||||
−0.949049 | + | 0.315128i | \(0.897953\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.249424 | 0.0124868 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.3287 | 1.11504 | 0.557521 | − | 0.830163i | \(-0.311753\pi\) | ||||
0.557521 | + | 0.830163i | \(0.311753\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 20.0800i | − | 1.00026i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.34274 | + | 1.78803i | 0.0667213 | + | 0.0888479i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.2898i | − | 0.906591i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.45818 | 0.220443 | 0.110221 | − | 0.993907i | \(-0.464844\pi\) | ||||
0.110221 | + | 0.993907i | \(0.464844\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.3515 | −0.954538 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.13503i | − | 0.0558513i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.78242 | − | 7.34621i | 0.480200 | − | 0.360611i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 20.0859i | − | 0.983613i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.0503944 | −0.00246193 | −0.00123096 | − | 0.999999i | \(-0.500392\pi\) | ||||
−0.00123096 | + | 0.999999i | \(0.500392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.0091 | 1.02392 | 0.511960 | − | 0.859009i | \(-0.328920\pi\) | ||||
0.511960 | + | 0.859009i | \(0.328920\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.7573i | 0.571658i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.8246 | − | 7.49775i | −1.25268 | − | 0.363694i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.89842i | − | 0.188658i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.5436 | 0.798730 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.8705 | −1.58332 | −0.791659 | − | 0.610963i | \(-0.790782\pi\) | ||||
−0.791659 | + | 0.610963i | \(0.790782\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.1919i | 1.30676i | 0.757030 | + | 0.653380i | \(0.226649\pi\) | ||||
−0.757030 | + | 0.653380i | \(0.773351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.81090 | − | 5.11472i | 0.326558 | − | 0.245232i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.32548i | − | 0.206916i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.84487 | −0.374415 | −0.187208 | − | 0.982320i | \(-0.559944\pi\) | ||||
−0.187208 | + | 0.982320i | \(0.559944\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.72788 | −0.320375 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.0129i | 0.903331i | 0.892187 | + | 0.451666i | \(0.149170\pi\) | ||||
−0.892187 | + | 0.451666i | \(0.850830\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.8610 | + | 26.4475i | 0.941503 | + | 1.25373i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.78079i | 0.415317i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.40771 | −0.255206 | −0.127603 | − | 0.991825i | \(-0.540728\pi\) | ||||
−0.127603 | + | 0.991825i | \(0.540728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.1136 | −0.805849 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 4.86906i | − | 0.228768i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.72420 | + | 4.95925i | 0.174593 | + | 0.232493i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.9620i | 1.68223i | 0.540854 | + | 0.841117i | \(0.318101\pi\) | ||||
−0.540854 | + | 0.841117i | \(0.681899\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.37821 | −0.251033 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3829 | 0.483578 | 0.241789 | − | 0.970329i | \(-0.422266\pi\) | ||||
0.241789 | + | 0.970329i | \(0.422266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.5835i | − | 1.04955i | −0.851242 | − | 0.524773i | \(-0.824150\pi\) | ||
0.851242 | − | 0.524773i | \(-0.175850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.75275 | − | 5.07105i | 0.313151 | − | 0.235164i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 21.7035i | − | 1.00432i | −0.864775 | − | 0.502159i | \(-0.832539\pi\) | ||
0.864775 | − | 0.502159i | \(-0.167461\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.521655 | 0.0240878 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.22949 | −0.379195 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.08648i | − | 0.417797i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.666574 | + | 2.29589i | −0.0305845 | + | 0.105343i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.8500i | 0.634148i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.9860 | 1.05026 | 0.525129 | − | 0.851023i | \(-0.324017\pi\) | ||||
0.525129 | + | 0.851023i | \(0.324017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.2533 | 1.42503 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.71914i | − | 0.214728i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.7315 | + | 25.3310i | −1.53167 | + | 1.15022i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.0187i | 1.63216i | 0.577937 | + | 0.816082i | \(0.303858\pi\) | ||||
−0.577937 | + | 0.816082i | \(0.696142\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.02693 | 0.0916608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.6698 | 0.797425 | 0.398713 | − | 0.917076i | \(-0.369457\pi\) | ||||
0.398713 | + | 0.917076i | \(0.369457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.4865i | 0.922665i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.17794 | + | 5.56346i | 0.187785 | + | 0.250059i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.16912i | − | 0.0972984i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.6980 | −0.523676 | −0.261838 | − | 0.965112i | \(-0.584329\pi\) | ||||
−0.261838 | + | 0.965112i | \(0.584329\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.5470 | −0.694590 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 37.6247i | − | 1.67760i | −0.544439 | − | 0.838800i | \(-0.683257\pi\) | ||
0.544439 | − | 0.838800i | \(-0.316743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.7186 | + | 19.5997i | 0.654969 | + | 0.872175i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.2694i | 0.678138i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.8119 | −1.14409 | −0.572046 | − | 0.820222i | \(-0.693850\pi\) | ||||
−0.572046 | + | 0.820222i | \(0.693850\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.34006 | 0.191993 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.478140i | 0.0211104i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.4413 | − | 17.6035i | 1.03295 | − | 0.775703i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.5828i | 1.60891i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.3736 | 0.806511 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.9851 | −0.525077 | −0.262539 | − | 0.964921i | \(-0.584560\pi\) | ||||
−0.262539 | + | 0.964921i | \(0.584560\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.9557i | 0.697692i | 0.937180 | + | 0.348846i | \(0.113426\pi\) | ||||
−0.937180 | + | 0.348846i | \(0.886574\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.727238 | + | 2.50484i | −0.0317393 | + | 0.109320i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.3116i | 0.884785i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −58.8388 | −2.55821 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.17583 | 0.0944231 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 29.2435i | − | 1.26668i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.9519 | + | 18.7379i | −1.07876 | + | 0.810110i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 17.2319i | − | 0.743611i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.9338 | −0.901684 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.6119 | 0.843180 | 0.421590 | − | 0.906787i | \(-0.361472\pi\) | ||||
0.421590 | + | 0.906787i | \(0.361472\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 19.1646i | − | 0.822431i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.4444 | + | 16.5713i | 0.533059 | + | 0.709837i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.4397i | 1.25875i | 0.777101 | + | 0.629376i | \(0.216689\pi\) | ||||
−0.777101 | + | 0.629376i | \(0.783311\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.47318 | 0.318947 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.82131 | 0.0775906 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.27571i | 0.139297i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.89278 | + | 10.5102i | 0.335030 | + | 0.446135i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.4467i | 1.12058i | 0.828296 | + | 0.560291i | \(0.189311\pi\) | ||||
−0.828296 | + | 0.560291i | \(0.810689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.5268 | 0.656716 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.7343 | −0.706523 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.06240i | 0.297645i | 0.988864 | + | 0.148822i | \(0.0475483\pi\) | ||||
−0.988864 | + | 0.148822i | \(0.952452\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.7489 | − | 13.3287i | 0.746700 | − | 0.560742i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.521655i | 0.0219074i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.9071 | −1.29569 | −0.647846 | − | 0.761772i | \(-0.724330\pi\) | ||||
−0.647846 | + | 0.761772i | \(0.724330\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.05811 | 0.169827 | 0.0849133 | − | 0.996388i | \(-0.472939\pi\) | ||||
0.0849133 | + | 0.996388i | \(0.472939\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.8740i | 0.454267i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 43.4386 | + | 12.6117i | 1.81152 | + | 0.525944i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.4193i | 0.641912i | 0.947094 | + | 0.320956i | \(0.104004\pi\) | ||||
−0.947094 | + | 0.320956i | \(0.895996\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.422686 | −0.0175662 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.85401 | 0.118404 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.0943i | 1.78479i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.50677 | + | 7.13921i | −0.393057 | + | 0.295170i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.6593i | 0.563778i | 0.959447 | + | 0.281889i | \(0.0909610\pi\) | ||||
−0.959447 | + | 0.281889i | \(0.909039\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.80576 | 0.0744052 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.02213 | −0.371121 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.36005i | 0.137981i | 0.997617 | + | 0.0689903i | \(0.0219778\pi\) | ||||
−0.997617 | + | 0.0689903i | \(0.978022\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.76715 | − | 5.01643i | −0.154438 | − | 0.205654i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 2.32112i | − | 0.0949969i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.0750 | 1.10625 | 0.553126 | − | 0.833097i | \(-0.313435\pi\) | ||||
0.553126 | + | 0.833097i | \(0.313435\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.20937 | −0.212495 | −0.106247 | − | 0.994340i | \(-0.533884\pi\) | ||||
−0.106247 | + | 0.994340i | \(0.533884\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.77045 | − | 2.35758i | −0.0719789 | − | 0.0958491i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 10.1446i | − | 0.411755i | −0.978578 | − | 0.205877i | \(-0.933995\pi\) | ||
0.978578 | − | 0.205877i | \(-0.0660048\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.98707 | 0.0805201 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −62.5122 | −2.52897 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 44.0310i | − | 1.77840i | −0.457523 | − | 0.889198i | \(-0.651263\pi\) | ||
0.457523 | − | 0.889198i | \(-0.348737\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.83436 | − | 7.38521i | 0.396559 | − | 0.297801i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.02385i | 0.363286i | 0.983364 | + | 0.181643i | \(0.0581416\pi\) | ||||
−0.983364 | + | 0.181643i | \(0.941858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.17585 | 0.288422 | 0.144211 | − | 0.989547i | \(-0.453936\pi\) | ||||
0.144211 | + | 0.989547i | \(0.453936\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.04648 | 0.363023 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.71602i | 0.309136i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.1130 | − | 13.3881i | −0.844519 | − | 0.535526i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.48773i | 0.0594144i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.6137 | −1.26052 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.2028 | 1.71988 | 0.859939 | − | 0.510397i | \(-0.170502\pi\) | ||||
0.859939 | + | 0.510397i | \(0.170502\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 9.63198i | − | 0.382837i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.6930 | + | 8.78097i | −0.464022 | + | 0.348462i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 35.7714i | − | 1.41732i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.15816 | 0.164494 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.226417 | −0.00894293 | −0.00447146 | − | 0.999990i | \(-0.501423\pi\) | ||||
−0.00447146 | + | 0.999990i | \(0.501423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.9852i | 0.867013i | 0.901150 | + | 0.433507i | \(0.142724\pi\) | ||||
−0.901150 | + | 0.433507i | \(0.857276\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.92118 | + | 5.22155i | 0.154396 | + | 0.205598i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 26.8931i | − | 1.05728i | −0.848847 | − | 0.528639i | \(-0.822702\pi\) | ||
0.848847 | − | 0.528639i | \(-0.177298\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.77012 | 0.265750 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.97010 | 0.0772144 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.0902i | 1.06012i | 0.847960 | + | 0.530060i | \(0.177831\pi\) | ||||
−0.847960 | + | 0.530060i | \(0.822169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.5812 | + | 16.7535i | 0.491588 | + | 0.654613i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.31980i | 0.324586i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.7849 | −1.58875 | −0.794376 | − | 0.607426i | \(-0.792202\pi\) | ||||
−0.794376 | + | 0.607426i | \(0.792202\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.4312 | 0.716889 | 0.358445 | − | 0.933551i | \(-0.383307\pi\) | ||||
0.358445 | + | 0.933551i | \(0.383307\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 28.5954i | − | 1.11055i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.445977 | + | 0.334911i | −0.0172943 | + | 0.0129873i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 34.4596i | − | 1.33428i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.1438 | −0.546832 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.2528 | 0.897665 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.6813i | 1.52960i | 0.644266 | + | 0.764802i | \(0.277163\pi\) | ||||
−0.644266 | + | 0.764802i | \(0.722837\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.80172 | − | 1.39410i | −0.184818 | − | 0.0536589i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.8173i | 1.26127i | 0.776079 | + | 0.630635i | \(0.217206\pi\) | ||||
−0.776079 | + | 0.630635i | \(0.782794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.84111 | −0.377667 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.52142 | −0.364862 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.83828i | 0.376451i | 0.982126 | + | 0.188226i | \(0.0602736\pi\) | ||||
−0.982126 | + | 0.188226i | \(0.939726\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.6010 | − | 25.9840i | 1.32204 | − | 0.992797i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.5476i | 0.555027i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −73.6390 | −2.80542 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.86946 | 0.337410 | 0.168705 | − | 0.985667i | \(-0.446041\pi\) | ||||
0.168705 | + | 0.985667i | \(0.446041\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.62313i | 0.0616577i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.9702 | + | 35.9143i | 1.02304 | + | 1.36231i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.5807i | 1.12045i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.7819 | 0.899514 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.8271 | −1.84418 | −0.922088 | − | 0.386981i | \(-0.873518\pi\) | ||||
−0.922088 | + | 0.386981i | \(0.873518\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.81056i | 0.106002i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.7870 | − | 21.0224i | −0.594571 | − | 0.791748i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.71818i | 0.215054i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.5117 | −0.845445 | −0.422723 | − | 0.906259i | \(-0.638926\pi\) | ||||
−0.422723 | + | 0.906259i | \(0.638926\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.27946 | −0.235498 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 34.1653i | − | 1.27950i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.5804 | + | 22.2137i | −1.10624 | + | 0.830745i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 5.68266i | − | 0.212223i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.9316 | −0.556855 | −0.278427 | − | 0.960457i | \(-0.589813\pi\) | ||||
−0.278427 | + | 0.960457i | \(0.589813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.83896 | 0.254696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 5.38321i | − | 0.200204i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.31036 | + | 18.2905i | −0.197222 | + | 0.679294i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 37.4214i | − | 1.38788i | −0.720031 | − | 0.693942i | \(-0.755873\pi\) | ||
0.720031 | − | 0.693942i | \(-0.244127\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.7059 | −0.580903 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 29.4317i | − | 1.08709i | −0.839381 | − | 0.543543i | \(-0.817083\pi\) | ||
0.839381 | − | 0.543543i | \(-0.182917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.0296 | − | 9.03379i | 0.443720 | − | 0.333216i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.11151i | 0.114614i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.3247 | −0.674084 | −0.337042 | − | 0.941490i | \(-0.609426\pi\) | ||||
−0.337042 | + | 0.941490i | \(0.609426\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.54222 | −0.0933908 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.6195i | 0.609710i | 0.952399 | + | 0.304855i | \(0.0986079\pi\) | ||||
−0.952399 | + | 0.304855i | \(0.901392\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.7903 | − | 15.7003i | −0.431964 | − | 0.575215i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.47106i | 0.200176i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.27968 | −0.265994 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.409716 | 0.0149507 | 0.00747537 | − | 0.999972i | \(-0.497620\pi\) | ||||
0.00747537 | + | 0.999972i | \(0.497620\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.4504i | 0.563044i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.53788 | + | 8.70602i | 0.237938 | + | 0.316845i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 14.2090i | − | 0.516434i | −0.966087 | − | 0.258217i | \(-0.916865\pi\) | ||
0.966087 | − | 0.258217i | \(-0.0831350\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.1482 | 1.02171 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.4596 | −1.75666 | −0.878330 | − | 0.478055i | \(-0.841342\pi\) | ||||
−0.878330 | + | 0.478055i | \(0.841342\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.83465i | 0.175026i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.61639 | − | 7.22153i | 0.347681 | − | 0.261095i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.5687i | 0.417721i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.46238 | 0.124857 | 0.0624283 | − | 0.998049i | \(-0.480116\pi\) | ||||
0.0624283 | + | 0.998049i | \(0.480116\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4600 | 0.412721 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.2434i | 1.05181i | 0.850542 | + | 0.525907i | \(0.176274\pi\) | ||||
−0.850542 | + | 0.525907i | \(0.823726\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.26502 | + | 18.1344i | −0.189125 | + | 0.651406i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.06635i | 0.110005i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.62982 | 0.0942231 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.9381 | 0.462963 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.80917i | 0.136129i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.7146 | − | 11.0501i | 0.525186 | − | 0.394394i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.1776i | 1.04007i | 0.854145 | + | 0.520035i | \(0.174081\pi\) | ||||
−0.854145 | + | 0.520035i | \(0.825919\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.5405 | −1.08727 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.17820 | 0.184116 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.7341i | 1.41100i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.5969 | − | 24.7642i | −0.659566 | − | 0.878296i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.1620i | 1.77683i | 0.459041 | + | 0.888415i | \(0.348193\pi\) | ||||
−0.459041 | + | 0.888415i | \(0.651807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 63.2330 | 2.23702 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.7914 | −0.522629 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.8871i | 0.913536i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.33658 | + | 8.43796i | 0.223335 | + | 0.297399i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.29684i | 0.256861i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.9515 | 1.12336 | 0.561678 | − | 0.827356i | \(-0.310156\pi\) | ||||
0.561678 | + | 0.827356i | \(0.310156\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.0335 | 1.79203 | 0.896014 | − | 0.444026i | \(-0.146450\pi\) | ||||
0.896014 | + | 0.444026i | \(0.146450\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.6066i | 0.442134i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.62420 | + | 2.72164i | −0.126950 | + | 0.0953347i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.39630i | 0.0488505i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.77358 | −0.0969169 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.40156 | −0.328117 | −0.164058 | − | 0.986451i | \(-0.552459\pi\) | ||||
−0.164058 | + | 0.986451i | \(0.552459\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.0765i | 1.71070i | 0.518050 | + | 0.855350i | \(0.326658\pi\) | ||||
−0.518050 | + | 0.855350i | \(0.673342\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.9406 | − | 4.33775i | −0.520164 | − | 0.151021i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25.9885i | − | 0.903709i | −0.892092 | − | 0.451854i | \(-0.850763\pi\) | ||
0.892092 | − | 0.451854i | \(-0.149237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.3498 | 1.26248 | 0.631240 | − | 0.775587i | \(-0.282546\pi\) | ||||
0.631240 | + | 0.775587i | \(0.282546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.6688 | 0.612925 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.1839i | 1.25370i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.7986 | − | 20.8756i | 0.962009 | − | 0.722431i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.77664i | 0.130540i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.3487 | −1.04775 | −0.523876 | − | 0.851794i | \(-0.675515\pi\) | ||||
−0.523876 | + | 0.851794i | \(0.675515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4902 | −0.499664 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 2.79446i | − | 0.0962463i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.5028 | − | 27.3021i | −0.705319 | − | 0.939222i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.687819i | − | 0.0236338i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.406056 | −0.0139358 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.1762 | 1.82286 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 22.2283i | − | 0.761084i | −0.924764 | − | 0.380542i | \(-0.875738\pi\) | ||
0.924764 | − | 0.380542i | \(-0.124262\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.642017 | − | 0.854928i | −0.0219565 | − | 0.0292379i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 50.9178i | − | 1.73932i | −0.493652 | − | 0.869659i | \(-0.664338\pi\) | ||
0.493652 | − | 0.869659i | \(-0.335662\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.6193 | −0.635284 | −0.317642 | − | 0.948211i | \(-0.602891\pi\) | ||||
−0.317642 | + | 0.948211i | \(0.602891\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.86916 | 0.0977806 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.8014i | 1.35485i | 0.735590 | + | 0.677427i | \(0.236905\pi\) | ||||
−0.735590 | + | 0.677427i | \(0.763095\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.8525 | + | 24.6710i | −1.11702 | + | 0.838838i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.9251i | 0.404997i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.5386 | −0.662801 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.31690 | −0.180156 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 18.8652i | − | 0.638490i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.06302 | − | 5.45522i | −0.0697429 | − | 0.184420i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.9132i | 1.44908i | 0.689235 | + | 0.724538i | \(0.257947\pi\) | ||||
−0.689235 | + | 0.724538i | \(0.742053\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.9198 | −0.368317 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.2117 | 1.22000 | 0.610002 | − | 0.792400i | \(-0.291169\pi\) | ||||
0.610002 | + | 0.792400i | \(0.291169\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 43.6256i | − | 1.46812i | −0.679085 | − | 0.734060i | \(-0.737623\pi\) | ||
0.679085 | − | 0.734060i | \(-0.262377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.89045 | + | 2.92158i | −0.130776 | + | 0.0982077i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.41060i | 0.181670i | 0.995866 | + | 0.0908351i | \(0.0289536\pi\) | ||||
−0.995866 | + | 0.0908351i | \(0.971046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.41141 | −0.114415 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.11151 | −0.104239 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.62162i | − | 0.188120i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.1380 | + | 30.8111i | 0.773416 | + | 1.02990i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 48.0992i | 1.60599i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.3859 | 0.479796 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 74.4881 | 2.48156 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.52338i | 0.0506949i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.7330 | + | 34.2668i | 0.855395 | + | 1.13907i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.2611i | 0.506736i | 0.967370 | + | 0.253368i | \(0.0815383\pi\) | ||||
−0.967370 | + | 0.253368i | \(0.918462\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.9616 | −0.363574 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.2436 | −0.935752 | −0.467876 | − | 0.883794i | \(-0.654981\pi\) | ||||
−0.467876 | + | 0.883794i | \(0.654981\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.0232i | 0.563387i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.3623 | + | 10.0345i | −0.441743 | + | 0.331731i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.88780i | 0.161409i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.8874 | −0.557063 | −0.278531 | − | 0.960427i | \(-0.589848\pi\) | ||||
−0.278531 | + | 0.960427i | \(0.589848\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.14641 | 0.0707267 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.1085i | 0.727710i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.2250 | − | 8.19467i | −0.928033 | − | 0.269439i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.1101i | 0.430593i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.2185 | 0.564922 | 0.282461 | − | 0.959279i | \(-0.408849\pi\) | ||||
0.282461 | + | 0.959279i | \(0.408849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.21687 | 0.105428 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.7310i | 0.809657i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.9214 | − | 22.4698i | 0.978536 | − | 0.734842i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36.4201i | − | 1.18979i | −0.803802 | − | 0.594896i | \(-0.797193\pi\) | ||
0.803802 | − | 0.594896i | \(-0.202807\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.4415 | −0.667083 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 60.5287 | 1.97318 | 0.986590 | − | 0.163220i | \(-0.0521879\pi\) | ||||
0.986590 | + | 0.163220i | \(0.0521879\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 49.7566i | − | 1.62030i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.700447 | − | 0.932734i | −0.0227855 | − | 0.0303418i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.9729i | 1.29894i | 0.760386 | + | 0.649472i | \(0.225010\pi\) | ||||
−0.760386 | + | 0.649472i | \(0.774990\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.2355 | −1.43595 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.1454 | −0.555979 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.76991i | − | 0.122119i | −0.998134 | − | 0.0610596i | \(-0.980552\pi\) | ||
0.998134 | − | 0.0610596i | \(-0.0194480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.6009 | − | 19.4430i | −0.472475 | − | 0.629161i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.8522i | 0.383129i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.0948 | 0.325978 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.7370 | −0.539902 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 13.9550i | − | 0.449693i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.755774 | − | 0.567557i | 0.0243292 | − | 0.0182703i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.5150i | 1.84956i | 0.380506 | + | 0.924778i | \(0.375750\pi\) | ||||
−0.380506 | + | 0.924778i | \(0.624250\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.57153 | 0.0826096 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.3873 | 1.36027 | 0.680137 | − | 0.733085i | \(-0.261920\pi\) | ||||
0.680137 | + | 0.733085i | \(0.261920\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.4779i | 0.335907i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.41228 | − | 25.5302i | 0.237383 | − | 0.817622i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 11.9310i | − | 0.381708i | −0.981618 | − | 0.190854i | \(-0.938874\pi\) | ||
0.981618 | − | 0.190854i | \(-0.0611257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −46.0236 | −1.47092 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.26791 | −0.295902 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.8452i | 1.01570i | 0.861445 | + | 0.507851i | \(0.169560\pi\) | ||||
−0.861445 | + | 0.507851i | \(0.830440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.1318 | − | 12.1144i | 0.514003 | − | 0.385996i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 6.13324i | − | 0.195223i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.4183 | 0.840053 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.8355 | 1.20188 | 0.600942 | − | 0.799293i | \(-0.294792\pi\) | ||||
0.600942 | + | 0.799293i | \(0.294792\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.2384i | 0.515310i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.11665 | + | 4.15022i | 0.0988046 | + | 0.131571i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.92135i | 0.314212i | 0.987582 | + | 0.157106i | \(0.0502165\pi\) | ||||
−0.987582 | + | 0.157106i | \(0.949784\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.87811 | −0.185975 |
(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 | 4020.2.g.c.1609.14 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.33 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.14 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.33 | yes | 38 | 5.4 | even | 2 | inner |