Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,4,Mod(649,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.f (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: | \(106.203438010\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.649 |
Dual form | 1800.4.f.q.649.1 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 24.0000i | 1.29588i | 0.761692 | + | 0.647939i | \(0.224369\pi\) | ||||
−0.761692 | + | 0.647939i | \(0.775631\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.0000 | 0.767483 | 0.383742 | − | 0.923440i | \(-0.374635\pi\) | ||||
0.383742 | + | 0.923440i | \(0.374635\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 74.0000i | − 1.57876i | −0.613904 | − | 0.789381i | \(-0.710402\pi\) | ||||
0.613904 | − | 0.789381i | \(-0.289598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 82.0000i | 1.16988i | 0.811077 | + | 0.584939i | \(0.198882\pi\) | ||||
−0.811077 | + | 0.584939i | \(0.801118\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −92.0000 | −1.11086 | −0.555428 | − | 0.831565i | \(-0.687445\pi\) | ||||
−0.555428 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 8.00000i | − 0.0725268i | −0.999342 | − | 0.0362634i | \(-0.988454\pi\) | ||||
0.999342 | − | 0.0362634i | \(-0.0115455\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −138.000 | −0.883654 | −0.441827 | − | 0.897100i | \(-0.645669\pi\) | ||||
−0.441827 | + | 0.897100i | \(0.645669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 80.0000 | 0.463498 | 0.231749 | − | 0.972776i | \(-0.425555\pi\) | ||||
0.231749 | + | 0.972776i | \(0.425555\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 30.0000i | − 0.133296i | −0.997777 | − | 0.0666482i | \(-0.978769\pi\) | ||||
0.997777 | − | 0.0666482i | \(-0.0212305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −282.000 | −1.07417 | −0.537085 | − | 0.843528i | \(-0.680475\pi\) | ||||
−0.537085 | + | 0.843528i | \(0.680475\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.0141859i | 0.999975 | + | 0.00709296i | \(0.00225778\pi\) | ||||
−0.999975 | + | 0.00709296i | \(0.997742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 240.000i | 0.744843i | 0.928064 | + | 0.372421i | \(0.121472\pi\) | ||||
−0.928064 | + | 0.372421i | \(0.878528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −233.000 | −0.679300 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 130.000i | 0.336922i | 0.985708 | + | 0.168461i | \(0.0538797\pi\) | ||||
−0.985708 | + | 0.168461i | \(0.946120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 596.000 | 1.31513 | 0.657564 | − | 0.753398i | \(-0.271587\pi\) | ||||
0.657564 | + | 0.753398i | \(0.271587\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −218.000 | −0.457574 | −0.228787 | − | 0.973476i | \(-0.573476\pi\) | ||||
−0.228787 | + | 0.973476i | \(0.573476\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 436.000i | 0.795013i | 0.917599 | + | 0.397507i | \(0.130124\pi\) | ||||
−0.917599 | + | 0.397507i | \(0.869876\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −856.000 | −1.43082 | −0.715412 | − | 0.698703i | \(-0.753761\pi\) | ||||
−0.715412 | + | 0.698703i | \(0.753761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 998.000i | − 1.60010i | −0.599935 | − | 0.800048i | \(-0.704807\pi\) | ||||
0.599935 | − | 0.800048i | \(-0.295193\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 672.000i | 0.994565i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32.0000 | 0.0455732 | 0.0227866 | − | 0.999740i | \(-0.492746\pi\) | ||||
0.0227866 | + | 0.999740i | \(0.492746\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1508.00i | 1.99427i | 0.0756351 | + | 0.997136i | \(0.475902\pi\) | ||||
−0.0756351 | + | 0.997136i | \(0.524098\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −246.000 | −0.292988 | −0.146494 | − | 0.989212i | \(-0.546799\pi\) | ||||
−0.146494 | + | 0.989212i | \(0.546799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1776.00 | 2.04588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 866.000i | − 0.906484i | −0.891387 | − | 0.453242i | \(-0.850267\pi\) | ||||
0.891387 | − | 0.453242i | \(-0.149733\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −270.000 | −0.266000 | −0.133000 | − | 0.991116i | \(-0.542461\pi\) | ||||
−0.133000 | + | 0.991116i | \(0.542461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1496.00i | − 1.43112i | −0.698552 | − | 0.715560i | \(-0.746172\pi\) | ||||
0.698552 | − | 0.715560i | \(-0.253828\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1692.00i | − 1.52871i | −0.644797 | − | 0.764354i | \(-0.723058\pi\) | ||||
0.644797 | − | 0.764354i | \(-0.276942\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −406.000 | −0.356768 | −0.178384 | − | 0.983961i | \(-0.557087\pi\) | ||||
−0.178384 | + | 0.983961i | \(0.557087\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 786.000i | − 0.654342i | −0.944965 | − | 0.327171i | \(-0.893905\pi\) | ||||
0.944965 | − | 0.327171i | \(-0.106095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1968.00 | −1.51602 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −547.000 | −0.410969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1744.00i | − 1.21854i | −0.792962 | − | 0.609272i | \(-0.791462\pi\) | ||||
0.792962 | − | 0.609272i | \(-0.208538\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −652.000 | −0.434851 | −0.217426 | − | 0.976077i | \(-0.569766\pi\) | ||||
−0.217426 | + | 0.976077i | \(0.569766\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2208.00i | − 1.43953i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1530.00i | 0.954137i | 0.878866 | + | 0.477068i | \(0.158301\pi\) | ||||
−0.878866 | + | 0.477068i | \(0.841699\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −516.000 | −0.314867 | −0.157434 | − | 0.987530i | \(-0.550322\pi\) | ||||
−0.157434 | + | 0.987530i | \(0.550322\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 2072.00i | − 1.21167i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1342.00 | 0.737859 | 0.368929 | − | 0.929457i | \(-0.379724\pi\) | ||||
0.368929 | + | 0.929457i | \(0.379724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −424.000 | −0.228507 | −0.114254 | − | 0.993452i | \(-0.536448\pi\) | ||||
−0.114254 | + | 0.993452i | \(0.536448\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 262.000i | − 0.133184i | −0.997780 | − | 0.0665920i | \(-0.978787\pi\) | ||||
0.997780 | − | 0.0665920i | \(-0.0212126\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 192.000 | 0.0939858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2292.00i | − 1.10137i | −0.834713 | − | 0.550685i | \(-0.814367\pi\) | ||||
0.834713 | − | 0.550685i | \(-0.185633\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1896.00i | − 0.878544i | −0.898354 | − | 0.439272i | \(-0.855236\pi\) | ||||
0.898354 | − | 0.439272i | \(-0.144764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3279.00 | −1.49249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2874.00i | 1.26304i | 0.775359 | + | 0.631521i | \(0.217569\pi\) | ||||
−0.775359 | + | 0.631521i | \(0.782431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1188.00 | −0.496063 | −0.248032 | − | 0.968752i | \(-0.579784\pi\) | ||||
−0.248032 | + | 0.968752i | \(0.579784\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3474.00 | −1.42663 | −0.713316 | − | 0.700843i | \(-0.752808\pi\) | ||||
−0.713316 | + | 0.700843i | \(0.752808\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2296.00i | 0.897862i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −192.000 | −0.0727363 | −0.0363681 | − | 0.999338i | \(-0.511579\pi\) | ||||
−0.0363681 | + | 0.999338i | \(0.511579\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4802.00i | 1.79096i | 0.445100 | + | 0.895481i | \(0.353168\pi\) | ||||
−0.445100 | + | 0.895481i | \(0.646832\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1518.00i | 0.549000i | 0.961587 | + | 0.274500i | \(0.0885123\pi\) | ||||
−0.961587 | + | 0.274500i | \(0.911488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5128.00 | −1.82670 | −0.913352 | − | 0.407170i | \(-0.866516\pi\) | ||||
−0.913352 | + | 0.407170i | \(0.866516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 3312.00i | − 1.14511i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2576.00 | −0.852563 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1084.00 | 0.353676 | 0.176838 | − | 0.984240i | \(-0.443413\pi\) | ||||
0.176838 | + | 0.984240i | \(0.443413\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1920.00i | 0.600636i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6068.00 | 1.84696 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 688.000i | 0.206600i | 0.994650 | + | 0.103300i | \(0.0329402\pi\) | ||||
−0.994650 | + | 0.103300i | \(0.967060\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4812.00i | 1.40698i | 0.710707 | + | 0.703488i | \(0.248375\pi\) | ||||
−0.710707 | + | 0.703488i | \(0.751625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2494.00 | −0.719686 | −0.359843 | − | 0.933013i | \(-0.617170\pi\) | ||||
−0.359843 | + | 0.933013i | \(0.617170\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 698.000i | − 0.196255i | −0.995174 | − | 0.0981277i | \(-0.968715\pi\) | ||||
0.995174 | − | 0.0981277i | \(-0.0312854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6320.00 | −1.71049 | −0.855244 | − | 0.518225i | \(-0.826593\pi\) | ||||
−0.855244 | + | 0.518225i | \(0.826593\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6510.00 | −1.74002 | −0.870012 | − | 0.493030i | \(-0.835889\pi\) | ||||
−0.870012 | + | 0.493030i | \(0.835889\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6808.00i | 1.75378i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −628.000 | −0.157924 | −0.0789622 | − | 0.996878i | \(-0.525161\pi\) | ||||
−0.0789622 | + | 0.996878i | \(0.525161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 224.000i | − 0.0556631i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 4862.00i | − 1.18009i | −0.807370 | − | 0.590045i | \(-0.799110\pi\) | ||||
0.807370 | − | 0.590045i | \(-0.200890\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 720.000 | 0.172736 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 5816.00i | − 1.36361i | −0.731533 | − | 0.681806i | \(-0.761195\pi\) | ||||
0.731533 | − | 0.681806i | \(-0.238805\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3526.00 | 0.799197 | 0.399599 | − | 0.916690i | \(-0.369150\pi\) | ||||
0.399599 | + | 0.916690i | \(0.369150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −256.000 | −0.0573834 | −0.0286917 | − | 0.999588i | \(-0.509134\pi\) | ||||
−0.0286917 | + | 0.999588i | \(0.509134\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 142.000i | − 0.0308013i | −0.999881 | − | 0.0154006i | \(-0.995098\pi\) | ||||
0.999881 | − | 0.0154006i | \(-0.00490237\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8842.00 | −1.87712 | −0.938558 | − | 0.345122i | \(-0.887838\pi\) | ||||
−0.938558 | + | 0.345122i | \(0.887838\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 7180.00i | − 1.50815i | −0.656788 | − | 0.754075i | \(-0.728085\pi\) | ||||
0.656788 | − | 0.754075i | \(-0.271915\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 6768.00i | − 1.39199i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1811.00 | −0.368614 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 7374.00i | − 1.47029i | −0.677912 | − | 0.735143i | \(-0.737115\pi\) | ||||
0.677912 | − | 0.735143i | \(-0.262885\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −592.000 | −0.114502 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −96.0000 | −0.0183832 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1500.00i | − 0.278858i | −0.990232 | − | 0.139429i | \(-0.955473\pi\) | ||||
0.990232 | − | 0.139429i | \(-0.0445268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7608.00 | 1.38717 | 0.693585 | − | 0.720374i | \(-0.256030\pi\) | ||||
0.693585 | + | 0.720374i | \(0.256030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 4758.00i | − 0.859227i | −0.903013 | − | 0.429614i | \(-0.858650\pi\) | ||||
0.903013 | − | 0.429614i | \(-0.141350\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4374.00i | 0.774979i | 0.921874 | + | 0.387489i | \(0.126658\pi\) | ||||
−0.921874 | + | 0.387489i | \(0.873342\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3864.00 | −0.678190 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 7544.00i | − 1.29956i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5760.00 | −0.965225 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7804.00 | −1.29591 | −0.647956 | − | 0.761678i | \(-0.724376\pi\) | ||||
−0.647956 | + | 0.761678i | \(0.724376\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 5106.00i | − 0.825346i | −0.910879 | − | 0.412673i | \(-0.864595\pi\) | ||||
0.910879 | − | 0.412673i | \(-0.135405\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2240.00 | 0.355727 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2640.00i | 0.415588i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4716.00i | − 0.729591i | −0.931088 | − | 0.364796i | \(-0.881139\pi\) | ||||
0.931088 | − | 0.364796i | \(-0.118861\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7302.00 | −1.11996 | −0.559982 | − | 0.828505i | \(-0.689192\pi\) | ||||
−0.559982 | + | 0.828505i | \(0.689192\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4382.00i | 0.660709i | 0.943857 | + | 0.330355i | \(0.107168\pi\) | ||||
−0.943857 | + | 0.330355i | \(0.892832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7224.00 | 1.06203 | 0.531014 | − | 0.847363i | \(-0.321811\pi\) | ||||
0.531014 | + | 0.847363i | \(0.321811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1408.00i | − 0.200264i | −0.994974 | − | 0.100132i | \(-0.968073\pi\) | ||||
0.994974 | − | 0.100132i | \(-0.0319266\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3120.00 | −0.436610 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1714.00i | − 0.237929i | −0.992899 | − | 0.118965i | \(-0.962043\pi\) | ||||
0.992899 | − | 0.118965i | \(-0.0379575\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10212.0i | 1.39508i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −884.000 | −0.119810 | −0.0599051 | − | 0.998204i | \(-0.519080\pi\) | ||||
−0.0599051 | + | 0.998204i | \(0.519080\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 10368.0i | − 1.38324i | −0.722263 | − | 0.691619i | \(-0.756898\pi\) | ||||
0.722263 | − | 0.691619i | \(-0.243102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 398.000 | 0.0518751 | 0.0259375 | − | 0.999664i | \(-0.491743\pi\) | ||||
0.0259375 | + | 0.999664i | \(0.491743\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 656.000 | 0.0848474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5098.00i | 0.644487i | 0.946657 | + | 0.322243i | \(0.104437\pi\) | ||||
−0.946657 | + | 0.322243i | \(0.895563\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10002.0 | −1.24558 | −0.622788 | − | 0.782391i | \(-0.714000\pi\) | ||||
−0.622788 | + | 0.782391i | \(0.714000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 5920.00i | − 0.731752i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 840.000i | − 0.102303i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9270.00 | 1.12071 | 0.560357 | − | 0.828251i | \(-0.310664\pi\) | ||||
0.560357 | + | 0.828251i | \(0.310664\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14304.0i | 1.70425i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6516.00 | −0.759731 | −0.379866 | − | 0.925042i | \(-0.624030\pi\) | ||||
−0.379866 | + | 0.925042i | \(0.624030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2626.00 | −0.303999 | −0.151999 | − | 0.988381i | \(-0.548571\pi\) | ||||
−0.151999 | + | 0.988381i | \(0.548571\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5232.00i | − 0.592961i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4304.00 | 0.481012 | 0.240506 | − | 0.970648i | \(-0.422687\pi\) | ||||
0.240506 | + | 0.970648i | \(0.422687\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11794.0i | 1.30897i | 0.756076 | + | 0.654484i | \(0.227114\pi\) | ||||
−0.756076 | + | 0.654484i | \(0.772886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 736.000i | 0.0805667i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5544.00 | 0.602735 | 0.301368 | − | 0.953508i | \(-0.402557\pi\) | ||||
0.301368 | + | 0.953508i | \(0.402557\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3788.00i | 0.406260i | 0.979152 | + | 0.203130i | \(0.0651115\pi\) | ||||
−0.979152 | + | 0.203130i | \(0.934889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13342.0 | −1.40233 | −0.701167 | − | 0.712997i | \(-0.747337\pi\) | ||||
−0.701167 | + | 0.712997i | \(0.747337\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7896.00 | −0.824408 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4390.00i | 0.449356i | 0.974433 | + | 0.224678i | \(0.0721330\pi\) | ||||
−0.974433 | + | 0.224678i | \(0.927867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5798.00 | −0.585770 | −0.292885 | − | 0.956148i | \(-0.594615\pi\) | ||||
−0.292885 | + | 0.956148i | \(0.594615\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 14656.0i | − 1.47111i | −0.677467 | − | 0.735553i | \(-0.736922\pi\) | ||||
0.677467 | − | 0.735553i | \(-0.263078\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8412.00i | 0.833535i | 0.909013 | + | 0.416768i | \(0.136837\pi\) | ||||
−0.909013 | + | 0.416768i | \(0.863163\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10464.0 | −1.03024 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 112.000i | 0.0108875i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14848.0 | 1.41633 | 0.708165 | − | 0.706047i | \(-0.249523\pi\) | ||||
0.708165 | + | 0.706047i | \(0.249523\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2220.00 | −0.210443 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 18568.0i | − 1.72771i | −0.503738 | − | 0.863857i | \(-0.668042\pi\) | ||||
0.503738 | − | 0.863857i | \(-0.331958\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14364.0 | 1.32024 | 0.660120 | − | 0.751160i | \(-0.270505\pi\) | ||||
0.660120 | + | 0.751160i | \(0.270505\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 11316.0i | − 1.03377i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 20544.0i | − 1.85417i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21660.0 | −1.94316 | −0.971578 | − | 0.236720i | \(-0.923928\pi\) | ||||
−0.971578 | + | 0.236720i | \(0.923928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17112.0i | 1.51687i | 0.651748 | + | 0.758436i | \(0.274036\pi\) | ||||
−0.651748 | + | 0.758436i | \(0.725964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11478.0 | 0.999516 | 0.499758 | − | 0.866165i | \(-0.333422\pi\) | ||||
0.499758 | + | 0.866165i | \(0.333422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23952.0 | 2.07353 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6720.00i | 0.571654i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13114.0 | −1.10275 | −0.551377 | − | 0.834256i | \(-0.685897\pi\) | ||||
−0.551377 | + | 0.834256i | \(0.685897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4508.00i | − 0.376905i | −0.982082 | − | 0.188452i | \(-0.939653\pi\) | ||||
0.982082 | − | 0.188452i | \(-0.0603471\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6560.00i | 0.542235i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12103.0 | 0.994740 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20868.0i | 1.69586i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6524.00 | −0.521352 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22950.0 | 1.82384 | 0.911920 | − | 0.410368i | \(-0.134600\pi\) | ||||
0.911920 | + | 0.410368i | \(0.134600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6580.00i | 0.514334i | 0.966367 | + | 0.257167i | \(0.0827890\pi\) | ||||
−0.966367 | + | 0.257167i | \(0.917211\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12696.0 | 0.981611 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 768.000i | 0.0590573i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7046.00i | 0.535994i | 0.963420 | + | 0.267997i | \(0.0863617\pi\) | ||||
−0.963420 | + | 0.267997i | \(0.913638\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 296.000 | 0.0223962 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 8252.00i | − 0.617727i | −0.951106 | − | 0.308864i | \(-0.900051\pi\) | ||||
0.951106 | − | 0.308864i | \(-0.0999486\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6838.00 | −0.503803 | −0.251901 | − | 0.967753i | \(-0.581056\pi\) | ||||
−0.251901 | + | 0.967753i | \(0.581056\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23316.0 | 1.70883 | 0.854417 | − | 0.519588i | \(-0.173915\pi\) | ||||
0.854417 | + | 0.519588i | \(0.173915\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10558.0i | 0.761760i | 0.924625 | + | 0.380880i | \(0.124379\pi\) | ||||
−0.924625 | + | 0.380880i | \(0.875621\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36192.0 | −2.58433 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3640.00i | 0.258582i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1028.00i | 0.0722830i | 0.999347 | + | 0.0361415i | \(0.0115067\pi\) | ||||
−0.999347 | + | 0.0361415i | \(0.988493\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7360.00 | −0.514879 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1202.00i | − 0.0832382i | −0.999134 | − | 0.0416191i | \(-0.986748\pi\) | ||||
0.999134 | − | 0.0416191i | \(-0.0132516\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3576.00 | −0.243926 | −0.121963 | − | 0.992535i | \(-0.538919\pi\) | ||||
−0.121963 | + | 0.992535i | \(0.538919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8650.00 | 0.587090 | 0.293545 | − | 0.955945i | \(-0.405165\pi\) | ||||
0.293545 | + | 0.955945i | \(0.405165\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 12656.0i | − 0.846279i | −0.906065 | − | 0.423139i | \(-0.860928\pi\) | ||||
0.906065 | − | 0.423139i | \(-0.139072\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17760.0 | 1.17593 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 3298.00i | − 0.217300i | −0.994080 | − | 0.108650i | \(-0.965347\pi\) | ||||
0.994080 | − | 0.108650i | \(-0.0346528\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5370.00i | 0.350386i | 0.984534 | + | 0.175193i | \(0.0560549\pi\) | ||||
−0.984534 | + | 0.175193i | \(0.943945\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16220.0 | 1.05321 | 0.526605 | − | 0.850110i | \(-0.323465\pi\) | ||||
0.526605 | + | 0.850110i | \(0.323465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 5904.00i | − 0.379677i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2460.00 | 0.155941 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20360.0 | −1.28450 | −0.642249 | − | 0.766496i | \(-0.721999\pi\) | ||||
−0.642249 | + | 0.766496i | \(0.721999\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17242.0i | 1.07245i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14498.0 | −0.893349 | −0.446674 | − | 0.894697i | \(-0.647392\pi\) | ||||
−0.446674 | + | 0.894697i | \(0.647392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21612.0i | 1.32550i | 0.748842 | + | 0.662748i | \(0.230610\pi\) | ||||
−0.748842 | + | 0.662748i | \(0.769390\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12184.0i | 0.740344i | 0.928963 | + | 0.370172i | \(0.120701\pi\) | ||||
−0.928963 | + | 0.370172i | \(0.879299\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16688.0 | 1.00934 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28122.0i | 1.68530i | 0.538464 | + | 0.842648i | \(0.319005\pi\) | ||||
−0.538464 | + | 0.842648i | \(0.680995\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5700.00 | −0.336935 | −0.168468 | − | 0.985707i | \(-0.553882\pi\) | ||||
−0.168468 | + | 0.985707i | \(0.553882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29458.0 | −1.73341 | −0.866705 | − | 0.498822i | \(-0.833766\pi\) | ||||
−0.866705 | + | 0.498822i | \(0.833766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1104.00i | 0.0640885i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6104.00 | −0.351181 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19810.0i | 1.13465i | 0.823494 | + | 0.567325i | \(0.192022\pi\) | ||||
−0.823494 | + | 0.567325i | \(0.807978\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 10450.0i | − 0.593244i | −0.954995 | − | 0.296622i | \(-0.904140\pi\) | ||||
0.954995 | − | 0.296622i | \(-0.0958601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20784.0 | 1.17469 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 23300.0i | − 1.30534i | −0.757641 | − | 0.652672i | \(-0.773648\pi\) | ||||
0.757641 | − | 0.652672i | \(-0.226352\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9620.00 | 0.531920 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14212.0 | −0.782417 | −0.391208 | − | 0.920302i | \(-0.627943\pi\) | ||||
−0.391208 | + | 0.920302i | \(0.627943\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 23124.0i | − 1.25665i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15978.0 | 0.860885 | 0.430443 | − | 0.902618i | \(-0.358357\pi\) | ||||
0.430443 | + | 0.902618i | \(0.358357\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2760.00i | 0.148073i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 6480.00i | − 0.344704i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8866.00 | 0.469633 | 0.234816 | − | 0.972040i | \(-0.424551\pi\) | ||||
0.234816 | + | 0.972040i | \(0.424551\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 640.000i | − 0.0336160i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7760.00 | 0.402502 | 0.201251 | − | 0.979540i | \(-0.435499\pi\) | ||||
0.201251 | + | 0.979540i | \(0.435499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35904.0 | 1.85456 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 13080.0i | − 0.667277i | −0.942701 | − | 0.333638i | \(-0.891724\pi\) | ||||
0.942701 | − | 0.333638i | \(-0.108276\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −328.000 | −0.0165958 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16934.0i | 0.853304i | 0.904416 | + | 0.426652i | \(0.140307\pi\) | ||||
−0.904416 | + | 0.426652i | \(0.859693\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12208.0i | 0.610159i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7060.00 | 0.351429 | 0.175715 | − | 0.984441i | \(-0.443776\pi\) | ||||
0.175715 | + | 0.984441i | \(0.443776\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12520.0i | 0.618189i | 0.951031 | + | 0.309094i | \(0.100026\pi\) | ||||
−0.951031 | + | 0.309094i | \(0.899974\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40608.0 | 1.98102 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9792.00 | −0.475786 | −0.237893 | − | 0.971291i | \(-0.576457\pi\) | ||||
−0.237893 | + | 0.971291i | \(0.576457\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 13166.0i | − 0.632135i | −0.948737 | − | 0.316068i | \(-0.897637\pi\) | ||||
0.948737 | − | 0.316068i | \(-0.102363\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23222.0 | 1.10617 | 0.553086 | − | 0.833124i | \(-0.313450\pi\) | ||||
0.553086 | + | 0.833124i | \(0.313450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9744.00i | − 0.462328i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 44104.0i | − 2.07628i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39934.0 | 1.87264 | 0.936318 | − | 0.351154i | \(-0.114211\pi\) | ||||
0.936318 | + | 0.351154i | \(0.114211\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17106.0i | 0.795938i | 0.917399 | + | 0.397969i | \(0.130285\pi\) | ||||
−0.917399 | + | 0.397969i | \(0.869715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25944.0 | 1.19325 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23968.0 | −1.09813 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9956.00i | 0.450944i | 0.974250 | + | 0.225472i | \(0.0723924\pi\) | ||||
−0.974250 | + | 0.225472i | \(0.927608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18864.0 | 0.847948 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16132.0i | 0.722401i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 9130.00i | − 0.405773i | −0.979202 | − | 0.202887i | \(-0.934968\pi\) | ||||
0.979202 | − | 0.202887i | \(-0.0650323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19680.0 | −0.871375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 27944.0i | − 1.22805i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11482.0 | 0.498993 | 0.249497 | − | 0.968376i | \(-0.419735\pi\) | ||||
0.249497 | + | 0.968376i | \(0.419735\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4612.00 | 0.199691 | 0.0998454 | − | 0.995003i | \(-0.468165\pi\) | ||||
0.0998454 | + | 0.995003i | \(0.468165\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 368.000i | − 0.0157585i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35010.0 | 1.48826 | 0.744128 | − | 0.668038i | \(-0.232865\pi\) | ||||
0.744128 | + | 0.668038i | \(0.232865\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13688.0i | 0.579749i | 0.957065 | + | 0.289875i | \(0.0936136\pi\) | ||||
−0.957065 | + | 0.289875i | \(0.906386\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11668.0i | 0.490612i | 0.969446 | + | 0.245306i | \(0.0788884\pi\) | ||||
−0.969446 | + | 0.245306i | \(0.921112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29306.0 | 1.22779 | 0.613896 | − | 0.789387i | \(-0.289601\pi\) | ||||
0.613896 | + | 0.789387i | \(0.289601\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 19106.0i | − 0.794698i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2664.00 | −0.109620 | −0.0548102 | − | 0.998497i | \(-0.517455\pi\) | ||||
−0.0548102 | + | 0.998497i | \(0.517455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5345.00 | −0.219156 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 13128.0i | − 0.532566i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −240.000 | −0.00966756 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26030.0i | 1.04484i | 0.852688 | + | 0.522421i | \(0.174971\pi\) | ||||
−0.852688 | + | 0.522421i | \(0.825029\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44202.0i | 1.76186i | 0.473249 | + | 0.880929i | \(0.343081\pi\) | ||||
−0.473249 | + | 0.880929i | \(0.656919\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32748.0 | 1.30075 | 0.650377 | − | 0.759612i | \(-0.274611\pi\) | ||||
0.650377 | + | 0.759612i | \(0.274611\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 45344.0i | − 1.78856i | −0.447507 | − | 0.894280i | \(-0.647688\pi\) | ||||
0.447507 | − | 0.894280i | \(-0.352312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 896.000 | 0.0349767 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32264.0 | 1.25514 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8778.00i | 0.337984i | 0.985617 | + | 0.168992i | \(0.0540512\pi\) | ||||
−0.985617 | + | 0.168992i | \(0.945949\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4142.00 | 0.158397 | 0.0791984 | − | 0.996859i | \(-0.474764\pi\) | ||||
0.0791984 | + | 0.996859i | \(0.474764\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22076.0i | 0.841355i | 0.907210 | + | 0.420678i | \(0.138208\pi\) | ||||
−0.907210 | + | 0.420678i | \(0.861792\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 40376.0i | − 1.52840i | −0.644978 | − | 0.764201i | \(-0.723133\pi\) | ||||
0.644978 | − | 0.764201i | \(-0.276867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41856.0 | 1.57908 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 22080.0i | − 0.827412i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11040.0 | −0.409571 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10660.0 | −0.394158 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26396.0i | 0.966334i | 0.875528 | + | 0.483167i | \(0.160514\pi\) | ||||
−0.875528 | + | 0.483167i | \(0.839486\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24368.0 | −0.886222 | −0.443111 | − | 0.896467i | \(-0.646125\pi\) | ||||
−0.443111 | + | 0.896467i | \(0.646125\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42224.0i | 1.53057i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 15648.0i | − 0.563514i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5096.00 | 0.182918 | 0.0914589 | − | 0.995809i | \(-0.470847\pi\) | ||||
0.0914589 | + | 0.995809i | \(0.470847\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 63344.0i | 2.25893i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18494.0 | −0.653142 | −0.326571 | − | 0.945173i | \(-0.605893\pi\) | ||||
−0.326571 | + | 0.945173i | \(0.605893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21436.0 | 0.754604 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33222.0i | 1.15829i | 0.815225 | + | 0.579144i | \(0.196613\pi\) | ||||
−0.815225 | + | 0.579144i | \(0.803387\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27846.0 | −0.964669 | −0.482335 | − | 0.875987i | \(-0.660211\pi\) | ||||
−0.482335 | + | 0.875987i | \(0.660211\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2256.00i | 0.0779061i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41052.0i | 1.40867i | 0.709868 | + | 0.704335i | \(0.248755\pi\) | ||||
−0.709868 | + | 0.704335i | \(0.751245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −73852.0 | −2.52617 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 5706.00i | − 0.193951i | −0.995287 | − | 0.0969756i | \(-0.969083\pi\) | ||||
0.995287 | − | 0.0969756i | \(-0.0309169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36720.0 | −1.23644 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23391.0 | −0.785170 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39352.0i | 1.30866i | 0.756209 | + | 0.654330i | \(0.227049\pi\) | ||||
−0.756209 | + | 0.654330i | \(0.772951\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33180.0 | 1.09660 | 0.548299 | − | 0.836282i | \(-0.315276\pi\) | ||||
0.548299 | + | 0.836282i | \(0.315276\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 12384.0i | − 0.408030i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 4014.00i | − 0.131442i | −0.997838 | − | 0.0657212i | \(-0.979065\pi\) | ||||
0.997838 | − | 0.0657212i | \(-0.0209348\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6888.00 | −0.224864 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 20328.0i | − 0.659575i | −0.944055 | − | 0.329788i | \(-0.893023\pi\) | ||||
0.944055 | − | 0.329788i | \(-0.106977\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0000 | 0.00102886 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11728.0 | 0.375936 | 0.187968 | − | 0.982175i | \(-0.439810\pi\) | ||||
0.187968 | + | 0.982175i | \(0.439810\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 50974.0i | − 1.61922i | −0.586968 | − | 0.809610i | \(-0.699679\pi\) | ||||
0.586968 | − | 0.809610i | \(-0.300321\pi\) | |||||||
\(998\) | 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 twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1800.4.f.q.649.2 | 2 | ||
3.2 | odd | 2 | 600.4.f.b.49.2 | 2 | |||
5.2 | odd | 4 | 72.4.a.b.1.1 | 1 | |||
5.3 | odd | 4 | 1800.4.a.bg.1.1 | 1 | |||
5.4 | even | 2 | inner | 1800.4.f.q.649.1 | 2 | ||
12.11 | even | 2 | 1200.4.f.p.49.1 | 2 | |||
15.2 | even | 4 | 24.4.a.a.1.1 | ✓ | 1 | ||
15.8 | even | 4 | 600.4.a.h.1.1 | 1 | |||
15.14 | odd | 2 | 600.4.f.b.49.1 | 2 | |||
20.7 | even | 4 | 144.4.a.b.1.1 | 1 | |||
40.27 | even | 4 | 576.4.a.v.1.1 | 1 | |||
40.37 | odd | 4 | 576.4.a.u.1.1 | 1 | |||
45.2 | even | 12 | 648.4.i.b.433.1 | 2 | |||
45.7 | odd | 12 | 648.4.i.k.433.1 | 2 | |||
45.22 | odd | 12 | 648.4.i.k.217.1 | 2 | |||
45.32 | even | 12 | 648.4.i.b.217.1 | 2 | |||
60.23 | odd | 4 | 1200.4.a.u.1.1 | 1 | |||
60.47 | odd | 4 | 48.4.a.b.1.1 | 1 | |||
60.59 | even | 2 | 1200.4.f.p.49.2 | 2 | |||
105.62 | odd | 4 | 1176.4.a.a.1.1 | 1 | |||
120.77 | even | 4 | 192.4.a.a.1.1 | 1 | |||
120.107 | odd | 4 | 192.4.a.g.1.1 | 1 | |||
240.77 | even | 4 | 768.4.d.o.385.2 | 2 | |||
240.107 | odd | 4 | 768.4.d.b.385.2 | 2 | |||
240.197 | even | 4 | 768.4.d.o.385.1 | 2 | |||
240.227 | odd | 4 | 768.4.d.b.385.1 | 2 | |||
420.167 | even | 4 | 2352.4.a.w.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.4.a.a.1.1 | ✓ | 1 | 15.2 | even | 4 | ||
48.4.a.b.1.1 | 1 | 60.47 | odd | 4 | |||
72.4.a.b.1.1 | 1 | 5.2 | odd | 4 | |||
144.4.a.b.1.1 | 1 | 20.7 | even | 4 | |||
192.4.a.a.1.1 | 1 | 120.77 | even | 4 | |||
192.4.a.g.1.1 | 1 | 120.107 | odd | 4 | |||
576.4.a.u.1.1 | 1 | 40.37 | odd | 4 | |||
576.4.a.v.1.1 | 1 | 40.27 | even | 4 | |||
600.4.a.h.1.1 | 1 | 15.8 | even | 4 | |||
600.4.f.b.49.1 | 2 | 15.14 | odd | 2 | |||
600.4.f.b.49.2 | 2 | 3.2 | odd | 2 | |||
648.4.i.b.217.1 | 2 | 45.32 | even | 12 | |||
648.4.i.b.433.1 | 2 | 45.2 | even | 12 | |||
648.4.i.k.217.1 | 2 | 45.22 | odd | 12 | |||
648.4.i.k.433.1 | 2 | 45.7 | odd | 12 | |||
768.4.d.b.385.1 | 2 | 240.227 | odd | 4 | |||
768.4.d.b.385.2 | 2 | 240.107 | odd | 4 | |||
768.4.d.o.385.1 | 2 | 240.197 | even | 4 | |||
768.4.d.o.385.2 | 2 | 240.77 | even | 4 | |||
1176.4.a.a.1.1 | 1 | 105.62 | odd | 4 | |||
1200.4.a.u.1.1 | 1 | 60.23 | odd | 4 | |||
1200.4.f.p.49.1 | 2 | 12.11 | even | 2 | |||
1200.4.f.p.49.2 | 2 | 60.59 | even | 2 | |||
1800.4.a.bg.1.1 | 1 | 5.3 | odd | 4 | |||
1800.4.f.q.649.1 | 2 | 5.4 | even | 2 | inner | ||
1800.4.f.q.649.2 | 2 | 1.1 | even | 1 | trivial | ||
2352.4.a.w.1.1 | 1 | 420.167 | even | 4 |